The second of two numbers is 7 times the first. Their sum is 72. Find the numbers.

Answer:

a) D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

b) C. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Step-by-step explanation:

a) We have a hypothesis test with the following hypothesis:

[tex]H_0: \mu=20\\\\H_a:\mu> 20[/tex]

The significance level is 0.05 for this right-tailed test.

The sample size is n=17.

This means we have 16 degrees of freedom.

[tex]df=n-1=17-1=16[/tex]

The test statistic has already been calculated and has a value of t=3.1.

This test is a right-tailed test, with 16 degrees of freedom and t=3.1, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>3.1)=0.0034[/tex]

As the P-value (0.0034) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.

b. The hypothesis are the same as point a:

[tex]H_0: \mu=20\\\\H_a:\mu> 20[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

The significance level is 0.01.

The test statistic has already been calculated and has a value of t=1.8.

This test is a right-tailed test, with 9 degrees of freedom and t=1.8, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>1.8)=0.0527[/tex]

As the P-value (0.0527) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.

Answer:

54

give me brainliest please please please and follow my page

Step-by-step explanation:

To find length of KC...we need to find the length of HM and MU first ...

so....HM= 96- 78 = 14

JU = 96 + HM = 96 + 14 = 110

....

KU = 110 - JK = 110 - 82 = 28

....

UN = 105+ 82 -( 96 + 14 )

187 - 110

= 77

UC = 77 - 51 = 26

KC = UC + KU = 26 + 28 = 54

The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.

To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.

[tex]\overline{HM}[/tex] = 96 - 78

[tex]\overline{HM}[/tex] = 14

[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]

= 96 + 14

[tex]\overline{JU}[/tex]= 110

[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]

= 110 - 82

[tex]\overline{KU}[/tex]= 28

[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )

=187 - 110

[tex]\overline{UN}[/tex]= 77

[tex]\overline{UC}[/tex] = 77 - 51

[tex]\overline{UC}[/tex]= 26

Thus,

[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]

[tex]\overline{KC}[/tex]= 26 + 28

[tex]\overline{KC}[/tex]= 54

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Answer:

The circle on the far left is the sum of 4x + 3y and 2x - y so the answer is 4x + 3y + 2x - y = 6x + 2y. The circle on the far left is the sum of x + 4y and something. To find that "something" we can do 4x + 5y - (x + 4y) = 3x + y which is the value of the bottom right rectangle. This means that the value of the bottom circle is 2x - y + 3x + y = 5x.

Answer:

Step-by-step explanation:

left circle=4x+3y+2x-y=6x+2y

right  bottom rectangle=4x+5y-(x+4y)=4x+5y-x-4y=3x+y

Bottom circle=2x-y+3x+y=5x

Answer:

We accept null hypothesis

Step-by-step explanation:

We assume a normal distribution

The population mean  μ₀ = 65 mph      

Sample mean     μ  = 63,2  mph ( calculated from data )

Sample standard deviation  σ  =  7,309

Sample size    n  = 8

Degree of freedom  is   n - 1         8 - 1   = 7

As n < 30  we have to use the t-student test

We will do our test with a confidence interval of  95 % that means            α = 5  %

or α = 0,05 and as we are going through a two-tail test α/2  = 0,025

Test Hypothesis:

Null Hypothesis:                                  H₀              μ  =   μ₀

Alternate Hypothesis                          Hₐ              μ  ≠   μ₀

From  t-student table for the degree of freedom 7,  α/2  = 0,025 two-tail test we find tc

tc = 2,365

And  calculate ts   as

ts = ( μ - μ₀ ) / σ /√n

ts = ( 63,2 - 65 ) / 7,309/ √8

ts = - 1,8 *2,828/ 7,309

ts = - 5,091 /7,309

ts = - 06965

Now we compare   ts and tc

tc = 2,365      or  tc = - 2,365    ( by simmetry)   tc = -2,37

and  ts = -0,06965      ts = - 0,07

As |ts| < |tc|

ts is in the acceptance zone so we accept null hypothesis

Answer:

-0.70

Step-by-step explanation:

For the tabulated value the mean is calculated as:

Mean = (60.5 + 63.2 + 54.7 + 51.6 + 72.3 + 70.7 + 67.2 + 65.4)/8

= 505.6/8

Mean \bar{x}= 63.2

and population mean as assumption u= 65

and given that the sample standard deviation is: s= 7.309

The test statistic is calculated as:

Ζ = Τ –μ 63.2 - 65 = -0.696 -0.70 S

Hence the T statistic would be -0.70

Answer: 57769.8 in²

Let A be the area of the shaded region

We have a relation that can help us calculate its area

A= 0.5*(θ-sin(θ))*r² where r is the radius and θ the angle

A= 0.5*(150-sin(150°))* 27.8² =57769.79≈57769.8 in²

Answer:

818.4

Step-by-step explanation:

Answer:

b. False.

