The number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula [tex]n^{p}[/tex] = n × n × n × ... × n, where n is the base number and p is the exponent. For example,[tex]4^{2}[/tex] = 16 and [tex]4^{3}[/tex]= 64.
The number of times a number is multiplied by itself is known as the power or exponent. For example, let's say we have the number 4. If we want to calculate 4 to the power of 2 ([tex]4^{2}[/tex]), we are essentially multiplying the number 4 by itself twice. This is written as 4 multiplied by 4, which is equal to 16. In mathematical notation, the calculation is written as [tex]4^{2}[/tex] = 16.To calculate the power of a number, we can use the exponent formula: [tex]n^{p}[/tex] = n × n × n × ... × n
where n is the base number and p is the exponent. For example, if we want to calculate[tex]4^{3}[/tex] (4 to the power of 3), we would write the formula as 4 × 4 × 4 = 64. The corresponding mathematical notation is [tex]4^{3}[/tex] = 64.
In summary, the number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula [tex]n^{p}[/tex] = n × n × n × ... × n, where n is the base number and p is the exponent. For example,[tex]4^{2}[/tex] = 16 and [tex]4^{3}[/tex]= 64.
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What is the conversion of 5.8 feet in cm?
Answer:
172.72 cm
Step-by-step explanation:
5 feet 8 inches in cm = [(5×12)+8] x 2.54 = 68 x 2.54 = 172.72 cm
help?????Miranda and Rory are multiplying 413
by different fractions. The table shows their work.
Rory's product is____
Mirandas because Rory is multiplying by a factor ______.
Rory's product is less than Maranda's because 13/9 is less than 13/3
Describe Fraction?In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.
The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.
Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.
A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.
An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.
A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.
Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.
From the table, it appears that Maranda multiplied 4 1/3 by 4 1/3 and then by 1/3, while Rory multiplied 4 1/3 by 1/3 and then by 4 1/3.
Multiplying by 1/3 first reduces the overall size of the number being multiplied, resulting in a smaller product. This is what Rory did, which is why their product is less than Maranda's.
On the other hand, Maranda multiplied by the larger numbers first and then by the smaller fraction, resulting in a larger overall product.
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The complete question is:
Maranda and rory are multiplying 4 1/3 by different fractions the table shows there work
maranda / rory why is rory's product less than maranda's
4 1/3 x 4 1/3 x 1/3
3/3 =4 1/3 1 4/9
how to convert 5/6 as percent?
5/6 can be expressed as 83% in percentage form.
Percentages are a way of expressing a fraction as a portion of 100. This makes it easier to compare fractions and understand their relative sizes. In this case, we will be converting the fraction 5/6 into a percentage.
To convert 5/6 into a percentage, we need to first divide the numerator (top number) by the denominator (bottom number) and then multiply the result by 100. This will give us the percentage equivalent of the fraction.
So, let's do the math:
5 ÷ 6 = 0.83333...
We can round this to two decimal places, giving us:
0.83
Now, we need to multiply this by 100 to convert it into a percentage:
0.83 × 100 = 83%
It's important to remember that percentages are a way of expressing a portion of 100. So, when we say that 5/6 is 83%, we are saying that 5/6 is equivalent to 83 out of 100. This means that if we were to divide something into 100 equal parts, 83 of those parts would be equivalent to 5/6.
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What is 64 times pi?
As per multiplication, the value of 64 times π is 200.96
Multiplication is a fundamental arithmetic operation that involves repeated addition. In this case, we are tasked with finding the result of multiplying 64 and pi. Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is commonly denoted by the Greek letter "π".
