Mathematics College

find the percent of change. Round to the nearest whole percent original:26 new:30

Answers

Answer 1

We want to find the percentage change;

We can do that using the formula;

[tex]\text{ \%P}=\frac{New-Original}{\text{Original}}\times100\text{\%}[/tex]

Given:

[tex]\begin{gathered} \text{Original = 26} \\ \text{New = 30} \end{gathered}[/tex]

Substituting the given values;

[tex]undefined[/tex]

Related Questions

Can someone help please

Answers

The maximum displacement of this cosine wave function is equal to 8 inches.

The frequency of this cosine wave function is equal to 1/8 Hertz.

The time (t) required for one cycle is equal to 8 seconds.

What is a cosine wave?

Mathematically, a cosine wave simply refers to an equation of simple harmonic motion (SHM) and it is modelled by this mathematical expression:

y = asinωt = asin2πft ......equation 1.

Where:

a represents the amplitude or maximum displacement of a cosine wave. f represents the frequency measured in Hertz.ω represents the angular velocity.t represents the time measured in seconds.

How to calculate the maximum displacement?

From the information provided, the equation for this simple harmonic motion (SHM) is given by:

d = -8cos(π/4)t ......equation 2.

By comparing equation 1 and equation 2, we have the following parameters:

Maximum displacement or amplitude, a = |-8|

Taking the absolute value of a, we have:

Maximum displacement or amplitude, a = 8

For the frequency, we have:

Angular velocity, ω = 2πf

Making frequency (f) the subject of formula, we have:

Frequency (f) = ω/2π

Frequency (f) = (π/4)/2π

Frequency (f) = π/8π

Frequency (f) = 1/8 Hertz.

Finally, we would calculate the amount of time (t) required for one cycle as follows:

Time (t) = 1/f

Time (t) = 1/(1/8)

Time (t) = 8 seconds.

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Complete Question:

An object moves in simple harmonic motion described by the equation d = -8cos(π/4)t, where t is measured in seconds and d in inches. Find the following:

maximum displacement

the frequency

the time required for one cycle.

result step by step of this simple but yet hard for me exercise

Answers

Answer:

The anser is

Step-by-step explanation:

DO IT YOURSELF BRO GO LEARN AND STOP USING BRAINLY PU_$$y

Over the interval [0,2pi), what are the solutions to cos(2x)=cos(x)? Check all that apply.

Answers

Answer:

x = 0 and 2pi/3

Explanation

Given the expression

cos(2x)=cos(x)

In trigonometry expression;

cos2x = 2xos^2x - 1

Substituting into the equation given;

cos(2x)=cos(x)

2xos^2x - 1 = cos x

Rearrange

2xos^2x - 1 - cosx - 1 = 0

Let P = cosx

2P^2 - P - 1 = 0

Factorize

2P^2 - 2P+P-1 = 0

2P(P-1)+1(P-1) = 0

2P+1 = 0 and P-1 = 0

P = -1/2 and 1

Recall that P = cosx

-1/2 = cosx

x = cos^-1(-1/2)

x = 120 degrees = 2pi/3

If P = 1

cosx = 1

x = cos^-1(1)

x = 0

Hence the value of x that satisfies the equation is 0 ad 2pi/3

Keandre wants to buy a new pair of shoes that costs $220. In order to earn money for this, Keandre babysits his neighbor for $10 an hour. He also has saved up his monthly allowance which totals $50. What is the minimum number of hours he should babysit in order to be able to afford the shoes?

Answers

Answer:

Step-by-step explanation:

$220=$10x+$50

x= hours

subtract $50 from both sides making sure to cancel the right side

$220-$50=$10x

$170=$10x

Divide both sides by $10 to leaving x by itself on the right side

$170/$10=x

17hrs=x

The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Cost of new pair of shoes = $220

In order to earn money for this, Keandre babysits his neighbor for $10 an hour.

And, He also has saved up his monthly allowance which totals $50.

Now,

Let number of minimum hours = x hour

So, We can formulate;

⇒ $10x + $50 = $220

Solve for x as;

⇒ $10x + $50 = $220

Subtract 50 both side, we get;

⇒ $10x + $50 - $50 = $220 - $50

⇒ $10x = $170

Divide by 10 both side, we get;

⇒x = 17

Thus, The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

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I just need to make sure 1-9 are correct so if you could confirm please.9 b)

Answers

Given:

[tex]2x^2+3x+9=0[/tex]

To find:

The roots.

