The lightest puppy in a litter weighs 12 ounces, which is
4/7
of the weight of the heaviest puppy.

The equation
4/7
w = 12 can be used to find the weight w in ounces of the heaviest puppy.

How much does the heaviest puppy weigh?

X goes left and right. Y goes up and down. Hope this help:)

Answer:

  49 = 7²

Step-by-step explanation:

A logarithm is an exponent. The base of the logarithm is the base of the exponent. The base to that exponent is the argument of the log function.

__

The logarithm (exponent) is 2. The base is 7. The argument of the log function is 49. In exponential form, this is written ...

  7² = 49

The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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Answer:

The correct answer is 14 yards.

Step-by-step explanation:

Area can be described as a measuring unit to measure the space in any flat surface. The square is a flat surface comprising of four equal sides. Area of a square would be the measure of the length of each size.

As per the question, the area of lawn is 196 yards and it is square shaped. This means that the length of each side would be would be 14 yards.

The area will be calculated by taking the square root of one of the equal sides. The square root of 14 is 196. hence, the correct answer is 14 yards.

- Sophia

The optimal number of necklaces for the necklace start-up to sell to make the most profit is 60.

Finding the maximum or minimum value of a function is known as optimization. In mathematical terms, optimization involves finding the values of the input variables that maximize or minimize a given output function, subject to some constraints.

In order to find the maximum or minimum value of a function, one commonly used method is to take the derivative of the function with respect to the input variable, and then set it equal to zero to find the critical points. The critical points can be either maximum or minimum points.

Here we have

A necklace start-up makes a profit, π, in dollars according to the following function of the number of necklaces, q, that they sell:

π(d) = 360q − 3q

To find the optimal number of necklaces that the necklace start-up should sell to make the most profit,  

Find the maximum value of the profit function π(q) = 360q - 3q^2.

To do this, take the derivative of the profit function with respect to q,

set it equal to zero, and solve for q:

=> π'(q) = 360 - 6q         [ derivation with respect to d ]

=> 0 = 360 - 6q

=> 6q = 360

=> q = 60

Therefore,

The optimal number of necklaces for the necklace start-up to sell to make the most profit is 60.

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Answer:

I am not sure but think that the answer is 1/20

I believe you convert the whole number into a mixed fraction.

5 converted into quarters is 20/4. Then you divided 1/4 by 20/4.

1/4 divided by 20/4 is 1/20 or 0.05.

Please, don't refrain to tell me if this is incorrect. Thank you.

Equation of the line that passes through points (-2, 0) and (0, 6) is y = 3x + 6

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

Given,

Line passes through (-2 , 0) and (0,6)

Equation of the line

y - y₁ = ((y₂ - y₁) / (x₂ - x₁)) (x - x₁)

y - 0 = ((6 - 0) / (0 - -2)) (x - -2)

y = (6/2)(x + 2)

y = 3x + 6

Hence, y = 3x + 6 is equation of the line.

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The location of the center and the radius will be (-1.5. -2) and 3, respectively. Thus, the correct option is A.

Given that:

Equation: (x + 1.5)² + (y + 2)² = 9

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

Compare the equation, then we have

Center: (-1.5, -2)

Radius: r² = 9 ⇒ r = 3

Thus, the correct option is A.

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Answer: m = -2.

The given equation is: \(\frac{m}{m+4}+\frac{4}{4-m}=\frac{m^{2}}{m^{2}-16}\).

The LCM of the denominators = \(m^{2}-16=(m+4)(m-4)\).

We multiply both sides by LCM.

\(\left(m+4\right)\left(m-4\right)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=\left(m+4\right)\left(m-4\right)\cdot\frac{m^{2}}{m^{2}-16}\)

\(m\left(m-4\right)-4\left(m+4\right)=m^{2}\)

\(m^{2}-4m-4m-16=m^{2}\)

\(8m=-16\\m=-2\)

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Answer:

M=-2 B

Step-by-step explanation:

trust me i took the quiz

The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

     *look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

    \(?^2+9^2 = 16^2\\?^2 + 81=256\\?^2 = 175\\? = 13.2\)

Thus the missing side length is 13.2 cm

Hope that helps!

Answer: I think that the answer is 3/4 miles

Step-by-step explanation:

Answer:

a) 8.23% probability that a piece of pottery will be finished within 95 minutes

b) 0.28% probability that it will take longer than 110 minutes.

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Two variables:

Means \(\mu_{a}, \mu_{b}\)

Standard deviations \(\sigma_{a}, \sigma_{b}\)

Sum:

\(\mu = \mu_{a} + \mu_{b}\)

\(\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}\)

In this question:

\(\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3\)

So

\(\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100\)

\(\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61\)

A) What is the probability that a piece of pottery will befinished within 95 minutes?

This is the pvalue of Z when X = 95.

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

\(Z = \frac{95 - 100}{3.61}\)

\(Z = -1.39\)

\(Z = -1.39\) has a pvalue of 0.0823

8.23% probability that a piece of pottery will befinished within 95 minutes.

