Mathematics College

## Answers

**Answer 1**

You have to replace the x value in the equation:

[tex]ŷ=2.9x-34.7[/tex][tex]ŷ=2.9(56)-34.7[/tex][tex]ŷ=127.7[/tex]

## Related Questions

Write the equation of aline parallel to3x + 3/4y = 2 andpassing through (0.1).

### Answers

parallel line has identical slope . Therefore parallel line passing through (0, 1) have the same slope.

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ 3x+\frac{3}{4}y=2 \\ \frac{3}{4}y=2-3x \\ mul\text{ltiply through by }\frac{4}{3} \\ y=2(\frac{4}{3})-3x(\frac{4}{3}) \\ y=\frac{8}{3}-4x \\ y-y_1=m(x-x_1) \\ m=-4 \\ y-1=-4(x-0) \\ y-1=-4x \\ y=-4x+1 \end{gathered}[/tex]

The equation is

**y = -4x + 1**

y varies inversely as the fourth root of x and when x = 81, y = 10. What would be y when x=29. Round your answer to two decimal places.

### Answers

**Answer:**

y=12.93

**Explanation: **

If y varies inversely as the fourth root of x, then we have:

[tex]y\propto\frac{1}{\sqrt[4]{x}}[/tex]

Introducing the constant of variation, k, we have the equation:

[tex]y=\frac{k}{\sqrt[4]{x}}[/tex]

When x = 81, y = 10

[tex]\begin{gathered} 10=\frac{k}{\sqrt[4]{81}} \\ \implies10=\frac{k}{3} \\ \text{Cross multipl}y \\ k=10\times3 \\ k=30 \end{gathered}[/tex]

Substitute k=30 into the equation of variation.

[tex]y=\frac{30}{\sqrt[4]{x}}[/tex]

When x=29.

[tex]\begin{gathered} y=\frac{30}{\sqrt[4]{29}}=\frac{30}{2.3206}=12.926 \\ y\approx12.93 \end{gathered}[/tex]

**The value of y when x=29 is 12.93 (correct to 2 decimal places).**

Two sides of a triangle measure 40 cm and 30cm. Which of the following could NOTbet the measure of the third and longest side?

### Answers

For a traingle, sum of two sides of triangle is always greater than the third side of triangle.

The sum of two sides of triange is,

[tex]40+30=70[/tex]

So length of thir side of triangle must be less than 70.

From the options, it can be observed that 70 is not possible length of third side of riangle.

So **70 cm ** is answer.

Write the slope-intercept form of the equation of the line passing through the point (4, -1) and perpendicular to the line y = 2x +2

### Answers

The given line has an equation y = 2x + 2

Comparing the equation above to y = mx + c

where m stands for the slope and c stands for the y-intercept

m = 2

c = 2

The equation of the line perpendicular to the equation y = mx + c and passing through the point (x₁, y₁) is given by:

[tex]y-y_1=\frac{-1}{m}(x-x_1)[/tex]

The line is passing through the point (4, -1).

That is, x₁ = 4, y₁ = -1

Substitute the values of m, x₁, and y₁ into the equation above:

[tex]undefined[/tex]

What are the vertices of (AABC). when it is translated by (x+6, y-2), graph thetransformation?BI.A'B'C'

### Answers

A translation is defined as:

[tex](x,y)\rightarrow(x+a,y+b)[/tex]

To do the translation we have to know the original vertexes coordinates. We have A(-6,2) B(-2,4) and C(-4,-4). Using the translation given we have:

[tex]\begin{gathered} A(-6,2)\rightarrow A^{\prime}(0,0) \\ B(-2,4)\rightarrow B^{\prime}(4,2) \\ C(-4,-4)\rightarrow C^{\prime}(2,-6) \end{gathered}[/tex]

**Therefore:**

[tex]\begin{gathered} A^{\prime}(0,0) \\ B^{\prime}(4,2) \\ C^{\prime}(2,-6) \end{gathered}[/tex]

**The graph is:**

the sum of the measure of the angels of a triangle is 180

### Answers

According to the question statement, the sum of the measures of the angles of a triangle is 180°, in this case, A B and C are the angles of the given triangle which means that:

[tex]m\measuredangle A+m\measuredangle B+m\measuredangle C=180[/tex]

John barley borrowed $25,000 for one year he borrowed some at 13% interest and the rest at 15% interest at the end of the year he owed $3,600 in interest how much did he borrow at each rate.?

