Answers
The quadratic equation written in vertex form is:
y = (x + 1)^2 - 9
How to write the quadratic equation?A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:
y = a*(x - h)^2 + k
On the graph we can see that the vertex is at (-1, -9), then we have:
y = a*(x + 1)^2 - 9
Now we also can see that the y-intercept is y = -8, then evaluating in zero we should get:
-8 = a*(0 + 1)^2 - 9
-8 = a - 9
-8 + 9 = a = 1
The quadratic equation is:
y = (x + 1)^2 - 9
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Related Questions
Zoe makes a total of $72.85 selling cookies and cupcakes at a bake sale. If she sells 17 cupckaes for $3.25 each, how many cookies does she sell at $1,60 each?
PLEASE SHOW WORK
and I have to pass it pls
Answers
Answer: 11 Cookies
Step-by-step explanation:
let C be cookies
17($3.25) + 1.60C = $72.85
$55.25 + 1.60C = $72.85
1.60C = $17.60
C=11
She sells 11 cookies
Answer:
11
Step-by-step explanation:
To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.
I AM SO SORRY IF THIS DIDN'T MAKE SENSE!
Anumeha knows the following information about a set of
20
2020 numbers:
9
99 numbers are a multiple of
3
33 but not a multiple of
4
44.
10
1010 numbers in total are a multiple of
3
33.
10
1010 numbers in total are a multiple of
4
44.
Can you help Anumeha organize the results into a two-way frequency table?
Answers
A
Step-by-step explanation:
There is 1 number that is a multiple of both 3 and 4.
9 numbers are a multiple of 4 and not 3.
9 numbers are a multiple of 3 and not 4.
1 number is not a multiple of 3 or 4.
Hope this helps!
Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 18sin^2(x)cos^2(x)
Answers
An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
How did we get the value?The power-reducing formulas state that:
sin^2(x) = (1 - cos(2x))/2
cos^2(x) = (1 + cos(2x))/2
Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:
18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]
Expanding the right-hand side of the equation, we get:
18[(1 - cos^2(2x))/4]
Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:
18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8
Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
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a senior math contest began at 6:00 am on a Sunday and ended 1000 min later then did the contest get over
Answers
The senior math contest ended at 10:40 pm on Sunday
What time did the contest get overIf the senior math contest began at 6:00 am on a Sunday and ended 1000 minutes later, we can add 1000 minutes to the starting time to find the ending time.
To do this, we can first convert the starting time of 6:00 am into minutes. There are 60 minutes in one hour, so 6:00 am is equivalent to:
6 hours × 60 minutes/hour = 360 minutes
Now, we can add 1000 minutes to this starting time:
360 minutes + 1000 minutes = 1360 minutes
Finally, we can convert this total number of minutes back into hours and minutes.
Since there are 60 minutes in one hour, we can divide 1360 minutes by 60 to get:
1360 minutes ÷ 60 = 22 hours and 40 minutes
Therefore, the senior math contest ended at 10:40 pm on the day (Sunday).
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A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
Answers
Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
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Classify the solid.
Explain your reasoning.
Image below.
Answers
The solid displayed in the image is a trapezoidal prism.
What is a trapezoidal prism?A trapezoidal prism is a three-dimensional solid with two parallel trapezoids as its bases, and rectangular or parallelogram sides connecting them. The top and bottom faces are identical, and the side faces are parallelograms.
To classify the solid, look at its properties. The solid has two parallel trapezoids as its bases, and the side faces are parallelograms. Therefore, it is a prism.
Since the bases are not identical rectangles or squares, it is not a rectangular or square prism. However, since the bases are trapezoids, it is a trapezoidal prism.
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Finding the Mean and Median 42,5,25,2,35
Answers
The mean of the given set of numbers is 21.8. and median is 25.
Define meanIn mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. The mean is also known as the arithmetic mean or average.
To find the mean and median of the given set of numbers, we can follow these steps:
Arrange the numbers in order from smallest to largest: 2, 5, 25, 35, 42.
To find the mean, add up all the numbers and divide by the total number of numbers:
Mean = (2 + 5 + 25 + 35 + 42) / 5
= 109 / 5
= 21.8
Therefore, the mean of the given set of numbers is 21.8.
To find the median, we need to find the middle number in the ordered list. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
In this case, there are 5 numbers, so the median is the middle number, which is 25.
Therefore, the median of the given set of numbers is 25.
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Is the following parallelogram actually a rectangle?
15 m
37 m
V 114
Answers
The given parallelogram is not a rectangle.
How to find a rectangle ?One of the tests for a rectangle is if a right angled triangle can be created by diagonally dividing the rectangle .
The test for a right - angled triangle is the Pythagorean Theorem which is :
Side ² + Side ² = Hypotenuse ²
Using, the dimensions, check to see if there is a right triangle :
7. 2 ² + 9. 1 ² = 12 ²
134. 65 ≠ 144
There is no right angled triangle so this is a parallelogram that is not a rectangle .
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Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
[1 mark]
(b) How much does Jack receive the following Christmas?
[1 mark]
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
Answers
a) Jill receives £45
b) Jack receives £20 the following Christmas
c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.
Explain the term years
Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.
According to the given information
(a) Let's first find the total ratio of their ages:
1 + 3 = 4
So Jack's share will be:
1/4 x £60 = £15
And Jill's share will be:
3/4 x £60 = £45
Therefore, Jill receives £45.
(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:
2/6 x £60 = £20
So Jack receives £20.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:
1/4 x £60 = £25
Multiplying both sides by 4/60, we get:x = 5/4
So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.
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PLEASE Help me answer these 2 math questions!!!
Answers
1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.
2. The range of the function is given as follows: The set of real numbers less than -5.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:
y = a(1/3)^x - 2.
When x = 0, y = -1, hence the parameter a is obtained as follows:
-1 = a - 2
a = 1.
Thus the function is:
g(x) = (1/3)^x - 2.
For item 2, we have that the function is:
Reflected over the y-axis, due to the negative sign of a.Has an horizontal asymptote at y = -5.Hence the range of the function is given as follows:
The set of real numbers less than -5.
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you want to hire a band for a school dance. The live band charges $75 to play for three hours and each student will pay a $2.00 admission prices, p. a, how much money will you make if 100 students attend the dance
b, how much money will you make if 100 students attend the dance
c, how many students would need to attend the dance for you to “break even” after you aging the band?
Answers
Answer:
38 stduentstudents
Step-by-step explanation:
2(100)=$200, if 100 students attend.
38(2)=$76
Breaking even means getting back the same amount you spent. The exact answer would be 37.5, but you can't have half a student.
PLEASE HELP
(a) How many total trees are included in the histogram?
(b) What is the least common height range of the trees?
Answers
Answer:
a. 31 total trees
b. Least common range is 85-90
Step-by-step explanation:
A. On the side of the chart it is labeled frequency. That is where you will find the number of tree per height range. The tops of the bars indicate the number is directly across.
B. Looking at the lowest bar or the smallest amount of trees indicate the lowest range or the least common range.
evaluate the expression 8 - 12 - (-6)
Answers
Answer:
2
Step-by-step explanation:
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
a) What is the probability that an American chosen at random died as a passenger car occupant last year?
Give your answer as a fraction or decimal. If decimal, make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 1. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
b) What is the probability that you died as a passenger car occupant last year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 2. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
c) What is the probability that you will die as a passenger car occupant next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 3. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
d) What is the probability that an American chosen at random will die as the result of a tornado next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 4. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
e) What is the probability that you will die as the result of a tornado next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
Answers
a) The probability that an American chosen at random died as a passenger car occupant last year is 0.0042.
b) The probability that you died as a passenger car occupant last year is 0.0042
c) The probability that you will die as a passenger car occupant next year P(C) is 0.0042.
d) The probability that an American chosen at random will die as the result of a tornado next year is 0.0000018
e) The probability that you will die as the result of a tornado next year is 0.0000018
What are the probabilities?The given probabilities are determined as follows:
The probability that an American chosen at random died as a passenger car occupant last year is:
P(A) = 13,100 / 312,000,000
P(A) = 0.0042
b) The probability that you died as a passenger car occupant last year is:
P(B) = 13,100 / 312,000,000
P(B) = 0.0042
c) The probability that you will die as a passenger car occupant next year P(C) would be 0.0042 since the values do not change.
d) The probability that an American chosen at random will die as the result of a tornado next year is:
P(D) = 553 / 312,000,000
P(D) = 0.0000018
e) The probability that you will die as the result of a tornado next year, P(E) = 0.0000018
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NO LINKS!! URGENT HELP PLEASE!!!
