What is the slope given: (-1, 1) and (6, -1)

Answer:

C: 120x+92y<1,300

Step-by-step explanation:

Since the band plays at an hourly rate of $120 for x hours, the total cost of the band playing is 120x.

Also the DJ can play for the remaining time at an hourly rate of $92 for y hours, the total cost of the band playing is 92y

The total cost of the band is DJ playing is thus 120x + 92y.

Since we require this to be under $1,300, we us the less than sign '<' to show the relation.

So, 120x + 92y < 1300

So, the answer is C

The answer is , the students in the sample were male is 50%.

To find the percentage of students in the sample who were male, we need to look at the total number of males and divide it by the total number of students in the sample, then multiply by 100 to get a percentage.
According to the table, the total number of males in the sample is 50,5050 and the total number of students in the sample is also 100,100,100.
So, the percentage of students in the sample who were male is:
50,5050 / 100,100,100 x 100% = 50%
Therefore, 50% of the students in the sample were male.

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The correct order of numbers from greatest to least is 746.211> 70.962> 28.19> 7.54> 0.419.

We are given 5 numbers and we have to give them a correct order from greatest to least. This means that we have to arrange them in descending order in which the first number that comes in the sequence is the largest one and the last number is the smallest one.

We will observe every number and see the range in which the number lies.

The number 0.419 is the smallest among the given numbers as its value is lesser than even 1. All the other numbers are greater than 1. Then, the number 7.54 is greater than 0.419 but lesser than all the other numbers.

After this, 28.19 is greater than 7.54 but lesser than the remaining numbers. The number 70.962 is greater than 28.19 but lesser than 746.211. The number 746. 211 is the greatest of all the numbers.

Therefore, arranging them in decreasing order we get  746.211> 70.962> 28.19> 7.54> 0.419.

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Answer:

15, 16, 17

Step-by-step explanation:

X

X + 1

X + 2

3X + 3 = 48

3X = 45

X = 15

Answer:

brand b is the better buy, brand a unit price is 0.0427, and brand b is 0.0346

Step-by-step explanation:

hope it helped :)

Answer:

You could say that -h=-2 and then divide both sides by -1 to get h=2.

:)

Answer:

Step-by-step explanation:

Given the vertex form of the quadratic function:

g(x) = - ½(x - 2)² + 5

Transform the vertex form of the quadratic function into its standard form, ax² + bx + c :

g(x) = - ½(x - 2)² + 5

g(x) =  - ½x² - 2(- ½)(2)x + - ½(2)² + 5

g(x) =  - ½x² - 2(- ½)(2)x - 2 + 5

g(x) = - ½x² + 2x + 3  (Standard form)

where a = - ½, b = 2, and c = 3  

In vertex form, we can say, x = h  since the axis of symmetry and vertex lies on the same line.  

To find the x-coordinate (h ) of the vertex:

\(x = \frac{-b}{2a} = \frac{-2}{2(-\frac{1}{2}) } = \frac{-2}{-1} = 2\)

Substitute the value of the x-coordinate (h ) of the vertex into the standard form to find the value of the y-coordinate, (k ):

k = - ½x² + 2x + 3

k = - ½(2)² + 2(2) + 3

k = -2 + 4 + 3 = 5

Therefore, the vertex (h, k) = (2, 5).

The correct answer is (c) Ali has a monthly net income of $2,088 after paying 28% in taxes.

.

To calculate Ali's net monthly income, we first need to find out the amount of tax she pays, and then we can subtract it from her annual income to get her net annual income. We'll then divide it by 12 to get her monthly net income.

Calculations: Ali's tax rate is 28%. 28% of 29,000 is 8,12029,000 - 8,120 = 20,88020,880 / 12 = 1,740

Therefore, Ali's net monthly income is $1,740. The correct answer is option D, $1,740. ($29,000 salary x 28% taxes = $8,120 in taxes annually; $8,120 / 12 months = $677 in taxes per month; $29,000 - $677 = $2,088 net monthly income).

Net income refers to the amount of money that a company or an individual has earned after deducting all the expenses and taxes from their gross income. In the context of a company, net income is also called profit, and it is an important measure of a company's financial performance.

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Given maximization problem is  Maximize profit The corresponding profit values at each point Optimal solution is (10,0) and the corresponding profit is $80(b) .

