Answer:
10 gallons
Step-by-step explanation:
84 ÷ 6.5 =12.9(The unit rate.)
Seeing as one gallon can get you 12.9 miles;
126÷12.9=9.7
So the answers 9.7 gallons, but if you need to round, then 10 to get a whole number.
Answer:
9.75
Step-by-step explanation:
We can write a ratio to solve
84 miles 126 miles
-------------- = -------------------
6.5 gallons x gallons
Using cross products
84 x = 6.5 * 126
84x=819
84x/84 = 819/84
x = 9.75
A survey sampled men and women workers and asked if they expected to get a raise or promotion this year. Suppose the survey sampled 200 men and 200 women. If 98 of the men replied Yes and 72 of the women replied Yes, are the results statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year?
a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.
b. What is the sample proportion for men? For women?
c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?
Answer:
a)
The null hypothesis is: [tex]H_0: p_M - p_W = 0[/tex]
The alternative hypothesis is: [tex]H_1: p_M - p_W > 0[/tex]
b) For men is of 0.49 and for women is of 0.36.
c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Men:
98 out of 200, so:
[tex]p_M = \frac{98}{200} = 0.49[/tex]
[tex]s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353[/tex]
Women:
72 out of 200, so:
[tex]p_W = \frac{72}{200} = 0.36[/tex]
[tex]s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339[/tex]
a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.
At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:
[tex]H_0: p_M - p_W = 0[/tex]
At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:
[tex]H_1: p_M - p_W > 0[/tex]
b. What is the sample proportion for men? For women?
For men is of 0.49 and for women is of 0.36.
c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?
From the sample, we have that:
[tex]X = p_M - p_W = 0.49 - 0.36 = 0.13[/tex]
[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error, so:
[tex]z = \frac{0.13 - 0}{0.0489}[/tex]
[tex]z = 2.66[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.
Looking at the z-table, z = 2.66 has a p-value of 0.9961.
1 - 0.9961 = 0.0039.
The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.
According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed.
a.) State the random variable.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
f.) What blood pressure do 90% of all people in China have less than?
Answer:
a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.
b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.
d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg
This means that [tex]\mu = 128, \sigma = 23[/tex]
a.) State the random variable.
Mean blood pressure for people in China, which has mean 128 and standard deviation 23.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
This is 1 subtracted by the p-value of Z when X = 135, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 128}{23}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a p-value of 0.6179.
1 - 0.6179 = 0.3821
0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
This is the p-value of Z when X = 141, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{141 - 128}{23}[/tex]
[tex]Z = 0.565[/tex]
[tex]Z = 0.565[/tex] has a p-value of 0.7140.
0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:
X = 125
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 128}{23}[/tex]
[tex]Z = -0.13[/tex]
[tex]Z = -0.13[/tex] has a p-value of 0.4483.
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 128}{23}[/tex]
[tex]Z = -0.35[/tex]
[tex]Z = -0.35[/tex] has a p-value of 0.3632.
0.4483 - 0.3632 = 0.0851
0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
From item b, when X = 135, Z = 0.3.
Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f.) What blood pressure do 90% of all people in China have less than?
The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 128}{23}[/tex]
[tex]X - 128 = 1.28*23[/tex]
[tex]X = 157.44[/tex]
90% of all people in China have a blood pressure of less than 157.44 mmHg.
which transformation of the red triangle on the graph maps it into the missing peice of the square?
A. a translation 16 units right
B. a reflection across the y-axis
C. a 90° counterclockwise rotation about the origin
D. a 90° clockwise rotation about the origin
E. a 180° rotation about the origin
Answer:
D
The missing piece (triangle) is facing right side up but the red triangle has its point facing left
TO get it facing up, turn it by 90 degrees clockwise
Which equation can be used to find 60 percent of 50
Answer:
x = 0.6 * 50
Step-by-step explanation:
x = 60% of 50
x = 60% * 50
x = 0.6 * 50
Answer:
60% of 50 = 60 / 100 × 50 = ⅗ × 50 = 150 / 5 = 30
________
x% of y = x / 100 × y = xy / 100
Taree fourts of the 64 books were math books. determine the percent of the books that were math books.
Answer: 75% - these are books on mathematics.
Step-by-step explanation:
[tex]\dfrac{3}{4} \cdot 64 = 48\\[/tex]
64 - 100%
48 - x%
[tex]\dfrac{64}{100} =\dfrac{48}{x}\\\\x=\dfrac{48 \cdot 100}{64} \\\\x=75 \%[/tex]
4 The equation of a curve is y= (3-20)^3 + 24.
(a) Find an expression for dy/dx.
g tau .......................
what is the average speed for the interval t=1 hour to t=3 hours
Step-by-step explanation:
2 hours
3+1 / 2 = 4/2 = 2 hours speed average
Which number produces an irrational number when added to 0.4
Answer:
0.31311311131111....
