Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b

Answer:

15.7 in  

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826  

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]

It checks.

Answer:

8x - 4

Step-by-step explanation:

8x - 4

Translated algebraically expression is 8x-4

What is expression?

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given verbal expression that,

8 times a number x is subtracted by 4

(1) Let x = the unknown number.

(2) "8 times a number of x" is translated algebraically as 8x

(3) "same number x is subtracted by 4" is translated algebraically as 8x -4

Putting analyses together translated algebraically into the following equation as the result : 8x-4

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Answer:

  the product of a number and 33

Step-by-step explanation:

The operation "times" is what is used to form the product of two operands.

  "t times 33" is "the product of t and 33"

Answer:

4

Step-by-step explanation:

Original coordinates:

A (0, 2)

B (2, 3)

The scale is what number the original coordinates was multiplied by to reach the new coordinates

1. Divide

(0, 8) ÷ (0, 2) = 4

(8, 12) ÷ (2, 3) = 4

AB was dilated by a scale factor of 4.

Answer:

A

Step-by-step explanation:

Let's find the ml per garlic for each sauce. Emily's has 1 clove of garlic for 62.5 ml. Raphael's has 1 clove of garlic for 7.438... ml. So, A, it will be too garlicky.

Answer:is the first answer 15.875 and the second answer 17 x 28 ÷5

Step-by-step explanation:

Answer: B) The linear speed is 4750 inches per second, so this car would qualify.

Step-by-step explanation: To determine linear speed using revolutions per second, i.e., angular speed (ω):

v = ω.r

where r is radius.

As ω is in revolutions per second, transform into rad/s:

ω = 36 revolutions/s

1 revolution = 2π rad

ω = 36.2π rad/s

ω = 72π rad/s

Radius is 21 inches, which can be written as

r = 21 inches/rad

Linear speed is

v = [tex]\frac{72.\pi rad}{s} .\frac{21 in}{rad}[/tex]

v ≈ 4750 inches per seconds

Converting to miles per hour:

v = [tex]4750.\frac{5}{88}[/tex]

v = 270mph

At linear speed of 4750 inches per second, a car with wheel of radius 21-inch can qualify.

Answer:

Above is correct

Step-by-step explanation:

Hey there! I'm happy to help!

Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.

We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.

If the line we are looking for is flat; it stays at the same y-value the entire time. We see that  the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.

I hope that this helps! Have a wonderful day!

Answer:

Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.

We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.

If the line we are looking for is flat; it stays at the same y-value the entire time. We see that  the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.

Step-by-step explanation:

; ) BELIEVE IN YOURSELF!!!!!!!!!!!!!!!!!

Answer:

A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

B) The method used is Relative frequency approach.

Step-by-step explanation:

From the question, we are told a sample of n kids line up for recess.

Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).

Since we are being asked about 3 kids from the class, let's assign a letter to each kid:

J: John

B: Betty

M: Mary

A) Now, we want to find the probability that Betty is first in line or Mary is last in line.

In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;

P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

Where;

The suffix 1 refers to the first position while the suffix n refers to the last position.

Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)

This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.

B) The method used is Relative frequency approach.

In this method, the probabilities are usually assigned on the basis of experimentation or historical data.

For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.

Also, let n_A be the number of times that A did occur.

Now, the relative frequency would be written as (n_A)/n.

Thus, in this method, we will define P(A) as:

P(A) = lim:n→∞[(n_A)/n]

Given this pair of probabilities, the probability that Mary is the first is  n(A) = n-1!, while the probability that Betty is last is  n(A) = n-1!

There are n! ways of making this arrangement

We have probability of A: Betty is the first person in this line

Probability of B: Mary is the last person

A U B = p(A) + p(B) - p(A ∩ B)

n(A) = n-1 that is given that Betty is the first person on the line.

then n(A) = n-1!

As the last person on the line P(B) = n-1!

Probability of (A∩B) =( n-2)!  this has Mary as the first and Betty as the last person.

Remaining students that would have to be on this line are n-2

Prob(A∪B) = n(A ∪ B)/n!

= 2(n-2)/n(n-1)

This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.

Read more on probability here: https://brainly.com/question/24756209

Answer:

a y = 2

b.y = 14

c. y =56

Step-by-step explanation:

a .6 (1)- 4=2

y=2

b. 6 (3)- 4

=18-4

y=14

c. 6 (10) - 4

= 60 - 4 =56

Answer:

x = [tex]10^{0}[/tex]

Step-by-step explanation:

From Δ MPL given that; <P = [tex]90^{0}[/tex], exterior angle to M = [tex]136^{0}[/tex] and <L = [tex](4x+6)^{0}[/tex].

