Answer:
The missing measures in triangle STU are:
SU = 14, ST = (2/3)TU, TU = (4/3)ST, m∠S = 70 degrees, m∠T = 64 degrees, m∠U = 46 degrees.
Step-by-step explanation:
Since triangles PQR and STU are similar, their corresponding sides are in proportion, and their corresponding angles are congruent. We can use this information to find the missing measures in triangle STU:
Since side PQ corresponds to side ST, we have:
ST/PQ = TU/PR
Substituting the given values, we get:
ST/14 = TU/21
Cross-multiplying, we get:
ST × 21 = 14 × TU
ST = (14/21)TU
Simplifying, we get:
ST = (2/3)TU
Since side QR corresponds to side TU, we have:
TU/QR = ST/RP
Substituting the given values, we get:
TU/28 = ST/21
Cross-multiplying, we get:
TU × 21 = 28 × ST
TU = (28/21)ST
Simplifying, we get:
TU = (4/3)ST
Since angle P corresponds to angle S, we have:
m∠S = m∠P = 70 degrees
Since angle R corresponds to angle U, we have:
m∠U = m∠R = 46 degrees
To find m∠T, we can use the fact that the angles in a triangle add up to 180 degrees:
m∠S + m∠T + m∠U = 180
Substituting the given values, we get:
70 + m∠T + 46 = 180
Simplifying, we get:
m∠T = 64 degrees
To find SU, we can use the fact that the corresponding sides are in proportion:
SU/PR = ST/PQ
Substituting the given values, we get:
SU/21 = (2/3)
Cross-multiplying, we get:
SU = 14
Therefore, the missing measures in triangle STU are:
SU = 14
ST = (2/3)TU
TU = (4/3)ST
m∠S = 70 degrees
m∠T = 64 degrees
m∠U = 46 degrees.
Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]
question jordan wondered if the bean burritos at restaurant a tend to be heavier than bean burritos at restaurant b. to investigate, she visited each restaurant at 10 randomly selected times, ordered a bean burrito, and weighed the burrito. the 95% confidence interval for the difference (a - b) in the mean weight of the burrito is 0.06 ounce 0.20 ounce. based on the confidence interval, which conclusion is most appropriate?
The conclusion of question as discuss below.
Define the term mean?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 values in the set and then dividing by the total number of values.
Based on the given information, we can say that there is a 95% chance that the true difference (a - b) in the mean weight of the bean burritos between Restaurant A and Restaurant B falls within the interval 0.06 ounce to 0.20 ounce.
Since the confidence interval does not include zero, we can conclude that there is a statistically significant difference between the mean weights of the bean burritos at the two restaurants. Specifically, we can say that the mean weight of the bean burritos at Restaurant A is likely to be heavier than the mean weight of the bean burritos at Restaurant B.
However, it's important to note that we cannot determine the magnitude of the difference or the direction of causation (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).
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We can infer that there is a statistically significant difference among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero.
Define the term mean?The mean, which reflects the average value of a group of numbers, is a metric of central tendency. It can be calculated by adding up all of the values in the collection, dividing by the total number of values, and then taking the remainder away.
Based on the information provided, we can state that there is a 95% chance that the actual difference (a - b) between Restaurant A and
Restaurant B's mean weight of the bean burritos will lie between 0.06 ounce and 0.20 ounce.
We can infer that there is a statistically significant variance among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero. We can specifically state that the bean burritos' average weight at Restaurant A is probably heavier than the average bean burrito's weight at Restaurant B.
It's crucial to remember that we cannot establish the size of the difference or the causal relationship. (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).
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Select the correct answer from each drop-down menu.
The approximate length of side XY is (3, 3. 16, 4, 4. 24) units.
The approximate length of side YZ is (3, 3. 16, 4, 4. 24) units.
The approximate length of side ZX is (3, 3. 16, 4, 4. 24) units.
The approximate perimeter of triangle XYZ is (9. 32, 10, 10. 32, 11. 4) units
The approximate length of side XY is 3.16 units, side YZ is 4 units, and side ZX is 4.24 units. The approximate perimeter of triangle XYZ is 10.32 units.
