Drag The Tiles To The Correct Boxes To Complete The Pairs. Not All Tiles Will Be Used.The Cafeteria Manager (2024)

The line are Parallel x+7y=-3 and y=7x+25 are perpendicular to each other

What is Parallel lines?

Parallel lines are straight lines that are coplanar and do not intersect at any point. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

Given,

x + 7y = -3

given equation in form of y = mx+c

where m is slope line

7 y = -x -3

y = -x/y - 3/7 ................(1)

slope equation (1)

m1 = -1/7

y = 7x +25 .................(2)

slope equation (2)

m2 = 7

two equation y = m1x + c1 and y = m2x+c2

parallel if m1 = m2

perpendicular if m1 *m2 = 1

here,

m1*m2 = -1/7*7

= -1

So given equation are perpendicular to each other

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The other endpoint of the line segment with the given endpoint and mid point is: (9,15)

We know how to find the midpoint coordinates by the following:

(a + b) / 2 = c, where a and b are the endpoints and c is the midpoint.

Well, in this case, instead of a and b and finding c, we have a and c, and need to find b. First the x-coordinate:

(3 + b) / 2 = 6

multiply both sides by 2:

3 + b = 12

Subtract both sides by 3:

b = 9

Now the y- coordinate. Follow the same rules as before, start by multiplying by 2:

(3 + b) / 2 = 9

3 + b = 18

Subtract 3:

b = 15

So our missing endpoint is (9, 15).

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Answer: x = -4 or 8

Step-by-step explanation:

To solve, we will isolate the x-variable. Since this is a parabola (as shown by the square) we will either have 1 or 2 answers.

Given:

6(x - 2)² + 7 = 223

Subtract 7 from both sides of the equation:

6(x - 2)² = 216

Divide both sides of the equation by 6:

(x - 2)² = 36

Square root both sides of the equation:

* Since we square rooted, we will have the positive and negative result

x - 2 = 6 x - 2 = -6

Add 2 to both sides of the equation, for both equations:

x = 8 x = -4

x = -4 or 8

Per pound of Red potatoes cost more by $0.485.

What is cost per pound ?

The cost function's generic formula is C(x)=F+V. (x) F is the sum of all fixed costs, V is the sum of all variable costs, x is the number of units, and C(x) is the sum of all production costs.

We have given :

Cost of 50 pounds of red potatoes = $27.50.

The price of 30 pounds of sweet potatoes is $22.50,

So, the price per pound of red potatoes is = 50/27.50 = $1.818

And, the price per pound of sweet potatoes is = 30/22.50 = $1.33

Therefore, the red potatoes are more expensive per pound by the amount of $1.818 - $1.33 = $0.485.

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The length of the mid segment of this trapezoid is 8 units.

What is trapezoid?

The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. The average of the bases multiplied by the height will yield the area of a trapezoid.

An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively.

According to, Trapezium Midpoint Theorem,

Mid segment of a trapezoid is equal to half of sum of its two parallel sides.

So, the length of the mid-segment : 1/2 (AB+CD)

Now, applying distance formula:

AB = [tex]\sqrt{(7-2)^2+(4-4)^2}[/tex] = 5 unit

CD = [tex]\sqrt{(9+2)^2 + (-1+1)^2}[/tex] = 11 unit

Hence, the length of the mid-segment : 1/2 (5 + 11)

= 1/2 × 16

= 8 unit

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The complete question is as follows:

Increase [tex]SS_{\text{within}}[/tex] and decrease the size of the F-ratio

[tex]SS_{\text{within}}[/tex] will increase,

The F test statistic is found by dividing the between group variance by the within group variance and F-ratio will decrease.

Sample Data:

[tex]M_1 = 10, \, M_2 = 20[/tex]

[tex]SS_1 = 50, \, SS_2 = 70[/tex]

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To create an equation for V as a function of x, you can use the tiles provided below:

Tile 1: V =

Tile 2: x

Tile 3: +

Tile 4: a

Tile 5: *

Tile 6: b

By placing the tiles in the following order: Tile 1, Tile 2, Tile 5, Tile 6, Tile 3, Tile 4, you can create the equation "V = b*x + a", where "b" and "a" are constants. This equation represents a linear relationship between V and x, where the slope of the line is "b" and the y-intercept is "a".

