What is the perimeter?

The cafeteria sold 41 corn chips and 80 potato chips.

Step-by-step explanation:

Let,

Corn chips = x

Potato chips = y

Price of corn chips = $0.80

Price of potato chips = $0.60

According to given statement;

x+y= 121   Eqn 1

0.80x+0.60y=80.80   Eqn 2

Multiplying Eqn 1 by 0.80

[tex]0.80(x+y= 121)\\0.80x+0.80y=96.80\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](0.80x+0.80y)-(0.80x+0.60y)=96.80-80.80\\0.80x+0.80y-0.80x-0.60y=16\\0.20y=16[/tex]

Dividing both sides by 0.20

[tex]\frac{0.20y}{0.20}=\frac{16}{0.20}\\y=80[/tex]

Putting y=80 in Eqn 1

[tex]x+80=121\\x=121-80\\x=41[/tex]

The cafeteria sold 41 corn chips and 80 potato chips.

Keywords: linear equation, subtraction

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Answer:

42.5 square centimeters

Step-by-step explanation:

The area of the parallelogram is

[tex]A=a\cdot b\cdot \sin \alpha,[/tex]

where a and b are adjacent sides and [tex]\alpha[/tex] is inckuded angle.

In your case,

[tex]a=11\ cm\\ \\b=5\ cm\\ \\ \alpha=50^{\circ}6'[/tex]

Thus,

[tex]A=11\cdot 5\cdot \sin 50^{\circ}6'\approx 42.5\ cm^2[/tex]

Answer:

Step-by-step explanation:

5r + 2b = 14 (5 lbs of oranges and 2 lbs of bananas = $14)

3r + 6b = 18 (3 lbs of oranges and 6 lbs of bananas = $18)

Let's use the elimination method. Multiply the first equation by -3:

-15r - 6b = -42

3r + 6b = 18

-----------------

12r = 24

Divide by 12:

r = 2

Answer:

The price per pound of the oranges is $ 2.

The price per pound of the bananas is $ 2.

Step-by-step explanation:

A system of linear equations is a set of equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all. In these equations the unknowns are related to each other.

In this case a system of equations is applied. For that, you must first define the unknowns (or also called variable):

The price of the 5 pounds of oranges, whose price is "x", and 2 pounds of bananas, whose price is "y", bought by Gail must add $ 14. Then expressed in an equation this represents: 5*x+2*y=14 Equation (A)

The price of the 3 pounds of oranges, whose price is "x", and 6 pounds of bananas, whose price is "y", bought by her husband must add $ 18. Then expressed in an equation this represents: 3*x+6*y=18 Equation (B)

Equation A and equation B form the equation system, where the variables are "x" and "y", which are the price of an orange and a banana:

[tex]\left \{ {{5*x+2*y=14} \atop {3*x+6*y=18}} \right.[/tex]

One of the ways to solve a system of equations is through the substitution method.  This method consists of isolating one of the unknowns (for example, "x") and replacing its expression in the other equation. In this way, a first degree equation is obtained with the other variable, "y".

In this case, x is isolated from the first equation, obtaining:

5*x+2*y=14

5*x=14-2*y

[tex]x=\frac{14-2*y}{5}[/tex]

[tex]x=\frac{14}{5} -\frac{2}{5}*y[/tex] Equation (C)

Replacing this equation (C) in the other equation you get:

[tex]3*[\frac{14}{5} -\frac{2}{5} *y]+6*y=18[/tex]

Isolating the value of "y" you get:

[tex]3*\frac{14}{5} -3*\frac{2}{5} *y+6*y=18[/tex]

[tex]\frac{42}{5} -\frac{6}{5} *y+6*y=18[/tex]

[tex]-\frac{6}{5} *y+6*y=18-\frac{42}{5}[/tex]

[tex]\frac{24}{5} *y=\frac{48}{5} \\[/tex]

[tex]y=\frac{\frac{48}{5} }{\frac{24}{5} }[/tex]

[tex]y=\frac{48}{5} *\frac{5}{24} \\[/tex]

y=2

Remembering that "y" is the price per pounds of the banana, then it is possible to say that the price per pound of the banana is $ 2.

Replacing the value of the variable "y" in equation (c) and isolating the value of the variable "x" gives:

[tex]x=\frac{14}{5} -\frac{2}{5}*2[/tex]

[tex]x=\frac{14}{5} -\frac{4}{5}[/tex]

[tex]x=\frac{14-4}{5}=\frac{10}{5}[/tex]

x=2

Remembering that "x" is the price per pounds of the oranges, then it is possible to say that the price per pound of the oranges is $ 2.

Answer:

Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units

Step-by-step explanation:

Given points:

[tex]P(-12,-2)[/tex]

[tex]Q(3,6)[/tex]

To determine the distance between points P and Q.

Steps to be carried out:

1) Plot the points P and Q on graph.

2) Construct a line from P towards right horizontally and a line from Q downwards vertically such that they meet at point [tex]O(3,-2)[/tex]

3) Join PQ thus forming a right triangle POQ.

4) We can find the distance of sides OP and OQ by counting the units between the points.

OP=[tex]|-12-3|=|-15|=15\ units[/tex]

OQ=[tex]|6-(-2)|=|6+2|=8\ units[/tex]

4)Now, we can apply Pythagorean theorem for triangle POQ.

[tex]PQ^2=OP^2+OQ^2[/tex]   [ [tex]Hypotenuse^2=Leg1^2+Leg 2^2[/tex]]

[tex]PQ^2=15^2+8^2[/tex]

[tex]PQ^2=225+64[/tex]

[tex]PQ^2=289[/tex]

Taking square root both sides:

[tex]\sqrt{PQ^2}=\sqrt{289}[/tex]

[tex]PQ=17\ units[/tex] [We take only the positive value as distance is always positive.

∴ Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units

Answer:

We can conclude that Δ ABC ≅ Δ DEF by SSS postulate.

Step-by-step explanation:

Δ ABC and Δ DEF are congruents because:

1. Their sides AB and DE are equal (9 units = 9 units)

2. Their sides BC and EF are equal (5 units = 5 units)

3. Their sides AC and DF are equal (10 units = 10 units)

Now, we can conclude that Δ ABC ≅ Δ DEF by SSS postulate.

Answer:

B

Step-by-step explanation:

When we see "square inches" in a statement (or squared centimeters, meters, feet, etc) this refers to an area measure. So we need to find which of the options are areas.

A is not, as it is width, is a longitude measure. I could never be in square inches.

C is volume and it measure should be in cubic inches. So, not.

D is perimeter and is the sum if the lengths of different sides of a figure, so is also in inches, not square inches.

Finally, B is the area,  so is our only chance. B in correct.

Answer:

AB = 9.6 cm

Step-by-step explanation:

ΔAPQ and ΔABC are similar triangles, thus ratio of corresponding sides are equal, that is

[tex]\frac{AP}{AB}[/tex] = [tex]\frac{PQ}{BC}[/tex], substitute values

[tex]\frac{8}{AB}[/tex] = [tex]\frac{10}{12}[/tex] ( cross- multiply )

10AB = 96 ( divide both sides by 10 )

AB = 9.6 cm

Answer:

See below

Step-by-step explanation:

To construct a confidence interval we use the following formula:

ci = (sample mean) +- z*(sd)/[n^(1/2)]

The sample mean is 57, the standard deviation is 2.36, n s 25 and z is the  upper (1-C)/2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C)/2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:

ci = 57 +- 1.65*(2.36)/[25^(1/2)]

ci = 57 +- 3.894*/(5) = 57 +- 0.78

ci => (56.22 , 57.78)

Step-by-step explanation:

You must exclude any intersecting faces (faces that are shared), because these faces are not on the surface.

For example, an ice cream cone can be approximated as a composite figure of a hemisphere on top of a cone.  The circular base of the hemisphere and the circular base of the cone are intersecting, so you must exclude it when finding the surface area.

Answer:When two figures are placed together, one of each of their surfaces meets. The surfaces come together on the inside of the figure, and are no longer a part of the surface. These surfaces are a part of the individual figures’ surface area, but not of

Step-by-step explanation:

Did the test (this is the sample response)

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

Step-by-step explanation:

Carla is saving money for a trip this summer. She already has some money in her savings account and will add the same amount to her account each week

Write a linear function in the form y = m x + b to represent the amount of money, m, that Carla has saved after w weeks

The linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are 2 points on the line

∵ The slope is the rate of change of y and x

∴ The same amount of money that Carla add every week = m

∵ At the end of 2 weeks, Carla has $130

∴ The first point is (2 , 130)

∵ At the end of 8 weeks, she has $280

∴ The second point is (8 , 280)

∵ [tex]m=\frac{280-130}{8-2}=\frac{150}{6}=25[/tex]

∴ The same amount of money that Carla add every week = $25

∵ The amount of money that Carla saved after w week is m

∴ m = 25 w + b, where b is the initial amount of money that she

   saved in her account

To find b substitute w and m by the coordinates of one of the two

given points, let us use the first point

∵ w = 2 and m = 130

∵ m = 25 w + b

∴ 130 = 25(2) + b

∴ 130 = 50 + b

- Subtract 50 from both sides

∴ 80 = b

∴ m = 25 w + 80

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

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Answer:

is is 20

Step-by-step explanation:

Answer:

[tex]CD=(3-\sqrt{3})\ cm[/tex]

Step-by-step explanation:

step 1

Find the length side AB

In the right triangle ABD

[tex]sin(30\°)=\frac{AB}{AD}[/tex]

[tex]AB=sin(30\°)(AD)[/tex]

we have

[tex]AD=2\sqrt{3}\ cm[/tex]

[tex]sin(30\°)=\frac{1}{2}[/tex]

substitute

[tex]AB=\frac{1}{2}(2\sqrt{3})[/tex]

[tex]AB=\sqrt{3}\ cm[/tex]

step 2

Find the length side BD

In the right triangle ABD

[tex]cos(30\°)=\frac{BD}{AD}[/tex]

[tex]BD=cos(30\°)(AD)[/tex]

we have

[tex]AD=2\sqrt{3}\ cm[/tex]

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]BD=\frac{\sqrt{3}}{2}(2\sqrt{3})[/tex]

[tex]BD=3\ cm[/tex]

step 3

Find the length side BC

In the right triangle ABC

we know that

BC=AB -----> is an 45°-90°-45° triangle

therefore

[tex]BC=\sqrt{3}\ cm[/tex]

step 4

Find the length side CD

we know that

[tex]BD=BC+CD\\CD=BD-BC[/tex]

substitute the values

[tex]CD=(3-\sqrt{3})\ cm[/tex]

Answer:

So the greatest common factor 42 and 98 is 14.

Answer:

6

Step-by-step explanation:

Answer:

28 students

Step-by-step explanation:

you get 28.3 if you divide 85 by 3

Final answer:

To express y in terms of x, rearrange the equations to isolate y. The equation expressing y in terms of x is (4x + 20)/3.

Explanation:

To express y in terms of x, we need to isolate y in the given equations.

From the first equation, x = 3t - 8, we can rearrange to solve for t: t = (x + 8)/3.

Substituting this expression for t into the second equation, y = 4 + t, gives us y = 4 + (x + 8)/3. Simplifying further, we have y = (4x + 20)/3.

Answer:

0.16

Step-by-step explanation:

Use long division

Answer:

0.16

Step-by-step explanation:

4÷25 = 0.16

Answer:

[tex]\displaystyle [\frac{9}{11}, 1\frac{111}{143}][/tex]

Step-by-step explanation:

{10x - 26y = −38

{6x + 13y = 28

½[10x - 26y = −38]

{5x - 13y = −19 >> New Equation

{6x + 13y = 28

___________

[tex]\displaystyle \frac{11x}{11} = \frac{9}{11}[/tex]

[tex]\displaystyle x = \frac{9}{11}[/tex][Plug this back into both equations above to get the y-coordinate of 1 111⁄143]; [tex]\displaystyle 1\frac{111}{143} = y[/tex]

I am joyous to assist you anytime.

Answer:

n=0

Step-by-step explanation:

6=1-2n+5-4n

Combine like terms

6=-6n+6

now move the +6 to other side

0=-6n

so divide to remove the n from the -6

0=n

No worries I tested it it's right! I hope :/

Answer:

Therefore, the percent error in 1.   20%

          and the percent error in 2.    6%  

Step-by-step explanation:

Given:

1. In estimation of 30 people only 25 people attended.

2. In estimated length of 150 feet the measurement was 142 feet.

Now, in first case for the percent error we would calculate the difference between the people attended:

[tex]30-25=5[/tex]

And then, we will get the percentage error :

[tex]\frac{5}{25} \times 100[/tex]

[tex]\frac{500}{25}[/tex][tex]=20[/tex].

Therefore, the percentage error is 20%.

Now, in second case for the percent error we would repeat the above process as done in first case:

[tex]150-142=8[/tex]

And then:

[tex]\frac{8}{142}\times 100[/tex]

[tex]\frac{800}{142}[/tex][tex]=5.63[/tex]

Therefore, the percentage error is 6% (approximately).

Therefore, the percent error in 1. is   20%

          and the percent error in 2. is  6%  

Answer:

The correct answer is s = 27.

