Consider the functions f (x )equals negative 9 x plus 3 and g (x )equals negative one ninth (x minus 3 ). ​(a) Find​ f(g(x)). ​(b) Find​ g(f(x)). ​(c) Determine whether the functions f and g are inverses of each other.

Answer:

Step-by-step explanation:

mean weight of baby = 4090 gms

standard deviation = √ 313600

= 560

z value = deviation / standard deviation

= 43 / 560

= .0767

Answer:

3.56 cm

Step-by-step explanation:

Cube is a 3D closed structure in which each adjacent side is perpendicular to each other and every side is equal to each other.

Let the side of cube be [tex]a[/tex] cm.

Please refer to attached image of cube for a clear look and feel of a cube with each side = a units.

Then, volume of cube is given by the formula:

[tex]V = a^3[/tex]

Here, we are given that:

[tex]V = 45\ cm^3[/tex]

[tex]\Rightarrow a^3 = 45\ cm^3\\\Rightarrow a =\sqrt[3] {45}\\\Rightarrow a ={45}^\frac{1}{3}\\\Rightarrow a = 3.56\ cm[/tex]

So, the answer is, Side of each petit four is, [tex]a = 3.56\ cm[/tex].

Answer:

Σx = 96

Σx² = 4280

Σy = 99

Σy² = 2593

Step-by-step explanation:

For this question, different values of x and corresponding values of y are provided.

X: 28 0 20 14 20 35 24 -11 -17 -17

Y: 18 -4 13 14 28 17 27 -6 -7 -1

X²: 784 0 400 196 400 1225 576 121 289 289

Y²: 324 16 169 196 784 289 729 36 49 1

Σx is the sum of all the variables given for x.

Σx = 28+0+20+14+35+24-11-17-17 = 96

Σx² is the sum of all the individual squares of each x-variable.

Σx² = 784+0+400+196+400+1225+576+121+289+289 = 4280

Σy is the sum of all the variables given for y.

Σy = 18-4+13+14+28+17+27-6-7-1 = 99

Σy² is the sum of all the individual squares of each y-variable.

Σy² = 324+16+169+196+784+289+729+36+49+1 = 2593

The attached image contains a spreadsheet of these variables, better shown, the squares, the sum, the sum of the squares and even a regression analysis is shown in the attached image.

Hope this Helps!!!

Answer:

[tex]0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419[/tex]  

[tex]0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481[/tex]  

And the 95% confidence interval would be given (0.419;0.481).   And the best option would be:

b. .419 to .481

Step-by-step explanation:

We know the following info:

[tex]n = 1000[/tex] sample size selected

[tex]X= 450[/tex] represent the number of people who favored Candidate AT

The sample proportion would be:

[tex]\hat p=\frac{450}{1000}=0.45[/tex]

The confidence interval would be given by this formula  

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]  

For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.  

[tex]z_{\alpha/2}=1.96[/tex]  

And replacing into the confidence interval formula we got:  

[tex]0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419[/tex]  

[tex]0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481[/tex]  

And the 95% confidence interval would be given (0.419;0.481).   And the best option would be:

b. .419 to .481

Answer:

48620

Step-by-step explanation:

There are 6 fruits and 18 non-fruits.  Cory wants to buy all 6 fruits, and 9 of the 18 non-fruits.

The number of ways he can choose 6 fruits from 6 is ₆C₆ = 1.

The number of ways he can choose 9 non-fruits from 18 is ₁₈C₆ = 48620.

The total number of combinations is 1 × 48620 = 48620.

Answer:

0.2613

Step-by-step explanation:

Use binomial probability.

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

P = ₇C₂ (0.6)⁵ (0.4)²

P = 0.2613

Answer:

8 hours

Step-by-step explanation:

because each hour that goes by the buses go a distance of 117 miles apart from each other (53+64) you must divide the total distance by the 117 mph distance for a total of 8 hours (936 / 117 = 8)

Answer:

8 hours

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

4 + 5 > 8

Answer:

yes

Step-by-step explanation:

For the lengths given to form a triangle, then the sum of any 2 sides must be greater than the measure of the third side.

4 + 5 = 9 > 8

4 + 8 = 12 > 5

5 + 8 = 13 > 4

The inequality theorem is true thus the 3 lengths form a triangle.