To calculate the approximate perimeter of triangle XYZ, we must first find the approximate length of each side. To do this, we can use the Pythagorean theorem. For side XY, we calculate 3² + 3² = 9 + 9 = 18. We then take the square root of 18, which is approximately 3.16. For side YZ, we calculate 4² + 3² = 16 + 9 = 25. We then take the square root of 25, which is approximately 4. For side ZX, we calculate 4² + 4² = 16 + 16 = 32. We then take the square root of 32, which is approximately 4.24. Finally, we add the lengths of all three sides together to get the approximate perimeter of triangle XYZ, which is 3.16 + 4 + 4.24 = 10.32.
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how do i write a linear equation to represent this relationship
Note that the linear equation that represents this relationship is y = -3x + 9.
What is the explanation for the above response?
To write a linear equation to represent this relationship, we need to find the slope and y-intercept of the line that passes through the given points.
Using the formula for slope, we have:
slope = (change in y) / (change in x)
= (0 - 9) / (3 - 0)
= -3
Now we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line. Let's use the point (0, 9):
y - 9 = -3(x - 0)
Simplifying, we get:
y - 9 = -3x
Adding 9 to both sides, we get:
y = -3x + 9
Therefore, the linear equation that represents this relationship is y = -3x + 9.
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??????????????????????question is on the pic
Answer:
Step-by-step explanation:
QR^2=PQ^2+PR^2
QR^2=(8[tex]\sqrt{3}[/tex])^2+(8)^2=8^2*(3+1)=8^2 * (4)
PR=8*2=16
answer is C
Two rectangles were used to form the following figure. Use the ruler provided to measure the dimensions of the figure to the nearest quarter of an inch.Which measurement is closest to the area of the shaded region of this figure in square inches
The measurement that is closest to the area of the shaded region is 19 square inches.
How to find the area of Shaded Region this figure?So to determine the area of shaded region. we first find by the area of the big rectangle.
Let the dimensions of rectangle are 10 by 15 inches.
The area would be
[tex]A = 10 *15\\= 150\ inches^{2}[/tex]
Now, we calculate the area of small rectangle.
Let the dimensions of rectangle are 10 by 13 inches.
The area would be
[tex]A = 10 *13\\= 130\ inches^{2}[/tex]
Now we calculate the difference between these two area,
= 150 - 130 inches²
= 20 inches²
19 value is the closest to 20.
So, 19 in² is the closest to the area of the shaded region.
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Complete Question :
Two rectangles were used to form the following figure. Use the ruler provided to measure the dimensions of the figure to the nearest quarter of an inch.
Which measurement is closest to the area of the shaded region of this figure in square inches?
a. 19 in²
b. 11 in²
c. 6 in²
d. 8 in²
12 In terms of л, work out the length of an arc which subtends an angle of 240° at the cen- tre of a circle of diameter 6 cm.
Answer:
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Class 10
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>>Areas Related to Circles
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Question
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Find the length of the arc in terms of π that subtends an angle of 30
∘
at the centre of a circle of radius 4 cm.
Easy
Updated on : 2022-09-05
Solution
verified
Verified by Toppr
⇒ θ=30
o
and r=4cm
⇒ Length of an arc =
360
o
θ
(2πr)
Where, θ is angle subtended at a center.
2πr is circumference of a circle.
⇒ Length of an arc =
360
o
30
o
×2π×4
⇒ Length of an arc =
12
2π×4
∴ Length of an arc =
3
2π
1. Defective DVDs From past experience, a company
Number of accidents X
Probability P(X)
found that in cartons of DVDs, 90% contain no defective DVDs, 5% contain one defective DVD, 3% contain two defective DVDs, and 2% contain three defective DVDs. Find the mean, variance, and standard deviation for the number of defective DVDs
The answer about number of defective DVDs in a carton are mean number is 0.15, the variance is 0.1575, and the standard deviation is 0.397.
Let X be the number of defective DVDs in a randomly chosen carton of DVDs. We know that:
P(X=0) = 0.90 (90% contain no defective DVDs)
P(X=1) = 0.05 (5% contain one defective DVD)
P(X=2) = 0.03 (3% contain two defective DVDs)
P(X=3) = 0.02 (2% contain three defective DVDs)
Mean: The mean of X is given by:
μ = E(X) = Σ(xi × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.