### Answers

**SOLUTION **

We want to find the principal money borrowed each at 13% and 15% from a total money of $25,000.

Now, let the money he borrowed at 15% be x

and, let the money he borrowed at 13% be y.

This means that

[tex]\begin{gathered} x+y=25,000 \\ \text{and } \\ y=25,000-x \end{gathered}[/tex]

From the simple interest formula

[tex]\begin{gathered} I=\frac{PRT}{100} \\ \text{Where, I = interest, P = principal, R = rate and T = time } \end{gathered}[/tex]

Interest on 15% will be

[tex]\begin{gathered} I_{15}=\frac{x\times15\times1}{100} \\ I_{15}=0.15x \end{gathered}[/tex]

Interest on 13% will be

[tex]\begin{gathered} I_{13}=\frac{(25000-x)\times13\times1}{100} \\ I_{13}=(25000-x)\times0.13 \\ I_{13}=3250-0.13x \end{gathered}[/tex]

Now, both interest should be = $3,600

That is

[tex]\begin{gathered} I_{15}+I_{13}=3,600 \\ 0.15x+(3250-0.13x)=3,600 \\ 0.15x-0.13x=3,600-3250 \\ 0.02x=350 \\ x=\frac{350}{0.02} \\ x=17,500 \end{gathered}[/tex]

So, **the money he borrowed at 15% is $17,500**

And the money he borrowed at 13% is

[tex]25000-17500=7,500[/tex]

Hence,** the answer is $17,500 at 15% and $7,500 at 13%. **

UseEquationY=2/3x-3y=-3/2x+2Which statement about the lines is true?A. The lines are the same.B. The lines are parallel.C. The lines are perpendicular.D. The lines intersect but are not perpendicular,

### Answers

The lines are not the same as thehy have different slope and y-intercept.

As the slopes are different, they are not parallel.

If the slopes are negative reciprocals, the lines are perpendicular.

We can test it by:

[tex]m_2=-\frac{1}{m_1}=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}[/tex]

The slopes are negative reciprocals, so they are perpendicular.

**Answer: C. The lines are perpendicular.**

Assume that blood pressure readings are normally distributed what the mean of 135 and a standard deviation of 4.8. If 35 people are randomly selected, find a probability that they’re mean blood pressure will be less than 137.

### Answers

**Step 1**

Given;

[tex]\begin{gathered} \mu=135 \\ \sigma=4.8 \\ X=137 \end{gathered}[/tex]

**Step 2**

State the z-score formula

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Find the z-score

[tex]z=\frac{137-135}{4.8}[/tex][tex]z=\frac{5}{12}[/tex]

**Step 3**

Find the probability based on the z-score

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Describe what a system with NOSOLUTION would look like on a graph.

### Answers

The solution of a system of equations is the point at which the graph for each equation intersect on the coordinate plane. When a system doesn't have a solution it means that the two graphs for this system don't have any point of intersection and that is only possible for parallel lines.** The correct answer is parallel lines.**

The table shows the probabilities of winning or losing when the team is playing away

Home

Away

Total

Win

0.63

0.27

0.9

Loss

0.07

0.03

0.1

Total

0.7

0.3

1.00

(a) Are the events "winning" and "playing at home independent? Show your calculations to justify why or why not

(b) Are the events "losing" and "playing away" independent? Show your calculations to justify why or why

not.

