Amelia bought a t-shirt for $15 and 3 pairs of pants. She spent a total of $117. Which equation matches this problem?

The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°.

Parallel lines are straight lines that never meet each other no matter how long we extend them

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).

The fundamental characteristics listed below make it simple to recognise parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

No matter how far apart they are from one another, parallel lines can never intersect.

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The slope of each of the perpendicular lines are:

a. 1/8

b. -5/2.

The slope of two lines that are perpendicular to each other have values that are negative reciprocals. That is to say, their product will be equal to -1.

For example, if the slope of two perpendicular lines are -a and 1/a, therefore, their product will be (-a)(1/a) = -1.

a. Line a has a slope that is equal to -8. The negative reciprocal of -8 is 1/8.

Therefore, the slope of the perpendicular to line a would be 1/8.

b. Line a has a slope that is equal to 2/5. The negative reciprocal of 2/5 is -5/2.

Therefore, the slope of the perpendicular to line a would be -5/2.

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Answer -

So since there are 3 balls that are in the bag, it makes the denominator 3 and since they get one- one chance each, so the answer will be-

yellow ball - 1/3

Red ball - 1/3

Blue Ball - 1/3

First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.

By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

Answer:

x=h+2 divided by d x = h+2/d

Step-by-step explanation:

Answer:

13. Given below is a graph showing the number of Hindi movies released in the first six months of 2005. Which of the following questions can be answered from this graph?

14. The table below gives the dimensions of some rectangles.

Step-by-step explanation:

Answer + Explanation:

13. A. can be answered - add all the monthly figures using the bar height.

     B. cannot be answered - the graph shows May has the least movies but the graph doesn't tell you WHY it has the least movies, it does not give any reason.

     C. can be answered - look at the highest bar height (it's February)

     D. can be answered - calculate March, April and May figures together.

As such, circle A , C and D.

14.

A. Wrong - perimeter does not change in the table despite increase in area (all the perimeters in the table are the same).

B. Wrong - none have equal areas that have equal perimeters.

C. Wrong - none of the rectangles with equal perimeters have equal areas.

D. Correct - All the rectangles with the equal perimeter do not have equal areas (areas can be different).

So circle only D.

The population proportion of women athletes who graduated from the university is more than 67%.

A random sample  of 40 women athletes at the school showed that 23 eventually graduated.

n=40 , X=23 , p0 =67% = 0.67 , alpha = 1% = 0.01

H0: : p0 = 0.67  Vs  H1 : p0 < 0.67

Test statistics = (p-p0) / (square root ((p0(1-p0) / n))

p=X/n

H0::p0=0.67  Vs  H1:p0<0.67

Test statistics = z = (p-p0) / ( square root ((p0(1-p0)/n))

p=X/n=23/40

z = (0.575-0.67) / (square root (0.67(1-0.67)/40))=-1.278

P - value = P(z < -1.278) = 0.1007

Since the p-value is  0.1007 that is less than the level of significance the decision is to reject the null hypothesis. In conclusion, there is a sufficient evidence to support that the population proportion of women athletes who graduated is now more than 67%.

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For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.

Properties of circumcenter of triangle are:

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The original price 1. $ 88.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means)

Given;

The cost of the product was reduced by 20%, leaving $ 70.4 as the final price.

Cost of phone after 80% off= $70.40

So, now we will do a cross-multiplication;

If the percent is 80% =70.40

Let, the original price 100% = x

80x = 70.40. 100

80x = 7040

X = 7040: 80

X = 88

Therefore, the 100 percent value of phone will be $88

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The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10

In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y

If a given number let's say Z is Y less than X then the value of Z will be

Z=X-Y

More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value

So, 3 more than 7 means 7+3 = 10

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As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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Answer: The leg-leg theorem, the hypotenuse-leg theorem, the hypotenuse-angle theorem, and the leg-angle theorem.

Step-by-step explanation: Search it up.

The number of simulation trials that would be likely to produce results that are  closest to the actual probability is 25. The correct option is C).

The following steps can be used  in order to determine the number of simulations:

Step 1 - Remember the maximum number of trials gives the maximum chance to produce results that are  closest to the actual probability.

Step 2 - Now, check all the options given in the question and choose the largest one.

From the above steps, it can be concluded that the correct option is C) 25.

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Full question :

Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.

A. 10

B. 15

C. 25

D. 20

The solutions or roots of the equation 2x² + 3x - 2 = 0 will be 1 and -2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic equation is given below.

