1. Does the graph below represent a function? Explain how you know.

Q1

A. Yes; the graph is linear.

B. No; the graph does not pass the vertical line test.

C. Yes; the graph passes the vertical line test.

D. No; the graph intersects the x and y axis.


p.s i might fail and retake 7th grade

Answer: 4.2 cups

Step-by-step explanation: 63 divided by 15=4.2

The four conditions of congruency of triangles would be SSS, SAS, ASA and AAS.

What is the congruency of triangles?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and angles of the two triangles.

Conditions of congruency of triangles:

1.) SSS (Side-Side-Side)

If all three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by the SSS rule.

2.) SAS (Side-Angle-Side)

If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by the SAS rule.

3.) ASA (Angle-Side- Angle)

If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

4.) AAS (Angle-Angle-Side)

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

Hence, the four conditions of congruency of triangles would be SSS, SAS, ASA and AAS.

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Answer:

45

Step-by-step explanation: Find what 80% of 25 is, you can do this by dividing 25 by 100. Then multiply the output by 80. Add that output to 25 and you should get an answer of 45.

Therefore, based on the information provided, the perpendicular distance from the x-axis to the center of Shape B, or the distance from the origin along the y-axis to the center of Shape B, is 1.5 units.

To determine the perpendicular distance from the x-axis to the center of Shape B or the distance from the origin along the y-axis to the center of Shape B, we need to consider the properties of Shape B.

In this context, when we say "center," we are referring to the midpoint or the central point of Shape B along the y-axis.

The given answer of 1.5 units suggests that the center of Shape B lies 1.5 units above the x-axis or below the origin along the y-axis.

The distance is measured perpendicular to the x-axis or parallel to the y-axis, as we are interested in the vertical distance from the x-axis to the center of Shape B.

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Answer:

1 / 14608440

Step-by-step explanation:

Given the following :

Winner has to select the five correct numbers between 1 and 35

Then, a single correct number between 1 and 45

Step1:

Number of ways to select 5 corre t numbers between 1 and 35; selecting 5 things from a total of 35 = 35C5

nCr = n! ÷ (n-r)!r!

35C5 = 35! ÷ (35-5)!5!

35C5 = 35! ÷ (30)!5!

= (35 * 34 * 33 * 32 * 31) / (5 * 4 * 3 * 2 * 1) = 324632 ways

Then find number of ways of selecting 1 correct number between 1 and 45:

45C1

45C1 = 45! ÷ (45-1)!1!

45C1 = 45! ÷ (44)!1!

45C1 = 45 ÷ 1 = 45

35C5 * 45C1 = 324632 * 45 = 14608440

Therefore, probability of winning the jackpot :

Required outcome / Total possible outcomes

= 1 / 14608440

Answer:

x=-12

Step-by-step explanation:

5x/5=1x = -60/5=-12

x=-12

Answer:

-12

Step-by-step explanation:

5x=-60

Divide both sides by 5 to isolate

X=-12

Answer:

Only external forces affect the motion of a system, according to Newton's first law. ... force applied to a car produces a much smaller acceleration than when ... Newton's second law states that a net force on an object is responsible for its ... A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.7 N on the Moon.

Step-by-step explanation:

Only external forces affect the motion of a system, according to Newton's first law. ... force applied to a car produces a much smaller acceleration than when ... Newton's second law states that a net force on an object is responsible for its ... A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.7 N on the Moon.

Answer:

C - 145

Step-by-step explanation:

This figure can be split into a trapezoid and a rectangle.

The rectangle has dimensions 7 x 11, and the trapezoid has bases of 11 and 6, and a height of 8 (15-7).

The area of the figure is the area of the rectangle + the area of the trapezoid, which is 7*11 + (11+6)/2 * 8 --> 77 + 17*4 --> 77+68 --> 145. The answer is C

The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).

= (41/10) × (- 4) × (5/12).

= (41×-4×5)/(10×12).

= (-820/120).

= - 82/12.

= - 41/6.

= \(-6\frac{5}{6}\).

