Multiply Rational Numbers Which story problem could be solved using the given equation?
\( \frac{1}{5} \times \frac{2}{3} = m\)
​

In the business world, running a takeaway, restaurant or any food business is one of the best and busiest ways to earn money. People need to eat and you could provide them with some delicious and hygienic food and earn profits at the same time.

Takeaways are those food services which provide food and snacks quickly and are on the go.The given data is:The takeaway sells 10-inch pizzas and 12-inch pizzas.

Here is the information about the number sold in 2 weeks:10-inch pizzas sold: 25012-inch pizzas sold: 170To find the average of the pizzas sold per day, we need to divide the total number of pizzas sold in two weeks by 14 days.

14 days because 2 weeks contain 14 days.

Therefore,Total pizzas sold in 2 weeks = 250 + 170 = 420Therefore, Average pizzas sold per day = 420 / 14 = 30 pizzas (approximately)

Therefore, the takeaway sells approximately 30 pizzas every day for 2 weeks with the given data.

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It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

I=$300

Step-by-step explanation:

P=1500

r=4%=0.04

t=5 years

I=p*r*t

I=1500*0.04*5

I=300

The covariance of X and Y when X = aU + bV and Y = cU + dV is ac + bd.

If U and V are independent random variables, both having variance 1, then the covariance of X and Y can be found using the formula for covariance of two random variables:

Cov(X, Y) = E[(X - E[X])(Y - E[Y])]

Since X = aU + bV and Y = cU + dV, we can substitute these values into the formula:

Cov(X, Y) = E[(aU + bV - E[aU + bV])(cU + dV - E[cU + dV])]

Using the properties of expected value, we can simplify this expression:

Cov(X, Y) = E[(aU + bV - aE[U] - bE[V])(cU + dV - cE[U] - dE[V])]

Cov(X, Y) = E[(a(U - E[U]) + b(V - E[V]))(c(U - E[U]) + d(V - E[V]))]

Cov(X, Y) = E[ac(U - E[U])² + ad(U - E[U])(V - E[V]) + bc(V - E[V])(U - E[U]) + bd(V - E[V])²]

Since U and V are independent, the expected value of the product of their deviations from the mean is zero:

E[(U - E[U])(V - E[V])] = 0

So the covariance of X and Y simplifies to:

Cov(X, Y) = E[ac(U - E[U])²] + E[bd(V - E[V])²]

Cov(X, Y) = acE[(U - E[U])²] + bdE[(V - E[V])²]

Cov(X, Y) = acVar(U) + bdVar(V)

Since the variance of both U and V is 1, the covariance of X and Y is:

Cov(X, Y) = ac + bd

Therefore, the covariance of X and Y when X = aU + bV and Y = cU + dV is ac + bd.

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Answer: 2(x+7)(x+2)

Step-by-step explanation:

2x² + 18x +28                            >Take out the Greatest Common Factor 2

2( x² + 9x +14)                           >Find 2 numbers that multiply to the 3rd

                                                   term, +14, and adds to +9.

                                                    +7 and +2 add to +14 and add to +9

                                                  Put +7 and +2 into factored form

2(x+7)(x+2)                                 >Don't forget the 2 that you factored out in

                                                     beginning

Kelly bought digital cameras for $56 each and applied a 65% price increase to determine the selling price. To find the selling price of one camera, we need to calculate the price increase and add it to the original purchase price.

To calculate the price increase, we first find 65% of the original purchase price ($56) by multiplying it by 0.65:
Price increase = 0.65 * $56 = $36.40
Next, we add the price increase to the original purchase price to find the selling price:
Selling price = $56 + $36.40 = $92.40
Rounded to the nearest dollar, the selling price for one camera is $92.
Therefore, the selling price for one camera, after a 65% price increase, is approximately $92.

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9514 1404 393

Answer:

  3/8 pound

Step-by-step explanation:

If Felicity started with 3/4 pound and used 1/2 of it, then the amount she used was ...

