Over three years ago Lucius a $550 $600 and $650 from Babysitting the polynomial 550 X to the 3rd+600 X squared +650 X represents her savings with interest after three years the annual interest rate equals X minus one find the interest needed so that she will have $200 after three years

Answer:

Step-by-step explanation:

DE*s=BA  24*s=35 s=35/24

(3x+7)35/24=6x-5

35/8x+5/24=6x-5

          -5/24    -5/24

Answer:

11. B

12. A

14. C

16. D

18. A

Answer:

42 liters

Step-by-step explanation:

Set up the ratios as fractions.

6/7 = 36/x

To get the volumes multiply the 6 and the 7 by 6.

This is how you got the 36 for the first volume.

The volume of the second container is 42.

7 x 6 = 42

Step-by-step explanation:

To solve this question I would use the sin rule.

The sin rule states that

[tex] \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) } [/tex]

Therefore if you substitute in your numbers you get:

[tex] \frac{a}{ \sin(90) } = \frac{15}{ \sin(60) } [/tex]

If you rearrange that you get:

[tex]a = \frac{15}{ \sin(60) } \times \sin(90) [/tex]

Therefore a = 17.3 Inches (to 3 sf)

This can also be done with basic trigonometry where you would get

[tex] \sin(60) = \frac{15}{h} [/tex]

Rearranging to

[tex]h = \frac{15}{ \sin(60) } [/tex]

meaning the answer is 13.7 inches

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

Work Shown:

h = unknown hypotenuse

sin(angle) = opposite/hypotenuse

sin(60) = 15/h

h*sin(60) = 15

h*sqrt(3)/2 = 15

h*sqrt(3) = 2*15

h*sqrt(3) = 30

h = 30/sqrt(3)

h = (30*sqrt(3))/(sqrt(3)*sqrt(3)

h = 30*sqrt(3)/3

h = (30/3)*sqrt(3)

h = 10*sqrt(3)

Answer:

P(A' U B) = 84/100

Step-by-step explanation:

We have, P(A) = 86/100

P(B) = 79/100

P(A') = 7/50

P(A U B) = 95/100

-: P(A intersection B) = P(A) + P(B) - P(A U B)

P(A intersection B) = 86/100 + 79/100 - 95/100

P(A intersection B) = (86+79-95)/100 = (165-95)/100

P(A intersection B) = 70/100

Now, P(A' U B) = P(A') + P(A intersection B)

P(A' U B) = 7/50+70/100

P(A' U B) = (7*2+70)/100 = (14 + 70)/100

P(A' U B) = 84/100

Answer:

d) Clothing prices decline because manufacturers shift to production in countries with lower wages.

Step-by-step explanation:

Demand is the quantity of goods or services consumers are able and willing and able to buy at a given price and at a particular time.

Movement along the demand curve also known as change in quantity demanded is an increase or decrease in the quantity demanded of goods or services due to change in the price of the good or service itself.

It is important to note that the only factor causing movement along the demand curve is change in the price of the product.

Answer:

Step-by-step explanation:

#2 the answer is B, -16/9

do 1/4-5/2

to do this, find the least common denominator. it's 4

1/4-10/4=-9/4

then divide 4 by -9/4. This is the same as 4*-4/9. That is -16/9

#3 the answer is A 9x/x-8

first factor the denominator of the first fraction using special products

x^2-6x-16=(x-8)(x+2)

if you look at the first fraction, you can simplify x+2 leaving you with the fraction 1/x+8

multiply that by 9x, and you get 9x/x-8

#4 the answer is C (2x+1)/2x^2

first add x/4 and 1/8

find the least common denominator. its 8

2x/8 + 1/8 is equal to (2x+1)/8

then multiply that by x^2/4 because dividing a fraction is the same as multiplying its reciprocal

you get (2x+1)/2x^2

#5 the answer is C (x-8)/(x+3)

using special products you can factor the numerator

x^2-4x-32 is the same as (x-8)(x+4)

then, using special products you can also factor the denominator

x^2+7x+12 is the same as (x+4)(x+3)

you can see that both the numerator and the denominator is multiplied by (x+4) you can simplify that. That leaves you with (x-8)/(x+3)

#7 the answer is D 3m

in the numerator in the second fraction, you can factor out 5m^2

leaving you with 5m^2(m-6)/5m^2. simplify the 5m^2 and the m-6

after you simplify both of those, you will get 3m

Answer: A) Stratified random sampling

Step-by-step explanation:

Since , the researchers divided college students into the four classes (freshman, sophomore, junior, and senior) and then took a random sample of students from each class.

