Find the total area of the prism.

Answer:

A: y = (x − 4)^2 − 4

Step-by-step explanation:

vertex=(4.-4)

A: y = (x − 4)^2 − 4

y=x^2-8x+16-4

y=x^2-8x+12 (a=1,b=-8,c=12)

the y intercept is (0,12)

vertex ( h, k)

h=-b/2a ⇒ h=-(-8)/2=4

plug the value of h in the equation y=x^2-8x+12

k=4²-8(4)+12

k=16-32+12

k=-4

v(4,-4)

The required equation of the given graph in vertex form is y = (x − 4)² − 4. which is the correct answer would be option (A).

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c.

The parabola equation into the vertex form:

(y-k) = a(x-h)²

Where (h,k) are the x and y-coordinates of the vertex.

The vertex = (4, -4) is given in the shown graph.

As per option (A),

y = (x − 4)² − 4

y = x²-8x+16-4

y = x²-8x+12 (a=1,b=-8,c=12)

the y-intercept is (0,12)

vertex ( h, k)

h = -b/2a ⇒ h=-(-8)/2=4

Substitute the value of h in the equation y = x²-8x+12

k = 4²- 8(4) + 12

k =16 - 32 + 12

k = -4

Thus, the vertex is (4,-4)

Hence, the correct answer would be option (A).

Learn more about the parabola here:

brainly.com/question/4074088

#SPJ2

Answer:

<M = 78°

Step-by-step explanation:

The sum of angles in a kite is 360°.

One of the properties of a kite is that one pair of opposite angles are equal.

Since it is not <L and <N, it must be <O and <M

Therefore:

<O = <M = x

=> x + x + 130 + 74 = 360

2x + 204 = 360

2x = 360 - 204

2x = 156

x = 156/2 = 78°

This means that <M = 78°

Answer:

[tex]\boxed{\sf \ \ x=-2, \ y=-3 \ \ }[/tex]

Step-by-step explanation:

Hello,

I assume that you want to solve this system of two equations

   (1) 5x - y  = -7

   (2) 4x + 2y = -14

We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y

2*(1)+(2) gives

   10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28

   <=>

   14x = - 28 we can divide by 14 both parts

   x = -28/14 = -2

and then we replace x in (1)

   5*(-2)-y=-7

   -10-y=-7 add 7

   -10-y+7=0

   -3-y=0 add y

   -3 = y

which is equivalent to y = -3

do not hesitate if you have any question

Answer:

x = -2, y = -3

Step-by-step explanation:

5x - y = -7

4x + 2y = – 14

Multiply the first equation by 2

2(5x - y) = 2*-7

10x -2y = -14

Add this to the second equation to eliminate y

10x -2y = -14

4x + 2y = – 14

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

14x = -28

Divide by 14

14x/14 = -28/14

x = -2

Now find y

4x+2y = -14

4*-2 +2y = -14

-8+2y = -14

Add 8 to each side

2y = -6

Divide by 2

2y/2 = -6/2

y = -3

Answer:

Perimeter = 54.6 cm

Area = 173 cm²

Step-by-step explanation:

sin 30 = x/20

x = 10

cos 30 = y /20

y = 17.3

perimeter = 10 + 17.3 + 10 + 17.3 = 54.6 cm

area = 10 * 17.3 = 173 cm²

Answer:  438.5L = 438000ml

Step-by-step explanation:

Answer:

(a) [tex]Q_1=36.5,M=Q_2=41,Q_3=46[/tex]

(b) [tex]IQR=9.5[/tex]

(c) 15

Step-by-step explanation:

The given data set is

41, 52, 37, 44, 42, 38, 41, 48, 43, 39, 36, 55, 42, 35, 15, 52, 39, 50, 29, 30

Arrange the data in ascending order.

15, 29, 30, 35, 36, 37, 38, 39, 39, 41, 41, 42, 42, 43, 44, 48, 50, 52, 52, 55

Divide the data in four equal parts.

