Mathematics College

## Answers

**Answer 1**

Explanation:

Decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point.

According to the table, Different guages with different fraction

Convert 15/32 to decimal

15/32 = 0.4686

17/64 = 0.2656

3/16 = 0.1875

1/8 = 0.1250

3/80 = 0.0375

13/1280 =

## Related Questions

question 6. find the slant height. round answer to 5 decimal places.

### Answers

see the attached figure to better understand the problem

Applying the Pythagorean Theorem

l^2=7.7^2+2.6^2

l=8.12712 ft

The graph of Flx) can be compressed vertically and shifted to the right toproduce the graph of G(X). If F(X) = x, which of the following could be theequation of G(x)?O A. GX) = *+B. G(X) = 2(x=69O C. G(X) = 36-6)D. G(X) = 212-6)

### Answers

Hello there. To solve this question, we need to remember some properties on functions and their graphs.

Starting with the function f(x) = x², we want to find a function g(x) such that it represents a shifted to the right and compressed vertically version of f(x).

First, graph f(x) and see what you want to have:

Shift a quadratic function to the right means changing the place of its vertex. In fact, for f(x), we can subtract values inside the square, or complete the square and then do it.

Notice that (x - a)² is a quadratic function with root a. If a is greater than 0, we have the case of the graph below:

So, when we want to shift to the right, you subtract a positive number. If you want to shift it to the left, subtract a negative number, thus it becomes a plus.

Now, talking about compressing it. We'd have something like follows:

This happens when we multiply the function by a factor between 0 and 1.

If the factor is less than 0, it will turn the parabola upside down (works for all types of graphs) and if it is greater than 1, it'll stretch the parabola, becoming bigger and not compressed.

In the options we have, the only option that satisfies both compressed vertically and shifted to the right version of f(x) is G(x) = 1/2 * (x - 6)².

Based on the graphs of functions fand g shown in the accompanying figure, what are all values of x between -3 and 3 for which f(x) = g(x)? I. -2 ≤ x ≤ 0II. 0 ≤ x ≤ 1III. 1 ≤ x ≤ 3A. I onlyB. II onlyC. III only D. I and IIE. II and III

### Answers

**D. I and II**

The values that satisfies this condition

[tex]f(x)\ge g(x)[/tex]

Are the values of y, or the Range that are higher than the values of g(x).

For these functions. we have

**I. -2 ≤ x ≤ 0 True**

Since according the graph all the values within this interval, f(x) is greater than or equal than f(x).

Because when x=-1 **y= 4** for f(x)

for g(x) x=-1 **y=2**

II. 0 ≤ x ≤ 1 **true**

Because

f(x) when x= 0 **y=6 **

g(x) when x=0 **y=4**

III. 1 ≤ x ≤ 3

f(x) when x= 1 y=6

g(x) when x=1 y=6

What are the steps for 8y^2=12y

### Answers

Given

The equation,

[tex]8y^2=12y[/tex]

To solve for y.

Explanation:

It is given that,

[tex]8y^2=12y[/tex]

That implies,

[tex]\begin{gathered} 8y^2-12y=0 \\ 4y(2y-3)=0 \\ 4y=0,\text{ }2y-3=0 \\ y=0,\text{ }y=\frac{3}{2} \end{gathered}[/tex]

**Hence the value of y is y = 0,3/2.**

a boat travels 33 miles Downstream in 4 hours. The return trip takes the boat 4 hours. Find the speed of the boat in still water.

### Answers

Let's use the following formula:

[tex]v=\frac{d}{t}[/tex]

We have two speeds in this case, the speed of the boat and the speed of the water, so:

[tex]\begin{gathered} v_b=Speed_{\text{ }}of_{\text{ }}the_{\text{ }}bo_{}at \\ v_w=Speed_{\text{ }}of_{\text{ }}the_{\text{ }}water \end{gathered}[/tex]

When the boat travels 33 miles downstream in 4 hours, we can say that their speeds add up:

[tex]v_b+v_w=\frac{33}{4}[/tex]

When the boat return, we can say that their speeds are subtracted:

[tex]v_b-v_w=\frac{33}{4}[/tex]

with this we can form a system of equations 2x2:

[tex]\begin{gathered} v_b+v_w=\frac{33}{4}_{\text{ }}(1)_{} \\ v_b-v_w=\frac{33}{4}_{\text{ }}(2) \end{gathered}[/tex]

Let's solve for vb:

