Find the value of x for which m || n.

The constant of proportionality, k, is 5.

In the next 8 seconds, the ball will drop 320 metres.

Given that the distance fallen, denoted as d, is directly proportional to the square of time, denoted as t, we can express this relationship as:

d ∝ t²

To find the constant of proportionality, we can use the information provided. It states that the ball drops 80 metres in the first 4 seconds. Substituting these values into the proportionality equation, we have:

80 ∝ 4²

Simplifying, we have:

80 ∝ 16

To determine the constant of proportionality, we divide both sides of the equation by 16:

80/16 = 5 = k

Therefore, the constant of proportionality, k, is 5.

Now that we have determined the constant of proportionality, we can use it to find the distance the ball drops in the next 8 seconds. We substitute the value of t = 8 into the proportionality equation:

d = k * t²

d = 5 * 8²

d = 5 * 64

d = 320

Therefore, in the next 8 seconds, the ball will drop 320 metres.

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Question

A ball, dropped vertically, falls d metres in t seconds. D is directly proportional to the square of t. The ball drops 80 metres in the first 4 seconds. How far does the ball drop in the next 8 seconds?

Answer:

On a coordinate plane, an absolute value graph has a vertex at (0, 0.5).

Step-by-step explanation:

properties of the given function

Answer: it's the second option

Step-by-step explanation:

Based on the random numbers given, the probability that 5 random digits will have at least 3 even digits is D. 3/5.

Based on the given numbers, the numbers that have at least 3 even digits are 6.

They are: 46370, 53480, 49126, 89212, 88241, and 37808.

The probability out of 5 of at least 3 even numbers is:

= Number of 3 digit numbers / Total random numbers

= 6 / 10

= 3 / 5

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Answer:

9/10

Step-by-step explanation:

Guy above is wrong, I took it just now.

Answer:

0

Step-by-step explanation:

Continuing from where Karissa stopped, solving for the value of x in the equation can be done as follows:

\(\frac{1}{2}x = \frac{-1}{2}x\)

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

Cross multiply

2x = -2x

2x + 2x = 0

4x = 0

Divide both sides by 4

\(\frac{4x}{4} = \frac{0}{4}\)

x = 0

The value of x in the equation Karissa was solving is 0

Answer:

0.2

Step-by-step explanation:

Convert the walking to percent

\(\frac{1}{2} \times 100 = 50\)

Add both skateboarding and walking

\(30\% + 50\%\\\\= 30 + 50\\\\= 80\)

Now, subtract that from a whole percent

\(100 - 80 = 20\\\\20\%\)

Convert it to a decimal

\(20\% = \frac{20}{100} \\\\=20 \div 100\\\\= 0.2\)

Therefore, in decimal, 0.2 is the number that shows the portion of the distance Sandy skips.

Answer: No

Step-by-step explanation: No because y is not the same as x.

Answer:

Second Graph.

Explanation:

It's the only graph that is concave down and the slope is decreasing.

Answer:

5. Is your answer for ur questions

Answer:

y= 56

Step-by-step explanation:

y=5a-3b+c

a=12, b=4, c=8

y= 5(12) - 3(4) + (8)

y= 60 - 12 + 8

y= 56

- I hope this helps have a great night

A high-quality paintbrush can hold a significant amount of paint without it running off the bristles due to its unique design and construction.

The bristles are designed to be absorbent and have a capillary action that helps retain the paint, allowing for controlled application and minimizing waste.The bristles of a good paintbrush are made of materials like natural or synthetic fibers that have absorbent properties. These materials are capable of holding and retaining a certain amount of liquid, including paint. The bristles are often packed densely, creating a large surface area for paint retention.

The capillary action plays a crucial role in preventing the paint from running off the bristles. Capillary action is the ability of a liquid to flow in narrow spaces, such as the gaps between bristles. When the brush is dipped into paint, the liquid is drawn up into the spaces between the bristles due to capillary forces. This action creates a reservoir of paint within the brush, allowing for a controlled release during painting.

