3. Working with Percent: Determine each amount. a) 1.6% of $150 b) 11.3% of $950 c) 0.29% of $2000 (3)​

The volume of the rectangular prism aquarium = 17 1/16 ft.

Volume of a rectangular prism = (l)(w)(h), where:

The aquarium is a rectangular prism. Its dimensions are given as:

Length (l) = 3 1/4 ft

Width (w) = 3 ft

Height (h) = 1 3/4 ft

Substitute

Volume of the rectangular prism aquarium = (3 1/4)(3)(1 3/4)

Volume of the rectangular prism aquarium = (13/4)(3)(7/4)

Volume of the rectangular prism aquarium = (13 × 3 × 7)/(4 × 4)

Volume of the rectangular prism aquarium = (273)/(16)

Volume of the rectangular prism aquarium = 17 1/16 ft.

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Answer:

c

Step-by-step explanation:

Answer:

[tex] \frac{\pi}{4} [/tex]

Step-by-step explanation:

[tex] \sf let \: y = { \tan }^{ - 1} ( \tan \frac{3\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan \frac{3\pi}{4} \\ \\ \sf \hookrightarrow \tan y = \tan(\pi - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan( - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = - \tan \frac{\pi}{4} \\ \\ \boxed {\hookrightarrow{ \bold{y = - \frac{\pi}{4} } } }[/tex]

Using the probability concept, we have that:

a) The experimental probability is of 0.75 = 75%.

b) The theoretical probability is of 0.5 = 50%.

c) As the number of trials increases, the probabilities are expected to get closer, though they might not be equal.

A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials. A theoretical probability is calculated before any trial, and as the number of trials increase, the experimental and theoretical probabilities get closer.

From the table, there were 20 trials, and 2 + 3 + 4 + 4 + 2 = 15 resulted in even numbers, hence the experimental probability is:

p = 15/20 = 0.75 = 75%.

For a fair machine, even and odd numbers should be equally as likely, hence the theoretical probability is of 0.5 = 50%.

For item c, we have that as the number of trials increases, the probabilities are expected to get closer, though they might not be equal.

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Answer:

no mode

Step-by-step explanation:

no number appears more than once

therefore there is no mode

Answer:

answer

x= 40°

Step-by-step explanation:

x= 40° [ base angle of isocles triangle]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{1000000} \: \: m {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{10 {}^{6} } \: \: m {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: cm {}^{3} = {}{10 {}^{ - 6} } \: \: m {}^{3} [/tex]

To find the missing numbers in the sequence, we must identify the rule by which they change.

The sequence starts at 8 and then decreases by 1, therefore, the second term is 7. The third term increases by 4 units with respect to the second, going from 7 to 11, and the fourth decreases again by 1, now remaining at 10.

The fifth term increases again by 4 units, from 10 to 14. This already gives us a clear idea of the rule that the sequence follows.

                                                  ₊₄              ₊₄

                                            ⁻¹             ⁻¹               ⁻¹  

In this way, the sixth element must decrease by 1, that is 13 and the seventh must increase by 4, that is 17.

8, 7, 11, 10, 14, 13, 17,…

The next numbers that the numerical sequence are 13 and 17, to complete. ✅

Using the substitution method, the system of equation that is easily solved is:

c. y = 2x + 3

2x + y = 5

Using the substitution method to solve a system of equations is best when one of the equations have one isolated variable that we can simply plug its value into the second equation.

For example, given the system of equations:

y = 2x + 3 --> eqn. 1

2x + y = 5 --> eqn. 2

Substitute y = (2x + 3) into eqn. 2 and find x:

2x + y = 5 --> eqn. 2

2x + 2x + 3 = 5

4x + 3 = 5

4x = 5 - 3

4x = 2

x = 2/4

x = 1/2

Substitute x = 1/2 into eqn. 1 to find y

y = 2x + 3 --> eqn. 1

y = 2(1/2) + 3

y = 1 + 3

y = 4

From the above, we can see that the system of equations that is quite easy to solve using the substitution method is:

c. y = 2x + 3

2x + y = 5

The rest of the equations are quite different and not as straightforward as solving as this using the substitution method.

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Answer:

376.99112cm²

Step-by-step explanation:

A=2 pi rh + 2 pi r²

A=(2 x pi x 5 x 7) + (2 x pi 5²)

pi 22/7

Step-by-step explanation: Given that the graph shows the side view of a water slide with dimensions in feet.

We are to find the rate of change between the points (0, ?) and (?, 40).

From the graph, we note that

the y co-ordinate for the x co-ordinate 0 is 80 and the x co-ordinate for the y co-ordinate 40 is 5.

So, the given two points are (0, 80) and (5, 40).

The rate of change for a function f(x) between the points (a, b) and (c, d) is given by

Therefore, the rate of change for the given function between the points (0, 80) and (5, 40) is

Thus, the required rate of change is -8.