When the right-hand side of constraint 1 is changed to 17, the profit increase or decrease: New profit=$80 Increase in profit When the right-hand side of constraint 1 is changed to 13, the profit decrease or increase: New profit=$65 Decrease in profit= $15If the right-hand-side value goes below 10, then the solution will not be feasible anymore .

When the right-hand side of constraint 2 is changed to 22, the profit decrease or increase from the original amount:

New profit= $88

Increase in profit= $8

New Solution is (11,5.5)(e)

If profits from X1 are reduced to $6, the new solution will change.The new optimal solution is (6,6) and the new profit is $72.(f) The dual price of constraint 1 is 2.5.The lower bound on dual price is $2.38. (g) Based on the results of the table, the conclusions that can be drawn regarding bounds of the right-hand-side values and the dual price are: When the RHS values of constraint 1 lie between 13 and 16, there is no change in the optimal solution.

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The estimate for the difference between the two population mean for 95% confidence interval is given by ( 3, 7 ).

The 95% interval estimate for the difference between the two population means,

Use the two-sample t-interval formula,

( X₁ - X₂ ) ± tα/2 × SE

where X₁ and X₂ are the sample means of the two branches,

tα/2 is the critical value of the t-distribution with degrees of freedom equal to the smaller of (n₁ - 1) and (n₂ - 1).

And α/2 = 0.025 for a two-tailed test at the 95% confidence level,

And SE is the standard error of the difference between the means, given by,

SE = √(s₁²/n₁ + s₂²/n₂)

Plugging in the given values, we get,

= ( 11 - 6 ) ± t0.025 × √(4²/25 + 1²/20)

Simplifying ,

5 ± t0.025 × 0.83

Using a t-table with 43 degrees of freedom the smaller of 25-1 and 20-1, find the critical value t0.025 = 2.017.

using calculator ( attached value)

Plugging this in, we get,

5 ± 2.017 × 0.83

So the 95% confidence interval for the difference between the two population means is (3.33, 6.67)

Nearest whole number = ( 3, 7 )

Therefore, 95% confidence interval that the true difference between the average hourly wages of employees of the downtown store and the north mall store is between  3 and 7.

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By solving two simultaneous linear equation, the result obtained is

There are 14 small rooms and 7 large rooms

What is Simultaneous Linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

A system of two simultaneous linear equation needs to be solved

Let the number of small rooms be x and the number of large rooms be y

The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 5 people.

Total number of guests = 63

2x + 5y = 63 ...... (1)

Fatoumata reserved twice as many small rooms as large rooms

x = 2y ....... (2)

Putting the value of x in (1)

\(2(2y) + 5y = 63\\4y + 5y = 63\\9y = 63\\y = \frac{63}{9}\\y = 7\)

Putting the value of y in (2)

x = \(2 \times 7\)

x = 14

There are 14 small rooms and 7 large rooms

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Answer:

option a 0.06 bared

The truth value of Vm³n P(m, n) is true.

Let P(m, n) be "n is greater than or equal to m" where the domain is all non-negative integers for both m and n.

V (for "universal quantification" which means "for all") states that "for all non-negative integers m and n, n is greater than or equal to m".

This statement is true since every non-negative integer n is always greater than or equal to itself, which implies that this statement holds true for all non-negative integers m and n. Therefore, the truth value of Vm³n P(m, n) is true.

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Answer:

x = 35 , y = 4

Step-by-step explanation:

since the quadrilaterals are similar then the ratios of corresponding sides are in proportion , that is

\(\frac{x}{10}\) = \(\frac{21}{6}\) ( cross- multiply )

6x = 210 ( divide both sides by 6 )

x = 35

and

\(\frac{y}{14}\) = \(\frac{6}{21}\) ( cross- multiply )

21y = 84 ( divide both sides by 21 )

y = 4

1) The standard deviation is 0.275

2) The approximate probability is 0.165

Sampling distribution: The sampling distribution is a probability distribution of a statistic determined from a larger number of samples. A statistic, such as a mean or a standard deviation, is a numerical quantity calculated from data and used to make inferences about the population's parameters.

For the first question, we can use the hypergeometric distribution to find the sampling distribution of the mean when we choose any 2 pumpkins out of 4.

Let X be the number of pumpkins preferred by the 2 children we sample. Then X follows a hypergeometric distribution with N = 4 (total number of pumpkins), n = 2 (number of pumpkins we choose), and K = {0, 1, 2} (possible number of pumpkins preferred).

