Mrs.Barkley has 75 feet ribbon. If each of the 18 students in her class gets an equal length of ribbon, how many inches of ribbon will each student get?

Answer:

[tex]y=35\cdot (1.6)^x.[/tex]

Step-by-step explanation:

Find the exponential function in a form [tex]y=a\cdot b^x.[/tex]

1. At x=0,

[tex]35=a\cdot b^0=a.[/tex]

2. At x=1,

[tex]56=35\cdot b^1\Rightarrow b=\dfrac{56}{35}=\dfrac{8}{5}=1.6.[/tex]

Therefore, the expression for the exponential function is

[tex]y=35\cdot (1.6)^x.[/tex]

Note that

[tex]y(-1)=35\cdot (1.6)^{-1}=\dfrac{35}{1.6}=21.875[/tex]

and

[tex]y(2)=35\cdot (1.6)^2=35\cdot 2.56=89.6.[/tex]

The exponential growth function represented by the provided set of ordered pairs is[tex]y = 35 \times 1.6^x,[/tex] where 'a' is the initial value and 'b' is the growth factor derived from the given points.

To begin determining the underline equation of this exponential growth function, we first need to recognize that the general form of an exponential function is[tex]y = ab^x[/tex] , where a is the initial value (the output when x=0) and b is the growth factor.

In the provided set of ordered pairs, when x = 0, y = 35.  Therefore, a = 35. Now, to calculate b, we could apply the function to the point (1,56). We know that[tex]56 = 35\times b^1,[/tex]which simplifies to 56 = 35b.  Solving for b gives us b ≈ 1.6 (approximation).

So, the exponential growth function that corresponds to these ordered pairs is[tex]y = 35\times 1.6^x.[/tex]

https://brainly.com/question/36376695

#SPJ3

The equation of proportional situation is y = ax.

Therefore your answer is y = 14x

Answer:

Mary's age is 16.8 years

Jane's age is 11.2 years

Step-by-step explanation:

Let's assume Jane was x years old

Mary is twice as old as Jane a long time ago

so, Marry's age =2x

difference in age =2x-x=x years

It means that Marry is x year older than Jane

now, we have

Mary was as old as Jane is now

or we can say that

Jane is as old as Mary was

we know that

Mary =2x years

so, Jane age becomes

Jane=2x years

and we have got

As Mary is x years older than Jane

so, Mary's age =2x+x=3x years old now

now, we are given

The sum of their ages is 28

So,

Mary's age + Jane's age =28

[tex]3x+2x=28[/tex]

[tex]5x=28[/tex]

[tex]x=5.6[/tex]

Mary's age is

[tex]=3\times 5.6[/tex]

[tex]=16.8[/tex]

Jane's age is

[tex]=2\times 5.6[/tex]

[tex]=11.2[/tex]

Answer:

V = 339.3 cm³; L = 203.9 cm²; A = 317.0 cm²  

Step-by-step explanation:

a) Volume

The formula for the volume (V) of a cone is

V = ⅓πr²h

V = ⅓π × 6² × 9

V = ⅓π × 36 × 9

V = 108π cm³

V ≈ 339.3 cm³

=====

Curved surface area  

The formula for the lateral surface area (L) of a cone is

L = πr√(r² + h²)

L = π×6√(36 + 81)

L = 6π√[9(4 + 9)]

L = 6π√(9 × 13)

L = 18π√13 cm²

L ≈ 203.9 cm²

===============

b) Base surface area

The base is a circle, so the formula for base surface area (B) is

B = πr²

B = π×6²

B = 36π cm²

B ≈ 113.1 cm²

=====

Total surface area

A = L + B

A = 18π√(13 +36π)

A = 18π(2 + √13) cm²

A ≈ 203.9 + 113.1

A ≈ 317.0 cm²

Answer:

[tex]\dfrac{5}{3}[/tex] cups

Step-by-step explanation:

Jacob mixes [tex]\dfrac{1}{3}[/tex] cup of yellow paint for every [tex]\dfrac{1}{5}[/tex] cup of blue paint to make green paint.

The ratio of yellow paint to blue paint = [tex]\dfrac{1}{3}:\dfrac{1}{5}[/tex]

                                                               = 5:3

[tex]\dfrac{1}{5}[/tex] cup of blue paint = [tex]\dfrac{1}{3}[/tex] cup of yellow paint

  1 cup of blue paint = [tex]\dfrac{1}{3}\div\dfrac{1}{5}[/tex] cup of yellow paint

[tex]\Rightarrow \dfrac{1}{3}\div\dfrac{1}{5}[/tex]

[tex]\Rightarrow \dfrac{5}{3}[/tex]

Hence, For 1 cup of blue paint needed [tex]\dfrac{5}{3}[/tex] cups of yellow paint.

