Answer:
1.12 meters
Step-by-step explanation:
Answer:
1.12
Step-by-step explanation:
each week it grows 0.16 m
so,in 7 weeks it will grow 0.16*7m
2/3 x G = 1/4
Solve for G!
(FIRST ANSWER GETS BRAINLIEST!)
Answer:
The value of G is 3/8 .
Step-by-step explanation:
In order to solve G, you have to divide 2/3 to both sides :
[tex] \frac{2}{3} \times G = \frac{1}{4} [/tex]
[tex] \frac{2}{3} \times G \div \frac{2}{3 } = \frac{1}{4} \div \frac{2}{3} [/tex]
[tex]G = \frac{1}{4} \times \frac{3}{2} [/tex]
[tex]G = \frac{3}{8} [/tex]
Answer:
3/8
Step-by-step explanation:
Convert to common denominator which would be 12.
8/12 x G=3/12
Then divide 3/12 by 8/12 and you get 3/8
What is 99 divided by 6
Answer: 16.5
Step-by-step explanation:
[tex]\frac{99}{6} = 16.5[/tex]
Answer:
What i got is 16.5 hope this helps!
Find the unit vector in the direction of v=(7,-3).
(enter exact answers with square roots)
Answer:
[tex]\binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} }[/tex]
Step-by-step explanation:
First, find the magnitude of the vector:
[tex] |v| = \sqrt{( {(7)}^{2} + {( - 3)}^{2}) } \\ = \sqrt{(49 + 9)} \\ = \sqrt{58} [/tex]
Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:
[tex]unit \: vector = \binom{ \frac{7}{ \sqrt{58} } }{ \frac{ - 3}{ \sqrt{58} } } \\ = \binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} } [/tex]
The formula for the surface area of a cylinder is SA= 2 pi r (h + r). What is the surface area of a cylinder when r = 3 centimetres and h = 4 centemeters?
The surface area of the cylinder, when the radius is 3 centimeters and the height is 4 centimeters, is approximately 131.88 square centimeters.
Use the provided formula for the surface area of a cylinder:
[tex]\[ SA = 2\pi r (h + r) \][/tex]
Given:
[tex]r = 3 \text{ centimeters}[/tex]
[tex]h = 4 \text{ centimeters}[/tex]
Now, substitute these values into the formula and calculate the surface area:
[tex]SA = 2\pi \times 3 \times (4 + 3)[/tex]
[tex]SA = 2\pi \times 3 \times 7[/tex]
[tex]SA = 6\pi \times 7[/tex]
[tex]SA = 42\pi[/tex]
Now, let's calculate the numerical value:
[tex]SA \approx 42 \times 3.14[/tex]
[tex]SA \approx 131.88 \text{ square centimeters}[/tex]
Therefore, the surface area of the cylinder, when the radius is 3 centimeters and the height is 4 centimeters, is approximately 131.88 square centimeters.
(1 point) Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with µ=106μ=106 and σ=24σ=24. (a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ? Answer: Round to four decimal places. (b) What score which marks the lowest 25 percent of the distribution? Answer: Round to two decimal places. (c) Enter the score that marks the highest 5 percent of the distribution. Answer: Round to two decimal places.
Answer:
a) 0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92
b) A score of 89.8 marks the lowest 25 percent of the distribution
c) A score of 145.48 marks the highest 5 percent of the distribution
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 106, \sigma = 24[/tex]
(a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ?
This is 1 subtracted by the pvalue of Z when X = 92. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 106}{24}[/tex]
[tex]Z = -0.58[/tex]
[tex]Z = -0.58[/tex] has a pvalue of 0.2810
1 - 0.2810 = 0.719
0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92
(b) What score which marks the lowest 25 percent of the distribution?
