Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Between y = x2 − 4x + 1 and y = −x2 + 4x − 5 for x in [0, 3]

The expression that represents the perimeter and the of the rectangle is: 14.6q - 13.4.

A rectangle's perimeter if the length of its surrounding borders. Thus, the perimeter of a rectangle is the sum of all the length of the sides of the rectangle which can be calculated using the formula below:

Perimeter of a rectangle = 2(length + width).

Given the following:

Therefore, substitute the expression for the width and length of the rectangle into the perimeter of the rectangle formula:

Perimeter of rectangle = 2(9.6q - 3.6 + 4.3q - 3.1)

Combine like terms

Perimeter of rectangle = 2(7.3q - 6.7)

Perimeter of rectangle = 14.6q - 13.4

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Answer:

\(\frac{43}{100}\)

Step-by-step explanation:

Think of it as a percentage. 43% is \(\frac{43}{100}\) , but it is also 0.43. Any number over 100 will be put into a similar decimal format (\(\frac{12}{100}\) = 0.12  and \(\frac{4}{100}\) = 0.04)

The fraction with a denominator of 100 is equivalent to 0.43 is,

\(\frac{43}{100}\).

Here,

We have to find fraction with a denominator of 100 is equivalent to 0.43.

What is Fraction?

A fraction is used to represent the portion/part of the whole thing.

Now,

Let a fraction with a denominator of 100 is \(\frac{x}{100}\).

And, its equivalent to 0.43.

Hence,

\(\frac{x}{100} = 0.43\)

\(x = 43\)

So, A fraction with a denominator of 100 is \(\frac{43}{100}\).

Which is equivalent to 0.43.

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Answer:

4x(a+1)(a-2)

Explanation:

Given the polynomial:

First, factor out 4x in all the terms:

Next, factor the expression in the parenthesis:

The factored form of the polynomial is 4x(a+1)(a-2).

Answer:

False

Step-by-step explanation:

7 4/10= 7.4

7.4<7.421

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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The median would be 22:

Step-by-step explanation: The median is the number that is in the middle

Simply defined, the median is the number right in the middle of a set.

But before I get down to finding the median, I will order the numbers from least to greatest:

15, 17, 19, 20, 21, 22, 23

Now, the middle number is 20. So that's the median.

As for the range, it's the difference between the largest number and the smallest one:

Range = Greatest number - Smallest number

           = 23 - 15

           = 6

In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.

Answer:

G is true is out divide 1/7 by 2 out get 1/14

H is false the product is always 1

I is false all numbers have a reciprocal besides 0

Answer:

g. True

h. False

i. False

Step-by-step explanation:  

g.  

\(\frac{1}{14}\) is half of \(\frac{1}{7}\)  

This would be true because half of a number can be found by multiplying by \(\frac{1}{2}\)  

If you multiplied \(\frac{1}{7} * \frac{1}{2}\)  

The numerator is 1 * 1 which is 1  

And then the denominator is 7 * 2 which is 14  

That would give you \(\frac{1}{14}\)

h.  

The products of two reciprocals is 0  

This is not true  

Reason being, reciprocals are just the number flipped. If you times the number by itself, you don't get 0, you get 1.  

Ex:  \(\frac{2}{8}\)

Its reciprocal is \(\frac{8}{2}\)  

So multiply them together

\(\frac{2}{8}* \frac{8}{2}\)  

2 * 8 = 16  

8 * 2 = 16  

\(\frac{16}{16} = 1\)

i.  

A whole number does not have a reciprocal  

This is incorrect. If you think about it, a whole number is just the number, over 1  

Ex: \(\frac{6}{1}\)

This is still a whole number even though its written in fraction form because if you divide 6 by 1, your still going to get 6.

If you an write it as a fraction, it has a reciprocal.

The reciprocal in this case would be \(\frac{1}{6}\)

I hope this helps, don't be afraid to reach out with any further questions!

Answer

His new position is 3.75 meters 12.25-8.5=3.75 her new position is 20ft 9 1/2 +10 1/2=20

Step-by-step explanation:

Answer:

d is the answer......................

Answer:

3 bookcases

Step-by-step explanation:

Answer:

1) Not Congruent

2) Congruent

3) Congruent

4) Congruent

5) Not Congruent

6) Congruent

(I tried my best, hope this helps. Good luck hun)

Step-by-step explanation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

The angle of the T in the ΔRST is 100° and the value of p is 11.

Define Triangle.

A triangle is a polygon that consists of three sides and three vertices. The fact that the interior angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. This characteristic is known as the angle sum property of a triangle.

i.e., In a give ΔABC, ∠A + ∠B + ∠C = 180°.

Given:

∠R = 37°; ∠S = 43°; ∠T = 10p-10°

Let's take ∠T = x

In ΔRST,

∠R + ∠S + ∠T = 180°

37 + 43 + x =  180°

x = 180 - 80 ⇒ 100

∴ ∠T = 100°

To find the value of p,

 ∠T = 100

10p - 10 = 100

10p = 110 ⇒ 11

∴ p = 11

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A sine function is as shown below

A cosine function is as shown below

The combination of both sine and cosine function is as shown below

It can be observed from the above combination that:

Cosine is better when the maximum is on the y- axis and sine is better if the midline is at the center.

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Let's assume that the distance from point A to the lighthouse is x feet and the distance from point B to the lighthouse is y feet. Also, let's assume that the height of the boat's crew's eye level is h feet above the water.