Explanation:

Here,

[tex]\begin{gathered} a=2 \\ b=3 \\ c=9 \end{gathered}[/tex]

Using the quadratic formula,

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

On substitution we get,

[tex]\begin{gathered} x=\frac{-3\pm\sqrt{(3)^2-4(2)(9)}}{2(2)} \\ =\frac{-3\pm\sqrt{9-72}}{4} \\ =\frac{-3\pm\sqrt{-63}}{4} \\ =\frac{-3\pm3i\sqrt{7}}{4} \end{gathered}[/tex]

Therefore, the solutions are,

[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]

Final answer:

The solutions are,

[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]

The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.

a. Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meet its goal.

b. List three different combinations of tickets sold that satisfy the inequalities.

Answers

The system of inequalities is x + y ≤ 300, 11x + 15y ≥ 3630, x ≥ 0 and y ≥ 0 while the three points are (70, 200), (150, 140) and (140, 150)

How to graph the system

From the question, we have the following parameters that can be used to determine system of inequalities

An adult ticket = $15Student ticket = $11. Auditorium capacity = 300 ticket-holdersAmount from sales = at least $3630 from ticket sales.

Represent the adult with y and the students with x

So, we have the following representations

x + y ≤ 300 ---- the ticket holders cannot exceed the capacity

11x + 15y ≥ 3630 --- the total sales cannot be less than $3630

x ≥ 0 -- the number of students cannot be negative

y ≥ 0 -- the number of students cannot be negative

Write out the inequalities

x + y ≤ 300

11x + 15y ≥ 3630

x ≥ 0

y ≥ 0

Next, we represent the inequalities on a graph

See attachment for the graph of the inequalities

The combinations from the graph

To get the combination, we make use of the coordinate points that are in the shaded region of the graph

Using the above as a guide, we have

(70, 200), (150, 140) and (140, 150)

There are other points too

Answers

The answer to the question is 4000

10x10x10=1000x4=4000

Explain how knowing the linear factor establishes that f(10) multiple of 12.

Answers

f(10) is a multiple of 12 because f(x) has a linear factor of x+2 and x+2 = 12, when x = 10

f(10) multiple of 12 is given as:

The first-degree equations that make up a polynomial's linear factors serve as the foundation stone for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. When paired with other linear factors, each linear factor represents a separate line, resulting in several sorts of functions with progressively more intricate graphical representations.

f(10) = (10+2)(100+20+2)

= (12)(122)

= 1220+244

= 1464

Hence, f(10) is a multiple of 12

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What number would you add to both sides of x2 + 7x = 4 to complete the square?2²0 72이를즐이

Answers

To complete the square, we want a number such that:

[tex]\begin{gathered} 2\sqrt{a}=7 \\ a=(\frac{7}{2})^2 \end{gathered}[/tex]

because in this way we can writte the square as follows:

[tex]\begin{gathered} x^2+7x+(\frac{7}{2})^2=4+(\frac{7}{2})^2 \\ (x+\frac{7}{2})^2=4+(\frac{7}{2})^2 \end{gathered}[/tex]

Hence the answer is the last option:

[tex](\frac{7}{2})^2[/tex]

Find the simple interest on $50,000 for 2 years at 7%

Answers

Answer:

$7,000

Explanation:

To find the simple interest on any principal, we use the formula:

[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]

From the given question:

• Principal = $50,000

• Rate= 7%

• Time = 2 years

Therefore:

[tex]\begin{gathered} \text{Interest}=\frac{50,000\times7\times2}{100} \\ =\$7,000 \end{gathered}[/tex]

The simple interest is $7,000.

given AC=XZ and AB=XY prove BC=YZ

Answers

119 that is it because Ac = 19 then Xz is 50 and AB = 54 and Xy is 6

Which two values of x are roots of the polynomial below?
4x² - 6x+1
A. x = -6-√52/16
B. x = 6+ √20/8
C. x = 6-√20/8
D. x = -8-√28/6
E. x = -8+ √28/6
F. x = -6 + √52/16

Answers

Roots are x = - 6 + √20/8 and x = - 6 - √20/8 of polynomial.

What in mathematics is a polynomial?

Sums of terms with the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered.

4x² - 6x+1 = 0

x = -b ± √b² - 4ac/2a

x = - (6) ± √(-6)² - 4 * 4 * 1/2 * 4

x = -( 6) ± √36 - 16/8

x = - 6 ± √20/8

So, roots are x = - 6 + √20/8 and x = - 6 - √20/8

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Find the slope of the line that passes through each of the following sets of points (0, 0) and (1, 4)

Answers

Answer:

slope would be 4/1

Step-by-step explanation:

its rise over run, so up 4 and out 1

have a good day!

help meeeeeee pleaseee !!!!