(15, 29, 30, 35, 36), (37, 38, 39, 39, 41), (41, 42, 42, 43, 44), (48, 50, 52, 52, 55)

Now,

[tex]Q_1=\dfrac{36+37}{2}=36.5[/tex]

[tex]M=Q_2=\dfrac{41+41}{2}=41[/tex]

[tex]Q_3=\dfrac{44+48}{2}=46[/tex]

[tex]IQR=Q_3-Q_1=46-36.5=9.5[/tex]

Range for outlier is

[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[36.5-1.5(9.5),46+1.5(9.5)][/tex]

                           [tex]=[22.25,60.25][/tex]

Since, 15 lies outside the interval [22.25,60.25], therefore 15 is an outlier.

[tex]\bold{Answer}:\quad \dfrac{24}{25}[/tex]

Step-by-step explanation:

There are 100 oranges.  4 of them are unripe which means 96 are ripe.

[tex]\dfrac{ripe}{total}=\dfrac{96}{100}\quad \div \dfrac{4}{4}=\large\boxed{\dfrac{24}{25}}[/tex]

Answer:

18 is the first multiple of 3,6, and 9.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

We need to find the LCM (lowest common multiple) of 3, 6, and 9. Let's count by multiples of 3 to find it.

3 (not a multiple of 6 or 9), 6 (not a multiple of 9), 9 (not a multiple of 6), 12 (not a multiple of 9), 15 (not a multiple of 6 or 9), 18.

Since 18 is the first number that is a multiple of 3, 6, and 9, that is the answer.

Answer:

123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134

Step-by-step explanation:

123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134

Answer: (a) When he turns 68 , the account will have = $1,179,415.39

(b) $ 288,000

Step-by-step explanation:

Formula: Future value of annuity =[tex]P[\dfrac{(1+r)^n-1}{r}][/tex], where P+ periodic payment, r = rate of interest per period, n= number of periods.

As per given, we have

P= $1800

rate of interest = 6% = 0.06

(a) n= 68-28 = 40

Rate per period : r= [tex]\dfrac{0.06}{4}=0.015[/tex]  

Number of periods: n = 4x 40 =160

Now, Future value of amount when Mr. Pink turns 28 years = [tex]1800(\dfrac{(1+0.015)^{160}-1}{0.015})[/tex]

[tex]=1800(\dfrac{10.8284615777-1}{0.015})\\\\=1800\times\dfrac{9.8284615777}{0.015}\\\\\approx\$1179415.39[/tex]

Hence, when he turns 68 , the account will have = $1,179,415.39

(b) Total contribution = P × n

=1800 × 160

=$ 288,000

Hence, Total contribution =$ 288,000

Answer:

[tex]y-4=2\,(x+1)[/tex]

which agrees with answer C in your list of possible answers.

Step-by-step explanation:

We can use the general point-slope form of a line of slope m and going through the point [tex](x_0, y_0)[/tex]:

[tex]y-y_0=m(x-x_0)[/tex]

which in our case, given the info on the slope (2) and the point (-1, 4) becomes:

[tex]y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)[/tex]

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

Graph A.

Step-by-step explanation:

Answer:

Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

Problem 1:

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%    {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%     {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is One-sample z-test for proportions;

                       T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53

           n = sample of adult Americans = 295

So, the test statistics =  [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]

                                    =  1.03

The value of z-test statistics is 1.03.

Also, the P-value of the test statistics is given by;

              P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)

                           = 1 - 0.8485 = 0.1515

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2:

We are given that a random sample of 35 trading days in 2014 resulted in a  sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let [tex]\mu[/tex] = mean daily volume in Google stock

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares    {means that the volume of Google stock has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares     {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                       T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares

            s = sample standard deviation = 1.68 million shares

           n = sample of trading days = 35

So, the test statistics =  [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                    =  -7.606

The value of t-test statistics is -7.606.

