Scott is driving to visit family. After 3 hours of driving, Scott traveled 180 miles. After driving for 5 hours at the same rate, he traveled 300 miles. Which equation represents this situation

Answer:   [tex]\dfrac{7}{1,337,220}=5.2\times 10^{-6}[/tex]

Step-by-step explanation:

Order does not matter so it is a Combination.

There are 14 men and we are going to choose 12 --> ₁₄C₁₂

There are 27 people and we are going to choose 12  --> ₂₇C₁₂

[tex]\dfrac{_{14}C_{12}}{_{27}C_{12}}\rightarrow\dfrac{14!}{(14-12)!}\div \dfrac{27!}{(27-12)!}=\large\boxed{\dfrac{7}{1,337,220}}[/tex]

Probabilities are used to determine the chances of an event

The probability of selecting 12 males is: [tex]\frac{7}{1337220}[/tex]

The parameters are given as:

[tex]n = 24[/tex] --- sample size

[tex]Male = 14[/tex]

[tex]Female = 13[/tex]

[tex]r = 12[/tex] ---- number of jury pool

The number of ways of selecting 12 members of the jury, from a total of 27 is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{27}C_{12} = \frac{27!}{(27 - 12)!12!}[/tex]

[tex]^{27}C_{12} = \frac{27!}{15! \times 12!}[/tex]

[tex]^{27}C_{12} = 17383860[/tex]

The number of ways of selecting 12 members of the jury, from a total of 14 male is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{14}C_{12} = \frac{14!}{(14 - 12)!12!}[/tex]

[tex]^{14}C_{12} = \frac{14!}{2! \times 12!}[/tex]

[tex]^{14}C_{12} = 91[/tex]

So, the probability of selecting 12 males is:

[tex]Pr = \frac{^{14}C_{12}}{^{27}C_{12}}[/tex]

[tex]Pr = \frac{91}{17383860}[/tex]

Simplify

[tex]Pr = \frac{91/13}{17383860/13}[/tex]

[tex]Pr = \frac{7}{1337220}[/tex]

Hence, the required probability is: [tex]\frac{7}{1337220}[/tex]

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Answer:

The graph of g( x ) is the graph of f(x) stretched vertically by a factor of 2.

Option C is the correct option.

Step-by-step explanation:

Solution,

f ( x ) = 2ˣ

g ( x ) = 2 ( 2 ˣ )

2 is multiplied with f(x)

2 is greater than 1

so, Vertical stretch by a factor of 2.

Option C is correct.

Hope this helps...

Best regards!!

We want to compare the functions f(x) and g(x), given that we know that g(x) is a transformation of f(x).

The correct option is B, "the graph of g(x) is the graph of f(x) stretched vertically by a scale factor of 2."

Here we know that:

f(x)  =2^x

g(x) = 2*f(x) = 2*2^x

First, remember that a general vertical dilation/stretch of scale factor k is written as:

g(x) = k*f(x)

So only by that and knowing that g(x) = 2*f(x), we can conclude that the graph of g(x) is the graph of f(x) dilated/stretched vertically by a scale factor of 2.

Then the correct option is B, "the graph of g(x) is the graph of f(x) stretched vertically by a scale factor of 2."

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Answer:

C.  y = 1

Step-by-step explanation:

For two line to be parallel, they have to have the same slope.  The slope for the equation y = 4 is 0.  This cancels out answer choices A, B, and D.  

A and B have an undefined slope since they are vertical lines.

D has a slope of 4.

Also, the line has to go through the point (-3, 1).  Since the line has a slope of 0, the equation will include the y-value.  The y-value for this point is 1.  This gives you an answer of y = 1.

Answer:

y = 1

Step-by-step explanation:

Just took the practice test and got it right

Answer:

B. y > 2/3x + 1

Step-by-step explanation:

To find slope we'll use the following formula,

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

(-3,-1) (3,3)

3 - -1 = 4

3 - -3 = 6

2/3x

The y intercept is 1,

we know this because that's the point the line touches the y axis.

Thus,

the answer is B. y > 1/3x + 1.

Hope this helps :)

The graph of the solution of an inequality is given .

The graph represents the inequality is [tex]y>\frac{2}{3} x+1[/tex]

Option B

Given :

The graph of an inequality. To find the inequality for the given graph we use linear equation [tex]y=mx+b[/tex]

where m is the slope and b is the y intercept

To find out slope , pick two points from the graph

(-3,-1) and (3,3)

[tex]slope =\frac{y_2-y_2}{x_2-x_1} =\frac{3+1}{3+3} =\frac{2}{3} \\m=\frac{2}{3}[/tex]

Now we find out y intercept b

The point where the graph crosses y axis is the y intercept

The graph crosses y axis at 1

so y intercept b=1

The linear equation for the given graph is

[tex]y=\frac{2}{3} x+1[/tex]

Now we frame the inequality . we use test point that lies inside shaded region

Lets take (4,5)

[tex]y=\frac{2}{3} x+1\\5=\frac{2}{3} (4)+1\\5=3.6\\5>3.6\\y>\frac{2}{3} x+1[/tex]

The inequality for the given graph is

[tex]y>\frac{2}{3} x+1[/tex]

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Answer: The rule of complements is apprising us that, the person selected will.eithwr have a type B blood or will not have a type B blood

Step-by-step explanations:

Find explanations in the attachment

Answer:

[tex]z=(-\sqrt{3}+i)^6[/tex] = -64

Step-by-step explanation:

You have the following complex number:

[tex]z=(-\sqrt{3}+i)^6[/tex]       (1)

The Demoivres theorem stables the following:

[tex]z^n=r^n(cos(n\theta)+i sin(n\theta))[/tex]      (2)

In this case you have n=6

In order to use the theorem you first find r and θ, as follow:

[tex]r=\sqrt{3+1}=2\\\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30\°[/tex]

Next, you replace these values into the equation (2) with n=6:

[tex]z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64[/tex]

Then, the solution is -64

Answer:

A) -64

Step-by-step explanation:

Edge 2021

Answer:

200.52 in^2

Step-by-step explanation:

to find the area of a circle, you square 6 and multiply it by pi in this case 3.14.

that gives you 113.04 but because this is only a half circle, it is 56.52 in^2.

Next, you need to find the rectangle. multiply 12(length) by 12(Width) to get 144 add 144 to 56.52 to get 200.52.

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Answer: A) 15

Step-by-step explanation:

Because of Pythagorean Theorem, 9^2+12^2=BC^2.  Thus, 81+144=BC^2.  Thus, 225=BC^2.  Thus, 15=BC.

Hope it helps, and ask if you want further clarification <3

x^3 - 3x^2 - 18x

Using the FOIL method, I arrived at my solution!

Answer:

Side length: 3 cm.

Surface area: 54 cm squared.

Step-by-step explanation:

The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.

So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.

There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.

Hope this helps!

Answer:

A) $0.11

Step-by-step explanation:

Since a dozen (12) eggs cost $1.35. You will divide $1.35 by 12. And it will equal 0.1125. Round it up it equals to 0.11.

Shortest is Vindale to Wildgrove to Clarksville

18.9 + 13.2 = 32.1 km.

Find attached to this answer the diagram of the Quadrilateral

Question:

If ABCD is a parallelogram, AD = 14, EC = 11, m∠ABC = 64°, m∠DAC = 71°, and m∠BDC = 25, find each measure.

a) BC =

b) AC =

c) m∠DAB =

d) m∠ABD =

e) m∠ACD =

f) m∠ADB =​

Answer:

a) BC = 11

b) AC = 22

c) m∠DAB = 116°

d) m∠ABD = 39°

e) m∠ACD = 45°

f) m∠ADB =​ 25°

Step-by-step explanation:

a) BC

In the question above, EC = 11

We can see that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Quadrilateral.

Hence, In a quadrilateral ABCD,

EC = BC

Hence BC = 11

b) AC

AC is one of the diagonal lines that divided parallelogram ABCD

AC = BC + EC

AC = 11 + 11

AC = 22

c) m∠DAB

m∠ABC = 64°

m∠ADC = 64°

For the two angles above, a diagonal bisects through those angles.