Step-by-step explanation:

According to the presented information, at the 95% confidence level, the mean number of coats owned will be between 3.1 and 5.2. That does not mean that there is a 95% chance that they will own that many coats; just that you are 95% confident that they will own the coats.

Hope this helps!

Answer:

15 49-cent stamps

Step-by-step explanation:

We can solve this problem with the equations 0.49(x) + 0.21(y) = 9.45 and x - 5 = y. Well, 0.49(15) + 0.21(10) = 9.45, so we know that there are 15 49-cent stamps and 10 21-cent stamps. The question is asking for the number of 49-cent stamps, so we can tell Travis bought 15 49-cent stamps.

Hope this helps! Plz give me brainliest, it will help me achieve my next rank.

The number of 49-cent stamps that Travis bought given the equation is 15.

Given this equation: 0.49s+0.21(s−5)=9.45 take the following steps to determine the value of s

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Answer:

864

Step-by-step explanation:

AT= 2Area base+ph

AT= 2(12*12) +(12*4)12

AT=2 (144)+576

AT= 288+576

AT=864"

Answer:

x = 2, y = 5

Step-by-step explanation:

Hello,

   y=6x-7

   9x-2y=8

can be written as

   (1) 6x - y = 7

   (2) 9x -2y = 8

(2)-2*(1) gives

   9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6

   <=> -3x=-6

   <=> x = 6/3=2

and we replace it in (1)

  y = 6*2-7=12-7=5

hope this helps

Answer:

x = 8

Step-by-step explanation:

To find the possible value of x in the given trapezoid MNOP with median QR, recall that one of the properties of a trapezoid is that the median length = ½ of the sum of the length of the parallel bases

Thus, ½ of [x + (3x + 8)] = 20

Let's find x

½*[x + (3x + 8)] = 20

½*[x + 3x + 8)] = 20

½*[4x +8] = 20

Multiply both sides by 2

4x + 8 = 20*2

4x + 8 = 40

Subtract 8 from both sides

4x = 40 - 8

4x = 32

Divide both sides by 4

x = 32/4

x = 8

Answer:

I think its 8 ‍♂️

Step-by-step explanation:

Answer:

9/26

Step-by-step explanation:

Answer:

Step-by-step explanation:

25-3 =22 have a cat or a dog

15 +16 =31 students are in the class if every person has either a cat or a dog

But we have 22

so 31 - 22 = 9 have both cat and dog

the probability is 9/25

Answer:

  17π/10

Step-by-step explanation:

To find a co-terminal angle in a specific range, add or subtract multiples of 2π until you have an angle in the desired range. Here, you can add 2π.

 -3π/10 +20π/10 = 17π/10 . . . . angle co-terminal with -3π/10

Answer:

2.5 meters per second

Step-by-step explanation:

9x1000=9000m/h

9000/60/60=2.5m/s

Answer:

2.5 m/s

Step-by-step explanation:

convert kilometers to meters and then use a conversion calc to do the rest

Answer:

QS

Step-by-step explanation:

The side opposite to the smallest angle must be the shortest side. The smallest angle is ∠R so the opposite side is QS.

Answer:

Hey there!

Smaller angles are opposite smaller sides, so the side opposite to angle R would be the shortest. (Or side SQ)

Hope this helps :)

Answer:

3.26%

Step-by-step explanation:

The computation of the probability that she is a student is shown below:

Percentage of student developers = 25.8% = SD

The Percentage of the developer is student = 7.4% = DS

The percentage of the developer is not student = 76.4% = ND

Based on this, the probability is

[tex]= \frac{SD \times DS}{SD \times DS + DS \times ND}[/tex]

[tex]= \frac{25.8\% \times 7.4\%}{25.8\% \times 7.4\% + 7.4\% \times 76.4\%}[/tex]

=3.26%

we simply considered all the elements

Answer:

y=2x+6

Step-by-step explanation:

The slope is 2x and the y-intercept is 6. It is shown how to graph it in the attachment.

