A simple random sample of 41 men from a normally distributed population results in a standard deviation of 10.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts​(a) through​ (d) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic; χ2 = ___ ​(Round to three decimal places as​ needed.)
c. Find the​ P-value; ​P-value = ____ ​(Round to four decimal places as​ needed.)
d. State the conclusion. (choose one from each ( x, y) set)
(Do not reject, Reject) Upper H0​, because the​ P-value is (greater than, less than, or equal to) the level of significance. There is
(sufficient, insufficient) evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to
10 beats per minute.

Answers

Answer 1

Answer:

H0 : σ²=10²

H1 : σ²>10²

χ² = 45.796

Pvalue = 0.2442

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Step-by-step explanation:

Given that :

Sample size, n = 41

Sample standard deviation, s = 10.7

Population standard deviation, σ = 10

Significance level, α = 0.10

The Hypothesis :

H0 : σ²=10²

H1 : σ²>10²

Using the χ² test for population variance :

The test statistic, χ² = (n-1)*s²/σ²

χ² = (41 - 1) * 10.7²/ 10²

χ² = (40 * 114.49) / 100

χ² = 4579.6 / 100

χ² = 45.796

The Pvalue ;

df = n - 1 ; 41 - 1 = 40

Pvalue(45.796, 40) = 0.2442

Since Pvalue > α ; WE fail to reject H0

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.


Related Questions

Solve the right triangle given that mZA= 30°, mZC = 90°, anda = 15. Round your result to one decimal place.​

Answers

Answer:

[tex]\angle B = 60^o[/tex]

[tex]b =17.3[/tex]

[tex]c = 20[/tex]

Step-by-step explanation:

Given

[tex]a= 15[/tex]

[tex]\angle A = 30^o[/tex]

[tex]\angle C = 90^o[/tex]

See attachment for illustration

Required

Solve the triangle

First, we calculate the measure of B

[tex]\angle A + \angle B + \angle C = 180^o[/tex] --- angles in a triangle

[tex]30^o + \angle B + 90^o = 180^o[/tex]

Collect like terms

[tex]\angle B = 180^o-90^o-30^o[/tex]

[tex]\angle B = 60^o[/tex]

Solve for (c) using sine function

[tex]\sin(30) = \frac{a}{c}[/tex]

Make c the subject

[tex]c = \frac{a}{\sin(30)}[/tex]

Substitute known values

[tex]c = \frac{10}{0.5}[/tex]

[tex]c = 20[/tex]

Solve for (b) using Pythagoras

[tex]c^2 = a^2 + b^2[/tex]

This gives:

[tex]20^2 = 10^2 + b^2[/tex]

[tex]400 = 100 + b^2[/tex]

Collect like terms

[tex]b^2 =400 - 100[/tex]

[tex]b^2 =300[/tex]

Take square roots

[tex]b =17.3[/tex]

what is 32⋅(12)x+1=2x−14?

Answers

Answer:

[tex]x=-\frac{15}{382}[/tex]

Step-by-step explanation:

32 × 12x + 1 = 2x - 14

384x + 1 = 2x - 14

384x + 1 - 1 = 2x - 14 - 1

384x = 2x - 15

384x - 2x = 2x - 2x - 15

382x = - 15

382x ÷ 382 = - 15 ÷ 382

[tex]x=-\frac{15}{382}[/tex]

x=cos(2t), y=sin(2t) find a rectangular coordinate equation for the curve by eliminating the parameter​

Answers

Answer:

x^2+y^2=1

Step-by-step explanation:

Since cos^2(x)+sin^2(x)=1, x^2+y^2=1

6/5 times 17/18 in lowest terms

Answers

Answer:

17/15

Step-by-step explanation:

6/5 * 17/18

1/5 * 17/3

17/15

We need to multiply 6/5*17/18. 6 x 17 is 102, 5 x 18 is 90. 102/90 can both be divided by 6. This gives us 17/15. 17/15 as a mixed number is 1 2/15.

