the number are in the ratio at is 8:7 their sum is 60 Find two numbers​

Answer:

After applying the distributive property, Ezra's expression was 8y + 16

After he used the commutative property, his expression was 16 + 8y

Step-by-step explanation:

Distributive property rule: a(x+y) = ax + ay
   Not much to explain here

Commutative property rule: a + b = b + a   or  xy = yx
   We use addition rule in this case, simply place 16 in front of 8y

Answer:

no looks confusing

Step-by-step explanation:

Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.

The z-score for a 97.5% confidence level is approximately 1.96. This means that a value that falls 1.96 standard deviations above the mean will have a cumulative probability of 0.975 or a 97.5% confidence level.

The z-score for a given confidence level represents the number of standard deviations away from the mean that corresponds to that level of confidence. To find the z-score for a 97.5% confidence level, we need to determine the area under the normal distribution curve that corresponds to a cumulative probability of 0.975.

The standard normal distribution has a mean of 0 and a standard deviation of 1. Using a standard normal distribution table or a statistical calculator, we can find that the area to the left of the z-score is 0.975.

Since the normal distribution is symmetric, the area to the right of the z-score is also 0.025. To find the z-score, we need to determine the value that corresponds to an area of 0.025. From the standard normal distribution table or calculator, we find that the z-score for a cumulative probability of 0.025 is approximately 1.96.

Therefore, the z-score for a 97.5% confidence level is approximately 1.96. This means that a value that falls 1.96 standard deviations above the mean will have a cumulative probability of 0.975 or a 97.5% confidence level.

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Answer:

The minimum exam score to be awarded an A is about 8.52.

Step-by-step explanation:

Let X represent the scores on a common final exam.

It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.

It is provided that according to the department policy is that the top 10% of students receive an A.

That is, P (X > x) = 0.10.

⇒ P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding z-score is:

z = 1.28

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52\)

Thus, the minimum exam score to be awarded an A is about 8.52.

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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Answer:

The restaurant bill before the service charge ​is: £69.55

Step-by-step explanation:

Service charge percentage = 8%

Total Bill including service charge = £75.60

Let us first determine the service amount using the formula

Service amount = 8% of 75.60

                          = 8/100 × 75.60

                          = £6.05

Thus, the restaurant bill before the service charge can be determined by subtracting the service amount from the total bill.

Restaurant bill before the service charge = Total Bill - Service amount

                                                                     = £75.60 - £6.05

                                                                      = £69.55

Therefore, the restaurant bill before the service charge ​is: £69.55

Answer:

Show that the ratios StartFraction UV/XY, WU/ZX, and WV/ZY are equivalent.

Step-by-step explanation:

I just took the quiz and got it right. Hope this helps :)

Two triangles are similar but not congruent if they have three congruent angles but the side lengths are not equal

The two triangles can be shown to be similar given that the ratios of the corresponding sides ΔWUV and ΔYXZ are constant

Reason:

Known parameters are;

ΔWUV and ΔXZY are shown

∠VUW ≅ ∠YXZ

∠UWV ≅ ∠XZY

∠UVW ≅ ∠ZYX

Length of side \(\overline {VW}\) = 60

Length of side \(\overline {VU}\) = 50

Length of side \(\overline {UW}\) = 40

Length of side \(\overline {ZY}\) = 48

Length of side \(\overline {YX}\) = 40

Length of side \(\overline {XZ}\) = 32

The ratio of the sides are;

\(\dfrac{\overline {VW}}{\overline {ZY}} = \dfrac{60}{48} = \dfrac{5}{4}\)

\(\dfrac{\overline {VU}}{\overline {YX}} = \dfrac{50}{40} = \dfrac{5}{4}\)

\(\dfrac{\overline {UW}}{\overline {XZ}} = \dfrac{40}{32} = \dfrac{5}{4}\)

Therefore, given that  the angles of ΔWUV and ΔXZY are all congruent, and the sides of triangle ΔWUV and ΔXZY have a constant proportion, we have that the two triangles are congruent by Side-Side-Side SSS congruency theorem,  and we have;

ΔWUV ~ ΔYXZ given that ΔYXZ is scaled drawing of ΔWUV

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Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).

