Complete the following questions on the picture

Answer:

absolute minimum = -749 and

absolute maximum = 467

Step-by-step explanation:

To get the absolute maximum and minimum of the function, the following steps must be followed.

First, we need to find the values of the function at the given interval [-4, 5].

Given the function f(x) = 6x³ − 9x² − 216x + 3

at x = -4;

f(-4) = 6(-4)³ − 9(-4)² − 216(-4) + 3

f(-4) = 6(-64) - 9(16)+864+3

f(-4) = -256- 144+864+3

f(-4) = 467

at x = 5;

f(5) = 6(5)³ − 9(5)² − 216(5) + 3

f(5) = 6(125) - 9(25)-1080+3

f(5) = 750- 225-1080+3

f(5) = -552

Then we will get the values of the function at the crirical points.

The critical points are the value of x when df/dx = 0

df/dx = 18x²-18x-216 = 0

18x²-18x-216 = 0

Dividing through by 18 will give;

x²-x-12 = 0

On factorizing the resulting quadratic equation;

(x²-4x)+(3x-12) = 0

x(x-4)+3(x-4) = 0

(x+3)(x-4) = 0

x+3 = 0 and x-4 = 0

x = -3 and x = 4 (critical points)

at x  = -3;

f(-3) = 6(-3)³ − 9(-3)² − 216(-3) + 3

f(-3) = 6(-27) - 9(9)+648+3

f(-3) = -162-81+648+3

f(-3) = 408

at x = 4

f(4) = 6(4)³ − 9(4)² − 216(4) + 3

f(4) = 6(64) - 9(16)-864+3

f(4) = 256- 144-864+3

f(4) = -749

Based on the values gotten, it can be seen that the absolute minimum and maximum are -749 and 467 respectively

for labor. Joni paid $85 less per hour for labor. explanation:

The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.

It refers to the total amount of the expenditure done on a product in manufacturing or procuring.

It refers to the expenditure done on procuring labor for the work.

In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,

labor cost Shannon Paid=339.50-112

=$227.50

labor cost per hour=227.50/3.5

=$6.5 per hour

Joni paid total $455 in which the cost of spare parts is $310 and rest is labor

labor cost paid by Joni=455-310

=$145

labor cost per hour=145/2.5

=$58 per hour

So by doing comparing we found that Shannon had paid $6 per hour extra for labor.

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Answer:

The probability is  [tex]P(X > x) = 0.0013499[/tex]

Step-by-step explanation:

From the question we are told that

     The mean is  [tex]\mu = 25[/tex]

      The standard deviation is [tex]\sigma = 5 \ minutes[/tex]

      The random number  [tex]x = 40[/tex]

Given that the time taken is  normally distributed  the probability is mathematically represented as

     [tex]P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ][/tex]

Generally the z-score for the normally distributed data set is mathematically represented as

        [tex]z = \frac{X - \mu}{\sigma }[/tex]

So  

     [tex]P(X > x) = P[Z > \frac{40 -25}{5 } ][/tex]

    [tex]P(X > x) = 0.0013499[/tex]

This value is obtained from the z-table

Answer:

A) 0.99413

B) 0.00022

Step-by-step explanation:

A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:

Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes

Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:

μ = n*μ_s ample = 42 × 5 = 210 minutes

While the standard deviation for the population would be:

σ = √nσ_sample = √(42 × 6) = 15.8745 minutes

To find the z-score, we will use the formula;

z = (x - μ)/σ

Thus;

z = (250 - 210)/15.8745

z = 2.52

From the z-distribution table attached, we have;

P(Z < 2.52) ≈ 0.99413

B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.

Thus, total time is now 250 + 10 = 260 minutes

Similar to the z-formula in A above, we have;

z = (260 - 210)/15.8745

z = 3.15

P(Z > 3.15) = 0.00022

Answer:

Your answer is B

Step-by-step explanation:

rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'

​Answer:

14.29cm

Step-by-step explanation:

Height of the building=10cm

Angle of depression=60°

We are therefore asked to find the distance from the stone to the

the foot of the building;Therefore we use Tan ratio which is opp/adj;

Let the distance from the stone to the foot of the building be x;

10/x=Tan60°

10/x=1.7/1

We then cross multiply to get 1.7x=10

x=10/1.7

=10*10/1.7*10

=100/17

=14.29cm.

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------             The frequency is ~7.5*1014 Hz

Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.

Step-by-step explanation:

Speed = wavelength × frequency

3×10⁸ m/s = (400×10⁻⁹ m) f

f = 7.5×10¹⁴

Answer:

0.76 or 19/25

Step-by-step explanation:

Convert 4/10 so that it has a common denominator with 36/100.

4/10 x 10/10 = 40/100

Now that the denominator is the same, just add the top values.

40/100 + 36/100 = 76/100

We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.

Answer:

Step-by-step explanation:

[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]

[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]

[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]

Answer:

The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.

Step-by-step explanation:

Convert to a mixed number:

209/8

Divide 209 by 8:

8 | 2 | 0 | 9

8 goes into 20 at most 2 times:

| | 2 | |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

8 goes into 49 at most 6 times:

| | 2 | 6 |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 |  

Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:

| | 2 | 6 | (quotient)

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 | (remainder)

The quotient of 209/8 is 26 with remainder 1, so:

Answer: 26 1/8° C

Step-by-step explanation:

(ax + b)² = a²x² + 2abx + b²

In this case, a = 1, so:

14 = 2b

b = 7

(x + 7)² = x² + 14x + 49

Answer:

30 years

Step-by-step explanation:

let the age of Ezekiel be x years

Given

Lily is 14 years older than her little brother Ezekiel

Age of Lily = x + 14 years

Next condition

after 8 years\

age of Ezekiel = x+8

age of Lily = x + 8 +14 = x + 22 years

Given

. In 8 years, Lily will be twice as old as Ezekiel will be then.

Thus,

x + 22 = 2(x+8)

=> x + 22 = 2x + 16

=> 22-16 = 2x -x

=> x = 6

Thus, age of  Ezekiel = 8 years

age of lily = 8+14 = 22 years

sum of their age = 22 + 8 = 30 years      answer.

Answer:

hope this is right y=74

Step-by-step explanation:

have not done this since two years ago so...

but anyway 148-180 = 32

32 is that angle

if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.

The correct answer is 90.

Answer:

The  confidence interval is  [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]

Step-by-step explanation:

From the question we are told that

    The first sample size is  [tex]n_1 = 146[/tex]

    The second sample size is [tex]n_2 = 180[/tex]

    The first sample mean is [tex]\= x_1 = 51.6[/tex]

    The second  sample  mean is  [tex]\= x_2 = 62.7[/tex]

     The first standard deviation is  [tex]\sigma _1 = 9.42[/tex]

     The second standard deviation is  [tex]\sigma _2 = 14.5[/tex]

Given that the confidence level is  98% then the significance level is mathematically evaluated as

      [tex]\alpha = (100 -98 )\%[/tex]

       [tex]\alpha = 2 \%[/tex]

        [tex]\alpha = 0.02[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is  [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]

The reason we are obtaining critical value of  

 [tex]\frac{\alpha }{2}[/tex]

instead of  

[tex]\alpha[/tex]

is because  

 [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (

[tex]1-\alpha[/tex]

) did not cover which include both the left and right tail while  

 [tex]\frac{\alpha }{2}[/tex]

is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

      [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }[/tex]

substituting values

      [tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]

substituting values

     [tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]

     [tex]E = 0.2405[/tex]

The 98% confidence interval is mathematically represented as

      [tex](\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E[/tex]

substituting values

      [tex](51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405[/tex]

     [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]

Answer:

x = 43

Step-by-step explanation:

125^(3x+7)=25^(5x−11)

Rewriting the bases as powers of 5

125 = 5^3  and 25 = 5^2

5^3 ^ (3x+7) = 5^2^(5x-11)

We know a^b^c = a^ (b*c)

5^(3 * (3x+7)) = 5^(2*(5x-11))

Distribute

5^(9x+21) = 5^(10x-22)

The bases are the same so the exponents are the same

9x+21 = 10x-22

Subtract 9x from each side

9x+21 -9x = 10x-9x-22

21 = x-22

Add 22 to each side

21+22 = x-22+22

43 = x

Answer:  B.  

