Given the function f(x) = -2x2 + 4x - 7, find f(-4).
-55
-7
25

Answer:

[tex]\sum ^{20} _{n \to \11} 4n[/tex]

Step-by-step explanation:

In order to write the series using the summation notation, first we need to find the nth term of the sequence formed. The sequence generated by the series is an arithmetic sequence as shown;

4, 8, 12, 16, 20...80

The nth term of an arithmetic sequence is expressed as Tn = a +(n-1)d

a is the first term = 4

d is the common difference = 21-8 = 8-4 = 4

n is the number of terms

On substituting, Tn = 4+(n-1)4

Tn = 4+4n-4

Tn = 4n

The nth term of the series is 4n.

Since the last term is 80, L = 4n

80 = 4n

n = 80/4

n = 20

This shows that the total number of terms in the sequence is 20

According to the series given 4 + 8 + 12 + 16 + 20+ . . . + 80 , we are to take the sum of the first 20terms of the sequence. Using summation notation;

4 + 8 + 12 + 16 + 20+ . . . + 80  = [tex]\sum ^{20} _{n \to \11} 4n[/tex]

The series 4 + 8 + 12 + 16 + 20 + ... + 80 can be expressed in summation notation as Σ[4 + (i - 1) × 4] for i = 1 to 20.

To write the series 4 + 8 + 12 + 16 + 20 + ... + 80 using summation notation, we first identify that it is an arithmetic series. An arithmetic series is a sequence of numbers in which the difference between consecutive terms is constant.

The given series: 4, 8, 12, 16, 20, ..., 80

We can observe that the common difference (d) is 4, and the first term (a) is 4. The nth term of an arithmetic series can be given by:

a + (n-1)d

Here, the nth term is 80. Setting up the equation for the nth term:

4 + (n-1)4 = 80

Simplifying this equation:

4 + 4n - 4 = 804n = 80n = 20

Thus, the series has 20 terms. We can write the series in summation notation as follows:

Σ[4 + (i - 1) × 4] for i = 1 to 20

To find the sum of this arithmetic series, we use the formula for the sum of an arithmetic series:

Sum = n/2 × (first term + last term)

Here, first term (a1) = 4, last term (an) = 80, and n = 20. So,

Sum = 20/2 × (4 + 80) = 10 × 84 = 840

Therefore, the summation notation for the series is Σ[4 + (i - 1) × 4] for i = 1 to 20, and its sum is 840.

Answer:

here are some notes to help

Recruitment has the GREATEST impact on raising labor productivity Because it is talking about labor productivity specifically. thus option D is correct.

Productivity is a measure of the amount of output produced by a given amount of inputs in a specific period of time.

Average Product of labor - It is the total output that a firm produces divided by the amount of workers required to produce that output.

Marginal Product of Labor - It is the additional output produced by a firm because of hiring extra workers .

Recruitment has the GREATEST impact on raising labor productivity Because it is talking about labor productivity specifically.

Hence, the option D is correct.

Learn more about the Productivity here;

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Answer:

The answer is B

Step-by-step explanation:

I have study Island too and the answer C is wrong

Final answer:

The survey conducted only among male customers at a music store is not valid because it's not representative of the entire customer base, thereby introducing a selection bias.

Explanation:

The question asks whether the results of a music preference survey conducted only among male customers at a music store are valid. Answer choice B, No, because the music store did not survey a sample that is representative of the population, is correct.

A valid survey must aim to avoid selection bias by ensuring that its sample represents the entire population it intends to make statements about.

Surveying only male customers introduces a bias, as it excludes female customers, making the sample not representative of all music store customers. This compromises the survey's ability to accurately reflect the preferences of the entire customer base.

Answer:

P = 16 inches

Step-by-step explanation:

The perimeter is given by

P = 2(l+w)

  = 2(2in+6in)

   = 2 ( 8in)

   = 16 in

Answer:

solution:  (3, 5)

Step-by-step explanation:

Solve this system of equations

{2x + y = 11

{5x - y = 10​

add the equations to use elimination method.

2x + 5x + y - y = 11 + 10;

7x = 21

x = 21/7 = 3

x = 3

y = 11 - 2x = 11 - 2*3 = 11 - 6 = 5

Answer:

C : 228 in³

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

The third side is called the hypotenuse, lets call that the x side.

So we are finding x.

The two other sides add up to the hypotenuse, x.

35 + 12 = 47

Answer:

Step-by-step explanation:

The result can be shown in multiple forms.

Exact Form:

√

6

−

√

2

4

Decimal Form:

0.25881904

…

Answer:

1st picture:

1st case: two triangles are similar (AAA), not congruent

2nd case: two triangles are congruent (SAS)

2nd picture:

both cases satisfy: two triangles are congruent (ASA)

3rd picture:

1st case: two triangles are congruent (SAS)

2nd case: neither congruent or similar

Hope this helps!

