Identify the range of the function.
A [-4,0]
B (-4,0)
C [-3,1]
D (-3,1)

Step-by-step explanation:

I assume the points D, E and C are also collinear (are on the same straight line).

that is something your teacher forgot to mention. but it is essential.

we have to remember :

1. the sum of all angles in a triangle is always 180°.

2. the sum of all angles around a single point on one side of a line is also always 180°.

3. the angles at the intersection point of 2 lines are the same on both sides of any of the intersecting lines, but they are left-right mirrored.

so,

angle A = 30°

angle DEB = 130°, so,

angle AED = 180 - DEB = 180 - 130 = 50°.

therefore, angle BEC = AED = 50°

therefore, angle D = 180 - 30 - 50 = 100°.

we know, angle B = 90° (AB is perpendicular to BC).

therefore,

angle C = 180 - 90 - 50 = 40°

Answer:

$2,000

Step-by-step explanation:

Amount invested in Fund A = 6000

Profit rate of return = 5%

Amount of profit = 6000 x 5% = 6000 x 0.05 = $300

Let amount invested in Fund B be $x

Profit amount = 0.01x

Total amount invested is 6000 + x

Total profit in $ = 300 + 0.01x

Total profit in percentage = Total Profit/Total investment x 100

= 4 %

So Total Profit/Total investment = 4/ 100 = 0.04

= (300 + 0.01x) / (6000 + x)  = 0.04

Multiply both sides by (6000 + x)

=> 300 + 0.01x = 0.04(6000 + x)

=> 300 + 0.01x = 240 + 0.04x

==> 300 - 240 = 0.04x - 0.01x

=> 60 = 0.03x

x = 60/0.03

x = $2,000

Amount invested in Fund B = $2,000

Step-by-step explanation:

Fund A

$6000 returned a 5% profit. that means it had at the end 105% of the original investment

the formally correct way

100% = 6000

1% = 100%/100 = 6000/100 = $60

5% = 1%×5 = 60×5 = $300

in short, if we knew what we are doing, we could have simply calculated 6000 × 0.05 = $300.

and by the way, 6000 × 1.05 = $6300. which is the current balance of the account (investment plus the returned profit). but we don't need this here. this is just FYI.

Fund B

x returned 1% profit.

Fund A + Fund B

6000 + x returned 4% profit.

so, we have

6000×0.05 + x×0.01 = (6000 + x)×0.04

300 + 0.01x = 240 + 0.04x

60 + 0.01x = 0.04x

60 = 0.03x

x = 60/0.03 = $2000

so, he invested $2000 into fund B.

Answer:

x = ± 3

Step-by-step explanation:

given y varies as [tex]\frac{1}{x^2}[/tex] , then

y = k × [tex]\frac{1}{x^2}[/tex] = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k use the condition x = 2 , y = 1

1 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

4 = k

y = [tex]\frac{4}{x^2}[/tex] ← equation of variation

when y = [tex]\frac{4}{9}[/tex] , then

[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x^2}[/tex] ( cross- multiply )

4x² = 36 ( divide both sides by 4 )

x² = 9 ( take square root of both sides )

x = ± [tex]\sqrt{9}[/tex] = ± 3

Answer:

[tex]X=\frac{-z}{m-y}[/tex]

Step-by-step explanation:

Answer:

x= -6

Step-by-step explanation:

1

Distribute

2

Distribute

3

Distribute

4

Multiply by 1

5

Combine like terms

6

Subtract the numbers

7

Move terms to the left side

8

Distribute

9

Add the numbers

10

Combine like terms

11

Multiply by 1

12

Combine like terms

13

Use the quadratic formula

14

Evaluate the exponent

15

Multiply the numbers

16

Subtract the numbers

17

Evaluate the square root

18

Add zero

19

Multiply the numbers

20

Cancel terms that are in both the numerator and denominator

The total distance Steve jogged is 5 miles.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Given:

Steve completed 60% of the Jog.

Also, he travelled 3 miles.

Let the total distance he travelled be x miles.

Then,

60% of x =3

60/100 x= 3

x= 3 x 100 / 60

x= 300/60

x= 5 miles.

Hence, total he had to jog 5 miles.

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Answer:

f g(x) = 12x^2 - 16x +5

Step-by-step explanation:

f(x) = 3x^2 + 2x

g(x) = -2x + 1

f g(x)

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

f g(x) = 3(-2x + 1)^2 + -4x + 2

f g(x) = 12x^2 - 12x +3 + -4x + 2

f g(x) = 12x^2 - 16x +5

Answer: [tex]x=5\sqrt{3}, y=15[/tex]

Step-by-step explanation:

[tex]\sin 60^{\circ}=\frac{x}{10}\\\\x=10 \sin 60^{\circ}\\\\x=5\sqrt{3}\\\\\\\tan 30^{\circ}=\frac{5\sqrt{3}}{y}\\\\\sqrt{3}=\frac{y}{5\sqrt{3}}\\\\y=15[/tex]

Answer:

9

Step-by-step explanation:

t < 13 - 4

t < 9

again as far as it goes

Answer:

The answer is 75 degrees

Step-by-step explanation:

Remember that the sum of the three angles of any triangle is 180 degrees.

