A group of six friends went out to eat. The final bill for the meal was $80.52. if they split the bill evenly, how much will each person pay?

The fraction in its lowest terms for 7 1/2 percent is 3/40.

To express the mixed number 7 1/2 percent as a fraction in its lowest terms, we need to convert it to a fraction and simplify.

First, we convert the mixed number to an improper fraction:

7 1/2 percent = 7 1/2 / 100

To simplify this fraction, we find the least common multiple (LCM) of the denominator (2) and the percent denominator (100), which is 200.

Now, we can rewrite the fraction with the common denominator:

7 1/2 / 100 = (7 * 2 + 1) / 200 = 15/200

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 200 is 5.

15/200 = (15 ÷ 5) / (200 ÷ 5) = 3/40

Therefore, the fraction in its lowest terms for 7 1/2 percent is 3/40.

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Answer:

63

Step-by-step explanation:

Answer:

117°

Step-by-step explanation: We know that the angles of a triangle have to equal 180°. We already know one angle (75°) and we can find the others. Vertical angles are congruents so the angle opposite 42° is also 42° So add 42 and 75 and you get 117. Keep in mind that all the angles have to equal 180 so 180-117 will get you the last angle measure. 180-117= 63. BUT that's not the answer because that is not x and it asks for x. So we know that a straight line also equals 180 that angle that we found that was 63 plus x should get us 180. To find that we do 180-63 and find that x=117° Hope this made sense!

Answer:

Step-by-step explanation:

total eggs= 600

2/5 ( total eggs)= duck eggs

2/5(600)= 240

duck eggs= 240

chicken eggs= 600-240= 360.

after eggs broke, let x be the new total eggs remaining.

8/15 (x) = 240

x= (240 x 15)/8

x= 450 total eggs.

450-240= chicken eggs remaining

chicken eggs remaining= 210

360-210= broken chicken eggs

broken chicken eggs= 150 Ans

Answer:

the numbers are 4 and 7

Step-by-step explanation:

"twice a number added to another number is 15" --- 4(2) + 7 = 15

"the sum of the two numbers is 11" --- 4 + 7 = 11

Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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Work Shown for problem 1

P(pink, then violet) = P(pink)*P(violet given 1st was pink)

= (4/14)*(2/13)

= 8/182

= 4/91

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

Work Shown for problem 2

P(gray, then gray)

= P(gray)*P(gray given 1st was gray)

= (3/14)*(2/13)

= 6/182

= 3/91

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

Work Shown for problem 3

P(not yellow, not yellow)

= P(not yellow)*P(not yellow given 1st was not yellow)

= (9/14)*(8/13)

= 72/182

= 36/91

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

Work Shown for problem 4

P(yellow, not yellow)

= P(yellow)*P(not yellow given 1st was yellow)

= (5/14)*(9/13)

= 45/182

Answer:

it's answer is D. 33°

Let the unknown angle be x Then.

x + 100° + 47° = 180° [ being sum of angles of triangle ]

x + 147° = 180°

x = 180° - 147°

x = 33°

Step-by-step explanation:

123-50=73

Step-by-step explanation:

its pretty basic, subtract the amount his uncle gave him from what he has now

Answer:

Pvalue > α ; We fail to reject the Null; hence no significant difference exists in the average prices of the two supermarkets.

(−68.1095 ; 57.8545)

Step-by-step explanation:

Given the data:

Week Advertiser ($) Competitor ($) 1 254.27 255.93 2 240.72 255.65 3 231.91 255.12 4 234.15 261.28

Difference, d :

254.27 - 255.93 = - 1 66

240.72 - 255.65 = - 14.93

231.91 - 255.12 = - 23.21

234.15 - 261.28 = - 27.13

d = -1.66, -14.93, 23.21, -27.13

Using calculator :

Mean difference , dbar = - 5.1275

Standard deviation of mean , Sd = 21.566

H0 : μd = 0

H1 : μd ≠ 0

Test statistic :

(dbar - μd) / s/√n

(-5.1275 - 0) / (21.566/√4)

-5.1275 / 10.783

= −0.475517

Using the Pvalue from Tscore Calculator ; df = 4 - 1 = 3

Pvalue = 0.66659

Pvalue > α ; We fail to reject the Null; hence no significant difference exists in the average prices of the two supermarkets.

Confidence interval :

dbar ± standard Error

Standard Error = Tcritical * Sd/√n

dbar = - 5.1275

Tcritical at 0.01 = 5.941

Standard Error = 5.8409 * 21.566/√4 = 62.982

Confidence interval :

Lower boundary : - 5.1275 - 62.982 = −68.1095

Upper boundary = - 5.1275 + 62.982 = 57.8545

(−68.1095 ; 57.8545)

The true population on difference exist within the interval

Answer:

y=4/3x-1

Step-by-step explanation:

Answer:

Yes.

because yea

Answer:

13

Step-by-step explanation:

Hence, the required inequality is x+y≤4, 7x+4y≤1150

inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Let x be the number of adults and y be the number of campers.

There are rooms for 450 people, so

x+y≤450.

Each adult costs $7, then x adults cost $7x.

Each camper costs $4, then y campers cost $4y.