μ = (00.90) + (10.05) + (20.03) + (30.02)
= 0.15
Therefore, the mean number of defective DVDs in a carton is 0.15.
Variance: The variance of X is given by:
σ² = E((X-μ)²) = Σ((xi-μ)² × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.
σ² = ((0-0.15)²⁰.⁹⁰) + ((1-0.15)²⁰.⁰⁵) + ((2-0.15)²⁰.⁰³) + ((3-0.15)²⁰.⁰²)
= 0.1575
Therefore, the variance of the number of defective DVDs in a carton is 0.1575.
Standard deviation: The standard deviation of X is given by:
σ = √(σ²)
σ = √(0.1575)
= 0.397
Therefore, the standard deviation of the number of defective DVDs in a carton is 0.397.
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What are the measures of angles 1 and 2? m∠1 = ° m∠2 = °
The measure of angle 1 is 50° and the measure of angle 2 is 130°.
Given that the chord intercepted arc RQ is 53° and the chord intercepted arc ST is 47°, we need to find the measures of angles 1 and 2.
According to a geometric property, the measure of the angle formed by two chords that intersect inside the circle is half the sum of the intercepted arcs. Applying this property, we can find the measure of angle 1:
measure of angle 1 = (53° + 47°) / 2
= 100° / 2
= 50°
Next, we can use the fact that the sum of angles 1 and 2 is 180° to find the measure of angle 2:
measure of angle 1 + measure of angle 2 = 180°
50° + measure of angle 2 = 180°
measure of angle 2 = 180° - 50°
measure of angle 2 = 130°
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Answer:
m∠1 =
✔ 50°
m∠2 =
✔ 130°
Step-by-step explanation:
edg2023
Assume you are the coach for a sports team. You have to decide the sports drink the team will use during practices and games. You obtain a sports magazine and Table 1 gives the list of most popular sports drinks and some important information about each. Compute the mean cost per container, and create a 90% confidence interval estimate for the mean. Do all costs per container fall inside the confidence interval? If not, which ones do not?
n= 7
values as follows: 1. 29, 1. 19, 0. 89, 0. 79, 1. 59, 1. 09, 01. 89
The mean cost per container is 1.13 dollars. A 90% confidence interval estimate for the mean is (0.66, 1.60) dollars. Not all costs per container fall inside the confidence interval. The costs of 1.89 and 0.89 dollars per container do not fall inside the confidence interval.
The coach for a sports team computed the mean cost per container of popular sports drinks, which was found to be $1.13. A 90% confidence interval estimate for the mean was calculated to be between $0.66 and $1.60. However, the costs of $1.89 and $0.89 per container did not fall within the confidence interval, indicating that they are not representative of the mean cost. This information could be used to make an informed decision on which sports drink to use for the team, considering factors such as cost and confidence in the mean cost per container.
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The same video is uploaded to a different website. There are also 100 views in day one ,but 400 views on day 2and 1,600 views on day 3. Explain how the explicit and rescursive formula change
The explicit formula is given by the equation a(n) = 50n² + 25n + 25 and the recursive formula is given by a(n) = a(n-1) + 200, with a(1) = 100.
What is the finite differences method?A approach for identifying patterns in numerical sequences is the method of finite differences. It entails first identifying the differences between each word in the sequence, then repeating the procedure with the sequence of differences that results. If a pattern forms where the gaps between the gaps are always the same, the initial sequence exhibits a polynomial pattern. Both the recursive formula, which enables us to compute any term by utilising the previous term in the series, and the explicit formula for the sequence, which allows us to calculate any term in the sequence directly, can be found using the procedure.
Given the views on different days we have:
First finite difference: 300-100 = 200
Second finite difference: 1200-300 = 900
We observe that second finite difference is constant and hence follows a quadratic pattern.
Using the explicit formula we have:
a(n) = 50n² + 25n + 25
where, a(n) is the views on day n.
Using recursive formula:
a(n) = a(n-1) + 200, with a(1) = 100
Hence, the explicit formula is given by the equation a(n) = 50n² + 25n + 25 and the recursive formula is given by a(n) = a(n-1) + 200, with a(1) = 100.
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what is the missing letter? high amount of points
Based on the pattern or sequence, it can be concluded that the missing letter is K.
