The two lines graphed below are not parallel. How many solutions are there to the system of equations?

Answer:

Step-by-step explanation:

2/5 và -1/2

It is important to ensure that the groups are assigned randomly to eliminate any potential sources of bias.

Rain increases the probability of a crash. A randomized experiment can be designed to address this question with the following steps:

Divide the drivers randomly into two groups of 20 drivers each. Prepare both groups by having them drive on dry asphalt and then on wet asphalt.

Measure and compare the stop time after pressing brakes for drivers in both groups.

Randomization is a process used to prevent bias in the selection of the participants or sample from the population. In a randomized experiment, participants are randomly assigned to different treatments or groups.

This helps to ensure that any differences between the groups are due to the treatments rather than other factors, such as differences in age or gender.

For the experiment designed above, randomization was used to ensure that the drivers were assigned to groups without any bias or influence. The two groups were prepared in the same way and were randomly assigned to either dry asphalt or wet asphalt.

This helps to eliminate any potential sources of bias, such as age, gender, or driving experience.

Dividing the drivers based on their driving experience could lead to biased results, as experienced drivers may react differently to wet conditions compared to less experienced drivers.

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To design a randomized experiment to address the question of whether rain increases the probability of a crash, we can use the following approach:

Randomly divide the drivers into two groups of 20 drivers each. Both groups are prepared by driving on the dry asphalt and then on the wet asphalt. Measure and compare the stop time after pressing brakes for drivers in both groups.

In this experiment, randomization is used to ensure that any differences observed between the two groups are due to the treatment (dry vs. wet asphalt) rather than other factors such as driving skills or experience. By randomly assigning drivers to either the dry or wet group, we minimize the chance of bias or confounding variables affecting the results. This helps establish a causal relationship between the treatment (rain conditions) and the response variable (stop time after pressing brakes) by isolating the effect of rain and controlling for other factors.

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Matching the reasons with the statements; we have the following;

CPCTE (Corresponding Parts of Congruent Triangles are Equal)

SAS (Side-Angle-Side) type of congruent triangles.

Reflexive property of equality

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Answer:

The flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.

Step-by-step explanation:

We can use the following formula to calculate the flow rate:

Flow rate (mL/hr) = Volume to be infused (mL) / Time of infusion (hr)

First, we need to convert the total volume of 2 liters to mL:

2 liters = 2000 mL

Next, we can plug in the values:

Flow rate = 2000 mL / 16 hours

Flow rate = 125 mL/hr

Therefore, the flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.

The probability that the same number appears twice is 0.16

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The fair die is thrown twice.

The total number of outcomes if a fair die is tossed twice is 36.

The favorable number of outcomes, which also contains six, is six.

Following is a calculation of the likelihood of the same number appearing twice.

Probability = (Number of possible outcomes)/(Total number of outcomes)

                  = 6/36

                  = 0.16

So, the probability is 0.16

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Answer:

130

Step-by-step explanation:

The solution is, the scale factor for the dilation is 1/3.

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

here, we have,

give that,

from the given figure, we get,

QRST is dilated and translated to form similar figure Q'R'S'T'.

now, we have,

QR = 6

and, Q'R' = 2

so, scale factor = Q'R'/QR

                         = 2/6

                         = 1/3

Hence, the scale factor for the dilation is 1/3.

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Answer:

one solution

Step-by-step explanation:

3x + 3 = -3x + 3

6x + 3 = 3

6x = 0

x = 0

Answer: 5 1/30

Step-by-step explanation:

8 + 4/5 - 2/3 - 3 - 1/10 = 5 + 1/30

Falcons had a more effective overall record because of the higher median. Thus, the answer is option B.

The median is usually used for the comparison of two data sets instead of the mean, as it is not affected by outliers.

Compare the total points earned by each team.

The Eagles data set is given below:

3, 7, 10, 10, 13, 14, 17, 21, 24, 24, 27, 27, 37, 40, 55.

As the data set has an odd cardinality, the median is the middle element, therefore it is for:

21.

For the Falcons, we use the same approach and obtain a median about:

24.

Therefore, we can say that the Falcons had a more effective overall record because of the higher median and the best measure of center to compare would be mean.

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Answer:

The answer is 476, so the third option is correct.

Step-by-step explanation:

Step 1: Recall the Order Of Operations

The order of operations tells us in which order we have to solve expressions, if there are different operations.

