1 a) Complete the equivalent fractions for each of the fractions below.


a) 3/5 18/? ?/25 27/?



b) 4/7 8/? ?/49 44/?




b) Explain how to calculate an equivalent fraction.








2. Use the butterfly method to solve the following equations. Show your work.

The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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Answer:

Last choice:

  3/10 · 2/9

Step-by-step explanation:

The total number of marbles and the number of red marbles is not provided but only one answer fits the problem solution

3/10 x 2/9 which is the last choice

It can be deduced that there are 10 marbles totally and 3 of them are red

The probability of a red marble on first draw = 3/10

After the first draw given a red marble was drawn, there are 2 red marbles and total of  marbles so the probability of a second red marble = 2/9

The combined probability is 3/10 x 2/9

The missing value, rounded to the nearest hundredth, is approximately 54.46 degrees.

The equation sin ___ = 7/12 suggests that we need to find an angle whose sine is equal to 7/12. To determine the missing value, we can use the inverse sine function, also known as arcsine or sin^-1.

Using the inverse sine function, we can write the equation as ___ = sin^-1(7/12). Evaluating this expression with a calculator or a trigonometric table, we find that sin^-1(7/12) is approximately 54.46 degrees.

It's important to note that trigonometric functions have periodicity, meaning that there are multiple angles that have the same sine value. Therefore, there are other angles, such as 180 degrees minus 54.46 degrees, that also satisfy sin ___ = 7/12. However, when finding a single missing value, we typically consider the principal value within a specified range, often from -90 degrees to 90 degrees.

Thus, rounding to the nearest hundredth, the missing value that satisfies sin ___ = 7/12 is approximately 54.46 degrees.

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Yes, there is sufficient evidence to conclude that the length of storage significantly influences sorbic acid residual concentrations by determining the t-test.

The review directed by the Division of Human Sustenance and Food sources at Virginia Tech explored the impact of capacity time on the centralization of sorbic corrosive residuals in ham. In view of the information gave, a matched t-test was directed to decide if there is a huge contrast between the sorbic corrosive lingering focuses when 60 days of capacity.

The aftereffects of the test showed that the determined t-test measurement of 4.35 was more prominent than the basic worth of 2.365 at the 0.05 degree of importance, demonstrating that there is adequate proof to dismiss the invalid speculation and infer that the length of capacity fundamentally impacts sorbic corrosive lingering fixations. This finding recommends that food makers ought to painstakingly consider the capacity states of their items to limit the degrees of additives and other substance buildups in the eventual outcome.

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Answer:

6x - 3 + 4x = 13

10x - 3 = 13

10x = 16

x = 1.6

Any equation whose solution is    x=1.6   has the same solution as this one has.

Step-by-step explanation:

Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.

In a linear equation, a first-degree polynomial is defined as the sum of a group of terms, where each term is the product of a constant as well as the initial power of a variable.

The linear equation using the slope intercept form is -

Y = mX + b,

where, Y - number of cards

Slope = (y2 - y1)/(x2 - x1),

y2=500 cards, y1=200 cards, x2=$35, and x1=$23.

m = (500-200)/(35-23) = 300/12

m = 25.

Now,  slope m = 25, apply slope-intercept formula to find y when x=0.

Y = mX + b,

25 = (200 - y)/(23-x),

At,  x=0,

25 = (200-y)/23

200 - y = 25*23

575 = 200 - y

y = -375 (y - intercept)

The linear equation :

Y = 25X -375.

Y = 700. Find X

700 = 25X - 375

25X = 325

X = $43

Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.

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Answers:

x = 40 and y = 40

========================================================

Explanation:

The three angles involving x add up to 180 since they form a straight line or straight angle.

3x+0.5x+x = 180

4.5x = 180

x = 180/(4.5)

x = 40

Then note how the 0.5x and 0.5y angles are vertical angle pairs. Vertical angles form when we have two lines cross to form an X shape, and vertical angles are always opposite one another. Also, vertical angles are always the same measure.

0.5x = 0.5y

x = y

40 = y

y = 40

In the second step, I multiplied both sides by 2. Then I plugged in x = 40 we found earlier.

The complete values on the similar triangles are given by the image shown at the end of the answer.

Similar triangles are triangles that share these two features given as follows:

The first step in this problem is obtaining the missing angle measures, considering that the sum of the three internal angles of a triangle is of 180º.

For triangle ABC, considering the similarity with PRQ, the length BC is given as follows:

x/19.19 = 11.28/25.44

x = 11.28 x 19.19/25.44

x = 8.51.

Considering the similarity of ABC and of MNO, the length NO is obtained as follows:

x/11.28= 32.78/16.39

x = 11.28 x 32.78/16.39

x = 22.56

Considering the similarity of PQR and of ABC, the length PR is obtained as follows:

x/16.39 = 19.19/8.51

x = 16.39 x 19.19/8.51

x = 36.96.

Triangles DEF and ABC are congruent, meaning that they have the same side lengths between the same angles.

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Answer:

haha

Step-by-step explanation:

Answer:

lol i got a dad joke for you

how can you get a country girl's attention?

