A medical researcher wants to compare the pulse rates of smokers and non-smokers. He believes that the pulse rate for smokers and non-smokers is different and wants to test this claim at the 0.01 level of significance. A sample of 75 smokers has a mean pulse rate of 76, and a sample of 73 non-smokers has a mean pulse rate of 72. The population standard deviation of the pulse rates is known to be 9 for smokers and 10 for non-smokers. Let µ1 be the true mean pulse rate for smokers and µ2 be the true mean pulse rate for non-smokers.
Step 1 of 5: State the null and alternative hypotheses for the test.
Step 2 of 5: Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 5: Find the p-value associated with the test statistic. Round your answer to four decimal places.
Step 4 of 5: Make the decision for the hypothesis test.
Step 5 of 5: State the conclusion of the hypothesis test.

Answer:

x = -2

Step-by-step explanation:

​x−3x=2(4+x)

Distribute

x - 3x = 8 +2x

Combine like terms

-2x = 8+2x

Subtract 2x from each side

-2x-2x = 8+2x-2x

-4x = 8

Divide by -4

-4x/-4 = 8/-4

x = -2

Answer:

x-3x=2(4+x)

-2x=8+2x

-2x-2x=8

-4x=8

x=8/-4

x=-2

hope it helps budy x=2

mark me brainliest

Answer: B. a = b .

First of all, let's think that a is equal to b.

Then, let's link up these two triangles.

Now, we have a parallelogram.

x+y = a+60

and 75 = b . So, a = b. Then, a is also = 75.

Now apply the basic triangle rule.

75+75+x=180 .. x = 30 degree.

and for the other triangle....

y+75+60=180 .. y= 45 degree...

Now, let's consider that we want to write a as b.

So, x+b+75=180 ...x+b=105

and..

y+b+60=180...y+b = 120..

Then, let's exit the b from these two equations.

-1/  x+b=105

    y+b=120

Finally, we found this: y-x =15

and we have already found y and x values.

y was 45 and x was 30 degree.

So when we put these two numbers into that equation y-x=15

we found the value of 15.

So, our answer is a=b.

Answer:

[tex]\huge \boxed{\mathrm{B.} \ a=b}[/tex]

Step-by-step explanation:

The two triangles form a parallelogram.

A parallelogram has opposite angles equal.

75 = b

Adjacent angles in a parallelogram are supplementary to one another.

They add up to 180 degrees.

a + 60 + 75 = 180

a + 135 = 180

Subtract 135 from both sides.

a = 75

Therefore, a = b.

Answer:

K=3.333

Step-by-step explanation:

-3=9(5-2k)/5

-3=45-18k/5

-15=45-18k

18k=60

K=60/18

K=3.3333

Answer:

Length of the rectangular prism = 4 meters

But other possible values = (-5meters or - 9 meters)

Step-by-step explanation:

The volume of a rectangular prism = Length × Width × Height

From the question above,

Length = x meters

Width = x - 1 meters

Height = x + 11 meters

Volume of the Rectangular prism = 180 cubic meters

Hence,

(x) × (x - 1) × (x + 11) = 180

We expand the brackets

(x)(x - 1) (x + 11) = 180

x² - x(x + 11) = 180

x² (x + 11) - x(x + 11) = 180

x³ + 11x² - x² + 11x =180

x³ +10x² - 11x = 180

x³ + 10x² - 11x -180 = 0

The above is a polynomial

We solve this polynomial to find x

x³ + 10x² - 11x -180 = 0

(x - 4)(x + 5) (x + 9) = 0

x - 4 = 0

x = 4

x + 5 = 0

x = -5

x + 9 = 0

x = -9

We are asked to find the various values for the length hence,

From the above question, we are told that

Length = x meters

Therefore, the length of this rectangular prism = 4 meters or -5 meters or -9 meters.

Answer:

(1, 4)

Step-by-step explanation:

If the three points all fall on the same straight line, then a triangle will not form. Instead, a line will. We call these points to be collinear.

