The Carter family just left the local pet store with Rex, their new family dog. The pet store owner told the Carter family that for the next 6 months, Rex would grow at an average rate of 9 pounds per month. Currently, Rex is 2 months old and weighs 6 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 6 Part A: Complete the given table that represents Rex’s current weight, in pounds, as a function of his age, in months Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. Part D: If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old? Upload your table, graph, and solution below.

The area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

It is defined as the four-sided polygon in geometry having four edges and four corners. It has one pair of opposite congruent angles and the diagonals of a kite are perpendicular.

We have a quadrilateral shown in the picture.

The diagonal divides the quadrilateral into two triangles

The area of the quadrilateral = area of the triangle ADC + area of the

                                                   triangle ADB

= (1/2)3.42×4.39 + (1/2)5.44×3.42

= 7.5069 + 9.3024

= 16.80 square units

Thus, the area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

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None of the options is true.

Three Different, Regular tessellation is formed 1. if we join regular polygons of side 3, called equilateral triangle,2. Regular polygon of side 4, called Square, and 3. Regular polygon of side,6 called hexagon,

to form a pattern.

A polygon is said to be regular if all interior angles and all sides are equal.

The regular polygon of side 3, when joined together can be named: 3.3.3.

The regular polygon of side 4, when joined together can be named 4.4.4.

The regular polygon of side 6, when joined together can be named 6.6.6.

So, a regular tessellation is formed, from a regular polygon having,3,4, and 6 Sides.

None of the sides of the polygon, which is given in the option, can be used to form a regular tessellation.

None of the options is true.

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Answer:

y = -7x

Explanation:

Take two points from table: (-4, 28), (-3, 21)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope\ (m): \dfrac{21-28}{-3-(-4)} = -7[/tex]

Now find equation:

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

[tex]\rightarrow \sf y - 21 = -7(x - (-3))[/tex]

[tex]\rightarrow \sf y = -7(x +3) + 21[/tex]

[tex]\rightarrow \sf y = -7x -21 + 21[/tex]

[tex]\rightarrow \sf y = -7x[/tex]

Slope

Equation of line

The question is incomplete. Below you will find the missing figure.

Two friends, Andrew and Liz, are playing a game using this spinner. If the

spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?

A. Yes. Each friend has a 1/4 probability of winning.

B. Yes. Each friend has a 1/6 probability of winning.

C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.

D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.

The correct option is Option A: Yes. Each friend has 1/4 probability of winning.

Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.

P = no. of favorable outcome/ total no. of outcome

Here given in the question,

If the spinner touches region 2 or 3, Andrew wins

If the spinner touches region 4, Liz wins.

This is fair play because both have the same size of region for winning.

If we cut the circle into 8 pieces,

as region 1 is the sum of 2 sub-parts of the circle,

possibility of spinner touching region 1= 2/8= 1/4

possibility of spinner touching the small region = 1/8

So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4

Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4

possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4

Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.

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Answer: Length = 9 cm, Width = 6 cm

Step-by-step explanation:

L - 3 + L - 3 + L + L = 30

2L - 6 + 2L = 30

4L - 6 = 30

4L = 36

L = 9

Length = 9 cm

Width = 9-3 = 6 cm

Answer:

width = 10 cm

Step-by-step explanation:

the ratio of width to length is 2 : 5 = 2x : 5x ( x is a multiplier )

the perimeter (P) of a rectangle is calculated as

P = 2 × width + 2 × length

given P = 70 then

2(2x) + 2(5x) = 70

4x + 10x = 70

14x = 70 ( divide both sides by 14 )

x = 5

Then

width = 2x = 2 × 5 = 10 cm and length = 5x = 5 × 5 = 25 cm

Answer: [tex]\frac{5\pi}{3}[/tex]

Step-by-step explanation:

[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]

The probability that the person has an IQ greater than 120 is 0.2524 of 25.24%

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

probability that the person has an IQ greater than 120,

P(x >120)

= P(Z > 120-100/ 15)

= P(Z > 0.667)

 P(x >120) = 1-  P(Z <  0.667)

                  = 1-0.7476

                 = 0.2524

                = 25.24%

Hence, the probability is 0.2524.

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Answer:

A.

Step-by-step explanation:

The parabola opens down, so the "a" value (the number in front of x^2) must be negative. The y-intercept is (0, 5) so the constant must be positive 5.