In the triangle, the exterior angle is equal to the sum of the two adjacent interior angles. So that;

[tex]136^{0}[/tex] = [tex]90^{0}[/tex] + [tex](4x+6)^{0}[/tex]

      = [tex]90^{0}[/tex] + 4[tex]x^{0}[/tex] + [tex]6^{0}[/tex]

[tex]136^{0}[/tex] = [tex]96^{0}[/tex] + [tex]x^{0}[/tex]

⇒      4[tex]x^{0}[/tex] = [tex]136^{0}[/tex] - [tex]96^{0}[/tex]

        4[tex]x^{0}[/tex]  = [tex]40^{0}[/tex]

Divided both sides by 4 to have;

[tex]x^{0}[/tex] = [tex]10^{0}[/tex]

The value of x is [tex]10^{0}[/tex].

Answer:

The correct answer is in fact 10 degrees.

Step-by-step explanation:

I hope this helps!

Have a great day! :)

Answer:

Average rate of change of the function will be = (-1.5)

Step-by-step explanation:

Average rate of change of a function f(x) is determined by the formula,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex] If a < x < b

We have to find the average rate of change of a function g(t) between the interval [-3, 1]

From the given table,

For t = -3,

g(-3) = 6

For t = 1,

g(1) = 0

Therefore, average rate of change of the function in the given interval

= [tex]\frac{g(1)-g(-3)}{1-(-3)}[/tex]

= [tex]\frac{0-6}{1+3}[/tex]

= [tex]-\frac{3}{2}[/tex]

= - 1.5

This problem is about creating a linear regression model.

First, we should take note of the points:

(-4,8)

(-2,4)

(-1,2)

(1,5)

(2,2)

(6,-5)

(7,6)

It's necessary to find a equation y = ax + b that brings us the least MSE (Mean Squared Error). You can calculate at hand, but I bet it is going to be tiresome.

So, basically intuitively you just need to choose a line that fits closer to the given points.

First: remember if y = ax+b, a is the slope which means if a > 0 the line is " / " and a < 0 the line is " \ ".

A) No, this equation is " / "

B) It could be this one.

C) It could be this one too.

D) Nope. " / "

B) a = -1/2

C) a = -4

You can draw those two lines and see that B) gets closer to the points.

Equation:

Y = -0.4957*X + 3.780

Answer:

[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]

Step-by-step explanation:

Using a graph,

we can see that the line y = -1/2x + 7/2 best fits for the data.

Answer:

[tex]\frac{x^{\frac{5}{6}} }{x^{\frac{1}{6}} } = x^{(\frac{5}{6} -\frac{1}{6}) }= x^{\frac{4}{6} }\\\sqrt{x} . \sqrt[4]{x} = x^{\frac{1}{2} } . x^{\frac{1}{4} } = x^{(\frac{1}{2} +\frac{1}{4}) } = x^{\frac{3}{4}[/tex]

Answer: -4

At 1, the parabola is at (1, 3). And at 3, it's at (3, -5). The rate of change is -4, since each time it moves right 1, it goes down 4.

Hope that helped,

-sirswagger21

Answer:

The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.

Answer:

7161

Step-by-step explanation:

7 + 7(2) + 7(2)² + ... + 7(2)⁹

= ∑₁¹⁰ 7(2)ⁿ⁻¹

= 7 (1 − 2¹⁰) / (1 − 2)

= 7161

Answer: 0.418 < p < 0.512

Step-by-step explanation: A 95% conifdence interval for a population proportion is given by:

[tex]p + z\sqrt{\frac{p(1-p)}{n} }[/tex]

where:

p is the proportion

z is score in z-table

n is sample size

The proportion for people who said "yes" is

[tex]p=\frac{202}{434}[/tex] = 0.465

For a 95% confidence interval, z = 1.96.

Calculating

[tex]0.465 + 1.96*\sqrt{\frac{0.465(0.535)}{434} }[/tex]

[tex]0.465 + 1.96*\sqrt{0.00057}[/tex]

0.465 ± 1.96*0.024

0.465 ± 0.047

Interval is between:

0.465 - 0.047 = 0.418

0.465 + 0.047 = 0.512

The interval with 95% of confidence is between 0.418 and 0.512.

