Mathematics College

## Answers

**Answer 1**

**Answer: d. m = 2**

**Step-by-step explanation:**

First, we will write a** slope-intercept equation** using the** y-intercept** given.

y = mx + 4

Next, we will **substitute **the given **point **and **solve **for m, the **slope**.

y = mx + 4

(8) = m(2) + 4

4 = 2m

m = 2

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**Answer 2**

**Answer:**

[tex]\boxed{\sf m=2}.[/tex]

**Step-by-step explanation:**

1. Identify the 2 given points.

In order to find the slope of any linear equation you need at least 2 points the line passes through. We're explicitly provided one, (2, 8), we just need to figure out the other one.

When the statement says that the line has a y-intercept of 4, it means that at a point with y=4 the function touches the y axis. The only way to touch the y-axis is if the x value is 0. Hence, another given point is (0, 4).

2. Calculate the slope.

Formula: [tex]\sf m=\dfrac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

**Naming the variables (can be done arbitrarily but always make sure the y's are actual y values from the ordered pairs and that x₁ goes with its corresponding y₁ value from the ordered pair):**

[tex]x_{1} =2;\\x_{2} =0;\\y_{1} =8;\\y_{2} =4.[/tex]

**Now substituting these values in the formula:**

[tex]\sf m=\dfrac{(4)-(8) }{(0) -(2) }=\dfrac{-4}{-2} =\boxed{\sf 2}.[/tex]

**Check out the attached image to see the graphed line.**

## Related Questions

Ali had 3469 bags of maize each weighing 90 kg.Hesold 2654 of them. How many kg of maize was he left with?

### Answers

The **number** of kg of maize was **left** with Ali is 73350 Kg.

Given that, Ali had 3469 bags of maize each weighing 90 kg.

Ali sold 2654 of them.

**Number** of bags left = 3469-2654

= 815

Number of Kg's of maize left = 815×90

= 73350 Kg

Therefore, the **number** of kg of maize was **left** with Ali is 73350 Kg.

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A side of an equilateral triangle is 20 cm long. What is the area of the triangle

### Answers

Should be 60 cm long in total. All sides are equal and it’s a triangle, so 20+20+20. Hope this helps

Andy saved $32 in June, $27 in July, and $38 in August. Then Andy spent $18 on school supplies and $47 on new clothes. How much money does

Andy have left?

### Answers

Andy has $32 **money **left after spending $18 on school supplies and $47 on new clothes.

To find out how much money Andy has left, we need to start with the total **amount **of money he saved and then subtract the amount he spent on school supplies and new clothes.

The total amount Andy saved is:

$32 + $27 + $38 = $97

The amount Andy spent is:

$18 + $47 = $65

To find out how much money Andy has left, we can **subtract **the amount he spent from the amount he saved:

$97 - $65 = $32

So, after spending $18 on school supplies and $47 on new clothes, Andy is left with $32.

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Find x. Simplify completely.

X

8

C

17

x = [?] √ [

Enter the number that belongs in the green box.

Enter

### Answers

**Answer:**

17/x = x/8

x^2 = 136, so x = 2√34

what is 2x multiplied by 7 with the exponent of 4

### Answers

The **simplified expression** of 2x multiplied by 7 with the exponent of 4 is 4,802x.

**What is the simplification of the expression?**

The **expression** is simplified by applying the rules of multiplication and **exponent rules**.

the expression = 2x(7⁴)

simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401

Multiply the **resultant solution** of 2,401 as follows;

= 2,401 x (2x)

= 4,802x

Thus, the **simplified expression** of 2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of **multiplication**.

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One respondent said they watched 10 movies. This seems to be an

symmetrical

This graph is

skewed

to the

left

because the data is stacked on the left with a "tail" going to the right.

Most people watched

[ Select ]

movies

### Answers

The graph seems to be a **left symmetrical **distribution and most people watched **action movies**

Calculating the skewness of the graph

From the question, we have the following parameters that can be used in our computation:

The **graph** (see attachment)

From the graph, we have the following readings and observations

The movie with the **highest frequency** is Action moviesThe data is **stacked** on the right with a "tail" going to the **left**.