From point A, we can use tangent function to find x:

tan(5°) = (119 + h) / x

From point B, we can use tangent function again to find y:

tan(18°) = (119 + h) / y

We want to find the distance between point A and point B, which is the difference between x and y:

distance AB = y - x

We need to eliminate h from these equations to solve for x and y. We can do this by solving for h in one equation and substituting it into the other equation:

h = x tan(5°) - 119

tan(18°) = (119 + x tan(5°) - 119) / y

tan(18°) = x tan(5°) / y

y = x tan(5°) / tan(18°)

distance AB = y - x = x (tan(5°) / tan(18°) - 1)

Now we can plug in the values and use a calculator to find the distance:

distance AB = x (tan(5°) / tan(18°) - 1)

distance AB = x (0.107 - 1)

distance AB = -0.893 x

Since the distance cannot be negative, we know that x must be greater than zero. Therefore, we can ignore the negative sign and solve for x:

x = distance AB / -0.893

Using a calculator, we get:

x ≈ 181.74 feet

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

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Answer:

3/8

Step-by-step explanation:

3/4 x 1/2 = 3/8

3/8 x 1/1 = 3/8

Hope that helps!

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

Answer:

2.85

Step-by-step explanation:

12.4% x 23 = 2.85

rounded to a maximum of 2 decimals

Answer:

all of the above

Step-by-step explanation:

A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.

A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.

Cone volume is calculated using the method V=1/3πhr².

Given that,

diameter(d) = 16 cm

radius (r) = d/2 = 8 cm

volume = 320π cubic centimeters

πr²h/3 = 320π

or, [π × (8)² × h]/3 = 320π

or,  h = (3 × 320)/(8)²

or, h = 15 cm

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Answer:

11/12

Step-by-step explanation:

ig not sure

the statement given 1/3 of the sum of 45 and a number is 16

In order to find the value of x, w

Answer:

No.

Step-by-step explanation:

hope u got it.........

Answer:

a)  Null hypothesis:  \(\mathbf{H_0 : \mu \leq 15}\)

Alternative hypothesis: \(\mathbf{H_1 = \mu > 15}\)

b) the test statistics is : 2.15

c) The p-value is 0.0158

d) NO, there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.

Step-by-step explanation:

The data in the  Microsoft Excel are:

17;11;12;23;20;23;15;

16;23;22;18;23;25;14;

12;12;20;18;12;19;11;

11;20;21;11;18;14;13;

13;19; 16;10;22;18;23.

a) Formulate the null and alternative hypotheses for this application.

From the question, Fowle Marketing Research Inc. is taking base charge from a client on the given assumption that if the mean time of telephone survey is 15 minutes or less.

The null and alternative hypotheses are therefore as follows:

Null hypothesis:  \(\mathbf{H_0 : \mu \leq 15}\)

The null hypothesis states that there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.

Alternative hypothesis: \(\mathbf{H_1 = \mu > 15}\)

The alternative hypothesis states that there is evidence that the mean time of telephone survey exceeds 15 and premium rate is justified.

b) Compute the value of the test statistic.

Given that:

\(\mu = 15\)

\(\sigma = 3.6\)

n = 35

The sample mean \(\bar x = \dfrac{ \sum x}{n}\)  is;

\(\bar x = \dfrac{ 17+11+12 ... 22+18+23}{35}\)

\(\bar x = 17\)

Thus:

\(z = \dfrac{ \bar x - \mu }{\dfrac{\sigma}{\sqrt{n}}}\)

\(z = \dfrac{ 17 - 15}{\dfrac{3.6}{\sqrt{15}}}\)

\(z = \dfrac{ 2}{0.9295}}\)

\(\mathbf{z =2.15}\)

Thus; the test statistics is : 2.15

c) What is the p-value?

p-value = P(Z > 2.15)

p-value = 1 - P(Z ≤ 2.15)

From the standard normal table, the value of P(Z ≤ 2.15) is 0.9842

p-value = 1 - 0.9842

p-value = 0.0158

The p-value is 0.0158

d)  At a = .01, what is your conclusion?

According to the rejection rule, if p-value is less than 0.01 then reject null hypothesis at ∝ = 0.01

Thus; p-value =  0.0158 >  ∝ = 0.01

By the rejection rule, accept the null hypothesis.

Therefore, there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.

Answer:

448

Step-by-step explanation:

A=((a+b)/2) h=(17+39)/2·16=448

Answer:

8n+12=36, triplets are 8 years old

Step-by-step explanation:

total age is 36

one of them is 12 years old so -> 36-12 = 24

three triplets so 24/3 = 8

there are three 8 years olds and one 12 year old. n = 3

Answer:

Step-by-step explanation:

3n + 12 = 36

3n = 24

n = 8 (the triplets)

another child: 12 years

If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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When something varies directly as something else, their ratio of change always stays the same.

56 / 7 = 8

Therefore,

8 * 3 = 24

If x = 3 then y = 24

Given:

given polynomial is

Find:

we have to find the leading coefficient and degree of the polynomial.

Explanation:

The lewading coefficient is the coefficient of highest power term of the polynomial.

Highest power of v is 8 and its coefficient is 4.

Therfore, leading coefficient is 4.

and the degree of the polynomial is equal to the highest power of v in the polynomial, which is 8.

Therefore, the leading coefficient of polynomial is 4 and degree is 8.