You can modify the equation by changing the values of the constants "a" and "b", or by adding additional terms to the equation using the available tiles. For example, you could add a Tile 7: "cx²" to the equation to create a quadratic relationship between V and x, resulting in the equation "V = bx + a + c*x²".

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Answer:

4/9

Step-by-step explanation:

y=4/9x+6

Slope is change in y in terms of x

Hence, 4/9 is slope since it affects x: for an increase in x by 1, y increases by 4/9.

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Answer:

If you're asking for the product of 2,031 by 75, then the product would be 152,325. 2,031 by 75 is 152,325.

Answer:

152,325

Step-by-step explanation:

in pictures :)

If the height of the cheese is 2.5 in and the base of the cheese is 4.75 in , then Area of the cheese shaped like the triangle is 38 cm² .

The piece of the cheese is shaped like triangle

The height of the triangle is = 2.5 inches = 2.5×2.54 cm = 6.35 cm

The base of the triangle = 4.75 inches = 4.75×2.54 cm = 12.065 cm

So , the Area is = (1/2)× base × height

Substituting the value of base and height of the cheese from above ,

= (1/2) × 12.065 × 6.35

= 38.3063 cm²

≈ 38 cm²

Therefore, the area of the cheese is 38 cm²

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Point c is the midpoint of ab and point b is between points a and d. If ad=17 and bd=9 , then cd = 13.

In the given question,

Point c is the midpoint of ab and point b is between points a and d.

If ad=17 and bd=9

We have to find the value of cd.

ac = cb

ad = 17

bd = 9

ad = ab+bd

17 = ab+9

Subtract 9 on both side, we get

ab = 8

cb = ab/2

cb = 8/2

cb = 4

Hence, cd = cb + bd

cd = 4+9

cd = 13

Hence, the value of cd is 13.

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The relations in this problem, regarding functions, are classified as follows:

Set {(-2,3) ...}: function.Discrete graph with the dots: Not a function.Continuous graph: function.Venn sets: Not a function.

When does a relation represents a function?

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

Hence the relations in this problem are classified as follows:

Set {(-2,3) ...}: function, as none of the inputs -2, -5, -7 and -9 are mapped to multiple outcomes.Discrete graph with the dots: Not a function, as the input -1 is mapped to the outputs 0 and 8.Continuous graph: function, as the graph contains no vertically aligned points, meaning that each input is mapped to a single output.Venn sets: Not a function, as the input dog is mapped to both outputs short hair and long hair.

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The width of the rectangle is 9 cm if the perimeter and length is 24 cm and 3 cm.

We have,

Length, l of the rectangle =3 cm

Perimeter of the rectangle, P = 24 cm

We have,

Perimeter of a Rectangle Formula = 2 (Length + Width) units

Let us assume w to be the width of rectangle.

Now,

P = 2(l + w) cm

Substituting the values, we get, P = 2(3 + w) cm

24 = (6 + 2w) cm

On solving, we get,

18 = 2w

w = 9 cm

Therefore, the width of rectangle is equivalent to 9 cm.

Hence we get the required width of the rectangle.

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Your question is incomplete. Please find the missing content below.

What is the Length of the Rectangle whose Perimeter is 24 cm and Width is 3 cm?

Pending money in a year = $1164.8

weekly pocket money of Michael = $28.

a percentage is a number or ratio that can be expressed as a fraction of 100.

If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Hence, the percentage means, a part per hundred. The word per cent means per 100.

It is represented by the symbol “%”.

Spend money = 20%

= 28*{20/100}

= 5.6

Therefor remaining money for a week = 28 - 5.6

=22.4 per week

there are 52 week in a year

pending in a year = 52 * 22.4

= 1164.8

Pending money in a year = $1164.8

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The p-value in the given scenario represents the proportion of California community college students who received federal grants.

