For what values of x is f(x) =-2x - 3 increasing? For what
values of x is it decreasing?

A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".

These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).

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Answer:

How many pink erasers do the students in your class have?

Answer:

Linear Pair Theorem

Step-by-step explanation:

Linear Pair Theorem:

If two angles form a linear pair, then they are supplementary, and the sum of their measures is 180°.

Answer:

1/1

Step-by-step explanation:

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

just start at like 220 i am pretty sure

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

\(\frac{4x}{4} = \frac{64}{4}\)

x = 16

Answer: -6x + 15 < 10-5x and the numberline with the 5---->

Step-by-step explanation:

Solving -3(2x-5) < 5(2-x)

Distribute the -3 to the 2x giving you -6x and -3 to the -5 giving you 15.

Distribute 5 to 2 giving you 10 and 5 to -x ginving you -5x.

Then just solve -6x+15 < 10-5x

                          +6x             +6x

10+x > 15

-10     -10

x>5

The numberline with the postive 5 is the correct answer.

Answer: c d

Step-by-step explanation:

Functions can be used to model real life scenarios

The function is given as:

\(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

(a) Sketch V(t)

See attachment for the graph of \(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

(b) The reasonable domain

t represents the number of weeks.

This means that: t cannot be negative.

So, the reasonable domain is: \(\mathbf{[0,\infty)}\)

(c) Average rate of change from t = 0 to 2

This is calculated as:

\(\mathbf{m = \frac{V(a) - V(b)}{a - b}}\)

So, we have:

\(\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}\)

\(\mathbf{m = \frac{V(2) - V(0)}{2}}\)

Calculate V(2) and V(0)

\(\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}\)

\(\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}\)

So, we have:

\(\mathbf{m = \frac{20 - 0}{2}}\)

\(\mathbf{m = \frac{20}{2}}\)

\(\mathbf{m = 10}\)

Hence, the average rate of change from t = 0 to 2 is 20

(d) The instantaneous rate of change using limits

\(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

The instantaneous rate of change is calculated as:

\(\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}\)

So, we have:

\(\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}\)

\(\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}\)

Expand

\(\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}\)\(\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}\)

Subtract V(t) from both sides

\(\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}\)

Substitute \(\mathbf{V(t) = -t^3 + t^2 + 12t}\)

\(\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}\)

Cancel out common terms

\(\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}\)

\(\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}\) becomes

\(\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}\)

\(\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}\)

Limit h to 0

\(\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}\)

\(\mathbf{V'(t) = -3t^2 + 2t + 12}\)

(e) V(2) and V'(2)

Substitute 2 for t in V(t) and V'(t)

So, we have:

\(\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}\)

\(\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}\)

Interpretation

V(2) means that, 20 people were infected after 2 weeks of the virus spread

V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week

(f) Sketch the tangent line at (2,V(2))

See attachment for the tangent line

The slope of this line is:

\(\mathbf{m = \frac{V(2)}{2}}\)

\(\mathbf{m = \frac{20}{2}}\)

\(\mathbf{m = 10}\)

The slope of the tangent line is 10

(g) Estimate V(2.1)

The value of 2.1 is

\(\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}\)

\(\mathbf{V(2.1) = 20.35}\)

(h) The maximum number of people infected at the same time

Using the graph, the maximum point on the graph is:

\(\mathbf{(t,V(t) = (2.361,20.745)}\)

This means that:

The maximum number of people infected at the same time is approximately 21.

The rate of infection at this point is:

\(\mathbf{m = \frac{V(t)}{t}}\)

\(\mathbf{m = \frac{20.745}{2.361}}\)

\(\mathbf{m = 8.79}\)

The rate of infection is 8.79 people per week

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Given:

The graph of a function.

To find:

The domain and range of the given function.

Solution:

Domain: It is the set of input values.

Range: It is the set of output values.

From the given graph, it is clear that the function is defined for all real values of x because it is a downwards parabola. So, domain is the function is the set of all real number.

\(Domain=\{x|x\in R\}\)

\(Domain=(-\infty,\infty)\)

The function is maximum at point (0,7). So, the maximum value of the function is 7. So, the range of the function is the set of all real numbers less than or equal to 7.