Step-by-step explanation:
We need to tell a number which when adds to 0.4 makes it a Irrational Number . We know that ,
Rational number :- The number in the form of p/q where p and q are integers and q is not equal to zero is called a Rational number .
Irrational number :- Non terminating and non repeating decimals are called irrational number .
Recall the property that :-
Property :- Sum of a Rational Number and a Irrational number is Irrational .
So basically here we can add any Irrational number to 0.4 to make it Irrational . One Irrational number is ,
[tex] \rm\implies Irrational\ Number = 0.31311311131111... [/tex]
So when we add this to 0.4 , the result will be Irrational . That is ,
[tex] \rm\implies 0.4 + 0.31311311131111 ... = 0.731311311131111 .. [/tex]
Counting numbers are to be formed using only the digits 1, 3, 7,5,4,8, and 2. Determine the number of different possibilities for two-digit numbers.
Answer:
11699 numbers and 42 two-digit numbers
The area of rectangle is 105cm².If it length is 21 cm,what is its length and perimeter.
Answer:
length of other side is 5cm and the perimeter is 52
Step-by-step explanation:
The area is side x times side y.
Knowing that the area A is 105cm2 and side x is 21cm
A= x*y
105cm2= 21 y /21
Arranging for y we get
y= 105/21
y= 5 cm
The perimeter is all sides added up
P= 21+21+5+5=52cm
Answer:
length 5cm and perimeter 52 cm
Step-by-step explanation:
length=area/breadth
=105/21
=5 cm
perimeter=2(length+breadth)
=2(5+21)
=52 cm
The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.
The restricted domain for ƒ is ?
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
Help please!!!!!A student needs to select 3 books from 3 different mathematics, 3 different physics and 1 history book. what is the probability that one of them is mathematics and the other 2 are either physics or history books ? A. 3/15 B.9/25 C. 15/35 D. 18/35
===========================================
Explanation:
There are 3 ways to select the single math book and 4*3/2 = 12/2 = 6 ways to pick the two other books that are either physics or history (order doesn't matter). This is effectively because we have 3+1 = 4 books that are either physics or history, and we're using the nCr combination formula.
Overall, there are 3*6 = 18 ways to select the three books such that one is math, and the other two are either physics or history.
-------------------
There are 3+3+1 = 7 books total. Since we're selecting 3 of them, we use the nCr formula again and you should get 35.
Or you could note how (7*6*5)/(3*2*1) = 210/6 = 35
This says there are 35 ways to select any three books where we can tell the difference between any subject (ie we can tell the difference between the math books for instance).
-------------------
We found there are 18 ways to get what we want out of 35 ways to do the three selections. Therefore, the answer as a fraction is 18/35
PLEASE HELP ME PLEASE AND BE CORRECT
Answer:
12 cm²
Step-by-step explanation:
area = L *B
a = 6 * 2
a = 12cm²
convert 2m 50cm 15mm in cm
Answer:
251.5 cm
Step-by-step explanation:
1 m = 100 cm
1 cm = 10 mm
2 m + 50 cm + 15 mm =
= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)
= 200 cm + 50 cm + 1.5 cm
= 251.5 cm
Hi please somebody help me with this equation with explanation thank you
Answer:
[tex]{ \tt{ \frac{1}{24} m - \frac{2}{3} = \frac{3}{4} }} \\ \\ { \tt{ \frac{1}{24} m = \frac{17}{12} }} \\ m = 34[/tex]
Step 1: Find a common denominator
---The common denominator here is 24. So, we need to transform all of the fractions to have a denominator of 24.
1/24m - 16/24 = 18/24
Step 2: Solve
1/24m - 16/24 = 18/24
1/24m = 34/24
m = 34/24 x 24/1
m = 34
Hope this helps!
graph a circle with General form.x^2 +y^2+8x-12y+24=0
Answer:
jhshejwjabsgsgshshsnsjs
Answer:
Step-by-step explanation:
Put the equation into center-radius form.
x² + y² + 8x - 12y + 24 = 0
x² + y² + 8x - 12y = -24
(x²+8x) + (y²-12y) = -24
(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24
(x+4)² + (y-6)² = 28
Center: (-4,6)
radius: √28
So for this problem, I almost got it however my rounding is off causing my answers to be wrong. Can someone please help me with the two that are wrong. Thank you for your help!
Answer:
it 94x26.2 i think it right if not sorry :/
Step-by-step explanation:
What is the answer to this? Is it d?
Answer:
Step-by-step explanation:
yeah of course..your answer is true.. it's part d and there is no solution for that system...w and v both of them remove in solution of system and we don't have any unknown variable for solving.