Answer:

The mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

In this case we need to test whether the mean commute time in the U.S. is less than half an hour.

The information provided is:

 [tex]n=45\\\bar x=25.5\\s=19.1\\\alpha =0.05[/tex]

(a)

The hypothesis for the test can be defined as follows:

H₀: The mean commute time in the U.S. is not less than half an hour, i.e. μ ≥ 30.

Hₐ: The mean commute time in the U.S. is less than half an hour, i.e. μ < 30.

(b)

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

 [tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{25.2-30}{19.1/\sqrt{45}}=-1.58[/tex]

Thus, the test statistic value is -1.58.

(c)

Compute the p-value of the test as follows:

[tex]p-value=P(t_{(n-1)}<-1.58)=P(t_{(45-1)}<-1.58)=0.061[/tex]  

*Use a t-table.

The p-value of the test is 0.061.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.061> α = 0.05

The null hypothesis will not be rejected at 5% level of significance.

Thus, concluding that the mean commute time in the U.S. is less than half an hour.

Answer:

"Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel"

a. The inference made involves estimation.  The question provided that the statements were made on the basis of the resulting data and not on the basis of some hypothesis testing.

This implies that some statistics were calculated from sample data to approximate the population parameter, as shown in the statements.  The statements were not an attempt to establish the statistical significance of some claims.

b. The population of interest is American teenagers between 12-17.

Step-by-step explanation:

An inference from data is a statistical estimation by which some statistics are calculated based on the sample data of 800 teens between the ages of 12 and 17.  The statistics serve as an approximation to the population parameter.

Inference based on hypothesis testing establishes if a claim has statistical significance by providing  statistical evidence in favor of the claim or against it.

Answer:

7

Step-by-step explanation:

The following range includes numbers from negative infinity to 8. But, 8 isn't included, because there is a parentheses not a bracket. So, basically you can have 7.9999999. But, it asks for an integer, so it is 7.

The largest integer which belongs to the interval: (−∞, 8) is 7

To determine the largest integer, we will first ascertain what the use of parentheses and brackets denote.

The use of parentheses ( ) stands for open interval, that is, the extreme numbers of the set are not included.

If the brackets [ ] were used instead, that will be closed interval, that is, the extreme numbers of the set are included.

Since ( ) were used in the question, that means the extreme numbers −∞ and 8 are NOT included in the set.

Now, let us define an integer.

An integer is a positive or negative whole number or zero.

Hence, the integers in the set will include: −∞+1, −∞ + 2, ... 5, 6, and 7.

The largest integer here is 7

Hence, the largest integer which belongs to the interval: (−∞, 8) is 7

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Answer:

The equation for a unit radius circle, centered at the origin is:

x^2 + y^2 = 1

Now, if we want to move it horizontally, you can recall to the horizontal translations:

f(x) -----> f(x - a)

Moves the graph to the right by "a" units.

A vertical translation is similar.

Then, if we want a circle centered in the point (a, b) we have:

(x - a)^2  + (y - b)^2 = 1.

Now, if you want to change the radius, we can actually write the unit circle as:

x^2 + y^2 = 1^2

Where if we set x = 0, 1 = y, this is our radius

So if we have:

x^2 + y^2 = R^2

And we set the value of x = 0, then R = y.

So our radius is R.

Then:

"A circle of radius R, centered in the point (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

Complete Question

Find the indicated area under the curve of the standard normal​ distribution, then convert it to a percentage and fill in the blank.

About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

Answer:

About 97.219% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

Step-by-step explanation:

From the question given we can see that they both are the same so 1  will just solve one

   Now the area under this given range can be represented mathematically as

  [tex]P ( -2.2 < z < 2.2) = P(z < 2.2 ) - P(z < -2.2 )[/tex]

Now  from the z-table  

        [tex]p(z < 2.2 ) = 0.9861[/tex]

and

        [tex]p(z < - 2.2 ) = 0.013903[/tex]

So

     [tex]P ( -2.2 < z < 2.2) = 0.9861 - 0.013903[/tex]

     [tex]P ( -2.2 < z < 2.2) = 0.97219[/tex]

So converting to percentage  

     [tex]P ( -2.2 < z < 2.2) = 0.97219 * 100[/tex]

    [tex]P ( -2.2 < z < 2.2) = 97.219 \%[/tex]

Answer:

[tex]\Large \boxed{{6x \ \mathrm{and} \ -3x}}[/tex]

Step-by-step explanation:

Like terms have identical variables and exponents, the coefficients don’t have to be the same.

