Answer:
To simplify the expression (5^-3/5^-1), we need to use the rule of exponents that states when dividing two powers with the same base, we can subtract the exponents.
Using this rule, we get:
(5^-3/5^-1) = 5^-3 ÷ 5^-1 = 5^-3 × 5^1 = 5^-2 = 1/25
Therefore, Hector gave the correct answer.
How do you convert this equation to rectangular form? The answer given in the book is (x-1)^2+y^2=9, but I need steps to show how you arrive at this answer.
The equation r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8 to rectangular form is (x - 1)² + y² = 9
Converting the equation to rectangular form?From the question, we have the following parameters that can be used in our computation:
r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8
The above equation is in its polar form, where
r² = x² + y²
cos(θ) = x/r
sin(θ) = y/r
Rearrange the terms in r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8
So, we have
r²cos²(θ) + r²sin²(θ) - 2rcos(θ) = 8
Factorize
r²(cos²(θ) + sin²(θ)) - 2rcos(θ) = 8
In trigonometry
cos²(θ) + sin²(θ) = 1
So, we have
r² - 2rcos(θ) = 8
Recall that
r² = x² + y²
cos(θ) = x/r
So, we have
x² + y² - 2r * x/r = 8
Evaluate
x² + y² - 2x = 8
Rearrange
x² - 2x + y² = 8
Express as perfect squares
(x - 1)² + y² = 8 + 1
So, we have
(x - 1)² + y² = 9
Hence, the equation to rectangular form is (x - 1)² + y² = 9
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Looking at the ping-pong ball toss board below, whats the probability of landing on a white square? (Note the board contains 5 rows of 5 squares.)
The probability of landing on a white square is 4/5.
We have toss board of measurement 5 x 5.
Total squares in board = 25
White square = 20
Black square= 5
So, the probability of landing on a white square
= 20 / 25
= 4/5
Thus, the required probability is 4/5.
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During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 10% per month.
State whether this increase was linear or exponential. If your food bill was $110 in one month during this period, what
was it three months later?
Step-by-step explanation:
Exponetial (compounding ) growth
New Price = original price ( 1 + .10)^n n is months .10 is 10% per month
= $ 110 ( 1.10)^3 = $ 146 . 41 three months later
Freemont run club surveyed a random sample of 30 of their members about their running habits
The reasonable estimate would be 25
How to solve for the estimateWe have to solve this using the rule of 3
9 out of 30 members said that they run more than 5 days a week.
We will form the equations
when 9 ran = 30 menbers
when n ran = 84 members
we will then cross multiply
84 x 9 = 30 x n
n = 25.2
When we round this, the reasonable estimate would be 25
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Complete question
Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.
There are 84 Freemont Run Club members.
Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?
A population of insects in an entomology lab experiment grows according to the formula P = h(t) = 100/1+4e^-0.05t with t given in days.
(a) Find a formula for h¹(P). Show your work.
(b) Calculate h-¹(90) and interpret its meaning in the context of the problem. Show your work. Round to 1 decimal.
The formula for the inverse function h⁻¹(P) is:
The population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is approximately 17.5 days.
To find the inverse function h⁻¹(P), we need to solve the equation P = h(t) for t in terms of P.
Starting with P = h(t) = [tex]100/1+4e^-^0^.^0^5^t[/tex]
we can first multiply both sides by [tex]1+4e^-^0^.^0^5^t[/tex] to get:
[tex]P(1+4e^-^0^.^0^5^t) = 100[/tex]
t = -20ln(4/(P-100)+1)
Therefore, the formula for the inverse function h⁻¹(P) is:
h⁻¹(P) = -20ln(4/(P-100)+1)
(b) To find h⁻¹(90)
we substitute P = 90 into the formula for h^-1(P):
h⁻¹(90) = -20ln(4/(90-100)+1)
= 17.5
This means that if the population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is 17.5 days.
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in how many ways can a student choose four questions from a question paper that contains six questions if
a. Question No. 1 is compulsory
b. Question No. 2 should not be chosen
c. There is no restriction on any of the questions
The student can choose four questions from a question paper that contains six questions as follow:
a. 10 ways.
b. 5 ways.
c. 15 ways.
How to choose how many ways can a student choose four questions?Combination is a way of selecting items from a collection where the order of selection does not matter.
a. If Question No. 1 is compulsory, then the student can choose three more questions from the remaining five. That is:
5C3 (i.e. 5 combination 3) ways = 10 ways.
b. If Question No. 2 should not be chosen, then the student can choose four questions from the remaining five. That is:
5C4 ways = 5 ways.
c. If there is no restriction on any of the questions, the student can choose any four questions from the remaining six. That is:
6C4 ways = 15 ways
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Find (v) x (w) if ||v||=8, ||w||=12, and the angle between v and w is 60 degrees
The product of two given vectors is 48.