B) What is the probability that it will take longer than 110 minutes?

This is 1 subtracted by the pvalue of Z when X = 110.

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

\(Z = \frac{110 - 100}{3.61}\)

\(Z = 2.77\)

\(Z = 2.77\) has a pvalue of 0.9972

1 - 0.9972 = 0.0028

0.28% probability that it will take longer than 110 minutes.

Answer: 9

Step-by-step explanation:

72÷9=8

9÷9=1

72/9 = 8/1

The expected value is ((18/37) x (2 x wager [we will receive the wager back and the winnings])) + ((19/37) x 0)

What is American roulette?

Guessing on which number on the wheel ball will come to rest is the objective of American Roulette. Every number contains the same chances as any other number of coming up on each spin (that is winning number on any spin has no effect on the outcome of next spin). The best chance of payout is provided by an outside bet. The possible outcomes of the game of roulette is covered by 'outside bets'. With the higher winning chances, the payout is not going to be incredibly generous(it's only 1:1 for bets like odd or even that covers almost like half the wheel).

Expected value is calculated by adding all the different possible outcomes multiplied by their probabilities.  

So, in this case (0.5 x $2) + (0.5 x $1).  

For specific example it would be determined by the number of options on a roulette wheel (generally 37).  

So winning on this bet in 18 outcomes (the even numbers) and losing on 19 outcomes (the odd numbers + 0).  

Putting it all together, the expected value is ((18/37) x (2 x wager [we will receive the wager back and the winnings])) + ((19/37) x 0).

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\(\frac{x}{3x}+\frac{8x}{3x}=\frac{1}{3}+\frac{8}{3}=3\)

Answer:

Step-by-step explanation:

y = ½(x-4)² + 13

y = ½(x² - 8x + 16) + 13

y = ½x² - 4x + 21

The exact same number of elements from Y is assigned to each element of X via a mathematical function from a set X to a set Y and with x=7 in the graph, the value of y is -5.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Initially, functions represented the idealized relationship between two changing quantities.

This is illustrated by the equation y=x².

Any input for x results in a single output for y.

Considering that x is the input value, we would state that y is a function of x.

So, according to the graph, y=-5 at x=7.

Therefore, the exact same number of elements from Y is assigned to each element of X via a mathematical function from a set X to a set Y and with x=7 in the graph, the value of y is -5.

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Correct question:

Find the value of f(7). y = f(x)

Answer:

She will be charged $180 once lets the account go past 6 months before making a payment.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

\(E = P*I*t\)

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

\(T = E + P\)

In this question:

If she pays within 6 months, she is not charged any interest.

However, if after 6 months she has not paid the balance, she is charged 20% interest for this period.

Barbara financed a new bedroom set at the furniture store for $1,800.

This means that \(P = 1800\)

20 percent interest

This means that \(I = 0.2\)

How much interest will she be charged once she lets the account go past 6 months?

6 months is half a year, so this is E when \(T = 0.5\)

\(E = P*I*t\)

\(E = 1800*0.2*0.5\)

\(E = 180\)

She will be charged $180 once lets the account go past 6 months before making a payment.

$960 per month on her entertainment budget

If Amy decides to live with her parents or a relative, she will save $8,640 compared to living on campus over the 9-month period ($12,798 living on campus minus $4,158 living with a relative).

Since we are wondering what she can now use for entertainment each month, we divide the number of dollars saved from living with a relative by 9 months.

$8,640 / 9 months = $960 per month

Amy is now able to reallocate $960 per month on her entertainment budget since she currently doesn't have an entertainment budget listed.

Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

Answer:

y=-2.5x-6 is the answer

Answer:

  1/60 gallon

Step-by-step explanation:

You want to know what is left of 4/5 gallon of paint if 3/4 gallon was used to paint a doghouse, and 2/3 of the remaining amount was used to paint a door.

To find the amount remaining we subtract the amount used for the doghouse from the original amount:

  4/5 -3/4 = (16 -15)/20 = 1/20 . . . . . gallon

2/3 of that was used, so 1/3 of it remains:

  (1/3)(1/20 gallon) = 1/60 gallon

There is 1/60 of a gallon of paint left in the can.

__

Additional comment

In a standard size gallon paint can, that's about 0.11 inches of paint in the bottom.

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Answer:

A

Step-by-step explanation:

A is a triangular prism

Using common factor method, sum of the given expressions is 17.14m + 9.37

what is common factor ?

In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.

In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.

According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:

(5.19 + 4.18) + (4m + 3.95m)

9.37 + 7.95m

So, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m

Now, we can use the distributive property to factor out a common factor of m from 7.95m:

9.37 + 7.95m = 4m + (5.19 + 7.95)m

We can factor out a common factor of 1 from (5.19 + 7.95)m:

4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m

Adding the coefficients, we get:

4 + 5.19 + 7.95 = 17.14

Therefore, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip