Given Information:
Mean test score = μ = 77
Standard deviation of test score = σ = 6.5 seconds
Answer:
The lower limit represents those 34% test scores which are below the mean test score.
The range of test scores will be (70.5 to 77)
The upper limit represents those 34% test scores which are above the mean test score.
The range of test scores will be (77 to 83.5)
Step-by-step explanation:
Normal Distribution:
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The Empirical Rule:
The empirical rule states that approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.
68% of all the data lie within 1 standard deviation from the mean, so that means 34% (half of 68%) of the test scores will be below the mean test score and remaining 34% of the test scores will be above the mean test score.
The confidence interval is given by
[tex]CI = \mu \pm 1 \cdot \sigma \\\\CI = 77 \pm 1 \cdot (6.5) \\\\CI = 77 \pm 6.5 \\\\Lower \: limit = 77 - 6.5 = 70.5 \\\\Upper \: limit = 77 + 6.5 = 83.5 \\\\[/tex]
The lower limit represents those 34% test scores which are below the mean test score.
So the range of test scores will be (70.5 to 77)
The upper limit represents those 34% test scores which are above the mean test score.
So the range of test scores will be (77 to 83.5)
How does the graph of g(x) = x+5+2 compare to the graph of the parent function f(x) =
х
g(x) is shifted 5 units left and 2 units up from f(x).
g(x) is shifted 5 units right and 2 units up from f(x).
g(x) is shifted 5 units left and 2 units down from f(x).
g(x) is shifted 5 units right and 2 units down from f(x).
g(x) is shifted 5 units right and 2 units up from f(x). Therefore, option B is the correct answer.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
The given functions are f(x)=x and g(x)=x+5+2.
Translation rules:
When the shape is moved towards the right by k units, then replace x with x + k.
When the shape is moved up by k units, then replace y with y + k.
So, the translation is g(x) is shifted 5 units right and 2 units up from the parent function.
Therefore, option B is the correct answer.
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Solve for x
8 (V2 - x) = 11
Answer:
V^2 - 11/8
Step-by-step explanation:
8(V^2 - x) =11
V^2 = 11/ 8 + X
X= V^2 - 11/8
Answer:
x= - [tex]\frac{11}{8}[/tex]+[tex]\sqrt{2[/tex]
Step-by-step explanation:
Distribute the 8, which becomes.... 8[tex]\sqrt{2}[/tex] - 8x = 11
Move the numbers to one side.... -8x= 11-8[tex]\sqrt{2}[/tex]
Divide by -8.......- [tex]\frac{11}{8}[/tex]+[tex]\sqrt{2[/tex]
unga oog boog ogah?
Answer:
ooage booge ohag
Step-by-step explanation:
oomago ooga booga
Answer:
I got a universal translator and got "Hello in caveman goodbye in caveman"
Step-by-step explanation:
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply.
Answer:
c and e
Step-by-step explanation:meow
Answer:
c and e
Step-by-step explanation:
WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
+ At time 0 (beginning), the volume is 5 (feet^3) of sand.
+ After 1 minute, it lefts: 90% of 5 = 0.9*5
+ After 2 minutes, it left 90% of (0.9*5) = 0.9*(0.9*5)
or
[tex]5.(0.9)^{2}[/tex]
+ After 3 minutes, it left 90% of [tex]5.(0.9)^{2}[/tex]
or
[tex]5.(0.9)^{3}[/tex]
.......
+ After x minutes, it left 90% of [tex]5.(0.9)^{x-1}[/tex]
or
[tex]5.(0.9)^{x}[/tex]
So the answer is [tex]5.(0.9)^{x}[/tex], that means C
The average cost of tuition plus room and board at small private liberal arts colleges is reported to be less than $18,500 per term. A financial administrator at one of the colleges believes that the average cost is higher. The administrator conducted a study using 150 small liberal arts colleges. It showed that the average cost per term is $18,200. The population standard deviation is known to be $1,400. Let α= 0.05. What are the null and alternative hypothesis for this study?
Answer:
The null and alternative hypothesis for this study are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The null hypothesis is rejected (P-value=0.004).
There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The significance level is 0.05.
The sample has a size n=150.
The sample mean is M=18200.
The standard deviation of the population is known and has a value of σ=1400.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-2.624)=0.004[/tex]
As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
What is the value of 5x+3 when x = 4?
Answer:
Step-by-step explanation:
5(4)+ 3
20+3
23
What the the Quotient 7/12 divided by 2/5
Answer:35/24
Step-by-step explanation:
7/12 ➗ 2/5
Next step we change divide sign to multiplication,with the numerator and denominator of the right hand fraction inverted
7/12 x 5/2
(7x5)/(12x2)
35/24
The quotient of 7/12 divided by 2/5 is 35/24.
To divide fractions, you need to multiply the first fraction by the reciprocal (or the multiplicative inverse) of the second fraction.
The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
So, to find the quotient of 7/12 divided by 2/5, you multiply 7/12 by the reciprocal of 2/5, which is 5/2.
Here are the steps:
Write down the first fraction: 7/12
Write down the reciprocal of the second fraction: 5/2
Multiply the first fraction by the reciprocal: (7/12) x (5/2)
Multiply the numerators: 7 x 5 = 35
Multiply the denominators: 12 x 2 = 24
Simplify the fraction, if possible: 35/24
Therefore, the quotient of 7/12 divided by 2/5 is 35/24.
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Find the compound interest on GHS 50,200 invested at 13% p.a. compounded annually for 3 years ( to the nearest
GHS).
Select one:
A. GHS 19,578
B. GHS 69,778
O
C. GHS 72,433
D. GHS 22.233
Answer:
D
Step-by-step explanation:
First found amount yielded
A = P(1+r)^nt
P is amount deposited 50,200
r is interest rate 13% = 13/100 = 0.13
t = 3
A = 50,200(1+0.13)^3
A = 50,200(1,13)^3
A = 72,433.42939999998
A is approximately 72,433.43
interest = A - P = 72,433.43-50,200 = 22,233.43= 22,233 to the nearest GHS
Find the area of the shape shown.
Answer:
well area is the space inside of a shape. so you would multiply 2 by 4 because there are 4 sides.
Step-by-step explanation:
Answer: area is 10
Step-by-step explanation:
add top and bottom base
8+2=10
then divide by 2
10/2 = 5
then times 5 by 2
5*2=10
8+2/2 * 2 = 10
10 = area
Katie runs 3 miles in 28 minutes. At this pace, how long will it take her to run 13.1 miles? Round to the nearest minute.
Answer:
122.6 min
Step-by-step explanation:
3 miles = 28 min
13.1 miles=x
28min x 13.1 miles=366.8/3=122.6 min
Answer:
122mins
Step-by-step explanation:
3 miles take 28mins
Therefore the pace refers to the speed of travel and is 3/28
The new time of travel = distance /speed
= 13.1 / 3/28
=13.1 * 28 /3
=122.27
=122minutes
How would you describe the translation from f(x)=x2 to f(x)=x2+5 ?
Answer:
5 units up
Step-by-step explanation:
Adding 5 to the y-value of an (x, y) coordinate moves it up 5 units.
f(x) = x^2 +5 is translated 5 units upward from f(x) = x^2.
Which angle has a positive measure?
Answer:
There are two qestions that both have different answers. Here are both of them. One is B one is A
Step-by-step explanation:
Answer:
A on Edge 2023
Step-by-step explanation:
$32 for a 14 2/19 km taxi ride
Answer:
What about it? If you need to know how much that is per km, it would be about $2.27 per km
Step-by-step explanation:
A theater can seat 160 people . If the theater is 60%full, how many more can fit in the theater
Answer:
64 people can fit in the theater.
Step-by-step explanation:
If 60% is full then calculate how many people is it
[tex] \frac{60}{100} \times 160 = 96 \\ 160 - 96 = 64[/tex]
64 is 40% of 160
So this many people can be accommodated in the theater
Answer:
64 more people can fit in the theater
Step-by-step explanation:
You need to find 60% of 160
10%=16 (divided by 10)
16×6=96
160 (total people)-96(60%)=64
There is one missing number in the “Which One Doesn’t Belong” game.
• Select a number that does not belong with any of the numbers. Explain your reasoning.
• Select a number that has a characteristic similar to the other two numbers. Explain your reasoning.
Answer:
I am not I understand the game but
1. 17 doesn't belong cause it a prime number and doesn't dived with any of the other numbers and double digit
2. 4 divides with 216 and 8 and single digit similar to 8
Step-by-step explanation:
A fair coin is flipped 10 times and lands on heads 8 times. Provide a reason to justify the difference between the experimental and theoretical
probabilities. Use the drop-down menus to explain your answer.
There should be a
Choose...
number of trials. With Choose...
flips of the coin, the experimental probability will likely
approach the theoretical probability of Choose...
Answer:
THere will be 8 heads and 2 tails
Step-by-step explanation:
I don't know
plzz help i hav a test after i need the answer quick plzz.
Answer:Oop
Step-by-step explanation:
Which expressions are equivalent to 7.7.7.7.7.7 ?
Answer:
1.84877
Step-by-step explanation:
tnvvvvvvvvvvv4kvjk5nvj5tnnjt5
Answer:
A and C
Step-by-step explanation:
Find the first five terms of the geometric sequence defined by a (n)=10
(.1)^n
Answer:
Step-by-step explanation:
a(1) = 10(.1)^1 = 1
a(2) = 10(.1)^2 = 10(0.01) = 0.1
a(3) = 10(.1)^3 = 10(0.001) = 0.01
a(4) = 0.001
a(5) = 0.0001
Solve for the variable 8x + 15 = 63
Answer:
6
Step-by-step explanation:
63-15 =48 48/8 is 6
Answer:
x = 6
Step-by-step explanation:
8x + 15 = 63
8x = 63 - 15
8x = 48
x = 48/8
x = 6
Mr. Cooper ask his students whether they prefer to go to the aquarium or the planetarium for a field trip. The table shows the result
table says:
response | percent
---------------------------------
aquarium | 50
---------------------------------
planetarium | 25
suppose the rest of the class had no preference what is the ratio of students who have no preference to the students who prefer to go to the aquarium
1:5 1:4 1:3 1:2
Answer:1/2
Step-by-step explanation:
It is 1/2 because 50 percent is the aquarium and the other 50 percent is unknown.
Unit 8: Right Triangles & Trigonometry Homework 2: Special Right Triangles...Please Help!
Answer:
x = 8√3y = z = 12√2Step-by-step explanation:
We presume you want the values of x, y, and z.
__
There are two "special triangles" in geometry and trigonometry. They are the 30°-60°-90° right triangle that is half of an equilateral triangle, and the 45°-45°-90° isosceles right triangle that is half a square (cut by the diagonal).
The side ratios of these special triangles are relatively easy to remember. It is useful to memorize them.
__
For the isosceles right triangle, the side lengths are the same. The Pythagorean theorem tells you that if they are both 1, then the hypotenuse is ...
√(1²+1²) = √2
That is, the side lengths of the 45-45-90 triangle are in the ratio ...
1 : 1 : √2
__
For the triangle that is half an equilateral triangle, you know the hypotenuse is twice the length of the shortest side (since we got that short side by cutting a long side in half). Then the longer side can be found from the Pythagorean theorem:
√(2²-1²) = √3
That is, the side lengths of the 30-60-90 triangle are in the ratio ...
1 : √3 : 2
_____
In this problem, we're given the hypotenuse of a 30-60-90 triangle, so we know the short side of it (x) will be half that length:
x = (16√3)/2
x = 8√3
The hypotenuse of the 45-45-90 triangle will be √3 times x, so will be ...
long side of small triangle = (√3)(8√3) = 24
The shorter sides of that 45-45-90 triangle will be this value divided by the square root of 2, so are ...
y = z = 24/√2
We can multiply this by (√2)/(√2) to "rationalize the denominator".
y = z = 12√2
Answer:
8\sqrt{3},\ 12\sqrt{2},\ 12\sqrt{2}
Step-by-step explanation:
The probability of event A is 0.5 and probability of event B is 0.2. Given that A and B are independent, then the probability of A and B (A intersection B) is:
A) 2.5%
B)7 %
C)10%
D) 14%
Help................!.!!.!.!.
Answer:
Step-by-step explanation:
it will be 5 * 14 = 70 cm in real life scale
Answer:
~ 70 cm of the width of the actual item ~
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. Given the information, let us create a proportionality as such:
1 = 14 ⇒ x - width of the actual item
5 x
2. Now let us cross multiply, and solve through simple algebra for x:
14 * 5= x,
x = 70 centimeters of the width of the actual item
How many sundaes did the shop make if they used 32 spoonfuls of sprinkles?
Answer:
32?
Step-by-step explanation:
Answer:
Depends on how many spoonfuls of sprinkles per sundae. Is there more details to this question?
If there is a strong correlation between the variables a and b, a may cause b.
True or false?
Answer:
true
Step-by-step explanation:
.
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
Angle-Angle-Side Postulate since two angles and one side is congruent to eachother.
Answer:
D. Angle-Angle-Side.
Step-by-step explanation:
The 2 sets of triangles have 2 angles and 1 side congruent so the reason is AAS.
if f(x)=-x^2 and g(x) = -x^2+4x+5 what is the product
Answer:
[tex]x^{4}[/tex] - 4x³ - 5x²
Step-by-step explanation:
-x²(-x² + 4x + 5) Distribute
[tex]x^{4}[/tex] - 4x³ - 5x²
If this answer is correct, please make me Brainliest!
Find the mean, median, and mode(s) of the data. 4, 6, 5, 4, 4, 5, 4, 8
Please Answer it Quickly :^)
Answer:
[see below]
Step-by-step explanation:
The Mean:Add all values together:
[tex]4+6+5+4+4+5+4+8 = 40[/tex]
There are 8 numbers in the data set.
40 ÷ 8 = 5
The mean of the data is 5.
The Median:Order the numbers in ascending order.
4, 4, 4, 4, 5, 5, 6, 8
There is no exact middle number.
[tex](4+5)/2 =4.5[/tex]
The median of the data is 4.5.
The Mode:'4' appears the most in the data set.
4, 4, 4, 4, 5, 5, 6, 8
The mode of the data is 4.