The 25th percentile, which is X when Z has a pvalue of 0.25. So it is X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 106}{24}[/tex]
[tex]X - 106 = -0.675*24[/tex]
[tex]X = 89.8[/tex]
A score of 89.8 marks the lowest 25 percent of the distribution
(c) Enter the score that marks the highest 5 percent of the distribution
The 100-5 = 95th percentile, which is X when Z has a pvalue of 0.95. So it is X when Z = 1.645
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 106}{24}[/tex]
[tex]X - 106 = 1.645*24[/tex]
[tex]X = 145.48[/tex]
A score of 145.48 marks the highest 5 percent of the distribution
Final answer:
Using z-scores and the properties of a normal distribution, it was calculated that approximately 71.90% of children score above 92. The score marking the lowest 25 percent is approximately 90.20, and the score that marks the highest 5 percent of the distribution is around 145.88.
Explanation:
To solve the problems about normal distribution and interpreting IQ scores, we use the properties of the normal curve and z-scores. Z-scores help us understand how far away a particular score is from the mean, in terms of standard deviations.
Part (a): Proportion of Children With Scores Above 92
We first calculate the z-score for 92 using the formula: z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. With μ = 106 and σ = 24, the z-score for 92 is (92 - 106) / 24 = -0.5833. Using a standard normal distribution table, we find that the proportion of children scoring above 92 corresponds to the area to the right of the z-score, which is approximately 0.7190. Therefore, the proportion of children aged 13 to 15 with scores above 92 is 0.7190.
Part (b): Lowest 25 Percent of the Distribution
The score marking the lowest 25 percent of the distribution corresponds to the 25th percentile or a z-score of about -0.675. We convert this z-score back to the original scale using the formula: X = μ + zσ, which yields X = 106 + (-0.675)(24) = 90.20. Thus, the score marking the lowest 25 percent is approximately 90.20.
Part (c): Highest 5 Percent of the Distribution
To find the score that marks the highest 5 percent, we locate the z-score that corresponds to the 95th percentile, which is about 1.645. Applying the conversion formula, we get X = 106 + (1.645)(24) = 145.88. Therefore, the score marking the highest 5 percent is approximately 145.88.
Determine between which consecutive integers the real zeros of y(x) = x2 - 4x – 2 are located.
Answer:
The zeros are x1=4.45 and x2=-0.45.
x1 is between 4 and 5.
x2 is between -1 and 0.
Step-by-step explanation:
We have the function:
[tex]y(x) = x2 - 4x-2[/tex]
As this is a quadratic function, we can calculate the zeros of the function with the quadratic equation:
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot 1\cdot(-2)}}{2\cdot 1}\\\\\\x=\dfrac{4\pm\sqrt{16+8}}{2}\\\\\\x=\dfrac{4\pm\sqrt{24}}{2}\\\\\\x=\dfrac{4\pm4.9}{2}=2\pm2.45\\\\\\x_1=2+2.45=4.45\\\\x_2=2-2.45=-0.45[/tex]
The zeros are x1=4.45 and x2=-0.45.
x1 is between 4 and 5.
x2 is between -1 and 0.
The two real zeros of the quadratic equation are located between -1 and 4.
Between which consecutive integers the real zeros located?To determine between which consecutive integers the real zeros of the function y(x) = x² - 4x - 2 are located, we can use the quadratic formula.
The quadratic formula is given as:
x = (-b ± √(b² - 4ac)) / (2a)
In the equation y(x) = x² - 4x - 2, we have a = 1, b = -4, and c = -2.
Let's substitute these values into the quadratic formula to find the values of x:
x = (-(-4) ± √((-4)² - 4(1)(-2))) / (2(1))
x = (4 ± √(16 + 8)) / 2
x = (4 ± √24) / 2
x = (4 ± 2√6) / 2
x = 2 ± √6
From the quadratic formula, we find that the real zeros of the function are x = 2 + √6 and x = 2 - √6.
To determine between which consecutive integers these real zeros are located, we can compare the values to the nearest integers.
x = 2 + √6 is approximately 4.45
x = 2 - √6 is approximately -0.45
Therefore, the real zeros of the function are located between the consecutive integers -1 and 4.
Learn more about quadratic equations at:
https://brainly.com/question/1214333
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Of the 3737 people at a basketball team party, 2525 of them play basketball, 1515 are under six feet tall, and 5 do not play basketball and are six feet or taller. Determine the number of people at the party who play basketball and are under six feet tall, |B∩????||B∩U| , where BB represents the set of people at the party who play basketball and ????U represents the set of people at the party who are under six feet tall.
Answer:
8
Step-by-step explanation:
Universal Set, U=37
Number who play basketball, n(B)=25
Number who are under six feet, n(U)=15
Number of those who do not play basketball and are six feet or taller, n(B∪U)'=5
From set theory.
U=n(B)+n(U)-n(B∩U)+n(B∪U)'
37=25+15-n(B∩U)+5
37=45-n(B∩U)
Therefore:
n(B∩U)=45-37=8
Therefore, the number of people at the party who play basketball and are under six feet tall is 8.
The number of people at the party who play basketball and are under six feet tall is 1510. These people belong to both the group of basketball players and the group of people under six feet tall.
Explanation:To answer this question, we first need to understand who are the people at the party who play basketball and are under six feet tall. This group of people belongs to both the basketball players group represented by BB and the group of people under six feet tall, represented by U. We are looking for the intersection of these two groups, represented by |B∩U|.
Out of the 3737 people at the party, 2525 of them play basketball. From these 2525 basketball players, we don't know directly how many are under six feet tall. However, we are told that 1515 people at the party are under six feet tall. We also know that 5 people are over six feet tall and do not play basketball.
Therefore, to find out how many under six feet basketball players there are, we can subtract the 5 people who are over six feet and do not play basketball from the total of the ones who are under six feet: 1515 - 5 = 1510. So, there are 1510 people at the party who play basketball and are under six feet tall.
Learn more about Intersection of Sets here:https://brainly.com/question/33193647
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The base of a cylinder has a radius of 9 centimeters. The cylinder is 12 centimeters tall. What is the approximate lateral area of the cylinder? Use 3.14 for π and round to the nearest whole number.
Answer:
The lateral area of the cylinder is 678cm²
Step-by-step explanation:
To calculate the lateral area of the cylinder we have to calculate the circumference and multiply it by the height
To solve this problem we need to use the circumferenc formula of a circle:
c = circumference
r = radius = 9cm
π = 3.14
c = 2π * r
we replace with the known values
c = 2 * 3.14 * 9cm
c = 56.52cm
The length of the circumference is 56.52cm
lateral area = c * h
56.52cm * 12cm = 678.24 cm²
round to the nearest whole number
678.24 cm² = 678cm²
The lateral area of the cylinder is 678cm²
Answer:
c-678 cm2
Step-by-step explanation:
what i got on edg 2020
Evaluate the following expression
40 -8 - 102
Answer:
-70
Step-by-step explanation:
40-8-102
= 32 - 102
= -70
To evaluate the expression 40 - 8 - 102, subtract 8 from 40 to get 32, then subtract 102 from 32 to arrive at -70.
40 - 8 - 102
To solve this expression, we need to follow the order of operations. In this case, since there are only subtraction operations involved, we can proceed from left to right.
40 - 8 = 32
32 - 102 = -70
This gives us the final answer: -70.
what are the first 5 terms of the sequence generated by the formula an= 2(n!)
Answer:
2, 4, 12, 48, 240
Step-by-step explanation:
We have the recursive formula a_n = 2*(n!)
Find:
a_1 = 2* 1! = 2
a_2 = 2*(2!) = 4
a_3 = 2*(3!) = 2*6 = 12
a_4 = 2*(4!) = 2*24 = 48
a_5 = 2*(5!) = 2*5*24 = 240
Question 5
A restaurant bill is $80. Juan leaves a $20 tip. What percent tip is that?
Answer:
25%
Step-by-step explanation:
Plz mark me brainliest.
Answer:
25%
Step-by-step explanation:
Which object has the mass of about one kilogram?
Answer:
A one-liter bottle of soda has a mass of about 1 kilogram.
In a large class of introductory Statistics students, the professor has each person toss a fair coin 1111 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. a) What shape would you expect this histogram to be? Why? b) Where do you expect the histogram to be centered? c) How much variability would you expect among these proportions? d) Explain why a Normal model should not be used here.