The order is (from first solved to lastly solved) Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

Step 2: Calculate the expression

As we can see, there are parentheses present, so we will solve the expression in them first:

\((6+4)\\=(10)\)

The expression becomes:

\(10\cdot 49 -7\cdot 2\)

Multiplication should occur first before the subtraction, so let's multiply the numbers:

\(10\cdot49-7\cdot2\\\\\text{Multiply the first expression:}\\=490-7\cdot 2\\\\\text{Multiply the second expression:}\\=490-14\)

Now, you can subtract the numbers:

\(490-14\\=476\)

Answer:

To find the total length of the two sides, we simply add them together:

Total length = Side 1 + Side 2

Total length = (8x^2 - 5x - 2) + (7x - x^2 + 3)

Total length = -x^2 + 8x^2 - 5x + 7x - 2 + 3

Total length = 7x^2 + 2x + 1

Therefore, the total length of the two sides of the triangle is 7x^2 + 2x + 1.

Step-by-step explanation:

To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle:

Perimeter = Side 1 + Side 2 + Side 3

We are given the perimeter of the triangle as 4x^3 - 3x^2 + 2x - 6 and we know the lengths of Side 1 and Side 2. Therefore, we can rewrite the formula as:

4x^3 - 3x^2 + 2x - 6 = (8x^2 - 5x - 2) + (7x - x^2 + 3) + Side 3

Simplifying the right-hand side:

4x^3 - 3x^2 + 2x - 6 = 7x^2 + 2x + 1 + Side 3

Side 3 = 4x^3 - 3x^2 + 2x - 6 - 7x^2 - 2x - 1

Simplifying further:

Side 3 = 4x^3 - 7x^2 - x - 7

Therefore, the length of the third side of the triangle is 4x^3 - 7x^2 - x - 7.

Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction.

Closure under addition means that when two polynomials are added, the result is also a polynomial. In Part A, we added the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 to get the total length of the two sides of the triangle, which is 7x^2 + 2x + 1. Since the total length is also a polynomial, this shows that the polynomials are closed under addition.

Closure under subtraction means that when one polynomial is subtracted from another polynomial, the result is also a polynomial. In Part B, we subtracted the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 from the given perimeter of the triangle, 4x^3 - 3x^2 + 2x - 6, to get the length of the third side of the triangle, which is 4x^3 - 7x^2 - x - 7. Since the length of the third side is also a polynomial, this shows that the polynomials are closed under subtraction.

Therefore, the answers for Part A and Part B demonstrate that the polynomials are closed under addition and subtraction.

Answer:

Use a graphing calc and plug in the equation.

Step-by-step explanation:

Answer:

It's C on EDGE

Step-by-step explanation:

The required slope or as represented in this answer m is equal to 0.

The given points are (9, 11) and (18, 11) since both x axis and y axis are positive

thus the given points lie in the first quadrant

Thus to find the slope of the coordinates

we will use the formula m = y₂ - y₁ / x₂ - x₁

Here  y₂ = 11

y₁ = 11

x₂ = 18

x₁ = 9

Thus the slope of the given coordinates is m = 11 - 11/ 18 - 9

m = 0

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Answers:

The total profit expression is a binomial.

The total profit expression is a polynomial.

The total profit expression has a constant term.

The total profit expression is a polynomial

The total profit expression is a binomial

The total profit expression has a constant term

The first step to determining which type of function it is, is to add the profits in both theatres together

(t³ - t² + 2t - 100) + (t² - 2t - 300) = t³ - 400

A polynomial function is a mathematical expression that is made up of different types of variables. They include non-zero coefficients, positive exponents, and constants.

Types of polynomials include :

1. Linear polynomial function : a linear function is a function that has a single variable raised to the power of 1.

An example is x + 2

The variable x is raised to the power of 1. 2 is the constant terms

2.  Quadratic polynomial function - A quadratic function is a function that usually has a single variable and it is raised to the power of 2.

An example is 2x² + 10x + 25

3. Cubic polynomial function : this is a function that usually has a single variable raised to the power of 3.

An example is 5y³ + y²

4. Binominal function: this  is a function that contains only two terms.

An example is   t³ - 400

t³ - 400

The above equation of the total profit has a constant term which is -400

The above equation is a polynomial. This is because it has different types of variables.