[tex]\begin{gathered} (1)+(2) \\ v_b+v_b+v_w-v_w=\frac{33}{4}+\frac{33}{4} \\ 2v_b=\frac{66}{4} \\ 2v_b=\frac{33}{2} \\ v_b=\frac{33}{4}=\frac{8.25mi}{h} \end{gathered}[/tex]

solve for the value of the variable-2-n-8 greater than -8

### Answers

[tex]\begin{gathered} -2n-8>-8 \\ -2n>-8+8 \\ -2n>0 \\ n>\frac{0}{-2} \\ n>0 \end{gathered}[/tex]

**Therefore n>0 or **

[tex]n\in(0,\infty)[/tex]

which point results when the point (-2, 8) is rotated 180 degrees around the point (0, 0)

### Answers

**(2,-8)**

**Explanation**

The rule for a rotation by 180° about the origin is:

[tex](x,y)\Rightarrow(-x,-y)[/tex]

in other words you have to change the sign of x component and y component, so

[tex](-2,8)\Rightarrow rotated\text{ 180 \degree}\Rightarrow(-(-2),-(8))=(2,-8)[/tex]

so, the point that results is

**(2,-8)**

I hope this helps you

-13×4a.find productexplain why you can find -13.(4) by finding 4.(-13)

### Answers

**Answer:**

The product is -52

The result is the same with 4.(-13) because multiplication is cummutative.

**Explanation:**

-13 × 4 = -52

This is the same as

4 × -13

because multiplication is cummutative.

For any numbers a and b,

a × b = b× a

a student uses data to find the exponential regression function y=18.21(1.29)^x to model the population of a herd of bighorn sheep y for each year x after the initial contact which is the best estimate of the time in years for the population to reach 65 sheep

### Answers

Given data:

The expression for the population of herds is y=18.21(1.29)^x.

Substitute 65 for y in the above expression.

[tex]\begin{gathered} (65)=18.21(1.29)^x \\ (1.29)^x=3.5695 \\ x\ln (1.29)=\ln (3.5695) \\ x=4.99 \\ x\approx5\text{ years} \end{gathered}[/tex]

Thus, the value of times in year are **, so option F is correct.**

Solve the problem down below. Round to the nearest cent.Don’t round until the final answer

### Answers

**Solution:**

The continuous compound interest is expressed as

[tex]\begin{gathered} P(t)=P_0\times e^{rt} \\ where \\ P(t)=value\text{ at time t} \\ P_0=principal\text{ amount} \\ r=annual\text{ interest rate} \\ t=length\text{ of time the interest is applied} \end{gathered}[/tex]

Given that

[tex]\begin{gathered} t=6 \\ r=3.5\%=0.035 \\ P_0=\$16000 \end{gathered}[/tex]

By substitution, we have

[tex]\begin{gathered} P(t)=16000\times e^{(0.035\times6)} \\ =19738.84895 \\ \Rightarrow P(t)\approx\$19738.8\text{ \lparen nearest cent\rparen} \end{gathered}[/tex]

**Hence, we have**

Determine the arc length.Leave your answer as an exact value.

### Answers

**SOLUTION**

**Write out the given information.**

[tex]\begin{gathered} \text{radius,r}=10\operatorname{cm} \\ \theta=4\pi\text{rad} \end{gathered}[/tex]

**The length of arc with radius and angle in radians is given by **

[tex]\begin{gathered} length\text{ of an arc=}\theta\times r \\ \text{Where }\theta\text{ is the angle in rads} \end{gathered}[/tex]

Substituting this value into the formula, we have:

[tex]\text{Length of an arc=4}\pi\times10=40\pi[/tex]

Therefore, **the length of arc is 40π rad**

**Answer:40π rad.**

Rewrite a new equivalent equation that is easier to solve !

### Answers

Solution:

Given the expression below

[tex]4|8x-2|=8[/tex]

Applying the absolute rule, which is

[tex]if\text{ \mid u\mid=a, a}>0,\text{ then u}=-a\text{ or u}=a[/tex]

Applying the rule above, the expression becomes

[tex]\begin{gathered} 4|8x-2|=8 \\ Divide\text{ both sides by 4} \\ |8x-2|=2 \\ -2=8x-2=2 \end{gathered}[/tex]

**Hence, a new equivalent equation that is easier to solve is**

[tex]-2=8x-2=2[/tex]

the table dispays the scores of students on a recent exam.find the mean of the scores to the nearest 10th

### Answers

To find the mean, we have to use the following formula

[tex]\bar{x}=\frac{\Sigma(x\cdot f)}{N}[/tex]

Where x represents each score and f represents the number of students. Using the given table, we have

[tex]\begin{gathered} \bar{x}=\frac{65\cdot8+70\cdot1+75\cdot2+80\cdot1+85\cdot1+90\cdot9+95\cdot4}{8+1+2+1+1+9+4} \\ \bar{x}=\frac{520+70+150+80+85+810+380}{26}=\frac{2095}{26} \\ \bar{x}\approx80.6 \end{gathered}[/tex]Hence, the mean is 80.6, approximately.

Save & Exit Certify Lesson: 4.1 Rates and Unit RatesQuestion 1 of 14, Step 1 of 10/14CorrectUse unit rates to determine the better buy and provide the unit price for your answer. Round your answer to the nearest hundredth, if necessary.$29.38 for 30 packs of gum$19.24 for 20 packs of gum

### Answers

**Solution: Better buy $ 19.24 for 20 packs of gum.**

Analysis: As we want to compare two purchase options of packs of gum, we need to find the rate of each option. In this case, we want to find the rate: Price per 1 pack of gum. We find it calculating the total price between the number of packs of gum.

Option 1:

[tex]Rate=\frac{29.38}{30}=0.9793\cong0.98[/tex]

Option 2:

[tex]Rate:\text{ }\frac{19.24}{20}=0.962\cong0.96[/tex]

After we find both rates, let's compare them:

[tex]0.98>0.96[/tex]

For that reason, we can assume the best purchase option is $ 19.24 for 20 packs of gum.

Im having hard problems with (function A) y=-3x+2 (Function B) X=0,2,4,6 Y=2,1,0,-1

### Answers

First, we find the equation of the function B:

The equation is of the form y = mx + b, where m is:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

We have the points P1(0,2) and P2(4,0), so

[tex]m=\frac{0-2}{4-0}=-\frac{2}{4}=-\frac{1}{2}[/tex]

And b is:

[tex]\begin{gathered} y=mx+b \\ \text{we use the point (0,2)} \\ 2=-\frac{1}{2}(0)+b \\ b=2 \end{gathered}[/tex]

Therefore, the function B is:

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

Next, we solve the system of equations:

[tex]\begin{gathered} y=-3x+2 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]

Substitute y:

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

Solve for x:

[tex]\begin{gathered} -3x+\frac{1}{2}x+2=-\frac{1}{2}x+\frac{1}{2}x+2 \\ -\frac{5}{2}x+2=2 \\ -\frac{5}{2}x+2-2=2-2 \\ -\frac{5}{2}x=0 \\ x=0 \end{gathered}[/tex]

Then for y:

[tex]y=-3(0)+2=0+2=2[/tex]

**Answer: **

x = 0

y = 2

Find the standard deviation for the sampling distribution of the sample proportion with n=75 and n=1500P=0.45

### Answers

The standard deviation of a sample portion is

[tex]\sigma_{\hat{p}}=\sqrt[]{\frac{pq}{n}}[/tex]

Where p = 45 and q = 1 - p.

[tex]q=1-0.45=0.55[/tex]

Let's find the standard deviation of the sample n = 75.

[tex]\sigma_{\hat{p}}=\sqrt[]{\frac{0.45\cdot0.55}{75}}\approx0.057[/tex]The standard deviation of the first sample is 0.057.

Repeat the process for n = 1500.

[tex]\sigma_{\hat{p}}=\sqrt[]{\frac{0.45\cdot0.55}{1500}}\approx0.0128[/tex]The standard deviation of the second sample is 0.0128.

Therefore,

• When n = 75, the standard deviation is 0.057.

,

• When n = 1500, the standard deviation is 0.0128.

Summer SwimmingPart C120Graph your two equations from Part Aand Part B.110100Total Cost80GraphingTools604020246810 12 14ONumber of Days

### Answers

We are required to graph out the equations from A and B.

In order to graph out the equations, we need a table of values for our x and y axes.

We can choose the values for our x-axis to be from 0 to 14 moving in steps of 2.

While there will be two corresponding y-values. One for y = 7x and the other for y = 30 + 4x

Therefore, we need to calculate these y values which we shall denote y1 and y2 respectively.

This is done below:

[tex]\begin{gathered} \text{when x = 0;} \\ y_1=7\times0=0 \\ y_2=30+4(0)=30 \\ \\ \text{when x = 2;} \\ y_1=7\times2=14 \\ y_2=30+4(2)=38 \\ \\ when\text{ x = 4;} \\ y_1=7\times4=28 \\ y_2=30+4(4)=46 \\ \\ \text{when x= 6;} \\ y_1=7\times6=42 \\ y_2=30+4(6)=54 \\ \\ \text{when x = 8;} \\ y_1=7\times8=56 \\ y_2=30+4(8)=62 \\ \\ \text{when x= 10;} \\ y_1=7\times10=70 \\ y_2=30+4(10)=70 \\ \\ \text{when x= 12;} \\ y_1=7\times12=84 \\ y_2=30+4(12)=78 \\ \\ \text{when x = 14;} \\ y_1=7\times14=98 \\ y_2=30+4(14)=86 \end{gathered}[/tex]

The calculated coordinates are:

(x, y1), (x, y2):

(0, 0), (0, 30)

(2, 14)(2, 38)

(4, 28)(2, 46)

(6, 42)(6, 54)

(8, 56)(8, 62)

(10, 70)(10, 70)

(12, 84)(12, 78)

(14, 98)(14, 86)

Now that we have calculated the values of the coordinates, we can create the table:

Now that we have the table of values, we can now plot the values:

The x values on the x-axis and the y-values on the y-axis

A picture of the plot is shown below:

Notice that on the table of values, both y1 and y2 have the same y-value at x = 10. This is the same point in which the graphs of y1 and y2 intersect i.e. at point x = 10, y = 70

Find the volume of a square pyramid with a height of 8 m and base edges of 5 m .v_m3(round to the nearest tenth as needed .)

### Answers

Answer:[tex]V\text{ = }66.7m^3[/tex]Explanations:

The volume of a square based pyramid is given by the formula:

[tex]\begin{gathered} V\text{ = }\frac{a^2h}{3} \\ \text{where V is the volume } \\ a\text{ is the }base\text{ edge} \\ \text{and h is the height} \end{gathered}[/tex][tex]\begin{gathered} V\text{ = }\frac{5^2\times8}{3} \\ V\text{ = }\frac{25\times8}{3} \\ V\text{ = }\frac{200}{3} \\ V\text{ = }66.7m^3 \end{gathered}[/tex]

After growing tired of squinting while driving, Donald went shopping for a pair of sunglasses. He tried glasses with different frames and lenses. Cat eye frames Browline frames Aviator frames Polarized lenses 2 5 2 2 4. 4 Regular lenses What is the probability that a randomly selected pair of sunglasses has regular lenses or cat eye fra Simplify any fractions,

### Answers

From our table, we have

[tex]P(\text{regular lenses)=}\frac{2+4+4}{19}=\frac{10}{19}[/tex]

similarly

[tex]P(\text{cat eye frame)=}\frac{2+2}{19}=\frac{4}{19}[/tex]

and the searched probability is

[tex]P(\text{regular lenses }\cup\text{ cat eye frame)=}P(\text{regular lenses)}+P(\text{ cat eye frame)-}P(\text{regular lenses }\cap\text{ cat eye frame)}[/tex]

which gives

[tex]\begin{gathered} P(\text{regular lenses }\cup\text{ cat eye frame)=}\frac{10}{19}+\frac{4}{19}-\frac{2}{19} \\ P(\text{regular lenses }\cup\text{ cat eye frame)=}\frac{12}{19} \end{gathered}[/tex]

then, **the answer is**

[tex]P(\text{regular lenses }\cup\text{ cat eye frame)=}\frac{12}{19}[/tex]

Work each problem according to the instructions given.A. Evaluate when x = 0: - 3/4x -4= B. Solve: -3/4x-4=-6C. Is 0 solution to -3/4x-4>-6?Select answerYes.No.D. Using interval notation, solve: -3/4x-4>-6

### Answers

Given the expression:

[tex]-\frac{3}{4}x-4[/tex]

We evaluate this expression for x = 0:

[tex]\begin{gathered} -\frac{3}{4}x-4=-\frac{3}{4}(0)-4=0-4 \\ \\ \therefore-4 \end{gathered}[/tex]

**Answer: -4**

If g(x) = 35 + 8x and t(x) = 13x + 5, find x when g(x) = t(x)

### Answers

g(x) = 35 + 8x

t(x) = 13x + 5

g(x) = t(x)

35 + 8x = 13x + 5 (Replacing)

35 - 5 + 8x = 13x (Subtracting 5 from both sides of the equation)

35 - 5= 13x - 8x (Subtracting 8x from both sides of the equation)

30= 5x (Subtracting)

30/5 = x (Dividing by 5 on both sides of the equation)

6= x

The answer is x= 6

during a garage sale, mrs.graham makes change with only 2 type of coins. two customers need the same amount of change. one customer receives 8 coins, 3 of which are nickels.the second customer receives 11 coins,7 of which are nickels. which equation could be used to determine c, the value of second coin?