Find the value of x. Show your work with proper statements and notation

Answers

Answer:  x = 14

====================================================

Explanation:

For any triangle, the three inside or interior angles always add to 180

M+N+P = 180

32+64+6x = 180

6x+96 = 180

6x = 180-96

6x = 84

x = 84/6

x = 14

1/2-5(2/3x + 6)+4/5x?

Answers

Answer:

[tex]-29.5-\frac{38}{15}x[/tex]

Step-by-step explanation:

First, we must expand out the -5.

-5 times 2/3x is equal to -10/3x, and -5 times 6 is equal to -30. 1/2 minus 30 is equal to -29.5, and 4/5x minus 10/3x is equal to -38/15x.

Which quadratic function has minimum value at x = -b/2a?
O y=-3x2 + 5 X + 6
O y=x2 + 5 x + 6
O y=-x2 + 5x + 6
O y = -4 x2 + 5x + 6

Answers

Answer:

The choose (2)

y=x²+5x+6

Step-by-step explanation:

y=x²+5x+6 —> (–5/2 , –1/4)

y=-3x² + 5 X + 6 —> (5/6, 97/12)

y=-x² + 5x + 6 —> (5/2,49/4)

y = -4 x² + 5x + 6 —> (5/8 , 121/16)

Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation. What is the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.

Answers

Answer:

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation.

This means that [tex]n = 3923, \pi = \frac{3196}{3923} = 0.8147[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 - 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.7987[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 + 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.8307[/tex]

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).

The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5. Calculate the probability of getting at least 4 calls between eight and nine in the morning.

Answers

Answer:

0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.

Step-by-step explanation:

We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.

This means that [tex]\mu = 5[/tex]

Calculate the probability of getting at least 4 calls between eight and nine in the morning.

This is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067[/tex]

[tex]P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337[/tex]

[tex]P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842[/tex]

[tex]P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735[/tex]

0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.

What is the simplified form of the following expression?

Answers

Answer:

-( cube root of 2x)-6(cube root of x)

Help please so lost!!!!!!!!!!!!

Answers

Answer:

hmmmmm please send the pic again

Select the correct answer
The equation of a line is y= 15x-2 What are its slope and y-intercept?
A.slope = 15 and y-intercept=-2
B.slope = 15 and y-intercept = 2
C.slope = 2 and y-intercept=15
D.siope =-2 and y-intercept=15
RES

Answers

Answer:

A

Step-by-step explanation:

Slope = term that multiply x

y intercept = the number without a variable

The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is 2630. Assume the standard deviation is$500 . A real estate firm samples 100 apartments. Use the TI-84 Plus calculator.a) What is the probability that the sample mean rent is greater than $27007?b) What is the probability that the sample mean rent is between $2450 and $2550? c) Find the 25th percentile of the sample mean. d) Would it be unusual if the sample mean were greater than $26457?e) Do you think it would be unusual for an individual to have a rent greater than $2645? Explain. Assume the variable is normally distributed.

Answers

Answer:

a) 0.0808 = 8.08% probability that the sample mean rent is greater than $2700.

b) 0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.

c) The 25th percentile of the sample mean is of $2596.

d) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

e) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

If |Z|>2, the measure X is considered unusual.

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.

The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2630. Assume the standard deviation is $500.

This means that [tex]\mu = 2630, \sigma = 500[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{500}{\sqrt{100}} = 50[/tex]

a) What is the probability that the sample mean rent is greater than $2700?

This is the 1 subtracted by the p-value of Z when X = 2700. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2700 - 2630}{50}[/tex]

[tex]Z = 1.4[/tex]

[tex]Z = 1.4[/tex] has a p-value 0.9192

1 - 0.9192 = 0.0808

0.0808 = 8.08% probability that the sample mean rent is greater than $2700.

b) What is the probability that the sample mean rent is between $2450 and $2550?

This is the p-value of Z when X = 2550 subtracted by the p-value of Z when X = 2450.

X = 2550

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2550 - 2630}{50}[/tex]

[tex]Z = -1.6[/tex]

[tex]Z = -1.6[/tex] has a p-value 0.0548

X = 2450

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2450 - 2630}{50}[/tex]

[tex]Z = -3.6[/tex]

[tex]Z = -3.6[/tex] has a p-value 0.0002

0.0548 - 0.0002 = 0.0546.