Express the statement as an inequality Part 4a^2
Answers
The correct answer is B) |x| > 6 for the given statement
What is meant by the statement?
A statement is a declarative sentence that can be either true or false. It is a proposition that can be proven using logical reasoning or evidence. Statements are the building blocks of mathematical proofs and are used to establish the truth of mathematical theories and concepts.
According to the given information
The statement “the absolute value of x is greater than 6” can be expressed as an inequality in the following way:
|x| > 6
This means that the distance between x and 0 on the number line is greater than 6 units. In other words, x can be any number that is either less than -6 or greater than 6.
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Halla el valor de (2+3) ² =
Identifica la base, el exponente y
resuelve: (-8) ² =
La siguiente fracción 3/5 expresado en porciento es:
5/a = 7/5 halla el valor de a:
El número mixto 20 0 a fracción impropia es igual a:
3
Answers
(2+3)²=25, base=2+3, exponente=2, (-8)²=64, 3/5 expressed as a percent is 60%, a=7, 20 0/3 = 60/3 = 20/1.
What is percentage?
Percentage is a way of expressing a fraction or decimal as a portion of 100. It is often used to describe proportions or rates in various fields, such as finance, economics, and statistics.
What is exponent?
An exponent is a mathematical operation that involves raising a number to a power. The exponent represents the number of times the base is multiplied by itself. For example, in 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, resulting in 8.
According to the given information:
(2+3)² = (5)² = 25. The base is (2+3), the exponent is 2, and the result is 25.(-8)² = 64. The base is -8, the exponent is 2, and the result is 64.To express 3/5 as a percentage, we multiply by 100: 3/5 x 100 = 60%. Therefore, 3/5 is equal to 60%.To solve 5/a = 7/5 for a, we cross-multiply to get 5 x 5 = 7a. Simplifying, we get 25 = 7a, so a = 25/7.To convert the mixed number 20 3/3 to an improper fraction, we first multiply the whole number (20) by the denominator of the fraction (3), which gives us 60. Then we add the numerator of the fraction (3) to get 63. So 20 3/3 as an improper fraction is 63/3, which simplifies to 21.To know more about percentage, exponent visit:
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Chau paid 13.88 for a -pound bag of shrimp at one store. The following week, he paid 38.99 for a 5.46 -pound bag at another store.
Answers
The first bag has a better unit price, at $7.01 per pound compared to $7.13 per pound for the second bag. Based on the unit price, the first bag is a better buy.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of variables, which are represented by letters or other symbols, to represent unknown quantities and to formulate and solve equations and inequalities.
The fundamental operations of algebra include addition, subtraction, multiplication, and division, which are used to manipulate the variables and simplify expressions. Algebra also involves the use of exponents, which are used to represent repeated multiplication, and logarithms, which are used to represent the inverse of exponents.
Algebra is used in a wide range of applications, including science, engineering, economics, and statistics, to model and analyze various phenomena. It is also used as a tool for problem-solving and decision-making, and it provides a powerful framework for reasoning and abstraction in many areas of mathematics and beyond.
To find the unit price, we divide the total price of each bag by its weight:
For the first bag:
Unit price = Total price / Weight = 13.88 / 1.98 = 7.01 dollars per pound
For the second bag:
Unit price = Total price / Weight = 38.99 / 5.46 = 7.13 dollars per pound
Therefore, the first bag has a better unit price, at $7.01 per pound compared to $7.13 per pound for the second bag.
Thus, based on the unit price, the first bag is a better buy.