:)

We have been given that the population of a town was 500 in 2010. The population grows at a rate of 9.6% annually.

We will use exponential growth formula to solve our given problem.

[tex]y=a\cdot (1+r)^x[/tex], where,

y = Final amount,

a = Initial value,

r = Growth rate in decimal form,

x = Time.

Let us convert 9.6% into decimal as:

[tex]9.6\%=\frac{9.6}{100}=0.096[/tex]    

We can see that initial value is 500.

[tex]y=500\cdot (1+0.096)^x[/tex]

[tex]y=500\cdot (1.096)^x[/tex]

Therefore, the equation [tex]P(t)=500\cdot (1.096)^t[/tex] represents the population t years after 2010.

To find the population of the town in 2020, we will substitute [tex]t=10[/tex] in our equation as:

[tex]P(10)=500\cdot (1.096)^{10}[/tex]

[tex]P(10)=500\cdot (2.5009530650806592)[/tex]

[tex]P(10)=1250.4765325403296\approx 1250[/tex]

Therefore, the population of the town would be approximately 1250 in 2020.

Answer:

(16  x  −  4  ,  x²  +  5x)  +  6

if we simplify it

but i don't know what your asking exactly..

Answer:

3 and 1/4

Step-by-step explanation:

Answer:

[tex]\sqrt136[/tex] (option D)

Answer:

1 - D

2- B

Simple just use a calculator

Answer:

1. B

2. B

Step-by-step explanation:

you add all of the money first

32.50

it says 18%

so you multiply 32.50 times 18%

PEMDAS

parenthesis

exponents

multiply or divide left to right

add or subtract left to right

5 times 69 - 9

336

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0

y-intercept: 1.5

Answer:

C. x = 6

Step-by-step explanation:

You are solving for x. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First subtract 4 from both sides:

2x + 4 (-4) = 16 (-4)

2x = 16 - 4

2x = 12

Next, isolate the variable, x. Divide 2 from both sides:

(2x)/2 = (12)/2

x = 12/2

x = 6

C. x = 6 is your answer.

~

Answer:

Step-by-step explanation:

The system of equation to be graphed is the following :

f(x) = Log_0.5 x

f(x) = Log_{3} (2 + x)

And the solution is the intersection point of the two graphs.

Check attachment for point of intersection.

Answer:

y1 = (Log x)/(Log 0.5)

y2 = [(Log 2)/(Log 3)] + x

Option D

Step-by-step explanation:

We are given;

Log_0.5_x = (Log_3_2) + x

To solve the equation graphically, we have to plot the graphs of these two functions and find the point of intersection of these graphs.

Using: log_a b = log b / log a

1) a = x, b=0.5

So, y1 = log0.5 x

Which gives; y1= (log x)/(log0.5)

2) a=2, b=3

So, y2 = (log_3 2) + x

So, y2 = (log 2 / log 3) +x

Hence, appropriate system is;

y1 = (Log x)/(Log 0.5)

And y2 = [(Log 2)/(Log 3)] + x

Looking at the options in the image attached, the correct solution that corresponds to our answer is Option D

Answer:

120

Step-by-step explanation:

Each square=x

6g-10g=4g       10g-12g=2g      12-14g=2g

15g-14g=1g       16g-15g=1g       20g-16g=4g

(4x3)+(2x8)+(2x11)+(1x23)+(1x19)+(4x20

12+16+22+23+19+8=1000

x=1000

1000÷100=10

1 box = 10

4×30=120

(I got this answer through help of others, it is not truly mine)

To find the number of mice with birth weights below 10 grams on a histogram, multiply the frequency by the given class width for that weight range and sum frequencies if multiple bars are relevant.

The student is asking how to work out the number of mice with birth weights below 10 grams, based on a given histogram. Since the histogram is not displayed here, I will explain the general process for determining the number of mice under a certain weight category using a histogram. First, find the bar that represents the birth weights below 10 grams. The height of this bar corresponds to the frequency density for this class interval. If the class width (the range of values within the category) is 1 gram, then the frequency (number of mice) in this bar can be found by multiplying the frequency density by 1 gram. If the histogram does not provide frequency directly and instead gives frequency density, you must also know the class width to calculate the number of mice. Multiply the frequency density by the class width to find the frequency. If multiple bars (class intervals) cover birth weights below 10 grams, sum the frequencies of all relevant bars to calculate the total number of mice with weights below 10 grams.

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Answer:

6.5 cm

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

26 = 1/2 (8) *h

26 = 4h

Divide each side by 4

26/4 = 4h/4

6.5 = h

Answer:

6.5 cm

Step-by-step explanation:

Area = ½ × base × height

26 = ½ × 8 × height

26 = 4height

height = 6.5 cm

Answer:

A: rolling a two and the coin landing on tails

Step-by-step explanation:

bc I got it right on edg 2020

Experimental probability: 3/10

The correct answer is rolling a two and the coin landing on the tails

A 3-column table with 10 rows.

Column 1 is labeled Trial with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Column 2 is labeled Outcome with entries H T, T T, H T, H H, H T, H T, T T, H T, T T, H H.

Column 3 is labeled Result with entries Fail, pass, fail, fail, fail, fail, pass, fail, pass, fail.

A pop quiz has 2 True/False questions. Paris used a 10-trial coin flip to simulate the results of guessing on the quiz. If T represents answering a question correctly, what is the experimental probability of correctly answering both questions by guessing?

Frequency of observed desired outcome: 3

Number of trials: 10

Experimental probability: 3/10

Therefore, the correct answer is

rolling a two and the coin landing on tails

To learn more about probability

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Answer:

1244 students

2064 students

hope it helped

Step-by-step explanation:

Thanks

you were right

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Step-by-step explanation:

Answer:

The area is [tex]78.54units^2[/tex]

The area would be 78.5[tex]units^2[/tex] (pi=3.14)

Step-by-step explanation:

The formula for the area of a circle is : [tex]\pi *radius^2[/tex]

To work the area of this quadrant you would first need to work out the area of the circle. You can do this by multiplying pi by the radius of 10 squared, this gives you 314.16.

The next step is to work out how much of the circle we need to work out the area for. As this is a right angle (90°) we know that this is [tex]\frac{1}{4}[/tex] of a circle. This is because the total of a circle is 360, and that by dividing 360 by 90, this gives you 4. This tells that this is a quarter of a circle.

The final step would be to divide the area of 314.16 by 4, this gives you 78.54. This is because we are using the area to work out the area of just one quadrant.

1) Multiply pi by 10 squared.

[tex]\pi*10^2=314.16^2[/tex]

2) Divide 360 by 90.

[tex]360/90=4[/tex]

3) Divide 314.16 by 4.

[tex]314.16/4=78.54^2[/tex]

Pi=3.14:

To work the area of this quadrant you would first need to work out the area of the circle. You can do this by multiplying pi by the radius of 10 squared, this gives you 314.

The next step is to work out how much of the circle we need to work out the area for. As this is a right angle (90°) we know that this is [tex]\frac{1}{4}[/tex] of a circle. This is because the total of a circle is 360, and that by dividing 360 by 90, this gives you 4. This tells that this is a quarter of a circle.

The final step would be to divide the area of 314. by 4, this gives you 78.5. This is because we are using the area to work out the area of just one quadrant.

1) Multiply pi by 10 squared.

[tex]\pi*10^2=314^2[/tex]

2) Divide 360 by 90.

[tex]360/90=4[/tex]

3) Divide 314.16 by 4.

[tex]314/4=78.5^2[/tex]

Answer:

A.   2,552,129 m^3.

Step-by-step explanation:

Volume of a pyramid = 1/3 * height * area of the square base

=  1/3 * 146 * 229^2

= 2552129 m^3.

We have been given two points. [tex]A(3,4)[/tex] and [tex]C(3,9)[/tex]. We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.

We will use segment formula to solve our given problem.

When a point P divides segment any segment internally in the ratio [tex]m:n[/tex], then coordinates of point P are:

[tex][\right x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}\left][/tex]

[tex](x_1,y_1)=(3,4)[/tex] and [tex](x_2,y_2)=(3,9)[/tex].

[tex]m=4,n=1[/tex]

Upon substituting our given information in above formula, we will get:

[tex][\right x=\frac{4(3)+1(3)}{4+1},y=\frac{4(9)+1(4)}{4+1}\left][/tex]

[tex][\right x=\frac{12+3}{5},y=\frac{36+4}{5}\left][/tex]

[tex][\right x=\frac{15}{5},y=\frac{40}{5}\left][/tex]

[tex][\right x=3,y=8\left][/tex]

Therefore, the coordinates of point B would be [tex](3,8)[/tex].

Answer:

9 - 24y

Step-by-step explanation:

12 ( 3/4 - 2y)

Distribute

12 * 3/4 - 12 * 2y

36/4 -24y

Simplfiy

9 - 24y

Step-by-step explanation:

The product of the original numbers: xy

The product of the altered numbers (.75x)(.5y), or 0.375xy

The product has decreased by 1 - 0.375, or 0.625, or 62.5%

Answer:

Original product:

P1 = a x b

Decreased product:

P2 = a x (100 - 20)/100 x b x (100 - 60)

    = a x b x 80/100 x 40/100

    = a x b x 8/25

=> P1/P2 = 8/25

or

P1 is decreased by: 1 - 8/25 = 17/25 = 68%

Hope this helps!

:)