There are two solutions, for a quadratic equation that represents the relation between distance and
time.
One of the solutions is positive and the other is negative.
If the values are associated with time, then we will choose
A the positive and the negative
solutions.
B the positive solution.
C neither the positive nor the.
D the negative solution.

Answer:

96

Step-by-step explanation:

12 colors times 2 possibilities of with or without air conditioning is 24.

24 times two possibilities of with or without automatic transmission is 48.

48 times two possibilities of with or power windows is 96.

96 times two possibilities of with or CD player is 192.

Answer:

Angle DCA = Angle CAB. (Alternate Interior Angle)

Angle DCA = 68°

Angles(DCA + ACB + BCE) = 180°. (Linear Pair)

Angle ACB + 68° + 33° = 180°

Angle ACB = 79°

Therefore,

Angle ABC = 33°. (Alternate Interior Angle)

If of the 2440 respondents to a survey. 1050 claimed to be worried about their health. The likelihood that a person selected at random will not be worried about their health is D. 56.97%.

The number of respondents who did not claim to be worried about their health is 2440 - 1050 = 1390.

So, the likelihood that a person selected at random will not be worried about their health is:

= 1390/2440 ×100

= 56.97%

Therefore there is a 56.97% chance that a person selected at random will not be worried about their health.

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Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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Answer:

The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.74

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 1.74\frac{26}{\sqrt{18}} = 10.66\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 140 - 10.66 = 129.34 cans per month

The upper end of the interval is the sample mean added to M. So it is 140 + 10.66 = 150.66 cans per month.

The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month

Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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The area of the semicircle is A = 1187.9 cm².

The area of a circle with a radius of r is A = πr².

Given that, the diameter of the semicircle is 55 cm.

The radius of the semicircle is,

r = 55/2

The area of a semicircle is given by,

A = (1/2)πr²

Substitute the values,

A = (1/2)π(55/2)²

A = 1187.9

Hence, the area of the semicircle is A = 1187.9 cm².

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Answer:

x = 20

Step-by-step explanation:

The triangle shown is an equilateral triangle.  An equilateral triangle has angles that are all the same.  Therefore, the expression 4x-20 equals the value of the angle, which is 60 degrees.  To find x, you just have to do some simple algebra.

4x - 20 = 60 ..... set the expression equal to 60, that's what the angle equals

4x = 80 .... add 20 to both sides

x = 20 .... divide both sides by 4, and you get your answer

Hope this helps! :)

The rate of the slower jet is 562 mi/h and the rate of the faster jet is 656 mi/h.

Distance is a measure of the physical separation between two objects or points. It is a fundamental concept in geometry, physics, and other sciences, and it is used to describe the length or size of objects, the speed of motion, and the magnitude of forces.

Let's call the rate of the slower jet "r" (in mi/h). Then the rate of the faster jet is "r+94" (since it's traveling 94 mi/h faster).

We know that after 2 hours, the two jets are 2436 miles apart. We can use the formula:

distance = rate x time

For the slower jet, the distance it has traveled is:

distance = rate x time = r x 2 = 2r

For the faster jet, the distance it has traveled is:

distance = rate x time = (r+94) x 2 = 2r + 188

The total distance between the two jets is the sum of these distances:

2r + (2r + 188) = 2436

Simplifying this equation, we get:

4r + 188 = 2436

Subtracting 188 from both sides:

4r = 2248

Dividing by 4:

r = 562

So the rate of the slower jet is 562 mi/h. The rate of the faster jet is:

r+94 = 562+94 = 656 mi/h

Therefore, the rate of the slower jet is 562 mi/h and the rate of the faster jet is 656 mi/h.

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Step-by-step explanation:

17. 21⁰ + 31⁰ + ?⁰ = 180⁰

= ?⁰ = 128⁰

18. ?² = 12² + 5²

? = √169

? = 13 TYPO

Answer:

17: 128
18: 13

Step-by-step explanation:

17: 21 + 31 = 52, 180 - 52 = 128.

18: a² + b² = c².
5² = 25
12² = 144
25 + 144 = 169
169 square rooted = 13
C (aka the missing side) = 13

edited to fix 17 from 121 to 128

Answer:  (x² - 5)(x - 7)

Step-by-step explanation:

Grouping the terms, we have:

(x^3 - 7x^2) + (-5x + 35)

Now, let's factor out the common factors from each pair:

x^2(x - 7) - 5(x - 7)

Notice that we have a common factor of (x - 7) in both terms. We can factor it out:

(x^2 - 5)(x - 7)

Therefore, the resulting expression after factoring by grouping is (x^2 - 5)(x - 7).