The combination of absorbent bristles and capillary action enables a high-quality paintbrush to hold a substantial amount of paint without it simply running off the bristles. This design feature ensures efficient paint application, reduced drips, and better control over the painting process.

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The next three terms in the sequence are 116 , 159 and 209

We are supposed to find the next 3 terms in the sequence:

5, 6, 14, 29, 51, 80, ___, ___, ___.

Here we can are first supposed to find the pattern which is as follows:

\(6-5=1\\14-6=8\\29-14=15\\51-29=22\\80-51=29\\\)

Therefore difference between the numbers is 7 more than the previous one i.e,

\(1+7=8\\8+7=15\\15+7=22\\22+7=29\)

Let required three numbers be x, y and z

So \(x-80=29+7=36\\x=116\)

    \(y-116=36+7=43\\y = 159\)

and \(z-159=43+7=50\\z=209\)

Hence x = 116, y = 159 and z = 209

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The second derivative, inflation point and slope of differential equation are explained below.

differential equation states how a pace of progress (a "differential") in one variable is connected with different factors. For example, when the position is zero (ie. the spring is neither extended nor compacted) then the  velocity isn't evolving.

We have,

dy/dx = 2x-y

Suppose f'(x) = 2x - y

d^2y/dx^2 = d(2x - y)/dx

⇒ 2

(b) To find the inflection points, equate f(x) to zero and solve for x.

f"(0) =0

f" (x)=2

So, the function defined on the interval (- ∞, 2) (2,  ∞)

In the interval (- ∞, 2), when x-1

f"(1)=2>0

So, the concave up wards on this interval.

In the interval (2,∞) when x=2

f"(2)=2>0

the concave up wards on this interval

Now, the slope of the function,

f(2)=3

here x-2y=3

Then, x = 2, y = 3

\(\frac{dy}{dx}|_{2, 3}\) = 2(2) - 3 = 1

Thus, the slope of the function is 1.

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The length of the shorter diagonal in the parallelogram is approximately 18 cm when rounded to the nearest centimeter.

To find the length of the shorter diagonal in the parallelogram, we can use the Law of Cosines. The Law of Cosines allows us to calculate the length of a side when we know the lengths of the other two sides and the included angle.

In this case, we know the lengths of the adjacent sides of the parallelogram: one side is 21 cm and the other side is 14 cm. We also know that the smaller angle measures 58°.

Let's denote the length of the shorter diagonal as d. According to the Law of Cosines, we have:

d^2 = a^2 + b^2 - 2ab * cos(C)

Where:

- d is the length of the diagonal.

- a and b are the lengths of the adjacent sides.

- C is the included angle.

Substituting the known values into the equation, we get:

d^2 = 14^2 + 21^2 - 2(14)(21) * cos(58°)

Simplifying:

d^2 = 196 + 441 - 588 * cos(58°)

Now, we can evaluate the expression on the right side using a calculator:

d^2 ≈ 196 + 441 - 588 * 0.532 (rounded to three decimal places)

d^2 ≈ 196 + 441 - 312.216

d^2 ≈ 324.784

To find the length of the shorter diagonal, we take the square root of both sides:

d ≈ √324.784

d ≈ 18.03 cm (rounded to the nearest centimeter)

Therefore, the length of the shorter diagonal in the parallelogram is approximately 18 cm when rounded to the nearest centimeter.

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Answer:

72 N

Step-by-step explanation:

From the question.

Force is directly proportional to acceleration, with the mass of the object constant.