That means each category is participating in the sample.

It means , they used stratified sampling method where each class denotes a strata.

Here ,  each category participates in researcher's analysis.

Hence, the correct answer is A) Stratified random sampling .

Answer: 0.383 and 0.6671

Step-by-step explanation:

Take 22%, that is 0.22 to be probability of success.

That means "1-0.22 = 0.78" is the probability of failure.

When dealing with selection in probability mathematics, the combination equation is used.

Probability of selecting number 'r' as a successful outcome from a given number 'n' is given as

nCr * p^r * q^n-r

Where p is the probability of success= 0.22

q is the probability of failure= 0.78

n is the total number of sample =10

r is the varying outcome of number of success.

For the first question, number of success is asked to be everything more than 2, that is probability of choosing 3,4,5,6,7,8,9,10 people with a successful outcome (adults who will pay more for environmentally friendly product.)

Instead of going through the long process of checking probability of success for choosing 3,4,5,6,7,8,9,10 adults who will pay more, we can simply find the probability of choosing 0,1,2 adults who will pay more and subtract the answer from 1.

By doing this, we first check for probability of choosing 0 adult that will pay More and this is gotten by putting r=0 in our probability Formula. The Formula becomes

=10C0 * 0.22^0 * 0.78^10

=1 *1 * 0.0834= 0.0834

Hence, Probability of Choosing 0 adult that will Pay more is 0.0834

To Check for probability of choosing 1 adult that will pay more becomes

=10C1 * 0.22^1 * 0.78^9

=10 * 0.22 * 0.1069 = 0.2352

Hence, Probability of choosing 1adult that will pay more = 0.2352

To Check for the probability of choosing 2adults that will pay more becomes

=10C2 * 0.22^2 * 0.78^8

=45 * 0.0484 * 0.1370 = 0.2984

Therefore the total sum of choosing 0,1,2 adults that are willing to pay more becomes

= 0.0834+ 0.2352+ 0.2984 = 0.617

So to determine the probability of choosing more than 2 adults, that is, 3,4,5,6,7,8,9,10 adults that are willing to pay more, we subtract 0.617 from 1.

This gives 1-0.617 = 0.383

Hence, probability of choosing more than 2 people that are willing to pay more than 2 = 0.383.

To determine the probability of choosing between two and five people inclusive, we follow the same probability formular but r becomes 2,3,4,5 differently.

For probability of choosing 2 adults, we already calculated it to be 0.2984 earlier.

For probability of choosing 3 adults, it becomes

10C3 * 0.22^3 * 0.78^7

=120* 0.0106 * 0.1757 = 0.2235

For the probability of choosign 4 adults, it becomes

10C4 * 0.22^4 * 0.78^6

= 210 * 0.0023 * 0.2252 = 0.1088

For the probability of choosing 5 adults, it becomes

10C5 * 0.22^5 * 0.78^5

= 252 * 0.0005 * 0.2887 = 0.0364

Hence, the probability of choosing between 2 and 5 adults becomes

0.2984 + 0.2235 + 0.1088 + 0.0364 = 0.6671

To find the probability of the number of adults who would pay more for environmentally friendly products, use the binomial probability formula.

To find the probability of the number of adults who would pay more for environmentally friendly products, we need to use the binomial probability formula.

The formula is: P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where:

Let's calculate the probabilities for the given scenario:

P(X > 2) = 1 - P(X <= 2)

P(X between 2 and 5 inclusive) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Question is Incomplete; Complete question is given below;

3 rectangular prisms have a combined volume of 518 cubic feet. Prism A has 1/3 the volume of Prism B. Prisms B and C have equal volume.What is the volume. What is the volume of each prism.