There is a maximum budget of $1,150, so

7x+4y≤1,150

Hence, you get the system of two inequalities:

         x+y≤4

         7x+4y≤1150

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Answer:

x + y \(\leq\) 450

7x + 4y \(\leq\) 1,150

Step-by-step explanation:

X and Y is the amount of people it can fit.

7 and 4 is the amount of money for each person.

7x is the amount per adult, 4y is the amount per camper.

Hope this helps.

Answer:

33%

Step-by-step explanation:

According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.

To find the wide variety of girl population, we will subtract the quantity of male population from the full population.

Total population = 88,51,84,692

Number of male = 45,40,34,570

Number of female = Total population - Number of male

= 88,51,84,692 - 45,40,34,570

= 43,11,50,122

Therefore, the number of female population is 43,11,50,122.

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Answer:

Step-by-step explanation:

Answer:111

Step-by-step explanation:

1111

Answer:

Alex can buy 12 bottles of lemon-lime soda and 6 bottles of cranberry juice.

Step-by-step explanation:

Since Alex found a new fruit punch recipe that calls for cranberry juice and lemon-lime soda, if cranberry juice costs $ 3.60 per bottle and lemon-lime soda costs $ 1.40 per bottle and the recipe calls for 2 times as many bottles of lemon-lime soda as cranberry juice, to determine at most how many bottles of cranberry juice can he buy if he only has $ 38.40 the following calculation must be performed:

20 x 1.40 + 10 x 3.60 = 64

10 x 1.40 + 5 x 3.60 = 32

12 x 1.40 + 6 x 3.60 = 38.40

Therefore, Alex can buy 12 bottles of lemon-lime soda and 6 bottles of cranberry juice.

Answer:

scale

Step-by-step explanation:

scales are used to measure weight

The tool that Caroline can use to Measure the mass of a dictionary is; Pan Balance.

When discussing measurements, there are different tools and equipment's that can be used such as  Ruler, Pan balance, Stopwatch, Liter container.

Now, the tools above can be used for measuring different things but our question wants the one that would be used to measure the mass of a dictionary and the correct tool is a Pan Balance.

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Answer:

Anything 5 and above.

Step-by-step explanation:

The sign that is shown is the less than or equal to sign, which means whatever is added to seven, the sum would have to be 12 or above? or it wouldn't work.

Answer:

blue and red

Step-by-step explanation:

hope it helped

Based on these considerations, it is necessary to assess the specific layout plan and the surrounding environment to determine whether the copier is suitably placed in room (3) at Hills Secondary.

To determine whether the copier is suitably placed in room (3) at Hills Secondary, we need to consider factors such as accessibility, noise, and convenience.

Firstly, we need to evaluate the accessibility of the copier in room (3). Is it easily accessible for all students and staff who need to use it? If the copier is located in a central position within the school or close to high-traffic areas, it would be considered suitable.

However, if it is tucked away in a corner or not easily visible, it may cause inconvenience and hinder access for users.

Secondly, we should consider noise levels. Copiers can be noisy machines, and if room (3) is located near classrooms or areas where students require a quiet environment, it may not be an ideal placement. Noise disturbances could disrupt learning activities and cause distractions.

Lastly, convenience plays an important role. Room (3) should be spacious enough to accommodate the copier and allow users to operate it comfortably. If the room is cramped or lacks proper ventilation, it may cause inconvenience for users and impact the overall workflow.

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After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.

The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted  measurement regarding the distance around the outside of a two-dimensional shape. In this system  the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22\)

Jace bought 4 cookies and 2 brownies from the bakery.

Let x represent the number of cookies and y represent the number of brownies.

Since he bought $9 worth of cookies and brownies. Each cookie costs $0.75 and each brownie costs $3. hence:

0.75x + 3y = 9      (1)

Also, he bought twice as many cookies as brownies, hence:

x = 2y

x - 2y = 0     (2)

Solving equation 1 and 2 simultaneously gives x = 4, y = 2

Hence Jace bought 4 cookies and 2 brownies from the bakery.

Answer:

96 square feet

Step-by-step explanation:

Area= length x width

So for the rug it would be 12x8

12x8=96

Answer:

600,000

Step-by-step explanation:

60,000 x 10

Answer:

hello

Step-by-step explanation:

have a great day...

Answer: The matrix A of the linear transformation T(f(t)) = f''(t) + 3f'(t) + 7f(t) from the space spanned by the functions cos(t) and sin(t) into itself with respect to the basis {cos(t), sin(t)} can be found by computing the images of the basis vectors under T and expressing those images as linear combinations of the basis vectors.

We have:

T(cos(t)) = -cos(t)'' - 3cos(t)' - 7cos(t) = -cos(t) - 3(-sin(t)) - 7cos(t) = -8cos(t) - 3sin(t)

T(sin(t)) = -sin(t)'' - 3sin(t)' - 7sin(t) = -sin(t) - 3cos(t) - 7sin(t) = -8sin(t) + 3cos(t)

So, with respect to the basis {cos(t), sin(t)}, the matrix A is:

A = [ -8, -3; 3, -8 ]

This is the matrix representation of the linear transformation T with respect to the basis {cos(t), sin(t)}.

Step-by-step explanation:

Answer:

2715

Step-by-step explanation:

10860/4 = 2715

if im wrong smite me