Step-by-step explanation:

A tractor

Answer:

The volume of the irregular figure would be 102 \(cm^3\).

Step-by-step explanation:

If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is \(l*w*h\), where \(l\), \(w\), and \(h\), represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be \(6*3*5=30*3=90 cm^3\), and the volume of the smaller rectangular prism would be \(3*2*2=6*2=12 cm^3\). So the volume of the entire irregular figure would be \(90+12=102 cm^3\).

Answer:

102

Step-by-step explanation:

Large rectangle:

6 × 3 × 5 = 18 × 5 = 90

Small rectangle:

7 - 5 = 2

3 × 2 × 2 = 6 × 2 = 12

90 + 12 = 102

Hope this helped.

The Wald test is a statistical test that can be used to test the significance of a group of coefficients in a multiple regression model.

The test statistic is calculated as the ratio of the estimated coefficient to its standard error. If the test statistic is significant, then the null hypothesis that the coefficient is equal to zero can be rejected.

Suppose we have a multiple regression model with three independent variables: age, gender, and education. We want to test the hypothesis that the coefficients for age and education are both equal to zero. The Wald test statistic would be calculated as follows:

Test statistic = (Estimated coefficient for age) / (Standard error of estimated coefficient for age) + (Estimated coefficient for education) / (Standard error of estimated coefficient for education)

If the test statistic is significant, then we can reject the null hypothesis that the coefficients for age and education are both equal to zero. This would mean that there is evidence that age and education are both associated with the dependent variable.

The Wald test is a powerful tool that can be used to test the significance of a group of coefficients in a multiple regression model. However, it is important to note that the test statistic is only valid if the assumptions of the multiple regression model are met. If the assumptions are not met, then the p-value of the Wald test may be inaccurate.

Here are some of the assumptions of the multiple regression model:

* The independent variables are independent of each other.

* The dependent variable is normally distributed.

* The errors are normally distributed.

* The errors have constant variance.

If any of these assumptions are not met, then the Wald test may not be accurate.

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Answer:

,

Step-by-step explanation:

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Answer:

40000 total visitors

Step-by-step explanation:

Let p represent a multiplier. Then the total number of visitors to the park is

4p + 7p + 9p = 40000.

This simplifies to 20p = 40000, so that p = 2000.

Then the number of children who visited is 4p = 8000; the number of women is 7p = 14000, and the number of men is 9p = 18000.

Summing up these results gives us the total number of chidren, women and men who visited the zoo last year: 8000 + 14000 + 18000, or 40000.

Solution

Question 1:

Question 2:

Final Answer

Question 1:

The exponential function to model the scenario is

Question 2:

The number of rabbits that will hop out of the hat on the 13th Day is 12,288 rabbits

To make the expression x² + 8x + ? a perfect square, we need to find the missing number that completes the square.

To complete the square, we take half of the coefficient of x and square it. The coefficient of x in this case is 8. Half of 8 is 4, and when squared, we get 4² = 16.

So, the missing number to make the expression a perfect square is 16.

The complete expression as a perfect square is:

x² + 8x + 16.

This expression can be factored as a perfect square: (x + 4)².

Therefore, by adding 16 to the expression x² + 8x, we obtain a perfect square expression of (x + 4)².

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The monthly payment for the loan is $1,013.16. After making 360 monthly payments, you will have paid a total of $364,137.64 to the bank. The total interest paid to the bank over the 360 months is $164,137.64.

To calculate the monthly payment, we can use the formula for calculating the monthly payment on a loan:

\(\[M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}\]\)

Where:

M is the monthly payment,

P is the principal loan amount,

r is the monthly interest rate, and

n is the total number of payments.

In this case, the principal loan amount is $200,000, the monthly interest rate is 0.35% (or 0.0035 as a decimal), and the total number of payments is 360. Plugging these values into the formula, we find that the monthly payment is $1,013.16.

To calculate the total amount paid to the bank over the 360 months, we simply multiply the monthly payment by the total number of payments: $1,013.16 * 360 = $364,137.64.

The total interest paid to the bank can be calculated by subtracting the principal loan amount from the total amount paid: $364,137.64 - $200,000 = $164,137.64.

Therefore, the monthly payment for the loan is $1,013.16, and after 360 monthly payments, the total payment to the bank is $364,137.64, with $164,137.64 being the total interest paid.

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Answer:

The value of p = -14

Step-by-step explanation:

Given the equation

\(-6\left(p+8\right)=36\)

Divide both sides by -6

\(\frac{-6\left(p+8\right)}{-6}=\frac{36}{-6}\)

simplify

\(p+8=-6\)

Subtract 8 from both sides

\(p+8-8=-6-8\)

simplify

\(p=-14\)

Therefore,

The value of p = -14

Answer:

p = -14

Step-by-step explanation:

-6 ( p + 8 ) = 36

Solve the brackets.

- 6p - 48 = 36

Add 48 to both sides.

- 6p = 36 + 48

- 6p =  84

Divide both sides by -6.

p = -14

There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.

