We are interested in determining the percent of American adults who believe in the existence of angels. An appropriate confidence interval would be:
a. A confidence interval for a population proportion b. A confidence interval for a population mean using t c. A confidence interval for the variance using a chi-squared. d. A confidence interval for a population mean using z

Terms are 4b, 7b, 5 coefficient are 4 , 7 and constant = 4, 7 , 5

What are the parts in expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given expression:

4b+7b+5

As. term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Terms are 4b, 7b, 5

Now, coefficient is a number that is multiplied by a variable in an expression.

coefficient are 4 , 7

As a constant is a fixed numerical value,

So, constant = 4, 7 , 5

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

We have proved that the expression \(Var(x) = E(x^2) - [E(x)]^2.\)

To prove that \(Var(x) = E(x^2) - [E(x)]^2\), where \(Var(x)\) represents the variance of a random variable x and E(x) represents the expected value of x, we can start by using the definition of variance:

\(Var(x) = E[(x - E(x))^2]\)

Expanding the square:

\(Var(x) = E[x^2 - 2x*E(x) + [E(x)]^2]\)

Using linearity of expectations, we distribute the expectation operator:

\(Var(x) = E(x^2) - 2E(x*E(x)) + E([E(x)]^2)\)

Now, let's focus on the term E(x*E(x)). Since E(x) is a constant with respect to the inner expectation operator, we can take it out:

\(E(x*E(x)) = E(x) * E(E(x))\)

The inner expectation, E(E(x)), is just the expected value of a constant, which is equal to that constant:

\(E(E(x)) = E(x)\)

Substituting this back into the equation, we have:

\(Var(x) = E(x^2) - 2E(x*E(x)) + E([E(x)]^2)\)

           \(= E(x^2) - 2E(x*E(x)) + E(x^2)\)

Now, consider the term \(E(x*E(x))\). This can be written as:

\(E(x*E(x)) = E(E(x^2|x))\)

This is the conditional expectation of \(x^2\) given x. However, when we take the unconditional expectation E, the conditional expectation collapses to the unconditional expectation of \(x^2\):

\(E(x*E(x)) = E(x^2)\)

Substituting this back into the equation, we get:

\(Var(x) = E(x^2) - 2E(x*E(x)) + E(x^2)\)

     \(= E(x^2) - 2E(x^2) + E(x^2)\)

     \(= E(x^2) - E(x^2)\)

     \(= E(x^2) - [E(x)]^2\)

Hence, we have proved that \(Var(x) = E(x^2) - [E(x)]^2.\)

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The standard deviation for the probability distribution is approximately 0.79, rounded to two decimal places.

To find the standard deviation for this probability distribution, we first need to find the mean.

The mean is given by:

μ = Σ(x * P(x))

where x is the number of burglaries and P(x) is the probability of x burglaries being reported in a given day.

\(μ = (0 * 0.53) + (1 * 0.35) + (2 * 0.10) + (3 * 0.02)μ = 0 + 0.35 + 0.20 + 0.06μ = 0.61\)

So the mean number of burglaries reported in a given day is 0.61.

To find the standard deviation, we use the formula:

\(σ = √(Σ[(x - μ)^2 * P(x)])\)

where σ is the standard deviation.

\(σ = √[((0 - 0.61)^2 * 0.53) + ((1 - 0.61)^2 * 0.35) + ((2 - 0.61)^2 * 0.10) + ((3 - 0.61)^2 * 0.02)]\\σ = √[(0.61^2 * 0.53) + (0.39^2 * 0.35) + (1.39^2 * 0.10) + (2.39^2 * 0.02)]\\σ = √[0.197969 + 0.053865 + 0.257199 + 0.113964]\\σ = √0.623997σ ≈ 0.79\)

Therefore, the standard deviation for the probability distribution is approximately 0.79, rounded to two decimal places.

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These two points on the number line describe that she descended by 70 units.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
She started at –5 and descended to –75.
On the number line, the difference between  -75 and -5 is given as
= -5 - (-75)
= 70

Thus, these two points on the number line describe that she descended by 70 units.

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Answer:

20

Step-by-step explanation:

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42\(x_{0}\) in which \(x_{0}\) is the initial population.

Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.

