10. Jordan wants to buy a pair of shoes that cost $150.99. The
shoes are 35% off, what will be the price of the shoes after the
discount?

Answer:

graph a and table a=B

Step-by-step explanation:

This is because for table a, if you subsite the numbers of x it would give you the answer for y such as y=2x, and since x is 2 y is 4, which is shown on the graph. And since it does not have any add ons, if you make x 0 it would be 0 so it would also be proportional through the orgin. so graph A is also correct.

Answer:

21,526 people

Step-by-step explanation:

Using the given data on the number of live multiple-delivery births for women aged 15 to 54, we need to calculate probabilities related to the age groups of the mothers. The probability of a randomly selected multiple birth involving a mother aged 30 to 39 will be determined, as well as the probabilities of not being in the age range, being less than 45, and being at least 40. Finally, we need to interpret whether a multiple birth involving a mother aged at least 40 is unusual.

(a) To calculate the probability of a randomly selected multiple birth involving a mother aged 30 to 39, we sum the number of multiple births in that age group and divide it by the total number of multiple births for women aged 15 to 54.

P(30 to 39) = 2822 / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(b) To find the probability of a randomly selected multiple birth involving a mother who is not aged 30 to 39, we subtract the probability found in part (a) from 1.

P(not 30 to 39) = 1 - P(30 to 39)

(c) To determine the probability of a randomly selected multiple birth involving a mother aged less than 45, we sum the number of multiple births for age groups below 45 and divide it by the total number of multiple births for women aged 15 to 54.

P(less than 45) = (89 + 508 + 1631 + 2822 + 1855 + 374) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(d) To find the probability of a randomly selected multiple birth involving a mother aged at least 40, we sum the number of multiple births for age groups 40-44 and 45-54, and divide it by the total number of multiple births for women aged 15 to 54.

P(at least 40) = (374 + 119) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

Interpretation: The answer to part (d) will determine whether a multiple birth involving a mother aged at least 40 is unusual. If the probability is less than 0.05, it can be considered unusual. Therefore, we need to compare the calculated probability to 0.05 and select the correct choice.

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The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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Using the formula;

H= ut + 1/2 gt²

The initial velocity = 0

Hence H= 1/2 gt²

g= 10m/s t= 5.78 s

H = 1/2 x 10 x 5.78²

H = 167.042 m

H = 167 m approximately

Answer:

X = 60

Y = 50

Step-by-step explanation:

The total degrees of a triangle is 180 degrees. For the middle triangle, 50+70=120 so 180-120=60.

On the far right, Y=50 because you take 50 degrees from the middle triangle, and insert it there.

Answer:

Given that, he will run at least total 30 miles this week. That means the minimum total distance, he will run in this week is 30 miles.

So, the inequality will be.....

t + 16 ≥ 30

t  ≥ 30 - 16

t  ≥ 14

Thus, he need to run at least 14 additional miles in this week.

Answer:

C. no solution

Step-by-step explanation:

Answer:

TIME FOr THE Ax? The Situation You are the sales manager for a well-established medical equipment company. You’ve been with the company a long time and, generally, you really enjoy your job. The company’s new president is interested in proving herself and has set a goal of 10 percent sales growth per year. Each sales representative has a quota that they are expected to meet. Those who exceed their quota will receive a bonus, and those who fall short of their quota will be fired or placed on probation.

The Dilemma

Your sales staff have worked really hard over the past year

to meet their new quotas. Six of the eight representatives met

their quotas and received bonuses. However, two others have

fallen below. Jane fell 2 percent short of her quota and you’re not surprised. She’s not hard working and often leaves work early to

play golf. Bill, on the other hand, has been with the company a

long time and is widely respected for his work ethic. However,

he’s struggling to care for his sick mother and fell 7 percent

below his quota. You know that control is an important part of

being a manager, but you’re unsure what to do. The company

president has asked to meet with you tomorrow to discuss the

situation.

QUESTIONS TO ADDRESS

5-21. Which management functions are involved in setting

goals and measuring performance?

5-22. What are the ethical issues in this situation?

5-23. What do you think most managers would do in this

situation?

Answer:

The linear function that models the population of rainbow smelt is y1 = −19.76x + 227, where x = the years since 1990 and y1 = the number of rainbow smelt.

Answers:

The linear function that models the population of bloater fish is y2 =  

–92.57x + 1,052 (D).

The linear equation that determines when the two populations were equal is

–19.76x + 227 = –92.57x + 1052.

The solution is x = 11.33 (D) years.

The highest point on the graph of the normal density curve is located at its mean represented by μ.

The highest point on the graph of the normal density curve is located at its mean. The normal density curve or the normal distribution is a bell-shaped curve that is symmetric about its mean. The mean of a normal distribution is the measure of the central location of its data and it is represented by μ. It is also the balancing point of the distribution. In a normal distribution, the standard deviation (σ) is the measure of how spread out the data is from its mean.

It is the square root of the variance and it determines the shape of the normal distribution. The normal distribution is an important probability distribution used in statistics because of its properties. It is commonly used to represent real-life variables such as height, weight, IQ scores, and test scores.

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The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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Answer:

Example 1:

A tank can be filled by pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. if the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?

Solution:

Step 1: Assign variables:

Let x = time taken to fill up the tank

Step 2: Use the formula:

Since pipe C drains the water it is subtracted.

1/3+1/5-1/4=1/x

Step 3: Solve the equation

The LCM of 3, 4 and 5 is 60

Multiply both sides with 60

solve the eqn

Answer: The time taken to fill the tank is 3 9/17 hours.

Work Problem: Pumps draining a tank

Example:

A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 5 hours more than the 10-horsepower pump to empty the pool when working by itself.

How long will it take to empty the pool using just the 10-horsepower pump?

Show Step-by-step Solutions

Cooperative Work Word Problems (Time to Finish)

Examples:

1. Pump A can empty a pool in 20 hours and pump B can empty it in 24 hours. Working together, how long will it take to empty the pool?

2. A painter can paint a building in 15 days and a coworker can do the same job in 10 days. If the first painter starts and 3 days later the coworker joins in to help finish the job, how many days doe it take to paint the building?

Show Step-by-step Solutions

Rates of Performing Work Problems

Example:

It takes 12 hours to fill a water tank. It takes 16 hours to drain the same water tank. How long will it take to fill the tank if the drain is left open?

Show Step-by-step Solutions

Step-by-step explanation:

Answer: neither are functions

Step-by-step explanation:

Answer:

Look below

Step-by-step explanation:

We can start by writing an equation.

Let x be the width. The length would be x+4.

The equation would be:

96=2(x+x+4)

Divide both sides by 2

48=x+x+4

Add like terms

48=2x+4

Subtract 4 from both sides

44=2x

Divide both sides by 2

x=22

x+4=26

The width is 22 inches and the length is 26 inches.

a) Since R satisfies reflexivity, symmetry, and transitivity, it is an equivalence relation.

1. Reflexivity: For any integer n ∈ Z, we need to show that nRn holds. Since the condition for R is mn > 0 or m = n = 0, we have two cases:

  Case 1: mn > 0

    - If n ≠ 0, we can choose m = n, and mn = n^2 > 0. Therefore, nRn holds.

    - If n = 0, then mn = 0, and 0 = 0 = 0 holds. Therefore, nRn holds.

2. Symmetry: For any integers m, n ∈ Z, if mRn holds, we need to show that nRm also holds. Let's consider the two cases:

  Case 1: mn > 0

    - If m ≠ 0 and n ≠ 0, then mn > 0 implies nm > 0. Therefore, nRm holds.

  Case 2: m = n = 0

    - In this case, we have mRn = 0R0, and since the condition is satisfied, 0R0 holds.

3. Transitivity: For any integers m, n, and p ∈ Z, if mRn and nRp hold, we need to show that mRp also holds. Let's consider the three cases:

  Case 1: mn > 0 and np > 0

    - If m ≠ 0, n ≠ 0, and p ≠ 0, then mn > 0 and np > 0 imply mp > 0. Therefore, mRp holds.

  Case 2: m = n = 0 and n ≠ 0 and p ≠ 0

    - In this case, we have mRn = 0R0 and nRp holds. Since n ≠ 0 and p ≠ 0, we can see that 0R0 and np > 0 imply 0p > 0, which holds. Therefore, mRp holds.

  Case 3: m ≠ 0 and n ≠ 0 and np > 0 and p = 0

    - In this case, we have mRn holds, and np > 0 and p = 0 imply that mp = 0. Since m ≠ 0, we have mn > 0, and mp = 0 = 0. Therefore, mRp holds.

Since R satisfies reflexivity, symmetry, and transitivity, it is an equivalence relation.

b) To determine the number of distinct equivalence classes and identify them, we need to analyze the relation R.

The relation R on Z divides the integers into three distinct equivalence classes:

1. The equivalence class [0]: This class contains the element 0 itself, along with any other integer that satisfies the condition mR0 if and only if m0 > 0 or m = 0 = 0. So, [0] = {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}.

2. The equivalence class of positive integers: This class contains all positive integers (excluding zero). For any positive integer p, [p] = {p, -p}.

3. The equivalence class of negative integers: This class contains all negative integers. For any negative integer q, [q] = {q, -q}.

Therefore, there are three distinct equivalence classes: {[0]}, {[p], -[p]}, and {[q], -[q]}.

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It can be solved using a Venn diagram. Total 8 students took both subjects.

A Venn diagram uses overlapping circles or other shapes to represent the relationships between two or more groups of objects. They typically serve to attractively organize objects, highlighting both the similarities and differences between the components. In the fields of mathematics, statistics, logic, education, linguistics, computer science, and business, Venn diagrams are extensively utilized.

It can be solved using a Venn diagram as

14 students take Physics, 6 students take mathematics and the rest 8 take both subjects.

where, 14(Physics) + 6(mathematics) + 8(both) = 28 (which is the total no. of students).

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Answer:

\(b^{2}\sqrt{30b}\)

Step-by-step explanation:

30 only has factors of 2×3×5, so the only perfect square here is \(b^{2}\), and so you factor that out.

Answer: -2115

Step-by-step explanation:

We can use the distributive property to simplify the calculation of -45 × 47 as follows:

\(\huge \boxed{\begin{minipage}{4 cm}\begin{align*}-45 \times 47 &= -45 \times (40 + 7) \\&= (-45 \times 40) + (-45 \times 7) \\&= -1800 - 315 \\&= -2115\end{align*}\end{minipage}}\)

Refer to the attachment below for explanation

Therefore, -45 × 47 = -2115 when using the distributive property.

________________________________________________________

To solve this problem using the distributive property, we can break down -45 into -40 and -5. Then we can distribute each of these terms to 47 and add the products:

\(\begin{aligned}-45 \times 47 &= (-40 - 5) \times 47 \\ &= (-40 \times 47) + (-5 \times 47) \\ &= -1{,}880 - 235 \\ &= \boxed{-2{,}115}\end{aligned}\)

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

If we pick 23 fruits at random, then 7% of the time, their mean weight will be greater than 210.8 grams.

To solve this problem, we need to use the Central Limit Theorem, which states that the sampling distribution of the means of a random sample from any population will be approximately normally distributed if the sample size is large enough.

In this case, since we are picking 23 fruits at random, we can assume that the sampling distribution of the mean weight of the fruits will be approximately normal with a mean of 204 grams and a standard deviation of 16/sqrt(23) grams.