Answer:

\(\text{27}\)

Step-by-step explanation:

Given that :

\(\text{Dimension of poster board} = 1 \ \text{yd} \ \text{by} \ 1 \ \text{yd}\)

\(\text{Dimension of each poster board} = \dfrac{1}{3} \ \text{yd} \ \text{by} \ \dfrac{1}{9} \ \text{yd}\)

Number of poster signs that can be cut :

\(\text{Area of poster sign} = \dfrac{1}{3} \times \dfrac{1}{9} = \dfrac{1}{27} \ \text{yard}^2\)

\(\text{Area of poster board} = 1 \ \text{yard}^2\)

Number of poster signs that can be cut :

\(\dfrac{\text{Area of poster board}}{\text{Area of poster sign}}\)

\(1 \ \text{yard}^2\div (\dfrac{1}{27} ) \ \text{yard}^2\)

\(1 \div \dfrac{1}{27}\)

\(1 \times \dfrac{27}{1}\)

\(\bold{= 27 \ poster \ signs}\)

Answer: \(34\pi m\)

Step-by-step explanation:

1.) First find the radius by square rooting the area and then divide it by pi

\(\pi \sqrt{289}\)

2.) Next find the circumference

\(C=2\pi 5.41127\)

A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:

a. Revenue Function:

Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.

The revenue function can be formulated as:

Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)

In equation form:

Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

b. Constraints:

The constraints for the availability of ingredients can be formulated as follows:

Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280

Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300

Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80

Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250

Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190

Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

c. Solve the system of linear inequalities using E x c e l Solver:

To solve the system of linear inequalities using E x c e l Solver, follow these steps:

1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:

| | A | B |

|-----|-----------|-----------------|

| 1 | Cakes | Selling Price |

| 2 | Cake 1 | $9 |

| 3 | Cake 2 | $12 |

| 4 | Cake 3 | $4 |

| 5 | Cake 4 | $5 |

| 6 | Cake 5 | $8 |

| | | |

| | | Formula |

| 9 | Milk | 280 |

| 10 | Sugar | 300 |

| 11 | Eggs | 80 |

| 12 | Flour | 250 |

| 13 | Cream | 190 |

2. In cell B16, enter the formula for the revenue:

=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11

3. In cell B18, enter the formula for the milk constraint:

=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6

4. In cell B19, enter the formula for the sugar constraint:

=7×B2 + 4×B3 + 5×B4

5. In cell B20, enter the formula for the egg constraint:

=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6

6. In cell B21, enter the formula for the flour constraint:

=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6

7. In cell B22, enter the formula for the cream constraint:

=4×B2 + 5×B4 + B5 + 3×B6

8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:

=B2

9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:

=B3

=B4

=B5

=B6

10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.

11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).

12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).

13. Click on the "Add" button in the "Subject to the Constraints" section.

14. In the Constraint window, select the range B18:B22 for the constraint cells.

15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.

16. Set the Solver options as desired, and click on the "Solve" button.

E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.

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Answer:

There were 5 phones sold and 10 accessories sold.

Step-by-step explanation:

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

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The probability of the Doubles" means both dice show the same number is 36.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.

The likelihood of rolling an even number or doubles is thus:

The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.

The odds of rolling an even number or two doubles are 19/36.

Therefore, the probability of the Doubles" means both dice show the same number is 36.

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Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining  $2,000 in her savings account.

Future value = $20,000

Simple interests rate = 1.5%

The return rate on bonds= 4.5%

The return rate on stocks = 6.2%

Total amount made on invests =  $942

Time period = 1 year

Let us assume that the amount of money Emily invested = x

Amount invested in stock = y

If the amount is twice = 2y

The interest earned = x * 0.015

Interest on bond = 2y * 0.045

Interest on stocks = y * 0.062

The equation will be:

(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942

0.015x + 0.152y = 942  ------ Equation 1

Total future value is given as $20,000

x + 2y + y = 20000

x + 3y = 20000

x = 20000 - 3y

Substituting the x value in the first equation:

0.015(20000 - 3y) + 0.152y = 942

300 - 0.045y + 0.152y = 942

0.107y = 642

y = 6000

Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.

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Answer:

Your answer is A.

Step-by-step explanation:

Absolute values of any number are positive.

|4| = 2

|-2| = 2

2 = 2 and 4 > -2

C and D can be true, but they are not since less than or greater than doesn't apply if they were less than/greater than or equal, then yes.

Answer:

$25000 * 40% = 100.000

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

Answer:

9.57

Step-by-step explanation:

Answer

Its A

Step-by-step explanation:

Answer:

c. 84 ft²

Step-by-step explanation:

lateral area = 1/2 * base perimeter * height

where

base sides = 6 ft.

height (L) = 7

lateral area = 1/2 x (4*6) * 7

lateral area = 84 ft²

LA = 1/2pl

p = base perimeter

l = length

p = (6 * 4)

p = 24

l = 7

Use the formula and solve.

LA = 1/2(24)(7)

LA = 1/2(168)

LA = 84

Therefore, the answer is C

Best of Luck!

The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.

Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.

Therefore, the intercepted arcs AD and CD have equal measures.

Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.

Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

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We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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Answer: B. 8

Step-by-step explanation: 3*2=6. What you have to do to the top you have to do to the bottom. So, 4*2=8