A student was asked to use the formula for the perimeter of a rectangle, P = 2ℓ + 2w, to solve for ℓ. The student came up with an answer, P − 2w = 2ℓ. What error did the student make? Complete the explanation. Then solve for ℓ.

The student only rearranged the formula so? but
did not ?

The formula for ℓ is ℓ = .

Answer:

91

Step-by-step explanation:

Answer:

His grandfather gave him 91 books

Step-by-step explanation:

?= number of books grandfather gave

13 + ? = 104

?= 104-13

?=91

Answer:

Conclusion:

Step-by-step explanation:

Given

Two similar quadrilaterals

To determine

x, y, and z

Given that the two quadrilaterals are similar,

so their corresponding ratios will be:

x/10 = 5/4

x = 5/4 × 10

x = 50/4

x = 25/2

x = 12.5

Thus, the value of x = 12.5

To determine the value of y, the corresponding ratio such as

y/4 = 8/10

y =  8/10 × 4

y = 32/10

y = 16/5

y = 3.2

Thus, the value of y = 3.2

To determine the value of z, the corresponding ratio such as

z/5 = 15/x

as x = 12.5, so substitute x = 12.5

z/5 = 15/12.5

z = 15/12.5 × 5

z = 75/12.5

z = 6

Therefore, the value of z = 6

Conclusion:

Answer:

b= (-6,-7)

c= (-6,-2)

d= (0,-2)

e= (4,-7)

Step-by-step explanation:

Answer:

56 is the answer

Step-by-step explanation:

bcz sum is equal to 90

hence 90-34 = 56

The value of the exponent (2/5)^3 is \(\frac{8}{125}\)

In the above question, it is given that

(2/5)^3

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2^3) signifies 2 x 2 x 2 = 8.

We need to solve it and then find the value of the exponent

(2/5)^3

= \(\frac{2}{5}\) x \(\frac{2}{5}\) x \(\frac{2}{5}\)

= \(\frac{2 . 2. 2}{5 . 5 . 5}\)

= \(\frac{8}{125}\)

Therefore the value of the exponent (2/5)^3 is \(\frac{8}{125}\)

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If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9

The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.

However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).

Therefore, p must end in 5. This means that p can be written in the form:

p = 10n + 5

where n is some integer. Now, let's consider what happens when we divide p by 10:

p/10 = (10n + 5)/10 = n + 0.5

Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.

To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).

Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.

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Answer:

If it is expression than answer 6x-6

If it is an equation 5x-16=x+10 than answer is 13/2

Step-by-step explanation:

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\(\\ \sf \longmapsto 5x-16=x+10\)

\(\\ \sf \longmapsto 5x-x=10+16\)

\(\\ \sf \longmapsto 4x=26\)

\(\\ \sf \longmapsto x=\dfrac{26}{4}\)

\(\\ \sf \longmapsto x=\dfrac{13}{2}\)

Answer:

A translation

Step-by-step explanation:

The rectangle doesn't change, it just scoots over.

Answer:

Its the A

first

Step-by-step explanation:

3 is positive ( + )

2 is Negative ( - )

Without the specific values, we cannot ascertain the true statement. The five-number summary typically includes the minimum, first quartile (Q1), median (second quartile or Q2), third quartile (Q3), and maximum values of a dataset.

Without the specific values provided for the credit hours, it is not possible to determine the true statement. However, I can explain the general interpretation of the five-number summary.

In the first paragraph, we are unable to determine which statement is true without the actual values for the five-number summary of credit hours for the statistics class.

The five-number summary provides a concise summary of the distribution of data. The minimum represents the smallest value, Q1 represents the lower quartile or the value below which 25% of the data falls, the median represents the middle value or the value below which 50% of the data falls, Q3 represents the upper quartile or the value below which 75% of the data falls, and the maximum represents the largest value. By analyzing these summary statistics, we can gain insights into the spread, central tendency, and skewness of the dataset.

