Mathematics College

## Answers

**Answer 1**

**Given:**

The probability that a word-recognition the program correctly interprets a hand-written word is:

[tex]=\frac{9}{10}[/tex]

**Find-:**

How many words out of 40 would the researcher expect the program to correctly interpret?

**Explanation-:**

the probability that a word-recognition the program correctly interprets a hand-written word is:

[tex]=\frac{9}{10}[/tex]

For 40 world is:

[tex]\begin{gathered} =\frac{9}{10}\times40 \\ \\ =9\times4 \\ \\ =36 \end{gathered}[/tex]

So,** there are 36 words.**

## Related Questions

School Supplies Pencils $0.25 each Notebooks $2.50 each Backpacks $32 each- . Hugh bought x notebooks. Write an expression for the cost of the notebooks.

### Answers

Pencils: $0.25 each

Notebooks: $2.50 each

Backpacks: $32 each

The cost of the notebooks (C) must be equal to the price of each notebook (2.50) multiplied by the number of notebooks bought (x)

**C = 2.50x**

Ingrid hit a golf ball. the height of the golf ball (in meters above the ground) t seconds after being hit is modeled by h(t)=-5t²+30tIngrid wants to know when the ball reached its highest point 1) rewrite the function in a different form (factored or vertex) where the awnser appears as a number in the equationh(t)=___2) How many seconds after being hit does the ball reach its highest point?____ seconds

### Answers

Write the equation in **vertex form** to find the maximum height, as well as the time when the maximum height is reached.

The vertex form of a quadratic equation is:

[tex]y=a(x-h)+k[/tex]

Where *(h,k)* is the vertex of the parabola, *k* is the maximum or minimum value and *h* is the value of *x* where that maximum or minimum is reached.

To write *h* in vertex form, complete the square:

[tex]\begin{gathered} h(t)=-5t^2+30t \\ =-5(t^2-6t) \\ =-5(t^2-6t+9-9) \\ =-5((t-3)^2-9) \\ =-5(t-3)^2-5(-9) \\ =-5(t-3)^2+45 \end{gathered}[/tex]

We can see that in this case, the vertex is (3,45).

Therefore:

**1)**

[tex]h(t)=-5(t-3)^2+45[/tex]

**2)**

The ball reaches the maximum height **3 seconds** after being hit.

A manager at a shipping company will purchase boxes in the shape of a right rectangle prisms he wants the volume of each box to be exactly 98 cubic ftwhich figure shows a box with the dimensions in feet that the manager will purchase

### Answers

We have that the general equation for the volume of a rectangle prism is:

[tex]V=lwh[/tex]

where l represents the length of the base, w represents the width of the base and h represents the height of the prism.

Since we need that the volume be equal to 98ft³, we have that the measures for the prism are:

[tex]V=(7)(3.5)(4)=98ft³[/tex]

therefore, the prism would look like this:}

A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)Part B: What is the equation for Sn? Show all necessary math work. (3 points)Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)

### Answers

**Answer with explanation**: A hiker has increased his distanced covered by **10%** each day since the start, the total distance covered at the end of the **7th** day is **75.897mile:**

**(A) The number of miles on the first day:**

[tex]\begin{gathered} \text{let x be the distance covered on first day:} \\ x,1.1x,1.21x,1.331x,\ldots. \\ \text{ This is a Geomatric sequence:} \\ S_n=\frac{a(r^n-1)}{r-1} \\ a=x \\ r=\frac{1.1x}{x}=1.1 \\ r=1.1 \\ n=7 \\ S_n=\frac{x((1.1)^7-1)}{1.1-1}\Rightarrow(0) \end{gathered}[/tex]

Substituting the total miles covered on the **7th** day in equation**(0)** gives:

[tex]\begin{gathered} 75.897=\frac{x((1.1)^7-1)}{1.1-1} \\ 7.5897=0.9487171x \\ x=7.9999612107761101807904590314647 \\ x\approx7.9999mi \end{gathered}[/tex]

Therefore on the first day, the hiker covered about **7.99 miles:**

**(B) The equation for the S:**

[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow(1) \end{gathered}[/tex]

The equation **(1)** gives the number of miles hiked on the **nth **day.

**(C) miles covered on 10th day:**

The number of miles covered on the **10th** day is calculated using the equation**(1)** as follows:

[tex]\begin{gathered} S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow n=10 \\ S_{10}=\frac{7.99((1.1)^{10}-1)}{1.1-1} \\ S_{10}=127.340mi \end{gathered}[/tex]

The number of miles covered on the **10th** day is **127.340miles**.

**About the formula used:**

[tex]\begin{gathered} S_n=\frac{a-ar^n}{1-r}\Rightarrow\text{ Your formula} \\ \text{Multiply by:} \\ \frac{(-1)}{(-1)} \\ \therefore\Rightarrow \\ S_n=\frac{(-1)}{(-1)}\times\frac{(a-ar^n)}{(1-r)}=\frac{(-1)\cdot(a-ar^n)}{(-1)\cdot(1-r)}=\frac{-a+ar^n}{-1+r}=\frac{ar^n-a}{r-1} \\ S_n=\frac{ar^n-a}{r-1}=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{a(r^n-1)}{r-1}\Rightarrow\text{ My formula} \end{gathered}[/tex]

In conclusion, the formula used is the same as the one that was required to be used.

Kathy Runde, age 66 and retired, receives a $20,000 partial distribution from her 401(k) plan. The plan does not pay out an annuity. Immediately before the distribution, her account balance is $50,000, including $10,000 in nondeductible contributions. How much of the $20,000 distribution must Kathy include in gross income?

### Answers

The whole** twenty thousand dollars** that were distributed has to be accounted for as part of the gross **revenue**.

This is further explained below.

What is gross income?

Generally, A person's or a household's gross income is the whole amount of **money earned **before any deductions or taxes are taken out of that income. This includes all wages, salaries, profits, interest **payments**, rentals, and other types of earnings.

Because it is treated as regular income, the amount that was **withdrawn **is subject to taxation at the same rate as ordinary income under the federal **income tax system.**

If, on the other hand, **Kathy **makes the decision to convert her 401(k) to a Roth 401(k), then any money she takes out of the account will not be subject to **taxes**.

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What is the rate of return when 25 shares of Stock A, purchased for $30/share, are sold for $825? The commission on the sale is $6. Rate of Return = [?] %

### Answers

**Given:**

The rate of return when 25 shares of Stock

A. purchased for $30/share, are sold for $825. The commission on the sale is $6.

**Required:**

What is the rate of return?

**Explanation:**

First step is to find the shares of stock price:

Shares of stock price=25 shares×$30/share

Shares of stock price= $750

Second step is to calculate the total sold price:

Total sold price= $825+$6

Total sold price= $831

Third step is to calculate the Rate of return:

[tex]\begin{gathered} \text{ Rate if return }=\frac{831-750}{750}\times100 \\ \text{ Rate if return }=\frac{81}{750}\times100 \\ \text{ Rate of return }=10.8\% \end{gathered}[/tex]

**Answer:**

Rate of return is 10.8%

If you roll a 6-sided die 72 times, what is the best prediction possible for the number of times you will roll a one?

### Answers

The **prediction **of **outcomes **of the number of 1 is 12

How to determine the number of times?

The given parameters are

Device = A die

Number of rolls = 72

From the question, the die is **six-sided**

This means that the **sample space **is

S = {1, 2, 3, 4, 5, 6}

So, the probability of **rolling **a 1 is

P(1) = 1/6

When the die is rolled 72 times, the number of outcomes of 1 is

Outcomes = P(1) * n

Where n = 72

So, we have

Outcomes = 1/6 * 72

Evaluate

Outcomes = 12

Hence, the **prediction **is 12

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Simplify the fractiom

7/21

4/38

### Answers

The answer is -3/1/6

1. 7/21 = 1/3

2. 4/38 = 2/19

The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of error

of 13%. What is the maximum the company can expect for returned items?

O $3268.20

$3668.30

O$4425.60

O $4902.30

### Answers

Using **proportions**, it is found that the **maximum **the company can expect for returned items is of:

$4,616.

What is a proportion?

A proportion is a **fraction **of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division along with the unit rates in the context of this problem.

The **lost amount **to returns each day is of 15% of 27235, and this amount is calculated as follows:

0.15 x 27235 = $4,085.25

(the decimal equivalent of the percentage is multiplied by the original amount to find the equivalent amount).

The **margin of error** is of 13%, hence this amount can still be increased by 113, that is, multiplied by 1.13, hence:

4085.25 x 1.13 = $4,616.

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**Answer:**

The answer is D $4902.30

**Step-by-step explanation:**

Find the distance between the two points rounding to the nearest tenth (if necessary). (5,-8) and (-3,-1)

### Answers

**Answer: **[tex]\sqrt{113}[/tex]

**Step-by-step explanation:**

You use the Pythagorean Theorem for problems like this.