2x² + 3x - 2 = 0

Factorize the equation, then we have

2x² + 3x - 2 = 0

2x² + 4x - x - 2 = 0

2x(x + 2) - 1(x + 2) = 0

(x - 1)(x + 2)

x = 1, -2

The solutions or roots of the equation 2x² + 3x - 2 = 0 will be 1 and -2.

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The roots of the quadratic equation 2x² + 3x - 2 = 0 are - 2, 1/2.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, A quadratic equation 2x² + 3x - 2 = 0.

Now, Two numbers that multiply to - 4 and add to 3 is 4, - 1.

Therefore,

2x² + 3x - 2 = 0.

2x² + 4x - x - 2 = 0.

2x(x + 2) - 1(x + 2) = 0.

(x + 2)(2x - 1) = 0.

x + 2 = 0 Or 2x - 1 = 0.

x = - 2 Or x = 1/2.

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If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

We know that the AAS (angle-angle-side) theorem says that when two angles and any side of a triangle are congruent to two angles and any side of other triangle, then the triangles are said to be congruent.

If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Whereas the Angle-Angle-Side Postulate (AAS) tells us that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

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The value of  p is 20

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = (Sum of all the observations/Total number of observations)

Is the mean of the following data is 18.75 then find the value of p?

Xi  10   15   p   25  30

Fi   5    10   7   8     2

We may prepare th frequency table as given below:

mean=(∑Fi *Xi) / ∑Fi

         = (5*10 + 10*15 + 7*p + 8*25 + 2* 30)/ (5 + 10 +7 +8 +2)

        = (460+7p)/ 32

        =18.75

460+7p=(18.75×32)

⇒(460+7p)=600

⇒7p=140

⇒p=20

The value of  p is 20

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To see the steps of  sum a column in Excel on a Mac.

Now, According to the question:

1. Click the first empty cell below a column of numbers.

2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click  AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...

3. Press RETURN .

How do you sum cells on a Mac?

Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.

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The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

So, we can say that the difference between any two consecutive odd numbers is:

= 2k+3 – (2k+1)

=2k+3-2k-1

=2

So, for every two consecutive odd numbers there is a difference of 2.

Now, let us take ‘n’ to be an odd number.

So, an odd number just before n will be (n-2).

And also an odd number just after n will be (n+2).

Since, it is given that the sum of these three consecutive odd numbers is 57. So, we can write the following equation:

n-2+n+n+2=57

3n=57

So, n = 19

The odd number before n will be = n -2 = 19-2 = 17

And the odd number after n will be = n+2 = 19 + 2 = 21

Therefore, The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.

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Answer:

Step-by-step explanation:

sean

The relative minimum of h(x) occurs at x = 2. Integrals can be used to solve a wide range of problems in mathematics and physics, such as finding the area under a curve

An integral is a mathematical concept that involves the concept of integration, which is a way to find the area under a curve or the volume of a solid of revolution. Integrals can be classified into two types: indefinite integrals and definite integrals.

To find the relative minimum of the function h(x), we need to find the value of x that minimizes the value of h(x).

First, let's find the derivative of h(x). We can do this by applying the chain rule to the function inside the integral:

[tex]h'(x) = (-4 * (t - 2)^2 + 8)' = (-4 * (t - 2)^2 + 8)' = -8 * (t - 2)[/tex]

Next, we need to find the points where h'(x) = 0 or is undefined. Setting h'(x) = 0 and solving for t, we find that t = 2. Substituting this value back into the original expression for h(x), we get:

[tex]h(x) = -4 * (2 - 2)^2 + 8 = 8[/tex]

Since h'(x) is undefined at t = 2, we need to check whether the function is increasing or decreasing at that point. To do this, we can take the second derivative of h(x):

[tex]h''(x) = (-8 * (t - 2))' = -8[/tex]

Since the second derivative is negative at t = 2, this means that the function is decreasing at that point.

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The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.

Given :

Let x represent the length of the garden and y represent the width of the garden.

Perimeter = 2(x + y)

32 = 2(x + y)

x + y = 16

y = 16 - x

Area (A) = length * width

A = xy

A = x(16 - x)

A = 16x - x²

Maximum area is at dA/dx = 0:

dA/dx = 16 - 2x

0 = 16 - 2x

2x = 16

x = 8.0 m

y = 16 - x = 15 - 7.5 = 8.0 m

The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.

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By using the concept of depreciation, it can be calculated that

Value of x is 3.6%

What is depreciation?

Depreciation is the exponential decrease in the value of an asset or population or cost of an article at a certain rate over  a certain period of time.

