What is the volume of the rectangular prism?

Answer:

4x^2 +9x/4 -7

Step-by-step explanation:

f(x) =x/4 - 3

g(x) = 4x^2 + 2x - 4

(f +g)(x) = x/4 - 3  +  4x^2 + 2x - 4

             = 4x^2 + 8x/4+x/4 -7

             = 4x^2 +9x/4 -7

Answer: (a): Good course, (b): Bad course

Step-by-step explanation:

Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.

Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.

Answer:

13/9

Step-by-step explanation:

Given

5/9 + 8/9

Both fractions have the same denominator.

Therefore, pick one of the denominator and add the numerators

5/9 + 8/9

= (5+8) / 9

= 13/9

5/9 + 8/9 = 13/9

Answer:

320 minutes (5 hours and 20 minutes).

Step-by-step explanation:

2 hours and 17 minutes = 137 minutes

137 + 84 + 99 = 320

Therefore, they will spend 320 minutes (5 hours and 20 minutes) watching movies.

Answer:

4/8= 2/4=1/2= 50%

Step-by-step explanation:

4 out of the 8 new cars have a fuel efficiency of less than 27 mpg. that is is 50%

Distance formula

[tex]\boxed{\sf AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(6 - 0) {}^{2} + {(8 - 0)}^{2} } \\ \\ \sf\longmapsto \sqrt{ {6}^{2} + {8}^{2} } \\ \\ \sf\longmapsto \sqrt{36 + 64 } \\ \\ \sf\longmapsto \sqrt{100} \\ \\ \sf\longmapsto 10[/tex]

Answer:

101

10+6+16+6*5

I hope it's correct

Answer:

9x-10y+60=0

Step-by-step explanation:

slope is,

m = (6-(-3))/(0-(-10))

= 9/10

b = -3-(9/10)×(-10)

= 6

So, the equation of the line is,

y = 9x/10+6

or, 9x-10y+60=0

Answered by GAUTHMATH

Answer:

(2, -6)

Step-by-step explanation:

u = (5, 0)

v = (-2, -1)

w = (-6, 6)

(5, 0) + 3(-2, -1) - 1/2(-6, 6)

= (5, 0) + (-6, -3) + (3, -3)

= (2, -6)

Answer:

A

Step-by-step explanation:

The answer is 0.6^(x)-2. Answered by Gauthmath

From the graph, the equation that's is represented is A. 0.6x - 2.

From the equation, on the coordinate plane, the curve opens up and to the right. It crosses the x-axis at (negative 1.5, 0) and then crosses the y-axis at (0, negative 1).

Here, based on the family the graph below belongs to, the equation represented is the first equation which is 0.6x - 2.

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Answer:

4, 7, 14

Step-by-step explanation:

Because it's were it decreases

Answer:

I think that there might be some complex differential equation

stuff going on here if this were in the real world, but for the sake of this problem... may I suggest that the tank is filling up  at a rate of

1/8 of a tank per hour...

it is evaporating at a rate of 1/12 tank per hour

you can subtract the rates

1/8 - 1/12 = 12/96- 8/96 = 3/96 = 1/32 tank/hr

so to fill the tank it should take 32 hours...

I think the logic and math work... lets see if someone else will verify this analysis?

Step-by-step explanation:

Answer:

y = 3 + 0.40x

Step-by-step explanation:

Fixed cost of taxi fare = $3

Additional cost = $0.40

Let

y = Total cost

x = number of kilometers

The equation:

Total cost = Fixed cost of taxi fare + (Additional cost * number of kilometers)

y = 3 + 0.40x

Answer:

(x+2,y-4)

Step-by-step explanation:

The correct answer is (x+2, y-4)

The translation of ABCD to A'B'C'D' is given by (x + 2,y - 4).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Translation is the movement of a point either up, left, right or down.

ABCD has vertices at A(-6, 2), B(-5, 4), C(-2, 4) and D(1, 2). If ABCD is translated 4 units down and 2 units right, the new point is A'(-4, -2), B'(-3, 0), C'(0, 0) and D'(3, -2)

The translation of ABCD to A'B'C'D' is given by (x + 2,y - 4).

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Answer:

copy and paste...