F α a

F = ka

F₁/a₁ = F₂/a₂....................... Equation 1

Where F₁ = Initial force, a₁ = initial acceleration. F₂ = final force, a₂ = Final acceleration.

make F₂ the subject of the equation

F₂ = (F₁/a₁)a₂................ Equation 2

Given; F₁ = 64 N, a₁ = 8 m/s², a₂ = 9 m/s²

Substitute these values into equation 2

F₂ = (64/8)(9)

F₂ = 72 N

Answer:

x = 0 or x = 1/4

Step-by-step explanation:

You are able to factor out 3x² from 12x³ - 3x² to get 3x²(4x-1).

Set everything to zero and solve.

The values of the terms, a₁, a₂, and a₁₀ of the sequence are;

(a) a₁ = 1, a₂ = 1/2, a₁₀ = 1/10

(b)  \(\lim\limits_{n\to {\infty}}\) aₙ = 0

A sequence is an ordered collection of objects such as numbers in which repetition of the object is possible, and the objects (or numbers) are referred to as the terms of the sequence.  

The sequence, \(\{a_n\}^\infty_{n = 1}\) with values, aₙ = \(\int\limits^{\infty}_1 {\frac{dx}{x^{n + 1}} }\)

(a) a₁ = \(\int\limits^{\infty}_1 {\frac{dx}{x^{1 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^2} } = -[\frac{1}{x} ]^{\infty}_1\)

\(-[\frac{1}{x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{1} ) = 0 + 1 = 1\)

Therefore; a₁ = 1

a₂ = \(\int\limits^{\infty}_1 {\frac{dx}{x^{2 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^3} } = -[\frac{1}{2\cdot x^2} ]^{\infty}_1\)

\(-[\frac{1}{2\cdot x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{2 \times 1} ) = 0 + \frac{1}{2} = \frac{1}{2}\)

Therefore; a₂ = 1/2

a₁₀ = \(\int\limits^{\infty}_1 {\frac{dx}{x^{10 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^{11}} } = [-\frac{1}{10\cdot x^{10}} ]^{\infty}_1\)

\([-\frac{1}{10\cdot x^{10}} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{10\times 1} ) = 0 + \frac{1}{10} = \frac{1}{10}\)

Therefore; a₁₀ = 1/10

b) The limit, \(\lim \limits_{n\to \infty} a_n\) can be evaluated as follows;

aₙ = \(\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx\)

\(\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx = [-\frac{1}{n\cdot x^n} ]^{\infty}_1 = -\frac{1}{n\times \infty } - (-\frac{1}{n\times 1^n} )= \frac{1}{n}\)

aₙ = 1/n

Therefore;

\(\lim \limits_{n\to \infty} a_n = \frac{1}{\infty}\) = 0

\(\lim\limits_{n\to {\infty}} a_n\) = 0

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The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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Answer:

3n + 2

Step-by-step explanation:

\(−n+(−4)−(−4n)+6\)

Open the parentheses

\( - n - 4 + 4n + 6 \\ \)

Add similar elements

\( - n + 4n - 4 + 6 \\ 3n + 2 \\ \)

Answer:

\( - n + 6\)

Step-by-step explanation:

\( - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6\)

Part A:  The amount of unearned interest is $3,225.

Part B: The amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C: To support our answers to Part A and Part B, the total interest that Christopher would have paid, which is 3,900$. the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

What is an interest?

To determine the amount of unearned interest, we need to find out how much interest Christopher would have paid if he made all 24 payments.

First, we can calculate the total amount he would have paid if he made all 24 payments:

Total amount paid = 475 x 24 = 11,400$

Next, we can subtract the amount borrowed from the total amount paid to find the total interest:

Total interest = Total amount paid - Amount borrowed

Total interest = 11,400$ - 7,500$

Total interest = 3,900$

Since Christopher paid off the loan after 18 months instead of 24 months, he did not pay the full amount of interest he would have paid if he made all 24 payments. The unearned interest is therefore:

Unearned interest = Total interest - (Number of remaining payments / Total number of payments x Total interest)

Unearned interest = 3,900 - (6 / 24 x 3,900)

Unearned interest = 3,225$

Therefore, the amount of unearned interest is $3,225.