Using the above as a guide, we have the following conclusions

**Most people** watched action moviesThe graph is **left skewed**

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Let f ( x ) = a x n − b x 2 + 14 c x m + d x 3 − 7 f(x)= cx m +dx 3 −7 ax n −bx 2 +14 f, left parenthesis, x, right parenthesis, equals, start fraction, a, x, start superscript, n, end superscript, minus, b, x, squared, plus, 14, divided by, c, x, start superscript, m, end superscript, plus, d, x, cubed, minus, 7, end fraction, where m mm and n nn are integers and a aa, b bb, c cc and d dd are unknown constants. Which of the following is a possible graph of y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis? Choose 1 answer:

### Answers

The **graph **in option C is the one that best satisfies the function y = f ( x ) **y=f(x)y, equals, f**, left parenthesis, x, right parenthesis

How to solve

The ultimate **exponent **of the equation**, **[tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.

If one between these **values is odd,** an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).

If both of these variables fit an** even figure,** the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).

**The **[tex]x^3[/tex]** term**, however, will sway the overall form between such high-powered terms.

Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive** flight path and curves.**

Solving the given problem:

f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]

At x= 0 on the y- axis

f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]

Thus, only **option C **satisfies this condition.

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3.4 MIXED FACTORING

1. Utilize all of the strategies for factoring in order to factor the following polynomials.

Reminder: Combine like-terms prior to factoring.

-7n + 5n^2 + 6 - 3n^2 - 11n + 30

### Answers

**Answer:**

2 (n - 3) (n - 6)

**Step-by-step explanation:**

[tex]-7n+5n^2+6-3n^2-11n+30[/tex]

Group like terms and combine...

[tex]2n^2-18n+36[/tex]

Observe that all terms contain a factor of 2. Factor out a 2...

[tex]2(n^2-9n+18)[/tex]

The leading coefficient is 1. The shortcut applies. Find the factors of "c" (18)

18 = 1 * 1818 = 2 * 918 = 3 * 6

Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").

Finish factoring the trinomial into two binomials:

[tex]2(n-3)(n-6)[/tex]

To verify that this is a valid factoring, distribute, and recombine terms:

[tex]2(n-3)(n-6)[/tex]

[tex]2(n^2-3n-6n+18)[/tex]

[tex]2(n^2-9n+18)[/tex]

18. Triangle GHJ has GH = 13, GJ = 15, and

m/G = 74. What is the area of the triangle?

SEE EXAMPLE 4

### Answers

Answer: 97.5

Step-by-step explanation:

Just do base times height divided by 2, which I'm assuming is 13x15 , that'd be 195. 195 divided by 2 is 97.5

Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.

A(-7,-2)A(−7,−2), B(-3,1)B(−3,1), C(-3,4)C(−3,4), D(5,4)D(5,4), E(5,-6)E(5,−6), F(-3,-6)F(−3,−6), G(-3, -2)G(−3,−2)

### Answers

The **total area **of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) has been found as **51 square units.**

What is a Graph?

A **graph** is described as a **mathematical representation** of a network and it describes the relationship between lines and points.

The first step is to divide the figure is into two **rectangles** and a **triangle.**

we notice that the points B, C, E, and F will form a rectangle with base BC and height of **7 units.**

We also notice that the points A, D, and G form a rectangle with base AG and height **5 units.**

we notice that points C, D, and E form a triangle with base CE and height **4 units**.

we notice that the length of BC is 4 - 4 = 0, therefore the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = **45 square units. **The area of the triangle with base CE is (4 - 1) x 4 / 2 =** 6 square units.**

In conclusion, the total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 45 + 6 = **51 square units.**

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MODELING REAL LIFE About 5.2% of a population

contracted the flu last year. A test used to diagnose the

flu was 92% accurate for people who had the flu and

85% accurate for people who did not have it. Find and

interpret the ratio of true positives to false positives.

### Answers

The** ratio** of true positives to false** positives**, given the accuracy of the test would be 239 : 711 .

Here. we have,

First, find the number of people who have the flu:

= 5. 2 % x 10, 000

= 520 people

Those who don't have it:

= 10, 000 - 520

= 9, 480 people

True **positive** :

= 92 % x 520

= 478 people

False negatives:

= 8 % x 520

= 42 people

False **positives**:

= 15 % x 9, 480

= 1, 422 people

Th**e ratio** of true **positives** to false positives is therefore:

478 : 1, 422

239 : 711

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All but 36 of the 120 state capitals have an interstate highway serving them. What percent of the capitals do not have interstates?

### Answers

Therefore, 70% of state **capitals **do not have **interstate **highways **serving **them.

What is percent?

**Percent **is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the **numerical **value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and **changes **in quantities.

Here,

If all but 36 of the 120 state capitals have an interstate highway serving them, then the number of capitals that do not have interstates is 120 - 36 = 84.

