George baked a cake to share with his family. Jenny ate 15 of the cake and Brett ate 13 of the cake. How much of the cake did Jenny and Brett eat in all? Responses 215 of the cake 2 over 15 of the cake 28 of the cake 2 eighths of the cake 815 of the cake 8 over 15 of the cake 85 of the cake 8 fifths of the cake

The width of the tent is twice the width of one side which is 10.5 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high and the sides of the tent make a 50° angle with the ground.

Here the opposite is the height with the reference angle of 50° and we have to determine the adjacent which is the width of the tent.

∴ tan50° = Height of the pole/width.

1.19 = 6.25/width.

width = 6.25/1.19.

width = 5.25 feet.

But the total width of the tent will be twice as we have obtained only one side width.

∴ Total width is (2×5.25) = 10.5 feet.

learn more about trig ratios here :

https://brainly.com/question/14977354

#SPJ1

The total number of residents that voted in the town election is 5275 votes

Total number of votes received = 2300 votes

Consider the total number of votes in the town election = x

She received 190 more than 2/5 of the total number of votes

2/5 of the total number of votes = (2/5)x

190 more than 2/5 of the total number of votes = (2/5)x + 190

The equation will be

(2/5)x + 190 = 2300

Move 190 to the right hand side of the equation

(2/5)x = 2300 - 190

(2/5)x = 2110

0.4x = 2110

x = 2110 / 0.4

x = 5275 votes

Hence, the total number of residents that voted in the town election is 5275 votes

Learn more about equation here

brainly.com/question/14603452

#SPJ1

Answer:

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 12 on the left side and the dividend 6 on the right side like this:

 12 ⟌ 6    

Step 2:

The divisor (12) goes into the first digit of the dividend (6), 0 time(s). Therefore, put 0 on top:

      0    

 12 ⟌ 6    

Step 3:

Multiply the divisor by the result in the previous step (12 x 0 = 0) and write that answer below the dividend.

       0    

 1 2 ⟌ 6    

       0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (6 - 0 = 6) and write the answer below.

      0    

 12 ⟌ 6    

  - 0    

   6    

You are done.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 6 divided by 12 calculated using Long Division is:

0

6 Remainder

The percentage change from 48 to 90 is 87.5%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, 48 to 90 represents a increase. The increase will be:

= 90 - 48

= 42

The percentage increase will be:

= Increase / Original number × 100

= 42 / 48 × 100

= 87.5%

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

The required permutations are given as 168 letters will be formed.

Given that,
How many different 8-letter permutations can be formed from 6 identical h's and two identical t's is to be determined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
A total number of combinations = 8!
The number of repetitions,  = 5!.2!
Permutation of letters = 8!/[5!.2!]

Thus, the required permutations are given as 168 letters will be formed.

Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ1

Answer:

Rule SAS; side angle side

Step-by-step explanation:

Since they give that DM and CM are equal, and BM and AM are equal, you already have two sides. And since you have already marked vertical angles (correct because of intersection), you have 2 sides and 1 angle that are equal. This is enough to prove they are equal so it is the rule SAS or side, angle, side.

Any number apart from 3 can be used to replace the ? to create a function.

In a function, the inputs do not repeat that is the input in all cases should be unique in nature.

The inputs are assigned to exactly one output for each.

Three is one of the options to create a non function as three is already an input in the given function.

Replacing the ? with 3 would create the a function would be to replace it with any number but 3.

(3,5) (2, 4) (9, 0) (3,6)

Any number apart from 3 can be used to replace the ? to create a function.

To learn more about function refer here

https://brainly.com/question/2328150

#SPJ4

The required slope of the given line is 1 which is shown in the graph.

The slope of the line is represented as the rise of the line.

Slope m = (y₂ - y₁)/(x₂ -x₁  )

Grab two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

We take the two points (4, 10) and (9, 22)

Let

x₁ = 0, y₁ = 1

x₂ = 8, y₂ = 9

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula

m = (9 - 1) / (8 - 0)

m = (8)/(8)

m = 1

Thus, the required slope of the given line is 1 which is shown in the graph.

Learn more about the Slope of the Line here:

brainly.com/question/14511992

#SPJ1

[tex]\fbox{3x}[/tex]

Simplify:

[tex]x+y+2x+-y[/tex]

Combine Like Terms:

[tex](x+2x)+(y+-y)[/tex]

[tex]=3x[/tex]

Natasha has left with 4.5 inches of oak boards.

What is a simplification?

The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining trade processes.

Here, we have

120 inches of oak boards

50.75 inches for shelves, 36 1/4 more inches of oak boards, and she didn’t use 401/2 inches for the top and 60.5 inches for the sides.

