Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k. Two lines labeled f(x) and g(x). Line f(x) passes through points (-4, 0) and (-3, 1). Line g(x) passes through points (-4, 0) and (-3, -3).
A.) 3
B.) 1/3
C.) -1/3
D.) −3

Answer:

3

Step-by-step explanation:

27^1/3 = cuberoot(27) = 3

Answer:

-The value of [tex]y[/tex]:

[tex]y = 1[/tex]

Step-by-step explanation:

-Find the value of [tex]y[/tex]:

[tex]11- 9y = -6y + 8[/tex]

-Add both sides by [tex]6y[/tex] and combine [tex]9y[/tex] and [tex]6y[/tex] together:

[tex]11- 9y + 6y = -6y + 6y+ 8[/tex]

[tex]11 - 3y = 8[/tex]

-Subtract both sides by [tex]11[/tex]:

[tex]11 - 11 - 3y = 8 -11[/tex]

[tex]-3y = -3[/tex]

-Divide both sides by [tex]-3[/tex]:

[tex]\frac{-3y}{-3} = \frac{-3}{-3}[/tex]

[tex]y = 1[/tex]

So the final answer is [tex]y = 1[/tex] .

Answer: 0.007

Step-by-step explanation:

Suppose that you have a ticket.

We have 3 prizes, and 300 tickets.

After the first tiket is drawn, someone win a prize, so now we have 299 tikets left and 2 prizes left.

Then, for the next draw, you have p = 1/299 of wining a prize.

If you did not win there, the probability for the third price is p = 1/298 (because there are 2 less tickets now)

Then the probability of winning at least one prize is:

P = 1/299 + 1/298 = 0.007

Answer:

Step-by-step explanation:

[tex]100 (0.96)^{25} =[/tex] around 36.04

Answer:

14.2% students

Step-by-step explanation:

279 / 1960 = 0.142

0.142 x 100% = 14.2 %

Answer:[tex]y=-\frac{3}{2} x+12[/tex]

Step-by-step explanation:

Perpendicular lines have inversely proportional slopes. So make the slope negative and switch it to its reciprocal.

2/3x would change into -3/2x

Lets write that down for a starting point for our perpendicular line.

y = -3/2x + b

We were given the x and y value via the coords. x = 12 and y = -6

Now we have -6 = -3/2(12) + b. Multiply -3 and 12 to get -36, then divide by 2 to get -18.  Now it's -6 = -18 + b. Solve for b by adding 18 to both sides to get b = 12

Answer:

(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.

(b) Roughly 16% of vehicle speeds exceeded 57 mph.

Step-by-step explanation:

We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.

For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.

Let X = vehicle speed at impact

SO, X ~ Normal([tex](\mu=42,\sigma^{2} = 15^{2}[/tex])

Here, [tex]\mu[/tex] = population average speed = 42 mph

         [tex]\sigma[/tex] = standard deviation = 15 mph

Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;

(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;

68% data values will lie between [ [tex]\mu-\sigma , \mu+\sigma[/tex] ] , i.e;

        [ [tex]\mu-\sigma , \mu+\sigma[/tex] ]  =  [42 + 15 , 42 - 15]

                                 =  [57 , 27]

So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.

(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.

It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.

This means that roughly 16% of vehicle speeds exceeded 57 mph.

Answer:

5,610 Miles

Step-by-step explanation:

To solve this you would need to multiply the average miles by how many tanks of gas she will use.

374 * 15 = 5,610

So, Eleanor can drive 5,610 miles with 15 tanks of gas.

Answer: recantagle

Step-by-step explanation:

Answer:

Length = 550 m

Width = 275 m

Area = 151,250 m2

Step-by-step explanation:

One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:

[tex]Perimeter = Length + 2*Width = 1100\ m[/tex]

And the area of the farmland is given by:

[tex]Area = Length * Width[/tex]

From the Perimeter equation, we have that:

[tex]Length = 1100 - 2*Width[/tex]

Using this in the area equation, we have:

[tex]Area = (1100 - 2*Width) * Width[/tex]

[tex]Area = 1100*Width - 2*Width^2[/tex]

Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:

[tex]Width = -b/2a[/tex]

[tex]Width = -1100/(-4)[/tex]

[tex]Width = 275\ m[/tex]

This width will give the maximum area of the farmland. Now, finding the length and the maximum area:

[tex]Length = 1100 - 2*Width = 1100 - 550 = 550\ m[/tex]

[tex]Area = Length * Width = 550 * 275 = 151250\ m2[/tex]

Answer:

only allow 3 decimals

90.284 is the answer we removed all others except for 3

Answer:

0.9940

Step-by-step explanation:

P(at least 1) = 1 − P(zero)

P(at least 1) = 1 − (1 − 0.64)⁵

P(at least 1) = 1 − (0.36)⁵

P(at least 1) = 0.9940

The probability that at least one of them has been vaccinated is 0.9939.