Answer:

Step-by-step explanation:

[tex]\sqrt{x-2}+8=x\\\\\sqrt{x-2}=x-8\\[/tex]

Square both sides,

[tex]x-2=(x-8)^{2}\\\\x-2=x^{2}-2*x*8+8^{2}\\\\x-2=x^{2}-16x+64\\\\x^{2}-16x+64=x-2\\\\x^{2}-16x+64-x+2=0\\\\x^{2}-17x+66=0[/tex]

Sum = - 17

Product = 66

Factors = -6 , -11

x² - 6x -11x + (-6)*(-11) = 0

x(x - 6) -11(x - 6) = 0

(x-6) (x - 11) = 0

x -6 = 0   ; x - 11 = 0

x = 6   ; x =11

Here,  x = 6 is a extraneous solution

When x = 1, the expression evaluates to 2/3.

When x = 4/9, the expression evaluates to 1.

When x = 1 1/3, the expression evaluates to 3/5.

Let's evaluate the expression 4/15 ÷ x + 0.4 for each given value of x.

1) When x = 1:

4/15 ÷ 1 + 0.4 = 4/15 + 0.4 = 4/15 + 6/15 = 10/15 = 2/3

So, when x = 1, the expression evaluates to 2/3.

2) When x = 4/9:

4/15 ÷ (4/9) + 0.4 = 4/15 * (9/4) + 0.4 = 36/60 + 0.4 = 3/5 + 0.4 = 3/5 + 2/5 = 5/5 = 1

So, when x = 4/9, the expression evaluates to 1.

3) When x = 1 1/3 (or 4/3):

4/15 ÷ (4/3) + 0.4 = 4/15 * (3/4) + 0.4 = 12/60 + 0.4 = 1/5 + 0.4 = 1/5 + 2/5 = 3/5

So, when x = 1 1/3, the expression evaluates to 3/5.

Learn more about expression here

https://brainly.com/question/16922619

#SPJ2

Answer:

0.77777777777...

Step-by-step explanation:

7/9 = 7 divided by 9

7 divided by 9 = 0.77777777777...

Answer:

Each tent site is 1/12 acre

Step-by-step explanation:

1/2 acre for tents divided by 6

1/2 ÷6

Copy dot flip

1/2 * 1/6

1/12

Each tent site is 1/12 acre

Answer:

StartFraction 1 Over 12 EndFraction acre

Step-by-step explanation:

Campground area= 1/2 acre

Campsite area= 1/6*1/2= 1/12 acre

Scarlett's campsite is same as others= 1/12 acre

Answer:

surface area = 74π

Step-by-step explanation:

The surface are of a cylinder is the sum of the area of the 2 circular base and the curved surface area.

A cylinder has 2 circular base and the curved surface region. Mathematically,

surface area = area of 2 circles + curved surface area

area of  2 circles = πr² + πr² = 2πr²

curved surface area = 2πrh

surface area = 2πr² + 2πrh

surface area = 2πr(r + h)

where

r = radius

h = height

assuming the r = 12 cm and h = 25 cm

Therefore, replacing the value in the formula

surface area = 2πr(r + h)

surface area = 2π(12 + 25)

surface area = 2π(37)

surface area = 74π

Answer:

1/8 of the buckets

Step-by-step explanation:

There's one X for 1 1/2 cups which is greater than 1 1/4 cups but less than 1 3/4 cups. There are 8 pieces of data in total so our answer is 1/8 of the buckets.

Answer:

tan 45° = 1 = true

cos 30° = 1/2 = false

sin 45° = 1/3 = false

sin 90° = 0 = false

Step-by-step explanation:

Answer:

0 < x < 8

Step-by-step explanation:

| x-4| < 4

There are two solutions one positive and one negative.  Remember to flip the inequality on the negative solution

x-4 <4     and   x-4 > -4

Add 4 to each side

x -4+4 <4+4   and x-4+4 > -4+4

x < 8 and x > 0

0 < x < 8

open circles at 0 and 8 and a line connecting them

Answer:

Part 1

a) Greatest possible weight range of gorillas = 60 kg.

b) 20 gorillas weigh 80 kg or less.

c) Midpoint weight of the modal group = 105 kg.

d) The estimate of the mean gorilla weight = 99 kg.