Step-by-step explanation:

This problem already gives us an equation so all we need to do is plug in the numbers:

c = 39.95 + 0.15(s + r) becomes 53.45 = 39.95 + 0.15(s + 63). Now to solve:

53.45 = 39.95 + 0.15(s + 63)

13.50 = 0.15(s + 63)                     Subtract 39.95 from both sides

13.50 = 0.15s + 9.45                    Distribute 0.15 to s and 63

4.05 = 0.15s                                 Subtract 9.45 from both sides

27 = s                                           Divide both sides by 0.15

Hope this helps,

❤A.W.E.S.W.A.N.❤

Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer

Step-by-step explanation:

Given fraction is:

[tex]\frac{\frac{x}{3}-\frac{y}{4}}{\frac{x}{4}+\frac{y}{3}}[/tex]

To solve the fraction, Taking LCM in denominator and numerator

[tex]=\frac{\frac{4x-3y}{12} }{\frac{3x+4y}{12}}[/tex]

When the numerator and denominator both have fractions, the simplified form is obtained be multiplying the numerator with reciprocal of the denominator. So,

[tex]= \frac{4x-3y}{12} * \frac{12}{3x+4y}\\=\frac{4x-3y}{3x+4y}[/tex]

Hence,

Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer

Keywords: fractions, simplification

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Answer:

a) $25,261

b) $25,156

Step-by-step explanation:

I'm sorry but I don't know how to show my work because I just searched up "Car Loan Calulator" :|

So don't put me up for Brainlist

Answer:

The percent increase is 157%

Explanation:

Average after tax income 20 years before: $263,700

Average after tax income after 20 years: $677,900

Increased average after tax  income : $677,900-$263,700

                                                            =$414,200

Hence,  

Percent increase = [tex]\frac{Increased amount}{original amount} \times 100[/tex]

=[tex]\frac{414,200}{263,700} \times 100[/tex]

=157.07%

After Rounding off:

=157%

157%  is the percent increase

Answer:

B) 113.1 cm³

Step-by-step explanation:

The cross-section of a sphere is a circle.  The area of a circle is:

A = πr²

The largest cross section passes through the center of the sphere, where the radius of the circle equals the radius of the sphere.

28.27 = πr²

r = 3.00

The volume of the sphere is therefore:

V = 4/3 π r³

V = 4/3 π (3.00)³

V = 113.1

Answer:

B

Step-by-step explanation:

They both will finish the work in 3.07 hours

Step-by-step explanation:

Time taken by Rachel = 5 hours

Work done by Rachel in one hour = 1/5

Time taken by Carl = 8 hours

Work done by Carl in one hour = 1/8

Let x hours be the time taken by both to do work

Then 1/x will be the work done by both in one hour

So,

[tex]\frac{1}{5} + \frac{1}{8} = \frac{1}{x}[/tex]

Taking LCM

[tex]\frac{8+5}{40} = \frac{1}{x}\\\frac{13}{40} = \frac{1}{x}\\13x = 40\\x = \frac{40}{13}\\x = 3.07\ hours[/tex]

They both will finish the work in 3.07 hours

Keywords: Linear Equation

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Answer:

12 hrs

Step-by-step explanation:

X/30+x/48=1

common denominator

x/1440+x/1440

2x/1440=1

2x=1440

x=720

when you convert to hrs  you get 12

A valid reason is :opposite sides of a parallelogram are equal

Step-by-step explanation:

It is possible to notice that RUTS is a parallelogram where RU=TS and RS = UT.

When you introduce a diagonal RT you form triangles RUT and TSR.

∠URT = ∠STR ----alternate angles

∠UTR=∠SRT------alternate angles

RU║ST and RS║UT

RT=TR -----Common

ΔRUT ≡ ΔTSR by AAS theorem

hence RS=UT matching sides of congruent triangles

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Properties of a parallelogram : https://brainly.com/question/12780093

Keywords : proof, parallelogram, reason

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Answer:

opposite sides of a parallelogram are equal

Step-by-step explanation:

got it right on odyssey

Answer:

A

Step-by-step explanation:

(3a^4-2a^2+5a-10)-(2a^4+4a^2+5a-2)

a^4-6a^2-8

The first group of points is not a function due to repetition of elements in domain while second group of points is a function because no element of domain is repeated in any ordered pair.

Step-by-step explanation:

Why {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function?

A relation is said to be a function if there is no repetition in the first elements of each ordered pair. In this group of points, 0 is repeated in two ordered pairs (0, 1), (0, 5) so it is not a function.

Why {(1, 4), (2, 7), (3, 1), (5, 7)} is a function?

The given group of points is a function because there is no repetition in first elements of each ordered pair i.e. there is not repetition in domain so it is a function

Keywords: Functions, Domain

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