Idrissa collected pennies in a fundraiser. He measured the mass of all the pennies he collected to be 2,400 grams. Two pennies put together have a mass of 5 grams. How much money did Idrissa raise in this fundraiser?

Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

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▹ Answer

43

▹ Step-by-Step Explanation

3³ + 4²

= 27 + 16

= 43

Hope this helps!

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Brainliest is greatly appreciated!

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Answer:

nine

Step-by-step explanation:

Answer: The width is 7 units.

Step-by-step explanation:

What we know:

- Area of the rectangle is 56

- The length of a rectangle is 1 unit more than the width

I will be using the variable w to represent the width.

Let's write it out:

Length = w + 1

Width = w

We know that the area is length x width

So the equation is (w + 1) x w = 56

Let's simplify this equation!

w^2 + w = 56

Now we need to find the solutions of this equation and see which one works.

Rewrite the eqaution:

w^2 + w - 56 = 0

Factor, find two factors of -56 whose sum equals the coefficient of the middle term (w):

-7, 8

Rewrite:

w^2 - 7w + 8w - 56 = 0

This part is a little tricky for me to explain, I apologize in advance for any confusion, but you want to do a little something like this:

(w+8) x (w-7) = 0

Now we solve both terms by = 0 seperately:

w + 8 = 0

= -8

w - 7 = 0

w = 7

Solutions:

w = 7, -8

Now that we have our solutions, we can choose which one best fits our scenario. In this case, 7 will fit the best.

To check this, we just plug it all in!

Length: 7 + 1 = 8

Width: 7

Area is length x width. So now we multiply:

8 x 7 = 56.

The width of this rectangle is 7 units.

Answer:90 shirts

Step-by-step explanation: do 1.5 x 1.6 = that answer and + 60 to that answer ok

Let's assign the variable "x" to the height of the smaller plant. Since we know that the larger plant grows twice as fast, its height would be "2x". Let's say the total height of the plants together is 90 cm, so we can write the equation: x + 2x = 90

Let's assign the variable "x" to the height of the smaller plant. Since we know that the larger plant grows twice as fast, its height would be "2x". Let's say the total height of the plants together is 90 cm, so we can write the equation:

x + 2x = 90

Simplifying the equation, we get:

3x = 90

x = 30

Therefore, the height of the smaller plant is 30 cm and the height of the larger plant is 2x = 60 cm.

To sketch a graph of the equation, we can plot the values of x (height of smaller plant) on the x-axis and the values of 3x (total height of the two plants) on the y-axis. The graph would be a straight line with a slope of 3 and intersecting the y-axis at 90 (the total height of the plants).

For the second equation, let's say we want to model the growth of the smaller plant over time. We can use the equation:

y = 0.5x + 10

where "y" is the height of the smaller plant (in cm) and "x" is the number of weeks since planting. The equation assumes that the plant starts at a height of 10 cm and grows at a rate of 0.5 cm per week. To sketch the graph, we can plot the values of x on the x-axis and the values of y on the y-axis. The graph would be a straight line with a slope of 0.5 and intersecting the y-axis at 10.

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The requried, percentage of students who study less than 2.50 hours a day is approximately 25.14 percent.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

We need to convert 2.50 hours to a standard score (z-score) using the formula,

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

z = (2.50 - 3.00) / 0.75

z = -0.67

This means that 2.50 hours is 0.67 standard deviations below the mean.

We can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls below this standard score. For example, using a standard normal distribution table, we can look up the area to the left of z = -0.67 and get:

P(z < -0.67) = 0.2514

So the correct answer is (a) 25.14 percent.

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Answer :

The answer is A.

Answer:

A) 140

Step-by-step explanation:

since angle RA is 40

and angle one seems the same so

<1+<2=140

40+<2=180

-40 -40

<2=140

The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

The given function is of the form

f(x) = x^(7/9), this is equivalent to ⁹√x⁷

say f(x) = y, then

f(x) = y = x^(7/9)

y = x^(7/9)

solving for the inverse, of y = x^(7/9)

y = x^(7/9)

y^(9/7) = x

interchanging the letters

y = x^(9/7)

hence the inverse function is solved to be f⁻¹(x) = x^(9/7)

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Answer:

Hope I helped!~

Step-by-step explanation:

To find the equation of the line, we can use the slope-intercept form of the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Using the two data points given, we can calculate the slope:

m = (11.25 - 8.35) / (1995 - 1993) = 1.95

To find the y-intercept, we can use one of the data points:

8.35 = 1.95(1993) + b

b = -3884.65

So the equation of the line is:

y = 1.95x - 3884.65

To predict the price of a box of two pieces on July 1, 1999, we can substitute x = 6 (since 1999 is 6 years after 1993) into the equation:

y = 1.95(6) - 3884.65

y = 11.7 - 3884.65

y = -3872.95

This gives us a negative price, which obviously does not make sense. It is likely that the price of a box of two pieces was not linearly increasing during this time period, or that there were other factors influencing the price. Therefore, we cannot use this equation to accurately predict the price of a box of two pieces on July 1, 1999.

Answer:

m=25/28

Step-by-step explanation:

Answer:

a) By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b) Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c) 0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less

d) 0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 0.9 and standard deviation 1.1.

This means that \(\mu = 0.9, \sigma = 1.1\)

Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.

This means that \(n = 1000, s = \frac{1.1}{\sqrt{1000}} = 0.035\)

a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.

By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b. What average numbers of children are reasonably likely in the sample?

By the Empirical Rule, 95% of the sample is within 2 standard deviations of the mean, so:

0.9 - 2*0.035 = 0.83

0.9 + 2*0.035 =  0.97

Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c. What is the probability that the average number of children per family in the sample will be 0.8 or less?

This is the p-value of Z when X = 0.8. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.8 - 0.9}{0.035}\)

\(Z = -2.86\)

\(Z = -2.86\) has a p-value of 0.0021

0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less.

d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?

p-value of Z when X = 1 subtracted by the p-value of Z when X = 0.8.

X = 1

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{1 - 0.9}{0.035}\)

\(Z = 2.86\)

\(Z = 2.86\) has a p-value of 0.9979

X = 0.8

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.8 - 0.9}{0.035}\)

\(Z = -2.86\)

\(Z = -2.86\) has a p-value of 0.0021

0.9979 - 0.0021 = 0.9958

0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Answer: the answer is u \(\geq\) 2

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

The value of y is 17.7

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal).

The sum of opposite angle of a parallelogram is 180. This means that the sum of opposite angle is supplementary.

Therefore ;

6y + 4y + 3 = 180

10y + 3 = 180

10y = 180 - 3

10y = 177

divide both sides by 10

y = 177/10

y = 17.7

Represent the opposite angle to 120 by x

therefore ,

120+x = 180

x = 180-120

x = 60

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Answer:

1/2 cups of apple juice.

Step-by-step explanation:

The ratio between apple juice to carrot juice is

1/4 : 1/2

By using this ratio we can find the number of cups of apple juice needed for one cup of carrot juice.

since 1 cup is twice the carrot juice in the ratio, we need twice the ratio in the apple juice as well.

1/4 * 2 = 2/4

This can be simplified to 1/2

C. For each term in this expression, you can just apply the power rule.

\(y = 3x^2 - \sqrt x + \dfrac2x = 3x^2 - x^{\frac12} + 2x^{-1}\)

\(\implies \dfrac{dy}{dx} = 2\cdot3x^{2-1} - \dfrac12 x^{\frac12-1} + (-1)\cdot2x^{-1-1}\)

\(\implies \dfrac{dy}{dx} = 6x - \dfrac12 x^{-\frac12} - 2x^{-2}\)

\(\implies \dfrac{dy}{dx} = 6x - \dfrac1{2\sqrt x} - \dfrac2{x^2}\)

Every other choice involves composite functions that do require the chain rule to differentiate.

Option C  : \(y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\\)  can be differentiated without using chain rule.

The differentiation of  \(y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\\)   without using chain rule can be done as follows:

\(\begin{aligned}\dfrac{dy}{dx} &= \dfrac{d}{dx}(3x^2 - \sqrt{x} + \dfrac{2}{x})\\\\&= \dfrac{d}{dx}(3x^2 - x^{\frac{1}{2}} + 2x^{-1})\\&= 6x - (1/2)x^{-\frac{3}{2}} -2x^{-2}\\\end{aligned}\)

The rest of the functions are composite, which means, that after differentiating them with some other base, you need to change the base and differentiate again, thus applying chain rule.

Thus, the function \(y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\\)   can be differentiated without using chain rule.

Thus, option C:   \(y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\\)   is correct option.