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Answer:

  D (0,4)​

Step-by-step explanation:

You want to know an ordered pair that could be added to the given relation such that it remains a function.

A function cannot have any two ordered pairs that have the same x-value. The given relation has x-values {1, 2, 3, 4}, so none of these can be repeated if the relation is to remain a function.

The only choice with a different x-value is ...

  D (0, 4)

__

Additional comment

The set of x-values is the "domain" of the function. It cannot have any repeats. The set of y-values is the "range" of the function. Those values can be repeated.

A function that is "one-to-one" cannot have any repeated range values, either.

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Lindsay's age (lll) is 156295 and Mark's age (mmm) is 156850.

To solve this problem, we can set up equations using the given information.

Let's assume Lindsay's age is L and Mark's age is M.

We know that Lindsay is 555 years younger than Mark, so we can write the equation: L = M - 555.

Seven years ago, Lindsay's age would have been L - 7, and Mark's age would have been M - 7.

We are also given that the sum of their ages seven years ago was 313131, so we can write the equation: (L - 7) + (M - 7) = 313131.

Now, we can substitute L = M - 555 into the second equation: (M - 555 - 7) + (M - 7) = 313131.

Simplifying the equation, we get: 2M - 569 = 313131.

Adding 569 to both sides, we have: 2M = 313700.

Dividing both sides by 2, we find: M = 156850.

Now, substituting this value back into L = M - 555, we get: L = 156850 - 555 = 156295.

Therefore, Lindsay's age (lll) is 156295 and Mark's age (mmm) is 156850.

In conclusion, Lindsay is 156295 years old and Mark is 156850 years old.

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The limit of the given expression as x approaches 1 is 0.

To evaluate the limit of the given expression as x approaches 1, we can use L'Hopital's rule, which states that if the limit of a quotient of functions is of the form 0/0 or ±∞/±∞, then the limit can be found by taking the derivative of the numerator and denominator and evaluating the new quotient at the same point.

Using L'Hopital's rule on the given expression, we get:

lim x→1 [5x/(x-1) - 5/x] = lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)]

Plugging in x = 1 directly to this expression, we get:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = (5 - 10 + 5)/(1 - 1) = 0/0

Since the limit is still in an indeterminate form, we can apply L'Hopital's rule once again:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = lim x→1 [(10x - 10)/(2x - 1)] = 0

Therefore, the limit of the given expression as x approaches 1 is 0.

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The graph the corresponds to the function f(x)=√(x - 1) is plotted and attached

A radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that calculates the square root of the input value.

key features of a radical graph is the shape: The shape of a square root graph is a concave upward curve. The steepness or flatness of the curve depends on the value of the constant a. A larger value of a results in a steeper curve, while a smaller value of a results in a flatter curve.

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To restore the original value of a computer after a 10% reduction, the new price should be increased by approximately 11.11%.



When a computer's price is reduced by 10%, the new price becomes 90% of the original value. To calculate the percentage increase needed to restore the original value, we can use the formula:Percentage Increase = (Original Value - New Value) / New Value * 100

In this case, the original value is 100% and the new value is 90%. Plugging these values into the formula, we get:Percentage Increase = (100 - 90) / 90 * 100 ≈ 11.11%

Therefore, the new value should be increased by approximately 11.11% to restore it to the original value.

The explanation is straightforward. If the price of a computer is reduced by 10%, it means the new price is 90% of the original value. To restore it to the original value, we need to find the percentage increase required. By using the formula mentioned above, we subtract the new value from the original value, divide it by the new value, and multiply by 100 to get the percentage increase. In this case, the percentage increase turns out to be approximately 11.11%. This means the new price needs to be increased by around 11.11% to bring it back to the original value.

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Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

The pair of (A) are orthogonal. (B) are parallel and (C) are orthogonal. In three-dimensional space, a plane is defined by a point and a normal vector. The normal vector is perpendicular to the plane, so we can use it to determine if two planes are parallel or orthogonal.

a) To determine if the planes are orthogonal or parallel, we need to compare their normal vectors. The normal vector of the first plane is <1, 1, -3>, and the normal vector of the second plane is <4, -6, 4>. To check if they are orthogonal, we need to take the dot product of the two vectors. 1(4) + 1(-6) + (-3)(4) = 0, which means they are orthogonal.
b) The normal vectors of the two planes are <-21, 14, 7> and <15, -10, -5>. To check if they are parallel, we need to see if one vector is a scalar multiple of the other. We can divide the first vector by -7 and get <3, -2, -1>, which is a scalar multiple of the second vector (we can multiply it by -5 to get the second vector). Therefore, they are parallel.
c) The normal vectors of the two planes are <1, -5, 4> and <-2, 6, 8>. To check if they are orthogonal, we need to take the dot product of the two vectors. 1(-2) + (-5)(6) + 4(8) = 0, which means they are orthogonal.
In three-dimensional space, a plane is defined by a point and a normal vector. The normal vector is perpendicular to the plane, so we can use it to determine if two planes are parallel or orthogonal. If the dot product of the normal vectors is zero, the planes are orthogonal. If one normal vector is a scalar multiple of the other, the planes are parallel. If the dot product is not zero and one normal vector is not a scalar multiple of the other, the planes are neither parallel nor orthogonal - they intersect in a line. These concepts are important in many areas of mathematics, including linear algebra and calculus. In linear algebra, we use these ideas to study systems of linear equations and to find the solutions to those systems. In calculus, we use them to study the behavior of surfaces and to calculate surface integrals.

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Answer:

he can buy 14 popcorn which will equal to have left 3 dollars

if he wants to spend all his money it will be

10 drinks and 12 popcorn

Step-by-step explanation:

Answer:

option

Step-by-step explanation:

THE THIRD GRAPH(X)

Answer:

Phillipa rode the most in May and rode the least in March.

Distance travelled by Phillipa on her cycle in May = 8 × Distance travelled by Phillipa on her cycle in March  

Step-by-step explanation:

Given:

In April, Phillipa rode 13 . 5 + 8 . 7 + 11 . 1 miles on her bicycle. In March, she rode ( 13 . 5 + 8 . 7 + 11 . 1 ) ÷ 2 miles, and in May, she rode 4 × ( 13 . 5 + 8 . 7 + 11 . 1 ) miles.

To find: the month when she rode the most and the month when she rode the least

Solution:

Distance travelled by Phillipa on her cycle in April = 13 . 5 + 8 . 7 + 11 . 1 = 65 + 56 + 11 = 132 miles

Distance travelled by Phillipa on her cycle in March = ( 13 . 5 + 8 . 7 + 11 . 1 ) ÷ 2 = \(\frac{132}{2}=66\) miles

Distance travelled by Phillipa on her cycle in May = 4 × ( 13 . 5 + 8 . 7 + 11 . 1 ) = 4 × 132 = 528 miles

So, she rode the most in May and rode the least in March

Distance travelled by Phillipa on her cycle in May = 8 × Distance travelled by Phillipa on her cycle in March  

Answer:

32

Step-by-step explanation:

u first do 120 divided by 2

which is 60 then subtract that by 28 which is 32

to check it add 28 plus 32 which is 60 then double it which is 120

hope this helps

sorry if this is late

Answer:

(3,1) (5,-3) (-4,4)

Step-by-step explanation:

The x values don't overlap or repeat so these can be plotted and still make it a function

Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.

How to solve?

To solve this problem, we can use the formula for the present value of a bond:

PV = (C/r) ×[1 - 1/(1+r)²n] + F/(1+r)²n

where PV is the present value of the bond, C is the semi-annual coupon payment, r is the semi-annual yield rate, n is the number of semi-annual periods, and F is the face value or redemption value of the bond.

We know that Mr. McMahon paid $880 for a $1000 bond, so the present value of the bond is PV = $880. The redemption value of the bond is F = $1000, and the yield rate that he desired was r = 8% per year, compounded semi-annually. Therefore, the semi-annual yield rate is:

i = 0.08/2 = 0.04

We can use the formula to solve for the number of semi-annual periods:

PV = (C/i) ×[1 - 1/(1+i)²n] + F/(1+i)²n

$880 = ($45/i) ×[1 - 1/(1+0.04)²(220)] + $1000/(1+0.04)²(220)

Solving for i gives:

i = 0.0517 or approximately 5.17%

This is the semi-annual yield rate that Mr. McMahon actually received on the bond. To find the semi-annual probability of default that he expected, we can use the formula for the expected yield rate of a bond:

yield = (1 - probability of default) ×(yield rate on the bond) + (probability of default) ×(recovery rate)

where the recovery rate is the percentage of the face value that would be recovered in the event of default.

Assuming that the recovery rate is zero (meaning that in the event of default, Mr. McMahon would receive nothing), we can solve for the probability of default:

0.08 = (1 - p) ×0.0517 + p ×0

Solving for p gives:

p = 0.357 or approximately 35.7%

Therefore, Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.

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To compute the line integral with respect to arc length of the function f(x, y, z) = xy^2 along the given parametrized curve, we can split it into two line segments.

Calculate the integral for each segment separately. Segment 1: Line from (1, 1, 1) to (2, 2, 2). Let's parameterize this line segment as r(t) = (1 + t, 1 + t, 1 + t), where t ranges from 0 to 1. The differential arc length ds along this segment is given by ds = ||r'(t)|| dt, where ||r'(t)|| represents the magnitude of the derivative of r(t). We have r'(t) = (1, 1, 1), so ||r'(t)|| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3). The line integral along this segment is given by: ∫[Segment 1] f(x, y, z) ds = ∫[0, 1] f(r(t)) ||r'(t)|| dt = ∫[0, 1] (t(1 + t)^2) sqrt(3) dt.

Evaluating this integral yields the result for the first line segment. Segment 2: Line from (2, 2, 2) to (−3, 6, 3). Similarly, parameterize this line segment as r(t) = (2 - 5t, 2 + 4t, 2 + t), where t ranges from 0 to 1. Calculate ||r'(t)|| for this segment, and set up and evaluate the integral as done for Segment 1. Add the results from both segments to obtain the final value of the line integral.

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Answer:

2:5  

12:30

Step-by-step explanation:

The group of things from which data are taken for a statistical research is referred to as a population in statistics. A data pool for study might consist of numerous things, many individuals, etc.

large-scale numerical data collection and analysis, especially with the aim of extrapolating proportions in the total from those in a representative sample.

The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are the focus of the science of statistics. It could be a collection of things, a gathering of people, etc. It serves as the study's data set.

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50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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The formula to calculate surface area is 2(Length × Width) + 2(Length × Height) + 2(Width × Height) and the length, width, and height of the sandbox is required to calculate rectangular area.

To determine how much sand your cousin will need to fill the rectangular prism-shaped sandbox, we first need to calculate its volume. To do this, we need the dimensions of the sandbox (length, width, and height). The formula for the volume of a rectangular prism is:

Volume = Length × Width × Height

Once we have the volume, we can determine the amount of sand needed to fill the sandbox in cubic units.

To find out how much paint is needed to paint all six surfaces of the sandbox, we need to calculate its surface area. The formula for the surface area of a rectangular prism is:

Surface Area = 2(Length × Width) + 2(Length × Height) + 2(Width × Height)

Once we have the surface area, we can determine the amount of paint required, usually measured in square units. Note that the amount of paint needed also depends on the coverage rate of the paint, which is typically listed on the paint container.

Please provide the dimensions of the sandbox (length, width, and height) so I can provide specific calculations for the sand and paint required.

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Answer:

Plz check in step by step

Step-by-step explanation: Hong Kong Island is the second-largest island of the territory, the largest being Lantau Island. Its area is 78.59 km2 (30.34 sq mi), including 6.98 km2 (2.69 sq mi) of land reclaimed since 1887 and some smaller scale ones since 1851.

Step-by-step explanation:

\( \sqrt{5} = 2.23\)

\( \frac{\pi}{3} = 1.04\)

\( \sqrt{3} = 1.73\)