What principle does the sequence follow?To understand the principle or fule the sequence follows, let's analyze the letters given:
A - C - E
These letters show the sequence follows the alphabet order but one of the letters is omitted. In the first case, the letter omitted is B and in the second case, the letter omitted is E. Based on this, the missing letter should be K.
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Solve for theta from [0, 2pi)
cos2theta = -1
Show work please
The solution for theta in the equation cos2theta = -1 in the range [0, 2π) is Ф = π/2
Solving for theta in the equationGiven the equation
cos2theta = -1
Express properly
cos(2Ф) = -1
Take the arc cos of both sides
So, we have
2Ф = π
Divide both sides by 2
Ф = π/2
Hence, the value of theta in the range is π/2
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Question 8, please help
8/10
6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.
We can set up a prοpοrtiοn using the given ratiο οf sugar tο baking sοda:
3 cups sugar : 2 teaspοοns baking sοda
We want tο find hοw many teaspοοns οf baking sοda are needed fοr 9 cups οf sugar, which we can represent as:
9 cups sugar : x teaspοοns baking sοda
Tο set up a prοpοrtiοn, we can crοss-multiply the ratiοs:
3 cups sugar * x teaspοοns baking sοda = 9 cups sugar * 2 teaspοοns baking sοda
Simplifying, we get:
3x = 18
Dividing bοth sides by 3, we get:
x = 6
Therefοre, 6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.
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Which equation represents the image of the line y= 1/2x+1 after a translation of -2 units on the y-axis?
Therefore , the solution of the given problem of equation comes out to be y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.
How do equations work?A variable term is typically used in complex variable algorithms to ensure agreement with both conflicting claims. Numerous academic numbers are shown to be equal using equations expression, which have been mathematical statements. In this case, the normalise technique offers b + 6 to use the info from y + 6 rather than splitting 12 into two parts.
Here,
By deducting 2 from each point's y-coordinate, one can acquire the image of the line after it has been translated -2 units on the y-axis.
The initial formula is
=> y = 1/2x + 1.
=> y = 1/2x + 1 - 2 when 2 is subtracted from it.
When we simplify, we obtain:
=> y - 2 = 1/2x - 1.
Consequently, y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.
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y = 1/2x - 1 is the equation for the image of the line.
Define the term equation ?A mathematical statement proving the equality of two expressions is known as an equation. Variables, constants, mathematical symbols, and operations like addition, subtraction, multiplication, and division are frequently used in it.
One can obtain the picture of the line after it has been translated -2 units on the y-axis by subtracting 2 from each point's y-coordinate.
The basic equation is given
y = 1/2x + 1
y - 2 = 1/2x + 1 - 2 [translated -2 units on the y-axis]
Simplify,
y - 2 = 1/2x - 1
Therefore, y = 1/2x - 1 is the equation for the image of the line.
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In a large population of adults_ the mean IQ is 119 with standard deviation of 18_ Suppose 50 adults are randomly selected for market research campaign: (Round to 2 decimal places for all z-values and round all other answers t0 decimal places, if needed ) (a) The distribution of IQ is exactly normal (b) The distribution of the sample mean IQ is approximately normal with mean of and standard deviation of (c) The probability that the sample mean IQ is less than 117 is (d) The probability that the sample mean IQ is greater than 117 is (e) The probability that the sample mean IQ is between 117 and 123 is
Standard deviation
a) The distribution of IQ is exactly normal.Trueb) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54c) The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886e) The probability that the sample mean IQ is between 117 and 123 is 0.773Step-by-step explanationa) The distribution of IQ is exactly normalGiven population mean IQ, µ = 119Standard deviation, σ = 18b) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54The standard error of the sample is calculated as:SE = σ/√nwhere σ = 18 and n = 50SE = 18/√50SE = 2.54The distribution of the sample means is approximated to normal with the help of central limit theorem. The mean of sample means is μ = 119 and standard deviation of sample means is σ/√n = 2.54.c) The probability that the sample mean IQ is less than 117 is 0.114We need to calculate the z-score using the formula:z = (x-μ)/SEz = (117-119)/2.54z = -0.79Now, using z-table, the probability is calculated as:P(Z < -0.79) = 0.2146The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886The probability that the sample mean IQ is greater than 117 is equal to one minus the probability of less than 117:P(Z > -0.79) = 1 - 0.2146 = 0.786The probability that the sample mean IQ is greater than 117 is 0.886.e) The probability that the sample mean IQ is between 117 and 123 is 0.773We need to calculate the z-score for 117 and 123 as:z1 = (117-119)/2.54 = -0.79z2 = (123-119)/2.54 = 1.57The probability of sample means between 117 and 123 can be found as:P(-0.79 < Z < 1.57) = 0.773The probability that the sample mean IQ is between 117 and 123 is 0.773.
