Janice got a raise in her hourly pay, from $9.75 to $11.50. Find the percent change. Round to the nearest tenth of a percent.

For the population to double, it takes around 7.07 hours.

The continuous exponential growth model is given by:

\(N(t) = N0 * e^{rt}\)

Where:

N(t) is the population size at time t

N is the initial population size (at t = 0)

r is the growth rate parameter

t is the time elapsed

We want to find the time t it takes for the population size to double, which means N(t) = 2N. Substituting into the growth model, we get:

\(2N = N * e^{rt}\)

Dividing both sides by N, we get:

\(2 = e^{rt}\)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2)/r

Substituting r = 0.098 (9.8% as a decimal), we get:

t = ln(2)/0.098

t ≈ 7.07 hours

Therefore, it takes approximately 7.07 hours for the population size to double.

Learn more about exponential growth and decay here:

https://brainly.com/question/17161065

#SPJ1

Answer:

Step-by-step explanation:

To calculate the simple interest on R600 at 5% p.a for 3 years, we use the formula:

Simple Interest = (Principal x Rate x Time)/100

where

Principal = R600 (the initial amount)

Rate = 5% per annum (p.a)

Time = 3 years

Plugging these values into the formula, we get:

Simple Interest = (600 x 5 x 3)/100 = 90

Therefore, the simple interest on R600 at 5% p.a for 3 years is R90.

Answer:

B

Step-by-step explanation:

So far, we know that:

∠D = ∠J.

And that:

DE:JK = 14:7 = 2:1

So, to prove that ΔDEF ~ ΔJKL by SAS, DF must be similar to JL, as those are the sides between the angle.  

So:

DF:JL = 2:1.

Our answer is B.

The percentage of women with weights that are within the limits is:

60.93%

Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:

z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74

z-score for upper limit = (217 - 168.7) / 48.8 = 0.99

Next, we can use a z-table to find the corresponding probabilities for these z-scores:

Probability for lower limit = 0.2296

Probability for upper limit = 0.8389

Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093

Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.

More information about the percentage here: https://brainly.com/question/28952121

#SPJ11

Answer:

40%

Step-by-step explanation:

formula=selected group number divided by the total number multipled by one hundred

22/55= 0.4

0.4×100=40

therefore, 40% of the members of the chess club are in 7th grade

Therefore , the solution of the given problem of probability comes out to be AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

(a) The voting box contains a total of seven slips, four of which are for candidate A and three for candidate B. Thus, there are 35 events that can occur from 7 choose 4 (or 7 choose 3) options.

Each vote can be represented by a letter, with A standing for a vote for candidate A and B for candidate B, so that all outcomes can be listed. These are the potential results:

AAAA

AAAB

AABA

ABAA

BAAA

AABB

ABAB

BABA

BBAA

ABBB

BABB

BBAB

BBBA

(b)

For instance, the following results could occur if the slips were removed in the following order:

A (1 vote for contender A) (1 vote for candidate A)

AA (2 ballots for candidate A) (2 votes for candidate A)

AAB (2 ballots for candidate A, 1 vote for candidate B) (2 votes for candidate A, 1 vote for candidate B)

AAAB (3 ballots for candidate A, 1 vote for candidate B) (3 votes for candidate A, 1 vote for candidate B)

AAAAB (4 ballots for candidate A, 1 vote for candidate B) (4 votes for candidate A, 1 vote for candidate B)

AAAABB (4 ballots for candidate A, 2 votes for candidate B) (4 votes for candidate A, 2 votes for candidate B)

AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ4

The quantity 2a 2c corresponds to the rate of change of the surface area with respect to a. So, Correct option is C.

When considering a rectangular prism with dimensions a, b, and c, there are three different measures that we can associate with the dimensions: the length, width, and height. These measures are important in determining both the volume and the surface area of the prism.

In this problem, we are given a quantity 2a 2c and asked to determine which measure of the rectangular prism it corresponds to. We can do this by considering the formulas for the volume and surface area of the prism, and taking the partial derivatives with respect to each of the three dimensions.

The volume of a rectangular prism is given by:

V = abc

Taking the partial derivative of this expression with respect to a, we get:

\(\frac {\partial v} {\partial a}\) = bc

This is not equal to 2a 2c, so we can eliminate the possibility of the quantity corresponding to the rate of change of the volume with respect to a.

Taking the partial derivative of the volume with respect to b and c gives:

\(\frac {\partial v} {\partial b}\) = ac

\(\frac {\partial v} {\partial c}\) = ab

Again, neither of these expressions is equal to 2a 2c, so we can eliminate the possibilities of the quantity corresponding to the rate of change of the volume with respect to b or c.

Next, we can consider the surface area of the prism, which is given by:

A = 2ab + 2ac + 2bc

Taking the partial derivative of this expression with respect to a, we get:

\(\frac {\partial v} {\partial a}\) = 2b + 2c

Substituting 2a 2c for 2b + 2c, we get:

\(\frac {\partial A} {\partial a}\) = 2a 2c

This is the same expression as the given quantity, so we can conclude that the quantity 2a 2c corresponds to the rate of change of the surface area with respect to a.

