Simplify. ‒36 ÷ (27 ÷ 3 ∙ 2)

Answer:

I dont know if this is right but i got -7/3.

Sorry if its wrong

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".

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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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. ✅

Answer:

c

Step-by-step explanation:

Answer:

answer

x= 40°

Step-by-step explanation:

x= 40° [ base angle of isocles triangle]

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.

Answer:

4 hours

Step-by-step explanation:

Hour1-

Bicycle = 24.50

ElectricScooter = 32

Hour2-

Bicycle = 34

ElectricScooter = 39

Hour3-

Bicycle = 43.5

ElectricScooter = 46

Hour4 -

Bicycle = 53

ElectricScooter = 53

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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so hmmm on average on the last 7 test, you get 82, so hmmm we could say that on each of the 7 tests you got 82, so you got 82, 7 times.

now, let's say in the 8th test, you get a grade of "g", now, if we were to get an average of all 8 tests, that means the average will simply be (82*7) + "g", and we know that's 84, so

[tex]\cfrac{(\stackrel{\textit{sum of all first seven tests}}{82+82+82+82+82+82+82})~~ + ~~g}{8}~~ = ~~84\implies \cfrac{(82\cdot 7)~~ + ~~g}{8}~~ = ~~84 \\\\\\ \cfrac{574+g}{8}=84\implies 574+g=672\implies g=672-574\implies g=98[/tex]

You must score 98 on the eighth test to raise your average to 84.

Average = Sum of all scores / Number of scores

The average score is given as 82, so the sum of the first 7 test scores would be 82 multiplied by 7.

The average to 84, we need to find the sum of all 8 test scores. Let's represent the score we need on the eighth test as "x."

Average = Sum of all scores / Number of scores

Using this equation, we can write:

84 = (Sum of the first 7 test scores + x) / 8

Multiply both sides of the equation by 8:

8 * 84 = Sum of the first 7 test scores + x

672 = Sum of the first 7 test scores + x

Subtract:

672 - Sum of the first 7 test scores = x

Substitute the sum of the first 7 test scores (82 * 7) into the equation:

x = 672 - (82 * 7)

x = 672 - 574

x = 98

Therefore, you must score 98 on the eighth test to raise your average to 84.

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Answer:

1/4 cups of milk and 1 1/3 Tbsp of butter.

Step-by-step explanation:

Milk : 3/4 multiplied by 1/3 = 3/12 = 1/4
Butter : 4 multiplied by 1/3 = 4/3 = 1 1/3

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)

Answer:

GC and GD

Step-by-step explanation:

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

GC and GD

Based on the data presented, it can be concluded out of the 52 females 26 prefer cats.

To read the graph we must take into account that the rows refer to the preference of men, preference of women and those who have no preference.

On the other hand, the columns refer to the number of students of both genders who prefer or do not prefer each animal. Additionally, adding all the students of each gender we have the total of the sample.

According to the above, the total sample of female students would be 52.

According to the above, the fraction that expresses this relationship correctly is:

[tex]\frac{26}{52}[/tex]

Note: This question is incomplete because the graph is missing. Here is  the graph.

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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:

[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 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?

Answer:

0.00018

Step-by-step explanation:

formula:Divide the volume by 1e+6

The solution to the given expression is x = -20/11

Logarithmic function are inverse of exponential functions. Given the equation below;

log (6 x + 10) = log 1/2 x

In order to determine the solution to the given logarithmic equation, we will first have to cancel the logarithm on both sides to have

6x + 10 = 1/2x

Collect the like terms

6x - 1/2x = 0 - 10

Find the LCD

12x-x/2 = -10
11x/2 = -10

Cross multiply

11x = -2 * 10

11x = -20

Divide both sides by 11

11x/11 = -20/11

x = -20/11

Hence the solution to the given expression is x = -20/11

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The critical value for the given confidence level, c = 0.90 and n = 21 is [tex]t_c=1.725[/tex].

The critical value is calculated as follows:

It is given that,

confidence level c = 0.90

sample size n = 21

Then,

degree of freedom,

(d.f) = n - 1 = 21 - 1 = 20

So, from the t-distribution table,

at d.f = 20 and the confidence level 0.90, the critical value is 1.725.

I.e., [tex]t_c[/tex] = 1.725

For this, α = (1 - 0.90)/2 = 0.05

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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:

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:

no mode

Step-by-step explanation:

no number appears more than once

therefore there is no mode

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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[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]

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

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 :-)

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The statements that apply to the algebraic expression are

The complete question is added as an attachment

The statement is given as:

Twice the difference of a number and six

Represent the number with n.

So, the statement becomes

Twice the difference of a n and six

Twice means 2 *

So, we have

2 * difference of a n and six

Express difference as minus i.e. -

So, we have

2 * (n - 6)

Hence, the expression is written as 2(n - 6)

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