Answer:
Given:
Sample size, n = 11
P = 0.5
a) The shape of the histogram will be symmetrical. This is because the probability of getting heads and tails is equal.
b) The histogram is centered at
p = 0.5 (because of equal probability of obtaining heads and tails).
c) How much variability would you expect among these proportions?
Here, we are to find the standard deviation.
Let's use the formula:
[tex] \sigma = \sqrt{\frac{pq}{n}} [/tex]
Where
p = 0.5(probability of getting heads)
q = 0.5 (probability of getting tails)
Therefore
[tex] \sigma = \sqrt{\frac{0.5 * 0.5}{11}} [/tex]
= 0.0227 ≈ 0.023
The standard deviation is 0.023
d) A normal model should not be use here because the success/failure condition is violated, since each student only flips the coin 11 times, it impossible to obtain both at least 10 heads and at least 10 tails. Here, the sample size is too small.
8.73e16 in standerd form
Answer:
Hello,
Here is your answer:
The proper answer to this question is 87300000000000000.
Here is how:
8.73e16=87300000000000000.
Your answer is 87300000000000000.
If you need anymore help feel free to ask me!
Hope this helps!
(P.S. REMEMBER E IS EXPONET OR ^)
using the method of gauss to find the sum 2 + 4 + 6 + ... + 300
Answer:
22650
Step-by-step explanation:
What is the total surface area of the solid?
A rectangular prism with a length of 14 centimeters, width of 10 centimeters and height of 6 centimeters. A rectangular pyramid with 2 triangular sides with a base of 14 centimeters and height of 11 centimeters, and 2 triangular sides with a base of 10 centimeters and height of 12 centimeters.
558 square centimeters
702 square centimeters
842 square centimeters
982 square centimeters
Answer:
so the answer is b i did the quiz
Step-by-step explanation:
What is the total surface area of the solid?
A rectangular prism with a length of 14 centimeters, width of 10 centimeters and height of 6 centimeters. A rectangular pyramid with 2 triangular sides with a base of 14 centimeters and height of 11 centimeters, and 2 triangular sides with a base of 10 centimeters and height of 12 centimeters.
558 square centimeters
702 square centimeters
842 square centimeters
982 square centimeters
Answer:
B but i could be wrong
Step-by-step explanation:
Mrs.Golden wants to cover her 6.5 by 4 bulletin board with silver paper that comes in 1-foot squares how many squares does Mrs.Golden need to cover her bulliten board will there be any pieces left over why or why not
Final answer:
Mrs. Golden will need 26 squares of silver paper to cover her bulletin board, and there will not be any pieces left over.
Explanation:
To find out how many 1-foot squares Mrs. Golden needs to cover her bulletin board, we first need to calculate the area of the bulletin board. The area of a rectangle can be found by multiplying the length and width. In this case, the length is 6.5 feet and the width is 4 feet, so the area is 6.5 feet x 4 feet = 26 square feet.
Since the silver paper comes in 1-foot squares, we can divide the area of the bulletin board by the area of each square to find out how many squares are needed. In this case, we divide 26 square feet by 1 square foot, giving us a result of 26 squares.
There will not be any pieces left over because 26 squares fully cover the area of the bulletin board. If there were any remaining space, we would need a fraction of a square to cover it.
Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight. The student who weighs his rock 5 times uses the mean to calculate the 95% confidence interval for the rock weight (in grams). His interval is (25.2, 29.1). What does a 95% confidence interval for rock weight tell us in this case? Group of answer choices We are 95% confident that this interval includes the mean of the 5 weight measurements taken by this student. We are 95% confident that most rocks of this type weigh between 25.2 g and 29.1 g. We are 95% confident that the true weight of the rock is between 25.2 g and 29.1 g.
Answer:
We are 95% confident that the true weight of the rock is between 25.2 g and 29.1 g.
Step-by-step explanation:
Hello!
A geology student weighted a rock 5 times and estimated the average weight using a 95% CI [25.2; 29.1]gr
The confidence interval is used to estimate the value of the population mean, it gives you a range of values for it.
The 95% level of confidence of the interval indicates that if you were to construct 100 confidence intervals to estimate the population mean, you'd expect 95 of them to include the true value of the parameter.
So with a 95% confidence level, you'd expect the true average weight of the rock to be included in the interval [25.2; 29.1]gr
I hope this helps!
A square of side length 7 cm is enlarged using the scale factor 6. Find the area of the enlarged square.
Answer:
The answer is 42 centimeters.
Step-by-step explanation:
HOPE THIS HELPED!
(Please be clear)
Solve the following cost minimization problems. For each of these find the conditional factor demands and c(w1, w2, y):
(a) f(x1, x2) = x ^1/4 1 x ^1/4 2 , and w1 = 1 and w2 = 2
(b) f(x1, x2) = x ^1/2 1 x ^1/2 2 , and w1 = 2 and w2 = 2
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
150 students in a tenth grade high school class take a survey about which video game consoles they own 60 students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox Out thesethere are who have both systems.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
150 students in a tenth grade high school class take a survey about which video game consoles they own. 60 students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox. Out of these, there are 20 who have both systems.
Let A be the event that a randomly selected student in the class has a Playstation and B be the event that the student has an XBOX. Based on this information, answer the following questions.
a) What is P(A), the probability that a randomly selected student has a Playstation?
b) What is P(B), the probability that a randomly selected student has an XBOX?
c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?
d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?
Answer:
a) P(A) = 2/5
b) P(B) = 1/3
c) P(A and B) = 2/15
d) P(A | B) = 2/5
Step-by-step explanation:
Total no. of students = 150
No. of students having playstation = 60
No. of students having xbox = 50
No. of students who have both playstation and xbox = 20
a) What is P(A), the probability that a randomly selected student has a Playstation?
P(A) = No. of students having playstation/Total no. of students
P(A) = 60/150
P(A) = 2/5
b) What is P(B), the probability that a randomly selected student has an XBOX?
P(B) = No. of students having xbox/Total no. of students
P(B) = 50/150
P(B) = 1/3
c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?
The probability that a students has a Playstation and an Xbox is given by
P(A and B) = P(A)*P(B)
P(A and B) = (2/5)*(1/3)
P(A and B) = 2/15
d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?
The conditional probability is given by
P(A | B) = P(A and B)/P(B)
P(A | B) = (2/15)/(1/3)
P(A | B) = 2/5
Alternatively:
P(A | B) = P(A∩B)/P(B)
Where P(A∩B) is given by
P(A∩B) = No. of students who have both playstation and xbox/Total no. of students
P(A∩B) = 20/150
P(A∩B) = 2/15
P(A | B) = P(A∩B)/P(B)
P(A | B) = (2/15)/(1/3)
P(A | B) = 2/5
My sister needs help
"Find the perimeter of the figure to the nearest hundredth."
Answer: 27.42 ft
Step-by-step explanation:
To find the perimeter first we must find the circumference of the circles.
You can easily find the diameter by subtracting and you get 6.
Using the circle circumference formula c=2piR you get 9.42.
9.42 is our circumference of one circle.
You don't need to divide this by 2 because you already have 2 halves of a circle.
Next add all the sides which is 18.
Add this to the circumference we calculated earlier which gives you 27.42 ft.
Tatiana made a two-way table to describe what her friends like at the amusement park. Which could be the columns and rows for Tatiana’s table? columns: likes roller coasters, likes water rides; rows: doesn’t like roller coasters, doesn’t like water rides columns: likes water rides, doesn’t like roller coasters; rows: doesn’t like water rides, likes roller coasters columns: likes roller coasters, doesn’t like roller coasters; rows: likes water rides, doesn’t like water rides columns: doesn’t like water rides, likes roller coasters; rows: doesn’t like roller coasters, likes water rides? HELP
Answer:
i think its c
Step-by-step explanation:
Answer:
C: Columns: likes roller coasters, doesn’t like roller coasters; rows: likes water rides, doesn’t like water rides
Step-by-step explanation:
Like variables need to be together on the columns and rows
How many minutes have passed between the time shown on the first clock and the time shown on the second clock
If you add a pic maybe I could help but for now I cant
Point B has coordinates (5, 1) The x coordinate of point A is 0 . The distance between point A and Point B is 13 units. What are the possible coordinates of point A?
Let y represent the y-coordinate of point A.
We have been given that point B has coordinates (5,1) The x-coordinate of point A is 0. So coordinates of point A would be (0,y)
The distance between point A and Point B is 13 units.
We will use distance formula to solve our given problem.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let point A [tex](0,y)=(x_2-y_2)[/tex] and point A [tex](5,1)=(x_1,y_1)[/tex].
Upon substituting coordinates of both points in distance formula, we will get:
[tex]13=\sqrt{(0-5)^2+(y-1)^2}[/tex]
[tex]13=\sqrt{25+y^2-2y+1}[/tex]
[tex]13=\sqrt{y^2-2y+26}[/tex]
Let us square both sides as:
[tex]13^2=(\sqrt{y^2-2y+26})^2[/tex]
[tex]169=y^2-2y+26[/tex]
[tex]169-169=y^2-2y+26-169[/tex]
[tex]0=y^2-2y-143[/tex]
[tex]y^2-2y-143=0[/tex]
Upon splitting the middle term, we will get:
[tex]y^2-13y+11y-143=0[/tex]
[tex]y(y-13)+11(y-13)=0[/tex]
[tex](y-13)(y+11)=0[/tex]
Now we will use zero product property.
[tex](y-13)=0, (y+11)=0[/tex]
[tex]y=13, y=-11[/tex]
Therefore, the possible coordinates of point A would be [tex](0,-11)[/tex] and [tex](0,13)[/tex].
Which statement best describes why the sale price is a function of the original price?
Answer:
see below
Step-by-step explanation:
A relation is a function when there is exactly one output for each input. That is the case in this table, so the relation between the original price and sale price is a function.
The equation having null set as its solution set is
A) x = cos x
B) x = e^x
C) x = sin x
D) x = tan x
Answer:
B) x = e^x
Step-by-step explanation:
The graphs of y = e^x and y = x never intersect, so the solution set will be the empty (null) set for ...
x = e^x
_____
There is one intersection of y=x with cos(x) and with sin(x). There are an infinite number of solutions for x = tan(x).
The hypotenuse of a right triangle is 10 feet long the longer leg is 2 feet longer than the shorter leg find the side side of the triangle
Answer:
square root of 96 or 9.79
Step-by-step explanation:
a2+b2=c2
2square+b2=10square
4+b2=100
(4-4)+b2=(100-4)
b2=square root96 or 9.79
Alice’s scores for five math test are: 85, 76, 81, 90, 88. What score must she achieve on the sixth test to give her an average of 85?
A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 81 graduating seniors and found the mean score to be 506 with a standard deviation of 83. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest tenth. (Do not write \pm±).
Answer:
The margin of error for the mean is of 165.18 points.
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9901
The margin of error is:
M = T*s = 1.9901*83 = 165.18.
In which s is the standard deviation of the sample.
The margin of error for the mean is of 165.18 points.
Final answer:
The answer discusses z-scores for SAT scores, calculating scores above the mean, and comparing performance on different tests.
Explanation:
Z-score for SAT score of 720:
Calculate the z-score: z = (720 - 520) / 115 = 1.74.
Interpretation: A score of 720 is 1.74 standard deviations above the mean.
Math SAT score 1.5 standard deviations above the mean:
Calculate the score: 520 + 1.5(115) ≈ 692.5.
The score of 692.5 is 1.5 standard deviations above the mean of 520.
Better performance on math tests:
For SAT: z = (700 - 514) / 117 ≈ 1.59.
For ACT: z = (30 - 21) / 5.3 ≈ 1.70.
Person with a z-score closer to 2 performed better relative to the test they took.