Answer:

x^2-10x+25=0

Step-by-step explanation:

Answer:

the answer is 25.9 round it to 26 if needed

Step-by-step explanation:

2.30 * 5 =11.50

3.60 * 4 =14.4

11.50+14.4=25.9

Well first let's do the small packages $2.30 * how many your sending which is 5.  $2.30 * 5 = $11.50 and do the same for the big packages 3.60 * 4 = $14.40. Now add up both $11.50 + $14.40 = 25.90

Hope That Helps

Answer:

Both answers are correct, depending on the angle taken as reference

Step-by-step explanation:

we know that

In a right triangle

The slope ratio of the triangle is equal to the function tangent

The function tangent in a right triangle is equal to the opposite side to the angle divided by the adjacent side to the angle

so

[tex]tan(35)=\frac{7}{10}[/tex] -----> Ben's ratio

and

[tex]tan(55)=\frac{10}{7}[/tex] ------> Carlissa's ratio

therefore

The slope will depend on the angle taken as a reference

so

Both answers are correct, depending on the angle taken as reference.

Answer:

The number is 34.

Step-by-step explanation:

Let the number be x.

As per the statement: if 5.5% of it is 17% of 11.

⇒ 5.5% of x is 17% of 11.

"5.5%of x" means [tex]\frac{5.5}{100} \times x[/tex]

"17% of 11" means [tex]\frac{17}{100} \times 11[/tex]

then;

[tex]\frac{5.5x}{100} = \frac{17 \times 11}{100}[/tex]

Multiply by 100 on both sides, we get;

[tex]\frac{5.5x}{100} \times 100 = \frac{17 \times 11}{100} \times 100[/tex]

Simplify:

[tex]5.5x = 187[/tex]

Divide both sides by 5.5 , we get;

[tex]\frac{5.5x}{5.5} = \frac{187}{5.5}[/tex]

Simplify:

x = 34

Therefore, the number is 34.

Answer:

Step-by-step explanation:

First we must find 17% of 11.

0.17 x 11 = 1.87

So we know 5.5% of "a number" or "x" is equal to 1.87

0.055x = 1.87

x = 1.87/0.055

x = 34

Answer:

√71

Step-by-step explanation:

Simplify 42÷6 to 7

√64+7

Simplify 64+7 to 71

=√71

Answer:

The total interest is £460.

Step-by-step explanation:

Formula

[tex]Simple\ interest = \frac{Principle\times Rate\times Time}{100}[/tex]

As given

£2300 is invested for 4 years at 5% per year simple interest.

Principle = £2300

Rate = 5%

Time = 4 years

Put in the formula

[tex]Simple\ interest = \frac{2300\times 5\times 4}{100}[/tex]

[tex]Simple\ interest = \frac{46000}{100}[/tex]

Simple interest = £460

Therefore the total interest is £460.

Answer: £460

Step-by-step explanation:

Use this formula to find the total interest [tex]I=\frac{P*R*T}{100}[/tex]

I stands for interest, P is principal, R is rate, and T is time.

Principle = £2300

Rate = 5%

Time = 4 years

[tex]\frac{2,300*5*4}{100} =\frac{46,000}{100} =460[/tex]

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)  

- Cutiepatutie ☺❀❤

Answer:

Let x = cost of your friend's lunch.

x + x + 3 = 19

x= 8

Answer:

Your friend lunch bill is $8

Step-by-step explanation:

The bill for you and your friend lunch = $19

Meaning the sum of your lunch bill and your friend bill is $19.

To find how much your friend bill is,

Let represent your friend bill to be x and your bill to be y.

Therefore: x + y = $19

Given that your bill is $3 more than your friend.

Simple means; your bill = your friend bill + 3

Since x represent your friend bill and y represent your bill

So

y = x + 3

Therefore from: x + y = $19

Substitute the value of y = x+3

x + y = $19

x + x + $3= $19

2x = $19 - $3

2x = 16

x = 16/2

x = $8

Since x = your friend bill.

Therefore:.