Now opposite of depreciation is growth.

Growth is the exponential increase in the value of an asset or population or cost of an article at a certain rate over  a certain period of time.

Here concept of depreciation has been used

Number of deer in 2005 = 1480

Rate = x%

Time = 7 years

Number of deer after 7 years = 1141

[tex]1141 = 1480(1-\frac{x}{100})^7\\(1 - \frac{x}{100})^7 = \frac{1141}{1480}\\(1-\frac{x}{100}) = (\frac{1141}{1480})^{\frac{1}{7}}\\1 - \frac{x}{100} = 0.964\\\frac{x}{100} = 1 - 0.964\\\frac{x}{100} = 0.036\\x = 0.036 \times 100\\[/tex]

x = 3.6 %

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ok

Answer:

the answer would be this 5,8,3

The rate of change is 1 and the y-intercept is 1/2.

How do you find the rate of change on a line graph?

To get the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.

The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.

It is frequently referred to as rate of change when determining the slope of real-world scenarios. "Rate of change" and "slope" have the same meaning. Use the slope formula or create a slope triangle if you are asked to determine the rate of change.

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The width of the rectangle is 2 units.

Despite having four sides, a rectangle only has two distinct dimensions since the sides are paired. Though the width is often the shorter of these two dimensions, it is more commonly referred to as the horizontal side when the rectangle is shown lying on its side.

Given the width of rectangle is length of rectangle - 5 units.

Let us suppose that length of rectangle is y and width of the rectange is y-5.

The formula of area of rectangle is l×b where l and b are length and breadth respectively.

So substituting in the equation we get

[tex]y* (y-5) = 14.\\y^2- 5y = 14\\y^2 - 5y - 14 = 0[/tex]

Solving the above quadratic equation we get y as 7 and -2.

As length cannot be a negative quantity we take length as 7 and it gives us the result that the width is 2 units.

The width of the rectangle is 2 units.

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Using percentage on the population size, the number of infected is 720

Probability sampling is a technique in which the researcher chooses samples from a larger population using a method based on probability theory. For a participant to be considered as a probability sample, he/she must be selected using a random selection.

In this question, we can find the percentage of infected in a sample size of 50.

Percentage of infected = (8 / 50) * 100

Percentage of infected = 0.16 * 100

Percentage of infected = 16%

Using this value, we can further calculate the total number of infected in the population.

16 % of 4500 = ?

16 / 100 = x / 4500

0.16 = x / 4500

x = 4500 * 0.16

x = 720

The number of infected are 720

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The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. When this expression is evaluated for x = 3, the result is 24, so the remainder is 0.

The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. To find the remainder when this expression is evaluated, we must first substitute in a value for x. For this example, let x = 3. When we substitute 3 for x, the expression becomes 3³ + 3x² - 4(3) - 6. We can simplify this expression by performing the operations in order of operations. First, we can calculate 3³, which is equal to 27. Next, we can calculate 3x², which is equal to 27. Subtracting 4(3) from 27 gives us 15. Finally, subtracting 6 from 15 gives us 9.

The remainder of evaluating

x³ 3x² 4x 6 for x = 3 is 9.

x³ 3x² 4x 6 = 3³ + 3x² - 4(3) - 6 = 27 + 27 - 12 - 6 = 24

Remainder = 24 - 3 = 0

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With the help of Trigonometry the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.

What is Trigonometry?

Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. From the use of geometry in astronomical research, the field first appeared in the Hellenistic world in the third century BC.

Dimensions are the measure of the length, width and height of a given object. Yes, a rectangular box of length 5 feet and height 2 feet can be stored underneath the ramp.

The measure of the sides of a given object is referred to as its dimensions. This can be with respect to its length, width, and height.

It has been given that the height of the ramp is 39 inches. But,

12 inches = 1 feet

So that,

39 inches = x feet

make x the subject of the formula to have;

x = 3.25 feet

Thus the dimensions of the ramp are ;

length = 12 feet

height = 3.25 feet

Therefore, the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.

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You can log into your My.SSS account to see the status of your SSS salary loan.

Your salary loan has been granted if you see the message "SSS Loan Application Has Been Granted." Logging into your My.SSS account will allow you to view the status of your SSS salary loan. Select "Inquiry" first, followed by "Loan Info." Your SSS loan status and other loan information can be found here. If the loan funds have already been credited to your disbursement account, you will also get another SMS message.

The loan must be repaid by the borrower in 24 monthly installments. The second month after the loan's origination date is when the monthly amortization starts.  

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