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. It helps to check the probability of getting “x” successes in “n” independent trials of a binomial experiment.

For the given situation,

Number of people vaccinated = 64% = 0.64

The formula of binomial distribution is

[tex]P(x:n,p) = nC_{x} p^x (1-p)^{n-x}[/tex]

Here x is the number of successes, x ≤ 1

n is the number of trials, n = 5

p is the probability of a success on a single trial, p = 0.64 and

where, [tex]nC_{x}=\frac{n!}{x!(n-x)!}[/tex]

The probability is [tex]P(X \leq 1)=1-P(X=0)[/tex]

[tex]P(X=0)= 5C_{0} (0.64)^{0} (1-0.64)^{5-0}[/tex]

⇒ [tex]P(X=0)= 1(1) (0.36)^{5}[/tex]

⇒ [tex]P(X=0)= 0.0060[/tex]

Thus, [tex]P(X \leq 1)=1-P(X=0)\\[/tex]

⇒ [tex]P(X \leq 1)=1-0.0060[/tex]

⇒ [tex]P(X \leq 1)=0.9939[/tex]

Hence we can conclude that the probability that at least one of them has been vaccinated is 0.9939.

Learn more about binomial distribution here

https://brainly.com/question/27939234

#SPJ3

Answer:

103.5

Step-by-step explanation:

Multiply x on both sides

xtan12 = 22

Now divide tan12 to isolate x

x = (22) / (tan(12))

Now we know that calculator should be in degree mode because the answer choices do not have the radian mode answer. When your calculator is in Degree mode and you calculate this value you get approximately 103.5

The value of x if tan 12 = 22/x is 103.5

Given the trigonometric expression:

tan 12 = 22/x

We need to get the value of "x"

Cross multiply

x tan12 = 22

x = 22/tan12

x = 22/0.2126

x = 103.529

Hence the value of x if tan 12 = 22/x is 103.5

Learn more here: https://brainly.com/question/25618616

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

Answer:

Option 4: at the vertices of the feasible region.

I completed the quiz

Answer:

at the vertices of the feasible region

Step-by-step explanation:

this is the correct answer

hope i helped

Answer:

Step-by-step explanation:

WITH THE GIVEN DATA

A ) using regression to investigate the relationship between the number of fatal accidents and the percentage of drivers under the age pf 21

to fit into a regression line we must have ∝ and β

where β = [tex]\frac{S_{xy} }{S_{xx} }[/tex]   = 0.2871

and ∝ = y - βx   =  - 1.5974

regression line = ∝ + β * x

insert values into regression line equation

regression line = -1.5974 + 0.2871 * x

we can conclude that for every single unit of : x, y would be increased by 0.2871.  and intersection of x and y will be through =1.5974

B ) conclusion and recommendations can you derive from your analysis

it  can be  concluded that they are strongly positively correlated. There is strong and positive correlation between them. i.e the number of fatal accidents and the drivers under the age of 21

using the correlation coefficient  ( r ) = [tex]\frac{S_{xy} }{\sqrt{S_{xx}*S_{xy} } }[/tex]    = 0.8394

Answer:

0.8394

Step-by-step explanation:

.

Answer:

  parallel lines both have slope 1/3; non-parallel lines both have length 5

Step-by-step explanation:

It generally works well to follow instructions.

A graph of the points shows you that the parallel sides are RA and PT. The difference between the end points of these segments are ...

  A - R = (6, 8) -(-3, 5) = (9, 3) = (Δx, Δy)

So, the slope of RA is Δy/Δx = 3/9 = 1/3

And the other difference and slope are ...

  P -T = (9, 4) -(-3, 0) = (12, 4)   ⇒   Δy/Δx = 4/12 = 1/3

The slope of RA is the same as the slope of PT, so those segments are parallel.

__

The length of segment TR can be found from the differences of the end point coordinates:

  R - T = (-3, 5) -(-3, 0) = (0, 5)

Since these points are on the same vertical line, this tells us the segment length is 5.

The other difference of coordinates is ...

  A - P = (6, 8) -(9, 4) = (-3, 4)

The distance formula tells us the length of AP is then ...

  AP = √((-3)² +4²) = √25 = 5

Non-parallel sides TR and AP have the same lengths, so the trapezoid is isosceles.