0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.

c) Find the 25th percentile of the sample mean.

This is X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-0.675 = \frac{X - 2630}{50}[/tex]

[tex]X - 2630 = -0.675*50[/tex]

[tex]X = 2596[/tex]

The 25th percentile of the sample mean is of $2596.

Question d and e)

We have to find the z-score when X = 2645.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2645 - 2630}{50}[/tex]

[tex]Z = 0.3[/tex]

|Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

In a certain town, 22% of voters favor the construction of a new hospital. For groups of 21 voters, find the variance for the number who did not favor the new hospital.
a. 1.9 voters
b. 4.6 voters
c. none of the given answers is correct
d. 3.6 voters
e. 13 voters

Answers

Answer:

Variance = 3.6 voteres

Step-by-step explanation:

Probability of favour voters, P = 0.22

Total number of voters, n = 21

The probability of voters who are in not favour of new hospital construction = 1  - P

The probability of voters who are in not favour of new hospital construction = 1  - 0.22

The probability of voters who are in not favour of new hospital construction, P* = 0.78

Variance = n x p* x (1 - p*)

Variance = 21 x 0.78 x 0.22

Variance = 3.6 voters

A shopkeeper bought a second-hand car for Rs 1,50,000. He spent Rs 10,000

on its painting and repair and then sold it for Rs 2,00,000. Find his profit or loss.

Answers

I am not sure about my answer as the placement of the zeros are confusing but hopefully it’s right

How many 10-letter words real or imaginary can. Be formed from the following letters R,S,P,Q,H,J,S,M,B,A

Answers

Answer: 3628800

Step-by-step explanation: there are 10 letters so we multiply each with the other 1x2x3x4x5x6x7x8x9x10 or 10! to know all possible combinations so the answer will be 3628800.

Hope it helped!

Answer:

[tex]1,814,400[/tex]

Step-by-step explanation:

The number of ways to arrange a word with [tex]d[/tex] distinct digits is each to [tex]d![/tex]. Since there are 10 letters, there are [tex]10![/tex] permutations initially formed.

However, there is one letter that is repeated, S. We need to account for that fact that switching the placement of the S's does not change the word, as they still appear the same. Therefore, divide [tex]10![/tex] by the number of ways you can arrange the 2 S's, which is simply [tex]2![/tex]. Therefore, our answer is:

[tex]\frac{10!}{2!}=10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3=\boxed{1,814,000}[/tex]

The population of a city has increased by 33% since it was last measured. If the current population is 39,900, what was the previous population?

=___

Answers

Answer:

26,733

Step-by-step explanation:

39,900 - Percentage decrease =

39,900 - (33% × 39,900) =

39,900 - 33% × 39,900 =

(1 - 33%) × 39,900 =

(100% - 33%) × 39,900 =

67% × 39,900 =

67 ÷ 100 × 39,900 =

67 × 39,900 ÷ 100 =

2,673,300 ÷ 100 =

26,733

Hope this helps :)

Flying with a tailwind, a flight crew flew 500 km in 4 hours. Flying against the tailwind, the crew flew 468 km in 4 hours. Find the speed of the plane in calm air and the speed of the wind, both in km per hour.

Answers

Answer:

spped of the plane in calm air=121 km/h

speed of the wind= 4km/h

Step-by-step explanation:

Let say V the speed of the plane in calm air

and v the speed of the wind

Flying with a tailwind, a flight crew flew 500 km in 4 hours ==> 500= (V+v)*4

Flying against the tailwind, the crew flew 468 km in 4 hours ==> 468 = (V-v)*4

We divide the 2 equations by 4 and then add the 2 results equations:

(500+468)/4=2V ==> V=121 (km/h)

We replace that value in the first equation:

V+v=500/4=125

v=125-121=4 (km/h)

How do i solve this quesiton 6(x − 2) > 15

Answers

Answer:  

Step-by-step explanation:

[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]

Need Help! ASAP!!! I gave a screen shot. Please someone give me the correct answer.