The probability mass function of X is given by:

P(X = k) = (K choose k) * (N - K choose n - k) / (N choose n)

where (a choose b) is the binomial coefficient "a choose b".

Using this formula and the given weights, we can calculate the probabilities for k = 0, 1, and 2:

P(X = 0) = (2 choose 0) * (2 choose 2) / (4 choose 2) = 1/6

P(X = 1) = (2 choose 1) * (2 choose 1) / (4 choose 2) = 2/3

P(X = 2) = (2 choose 2) * (2 choose 0) / (4 choose 2) = 1/6

Now we can find the mean and standard deviation of the sampling distribution of the mean, which is approximately normal by the central limit theorem since the sample size is relatively small:

Mean = E(X) = n * (K/N) = 2 * [(00.2)+(10.3)+(2*0.35)] / 4 = 0.95

Standard deviation = sqrt(n * K/N * (1 - K/N) * (N - n)/(N - 1))

= sqrt(2 * 0.95 * (1 - 0.95) * 2/3)

= 0.275

For the second question, we can use the central limit theorem to approximate the sampling distribution of the sample mean. Since we have a large sample size (n = 50), the sample mean X follows an approximately normal distribution with mean μ = 4.0 g and standard deviation

σ/sqrt(n) = 1.5/sqrt(50) ≈ 0.212 g.

Then, we can calculate the z-scores for the lower and upper bounds of the interval:

z_1 = (3.5 - 4.0) / 0.212 ≈ -2.36

z_2 = (3.8 - 4.0) / 0.212 ≈ -0.94

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(Z < -2.36) ≈ 0.009

P(Z < -0.94) ≈ 0.174

Then, we can find the probability that X falls within the interval [3.5, 3.8] by taking the difference between these probabilities:

P(3.5 ≤ X ≤ 3.8) ≈ P(-2.36 ≤ Z ≤ -0.94) ≈ 0.174 - 0.009 ≈ 0.165

Therefore, the approximate probability that the sample average amount of impurity X is between 3.5 and 3.8 g is 0.165.

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Answer:

y = -x - 5

Step-by-step explanation:

To find the equation of the line passing through two given points, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Where m is the slope of the line, and (x1, y1) are the coordinates of one of the points on the line.

We first need to find the slope of the line passing through the two given points. We can use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (-8, 3) and (x2, y2) = (-2, -3)

m = (-3 - 3) / (-2 - (-8)) = -6 / 6 = -1

Now, we can use the point-slope form of the equation with one of the given points, say (-8, 3):

y - 3 = -1(x - (-8))

Simplifying:

y - 3 = -x - 8

y = -x - 5

Answer:

(-8, 3) and (-2, -3) is y = -x - 5

Step-by-step explanation:

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.

Given the points (-8, 3) and (-2, -3), we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates into the formula:

m = (-3 - 3) / (-2 - (-8))

m = (-3 - 3) / (-2 + 8)

m = (-6) / (6)

m = -1

Now that we have the slope (m = -1) and one of the points (x1, y1) = (-8, 3), we can use the point-slope form to write the equation:

y - 3 = -1(x - (-8))

y - 3 = -1(x + 8)

y - 3 = -x - 8

y = -x - 8 + 3

y = -x - 5

Therefore, the equation that represents a line passing through the points (-8, 3) and (-2, -3) is y = -x - 5.

Hope this helped :)

The given points, only the point (4, -9, -8) lies on line 1.

To determine whether certain points lie on the line 1, which is perpendicular to the plane x - 2y - 4z = 5 and contains the point (2, -5, 0), we can check if the coordinates of those points satisfy the equation of the line.

The direction vector of the line 1 is perpendicular to the plane and can be determined from the coefficients of x, y, and z in the plane equation. In this case, the direction vector of the line is (1, -2, -4).

Now, we can write the parametric equation of the line l as:

x = 2 + t * 1

y = -5 + t * (-2)

z = 0 + t * (-4)

To check if a point (x₀, y₀, z₀) lies on the line 1, we need to find a value of t that satisfies the parametric equations.

Let's consider the following points and determine if they lie on line 1:

Point (3, -6, -4)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (3, -6, -4) into the parametric equations:

x₀ = 2 + t * 1 --> 3 = 2 + t --> t = 1

y₀ = -5 + t * (-2) --> -6 = -5 - 2 --> t = -1

z₀ = 0 + t * (-4) --> -4 = 0 - 4t --> t = 1

The value of t is not consistent across all equations, so the point (3, -6, -4) does not lie on line 1.