We have to find how many inches of oak boards Natasha has left.

We use here simplification, we get

= 120 + 36 1/4 - 50.75 - 40 1/2 - 60.5

= 4.5 inches

Hence, Natasha has left with 4.5 inches of oak boards.

To learn more about the simplification from the given link

https://brainly.com/question/1280754

#SPJ1

Answer:

3w - 2j

Step-by-step explanation:

twice the length j less of three times the width

Answer:

3/10

Step-by-step explanation:

4/5 - ½

The l.c.m of the Denominator is 10

=8-5/10

=3/10

Answer:

3:1

Step-by-step explanation:

bc the lcm is 3

Answer:

the ratio is 3/1

The balance of the account after 1 year and after 2 years  16400 and 16820 is respectively.

A bank account starts with a balance, P = $8000

rate of interest = 5%

compound interest for 1 year is :

[tex]CI = P(1 + R/100)^n[/tex]

CI = 8000(1 + 5/100)

CI = 8000(1 + 1/20)

CI = 8000(21/20) = 8400

A = CI + P = 8000 + 8400 = 16400

compound interest for 1 year is :

[tex]CI = P(1 + R/100)^{2n}[/tex]

CI = 8000(1 + 5/100)^2

CI = 8000(1 + 1/20)^2

CI = 8000(21/20)^2 = 8820

A = CI + P = 8000 + 8820 = 16820

The balance of the account after 1 year and after 2 years  16400 and 16820 is respectively.

To know more about interest

https://brainly.com/question/25845758

#SPJ1

Answer:

95%

Step-by-step explanation:

An equation which has an extraneous solution is: C. √x = -5.

In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that isn't a direct solution (root) of the original equation.

This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that aren't solutions to the original equation as shown below:

Taking the fifth root of both sides of the equation, we have:

[tex]\sqrt[5]{x} = -2\\\\(\sqrt[5]{x})^5 = -2^5\\\\[/tex]

x = -32.

Taking the cubic root of both sides of the equation, we have:

∛(x + 1) = 10

[∛(x + 1)]³ = 10³

x + 1 = 1000

x = 1000 - 1

x = 999.

Taking the fourth root of both sides of the equation, we have:

[tex]\sqrt[4]{x-5} =3\\\\(\sqrt[4]{x-5})^4 =3^4[/tex]

x - 5 = 81

x = 81 + 5

x = 86.

Read more on extraneous solutions here: https://brainly.com/question/26218294

#SPJ1

Answer: 40%

Step-by-step explanation:

100(175-125/125)

Simplify: 100(50/125)

Simplify: 100(0.4)=40

Abe jogs 1. 8 miles on Monday, 1. 3 miles on Tuesday, and 1. 2 miles on Wednesday.

Beth will jog 8.6 miles, if she jogs twice as far as Abe.

The answer provided below has been developed in a clear step by step manner.

Step: 1

Given that,

Abe jogs 1.8 miles on Monday, 1.3 miles on Tuesday and 1.2 miles on Wednesday.

So,

Total miles jog by Abe =1.8+1.3+1.2

Step: 2

Adding, we get,

Total miles jog by Abe = 4.3 miles

To find :-

The number of miles Beth jogged.

Step: 3

Since Beth jogs twice as far as Abe, we have,

Number of miles Beth jog = 2×4.3 miles = 8.6 miles

Since Abe jog 4.3 miles in total, Beth will jog (2* 4.3) miles

Hence the answer is, Beth will jog 8.6 miles, if she jogs twice as far as Abe.

To learn more about probability click here https://brainly.com/question/24756209

#SPJ4

Step-by-step explanation:

-5x + 18 < -12

subtract 18 from both sides:

-5x + 18 - 18 < -12 - 18

-5x < -30

divide both sides by -5: [remember, when dividing by a negative number you must FLIP the sign direction]

(-5x)/-5 > (-30)/-5

x > 6

or

(6 , ∞)

The measure of the obtuse angle is 128 degrees

From the question, we have the following statement that can be used in our computation:

Acute angle = 52  degrees

The measure of the obtuse angle is calculated as

Obtuse angle = 180 - Acute angle

Substitute the known values in the above equation So, we have the following equation

Obtuse angle = 180 - 52

Evaluate

Obtuse angle = 128

Hence, the angle is 128 degrees

Read more about angles at

https://brainly.com/question/7620723

#SPJ1

The total number of small boxes is 2.1 and the large boxes is 6.3.

Given;

To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 150 nails in each small box and 400 in each large box. The contractor purchased 3 more tiny boxes than large boxes. Totaling 2850 nails.

To calculate the proportion of small and large boxes that were bought,

Let's assume the small boxes as 's' and the big boxes as '3s'.

∴ s(150) + 3s(400) = 2850

  150s + 1200s = 2850

  1350s = 2850

  s = 2850/1350

  s = 2.1

∴ 3s = 2.1 * 3

      = 6.3

Hence, the total number of small boxes is 2.1 and the number of large boxes is 6.3.

To learn more about proportion click here:

brainly.com/question/12235587

#SPJ4

Answer:

The number of small boxes purchased are 3 and the number of large boxes purchased are 6.

Step-by-step explanation:

Let the small boxes bought be x

Therefore the large boxes will be 2x

Total nails bought = 2850

Nails in x small boxes = 150x

Nails in 2x large boxes = 400. 2x = 800x

2850 = 150x + 800x

2850 = 950x

x= 2850/950 =  3

2x = 2x3= 6

Equation with option B and C has no solution.

What is equation?

When two expressions are connected with the equals sign, a formula known as an equation is created.

Main Body:

A) -3(x+5) = x-15 -2x

⇒ -3x -15 = x-15-2x

⇒ -3x = -x

⇒ -2x= 0

⇒ x = 0, this means it has a solution.

B) -3(x+5) = x- 15 -4x

⇒ -3x -15 = -3x -15

So this equation also has no solution.

as L.H.S cancels out R.H.S completely so this equation has no solution.

C) -3(x+5) = x-10 -4x

⇒ -3x -15 = -3x -10

⇒ -15 ≠ 10

hence the equation with no solution is option b and c.

To learn more about equation click on the link below

https://brainly.com/question/25896797

#SPJ9

The 12 terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

The formula to calculate the nth term of an Arithmetic Sequence is -

a(n) = a + (n - 1)d

a - first term of A.P.

d - Common difference of A.P.

n - position of term

We have -

a[1] = 3

a[12] = 25

Then, using the formula to calculate the nth term, we get -

a(n) = a + (n - 1)d

a[1] = 3

AND

a(12) = 3 + 11 x d

25 = 3 + 11d

22 = 11d

d = 2

So, the terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

Hence, the 12 terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

To solve more questions on Arithmetic Sequences, visit the link below-

brainly.com/question/19828148

#SPJ1

I gotchu :)

So, the base equation is: ax+by=c

x int is c/a

y int is c/b

and the slope is -a/b

So basically, what I wrote above is how to get each aspect of the line using the standard form formula.

The "nonzero" part means that each integer (the A, B, AND C in the formula above) cannot be 0, as that would mean that everything will end up equaling to 0, which does not create the line. So basically, the answer would be:

x int is c/a

y int is c/b

and the slope is -a/b

^ if you apply these to any standard form, you will get the thing I stated next to it. For example, if the standard form equation is:

5x+6y=5

if you want to find the slope, you will do -a/b, and that will give you -5/6, which is your slope

Hope this helps :)

Answer:

c = 121

Step-by-step explanation:

Take half of the middle term coefficient: -22/2 = -11

Now square it: (-11)² = 121

c = 121

Answer:  a)  y - 4 = 2/3(x) - 2

b)  y - 4 = -3/2(x) -2

Step-by-step explanation:

equation of original line:  y = 2/3x -5

point on a line parallel to original line:  (3,4)

The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:

(y - y1) = 2/3(x - x1)

point (x1, y1) is (3, 4)

plug (3,4) into the equation:

y - 4 = 2/3(x - 3)

y - 4 = 2/3(x) - 2

rewrite in slope-intercept form:  y = 2/3(x) + 2

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line:  - 1/m

Therefore, the slope of the perpendicular line = -3/2

Equation for the perpendicular line is:

y - 4 = -3/2(x) -2

Answer: D. 16/25

Step-by-step explanation:

The time taken in minutes to fill a tank having a capacity or work of 1.5m³ is 1.2 minutes;

What are Time and Work?

According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.

The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.

W is the amount of work done.

N is the number of people.

D is the number of days or hours needed.

In the question, It is given that:

water flowing off a certain pipe is 75 liters per minute;

and;

the tank has a capacity of 1.5m³

First converting the Efficiency in liters per second,

So,

water flowing off a certain pipe is 75 liters per minute;

So, dividing it by 60 ;

Water flowing off the pipe = 1.25;

Now using the work-time relationship:

Efficiency × Time = work;

So,

1.25×Time = 1.5

⇒Time = 1.2

So, the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;

Hence,

the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;

To learn more about work and time, visit:

https://brainly.com/question/25748643

#SPJ1