Word Problems
1. The sum of 21 and three times a number is 60. What is that number?

2. Three times the difference between a number and three is equal to four times the number.
That is that number?

3. The sum of three consecutive integers is 48. Once you find them, answer this question: What
is > times the 3m as minus z times the 1St ?

4. Twice the smallest of three consecutive odd integers is seven more than the largest. What is the middle number?

5. The length of a rectangle is 3 cm more than the width. The perimeter is 22 cm. What is the
AREA of this rectangle? Note: A = (L)(W)

6. The perimeter of a triangle is 43 in. Side b is 3 times the length of side a. Side c is 1 more than twice the length of side a. What is the SUM of sides a and b?

The slope for:

1 = 1/2  (Option E)

2 = 2 (Option C)

3 = -1/2 (Option H)

4 = -2 (Option A)

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

The formula for slope (m) is given as:

m = Rise/Run = y2-y1/x2-x1

(x1,y1) = Coordinates of the first point in the line

(x2,y2) = Coordinates of the second point in the line.

1) The points are:

x1= -2

y1 = 2

x2 =2

y2  = 4

m = (4 - 2) / (2 - (-2))

m = 2 / 4

m = 1/2

Thus, Δy/Δx = 1/2

2) The points are:

x1= -1

y1 = -12

x2 =5

yx  = 0

m = (y2 - y1) / (x2 - x1)

Substituting the given values, we get:

m = (0 - (-12)) / (5 - (-1))

m = 12 / 6

m = 2

Thus, Δy/Δx = 2


3) Where the points are:
x1= 2

y1 = -6

x2 = - 4

y2  = -3

Substituting the given values, we get:

m = (-3 - (-6)) / (-4 - 2)

m = 3 / (-6)

m = -1/2

Thus, Δy/Δx = -1/2


4)  Where the points are:
x1= 0

y1 = 3

x2 = 1.5

y2  = 0

Substituting the given values, we get:

m = (0 - 3) / (1.5 - 0)

m = -3 / 1.5

m = -2


Thus, Δy/Δx = -2

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Answer:

$ 546.00

Step-by-step explanation:

Simple Interest = P x r x  t

where t = number of years

r = interest rate per year as a decimal

P = amount invested(deposit)

We are given that r = 7.8% per year = 7,8/100 = 0.078

However, since this is the yearly interest, the monthly interest = 0.078/12

The time period is 42 months

Initial deposit = $2,000

Therefore interest
I = 2000x (0.078/12) x 42 =  $ 546.00

The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

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Answer:

R207

Step-by-step explanation:

R180 times 15% =27

27+180=207, therefore, R270 ir correct

Answer:

Below

Step-by-step explanation:

Rectangular area = L x W =  10 x 20 = 200 ft^2

  PLUS triangular area = 1/2 b h = 1/2 * 10 * 10  = 50 ft^2

      TOTAL = 250 ft^2

The value of k is given as follows:

k = 2x.

The exponential function that models the growth of the first virus is given as follows:

y = P(3)^x.

The exponential function that models the growth of the second virus is given as follows:

y = P(9)^x = P(3)^k.

We have that 9 is the second power of 3, hence we have that:

y = P(3²)^x = P(3)^k.

Applying the power of power rule, we have that:

y = P(3)^(2x) = P(3)^k.

Hence the value of k is given as follows:

k = 2x.

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Answer:

4,233,000

Step-by-step explanation:

4,232,000                 4,4232,852                  4,233,000

4,4232,852 is between 4,232,000 and 4,233,000.  It is closer to 4,233,000.

The rule is to look a the digit in the hundreds' place.  That number is 8.  If the digit in the hundreds' place is 5 or larger, you round up.

Answer:

(B) "1 to 5."

Step-by-step explanation:

The ratio of single to married instructors is 1 to 5. Since 4 instructors are single out of 24 total instructors, the ratio of single instructors to married instructors is 4 to (24 - 4) = 4 to 20. Simplifying the ratio to its simplest form, we get 4:20 = 1:5, which is the answer choice (B) "1 to 5."

Based on the information, it can be inferred that the area of the figure is 310 yards²

To calculate the surface area of this figure we must find the area of all the faces of the figure:

Then we must multiply the area of each face by the number of faces with that area.

Finally we must add the areas of the faces

According to the above, the total surface area of this figure is 310 yards ²

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[tex]\cfrac{6}{4+\sqrt{2}}\implies \cfrac{6}{4+\sqrt{2}}\cdot \cfrac{4-\sqrt{2}}{4-\sqrt{2}}\implies \cfrac{6(4-\sqrt{2})}{\underset{\textit{difference of squares}}{(4+\sqrt{2})(4-\sqrt{2})}} \implies \cfrac{6(4-\sqrt{2})}{(4)^2 - (\sqrt{2})^2} \\\\\\ \cfrac{6(4-\sqrt{2})}{16 - 2}\implies \cfrac{6(4-\sqrt{2})}{14}\implies \cfrac{3(4-\sqrt{2})}{7}\implies \cfrac{12-3\sqrt{2}}{7}[/tex]

If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that  can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is:  x=≤ 477.5.

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

Inequality

x is the integer

First step is to formulate the inequality

40x≤ 25,500-6,400

Now let determine the x by using the inequality

40x≤ 25,500-6,400

40x≤19,100

x=≤19,100/40

x=≤ 477.5

Therefore If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that  can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is:  x=≤ 477.5.

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The graph of the function is added as an attachment

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

h(x) = (1/3)ˣ - 4

The above function is an exponential function shifted down from the origin by 4 units

An exponential function of this form is represented as

h(x) = a(b)ˣ + c

Where

Initial value = a

Rate = b

Shift = c

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

a = 1

b = 1/3

c = -4

Next, we plot the graph

See attachment for the graph of the function

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.

In the given figure, there are two pairs of vertical angles~

That are :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \: \: and \: \: \angle3[/tex]

and

[tex]\qquad \sf  \dashrightarrow \: \angle2 \: \: and \: \: \angle4[/tex]

Also, vertical opposite angles are equal in measure.

The probability of getting exactly one head after flipping a coin three times is equal to ( 3 / 8 ) .

Possible outcomes of flipping a coin three times are :

= { HHH, THH, HTH, HHT, TTH, THT, HTT, TTT }

Possible outcomes of getting exactly one head are:

= { TTH, THT, HTT }

Total number of outcomes are equal to 8

Favourable number of outcomes are 3

Probability of getting exactly one head is equal to

= ( Number of favourable outcomes ) / ( total number of outcomes)

= 3 / 8

Therefore, the probability of getting exactly one head by flipping a coin three times is equal to ( 3 / 8 ).

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After answering the provided question, we can say that the function's midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2. midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5

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Answer:

Option C. (x + 5)

Step-by-step explanation:

This quadratic equation can either be solved using the quadratic formula or be factorised using The Double Bubble Method.

Double Bubble Method:

After listing the different pairs of factors 10, the pair (that would add together to give 7) are 2 and 5. These two factors will be used to rewrite +7x:

[tex]x^{2} + 2x + 5x + 10[/tex]

Factorization by grouping (i.e factorising each separate group sharing a common factor) will then be applied:

[tex]= x(x + 2) + 5(x + 2)[/tex]

The common factor, which is the (x + 2) expression, will be extracted:
[tex]= (x + 2)(x + 5)[/tex]

∴ [tex]x^{2} + 7x + 10[/tex] can be factorised to [tex](x + 2)(x + 5)[/tex]

It is observed that a factor of the given quadratic equation is x + 5

∴Option C

The conditional probability P(B|F) of the two way table is; P(B|F) = 0.37 given that the students prefer to write with block letters, there is a 0.37 probability that they have fair dancing skills

Two-way tables are a way of sorting data so that the frequency of each category can be seen quickly and easily.

Conditional probability is defined as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

Now, from the given two way table,

B = the student prefers writing in block letters.

F = the student's dancing skills are fair.

Thus;

P(B|F) = 17/45

P(B|F) = 0.37

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The Shanika Company's inventory levels changed during 20Y6. The materials inventory increased, the work in process decreased, and the finished goods slightly increased.

Based on the information provided, it appears that the Shanika Company has gone through some changes in its inventory levels during the 20Y6 period.

The company's materials inventory has increased from $274,730 on January 1 to $346,160 on December 31, indicating that the company has acquired more raw materials over the course of the year.

On the other hand, the work-in-process inventory has decreased from $494,510 to $470,780, suggesting that the company has been able to efficiently process its raw materials into partially completed goods over the year.