1. First you figure out the distance between the points.

2. As seen in the picture, the yellow line is 7 units long and the blue line is 8 units long.

3. From here you substitute the numbers into the Pythagorean Theorem. [tex]7^{2} +8^{2} =c^2[/tex]

4. Now solve. This gives you [tex]\sqrt{113}[/tex]

3] If the p.d.f., of the random variable X is given byf(x)= K sqrt x &0 1)(c) P(|X| < 3)(d) E(2X - 2)(e) V(3X)

### Answers

[tex]undefined[/tex]

What is the area of ΔABC given m∠B = 95°, a = 22 feet, and c = 17 feet?use area = 1/2 ac sin B

### Answers

area = 1/2 ac sin B

1/2 ( 22) ( 17) * (sin 95)

187 sin 95

186.2884085 ft^2

Please help me work this out and explain it.

### Answers

So triangle ABC and triangle CDE are the same triangle. The triangle ABC is just a simplified version of triangle CDE. So, for the length of C,E it is 24in. The length of the equivalent side of C,E is A,C which equals 8cm. So we will do the length of side C,E divided by the length of side A,C. (24 divided by 8)= 3. Since the anwser is 3 we now know that side A,C multiplied by 3 equals side C,E. So now you just do Side B,C multiplied by 3 to get the D,E side. (5 x 3) = 15. So side D,E equals 15in. To find Side B,A you will need to do the same as you did for side C,E earlier. So take side D,C and divide it by 3 (18 divided by 3 = 6) Side D,E now equals 6in.

**Answer:**

a) DE = 15 cm

b) AB = 6 cm

**Step-by-step explanation:**

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- Relating the triangle ABC with triangle DCE, a scale factor fomula is used;

[tex]{ \rm{ \frac{ \bar{DE}}{ \bar{BC} }} = \frac{ \bar{CE}}{ \bar{AC} } } \\ \\ { \rm{ \frac{\bar{DE}}{5} = \frac{24}{8} }} \\ \\ { \rm{\bar{DE}} = \frac{24 \times 5}{8} } \\ \\ { \rm{\bar{DE}} = 15 \: cm}[/tex]

**E****x****p****l****a****n****a****t****i****o****n**** ****#****b****)**

[tex]{ \rm{ \frac{ \bar{CE}}{ \bar{AC}} } = \frac{ \bar{CD}}{ \bar{AB} }} \\ \\ { \rm{ \frac{24}{8} = \frac{18}{\bar{AB}} }} \\ \\ { \rm{\bar{AB} = \frac{18 \times 8}{24} }} \\ \\ { \rm{\bar{AB} = 6 \: cm}}[/tex]

- Therefore, the scale factor is **2****,**** **triangle CDE = 2ABC

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what is the daily recommended amount of vitamin A if 15% is 150 mcg?

### Answers

If x is the daily amount of Vitamin A and we know that 15% of x is 150 mcg, we can calculate x as:

[tex]\begin{gathered} 15\%\cdot x=\frac{15}{100}x=0.15x=150 \\ x=\frac{150}{0.15} \\ x=1000 \end{gathered}[/tex]

**Answer: the recommended daily amount of Vitamin A is 1000 mcg.**

aIn a class of students, the following data table summarizes how many students passeda test and complete the homework due the day of the test. What is the probability thata student who passed the test did not complete the homework?Passed the test Failed the testCompleted the homework112.2Did not complete the homework3N

### Answers

According to the given table, the number of students that passed the test and did not complete the homework is

[tex]3.[/tex]

Also, from the table, we get that the total number of students that passed the test is

[tex]11+3=14.[/tex]

Therefore, the probability that a student that passed the test did not complete the homework is:

[tex]\frac{3}{14}\text{.}[/tex]

**Answer:**

[tex]\frac{3}{14}\text{.}[/tex]

Write the equation of the line with a slope of -3 that passes through (-5,20)

### Answers

SUBSTITUTE THE KNOWNS IN THE GIVEN GENERAL EQUATION BELOW AND SIMPLIFY TO GET **c**

[tex]y = mx + c \\ 20 = - 3( - 5) + c \\ 20 = 15 + c \\ c = 20 - 15 \\ c = 5[/tex]

Meaning

[tex]y = - 3x + 5[/tex]

IS THE EQUATION

Bridget sold a total of $135 at her yard sale. If she sold a lamp for $35.50 more than the cost of everything else, what was the cost of the lamp and everything else.

### Answers

The cost of** lamp** and **everything else** will be equal to $85.25 and $49.75 respectively.