Answers

9514 1404 393

Answer:

  x ∈ {-35, 0, 35}

Step-by-step explanation:

We can solve for x and equate those values to find corresponding y-values. Substituting into the original expressions for x gives the possible x-values.

  [tex]x+xy^2=250y\ \Rightarrow\ x=\dfrac{250y}{1+y^2}\\\\x-xy^2=-240y\ \Rightarrow\ x=\dfrac{-240y}{1-y^2}\\\\\dfrac{250y}{1+y^2}+\dfrac{240y}{1-y^2}=0\\\\\dfrac{25y(1-y^2)+24y(1+y^2)}{(1+y^2)(1-y^2)}=0\\\\y(-y^2+49)=0=y(7-y)(7+y)\ \Rightarrow\ y\in\{-7,0,7\}\\\\x=\dfrac{250(\pm 7)}{1+(\pm7)^2}=\pm35,\quad=\dfrac{250(0)}{1+0^2}=0\\\\\boxed{x\in\{-35,0,35\}}[/tex]

Which graph shows data that would allow the most accurate prediction for the number of water bottles a vendor sells based on the daily high temperature?

Graph A
Daily High Temperatures and Bottled Water Sales

On a graph, points are scattered all over the graph.

Graph B
Daily High Temperatures and Bottled Water Sales

On a graph, points are scattered all over the graph.
Graph C
Daily High Temperatures and Bottled Water Sales

On a graph, points are grouped together and form a line with positive slope.
Graph D
Daily High Temperatures and Bottled Water Sales

On a graph, points are grouped together and increase.
PLS HELP ILL GIVE BRAINLIEST FAST

Answers

9514 1404 393

Answer:

  Graph C: Daily High Temperatures and Bottled Water Sales

  On a graph, points are grouped together and form a line with positive slope.

Step-by-step explanation:

Apparently, Graph C shows data with the greatest degree of correlation. This suggests that any model of the data is likely to have less error than if the data were less well correlated.

Answer:

Graph C: Daily High Temperatures and Bottled Water Sales

On a graph, points are grouped together and form a line with positive slope.

Step-by-step explanation:

Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.

0.010

0.354

0.424

0.25

Answers

Total People=5+7+4=16

Women=7

We know

[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]

[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]

Write an equation of the line through each pair of points in slope-intercept form.
a(– 3,–2) and (–3,4)

b(3,2)and (–4,–5)



Answer and I will give you brainiliest ​

Answers

Answer:

see below

Step-by-step explanation:

a) (– 3, –2) and (–3, 4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - (-2) / (-3 - (-3))

Simplify the parentheses.

= (4 + 2) / (-3 + 3)

Simplify the fraction.

(6) / (0)

= undefined

If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.

In this case, the x-coordinate for both points is -3.

Therefore, your equation is x = -3.

b) (3, 2) and (–4, –5)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-5 - 2) / (-4 - 3)

Simplify the parentheses.

= (-7) / (-7)

Simplify the fraction.

-7/-7

= 1

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 1(3) + b

To find b, multiply the slope and the input of x(3)

2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-1 = b

Plug this into your standard equation.

y = x - 1

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, -5).

y = 1x - 1

-5 = 1(-4) - 1

-5 = -4 - 1

-5 = -5

Your equation is correct.

Hope this helps!

Please Help me and don't report this

Answers

8 < x < 8.5 is your answer

other sides has to always be less than the hypotenuse

9514 1404 393

Answer:

  0.5 < x < 16.5

Step-by-step explanation:

The sum of the two shortest sides of a triangle must always exceed the length of the longest side.

If x and 8.0 are the short sides, then ...

  x + 8.0 > 8.5

  x > 0.5

If 8.0 and 8.5 are the short sides, then ...

  8.0 +8.5 > x

  16.5 > x

So, for the given triangle to exist, we must have ...

  0.5 < x < 16.5

_____

Additional comment

You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.

A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280π⁢cm3. Find the radius of the can if the height is 16cm16⁢cm. Keep your answers in simplified radical form.

Answers

Answer:

The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]

Step-by-step explanation:

Radius of the can:

The radius of the can is given by:

[tex]r^2 = \frac{V}{h\pi}[/tex]

In which V is the volume and h is the height.

