Let f(x)= |x| and g(x) = x+2. What are the domain and range of (fog)(x)?

Answer:

x = 7

y = 8

Step-by-step explanation:

4y-4 = 28

4y = 32

y = 8

10x+65 = 135

10x = 70

x = 7

Answer:

Step-by-step explanation:

(4y-4)=28

4y=32

y=8

(10x+65)=135

10x=70

x=7

Answer:

240cm³

Step-by-step explanation:

First, let's assume the entire shape is full rectangular prism without that has the middle being cut out.

What this means is that, to get the volume of the solid made out of clay, we would calculate the solid as a full rectangular prism, then find the volume of the assumed middle cut-out portion. Then find the difference between both.

Let's solve:

Find the volume of the rectangular prism assuming the solid is full:

Volume of prism = width (w) × height (h) × length (l)

w = 4cm

h = 7cm

l = 3+6+3 = 12cm

Volume of full solid = 4*7*12 = 336cm³

Next, find the volume of the assumed cut-out portion using same formula for volume of rectangular prism:

w = 4cm

h = 7-3 = 4cm

l = 6cm

Volume of assumed cut-out portion = 4*4*6 = 96cm³

Volume of solid made from clay = 336cm³ - 96cm³ = 240cm³

Answer:

1:27 (D)

Step-by-step explanation:

Given:

Sphere A has a diameter of 2

Sphere A is dilated to create sphere B

Scale factor = 3

Volume of a sphere = 4/3 πr³

Radius = r = diameter/2 = 2/2

r = 1

Volume of sphere A = 4/3 ×π(1)³

Volume of sphere A = 4/3 × π

Volume of sphere B = 4/3 πR³

Since the diameter was dilated, the diameter of B = diameter of A × scale factor

diameter of B = 2×3 = 6

Radius of B = R = diameter/2 = 3

Volume of sphere B = 4/3 × π(3)³

Volume of sphere B = (4/3)(27)π

Ratio of the volume of sphere A to volume of sphere B

= [4/3 ×π]: [(4/3)(27)π]

= (4π/3)/[(4π/3)×27] = 1/27

= 1:27

Answer: 1:27

Step-by-step explanation:

The original volume * scale factor cubed = new volume.

The scale factor is 3 and 3^3 is 27, so the ratio is 1:27

Answer:

Step-by-step explanation:

The spread of the height of each person in the group depends on the standard deviation. A low standard deviation means that the heights are closer to the mean than that of a high standard deviation. If an individual is picked, the probability of picking one who is more than 68 inches tall is small as this depends on the number of individuals in this category. The probability of picking a sample of four people who average more than 68 inches tall would be higher since average would be taken. Therefore, it is more likely to pick a sample of four people who average more than 68 inches tall

Answer:

The required matrix is[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Step-by-step explanation:

Matrix of rotation:

[tex]P = \left[\begin{array}{ccc}cos\pi/4&-sin\pi/4\\sin\pi/4&cos\pi/4\end{array}\right][/tex]

[tex]P = \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

x' + iy' = (x + iy)(cosθ + isinθ)

x' = x cosθ - ysinθ

y' = x sinθ + ycosθ

In matrix form:

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos\theta&-sin\theta\\sin \theta&cos\theta\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

The matrix stretches by 1.8 on the x axis and 0.7 on the y axis

i.e. x' = 1.8x

y' = 0.7y

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

[tex]Q = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right][/tex]

According to the question, the result is rotated by pi/3 clockwise radians

[tex]R = \left[\begin{array}{ccc}cos(-\pi/3)& -sin(-\pi/3)\\-sin(\pi/3)&cos(\pi/3)\end{array}\right][/tex]

[tex]R = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right][/tex]

To get the matrix A, we would multiply matrices R, Q and P together.

[tex]A = RQP = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right] \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Answer: C

Step-by-step explanation:

We can automatically eliminate D because since both matrices are 2x2, the product exists.

[tex]\left[\begin{array}{ccc}1&5\\-3&4\end{array}\right] \left[\begin{array}{ccc}2&6\\6&-1\end{array}\right] =\left[\begin{array}{ccc}1*2+5*6&1*6+5*(-1)\\(-3)*2+4*6&(-3)*6+4*(-1)\end{array}\right]=\left[\begin{array}{ccc}32&1\\18&-22\end{array}\right][/tex]

Answer:

3x - 300

Step-by-step explanation:

Expand the brackets or use distribute law.

Answer:

solution,

[tex]3(x - 100) \\ = 3 \times x - 3 \times 100 \\ = 3x - 300[/tex]

hope this helps..

Answer:

Step-by-step explanation:

A standard normal probability distribution is a normal distribution that has a mean of zero and a standard deviation of 1.

Answer:

7.75

Step-by-step explanation:

6-4=2

2 times the square root of 3=3.46410161514

square root of 5 times 3.46410161514=7.74596669242

to 2dp=7.75

Answer/Step-by-step explanation:

Let's highlight the dimensions of the bedroom and living room using the information given in the question:

==>Squared Bedroom dimensions:

Side length = w = x ft

Area = x*x = x²

==>Rectangular living room dimensions:

width = side length of the squared bedroom = x

length = (x + 9) ft

Area = L*W = x*(x+9) = x² + 9x

Now let's match each given expression with what they represent:

==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"

As we have shown in the dimensions of the squared bedroom above.

==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room

==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"

i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.

==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".

i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x

Answer:

The answer is option B.