What is repay?

Part B:

To determine the amount needed to repay the loan using the Rule of 78, we need to calculate the proportion of the total interest that has been earned by the lender up to the point when Christopher repays the loan.

The Rule of 78 is a method of allocating interest charges based on the sum of the digits of the loan term. In this case, since the loan term is 24 months, the sum of the digits is:

1 + 2 + ... + 4 + 5 = 15

We can use this sum to calculate the proportion of the total interest earned by the lender up to the point when Christopher repays the loan:

Proportion of earned interest = (Number of payments made / Total number of payments) x (Sum of digits of loan term / Total sum of digits)

Proportion of earned interest = (18 / 24) x (15 / 120)

Proportion of earned interest = 0.09375

The total interest paid is 3,900$, so the amount needed to repay the loan using the Rule of 78 is:

Amount needed to repay loan = Amount borrowed + Total interest x Proportion of earned interest

Amount needed to repay loan = 7,500$ + 3,900$ x 0.09375

Amount needed to repay loan = 8,443.75$

Therefore, the amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C:

To support our answers to Part A and Part B, we calculated the total interest that Christopher would have paid if he made all 24 payments, which is 3,900$. We also calculated the unearned interest, which is the difference between the total interest and the interest that Christopher actually paid when he paid off the loan early.

Using the Rule of 78, we calculated the proportion of the total interest earned by the lender up to the point when Christopher repaid the loan, which is 0.09375. We then used this proportion to calculate the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

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Answer:

1) 1/2or 50%
2) 38/50 or 76%
3) 38/60 or 63%
4) not sure tbh

Step-by-step explanation:

Answer:

43/90

Step-by-step explanation:

We want to express 0.47777... as a ratio of two integers. To do so, we need to multiply by 10^n, where n is the number of repeating decimals. Only 7 is repeating so we multiply 0.47777... by 10. The trick to do this is to let x=0.47777... In other words, what we are doing is the following:

\(x=0.47777...\\10x=4.7777....\\\text{Subtract x}\\10x-x=4.7777...-x\\9x=4.7777...-0.4777...\\9x=4.3\\x=4.3/9=43/90=0.4\overline{7}\)

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

|h - 1.6| ≤ 0.2

Step-by-step explanation:

Given:

1.4≤ h ≤ 1.8

To write the compound inequality as an absolute value inequality, follow the following steps:

(i) Find the mid-point between the given extremes of the inequality.

The given extremes are 1.4 and 1.8

The mid-point is therefore, (\(\frac{1.4 + 1.8}{2}\)) = 1.6

(ii) With the mid-point value calculated in (i) above, form the inequality around that by subtracting 1.6 from each term in the given compound inequality. i.e

1.4 - 1.6 ≤ h - 1.6 ≤ 1.8 - 1.6

(iii) Solve the result from (ii) above.

-0.2 ≤ h - 1.6 ≤ 0.2

(iv) Re-write the result from (iii) above in absolute value inequality. i.e

-0.2 ≤ h - 1.6 ≤ 0.2 becomes

|h - 1.6| ≤ 0.2

Therefore, the absolute value inequality of the given compound inequality is |h - 1.6| ≤ 0.2

The 95% confidence interval for the true mean weight of all packages received by the parcel service is: 17.17 to 18.63 pounds.

The formula to find the 95% confidence interval for the true mean weight of all packages received by the parcel service is:

Confidence Interval = sample mean ± (critical value * standard error)

The standard error (SE) is calculated using the formula:

SE = standard deviation/√sample size

The parameters are given as:

Sample mean weight: x' = 17.9 pounds

Standard deviation: σ = 2.1 pounds

Sample size: n = 32

Thus:

SE = 2.1/√32

SE ≈ 0.3717

The critical value for a 95% confidence level with a sample size of 32 is: z = 1.96

Thus:

Confidence Interval = 17.9 ± (1.96 * 0.3717)

Lower bound = 17.9 - (1.96 * 0.3717) = 17.17

Upper bound = 17.9 + (1.96 * 0.3717) = 18.63

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Complete question is:

32 packages are randomly selected from packages received by parcel service. the sample has a mean weight of 17.9 pounds and a standard deviation of 2.1 pounds. What is

The probability that the mean weight of the 17 fruits will be between 489 grams and 500 grams is approximately 0.0322 - 0.0322 = 0.0000 (rounded to four decimal places).

