12. A summer soccer camp ordered a total of 84 soccer balls and t-shirts for the season. Soccer balls cost $25 each and t-shirts cost $9.50 each. If they payed $1,046 total for the purchase, how many of each item was ordered?

Answers

Answer 1

Answer:

16 Soccer balls

68 T-shirts

Step-by-step explanation:

Given information:

Total order = 84 itemsCost of a soccer ball = $25Cost of a t-shirt = $9.50Total bill = $1,046

Define the variables:

Let x = the number of soccer balls ordered.Let y = the number of t-shirts ordered.

Create two equations from the given information:

\(\textsf{Equation 1}: \quad x + y = 84\)

\(\textsf{Equation 2}: \quad 25x+9.5y=1046\)

Rewrite Equation 1 to make y the subject:

\(\implies y=84-x\)

Substitute this into Equation 2 and solve for x:

\(\implies 25x+9.5(84-x)=1046\)

\(\implies 25x+798-9.5x=1046\)

\(\implies 15.5x+798=1046\)

\(\implies 15.5x=248\)

\(\implies x=16\)

Substitute the found value of x into the rewritten form of Equation 1 and solve for y:

\(\implies y=84-16\)

\(\implies y=68\)

Solution

Soccer balls ordered = 16T-shirts ordered = 68

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Related Questions

help me to answer this​

help me to answer this

Answers

Answer: The answer would be 20

Step-by-step explanation:

NEED HELP ASAP!! Which expressions are equivalent to the one below? Check all that apply.
21x/7x

NEED HELP ASAP!! Which expressions are equivalent to the one below? Check all that apply.21x/7x

Answers

The equivalent expressions \($\frac{21^x}{7^x}\) is \($3^{x}$$\).

What is an equivalent expression?

Equivalent expressions exist as expressions that work exactly even though they look different. If two algebraic expressions exist as equivalent, then the two expressions contain the exact value when we plug in the same values for the variables.

Given: \($\frac{21^x}{7^x}\)

Factor \($21^{x} = 7^{x} \cdot 3^{x}$\)

\($=\frac{7^{x} \cdot 3^{x}}{7^{x}}$$\)

Cancel the common factor: \($7^{x}$\)

\($=3^{x}$$\)

Therefore, the correct answer is option B. \($3^{x}$$\).

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PLEASEEEE HELPPPPP!!!!!!!!

PLEASEEEE HELPPPPP!!!!!!!!

Answers

Answer:

C, thoughtful and grntle

Answer:

B

Step-by-step explanation:

Vain is defined as having a high opinion of oneself.

Conceited is a synonym for vain.

HURRY PLS 7TH GRADE MATH I NEED HELP I HAVE LESS THAN 5 MINS TO DO THIS

HURRY PLS 7TH GRADE MATH I NEED HELP I HAVE LESS THAN 5 MINS TO DO THIS

Answers

Answer:

35 = 8 + x + x + x + x + x +x

35 = 8 + 6x

6x + 8 = 35

35 - 8 = 6x

Step-by-step explanation:

hope this helps:)

What number would come next in this sequence? 1, 2, 6, 22

Answers

The next number in the sequence 1, 2, 6, 22 is 86.

What is Sequence?

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 1, 2, 6, 22

Consider the provided sequence 1, 2, 6, 22, ____ ?

Observe the pattern of the sequence.

To obtain the sequence you need to add the next even square of 2 in the previous number.

1+2⁰=2

Now the next even number is 2.

2+2²=6

Now 6+2⁴=6+16=22

Therefore, the next number should be:

22+2⁶=86

Hence, the next number in the sequence 1, 2, 6, 22 is 86.

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Identify the steps for proving ADDC.
A. 1. BD BD by the reflexive property
2. AABD=ACBD by SAS
3. ADDC by CPCTC
B. 1. BD BD by definition of an isosceles triangle
2. AABD = ACBD by SAS
3. ADDC by CPCTC
C. 1. BD BD by the reflexive property
2. AABD = ACBD by CPCTC
3. ADDC by SAS
D. 1. BD BD by definition of an isosceles triangle
2. AABD = ACBD by CPCTC
3. ADDC by SAS

Identify the steps for proving ADDC.A. 1. BD BD by the reflexive property2. AABD=ACBD by SAS3. ADDC by

Answers

I thinks it’s BD BD by reflex is


Divide 3.87 x 10 by 6.28 x 10 Express your answer in scientific
notation. Round the coefficient to two decimal places.

Answers

Answer:

oo my god the points are more

Answer:

PLEASE MARK AS BRAINLIEST!!!!

Step-by-step explanation:

DIVISION ANSWER = 0.61624203821

SCIENTIFIC NOTAION =

6.1624203821 × 10-1

(scientific notation)

= 6.1624203821e-1

(scientific e notation)

= 616.24203821 × 10-3

(engineering notation)

(thousandth; prefix milli- (m))

= 0.61624203821

(real number)

I DON'T KNOW HOW TO ROUND THE COEFFICIENT

Please solve 13 and 14 I need help

Please solve 13 and 14 I need help

Answers

Answer:

13. a

14.c

Step-by-step explanation:

It is shown in figure

Please solve 13 and 14 I need help
Please solve 13 and 14 I need help

A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 528,000 feet. The square of the height of the pylon is 19,600 feet. So the length of the guy wire can be found by evaluating sqrt(528,000 + 19,600) . What is the length of the guy wire?​

Answers

Answer:

740

Step-by-step explanation:

\( {hyp}^{2} = {opp}^{2} + {adj }^{2}\)

Opp=528, 000 feet

Adj = 19,600feet

Hyp=?

\( {x}^{2} = 528000 + 19600\)

\( {x}^{2} = 547600\)

\(x = \sqrt{547600} \)

Therefore,

\(x = 740\)

The data below shows the money Paritosh spends on a weekend. What will be the central angles of each of these categories?with the numbers 40 100 50 50

Answers

The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:

Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.

Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).

Central angle for the first category: (40/240) * 360 = 60 degrees.

Central angle for the second category: (100/240) * 360 = 150 degrees.

Central angle for the third category: (50/240) * 360 = 75 degrees.

Central angle for the fourth category: (50/240) * 360 = 75 degrees.

The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.

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Note the search engine cannot find the complete question

What is the equation of a hyperbola with a = 7 and c = 9? Assume that the transverse axis is horizontal.

Answers

The equation of a hyperbola with a=7 and c=9 is (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.

Define Hyperbola.

A hyperbola is a kind of smooth curve that appears to lie in a plane. It is made up of two connected components or branches that are mirror reflections of one another and look like two infinite bows. A hyperbola is a collection of points whose difference in distance between two foci is a fixed amount. This discrepancy is calculated by subtracting the distance from the farther focus from the distance from the closest focus.

As we know the standard equation of the hyperbola with a horizontal transverse axis is:

(x-h)²/a²-(y-k)²/b²

Now, put the given values a=7 and c=9 in the Pythagorean theorem to get the value of b.

c²=a²+b²

(9)²=(7)²+b²

81=49+b²

81-49=b²

32=b²

Now square root both sides:√

32=√b²

√32=b

Assuming that the center of a hyperbola is (0,0):

(x-0)²/a²-(y-0)²/b²=1

x²/a²-y²/b²=1

x²/(7)²-y²/(√32)²=1

x²/49-y²/32 = 1

Therefore, the equation of a hyperbola with a=7 and c=9 (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.

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What interest could be earned by a deposit of $1,500 for 6 months at a bank that pay a 4 1/8% annual interest rate, compounded semiannually?

Answers

Answer:

Interest = $720

Balance = $9,720

Step-by-step explanation:

P = $9,000, the principal

r = 8% = 0.08, the interest rate

n = 2, semiannual compounding

After 6 months, the interest is

9000 * 0.08 = $720

The balance after 6 months is

9000 + 720 = $9720

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can someone please help

can someone please help

Answers

Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Aliana is supposed to get back to a customer with an answer about a refund by the end of the day, but she won't have all the approvals she needs to process the refund by that time. What should she do? O a) Call the customer only when she has processed the refund Ob Tell the customer that she should have called about the problem earlier Oc) Explain to the customer that her bosses are the ones that are taking forever O di Apologize to the customer and say that she will call her tomorrow with an update

Answers

Answer:

"ob" is the answer of this long question

Answer:

D

Step-by-step explanation:

reason:

not A cuz the customer has to wait for a long time, and she feel waste of time

not B cus it's the store's responsiblity, not customer. if she said that, the customer would feel be disrespected. and i swear she never comes back that store.

C if she said that, customer also feel waste of time when she has to talk with Aliana who cant solve her problem

and the boss will think Ali couldnt have no problem-solving skills

The following are the ages (years) of 5 people in a room: 13 , 22 , 15 , 14 , 15 A person enters the room. The mean age of the 6 people is now 16. What is the age of the person who entered the room?

Answers

Answer:

17

Step-by-step explanation:

Add up the values (13, 22, 15, 15, 14) and subtract from the product of 16 and 6

Answer:

17

Step-by-step explanation:

the mean is calculated as

mean = \(\frac{sum}{count}\)

let x be the age of the person entering the room, then sum of 6 is

sum = 13 + 22 + 15 + 14 + 15 + x = 79 + x

\(\frac{79+x}{6}\) = 16 ( multiply both sides by 6 to clear the fraction )

79 + x = 96 ( subtract 79 from both sides )

x = 17

the age of the person who entered the room is 17

Together Elizabeth and Norman have 45 postcards. Norman has 4 Times as many postcards as Elizabeth. How many postcards are in Norman's collection? how many postcards are in Elizabeth's collection?

Answers

Answer:

boy 36

girl 9

............

Fred brought a shirt and a wallet for a total of 34.26 before tax. The price of the wallet was $15 less than the price of the shirt. What was the price of the shirt?

Answers

Answer:

The price of the shirt is $24.63.

Step-by-step explanation:

Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:

x + (x - 15) = 34.26

Simplifying, we get:

2x - 15 = 34.26

Adding 15 on both sides:

2x = 49.26

Dividing by 2:

x = 24.63

Therefore, the price of the shirt is $24.63.

Which numbers can be placed in the blank to make the value of this expression a negative number? (-16) -​

Answers

Answer:

All numbers greater than -16.

Step-by-step explanation:

Hello!

To keep this expression negative, we can subtract a positive number (numbers greater than or equal to 0), to give us an even smaller negative number.

Another option is to add a negative number so that the value is still negative. We can add any number that is larger than -16.

Answer: All numbers greater than -16

solve In 2010, the percentage of assisted living residents who had both heart disease and depression was 9%, the percentage with only heart disease was 25%, and the percentage with either condition was 48%. What percentage of assisted living residents had only depression

Answers

Answer:

The percentage of assisted living residents had only depression

P(D) =0.32

Step-by-step explanation:

Explanation:-

Given  the percentage of assisted living residents who had both heart disease and depression was 9%

Let The event 'H' be the event of heart disease and 'D' be the event of depression

P(H ∩D) = 9% =0.09

The  percentage with only heart disease was 25%

P(H) = 0.25

The percentage with either condition was 48%.

P(H∪D) = 48%=0.48

By addition theorem on probability

       \(P(H UD) = P(H) +P(D) - P(H n D)\)

              \(0.48 = 0.25 + P(D) -0.09\)

            P(D) = 0.48 -0.16

            P(D) = 0.32  

The percentage of assisted living residents had only depression

P(D) =0.32

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3. Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3. To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and ∠DFE is 4 times greater than ∠GFH. ∠FHG is One-fourth the measure of ∠FED. ∠DFE is congruent to ∠GFH. ∠FHG is congruent to ∠EFD.

Answers

To prove that △DFE ~ △GFH by SAS similartiy theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: \(\frac{DF}{GF}\) = \(\frac{EF}{HF}\) and ∠DFE is congruent to ∠GFH.

Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:

By comparing ΔDEF and ΔGFH

DF = DG + GF

     = 12 + 4

DF = 16

Also,

EF = EH + HF

    = 9 + 3

EF = 12

Comparing the sides of ΔDEF and ΔGFH, we have;

\(\frac{DF}{GF}\) = \(\frac{EF}{HF}\)

\(\frac{16}{4}\) = \(\frac{12}{3}\)

4 = 4

Thus, the two triangles have similar sides.

Comparing the included angle <DFE and <GFH, then;

∠DFE is congruent to ∠GFH

So that the appropriate answer to the given question is option C. ∠DFE is congruent to ∠GFH

Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;

\(\frac{DF}{GF}\) = \(\frac{EF}{HF}\) and ∠DFE is congruent to ∠GFH.

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In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3. Triangle D E F is shown. Line G H is drawn parallel

Answer: C

Step-by-step explanation:

Read the following description of a relationship:
The maple tree in Maggie's backyard is 5 years younger than the willow tree.
Let w represent the willow tree's age and m represent the maple tree's age.
Use the function m = w - 5 to find the value of m when w = 6.
m =
Submit
Sh

Read the following description of a relationship:The maple tree in Maggie's backyard is 5 years younger

Answers

The Maple tree would be 1, it claims that the Willow tree is 6 years old and if you did 6-5 it would be 1. Hope this helped.

Which sizes can he display? Choose all that apply.
linch
4
0.5 inch
3 inch
8
1 inch
1.5 inch

Which sizes can he display? Choose all that apply.linch40.5 inch3 inch81 inch1.5 inch

Answers

Step-by-step explanation:

He can choose the dispay boxes that are 0.5 in, 1/4 in, and 3/8 in

Hope this helps

May I get braineist pls?

Each machine at a certain factory can produce 90 units per hour. The setup cost is 20 dollars for each machine and the operating cost is 26 dollars per hour (total, not 26 dollars per machine per hour). You would like to know how many machines should be used to produce 40000 units, with the goal of minimizing production costs.
First, find a formula for the total cost in terms of the number of machines, n:_______
TC = ______
machines for a total cost of The minimum total cost is achieved when using dollars.

Answers

Answer:

a)  \(Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}\)

b)  \(n=24\)

Step-by-step explanation:

From the question we are told that:

Rate r=90 units per hour

Setup cost =20

Operating Cost =26

Units=40000

Generally the equation for Total cost is mathematically given by

\(Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}\)

\(T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1\)

Differentiating

\(T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2\)

Equating equ 1 to zero

\(0=\frac{20n^2+11556}{n}\)

\(n=24\)

Therefore

Substituting n

For Equ 1

\(T_n=\frac{20(24)^2+11556}{24}\)

F(n)>0  

For Equ 2

\(T_n'=\frac{20(24)^2-11556}{24^2}\)

F(n)'<0

Bryan drew a triangle with vertices at (4,1), (1, 3), and (2,-3). He slides the triangle 3 units to the left to create an image. What are the vertices of the image?

Answers

you are sliding it along the x axis, so subtract three from each z coordinate. (1,1) (-2,3) (-1,-3)

change the height for Ramp 2 to make a smooth slide

Answers

First answer:

If you look carefully to the measures of the three triangles that are the ramps of the exercise, you will notice they are similar after comparing them.

• Ratio of Ramp 1 = 2/3

,

• Ratio of Ramp 2 = 4/6

,

• Ratio of Ramp 3 = 6/9

Second answer

The information is given on the image and we can calculate the missing measures for make a smooth slide:

• Ramp 1 - Base 10 - Height 12

,

• Ramp 2 - Base 15 - Height 18

,

• Ramp 3 - Base 30 - Height 36

We used the ratio 2/3 for answering the first question, now we have the ratio

5/6, as follows:

• Ramp 1 - 5/6 * 2/2 = 10/12

,

• Ramp 2 - 5/6 * 3/3 = 15/18

,

• Ramp 3 - 5/6 * 6/6 = 30/36

Question
A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When
she plants 3 stalks, each plant yields 115 ounces of beans. When she plants 8 stalks, each plant yields 190 ounces of beans.
Write the linear equation, Y(n), that correctly represents this situation.
Provide your answer below:
Y(n)=
Content attribution
evious
FEEDBACK
MORE INSTRUCTION
SUBMIT

Answers

The equation that represent the given situation is y = 15x + 70

When she plants 3 stalks, each plant yields 115 ounces of beans

The first point = (3, 115)

When she plants 8 stalks, each plant yields 190 ounces of beans

The second point = (8, 190)

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Substitute the values in the equation

The slope of the line m = (190-115) / (8-3)

= 75/5

= 15

The point slope form is

\(y-y_1=m(x-x_1)\)

Choose one point and substitute the values in the equation

y - 115 = 15(x - 3)

y - 115 = 15x - 45

y = 15x - 45 + 115

y = 15x + 70

Hence, the equation that represent the given situation is y = 15x + 70

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In each diagram, line f is parallel to line g, and line t intersects lines f and g

Answers

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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You brought three erasers and a magazine for $4. You spent a total of $13. How much did each eraser cost?

Answers

Answer:

$3

Step-by-step explanation:

3x + 4 = 13

X=3

I believe that the answer is 3 (:

Sean runs a marathon, which is 26.2 miles long. A mile is about 1.61 kilometers. What is the distance to the nearest kilometer?

Answers

No of miles=26.21mile=1.61km

26.2miles:-

\(\\ \sf\longmapsto 26.2(1.61)\)

\(\\ \sf\longmapsto 42.182\)

\(\\ \sf\longmapsto 42km\)

The given distance to the nearest kilometer is 42 kilometers.

Given that, Sean runs a marathon, which is 26.2 miles long.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, a mile is about 1.61 kilometers.

Here, number of kilometers = 26.2×1.61

= 42.182 kilometers

≈ 42 kilometers

Therefore, the given distance to the nearest kilometer is 42 kilometers.

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Is 7. 787887888. A rational number?


A. Yes; it has a pattern which is repeating.


B. Yes; it has a pattern which is terminating


C. No; it has a pattern which is predictable, but no repeating


D. No; it has a pattern which is non repeating and non termination

Answers

The number 7.787887888 is option (C) not a rational number, it has a pattern which is predictable, but not repeating

The given number is 7.787887888

The rational numbers is a number that can be expressed as the p/q format, where p and q are integers and p will not be equal to zero. So the rational number is the ratio of the two integers.

Here the given number is 7.787887888.

So this is an non terminating number

But here we can see that there is a pattern which is predictable but its not repeating

Therefore, it is not a rational number ,but it has a pattern which is predictable, but not repeating

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