Therefore, the answer is option b) The proportion of California community college students who received federal grants.

The p- value in a hypothesis is a statistical measurement that helps to validate the hypothesis against the data observed. It represents the probability of the null hypothesis being true.

Here the hypothesis is made for the population of California students and it is that the California community college students receive federal grants and the p-value here is 0.23 which is the ratio found for the whole country.

-- The question is incomplete, the correct question is as follows --

"According to the American Association of Community Colleges, 23% of community college students receive federal grants. The California Community College Chancellor’s Office anticipates that the percentage is smaller for California community college students. They collect a sample of 1,000 community college students in California and find that 210 received federal grants.

What does p represent in the hypotheses?

a) The proportion of community college students who received federal grants

b) The proportion of California community college students who received federal grants"

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Graph the following features: Slope = -2 Y-intercept = 2 is y = 2x - 5.

What is Slope?

A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two locations, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is typically used to signify slope.

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b).

y = mx + b

y = 2x - 5

you can go to desmos calculator online and simply put in the equation. but what you're going to do is find -5 on the y axis. then you will go up 2 and then 1 to the right.

it should look like this:

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Answer: Bar graph

Step-by-step explanation: You can show each phone on the bottom row and the number of sold phones on the side to compare them to one another

There are 25,053,600 different tests of 5 questions each that can be made from Ms. Wood's collection of 25 questions.

To find the number of different tests of 5 questions each that can be made from a set of 25 questions, you can use the combination formula. The combination formula is:

n! / (r! * (n-r)!)

Where n is the total number of items and r is the number of items being chosen at a time.

In this case, n is 25 (the total number of questions) and r is 5 (the number of questions per test). Plugging these values into the formula gives:

25! / (5! * (25-5)!) = 25! / (5! * 20!) = 25 * 24 * 23 * 22 * 21 / (5 * 4 * 3 * 2 * 1) = 25,!053,!600

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The probability that the machine will be working is (b) 0.795.

The probability of success in x trials under a binomial distribution is given by:-

P( X = x) = [tex]^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

,where n is the overall number of trials and p is the likelihood that each trial will be successful.

Given,

Probability that the component will fail, p = 0.2

n = 12

Let the no. of component that stop working = x

Due to the fact that if more than three components fail, the machine would stop functioning.

The likelihood that the device will malfunction then is:

P( X > 3) = 1 - P(X ≤ 3)

= 1 - [ P(0) + P(1) + P(2) + P(3) ]

[tex]= 1 - [ ^{12}C_{0}(0.2)^{0}(0.8)^{12}+^{12}C_{1}(0.2)^{1}(0.8)^{11} +^{12}C_{2}(0.2)^{2}(0.8)^{10} +^{12}C_{3}(0.2)^{3}(0.8)^{9} ][/tex]

[tex]= 1-[ (1)(0.8)^{12}+(12)(0.2)(0.8)^{11} + \frac{12!}{2!10!}(0.2)^{2} (0.8)^{10}+ \frac{12!}{3!9!}(0.2)^{3} (0.8)^{9}][/tex]

[tex]= 1 - (0.068719476736+0.206158430208+0.283467841536+0.23622320128)[/tex]

= 1 - 0.79456894976

= 0.20543105024

≈ 0.205

P(machine is working) = 1 - 0.205

= 0.795

The probability that the machine will stop working is 0.205.

Hence, The probability that the machine will be working is 0.795.

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Option D is the correct answer. all angles in a triangle are acute

A triangle in which all three internal angles of the triangle are acute is also called an acute-angled triangle.

Properties are Acute angles:

The interior angles of a triangle will always be less than 90° different side measures.In this triangle, a line drawn from the base of the triangle to the opposite vertex will be always perpendicular.

We have the formula to calculate the area of the acute angle triangle = (½) × b × h square units.

Where,

“b” is the base of the triangle.

“h” is to be the height of a triangle.