Answers

The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:

y = -5*x + 3

How to find the linear function?

We can find a general linear function in the slope-intercept form as:

y = m*x + k

Where m is the slope and k is the intercept of the y-axis.

If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:

m = (d - b)/(c - a)

In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:

m = (-7 - 18)/(2 + 3) = -5

So the line is something like:

y = -5*x + k

To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:

-7 = -5*2 + k

-7 = -10 + k

-7 + 10 = k

3 = k

So the linear function is:

y = -5*x + 3

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help please

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample 50 of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.

5 9 10 2 2 2 2 7 7 7 7 6 7

8 9 9 2 10 2 7 6 9 8 10 9 2

7 5 7 2 2 7 7 6 2 10 8 2 6

6 9 5 2 10 7 10 2 2 6 6

Develop a confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.

Answers

Using the t-distribution, the 95% confidence interval estimate of the population mean rating for Miami is of:

(4.29, 7.71).

What is a t-distribution confidence interval?

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the meaning of the parameters are:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

Using a calculator from the 50 observations given in this problem, the values of the parameters are as follows:

[tex]\overline{x} = 6, s = 2.86, n = 50[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Hence the lower bound of the interval is given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6 - 2.0096\frac{6}{\sqrt{50}} = 4.29[/tex]

The upper bound of the interval is given by:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6 + 2.0096\frac{6}{\sqrt{50}} = 7.71[/tex]

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Ward is planning to install a new counter top in kitchen, as shown in the figure. Determine the area of the countertop.

Answers

[tex]\begin{gathered} A=\frac{a+b}{2}\cdot h \\ A=\frac{6+8}{2}\cdot2 \\ A=14ft^2 \end{gathered}[/tex][tex]\begin{gathered} A=h\cdot l \\ A=2\cdot3 \\ A=6ft^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Total area:} \\ A_T=6ft^2+14ft^2+6ft^2=26ft^2 \end{gathered}[/tex]

I inserted a image of the question I’m very confused and need help with homework so I do good on test

Answers

To find the magnitude of a vector we use the following equation

[tex]\lvert\vec{v}\rvert=\sqrt[]{(v_x)^2+(v_y)^2}[/tex]

This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:

In the case of your exercise, the values would be

[tex]\begin{gathered} v_x=x \\ v_y=y \\ \lvert\vec{v}\rvert=\sqrt[]{(x_{})^2+(y)^2} \end{gathered}[/tex]

Translate the sentence into an equation. Use the variable w for the unknown number.Two times the sum of a number and 7 equals 6.

Answers

we have that

Two times the sum of a number and 7 -----> 2(w+7)

Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6

the answer is

2(w+7)=6

9y-(2y-3)=5(y-2)+2
Should equal ‘no solution’

Answers

[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]

ATTACHED IS THE SOLUTION OF Y

BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.

Your lunch in the hospital cafeteria cost $6.50. How much will you spend each week if you average spending $6.50 per meal every day for your five day work week?

Answers

$32.50 per week because you take $6.50 x 5 days a week

a line goes through the point (5, -7) and has slope m = -3. write the equation that represents the line.

Answers

We are given the following information

Slope of the line = m = -3

The line passes through the point (5, -7)

Recall that the equation of a line in the point-slope form is given by

[tex](y-y_1)=m(x_{}-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point on the line.

Let us substitute the given values into the above equation

[tex]\begin{gathered} (y-(-7)_{})=-3(x_{}-5_{}) \\ (y+7)=-3(x_{}-5_{}) \\ y+7=-3x+15 \\ y=-3x+15-7 \\ y=-3x+8 \end{gathered}[/tex]

Therefore, the equation of the line in slope-intercept form is

[tex]y=-3x+8[/tex]

12. In the diagram below, transversal TU intersects PQ and RS at V and W, respectively. If mZTVQ = 5x - 22 and mZTVQ = 3x + 10, for which value of x is PQ parallel to RS? P_ R W A. 6 B. 16 C. 24 D. 28

Answers

ANSWER:

The value of x is 16

STEP-BY-STEP EXPLANATION:

With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.