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In a certain fraction, the denominator is 6 more than the numerator. If 3 is added to both the numerator and denominator, the resulting fraction is equivalent to 1. What was the original fraction (not written in lowest terms)+
The original fraction is 5/8. The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.
Let the numerator be 'n'. The denominator is 6 more than the numerator, so the denominator is (n + 6).
We can represent this as an equation:
n/(n + 6) = 1
We can solve for the value of n by multiplying both sides by the denominator, (n + 6):
n*(n + 6) = 1*(n + 6)
Simplifying, we get:
n^2 + 6n = n + 6
Subtracting 6n from both sides gives us:
n^2 = 6
Taking the square root of both sides yields:
n = √6
The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.
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what is the sin 0 if cos =-6/10 and 0 is in quadrant 2?
Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is: sin 0 = 0.8
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles. It is used tο study and sοlve prοblems invοlving triangles, especially right triangles.
Since cοsine is negative and the angle is in quadrant 2, we knοw that the sine will be pοsitive. We can use the Pythagοrean identity tο find the value οf sine:
sin²θ + cοs²θ = 1
Substituting the value οf cοsine, we get:
sin²θ + (-6/10)² = 1
Simplifying, we get:
sin²θ + 36/100 = 1
sin²θ = 1 - 36/100 = 64/100 = 0.64
Taking the square rοοt οf bοth sides, we get:
sin θ = ±0.8
Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is:
sin 0 = 0.8
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Choose the most likely correlation value for this scatterplot:
r=−0.127
r=−0.383
r=−0.828
r=0.678
r=0.845
r=0.941
Based οn the given οptiοns, the mοst likely cοrrelatiοn value fοr this scatterplοt wοuld be r = -0.383.
What is cοrrelatiοn?Cοrrelatiοn refers tο the statistical relatiοnship between twο οr mοre variables. In οther wοrds, it measures hοw strοngly twο variables are related tο each οther. A cοrrelatiοn value ranges frοm -1 tο +1, with -1 indicating a perfectly negative cοrrelatiοn, 0 indicating nο cοrrelatiοn, and +1 indicating a perfectly pοsitive cοrrelatiοn. A cοrrelatiοn cοefficient οf 0 means there is nο linear relatiοnship between the twο variables.
The cοrrelatiοn cοefficient ranges frοm -1 tο +1, where -1 indicates a perfect negative cοrrelatiοn, 0 indicates nο cοrrelatiοn, and +1 indicates a perfect pοsitive cοrrelatiοn. Based οn the given οptiοns, the mοst likely cοrrelatiοn value fοr this scatterplοt wοuld be r = -0.383. This indicates a mοderate negative cοrrelatiοn between the variables.
The absοlute value οf the cοrrelatiοn cοefficient (0.383) suggests that the relatiοnship is nοt particularly strοng, but there is sοme evidence tο suggest that as οne variable increases, the οther variable tends tο decrease.
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According to Centers for Disease Control and Prevention (CDC), the weights for boys in kindergarten are
normally distributed with a mean of 44 pounds and a standard deviation of 3.2 pounds.
(a) What is the probability of selecting a boy in kindergarten whose weight is between 38 pounds and 48 pounds?
(b) Boys weighted over 52 pounds are considered as obesity. What is the probability of selecting an obese kindergarten boy?
(c) What is the cut off value for the top 5% of the weights? If the weight of Philip is 50 pounds, will he be in the top 5%?
Philip is not in the top 5% of weights.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. Probability can also be expressed as a percentage, ranging from 0% to 100%.a) We need to find the probability of selecting a boy in kindergarten whose weight is between 38 pounds and 48 pounds. This can be done by calculating the z-scores and using the z-table.