The above equation is a binomial equation because it has only two terms  t³ and 400

In order to determine the type of expression the total profit is, the first step is to add the two profit expressions provided in the question. Based on the expression derived, the type of expression it is can then be deduced.

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Since the marginal cost and average total cost are both constant at 2, the optimal price for the firm to set is $5.00.

[32] At p=6, quantity demanded equals 18 as below: When the price charged by the firm is greater than or equal to 5, then q = 24 - 4p​ for which p=6 satisfies the condition; thus, we can substitute the given value of p into the second equation and solve for q:

q = 24 - 4(6)q = 24 - 24q = 0

Thus, when p=6, the quantity demanded of the firm's product is 0.

[33] Suppose the firm's marginal cost and average total cost are both constant at 2.

The profit-maximizing price is where marginal cost is equal to marginal revenue. To obtain the marginal revenue function, first, we must obtain the inverse demand function and then take the derivative of it. For p ≤ 5, the demand function is q = 9 - p, and for p ≥ 5, the demand function is q = 24 - 4p​.

To find the inverse demand function, solve each of the above demand functions for p in terms of q. For p ≤ 5, p = 9 - q, and for p ≥ 5, p = (24 - q)/4.

For p ≤ 5:

R(q) = pq

= (9 - q)q

= 9q - q^2M

R(q) = dR(q)/dq = 9 - 2q

For p ≥ 5:

R(q) = pq

= ((24 - q)/4)

q = 6q - q^2/4M

R(q) = dR(q)/dq

= 6 - q/2

The optimal price charged by the firm is where marginal cost equals marginal revenue:

For p ≤ 5:

2 = 9 - 2q2 + 2q - 9

= 0

q = 7/2

p = 9 - q

= 9 - (7/2)

= 11/2

= 5.50

For p ≥ 5:2 = 6 - q/22 + q/2 - 6 = 0

q = 4p = (24 - q)/4 = (24 - 4)/4 = 5

Since the marginal cost and average total cost are both constant at 2, the optimal price for the firm to set is $5.00.

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Answer:

Question 1:

a. The answer is B because the graph inclined really quickly and then it inclined at a much slower pace, suggesting that the person was running and then walking.

b. The answer is C because you can see on the graph that after a while, the distance from the starting point goes back to 0, indicating that the person forgot something at home.

Question 2:

a. The dashed line reaches the bottom at 15:30 so the answer is C.

b. Siobhan travels 8 km to go from home to school so the answer is 2 * 8 = 16 which is option D.

Question 3:

The answer is C because after the distance from the starting point increased, it then decreased and came back to the original point suggesting that he walked, turned around and walked back to the starting point.

Answer:

first page : a) A because it is the shortest time with no stop

b) C the graph goes up and return to the start point after a while

second page : it is at 3:30 0r 15:30

b): 8 km going to schools and 8 coming back is 16

third page it is C because he walk up a certain distance and come back to the starting point

Answer:

Electricity makes work easier.

We do not have to walk to a river to get water or wash our clothes and we can cook foods by switching a button.

Step-by-step explanation:

Answer:

hi how are you fineeeeee

Answer:

24 and 1 (1 x 24 = 24)

12 and 2 (2 x 12 = 24)

6 and 4 (4 x 6 = 24)

8 and 3 (3 x 8 = 24)

Answer:

The area will decrease by 9%.

Step-by-step explanation:

The area of a rectange is given by the formula below.

\(\boxed{\text{Area of rectangle}= \text{length}×\text{width}}\)

Let the original length and width of the rectangle be L and W respectively.

Start by finding the original area:

Original dimensions

Length= L= 100%L

Width= W= 100%W

Original area= LW

Let's find the dimensions of the new rectangle in terms of L and W.

New dimensions

Length= (100% +30%)L= 130%L

Width= (100%-30%)W= 70%W

New area

\( = \frac{130}{100} L \times \frac{70}{100} W\)

\( = \frac{91}{100} LW\)

= 91% LW

Comparing the new area with the original area:

100% LW- 91% LW= 9% LW

∴ The area will decrease by 9%.

*Note that percentage is equivalent to dividing a number by 100.

Answer:

b cot

Step-by-step explanation:

csc= 1 over sin

so

cos x  1    =  cos  =  cot

 1      sin      sin

90 intervals are expected to include the unknown parameter.

