In the pair competition of Olympic figure skating, a 60-kg male skater pushes a 45-kg female skater. If the push caused the female to accelerate at 2.0 m/s, what is the acceleration of the male skater?

Answer:

(3,1)

Step-by-step explanation:

Answer:

n = 1

Step-by-step explanation:

n - 6 = 5(n-2)

n - 6 = 5n - 10

-6 +10 = 5n - n

4 = 4n

n = 4/4

Answer:

\(Area = 129.5m^2\)

\(Perimeter = 48m\)

Step-by-step explanation:

Given

See attachment

Required

Determine the area and the perimeter of the garden

Calculating Area

First, we calculate the \(area\ of\ the\ rectangle\)

\(A_1 = L * B\)

Where:

\(L = 20-(3.5 +3.5)\)

\(B = 7\)

So:

\(A_1 = (20 - (3.5 + 3.5)) * 7\)

\(A_1 = (20 - 7) * 7\)

\(A_1 = 13 * 7\)

\(A_1 = 91\)

Next, we calculate the area of the two semi-circles.

Two semi-circles = One Circle

So:

\(A_2 = \pi r^2\)

Where

\(r = \frac{7}{2}\)

\(A_2 = \frac{22}{7} * (\frac{7}{2})^2\)

\(A_2 = \frac{22}{7} * \frac{49}{4}\)

\(A_2 = \frac{22}{1} * \frac{7}{4}\)

\(A_2 = \frac{22*7}{4}\)

\(A_2 = \frac{154}{4}\)

\(A_2 = 38.5\)

Area of the garden is

\(Area = A_1 + A_2\)

\(Area = 91 + 38.5\)

\(Area = 129.5m^2\)

Calculating Perimeter

First, we calculate the perimeter of the rectangle

But in this case, we only consider the length because the widths have been covered by the semicircles

\(P_1 = 2 * L\)

Where:

\(L = 20-(3.5 +3.5)\)

So:

\(P_1 =2 * (20-(3.5 +3.5))\)

\(P_1 =2 * (20-7)\)

\(P_1 =2 * 13\)

\(P_1 =26\)

Next, we calculate the perimeter of the two semi-circles.

Two semi-circles = One Circle

So:

\(P_2 = 2\pi r\)

Where

\(r = \frac{7}{2}\)

\(P_2 = 2 * \frac{22}{7} * \frac{7}{2}\)

\(P_2 = \frac{2 * 22 * 7}{7 * 2}\)

\(P_2 = \frac{308}{14}\)

\(P_2 = 22\)

Perimeter of the garden is

\(Perimeter = P_1 + P_2\)

\(Perimeter = 26 + 22\)

\(Perimeter = 48m\)

Answer:

0.00005

Step-by-step explanation:

Answer:

0.01

.......................

The rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.

The volume of a sphere can be found using the equation V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere.

The surface area of a sphere can be found using the equation A = 4 * pi * r^2, where A is the surface area.

To find the rate of change of the surface area, we can use the chain rule of calculus:

dA/dt = dA/dr * dr/dt

We know that dr/dt = 2409 cubic inches per minute (from the problem statement). To find dA/dr, we can take the derivative of the surface area equation with respect to r:

dA/dr = 8 * pi * r

Now we can substitute these values into the chain rule equation:

dA/dt = 8 * pi * r * dr/dt

When the radius of the sphere is 99 inches, we can substitute this value into the equation:

dA/dt = 8 * pi * 99 * 2409 cubic inches^2 per minute

So, the rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.

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One-half of the dogs in each shelter are between the weights represented by the first and third quartiles, which are approximately 20-55 pounds for the first shelter and 25-65 pounds for the second shelter, respectively.

A box plot is a visual representation of a set of data that shows the median, quartiles, and outliers of the data. The box represents the middle 50% of the data, with the bottom and top edges of the box representing the first and third quartiles, respectively. The line inside the box represents the median, or the middle value of the data set. The "whiskers" extend from the edges of the box to the minimum and maximum values of the data set, but outliers beyond the whiskers are represented as individual points.

Now, let's look at the two box plots showing the weights of dogs in two different animal shelters. One-half of the dogs in each shelter are between the first and third quartiles, which are represented by the edges of the box in each plot.

If we take the first box plot, we can see that the first quartile is approximately 20 pounds and the third quartile is approximately 55 pounds. Therefore, one-half of the dogs in this shelter weigh between 20 and 55 pounds.

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If a number cube is rolled 25 times and 6 appears only four times, then the experimental probability of getting 6 is 4/25.