Also the sum of angles in a triangle = 180°

Hence,

180° = 1/2m∠ABC + 1/2m∠ADC +

m∠DAB

m∠DAB = 180° - ( 1/2 (64) + 1/2(64))

m∠DAB = 180 ° - 64°

m∠DAB = 116°

d) m∠ABD

Since,

m∠ABC = 64° and m∠BDC = 25

m∠ABC = m∠BDC + m∠ABD

64 = 25+ m∠ABD

m∠ABD = 64° - 25°

m∠ABD = 39°

e) m∠ACD

In the above question,

m∠ABC = 64°,

m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral are congruent and equal to each other.

Hence, m∠ADC = 64°

m∠DAC = 71°,

In a triangle , all the angles in a triangle = 180°

Hence,

180° = m∠DAC + m∠ADC + m∠ACD

180° = 71° + 64 ° + m∠ACD

m∠ACD = 180° -(71 + 64)°

m∠ACD = 180° - 135°

m∠ACD = 45°

f) m∠ADB

Since

m∠DAB = 116°

m∠ABD = 39°

The sum of angles in a triangle = 180°

180° = m∠ABD + m∠DAB + m∠ADB

180° = 39 ° + 116° + m∠ADB

m∠ADB = 180° - ( 116 + 39)°

m∠ADB = 25 °

a) BC = 11

b) AC = 22

c) m∠DAB = 116°

d) m∠ABD = 39°

e) m∠ACD = 45°

f) m∠ADB =​ 25°

Given : AD=14 , EC=11, m∠ABC= 64°, m∠DAC=71° and m∠BDC=25°

To find:  BC =?  , AC =? , m∠DAB =?, m∠ABD =?  ,m∠ACD =?  ,m∠ADB =​?

Consider the figure given below ABCD is a parallelogram

To find a) BC

Given, EC = 11

As seen in figure that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Parallelogram.

Hence, In a Parallelogram ABCD,

EC = BC

Hence BC = 11

To find b) AC

AC is one of the diagonal lines that divided parallelogram ABCD

AC = BC + EC

AC = 11 + 11

AC = 22

To find c) m∠DAB

Given, m∠ABC = 64°

m∠ADC = 64°

(For the two angles above, a diagonal bisects through those angles)

Also From Angle sum property;

Hence,

180° = 1/2m∠ABC + 1/2m∠ADC +  m∠DAB

m∠DAB = 180° - ( 1/2 (64) + 1/2(64))

m∠DAB = 180 ° - 64°

m∠DAB = 116°

To find d) m∠ABD

Since,

m∠ABC = 64° and m∠BDC = 25  

m∠ABC = m∠BDC + m∠ABD

64 = 25+ m∠ABD

m∠ABD = 64° - 25°

m∠ABD = 39°

To find e) m∠ACD

Given,  m∠ABC = 64°;

m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral (here parallelogram) are congruent and equal to each other

Hence, m∠ADC = 64°

m∠DAC = 71°,

In a triangle , all the angles in a triangle = 180°(Angle sum property)

Hence,

180° = m∠DAC + m∠ADC + m∠ACD

180° = 71° + 64 ° + m∠ACD

m∠ACD = 180° - (71 + 64)°

m∠ACD = 180° - 135°

m∠ACD = 45°

To find f) m∠ADB

Since  ,m∠DAB = 116°  and m∠ABD = 39°

From Angle sum property;

180° = m∠ABD + m∠DAB + m∠ADB

180° = 39 ° + 116° + m∠ADB

m∠ADB = 180° - ( 116 + 39)°

m∠ADB = 25 °

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Answer: not enough data shown to proceed with this question

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Let s be the price of snickers, g the price of galaxy and k the price of kitkat.

●For Mariam the equation will be:

8 s + 3 g + 3k = 8

●For Zainab the equation will be:

4 s + 9 g + 4 k = 10.9

Take the first equation and divide both sides by 4 to make it easier.

You get:

● 2s + 0.75 g + 0.75k = 2

Take the second equation and divide both sides by 2 to make easier.

You get:

● 2s + 4.5g + 2k = 5.45

The new system of equation is:

● 2s +0.75g + 0.75k = 2

● 2s + 4.5g + 2k = 5.45

Express s in the first equation using the other variables.

● 2s +0.75g +0.75k = 2

● 2s + 0.75(g+k) = 2

● 2s = 2-0.75(g+k)

● s = 1- 0.325 (g+k)

Replace s by the new expression in the second equation:

●2 [1-0.325(g+k)] +4.5 g +2k = 5.45

●2-0.75(g+k) +4.5g + 2k = 5.45

●2- 0.75g -0.75k +4.5 g +2k = 5.45

●2+ 3.75g + 1.25k = 5.45

● 3.75g +1.25k = 3.45

We have eliminated one variable (s)

We will keep (3.75g+1.25k=3.45) and use it.

Now that we eliminated in the second equation do it again in the first one.

You will get a system of equations with two variables.

Solve it and replace g and k with the solutions.

Finally solve the equation and find s.

Answer: C. p = p

Step-by-step explanation:

A tautology is a statement that is always true.

A. p = q

This is not always true. Counterexample: p = 1 & q = 2

B. p = q

This is the same as A (above)

C. p = p

This is ALWAYS true!

D. q = p

This is the same as A but in reverse order.

Answer:

The 95%   confidence interval is   [tex]768.44 < \mu <777.55[/tex]

Step-by-step explanation:

From the question we are told that  

    The  sample size is n = 48

    The sample mean is  [tex]\= x = 773 \ lb[/tex]

     The standard deviation is  [tex]\sigma = 16.1 \ lb[/tex]

Now given that the confidence level is  95% , then the level of significance is mathematically represented as

          [tex]\alpha = 100 - 95[/tex]

          [tex]\alpha = 5 \%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the  critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is

              [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The reason we are obtaining critical values of   [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (   [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while

[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error

 The  margin of error is mathematically represented as

      [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

     [tex]MOE = 1.96 * \frac{ 16.1 }{ \sqrt{48} }[/tex]

     [tex]MOE = 4.555[/tex]

The 95% confidence interval to estimate the mean breaking weight for this type cable is mathematically evaluated as

      [tex]\= x - MOE < \mu < \= x - MOE[/tex]

substituting values

    [tex]773 - 4.555 < \mu < 773 + 4.555[/tex]

     [tex]768.44 < \mu <777.55[/tex]

Answer:

288 possible seating arrangements.

Step-by-step explanation:

There are 4 possible choices for the first seat.

There are 3 possible choice for the sixth seat.

There are 4 possible choices for the second seat.

There are 3 possible choices for the third seat.

There are 2 possible choices for the fourth seat

There is only 1 possible choices for the fifth seat.

4×3×4×3×2×1=

12×4×3×2×1=

48×3×2×1=

144×2×1=

288×1=

288 possible seating arrangements.

Answer:

7.8 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 48 = x/7

7 tan 48 = x

7.774287604 = x

To the nearest tenth

7.8 =x

Answer:

An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5

Step-by-step explanation:

Start at 0 and move 3 units to the left since it is negative

Move 1.5 units to the left since we are subtracting

We end up at - 4.5

Answer:

An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5

Step-by-step explanation:

-3 is also 0-3

arrow goes from 0 to -3 backwards.

arrow goes from -3 to -4.5 because -3-1.5=-4.5

Answer:

C = 150S + 3,500.

$6,050.

Step-by-step explanation:

It costs $3,500 to rent the trucks, so your constant/y-intercept will be $3,500.

It will cost $150 for every ton of sugar, so your slope will be $150.

You then have your equation:

C = 150S + 3,500.

If you were to transport 17 tons of sugar...

C = 150 * 17 + 3,500

C = 2,550 + 3,500

C = $6,050.

Hope this helps!

Answer:

C = $6050

Equation:

To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:

[tex]3500+150(S)=C[/tex]

3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.