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The complete question is:
Chau paid 13.88 for a 1.98- pound bag of shrimp at one store. The following week, he paid 38.99 for a 5.46 -pound bag at another store.
Find the unit price for each bag. Then state which bag is better buy based on the unit price.
Trigonometry help me please!
Answers
As per the question of trigonometry the another equation that describes the given graph is
y = -cos5x. And after verifying the equation given in the question as well as the new equation we conclude that both equations are equal.
In trigonometry what are the domain and range of the standard functions?The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental geometrical operations in trigonometry. These functions' domain and range are as follows:Sine Function (sin x): All real numbers are its domainRange: [-1, 1]The domain of the cosine function (cos x): all real numbersRange: [-1, 1]Domain: All real numbers, excluding x = (n + 1/2), where n is an integer. Tangent Function (tan x):the entire real number rangeDomain: All real numbers except for x = n, where n is an integer. Cotangent Function (cot x)the entire real number rangeDomain: All real numbers, excluding x = (n + 1/2), where n is an integer. Secant Function (sec x)Range: (-∞, -1] U [1, ∞)Domain: All real numbers except x = n, where n is an integer. What distinguishing characteristics can be found in the sine and cosine function graphs?The sine and cosine function graphs' main characteristics are:
The sine and cosine functions are both periodic, which means that their graphs repeat at regular intervals. The maximum distance between the function value and the horizontal axis is determined by the sine and cosine functions' amplitudes. Zeros: The positions where the sine and cosine functions intersect the horizontal axis are known as the zeros.The functions' maximum and minimum values occur at the period's endpoints. For charting and analyzing the behavior of the sine and cosine functions, it is crucial to comprehend these fundamental characteristics.a. We can use trigonometric identities to simplify the given equation in order to describe the graph using a different equation.
[tex]cos((a+b)/2) = 2 cos(sin(a-b)) sin((a-b)/2)[/tex][tex]Sin((a+b)/2) = cos(a) - cos(b) sin((a-b)/2)[/tex]Using this identity, the given equation can be made simpler:[tex][(2 cos(5x) sin(-4x))/(-2 sin(5x) sin(-4x)] gives y.\\y = -cos(5x)[/tex]So, the equation [tex]y = -cos(5x)[/tex] can be used to describe the graph.b. We can simplify the following equation and compare it with [tex]y = -cos(5x)[/tex]to see if the two equations are equivalent.
We obtain this by applying the same trigonometric identity as before.
Y is equal to [tex][((sinx - sin9x)/(cosx - cos9x)][/tex]Y is equal to [tex][(2 cos5x sin(-4x))/(-2 sin5x sin(-4x)][/tex] (using the identities [tex]cos(a) - cos(b) and sin(a) - sin(b))[/tex][tex]y = -cos5x[/tex]As we can see, the following equation's shortened form is equal.To know more about trigonometric functions visit:
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Luka and Dana are making cookies for the Westland pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour(x), and 20 snickerdoodle cookies in an hour(y). They need it make at least 150 cookies. Which inequality represents the situation?
Answers
Option 3. x+y≤6 , 32x + 20y ≥ 150. The inequality 32x + 20y ≥ 150 ensures that they bake enough cookies to meet the requirement of making at least 150 cookies.
The right disparity that addresses what is happening is:
32x + 20y ≥ 150
To see the reason why, we want to consider the quantity of treats Luka and Dana can heat in every hour and the all out number of hours they need to prepare. We should expect they have H hours to prepare, where H = 6 for this situation.
Luka and Dana can prepare 32 chocolate chip treats in 60 minutes, so they can heat a sum of 32x treats in x hours. Likewise, they can prepare a sum of 20y snickerdoodle treats in y hours. To make no less than 150 treats, they need to prepare a mix of chocolate chip and snickerdoodle treats in every hour, with the end goal that the complete number of treats they make in H hours is something like 150.
Thus, the imbalance 32x + 20y ≥ 150 guarantees that they heat an adequate number of treats to meet the necessity of making somewhere around 150 treats.
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F(x)=x-1/x+1 show that f(2x)=3f(x)+1/f(x)+3?