Part 2

a) The greatest range of the lengths of snakes = 250 cm.

b) 40 snakes have lengths between 1.5 m and 2.5 m.

c) Midpoint length of the modal group = 175 cm.

d) The estimate of the mean gorilla length = 154 cm.

Step-by-step explanation:

Part 1 - The Gorilla part

a) Greatest possible weight range of gorillas = (Maximum weight of gorillas on the table) - (Minimum weight of gorillas on the table)

= 120 - 60 = 60 kg

b) How many gorillas weigh 80 kg or less

6 gorillas weigh between 60 < W ≤ 70

14 gorillas weigh between 70 < W ≤ 80

So, 6 + 14 = 20 gorillas weigh 80 kg or less.

c) Midpoint weight of the modal group

To find the modal class, we first use (n+1)/2 th

where N = number of variables = 160

Modal weight will be (160+1)/2 = 80.5 weight

The 80.5th weight is in the 100 to 110 class. This is how we know

6 + 14 + 22 + 34 = 76

Indicating that the 80.5th weight is in the next class (100 < W ≤ 110)

The midpoint weight of the modal class is then

(100+110)/2 = 105 kg

d) To calculate the mean weight, we use the midpoint theory where we replace all the groups with the midpoint weight of each weight class.

Midpoint weight is W, frequency is f

W | f

65 | 6

75 | 14

85 | 22

95 | 34

105 | 40

115 | 44

The mean is given as

Mean = (Σfx)/(Σf)

Σfx = (65×6) + (75×14) + (85×22) + (95×34) + (105×40) + (115×44) = 15800

Σf = 160

Mean = (15800/160) = 98.75 kg = 99 kg to the nearest whole number.

Part 2 - The Snake part

a) Greatest possible range of lengths of snakes = (Maximum length of snakes on the table) - (Minimum length of snakes on the table)

= 250 - 0 = 250 cm

b) How many snakes are between 1.5 m and 2.5 m in length?

1.5 m = 150 cm, 2.5 m = 250 cm

19 snakes have lengths between 150 < L ≤ 200

21 snakes have lengths between 200 < L ≤ 250

So, 19 + 21 = 40 snakes have lengths between 1.5 m and 2.5 m

c) Midpoint length of the modal group

To find the modal class, we first use (n+1)/2 th

where N = number of variables = 72

Modal length will be (72+1)/2 = 36.5th length

The 36.5th length is in the 150 to 200 class. This is how we know

4 + 11 + 17 = 32

Indicating that the 36.5th length is in the next class (150 < L ≤ 200)

The midpoint length of the modal class is then

(150+200)/2 = 175 cm

d) To calculate the mean length, we use the midpoint theory where we replace all the groups with the midpoint length of each length class.

Midpoint length is L, frequency is f

L | f

25 | 4

75 | 11

125 | 17

175 | 19

225 | 21

The mean is given as

Mean = (Σfx)/(Σf)

Σfx = (25×4) + (75×11) + (125×17) + (175×19) + (225×21) = 11100

Σf = 72

Mean = (11100/72) = 154.167 cm = 154 cm to the nearest whole number.

Hope this Helps!!!

Answer:

Step-by-step explanation:

in a square pyramid the base area plus the area of the triangular faces is equal to the total area so we take (9*5) *1/2=22.5 then we multiply 22.5 *4= 90 so we take 90 + 5*5 = 115 so the total area is 115

Answer:

  dh/dt ≈ 0.55 ft/min

Step-by-step explanation:

The volume is given by the formula ...

  V = (1/3)πr²h

We have r = h/2, so the volume as a function of height is ...

  V = (1/3)π(h/2)²h = (π/12)h³

Then the rates of change are related by ...

  dV/dt = (π/4)h²·dh/dt

  dh/dt = (4·dV/dt)/(πh²) = 4(35 ft³/min)/(π(9 ft)²)

  dh/dt ≈ 0.55 ft/min

Answer:

35

Step-by-step explanation:

Angle 4 and angle 2 are alternate interior angles.

Alternate interior angles are equal.

Answer:

m∠2 = 35°

Step-by-step explanation:

∠4 is the corresponding angle to the angle right of ∠3. The angle right of ∠3 is vertical to ∠2, so they are both congruent. Therefore, m∠2 = 35°

You can also use the Alternate Interior Angles Theorem to state that ∠4 and ∠2 are congruent.