To learn more about rectangular prism click on,

https://brainly.com/question/18233448

#SPJ4

Step-by-step explanation:

As my previous answer got deleted for being wrong (in which it was right), I will answer again.

The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.

This is proof that it is right, and that there are some corrupt admins on brainly.

How to get to this solution?

Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).

If we do so, we get 2a + 5 = 7.

Solving this equation, we get a = 1.

Answer:

The null hypothesis will not be rejected at 5% significance level.

Step-by-step explanation:

Consider a Chi-square test for goodness of fit.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

 \(\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}\)

The information provided is:

Observed values:

Half Pint: 36  

XXX: 35  

Dark Night: 9  

TOTAL: 80

The expected proportions are:  

Half Pint: 40%

XXX: 40%  

Dark Night: 20%  

Compute the expected values as follows:

E (Half Pint)  

 \(=\frac{40}{100}\times80=32\)

E (XXX)  

 \(=\frac{40}{100}\times80=32\)

E (Dark night)  

 \(=\frac{20}{100}\times80=16\)

Compute the test statistic as follows:

 \(\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}\)

     \(=\frac{(36-32)^{2}}{32}+\frac{(35-32)^{2}}{32}+\frac{(9-16)^{2}}{16}\\\\=3.844\)

The test statistic value is, 5.382.

The degrees of freedom of the test is:

n - 1 = 3 - 1 = 2

The significance level is, α = 0.05.

Compute the p-value of the test as follows:

p-value = 0.1463

*Use a Chi-square table.

p-value = 0.1463 > α = 0.05.

So, the null hypothesis will not be rejected at 5% significance level.

Answer:

sorryajaajqiqoqoqiqsjsjwuwuqqu

Answer:

A - C(-3, -2), D(1, -2)

Step-by-step explanation:

Answer:

Length: 18

Width: 9

Step-by-step explanation:

Denote the width as x, hence the length is x+9. As a result, you can create the equation x(x+9) = 162. Solving, you find x = 9.

Answer:

1/12 gallons

Step-by-step explanation:

We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.

Step 1:  Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2

(1/6) * (2/2) = 2/12

Step 2:  Now we can subtract 1/12 from 2/12:

2/12 - 1/12 = 1/12

Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.

The amount of Bruno's yearly pay deducted for FICA is approximately

A. $4,524.15. The closest option provided is A. $4521.15.

To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.

As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.

Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:

Yearly gross income = $4925 * 12 = $59,100

To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:

Social Security deduction = $59,100 * 6.2% = $3,667.20

Medicare deduction = $59,100 * 1.45% = $856.95

Adding these two deductions together:

FICA deduction = $3,667.20 + $856.95 = $4,524.15

Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.

The closest option provided is A. $4521.15.

for such more question on amount deducted

https://brainly.com/question/25821437

#SPJ8

Answer:

1988 years ago

Step-by-step explanation:

2021 - 33 =

1988

Hope that helps!

Answer:

x²+17x+6=xx+17x+6=(17+x)x +6=17+xx+6= 17+x²+6=23+x²

=>x²+17x+6=23+x²

The meaning is that "If you share seven apples equally with three people, there are 2 1/3 apples for each person."

In this context, a "whole number to the denominator of three and the numerator one" refers to the fact that when the seven apples are divided equally among the three people, each person receives a whole number of apples, plus a fraction.

The denominator of the fraction is three because there are three people sharing the apples,

Tthe numerator of the fraction is one because each person receives one of the three equal parts.

The fraction 1/3 represents the amount of the seventh apple that each person receives. So, each person receives 2 whole apples and 1/3 of another apple, for a total of 2 1/3 apples.

Read more about fraction at

https://brainly.com/question/1330447

#SPJ1

If Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint

A word problem in mathematics is a maths question written as one sentence or more that requires the application of mathematics knowledge to a 'real-life' scenario.

Given that 6 gallons of light green paint use 3/8 gallon of white paint, this can be expressed as:

3/8 gallons of white paint = 6 gallons of light green

We are to determine if 9/16 gallons will be enough to make 8 gallons of light green paint. This can be expressed as

9/16 gallons of white paint = x

Divide both expressions

3/8 x 16/9 = 6/x

2/3 = 6/x

By cross multiplying

2x = 3 x 6

2x = 18

x = 18/2

x = 9

This shows that if Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint

Learn more about word problem on:https://brainly.com/question/21405634

#SPJ1

A scatter plot visually represents the relationship between two variables. It shows a positive correlation between the number of books read per month and SAT Verbal Test scores, with the equation y = 6.4828x + 520.6962.

A scatter plot is a graphical representation of a set of data that allows the observer to observe the relationship between two variables. It is used to graphically display how one variable is affected by the other. It is a chart of data points plotted on a two-dimensional graph with one variable represented on the X-axis and the other variable on the Y-axis.

