Answer:
Let's first calculate the number of students who passed the test and completed the assignment. We know that 15 students passed the test and 6 students who failed the test and did not complete the assignment. Therefore, there are 25 - 15 - 6 = 4 students who failed the test but completed the assignment.
Now we can calculate the probability that a student who completed the homework passed the test by dividing the number of students who passed the test and completed the assignment by the total number of students who completed the assignment.
The number of students who passed the test and completed the assignment is 15 - 6 = 9. The total number of students who completed the assignment is 16 - 6 = 10. Therefore, the probability that a student who completed the homework passed the test is 9/10 or 0.9.
Step-by-step explanation:
the dean's secretary receives an average of 3 calls per hour. assuming the poisson distribution applies, what is the probability that th secretary will receive 6 calls next hour?
The probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.
The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed time interval, given the average rate at which events occur and the independence of events. In this case, the average rate of calls is 3 calls per hour.
The probability of receiving exactly 6 calls next hour can be calculated using the Poisson probability formula:
[tex]P(X = 6) = (e^(-λ) * λ^6) / 6![/tex]
where λ is the average rate of calls, e is the base of the natural logarithm, and 6! is the factorial of 6.
Substituting the values, we get:
[tex]P(X = 6) = (e^(-3) * 3^6) / 6! ≈ 0.090[/tex]
Therefore, the probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.l
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The probability that the secretary will receive 6 calls next hour is approximately 0.0504, or 5.04%
To calculate the probability that the secretary will receive 6 calls next hour, given that the average is 3 calls per hour
and the Poisson distribution applies, follow these steps:
Identify the given information: λ (average calls per hour) = 3, k (number of calls to calculate the probability for) = 6.
Use the Poisson probability formula:
P(k) =[tex](e^{(-\lambda)} \times\lambda^k) / k!,[/tex]
where P(k) is the probability of k calls,
e is the base of the natural logarithm (approximately 2.71828),
λ is the average rate (3 calls per hour), and
k! is the factorial of k (6 in this case).
Calculate [tex]e^{(-\lambda)}: e^{(-3)} = 0.04979.[/tex]
Calculate [tex]\lambda^k: 3^6 = 729.[/tex]
Calculate k!: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Substitute these values into the formula: P(6) = (0.04979 × 729) / 720 ≈ 0.0504.
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!!!!PLEASE HELP!!!!
Lesson 4.06
The number of people that enter a contest on the 1st day is 23. On the 2nd day 30 people entered, and 37
people entered on the 3rd day. This pattern continues and the contest lasts 28 days.
What is the total number of people that enter the contest? Write the arithmetic series formula you used
to determine the total number of people and show all steps used to find the solution.
Thus, 3290 persons in total have entered the contest. We calculated the sum using the following arithmetic series formula: [tex]S = (n/2) * [2a + (n-1)d][/tex]
what is arithmetic progression ?The phrase "arithmetic progression" (AP) describes a series of numbers in which every term—aside from the first—is derived by multiplying the previous term by a set value. The common difference is a constant number. The following equation can be used to symbolise an arithmetic progression: a n = a 1 + (n-1)d where d is the clear differentiation, a n is the n - th term, a 1 represents the initial term, and n is the total number of terms. For instance, an arithmetic progression with 5 terms and a common difference of 3 starting at 1 would be: 1, 4, 7, 10, 13
given
The formula for the sum of an arithmetic series can be used to determine the total number of contestants:
[tex]S = (n/2) * [2a + (n-1)d][/tex]
Here are the facts:
a = 23 (the first phrase) (the first term)
d = 7 (the usual difference, since each day 7 more participants enter the contest) (the common difference, since each day 7 more people enter the contest)
n = 28 (the number of terms, since the contest lasts 28 days) (the number of terms, since the contest lasts 28 days)
With these values entered into the formula, we obtain:
S = (28/2) * [2(23) + (28-1)(7)]
S = 14 * [46 + 189]
S = 14 * 235
S = 3290
Thus, 3290 persons in total have entered the contest. We calculated the sum using the following arithmetic series formula: S = (n/2) * [2a + (n-1)d].
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USE A MODEL In a mathematics exam with a maximum score of 100, Machelle loses less than 27 points. The table shows the grade that matches the exam score. Compare points to grades and identify which grade Machelle can get.