To find the weight of the fruits such that their mean weight will be greater than a certain amount 7% of the time, we need to find the z-score associated with that probability using a standard normal distribution table. The z-score can be calculated as:

z = invNorm(0.93) = 1.475

where invNorm is the inverse normal function. This means that the weight of the fruits such that their mean weight will be greater than this amount 7% of the time is:

x = 204 + 1.475*(16/sqrt(23)) = 210.8 grams (rounded to one decimal place)

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Answer:

1 Simplify  \frac{24}{5}x  

5

24

​  

x  to  \frac{24x}{5}  

5

24x

​  

.

\frac{24x}{5}=-\frac{11}{4}

5

24x

​  

=−  

4

11

​  

2 Multiply both sides by 55.

24x=-\frac{11}{4}\times 5

24x=−  

4

11

​  

×5

3 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}  

b

a

​  

×c=  

b

ac

​  

.

24x=-\frac{11\times 5}{4}

24x=−  

4

11×5

​  

4 Simplify  11\times 511×5  to  5555.

24x=-\frac{55}{4}

24x=−  

4

55

​  

5 Divide both sides by 2424.

x=-\frac{\frac{55}{4}}{24}

x=−  

24

4

55

​  

​  

6 Simplify  \frac{\frac{55}{4}}{24}  

24

4

55

​  

​  

  to  \frac{55}{4\times 24}  

4×24

55

​  

.

x=-\frac{55}{4\times 24}

x=−  

4×24

55

​  

7 Simplify  4\times 244×24  to  9696.

x=-\frac{55}{96}

x=−  

96

55

​  

Step-by-step explanation:

Answer:

2 cos (x + pi/2)

Step-by-step explanation:

Of the choices given, this looks like a cos curve that is shifted to the Left by pi / 2  and   multiplied to give an amplitude of 2

Answer:

Water level before > 31

Step-by-step explanation:

The value of the cosine ratio cos(L) is 5/13

The complete question is added as an attachment

Start by calculating the hypotenuse (h) using

h^2 = 5^2 + 12^2

Evaluate the exponent

h^2 = 25 + 144

Evaluate the sum

h^2 = 169

Evaluate the exponent of both sides

h = 13

The cosine ratio is then calculated as:

cos(L) = KL/h

This gives

cos(L) =5/13

Hence, the value of the cosine ratio cos(L) is 5/13

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A list of steps, in order, that will solve the following equation include the following:

In order to create a list of steps and determine the solution to the equation, we would have to add 5 to both sides and divide both sides by 2 in order to open the parenthesis as follows;

2(x + 3) – 5 = 123

2(x + 3) – 5 + 5 = 123 + 5

2(x + 3) = 128

By dividing both sides of the equation by 2, we have the following:

2(x + 3)/2 = 128/2

x + 3 = 64

By subtracting 3 from both sides of the equation, we have the following:

x + 3 - 3 = 64 - 3

x = 61

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Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

2 different expressions that involve only outs and powers of 2 which are equivalent 4 2/3 / 8 1/4

1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)

2) (2^5 * 3^1) / (2^6 * 4^-1)

1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)

This expression is equivalent to 4 2/3 / 8 1/4 because it is written in terms of powers of two. 4^2 is equal to 16, which is the numerator in 4 2/3. 2^-1 is the same as 1/2, which is the second fraction in 4 2/3. 3^1 is equal to 3, which is the numerator in 8 1/4. 8^1 is equal to 8, which is the denominator in 8 1/4. 2^-2 is the same as 1/4, which is the second fraction in 8 1/4. 4^-1 is equal to 1/4, which is the first fraction in 8 1/4. When all the terms are multiplied and divided, it is the same as 4 2/3 / 8 1/4.

2) (2^5 * 3^1) / (2^6 * 4^-1)

This expression is also equivalent to 4 2/3 / 8 1/4 because it is written similar to above equation.

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