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Step 1

given

a): Group the like terms. Like terms are terms whose variables and exponents are the same

so

b)Simplify by combining like terms.

therefore, the answer is

I hope this helps you

The linear function for the total cost C is:

A function is an expression, rule, or law that defines a relationship between one variable.

Example:

\(f(\text{x}) = 2\text{x} + 1\)

\(f(1) = 2 + 1 = 3\)

\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The total cost for x cubic yards.

\(\bold{C = 28 + 48x}\)

Thus, the function is C = 28 + 48x.

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The rate of change for company A is 8.

The rate of change for company B is 15

Company A is better as it is charging less by a value of $18

What is rate of change?

Rate of change is the changes in the dependent variable when the independent variable changes by a unit value.

We are given 2 companies

A) equation for charges applied by company A is given by c=8h+10

Cost is a function of hours

To find the rate of change we differentiate the function

We get c' = 8

Rate of change for company A is 8

The cost for 4 hour rental is

c= 8(4)+10

c=32+10

c=$42

B) Company B charges $15 per hour

Rate of change for company B is 15

The cost for 4 hour rental is

c= 15(4)

c=$60

C) Company A is better to buy by $18 as the difference between the four hours price between company A and company B is $ 18

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The difference, in euros, between the cost of the newspaper in France and the cost of the newspaper in England is 2.10 euros.

Exchange rate is the rate at which one currency is exchanged for another currency.

Cost of the newspaper in England in euros = 2.50 x 1.16 = 2.90

Difference in costs = 5 euros - 2.90 euros = 2.10 euros

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Answer:

y=-2x+12

Step-by-step explanation:

Count how much the y raises for each x through division for the slop, and then plug that in to the x on either one of the pairs to get the number, and then add or subtract whatever the actual y is to get the y intercept.

Answer:

5 feet + 12 inches = 2 yards

48 inches = 1 foot + 1 yard

5 feet = 3 feet + 24 inches

Step-by-step explanation:

To help solve these equations, you must know how to convert feet to inches, inches to yards, etc. Use the information below:

1 feet = 12 inches

3 feet = 1 yard

To solve 5 feet + 12 inches = blank yard(s), convert 5 feet & 12 inches to yards. Since 5 feet would be complicated to convert, let's convert 12 inches to feet first.

12 inches = 1 feet

Instead of 12 inches, we can substitute it as 5 feet + 1 feet = blank yard(s). That would be 6 feet = ? yards. 3 feet = 1 yard, which tells us we must divide both sides by 3. Thus, 5 feet + 12 inches = 2 yards.

Blank inches = 1 foot + 1 yard

To find the # of inches in a yard, you must first know that 3 feet = 1 yard. If there are 12 inches in a foot, we must multiply 3 by 12, getting us 36. You add 12 inches (1 foot), getting us 48 inches in total. Thus 48 inches = 1 foot + 1 yard.

Blank feet = 3 feet + 24 inches

Since 3 feet is already feet, we do not need to convert it. If 12 inches is 1 foot, we must divide 24 inches by 12. So, there is 2 feet in 24 inches. 2 + 3 is 5. Thus, 5 feet = 3 feet +24 inches.

The equation that represents the distance, d, between the friends after t hours is d = √(3250t²)

From the question, we are to write an equation for the distance between the friends after t hours

From the given information,

"One heads North at 45 miles per hour, while the other heads East at 35 miles per hour"

First, we will calculate the distance each of them has traveled after t hours

Using the formula,

Distance = Speed × Time

Distance covered by the friend that heads North is

Distance = 45 × t

Distance = 45t

Distance covered by the friend that heads East is

Distance = 35 × t

Distance = 35t

Now, for the distance, d, between the two friends after t hours

Using the Pythagorean theorem, we can write that

d² = (45t)² + (35t)²

d² = 2025t² + 1225t²

d² = 3250t²

d = √(3250t²)

Hence, the equation that represents the distance, d, between the friends after t hours is d = √(3250t²)

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Answer: D

Step-by-step explanation:

m – 11

A. 11 more than a number ( m+11 )

B. the difference of a number and 11 ( 11/m )

C. the quotient of a number and 11  ( m/11 )

D. 11 less than a number ( m-11 )

Answer:

− 25 /27

Step-by-step explanation:

Answer:

-25/27

Step-by-step explanation:

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