Machelle can get a grade of D or higher on her exam.
Describe Inequality?In mathematics, an inequality is a mathematical statement that describes a relationship between two quantities that are not necessarily equal. An inequality can express that one quantity is less than, less than or equal to, greater than, greater than or equal to, or not equal to another quantity.
Inequalities can be represented using various symbols. For example, the symbol < represents "less than," the symbol > represents "greater than," the symbol ≤ represents "less than or equal to," and the symbol ≥ represents "greater than or equal to." The symbol ≠ represents "not equal to."
Inequalities are also used in algebra to solve equations and to represent the solution set of an equation. In this context, an inequality can represent all the possible values of a variable that satisfy the equation. For example, the inequality x > 5 represents all the values of x that make the expression x - 5 positive.
We can write an inequality to represent the number of points, m, obtained by Machelle on her exam:
m > 100 - 27
Simplifying this expression, we get:
m > 73
This means that Machelle must have scored more than 73 points on her exam. Based on the table, we can see that a score of more than 73 points corresponds to a grade of at least a D. Therefore, Machelle can get a grade of D or higher on her exam.
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The complete question is:
What are all values of x for which the function f is defined by f(x)= x^3 +3x^2 -9x +7 is increasing?a) -31d) x <-1 or x > 3e) all real numbers
The values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing are (-∞, -3) and (1, +∞).
To find the values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing, we need to take the derivative of the function and determine where the derivative is positive.
f(x) = x³ + 3x² - 9x + 7
f'(x) = 3x² + 6x - 9
To find where f(x) is increasing, we need to find the values of x where f'(x) > 0.
3x² + 6x - 9 > 0
Simplifying this inequality, we get
x² + 2x - 3 > 0
Factoring the left side of the inequality, we get
(x + 3)(x - 1) > 0
The critical points of f(x) occur when f'(x) = 0 or when the denominator of f'(x) is undefined. The denominator of f'(x) is always defined, so we only need to find where f'(x) = 0
3x² + 6x - 9 = 0
Dividing both sides by 3, we get
x² + 2x - 3 = 0
Factoring the left side of the equation, we get
(x + 3)(x - 1) = 0
So the critical points of f(x) are x = -3 and x = 1.
Now we can use a sign chart to determine the intervals where f'(x) > 0.
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The given question is incomplete, the complete question is:
What are all values of x for which the function f is defined by f(x)= x³ +3x² -9x +7 is increasing?
Given that ZQRP = (2x + 20) and ZPSQ = 30°, find the value of x.
The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.
We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.
If angles QRP and PSQ are supplementary, their sum is 180°:
(2x + 20)° + 30° = 180°
Now, we can solve for x:
2x + 50 = 180
Subtract 50 from both sides:
2x = 130
Divide by 2:
x = 65
3. Given: Line segment PQ.
Construct: Circle with center Q and equilateral triangle NOP so that points N and O are on circle Q.
A circle with center Q and equilateral triangle NOP, where points N and O lie on the circle
What is a circle?
A circle is a two-dimensional shape with a perfectly round boundary that has no corners or edges. It is defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the boundary of the circle is called the radius.
The circumference of a circle is the distance around the boundary of the circle, and it is calculated as 2π times the radius. Circles are found in many natural and man-made objects, such as wheels, planets, and coins, and they have a wide range of applications in mathematics, science, and engineering.
To construct a circle with center Q and equilateral triangle NOP where points N and O lie on the circle, follow these steps:
Draw line segment PQ as the base of the equilateral triangle NOP.
Draw a perpendicular bisector of PQ, which intersects PQ at its midpoint, say M. This bisector will be the axis of symmetry of the equilateral triangle NOP.
With M as the center and MP (or MQ) as the radius, draw a circle that intersects PQ at two points, say X and Y.
Using Q as the center and QX (or QY) as the radius, draw two arcs that intersect the circle drawn in step 3 at two points, say N and O.
Draw the lines NQ and OQ to complete the equilateral triangle NOP.
Now, you have a circle with center Q and equilateral triangle NOP, where points N and O lie on the circle.
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PLEASE is due very soon please explain 50pts
Answer:
3
Step-by-step explanation:
Because same numbers = same y intercept but I'm not sure
Answer:
1) The image has the same slope, different y-intercept
Step-by-step explanation:
You want the relationship between the line 3x -5y = 4 and its image dilated by a factor of 5/3 centered at the origin.
DilationDilation about the origin multiplies every coordinate by the dilation factor. Dilation does not change slopes or angles, but it changes lengths by the dilation factor.
Dilation of a lineWhen the equation of a line is written in standard form, the dilation of it effectively multiplies the constant by the dilation factor.
The given line has intercepts ...
ax +by = c
x-intercept = c/a = 4/3
y-intercept = c/b = -4/5
If these values are multiplied by the dilation factor 5/3, they become ...
x-intercept' = (5/3)(4/3) = 20/9 = 2 2/9
y-intercept' = (5/3)(-4/5) = -4/3 . . . . . note the y-intercept has changed
SlopeThe slope of the given line can be determined from its intercepts:
m = (-y intercept)/(x intercept) = -(-4/5)/(4/3) = 3/5
Since both of these intercepts are multiplied by the same dilation factor, their ratio remains unchanged. The slope of the dilated line is the same.
EquationEffectively, the dilated line's equation is ...
3x -5y = 4(5/3)
3x -5y = 20/3
__
Additional comment
The original (dashed) line and its dilated image are shown in the attachment.
standard error of an estimator is not affected by the multiple choice question. population standard deviation. sample size. population size
The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.
The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.
It is calculated simply by dividing the standard deviation by the square root of the sample size. That is [tex]SE = \frac{σ }{\sqrt{n}}[/tex]
where , n --> sample size
σ --> population standard deviations
Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.
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Complete question:
standard error of an estimator is not affected by the multiple choice question.
a) population standard deviation
b) sample size
c) population size
A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0. 4. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot. Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?
A Yes, because a difference in proportions of 0. 4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
B Yes, because a difference in proportions of 0. 4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
C No, because a difference in proportions of 0. 4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
D No, because a difference in proportions of 0. 4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective
Yes, since the new additive is more efficient and a proportional difference of 0.4 or more occurred 7 times out of 200, making the difference statistically significant. The correct answer is A) .
The dotplot can be used to determine whether the 0.4 observed proportional difference is statistically significant. Few dots are at or above 0.4 in any direction, as can be seen by looking at the dotplot. In particular, it appears that there are no dots to the left of the observed difference and only roughly 7 dots that are at or beyond 0.4. Therefore, at the 5% level of significance, the observed proportional difference of 0.4 is statistically significant. Hence the correct answer is option: A.
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Rihanna worked for 3 hours 35 minutes
on Monday. She worked for 2 hours
50 minutes on Wednesday. She wants
to work enough hours on Friday so she
works a total of 8 hours. How much
longer does she need to work?
Answer:
1 hour and 35 minutes
Step-by-step explanation:
3 hours and 35 minutes + 2 hours and 50 minutes = 6 hours and 25 minutes.
8 hours - 6 hours and 25 minutes = 1 hour and 35 minutes
given u=5i+4j and v = 4i-3j, determine -9u-v
-9u - v = -49i - 33j
To find -9u - v, you need to multiply the vector u by -9 and subtract the vector v from the result.
Given u = 5i + 4j and v = 4i - 3j, first multiply u by -9:
-9u = -9(5i + 4j) = -45i - 36j
Now, subtract the vector v from -9u:
-9u - v = (-45i - 36j) - (4i - 3j) = (-45i - 4i) + (-36j + 3j) = -49i - 33j
Choose ALL answers that describe
The answer choices which fit into the descriptions as given in the task content are; Squares and Rhombus.
Which answer choices describe the given quadrilateral?It follows from the task content that the given quadrilateral is such that; FG || HI, GH || IF and FH = GI. However, since the diagonals are perpendicular.
Consequently, it can be inferred that the diagonals of squares and Rhombuses are perpendicular. On this note, the shapes which best align with the given descriptions are; Square and Rhombus.
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Find the geometric mean of the two lo and 90
Write the following in expanded form.
369.964
A.
B.
C.
D.
The number 369.964 in expanded form as 369.964 = 300 + 60 + 9 + 0.9 + 0.06 + 0.004
To express 369.964 in expanded form, we must break down the number by its place value. The digits to the left of the decimal point represent whole numbers, while the digits to the right represent fractions or decimals.
So let's start with the whole number part, 369. We can express this in expanded form by breaking it down into its component parts according to its place value. The digit 3 is in the hundreds place, which means it has a value of 300. The digit 6 is in the tens place, which means it has a value of 60. The digit 9 is in the ones place, which means it has a value of 9. Therefore, we can write 369 in expanded form as:
369 = 300 + 60 + 9
Now let's move on to the decimal part, 0.964. The digit 9 is in the tenths place, which means it has a value of 0.9. The digit 6 is in the hundredths place, which means it has a value of 0.06. The digit 4 is in the thousandths place, which means it has a value of 0.004. Therefore, we can write 0.964 in expanded form as:
0.964 = 0.9 + 0.06 + 0.004
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simply the following expression below.
(5x^2 + 5x -6)
Answer: It is simplified the way it is it can not be simplified anymore. its a trick question
Step-by-step explanation:
Help on this pls due tmrw
5. The value of x in the figure is
C. 6√77. Length of arc AD is 125 degrees
8. Angle ROT is 36.87 degrees
How to find the length of chord xThe length of chord x is solved using Pythagoras theorem as follows
5.
let x/2 = y then we have
y² = 12² - 9 ² = 144 - 81 = 63
y = √63 = 3√7
and x/2 = y = 3√7. so x = 6√7
7. BD is the diameter hence arc BAD = 180 degrees
if arc ABC is 110 then arc BA = 110 /2 = 55
Arc AD = arc BAD - arc BA
Arc AD = 180 - 55
Arc AD = 125 degrees
8. Angle ROT = arc sin (3/5)
Angle ROT = 36.87 degrees
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Solve the system of linear equations using any method
Answer:
(-1,-1)
Step-by-step explanation:
Rearange the equation
5y=6x+1 + 4y=-6x-10
9y = -9
y = -1
The only option with y as -1 is the second one
You can plug in -1 as x into any of the equations
5y=6x+1
-5 = -6+1
Hope this helps
PLEASE HELP FAST!!!!!
Lucy received a $1300 bonus. She decided to invest it in a 3-year certificate of deposit (CD) with an annual interest rate of 1.27% compounded monthly.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Assuming no withdrawals are made, how much money is in Lucy's account after 3 years?
$____
(b) How much interest is earned on Lucy's investment after 3 Years?
$____
Answer:
(a) $1350.46
(b) $50.46
Step-by-step explanation:
You want to know the future value of a $1300 CD earning 1.27% compounded monthly for 3 years, along with the amount of interest earned.
Future valueThe compound interest formula tells you the future value is ...
FV = P(1 +r/12)^(12·t)
where r is the annual interest rate and t is the number of years.
ApplicationUsing the given values, we have ...
FV = $1300(1 +0.0127/12)^(12·3) ≈ $1350.46
(a) The value after 3 years is $1350.46.
The interest earned is the difference between the final value and the amount of the original investment:
Interest = $1350.46 - 1300.00 = $50.46
(b) The interest earned by the CD is $50.46.
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С
Complete each statement given w = 2(cos(90°) + i sin (90°)) and z= √ (cos(250) + i sin(225°)).
Answer:
To complete each statement, we will need to perform some operations on the given complex numbers w and z.
1. Find w^3:
We can use De Moivre's theorem to raise w to the third power:
w^3 = [2(cos(90°) + i sin(90°))]^3
= 2^3(cos(90°3) + i sin(90°3))
= 8(cos(270°) + i sin(270°))
Therefore, w^3 = 8(cos(270°) + i sin(270°)).
2. Simplify z^2:
To simplify z^2, we can use the identity cos(2θ) = 2cos^2(θ) - 1 to simplify the cosine term:
z^2 = [√(cos(250°) + i sin(225°))]^2
= cos(2250°) + i sin(2225°)
= cos(500°) + i sin(450°)
= cos(140°) - i sin(90°)
Therefore, z^2 = cos(140°) - i sin(90°).
Note: We can also simplify the square root of the cosine term using the identity cos(2θ) = 1 - 2sin^2(θ), but this would result in a more complicated expression for z^2.
3. Find the product wz:
We can simply multiply w and z using the distributive property:
wz = 2(cos(90°) + i sin(90°)) * √(cos(250°) + i sin(225°))
= 2√(cos(90°)cos(250°) - sin(90°)sin(250°) + i(cos(90°)sin(250°) + sin(90°)cos(250°)))
= 2√(-sin(250°) + i cos(250°))
Therefore, wz = 2√(-sin(250°) + i cos(250°)).
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
For the given data correct option is option a.) The range is the best measure of variability, and it equals 8.
How to find the measure of variability?The dots on the line plot reflect the quantity of roses purchased every day at a grocery shop based on the supplied data. The dots are scattered horizontally, with some dots above specific numbers.
1, 2, 6, 7, 8, and 9 have dots above them , thus,
for given problem,
[tex]\text{Number of Rose Bouquets: 1, 2, 6, 7, 8, 9}[/tex]
[tex]\text{The range is the difference between the highest and lowest values:}[/tex]
[tex]Range = \text{Highest value} - \text{ Lowest value}\\Range = 9 - 1\\Range = 8[/tex]
The Interquartile Range (IQR) is a measure of variability that considers the difference between the data set's 25th and 75th percentiles (Q3).
The median (Q2) would be towards these digits since there are dots above numbers 6, 7, and 8. As a result, using the information provided, the IQR cannot be computed precisely.
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The graph shows a line of best fit for data collected on the number of students enrolled at a university as a function of the number of faculty employed there. Which equation represents the line of best fit? A. y= 20x B. y=1/50 C. y=2x D. y=x
The equation that represents the line of best fit is given as follows:
y = 50x.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.From the graph, when x = 0, y = 0, hence the intercept b is given as follows:
b = 0.
When x = 10, y = 500, hence the slope m is given as follows:
m = 500/10
m = 50.
Hence the equation is given as follows:
y = 50x.
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A musician on tour exchanges American dollars for British pounds. The equation y = 1.25 x models the relationship between pounds ( x ) and dollars ( y ). Positive numbers represent bank deposits, and negative numbers represent bank withdrawals.
The y-intercept of 0 indicates that if the musician does not exchange any pounds, they will not receive any dollars.
What is the meaning of the slope and y-intercept in this context?In the given equation, y = 1.25x, the slope is 1.25, and the y-intercept is 0.
The slope represents the exchange rate between pounds and dollars. Specifically, it tells us that for every pound exchanged, the musician receives 1.25 dollars.
The y-intercept of 0 indicates that if the musician does not exchange any pounds, they will not receive any dollars.
Keep in mind that positive numbers in this context reflect bank deposits, whereas negative numbers represent bank withdrawals
. As a result, a positive value for y indicates money received, whereas a negative value for y indicates money taken out.
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Carly wants to fly to Canada, rent a car, and drive 568 miles to visit her sister in a truck that gets 21 miles per gallon. If gas costs $1. 02 per liter, how much will the road trip cost her? There are 3. 79 liters in 1 gallon. Round your answer to the nearest cent
Carly will need to buy 27.05 gallons of gas for the trip, which will cost her $7.28.
To calculate the total cost of the road trip, we need to find out how many gallons of gas Carly will need and then multiply that by the cost per gallon.
First, we need to convert the distance from miles to gallons, using the truck's fuel efficiency of 21 miles per gallon
568 miles ÷ 21 miles per gallon = 27.05 gallons
So Carly will need approximately 27.05 gallons of gas for the trip.
Next, we need to convert the cost of gas from liters to gallons. There are 3.79 liters in 1 gallon, so the cost of gas is:
$1.02 per liter ÷ 3.79 liters per gallon = $0.269 per gallon
Finally, we can calculate the total cost of the road trip by multiplying the number of gallons of gas by the cost per gallon
27.05 gallons × $0.269 per gallon = $7.28
Therefore, the road trip will cost Carly approximately $7.28.
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The button on Ted's jacket has a diameter of 10 millimetres. What is the button's radius?
Answer:
To find the button's radius, we need to divide its diameter by 2, since the radius is half the size of the diameter.
radius = diameter ÷ 2
Given that the diameter of Ted's button is 10 millimeters, we can substitute it into the above formula to get:
radius = 10 mm ÷ 2
radius = 5 mm
Therefore, the button's radius is 5 millimeters.
A clothing store has these items on sale:
5 hats
10 jackets
15 pants
20 sweaters
A customer randomly selects one of the sale items. Complete each statement
Select the correct answer for each box. Each answer may be used more than once. Not all answers will be used. a 0.10 b 0.20 c 0.40 d 0.50 e 0.70 f 0.80
The probability that the customer will randomly select a sweater or a hat is
The probability that the customer will randomly select a jacket is
Answer:
To find the probability of choosing a hat, we divide the number of hats by the total number of choices = #hat / #clothes = 5 / (5+10+15+20) = 5 / 50 = 1 / 10 = 0.1.
Step-by-step explanation:
Marina is drawing a plan for a new garden. The rectangle plotted in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need? 4 feet 6 feet 10 feet 20 feet
If Mariana needs to surround the garden with a stone-path, then she would need 20 feet of stone, Option (d) is correct.
The "Perimeter" of a rectangle is defined as the "total-length" of the outer boundary.
The length of the rectangle can be calculated as the difference between the x-coordinates of the vertices on the same vertical side.
In this case, the "x-coordinates" of vertices on same vertical side are 4 and -2.
So, the length of the rectangle is = 4 -(-2) = 6 feet.
Similarly, the width of rectangle is calculated as difference between "y-coordinates" of vertices on same horizontal side.
In this case, the "y-coordinates" of vertices on same horizontal side are 1 and -3.
So, the width of the rectangle is = 1 -(-3) = 4 feet,
To surround rectangle with a stone path, Marina need to add length of stone needed for the perimeter of rectangle, which is sum of all four sides.
The perimeter (P) is ⇒ P = 2(length + width),
Substituting the values,
We get,
⇒ P = 2(6 + 4) = 2(10) = 20 feet
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
Marina is drawing a plan for a new garden. The rectangle with the vertex (4,1) , (4,-3) , (-2,-3) , (-2,1)in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need?
(a) 4 feet
(b) 6 feet
(c) 10 feet
(d) 20 feet
Answer:
20 feet because ik from experience
Solve each one of the following equations and check your result. 4x+7=9
Solving the equation 4x + 7 = 9 will give value of x = 1/2
To solve we will use the equation
4x + 7 = 9
By subtracting 7 from both side we get
4x + 7 -7 = 9 -7
4x = 2
By diving 4 from both sides we get
4x/4 = 2/4
x = 1/2
To check we put the value of x in the equation we get
4(1/2) + 7 = 9
2 + 7 = 9
9 = 9
Hence the value of x is satisfying the equation
Therefore, the value of x is 1/2
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which linear graph represents a proportional relationship?
Question 6
Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car
results in 310 miles on 20 gallons of gas. Which equation below represent the gas milage of the
car? Select ALL answers that apply.
Oy=310-20x
Oy = 15.5x
Oy = 310x + 20
Oy = 31/2x
Answer: Oy = 15.5x
Step-by-step explanation: Gas mileage refers to the quantity of miles driven per unit volume of gasoline, typically expressed as "miles per gallon." In the context of the present inquiry, the vehicle in question exhibited a capacity to traverse a distance of 310 miles subsequent to the utilization of 20 gallons of gasoline. Thus, it is possible to calculate the gas mileage through the division of the quantity of gas consumed by the distance elapsed, resulting in:
The fuel efficiency of a vehicle, represented by the metric of gas mileage, is typically calculated by the ratio of distance traveled in miles to the amount of fuel consumed in gallons. In the present case, the gas mileage is equivalent to the quotient of 310 miles by 20 gallons, resulting in an efficiency rating of 15.5 miles per gallon.
The theoretical probability of an albino Galapagos tortoise being born is 0.001%. If 500,000 Galapagos tortoises hatch, how many would you expect to be albino?
So, we would expect about 5 albino Galapagos tortoises to be born out of 500,000 Galapagos tortoises hatched, assuming that the theoretical probability holds true in practice.
What is probability?Probability is a branch of mathematics that deals with the measurement and analysis of random events. It is the study of how likely an event is to occur, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used in many areas of mathematics, science, and engineering, such as statistics, physics, finance, and computer science. It is a fundamental concept for understanding and predicting the behavior of random events and systems.
Here,
To find the expected number of albino Galapagos tortoises, we can use the formula:
Expected value = Probability of event * Total number of trials
In this case, the probability of an albino Galapagos tortoise being born is 0.001 or 0.001/100 = 0.00001 (as a decimal). The total number of trials is 500,000, since that is the number of Galapagos tortoises that hatched.
Therefore, the expected number of albino Galapagos tortoises is:
Expected value = 0.00001 * 500,000
= 5
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