Answers
The proof that f(2x)=3f(x)+1/f(x)+3 is shown below.
Mathematical functionTo show that f(2x) = 3f(x) + 1/f(x) + 3, we substitute 2x for x in the expression for f(x):
f(x) = x - 1 / x + 1
f(2x) = 2x - 1 / 2x + 1
Next, we substitute x into the expression for f(x) and add the result to itself twice:
f(x) = x - 1 / x + 1
f(x) + f(x) + f(x) = (x - 1 / x + 1) + (x - 1 / x + 1) + (x - 1 / x + 1)
= 3x - 3 / 3x + 3
We can simplify the expression by dividing both the numerator and denominator by 3:
f(x) + f(x) + f(x) = x - 1 / x + 1
= (1/3) (3x - 3) / (1/3) (3x + 3)
= (x - 1) / (x + 1)
= f(x)
Now, we substitute f(x) and f(2x) back into the original equation:
f(2x) = 2x - 1 / 2x + 1
3f(x) + 1/f(x) + 3 = 3(x - 1 / x + 1) + 1/(x - 1 / x + 1) + 3
= (3x - 3 / x + 1) + (1 / (x - 1 / x + 1)) + 3
= (3x - 3 + (x + 1) / (x - 1)) / (x + 1)
= (2x + 2) / (x + 1)
= 2(x + 1) / (x + 1)
= 2
Thus, we have shown that f(2x) = 3f(x) + 1/f(x) + 3.
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Jason is planning to surprise his wife with a trip to Turkey this summer. He had difficulty making hotel reservations during
tourist season, but managed to reserve a room for two weeks in a nice hotel in Cappadocia in central Turkey. From there, he
plans to rent a car to take him and his wife to see the sights. After making all of his hotel and rental car reservations, Jason
is surprised to see that the trip will cost much more than he anticipated. What change(s) should Jason make to his vacation
to lower the overall cost?
Answers
The changes that Jason should make are:
1. Plan a trip not during the tourist season.
2. In place of renting car, use transportation services of the country.
3. He should go to other places to find a nice hotel.
The solution has been obtained by using cost planning.
What is cost planning?
Estimating expenses, establishing an agreed-upon budget, and managing actual and projected expenditures in relation to that budget are all parts of cost planning and control.
The changes that Jason should make are:
1. Plan a trip not during the tourist season. This is because during the tourist season prices are high.
2. In place of renting car, use transportation services of the country. This is because the local transport will cost him less that the rental.
3. He should go to other places to find a nice hotel. This is because central Turkey is costly and he might find a nice hotel in other areas in less price.
Hence, the required solution has been obtained.
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Find the area of the regular polygon.
Answers
Answer:
This is a right angle
Step-by-step explanation:
There is a square inside of the triangle.
Please help if your good at (FUNCTION TABLE) and (nonlinear or liner or nor or both)
Please help ASAP look at the picture !
Answers
Answer:
Linear
Step-by-step explanation:
The table represents a consistent function and is therefore linear.
A digital thermometer in Olivia's car says the temperature outside is –5°C. Which statement BEST describes the meaning of the value –5 in this context?
Answers
The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.
Which statement describes the meaning of the valueIn this context, the value -5 represents the temperature outside in Celsius degrees.
The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.
Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.
The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.
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[tex]\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}[/tex]
Find max, min, sup and inf
Answers
The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.
The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]
To find the maximum and minimum values of the sequence, we can start by taking the first few terms and looking for patterns:When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]
When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]
When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]
When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]
It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.
Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.
The maximum value occurs at n = 2, where it evaluates to 1/6.
To find the supremum and infimum of the sequence, we can start by considering the upper and lower bounds of each term separately.The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.
The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].
Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].
The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]
In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]
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According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average
of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of
the individual
The middle 40% of heights fall between what two values? Sketch the graph, and write the probability statement
Answers
The probability statement is written below:
P(62.8 ≤ X ≤ 69.2) = 0.4What is the probability statement?The middle 40% of heights fall between the 10th and 90th percentiles of the standard normal distribution.
The z-scores of the 10th and 90th percentiles are -1.28 and 1.28 respectively.