\(Range=-\infty<y\leq 7\)

\(Range=(-\infty,7]\)

Therefore, the domain of the function is \((-\infty,\infty)\) and the range of the function is \((-\infty,7]\).

Answer:

The probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

Step-by-step explanation:

We have a cube, with the faces painted black, that each side is divided in 5, so we end up with 125 cubes.

We have to calculate the probability that a randomly selected cube is rolled and the face on the top is black.

This probability is equal to the proportion of black area in the total area of the cube.

We can define the side of the original cube as A=5a, being a the side of the small cubes.

The area that is painted black is equal to the sum of 6 squares of side A. In terms of a, that is:

\(S_b=6\cdot A^2=6\cdot(5a)^2=6\cdot25a^2=150a^2\)

The total area of the 125 small cubes is:

\(S=125(6a^2)=750a^2\)

Then, the ratio of black surface to the total surface is:

\(s_b/s=(150a^2)/(750a^2)=0.2\)

Then, we can conclude that the probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

At the district competition for 5th grade jump-roper of the year, the mean number of jumps, rounded to the nearest hundredth is 242.83 and the median number of jumps is 265

The mean can be calculated as follows:

Observations (the number of jumps each student without pausing was counted); There were 24 observations

Mean is calculated by adding all of the observations together.

Mean = (203 + 245 + 237 + 233 + 90 + 100 + 100 + 277 + 265 + 264 + 265 + 285 + 288 + 291 + 291 + 290 + 300 + 224 + 200 + 257 + 290 + 279 + 266 + 288)/24

Mean = 5828/24

Mean = 242.83

to figure out the median;

The observations must first be put into either ascending or descending order.

Ordered in descending order

90, 100, 100, 200, 203, 224, 233, 237, 245, 257, 265, 265, 265, 266, 277, 279, 285, 288, 288, 290, 290, 291, 291, 300

Given that there have been 24 observations (an even number).

The middle number, 265 and 265 at the midway of items 12 and 13, is used to calculate the median.

The average of these figures is then determined.

Median = 1/2 (265 + 265)

Median = 265

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here's half of them:

1: 15 - (3r) = 6

2: q + 4f = 29

3: \(n^{2}\) + 12 = p/4

4: 0.5j - 5 = k + 13

for the rest, just know that:

sum means addition

times/product means multiplying

quotient means division

less than means subtraction

The distance between E and the bottom of the tree, given the distance above the ground, is 7 m.

We are told that the tree is midway between points E and F. We are also told that points E and F are 14 meters away from each other.

The distance between E and the bottom of the tree would be half of the distance between E and point F because the tree is located midway between both points.

The distance between E and the bottom of the tree is therefore:

= 14 / 2

= 7 m

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Answer:5.666666667

Step-by-step explanation:

Answer:

-9 and -10

Step-by-step explanation:

x + x+1=-19

2x+1=-19

2x=-19-1

2x=-20

x=-10

x+1

-10+1=-9

Answer:

\(-9\)

\(-10\)

Step-by-step explanation:

\(x+x+1=-19\)

\(2x+1=-19\)

\(2x=-19-1\)

\(2x=-20\)

\(x=-20 \div 2\)

\(x=-10\)

\(x+x+1=-19\)

\(x+1=-19-x\)

\(-10+1=-19-(-10)\)

\(-9=-19+10\)

\(-9=-9\)

The center of the circle is (13, 2)

The radius of the circle is 9

To find the center and radius of the circle described by the equation:

(x + 13)² + (y + 2)² = 81

We can compare with the standard form of the equation of the circle which is

(x - h)² + (y - k)² = r²

it can be deduced that

-h = 13, h = -13

-k = 2, k = -2

r² = 81, r = 9

This is the equation for a circle with center at (13, 2) and radius 9. So the center of the circle is (13, 2) and the radius is 9.

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Answer:

Center = (-13,-2)
Radius = 9

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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Answer:

d = 115.4 mi

Step-by-step explanation:

Since it gives us the distance in between the locations, we simply label the distances:

From the Garbage to the Hotel is 58.3 miles.