Also, the P-value of the test statistics is given by;

              P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the volume of Google stock has changed.

Answer:

13°

Step-by-step explanation:

The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.

The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft

Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:

[tex] tan x = \frac{opposite}{adjacent} [/tex]

[tex] tan x = \frac{6}{26} [/tex]

[tex] tan x = 0.2308 [/tex]

x = tan-¹(0.2308)

x = 12.996

x ≈ 13° (to the nearest whole degree)

The angle of elevation of the sun = 13°

Answer: True

Step-by-step explanation:

The probability of an event occurring lies between zero and one. A probability of 0 means that the event has no chance of happening for example, rolling a die once and getting a number greater than 6 while a probability of 1 means the event will definitely happen for example, getting a number less than 7 when you roll a die once.

Every other probability falls in-between this range so probability can never be 154.

Answer:

A= 66.6667

B = 333.3333

Step-by-step explanation:

Initial value of A = $20

Initial value of B = $80

Initial total=$ 28000

A moves up 50%= 20+(0.5*20)

A moves up 50% = 20+10

A moves up 50% =$ 30

B double it values = $80*2

B double it values = $160

Now total value is = $54000

A20+B80= 28000... equation 1

A30+B160= 54000.... equation 2

Multiplying equation 1 * 2

Multiplying equation 2 * 1

A40 +B160 = 56000

A30+B160= 54000

A30 = 2000

A= 2000/30

A= 200/3

A= 66.6667

A20+B80= 28000

Substituting A

200/3 (20) +B80= 28000

B80= 28000-4000/3

B80= 80000/3

B= 80000/240

B = 333.3333

Answer:

B = 26.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin B = 4/9

Take the inverse sin of each side

sin ^-1 sin ( B) = sin ^-1 ( 4/9)

B = 26.38779996

B = 26.4

Answer:

[tex]26.4\º[/tex]

Step-by-step explanation:

[tex]\theta=?[/tex]

[tex]$\sin(\theta)=\frac{opp}{hyp} = \frac{4}{9} $[/tex]

[tex]$\theta=\sin^{-1}\frac{4}{9} =\arcsin\frac{4}{9} \approx 26.4\º$[/tex]

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]

Answer:

I did my best with the information! The Man died at around 11:20 am.

Step-by-step explanation:

So due to the algus mortis process, after death, a body can stay at its regulated temperature for up to 2 to 3 hours postmortem. But after that, the body soon drops at about 1 degrees celsius each hour. 1 degrees celsius is about -33 . So he was found at 42 degrees fahrenheit, which means he died somewhere around 11 o-clock. We do not know how long the postmortem process had his temperature delayed, so it would be roughly I say around 11: 20 am.

Answer:

There is no significant interaction between the number of sales calls and the miles driven.

Step-by-step explanation:

The variables are defined as follows:

Dependent (Y) = amount earned in commissions last month

Independent (X₁) = number of miles driven last month

Independent (X₂) = number of sales calls made last month

In this case we need to test whether there is a significant interaction between the number of sales calls and the miles driven.

The hypothesis can be defined as follows:

H₀: There is no significant interaction.

Hₐ: There is a significant interaction.

Assume that the significance level of the test is, α = 0.05.

Use the Data Analysis tool in Excel to form the regression equation.

For the regression equation, we need to compute the values of (X₁ × X₂).

Steps:

The output of the regression analysis is attached below.

The regression equation is:

[tex]Y=-455.07+3.128\cdot X_{1}+0.143\cdot X_{2}-0.001\cdot X_{1}X_{2}[/tex]

Consider the third table in the regression output.

The test statistic corresponding to the interaction term is:

t = -1.85

The p-value for the test of the interaction term is:

p-value = 0.078.

The p-value of the test is more than the significance value.

The null hypothesis will not be rejected.

Thus, concluding that there is no significant interaction between the number of sales calls and the miles driven.