The experimental probability of an event happening is the number of times the event occurred divided by the total number of trials. In this case, a number cube is rolled 25 times and lands on 6 four times. Here are the steps to determine the experimental probability of landing on 6:

So, the experimental probability of landing on 6 is 4/25, which means that if we roll the number cube many more times, we would expect to get a 6 approximately 4 out of every 25 rolls.

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the monthly payments for the loan are approximately $2,372.51.

To calculate the monthly payments for the loan, we need to use the following formula:

PMT = (r * PV) / (1 - (1 + r)^(-n))

where PMT is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (in this case, $100,000), and n is the number of monthly payments (in this case, 4 years * 12 months/year = 48 months).

To calculate the monthly interest rate, we need to first calculate the nominal annual interest rate, compounded monthly. We can do this using the following formula:

r_nom = (1 + r_eff)^(1/12) - 1

where r_eff is the effective annual interest rate, which is given as 9.25%. Substituting:

r_nom = (1 + 0.0925)^(1/12) - 1 = 0.007449

So the monthly interest rate is 0.7449%.

Now we can plug in the values to the formula for PMT:

PMT = (0.007449 * 100000) / (1 - (1 + 0.007449)^(-48)) = $2,372.51

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There are three defects, and two pencils can be considered defectives.  a crack with broken lead, being broken in half, and a missing eraser. Each defect represents a unique issue or imperfection in the respective pencil.

Examining the three pencils, we can identify three distinct defects: a crack with broken lead, being broken in half, and a missing eraser. Each defect represents a unique issue or imperfection in the respective pencil.

Now, considering the term "defectives," it refers to the number of pencils that have defects. In this case, two out of the three pencils exhibit defects. The pencil with the crack and broken lead, as well as the pencil broken in half, can be categorized as defectives since they possess flaws affecting their functionality or appearance.

there are three defects present among the three pencils, representing the specific issues each pencil has. Additionally, two pencils can be classified as defectives, indicating the number of pencils that possess one or more defects.

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Answer:

probability distribution

There are no restrictions on the value of h for which b is in the plane spanned by a1 and a2

To determine if vector b is in the plane spanned by vectors a1 and a2, we need to see if there exist scalars c1 and c2 such that b = c1a1 + c2a2.

Let's set up this equation and solve for h:

b = c1a1 + c2a2

⇔

left bracket Start 3 By 1 Matrix 1st Row 1st Column 4 2nd Row 1st Column 8 3rd Row 1st Column h End Matrix right bracket

c1 * left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 4 3rd Row 1st Column −1 End Matrix right bracket

c2 * left bracket Start 3 By 1 Matrix 1st Row 1st Column −7 2nd Row 1st Column −24 3rd Row 1st Column 3 End Matrix right bracket

This gives us the system of equations:

c1 - 7c2 = 4

4c1 - 24c2 = 8

-c1 + 3c2 = h

We can solve this system using Gaussian elimination or another method to get:

c1 = -2h/5

c2 = -(3h + 20)/35

Now, we need to ensure that there exist values of c1 and c2 that satisfy these equations for any value of h. In other words, we need to make sure that the system of equations has a solution for any value of h.

One way to do this is to use the determinant of the coefficient matrix of the system. If the determinant is nonzero, then the system has a unique solution for any value of the constants on the right-hand side (in this case, the vector b).

The determinant of the coefficient matrix is:

left| Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column negative 7 3rd Column negative 1 2nd Row 1st Column 4 2nd Column negative 24 3rd Column 3 3rd Row 1st Column negative 1 2nd Column 3 3rd Column 0 End Matrix End| right| equals 100 \(\neq\) 0

Since the determinant is nonzero, there exists a unique solution for any value of b, and therefore a unique value of h that satisfies the system of equations.

Therefore, b is in the plane spanned by a1 and a2 for any value of h.

In other words, there are no restrictions on the value of h for which b is in the plane spanned by a1 and a2

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Answer:

163 times

Step-by-step explanation:

Let us first find how many minutes she was on the International Space Station:

1 hour = 60 minutes

114.1 hours = 114.1 * 60 = 6846 minutes

The station orbits earth every 42 minutes. Therefore, the number of times the station will orbit the earth during her stay is:

6846 / 42 = 163 times

ANSWER

EXPLANATION

Given that;

Let U(x) = 2x and V(x) = x^2 + 1

Apply the quotient rule to find the derivative of f(x)

Differentiate U and V with respect to x

Hence, we have

Answer:

1.8%

Step-by-step explanation:

2.85-2.80=$0.05

$0.05 x 100 = 5

5/2.80=1.78

1.8

1/2 is the probability that the sum of the two recorded numbers will be odd, given that the first recorded number is odd

First, let's find the total number of possible outcomes when the computer makes two selections from the set {12, 13, 15, 17}.