### Answers

From the given table, we can deduce the following:

P(win) = 0.9

P(loss) = 0.1

P(Playing at home) = 0.7

P(Playing away) = 0.3

P(win at home) = 0.63

P(win away) = 0.27

P(Loss away) = 0.03

P(loss home) = 0.07

• (a) Are the events winning and playing at home independent.

Independent events are events that do not affect the probability of each other occuring.

We have:

P(winning) = 0.9

P(playing at home) = 0.7

P(win and playing at home) = 0.63

To determine if the events **winning **and **playing at home ** is independent, we have:

P(win and playing at home) = P(win) x P(playing at home) = 0.9 x 0.7 = 0.63

0.63 = 0.9 x 0.7

0.63 = 0.63

Since the equation is true, the events winning and playing at home are **independent.**

• (b) Are the events "losing" and "playing away" independent? Show your calculations to justify why or why not.

From the table, we hae:

P(losing) = 0.1

P(Playing away) = 0.3

P(Losing and playing away) = 0.03

To determine if the events are independent or not, we have:

P(losing and playing away) = P(losing) x P(playing away)

0.03 = 0.1 x 0.3

0.03 = 0.03

SInce the equation is true, both events are **independent.**

**ANSWER:**

**(a) The events are indepedent**

**(b) The events are indepedent**

If it is given that AB¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯, how can it be proved that m∠A=m∠C?

### Answers

Given:

Line AB ≅ Line CB

Let's prove that m∠A ≅ m∠C.

Given that side AB is congruent to side CB, to prove that the measure of angle A is congruent to the measure of angle C, we have:

The first step is to draw an angle bisector from B to a point D such that point D is on AC.

The next step is to show that the corresponding sides and the angle between the sides of the new triangles ABD and CBD are congruent.

Since triangle ABD and triangle CBD are congruent, we are to use the Side-Angle-Side Congreunce postulate and the definition of congruent angles to show that measure of angle A is congruent to the measure of angle C.

**ANSWER:**

**Draw an angle bisector from B to a point D such that point D is on AC. Then show that corresponding sides and the angle between the sides of the new triangles ABD and CBD are congruent. Finally, use the Side-Angle-Side postulate and the definitio**

Find the surface area Of the figure. 9 cm 1 cm Insert Answer 5 cm 5 cm 1 cm

### Answers

The formula to find the surface area of a rectangular prism is

[tex]\begin{gathered} SA=2lw+2wh+2lh \\ \text{ Where SA is the surface area}, \\ l\text{ is the length,} \\ w\text{ is the width and} \\ h\text{ is the height of the rectangular prism} \end{gathered}[/tex]

In this case, you have

[tex]undefined[/tex]

Six campers -- Hernan, Jonelle, Kwong, Lisette, Mohammed, and Nestor -- are assigned to the following three activities: swimming, tennis, and volleyball. Each camper is assigned to exactly one activity, and each activity is assigned exactly two campers. No other campers are assigned. The following conditions must be met:Kwong is not assigned to the same activity as Lisette.Mohammed is not assigned to volleyball.If Lisette is assigned to swimming, then Hernan is assigned to volleyball.Jonelle is assigned to volleyball.If Kwong is assigned to volleyball, each of the following could be true EXCEPT: A. Mohammed is assigned to tennis. B. Hernan is assigned to swimming. C. Nestor is assigned to swimming. D. Nestor is assigned to tennis. E. Lisette is assigned to swimming.

### Answers

Hernan, Jonelle, Kwong, Lisette, Mohammed, and Nestor

swimming, tennis, and volleyball.

Kwong is not assigned to the same activity as Lisette.

Mohammed is not assigned to volleyball.

If Lisette is assigned to swimming, then Hernan is assigned to volleyball.

Jonelle is assigned to volleyball.