Given that,

If 100 separate simple random samples of size n were used to create 100 90% confidence intervals,

What is confidence interval ?

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence. Confidence is another name for probability in statistics.

90 % Confidence Interval means that we are 90% confident that true parameter lies between that interval.

If we construct 100, 90% confidence interval based on 100 random samples.

So, 90 of the intervals include the true parameter.

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Answer:

-1/3

Step-by-step explanation:

Multiply by root 3 on the top and bottom. Root 3 times root 3 is 3. 2-3 is -1.

x - intercept of the lines based on the given points is :

x intercept at 22 .

Given coordinates (48 , 30) , (61 , 45) , (74 , 60)

Take any two points,

Consider (48, 30) and (61, 45).

We have to find the slope of  line joining them:

Slope = (y2 - y1)/(x2 - x1)  

= (45 - 30)/(61 - 48)

= 15/13

Since all points are in same line,  we will get same slope for (48 ,30) and (74 , 60) and to other combination .

So the equation of line joining them:

y - y1 = m(x - x1)

y - 30 = (15/13) (x - 48)

=> 13(y - 30) = 15(x - 48)

=> 15x - 13y = 330

=> (15x)/330 - (13y/330) = 1

=> x/22 + (-y/330/13) = 1

We know that  x/a + y/b = 1 .

a is x intercept and b is y intercept.

∴ x intercept is 22.

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The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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The two transformations are:

For a function f(x) we define:

Vertical translation of N units as:

g(x) = f(x) + N

if N > 0, the translation is up.

if N <0, the translation is down.

Horizontal translation of N units as:

g(x) = f(x + N)

if N > 0, the translation is to the left.

if N <0, the translation is to the right.

Here we have two transformations:

f(x + 5/4)   this is a translation of 5/4 units to the left.

f(x) - 5/4  this is a translation of 5/4 units down.

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The required probability is 0.0828.

The probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1 thousand is 0.0828 (rounded to four decimal places).

Solution:

Given that,Mean annual salary of (public) classroom teachers = $54.7 thousand Standard deviation = $8.0 thousand

The sample size of the classroom teachers = 64Sample error = $1 Thousand The standard error is given by the formula;\( \large \frac{\sigma}{\sqrt{n}} = \frac{8}{\sqrt{64}}\)  = 1

And the Z-score is given by the formula;\( \large Z = \frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\)Substituting the given values, we getZ = \( \large \frac{55.7-54.7}{1}\) = 1

The probability of sampling error is the area between 53.7 and 55.7. Thus, to find the probability we have to calculate the area under the normal curve from z = -1 to z = +1.

That is;P ( -1 ≤ Z ≤ 1) = 0.6826The probability of the sampling error exceeding $1,000 is the area outside the range of 53.7 to 55.7. Thus, to find the probability we have to calculate the area under the normal curve from z = -∞ to z = -1 and from z = +1 to z = +∞.

That is;P(Z < -1 or Z > 1) = P(Z < -1) + P(Z > 1)P(Z < -1) = 0.1587 (from the standard normal table)P(Z > 1) = 0.1587Hence, P(Z < -1 or Z > 1) = 0.1587 + 0.1587 = 0.3174

Therefore, the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1 thousand is 0.6826 and

the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be more than $1 thousand is 0.3174.

The probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1 thousand is 0.0828 (rounded to four decimal places).

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The relation declares that (m,n) ~ (I, k) if and only if M'k. The equivalence class of an element (m,n) is the set of all pairs (a,b) such that (a,b) ~ (m,n). To determine the elements in the equivalence class [(4,6)], we need to find all pairs (a,b) such that (a,b) ~ (4,6).

The given equivalence relation ~ is helpful in grouping pairs of integers based on their powers. If two pairs of integers are related by this equivalence relation, then they have the same power and belong to the same equivalence class. The equivalence class [(m,n)] of a pair (m,n) consists of all pairs (a,b) such that \(a^n = b^m\).

To find the elements in the equivalence class [(4,6)], we need to find all pairs (a,b) such that \(a^6 = b^4\). Checking each option, we can see that (1,2), (3,2), (3,9/2), (3,5/2), (10,15), (10,18), (12,18), and (12,20) satisfy this condition. Therefore, these pairs are all elements of [(4,6)]. The pairs (1,3), (2,3), and (2,4) do not satisfy the condition and are not elements of [(4,6)].

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The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.

AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.

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