Answer:

Volume of prism A is [tex]74\ ft^3[/tex] and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].

Step-by-step explanation:

Let the Volume of 3 prism be A,B,C.

Now Given:

3 rectangular prisms have a combined volume of 518 cubic feet.

so we can say that;

[tex]A+B+C=518 \ ft^3 \ \ \ \ equation \ 1[/tex]

Also Given:

Prisms B and C have equal volume.

[tex]B = C[/tex]

Also given:

Prism A has 1/3 the volume of Prism B.

so we can say that;

[tex]A=\frac{B}{3} = \frac{C}{3}\\\\B=C=3A[/tex]

Now Substituting the value of B and C in equation 1 we get;

[tex]A+B+C=518\\\\A+3A+3A=518\\\\7A=518[/tex]

Dividing both side by 7 we get;

[tex]\frac{7A}{7}=\frac{518}{7}\\\\A= 74 \ ft^3[/tex]

Now Substituting the value of A to find B and C we get;

[tex]B=C=3A=3\times74=222\ ft^3[/tex]

Hence Volume of prism A is [tex]74\ ft^3[/tex]  and Volume of Prism B and Volume of Prism C is [tex]222\ ft^3[/tex].

Answer:

152.6$

Step-by-step explanation:

35*4=140

Need to find the new amount since it was decreased by 18%

35*18/100=6.30

6.30+6.30

12.6

140+28.7=152.6

Answer:

Kim and Lauren have 5 more hours to reach Pennsylvania.

Step-by-step explanation:

Given,

Total distance = 680 miles

We have to find the number of hours taken by them to reach Pennsylvania.

Solution,

For Day 1:

Speed = [tex]60\ mi/h[/tex]

Time = 3 hrs

We know that the distance is equal to speed multiplied with time.

So the equation is;

[tex]Distance = 60\times3=180\ miles[/tex]

For Day 2:

Speed = [tex]65\ mi/h[/tex]

Time = 5 hrs

We know that the distance is equal to speed multiplied with time.

So the equation is;

[tex]Distance = 65\times5=325\ miles[/tex]

Now the total distance traveled in two  days is the sum of distance traveled in day 1 and distance traveled in day 2.

Distance traveled in 2 days = [tex]180+325=505\ miles[/tex]

So the remaining distance they have to travel is equal to total distance minus distance traveled in 2 days.

Remaining distance =[tex]680-505=175\ miles[/tex]

Now also given that the speed on day 3 is [tex]35\ mi/h[/tex].

So the time taken to cover the distance is equal to distance divided by speed.

[tex]\therefore time=\frac{175}{35}=5\ hours[/tex]

Hence Kim and Lauren have 5 more hours to reach Pennsylvania.

Answer:

Option C) -cosu is correct

Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]

Step-by-step explanation:

Given expression is [tex]cos(u+\pi)[/tex]

To find the value of the given expression :

By using the formula [tex]cos(A+B)=cosAcosB-sinAsinB[/tex]

Substitute A=u and [tex]B=\pi[/tex] in the above formula we get

[tex]cos(u+\pi)=cosucos\pi-sinusin\pi[/tex]

[tex]=cosu(-1)-sinu(0)[/tex]  ( here [tex]cos\pi=-1[/tex] and [tex]sin\pi=0[/tex] )

[tex]=-cosu-0[/tex]

[tex]=-cosu[/tex]

[tex]cos(u+\pi)=-cosu[/tex]

Therefore option C) -cosu is correct

Therefore the simplified expression is [tex]cos(u+\pi)=-cosu[/tex]

Answer:tony was billed for 154 minutes.

Step-by-step explanation:

Let x represent the number of minutes for which Tony was billed.

For his long distance phone service, Tony pays an $8 monthly fee plus 6 cents per minute. Converting 6 cents to dollars, it becomes 6/100 = $0.06

This means that if he made x minutes of long distance call in a month, the total cost would be

8 + 0.06x

Last month, Tony's long distance bill was $17.24. It means that

8 + 0.06x = 17.24

0.06x = 17.24 - 8 = 9.24

x = 9.24/0.06

x = 154

Step-by-step explanation:

Given  

    2. and w = max (10,w)

From the first equation we get that w= 20

and it also satisfies the second equation.