9514 1404 393
Answer:
D. no solutions
Step-by-step explanation:
The first equation can be simplified to standard form:
0.5(8w +2v) = 3
4w +v = 3 . . . . . . . eliminate parentheses
__
The second equation can also be simplified to a comparable standard form:
8w = 2 -v +4w
4w +v = 2 . . . . . . add v -4w
__
Comparing these two equations, we find the variable expressions to be the same, but the constants to be different. If any set of variable values were to satisfy one of these equations, it could not satisfy the other equation. There are no solutions to the system.
he ride a bike for 15 miles oer hour how many miles did he ride
A friend wants to buy a pool and has two places she wants to purchase the pool with the largest volume which pool should she buy a rectangular pool that is 20' x 15' in 54 inches deep or a cylindrical pool that has a 3.3 m radios and is 1.8 m deep
Answer:
20'×15 in 54 inches
Step-by-step explanation:
The Best as a pool should be rectangular in shape and 54inches deep for safety of life's
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2}[/tex]h
The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;
= [tex]\pi r^{2}[/tex]h
[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]
The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;
V = 20 x 15 x 54
V = 16,200 cubic meter.
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
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Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Express a simplified ratio
Answer:
5:12
Step-by-step explanation:
125:300 simplified = 5:12
I hope this helps
Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?
∠P
∠Q
∠T
∠U
Answer:
[tex]\angle P[/tex]
Step-by-step explanation:
Given
[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]
[tex]PQ = 20[/tex] [tex]QR = 16[/tex] [tex]PR = 12[/tex]
[tex]ST = 30[/tex] [tex]TU = 34[/tex] [tex]SU = 16[/tex]
See attachment
Required
Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]
Considering [tex]\triangle PQR[/tex]
We have:
[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse
So, we have:
[tex]\sin(P) = \frac{16}{20}[/tex]
Divide by 4
[tex]\sin(P) = \frac{4}{5}[/tex]
Hence:
[tex]\angle P[/tex] is correct
Answer:
A or <P
Step-by-step explanation:
on edge 2021
Martinez' General Store is having a 45% off sale on men's clothing. John paid $70.95 for a jacket that was on sale. What was the original price of the jacket?
Answer:
$129
Step-by-step explanation:
We can use this equation:
x - 0.45x = 70.95
0.55x = 70.95
x = $129
Find the value of x in each case and give an explanation plzzz, thank youu :)
Answer:
Step-by-step explanation:
the arrows from the picture tells us that TV is parallel to RS
since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x
(alternate interior angles)
sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°
2x = 45*2 = 90°
3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(X) is shown on the provided graph.
Graph the result of the following transformation on fx).
f(x)+6
10% of 360 is how much more than 5% of 360
10% of 360 is 18 more than 5% of 360.
What is the percentage?The percentage is defined as ratio expressed as a fraction of 100.
What are Arithmetic operations?
Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Given data as :
10% of 360
5% of 360
Firstly, we have to determine 10% of 360,
⇒ 10% of 360
⇒ (10/100)360
⇒ (0.10)360
So, 10% of 360 is 36.
⇒ 5% of 360
⇒ (5/100)360
⇒ (0.05)360
So, 5% of 360 is 18.
Since 10% of 360 is more than 5% of 360
So, substract 18 from 36, and
⇒ 36 - 18
⇒ 18
Hence, 10% of 360 is 18 more than 5% of 360.
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The sum of the 3rd and 7th terms of an A.P. is 38, and the 9th term is 37. Find the A.P?
Let a be the first term in the arithmetic progression. Then each successive term differs from a by a fixed number c, so that
• first term = a
• second term = a + c
• third term = (a + c) + c = a + 2c
• fourth term = (a + 2c) + c = a + 3c
and so on. In general, the n-th term in the AP is a + (n - 1) c.
The sum of the 3rd and 7th terms is 38, so that
(a + 2c) + (a + 6c) = 38
==> 2a + 8c = 38
==> a + 4c = 19 … … … [1]
The 9th term is 37, so
a + 8c = 37 … … … [2]
Subtracting [1] from [2] eliminates a and lets you solve for c :
(a + 8c) - (a + 4c) = 37 - 19
4c = 18
c = 18/4 = 9/2
Solve for a using either equations [1] or [2] :
a + 8 (9/2) = 37
a + 36 = 37
a = 1
Then the n-th term in the AP is 1 + 9/2 (n - 1) or 9/2 n - 7/2, where n ≥ 1.
can someone help me with this question
9514 1404 393
Answer:
local minima: at x=-1, x=3local minimum values: -2 and -1 (respectively)Step-by-step explanation:
A local minimum is where the curve stops going down and starts going up. It is the bottom of any U-shaped spot. Here, those are identified with dots at the coordinates (-1, -2) and (3, -1).
(a) the x-values at which f has a local minimum are -1 and 3.
(b) the local minimum values of f are -2 and -1 at those x-values.
The length of a rectangle is 4 meters and the width is 4 meters. What is the perimeter of the rectangle? Do not include units in your answer.
Answer ASAP
Will give brainliest!
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