To find the product of 64 and pi, we simply need to multiply these two numbers. Multiplication is typically represented using the "×" symbol or the "dot" symbol ( · ). In this case, we can write:
64 × π
Since pi is a mathematical constant, we typically use an approximation of its value in calculations. The commonly used approximation is 3.14, which is accurate to two decimal places. Thus, we can substitute 3.14 for pi and obtain:
64 × 3.14
Using the distributive property of multiplication, we can break down 64 into smaller factors that are easier to multiply with 3.14. For example, we can write:
64 = 60 + 4
Then, we can use the associative property of multiplication to group the factors in a way that makes the calculation easier. For instance, we can write:
64 × 3.14 = (60 × 3.14) + (4 × 3.14)
Now, we can use our knowledge of multiplication tables to calculate the products on the right-hand side. We get:
60 × 3.14 = 188.4
4 × 3.14 = 12.56
Therefore, the final result is:
64 × π = 188.4 + 12.56 = 200.96
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Last month, Ed spent $50 in all. He spent 40% of the money at the movies. How much money did Ed spend at the movies
A loading dock at a warehouse has a ramp that is 16 feet in length. The length from the edge of the loading dock to the end of the ramp is 14 feet. What is the height of the loading dock to the nearest tenth of a foot?
The required height of the loading dock is approximately 7.746 feet (to the nearest tenth of a foot).
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. Let's call the height of the loading dock "h". The ramp, the distance from the edge of the loading dock to the end of the ramp, and the height of the loading dock form a right triangle. The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the ramp in this case) is equal to the sum of the squares of the other two sides (the height and the distance from the edge of the loading dock to the end of the ramp).
In this case, we can write:
16² = h² + 14²
256 = h² + 196
60 = h²
Taking the square root of both sides, we get:
h = √60
h ≈ 7.746
Therefore, the height of the loading dock is approximately 7.746 feet (to the nearest tenth of a foot).
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The quadratic equation x x4 3 2 0 2 − − = has what roots
The quadratic equation x2 - 4x + 3 = 0 has two roots. The roots are given by the quadratic formula as x = [4 ± √(16 - 12)]/2, which gives x = [4 ± 2√3]/2. Therefore, the roots are x = 2 ± √3.
The quadratic equation x^2 - 4x - 3 = 0 has two roots.
To find the roots of this equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 1, b = -4, and c = -3. Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-3)))/(2(1))
x = (4 ± √(16 + 12))/2
x = (4 ± √28)/2
x = (4 ± 2√7)/2
Simplifying further, we get:
x = 2 ± √7
Therefore, the two roots of the equation are x = 2 + √7 and x = 2 - √7.
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Please help I’ll give brainliest
The sum of the expressions 8x - 2 and - 3x² - 7 is, - 3x² + 8x - 9.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
Given, Two expressions, 8x - 2 and - 3x² - 7.
Now, Sum implies adding.
Therefore, The sum of 8x - 2 and - 3x² - 7 is,
(8x - 2) + (- 3x² - 7).
= - 3x² + 8x - 2 - 7.
= - 3x² + 8x - 9.
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in a study of environmental lead exposure and iq, the data was collected from 221 221 children in cincinnati, ohio. their iq scores at age of 7 7 approximately follow a normal distribution with mean of 87.0 87.0 and standard deviation of 11.4. 11.4 . suppose one child had an iq of 55. 55 . the researchers would like to know whether an iq of 55 55 is an outlier or not. calculate the lower fence for the iq data, which is the lower limit value that the iq score can be without being considered an outlier. keep a precision level of two decimal places for the lower fence.
The lower fence is 56.2428
As the Iq score < lower fence, Iq score is outlier
What is average/mean?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
data was collected from 221 children
iq scores at age of 7 approximately follow a normal distribution with mean of 87.0 and standard deviation of 11.4.
Let X=iq scores
distribution is
X ~ [tex]N( \mu=87, \sigma=11.4)[/tex]
If one child has iq of 55,
To find outlier, find the lower fence
lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]
[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]
[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]
Using excel function,
[tex]Z_{0.25} = -0.67[/tex]
[tex]Z_{0.75} = 0.67[/tex]
[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]
=87+(-0.6745)11.4
= 79.3107
[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]
= 87+(0.6745)11.4
= 94.6893
lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]
= 79.3107 -1.5(94.6893 - 79.3107 )
= 56.2428
So, the lower fence is 56.2428
As the Iq score < lower fence, Iq score is outlier
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evaluate the expression 5 ⋅ � 3 � 2 x 2 5⋅x 3 start fraction, 5, dot, x, cubed, divided by, x, squared, end fraction for � = 2 x=2x, equals, 2.
The value of the expression is found to be 1 0 when the value of x is equal to 2.
The expression provided to us is 5.x³/x² for x = 2.
Now, in order to evaluate this expression, we will follow the simple,
5.x³/x² = 5x.
First as we can see, x³ can be divided by x²and then we will get x as the outcome of the simple division operation,
So, we will get,
5x
Now, we have to put the value of x equal to 2 so that we get to know about the exact value of the expression,
x = 2,
= 5(2)
= 10
So, the value of the expression is found to be 10 when the value of x was 2.
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Complete question - Evaluate the expression 5.x³/x² for x equals to 2.
WORKING OUT!!! I cannot stress ts enough, it’s also the whole basis of my assignment. Please show working out
Answer:
$7500
Step-by-step explanation:
So to find mean the formula is total divided by no. of items or values so therefore the total no. of people is 310+390+380+420 which is 1500 people and if one ticket is $20 ,1500 tickets is 1500 multiplied by 20 which is $30,000 and the mean of one night would by 30,000 divided by 4 nights which is $7500 per night.Hope this helped!
Measurement & space math questions. 20 pts, show working out!
Based on the information, the probability that the next buyer did not buy apples last week is: 0.23
How to calculate the probability that the next buyer did not buy apples last week?To calculate the probability that the next buyer did not buy apples last week we must carry out the following mathematical procedure:
Add up all the values.
17 + 12 + 5 + 8 + 2 + 8 + 3 = 55Now we add the number of buyers who bought apples
17 + 12 + 5 + 8 = 42Finally, to find the probability we must divide the number of people who bought apples by the total number of buyers.
42 / 55 = 0.76However, to find the value of those who did NOT buy apples we must subtract this value from 1.
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Write the solution set of the given homogeneous system in parametric vector form.3x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=03x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=0 where the solution set is x=⎡⎢⎣x1x2x3⎤⎥⎦x=[x1x2x3]
The solution set of the given homogeneous system in parametric vector form is x = (0, 0, t), where t is a real number
Vectors are an important mathematical tool for representing complex data and equations. In this problem, we are given a homogeneous system of equations and asked to write the solution set in parametric vector form.
The homogeneous system consists of three equations: 3x₁ + 3x₂ + 6x₃ = 0, -6x₁ - 6x₂ - 12x₃ = 0, and -4x₂ + 4x₃ = 0. To solve this system, we need to use linear algebra techniques, such as Gaussian elimination, to find the solution set.
By using Gaussian elimination, we can reduce the system to a simpler system, which has the form x₁ = 0, x₂ = 0, and x₃ = t, where t is a real number. This can be written as a parametric vector form as x = (0, 0, t).
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A gem is cut in the shape of two square pyramids that are joined at their base. The length of each side of the base is 6cm and the height of each pyramid is 4cm. Determine the surface area of the composite solid. (A)72cm2 (B)87cm2 C)103cm2 D)120cm2
The solution is, pyramid's volume is 96 cm^3.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
from the given information we get,
So we know that the bar edge length is 8 cm (6+2) and the height is 6 cm....
And a pyramid's volume is 1/3 of a prism's volume.
If the base is square and both sides are 6 cm, the area is 36 cm^2.
Then you multiply that area by the height: 288 cm^3.
BUT you have divide that by 3,
because a pyramid's volume is 1/3 of a prism's volume:
288/3= 96 cm^3.
Answer: 96 cm^3
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A pets shop amount of rabbits is approximated by R(t)=2t2/3+10 in t weeks. After how many weeks, t, will the pet shop have 18 rabbits.
For a pet shop to approximate 18 rabbits, it would take 6 weeks.
In the question, we have a formula that represents the number of rabbits available with them.
The amount of rabbits is dependent on another variable, Time.
The variables depend on each other, and the number of rabbits with the pet shop relies on the number of weeks.
R(t)= 2t(2/3) + 10
If the number of rabbits is 18, then the value of the equation would be equal to 18. [R(t) = 18]
18= 2t(2/3) +10
18= 4t/3 + 10
8 X 3 = 4t
24/4 = t
6 = t
Therefore, 18 rabbits are approximated by the pet store in 6 weeks.
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The measure of each exterior angle of a regular polygon of 12 sides is ______ .
A.45°.
B 75°.
C 60°.
D 30°.
Answer:
Step-by-step explanation:
The sum of exterior angles of a polygon is 360
Each exterior angle = 360/n
where n is the number of sides
360/12 = 30
Answer is D
What is the conversion of 135 kg to lbs ?
The value of 135 kg into lbs can be converted by multiplying kilogram by 2.204622 so the answer is 297.624 pounds.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.
The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.
Pounds = kilograms × 2.20462262184878
= 135 x 2.20462262184878
= 297.624 pounds or lbs.
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Tyler takes his friends out for pizza and wings. He pays the whole bill of $71.46. He wants to leave an 18% tip. How much does the bill and tip cost Tyler?
The total cost of the bill and tip for Tyler is $71.46. This means that Tyler paid $58.6 for the food and drinks, and an additional $12.86 as a tip for the service.
To calculate how much the bill and tip cost Tyler, we first need to calculate the amount of the tip. We can do this by multiplying the total bill by the percentage of the tip, which is 18% or 0.18 as a decimal.
Tip amount = $71.46 x 0.18 = $12.86
Once we know the tip amount, we can add it to the total bill to find the final cost.
Bill and tip cost = $71.46 - $12.86 = $58.6
Therefore, total bill is $84.32 with tip as $12.86 and bill as $58.6
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If the dimensions of a rectangular playground ca be represented as (3x + 16) and (2x + 3), then what is the area of the playground?
Answer:
6x² + 41x + 48
Step-by-step explanation:
Area (A) = l × w
Therefore,
A = (3x + 16)(2x + 3) (distribute)
A = 6x² + 9x + 32x + 48 (combine like terms)
A = 6x² + 41x + 48
Therefore, the area of the playground is 6x² + 41x + 48.
5+5multiplied 5-5 divided by 5
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C
and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P91, the 91-
percentile. This is the temperature reading separating the bottom 91% from the top 9%.
P91
=
The temperature separating the bottom 91% from the top 9% is given as follows:
P91 = -1.34ºC.
How to obtain the measure using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
For the P91, the temperature is obtained as X when Z has a p-value of 0.91, so X when Z = 1.34, hence:
1.34 = X/1
X = 1.34ºC.
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An organization promoting good nutritional habits collected data on fat calories in foods from 9 fast food
staurants. The values represent the number of fat calories in a small order of french fries from each restaurant.
160, 106, 104, 113, 160, 103, 161, 89, 96
What is the median number of fat calories in a small order of fries at these restaurants?
to find the MEDIAN, arrange the #s in order and find the middle #.
If the total number of calories is X, then the lowest number is 89, which is 43% of the total, or 206.98 calories. Thus, the response is A.
The middle value of the provided collection of data, when organised in order, is known as the median in statistics. It is possible to arrange the data or observations in either ascending or descending order. For instance, the median of 2,3,4, is 3. The median, a form of average used to determine the center value in mathematics, is another average.
Two easy steps are used to determine the median of a dataset. Put the information provided in ascending order first. The middle data must be chosen next.
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How many inches are in 52 cm?
52 cm is equivalent to nearly 20.47 inches, rounded to two decimal places.
The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.
It is the unit of length.
Furthermore, length is measured in centimeters,
Used in the International System of Units,
This is the metric system's present configuration.
52 centimetres equal 20.47 inches (centimeters).