Thanks to this we can make the following equality:

[tex]5x-22=3x+10[/tex]

Solving for x:

[tex]\begin{gathered} 5x-3x=22+10 \\ 2x=32 \\ x=\frac{32}{2} \\ x=16 \end{gathered}[/tex]

Answer:

16 is the answer

A square napkin has sides of length 8 inches. To the nearest inch, what is the length of the diagonal of the (1
napkin?
O8 inches
09 inches
O11 inches
O16 inches

Answers

The length of the diagonal of the napkin is 11 inches.

Here, we are given that a square napkin has a side of length 8 inches.

All the sides of a square are equal and the measure of angle formed by any two adjacent sides is also equal and 90°.

Thus, by using Pythagoras theorem, we can form the following equation-

[tex]side^{2} + side^{2} = diagonal^{2}[/tex]

Let the diagonal of the square be d. Then, we have-

[tex]8^{2} +8^{2} =d^{2}[/tex]

64 + 64 = [tex]d^{2}[/tex]

128 = [tex]d^{2}[/tex]

[tex]d^{2}[/tex] = 128

d = [tex]\sqrt{128}[/tex]

d = [tex]8\sqrt{2}[/tex]

the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,

d = 8 × 1.41

= 11.28

Thus, the length of the diagonal of the napkin to the nearest inch comes out to be 11.

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A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Dallas, Houston, and San Antonio (see figure).
If the actual distance from San Antonio to Houston is approximately 192 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate
a. the actual distance from Dallas to Houston.
b. the actual distance from Dallas to San Antonio.

Answers

a. The actual distance from Dallas to Houston is 0.058 mi. b. The actual distance from Dallas to San Antonio is 0.064 mi

What is the scale factor?

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given that the actual distance from San Antonio to Houston is approximately 192 miles.

The scale factor from the map to the real world is;

(actual)/( map) = (192mi)/(3 in) = 64 mi/in

Then the actual distance from Dallas to Houston will be;

(3.75 in)(64 mi/in) = 0.058 mi

And from Dallas to San Antonio, the distance will be;

(4.125 in)(64 mi/in) = 0.064 mi

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write the following in the form a+bi (2+5) - (-6 +bi)

Answers

The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi

How to evaluate the expression?

The expression is given as

(2+5) - (-6 +bi)

The above expression is a complex expression

So, we have the following expression

(2+5) - (-6 +bi)

Remove the brackets in the above expression

So, we have the following expression

(2+5) - (-6 +bi) = 2 + 5 + 6 - bi

Evaluate the like terms in the above equation

So, we have the following expression

(2+5) - (-6 +bi) = 13 - bi

Hence, the solution to the complex expression is 13 - bi

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A coin has 2 sides: heads (H) and tails (T). A bag has 3 balls: 1 red (R), 1 green (G), and 1 blue (B). You toss a coin and randomly pick a ball. What is the sample space?

Answers

The space sample is the total quantity of possible results

for each toss there are 3 possible results

so the total results are 2x 3 = 6

The only option with 6 elements is B

so the answer is B.

The sum of two whole numbers is 63. The difference between the numbers is less than 10. Find as many solutions

Answers

Answer:

hmmph..

(32, 31)

(33,30)

(34, 29)

(35, 28)

(36,27)

(37, 26)

Step-by-step explanation:

That all I got....

A cricket pitch measures $1$ chain by $10$ feet. What is the area of a cricket pitch in square feet?

(Useful information: there are $3$ feet in a yard, and there are $22$ yards in a chain.)

Answers

Area of the cricket pitch is 660 square feet

Given

1 chain is equal to 10 feet

There are 3 feet in a yard

And 22 yards in a chain

Hence it is evident that

One chain is equal to 22 x 3

1 chain = 66 Feet

Area of a rectangle is Length x Width

Length = 66

Width = 10

Hence Area = 66 x 10

Area = 660 Square feet

Hence area of the cricket pitch is 660 square feet.

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a standard number cube number 1 through 6 on east side is rolled 3 times what is the probability of rolling a 2 on all three rolls express your answer as a fraction

Answers

the probability of getting a 2 tree times is

[tex]\frac{1}{6}\cdot\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{216}[/tex]

15
A principal needs to order 1,437 T-shirts for students at her school. She rounds to the nearest hundred
to estimate the number of T-shirts to order. Will there be enough T-shirts for all the students? Explain.

Answers

There will not be enough T-shirts for all the students

How to determine if the T-shirts will be enough?

From the question, the given parameters are:

Number of T-shirt = 1437

From the question, we understand that the principal approximates the number of T-shirts to the nearest hundred

When the number of T-shirts is approximated to the nearest hundred, we have

Approximation = 1400

By comparison, 1400 is less than 1437

This means that the T-shirts will not be enough