Volleyball:

Kwong, Jonelle

Tennis

Swimming

Lissette

**The answer is E. Lissette is assigned to swimming. **

Because Kwong and Lissette are not assigned to the same activity and if Lissette was assigned to swimming then Hernan should be assigned to volleyball, but in this case it cannot be possible because Kwong and Jonelle are already assigned to volleyball.

I need to know number 7 it says find the sum of the first 9 terms

### Answers

**Given**:

[tex]1+8+27+64+125+.....[/tex]

**To find:**

The sum of the first 9 terms

**Explanation:**

The series is of the form,

[tex]1^3+2^3+3^3+4^3+5^3+......[/tex]

Using the formula,

[tex]1^3+2^3+.....+n^3=(\frac{n(n+1)}{2})^2[/tex]

Here, n = 9.

On substitution we get,

[tex]\begin{gathered} 1^3+2^3+......+^3=(\frac{9(9+1)}{2})^2 \\ =(\frac{9(10)}{2})^2 \\ =(\frac{90}{2})^2 \\ =45^2 \\ =2025 \end{gathered}[/tex]

**Final answer:**

**The sum of the first 9 terms is 2025.**

I need help on this question[tex] - \frac{2}{3} a = - 12[/tex]"Solve for a and Simplify your answer."

### Answers

[tex]\begin{gathered} -\frac{2}{3}a=-12 \\ \text{cross multiply} \\ -2a=-36 \\ a=\frac{-36}{-2} \\ a=18 \end{gathered}[/tex]

A bird flies from the bottom of a canyon that is 63 1/5feet below sea level to a nest that is 857 7/10feet above sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest?

### Answers

step 1

we have that

above sea level is positive

below sea level is negative

so

The difference in elevation between the bottom of the canyon and the bird's nest is equal to

857 7/10-(-63 1/5)

857 7/10+63 1/5

To adds the fractions convert to an improper fraction or decimal number

857 7/10=857+7/10=857+0.7=857,70

63 1/5=63+1/5=63+0.20=63.20

Find the sum

857.70+63.20=920.90 ft

Convert to mixed number

920.90 ft=920+0.90=920+9/10=920 9/10 ft

Select the true statement about triangle ABC.135B12АO A. sin C = cos AO B. sin C = tan AO c. sin C = cos BO D. sin C = sin A

### Answers

Answer:

The correct optio

Explanation:

From the given right triangle,

[tex]\sin C=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{12}{13}[/tex]

and

[tex]\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{12}{13}[/tex]

Clearly, we see that sin C = cos A

Streets A and B run parallel to each other. The measure of <3 is 153 degrees. Find the measure of <5

### Answers

Given:

[tex]\angle3=153^{\circ}[/tex][tex]\angle3\text{ and }\angle5\text{ are same side interior angles.}[/tex][tex]\begin{gathered} \angle3+\angle5=180^{\circ} \\ 153+\angle5=180 \\ \angle5=180-153 \\ \angle5=27^{\circ} \end{gathered}[/tex]

Stephan owns a landscaping company. Today, he is mowing three lawns: one is of an acre, one is į of an acre, and oneis 14 acres. How many acres of lawn is Stephan going to mow today? Simplify your answer and write it as a mixedfraction if necessary.Oacreso 25acresOacresO2 acres

### Answers

Stephen is mowing three lawns: one is 1/4 th of an acre, one is 1/2 of an acre and another is 1 1/3 acres.

Now, let us add.