If the sides are given, then we have to apply Heron’s formula:

The area of the acute triangle:

A=√S(S-a)(S-b)(S-c)

square units

Where S defines the semi-perimeter of a triangle

The S can be solved by using the formula:

S = (a + b + c)/2

The perimeter of an acute triangle is equal to the sum of the length of the sides of a triangle,

The perimeter is given as:

Perimeter = a + b + c

It is measured in units.

a, b, and c are the sides of the triangle.

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The city block draw should be composed of a square of side lengths of 20 units.

How to obtain the scale?

An scale represents a proportion between the drawn length and the atual length of a building/block/...

The parameters for this problem are given as follows:

Actual length: 100 meters.Scale: 1 unit = 5 meters.

Hence the length of the sides of the square, in meters, is calculated applying the proportion as follows:

100/5 = 20 units.

Thus the drawing should be composed by a square in which all four side lengths are of 20 units, due to the scale calculated above.

Missing Information

The grid is not given, hence the format of the drawing is stated in this problem, along with the calculation of the scale.

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Assume that jessie and lester have formed a contract whereby jessie agrees to deliver 10,000 dozen grade a large eggs to be shipped in paper cartons. a shortage of paper makes paper cartons much more expensive, so jessie uses styrofoam cartons and ships the eggs. lester is entitled to cancel the contract based on a material breach of the contract: False.

What is paper cartons?

A carton is a box or container that is typically composed of paperboard, corrugated fiberboard, or liquid packaging board. For packing, a variety of carton types are employed. A box may also be used to describe a carton.

A carton is a food or beverage container that is made of cardboard or plastic. A carton is a large, durable cardboard box used for storage and transportation of products.

The answer is false since Lester lacks the authority to terminate the agreement due to a substantial breach.

Thus, the given statement is false.

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The correct expression are

1. 6/9 = 3/9 + 3/9 (fraction as the sum of two equal fractional Parts)

2. 15/4 = 3/4 + 3/4 + 3/4 + 3/4 + 3/4 (fraction as the sum of more then three equal fractional Parts)

Given that,

Each fraction should be written as the addition of two or three equal fractional parts. As a multiplication equation, rewrite each.

We know that,

The fraction are

a. 6/9

b. 15/4

Each fraction is expressed as the sum of two or three equally sized fractional parts;

1) 6/9

⇒ 6/9 = 3/9 + 3/9

2) 15/4

⇒ 15/4 = 3/4 + 3/4 + 3/4 + 3/4 + 3/4

Therefore, The correct expression are

1. 6/9 = 3/9 + 3/9 (fraction as the sum of two equal fractional Parts)

2. 15/4 = 3/4 + 3/4 + 3/4 + 3/4 + 3/4 (fraction as the sum of more then three equal fractional Parts)

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Answer:

Step-by-step explanation:

y=180'-(59.3'+78.5')

y=180'-(137.8')

y=42.2'

degree='

Answer: y = 42.2°

Step-by-step explanation:

We know that a straight line is equal to 180 degrees. We will set up an equation with the given values and solve.

59.3° + y + 78.5° = 180°

137.8° + y = 180°

(137.8° + y) -137.8° = (180°) - 137.8°

y = 42.2°

The correct option regarding the scale factor and the statement in this problem is given as follows:

D. The statement is false. Because there are 3 feet in one​ yard, there are 9 square feet in one square yard.

How to obtain the correct scale factor?

The scale factor between the length dimensions of the yard are given as follows:

3 feet = 1 yard.

(as these length dimensions are given in yards).

Then for the square units, the correct scale factor is found applying the proportion as follows:

(3 feet)² = (1 yard)².

9 feet squared = 1 square yard.

Hence the statement given in this problem, that because there are 3 feet in one​ yard, there are also 3 square feet in one square yard, is false, and the correct option is given by option D.

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Answer:

The rational zeros of the polynomial function f(x) = x^3 + 2x^2 - 13x + 10 are x = -1, x = 1, and x = 10/3.