To find the percentage of capitals that do not have interstates, we need to divide the number of capitals without interstates by the total number of capitals and then multiply by 100:

84 / 120 x 100% = 70%

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Bad gums may mean a bod mood. Researchers discovered that 85% of people who have suffered a bad mood had periodontal disease. Only 29% of healthy people have this disease. Suppose that in a certain community bad moods are rare, occuring with only 10% probability. If someone has periodontal disease, what is the probability that he or she will have bad mood?

### Answers

**Answer:**

24.6%

**Step-by-step explanation:**

denote B: bad mood; H: healthy; D: periodontal disease

P(B|D)

=P(B,D) / P(D)

=P(B,D) / [P(D,B)+P(D,H)] ### law of total probability ###

=P(D|B)P(B) / [P(D|B)P(B) + P(D|H)P(H)]

=(0.85)*(0.1)/[(0.85)*(0.1) + (0.29)*(0.9)]

=0.245664739

A model rocket is launched with an initial upward velocity of 60 m/s the rocket's height h meters after t seconds h=60t-5t^2 find values for which rockets height is 30 meters

### Answers

The model **rocket** will have a **height** of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.

How to determine the time associated with the height of a rocket on air

In this problem we have the case of a model **rocket** being launched, the **height** of the rocket in **time** is described by the following **quadratic equation**:

h(t) = 60 · t - 5 · t²

Where:

h - Height, in meters.t - Time, in seconds.

We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:

30 = 60 · t - 5 · t²

6 = 12 · t - t²

t² - 12 · t + 6 = 0

(t - 11.477) · (t - 0.523) = 0

t = 11.477 s. or t = 0.523 s.

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A chef has 5 containers of rice. Each container has 2 cups of rice in it. If the chef uses cup of rice for a recipe, how many cups of rice do they have left?

### Answers

**Answer:10-x**

**Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.**

Can someone please help me with this problem? I'm struggling and the assignment is already late :(

### Answers

Bottom right because both are for ever 1x there is 0.5 y

Suppose that the function is defined as follows.

### Answers

**Answer:**

**Step-by-step explanation:**

200 000+40 000+8 000+10+8 in standard form

### Answers

**Answer:**

240 8018

**Step-by-step explanation:**

two hundred forty eight thousand and eighteen

200 000+40 000+8 000+10+8= 248018.

Standard form is represented in the format a x 10^b. a represents any number bigger than 1, but smaller than 9.9. B is what 10 is to the power of, it represents any whole number. It can also be negative.

Try and get a to a number bigger than 1, but smaller than 9.9. Then if you multiplied the new number by 10 to the power of something to get the old number, what would it be?

In standard form, it would be 2.48018 x 10^5 (so sorry if i’m wrong!!)

Based on a survey of 1250 employees at a software company, the average number of hours spent in meetings per week is 4.3 with a margin of error of 1.1.

What is the range of values for the actual mean numbers of hours spent in meetings in a week? Enter your answer by filling in the blanks to correctly complete the statement.

The actual mean number of hours spent in meetings in a week is between______and______hours

### Answers

**Answer:**

**Step-by-step explanation:**

The margin of error represents the range of values within which the true population mean is likely to fall with a certain level of confidence. To calculate the range of values for the actual mean number of hours spent in meetings in a week, we can use the formula:

(actual mean) = (sample mean) ± (margin of error)

Substituting the given values, we get:

(actual mean) = 4.3 ± 1.1

To find the range of values, we need to compute the upper and lower bounds of this interval:

Lower bound = 4.3 - 1.1 = 3.2 hours

Upper bound = 4.3 + 1.1 = 5.4 hours

Therefore, the actual mean number of hours spent in meetings in a week is between 3.2 and 5.4 hours.

Tickets of a program at college cost $3 for general admission or $2 with student ID. If 181 people paid to see a performance and $435 was collected, how many of each type of ticket were sold.

### Answers

2 times 181 =363 435-363=71

which fraction is the smallest? 3to4, 2/3, 10:12, 2to1

### Answers

The smallest** fraction** is 8/12, which is equivalent to 2/3.

How to determine the smallest fraction

To compare fractions, it's best to convert them all to a** common denominator. **

3/4 is equivalent to 9/12

2/3 is **equivalent **to 8/12

10/12 is equivalent to 5/6

2/1 is equivalent to 24/12

So, the smallest **fraction **is 8/12, which is equivalent to 2/3.

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HELP ASAP PLEASE 20 POINTS!!!!!

### Answers

**Answer:**

5.6 mi

**Step-by-step explanation:**

1 km is around 0.6 (estimate) miles so just multiply both sides by 9 and 9km = around 5.4 miles and 5.6 is the closest so it is most likely that

18. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?