To convert centimeters to inches,
We can use the following conversion:
1 inch = 2.54 cm
Therefore,
To convert 52 cm to inches,
You can divide 52 by 2.54:
52 cm / 2.54 = 20.47 inches
So, 52 cm is equivalent to nearly 20.47 inches,
rounded to two decimal places.
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Find −2⋅[4x+1(−2)]
.Select one:
a. 8
b. -40
c. 20
d. -16
The expression −2⋅[4x+1(−2)] is d. -16.
How to find the expression?To simplify the expression −2⋅[4x+1(−2)], we first need to evaluate the expression inside the square brackets:
4x + 1(-2) = 4x - 2
Then we can substitute this back into the original expression:
−2⋅[4x+1(−2)] = −2⋅(4x - 2)
Using the distributive property, we can multiply -2 by each term inside the brackets:
−2⋅(4x - 2) = -8x + 4
Therefore, the answer is d. -16.
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a company has two locations with a total of 23 employees. if four times the number of employees at the larger location is four greater than seven times the number of employees at the smaller location, how many employees are at each location, how many employees are at each location??
Consider that X is the staff so at tinier location while Y is workforce at the origin. 9 people are employed at tiny site, compared to 24 at larger location (s).Is the right answer.
X + Y = 33
It is assumed that two times the number of employees at the larger location is three times the number at the smaller location. The equation for this is as follows:
2Y = 5X + 3
Because we already know that X + Y = 33, we can write it as X = 33 - Y.
Let us now plug X into the above equation.
2Y = 5*(33 - Y) + 3
2Y = 165 - 5Y + 3
7Y = 168
Y = 168 / 7
Y = 24
Let us now compute the value of X.
X + Y = 33
X + 24 = 33
X = 9
The smaller location employs 9 people, while the larger location employs 24 people (s).
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Express the following fraction in simplest form using only positive exponents. \frac{12u^{10}}{4(u^{3})^4}
4(u
3
)
4
12u
10
The simplified form of the fraction is 3/u², where u is a positive real number.To simplify this fraction, we can first simplify the denominator by using the exponent rule that says: [tex](a^{m}) ^{n} =(a^{m*n})[/tex]. Applying this rule, we get:
4(u³)⁴ = 4u³*⁴ = 4u¹²
Now, we can substitute this value back into the original fraction and simplify further:
(12u¹⁰)/(4(u³)⁴) = (12u¹⁰)/(4u¹²)
We can simplify the fraction further by dividing both the numerator and the denominator by the greatest common factor (GCF) of 12 and 4, which is 4. Also, we can simplify the exponent by using the exponent rule that says: [tex]\frac{a^{m} }{a^{n}} =a^{m-n}[/tex]. Applying these steps, we get:
(12u¹⁰)/(4u¹²) = (3u¹⁰)/(u¹²) = 3/u²
Therefore, the simplified form of the fraction is 3/u², where u is a positive real number.
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Yaqub has a bag only containing green and yellow pins
3/7 of the pins are green
He picks out a green pin from his bag and gives it to his sister
2/5 of the remaining pins in his bag are green
how many of the remaining pins in his bag are green and how many are yellow
The answer is that there are 8 green pins and 12 yellow pins remaining in the bag after Yaqub gives a green pin to his sister.
Describe Probability?Probability is a branch of mathematics that deals with the study of random events or phenomena. It is used to measure the likelihood or chance of an event occurring. Probability is represented as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if a fair coin is flipped, the probability of getting heads is 1/2, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
There are two main types of probability: theoretical probability and empirical probability.
Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. For example, the theoretical probability of rolling a six on a fair die is 1/6, since there is one favorable outcome out of six possible outcomes.
Empirical probability is based on observations and experiments and reflects the actual frequency of an event occurring. For example, the empirical probability of rolling a six on a particular die after many rolls may be different from the theoretical probability due to factors such as bias or chance.
Probability is used in many real-life situations, such as in games of chance, insurance, stock market analysis, and weather forecasting. It is also used in various fields of science, such as physics, biology, and chemistry, to model and analyze the behavior of complex systems.