Given that, |v|=8, |w|=12 and the angle between v and w is 60 degrees.
We know that, |a|·|b|=|a|×|b|×cosθ.
Here, |v|·|w|=8×12×cos60°
= 96× 1/2
= 48
Therefore, the product of two given vectors is 48.
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What is the volume of the resulting solid
Note that the volume (V) of the resulting solid which is revolved around it's axis is given as V = 37.699 cubic units.
How do you compute the above?If we used the distance formula, to computer the distance between the coordinates, we'd arrive at the following side lenghts:
3, 4, and 5.
Since we are looking at a right triangle, it is correct to infr that the hypotenuse is the longer side, which is 5.
We can assume the height to be four units and the radius to be 3 units.
Thus, using the formula fo rthe volume of a cone:
V = (1/3) * π * r² * h
Inputting values, we have
V = (1/3) * 3.14159 * 3² * 4
V = 1.0472 * 9 * 4
V = 37.6992
If we approximate to the nearest thousandth, we have:
V = 37.699 cubic units
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Need help with this please. Be creative!!
The picture for reduction and enlargement is attached
What is scale factor?Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying. while that of decrease is reduction.
The drawing of the the reduction is a square of side 8 units. The scale factor given is 1/2 hence we have the dimensions are as follows
preimage: 8 units x 8 units
image: 4 units x 4 units
The drawing of the the enlargement is a circle of radius 2 units. The scale factor given is 2, hence we have the dimensions are as follows
preimage: radius = 2 units
image: radius = 4 units
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AYOde deposit 600 at the end of each quarter for 15 year in a bank whose annual interest rate is 12% and compounding is done at each deposit
Find the total with of the account 60th deposit
Find the accumulate interest
The account's total value is $498,174.72.
The total interest paid is $174,174.72.
To solve this problemWe can utilize the calculation for the future value of a compound interest annuity to resolve this issue:
FV = P*(((1 + r/n)(n*t))-1) / (r/n).
where
FV is the future value of the annuityP is the periodic payment deposit, which is 600 in this caser is the annual interest rate, which is 12%n is the number of times the interest is compounded per year, which is 4 since the deposits are made quarterlyt is the total number of periods, which is 60 since there are 15 years and 4 deposits per yearWhen we enter the values, we obtain:
FV = 600 * (((1 + 0.12/4)^(4*60)) - 1) / (0.12/4) = 498,174.72
After the 60th deposit, the account's total value is $498,174.72.
We can deduct the total amount deposited from the account's total value to calculate the cumulative interest:
Added interest is calculated as follows: FV - (P * t * n) = 498,174.72 - (600 * 60 * 4) = 174,174.72
Therefore, the total interest paid is $174,174.72.
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Suppose you decide to invest in an annuity that pays 5% interest, compounded annually. How much money do you need to invest semiannually to reach a savings goal of $300,000 at the end of 25 years.
If your objective is to save $300,000 over 25 years, you would need to put away around $3077.41 every six months.
To solve this problem, we can use the formula for the future value of an annuity:
[tex]FV = P *\frac{((1 + r/n)^{(n*t)} - 1)}{(r/n)}[/tex]
where FV is the future value, P is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Since the interest is compounded annually, we have n = 1 and r = 0.05. To find the periodic payment P, we can rearrange the formula:
P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)
Plugging in the given values, we have:
[tex]P = 300000 * (0.05/2) / ((1 + 0.05/2)^{(2*25)} - 1)[/tex]
P ≈ $3077.41
Therefore, you would need to invest approximately $3077.41 every six months to reach a savings goal of $300,000 at the end of 25 years.
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Use the equation of the line of best fit, =y+−0.76x8.76, to answer the questions below. Give exact answers, not rounded approximations. (a) For an increase of one hour in the time spent texting, what is the predicted decrease in the time spent exercising? hours (b) What is the predicted time spent exercising for a student who doesn't spend any time texting? hours (c) What is the predicted time spent exercising for a student who spends 5 hours texting?
For an increase of one hour in time worked, the predicted increase in the amount of money spent on entertainment will be; 1.86 units.
To Determine the predicted increase in the amount of money spent on entertainment for an increase of one hour in time worked, we need to find the slope of the line, which is the coefficient of x in the equation.
We are given that the equation of the line of best fit, y = −0.76x8.76
The slope is 1.86, that means that for every one unit increase in x (which in this case is one hour worked), y (in this case is the amount of money spent on entertainment) is predicted to increase by 1.86 units.
This is the change in the dependent variable (y) for a unit increase in the independent variable (x),
Based on the linear relationship described by the equation of the line fit.
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P
60°
30°
8 yd
Write your answer in simplest radical form.
yards
Using the sine ratio, the value of p in the right triangle, in simplest form is: p = 4.
How to Find the Missing Side in Simplest Radical Form?To find the value of p, we have to determine what formula to use. We would apply the sine ratio, which is:
sin ∅ = opposite side / hypotenuse.
From the right triangle in the diagram, we have:
sin 30 = p / 8
p = sin 30 * 8
Note: sin 30 = 1/2
Therefore, we have:
p = 1/2 * 8
p = 4
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A married couple would like to examine the potential of using their home equity to borrow funds in order to remodel their kitchen at a cost of $17,000. The couple purchased the home 3 years ago for its market value of $135,000. The interest rate on their 30-year fixed-rate mortgage is 4.25% and they were able to put down a 5% down payment towards the purchase. The market value of the home has grown at 2.5% per year and the current balance owed on the mortgage is $121,478. If the local Credit Union is offering to lend the couple up to 80% of their home equity in the form of a home equity loan to remodel their kitchen, will they be able to borrow the money necessary to complete the project this third year? Please explain how you calculated the answer.
Only afford a home with a market value of about $375,000, and she would require a down payment of $75,000 to do so.
First, we have to ascertain how much Kelly can comfortably afford to pay for her mortgage each month. Her income, expenses, and other financial commitments will determine this. Her monthly mortgage payment should not be more than 28% of her total monthly income, on average.
The loan is interest rate is the next thing we need to think about. Kelly will have a constant monthly payment for the duration of the loan thanks to a 30-year fixed rate loan at the current market rate of 4.25%.
With a 20% down payment and a loan with a 4.25% interest rate, we could be calculate the maximum purchase price to be roughly $375,000 using a mortgage calculator.
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Two fair dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9?
A)11/12. B)5/6. C)1/12. D)1/6
Answer:
There are 36 possible outcomes when two dice are rolled (6 outcomes for the first die and 6 outcomes for the second die). To find the probability that the sum of the two numbers on the dice will be greater than 9, we need to count the number of outcomes where the sum is greater than 9.
The possible outcomes where the sum is greater than 9 are (4,6), (5,5), (5,6), and (6,5), for a total of 4 outcomes. Therefore, the probability of getting a sum greater than 9 is 4/36 or 1/9.
Answer: C) 1/12.
ayer compre 3/4 kg de papas y hoy 1/2 kg cuantos kg tengo en total
Jada is designing a study to determine whether mold grows faster in tap water or bottled water. To do this she compares growth rate of mold growing in a glass of tap water to the growth rate of mold growing in a glass of bottled water.
What type of study is Jada designing?
How could her design be improved to collect date that would be better for answering question of interest?
Jada is directing a comparative analysis to identify whether mold thrives faster in tap water or bottled water.
How to improve her designTo upgrade her design and procure data that would be more viable for addressing the question of interest, Jada might reflect on the following:
Randomized Controlled Trial (RCT): Preferably of just contrasting the rate of growth of mold in tap water versus bottled water in a glass, Jada could arbitrarily allote separate glasses to either tap water or bottled water categories.
Replicates and Sample Size: Jada may utilize several copies for each type of water to escalate the probabilistic force of her study.
Control Group: Jada should integrate a control group in her study, where no water is integrated into the glass.
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Which is the best reason why 2/5 is the exact quotient for 1/4 divided by 5/7
The best reason why 2/5 is the exact quotient for 1/4 divided by 5/8 is: ²/₅ * ⁵/₈ = ¹/₄
How to divide fractions?To divide fractions, firstly, you need to turn the 2nd fraction upside down. For example, 3/8 divided by 3/4 would be 3/8 divided by 4/3. After you have flipped the second fraction, you multiply them - 3*4 = 12. 8*3 = 24 so the answer would be 12/24. Which then could be cancelled down to 1/2.
Now, from the given question, we can say that:
1/4 ÷ 5/8
Now, from the earlier step in dividing fractions, the next step is to turn the 2nd fraction upside down and multiply by the first to get:
¹/₄ * ⁸/₅ = ²/₅
Rearranging, we have:
²/₅ * ⁵/₈ = ¹/₄
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Complete question is:
Which is the best reason why 2/5 is the exact quotient for 1/4 divided by 5/8
Let's say you wanted to make a flute from one-inch PVC pipe. If the lowest desired note is C5 on the Equal Temperament Scale (523.25 Hz), what length should it be cut?
The length the one-inch pipe should be cut to make a flute with a lowest desired note of 523.25 Hz, based on the acoustic length formula is 12.9 inches
What is the acoustic length?The acoustic length is the length obtained from the sum of the bore length and the corrections at the foot and the sound hole.
The frequency of the lowest note = 523.25 Hz
Whereby the frequency of the lowest note = The fundamental frequency
The acoustic length formula for finding the length of the pipe, L, can be presented as follows;
L = (v/(2·f)) × √(1 + 4·A²/v²)
Where;
L = The length of the pipe
f = The frequency = 523.25 Hz
A = The cross-sectional area of the pipe = π × 1.315²/4 ≈ 1.36 in²
v = The speed of sound ≈ 343 m/s ≈ 13503.9 in/s
L = (v/(2·f)) × √(1 + 4·A²/v²)
L = (13503.9/(2×523.25)) × √(1 + 4×1.26²/13503.9²) ≈ 12.9
The length of the pipe is about 12.9 inches
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2. A 18 kg rock starting from rest free falls through a distance of 7.0 m with no air resistance. Find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earth’s velocity. Earth’s mass is 6.0 × 1024 kg. Show all your work, assuming the rock-earth system is closed.
The momentum change of the rock caused by its fall will be 35.49 x [tex]10{-24[/tex] m/sec and the magnitude of the earth velocity will be 212.94 kgm/s
We have,
Mass of the rock = 18 kg
Distance traveled = 7 m
Mass of earth = 6 x [tex]10^{24[/tex] Kg
Using second equation of motion
S= ut + 1/2 at²
If the body freely falls initial velocity will be zero.
u = initial velocity = 0
Then, S = 1/2 at²
7 = 1/2 x 10 x t²
14/ 10= t²
t= 1.183 sec
Now, Change in the momentum of the rock will be,
ΔP= FΔT
ΔP = (mg ) ΔT
ΔP= (18) x 10 x 1.183
ΔP=212.94 kg-m/s²
Now, Earth will also have same momentum change
ΔP(earth)= ΔP(rock)
6 x [tex]10^{24[/tex] Kg x Δv = 212.94
Δv = 35.49 x [tex]10{-24[/tex] m /sec
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The correct statements regarding the scatter plot are given as follows:
The line of best fit gives the best approximation between the SAT score and the GPA.The line of best fit can be used to predict the GPA based on the SAT score.A reasonable prediction of GPA for a SAT score of 2100 is a GPA of 3.5.What is the scatter plot?The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:
(SAT score, GPA).
There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.
For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.
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The following data relate to a firm’s purchase of a machine used in the manufacture of its product:
Invoice price $299,000
Applicable sales tax 2,100
Cash discount taken for prompt payment 1,300
Freight paid 1,160
Cost of insurance coverage on machine while in transit 1,025
Installation costs 1,900
Testing and adjusting costs 1,375
Repair of damages to machine caused by the firm's employees 1,450
Prepaid maintenance contract for first year of machine's use 1,200
Determine the acquisition cost of the machine.
The machine's purchasing cost is $309,210.
The acquisition cost of the machine is the total cost incurred by the firm to purchase and put the machine into service.
To determine the acquisition cost of the machine, we need to add up all the costs listed in the question.
Invoice price = $299,000
Applicable sales tax = $2,100
Freight paid = $1,160
Cost of insurance coverage = $1,025
Installation costs = $1,900
Testing and adjusting costs = $1,375
Repair of damages caused by the firm's employees = $1,450
Prepaid maintenance contract = $1,200
Total acquisition cost = Invoice price + Sales tax + Freight paid + Cost of insurance coverage + Installation costs + Testing and adjusting costs + Repair of damages caused by the firm's employees + Prepaid maintenance contract
Total acquisition cost = $299,000 + $2,100 + $1,160 + $1,025 + $1,900 + $1,375 + $1,450 + $1,200
Total acquisition cost = $309,210
Therefore, the acquisition cost of the machine is $309,210.
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The sun is a even number
The probability that the sum would be an even number, can be found to be 1 / 2 .
How to find the probability ?There are six sides on each die so the total number of outcomes is:
= 6 x 6
= 36 outcomes
We will get an even number if we get two odd numbers, and two even numbers. We will not get even, with an even number and an odd number.
The number of two odd number outcomes is:
= 3 x 3
= 9 outcomes
The two even outcomes:
= 3 x 3
= 9 outcomes
The probability that the sum is even is:
= ( 9 + 9 ) / 36 total outcomes
= 18 / 36
= 1 / 2
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write an exponential model given two points. (6,85) (7,92)
The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]
We have,
To write an exponential model given two points (6,85) and (7,92), we can use the general exponential function form:
y = a[tex]b^x[/tex]
where y is the dependent variable, x is the independent variable, a is the initial value (when x = 0), and b is the base of the exponential function.
To find the values of a and b, we can use the two given points as follows:
When x = 6, y = 85:
85 = a b^6
When x = 7, y = 92:
92 = a b^7
We now have a system of two equations with two unknowns (a and b).
We can solve for a by dividing the second equation by the first equation:
92/85 = (ab^7) / (ab^6)
1.0824 = b
Substitute this value of b into one of the equations to solve for a:
85 = a (1.0824)^6
a = 41.62
Therefore,
The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]
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20x+4y=8 in slope-intercept form, simplifying all fractions.
slope = -5, y intercept = 2
The graph is below.
======================================
Work Shown:
20x+4y = 8
4y = 8-20x
4y = -20x + 8
y = (-20x+8)/4
y = -20x/4 + 8/4
y = -5x + 2 is the final answer
slope = -5, y intercept = 2
Two points on this line are (0,2) and (1, -3)
The graph is below. I used GeoGebra to make it, but Desmos is another good choice.
if f(x)=-4x-2 is vertically tranfered up 6 units to g(x), what is the y intercept of g(x)
The y-intercept for the function g(x) is 4.
The y-intercept of a function is a point where the line crosses the y-axis. The linear function can be given as below.
f(x) = mx+n
Where m is the slope of the line and n is a real number and y-intercept of the line.
The given function is f(x)=-4x—2.
The function is vertically translated 6 units up to g(x).
The y-intercept of the function f(x) is -2. Then the y-intercept for the function g(x) can be given as below.
y-intercept g(x) = -2+6
y-intercept g(x) = 4
Hence, the y-intercept for the function g(x) is 4.
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this figure represents a garden box.
How much soil will it take to fill the garden box?
The amount of soil to fill the garden box is V = 1,134 inches³
Given data ,
Let the volume of the first rectangular box be V₁
Let the volume of the second rectangular box be V₂
where Volume of Rectangle = Length x Width x Height
So , V₁ = 21 x 7 x 2
V₁ = 294 inches³
And , V₂ = 12 x 10 x ( 7 )
V₂ = 120 x 7
V₂ = 840 inches³
And , the total soil in the garden box = V₁ + V₂
Amount of soil in garden box = 1,134 inches³
Hence , the volume is V = 1,134 inches³
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Determine the Y intercept:
The y-intercept of the line is 2.
In the equation y = 9x + 2, x and y are variables that represent the coordinates of any point on the line.
To find the Y-intercept, we need to find the value of y when x equals 0.
When x equals 0, the equation becomes:
y = 9(0) + 2
Any number multiplied by 0 is 0, so the first term drops out and we are left with:
y = 0 + 2
Which simplifies to:
y = 2
Therefore, when x equals 0, y equals 2. This means that the point (0, 2) is on the line. In other words, the line intersects the y-axis at y = 2, which is the Y-intercept of the line.
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Write four math sentences that have an answer of 2.4. Use a different operation in each sentence.
The four math sentences that have an answer of 2.4 are 1.2 + 1.2, 1.2 * 2, 3.6 - 1.2 and 4.8/2
Writing four math sentences that have an answer of 2.4.From the question, we have the following parameters that can be used in our computation:
An answer of 2.4
Using a different operation in each sentence., we have the following math sentences
1.2 + 1.2
1.2 * 2
3.6 - 1.2
4.8/2
The solution to each of the above sentences is 2.4
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Anna ordered a large pizza with 2 toppings. What was the total cost of her pizza? Write an equation and solve it to find the total cost.
Answer: The cost of a large pizza with 2 toppings depends on the pizza place. Let's say the cost is $15 per pizza, and each additional topping costs $2.
Let t be the number of toppings Anna has on her pizza. Then, the total cost of her pizza can be expressed as:
Total cost = $15 + $2t
Since Anna has 2 toppings on her pizza, we can substitute t = 2:
Total cost = $15 + $2(2)
Total cost = $15 + $4
Total cost = $19
Therefore, the total cost of Anna's pizza with 2 toppings is $19.