To determine which statement is true, we would need the actual values for the five-number summary. For example, if the minimum value is 2, Q1 is 4, the median is 6, Q3 is 8, and the maximum value is 10, we can make statements about the distribution of credit hours based on these values. However, without the specific values, we cannot ascertain the true statement.

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

if it's .2472/24 it is = .0103

but if it's 2472/24 it is = 103

Complete question :

Jason makes a fruit salad using only strawberries and blueberries. The ratio of strawberries to blueberries in Jason's fruit salad is 4 cups to 5 cups.

Options is in the attached picture

Which statement describes the contents of Jason's fruit salad?

Answer:

Blueberry makes up 5/9 of the fruit salad

Step-by-step explanation:

Ratio of strawberries to blue berries is 4cups to 5 cups

Hence, in a fruit salad makeup ;

We can say we have 4 cups of strawberry for every 5 cups of blue berry

Fraction of strawberry and blueberries :

Total ratio = (4 + 5) = 9

Fraction of strawberry = 4/ 9

Fraction of blueberry = 5/9

Hence, from the option  , the statement ;

Blueberry makes up 5/9 of the fruit salad is true since both are the only ingredients used

Answer: Let the side length of the square rug be x, and the dimensions of the rectangular rug be l and w.

In the first arrangement, the three rugs are arranged side by side, with the rectangular rugs aligned vertically and the square rug aligned horizontally. The length of this arrangement is l + 2x, and the width is w. We know that the length is 3 times the width, so we can write:

l + 2x = 3w

In the second arrangement, the two rectangular rugs are arranged side by side, with the square rug placed on top. The length of this arrangement is l, and the width is w + x. We know that the length is twice the width, so we can write:

l = 2(w + x)

We now have two equations with two unknowns, l and w:

l + 2x = 3w

l = 2(w + x)

Substituting the second equation into the first, we get:

2(w + x) + 2x = 3w

4x = w

Substituting this value of w into the second equation, we get:

l = 2(4x) = 8x

So the dimensions of the rectangular rug are 4x by x, and the dimensions of the square rug are x by x.

To find the value of x, we use the measurements given in the diagram:

l + 2x = 60

l = 36

Substituting into the equation l = 2(w + x), we get:

36 = 2(4x + x)

36 = 10x

x = 3.6

So the side length of the square rug is 3.6 feet.

Step-by-step explanation:

To write the equation in standard form for the circle passing through (–2, 4) centered at the origin, we need to find the radius and the center of the circle.

Since the circle passes through (–2, 4), we can use the distance formula to find the radius, which is the distance from the origin to (–2, 4).

The distance formula is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, x1 = 0, y1 = 0, x2 = –2, and y2 = 4. So, the radius is:

radius = sqrt((-2 - 0)^2 + (4 - 0)^2) = sqrt(20) = 2sqrt(5)

The center of the circle is the origin, since the circle is centered at the origin. Therefore, the equation of the circle in standard form is:

x^2 + y^2 = (2sqrt(5))^2 = 20

So, the equation of the circle passing through (–2, 4) centered at the origin is x^2 + y^2 = 20.

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By evaluating the expression for s(tB), we can determine whether driver A crossed the finish line before or after driver B. If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.

To solve the initial value problem, we start with the equation vA'(t) = -k(vA(t))^2, where vA'(t) represents the derivative of vA with respect to t.

This equation describes the deceleration of driver A, proportional to the square of his remaining speed. Rearranging and solving the differential equation, we get vA(t) = 1 / (kt + C), where C is a constant determined by the initial conditions.

To find the expression for s(t), we integrate vA(t) with respect to t: s(t) = ∫(1 / (kt + C)) dt. Integrating this expression gives us s(t) = (1/k) ln(kt + C) + D, where D is another constant determined by the initial conditions.