  (1/2)(3/4 pound) = (1·3)/(2·4) pound = 3/8 pound

Felicity used 3/8 pound of hamburger for dinner.

Answer:

Chandler will need 82.2  cm of fabric.

Step-by-step explanation:

Given that,

Chandler has 822 millimeters of fabric.

We know that,

1 mm = 0.1 cm

To convert 822 mm to cm, use the unitary method.

822 mm = (0.1×822) cm

= 82.2  cm

So, Chandler will need 82.2  cm of fabric.

Answer:

Commutative Property of Addition

Step-by-step explanation:

3(x − 4) + 5x = 9x − 36

3x − 12 + 5x = 9x − 36  Distribute

3x + 5x − 12 = 9x − 36 Commutative Property of Addition

The measure of angle POQ is 118°.

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given ΔPQR

∠R = 62°

QS and PT are altitudes,

Take ΔQRS

∠R = 62°

∠QSR = 90°

so, ∠SQR + ∠QSR + ∠R = 180°

∠SQR = 180 - 90 - 62

∠SQR = 28°

Taking ΔPRT

∠R = 62°

∠PTR = 90°

so, ∠RPT + ∠PTR + ∠R = 180°

∠RPT = 180 - 90 - 62

∠RPT = 28°

now let  ∠TPQ = x° and ∠SQP = y°

in ΔPQS,

∠SPQ = 28 + x

∠PQS = y°

∠QSP = 90°

∠QSP + ∠PQS + ∠SPQ = 180°

90 + y + 28 + x = 180

x + y = 180 - 90 - 28

x + y = 62°

now in  ΔPOQ

∠OPQ = x°, ∠OQP = y°

∠POQ + ∠OPQ + ∠OQP = 180°

∠POQ + x + y = 180

sunstitute value of x + y =  62°

∠POQ = 180 - 62

∠POQ = 118°

Hence the value of angle POQ is 118°.

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Answer: 12

Step-by-step explanation:

When Omar does not have a common factor while factoring a polynomial, he should consider regrouping terms, factoring out a common factor, or adjusting signs to simplify the expression. The absence of a common factor does not necessarily mean the polynomial is prime.

If Omar noticed that he does not have a common factor when factoring a polynomial, there are a few possible next steps to consider. It is important to note that the absence of a common factor does not necessarily mean that the polynomial is prime.

One option for Omar is to go back and regroup the terms in step 1, as (3x³ – 15x²) – (4x + 20). By rearranging the terms, he may be able to identify a common factor or a different factorization approach.

Another possibility is for Omar to factor out a common factor from the first expression in step 2. He can examine the terms in the expression and determine if there is a factor that can be pulled out.

It is also worth considering whether Omar needs to factor out a negative from one of the groups so that the binomials become the same. This step can help simplify the expression and make the factoring process easier.

Overall, Omar should explore different factorization strategies, regroup terms if necessary, and look for common factors or patterns to continue factoring the polynomial. The absence of a common factor does not necessarily imply that the polynomial is prime.

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The probability a player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue). Option C is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Probabilities of wearing specific jersey colors,
Yellow 0.47

Blue 0.18

White 0.35

So,
P(Yellow)> P(White) > P(Blue).

It implies that, from the options, the player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue).

Thus, option C is correct.

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Answer: C: The player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue).

Step-by-step explanation:

The length of the fence in feet if he uses all 72 feet of material is 33 feet.

Perimeter = 2(length + width)

72 = 2(x + 3)

72 = 2x + 6

72 - 6 = 2x

68 = 2x

x = 68/2

x = 33 feet

Therefore, the length of the fence in feet if he uses all 72 feet of material is 33 feet.

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The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

To perform u-substitution with indefinite integrals, follow these steps:

Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.

Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.

Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.

Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.

Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.

Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.

Let's illustrate these steps with an example:

Consider the integral ∫(2x + 3)² dx.