The number of times that Greg is on time to class is 4

The given parameters are:

Probability that Greg is on time, p = 14%

The sample size, n = 30

The estimate of the number of times that Greg is on time to class is

E(x) = np

Substitute the known values in the above equation

E(x) = 30 * 13%

Evaluate the product

E(x) = 3.9

Approximate

E(x) = 4

Hence, the number of times that Greg is on time to class is 4

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Answer:

92 degrees

Step-by-step explanation:

The sum of the exterior angles will be 360.  

67 x 4 = 268.  That means that the last angles must be 92 (360 - 268)

Using the z-distribution, it is found that a sample size of n = 18,805 is required.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]z = 2.81, \sigma = 24.4, M = 0.5[/tex].

Hence we solve for n to find the needed sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 2.81\frac{24.4}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 24.4 \times 2.81[/tex]

[tex]\sqrt{n} = 48.8 \times 2.81[/tex]

[tex](\sqrt{n})^2 = (48.8 \times 2.81)^2[/tex]

n = 18,805.

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Answer:

Step-by-step explanation:

What if the estimate is within 1 of the population mean?

===========================================================

Explanation:

Let's use the distance formula to find the distance from D to E

[tex]D = (x_1,y_1) = (-7,2) \text{ and } E = (x_2, y_2) = (3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-7-3)^2 + (2-4)^2}\\\\d = \sqrt{(-10)^2 + (-2)^2}\\\\d = \sqrt{100 + 4}\\\\d = \sqrt{104}\\\\d = \sqrt{4*26}\\\\d = \sqrt{4}*\sqrt{26}\\\\d = 2\sqrt{26}\\\\d \approx 10.198\\\\[/tex]

Note: uppercase D refers to the point, while lowercase d is the distance from D to E.

The length of segment DE is roughly 10.198 units long.

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

Repeat for the distance from E to F.

[tex]E = (x_1,y_1) = (3,4) \text{ and } F = (x_2, y_2) = (5,-7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-5)^2 + (4-(-7))^2}\\\\d = \sqrt{(3-5)^2 + (4+7)^2}\\\\d = \sqrt{(-2)^2 + (11)^2}\\\\d = \sqrt{4 + 121}\\\\d = \sqrt{125}\\\\d = \sqrt{25*5}\\\\d = \sqrt{25}*\sqrt{5}\\\\d = 5\sqrt{5}\\\\d \approx 11.1803\\\\[/tex]

Segment EF is roughly 11.1803 units long.

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

Repeat for the distance from F to D.

[tex]F = (x_1,y_1) = (5,-7) \text{ and } D = (x_2, y_2) = (-7,2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(5-(-7))^2 + (-7-2)^2}\\\\d = \sqrt{(5+7)^2 + (-7-2)^2}\\\\d = \sqrt{(12)^2 + (-9)^2}\\\\d = \sqrt{144 + 81}\\\\d = \sqrt{225}\\\\d = 15\\\\[/tex]

Unlike the others, this result is exact.

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

Add up the three segment lengths to get the perimeter

DE + EF + FD

10.198 +  11.1803 + 15

36.3783

The perimeter is approximately 36.3783 units which rounds to 36.4

The answer has been confirmed with GeoGebra.

Step-by-step explanation:

since the y- axis stands for velocity (and the x-axus for time), speeding up means when the curve goes up (increasing velocity), and slowing down means when the curve goes down (decreasing velocity), all when reading the graph from left to right (small time values to larger time values).

(a)

speeding up

t in [0, 1)

or

0 <= t < 1

I would exclude t = 1, because at that point the slope is 0, there is no speeding up there.

slowing down

t in (1, 3)

or

1 < t < 3

the same argumentation for excluding 1 and 3, because there the slope of the curve turns 0 (just the turning point from one tendency to the other), and there is no speeding up or slowing down at these points.

(b)

speeding up

t in (1. 2)

or

1 < t < 2

slowing down

t in [0, 1) or in (2, infinity)

or

0 <= t < 1 || 2< t < infinity

we could use 3 instead of infinity, as this seems to be the last point of the drawn curve, but normally this kind of drawing tells me "infinity".

The computation shows that the number of weeks that it take to repair this stretch of road will be 4 weeks.

From the information given, we are told that a thirteen kilometers stretch of road needs repairs and that the workers can repair three and half kilometers of road per week.

The question is simply for us to calculate the number or weeks that it will take to be able to repair the stretch of road.

Therefore, based on the information given, it should be noted that to get the number of weeks that will be used to repair the road, we simply have to divide the total distance or the road by the distance that is repaired every week.

Therefore, the number of weeks that it will take to be able to repair this stretch of road will be:

= 13/3.5

= 3.7

= 4 weeks approximately

Therefore, based on the information given, the number of weeks that's required is 4 weeks.

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Answer:

Option 3: -2

Step-by-step explanation:

The slope of the graph is negative, and the only option with a negative term for the slope is -2.

So the slope of the graph is -2.

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Evaluate by substituting :

[tex]\begin{gathered} \boldsymbol{f(x)=-2x^2-3x+5; \ evaluate \ when \ x=-3} \\\boldsymbol{Write \ -3 \ everywhere \ you \ see \ and \ x :}\\\boldsymbol{f(-3)=-2(-3)^2-3(-3)+5}\\\boldsymbol{Evaluate \ using \ Order \ of \ Operations :}\\\boldsymbol{f(-3)=-2(9)+9+5= > -18+9+5= > -18+14= > -4}\end{gathered}[/tex]

Therefore, the answer is [tex]\LARGE\textbf{-4}[/tex].

I hope the answer - and steps - made sense to you !!

Happy Learning !!

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

The equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60

From the question, we are to determine the equation that will give the number of boxes, x, that Joe needs to buy

From the given information,

Joe needs 60 donuts to feed his construction crew

Also,

There are 12 donuts per box

This means he needs to buy 60/12 boxes of donut

Since the number of boxes Joe needs to buy is x

∴ 60/12 = x

60 = 12x

12x = 60

Hence, the equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60

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Answer:

0.00018

Step-by-step explanation:

formula:Divide the volume by 1e+6

Answer:

GC and GD

Step-by-step explanation:

The only points on plane L are: J, C, G, D

GC and GD

A. The pair of linear equations are: x + y = 55 and y = x + 25

B. Number of time she spend running everyday is: 15 minutes.

C. It is not possible.

A system of equations consist of linear equations that have unknown variables whose values make the linear equations in the system true.

Part A: To write a pair of linear equations, do the following,

Let x represent the time Jackie runs

Let y represent the time Jackie dances

We are given that, Jackie runs and dances for a total of 55 minutes every day, therefore, the first linear equation would be:

x + y = 55 --> equation 1

We are also given that Jackie dances for 25 minutes longer than she runs, therefore, the second linear equation would be:

y = x + 25 --> equation 2

Therefore, the two pair of linear equations that shows the relationship between the number of minutes Jackie runs and dances everyday are:

x + y = 55

y = x + 25

Part B: Substitute y = (x + 25) into equation 1

x + y = 55 --> equation 1

x + x + 25 = 55

2x + 25 = 55

2x = 55 - 25

2x = 30

x = 15

Therefore, the number of time she spend running everyday is: 15 minutes.

Part C:

If she spent 45 minutes dancing (y = 45), and x = 15, substitute the values into x + y = 55 to find out if it is possible.

15 + 45 = 55

60 = 55 (not true)

Therefore, it is not possible.

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The number of ways men can be selected from the team of 18 is 48,620ways

Permutation has to do with arrangement while combination has to do with selection.

If a baseball team consists of 18 players and 9 man are possible in the team, the number of ways the men can be chosen is calculated using the combination formula below;

nCr = n!/(n-r)!r!

Given the following

n =18

r = 9

Substitute

18C9 = 18!/(18-9)!9!
18C9 = 18!/9!9!
18C9 = 48,620

Hence the number of ways men can be selected from the team of 18 is 48,620ways

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Answer:

y = 3/2x + 2

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y = 3/2x + 2

Answer:

[tex]\sf y =\dfrac{3}{2}x+2[/tex]

Step-by-step explanation:

 Pick any two points on the line.

 (0,2) and (2 , 5)

  (0,2) ⇒ x₁ = 0  & y₁ = 2

  (2,5) ; x₂ = 5 & y₂ = 5

[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

            [tex]\sf =\dfrac{5-2}{2-0}\\\\=\dfrac{3}{2}[/tex]

Equation of line in point slope form:

         [tex]\sf y - y_1 =m(x -x_1)[/tex]

        Point(0 ,2) and m = 3/2

       [tex]\sf y - 2 = \dfrac{3}{2}(x -0)\\\\ y - 2 = \dfrac{3}{2}x\\\\[/tex]

Equation of line in slope y-intercept form:

              [tex]\sf y =\dfrac{3}{2}x+2[/tex]

Answer:

{(4,1), (-6, 6), (5,-2), (-4,1)} set of ordered pairs represents a function.

Step-by-step explanation:

Because every element or component of domain has unique image in co-domain.

Hope its helpful :-)

If so, please mark me as brainlist :-)

For only 4 wire transfers, Checking account A has a monthly fee of $54, while checking account B has a monthly fee of $55, so the correct option is D.

Checking account A charges a monthly fee of $12, plus $10.50 for each wire transfer, then the total cost if you make 4 wire transfers is:

C = $12 + $10.50*4 = $54

For checking account B, we have a fixed cost of $21, plus $8.50 per each wire transfer, then the total cost for 4 wire transfers is:

C'  = $21 + 4*$8.50  = $55

So, if you make only 4 wire transfers per month, checking account A is a better option.

Then we can see that the correct option is D.

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Answer:

[tex]y=-2x+1[/tex]

Step-by-step explanation:

Looking at the line can ensure that the slope is negative

The rise/run is 4/-2, ten the slope is:

[tex]s=\frac{-4}{2} =-2[/tex]

b intercept is 1

The equation:

[tex]y=-2x+1[/tex]

Hope this helps