Molly rode her bike 15 miles in 1.75 hours. Then she rode it for 10 miles in .75 hours. What is her average speed?

Answer:

55 L

Step-by-step explanation:

Step-by-step explanation:

hg=4

if correct then can we become friends

Answer: Complex

Step-by-step explanation:

Answer:

I think the answer is complex number.

Step-by-step explanation:

The set of complex numbers is denoted by either of the symbols ℂ or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.

Hope this helps!!

The payback period of the project is 2 years.

The payback period is a financial metric used to evaluate the time it takes for an investment to recoup its initial cost. It measures the length of time required for the cash inflows from the investment to equal or surpass the initial investment amount. In this case, the initial investment is $35,000, and the cash flows are $10,000 in year 1, $20,000 in year 2, and $10,000 in year 3. To calculate the payback period, we need to determine in which year the cumulative cash inflows will equal or exceed the initial investment.

By adding the cash flows year by year, we can see that at the end of year 1, the cumulative cash inflow is $10,000. By the end of year 2, the cumulative cash inflow becomes $30,000 ($10,000 from year 1 + $20,000 from year 2). Finally, at the end of year 3, the cumulative cash inflow reaches $40,000 ($10,000 from year 3).

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Using the laws of exponents, we can find that the equation holds true when the value of a=3 and b=3.

A number's exponent shows how many times the initial number has been multiplied by itself. For instance, the number 4 has been multiplied by itself three times in the formula 4 × 4 × 4 = 4³, where 3 is the exponent of 4. The term 4 to the power of 3 denotes an exponent, also referred to as the power of a number. Whole numbers, fractions, decimals, and even negative values can be exponents.

Here in the question,

Given equation:

\(\frac{(2xy)^{4}}{4xy}\) = \(4x^{a}y^{b}\)

To find the value of a and b the equation must hold true. So, we must prove LHS = RHS.

Taking LHS,

\(\frac{(2xy)^{4}}{4xy}\)

= \(\frac{2^{4}x^{4}y^{4}}{4xy}\) (Using the rule: \(ab^{m}\) = \(a^{m} b^{m}\) )

= \(\frac{16x^{4}y^{4}}{4xy}\)

= \(4x^{4}y^{4}x^{-1}y^{-1}\) (Using the rule: \(\frac{1}{a^{m}}\) = \(a^{-m}\))

= \(4x^{4-1}y^{4-1}\) (Using the rule: \(a^{m}.a^{n}\) = \(a^{m+n}\))

= 4x³y³

Comparing this with the RHS of the main equation, we can get the values of a and b to be 3.

Therefore, when a=3 and b=3 the equation holds true.

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The complete question is:

Which values of a and b make the equation true?

a = 0, b = 0

a = 3, b = 3

a = 4, b = 4

a = 5, b = 5

Answer:

0.136

Step-by-step explanation:

Answer:

3/22

Step-by-step explanation:

for decimal dorm it is 0.136

Answer:

The common ratio of a geometric series is \dfrac14

4

1 ​

start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

\(r = \frac{1}{4}\)

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

\(s_n=\frac{a_1(1-r^n)}{1-r}\)

common ratio, n=4 and equate to 170.

\(\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170\)

\(\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4} \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2} \\\\\frac{1}{256} a_1 = \frac{1}{2} \\\\ a_1 = \frac{1}{2} \times 256\\\\a_1 = \frac{1}{2} \times 256 \\\\= 128\)

Answer:

The first term is 128

Stokes' Theorem states that the line integral of a vector field F along a closed curve C is equal to the surface integral of the curl of F over the surface S bounded by C.

To evaluate the line integral C F.dr using Stokes' Theorem, we can first calculate the curl of the vector field F. Then, we find the surface that is bounded by the given curve C, which is a triangle in this case. Finally, we evaluate the surface integral of the curl of F over that surface to obtain the result.

Stokes' Theorem states that the line integral of a vector field F along a closed curve C is equal to the surface integral of the curl of F over the surface S bounded by C. In this problem, we are given the vector field F(x,y,z) = (x+y^2)i + (y+z^2)j + (z+x^2)k and the curve C, which is a triangle with vertices (1,0,0), (0,1,0), and (0,0,1).

To apply Stokes' Theorem, we first need to calculate the curl of F. The curl of F is given by the determinant of the curl operator applied to F: ∇ × F = ( ∂F₃/∂y - ∂F₂/∂z )i + ( ∂F₁/∂z - ∂F₃/∂x )j + ( ∂F₂/∂x - ∂F₁/∂y )k.

After finding the curl of F, we need to determine the surface S bounded by the curve C. In this case, the curve C is a triangle, so the surface S is the triangular region on the plane containing the triangle.

Finally, we evaluate the surface integral of the curl of F over S. This involves integrating the dot product of the curl of F and the outward-pointing normal vector to the surface S over the region of S.

By following these steps, we can use Stokes' Theorem to calculate the integral C F.dr for the given vector field F and curve C.