Step-by-step explanation:

Using the expression

[tex] {e}^{ ln(x) } = x[/tex]

[tex] {e}^{ ln(4) } = 4[/tex]

Hope this helps you

Answer:

A translation; (x,y) --> (x-4,y-5)

Step-by-step explanation:

This is because the figures are congruent and in the same orientation but just in different locations on the coordinate plane.

A(0,3) --> A'(-4,-2)

So, the rule is (x,y) --> (x-4,y-5)

Answer:

If r = 6 cm, the the circumference is c = 2π(6) = 12π cm

HOPE THIS HELPS AND PLS MARK AS BRAINLIEST

THNXX :)

Answer:

No solutions.

Step-by-step explanation:

5x = 8x^-1/3

Divide 8 into both sides.

5/8x = x^-1/3

Divide both sides by x.

5/8 = x^-4/3

Multiply both sides by the exponent -3/4.

5/8^-3/4 = x

1.422624 = x

Plug in 1.422624 for x to check.

It does not work. There are no real solutions.

Answer:

Step-by-step explanation:

Try this:

    1 wall                           1                   288

------------------------ =  ---------------  =  --------------- min  =  8 min

1 wall        1 wall         24 + 12                 36

(---------) + (---------)      ------------

12 min      24 min           288

Answer:

The population under consideration in the data set are all the adults in the United States.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

The population of interest are all the residents of New York State.

In this question:

Sample of 765 adults in the United states.

So the population under consideration in the data set are all the adults in the United States.

Answer:

140

Step-by-step explanation:

The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84

Answer:

the other person is correct!

Step-by-step explanation:

Answer:

V= 452.39cm³ (to 2 d.p. )

S.A. = 326.73cm² (to 2 d.p. )

Step-by-step explanation:

Vcylinder = π r² h = π (4)² (9) = 144 π = 452.3893421cm³ = 452.39cm³ (to 2 d.p. )

S.A. cylinder = 2π r h + 2π r² = 2π (4)(9) + 2π (4)² = 104π = 326.725636cm² = 326.73cm² (to 2 d.p. )

Answer:

26,400 N

Step-by-step explanation:

PLEASE CHECK ATTACHMENT FOR COMPLETE SOLUTION

Answer:

The description is provided following.

Step-by-step explanation:

The given question is incomplete. The complete question will be:

                                     Brain tumors                      No Brain tumors

Cell Phones                          63                                          185

No Cell Phones                    96                                          292                  

The further explanation is given below.

a...

Subjects with these symptoms/diseases are recognized as "cases." Consequently, the majority of the instances would be as follows:

⇒  [tex]63+96[/tex]

⇒  [tex]159[/tex]  

b...

Subjects who might not have the disorder or infection are classified as "controls." Therefore, the amount of controls is as follows:

⇒  [tex]185+292[/tex]

⇒  [tex]477[/tex]

c...

The proportion of control and monitoring of instances:

⇒  [tex]\frac{478}{159}[/tex]

⇒  [tex]3.006[/tex]

Using the percentage concept, it is found that 51% of 10th graders surveyed preferred robotics, hence option B is correct.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, we have that 33% out of 65% of the students are 7th graders who preferred robotics, hence the percentage is given by:

[tex]P = \frac{33}{65} \times 100\% = 51%[/tex]

Which means that option B is correct.

More can be learned about percentages at https://brainly.com/question/14398287

#SPJ1

Answer:

It's A. 61% The dude above me is wrong.

Step-by-step explanation:

I just took the test

Answer:

x=-2

Step-by-step explanation:

2 times -2=-4+3=-1

Answer:

[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]

Step-by-step explanation:

Sample space, n = 100

Let the number of students signed up for CSE 311 = a

Let the number of students signed up for CSE 312 = b

Let the number of students signed up for CSE 331 = c

Let the number of students signed up for CSE 332 = d

Probability of taking CSE 311, [tex]P_a[/tex] = 0.3

Probability of taking CSE 312, [tex]P_b[/tex] = 0.4

Probability of taking CSE 331, [tex]P_c[/tex] = 0.1

Probability of taking CSE 332, [tex]P_d[/tex] = 0.2

[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]

Answer:

(5x + 6) (x² + 5)

Step-by-step explanation:

5x³ + 6x² + 25x + 30

= x² (5x + 6) + 25x + 30    -- Group 5x³ and 6x²

= x² (5x + 6) + 5 (5x + 6)    -- Group 25x and 30

= (5x + 6) (x² + 5)  -- Both terms have a common factor of 5x + 6

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

[tex]x - h = 4\cdot p \cdot (y-k)^{2}[/tex]

Where:

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

[tex]p[/tex] - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

[tex]p = x_{D} - x_{V}[/tex]

[tex]p = \frac{1}{48}-0[/tex]

[tex]p = \frac{1}{48}[/tex]

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

Answer:

Answer is Y

Step-by-step explanation:

Answer:

In that year approximately 2114 thousand people visited the park.

Step-by-step explanation:

Since the expression [tex]y(x) = -7.5*x^2 + 103*x + 2142[/tex] models the number of visitors in the park, where x represents the number of years after 2007 and 2021 is 14 years after that, then we need to find "y" for that as shown below.

[tex]y(14) = -7.5*(14)^2 + 103*14 + 2142\\y(14) = -7.5*196 + 1442 + 2142\\y(14) = -1470 + 3584\\y(14) = 2114[/tex]

In that year approximately 2114 thousand people visited the park.

Answer:

99% chance tommy has it

Step-by-step explanation:

cuz do da math