The z-score for a weight of 38 pounds is:
z = (38 - 44) / 3.2 = -1.875
The z-score for a weight of 48 pounds is:
z = (48 - 44) / 3.2 = 1.25
Using the z-table, the probability of selecting a boy whose weight is between -1.875 and 1.25 is approximately 0.8365.
(b) We need to find the probability of selecting an obese kindergarten boy, which means a boy with a weight over 52 pounds. We can calculate the z-score for a weight of 52 pounds as:
z = (52 - 44) / 3.2 = 2.5
Using the z-table, the probability of selecting a boy whose weight is over 52 pounds is approximately 0.0062.
(c) We need to find the cut-off value for the top 5% of weights, which corresponds to a z-score of 1.645. We can use the z-score formula to solve for the weight value:
z = (x - 44) / 3.2
1.645 = (x - 44) / 3.2
x - 44 = 1.645 * 3.2
x = 49.276
So the cut-off weight value for the top 5% of weights is approximately 49.276 pounds.
Philip's weight of 50 pounds is greater than the mean weight of 44 pounds, but it is less than the cut-off weight value for the top 5% of weights.
Therefore, Philip is not in the top 5% of weights.
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A large soda cup holds 32 ounces. What is this capacity in cubic
inches?
Answer:
57.7 cubic inches
Step-by-step explanation:
1 ounce = 1.8 cubic inches
32 ounces = 57.7 cubic inches
So, the capacity is 57.7 cubic inches.
Suppose that the Local sales tax rate is 4% and you purchase a car for 24,500. A. How much Tax is paid?
B. What is the car’s total cost?
The purchase cost of a car 24,500 with local sales tax rate 4% has following answer,
Total tax paid = $980
Total cost of a car including tax = $25.480.
Purchasing cost of a car = $24,500
Local sales tax rate on a car = 4%
Tax paid on the car purchase = (Purchase price) × (tax rate)
Substitute the value we get,
⇒ Tax amount = 4% of 24,500
⇒ Tax amount = 0.04 x 24,500
⇒ Tax amount = $980
Total cost of a car including tax = ( Tax amount ) + (Purchase price )
Substitute the value we have,
⇒ Total cost of a car = Purchase price + Tax amount
⇒ Total cost of a car = 24,500 + 980
⇒ Total cost of a car = $25,480
Therefore, the tax paid on the car purchase and the car's total cost including tax is equal to $980 and $25,480 respectively.
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Alex has 1/3 bag of cat food. If he feeds his cat an equal amount of food for 7 days, what fraction of the bag does he feed his cat each day
Alex feeds his cat 1/21 of the bag each day.
The fraction of the bag that Alex feeds his cat each day is 1/21. This can be calculated using the following formula:
Fraction of Bag = 1/3 / 7
Using algebra, we can solve this equation by multiplying both sides of the equation by 7, which results in the following equation:
1/3 = (1/21) * 7
Simplifying the equation, we get
1/3 = 1/21
Therefore, the fraction of the bag that Alex feeds his cat each day is 1/21.
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a line has a slope of 3 and a y-intercept of 5. what is its equation in slope-intercept form? write your answer using integers, proper fractions, and improper fractions in simplest form
Answer:
y = 3x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 3 and c = 5 , then
y = 3x + 5
In ΔJKL, \text{m}\angle J = (8x-7)^{\circ}m∠J=(8x−7)
∘
, \text{m}\angle K = (x+7)^{\circ}m∠K=(x+7)
∘
, and \text{m}\angle L = (2x+15)^{\circ}m∠L=(2x+15)
∘
. What is the value of x?x?
Answer:
x=15
Step-by-step explanation:
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a plane has 360 360360 total seats, which are divided into economy class and business class. for every 13 1313 seats in economy class, there are 5 55 seats in business class. how many seats are there in each class?
There are 100 seats in business class and 260 seats in economy class on the plane. As,we know that for every 13 seats in economy class, there are 5 seats in business class. We can write this as a fraction:5/13. This fraction represents the ratio of seats in business class to seats in economy class.
We can use this ratio to find the actual number of seats in each class, let's start by finding the total number of seats in business class. To do this, we need to know what fraction of the total number of seats is in business class. We can write this as: 5/18. This fraction represents the ratio of seats in business class to the total number of seats and can use this fraction to find the actual number of seats in business class:5/18 * 360 = 100. So there are 100 seats in business class.
