A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received vaccinations; the other did not. During the following year, only 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group. a) Are the conditions for inference satisfied? b) Find a 95% confidence interval for the difference in rates of ear infection. c) Use your confidence interval to explain whether you think the vaccine is effective.

Answer:

C

Step-by-step explanation:

In the attached file

Answer: A

I just love your questions. You always put "No guessing" haha.

Step-by-step explanation:

[tex]f(x)=3^x+10x\\g(x)=2x-4[/tex]

[tex](f+g)(x)=[/tex]

This basically means you have to take both functions and add them together.

[tex](f+g)(x)=(3^x+10x)+(2x-4)\\(f+g)(x)=3^x+10x+2x-4\\[/tex]

Combine like terms;

[tex](f+g)(x)=3^x+12x-4[/tex]

Answer:

SA=571.77

Step-by-step explanation:

SA==2πrh+2πr2=2·π·7·6+2·π·72≈571.76986

pls mark brainliest

Answer:

Correct answers are Marci's monthly payment: $227.30, and total finance charge: $455.20.

Step-by-step explanation:

24 months (2 years)

$45.46 x 5 = $227.30

$227.30 x 24 = $5,455.20

$5,455.20 - $5,000 = $455.20

Answer:

2 1/4 ,2 1/2, 2 3/4, 3 1/4 ,3 1/2, 3 3/4, 4 1/4 , 4 1/2, 4 3/4

Step-by-step explanation:

These are the mixed numbers.

Answer:

The area of the riders field of view is 987.5 square yards.

Step-by-step explanation:

The human has a 180° arc view. If the rider can see only 25 yards, the area of the riders field of view is a semi-circle (180° arc) of 25 yards of radius.

The semi-circle of 25 yards of radius has an area of:

[tex]S=\dfrac{1}{2}\pi r^2=\dfrac{1}{2}\cdot3.16\cdot (25)^2=\dfrac{1}{2}\cdot3.16\cdot625=987.5[/tex]

The area of the riders field of view is 987.5 square yards.

Answer:

905

Step-by-step explanation:

So your original equation is f(x) = x² + 5

First lets work with the stuff inside the parentheses.

f(5) = 5² + 5 = 30

So now you are finding,

f(f(5)) => f(30)

f(30) = 30² + 5 = 900 + 5 = 905

Answer:

a = 250 ; b = 10

Step-by-step explanation:

a = 5 × 10² / 2

a = 5 × 100 / 2

a = 500 / 2

a = 250

b = 2 × 10² (10-5) / 10×10

b = 2 × 100 × 5 / 100

b = 1000 / 100

b = 10

Answer:

k= -6.48 approx

Step-by-step explanation:

(5k+35) -8=12

opening bracket

-45k-280=12

-45k=12+280

-45k=292

k=-6.48 approx

Answer:

Step-by-step explanation:

I don't say you have to mark my ans as brainliest but if you think it has really helped you plz don't forget to thank me...

Answer: the numbers are 5,111.3 and 35.74

Step-by-step explanation:

I will answer this in English.

We have the numbers X and Y, ad we have that:

X + 2*Y^2 = 7776

X = 7776 -  2*Y^2

Now we also want that the product of X and Y is a maximum.

The equation of maximum product is

P(Y) = X*Y = (7776 -  2*Y^2)*Y

       = 7776*Y - 2*Y^3

Now, to find the maximum we must derivate and find the value where P'(Y) is equal to 0

P'(Y) = 7776 - 6*Y^2 = 0

7776 = 6*Y^2

Y = √(7776/6) = 35.74

Now, we replace this value in the equation for X and we can find X:

X = 7776 -  2*Y^2  = X = 7776 -  2*(35.74)^2 = 5,111.3

Answer:

a) (1,3)

b) x=1

Step-by-step explanation:

The general form of a parabola in vertex form is f(x)=a(x-h)^2+k, where h is the x coordinate of the vertex, and k is the y coordinate, while a indicates how "squished" the graph is, or how quickly it grows in relation to the parent graph. In this case, h is shown to be 1, and k is 3, meaning that the vertex is at (1,3). The axis of symmetry , for a vertical parabola, just runs vertically through the vertex, meaning that in this case it is at x=1. Hope this helps!

Answer:

(1,3) and y-axis

Step-by-step explanation:

The vertex is the value of x at maximum or minimum point

At maximum point

dy/ dx = 0;

dy/dx = 4(x-1)= 0

=>x= 1 and is the vertex

Y when x = 1; we substitute x=1 in the original equation.

f(x) =y =2(x-1)^2+3

y = 2(1-1)^2 +3

y = 0 + 3= 3

The vertex is (1,3)

2.

A symmetrical equation is given by

b^2 = 4ac

Looking at the equation above x has an order of 2 meaning a possibility of cutting the x axis on two values of x

Hence the axis of symmetry is the y-axis

Assuming this was the expression; the axis of rotation would have been the x-axis.

f(y)=2(y-1)^2+3

The surface area of the new figure is,

⇒ 1550 cm²

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

The surface area of a figure is 62cm².

And, the dimensions are multiplied by 5.

Here, The surface area of a figure is 62cm².

After multiply by 5, surface area of the new figure is,

⇒ 5² × 65

⇒ 25 × 65

⇒ 1550

Thus, The surface area of the new figure is,

⇒ 1550 cm²

Learn more about multiplication visit:

https://brainly.com/question/1135170

#SPJ6

Answer:

7 lbs   4 oz

Step-by-step explanation:

6 lb 10 oz

   + 10 oz

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

6 lbs  20 oz

But we know that there are 16 oz in 1 lb

So subtract 16 oz and add 1 lb

6 lbs  20 oz

+1 lb   - 16 oz

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

7 lbs   4 oz

Answer:

m<10 = 92°

m<5 = 106° (I think because of correspondence)

m<8 =92°

m<14 = 74°

m<3 = 106°

<1 and <4 are corresponding angles

<2 and <3 are same side interior angles

<3 and <4 are vertical angles

<4 a d <6 are Alt. Interior Angles

Answer:

157 cm

Step-by-step explanation:

El valor que se necesita para el borde del mantel es equivalente al perímetro del mantel.

Para un circulo de 50 cm de radio, el perímetro es:

[tex]P=\pi r=3.14\cdot 50=157[/tex]

Se necesitan 157 cm de encaje.

The value needed for the edge of the tablecloth is equivalent to the perimeter of the tablecloth.

For a circle with a radius of 50 cm, the perimeter is:

[tex]P=\pi r=3.14\cdot 50=157[/tex]

157 cm of lace are required.

Answer:

With replacement, 0.037, independent

Without replacement, 0.031, dependent

Step-by-step explanation:

There are 5 vowels (not including y).

The probability the first letter is a vowel is 5/26.

With replacement, the probability the second letter is a vowel is also 5/26.

The total probability is (5/26) (5/26) = 0.037.

Since the first letter is replaced, the probability of the second letter is not affected, so the events are independent.

Without replacement, the probability the second letter is a vowel is 4/25.

The total probability is (5/26) (4/25) = 0.031.

Since the first letter is not replaced, the probability of the second letter is affected, so the events are dependent.

Answer:

(1, 9/2) or (1, 4.5)

Step-by-step explanation:

To find the midpoint, take the x1 and x2 values and divide it by 2, same for the y values.

(4-2)/2  and (6 + 3)/2

1 and 4.5

(1, 4.5)

Answer:

[tex] = 3053.6[/tex]

Answer D is correct

Step-by-step explanation:

[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times \pi \times {9}^{3} \\

≈3053.62806 [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

The right answer is of option D

Look at the attached picture

hope it will help you

Good luck on your assignment

Answer:

P(seventh grade winner) = 3/8

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

8 • (5x - 1)

Step-by-step explanation:

Step  1  :  See below

Step  2  : See below

Pulling out like terms/ factors

8x - 4  =   4 • (2x - 1)

Equation at the end of step  2  :

20 • (2x - 1) +  12

Step  3  :  See below

Step  4  : See below

Pull out like factors:

40x - 8  =   8 • (5x - 1)

Answer:  8 • (5x - 1)

Hope this helps.

Answer:

i think its B

Step-by-step explanation:

i think itd most accurate t b

Answer:

Check the explanation

Step-by-step explanation:

The distribution is right skewed but the sample size is large so we can use t - test here. The statistical software output for this problem is:

One sample T hypothesis test:

μ : Mean of population

[tex]H_0[/tex] : μ = 27

[tex]H_A[/tex] : μ < 27

Hypothesis test results:

Mean         Sample Mean          Std. Err.        DF         T-Stat         P-value

μ                         26.8            0.29014496     653   -0.68931061   0.2454

Since p - value > 0.05, do not reject .

Hence,

With a mean BMI of 26.8, the data supports the claim that the average BMI is less than 27, but the difference is not statistically significant. We fail to reject the null hypothesis that the mean BMI for women aged 20 to 29 in U.S. is 27.

Answer:

67

Not exactly sure on how to write it in though

Step-by-step explanation:

Answer:

We conclude that a compact microwave oven consumes a mean of more than 250 W.

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let [tex]\mu[/tex] = mean power consumption for microwave ovens.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 250 W     {means that a compact microwave oven consumes a mean of no more than 250 W}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W     {means that a compact microwave oven consumes a mean of more than 250 W}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                                T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean power consumption for ovens = 257.3 W

            σ = population standard deviation = 15 W

            n = sample of microwave ovens = 20

So, the test statistics  =  [tex]\frac{257.3-250}{\frac{15}{\sqrt{20} } }[/tex]

                                      =  2.176

The value of z test statistics is 2.176.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.

Answer:

The equivalent expression is: (6x + 5)*(6x - 5)

Step-by-step explanation:

This expression is called the difference of two squares.

It has the following format: [tex]a^{2} - b^{2}[/tex]

It is factored as: [tex]a^{2} - b^{2} = (a-b)*(a+b)[/tex]

In this question:

[tex]a^{2} - b^{2} = 36x^{2} - 25[/tex]

So

[tex]a^{2} = 36x^{2}[/tex], then [tex]a = \sqrt{36x^{2}} = 6x[/tex]

[tex]b^{2} = 25[/tex], then [tex]b = \sqrt{25} = 5[/tex]

So

The equivalent expression is: (6x + 5)*(6x - 5)

Answer: (6x)^2 − (5)^2

Step-by-step explanation:

edge. 2022 got it right

Answer:

99cm²

Step-by-step explanation:

Area of a Triangle: [tex]A=\frac{1}{2} bh[/tex]

B- base

H- height

We are given a base of 18 cm and a height of 11cm.

[tex]A=\frac{1}{2} 18*11\\\\A=\frac{1}{2} 198\\\\\boxed{A=99}[/tex]

The area of the triangle should be 99cm².

Answer:

Arc = 20 / 3°

Step-by-step explanation:

Say the angle is = x

The sector = πr^2 / x

Sector = 100π / x

15π = 100π / x

15πx = 100π

x = 20 / 3

Arc is = to the central angle

Answer:

Area = base × height

31.5 = base × 6.3

base = 5 ft

Answer:

5 feet

Step-by-step explanation:

The area formula is A = b * h, where A is the area, b is the length of the base, and h is the height. Since we want to know the length of the base, we are solving for b. Thankfully, we know that A = 31.5 and h = 6.3. When we plug them into the equation, we get 31.5 = b * 6.3. Because we want b on one side without any coefficients and numbers on the other side, we can divide the equation by 6.3 on both sides. The equation will remain the same because we are doing the same thing to both sides. When we divide, we get b = 31.5 / 6.3 = 5 feet. Hope this helps!