The given functions are f(x) = 3x² and g(x) = -2².

To understand the difference between their graphs, let's examine the characteristics of each function individually:

Function f(x) = 3x²:

The coefficient of x² is positive (3), indicating an upward-opening parabola.

The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.

The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.

Function g(x) = -2²:

The coefficient of x² is negative (-2), indicating a downward-opening parabola.

The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.

The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.

Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.

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Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

m<20

Step-by-step explanation:

m must be less than 20

m < 20

or

20 > m

The probability of picking an ace of hearts from a standard deck of playing cards is 1/52.

Consider a standard deck of cards.

We know that a standard deck of cards contains 52 cards.

So, total number of cards in the standard deck of cards = 52 cards

Now, we have to assume that there are no jokers in the set of cards.

We have to find the probability of picking an ace of hearts from a standard deck of playing cards.

For that we need to first find the number of cards which are ace of hearts.

Number of cards which are ace of hearts = 1

Probability of picking an ace of hearts from a standard deck of playing cards is,

P = Number of ace of hearts / Total number of cards

  = 1/52

Hence the probability is 1/52.

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Answer:

Step-by-step explanation:

Find the slope of the line by formula:

Substitute and calculate:

Use point-slope equation to determine the line:

Substitute and find:

Answer:

B. Q and S

Step-by-step Explanation:

Given the below equation;

We'll follow the below steps to solve the above equation;

Step 1: Subtract 36 from both sides of the equation;

Step 2: Divide both sides of the equation by 4;

Step 3: Take the square root of both sides;

We can see that the solutions are imaginary numbers so we'll need to plot the two points on the imaginary axis, so points Q and S give the solutions to the given equation.

Answer:

the answer is zero property

Answer:

Zero Property.

Step-by-step explanation:

Communitive is where you switch the numbers around but still have the same result. For example: 4 times 5 is the same as 5 times 4

Associative is this 4+ (3 +5 ) = 3 + (4+5)

price of one message = 1.35 ÷ 9

1.35 ÷ 9 = 0.15

0.15 • 118 = ( 3 ÷ 20 ) • 118

118 • 3 = 354

354 ÷ 20 = 177 ÷ 10 = $17.7 to send 118 messages

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Janet's savings in January is $800

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Represent Mary's savings by x and Janet's savings by y

7/4 = x/y

40/100 × x = 40x/100 = 2x/5

New savings for Mary =

x -2x/5 = 5x - 2x)/5 = 3x/5

50/100 × y = y/2

New savings for Janet =

y + y/2 = 3y/2

3y/2 + 3x/5 = 2040

15y + 6x = 20400

7y = 4x

y = 4/7x

Substitute (4/7)x for y

15( 4/7) x + 6x = 20400

(60/7 )x + 6x = 20400

60x + 42x = 142800

102x = 142800

x = 142800/102

x = $ 1400

y = 4/7 × 1400

y = $800

Therefore, the savings for Janet in January is $800.

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Answer:

Step-by-step explanation:

is there more information to the question??

The likelihood that a random cumulative variable will fall within a specific range of values rather than taking on a single value is specified by the Probability Density Function.

The probability density function (PDF), also known as the density of a continuous random variable, is a function whose value at any specific sample (or point) in the data point (the range of potential values for the random variable) can be understood as having given a relative likelihood that the value of something similar to the random variable would be closer to that sample.

There is no absolute probability that a random variable will take on any specific value because there are an unlimited number of alternative values to begin with. However, the PDF value at two samples can be used to estimate how much more likely it is for the random variable to have that particular value in any given draw.

The Cantor distribution, which although having no discrete component, does not assign positive probabilities to any specific locations, and discrete random variable probability distributions do not all have a density function.