So, 180=58+47+x

180=105+x

75=x

The answer is not 1 so it is not that simple that you can divide it into 2 equal size subsets and ask whether the final sequence is in there. From what I got through his hints, it should be related to Central Limit theorem.

Given that,

One hundred coins are flipped, but the outcome is kept a secret. I am able to pose one yes/no query. I'll begin speculating on the outcomes of the coin toss following the response. I receive $1 for each accurate guess, and I lose $1 for each unreliable guess.

To find:

What is the most effective gaming approach and what is the highest possible return on investment

By Central Limit Theorem,

It is not straightforward to divide the response into two subsets of equal size and then check to see if the final sequence is present because the answer is not 1. His indications led me to believe that it should be connected to the Central Limit theorem.

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The fraction of oranges eaten by the family is 3/5

Given,

Number of oranges in a bag = 8 oranges

Number of bags sold to a family = 10 bags

Number of members in the family = 6 members

Number oranges ate by each member of the family = 6 oranges

We have to find the fraction of the oranges eaten by the family members;

Here,

8 oranges in 1 bag and 10 bags sold.

So, total number of oranges sold = 8 x 10 = 80 oranges

Each member ate 6 oranges and there are 8 members.

So, total number of oranges eaten by them = 6 x 8 = 48 oranges

Now,

The fraction of oranges eaten by the family = 48/80 = 6/10 = 3/5

That is,

3/5th of oranges were eaten by the family.

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The person that has the higher average speed is Teresa.

The average speed is the total distance travelled by the object in a particular time interval.

Average speed measures the average rate of speed over the extent of a trip.

Therefore,

average speed = distance / time

Hence, Karl drove 40 miles in 50 minutes.

Therefore,

average speed of Karl = 40 / 50

average speed of Karl = 4 / 5 miles per minute

Teresa drove 35 miles in 42 minutes.

Therefore,

average speed of Teresa = 35 / 42

average speed of Teresa  = 5 / 6 miles per minutes

Therefore, Teresa had the higher average speed.

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La ganancia aproximada del estadio por concepto de la venta de boletos para un partido de fútbol es $ 502,968.

En esta pregunta se nos solicita determinar la ganancia aproximada por la venta de boletos para un partido de fútbol en un estadio. La ganancia aproximada es igual al producto del aforo del estadio y el costo de cada boleto. Entonces,

c = ($ 19) · (26,472)

c = $ 502,968

La ganancia aproximada por el partido de fútbol es $ 502,968.

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The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

Given,

We have to expand the given polynomials and simplify them.

1. The polynomial: (a² - 3a)²

Here,

The polynomial is in the form of (a - b)²

So,

(a - b)² = a² - 2ab + b²

Then,

(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²

(a² - 3a)² = a⁴ - 6a³ + 9a²

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.

a = 1, b = -6 and c = 9

[tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex] = [tex]\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}[/tex] = [tex]\frac{6(+-)\sqrt{36 - 36} }{2}[/tex] = [tex]\frac{6(+-)\sqrt{0} }{2}[/tex] = (6±0) / 2

= 6/2 = 3

Then,

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) = 3

So,

(a² - 3a)² = 3a²

2. The polynomial: (1/2x³ + 6x)²

Here, the polynomial is in the form (a + b)²

(a + b)² = a² + 2ab + b²

Here,

(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²

(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

a = 1/4, b = 6 and c = 36

Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex]

= [tex]\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}[/tex] = [tex]\frac{-6(+-)\sqrt{36-36} }{1/2}[/tex] = (-6±0) / (1/2) = -6 × 2 = -12

Therefore,

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

Here,

(1/4x⁴ + 6x² + 36) = -12

Then,

(1/2x³ + 6x)² = -12x²

That is,

The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

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Least number (sample size) of viewers that should be randomly selected to ensure that a 95% confidence interval for the true proportion of viewers will have a width of 0.06 or less is 225.

E = 0.06,

P = 0.30

c= 95%

& = 1 - 0. 95

To x/2 = 0-025

21096*/ 2 = 0-025

Margin of error

P ( 1 - P )

To ac / 2 ) 2 P ( 1 - P )

E= ( 1. 96* 0 . 30 x ( 1 - 0 - 30 )0-06

=224.09 ~ 225

round to next number

225

In order to guarantee that a 95% confidence interval for the true proportion of viewers would have a width of 0.06 or less, the minimum number of viewers (sample size) that should be chosen at random is 225.

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Answer:

a. 5.6

b. 38.4

c. 8.25

d. 24

Step-by-step explanation:

Explanation

By observation, we can see that the transformation from the original to the image, is a rotation of 90 degrees counterclockwise about the origin.

Answer: Option D

P(A) = P(6) = 0.003

answer: 0.003

You can see the three points where the result is equal to an integer in the photo below. Good luck!

Answer: Richard is 29 and Teo is 9.

Step-by-step explanation: Use Substitution

The constant of proportionality between x and y in the given graph above is determined as: 2.

The constant of proportionality of a proportional relationship between two variables, x and y, can be defined as the ratio of y to x, which is expressed as, k = y/x, where x and y are the coordinates of one point one the line that represents the proportional relationship.

Using the coordinates of a point on the graph, (2, 4), find the constant of proportionality, k:

Constant of proportionality (k) = y/x = 4/2

Constant of proportionality (k) = 2

Therefore, the constant of proportionality that represents the proportional relationship between the variables, x and y, is calculated as, 2.

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Answer:

Step-by-step explanation:

triangle area formula: A = 1/2 × b × h

7 +3 = 10 ft

1/2 10 × 4 =

5 × 4 =

20 feet²

If the remaining balance for 48 months with an APR of 4.5%. the monthly payment that Jenna pays is: $595.17.

Using this formula to determine the monthly payment

P = A ×r × ( 1 +r)^n  ÷( 1+ r)^n -1

Where:

P = Principal = ?

A = Amount = $29,000 × ( 1- .10) = 26,100

r = Interest rate = 4.5% / 12 = 0.00375

n = number of months = 48 months

Let plug in the formula

P = 26,100 × 0.00375 × ( 1+ 0.00375)^ 48 ÷ ( 1+ 0.00375)^ 48 -1

P = 26,100 × 0.00375 × ( 1.00375)^ 48 ÷ ( 1.00375)^ 48 -1

P = 26,100 × 0.00375 × 1.196814377  ÷  1.196814377 -1

P = 26,100 × 0.00375 × 1.196814377  ÷  0.196814377

P = $117.1382456  ÷  0.196814377

P = $595.17

Therefore $595.17 is the monthly payment.

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The angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.

The table shows the votes of 900 people in the last elections.

Political Party    Frequency     Angle in

Labour                    345

Conservative          480

Lib Democrat           60

Other                        15

345 + 480 + 60 + 15 = 900

The total angle in a pie chart is 360

The angle for labour is = 360 (345 / 900) = 138 degree

The angle for Conservative is = 360 (480 / 900) = 192 degree

The angle for Lib democrate is = 360 (60 / 900) = 24 degree

The angle for others is = 360 (15 / 900) = 6 degree

Therefore, the angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.

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Answer:

Since you do not have any answer choices, I will step-by-step solve the equation for you. Typically what happens with problems like this is the answer choices will match the work when solving. So, pay attention to my scratch-work and if any answers match the answer choices, then that is most likely the correct answer. (Hint: the solution to the equation is most likely the correct answer)

Write the equation:

(2x^2 + 4x – 7)(x – 3)

Simplify and Distribute:

(2x^2 + 4x – 7)(x – 3)

2(x – 3)^2 + 4x(x – 3) – 7(x – 3)

2x^3 – 6x^2 + 4x

(x – 3) – 7(x – 3)

2x^3 – 6x^2 + 4

x^2 – 12x – 7(x – 3)

2x^3 – 6x^2 + 4

x^2 – 12x – 7x + 21

Combine Like Terms:

2x^3 – 2x^2 – 12x – 7x + 21

2x^3 – 2x^2 – 19x + 21

Solution:

2x^3 – 2x^2 – 19x + 21

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The slope of the line is given as -2/3.

We are also given the point (1, 1) in which this line passes through.

Before we can plot the graph of the line, we need to know the equation of the line first.

The values given are more than enough to find the equation of the line.

The formula used to get the equation of the line is given below:

Now, with this formula, let us find the equation of the line.

Thus, the equation of the line is:

Now, using a graph calculator, let us plot this equation.

After doing this, the following is the result:

Answer:

Step-by-step explanation:

$17.64 for 147 text messages

Therefore 1 text message will cost $17.64 ÷ 147 Text messages = $0.12 per text message

The weight of the largest piece of pie is 250 gram.

Let the weights of others be illustrated as x.

Therefore, the weight of the largest weight is the addition of the others weight. This will be:

= x + x + x = 3x

Therefore, the weights will be:

3x + x + x + x = 500

6x = 500.

Divide

x = 500 / 6

x = 83.33.

The larger weight will be:

= 3x

= 3 × 83.33

= 250

The pie weights 250g.

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The table shows different flood types and their frequencies.

Total frequency of all flood types = 18 + 6 + 4 + 2 = 30

frequency of river flood = 6

Recall, probability is expressed as

number of favorable outcomes/number of total outcomes

Thus, the estimated probability that a flood in 2021 in that state will be a river flood is

6/30 = 0.2

By changing 0.2 to percentage, we have

0.2 x 100 = 20%

The correct option is C. 20%