Now we can use the ratio of seats in economy class to find the actual number of seats in that class. We know that there are 13 seats in economy class for every 5 seats in business class. So the ratio of seats in economy class to seats in business class is:13/5, We can use this ratio to find the actual number of seats in economy class: 13/5 * 100 = 260, so there are 260 seats in economy class.
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56 is 69% of what number? Round your answer to the nearest hundredth if necessary.
Incorrect answer:124
Answer:
Approximately 81.159
Step-by-step explanation:
First, set up the equation
56 = (0.69)(x)
^ is 69% of a number
Divide each side by 0.69 to simplify
56 / 0.69 = x
x ≈ 81.159420...
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 168 pages if the mean (μ) is 190 pages and the standard deviation (σ) is 22 pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary.
Provide your answer below:
To find the probability that a randomly selected book has fewer than 168 pages, we need to use the empirical rule, which is a guideline for how data is distributed in a normal distribution.
The empirical rule states that (approximately):
68% of the data points will fall within one standard deviation of the mean.95% of the data points will fall within two standard deviations of the mean.99.7% of the data points will fall within three standard deviations of the mean.In this case, we have:
Mean (μ) = 190 pagesStandard deviation (σ) = 22 pagesLower bound (x) = 168 pagesWe can calculate how many standard deviations away from the mean x is by using this formula:
z = (x - μ) / σPlugging in our values, we get:
z = (168 - 190) / 22z = -1This means that x is one standard deviation below the mean.
So, we are looking for the probability that a randomly selected book has a value less than -1 standard deviations from the mean. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 34% of the data falls between the mean and -1 standard deviation.
To find the area under the normal distribution curve to the left of -1 standard deviation, we can use a standard normal distribution table (z-table) or calculator. The area to the left of -1 standard deviation is approximately 15.87%.
Therefore, the probability that a randomly selected book has fewer than 168 pages is approximately 15.87%.
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Let the random variable Z follow a standard normal distribution. Find the value u , such that P(−0.62
We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392
Given, Random variable Z follows standard normal distribution. To find the value of u such that P(−0.62-0.62)Now, we will find the Z value for -0.62 using standard normal table as follows:-We get the value of P(Z<-0.62) as 0.2676Now, P(Z>-0.62)=1-P(Z<-0.62)=1-0.2676=0.7324Now, P(-Z<0.62)=P(Z<0.62)=0.7324We know, 0.62 lies between u=0 and u', we can find u' using standard normal table as follows:-From the standard normal table, we get that P(Z<0.62)=0.7315P(Z<0)=0.5Now, Z follows standard normal distribution, Z~N(0, 1) => 0.62=(u'-0)/1 => u'=0.62To find the value of u, let's use the formula Z = (X - μ) / σ where X is the observation, μ is the mean and σ is the standard deviation. We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392Now, using standard normal table, we get the value of Z when P(Z
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The Hair Care Salon charges a stylist $30 per day to rent a station at the salon. Rhonda, a stylist, makes $12 on each haircut.
Answer: I got it :)
The equation that represents the number of haircuts she needs to do is 10.5x = 168.
Step-by-step explanation:
Given, The Hair Care Salon charges a stylist $30 per day to rent a station at the salon, Rhonda, a stylist makes $10.50 on each haircut.
Therefore, She needs to earn $138 + $30 to make a profit of $138 and let
'x' be the number of haircuts.
Therefore, the equation that equation that represents this situation is.
10.50x = 138 + 30.
10.5x = 168.
If x = 4 units, y = 5 units, and h = 6 units, find the area of the rhombus shown above using decomposition.
The area of a rhombus is 15 units².
What is the rhombus?A rhombus is a quadrilateral with four sides that are all the same length. It is sometimes referred to as a lozenge or a diamond. A rhombus has equal opposite angles, and its diagonals form a right angle cut across one another.
Rhombus area can be express using the formula:
Area = (base x height) / 2
where the base and height refer to any two sides of the rhombus that form a right angle.
Given figure: base = 5 units and height = 6 units
Area of a rhombus = (5 × 6) / 2 = 30/2
Area of a rhombus = 15 units²
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