Point (2, -5, 0)

This point is given as the point that line 1 contains. Therefore, it lies on line 1.

Point (4, -9, -8)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (4, -9, -8) into the parametric equations:

x₀ = 2 + t * 1 --> 4 = 2 + t --> t = 2

y₀ = -5 + t * (-2) --> -9 = -5 - 2t --> t = 2

z₀ = 0 + t * (-4) --> -8 = 0 - 8t --> t = 1

The value of t is consistent across all equations, so the point (4, -9, -8) lies on line 1.

Therefore, among the given points, only the point (4, -9, -8) lies on line 1.

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The complete question is:

Let l be the line perpendicular to the plane x - 2y - 4z = 5 and containing the point (2, -5, 0). determine whether the following points lie on line l.

Statement I is correct, while statements II and III are false. The longer-term bond (Bond L) fluctuates more due to its higher interest rate risk compared to the shorter-term bond (Bond S).

To calculate the value of Bond L and Bond S, we need more information, specifically the interest rate or yield associated with these bonds.

a. Bond prices are influenced by various factors, including the bond's face value, coupon payments, time to maturity, and prevailing interest rates. Without the interest rate or yield, we cannot determine the exact values of Bond L and Bond S.

The bond price can be calculated using the present value formula, which discounts the future cash flows of the bond to their present value.

b. The longer-term bond (Bond L) tends to fluctuate more when interest rates change compared to the shorter-term bond (Bond S) due to interest rate risk. Interest rate risk refers to the impact of changes in interest rates on the value of a bond.

I. Longer-term bonds have more interest rate risk than shorter-term bonds. This statement is true. Longer-term bonds are exposed to changes in interest rates for a more extended period, which makes their prices more sensitive to interest rate movements. When interest rates rise, the value of longer-term bonds tends to decrease more than shorter-term bonds.

II. Longer-term bonds have less reinvestment rate risk than shorter-term bonds. This statement is false. Reinvestment rate risk refers to the risk of reinvesting coupon payments at lower interest rates when the bond matures. Longer-term bonds have a higher reinvestment rate risk because they have more coupon payments to reinvest over the bond's longer lifespan.

III. Longer-term bonds have less interest rate risk than shorter-term bonds. This statement is false. As mentioned earlier, longer-term bonds have more interest rate risk because their prices are more sensitive to changes in interest rates compared to shorter-term bonds.

In summary, statement I is correct, while statements II and III are false. The longer-term bond (Bond L) fluctuates more due to its higher interest rate risk compared to the shorter-term bond (Bond S).

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Answer:

4 + 2 = 6

Step-by-step explanation:

If you put up 4 figers and 2 figers and count it

will give you the sum of 6

In a paired design, each pair of observations does not necessarily consist of measuring the same individual twice. Instead, a paired design involves matching pairs of individuals or units based on certain criteria or characteristics and then measuring each individual in the pair under different conditions or at different time points.

This design is often used to compare the effects of different treatments or interventions within the same individuals or to control for individual-specific factors. In a paired design, the pairing could be based on various factors such as age, gender, pre-existing conditions, or other relevant characteristics. For example, in a study evaluating the effectiveness of a new medication, researchers may pair individuals with similar characteristics (e.g., age, gender, severity of the condition) and then administer the new medication to one individual in each pair while providing a placebo to the other individual. By measuring the outcomes within each pair, the researchers can directly compare the effects of the medication and the placebo within the same individuals.

The key aspect of a paired design is that the pairs are matched based on certain criteria, and each pair represents a unique combination of individuals. This allows for a more controlled comparison within the pairs and helps minimize the influence of individual-specific factors on the outcomes of interest.

In summary, a paired design involves matching pairs of individuals based on certain characteristics and comparing the outcomes within each pair. It does not require measuring the same individual twice but rather focuses on comparing different conditions or treatments within matched pairs of individuals.

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When a plane intersects only one nappe of a double-napped cone such that it is parallel to a generating line, it forms a parabola.

When a plane intersects only one nappe of a double-napped cone parallel to a generating line, it forms a conic section known as a parabola. This is because a parabola is defined as the set of all points that are equidistant to a fixed point (known as the focus) and a fixed line (known as the directrix).

When a plane intersects a double-napped cone parallel to a generating line, it intersects all the generatrices at the same angle, resulting in a curve that is symmetric and opens in one direction. This curve is a parabola, and it is commonly found in nature, such as the path of a thrown ball, the shape of a satellite dish, or the reflector of a car's headlights.

