After Many Studies, A Researcher Finds Thatthe Probability That A Word-recognitionprogram Correctly Interprets (2024)

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

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.

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:}

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.

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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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%

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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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:

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]

[tex]undefined[/tex]

area = 1/2 ac sin B

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

187 sin 95

186.2884085 ft^2

Answer:

a) DE = 15 cm

b) AB = 6 cm

Step-by-step explanation:

Explanation #a)

- 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]

Explanation #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

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]

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.

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]

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

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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We solve as follows:

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

So, the value of "blank" is 80.

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 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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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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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.

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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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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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]

Answer:

Step-by-step explanation:

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.

-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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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:

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