### Answers

**Input data**

2 type of coins

Customer 1

8 coins, 3 of which are nickles

Customer 2

11 coins, 7 of which are nickles

**Procedure**

V = total value

Customer 1

V = (8-3)c + (3)*0.05

Customer 2

V = (11-7)c + (7)*0.05

Now we are going to equal the equations

[tex]\begin{gathered} 5c+3\cdot0.05=4c+7\cdot0.05 \\ 5c-4c=7\cdot0.05-3\cdot0.05 \\ c=4\cdot0.05 \\ c=\text{0}.20 \end{gathered}[/tex]

The coin c would be **c = 0.20**

Graph the image of AKLM after a translation 1 unit right and 4 units down.

### Answers

Answer:

Explanation:

From the graph, we can read off the vertices of triangle KLM as;

[tex]\begin{gathered} K(0,4) \\ L(9,4) \\ M(-1,-6) \end{gathered}[/tex]

To translate 1 unit right, we have to add 1 to each of the x-coordinates of the vertices of triangle KLM.

To translate 4 units down, we have to subtract 4 from each of the y-coordinates of the vertices of triangle KLM.

So we'll have;

[tex]K^{\prime}(0+1,4-4)\rightarrow K^{\prime}(1,0)[/tex][tex]L^{\prime}(9+1,4-4)\rightarrow L^{\prime}(10,0)[/tex][tex]M^{\prime}(-1+1,-6-4)\rightarrow M^{\prime}(0,-10)[/tex]

Therefore, the graph of t

If a number cube is rolled once, which is the more likely outcome, a prime number or a composite number?

### Answers

Remember that

we have 3 prime numbers (2,3,5)

and

we have two composite numbers on a 6 sided die (4,6)

therefore

The probability of getting a prime number is P=3/6=1/2=0.5

The probability of getting a composite number is P=2/6=1/3=0.33

therefore

The more likely outcome is a prime number

Sixth grade Which sign makes the statement true? 1 ? 1.2

### Answers

1 < 1.2

This may be interpreted as 1 is less than 1.2

Solve the quadratic equation: 3x^2-2=25

### Answers

The question is given as :

[tex]3x^2-2=25[/tex]

collect like terms as;

[tex]3x^2=25+2[/tex][tex]3x^2=27[/tex]

Divide both sides by 3 as

[tex]x^2=\frac{27}{3}[/tex][tex]\begin{gathered} x=\sqrt[\square]{9} \\ \end{gathered}[/tex][tex]x=3[/tex]

The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is greater than 2". Find P(A). Outcome Probability 1 0.2 2 0.2 3 0.3 4 0.3

### Answers

According to the problem, the event is "the outcome is greater than 2", so the probability is

[tex]P(A)=0.3+0.3=0.6[/tex]Hence, event A has 0.6 chances.

The question is in the image. Answer the question 5.

### Answers

Explanation

Question 5

If the data values are multiplied by a factor, the center and measure ofspread of the graph will NOT increase proportionally.

### Answers

The answer is False. When any data value in a **distribution **provided is multiplied by a factor, the **center** and measure of **spread** of the graph will increase proportionally.

Center and Spread of the graph are a part of summary statistics because they can shortly define the data sets provided. A specific value in a given data set is represented by the Center. The Center of a graph can be **Mean**, or **Median**, or **Mode**.The variation observed in the data set is represented by the Spread. The Spread of a graph can be **Range** or **Standard Deviation**.

Now that we have an idea about the Center and Spread of the graph, it can be understood that -

When the values in a data set are multiplied by a factor -

There will be increase in the value of the mean or median and thus, correspondingly, the center of the graph.There will be increase in the value of variation of the data set and thus, correspondingly, the spread of the graph.

Thus, the answer is false. Whenever the data values in a **distribution **are multiplied by a factor, the center and measure of spread of the graph will NOT increase proportionally.

To learn more about **distribution** visit https://brainly.com/question/14926605

#SPJ9

On number 8 I’m a bit confused and please explain it to me so I can grasp it I listen all the way through

### Answers

**SOLUTION **

(8). From the question, Jenny rode 8km, changed direction and rode another 15km and then turned, by changing direction and rode 17km before checking her map.

Could her path be a right angle?

For her path to be a right angle, then the square of the longest path (17km) must be equal to the sum of the squares of the other two paths (8km and 15km). That is, according to Pythagorean theorem.

Let's check

[tex]\begin{gathered} 17^2=289 \\ 8^2+15^2=64+225=289 \end{gathered}[/tex]

So, since we got 289 as the sum of 8 square and 15 square,

**Hence her path is a right-angle. YES**

The right-angle is shown below

**Following the arrow indicating the direction she moved, we can see that Jenny will be back at her starting point. **

Could Jenny be back at her starting point?

**The answer is YES**