The properties of a parabola make it useful in various fields, including optics, physics, and engineering, where it is used to model and analyze a wide range of phenomena, such as the trajectory of projectiles, the behavior of lenses and mirrors, and the design of antennas and reflectors.

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Answer:

option C

Step-by-step explanation:

Here, we want the first best step

looking at the expression, we can see that if we divided both sides by -2, we will have to answer a regular

Thus, by dividing both sides by -2, then we have the answer

Answer:

Quadrant III

Step-by-step explanation:

Because both numbers are negative, the point lands in Quadrant III.

Y = 18.50

Please tell me if it is right XD <3

Answer:

x^2

Step-by-step explanation:

Any even number raised to two is even.

Eg: 4^2 = 16

12^2 = 144

Etc...

And

Any odd number raised to two is odd.

Eg: 5^2 = 25

13^2 = 169

Etc...

And also x^2 is greater than 2x & x+3 & x+2

Answer:

Please see below.

Step-by-step explanation:

First, let us find the cost of ONE soft drink.

We have the relation:

4 drinks for $2.20

We can divide the amount of money by the amount of drinks.

2.20 / 4 = 0.55

With this, we can conclude that each drink costs $0.55

A.)

Fill in the table.

For this, we just need simple multiplication.

1 drink = $0.55

2 drinks = $1.10

3 drinks = $1.65

4 drinks = $2.20

B.)

What is the constant of proportionality?

We have y = 2.20 and we have x = 4. Using the equation of proportional relationship, y = kx, we can plug in these numbers.

The constant of proportionality is 0.55.

C.)

If you were to buy 22 soft drinks, how much would it cost?

We can use multiplication.

22 x 0.55 = 12.10

22 soft drinks cost $12.10.

I hope this helps you. Please inform me of any mistakes.

Answer:

73°

Step-by-step explanation:

Angles on a straight line add up to 180°

angle ABC= 180-146= 34°

Angles in a traingle add up to 180°

180-34= 146°

y= 146÷2= 73°

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Answer:

Option D (73°)

Step-by-step explanation:

According to Exterior Angle Property , the measure of exterior angle is the sum of the opposite interior angles.

So, according to the question -

\(y + y = 146\)

\( = > 2y = 146\)

\( = > y = \frac{146}{2} = 73\)

Therefore, the probability of landing on a blue and a number greater than 3 is 1/24 or approximately 0.042.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there is one favorable outcome (heads) out of two possible outcomes (heads or tails). Probability is used in many fields, including mathematics, statistics, physics, engineering, and finance. It is used to make predictions and to estimate the likelihood of various outcomes. In addition, probability theory provides a framework for analyzing and understanding random processes, which occur in many real-world situations.

Here,

To find the probability of landing on a blue and a number greater than 3, we need to first identify all the possible outcomes when spinning both spinners.

The first spinner has four equally likely outcomes (red, blue, green, and yellow), and the second spinner has six equally likely outcomes (1, 2, 3, 4, 5, and 6). Therefore, there are a total of 4 x 6 = 24 possible outcomes.

We need to find the number of outcomes where we spin a blue on the first spinner and a number greater than 3 on the second spinner. There is only one blue section on the first spinner, and there are three sections with numbers greater than 3 on the second spinner (4, 5, and 6). Therefore, there is only one possible outcome that satisfies both conditions, which is landing on blue and a number greater than 3.

So the probability of landing on a blue and a number greater than 3 is 1 out of 24 possible outcomes:

P(blue and number > 3) = 1/24

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Absolute increase in population will be 2050

And percentage increase will be 56.94 %

We have given population in 2005 is 3600

And population in 2011 is 5650

So absolute increase in population = 5650-3600 = 2050

We have to find the percentage increase in population

So relative percentage increase in population will be 2050/3600 *100 = 56.94  %

So population will increase by 60 %

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Answer:

174 CM²

Step-by-step explanation:

First we split up the triangular prism into shapes we can better understand (2 triangles, and 2 rectangles)

We solve the area of the triangles by using the formula to the area of a triangle (B·H÷2) 8·6÷2=24

There are 2 triangles therefore we get 2*24 which is 48 CM²

Now we calculate the area of the rectangles (7·10=70, 8·7=56)

Finally we add up all the numbers (70+56+48=174 CM²)

Therefore the surface area of the triangular prism is 174 CM², respectively.