7x - y = 10
x - 4y = - 14

Answer:

8/9

Step-by-step explanation:

In the standard form of line y = mx + b

m is the slope and b is the y-intercept

so just compare these two equations and you will see that the slope here is just 8/9

Answer:

L = 22     W = 4

Step-by-step explanation:

It says that the length is 6 more than 4 times its width, this means

4W + 6 = L

Perimeter is 52, this means

2W + 2L = 52

and Area is 88, this means

W*L = 88

2W = 52 - 2L

W = 26 - L

4(26 - L) + 6 = L

104 - 4L + 6 = L

104 + 6 = L + 4L

110 = 5L

L = 22

W = 26 - 22

W = 4

The probability that the student makes it to the second class before it starts is very close to 0.

To find the probability that the student makes it to the second class before it starts, we can use the concept of linear combinations of random variables and the properties of normal distributions.

Let's define the random variable X as the total time it takes for the student to transition from the end of the first class to the start of the second class. Since X is a linear combination of independent normally distributed random variables (X1, X2, X3), we can use their means and variances to calculate the mean and variance of X.

The mean of X is the sum of the means of X1, X2, and X3:

μX = μ1 + μ2 + μ3 = 9:02 + 9:15 + 10 = 28:17 minutes.

The variance of X is the sum of the variances of X1, X2, and X3:

σX^2 = σ1^2 + σ2^2 + σ3^2 = (2.5)^2 + (3)^2 + (2.5)^2 = 15.25 minutes^2.

Now, we need to calculate the probability that X is less than or equal to 0, meaning the student arrives before the second lecture starts. Since X follows a normal distribution, we can standardize the variable and calculate the probability using the standard normal distribution table.

Z = (0 - μX) / σX = (0 - 28:17) / √15.25 ≈ -9.43.

Using the standard normal distribution table or a calculator, we can find the probability corresponding to Z = -9.43. The probability is essentially 0, as the value is significantly far in the left tail of the standard normal distribution.

Therefore, the probability that the student makes it to the second class before it starts is very close to 0.

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Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.

So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~

Answer: your credit utilization ratio on that card would be 50% but the answer is 450

Step-by-step explanation:

900-450 = 450

The similarity property that can be used for the triangles is SAS.

The congruence of any two figures is generally understood as two figures which can perfectly overlap each other. Congruent triangles are triangles that are perfect copies of one another. Various congruence rules are used to prove the congruency in two triangles

One of the conditions that make triangles congruent is:

if the two sides and the included angle of one triangle are respectively equal to the two sides and the included angle of the other( SAS).

Considering the given image:

If two triangles ABC and DEF are drawn in which AB/DE = AC/DF and the included angles <A and <D are equivalent i.e. <A ≅ <D

Since the two sides and the included angle of ΔABC are respectively equal to the two sides and the included angle of the ΔDEF

Therefore, the similarity property that can be used is SAS. The  3rd option is the answer

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Given that x = 7.7 m and = 25° the value of  AB is given as 3.254

We have the following data to work with

x = 7.7 m and = 25°,

then we have sin 25 = ∅ = 25 degrees

sin 25 = ab / 7.7

cross multiply from here

AB = sin25 x 7.7

= 0.4226 x 7.7

= 3.254

Hence we would say that in the triangle if x = 7.7 m and = 25°, the value of AB would be solved to be 3.254

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The surface area of the complex shape is 3,737,996 square feet.

To find the surface area of this complex shape, we need to break it down into simpler shapes and calculate their individual surface areas.

First, we can see that the shape consists of a rectangular prism (the block) and two triangular prisms (the roofs).

The rectangular prism has dimensions of 408 ft x 458 ft x 545 ft, and the triangular prisms have a height of 720 ft and a base of 680 ft.

The surface area of the rectangular prism is given by:

2lw + 2lh + 2wh = 2(408 x 458) + 2(408 x 545) + 2(458 x 545)

                          = \(1,739,276 ft^2\)

The surface area of one of the triangular prisms is given by:

2(lw/2) + lh + wb = 2(680 x 720/2) + 720 x 408 + 680 x 545

                           = \(999,360 ft^2\)

Since there are two triangular prisms, we need to multiply this by 2:

2(999,360) = 1,998,720 \(ft^2\)

Therefore, the total surface area of the complex shape is:

1,739,276 + 1,998,720 = 3,737,996 \(ft^2\)

So, the surface area of the complex shape is 3,737,996 square feet.

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Answer:

4z+4x

Step-by-step explanation:

Answer:

4x + 4z  

Step-by-step explanation

Answer:

456

Step-by-step explanation:

the dog was red

Answer:

24

Step-by-step explanation:

let \(\ell=length\)

then \(width=\frac{3}{4}\ell\)

since the perimeter is 84, then

\(2(length+width)=84\\ 2(\ell+\frac{3}{4}\ell)=84\\ 2(\frac{4}{4}\ell+\frac{3}{4}\ell)=84\\2(\frac{7}{4}\ell)=84\\ \frac{7}{2}\ell=84\\ \ell=\frac{84\times 2}{7}\\ \ell=24\)

Answer:

The 90% confidence interval

(74.71, 82.63)

Step-by-step explanation:

Confidence Interval Formula is given as:

Confidence Interval = μ ± z (σ/√n)

Where

μ = mean score

z = z score

N = number of the population

σ = standard deviation

The mean is calculated as = The average of their scores

N = 6 students

(71.6 + 81.0 + 88.9 + 80.4 + 78.1 + 72.0 )/ 6

Mean score = 472/6

= 78.666666667

≈ 78.67

We are given a confidence interval of 90% therefore the

z score = 1.645

Standard Deviation for the scores =

s=(x -σ)²/ n - 1 =(71.6 - 78.67)²+(81.0 - 78.67)²+(88.9 - 78.67)² + (80.4 - 78.67)²+ (78.1 - 78.67)²+( 72.0 - 78.67)2/ 6 - 1

= 5.886047531

= 5.89

The confidence interval is calculated as

= μ ± z (σ/√N)

= 78.67 ± 1.645(5.89/√6)

= 78.67 ± 3.9555380987

The 90% confidence interval

is :

78.67 + 3.9555380987 = 82.625538099

78.67 - 3.9555380987 = 74.714619013

Therefore, the confidence interval is approximately between

(74.71, 82.63)

Answer:

cost price = $262.57

selling price = $302.48

Explanation:

The selling price is

Selling price = cost + markup

We know that markup is 15.2% of the cost price. Since the markup is $39.91,

dividing both sides by 0.152 gives

The selling price is

cost price + 15.2% of the cost price

= (100% + 15.2%) cost price

=115.2% cost price

Now, 115.2% of the cost price is

Hence the selling price is $302.48.

Therefore, to summerise,

cost price = $262.57

selling price = $302.48

Answer:

E'(0,-2),F'(-3,-1),G'(-4,-3)

H'(3,-2),I'(1,-5),J'(-2,-1)

Step-by-step explanation:

You have to reflect the given coordinates.

For example:

W(-3,5)

The reflection of the coordinate would be W'(3,-5)

Answer: -1

Step-by-step explanation:

Answer: -1

Step-by-step explanation: I got it right :))

S = 10x^2

S/10 = x^2

+or-sqrt(S/10) = x

+or- sqrt(S10)/10 = x

so

_inverse = +or-sqrt(10x)/10

The dimensions for the maximum possible area that is 6.25 m² are L = 2.5 m and W = 2.5 m.

Area is the measure of the surface enclosed by a closed two-dimensional figure. It is typically measured in square units, such as square meters, square feet, or square inches. The formula for finding the area of various shapes depends on their geometrical structure. For example, the area of a rectangle is given by multiplying its length and width, the area of a triangle is given by multiplying its base and height and dividing by 2, and the area of a circle is given by π times the square of its radius.

Here,

To find the maximum area of the rectangular exercise area, we need to use the given amount of fencing to enclose the largest possible area.

a) Let the length of the rectangle be L and the width be W. We know that the perimeter of the rectangle is 10 m, so:

2L + 2W = 10

Simplifying, we get:

L + W = 5

We want to maximize the area of the rectangle, which is given by:

A = LW

Using the equation L + W = 5, we can solve for L in terms of W:

L = 5 - W

Substituting into the area equation, we get:

A = (5 - W)W = 5W - W²

To find the maximum area, we need to take the derivative of A with respect to W, set it equal to zero, and solve for W:

dA/dW = 5 - 2W = 0

Solving for W, we get:

W = 2.5

Substituting this value back into the equation L + W = 5, we get:

L = 2.5

So the maximum possible area is:

A = LW = (2.5)(2.5) = 6.25 square meters

b. To find the dimensions of the maximum possible area, we can use the fact that the maximum area occurs when the rectangle is a square.

Let x be the length and y be the width of the rectangle. We know that the perimeter is 10m, so:

2x + 2y = 10

Simplifying this equation, we get:

x + y = 5

To maximize the area, we want to find the values of x and y that satisfy this equation and also make the area as large as possible. Since we know that the rectangle is a square, we can set x = y:

x + y = 5

x + x = 5

2x = 5

x = 2.5

Therefore, the dimensions of the maximum possible area are 2.5m by 2.5m.

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One reason a sample may fail to represent the population of interest is sampling error.

The correct answer is an option (c)

We know that the sampling error is a statistical error that occurs when an analyst does not select a sample which represents the entire population of data.

So, the results found in the sample and the results obtained from the entire population would be different.

This error occurs when the sample used in the study is not representative of the entire population.

A sampling error is nothing but a deviation in the sampled value vs. the true population value.

Even randomized samples might have some degree of sampling error because in randomized samples, sample is only an approximation of the population from which it is drawn.

There are different categories of sampling errors.

- Population-Specific Error

- Selection Error

- Sample Frame Error

- Non-response Error

- Eliminating Sampling Errors

Therefore, One reason a sample may fail to represent the population of interest is sampling error.

The correct answer is an option (c)

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Answer:

     j/k + 6

Step-by-step explanation:

Add 6 to the quotient of j and k comes out to:

                                  j/k + 6

To find the values of y for which the binomial expression 5y - 7 belongs to the interval (-5, 13), we need to solve the inequality:

-5 < 5y - 7 < 13

Adding 7 to all sides of the inequality, we get:

2 < 5y < 20

Dividing all sides by 5, we have:

2/5 < y < 20/5

Simplifying the fractions, we get:

0.4 < y < 4

Therefore, the values of y that satisfy the inequality and make the binomial expression 5y - 7 belong to the interval (-5, 13) are in the range of 0.4 < y < 4. In interval notation, this can be expressed as (0.4, 4).

Note: The solution assumes that y is a real number.

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Answer:

Step-by-step explanation:

y=10

Answer:

(6, 6)

Step-by-step explanation:

Answer:

The distance is 8.4853

Step-by-step explanation:

Input Data :

Point 1 (xA, yA) = (0, -1)

Point 2 (xB, yB) = (6, 5)

Objective :

Find the distance between two given points on a line?

Formula :

Distance between two points = √(xB − xA) ^ 2 + (yB − yA) ^ 2

Solution :

Distance between two points = √ (6 − 0)^2 + (5− −1) ^ 2

= √6^2 + 6^2

= √36 + 36

= √72

= 8.4853

Distance between points (0, -1) and (6, 5) is 8.4853

hope this helps and is right :)

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

okay so,

Step-by-step explanation:

My computer screen is broken and I could not see the equation for 11, 13, and 16

10. 81

12. -1/5 or -0.2

14. 9/64 or 0.140625

15. 27

17. -8

18. 1

Answer:

1.  81

2.  1/144

3.  -5

4.  1/64

5.  9/64

6.  27

7.  0

8. -16

9.  3

Answer:

T= (-4 ,2)

U= (2 ,4)

V= (3 ,1)

W= (-3, -1)

1 . LENGTH OF EACH SIDES

 \(length \ of \ sides =\sqrt{(x_{2} -x_{1} )^2+(y_{2} -y_{1})^2}\)

\(length \ of \ TU = \sqrt{(2--4 )^2+(4-2)^2} = \sqrt{40}\)

\(Length \ of \ UV =\sqrt{(3-2 )^2+(1-4)^2} = \sqrt{10}\)

\(Length \ of \ VW =\sqrt{(-3-3)^2+(-1-1)^2} = \sqrt{40}\)

\(length \ of \ TW =\sqrt{(-3--4 )^2+(-1-2)^2} =\sqrt{10}\)

2. SLOPE OF CONSECUTIVE SIDES

\(Slope \ of \ the \ line \ passing \ through \ (x_{1}, y_{1} ) \ and \ (x_{2}, y_{2}) = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

\(Slope \ of \ TU = \frac{4-2}{2--4} = \frac{2}{6} =\frac{1}{3}\)

\(Slope \ of \ UV = \frac{1-4}{3-2} = -3\)

\(Slope \ of \ VW = \frac{-1-1}{-3-3} = \frac{-2}{-6} =\frac{1}{3}\)

\(Slope \ of \ TW = \frac{-1-2}{-3--4} = -3\)

\(Slope \ of \ lines \ parallel \ to \ each \ other = m_{1}\cdot m_{2} = 1\\Slope\ of \ lines\ perpendicular \ to \ each \ other =m_{1}\cdot m_{2} = -1\\\)

\(Slope \ of \ TU * UV = \frac{1}{3}*-3 = -1\\\\Slope \ of \ UV *VW = -3 *\frac{1}{3}= -1\\\\ Slope \ of \ VW * TW = \frac{1}{3}*-3 = -1\\\\Slope \ of \ TW * TU = -3 *\frac{1}{3}= -1\\\\\)

Therefore the consecutive sides are perpendicular to each other.

3. TYPE OF PARALLELOGRAM

The opposite sides are of same length.  The consecutive sides are perpendicular to each other. So the parallelogram is a RECTANGLE.

Answer:

-6x+19

Step-by-step explanation:

-6(x-4) = -6x+24

-6x+24-5 = -6x +19

Answer:

x=9-3y

Step-by-step explanation:

- Move the variable to the right & change its sign

3x + 9y = 27

- Divide both sides by 3

3x = 27 - 9y

- Write the solution x in parametric form

x=9-3y

- Solution:

x= 9-3y

Barbara can buy a combination of earrings and necklaces with a total cost of no more than $144. We need to determine how many of each item she can buy within her budget.

Let's assume Barbara buys x earrings and y necklaces. The cost of earrings will be 12x, and the cost of necklaces will be 24y. According to the problem, the total cost must be no more than $144, so we have the inequality:

12x + 24y ≤ 144

To find the possible combinations, we can test different values of x and y that satisfy this inequality. Since we want to maximize the number of items Barbara can buy, we can start by setting x and y to their maximum possible values.

The maximum number of earrings Barbara can buy is 144/12 = 12 pairs. The maximum number of necklaces she can buy is 144/24 = 6 necklaces.

By trying different combinations within these limits, we find that Barbara can buy 0 earrings and 6 necklaces, spending a total of $144, or she can buy 6 earrings and 0 necklaces, also spending a total of $144.

Therefore, Barbara can either buy 6 necklaces or 6 earrings within her budget of $144.

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a) The given statement is true b) The given statement is true c) The given statement is false d) The given statement is true e) The given statement is true f) The given statement is true.

(a) True. If a set S is linearly dependent, it means that there exists at least one element in S that can be expressed as a linear combination of the other elements in S.

(b) True. Any set that contains the zero vector is linearly dependent because the zero vector itself can be expressed as a linear combination of its elements (in this case, just the zero vector itself multiplied by the scalar 1).

(c) False. The empty set is considered linearly independent by convention. Since it contains no elements, there are no vectors to form a nontrivial linear combination, and thus it is vacuously linearly independent.

(d) True. If a set S is linearly dependent, then any subset of S will also be linearly dependent. This is because if a set of vectors can be expressed as a linear combination of other vectors, removing some vectors from that set will not change its linear dependence.

(e) True. Subsets of linearly independent sets are also linearly independent. If a set is linearly independent, it means that no vector in the set can be expressed as a linear combination of the other vectors. Therefore, any subset of this set will still retain the property of linear independence.

(f) True. If the equation a1x1 + a2x2 + ... + anxn = 0 holds, where x1, x2, ..., xn are linearly independent, then the only solution is when all the scalars ai are zero. This follows from the definition of linear independence, which states that a set of vectors is linearly independent if the only solution to the equation c1v1 + c2v2 + ... + cnvn = 0 is when all the scalars ci are zero.

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Answer:

9/20 or 45%

Step-by-step explanation:

If we make common denominators (for this example, we will make each denominator 20), this would make 7/10 = 14/20 and 1/4 = 5/20. From there, we subtract the numerators from each other (14-5) and leave the denominators alone. The difference comes out to 9/20 and there is no way to simplify it further, making it the final answer.