Step-by-step explanation:

Answer:

bạn cực ngu

Step-by-step explanation:

bạn cực kì ngu

Answer:

[tex]n=35[/tex]

Step-by-step explanation:

From the question we are told that:

Standard Deviation [tex]\sigma=4min[/tex]

Let

[tex]CI=95\%[/tex]

Since

Significance level [tex]\alpha[/tex]

[tex]\alpha =1-CI[/tex]

[tex]\alpha =1-0.95[/tex]

Therefore

[tex]Z_{\alpha/2}=Z_{0.025[/tex]

[tex]Z_{\alpha/2}}=1.96[/tex]

Generally the equation for Sample size is mathematically given by

[tex]n = (Z_{\alpha/2}* \frac{\sigma}{E})^2[/tex]

[tex]n= \frac{1.96 * 3}{1}^2[/tex]

[tex]n=35[/tex]

Answer:

It's A

Step-by-step explanation:

Answer:

The Constant is 9/2

Answer:

Area=9:25 Volume=81:625

Step-by-step explanation:

Should be squared, might be wrong.

Answer:

B. decrease of 12

Step-by-step explanation:

Number of people who left the store = 14

Number of people who entered the store = 10

Again,

Number of people who left the store = 13

Number of people who entered the store = 5

Total people who left the store = 14 + 13

= 27 people

Total people who entered the store = 10 + 5

= 15 people

Number of people remaining in the store = Total people who entered the store - Total people who left the store

= 15 - 27

= -12

This means there is a net decrease in the number of people in Carmen's Computer Store

Answer:

I say the fourth one just because

Answer: y = -1x + 1

Step-by-step explanation:

(choose two points on the line to find the slope)

(0,1) and (2,-1)

(slope = m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-1}{2-0}=\frac{-2}{2} =-1[/tex]

y = mx + b, (0,1), (2,-1), m=-1

(both points work and yield the same equation)

[tex]y=mx+b\\1=-1(0)+b\\b=1\\y=-1x+1[/tex]

Answer:

B.5: 5^2(-3)(+7)

Step-by-step explanation:

1. 5 is the HCF of the three numbers, so it goes outside the brackets. 5(^4+4^3−21^2).

2. ^2 is also a factor, so now its 5^2(^2+4-21)

3. Factor by Grouping 5^2(^2−3+7−21)

4. Factor by Grouping 5^2((−3)+7(−3))

5. Factor by Grouping 5^2(−3)(+7)

Thats your final answer.

Answer:

C

Step-by-step explanation:

The angles are congruent by CPCTC as they correspond with one another.

Answer:

The final answer, D

Step-by-step explanation:

Source: Done this question before

Answer:

$21,616.26.

Step-by-step explanation:

24000 =P(1 + 0.03/4)^14

P = 24000 / (1 + 0.03/4)^14)

21,616.26.

=

The present value that will grow to ​$24000 if interest is 3​% compounded quarterly for 14 quarters is $21,482.40

To find the present value that will grow to $24,000 at 3% interest compounded quarterly for 14 quarters, we use the formula for compound interest:

[tex]PV = FV / (1 + r/n)^{(n*t)}[/tex]

Where:

PV = Present Value

FV = Future Value ($24,000)

r = Annual interest rate (3% or 0.03 as a decimal)

n = Number of compounding periods per year (quarterly, so n = 4)

t = Number of years (14 quarters = 14/4 = 3.5 years)

Substitute the values into the formula:

PV = [tex]$24,000 / (1 + 0.03/4)^{(4*3.5)}[/tex]

PV = [tex]$24,000 / (1 + 0.0075)^{(14)}[/tex]

PV = [tex]$24,000 / (1.0075)^{14}[/tex]

PV ≈ $21,482.40 (rounded to the nearest cent)

Therefore, the present value required for it to grow to $24,000 in 14 quarters at 3% interest compounded quarterly is approximately $21,482.40.

In this explanation, we used the formula for compound interest to calculate the present value (PV). The formula accounts for the future value (FV), the annual interest rate (r), the number of compounding periods per year (n), and the time in years (t). By plugging in the given values and performing the calculations, we arrived at the present value of approximately $21,482.40.

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y = -2x-3

Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope  , then a line perpendicular to this has slope . That means the slope of our perpendicular line is

The equation of the line that is perpendicular to 8x - 2y = 4 and passes through the point (4, 3) is y = (-1/4)x + 4.

To find the equation of a line that is perpendicular to the line 8x - 2y = 4 and passes through the point (4, 3), we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope:

8x - 2y = 4

-2y = -8x + 4

Divide both sides by -2:

y = 4x - 2

The slope of the given line is 4.

The slope of a line perpendicular to this line would be the negative reciprocal of 4, which is -1/4.

Now, we have the slope (-1/4) and a point (4, 3). We can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Substituting the values, we have:

y - 3 = (-1/4)(x - 4)

Expanding and simplifying, we get:

y - 3 = (-1/4)x + 1

Adding 3 to both sides, we have:

y = (-1/4)x + 4

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