There are four choices for the first selection and four choices for the second selection,

so there are 4 x 4 = 16 possible outcomes.

Now, let's consider the outcomes where the first recorded number is odd.

There are two odd numbers in the set, 13 and 15,

so there are 2 x 4 = 8 outcomes where the first recorded number is odd.

Of these 8 outcomes, we need to count the number of outcomes where the sum of the two recorded numbers is odd.

The sum of two numbers is odd if and only if one number is odd and the other number is even.

There are two even numbers in the set, 12 and 16, so there are 2 x 2 = 4 outcomes where the sum of the two recorded numbers is odd.

Therefore, the probability that the sum of the two recorded numbers will be odd, given that the first recorded number is odd, is: 4/8 = 1/2

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Answer:

14.76482306

Step-by-step explanation:

distance equals the square root of (x2-x1)^2 + (y2-y1)^2.

think of your ordered pairs as set 1 and set 2. (-4, 6) would be set 1 and (3, -7) would be set 2. so your equation will look similar to: (3- -4)^2 + (-7-6)^2 then you square root the whole thing and you will have your answer.

A repeated-measures experiment involves measuring the same participants multiple times, which can introduce carry-over effects. This means that the experience or treatment received in one condition may affect the results of the subsequent conditions. To avoid this issue, researchers may use counterbalancing techniques or a randomized order of conditions. Another concern with repeated-measures experiments is obtaining negative values for difference scores, which may be an indication of a ceiling or floor effect. Additionally, individual differences between participants can impact the results, leading to a mean difference that is not solely due to the treatment. To address this concern, researchers may use statistical methods such as ANOVA or MANOVA to control for individual differences. Lastly, obtaining a large enough sample is important to ensure that the results are representative of the population and that any effects are not due to chance.
A major concern with a repeated-measures experiment is the possibility of carry-over effects, which can occur when the influence of one treatment persists into the subsequent treatment, potentially skewing the results. Additionally, negative values for difference scores might complicate the interpretation of the data. Another concern is obtaining a mean difference due to individual differences rather than treatment differences, which could lead to misleading conclusions. Lastly, securing a large enough sample size is crucial for obtaining reliable and generalizable results in such experiments.

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Answer:

5

Step-by-step explanation:

x - 1= 0 → x = 1 We paste this value.

3(1)⁵ + 4(1)⁴ - 2= 3 + 4 - 2 = 5

There is another method that is longer. As shown in the picture

We will have that the odds that are less generous are:

*17:1

*16:1

*18:1

If A does not equal B, then the outcome of the formula =if(a1=b1, c1, c2) will be c2.

One of the most well-known Excel functions is certainly the IF one. The "IF Function" typically enables us to compare values logically to what we anticipate. This implies that an IF statement may produce one of two outcomes. If your comparison is True, the first result will be the case; if it is False, the second result will be the case.

Now, this indicates hat the IF function takes 3 arguments namely;

Comparing data or determining whether a condition is met is a logical test.

If this argument were defined, Excel would be instructed to return a specific value if the logical test's condition was satisfied.

if false, value.

From the above definitions when they are applied to the question, since a1 = b1, then we can say that the result can be c2 if A is not equal to B.

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Answer: 4x√5

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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Given that the bacteria culture initially contains 50 cells and grows at a rate proportional to its size.

After an hour the population has increased to 120.

We need to find an expression for the number P(t) of bacteria after t hours.

P(t) = 50+70t

For t = 3,

P(t) = 50+70t

= 50 + 70 × 3

= 260.

So, the number of bacteria after 3 hours is 260. To find the rate of growth after 3 hours, we can use the expression for P(t).

P(t) = 50+70t

Differentiating P(t) w.r.t. t, we get dP/dt = 70.

So, the rate of growth after 3 hours is 70.

Now, we need to find when the population will reach 5000.

Let t be the number of hours it takes to reach 5000 bacteria.

P(t) = 5000.Substituting the given values in the above equation, we get

50 + 70t = 5000

Solving the above equation for t, we get

t = (5000 - 50)/70

= 450/7.

So, the population will reach 5000 after approximately 64.3 hours.

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