Answer:

78 grams

Step-by-step explanation:

20% is 1/5

1/5 of 65 is 13

65 + 13 = 78

brainliest?

Trigonometry is the study of the properties of triangles and trigonometric functions and of their applications.  

I'm not sure how you'd want me to answer your question though, but stay safe!!

- eli <3

Answer:

A. [tex]\frac{9}{10}[/tex]

B. 1

C. [tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]

D. [tex]\frac{2}{30}[/tex] or [tex]\frac{1}{15}[/tex]

E. [tex]\frac{12}{70}[/tex] or [tex]\frac{6}{35}[/tex]

F. [tex]\frac{6}{90}[/tex] or [tex]\frac{1}{15}[/tex]

G. [tex]\frac{9}{32}[/tex]

H. [tex]\frac{4}{15}[/tex]

Answer:

Step-by-step explanation:

Reducing the given expressions to the lowest terms:

A. 3/10 + 6/10:

B. 1/3 + 1/4 + 1/6:

C. 5/6-3/6:

D. 2/3-6/10:

E. 4/10*3/7:

F. 1/6*6/15:

G. 1/8 divided by 4/9:

H. 1/5 divided by 3/4:

Answer:

A) Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

B) Test statistic = t = 1.878

C) p-value is 0.038823.

D) Reject the Null hypothesis H0

Step-by-step explanation:

We are given;

α = 0.05

n1 = 16

n2 = 10

bar x1 = 6.82

bar x2 = 6.28

s1 = 0.65

s2 = 0.75

A) The hypothesis is as follows;

Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

B) Formula yo determine the test statistic is;

t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))

Plugging in the relevant values, we have;

t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))

t = 0.54/√(0.02640625 + 0.05625)

t = 0.54/0.2875

t = 1.878

C) The formula for the degree of freedom is;

Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))  

Plugging in the relevant values, we have;

Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))  

Δ = 0.00683205566/(0.000046486 + 0.0003515625)

Δ ≈ 17

Thus, the P-value;

From online p-value calculator from t-score and DF which i attached, we have the p-value as;

The p-value is 0.038823.

D) The p-value result is significant at p < 0.05

Thus, we reject the Null hypothesis H0

A) Null hypothesis: μ1 − μ2 ≤ 0

B) Test statistic = t = 1.878

C) The p-value is 0.038823.

D) Reject the Null hypothesis H0.

What all information we have ?

α = 0.05

n1 = 16

n2 = 10

bar x1 = 6.82

bar x2 = 6.28

s1 = 0.65

s2 = 0.75

Part A)

The hypothesis is as follows;

Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

Part B)

The formula to determine the test statistic is :

t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))

t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))

t = 0.54/√(0.02640625 + 0.05625)

t = 0.54/0.2875

t = 1.878

The formula to determine the test statistic is t = 1.878.

Part C)

The formula for the degree of freedom is;

Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))  

Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))  

Δ = 0.00683205566/(0.000046486 + 0.0003515625)

Δ ≈ 17

Thus, the P-value is 0.038823.

Part D)

The p-value result is significant at p < 0.05 is :

Thus, we reject the Null hypothesis H0.

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Answer:

The total number of ways to select 2 CDs from 8 CDs is 28.

Answer:

a) Expected Value of Claims = $32,000

b) Average premium per claim, in order to break-even on claim costs

= $5,333.33

c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:

= $5,393.33 per policy

Step-by-step explanation:

a) Data and Calculations:

Amount of Claim      Probability   Expected Value

$0                               0.60             $0

$50,000                     0.25             $12,500

$100,000                   0.09                 9,000

$150,000                   0.04                 6,000

$200,000                  0.01                 2,000

$250,000                 0.01                 2,500

Expected Cost of claims =          $32,000

b) Average premium per claim, in order to break-even on claim costs

= Total Claim cost divided by number of policies

= $32,000/6 = $5,333.33

c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:

Total Claim cost + Total profit / 6 or Average Premium plus Profit per policy =

= ($32,000 + $360)/6 or $5,333.33 + $60

= $32,360/6 or $5,393.33

= $5,393.33

The total expected value is $32000, the average premium so that it breaks even on its claim  costs are $5333.33 and the company charge to make a profit of $60 per policy is $5393.33.