From the Hotel to the Hardware Store is 57.1 miles.

We are trying to find the distance from the Garbage to the Hardware Store, we simply add the distances between:

58.3 mi + 57.1 mi = 115.4 mi

Answer:

He will be at a loss of $160

Explanation:

Here, we want to check if he can get the profit or loss

If the purchase price is $1000, 40% of this is $400, and that makes the initial asking price as $1,400

He was unable to sell and decide to reduce his asking price by 40%

That would be:

The difference between the final sales price and the cost price will be:

What that simply means is that he will be at a loss of $160

Answer:

The correct option is D

D) She may not be correct because means cannot be determined from the box plots

Step-by-step explanation:

The question is incomplete because the box plots are not attached in the question. I've attached the box plots of this question at the bottom.

The box plot, also know as box and whisker plot, displays only five type of values, which are:

Mean cannot be determined by just lookin at the box plots. To find the mean, we need to know the values of data and total number of values.

As mean cannot be determined from the box plot, correct option is D

Answer:

D

Step-by-step explanation:

Box plots do not show the value of the mean.

Answer:

7· 5n + 55 ≥ 100 is required inequality

Step-by-step explanation:

Let he visit be theater x time

→ for new movie ticket

→55+7·5xn≥100

→7·5n+55≥100

Hence, 7· 5n + 55 ≥ 100 is required inequality  

Answer:

Inequality: 7.5v+55≥100

Answer: v≥6

Step-by-step explanation:

Have a good day :)

The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.

The given polynomial expression is 3x² + 3bx - 6x - 6b.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factors of given polynomial can be find using grouping method, that is

(3x² + 3bx) - 6x - 6b

=3x(x+b)-6(x+b)

=(x+b)(3x-6)

=3(x-2)(x+b)

The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.

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Answer:

-1,0

Step-by-step explanation:

We have to put values of domain to find range

\(\\ \ast\sf\longmapsto y=3x+1\)

\(\\ \ast\sf\longmapsto D_R=[-1,0,1]\)

\(\\ \ast\sf\longmapsto y=3(-1)+1=-3+1=-2\)

\(\\ \ast\sf\longmapsto y=3(0)+1=0+1=1\)

\(\\ \ast\sf\longmapsto y=3(4)+1=12+1=13\)

Now

\(\\ \ast\sf\longmapsto R_R=[-2,1,13]\)

75=14y+5

or, -14y=5-75

or, -14y = -70

or, y = -70/-14 = 5

The answer is 5.

Answer: Slove for the y in 75

= (14y + 5)

Then subsitute the y = 5 into 75 = (14y + 5)

75 = 75

Since 75 = 75 is redudat information , this seems to be a dependent system.

Infinitely Many solutions.

According to the information we can infer that the parallel line would be AD or CF. Additionally, the perpendicular lines would be CB or FE.

To identify the parallel lines we must look at the figure and find the lines that have the same direction as the line BE and that would never intersect with the segment BE, according to the above, we can infer that the parallel lines would be:

On the other hand, the lines perpendicular to CF would be CB or FE because they make 90° angles with segment CF. Additionally, the face that would be parallel to ABC is DEF.

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Kirk can spend $695.89 each month.

Given that Kirk worked hard over the summer and saved $3,251.35 to live on during the next two semesters of school, and Kirk will receive a scholarship each semester for $1,157.9, to determine, if he plans to use up all of his savings while at school, how much money can Kirk spend each month, on average, for things like groceries, entertainment, and miscellaneous items, assuming two semesters equals 8 months total, the following calculation must be made:

Therefore, Kirk can spend $695.89 each month.

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Answer:

Kirk can spend $695.89 each month.

Step-by-step explanation:

There are 28 units in total between the first and last clothespin.

The resulting displacement may be measured using the distance. It represents the distance between the two places. It may be measured using a variety of units, including meters and centimeters.

The specified parameter is shown as intervals in the query. The phrase can be written as follows:

There are 15 total clothespins.

The distance between clothing pegs is 2 feet.

No, the following is the distance from the initial location to the last one:

0 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 28 units

There are 28 units in total between the first and last clothespin.

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