Scatter Plot of the Data: From the data provided by the Language Arts department, we can create the scatter plot as shown below:
Equation of the line of best fit: The line of best fit is a straight line that is used to model the relationship between the two variables. It is determined by minimizing the sum of the squares of the differences between the observed values and the predicted values.

From the scatter plot, we can see that there is a positive correlation between the number of books read per month and the score on the SAT Verbal Test. This suggests that the more books a student reads per month, the higher their score on the SAT Verbal Test.

The equation of the line of best fit for the given data set is y = 6.4828x + 520.6962. Here, y represents the score on the SAT Verbal Test and x represents the number of books read per month.

To find the equation of the line of best fit, we can use a regression analysis tool such as Excel. The regression analysis will give us the values of the slope and intercept of the line of best fit, which we can use to write the equation of the line.

For more questions on a scatter plot

https://brainly.com/question/30756481

#SPJ8

The range of the possible length of the third side is between 10 and 22

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

Lengths = 6 and 16

The possible length of the third side can be calculated using the triangle inequality theorem

For this triangle, the length of the third side must be greater than

16 - 6 = 10

Also, the length of the third side must be less than

16 + 6 = 22

Hence, the possible length of the third sides is between 10 and 22

Read more about triangles at:

brainly.com/question/1058720

#SPJ1

The reasoning for the third step of the proof would be "Corresponding parts of congruent triangles are congruent." Let's go through the explanation:

1. Given: Quadrilateral ABCD is a rectangle.

2. Given: AB & CD (Opposite sides of a rectangle are equal).

3. To prove: AC & BD.

To prove that AC is equal to BD, we can utilize the property that opposite sides of a rectangle are equal (step 2). In a rectangle, opposite sides are parallel and congruent. Therefore, we have AB || CD and AB = CD.

Now, we need to show that the triangles ABAD and ACDA are congruent, specifically using the SAS (Side-Angle-Side) congruence theorem. The congruence of these triangles will allow us to establish the equality of their corresponding parts, including AC and BD.

4. Given: AD = AD (Reflexive Property of Equality).

5. By step 2, we know AB = CD. Additionally, AD = AD is given (Reflexive Property of Equality).

6. By step 3, ZBAD = ZCDA.

7. Using SAS triangle congruence theorem, we can conclude that triangles ABAD and ACDA are congruent.

Finally, according to the "Corresponding parts of congruent triangles are congruent" property, we can state that AC = BD. This establishes the equality of the diagonals of the rectangle.

Therefore, the correct reasoning for step 3 is "Corresponding parts of congruent triangles are congruent."

For more such questions on congruent triangles.

https://brainly.com/question/29789999

#SPJ8

Answer:

m = 2

Step-by-step explanation:

Given:

x = 4

y = 6m - 2

a = 8

b = 5

Required:

Value of m

SOLUTION:

x and y are segments of a chord divided when it intersects another chord that also has segments a and b.

According to the Intersecting chords theorem, \( a*b = x*y \)

Thus:

\( 8*5 = 4*(6m - 2) \)

Solve for m

\( 40 = 24m - 8 \)

\( 40 + 8 = 24m - 8 + 8 \)

\( 48 = 24m \)

\( \frac{48}{24} = \frac{24m}{24} \)

\( 2 = m \)

The value of m = 2

The goal is to find the radius of a circle which also helps to get the diameter. Finding the center helps to measure and know the circumference.

When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

To learn more about ratio refer to :

https://brainly.com/question/2328454

#SPJ1

The Distance between point A and Point B is √10 units.

Distance is a numerical measurement of how far apart objects or points are. In Physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

Here, Coordinates of A is (1, 8) and B is (4, 9).

Distance formula = √(x₂-x₁)² + (y₂-y₁)²

                              = √(4 - 1)² + (9 - 8)²

                             = √9 +1

                   AB     = √10

Thus, the Distance between point A and Point B is √10 units.

Learn more about Distance from:

https://brainly.com/question/12319416

#SPJ2

The perimeter of triangle N is 72 inches.

Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.

Here given the triangles M and N are similar, the ratio of sides N:M is 4:3

We can say that M and N with constant term x is, (by ratio proportion rule)

M = 3x and N = 4x and

Given the lengths of triangle M are 12 inches, 18 inches and 24 inches

for triangle M = 3x, (Using above ratio proportion rule)

3x = 12 inches                    3x = 18 inches                    3x = 24 inches

x = 4                                    x = 6                                    x = 8

Similarly, for similar triangle N = 4x, (Using above ratio proportion rule) put all values of x = 4, 6, 8

for x =4                                for x =6                                for x =8

4x = 4×4                               4x = 4×6                              4x = 4×8  

16 inches                             24 inches                            32 inches

Length of triangle N is 16 inches, 24 inches and 32 inches

Perimeter of triangle N = 16+24+32 = 72 inches

Therefore, the Perimeter of triangle N is 72 inches.

To know more about triangle, visit:

brainly.com/question/17815056

#SPJ1

Answer:

8 hours

Step-by-step explanation:

9 kg dough...........................3 hours

24 kg dough.........................?

9/3=24/x

x=(24*3)/9=8