Your friend lunch bill is $8

It'a an arithmetic sequence:

[tex]a_1=-1\\\\a_2=-1+\dfrac{5}{3}=-\dfrac{3}{3}+\dfrac{5}{3}=\dfrac{2}{3}\\\\a_3=\dfrac{2}{3}+\dfrac{5}{3}=\dfrac{7}{3}\\\\a_4=\dfrac{7}{3}+\dfrac{5}{3}=\dfrac{12}{3}=4\\\\a_5=4+\dfrac{5}{3}=\dfrac{12}{3}+\dfrac{5}{3}=\dfrac{17}{3}\\\vdots\\\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=-1\ \text{and}\ d=\dfrac{5}{3}.\\\\\text{Substitute}\\\\a_n=-1+(n-1)\left(\dfrac{5}{3}\right)=-1+\dfrac{5}{3}n-\dfrac{5}{3}=\dfrac{5}{3}n-\dfrac{3}{3}-\dfrac{5}{3}[/tex]

[tex]\boxed{a_n=\dfrac{5}{3}n-\dfrac{8}{3}}[/tex]

Final answer:

The sequence increases by 5/3 with each term. Using the formula T(n) = T(1) + (n-1)d, where T(1) is the first term, n is the term number, and d is the common difference, the tenth term of the sequence is determined to be 14.

Explanation:

The sequence provided is -1, 2/3, 7/3, 4, 17/3. To find the pattern, let's examine the differences between the terms:

2/3 - (-1) = 5/3

7/3 - 2/3 = 5/3

4 - 7/3 = 5/3

17/3 - 4 = 5/3

It appears that this sequence increases by 5/3 with each term. To find the tenth term, we start by finding the number of steps to get from the first term to the tenth term, which is 9 steps (since we are already given the first term).

To calculate the tenth term, we use the formula for the nth term of a sequence with a common difference: T(n) = T(1) + (n-1)d, where T(1) is the first term, n is the term number, and d is the common difference.

T(10) = -1 + (10-1)(5/3) = -1 + 45/3 = 14

Therefore, the tenth term of the sequence is 14.

Answer:

7/32 square meters

Step-by-step explanation:

Multiply the fractions. The numerators multiply to 7*1 = 7. The denominators multiply to 4*8 = 32. This is why (7/8)*(1/4) = 7/32. The units are "square meters" to indicate we're dealing with area instead of a linear measurement.

note: 7/32 = 0.21875

Answer:

7/32 square meters

Step-by-step explanation:

The area of a rectangle is A = L * W.

Here, that area is A = (7/8)(meter)(1/4)(meter) = 7/32 meter^2.

Answer:

The expression = 6

Step-by-step explanation:

The expression is 30/r

30/r

Substitute r=5

30/5

6

Hello.

Y= 2/7

Step 1: Simplify both sides of the equation.

5y+2−3(4y)=0

5y+2+−12y=0

(5y+−12y)+(2)=0(Combine Like Terms)

−7y+2=0

Step 2: Subtract 2 from both sides.

−7y+2−2=0−2

−7y=−2

Step 3: Divide both sides by -7.

−7y/−7=−2/−7

y=2/7

Have a nice day.

Answer:

x = [tex]\frac{13}{2}[/tex]

Step-by-step explanation:

distribute parenthesis on both sides of the equation

6x - 9 = 4x + 4 ( subtract 4x from both sides )

2x - 9 = 4 ( add 9 to both sides )

2x = 13 ( divide both sides by 2 )

x = [tex]\frac{13}{2}[/tex]

Answer:

Step-by-step explanation:

2÷20= 10 × 300= 3,000 miles

The distance between her house and her cousin's house is 3000 miles.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 seconds

1 minute = 60 seconds

1 km = 1000 m

We have,

2 cm = 300 miles

The distance between her house and her cousin's house.

= 20 cm

= 10 x 2 cm

= 10 x 300

= 3000 miles

Thus,

3000 miles is the distance between her and her cousin's house.

Learn more about unit conversion here:

https://brainly.com/question/13899873

#SPJ3

Answer:

p=2

Step-by-step explanation:

3(p+1)=9

3 x ? = 9

3x3=9

p+1 = 3

P=2

3(2+1)=9

3(3)=9

9=9

BRAINLIEST?

Answer:

Step-by-step explanation:

divide by three on both sides of the equal sign.

Then subtract one from from both sides of the equal sign.

the answer is    p=2

3(p+1)=9

(p+1)=3

p=2

Problem 1)

This question is incomplete. It asks us to find something, but doesn't say what to find. It's literally blank after the word "find" which suggests your teacher made a typo. Please get back to me on this. Thanks.

===================================

Problem 2)

Angles GAR and GAT are supplementary because they are a linear pair. They form a straight angle. So we add up the expressions of x for each of these angles, solve for x, and use this to find angle GAR.

(angle GAR) + (angle GAT) = 180

(5x) + (3x+4) = 180

8x+4 = 180

8x+4-4 = 180-4

8x = 176

8x/8 = 176/8

x = 22

Note: now that I reached this point I realize that this might be the answer to problem 1; however, I'm not 100% sure because of the incomplete problem.