[tex]\begin{gathered} \frac{1}{4}+\frac{1}{2}+\frac{4}{3}=\frac{3+6+16}{12} \\ =\frac{25}{12} \\ =2\frac{1}{12} \end{gathered}[/tex]

**Hence, the correct option is (D)**

**N.B - Since it is asked to convert the answer into mixed fraction, D is correct and B is not**

Could someone please help me solve this question? Thanks! (Click image to see question)

### Answers

We will have the following:

*First: From properties of the rhombus the following is true:

[tex]m<1=m<6\Rightarrow m<1=65[/tex][tex]m<2=m<6\Rightarrow m<2=65[/tex]

*Second: We know that the sum of all internal angles of a quadrilateral add 360°, so the following is true:

[tex]2(m<1+m<2)+4(m<3+m<4)=360[/tex]

So:

[tex]4(65)+4(m<3)=360[/tex]

This, since from properties of the rhombus m<3 = m<4, now we wil have:

[tex]260+4(m<3)=360\Rightarrow4(m<3)=100[/tex][tex]\Rightarrow m<3=25[/tex]

Now, we will have the following:

[tex]m<3=25[/tex][tex]m<4=25[/tex]

And finally, we can see that the measurement of angle 5 is:

[tex]m<5=90[/tex]

Can you please help me with 24Find the x and y-intercepts

### Answers

**ANSWER**

• x-intercepts: (-√47, 0), and ,(√47, 0)

,

• y-intercept: (0, -47/6)

**EXPLANATION**

The y-intercept is the point where the graph of the function intersects the y-axis, so the x-coordinate is 0. To find the y-coordinate, we have to find f(0),

[tex]f(0)=\frac{94-2\cdot0^2}{3\cdot0^2-12}=\frac{94-0}{0-12}=\frac{94}{-12}[/tex]

Simplify the fraction,

[tex]f(0)=-\frac{47}{6}[/tex]

Hence, the **y-intercept** is **(0, -47/6)**.

The x-intercepts are the values of x where the function is 0. To find them, we have to solve f(x) = 0. In the case of rational functions, the zeros are all the zeros of the numerator that are not zeros of the denominator,

[tex]0=94-2x^2[/tex]

To solve this, add 2x² to both sides of the equation,

[tex]2x^2=94[/tex]

Divide both sides by 2,

[tex]\begin{gathered} \frac{2x^2}{2}=\frac{94}{2} \\ \\ x^2=47 \end{gathered}[/tex]

And take the square root of both sides,

[tex]x=\pm\sqrt[]{47}[/tex]

Hence, the **two x-intercepts** are **(-√47, 0)** and **(√47, 0)**.

Which point is collinear to the point (2, 1)? OA) (1,0) B) (3,2) C) (4,1) D) (1,3)

### Answers

Answer : (4, 1)

They both lie on the same y - axis

jeon jumped 2 meters from the diving board into the swimming pool About how many feet did he jump?

### Answers

[tex]\begin{gathered} \text{jeon jumped}\Rightarrow\text{2 meter} \\ In\text{ 1 meter}\Rightarrow3.28ft \\ In\text{ 2 meter}\Rightarrow2\times3.28=6.56ft \end{gathered}[/tex]

There is a answer i need help with can u help me?

### Answers

first we name the horizontal number and then the vertical, so the point is

[tex](2,4)[/tex]

then, the right option is C

A parallelogram can be represented by ... What is its area?

### Answers

Answer:

**35 square units**

Explanations:

The area of the parallelogram represented by the** 2*2 matrix** is the** determinant** of the matrix as shown:

[tex]Area=|A|[/tex]

where A is the** 2*2 matrix given**

**Find the area of the parallelogram**

[tex]\begin{gathered} |A|=7(3)-2(-7) \\ |A|=21+14 \\ |A|=35square\text{ units} \end{gathered}[/tex]

Hence the a**rea of the parallelogram** is **35 square units**

what do I multiply 3P + 2D = 16.50 with??