### Answers

Answer:

64.14

Step-by-step explanation:

Reading the passage I see that you have to multiply then divide

The **surface area** of the larger solid is, 171.7 mm²

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The **volumes** of two similar solids are 857.5 mm³ and 540 mm³.

And, The surface area of the smaller solid is 108 mm².l

Now, Let us assume that;

The **surface area **of the larger solid is, x

Hence, We get;

857.5 / x = 540 / 108

Solve for x as;

857.5 x 108 = 540 x

92,718 = 540x

x = 171.7 mm²

Thus, The **surface area** of the larger solid is, 171.7 mm²

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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get

�

x small greeting cards and

�

y large greeting cards?

### Answers

**Answer: 18.75**

**Step-by-step explanation:**

small greeting cards = 1.80

large greeting cards = 3.85

1.80 x 4 = 7.20

3.85 x 3 = 11.55

7.20 + 11.55 = 18.75

Find the volume of the composite solid. Round your answer to the nearest hundredth.

### Answers

To the nearest hundredth, the **volume** of composite **solid,** giving us 904.600 cubic metres.

specify the solid volume?

How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many **unit cubes **are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.

For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:

**V = l × w ×h**

The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and **two hemispheres**. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.

Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.

V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.

We arrive at a total volume of 792 cubic meters by adding these volumes together.

To the nearest hundredth=904.600 cubic meters.

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True or False Deductive reasoning is when someone uses lots of data to make a conjecture.

### Answers

False.

Deductive reasoning is a logical process in which a conclusion is drawn from a set of premises, statements, or propositions, using facts, definitions, and rules. It involves starting with general principles or premises, and then deriving specific conclusions based on those premises.

Answer:

Step-by-step explanation:

To the nearest ten dollars, what can Carlos expect the value of the computer to be 3 years after purchase

### Answers

Carlos can expect the value of the **computer** to be $580 three **years** after purchase.

To model the value of the **computer**, we can use the formula:

y = abˣ

We know that the initial value of the computer is $1,350, so a = 1350.

We also know that one **year** after purchase, the value of the computer is $810, so we can use this to find the value of b:

810 = 1350b

b= 0.6

b = 0.6

So our exponential equation is:

y = 1350(0.6)ˣ

To find the value of the **computer** 3 years after purchase, we can substitute x = 3:

y = 1350(0.6)³

y = 583

Hence, Carlos can expect the value of the **computer** to be $580 three years after purchase.

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PLEASE HELP

Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed.

C=0.90, x=13.7, s =3.0, n= 10

### Answers

The 95% **confidence interval** using a t-distribution for the population** **mean μ using the **t-distribution** is (9.7, 14.7).

Here, we have,

1. Identify the given information:

- **Confidence level** (c) = 0.95

- Sample mean (x) = 12.2

- Sample standard deviation (s) = 3.0

- Sample size (n) = 8

2. Determine the degrees of freedom (df) for the **t-distribution**:

- df = n - 1 = 8 - 1 = 7

3. Find the t-value corresponding to the 0.95 **confidence level** and 7 degrees of freedom:

- You can use a t-table or an online calculator for this.

- The t-value for a 0.95** confidence level **and 7 df is approximately 2.365.

4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):

- ME = t-value * (s / sqrt(n))

- ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5

5. Construct the 95% **confidence interval **using the sample mean (x) and the margin of error (ME):

- Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7

- Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7

So, the 95% **confidence interval** for the population mean μ using the **t-distribution** is (9.7, 14.7).

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Work out the value of fg^2 when:

f = -5 and g = -4

### Answers

-5*-4=20

20^2 =400

ANSWER=400

Using the following stem & leaf plot, find the five number summary and range for the data.

1 0 2

2 1 2 5 9 9

3

4 2 2 7 9

5 0 2 3 4 8 9

6 0 7

### Answers

Note that the **five number summary** and range for the **data** are given as follows:

Minimum: 102First Quartile (Q1): 225Median (Q2): 329Third Quartile (Q3): 458Maximum: 607.

What is the explanation for the above response?

The **five**-**number summary **and range were calculated using the given stem and leaf plot. The minimum value is 102, the first quartile (Q1) is 226, the median (Q2) is 340, the third quartile (Q3) is 492, and the maximum value is 670. The range is the difference between the maximum and minimum values, which is 568.

The range is calculated by subtracting the **minimum value **from the maximum value:

**Range**: 607 - 102 = 505

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