Identify a suitable substitution: Let u = 2x + 3.

Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.

Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).

Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.

Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.

Simplify and solve: Further simplify the expression if necessary to obtain the final result.

In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

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Answer:

The answer is below

Step-by-step explanation:

a) The graph is attached

b) The table shows a linear relationship between x and y.

A linear equation is in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change (slope) and b is the value of y when x = 0.

x represent the distance on map in mm and y represent the actual distance in mile. The table (x, y) has the points (10, 25) and (20, 50). The equation is given by:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-25=\frac{50-25}{20-10} (x-10)\\\\y-25=2.5(x-10)\\\\y-25=2.5x-25\\\\y=2.5x\)

The slope m = 2.5. This means that for every 1 mm on the map, the actual distance increases by 2.5 miles.

c) y = 2.5x

put x = 48 mm

y = 2.5(48)

y = 120 miles

The actual distance between Toledo and Columbus is 120 miles

d) y = 2.5x

Put y = 225 miles

225 = 2.5x

x = 225/2.5

x = 90 mm

The distance on map between Cincinnati and Cleveland is about 90 mm.

Answer:

45

Step-by-step explanation:

1/4 of a number means the number divided by 4. 60/4=15. That's how much she spent, and we have to find the rest. So we do 60-15=45.

A simple linear regression model is appropriate when the response variable is influenced by only one explanatory variable.

A simple linear regression model assumes a linear relationship between the response variable (y) and a single explanatory variable (x).

It is suitable when we want to understand how changes in the explanatory variable affect the response variable.

In the given options, the situation where the response variable y is influenced by one explanatory variable aligns with the requirements of a simple linear regression model.

This means that the relationship between y and x can be adequately described by a straight line.

The model aims to estimate the slope and intercept of this line, allowing us to make predictions and draw conclusions about the impact of the explanatory variable on the response variable.

If the response variable y is influenced by two or more explanatory variables, a multiple linear regression model would be more appropriate.

Multiple linear regression allows for the analysis of the combined effects of multiple predictors on the response variable, accounting for their individual contributions.

Similarly, if the explanatory variable x is influenced by two or more response variables, a different modeling technique, such as multivariate regression, would be more suitable.

Therefore, the situation where the response variable y is influenced by one explanatory variable is the scenario where a simple linear regression model is appropriate.

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Answer:

Let x be the number of $10 CDs and y be the number of $15 CDs. Then, the system of inequalities representing this situation is:

10x + 15y ≥ 30 (the customer wants to spend at least $30)

10x + 15y ≤ 60 (the customer wants to spend at most $60)

x ≥ 0 (the customer can't buy a negative number of CDs)

y ≥ 0 (the customer can't buy a negative number of CDs)

Simplifying the first two inequalities:

2x + 3y ≥ 6

2x + 3y ≤ 12

To graph the solution region, we first graph the boundary lines:

2x + 3y = 6 (or y = (-2/3)x + 2)

2x + 3y = 12 (or y = (-2/3)x + 4)

Then, we shade the region that satisfies both inequalities (the region below the upper line and above the lower line), as well as the regions to the right and above the x and y axes:

Let x be the number of $10 CDs and y be the number of $15 CDs. Then, the system of inequalities representing this situation is:

10x + 15y ≥ 30 (the customer wants to spend at least $30)

10x + 15y ≤ 60 (the customer wants to spend at most $60)

x ≥ 0 (the customer can't buy a negative number of CDs)

y ≥ 0 (the customer can't buy a negative number of CDs)

Simplifying the first two inequalities:

2x + 3y ≥ 6

2x + 3y ≤ 12

To graph the solution region, we first graph the boundary lines:

2x + 3y = 6 (or y = (-2/3)x + 2)

2x + 3y = 12 (or y = (-2/3)x + 4)

Then, we shade the region that satisfies both inequalities (the region below the upper line and above the lower line), as well as the regions to the right and above the x and y axes:

inequality graph

As an example of one possible production situation within these restrictions, let's say the customer buys 2 $10 CDs and 2 $15 CDs. This would cost $50, which falls within the customer's desired spending range of $30 to $60. Plugging in x = 2 and y = 2 into the inequalities:

10x + 15y = 10(2) + 15(2) = 50, which satisfies 10x + 15y ≥ 30 and 10x + 15y ≤ 60

x = 2 ≥ 0

y = 2 ≥ 0

Therefore, (2,2) is a valid solution within the given restrictions.

Step-by-step explanation:

The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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Answer:

a = 254.5 mm² ( if using accurate value of π)

a = 254.4 mm² (if using 3.14 as approximate value of π)

Step-by-step explanation:

a = πr²

a = π * 9²

a = π * 81

(note using π = 3.1415926536)

a = 254.4690049408

Rounded

a = 254.5 mm²

(a = 254.4 If using π = 3.14)

Answer: 1- function 1 has the greater rate of change but function 2 has the greater y-intercept

Step-by-step explanation:

We know that function 1 is:

y = f₁(x) = 0.75*x - 1

And for the second linear equation we can see that it passes through the points (-3, -1) and (0,1)

Then the slope is:

a = (1 - (-1))/(0 - (-3)) = 2/3

then the equation is something like:

y = f₂(x) = (2/3)*x + b

To find the value of b, we use the fact that when x = 0, we have y = 1.

Then:

1 = (2/3)*0 + b

1 = b

Then the equation for function 2 is:

f₂(x) = (2/3)*x + 1

So the two equations are:

f₁(x) = 0.75*x - 1

f₂(x) = (2/3)*x + 1

Where we can see that function 1 has a greater slope (rate of change) and function two has a greater y-intercept.

Then the correct option is

(1- function 1 has the greater rate of change but function 2 has the greater y-intercept)

The correct answer is:A. 10% of males weigh 11.0 kg or less, and 90% of 36-month-old males weigh more than 11.0 kg.

In statistical terms, percentiles represent points in a distribution that divide the data into specific percentages. They indicate the relative position of a particular value within a dataset.

(a) The 10th percentile of the weight of males 36 months of age in a certain city is 11.0 kg. This means that 10% of males who are 36 months old or younger weigh 11.0 kg or less.

(b) The 90th percentile of the length of newborn females in a certain city is 54.3 cm. This means that 90% of newborn females in that city have a length less than or equal to 54.3 cm.

Therefore, the correct answer is:

A. 10% of males weigh 11.0 kg or less, and 90% of 36-month-old males weigh more than 11.0 kg.

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The time it will take for Helen and Reid to meet is given as follows:

3/7 of an hour = 26 minutes.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

The parameters for this problem are given as follows:

Hence the time is obtained as follows:

7 = 3/t

7t = 3

t = 3/7 of an hour = 26 minutes.

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d. 7/11 is not a unit fraction

The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

Given,

A spherical golf ball is measured to have a radius of $$5 mm, with a possible measurement error of $$0.1 mm

How to determine the volume

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

r is the radius of the sphere

pi takes the value 3.14

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

v = 4/ 3 (392.5)

v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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Explanation

Question 57

We are asked to get the absolute maxima and minima of the function.

An absolute extremum (or global extremum) of a function in a given interval is the point at which a maximum or minimum value of the function is obtained. Frequently, the interval shown is the function's domain, and the absolute extremum is the point corresponding to the maximum or minimum value of the entire function.

To get the absolute maxima and minima, we will use the graph below

From the graph, we can observe that

Answer:

A is 90 degrees because of the box

Answer:

a = 34.64

Step-by-step explanation:

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Answer:

x = 2

y = 5

Step-by-step explanation:

when you think of how many times 5 can go into 10 it is 2

then think of how many times 2 can go into 10 which is 5

then you add the two and it equals 20$