This question can be solved by converting it into the form of **linear equation**. A linear equation can be expressed in the form of y = ax + b where a, b are coefficients and x, and y are **independent** and** dependent **variables. We know the total sale which is equal to $135. Let us assume the cost of everything else as x. Now, the cost of lamps is $35.50 more than cost of everything else that is equal to x + 35.50. Now, the linear equation will be written as

135 = x + (x + 35.50)

135 = 2x + 35.50

=> 2x = 99.5

=> x = $49.75 which is the cost of everything else and cost of lamp = x + 35.50 = $85.25.

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4/5 equals blank over 100

### Answers

We solve as follows:

[tex]\frac{4}{5}=\frac{x}{100}\Rightarrow x=80[/tex]

So, the value of "blank" is 80.

If you could please help me with this it makes no sence to me.

### Answers

**Answer:**

A = 7986 m²

**Step-by-step explanation:**

the field is in the form of a trapezium.

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular distance between the bases b₁ and b₂

here h = 66 , b₁ = 102, b₂ = 140 , then

A = [tex]\frac{1}{2}[/tex] × 66 × (102 + 140) = 33 × 242 = 7986 m²

**Answer:**

7986 m²

**Step-by-step explanation:**

The field geometric shape is a trapezoid whose bases are 102 m and 140 m and height of 66m

The equation for the area of a trapezoid is given by

[tex]A = \dfrac{a + b}{2} h\\\\[/tex]

where a and b are the two sides and h is the height

Here a = 102, b = 140 and h = 66

Substitute these values directly into the equation for area

[tex]A = \dfrac{102 + 140}{2} \times 66\\\\A = (102 + 140) \times \dfrac{66}{2}\\\\\\102 + 140 = 242\\\\\dfrac{66}{2} = 33\\\\\\A = 242\ \times 33 = 7986\; m^2[/tex]

Tristan is building steps up to a deck that is 1 yards above the ground. The steps must all be the same height. If he wants to make 8 steps, how high should he make each step?

### Answers

Tristan should make **8 pieces** of length **0.125** **yards** each to make a steps to the deck **1 yards** above.

What is division?

Division is breaking a number up into an **equal number **of parts. Mathematically, we can write "**[a]** divided by** [b]**" as **a ÷ b**. The division algorithm is given by -

**D = dq + r**

**[D] **- Dividend

**[d]** - Divisor

**[q] **- Quotient

**[r] **- remainder

Given is Tristan who is building steps up to a deck that is** 1 yards** above the ground. The steps must all be the **same height** an he wants to make **8 steps.**

Total number of steps to be made =** [n] = 8**

Height of deck = **[h] = 1 yard.**

Now, we have to divide **1 yard** into **8 equal** parts. Therefore, assume

that -

**A = 1 ÷ 8**

A = 1/8

0.125

We get the length of each **step **to be **0.125 yards.**

Therefore, Tristan should make **8 pieces** of length **0.125** **yards** each to make steps to the deck **1 yards** above.

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Find the product of 21 and the difference between one whole number 1/2 and -1/2

### Answers

The** product** of 21 and the difference between one whole number 1/2 and -1/2 is; 42

What is the product of the two numbers?

We want to find the **product **of 21 and the **difference** between one whole number 1/2 and -1/2. This can be expressed as;

21 * (1¹/₂ - (-¹/₂))

Let us first solve the **bracket** out using the **order of operations** rule named PEMDAS which stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction to get;

1¹/₂ - (-¹/₂)

= 1¹/₂ + ¹/₂

= 2

Thus;

21 * (1¹/₂ - (-¹/₂)) = 21 * 2

= 42

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please help me with this. I have been trying to figure it out for a long time and I need to have dinner with my family very soon.

### Answers

To subtract this polynomial, we would have to open the bracket

[tex]\begin{gathered} 9x^4+8x^3-6-(5x^2-8x+6) \\ 9x^4+8x^3-5x^2+8x-6-6=9x^4+8x^3-5x^2+8x-12^{} \end{gathered}[/tex]

Remember, we only add and subtact directly , Algebraic characters of the same type only

and the same power only.

Elinor wanted to order an 18 inch hoagie, which cost $7.99. The sandwich shop is out of 18 inch buns. They only have 12 inch buns.

### Answers

The price of **12 inch bun** purchased by **Elinor **is $5.32.

What is defined as the method of unitary?The unitary method determines the value of a unit and afterwards the value of such a necessary number of units. The value of a unit amount is determined first in the unitary method before calculating the value of many other units. It comes in two varieties.Variation in DirectVariation in the inverse

For the given question;

**Elinor **wanted to have a bun.

The cost of 18 inch **hoagie **bun is $7.99.