In this question:

[tex]V = 1280\pi, h = 16[/tex]

Thus

[tex]r^2 = \frac{V}{h\pi}[/tex]

[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]

[tex]r^2 = 80[/tex]

[tex]r = \sqrt{80}[/tex]

[tex]r = \sqrt{5*16}[/tex]

[tex]r = \sqrt{5}\sqrt{16}[/tex]

[tex]r = 4\sqrt{5}[/tex]

The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]

If it's possible to tell, decide if a and b are positive or negative: a-3>b-3 and b>4

PLEASE HELP NEED ASAPPPPPPP

Answers

Answer:

a and b are positive

Step-by-step explanation:

We are given that

[tex]a-3>b-3[/tex]

[tex]b>4[/tex]

We have to find that a and b are positive or negative.

We have

[tex]b>4[/tex]

It means b is positive and greater than 4.

[tex]a-3>b-3[/tex]

Adding 3 on both sides

[tex]a-3+3>b-3+3[/tex]

[tex]a>b>4[/tex]

[tex]\implies a>4[/tex]

Hence, a is positive and greater than 4.

Therefore, a and b are positive

Charles spent 1/4 of his allowance on a shirt, and 2/5 of the remainder on a book. A.What fraction of his allowance did he have left? B.If he spent $18 on the book, how much did he have at first?

Answers

Answer:

18.65

Step-by-step explanation:

1/4+2/5+18=18.65

18.65

hope it helps you good luck

URGENT 100 POINTS AND BRAINIEST
Question 9 (Essay Worth 10 points)
(04.01, 04.02 HC)

Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)

Part B: How much time does Ted spend practicing the breaststroke every day? Show your work. (3 points)

Part C: Is it possible for Ted to have spent 45 minutes practicing the butterfly stroke if he practices for a total of exactly 50 minutes and practices the breaststroke for 20 minutes longer than he practices the butterfly stroke? Explain your reasoning. (2 points)

Answers

Answer:

Part A:

x + y = 50

y = x + 20

Part B:

Ted spends 35 minutes practicing the breaststroke every day.

Part C: It is not possible, as 45 + 65 isn't 50.

Step-by-step explanation:

Clear parentheses by applying the distributive property.

-(-4s + 9t + 7)

Answers

Answer:

4s-9t-7

Step-by-step explanation:

multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same

Write an equation for a line containing (–2,8) that is perpendicular to the line containing the points (3,–4)and (–7,1).





Answer and I will give you brainiliest

Answers

Answer:

y = 2x + 12

Step-by-step explanation:

the formula for a line is typically

y = ax + b

a is the slope of the line (expressed as y/x ratio describing how many units y changes, when x changes a certain amount of units).

b is the offset of the line in y direction (for x=0).

we have the points (3, -4) and (-7, 1).

to get the slope of the line let's wander from left to right (x direction).

to go from -7 to 3 x changes by 10 units.

at the same time y changes from 1 to -4, so it decreases by 5 units.

so, the slope is -5/10 = -1/2

and the line equation looks like

y = -1/2 x + b

to get b we simply use a point like (3, -4)

-4 = -1/2 × 3 + b

-4 = -3/2 + b

-5/2 = b

so, the full line equation is

y = -1/2 x - 5/2

now, for a perpendicular line the slope exchanges x and y and flips the sign.

in our case this means +2/1 or simply 2.

so, the line equation for the perpendicular line looks like

y = 2x + b

and to get b we use the point we know (-2, 8)

8 = 2×-2 + b

8 = -4 +b

12 = b

so, the full equation for the line is

y = 2x + 12

Answer:

2x-y+12= 0 or y = 2x+12 is the answer

Step-by-step explanation:

slope of the line joining (3,-4) and (-7,1) is 1-(-4)/-7-3

= -5/10

= - 1/2

slope of the line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) = 2

Equation of the line line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) is y-8 = 2(x-(-2))

y-8 = 2(x+2)

y- 8 = 2x+4

y=2x+12 (slope- intercept form) or 2x-y+12= 0 (point slope form)

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