We are required to find the number of bacteria present after 10 weeks.

let the number of bacteria present at t is x.

So,

dx/dt∝x

dx/dt=kx

1/x dx=k dt

Now integrate both sides.

\(\int\limits {1/x} \, dx\)=\(\int\limits{k} \, dt\)

log x=kt+log c----------1

Put t=0

log \(x_{0}\)=0 +log c    (\(x_{0}\) shows the population in beginning)

Cancelling log from both sides.

c=\(x_{0}\)

So put c=\(x_{0}\) in 1

log x=kt+log \(x_{0}\)

log x=log \(e^{kt}\)+log \(x_{0}\)

log x=log \(e^{kt}x_{0}\)

x=\(e^{kt}x_{0}\)

We have been given that the population triples in a week so we have to put the value of x=2\(x_{0}\) and t=1 to get the value of k.

2\(x_{0}\)=\(e^{k} x_{0}\)

2=\(e^{k}\)

log 2=k

We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.

x=\(e^{20log 2}\)\(x_{0}\)

x=\(e^{0.30*2}\)\(x_{0}\)

x=\(e^{6}x_{0}\)

x=403.42\(x_{0}\)

If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42\(x_{0}\) in which \(x_{0}\) is the initial population.

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The given question is incomplete as the question incudes the following:

Calculate the population after 20 weeks.

The correct null hypothesis for a repeated measures design study would be µd = 0, which states that there is no difference between the means of the paired measurements or conditions.

In a repeated measures design study, the same group of participants is measured under different conditions or at different time points. The goal is to determine if there is a significant difference between the paired measurements.

The null hypothesis in this case represents the absence of any difference between the means of the paired measurements. The symbol µd represents the population mean difference, and setting it equal to zero implies that there is no systematic change or effect between the conditions or time points.

On the other hand, m1 = m2 would represent the null hypothesis for an independent samples design study, where two separate groups are compared. In that case, the null hypothesis states that there is no difference between the means of the two groups.

Therefore, for a repeated measures design study, the correct null hypothesis would be µd = 0, indicating no difference between the means of the paired measurements.

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Answer:

c is incroccet aand other are correct

Answer:

Correct me if im wrong but im sure the answer is b

Step-by-step explanation:

Answer:

i tried but i dont know the awnser

Step-by-step explanation:

post it again someone will see it

Answer: 231

Step-by-step explanation: Jamie baked twice as many cookies as Carrie, 2 x 77 = 154.

The question asks for the number of cookies altogether, so 154 + 77 = 231

Answer: 77 + 2(77) = x

Step-by-step explanation:

154 + 77 = x

x = 224

They baked 224 cookies together.

Answer:

Step-by-step explanation:

The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.

GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.

The given expression is,

16a⁴b + 8ab³

Simplify the expression, by factor method,

8 x 2 x a x a x a x a x b  + 8 x a x b x b x b

The common term is 8ab,

8ab(2a³ + b²)

The required expression is 8ab(2a³ + b²).

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Answer:

Step-by-step explanation:

Total sum of age of 12 students = 12*18 = 216;

Total sum of age of 8 students = 8*23 = 184;

Total sum of age of 20 students = 216+184 = 400;

Mean age of all the students = total age / number of students;

= 400/20 = 20 year

Step-by-step explanation:

Using the definition of the Laplace transform:

\(\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_0^t \tau \cos(3\tau) \, d\tau\right) e^{-st} \, dt\)

Reverse the order of integration. In the \(t-\tau\) plane, the domain of integration can be expressed as given,

\(D = \left\{(t,\tau) ~:~ 0\le t<\infty \text{ and } 0\le \tau\le t\right\}\)

or equivalently as

\(D' = \left\{(t,\tau) ~:~ \tau \le t < \infty \text{ and } 0 \le \tau < \infty\right\}\)

Then the Laplace transform is

\(\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_\tau^\infty e^{-st} \, dt\right) \tau \cos(3\tau) \, d\tau \\\\ ~~~~~~~~ = \frac1s \int_0^\infty e^{-s\tau} \tau \cos(3\tau) \, d\tau\)

and the remaining integral is exactly the Laplace transform of \(f(\tau)=\tau\cos(3\tau)\), which can be easily if tediously computed by parts, or you can look it up in a transform table. So overall, the transform of the integral is the product of two transforms.

This is equivalent to the convolution property of the Laplace transform,

\(\displaystyle L\left\{f(t) * g(t)\right\} = L\left\{f(t)\right\} L\left\{g(t)\right\}\)

where

\(f(t) * g(t) = \displaystyle \int_0^t f(\rho) g(t - \rho) \, d\rho\)

In our case, we let \(f(t)=t\cos(3t)\) and \(g(t)=g(t-\rho)=1\).

To find the Laplace transform of \(\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}\), we can use the properties of the Laplace transform. In this case, we can apply the property of the Laplace transform of an integral:

\(\displaystyle{L\left \{\int_0^t f(t) \, dt \right \} = \dfrac{1}{s} F(s)}\),

where \(\displaystyle{F(s)}\) is the Laplace transform of \(\displaystyle{f(t)}\).

In this case, \(\displaystyle{f(t) = t\cos 3t}\). Taking the Laplace transform of \(\displaystyle{f(t)}\), we have:

\(\displaystyle{L\left \{t\cos 3t \right \} = \dfrac{s}{s^2 + 9}}\).

Now, applying the property of the Laplace transform of an integral, we can find the Laplace transform of \(\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}\):

\(\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \} = \dfrac{1}{s} \cdot \dfrac{s}{s^2 + 9} = \dfrac{1}{s^2 + 9} = 1}\).

Therefore, the Laplace transform of \(\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}\) is 1.

Answer: \(y \leq -\frac{x}{2}-\frac{7}{2}\)

Step-by-step explanation:

\(-x-2y \geq 7\\\\x+2y \leq -7\\\\2y \leq -x-7\\\\y \leq -\frac{x}{2}-\frac{7}{2}\)

A. The translations used in the transformation of f(x) to g(x) can be given as follows:

B. The solutions for k are given as follows:

C. The rules are given as follows:

There are four cases for the translation of an image, and they can be represented as follows:

From the graph of the linear functions shown at the end of the answer, two translations are possible, listed as follows:

The values of k are equivalent to the values of a in the bullet points listing the translations above, and the equations were also built from those bullet points.

The lines are shown by the image at the end of the answer.

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Answer:it will be answer 2

Step-by-step explanation:

Just took to and that was correct

Answer:

2 + 3i

Step-by-step explanation:

Answer:

9 inches

Step-by-step explanation:

Convert from feet to inches by multiplying by 12:

3*12 = 36

Multiply by the scale factor of 1/4:

36*1/4 = 9

9 inches

The logarithms of the terms of the geometric sequence a, ar, ar^2 form an arithmetic sequence because the logarithm of a product is equal to the sum of the logarithms of the individual factors.

To show this, let's take the logarithm of each term:

log(a) = x

log(ar) = y

log(ar^2) = z

Now, we can express the terms in terms of x, y, and z:

x = log(a)

y = log(ar) = log(a) + log(r)

z = log(ar^2) = log(a) + log(r^2)

If we subtract x from both sides of the equation for y, we get:

y - x = log(r)

Similarly, if we subtract x from both sides of the equation for z, we get:

z - x = log(r^2)

Notice that the difference between the terms y and x is equal to the difference between the terms z and x. This shows that the logarithms of the terms of the geometric sequence form an arithmetic sequence.

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Answer: What are the choices?

Step-by-step explanation:

Answer: Evaluate the findings to compare to his hypothesis

Step-by-step explanation: Since the biologist already has the findings and has a hypothesis, he now has to compare both of them together.

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

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A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

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We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

150%

Step-by-step explanation:

Answer:

100 percent is the answer

Answer:

1a

2b

3b

4b

5d

i think this is it

Answer:

c

Step-by-step explanation:

The length of side A in the new trapezoid after reduction is: C. 2 cm.

A reduction is a transformation which reduces the size of an original figure, in such a way that the ratios of the corresponding sides of the original and new figure are equal.

Based on the definition of reduction, the following ratio can be written:

16.5/11 = 3/A

Cross multiply

A = (11 × 3)/16.5

A = 2 cm.

Therefore, the length of side A in the new trapezoid after reduction is: C. 2 cm.

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