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Answer:

B. 5

Step-by-step explanation:

This table does not describe a linear relationship. This is because the table does not have a constant rate of change; between the first two points, the function changes by

(1/2 - 1/10)/(0--1) = (5/10 - 1/10)/(1) = 5/10 - 1/10 = 4/10 = 2/5

Between the second two points, the function changes by

(5/2-1/2)/(1-0) = (4/2)/1 = 4/2 = 2

Comparing the first two y-coordinates, we have 1/10 and 1/2 = 5/10. This is the result of multiplication by 5.

Comparing the second two y-coordinates, we have 1/2 and 5/2. This is the result of multiplication by 5.

Comparing the rest of the y-coordinates, we can see that each time, the y-coordinate is multiplied by 5. This means the rate of change is 5.

Answer:

28

Step-by-step explanation: So 21 miles to 3 first i divided 21 by 3 and got 7 and i just added seven 1 more time to get 28

A. y = 4x-7, the inverse function is, x = (y + 7)/4

B. y = 7x, the inverse function is, x = y/7

C. y = 7x-4, the inverse function is, x = (y + 4)/7

D. y = x-4, the inverse function is, x = y + 4

E. y = x+4, the inverse function is, x = y - 4

F. y = x-4/7, the inverse function is, x = 7y + 4

The inverse of each of the functions is calculated as follows;

y = 4x - 7

x = 4y - 7

4y = x + 7

y = (x + 7)/4  

⇒ x = (y + 7)/4

Second function;

y = 7x

x = 7y

y = x/7

⇒ x = y/7

Third function;

y = 7x - 4

x = 7y - 4

7y = x + 4

y = (x + 4)/7

⇒ x = (y + 4)/7

Fourth function;

y = x - 4

x = y - 4

y = x + 4

⇒ x = y + 4

Fifth function;

y = x + 4

x = y + 4

y = x - 4

⇒ x = y - 4

Sixth function;

y = (x - 4)/7

x = (y - 4)/7

7x = y - 4

y = 7x + 4

⇒ x = 7y + 4

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40.13  percentage of the bottles contain less than 32 oz of soda.

Mean (μ) = 32.3 oz

Standard Deviation (σ) = 1.2 oz

Threshold value (X) = 32 oz

We can use the standard normal distribution (Z-distribution) to calculate the cumulative probability.

First, let's standardize the threshold value using the formula

Z = (X - μ) / σ

Z = (32 - 32.3) / 1.2 Z ≈ -0.25

Next, we'll look up the cumulative probability corresponding to Z = -0.25 in the standard normal distribution table or use a calculator.

From the standard normal distribution table or calculator, we find that the cumulative probability for

Z = -0.25 is approximately 0.4013.

This means that approximately 40.13% of bottles contain less than 32 oz of soda.

Therefore, about 40.13% of the bottles contain less than 32 oz of soda.

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Answer:

Sum of interior angles of a pentagon

Angles H and G are same as the trapezoid is isosceles

The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

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To calculate Joey's current grade, we need to apply the weighted average formula. We'll multiply each category (tests, quizzes, and homework) by its respective weight and then sum up the results.

Test average contribution = 82 * 0.60 = 49.2

Quiz average contribution = 77 * 0.25 = 19.25

Homework average contribution = 98 * 0.15 = 14.7

Joey's current grade = Test average contribution + Quiz average contribution + Homework average contribution

= 49.2 + 19.25 + 14.7

= 83.15

Therefore, Joey's current grade is 83.15. Rounding it to the nearest tenth, we get 83.2.

The closest option to 83.2 is Option B: 83.15%. So the correct answer is B. 83.15%.

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

(b) 217 cm

Step-by-step explanation:

The computation of the number of centimeters will each have is shown below:

= Length of the string ÷ number of pieces

= 10.85 meters ÷ 5

= 2.17 meters

= 217 centimeters

hence, the correct option is b.

To find the greatest volume under the given conditions, we need to optimize the volume function V in terms of the edge length of the square base (denoted by L) and the height of the box (denoted by H).

The volume V of the box is given by V = L^2 * H. We want to find the values of L and H that maximize this volume.

To optimize the volume function, we can take the derivative of V with respect to L and H, respectively, and set the derivatives equal to zero to find the critical points.

Taking the derivative of V with respect to L:

dV/dL = 2LH

Setting this derivative equal to zero:

2LH = 0

Since we are looking for positive values of L and H, we can conclude that L = 0 does not yield the maximum volume.

Next, let's take the derivative of V with respect to H:

dV/dH = L^2

Setting this derivative equal to zero:

L^2 = 0

Again, since we are looking for positive values of L and H, we can conclude that H = 0 does not yield the maximum volume.

Therefore, the critical points are L = 0 and H = 0, but they do not yield the maximum volume.

To find the maximum volume, we need to consider the boundary conditions. In this case, the length of the square base, L, and the height of the box, H, are constrained. However, the specific values or constraints for L and H are not provided in the question.