At t = t1 (when driver A's speed is halved, i.e., one mile after running out of gas), we have vA(t1) = vA(0) / 2. Plugging this into the expression for vA(t) from step 1, we find 1 / (k * t1 + C) = (1 / (k * 0 + C)) / 2. Simplifying, we get k = ln(2) / t1.

Using the expression for s(t) from step 2, we can find tB by settings S(tB) = 3 (since driver A was leading by 3 miles). Simplifying this equation, we find tB = (e^(3k) - C) / k. Plugging in the value of k we found in step 3, we have tB = (e^(3ln2 / t1) - C) / (ln2 / t1).

To evaluate s(tB), we substitute t = tB into the expression for s(t) from step 2, resulting in s(tB) = (1/k) ln(ktB + C) + D. Since tB depends only on vB and t1, and C and D are constants determined by the initial conditions, s(tB) depends only on vB.

If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.

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Answer:

452.389342 cubic inches

Step-by-step explanation:

The volume of a sphere is calculated using the formula V = 4/3 pi r^3

to determine the radius, you can notice that 4 spheres take up 24 in in length. This means that the radius of 1 sphere is 24/4/2 = 3 inches.

from there we plug and play: V = 4/3 * pi * 3^3 = 113.097336 cubic inches.

Note that this is only the volume of 1 sphere, so we multiply by 4

and we get 452.389342 cubic inches

Answer:

452.4

Step-by-step explanation:

Radius of each sphere: 24/4/2=3

Formula for volume: (4pir^3)/3

Formula for 4 spheres: 4 times (4pir^3)/3

Substitute 3 for r

Step-by-step explanation:

1.2.4) From the above information give and calculation done, which house would you recommend to Mrs Bhengu to buy .give reason for your answer.

Since McKenzie fills the 2-quart pitcher 2 times, there are a total of 4 quarts.

2 quarts × 2 times filled = 4 quarts

Recall that

1 quart = 4 cups

Since each quart is 4 cups, having 4 quarts is equivalent to

4 quarts × 4 = 16 cups

Therefore, there are a total of 16 cups of juice that was made.

Answer:

Step-by-step explanation:

you can find videos on yt for that

Answer:

sorry, I'm not sure. you need a little more description though

Teresa picked a total of 3 marbles because there are three bags shown and she picked one marble from each bag. Since each bag contains 8 marbles, the probability of picking any one marble from a bag is 1/8. So the probability of Teresa picking three specific marbles from each bag is (1/8) x (1/8) x (1/8) = 1/512.

If we assume that each bag contains marbles of a different color, then the probability of picking three different colors is 1, since there are 8 different colored marbles in each bag. If we assume that all the marbles in the bags are the same color, then the probability of picking three of the same color is (1/8) x (1/8) x (1/8) = 1/512.

In either case, the probability of Teresa picking three marbles with a specific color or pattern is very low. However, if she picked randomly without any specific pattern, then the probability of picking any three marbles is 1, since she can pick any three marbles from the bags.

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Answer:

-11 < x < 11

Step-by-step explanation:

The domain is the two points of the x, where one is the smallest and the biggest. In this case, -11 and 11 are the domains of this graph. And because this is not a close circle, there will not be an equal sign.

So, our answer is

-11 < x < 11

Answer:

if they are right angles

The ratio of collectible figures in a box to collectible figures not in a box is 1.5:1.

A ratio describes the relative size of one quantity or value compared to another.

Ratios can be determined as the quotient of two values or quantities related to each other.

Ratios are denoted in decimals, percentages, or fractions, just like proportions because they are fractional values.

The proportion of secondhand figures in a box = 60%

The remaining proportion of secondhand figures not in a box = 40% (1 - 60%)

The ratio of figures in a box to figures not in a box = 60:40 = 6:4 = 3:2

= 1.5:1

The sum of ratios is 5 (3 + 2).

Thus, 60% of the collectible figures in a box and 40% not in a box can be reduced to a ratio of 1.5:1 or 3:2.