### Answers

we need to solve the system of equations, there are different methods, I think here the simplest one is multiplying the first equation by 2 and then substract the second equation

[tex]\begin{gathered} 2(3P+2D=16.5) \\ 6P+4D=33 \end{gathered}[/tex]

Then, we have the equation

[tex]\begin{gathered} 2P=7 \\ P=\frac{7}{2} \\ P=3.5 \end{gathered}[/tex]

So, replacing P in the first equation

[tex]\begin{gathered} 3(3.5)+2D=16.5 \\ 10.5+2D=16.5 \\ 2D=16.5-10.5 \\ 2D=6 \\ D=\frac{6}{2} \\ D=3 \end{gathered}[/tex]

We can check our result replacing P=3.5 and D=3 in the second equation

[tex]4(3.5)+4(3)=14+12=26[/tex]

Then, our answer is correct and P=3.5 and D=3

Three sodas and one hamburger cost $4.50. Two sodas and 2 hamburgers cost $4.00. One soda costs:

### Answers

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**1) **We can solve this problem using a system of equations. So let's cal h for hamburger and s for sodas.

**2) **So let's set the system:

[tex]\begin{gathered} 3s+h=4.5 \\ 2s+2h=4 \end{gathered}[/tex]

Hence, we can solve them by **the Elimination Method.**

Let's multiply the first equation by -2 to eliminate the *h* terms

[tex]undefined[/tex]

Since the question is about the soda's price, we can stop it here.

**Answer:**

$1.25

**Step-by-step explanation:**

1)We can set two equatons for each statement.

Three sodas and one hamburger cost $4.50:

3s + h = 4.5

Two sodas and 2 hamburgers cost $4.00:

2s + 2h = 4

2) Solve using simultaneous equations. To find out the cost of one soda we need to make the number of hamburgers the same in both equations to eliminate them.

3s + h = 4.5

2s + **2h** = 4

To do this multiply the first equation across by 2 because in the second equation there is **2h**, which also makes the first equation **2h**.** **This gives us:

6s + 2h = 9

2s + 2h = 4

3) subtract across to eliminate the h.

6s - 2s = 4s, 2h - 2h = 0h, 9 - 4 = 5, so we now have:

4s = 5

4) divide by 4 to solve for s:

s = 5/4 = $1.25

A turtle travels 5/12 mile in 1/3 hour and a snail travels 1/8 mile in 3/4 hour. Which animal is faster?• The turtle's rate is ____ 1 mile per hour( greater than or less than)• The snail's rate is ____ 1 mile per hour( greater than or less than)• Find the turtle's speed in miles per hour.• The turtle's speed is ____ miles per hour.

### Answers

A turtle travels 5/12 mile in 1/3 hour and a snail travels 1/8 mile in 3/4 hour. Which animal is faster?

Part A

Find out the turtle's rate

divide the total miles by the total time

so

(5/12)/(1/3)=15/12=1.25 miles per hour

that means

The turtle's rate is **greater than** 1 mile per hour

Part B

Find the snail's rate

so

(1/8)/(3/4)=4/24=0.17 miles per hour

that means

The snail's rate is **less than** 1 mile per hour

Part C

the turtle's speed in miles per hour is 1.25 miles per hour

Part D

the turtle is faster than the snail

Answer:

The turtle's speed is 1 1/4 mile(s) per hour.

Step-by-step explanation:

i got it right on iready

Suppose that P(A) = 0.1 and P(B) = 0.6. If events A and B are mutually exclusive, find the following probabilities. (a) P(A ∩ B) Incorrect: Your answer is incorrect. (b) P(A ∪ B)

### Answers

a) The **value **of P(A ∩ B) =0.

b) P(A ∪ B)= 0.9

What is Conditional Probability?

The **possibility **of an **event **or **outcome **happening contingent on the occurrence of a prior **event **or **outcome **is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.

If A and B are two **events **in a **sample** space S, then the **conditional probability **of A given B is defined as P(A|B)=P(A∩B)P(B), when P(B)>0.

Given:

P(A) = 0.1 and P(B) = 0.6

Now, By **definition **

P(AUB)=P(A)+P(B)-P(AՈB).

As, the **events **A and B are **mutually **exclusive,

P(AՈB)=0.

So,

P(AUB) =0.3+0.6

P(AUB) =0.9.

Learn more about **conditional probability **here:

https://brainly.com/question/11899923

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