14 friends go out for dinner and the bill for food and drink comes to £130. The friends decided to add a 5% tip on the top of this total. If they divide this expense equally between them, How much does each friend pay?

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]

Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.

According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.

90 + 7x - 20 + 4x = 180

70 + 11x = 180

11x = 180 - 70

11x = 110

11x/11 = 110/11

x = 10

m∠ACB = 7x - 20

Plug in the value of x

m∠ACB = 7(10) - 20

m∠ACB = 50° (option B).

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Answer:

see the attachment photo!

Answer:

360 people out of 1200 are likely to have red hair.

Step-by-step explanation:

So I just saw that 100 x 120 equals 1200. So I just need to multiply 3 x 120 and I got 360. I think this is how to solve?

If Tyler sold his car for $9200, then the approximate percentage profit for this product is 33.3%.

Final price - initial price

Calculate the percentage $2300 is equivalent to by using the information you already have.

33.3% is the profit percentage.

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If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-3, 6), (-3, 3) and (-1, 3)

Translation is a way of changing the position of an object on the xy plane

Given the coordinates of the vertices (1, 4), (1, 1), (3,1)

If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-3, 6), (-3, 3) and (-1, 3)

Note that 4 was subtracted from the x-axis and 2 added to the y-coordinates.

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Those two have both two formulas but when dealing with a not-right triangle which is a particular case you use this formula for sines.

[tex]\frac{SinC}{c} =\frac{SinR}{r}[/tex]

Substitute

Note: the capital letters are for the angles and the small letter are for the sides.

But since we used side R and there is no angle to substitute. you will basically have to find it by adding the two angles given and subtracting it by 180, which is a 100.

[tex]\frac{Sin(7)}{1.9} =\frac{Sin100}{x}[/tex]

now you do the butterfly method or cross multiplication method.

[tex]xsin(7)=1.9sin(100)[/tex]

You have to isolate the x

[tex]\frac{xsin(7)}{sin(7)} =\frac{1.9sin(100)}{sin(7)}[/tex]

now cancel and plug the right side of the equation into your calculator and u get the answer for the missing side.

[tex]x= 15.35[/tex] or if u want to round it [tex]15.4[/tex]

<R = 100 and side CK= 15.35 or 15.4

Hope I helped! ^w^

TheOneAndOnlyLara~

Answer:

Sasha has used the theoretical probability which assumes that all the possibilities have an equal chance of occurring but in reality, the chances of each probability happening are not going to be equally split with the chances of the bus being on time being slightly higher than being early or late. This is called the experimental probability where you actually test out the probability of the bus being on time, early or late which is much more accurate than the general, theoretical probability.

Answer:

The distribution of the ages of vice president shows that the youngest age is about 36 while the oldest age is around 72. The median age of vice president is 53. On the lower end, the common age is 48 while the age of 60 is upper median age.

Answer:

a) 3x⁴-4x³-8x²-35x-10

Step-by-step explanation:

3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10

3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10

3x⁴-4x³-8x²-35x-10

The expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

An expression is combination of variables, numbers and operators.

The area (w) of Vanessa's patio can be found by multiplying the length and width expressions:

w = (3x² + 5x + 10)(x² – 3x - 1)

Expanding this expression using the distributive property, we get:

w = 3x⁴ - 4x³ - 8x² + 15x³ - 25x² - 10x + 10x² - 30x - 10

Simplifying this expression, we get:

w = 3x⁴ + 11x³ - 15x² - 40x - 10

Hence, the expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

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The class which has a greater percent of students who ride the bus is Walter's class

Walter's class:

Percentage of students who ride bus = 14 / 15 × 100

= 0.933 × 100

= 93.3%

Sasha's class:

Percentage of students who ride bus = 11 / 20 × 100

= 0.55 × 20

= 55%

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Answer:

I think the answer is 1,714 tubes

Step-by-step explanation:

The number of second it takes the apple to hit the ground is 4 seconds

To answer the question, we need to know what functions are

Functions are mathematical equations that show the relationship between two variables

Given that when an apple is dropped from a tower 256 feet high, the function h(t) = -16t² + 256 modelshe height of the apple, in feet, after t seconds.

The time it takes the apple hits the ground is when h(t) = 0

So, h(t) = 0

-16t² + 256 = 0

-16t² = -256

t² = -256/-16

t² = 16

t = ±√16

t = ±4

Since t ≥ 0, t = 4 seconds

So, the number of second it takes the apple to hit the ground is 4 seconds

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Answer:

i just need points

Step-by-step explanation:

sorrry ehburbvuygvuywhefe2b yvfb we

Answer:

360 g

Step-by-step explanation:

Amount of Salt = 2.5% x Amount of Mango

Taking 9 g as the amount of salt :

Answer:

the answer is  4.979

Step-by-step explanation:

Answer:

The answer is 4.979

Step-by-step explanation:

The area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively, option (a) is correct.