Given :

The table shows claims and their probabilities for an insurance company.

Amount of Claim          Probability               Expected Value

$0                                      0.60                             0

$50000                             0.25                            $12500

$100000                            0.09                            $9000

$150000                            0.04                             $6000

$200000                           0.01                              $2000

$250000                            0.01                             $2500

A) So, the total expected value is = 12500 + 9000 + 6000 + 2000 + 2500

                                                   =  $32000

B) The average premium is given by:

[tex]=\dfrac{32000}{6}[/tex]

= $5333.33

C) The company charge to make a profit of $60 per policy is:

[tex]= \dfrac{32000+360}{6}[/tex]

[tex]=\dfrac{32360}{6}[/tex]

= $5393.33

For more information, refer to the link given below:

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Answer:

Step-by-step explanation:

First off, you need to add up AB and BC. You would get the equation:

2(3x-4)=62, since there are two segments. Solve it/simplfy.

6x-8=62 => 6x=70 => x= 11.66666(forever)

Since you alreday solved one, you easily know the answer is c.

Answer:

35 students

Step-by-step explanation:

Take the number of students in the class and multiply by 60% and see if you get an integer number

28 * .60 =16.8  not an integer

32 * .6 =19.2

35 * .6 =21  yes

39*.6 =23.4

━━━━━━━☆☆━━━━━━━

▹ Answer

-17 isn't a natural number

▹ Step-by-Step Explanation

Positive integers are only natural numbers, meaning negative numbers aren't natural numbers.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

Given that:

mean (μ) = 476 grams, standard deviation (σ) = 36 grams. P(z) = 19%

The z score shows by how many standard deviation the raw score is above or below the mean. It is given by the equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Since the 19% weigh more, therefore 81% (100% - 19%) weigh less.

From the normal distribution table, the z score that corresponds to a probability of 81%(0.81) = 0.87

We substitute z = 0.88 in the z score equation to find the raw score. Therefore:

[tex]z=\frac{x-\mu}{\sigma}\\0.87=\frac{x-476}{36}\\ x-476=31.32\\x=31.32+476\\x=507.32\\[/tex]

x ≅ 507 grams

Therefore 19% of fruits weigh more than 507 grams

Answer:

0.3 m/s

Step-by-step explanation:

The first thing is to attach the allusive graphic to the question. Now yes, let's move on to the solution that would be:

If the through is completely filtered the its volume will:

V = l * [1/2 w * h] = 1/2 l * w * h

Now we derive with respect to time and we are left with:

dV / dt = 1/2 * l * w * dh / dt

We solve by dh / dt and we have:

dh / dt = (2 / (l * w)) * (dV / dt)

We know that l = 8 and w = 5, in addition to dV / dt = 6, we replace:

dh / dt = (2 / (8 * 5)) * (6)

dh / dt = 0.3

Therefore the rate at which the height of the water changes is 0.3 m / s

Answer:

C(d) = d(2.25) + m(0.3)

Step-by-step explanation:

A taxi company charges $2.25 per ride plus $0.30 per mile.

Let d represent number of rides..

Let m represent number of Miles...

Then let C represent the total cost for each ride at a specific number of Miles.

The linear model representing the cost as a function of d the total ride

C(d) = d(2.25) + m(0.3)

The values stand independently because the customer can choose a different right and a different mile.

Answer:

B

Step-by-step explanation:

Answer:

[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

Step-by-step explanation:

Given

[tex]f(b) = b^2 - 75[/tex]

Required

Determine the roots

To get the root of the function, then f(b) must be 0;

i.e. f(b) = 0

So, the expression becomes

[tex]0 = b^2 - 75[/tex]

Add 75 to both sides

[tex]75 + 0 = b^2 - 75 + 75[/tex]

[tex]75 = b^2[/tex]

Take square roots of both sides

[tex]\sqrt{75} = \sqrt{b^2}[/tex]

[tex]\sqrt{75} = b[/tex]

Reorder

[tex]b = \sqrt{75}[/tex]

Expand 75 as a product of 25 and 3

[tex]b = \sqrt{25*3}[/tex]

Split the expression

[tex]b = \sqrt{25} *\sqrt{3}[/tex]

[tex]b = \±5 *\sqrt{3}[/tex]

[tex]b = \±5 \sqrt{3}[/tex]

[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

The options are not clear enough; however the roots of the equation are [tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]