∴ The value of min(10,w) = min(10,20) ∵w=20

                                        = 10

Considering both conditions, our w value could be 10 or greater. As we are looking for the minimum value between 10 and w, the result of min(10, w) will be 10.

Let's look at the two provided conditions:

Since both conditions suggest that w could be a value 10 or greater, the exponent w in min(10, w) will be at least 10. However, because we're finding the minimum between 10 and w, the value of min(10, w) will be 10.

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Answer:

The difference between the number of pages that Darla and Juan read are VI pages.

Step-by-step explanation:

Given:

Darla told her teacher that she had read XLV pages in her library book.

Juan said that he had read XXXIX pages.

Now, to get the difference between the number of pages that Darla read and Juan read.

As, we see the number of pages are in roman numeral symbols.

So, we convert them in numbers first to calculate:

Darla read = XLV pages.

Darla read = 45 pages.

Now,

Juan read = XXXIX pages.

Juan read = 39 pages.

So, to get the difference between the number of pages by subtracting:

[tex]45-39=6[/tex]

Thus, the difference between the number of pages = 6 pages.

Now, converting it into roman numerals:

6 pages = VI pages.

Therefore, the difference between the number of pages that Darla and Juan read are VI pages.

Answer:

A

Step-by-step explanation:

Answer:

the choice of consumers regarding what to purchase to satisfy their wants and the choice of producers regarding what to produce to maximize profits.

Step-by-step explanation:

Answer:

It's descriptive.

Step-by-step explanation:

inferential statistic, means we are inferring based on a sample of our population. Many times we need to infer because the data we need to collect is too large, i.e. the population is too large e.g. the average age of high school students in the US. so we take a sample, a portion of this population and we calculate their mean age. If our sample is random enough, we can "infer" to a certain degree of accuracy the mean

But descriptive statistics, describes the data. They are numbers used to summarise and describe a data. 60% describes the data.

Answer:

1,440,000 cubic feet

Step-by-step explanation:

Proportions

We are told that 90% of the volume of an iceberg is below water. It means that 10% is above water. The proportion between the sunk/floating volumes is 90/10=9. The underwater volume of the iceberg is 9 times the above water volume. Thus, the volume of the iceberg below water is 9*160,000 = [tex]\boxed{1,440,000\ cubic feet}[/tex]

The volume of the iceberg below water is 1,440,000 cubic feet.

To determine the volume of the iceberg below the water's surface, we can use the fact that 90% of the iceberg's total volume is submerged underwater.

We are given that the volume of the part above water is 160,000 cubic feet.

Let V be the total volume of the iceberg and V_sub be the volume submerged below the water.

We can set up the following equation based on the given information:

V_sub = 0.9 * V

We know that V_sub + V_above = V, where V_above is the volume above the water's surface. We are given that V_above is 160,000 cubic feet, so we can rewrite the equation as:

V_sub + 160,000 = V

Now, substitute the expression for V_sub from the first equation:

0.9 * V + 160,000 = V

To isolate V_sub, subtract 160,000 from both sides of the equation:

0.9 * V = V - 160,000

Now, subtract V from both sides:

0.9 * V - V = -160,000

0.1 * V = -160,000

Now, divide both sides by 0.1 to find V_sub:

V_sub = (-160,000) / 0.1 = -1,600,000 cubic feet

However, it's important to note that the volume cannot be negative, and this result doesn't make physical sense.

This suggests there might be an issue with the given information or calculations.

For similar question on volume.

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Answer:A=183cm^

Step-by-step explanation:

The area of square is :

Let s be side

A= s^2

144= s^2

Square both side

Therefore

s=sqrt(144)

s=12 cm

The perimeter of the square is : 4× s= 4×12= 48cm

So the perimeter of the square is equal to the circumference of the circle.

