Use the functions m(x) = 4x + 5 and n(x) = 8x − 5 to complete the function operations listed below. Part A: Find (m + n)(x). Show your work. (3 points) Part B: Find (m ⋅ n)(x). Show your work. (3 points) Part C: Find m[n(x)]. Show your work. (4 points)

Answer: 32

Step-by-step explanation:

Answer:  A) N'=(-2, 2) M'=(-1, 0)  L'=(-5, -2)

Step-by-step explanation:

N = (-2, -4)      M = (-3, -2)       L = (1, 0)

Reflection over y = -1

N' = (-2, 2)      M' = (-3, 0)       L' = (1, -2)

Reflection over x = -2

N'' = (-2, 2) M'' = (-1, 0)  L'' = (-5, -2)

Answer:isosceles is the correct

Step-by-step explanation:

According to the given conditions the triangle ABC is an isosceles triangle.

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles  ADB and CBD congruent by SAS rule,

So, the proof is as follows,

AD = CD [definition of median]

∠ ADB = ∠ CDB [definition of altitude]

BD = BD [reflexive property]

∴ Δ ADB ≅ Δ CBD by SAS rule

AB = BC by CPCT

According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.

Hence, according to the given conditions the triangle ABC is an isosceles triangle.

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Answers:

sin a=12/15=4/5

step by step explanation:

AB=9, and BC=12

find c: hyp.=√12²+9²=c²

c=15

sin a=opp/hyp.=12/15=4/5 ( convert to degrees)

a=41.10

Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

[tex]a^2+ b^2 = c^2[/tex]

[tex]5^2+ 9^2 = 13^2[/tex]

[tex]25+81=169[/tex]

[tex]106=109[/tex]

False statement.

The triangle is not a right triangle.

Answer:

26 × 26 × 10 × 10 × 10 = 676 , 000  possibilities

Step-by-step explanation:

There is nothing stating that the letters and numbers can't be repeated, so all  26  letters of the alphabet and all  10

digits can be used again.

If the first is A, we have  26  possibilities:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

If the first is B, we have  26  possibilities:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

And so on for every letter of the alphabet.  There are  26  choices for the  first letter and  26  choices for the second letter. The number of different combinations of  2  letters is: 26 × 26 = 676

The same applies for the three digits. There are  10  choices for the first,  10

for the second and  10  for the third:

10 × 10 × 10 = 1000  

So for a license plate which has  2  letters and  3  digits, there are:  26 × 26 ×  10 × 10 × 10 = 676 , 000  possibilities.

Hope this helps.

Answer:

Number of term N = 9

Value of Sum = 0.186

Step-by-step explanation:

From the given information:

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]

here;

m = 5

n = 9

r = 0.5

Then:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]

For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,

the responses are;

(1) The number of terms are 9

(2) The value of the sum is approximately 0.374

The given geometric series is presented as follows;

3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³

(1) The number of terms in the series = 13 - 4 = 9

Therefore;

(2) The value of the sum can be found as follows;

The common ratio, r = 0.5

The sum of the first n terms of a geometric progression is presented as follows;

[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]

The sum of the first 4 terms are therefore;

[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]

The sum of the first 13 terms is found as follows;

[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]

Which gives;

The sum of the 5th to the 13th term = S₁₃ - S₄

Therefore;

[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]

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Answer:

[tex]z = \frac{x}{y} [/tex]

Step-by-step explanation:

Let x be the price of carton of ice cream

Let y be the number of grams in carton

Let z be price per gram.

[tex]z = \frac{x}{y} [/tex]

Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.

Hope this helps ;) ❤❤❤

Answer:

A: True

B, C and D: False

Step-by-step explanation:

We have a total sales tax for Alabama that is:

[tex]T_A=4.225+1.375+3=8.6[/tex]

The total sales tax for Florida is:

[tex]T_F=6.5+1+1.625=9.125[/tex]

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

The sales tax difference in this purchase can be calculated as:

[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).

Answer:

Hey there!

A=1/2bh

14=1/2(28)h

14=14h

h=1

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

where b is the base

h is the height

From the question

Area = 14in²

b = 14 inches

So we have

[tex]14 = \frac{1}{2} \times 28 \times h[/tex]

which is

[tex]14 = 14h[/tex]

Divide both sides by 14

That's

[tex] \frac{14}{14} = \frac{14h}{14} [/tex]

We have the final answer as

h = 1

Therefore the height is 1 inch

Hope this helps you

The complete question is;

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer:

A) P (x < 10) = 0.6700

B) P (x > 5 ) = 0.9406

C) P (8.0000 < x < 15.0000) = 0.6332

Step-by-step explanation:

A) we are given;

Mean;μ = 8.9 minutes

Standard deviation;σ = 2.5 minutes

Normal random variable;x = 10

So to find;P(x < 10) we will use the Z-score formula;

z = (x - μ)/σ

z = (10 - 8.9)/2.5 = 0.44

From z-distribution table and Z-score calculator as attached, we have;

P (x < 10) = P (z < 0.44) = 0.6700

B) similarly;

z = (x - μ)/σ =

z = (5 - 8.9)/2.5

z = -1.56

From z-distribution table and Z-score calculator as attached, we have;

P (x > 5 ) = P (z > -1.56) = 0.9406

C)between 8 and 15 minutes

For 8 minutes;

z = (8 - 8.9)/2.5 = -0.36

For 15 minutes;

z = (15 - 8.9)/2.5 = 2.44

From z-distribution table and Z-score calculator as attached, we have;

P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332

A slope is also known as the gradient of a line is a number. The correct option is B.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The rate of change shown in the graph is the slope of the given line.

Now, to know the slope of the line consider any two points on the line, such as (0,0) and (5,400).

Therefore, the slope of the line can be written as,

Slope, m = ($400 - $0)/(5-0) hour

               = $400/5 hour

               = $80/hour

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Answer:

option: D

51200

Step-by-step explanation:

64000 x 80/100 = 51200

Answer:

Hi there!!!

your required answer is option D.

explanation see in picture.

I hope it will help you...

It's adding 3 and subtracting 2 every time.

This means the next two terms would be +3 and -2 since the last one was -2.

The next term = 4+3=7

The next next term = 7-2=5

Answer:

Please see the attached picture.

Hope it helps...

Best regards!!

Answer:

Step-by-step explanation:

Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answer:

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Step-by-step explanation:

To identify outliers the interquartile range of the dataset can be used

Outliers can be identified as data values that are

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Using the interquartile range concept, it is found that:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

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

[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]

Thus:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

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Answer: hundredths place

Step-by-step explanation:

Answer:

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Step-by-step explanation:

(i) probability with 16 success out of 24 = 16/24 = 2/3

(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3

Since the two experiments have the same probability, the observed probabilities are the same.

HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.

Using the binomial distribution,

(i)

p = 1/2

N = 24

x = 16 (number of successes)

P(16,24) = C(24,16) p^16* (1-p)^8

= 735471* (1/65536)*(1/256)

= 0.0438

(ii)

p = 1/2

N = 12

x = 8 (number of successes)

P(8,12) = C(12,8) p^8* (1-p)^4

= 495*1/256*1/16

= 0.1208

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Note: It would help to mention the topic you're on so answers will correspond to what is expected.  Here we cover probability and binomial distribution.

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.

Answer:

[tex]\boxed{y\leq 6}[/tex]

Step-by-step explanation:

[tex]y-8 \leq -2[/tex]

Adding 2 to both sides

[tex]y \leq -2+8[/tex]

[tex]y \leq 6[/tex]

Answer:

14 Quarters and 28 dimes

Step-by-step explanation: 14 quarters $3.50

28 dimes is $2.80 total is $6.30

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

You probably want the unsigned area, which means you don't compute the integral

[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]

but rather, the integral of the absolute value,

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]

[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]

Answer:

5 games

Step-by-step explanation:

To find how many games the team scored at least 70 points, we need to look at the 7 on the stem side. The 7 means 70, and we add the digits on the leaf side. For example, 7 | 2 is 72. The numbers on the leaf side are: 1, 1, 2, and 3.

There are no points for the 8 on the stem side, but on 90, there is one digit on the leaf side: 1. So, the points they scored over 70 are 71, 71, 72, 73, and 91, which equals to five games.

Answer:

[tex]\boxed{\mathrm{5 \ games}}[/tex]

Step-by-step explanation:

At least 70 points makes it 70 and more. It should be at least 70 and at most anything above then 70.

So, In 5 games, the team scored at least 70. (71,71,72,73 and 91)

Answer:

Correlation Coefficient

Step-by-step explanation:

Answer:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Step-by-step explanation:

For this problem we have the following function given:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

Have a good day! :)

Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

Answer:

The center is (1,4)

Step-by-step explanation:

The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.

Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:

[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]

So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:

[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]