As there is only 12 inch bun present, the price of 12 inch bun is calculated by **unitary method.**

The price can be written as;

18 inch -------> $7.99

For 1 inch bun, divide both side by 18.

18/18 inch -------> $7.99/18

1 inch -------> $7.99/18

For 12 inch, multiply each side by 12.

12 inch -------> $7.99×12/18

12 inch -------> $5.32

Thus, the price of** 12 inch bun** is $5.32.

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Nicholas is typing a book report at an average of 30 words per minute. Which equation could Nicholas use to find tea the amount the amount of time in minutes he will spend typing his report has W words?

### Answers

The **equation **could Nicholas use to find tea the amount the amount of time in minutes he will spend typing his report has W words is w = 30t .

What is speed?

In contrast to **velocity**, which describes the speed and **direction** of an object's movement, speed is the **rate of movement** along a path. Alternatively, velocity is a **vector** while speed is a **scalar** quantity. Velocity and speed are denoted by the letters v and v, respectively (boldface). The symbol has a bar over it for **average values**. How swiftly something is going, being done, or something that is moving quickly is measured in terms of speed. Driving an automobile 45 miles per hour is an illustration of speed. Someone cleaning a room in 10 minutes would be an example of quickness. the definition of speed. a **direction** or speed at which an object's location changes.

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Ben has £24

He gives £16 to Rhys.

a) What fraction of the £24 does Rhys get?

Give your answer in its simplest form.

b) What fraction of the £24 does Ben have now?

Give your answer in its simplest form.

### Answers

**Answer:**

[tex]\frac{2}{3}[/tex] and [tex]\frac{1}{3}[/tex]

**Step-by-step explanation:**

(a)

fraction Rhys gets is [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]

(b)

Ben is left with £24 - £16 = £8

then fraction Ben has left is

[tex]\frac{8}{24}[/tex] = [tex]\frac{1}{3}[/tex]

A country's education department reported that in 2015, 64.8% of students enrolled in college or a trade school within 12 months of graduating high school. In 2017, a random sample of 179 individuals who graduated from high school 12 months prior was selected. From this sample, 112 students were found to be enrolled in college or a trade school. Complete parts a through c. a. Construct a 90% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2017.

The confidence interval has a lower limit of

and an upper limit of

(Round to three decimal places as needed.)

### Answers

**Answer:**

**Step-by-step explanation:**

Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again.(a) What is the probability that the second roll is also a "4".P(4 | 4) =(b) What is the probability that the second roll is a "1".P(1l4)

### Answers

The probability of getting a 4 again means is given by the product of the probabilities to obtain 4 twice (because in this case we have independent events)

**(a) P(4I4) = P(4)*P(4) = (1/6)(1/6) = 1/36**

**(b) P(1l4) = P(1)*P(4) = (1/6)(1/6) = 1/36**

In the previous calculations we have considered that the probability for getting any number is the same and it is 1/6.

Which number comes first

5

1/3 -1. √3. - 12/21

6

3.4

### Answers

-3.4 is the **number** which will come first.

What is simplifying?

To simplify simply means to make anything easier. In mathematics, **simplifying** an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. the act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired.

Given Data

5, 1/3 -1. √3. - 12/21,6,3.4

**Simplifying**,

5, [tex]\frac{1}{3}[/tex] - 1, √3. -[tex]\frac{12}{21}[/tex], 6, -3.4

5, -0.6 , [tex]\sqrt{3}[/tex] , -0.5 ,6,-3.4

-3.4 is the **number** which will come first.

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For what value of x will 3x + 4 = x - 6 be a true statement?

A x = -5

В. x = -5/2

C x = -1

D x = - 1/2

### Answers

**Answer:**

A

**Step-by-step explanation:**

3x + 4 = x - 6 ( subtract x from both sides )

2x + 4 = - 6 ( subtract 4 from both sides )

2x = - 10 ( divide both sides by 2 )

x = - 5

**Answer:x 1= x. Examples: 41=4. 5)**

**Step-by-step explanation:**

Are the triangles similar! If yes state how?are the triangles similar if yes State how

### Answers

Part 1

Remember that

If two triangles are similar , then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

Verify the proportion

38.5/14=22/8

38.5*8=14*22

308=308 -----> is true

that means

the triangles are similar

Part 3

Verify the proportion

22/9=30/12=25/10

2.44=2.5=2.5 ------> is not true

that means

the triangles are not similar