Answer:

first option

Step-by-step explanation:

[tex]\frac{(2g^5)^3}{(4h^2)^3}\\= \frac{8g^1^5}{64h^6} \\= \frac{g^1^5}{8h^6}[/tex]

The correct answer is option B which is 3

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

Given data:-

4,3,2

The mean will be calculated as:-

Mean = (4 + 3 + 2) / 3

Mean =  9 / 3

Mean = 3

Therefore the correct answer is option B which is 3

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Answer:

Step-by-step explanation:

[tex] \bf {x}^{2} + 5x + 6 = 0[/tex]

Write the equation in factored form.

[tex]\bf (x + 2)(x + 3) = 0[/tex]

Separate equations, and set each factor to zero.

[tex]\bf x + 2 = 0[/tex]

[tex]\bf x + 3 = 0[/tex]

Rearrange and isolate the variable to find the solutions

[tex]\bf x = - 2[/tex]

[tex]\bf x = - 3[/tex]

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

Answer:

x=-3           x=-2

Step-by-step explanation:

x^2 +5x+6 =0

We need to factor the equation

What two numbers multiply to 6 and add to 5

3*2 = 6

3+2 =5

(x+3)(x+2)

Using the zero product property

x+3 =0  x+2 =0

x=-3           x=-2

Answer:

[tex]\frac{2}{3}|2-x|=\frac{1}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5} + \frac{2}{3} |2-x| = \frac{4}{15} \\\\\frac{1}{5}*(\frac{3}{3}) = \frac{3}{15}\\\\\frac{3}{15}-\frac{3}{15} + \frac{2}{3}|2-x| =\frac{4}{15}-\frac{3}{15}\\\\\frac{2}{3}|2-x|=\frac{1}{15}[/tex]

[tex](6^-^8)^4[/tex]

[tex]=6^-^2^4[/tex]

[tex]=\frac{1}{6^2^4}[/tex]

Therefore,

We know that :

Substituting the values :

>> V = π × (7 / 2)^2 × 8

>> V = π × (49 / 4) × 8

>> V = π × 49 × 2

>> V = 98π

Henceforth,

We know , the volume of a cylinder is given by the formula – πr²h, where r is the radius of the cylinder and h is the height.

Therefore, putting the values, we get,

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: {r}^{2}h[/tex]

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \times \: \bigg(\frac{7}{2} \bigg)^{2} \: \times \: 8 \\ [/tex]

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{2} \: \times \: 8 \\ [/tex]

[tex] \Large \mathcal \purple {Volume } \large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{ \cancel2} \: \times \: \cancel{8} \: ^{ \orange4} \\ [/tex]

[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{ \cancel2} \: \times \: {7} \: \times \: \cancel4 \: ^{ \orange2} \\ [/tex]

[tex] \\ \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: 7 \: \times \: 7 \: \times \: 2[/tex]

[tex]\Large \mathcal \purple {Volume }\ \large\red\implies \tt \large \:\pi \: \times \: 49 \: \times \: 2[/tex]

[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:98 \:\pi[/tex]

Hence , the volume of cylinder is 98 pi

Answer:

[tex]\text{B}) \text{ } -3 < x < -1\\\text{D}) \text{ } 2 < x < \infty[/tex]

Step-by-step explanation:

The graph lies below the x-axis.

Answer:

First figure out the angle measure of CBA and DBE to find out what Angle measure of ABE is.

Angle CBA and DBE are vertical angles, meaning they are congruent.

so set the equation as:

(2x+21)=(5x)

21=5x-2x

21=3x

x=7

It doesn't matter in which angle you plug 7 you get the same angle measure, so : 5x=5(7)=35 degrees

So to find angle measure of ABE:

We know that ABE and DBE form linear pair, so

180-35=145 degrees

145 degrees is the answer.

Hope it helps!

Answer:

∠ABE = 145°

Step-by-step explanation:

because angle CBA and ABE form a straight line, we know that they must add together to 180 degrees

and because DBE and ABE also form a straight line/angle, they must add together to 180 degrees

we can set this up as a system of equations (I will be writing ABE as "y")

2x + 21 + y = 180

5x + y = 180

We can combine this to beL

2x + 21 + y = 5x + y

 - 2x              -2x

21 + y = 3x + y

   - y       - y

21 = 3x

x = 7

If we plug this back into our original equations (which is set to 180 degrees), we can find y

2(7) + 21 + y = 180

14 + 21 + y = 180

35 + y = 180

- 35       - 35                  

y = 145

(remember, "y" is angle ABE)

we can check this value (ABE = 145) by substituting our second equation

5(x) + ABE = 180

35 + 145 = 180

       180 = 180

(TRUE)

so, the measure of ∠ ABE is 145°

hope this helps!!

Step-by-step explanation:

[tex] \sqrt{10} = 3.2 \\ then \: the \: sign \: there \: is \: = \\ \sqrt{10 } = 3.2 \\ \\ \: \sqrt{12} = 3.5 \\then \: the \: sign \: there \: is \: = \\ \: \sqrt{12} = 3.5 \\ \\ 6 \frac{1}{3} = 6.3 \: and \: \sqrt{40 } = 6.3 \\ therefore \: 6 \frac{1}{3} = \sqrt{40} \\ \\ 2 \frac{2}{5} = 2.4 \: and \: \sqrt{5.76} = 2.4 \\ then \: \: 2 \frac{2}{5} = \sqrt{5.76} \\ \\ 5 \frac{1}{6} = 5.16 \: and \: 516 \: \: therefore \: \\ 5 \frac{1}{6} = 5.16 \\ \\ \sqrt{6.2} = 2.5 \\ and \: 2.4 \: therefore \: \\ \sqrt{6.2} > 2.4[/tex]

Answer:

8x + 100

Step-by-step explanation:

Your answer is correct! But because the equation is already set to "y =", you do not need the "f(x)" in your equation.

The count of patients needing a blood transfusion can be modelled as a continuous distribution.

A continuous distribution is a distribution that can take on an infinite number of possible values. A continuous distribution is not defined at specific values. The number of patients can be 1 or 10 or 50 or even 0.

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Answer: 4.2%

Step-by-step explanation:

Multiplying these, we get (1/6)(1/4), which is about 4.2%

A function assigns the values. The correct option is C, x=-6.

A function assigns the value of each element of one set to the other specific element of another set.

A.) When the value of x is -12,

f(-12) = 2/3(-12) + 7 = -1

g(-12) = 2(-12) + 15 = -9

B.) When the value of x is -9,

f(-9) = 2/3(-9) + 7 = 1

g(-9) = 2(-9) + 15 = -3

C.) When the value of x is -6,

f(-6) = 2/3(-6) + 7 = 3

g(-6) = 2(-6) + 15 = 3

D.) When the value of x is -3,

f(-9) = 2/3(-3) + 7 = 5

g(-9) = 2(-2) + 15 = 11

Hence, the correct option is C, x=-6.

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The probability that both are smokers is 6903/180000

The given parameters are:

Male smoker = 177

Female smoker = 78

Total student = 78 + 522 = 600

The probability of a male smoker is

P(Male) = 177/600

The probability of a female smoker is

P(Female) = 78/600

The probability that both are smokers is

P(Smoker) =P(Male) *P(Female)

So, we have:

P(Smoker) = 177/600 * 78/600

Simplify

P(Smoker) = 177/600 * 39/300

Evaluate the product

P(Smoker) = 6903/180000

Hence, the probability that both are smokers is 6903/180000

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Answer:

(4, -3)

Step-by-step explanation:

A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)

The cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.

a. Cost of goods sold

Cost of Goods Sold=Beginning Inventories + Purchases – Ending Inventories

Cost of goods sold = $1,997 + $10,392 - $2,131

Cost of goods sold = $10,258

b. Cash paid to supplier

Cash paid=2015 Beginning balance  + Purchases - 2015 Ending balance

Cash paid = $1,181 + $10,392 - $1,126

Cash paid = $10,447

Therefore the cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.

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Answer: Right iscoleces triangle

Step-by-step explanation: The square on the left bottom side means it is a right angle. The lines means that a side is congruent to the other side. By definition, iscoleces triangles have two congruent sides, so this must be it.

Answer:

right isosceles

Step-by-step explanation:

the right angle and the two sides that are equal make the triangle a right isosceles

Answer:

The plots are (0,2) (1,-1)

Step-by-step explanation:

a slanted line starting from top left corner ending in the bottom right

Answer:

vector VW= w - v

vector WV= v - w

Step-by-step explanation:

there are no figures to solve the question so i'll just write the formula..

vector VW= w - v

vector WV= v - w

The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the function f(x) = x² + 6x + 7. This is a quadratic equation,that is of degree two.

The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.

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