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The value 2,649 represents the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 and the estimated population was 618.4.

The formula for population growth can be represented as:

P = P0ert

Here, P is the population of elephants, P0 is the initial population, e is the base of the natural logarithm, r is the rate of growth or decay, and t is the time in years.

Now, as per the given data, P = 2,649P0 = initial population r = 1.045 (as per the given expression)b = t - 1995 (as per the given formula)Now, putting these values in the population growth formula,

P = P0ert2,649 = P0e1.045(b-1995)Dividing by P0 on both sides, we get:e1.045(b-1995) = 2649/P0

Taking the natural logarithm on both sides,

ln e1.045(b-1995) = ln (2649/P0)

Applying the property of logarithm,1.045(b-1995) ln e = ln (2649/P0)1.045(b-1995) = ln (2649/P0)

vAs we need to find the value of P0, substitute the value of b = 0,1.045(0-1995) = ln (2649/P0)-1.045*1995 = ln (2649/P0)ln (2649/P0) = -2069.95

Taking anti-logarithm or exponentiation on both sides,2649/P0 = eln (2649/P0) = e^(-2069.95)2649/P0 = 4.29P0 = 2649/4.29P0 = 618.4

Therefore, the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 was 618.4.


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Answer:

A

Step-by-step explanation:

when you divide a fraction, you actually multiply by the reciprocal

Answer:

The correct answer is A, 4/5 x 5/4.

Step-by-step explanation:

I just remember to Keep Change Flip which means keep the first fraction exactly how it is, change the sign to a division sign, and flip the last fraction. So, go from 4/5 ÷ 4/5 = 4/5 x 5/4.

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Applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees

Based on the linear angles theorem, we have the following equation which we will use to find the value of y:

3y + 11 + 10y = 180

Add like terms

13y + 11 = 180

Subtract 11 from both sides

13y + 11 - 11 = 180 - 11

13y = 169

13y/13 = 169/13

y = 13

Plug in the value of y

3y + 11 = 3(13) + 11 = 50 degrees

10y = 10(13) = 130 degrees.

Therefore, applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees.

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The inverse Laplace transform of G(s) is \(g(t) = 10e^{-t} - 10e^{-3t}\).

To find the inverse Laplace transform of the given function G(s), we can use partial fraction decomposition and known Laplace transforms. The partial fraction decomposition of G(s) is:

\(G(s) = 10s^2e^{-s} / (s+1)(s+3)\)

To perform the partial fraction decomposition, let's write G(s) in the following form:

G(s) = A/(s+1) + B/(s+3)

To find the values of A and B, we need to find a common denominator for the two fractions on the right-hand side:

\(10s^2e^{-s} = A(s+3) + B(s+1)\)

Expanding the right-hand side:

\(10s^2e^{-s} = As + 3A + Bs + B\)

Now, equating the coefficients of \(s^2\), s, and the constant term:

Coefficient of \(s^2\):

10 = A

Coefficient of s:

0 = A + B

Constant term:

0 = 3A + B

From the first equation, A = 10. Substituting this value in the second and third equations:

0 = 10 + B

0 = 3(10) + B

From the second equation, B = -10. Substituting B = -10 into the third equation:

0 = 3(10) - 10

0 = 30 - 10

0 = 20

Now that we have the values of A and B, we can rewrite G(s) as:

G(s) = 10/(s+1) - 10/(s+3)

To find the inverse Laplace transform of G(s), we can use the known Laplace transform pairs. The inverse Laplace transform of 10/(s+1) is 10e^(-t), and the inverse Laplace transform of \(-10/(s+3) is -10e^{-3t}\). Therefore, the inverse Laplace transform of G(s) is:

\(g(t) = 10e^{-t} - 10e^{-3t}\)

So, the inverse Laplace transform of G(s) is \(g(t) = 10e^{-t} - 10e^{-3t}\).

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Answer:

ccccc

Step-by-step explanation:

cccccc