Solving the equation

To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.

[tex]3500+150(17)=C[/tex]

150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.

C = $6050

Answer:

5 1/7

Step-by-step explanation:

To find the mean, add up all the numbers and then divide by the number of numbers

(10+ 6+ 9+ 6+ 2+ 0+ 3)/7

The sum of all the numbers is 36 and there are 7 numbers

36/7 =

7 goes into 36  five times with 1 left over

5 1/7

Answer:

5.143

Step-by-step explanation:

Add them all up then divide by the amount of numbers there are.

Answer:

X+3=-5

Step-by-step explanation:

Once you solve the initial equation for x, you will find that the value for x is -8. You can confirm this by doing 2^-5, which will in turn give you 1/32.

Once you know the value of x, you can plug it into the equation and see which one is true, which in this case is the first one, because -8+3 gives you -5

Answer:

b

Step-by-step explanation:

Altitude- 0n- hypotenuse theorem

(leg of big Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse ), that is

x² = (30 - 6) × 30 = 24 × 30 = 720 ( take square root of both sides )

x = [tex]\sqrt{720}[/tex]

  = [tex]\sqrt{144(5)}[/tex] = [tex]\sqrt{144}[/tex] × [tex]\sqrt{5}[/tex] = 12[tex]\sqrt{5}[/tex] → b

Answer:

A:-4

Step-by-step explanation:

If you simplify 9(2x+1)<9x-18 you will get 9x<-27. That will mean x<-3 and the only answer for something less than -3 is -4.

If the answer was right, please put 5 stars.

Answer:

The answer would be-4

Step-by-step explanation:

Here,

9(2x+1) < 9x-18

or, 18x+9 < 9x-18

or, 18x-9x<-18-9

or, 9x<-27

or, x= -27/9

Therefore, the value of x is -4.

Hope it helps...

Answer:

In 10 years she'll have approximately $21865.4 in her account.

Step-by-step explanation:

When an amount is compounded continuously its value over time is given by the following expression:

[tex]v(t) = v(0)*e^{rt}[/tex]

Applying data from the problem gives us:

[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]

In 10 years she'll have approximately $21865.4 in her account.

Answer:

21,865.43

previous answer left out the last digit

Step-by-step explanation:

Answer:

Number is yellow box=3

Step-by-step explanation:

We know this because the way we get that number is subtracting the two numbers above it, which is 8 and 5, which give us 3.

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Answer:

h(x) = -x^2 - 1

Step-by-step explanation:

well y, h(x), f(x), n(x), or any other something of x is all the same thing y.

So if f(x) is -x^2 - 1,

Then h(x) is also -x^2 - 1

Answer:

40

Step-by-step explanation:

The measure of m∠B in the triangle is 40°.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Since the triangles are congruent, we know that their corresponding angles are congruent as well.

Therefore, we have:

m∠B = m∠F = 40°.

Note that we also have:

m∠C = m∠A = 80° (by corresponding angles)

m∠H = m∠G = 60° (by corresponding angles)

Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle D:

m∠D = 180° - m∠B - m∠C = 180° - 40° - 80° = 60°.

Therefore,

m∠B = 40°.

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Answer:

Maximum value of r = 7

Step-by-step explanation:

We have this function:

[tex]r=7\cos(4\theta)[/tex]

and we want to calculate the maximum values for r.

This can be done by deriving, but there is a simpler way.

If we look at the function, the maximum values of r will be found when the cosine function is maximum.

The maximum values for the cosine function is 1, so the maximum values for r are:

[tex]r_{max}=7\cdot 1=7[/tex]

This maximum values happen when the cosine function has a value of 1.

We know that this happens for every natural number n that satisfies:

[tex]\cos(\dfrac{n\pi}{2})=1[/tex]

Then, we can calculate the values of theta that satisfy this condition:

[tex]4\theta=\dfrac{n\pi}{2}\\\\\\\theta=\dfrac{n\pi}{8}[/tex]

For every natural n, when theta has a value of (nπ/8), the values of r are maximum.