Without specific constraints, we cannot determine the exact values of L and H that yield the greatest volume. To find the greatest volume, we need additional information or constraints related to the specific dimensions or limitations of the box.

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Answer:

i think let me see

Step-by-step explanation:

For a larger input size of 320,000 elements, it will take 240 ms to sort each half and 24 ms to merge the sorted halves, resulting in a total time of 264 ms.

The given information describes the time required for sorting and merging operations on two different input sizes. For 80,000 elements, it takes 18 ms to sort each half, resulting in a total of 36 ms for sorting. Merging the two sorted halves with 80,000 numbers in each takes 40 - 18 = 22 ms.

When the input size is doubled to 320,000 elements, the sorting time for each half increases to 240 ms, as it scales linearly with the input size. The merging time, however, remains constant at 4 ms since the size of the sorted halves being merged is the same.

Thus, the total time for sorting and merging 320,000 elements is the sum of the sorting time (240 ms) and the merging time (4 ms), resulting in a total of 264 ms.

Therefore, based on the given information, the total time required for sorting and merging 320,000 elements is 264 ms.

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Step-by-step explanation:

Distance between (5,-3) and (9,1)=√(9-5)^2+(1-(-3))^2

=√4^2+4^2

=√16+16

=√32 units

It's not possible to calculate the distance between these points by pythagoras theorem .We can easily calculate it by distance formula I.e.√(x2-x1)^2+(y2-y2)^2

The expression √(128x⁸y³z⁹) is equivalent to the expression 8x⁴yz⁴ √(2yz). Then the correct option is C.

The missing options are given below.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ √(128x⁸y³z⁹)

Then the expression is given below.

⇒ √[(64 × 2)(x⁴)²(y²y)(z⁸z)]

⇒ 8x⁴yz⁴ √(2yz)

Then the correct option is C.

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so hmmm say A(-10 , 5) , B(8 , 2) and the point that partitions them is point C.

\(\textit{internal division of a line segment using ratios} \\\\\\ A(-10,5)\qquad B(8,2)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-10,5)=1(8,2)\)

\((\stackrel{x}{-20}~~,~~ \stackrel{y}{10})=(\stackrel{x}{8}~~,~~ \stackrel{y}{2}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-20 +8}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{10 +2}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -12 }{ 3 }~~,~~\cfrac{ 12}{ 3 } \right)\implies \boxed{C=(-4~~,~~4)}\)

Answer:

Data collected shows that the more you water, the larger your plant will grow. If you use the following Equation, y = 1/2x + 2 How tall will a plant be at 25 weeks if x is the number of weeks watered and y represents the height of the plant? Show your work.

Step-by-step explanation:

The solution to -3 ≤ x ≤ 1 is represented by graph A.

aph A.

'In math, a

'In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.'

According to the given problem,

we know,

-3 ≤ x < 1 means, the values of x will lie between -3 and less than 1 because x is less than 1. The darkened region of the number line signifies that the value of x includes all real numbers between -3 and less than 1.

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Answer:

mean is 19

Step-by-step explanation:

sorry that's all I know

The ratio of yellow to all skittles is

Answer:

\(0.2\ km\ per\ minute\)

Step-by-step explanation:

\(As\ we\ are\ given\ that,\\Time\ Jerry\ takes\ with\ the\ Force\ of\ Wind\ in\ his\ direction=10\ minutes\\Time\ Jerry\ takes\ with\ the\ Force\ of\ Wind\ against\ his\ direction=15\ minutes\\Considering\ only\ the\ direction\ of\ the\ forces\ are\ opposite\ and\ the\\ magnitudes\ equal,\\Let\ the\ time\ Jerry\ take\ travelling\ through\ a\ still\ wind\ be\ x\\Let\ the\ Force\ of\ wind\ be\ F.\\Hence,\\x+F=10\\x+(-F)=15\\By\ simply\ adding\ the\ equations,\\2x=10+15\\2x=25\\x=\frac{25}{2}\\\)

\(x=12.5\\Hence,\\Time\ taken\ by\ Jerry\ during\ a\ still\ wind=12.5\ seconds.\\We\ also\ observe\ that\ 12.5\ is\ the\ mean\ of\ 10\ and\ 15\ and\ lies\ between\\ the\ two\ extremes.\\Hence,\\As\ we\ now\ know\ that,\\Distance\ from\ the\ library=2.5\ km\\Time\ taken\ by\ Jerry\ during\ the\ still\ wind=12.5\ minutes\\Hence,\ we\ know\ that\\Speed=\frac{Distance}{Time}\\Here,\\Speed=\frac{2.5}{12.5}\\Speed=\frac{1}{5}\ or\ 0.2\ km\ per\ minute\)

Answer:

y= 1/2x + 2

an equation set up is y= mx + b. the line started at 2 so b=2. then you look at see how much you increased each time, which in this case was 1/2. m=1/2