The heights in the given normal distribution are found using the formula:
X = μ + zσwhere
X is the height,μ is the mean height = 66 inchesσ is the standard deviation = 2.5 inchesz is the z-score.The height of the 10th percentile is:
X = 66 + (-1.28)(2.5)
X = 62.8 inches
The height of the 90th percentile is:
X = 66 + (1.28)(2.5)
X = 69.2 inches
Therefore, the middle 40% of heights fall between 62.8 inches and 69.2 inches and the probability statement will be P(62.8 ≤ X ≤ 69.2) = 0.4
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francine can type 3,420 words in 1 hour and 30 minutes at this rate how any words can she type per minute
Answers
Francine can type 38 words per minute at this rate.
To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.
Next, we can use the formula:
words per minute = total words / total minutes
where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).
Substituting these values into the formula, we get:
words per minute = 3,420 / 90 = 38
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A cube is shown. Describe the shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section.
horizontal cross section: _____
vertical cross section: _____
angled cross section: _____
Answers
The shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section of the cube are:
horizontal cross section: square.
vertical cross section: square.
angled cross section: rectangle.
How to determine the cross section?In this exercise, you are required to use a graphing tool to investigate and determine the cross-sections of the given three-dimensional geometric object (cube), by passing different planes through them.
By critically observing the cross-sections of the three-dimensional geometric object (cube) I used, we can reasonably infer and logically deduce the following types of quadrilateral based on the cross-sections;
A horizontal cross section would produce a square.
A vertical cross section would produce a square.
An angled cross section would produce a rectangle.
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Need answers ASAP!!!
Also, I will give Brainliest to whoever includes an explanation on what 9 ⁻³ means.
Answers
The given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.
What is Exponentiation?A number's power or exponent, in other words, tells how many times it must be multiplied by itself.
Any integer, fraction, or decimal can serve as the basis in this situation.
Additionally, the exponent might have either a positive or negative value.
Subtract the exponents to divide exponents (or powers) with the same base.
Given that division is the inverse operation of multiplication, it stands to reason that, just as exponents are added when multiplying numbers with the same base, exponents are subtracted when dividing numbers with the same base.
So, we have the exponents as;
9⁻³/9¹²
Then, solve as follows:
9⁻³/9¹²
9⁻³⁻¹²
9⁻¹⁵
Therefore, the given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.
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A movie theater has a seating capacity of 257. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 1870, How many children, students, and adults attended?
Answers
The attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given:
Seating capacity = 257
Charges: Children = $5.00; Students = $7.00; Adults = $12.00
Total sales of ticket = $1870
A number of children, students, and adults were present in the theatre.
Let A, C, and S represent adults, children, and students respectively.
There are half as many adults as there are children; this means that
A = ½C
If the total seat capacity is 257, then
A + C + S = 257
Also, if the total sales of tickets are $1870, then
12A + 7S + 5C = 1870
So, we have two equations to be solved simultaneously.
A + C + S = 257 --- (1)
12A + 7S + 5C = 1860 --- (2)
Substitute ½C for A in (1) and (2)
½C + C + S = 257
Multiply both sides by 2
2(½C + C + S) = 2 * 257
C + 2C + 2S = 514
3C + 2S = 514 ----- (3)
12(½C) + 7S + 5C = 1870
6C + 7S + 5C ,= 1870
6C + 5C + 7S = 1870
11C + 7S = 1870 --- (4)
Make S the subject of the formula in (3)
2S = 514 - 3C
S = ½(514 - 3C)
S = 257 - 1.5C
Substituton 257 - 1.5C for S in (4)
11C + 7(257- 1.5C) = 1870
11C + 1799 - 10.5C = 1870
Collect like terms
11C - 10.5C = 1870 - 1799
0.5C = 71
Multiply both sides by 2
2 * 0.5C = 2 * 71
C = 142
Recall that
S = 257 - 1.5C
S = 257 - 1.5(142)
S = 257 - 213
S = 44
Also, recall that
A = ½C
A = ½ * 142
A = 71
Hence, the attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
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