Explanation:

To find the rational zeros of the polynomial function f(x) = x^3 + 2x^2 - 13x + 10, we can use the rational zero theorem, which states that if p/q is a rational zero of a polynomial function f(x) with integer coefficients, then p is a factor of the constant term of f(x) (in this case, 10) and q is a factor of the leading coefficient (in this case, 1).

We can then use this information to create a list of potential rational zeros by listing out the factors of 10 (which are -1, 1, -2, 2, -5, 5, and -10) and dividing them by the factors of 1 (which are -1 and 1). This gives us the following list of potential rational zeros: -1, 1, -2, 2, -5, 5, and -10.

To determine which of these values are actually zeros of the polynomial function, we can substitute each value into the function and see if it makes the function equal to 0. We find that x = -1, x = 1, and x = 10/3 are zeros of the function, but the other values are not.

We can then use these zeros to factor the polynomial function:

f(x) = (x + 1)(x - 1)(x - 10/3)

This is the factored form of the polynomial function.

If the yearly cost for the dental claims are normally distributed , then the yearly cost at which 35% of the employee fall at or below is $91.35 .

In the question ,

it is given that ,

the yearly cost for the dental claims are normally distributed ;

and the mean (μ) is 105 , standard deviation(σ) is 35 .

we know that the z value that corresponds to 35th percentile from standard normal table is : z = -0.385 ;

let the yearly cost be "x" ;

the yearly cost can be calculated using the formula ;

x = z×(σ) + μ

x = (-0.385)×35 + 105

Simplifying further ,

we get ;

x = 91.525

x ≈ 91.53

Therefore , the correct option is (d) 91.53 .

The given question is incomplete , the complete question is

The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of $105 and a standard deviation of $35. what is the yearly cost at which 35% of the employees fall at or below is ?

(a) $118.48

(b) $127.29

(c) $82.71

(d) $91.53

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If we have an angle and an opposite side, we can divide the length of the side by sin(θ) to get the hypotenuse. Alternatively, divide the length by tan(θ) to get the side length adjacent to the angle.

The side lengths and angles of a triangle satisfy two laws namely Law of sines and Law of Cosines.

Law of sines:

If we know two angles and one side, you can use the law of sine to calculate the remaining side of the triangle. This is a technique known as triangulation. It can also be used if you know two sides and one of the angles that are not included. In such cases the triangle is not uniquely determined by this data (called an ambiguous case) and the technique provides two possible values ​​for the included angle.

According to the Law:

[tex]\frac{a}{sin\alpha } = \frac{b}{sin\beta } = \frac{c}{siny} = 2R[/tex]

where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles and R is the radius of triangle circumcircle.

Now,

(sin A)/a = (sin B)/b = (sin C)/c where A, B, and C are the angles and

a = BC, b = CA, and c = AB

And,

AB = sqrt(BC² + CA² + 2*BC*CA*cos(C) . . . . . . . . (1)

Law of cosines is cyclic in A,B, and C

i.e.

We get equation for BC by changing

A=>B, B=> C , and C=> A in (1) i.e.

BC = sqrt(CA² + AB² + 2*CA*AB*cos(A) . . . . . . . (2)

and

equation for CA by a similar change in the equation (2) for BC i.e.

CA = sqrt(AB² + BC²+ 2*AB*BC*cos(B) . . . . . . (3)

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The interpretation of the x-intercept in the context of the given problem is: B. After 14 months, the business will have $0 remaining in their technology budget.

How to Find and Interpret the X-intercept of an Equation?

To find the x-intercept of an equation, substitute the value of y = 0, and solve for x. It is the value of x when y or the output = 0.

Given the equation, T(x) = −135x + 1890, where T(x) is the amount of money remaining in the budget for technology, and x is the number of months, the x-intercept would be the number of months that the business will have $0 in their budget for technology.

To find the x-intercept, substitute T(x) = 0, into T(x) = −135x + 1890:

0 = −135x + 1890

135x = 1890

Divide both sides by 135

135x/135 = 1890/135

x = 14

This means after 14 months, the technology budget that the company will have remaining is $0.

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