Answer:

It’s a 1/2 chance it’s heads.

Step-by-step explanation:

Because there’s two sides

Answer:

1/2

Step-by-step explanation:

The probability of getting heads is 1 out of 2.

1/2

When you flip a coin, you either get heads or tails.

Hey there! :)

Answer:

P(factor of 40) ≈ 66.7%

Step-by-step explanation:

Begin by finding factors of 40 on the die:

1, 2, 4, 5.

Find probability of a factor of 40:

[tex]\frac{factors}{total}[/tex]

There are 4 possible factors on a 6-sided die. Therefore:

[tex]\frac{4}{6} = \frac{2}{3}[/tex]

Convert to percentage:

2/3 × 100 ≈66.7%. This is the probability for a factor of 40.

An angle is the intersection of two noncollinear rays at a common endpoint. The rays are called sides and the common endpoint is called the vertex.

Answer:

Step-by-step explanation:

Let x represent the walking rate of the cyclist.

If the cycling rate was four times the walking rate, it means that the cycling rate is 4x mph.

Time = distance/speed

Time spent during cycling is

Time = 40/4x = 10/x

Time spent during walking is

5/x

Since the total time spent cycling and walking is 5 hours, it means that

10/x + 5/x = 5

Cross multiplying by x, it becomes

10 + 5 = 5x

5x = 15

x = 15/5

x = 3

The cycling speed is 4x = 4 × 3 = 12 mph

Answer:

A

Step-by-step explanation:

ITS A

Answer:

On a coordinate plane, the point (0, 3) is graphed. Also known As A .

Step-by-step explanation:

The answer is A ,I just did the test and got it correct .

Answer:

The answer is C.

Step-by-step explanation:

[tex]50-x^2=0[/tex]

[tex]x^2=50[/tex]

[tex]x=\pm \sqrt{50} =\pm \sqrt{25*2}=\pm 5\sqrt{2}[/tex]

The answer is C (I am assuming that it isn't 5/2).

Answer:

The least squares regression minimizes the sum of squared differences between actual and predicted y-values. This is the last option in your list of possible answers.

Step-by-step explanation:

Recall that when one performs the least square regression, one deals with what are called the "residuals". These are the differences in between the predicted "y-value" from the best fitting function, and the actual value of the dependent variable plotted (the actual y-value of the plotted points)

What the least square regression does is to find the best function parameters that minimize the sum of these squared residuals.

Answer:

4) 69

Step-by-step explanation:

Nos dicen que en una fiesta hubo 25 ordenes mas de coca cola que de pepsi y que en total fueron 113 pedidos, por lo tanto:

Sea C pedidos de coca cola

Sea P pedidos de pepsi

C + P = 113

C = P + 25

Reemplazamos:

P + 25 + P = 113

2*P = 113 - 25

P = 88/2

P = 44

Ahora para saber el numero de pedidos de coca cola:

C = 44 + 25

C = 69

Lo que quiere decir que fueron 4) 69 pedidos la respuesta correcta.

Answer:

Step-by-step explanation:

The tangent lines meet the radii at 90 degrees.

The way the diagram is drawn, the following formula will work

<AOB + <OAC + OBC + 10 = 360

<OAC = 90

<OBC = 90

<AOB + 90 + 90 + 10 = 360

<AOB + 190 = 360

<AOB = 360 - 190

<AOB = 170

Answer:

(C)12 Units

Step-by-step explanation:

Triangle WRS has points W(0, -1), R(1.75, 1.5), and S(5, -1).

[tex]WR=\sqrt{(1.75-0)^2+(1.5-(-1))^2}=\dfrac{\sqrt{149}}{4}[/tex]

[tex]WS=\sqrt{(5-0)^2+(-1-(-1))^2}=\sqrt{25}=5[/tex]

[tex]RS=\sqrt{(5-1.75)^2+(-1-1.5)^2}=\dfrac{\sqrt{269}}{4}[/tex]

Perimeter of Triangle WRS

[tex]= \dfrac{\sqrt{149}}{4}+5+\dfrac{\sqrt{269}}{4}\\\approx 12$ Units[/tex]

Answer:

c

Step-by-step explanation:

took it on edge