A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.

If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.

The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.

In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.

The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.

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Answer:

C

Step-by-step explanation:

1. Identfiy The type therom it is which is alternate interior

2. Find the converse of the alternate interior which is the oppoiste so it has to be alternate exterior angle

Therefore, the final code would be:values = [ 14, 10, 8, 19, 7.13] print(values[2], values[-2])This code would print the following output:8 19

Indices, also known as exponents or powers, are mathematical symbols that express the repeated multiplication of a number. These numbers show how many times the base number has been multiplied by itself. For example, the index of 2 in the formula 23 is 3, which indicates that 2 is multiplied by itself three times to provide the value 8. Indices are often written as little numbers to the right and above the base number, with the latter enclosed in parentheses or brackets. Indices are often used to indicate the size or quantity of a number in mathematical model, but they may also be used to represent the degree of a polynomial function or the order of a derivative in calculus.

How to solve?

To print the integer at index 2 of the values list, we can use the following code: print(values[2])

To print the integer at index -2 of the values list, we can use the following code: print(values[-2])

Here, the index -2 refers to the second-to-last element in the list, which is the integer 19.

Therefore, the final code would be:

values = [ 14, 10, 8, 19, 7.13]

print(values[2], values[-2])

This code would print the following output:

8 19

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Answer:

The code is 571113

Step-by-step explanation:

The problem requires that we find the prime factors of 5005

1. 5005 is a multiple of 5 since it ends with a number 5

5 is one of the numbers

Dividing 5005/5 = 1001

the next prime number after 5 is 7

so 1001/7= 143

7 is one of the numbers

the next prime number after 7 is 11

so 143/11= 13

13 is one of the numbers

In all the prime factorization of 5005 is found as follows

5,7 11,13

Combining these numbers gives the 6 digit code

571113

A measure of the dispersion of observations in a process distribution is called: range.

This is further explained below.

Generally, The range of a collection of data is the difference between the highest and smallest values in the set. This difference is calculated by subtracting the sample maximum and minimum from the sample size. It is written out using the same units that were used for the data.

In conclusion, The term "range" refers to a measure of the dispersion of observations included within a process distribution.

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Answer: D

Step-by-step explanation:

Answer:

Area A = 12 = 1/2 × x × (5x-2)

5x^2 - 2x -24 = 0

Solution;

Base x = 2.4

Height h = 10 ft

Step-by-step explanation:

Given;

base of the triangle is x feet;

Base = x

The height of a triangle is 2 less than 5 times it's base;

Height = 5x - 2

the area of the triangle is 12 square feet;

Area A = 12 ft^2

The area of a triangle is;

Area A = 1/2 × base × height

Substituting the base and height;;

Area A = 1/2 × x × (5x-2)

Area A = 1/2 × (5x^2 - 2x)

Area A = 12

12 = 1/2 × (5x^2 - 2x)

Multiply through by 2.

24 = (5x^2 - 2x)

5x^2 - 2x -24 = 0

Solving the simultaneous equation;

x = 2.4 or -2

Since the base cannot be negative;

x = 2.4 ft

Height h = 5x -2 = 5(2.4) - 2 = 12 - 2 = 10 ft

Base x = 2.4

Height h = 10 ft

Answer:

Probably puberty

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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Let x be the number of adult tickets sold and y be the number of student tickets sold. From the problem, we can form the following system of equations :x + y = 12 (total number of tickets sold)7x + 4y = 75 (total amount of money collected)

We can use substitution method to solve for x and y. Solving for x in the first equation gives: x = 12 - y Substituting this expression for x into the second equation gives:7(12 - y) + 4y = 75Simplifying and solving for y gives :y = 5Substituting this value of y into the equation x + y = 12 gives :x + 5 = 12x = 7Therefore, there were 7 adult tickets and 5 student tickets sold.

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Answer:

x = 200

Step-by-step explanation:

\(\frac{x}{5} = \frac{120}{3}\)

so you cross multiply

5 × 120 = 600

x × 3 = 3x

so

3x = 600

x = 200

Answer:

\(\huge\boxed{\sf 126\° \ OR \ 145 \°}\)

Step-by-step explanation:

m∠4 + m∠7 = 180    (Adjacent Angles of a parallelogram)

Given that m∠4 = x + 45, m∠7 = x² + 45

x + 45 + x² + 45 = 180

x² + x + 90 = 180

x² + x = 180 - 90

x² + x = 90

x² + x - 90 = 0

Using mid-term break formula

x² + 10x - 9x - 90 = 0

x(x+10) - 9(x+10) = 0

(x - 9)(x + 10) = 0

Either,

x-9 = 0       OR      x+10 = 0

x = 9          OR        x = -10

\(\rule[225]{225}{2}\)

Now,

m < 7 = x² + 45

For x = 9

m < 7 = (9)² + 45

m < 7 = 81 + 45

For x = -10

m < 7 = (-10)² + 45

m < 7 = 100 + 45

\(\rule[225]{225}{2}\)

Hope this helped!