A distribution has a density function if and only if the cumulative distribution function F(x) is fully continuous. In this case, F is typically always differentiable, and its derivative can be used to symbolize the probability density.

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Step-by-step explanation:

anewer is 30 cubic inches.

Measure of the angle m ∠ RQS = 58 ° for the given circle with arc RS subtending m ∠RPS=14 x + 46 ° at the center P and m ∠ RQS = 3 x + 43 ° at Q, on the circumference.

As given in the question,

Measure of the angle is given by :

m ∠ RPS=14 x + 46 °                                  

m ∠ RQS=3 x + 43 °                                      

m ∠ RPS = twice m ∠RQS (angle subtended at center of the circle)

14 x +46 =2(3 x + 43)

⇒ 14x + 46 = 6x +86

⇒ 14x-6x=86-46

⇒8x=40

⇒ x=5°

m ∠ RQS = (3 x + 43) °  

                 =[3(5) + 43 ]°

                 = 58°

Therefore, measure of the angle in the given circle m ∠RQS is equal to the  58 °

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The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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Answer:

What is the average rate of change from x = −4 to x = 1? x= -4 x + 5

Step-by-step explanation:

Three coordinates of triange are given to us and we need to find its perimeter . We know that perimeter is the sum of all sides . Lets find the distance between each sides using distance formula .

• Distance between A and B :-

\(\tt\to D_{(AB)} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\tt\to D_{(AB)} =\sqrt{(3-2)^2+(4-4)^2}\\\\\tt\to D_{(AB)} =\sqrt{( 1^2+0^2 )} \\\\\tt\to D_{(AB)} =\sqrt{1} \\\\\tt\to \boxed{\orange{\tt D_{(AB)} = 1\ units }}\)

_________________________________

• Distance between A and C :-

\(\tt\to D_{(AC)} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\tt\to D_{(AC)} =\sqrt{(3-2)^2+(4+4)^2}\\\\\tt\to D_{(AC)} =\sqrt{( 1^2+8^2 )} \\\\\tt\to D_{(AC)} =\sqrt{65} \\\\\tt\to \boxed{\orange{\tt D_{(AC)} = \sqrt{65}\ units }}\)

_________________________________

• Distance between C and B :-

\(\tt\to D_{(CB)} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\tt\to D_{(CB)} =\sqrt{(3-3)^2+(4+4)^2}\\\\\tt\to D_{(CB)} =\sqrt{( 8^2+0^2 )} \\\\\tt\to D_{(CB)} =\sqrt{65} \\\\\tt\to \boxed{\orange{\tt D_{(CB)} = \sqrt{65}\ units }}\)

Hence the total perimeter will be ,

\(\to\tt D_{(AB)}+D_{(BC)}+D_{(CA)}\\\\\tt\to \sqrt{65}+\sqrt{65}+1 \\\\\tt\large\to\underline{\boxed{\green{\tt 1 +2\sqrt{65} \:\:units }}}\)

Answer:

the opposite number is going to be negative because if  x is to the right of the number line then the opposite will be of the left of 0 making the opposite number negative.

Step-by-step explanation:

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(Option A) 1/2 - This is a rational number because it is a fraction with both numerator and denominator being integers.

A rational number is any number that can be written as a fraction of two integers (where the denominator is not equal to zero). Examples of rational numbers include:

A rational number can be represented in many different forms. It can be written as a fraction, with both the numerator and denominator being integers, or as a decimal, with the decimal part either terminating or repeating. A rational number can also be written as a mixed number, which is a combination of an integer and a fraction.

Which of the following is a rational number?

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Answer:

She will need a time of 1024 units to complete the 10th station.

Step-by-step explanation:

A. As the quotient between consecutive terms is the same, the data is a geometric sequence.

B. The recursive formula is:

C. She will need a time of 1024 units to complete the 10th station.

In a sequence, if the difference between consecutive terms is the same, the sequence is arithmetic.

If the quotient between consecutive terms is the same, the sequence is geometric.

Item a:

When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.