The equation will be:

4×s=2×pi×r

4×12=2× (22/7)×r

r=48/6.29

r=7.63

Area of a circle is:

A=pi× r^2

A= (22/7) × (7.63)^2

A=182.9674cm^2

A=183cm^

Final answer:

To find the area of the largest circle from a string around a square, calculate the square's perimeter to get the string's length, which is also the circle's circumference. Then determine the circle's radius and use it to calculate the circle's area, which rounds to 183 square units.

Explanation:

To find the area of the largest circle that can be formed from a piece of string that fits around a square with an area of 144, first we must determine the perimeter of the square. Since the area of the square (A) is 144, the side length (s) can be found by taking the square root of the area: s = √A = √144 = 12. Therefore, the perimeter (P) of the square is P = 4s = 4 × 12 = 48.

The string that fits around the square is the same length as the perimeter, so it will also be 48 units long. This string will become the circumference (C) of the circle. The formula for the circumference of a circle is C = 2πr, where π is approximately 3.14 and r is the radius of the circle. We can solve for r by setting the circumference equal to the length of the string: C = 2πr = 48 → r = 48 / (2π) → r ≈ 7.64. So the radius of the circle is approximately 7.64 units.

Finally, to find the area (A) of the circle, we use the formula A = πr². Substituting the value of the radius, we get A = π × (7.64)² ≈ 183.47. However, since we need to round to the nearest whole number, the largest circle area is approximately 183 square units.

Answer:

f(x) = 100(0.50)x

Step-by-step explanation:

f(1) = 100(0.50)1

f(2) = 100(0.50)2

Therefore f(x) = 100(0.50)x

To make at least a 25% profit, Cameron should charge a minimum of $1.22 per bag for the mixed candy. The cost per bag is found by adding the total cost of candy corn and M&Ms, then multiplying by 125% and dividing by the number of bags to distribute the cost and profit evenly.

The student's question involves calculating the minimum selling price for candy bags to achieve a certain profit margin, which is a common type of problem in Mathematics, specifically in the field of algebra and business mathematics.

To find the least price Cameron can charge for each of the thirty bags to make at least a 25% profit, we first calculate the total cost of the candy. Cameron bought twelve pounds of candy corn at 79 cents a pound and eighteen pounds of M&Ms at $1.09 a pound.

Now, we calculate the total cost including the desired 25% profit.

Total cost with profit: $29.10 × (1 + 0.25) = $36.375

Since Cameron is making thirty bags, we divide the total cost with profit by the number of bags.

Minimum selling price per bag: $36.375 / 30 bags = $1.2125

However, as prices are generally rounded to the nearest cent, the minimum charge per bag would be $1.22 to ensure a 25% profit.

Answer:length = 11 feet

Width = 5 feet

Step-by-step explanation:

Let L represent the length of the rectangular box.

Let W represent the width of the rectangular box.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The length of the batter's box on a softball field is 1 ft more than twice the width. It means that

L = 2W + 1

The areas of the batter's box is 55 ft^2. It means that

LW = 55

Substituting L = 2W + 1 into LW = 55, it becomes

W(2W + 1 ) = 55

2W² + W = 55

2W² + W - 55 = 0

2W² + 11W - 10W - 55 = 0

W(2W + 11) - 5(2W + 11) = 0

(W - 5) = 0 or 2W + 11 = 0

W = 5 or W = - 11/2

The width cannot be negative, hence, it is 5 ft

L = 2W + 1 = 2 × 5 + 1 = 10 + 1

L = 11 feet

Answer:

[tex]Down\ payment = 7,344[/tex]

Step-by-step explanation:

Let x be the amount of 15% of gross income.

Given:

Jessica gross income = 48,960.00

She decided to use 15% amount as down payment.

We need to find the amount of 15% of gross income.

Solution:

Using percentage formula.

[tex]percentage = (\frac{Value}{Total\ value})\times 100[/tex]

Now we substitute 15 in the place of percentage and 48,960 in the place of Total value.

[tex]15=(\frac{x}{48960})\times 100[/tex]

Now, we apply cross multiplication rule.

[tex]x= \frac{48960\times 15}{100}[/tex]

[tex]x=48960\times 0.15[/tex]

[tex]x =7,344[/tex]

Therefore: Down payment is 7,344.

Final answer:

Jessica allocated $7,344 for the down payment on a house based on her 15% gross income allocation.

Explanation:

The budget that Jessica allocated for her down payment on a house is calculated as follows:

Calculate 15% of Jessica's gross income: 15% of $48,960 is $48,960 * 0.15 = $7,344.

Therefore, the budget that Jessica allowed for the down payment on a house is $7,344.

Answer:

Step-by-step explanation:

The total number of ducks in the pond is 75. 25 ducks are marked as a winner.

Probability is expressed as number of possible outcomes/total number of outcomes.

if you take 2 ducks out but don't replace them, the probability that the first duck that you took out is a winner is

25/75 = 1/3

The total number of ducks left would be 74 and the number of winners would be 24.

the probability that the second duck that you took out is a winner is

24/74 = 12/37

Therefore, the probability that both are winners is

1/3 × 12/37 = 4/37

Answer:

Option B) False            

Step-by-step explanation:

We define the following terms:

Range:

It is the difference between the minimum and maximum value of data.

It is effected by presence of outliers.

Interquartile range:

It is the difference between the third quartile and the first quartile of data.

Variance:

[tex]\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

It is a measure of spread of the data. It is effected by presence of outliers as they increase the variation in the data.

Thus, the given statement is false.

1/3 shows the spots that are black as compared to all the spots

Step-by-step explanation:

The simple fraction will consist of number of black spots as numerator and the total number of spots on the dog in denominator.

Given

Number of black spots = b = 8

Number of white spots = w = 13

Number of Gray spots = g = 3

Total spots are:

[tex]t=b+w+g = 8+13+3 = 24[/tex]

So the fraction will be:

[tex]\frac{Number\ of\ black\ spots}{Total\ spots}\\= \frac{b}{t}\\=\frac{8}{24}\\= \frac{1}{3}[/tex]

Hence,

1/3 shows the spots that are black as compared to all the spots

Keywords: Fractions, sum

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Answer:

The answer to your question is picture 1

Step-by-step explanation:

- This is a quadratic equation, so we look for a parabola. The four graphs show parabolas.

- We can notice a negative sign before the term (x - 3)², which indicates that it is a down-parabola. We discard the second and the fourth pictures.

- Get the vertex

                         y = -(x - 3)² - 5

                         y + 5 = - (x - 3)²      Vertex = (-5, 3)  

                                                         because we change signs

- With all this information, we conclude that the answer is picture 1 because its vertex is (-5, 3)

Answer: he invested $6000 in the account earning 5% interest and $2100 in the other account earning 2% interest

Step-by-step explanation:

Let x represent the amount invested in the account earning 5% interest.

Let y represent the amount invested in the account earning 2% interest.

In an account earning 5% interest, George invested $1800 more than twice the amount he invested in an account earning 2%. It means that

x = 2y + 1800

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

Assuming the duration for both investments is 1 year,

The interest on the first account would be

I = (x × 5 × 1)/100 = 0.05x

The interest on the second account would be

I = (y × 2 × 1)/100 = 0.02y

George earned a total of $342 in simple interest from two separate accounts. This means that

0.05x + 0.02y = 342 - - - - - - - - - - 1

Substituting x = 2y + 1800 into equation 1, it becomes

0.05(2y + 1800) + 0.02y = 342

0.1y + 90 + 0.02y = 342

0.1y + 0.02y = 342 - 90

0.12y = 252

y = 252/0.12 = 2100

x = 2y + 1800 = 2 × 2100 + 1800 = $6000

Answer:

Sum = 1,023

Step-by-step explanation:

The given series is:

1 + 2 + 4 + 8 + ........ + a₁₀

The given series is a geometric series.

It is required to find the sum of the first 10 terms

The sum to n terms of a geometric series given by:  [tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex]

Where: a = the first term = 1

            r = common ratio = 2/1 = 2

           n = number of terms = 10

So,

[tex]S_{n} = \frac{a(r^n-1)}{r-1}[/tex] = [tex]\frac{1*(2^{10} -1)}{2-1} = 2^{10} -1 = 1024 - 1 = 1,023[/tex]

So, the summation of the series = 1,023