The like terms from the expression are 6x and -3x.

Step-by-step explanation:

Hey, there!!

6x and -3x are like terms.

Like terms in algebraic terms are those terms which has same variable or exponents. In This expression "6x+8xy-3x+9y4x^2"

6x and -3x has "x" common in them so, The answer is 6x and -3x.

Hope it helps..

Answer: E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)

Step-by-step explanation:

According to the combinations: Number of ways to choose r things out of n things = C(n,r)

Given word: "georgianna"

It is a sequence of 10 letters with 2 a's , 2 g's , 2 n's , and one of each e, o,r, i.

If we think 10 blank spaces, then in a sequence we need 2 spaces for each of g.

Number of ways = C(10,2)

Similarly,

1 space for 'e' → C(8,1)

1 space for 'o' → C(7,1)

1 space for 'r' → C(6,1)

1 space for 'i' → C(5,1)

1 space for 'a' → C(4,2)

1 space for 'n' → C(2,2)

Required number of different sequences  = C(10,2) ×C(8,1)× C(7,1)× C(6,1)×C(5,1)×C(2,2).

Hence, the correct option is E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)

Answer:

Step-by-step explanation:

[tex]-3\left(x+1\right)=-3\left(x+1\right)-5\\\\\mathrm{Add\:}3\left(x+1\right)\mathrm{\:to\:both\:sides}\\\\-3\left(x+1\right)+3\left(x+1\right)=-3\left(x+1\right)-5+3\left(x+1\right)\\\\\mathrm{Simplify}\\\\0=-5\\\\\mathrm{The\:sides\:are\:not\:equal}\\\\\mathrm{No\:Solution}[/tex]

Answer:

-35 and 37

Step-by-step explanation:

If you start with negative 35 and count up (including zero), you’ll cancel out when you get to positive 35 and have 71 numbers.  Then you continue on with 36 and 37 which equals 73, and you have 73 consecutive integers.

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = probability of obtaining head.

So, Null Hypothesis, [tex]H_0[/tex] : p = 0.5

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.5

(a) The significance level of the test which is represented by [tex]\alpha[/tex] is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

            P(Type I error) = [tex]\alpha[/tex]

         P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]

[tex]\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}[/tex]  = [tex]\alpha[/tex]

[tex](1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})[/tex] = [tex]\alpha[/tex]

[tex]\alpha[/tex] = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - [tex]\beta[/tex]).

So, here, X ~ Binom(n = 10, p = 0.1)

[tex]1-\beta[/tex] = P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true)

[tex]1-\beta[/tex] = [tex]\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}[/tex]  

[tex]1-\beta[/tex] = [tex](1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})[/tex]

[tex]1-\beta[/tex] = 0.3487

Hence, the power of the test is 0.3487.

Answer:

[tex]\large \boxed{-40, \ 4, \ -4}[/tex]

Step-by-step explanation:

[tex]f(x)=-9x+14[/tex]

[tex]\sf Put \ x \ as \ 6.[/tex]

[tex]f(6)=-9(6)+14[/tex]

[tex]f(6)=-54+14[/tex]

[tex]f(6)=-40[/tex]

[tex]g(x)=-3x^2[/tex]

[tex]\sf Put \ g(x) \ as \ -48.[/tex]

[tex]-48=-3x^2[/tex]

[tex]\displaystyle \frac{-48}{-3} =\frac{-3x^2 }{-3}[/tex]

[tex]16=x^2[/tex]

[tex]\sqrt{16} =\sqrt{x^2 }[/tex]

[tex]x= \pm 4[/tex]

Answer:

F(6) = -9(6) + 14 = -54 + 14. f(6) = -40

G(x) = -48 / g(x) = -3(16) / g(4) = -48

Step-by-step explanation:

For the first one the drop answer is -40

For the second one its 4 then 16

I think because that whats im seeing but these are the right answers :)

Answer:

[tex]\large \boxed{\mathrm{B. \ \ \{-10, -6, 10\} }}[/tex]

Step-by-step explanation:

The domain is the x values.

D = {-1, 0, 4}

y = 4(-1) - 6 = -4 - 6 = -10

y = 4(0) - 6 = 0 - 6 = -6

y = 4(4) - 6 = 16 - 6 = 10

The range is the y values.

R = {-10, -6, 10}