Let's start by using algebra to represent the information given in the problem.
Let G be the number of green pins in the bag, and Y be the number of yellow pins in the bag. We know that:
G + Y is the total number of pins in the bag.
G/(G + Y) = 3/7, since 3/7 of the pins are green.
(G - 1)/[(G - 1) + Y] = 2/5, since after Yaqub gives a green pin to his sister, there are (G - 1) green pins remaining out of (G - 1 + Y) total remaining pins.
To solve for G and Y, we can use algebra to manipulate the equations:
G/(G + Y) = 3/7 can be simplified to 7G = 3(G + Y), which gives us 4G = 3Y.
(G - 1)/[(G - 1) + Y] = 2/5 can be simplified to 5(G - 1) = 2(G - 1 + Y), which gives us 3G - 2Y = 3.
We now have two equations with two variables, so we can solve for G and Y using substitution or elimination. For simplicity, we will use substitution.
From 4G = 3Y, we can solve for Y in terms of G:
Y = (4/3)G
Substituting this into 3G - 2Y = 3, we get:
3G - 2(4/3)G = 3
Simplifying, we get:
G = 9
Therefore, there are 9 green pins in the bag. Using the equation Y = (4/3)G, we get:
Y = (4/3)(9) = 12
So there are 12 yellow pins in the bag. After giving one green pin to his sister, Yaqub has 8 green pins and 12 yellow pins remaining in his bag. To check that 2/5 of the remaining pins are green, we can calculate:
8/(8+12) = 4/10 = 2/5
Therefore, the answer is that there are 8 green pins and 12 yellow pins remaining in the bag after Yaqub gives a green pin to his sister.
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On a coordinate plane, 2 triangles are shown. The first triangle has points X (2, 5), Y (2, 3), Z (4, 3). The second triangle has points X prime (negative 2, negative 5), Y prime (negative 2, negative 3), Z prime (negative 4, negative 3). What are the vertices for the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ?
Herefore, the vertices of the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ are X''(-2, -1), Y''(0, -1), and Z''(0, 1).
First, we need to perform a reflection over the x-axis and then a translation of 2 units to the left and 4 units up. This is the transformation T−2,4.
Next, we need to perform a rotation of 180 degrees about the origin. This is the transformation RO,180°.
We can apply these transformations to each vertex of the first triangle ΔXYZ to obtain the coordinates of the final image.
Applying T−2,4 to each vertex:
T−2,4(X) = (2, 5) → reflection over x-axis → (2, -5) → translation 2 units left and 4 units up → (0, -1)
T−2,4(Y) = (2, 3) → reflection over x-axis → (2, -3) → translation 2 units left and 4 units up → (0, 1)
T−2,4(Z) = (4, 3) → reflection over x-axis → (4, -3) → translation 2 units left and 4 units up → (2, 1)
Applying RO,180° to each vertex:
RO,180°(0, -1) = (0 × cos(180°) - (-1) × sin(180°), 0 × sin(180°) + (-1) × cos(180°)) = (0, 1)
RO,180°(0, 1) = (0 × cos(180°) - 1 × sin(180°), 0 × sin(180°) + 1 × cos(180°)) = (0, -1)
RO,180°(2, 1) = (2 × cos(180°) - 1 × sin(180°), 2 × sin(180°) + 1 × cos(180°)) = (-2, -1)
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Answer:
x is (-4,-1)
y is (-4,1)
z is (-6,1)
Step-by-step explanation:
mike wrote 4 checks for $30 each, withdrew another $40 and deposited $80. What was the overall change in the amount of money he had?
((30$ x4)+40$)-80$=80$
Solve. It’s all real numbers are solutions, click on all reels if there’s no solution click on no solution.
Answer:
no solution
Step-by-step explanation:
7 | y + 6 | + 3 < - 18 ( subtract 3 from both sides )
7 | y + 6 | < - 21 ( divide both sides by 7 )
| y + 6 | > - 3
the absolute value function cannot be negative
thus the equation has no solution