If the points aren't collinear, then a triangle forms.

Answer:

No.

Step-by-step explanation:

The points may be in a straight line, and that doesn't form a triangle.

A)78°

135°+a° =180°

a°=45°

57°+x°+a°=180°

57°+x°+45°=180°

102°+x°=180°

x°=180°-102°

x°=78°

Answer:

x = 1/25

Step-by-step explanation:

2/5x+1/x=35

[tex]2/5x+1/x=35[/tex]

taking 1/x common

[tex]1/x(2/5+1)=35[/tex]

[tex](2+5)/5=35x\\7/5 = 35x\\x = 7/(5*35) = 1/(5*5) = 1/25[/tex]

Thus, value of x is 1/25

Answer: 11

Step-by-step explanation:

30 - 2(7+2)- 1        Distribute or  solve parentheses

30 - 14 -4 - 1  

30 - 19 = 11  

Answer:

C. Why? No repeating x values.

First set up the ratio 2/5 = 10/x where x is the number of girls.

Now, we can use cross-products to find the missing value.

So we have (2)(x) = (5)(10).

Simplifying, we have 2x = 50.

Dividing both sides by 2, we find that x = 25.

So there are 25 girls in the class if there are 10 boys.

Answer:

− 4 y  − 7

Step-by-step explanation:

Remove parentheses.

− 4 y − 4 − 3

Subtract  3  from  − 4

− 4 y  −  7

.

Answer:

1 week= 7 days

number of days= 9

number of weeks= 1 week and 2 days

hope it helps :)

please mark it the brainliest!

Answer:

1 week and 2 days

Step-by-step explanation:

Answer: d) Neither of the answers are correct

Step-by-step explanation:

Law of Cosines: a² = b² + c² - 2bc · cos A

Note: The letters can be swapped but the letters on the outside must be the same.

Answer:

False the conjugate of 2+5i is 2-5i .

Step-by-step explanation:

Hope it will help you :)

Answer: 300%

Step-by-step explanation:

percent of increase: new/old×100%-100%

Since it is percent of increase, you need to subtract the original percent (100%) from the current percent.

------------------

new (current)=2000

old (original)=500

 new/old×100%-100%

=2000/500×100%-100%

=4×100%-100%

=400%-100%

=300%

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

Calculated z= 3.515

The Z∝/2 = ±1.96  for ∝= 0.05

The Z∝/2 = ± 2.58  for ∝= 0.01

Yes the company claims valid at a level of significance of 0.05 and 0.01

Step-by-step explanation:

Here p1= 70% = 0.7

p2= 20/45= 0.444   q= 1-p= 1-.444= 0.56

The level of significance is 0.05 and 0.01

The null and alternative hypotheses are

H0; p1= p2                Ha: p1≠p2

The test statistic used here is

Z= p1-p2/ √pq/n

Z= 0.7-0.44/ √ 0.44*0.56/45

z= 0.26/ √0.2464/45

z= 3.515

The Z∝/2 = ±1.96  for ∝= 0.05

The Z∝/2 = ± 2.58  for ∝= 0.01

For the significance level 0.05 reject null hypothesis

For the significance level 0.01 reject null hypothesis

Yes the company claims valid at a level of significance of 0.05 and 0.01

Step-by-step explanation:

(A) Let a triangle be formed with height of pole h, length of base b and angle of elevation 58°. (Due to lack of a figure).

Tan 58° = h / b = 1.6

(B) Let another triangle be formed with height of pole h, length of base (b + 90) and angle of elevation 36°. (Due to lack of a figure).

Tan 36° = h / (b + 90) = 0.72

(C) Simplifying the two equations :

1.6b = 0.72b + 64.8

b = 64.8 / 0.88 = 73.6 m

h (height of pole) = 1.6 * 73.6 = 117.76 m

Answer:

Option (B)

Step-by-step explanation:

Since all the four rays A, E, D and F are diverging from a point C in the different directions.

Therefore, sum of all the angles formed at a point C will be equal to 360°

m∠1 + m∠4 + m∠6 + m∠9 = 360°

25° + 34° + 146° + m∠9 = 360°

m∠9 = 360° - 205°

        = 155°

Therefore, measure of angle 9 is 155°.

Option (B) will be the correct option.

Answer:   A) a² = b² - w² + 2wx

Step-by-step explanation:

b² - (w - x)² = a² - x²

b² - (w² - 2wx + x²) = a² - x²

b² - w² + 2wx - x² = a² - x²

b² - w² + 2wx       = a²

Answer:

Option B

Option E

Step-by-step explanation:

By the use of following postulates we can prove the two right triangles to be congruent.

1). HA - [Equal hypotenuse and an cute angles]

2). LL - [Two legs should be equal]

3). LA - [One leg and one angle must be equal]

4). ASA - [Two angles and the side containing these angles should be equal]

In the given right triangles,

1). OJ ≅ IL

2). ∠O ≅ ∠I

3). ∠J ≅ ∠L

Therefore, two postulates HA, ASA will be applicable for the congruence of the two triangles given.

Options A and E will be the answer.

Answer:

asa, ha, aas

Step-by-step explanation:

Answer:

The number of ways to distribute 30 batteries among the six different types is 33,649.

Step-by-step explanation:

It is provided that a camera shop stocks six different types of batteries, one of which is type A7b.

Also, the camera shop has only twelve A7b batteries but at least 30 of each of the other types.

Combinations would be used to determine the number of ways to distribute 30 batteries among the six different types. Here repetition is allowed.

[tex]C(n+r-1, r)={n+r-1\choose r}=\frac{(n+r-1)!}{r!(n-1)!}[/tex]

The number of A7b batteries is 12.

Then the number of ways to distribute 30 batteries among the six different types is:

[tex]C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}[/tex]

The number of ways is:

[tex]C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}[/tex]

                                          [tex]=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}\\\\=\frac{(6+(30-12)-1)!}{(30-12)!\times (6-1)!}\\\\=\frac{23!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19\times 18!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19}{ 5!}\\\\=33649[/tex]

Thus, the number of ways to distribute 30 batteries among the six different types is 33,649.

Answer:

[see below]

Step-by-step explanation:

A function is a relation where one domain value is assigned to exactly one range.

An x-value in a function must not repeat.

Hope this helps.

Answer:

1. Yes, there is sufficient evidence to support the claim that student cars are older than faculty cars.

2. The 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].

Step-by-step explanation:

We are given that randomly selected 110 student cars to have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars to have ages with a mean of 5.3 years and a standard deviation of 3.7 years.

Let [tex]\mu_1[/tex] = mean age of student cars.

[tex]\mu_2[/tex]   = mean age of faculty cars.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \leq \mu_2[/tex]      {means that the student cars are younger than or equal to faculty cars}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1>\mu_2[/tex]      {means that the student cars are older than faculty cars}

(1) The test statistics that will be used here is Two-sample t-test statistics because we don't know about the population standard deviations;

                             T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)} {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~   [tex]t_n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean age of student cars = 8 years

[tex]\bar X_2[/tex] = sample mean age of faculty cars = 5.3 years

[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years

[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years

[tex]n_1[/tex] = sample of student cars = 110

[tex]n_2[/tex] = sample of faculty cars = 75

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(110-1)\times 3.6^{2}+(75-1)\times 3.7^{2} }{110+75-2} }[/tex]  = 3.641

So, the test statistics =  [tex]\frac{(8-5.3)-(0)} {3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} } }[/tex]  ~ [tex]t_1_8_3[/tex]

                                     =  4.952    

The value of t-test statistics is 4.952.

Since the value of our test statistics is more than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we support the claim that student cars are older than faculty cars.

(2) The 98% confidence interval for the difference between the two population means ([tex]\mu_1-\mu_2[/tex]) is given by;

98% C.I. for ([tex]\mu_1-\mu_2[/tex]) = [tex](\bar X_1-\bar X_2) \pm (t_(_\frac{\alpha}{2}_) \times s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} })[/tex]

                                 = [tex](8-5.3) \pm (2.326 \times 3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} })[/tex]

                                 = [tex][2.7 \pm 1.268][/tex]

                                 = [1.432, 3.968]

Here, the critical value of t at a 1% level of significance is 2.326.

Hence, the 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].

Answer:

The correct answer is:

It is a continuous random variable. (B)

Step-by-step explanation:

Continuous random variables are variables that take on infinite possibility of values, hence the number of possible outcomes of a random variable cannot be counted. For instance, in this example, the amount of rainfall measured using a rain guage or a pluviometer has infinite possibilities of outcomes. it can either be 22.3 Liters, 20.1 Liters etc, up to infinity, in fact between 20 and 21 litres, there is an infinite possibility of outcomes.

Discrete random variables are variables that have a finite possibility of outcomes. the possibilities of occurrences can be counted. For example, if a coin is tossed, the coin can either land on its head or tail, hence there are two possibilities, making the variables discrete

The correct answer is:

It is a continuous random variable (B)

Step-by-step explanation:

Continuous Random Variables are variables that take on a number of possibilities of values that cannot be counted. The values have infinite possibilities. In this example, the height of a Giraffe measured in meters can be an unlimited possibility if values say, 10.5m, 15.22m 12.0m etc. The possibilities are endless.

Discrete Random variables are variables that take on a number of possibility of occurrences that can be counted. For instance, if a dice is rolled, the possibilities can either be a 1, 2, 3, 4, 5 or 6. There are six values that can be gotten, nothing in-between.

THANKS

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Answer:

x = -4

Step-by-step explanation:

This vertical line is x = -4.  That's all we need here.

Answer:

0.185185185185185185.........

Step-by-step explanation:

i used a  calculator, to the nearst tenth is 0.18 to the nearest 100th is 0.185 also the 185 is repeating so u put a line over the numbers 185

Answer:

3 ÷ 162 = 0.01851851851

If you meant 162 ÷ 3 it is 54

If niether of the two answers above didnt answer your question, then sorry

[tex](0,-4)[/tex] fits the linear equation perfectly.

Hope this helps.

Answer:

the y-intercept is the point (0, -4) on the plane

Step-by-step explanation:

In order to find the y-intercept, write the equation in "slope intercept form"  solving for "y":

[tex]2\,y=x-8\\y=\frac{x-8}{2} \\y=\frac{x}{2} -\frac{8}{2} \\y=\frac{x}{2} -4[/tex]

Recall now that the y-intercept is the value at which the line crosses the y-axis (when x = 0), therefore:

[tex]y=\frac{x}{2} -4\\y=\frac{0}{2} -4\\y=-4[/tex]

So the y-intercept is the point (0, -4) on the plane.

Hey there! I'm happy to help!

Let's create a basic rectangle with this length to width ratio.

Two sides are 3 and two of them have a length of 2. This would give us a perimeter (distance around) of 10.

We want to find a rectangle with a perimeter of 35 meters with this same ratio. What we can do is multiply all of the dimensions of our first rectangle by 3.5 (to get our perimeter of 10 to 35, we multiply by 3.5).

3×3.5=10.5

2×3.5=7

If we simplify 10.5:7, we have 3:2, and the perimeter of a rectangle with a length of 10.5 and a width of 7 would equal 35 meters.

Have a wonderful day! :D

Answer:

There is sufficient evidence that there is linear  correlation between two variable

Step-by-step explanation:

From the question we are told

   The significance level is  [tex]\alpha = 0.01[/tex]

   The critical value  is  [tex]a = 0.590[/tex]

   The  test statistics is  [tex]r = 0.591[/tex](linear correlation coefficient )

Now  from the data given in the value we see that

     [tex]r > a[/tex] so  the null hypothesis is rejected

Hence the conclusion is that there is  sufficient evidence that there is linear   correlation between two variable