Finally, the finished goods inventory has increased slightly from $475,280 to $481,160, indicating that the company has been able to produce more finished products over the course of the year and has had sufficient demand for its products to keep the finished goods inventory at a relatively stable level.

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The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.

We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of

y² = x, x = 3y.

=> x = 3y --(1)

=> y² = 3y

=> y² - 3y = 0

=> y( y - 3 ) = 0

=> y = 0 or y - 3 = 0

=> y = 0 , y = 3

from (1), x = 3y => x = 0, x = 9

Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is

[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]

where R = 3y , r = y²

[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]

[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]

[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]

[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]

[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]

Hence, the required volume is 162π/5 cubic units.

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Answer:

563

Step-by-step explanation:

The time Jim takes alone to mow the lawn is 10 hours.

Jim and Craig, working together  can mow the lawn in 8 hours. Working alone, Craig take 4 times as long as Jim.

Therefore, the time it takes Jim to mow the lawn alone can be calculated as follows:

let

x = time use by Jim to mow the lawn

Therefore,

time Craig use to mow the lawn = 4x

Hence,

1 / 8 = 1 / 4x + 1 / x

1 / 8 =  1 + 4/ 4x

1 / 8 = 5 / 4x

cross multiply

4x = 40

x = 40 / 4

x = 10

Therefore,

time Jim takes alone to mow the lawn = 10 hours.

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Answer:

2 . of(0)=2/1/2 this is answer number 2

The solution is, option 2 neither linear nor exponential.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The given function is

x    : -5       -3      -1       1      3

f(x) :8192   512   32      2    18

when we plot this function in the excel we get to know that it a regression as shown in the figure attached  

because value of  lies between (0,1)

which shows regression

therefore it is neither linear nor exponential.

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The solution to the system of equations is x = -1 and y = 1.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

The system of equation is given as:

2x - 3y = -5 .........(1)

3x + y = -2 ........(2)

Equation 2 can be written as:

y = -2 - 3x

Substituting the value of y in equation 1 we have:

2x - 3(-2 - 3x) = -5

2x + 6 + 9x = -5

11x + 6 = -5

11x = -5 -6

11x = -11

x = -1

Substituting the value of x in equation 2 we have:

3x + y = -2

3(-1) + y = -2

-3 + y = -2

y = -2 + 3

y = 1

Hence, the solution to the system of equations is x = -1 and y = 1.

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The range is the set of y-coordinates of the function.

As per graph we can see:

Add all together to get the range:

As interval the range is:

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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Percentage of change in the stock's price since the beginning of the year is: 12.32%

The price at which a stock's share is currently trading on the market is referred to as the stock price. Every publicly listed company issues its shares at a price, which is an estimation of their value that, ideally, corresponds to the worth of the firm itself.

The market forces of supply and demand govern a company's share price once it becomes public and its shares begin trading on a stock exchange. Price increases will occur if there is a large demand for its shares. A stock's price might be reduced by sellers if the company's prospects for future growth appear uncertain.

Given that,

Closing price today = $21.20

Closing price on the previous trading day= $28.83

Difference between closing price today and closing price on the previous trading day= $21.20 - $28.83

= $7.63

Percentage of change in the stock price since the beginning of the year

= Year-to-date % change

= 12.32%

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Answer:because angles in a triangle add up to 180 degrees.

Step-by-step explanation:

A=40

C=30

So 180-40-30=110

The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

where:

μ1 = mean bumper repair cost for small pickups ($1090)

μ2 = mean bumper repair cost for small utility vehicles ($485)

s1 = standard deviation of bumper repair cost for small pickups ($403)

s2 = standard deviation of bumper repair cost for small utility vehicles ($382)

n1 = sample size for small pickups (5)

n2 = sample size for small utility vehicles (8)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator. Since the degrees of freedom (df) for a Welch's t-test are unequal, the critical value can be approximated using the degrees of freedom formula:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / (((s1^2 / n1)^2) / (n1 - 1) + ((s2^2 / n2)^2) / (n2 - 1))

Plugging in the values, we get:

df = ((403^2 / 5) + (382^2 / 8))^2 / (((403^2 / 5)^2) / (5 - 1) + ((382^2 / 8)^2) / (8 - 1)) = 9.57

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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