Answer:

Graph 2

Step-by-step explanation:

You can see that all the shaded numbers are above negative 25 in that graph. Hope this helped!

Answer:

220

Step-by-step explanation:

If we lost 12% we still have 100 - 12 = 88% of the employees left. 88% can be written as 0.88. 0.88 * 250 = 220 employees left.

Answer:

Here are the formulas

Cube/Rectangular Prism:

Volume = Length*width*height

Surface area = 2(wl+hl+hw)

Lateral area= Area of vertical faces

Base area = length*width

Regular hexagonal prism:

Volume : (3sqrt3/2)*a^2*h

Surface Area  = 6ah+3sqrt(3)a^2

lateral area: 6ah

base area = 3sqrt(3)s^2/2

Triangular prism

Volume: The volume of a triangular prism can be found by multiplying the base times the height.

Surface area: A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.

Etc.

Answer:

A) 13/20

Step-by-step explanation:

65% in simplest form,

65/100

= 13/20 (Divided by five)

Answer:

[tex]\frac{13}{20}[/tex].

Step-by-step explanation:

We can begin by converting 65% to a fraction over 100. 65% converts to 0.65, or [tex]\frac{65}{100}[/tex].

We can simplify this down. Both 65 and 100 share a common factor of 5, which allows us to produce a new fraction:

[tex]\frac{65}{100} = \frac{13}{20}[/tex]

Therefore, the simplified version is [tex]\frac{13}{20}[/tex].

Answer:

x = -6

Step-by-step explanation:

-2/3x + 9 = 4/3x - 3

First we need to simplify to where we have x on one side and a constant (number not connected to a variable) on the other side.

Subtract 4/3x from both sides:

-2/3x + 9 - 4/3x = -3

-6/3x + 9 = -3

Now subtract 9 from both sides:

-6/3x + 9 - 9 = -3 - 9

-6/3x = -12

Now turn -6/3 into a whole number to make things more simple:

-6/3 = -2

-2x = -12

Now divide both sides by -2 to get x by itself

-2x/-2 = -12/-2

x = -6

Answer:

0

Step-by-step explanation:

In a suit of 52 cards

The experiment consists of drawing 1 card from the standard deck.

Since diamonds are red, there is no black jack of diamonds.

Therefore:

P(drawing a black jack of diamonds)

[tex]=\dfrac{0}{52}\\\\ =0[/tex]

Answers:

In photo below

Explanation:

I got it correct in my test :)

Answer:

[tex]y=50x+75[/tex]

Step-by-step explanation:

When writing a linear equation from a graph, we need to find two things: the y-intercept (what y is when x is 0) and the slope.

First, let us find the y-intercept.

To do this, we can just look at the graph. When x=0, y=75, so 75 is our y-intercept, which is also known as b.

To find the slope of this line, we will need to look at two points

We already know that (0,75) is a point. From the graph, we can see that (1,125) is also a point on this line.

Now, we can find the slope of this line using the following formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{125-75}{1-0} \\\\m=\frac{50}{1} \\\\m=50[/tex]

Now that we have both the y-intercept and slope, we can put them together in the form of [tex]y=mx+b[/tex]

[tex]y=50x+75[/tex]

Answer:

Slope: 50

Equation: y = 50x + 75

Step-by-step explanation:

Take two points:

(2,175)

(3,225)

Find the slope:

225 - 175/3 - 2

50/1 = 50

So we get this equation:

y = 50x + b

Now to find b, insert one of those points from before back in:

175 = 50(2) + b

175 = 100 + b

b = 75

So the equation is:

y = 50x + 75

Answer:

The bottom left table

Step-by-step explanation:

the same x value cannot have different y values

Answer:

√130 is the distance between (9,-3) (0,-10)

Answer:

C

Step-by-step explanation:

Measure of Arc FED = 51+79

= 130°

Since the measures of arcs and angles are the same

Hence

<FED = 130°

Answer:

Eve gets 1.47 and Amelie gets 0.81

Step-by-step explanation:

the ratio is 9 to 5 so we can say 9x + 5x=2.28

14x=2.28

x=0.16

so eve gets 9x = 9(2.28/14) = 1.47

and amelie gets 5x = 5(2.28/14) = 0.81

Answer:

B. The radius

Step-by-step explanation:

The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle so we need to know the radius for it

Answer:

Air resistance

Step-by-step explanation:

Air resistance is a type of friction that occurs when air pushes against a moving object causing it to negatively accelerate

Answer:

Air resistance

Step-by-step explanation:

Air resistance is a type of friction that occurs when air pushes against a moving object causing it to negatively accelerate.