The probability that the mean weight of 17 randomly picked fruits falls between 489 grams and 500 grams can be calculated using the Central Limit Theorem.

The mean weight of the 17 fruits will follow a normal distribution with a mean equal to the population mean (494 grams) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (√17).

First, we calculate the z-scores for the lower and upper bounds:

Lower z-score:

z_lower = (489 - 494) / (8 / √17)

Upper z-score:

z_upper = (500 - 494) / (8 / √17)

Then, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability that the mean weight falls between 489 grams and 500 grams is equal to the difference between these two probabilities.

Let's calculate the probabilities:

z_lower = (489 - 494) / (8 / √17) ≈ -1.8409

z_upper = (500 - 494) / (8 / √17) ≈ 1.8409

Using a standard normal distribution table or a calculator, we find that the probability corresponding to z_lower is approximately 0.0322 and the probability corresponding to z_upper is also approximately 0.0322.

The problem presents a normal distribution of fruit weights, with a given mean of 494 grams and a standard deviation of 8 grams. When we randomly select a sample of 17 fruits, the mean weight of this sample will also follow a normal distribution. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

In this case, since the range is relatively narrow and the sample size is moderate, the probability of the mean weight falling between 489 grams and 500 grams is quite low, approximately 0.0000.

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The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle.

The orthocenter is the intersection of the three altitudes of the triangle. It is a point on the plane of the triangle that is equidistant from the three sides of the triangle.

To find the orthocenter of a triangle, you can draw the altitudes of the triangle and find the point where they intersect. The orthocenter is the point of concurrency for the three altitudes.

An orthocenter of a triangle is a point where the three lines that are perpendicular to the sides of the triangle intersect. These lines are called altitudes of the triangle.

Alternatively, you can use the following formula to find the coordinates of the orthocenter:

Let's say that the vertices of the triangle are A(x1, y1), B(x2, y2), and C(x3, y3). The coordinates of the orthocenter (H) can be found using the following formula:

Hx = ( (y1 - y3) (x1^2 + y1^2 - x3^2 - y3^2) - (y1 - y2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (y1 - y3) - 2 * (y1 - y2))

Hy = ( (x1 - x3) (x1^2 + y1^2 - x3^2 - y3^2) - (x1 - x2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (x1 - x3) - 2 * (x1 - x2))

Therefore, The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle

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In complex number a+ib a is real and ib is the imaginary part.

Complex numbers are the numbers that are communicated as a+ib where, a,b are genuine numbers and 'I' is a fanciful number called "particle". The worth of I = (√-1). For instance, 2+3i is a complicated number, where 2 is a genuine number (Re) and 3i is a imaginary number (Im).

We have, a + ib is a complex number in mathematics

where a is the real part and ib is the imaginary part of the complex number.

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The Mean Value Theorem is a crucial theorem of calculus that reveals a relationship between the gradient of a curve and the values of its associated function at the endpoint.

Specifically, it states that provided f(x) is steady on the enclosed interval [a, b], and differentiable on (a, b), then there must exist a point c within the range of (a, b) such that

f(b) - f(a) = f'(c) * (b - a)

which translates to there being an individual c inside the parameterized region (a, b), such that the inclined angle of the tangent line to the graph at c is equal to the general incline of the graph between a and b.

The Mean Value Theorem possesses a plethora of utilities in mathematical analysis and calculus alike.

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