It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.

We know the area of the kite = pq/2

Where p and q are the length of the diagonals

p = 10+10 = 20 ft

q = 7+11 = 18 ft

Area = (20×18)/2

Area = 180 square feet

Thus, the area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively option (a) is correct.

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Answer:

10 degrees

Step-by-step explanation:

A straight line equals 180 degrees. We already know we have 110 degrees, so we subtract 180-110 and get 70. Now, we can set up an equation:

We have to isolate x, so divide both sides by 7

70=7x

_____  =  10=x

   7

x=10 degrees

Hope this helps!

Answer:

$42.80

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 9.75%/100 = 0.0975 per year.

Solving our equation:

A = 39(1 + (0.0975 × 1)) = 42.8025

A = $42.80

The total amount accrued, principal plus interest, from simple interest on a principal of $39.00 at a rate of 9.75% per year for 1 years is $42.80.

Answer:

Sales tax is $3.8.  So total would be 39.00+3.8= $42.8

Step-by-step explanation:

Answer:

Point C

Step-by-step explanation:

Answer: Point C

Step-by-step explanation: I hope this helped! :D

Answer:

3

Step-by-step explanation:

got it on edge

Answer: -7 < x < 3

Step-by-step explanation:

-21 < 3x < 9

-7 < x < 3

Answer: See the screenshots below

I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).

All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.

[tex]\large\boxed{Formula: I= \frac{PRT}{100}}[/tex]

First, we'll have to multiply, principal amount (12500), rate (10) and time period (3).

[tex]12500×10×3[/tex]

[tex]=375000[/tex]

Now, we'll have to divide the amount (375000) by 100.

[tex]\frac{375000}{100}[/tex]

I=$3750

Now, we can find the total amount paid.

[tex]\large\boxed{A=SI+P}[/tex]

Let's substitute according to the formula.

[tex]A=3750+12500[/tex]

A=$16250

Therefore, simple interest is $3750 and $16250 was paid in total.

Answer:

9 is 15% of 60.

Step-by-step explanation:

[tex]\text{Formula}=\frac{\text{Number x 100}}{\text{Percent}} =\frac{9 \times100}{15} =60[/tex]

Following shows the steps on how to derive this formula and find out 15% of what number is 9.

Step 1: If 15% of a number is 9, then what is 100% of that number? Setup the equation.

[tex]\frac{9}{15} = \frac{Y}{100}[/tex]%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

[tex]15Y=6\times100\\15Y=600[/tex]

Y = [tex]\frac{600}{100} =60[/tex]

The requried 15% of 60 is equal to 9, as of the given percentage situation.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To find the number that 15% of is equal to 9, we can set up a proportion:

15% of x = 9

Converting 15% to a decimal:

0.15x = 9

Dividing both sides by 0.15 gives:

x = 60

Therefore, 15% of 60 is equal to 9.

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Answer:

28

Step-by-step explanation:

[tex]sin=\frac{opp}{hyp}[/tex]

[tex]cos = \frac{adj}{hyp}[/tex]

[tex]cos^{-1}\left(\frac{45}{51}\right)[/tex]

which is 28.07 degree

[tex]sin\left(28.07\right)=\frac{x}{51}[/tex]

x= 23.99

23.99+4=h=28

Answer:

The slope of the line y = x + 1 is equal to 1.

General Formulas and Concepts:
Algebra I

Slope-Intercept Form:
[tex]\displaystyle y = mx + b[/tex]

Step-by-step explanation:

Step 1: Define

Identify given equation.

[tex]\displaystyle y = x + 1[/tex]

Step 2: Find Slope m

Let's compare our given equation to the general equation Slope-Intercept Form to identify our values for slope m and y-intercept b:

We can see that our y-intercept b is equal to 1. Let's rewrite our given expression:

Here, we can identify our slope m to be 1.

∴ the slope of the given line is equal to 1.

___

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Topic: Algebra I

50 students preferred science...

Explanation:

we can consider the numbers 5 and 4 in the ratio as units

now we need to know how much each unit represent

units = 5 + 4 = 9

my sample = 90 students

each unit = 90/9 = 10 students

so each unit represents 10 students

back to the ratio

who preferred science = 5

who preferred English = 4

Number of students choose Science = 5 * 10 = 50