Four students won 12, 13, 14, 15, 16, or 17 prizes

Answer:

Four students won 12, 13, 14, 15, 16, or 17 prizes!

Step-by-step explanation:

Answer:

C. It is an angle that has its vertex at the center of a circle.

Step-by-step explanation:

That's the definition.

A. is wrong. An angle with a measure greater than 180° is an obtuse angle,

B. is wrong. An angle that has its vertex on the circle is an inscribed angle.

D. is wrong. Part of the circumference of a circle is an arc.

Answer: 1/4≤x

Step-by-step explanation:

-5/(2x-3)≤2

Multiply by (2x-3)

-5≤4x-6

Add 6

1≤4x

1/4≤x

Hope it helps <3

Answer:

[tex]x \geq 1/4[/tex]

Step-by-step explanation:

=> [tex]\frac{-5}{2x-3} \leq 2[/tex]

Multiplying both sides by (2x-3)

=> [tex]-5 \leq 2(2x-3)[/tex]

=> [tex]-5 \leq 4x-6[/tex]

Adding 6 to both sides

=> [tex]-5+6 \leq 4x[/tex]

=> [tex]4x\geq 1[/tex]

Dividing both sides by 4

=> [tex]x \geq 1/4[/tex]

Hey there! :)

Answer:

m = 4.

Step-by-step explanation:

We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)

Where 'm' is the slope and 'b' is the y-intercept. Therefore:

y = -5 + 4x becomes y = 4x - 5

The 'm' value is equivalent to 4, so the slope of the equation is 4.

Answer:

4

Step-by-step explanation:

because of y= mx + b where m is the slope

m= 4 in the equation

Answer:

I think D

Step-by-step explanation:

Verticle or horizontal line test, it would be a function either way

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           Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

The statement for [tex]6x - 3 = 9[/tex] is :

[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

A

Step-by-step explanation:

Answer:

when we add all the angles.

=58+94+15=167

so it's a 180..

180_167

=13

round to nearest tenth.

=10..

Answer:

answer there

Step-by-step explanation:

hope it. was. helpful

Answer:

Hey there!

The line can be expressed into y intercept form, y=3x+1.

Thus, in y=mx+b form, m is the slope, and we see that 3 is the slope of the line.

Let me know if this helps :)

Answer:

The volume of sphere is 267.95 units³.

Step-by-step explanation:

Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :

[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]

[tex]let \: r = 4[/tex]

[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times 64[/tex]

[tex]v = \frac{256}{3} \times 3.14[/tex]

[tex]v = 267.95 \: {units}^{ 3} [/tex]

Answer:

You need to use the AAS (angle angle side) congruency theorem

Step-by-step explanation:

youre welcome!!!

Answer:

The Angle-Angle-Side Postulate (AAS)

Step-by-step explanation:

It is given that angle 1 and 2 are equivalent so that is angle #1

It is given that angle 3 and 4 are also equivalent so that is angle #2

And finally, it is given that side TS and side TR are equivalent giving you that last side you need to prove the type of Postulate it is

If this helped, please consider giving me brainliest, it will help me a lot

Have a good day! :)

Answer:

a(n)= a(n+1)+4

Step-by-step explanation:

The first terms of this sequence are: 4,0, -4, -8, -12

Let 4 be a0 and 0 a1.

● a1-a0 = 0-4

●a1-a0 = -4

●a1 = -4+a0

So this relation links the first term with the second one.

replace 1 in a1 with n.

0 in a0 will be n-1

● an = -4+a(n-1)

Add one in n

● a(n+1) = a(n)-4

● a(n) = a(n+1)+4