Answer:

120

Step-by-step explanation:

Answer: 120

Hope that helped!(:

Answer:

1)  m = negative StartFraction 10 over 4 EndFraction

2) m = negative five-halves

3) m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]

Step-by-step explanation:

The given equation is:

=> [tex]\frac{3}{4} +m = -\frac{7}{4}[/tex]

Subtracting 3/4 to both sides

=> m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]

=> m = [tex]\frac{-10}{4}[/tex]

=> m = [tex]-\frac{5}{2}[/tex]

Answer:

-5/2 ye

cause ya do the math

Step-by-step explanation:

Answer: 0.0668

Step-by-step explanation:

Given the following :

Mean (m) Cost = RS385

Standard deviation (s) = RS110

Assume a normal distribution, Probability that domestic airfare is RS550 or more?

P(x > 550)

Find the z - score

Z - score = (x - m) / s

Where x = 550

Z = (550 - 385) / 110

Z = 165 / 110 = 1.5

P(Z > 1.5) = 1 - P(Z ≤1.5)

Using the z table : 1.5 = 0.9332

Therefore,

1 - P(Z ≤1.5) = 1 - 0.9332 = 0.0668

P(x > 550) = 0.0668

Answer:

[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all, let's find the factors of these two numbers and I will put in boxes the common factors.

[tex]15a^2b^2=\boxed{3}\cdot 5\cdot \boxed{a} \cdot a \cdot \boxed{b} \cdot b \\ \\ \\-24ab=(-1)\cdot 2 \cdot \boxed{3} \cdot 4 \cdot \boxed{a} \cdot \boxed{b}[/tex]

The Highest Common Factor (HCF) is found by finding all common factors and selecting the largest one. So, in this case, it gives

[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

I suppose this is saying that 20%, 25% and 55% are each a whole number of science students.  The GCD is 5%, 1/20th, so minimum 20 people total.  55% are studying biology, that's 11.

Answer: C. 11

Answer:

20%

Step-by-step explanation:

When you divide 40 by 8, you get 0.2. To convert a decimal into a percent, you multiply by 100 to get 20.

Hence,

8 is 20% of 40.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

The answer is option B.

Step-by-step explanation:

Let the percentage be x

We have

[tex] \frac{x}{100} \times 40 = 8 \\ \\ \frac{4}{10} x = 8 \\ \\ 4x = 80 \\ \\ x = \frac{80}{4} \\ \\ x = 20[/tex]

Hope this helps you

Answer:

Step-by-step explanation:

Given the following geometric progression; 1/2 + 1/10 + ( 1/50) + (1/250 ) + ... + (1/31,250),the sum of the arithmetic geometric progression is expressed using the formula below;

Sn = a(1-rⁿ)/1-r  for r less than 1

r is the common ratio

n is the number of terms

a is the first term of the series

In between the mid-line ellipsis there are 2 more terms, making the total number of terms n to be 7]

common ratio = (1/10)/(1/2) =  (1/50)/(1/10) =  (1/250)/(1/50) = 1/5  

a = 1/2

Substituting the given values into the equation above

S7 = 1/2{1 - (1/5)⁷}/1 - 1/5

S7 = 1/2(1- 1/78125)/(4/5)

S7 = 1/2 (78124/78125)/(4/5)

S7 = 78124/156,250 * 5/4

S7 = 390,620/625000

S7 = 39062/62,500

Hence the geometric sum is 39062/62,500

85% x 1600/100 = 1360 number of seats sold

Answer:

50% of 100<75% of 104

50% of 100>75% of 60

Step-by-step explanation:

For the inequality to support the statement, we can use 50% of 100 which is 50

Now we need to find "any other number" that is greater. I'll use 104 since it divides evenly. 75% of 104 is 78, 50<78

Now for the second one, we can use 50% of 100 again which is 50.

This time we need to find another number that is less than. I'll use 60. 75% of 60 is 45. 50>45