Use this x value to find angle GAR

angle GAR = 5*x

angle GAR = 5*22

angle GAR = 110

Unfortunately this answer isn't listed. I'm thinking your teacher made another typo.

===================================

Problem 3)

Answer: angle GAR and angle ABQ are corresponding angles.

Thankfully this answer is listed. Corresponding angles are angles that are on the same side of the transversal line and they are either both above or below the parallel lines they are next to. In this case, they are both above the parallel line counerparts.

===================================

Problem 4)

Corresponding angles are congruent as long as we have a set of parallel lines. So that means angle ABQ is equal to angle GAR. So angle ABQ is also 110 degrees

===================================

Problem 5)

angle BAT = angle GAR,  because they are vertical angles

angle BAT = 110

angle BAT = (angle BAD) + (angle DAT)

(angle BAD) + (angle DAT) = angle BAT

(100) + (angle DAT) = 110

angle DAT = 110-100

angle DAT = 10

angle ADB = angle DAT,  because they are alternate interior angles

angle ADB = 10

--------

Final Answer: 10 degrees

Answer:

see below    PLEASE GIVE BRAINLIEST

Step-by-step explanation:

Aiden's father will be 61 in 5 years:

61 - 5 = 56

Since Aiden is 1/7 of his father's age just divide his father's age by 7:

56 ÷ 7 = 8     Aiden is currently 8 years old.

Aiden                 his father                         is he 1/5 his fathers age

9                           57                                   9 x 5 = 45  NO

10                          58                                  10 x 5 = 50  NO

11                            59                                  11 x 5 = 55   NO

12                            60                                 12 x 5 = 60  YES

Aiden is 1/7 of his father's current age, and his father is currently 56. Given that we want Aiden's age to be 1/5 of his father's, the number of years that would need to pass is 14 years.

Firstly, let's determine Aiden's current age and his father’s current age. We know that Aiden's age is 1/7 of his father’s age, and that his father will be 61 in five years, meaning that his father is currently 56. Thus, Aiden, being 1/7 of his father’s age, is 8 years old.

Let's denote the number of years that we are looking for as 'x'. In 'x' years, Aiden will be 8+x years old, and his father will be 56+x. For Aiden’s age to be 1/5 of his father’s age, the following must be true: (8+x) = 1/5*(56+x). Solving this equation gives us x = 14. Therefore, in 14 years, Aiden's age will be 1/5 of his father's age.

https://brainly.com/question/23355172

#SPJ3

[tex]f(x)=-2x+7\\\\g(x)=x^2-2\\\\\ [f\ \circ\ g](x)=-2(x^2-2)+7=-2x^2+4+7=-2x^2+11\\\\\text{Put x = 3 to the equation of the function}\\\\\ [f\ \circ\ g](3)=-2(3^2)+11=-2(9)+11=-18+11=-7\\\\Answer:\ \boxed{-7}[/tex]

Answer:

The value of [f o g](3) is -7

Step-by-step explanation:

Given two functions

[tex]f(x)=-2x+7, g(x)=x^2-2[/tex]

we have to find [f o g](3)

[tex]f(x)=-2x+7[/tex]

[tex][f o g](x)=f(g(x))=f(x^2-2)=-2(x^2-2)+7[/tex]

[tex][f o g](x)=-2x^2+4+7=-2x^2+11[/tex]

Put x=3

[tex][f o g](3)=-2(3)^2+11=-7[/tex]

The value of [f o g](3) is -7

Option 1 is correct

Answer:

12+n+n+n

Step-by-step explanation:

3(n+4)

Distribute 3.

3 x n = n+n+n

3 x 4 = 12

12+n+n+n

Answer:

n/3 ≤ 15

Step-by-step explanation:

Quotient = n/3

The quotient cannot be greater than 15, but it can equal 15.

n/3 ≤ 15

The quotient of a number and 3 is no more than 15 represented by x/3 ≤ 15.

Problem-solving is defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. For example, a trainer may need to figure out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Solution:

let the number be X

x/3 ≤ 15

Quotient = x/3

Since the quotient cannot be greater than 15, it can equal 15.

                ∴ x/3 ≤ 15

Learn more about inequality here:-https://brainly.com/question/24372553

#SPJ2

Good morning Sir/Ma'am!

Answer:

A plane is a flat surface made up of points that extends infinitely in all directions.

Hope this helps! Have a great day!

~Sky

Answer: B

Step-by-step explanation:

Answer:

$16

Step-by-step explanation:

$10 is the original price when it is out of the factory. If they are marking it up, they are raising the price by 60%. 160% of 10 is 16, so your answer is $16. Please mark my answer as brainliest

Plz provide a 'Table'

Answer:

the answer is A.(4-g)1.5

Step-by-step explanation: