A point is located in a polar coordinate system by the coordinates r = 2.8 m and θ = 18°. find the x- and y-coordinates of this point, assuming that the two coordinate systems have the same origin.

1,330,000 is the answer.

Probably late lol

To subtract 7 from 13 you use the fact that 13 is one ten plus three units, i.e. 13 = 10 + 3. then you can subtract 7 from 10 which is 3, and then add the 3 other 3 units to get 3 + 3 = 6. In this way, you have subtracted 7 from 13 using the fact that 13 is one ten plus 3 units.

The probability that at least one of the five light bulbs is defective is approximately 26.61%. This is found by calculating the probability that all bulbs work ([tex]0.94^5[/tex]) and subtracting that from 1.

The student is asking about the probability of having at least one defective light bulb in a pack of five, given a defect rate of 6%. To calculate this, we will use the complement rule, which states that the probability of at least one success is equal to 1 minus the probability of zero successes (no defective bulbs).

First, we calculate the probability that a bulb is not defective, which is 94% or 0.94 (since 100% - 6% = 94%). Since the bulbs are independent, the probability that all five bulbs are not defective is:

[tex](0.94)^5[/tex]

The probability that at least one bulb is defective is thus:

1 - [tex](0.94)^5[/tex]

Using a calculator, this gives us:

[tex]1 - (0.94^5) \approx 1 - 0.7339 \approx 0.2661 or 26.61%[/tex]

So, there is approximately a 26.61% chance that at least one of the five light bulbs is defective.

The probability that at least one of the light bulbs is defective is approximately 0.264909 or 26.49%.

To find the probability that at least one of the light bulbs is defective, we can use the complement rule.

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

In this case, the event of interest is that at least one light bulb is defective. The complement of this event is that none of the light bulbs are defective.

Given that 6% of the light bulbs are defective, the probability that any one light bulb is not defective is 1 - 0.06 = 0.94.

Since each light bulb operates independently of the others, the probability that none of the five light bulbs are defective is [tex]\((0.94)^5\)[/tex].

Therefore, the probability that at least one of the light bulbs is defective is [tex]\(1 - (0.94)^5\)[/tex].

Let's calculate it:

P(at least one defective) = 1 - (0.94)^5

P(at least one defective) = 1 - 0.735091 = 0.264909

So, the probability that at least one of the light bulbs is defective is approximately 0.264909 or 26.49%.

2 and 10 are 4 units from 6.

Two sets of real numbers are more than 4 units from 6:  (-inf., 2) and (10, inf.)

goes up five everytime

i see a pattern that each number increases by 5

38 is quotient and 6 is remainder

Hi. This is a simple division problem.  You divide 9 into 348 which goes 38 times (9x3=27 which you subtract from the 34 leaving 7. Now bring the 8 down and divide 9 into 78, which goes in 8 (9x8=72) leaving you with a remainder of 6.

348/9 = 38 R6

I hope this helps.
Take care,
Diana

The answer is 4.875

Sent a picture of the solution to the problem (s).

Answer:

Sample Response: With integer tiles, you would add 5 groups of negative 2 tiles or remove 2 groups of 5 positive tiles. On the number line, you would bounce by 5 to the left 2 times.

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The answer is incorrect because there are 1000 meters in 1 kilometer, not 1000 kilometers in a meter, the answer should've been 68 times 10^3 which makes it 6,800 meters.

Final answer:

The conversion of 68 kilometers into meters gives 68000 meters, not 0.068 meters. The error arises due to dividing instead of multiplying the kilometers by 1000 (because 1 km equals 1000m).

Explanation:

When you are converting from kilometers to meters, you need to understand that 1 kilometer is equal to 1000 meters. Therefore, to convert 68 kilometers to meters, you should multiply 68 by 1000, not dividing it. You calculate 68km * 1000 = 68000m. So, 68 kilometers is equal to 68,000 meters, not 0.068 meters. The response 0.068 meters is incorrect because it is vastly smaller than the actual conversion result.

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first we have to put the numbers in order

1/2, 3/5, (5/8, 1 1/4), 1 1/2, 1 3/4

the median is the middle number. when there is an odd number of numbers, u will have 1 middle number. But when there is an even number of numbers, like this one, there will be 2 middle numbers. So u have to take ur 2 middle numbers, add them, then divide them by 2 to get the average median.

are 2 middle numbers are : 5/8 and 1 1/4..

(5/8 + 1 1/4) / 2 = (5/8 + 5/4) / 2 = (5/8 + 10/8) / 2 = 
(15/8) / 2 = 15/8 * 1/2 = 15/16 <==

Answer:

Step-by-step explanation:

answer is 15/16

a. Yule-Simons PMF is valid due to non-negativity and sum 1 proof.

b. E[X] = 2 calculated through partial fraction and cancellation.

c. E[X^2] = ∞ shown using comparison test with p-series.


a. Proving it's a Probability Mass Function (PMF):

Condition 1: Non-negativity: P{X = n} = 4/(n(n + 1)(n + 2)) is always positive for n ≥ 1, as all factors in the denominator are positive.

Condition 2: Sums to 1:

We need to show ∑_(n=1)^∞ P{X = n} = 1.

Use partial fraction decomposition:

4/(n(n + 1)(n + 2)) = 1/(n) - 1/(n + 1) + 1/(2(n + 2))

Expand the infinite series:

∑_(n=1)^∞ P{X = n} = (1/1 - 1/2 + 1/6) + (1/2 - 1/3 + 1/8) + ...

Notice terms cancel out:

= 1 + (1/6 - 1/6) + (1/8 - 1/8) + ... = 1

Therefore, P{X = n} is a valid PMF.

b. Expectation E[X] = 2:

E[X] = ∑_(n=1)^∞ n * P{X = n}

Substitute P{X = n} with its expression:

E[X] = ∑_(n=1)^∞ n * (4/(n(n + 1)(n + 2)))

Apply partial fraction decomposition (as in a) and simplify:

E[X] = ∑_(n=1)^∞ (1/(n + 1) - 2/(n + 2))

Expand the series and observe cancellations:

E[X] = (1/2 - 2/3) + (1/3 - 2/4) + ... = 1 - 1/2 = 1/2

Multiply by 4 to account for the 4 in the original PMF:

E[X] = 4 * (1/2) = 2

Therefore, E[X] = 2.

c. Expectation E[X^2] = ∞:

E[X^2] = ∑_(n=1)^∞ n^2 * P{X = n}

Substitute P{X = n} and simplify:

E[X^2] = ∑_(n=1)^∞ (4n/(n + 1)(n + 2))

Use the comparison test:

4n/(n + 1)(n + 2) > 4n/(n^3) = 4/(n^2) for n ≥ 1

Since ∑_(n=1)^∞ 4/(n^2) (p-series with p = 2) converges, so does E[X^2].

Therefore, E[X^2] = ∞.

The probable question is in the image attached.

check the picture below.

The distance of the bird from its starting point will be 29.15 miles.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

A bird flies 25 miles Due West then turns due south and flies for another 15 miles and lands.

Now,

Since, A bird flies 25 miles Due West then turns due south and flies for another 15 miles and lands.

Let the distance of the bird from its starting point = x

So, By using Pythagoras theorem, we get;

⇒ x² = 15² + 25²

⇒ x² = 225 + 625

⇒ x² = 850

⇒ x = √850

⇒ x = 29.15 miles

Thus, The distance of the bird from its starting point = 29.15 miles.

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C. y=3x+1 is the answer.

Answer:

[tex]y=3x+1[/tex]

Step-by-step explanation:

The line has positive slope, therefore the variable in the equation must be positive ([tex]y=-3x+1[/tex] and [tex]y=-3x-1[/tex] must be discarded)

Now, in the graph we can see that the line passes over the following points:

[tex](0,1) \rightarrow x=0, y=1\\(1,4) \rightarrow x=1, y=4[/tex]

With the point [tex](0,1)[/tex], we can discard [tex]y=3x-1[/tex] because:

in the equation  [tex]y=3x-1[/tex], we have: [tex]x=0 \rightarrow y=3(0)-1=0-1=-1\rightarrow y=-1[/tex]

The line doesn't pass over the point [tex](0,-1)[/tex]

Therefore, the equation is [tex]y=3x+1[/tex].

We can verify the answer with the points [tex](0,1)[/tex] and [tex](1,4)[/tex], replacing values in the equation:

[tex](0,1):\\x=0\rightarrow y=3(0)+1=0+1=1\rightarrow y=1\\\\(1,4):\\x=1\rightarrow y=3(1)+1=3+1=4\rightarrow y=4[/tex]

3.14 is the answer
hope it helped!

pi is equal to 3.14159265....

or just 3.14

3.14 is your answer

hope this helps

[tex]\displaystyle\int_{x=-1}^{x=1}\int_{y=0}^{y=2}(4+x^2-y^2)\,\mathrm dy\,\mathrm dx=12[/tex]

The volume of the solid under the hyperbolic paraboloid [tex]z = 4 + x^2-y^2[/tex] and above the square r = [−1, 1] × [0, 2] is [tex]20\text{ cubic units}[/tex]

The question is asking us to find the volume bounded by the following surfaces

The plane [tex]z=0[/tex] and the surface [tex]z = 4 + x^2 - y^2[/tex]The planes [tex]x=-1[/tex] and [tex]x=1[/tex]The planes [tex]y=0[/tex] and [tex]y=2[/tex]

To do this, we have to evaluate the triple integral

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy\int\limit_0^{4+x^2-y^2}\,dz[/tex]

Evaluating the triple integral

First, we integrate with respect to [tex]z[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy\int\limit_0^{4+x^2-y^2}\,dz\\\\=\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy(4+x^2-y^2)[/tex]

Next, we integrate with respect to [tex]y[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy(4+x^2-y^2)\\\\=\displaystyle \int\limit_0^2\,dx \left[4y+x^2y-\dfrac{y^3}{3} \right]_{-1}^1\\\\=\displaystyle \int\limit_0^2\,dx \left[ \left(4(1)+x^2(1)-\dfrac{(1)^3}{3} \right)- \left(4(-1)+x^2(-1)-\dfrac{(-1)^3}{3} \right)\right]\\\\=\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\[/tex]

Finally, we integrate with respect to [tex]x[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\=\left[\dfrac{22}{3}x+\dfrac{2x^3}{3}\right]_0^2\\\\=\left(\dfrac{22}{3}(2)+\dfrac{2(2)^3}{3}\right) - \left(\dfrac{22}{3}(0)+\dfrac{2(0)^3}{3}\right)\\\\=20 \text{ cubic units}[/tex]

The volume of the solid is [tex]20\text{ cubic units}[/tex]

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Answer:

2/35

Step-by-step explanation:

The only way we can solve this problem is to assume that the given complement of pieces is of a full kit before one went missing. The total number of pieces in the kit is ...

... 9 + 8 + 12 + 6 = 35

Of those, 2 are red with four holes. Thus the probability that a randomly chosen piece is red with 4 holes is 2 out of 35, or 2/35.

____

If this is the kit contents after the piece went missing, we have no way of knowing the color or hole count of the missing piece. If the kit is supposed to contain 13 blue pieces, for example, then the probability is zero that the missing piece is red.

Final answer:

The probability of a specific event is determined by dividing the number of ways this event can occur by the total number of possible outcomes. In this case, the probability of selecting a red piece with four holes from the toy building kit is the ratio of the quantity of four-holed red pieces to the total quantity of pieces in the kit.

Explanation:

The question refers to the probability of a specific event in a set of outcomes related to a toy building kit. In this case, the event is selecting a red piece with four holes. Probability can be defined mathematically as (Number of ways event can occur)/(Total number of outcomes). Specifically, in your case, you would calculate the number of four-holed red pieces within the whole toy building kit. Divide that by the total number of pieces in the entire kit, including the missing one.

Using an example with different objects for clarity, consider if there are 10 pieces in the set, and 3 of them are four-holed red pieces, the probability of the selected piece being a four-holed red piece would be 3/10 or 0.3 (once converted to decimal form). This method can now be applied to your toy building set once you identify the total number of pieces in the set and the number of these that are four-holed red pieces.

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so false would be your answerA sample of n = 4 scores has a mean of M = 8. If one new score with a value of X = 3 is added to the sample, what will be the value for the new mean?A. M=7.0A normal distribution has a mean of μ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 58?A. 0.8413On an exam with μ = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution?σ = 2Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean?When the population standard deviation is much smaller than 15For a sample of n = 16 scores, how many scores are used to calculate the sample variance?D. 16A normal distribution has a mean of μ = 80 with σ = 20. What score separates the lowest 30% of the distribution from the rest of the scores?B. X=69.6A normal distribution has a mean of μ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 80 and X = 100?B. 0.1587If sample variance is computed by dividing SS by df = n - 1, then the average value of the sample variances from all the possible random samples will be ____ the population variance.C. exactly equal toA population of N = 6 scores has ΣX = 12 and ΣX2 = 54. What is the value of SS for this population?C. 30One sample has n = 4 scores and M = 10. A second sample has n = 6 scores and M = 5. If the two samples are combined, then what is the weighted mean for the combined sample?C. 70/10 = 7.0A jar contains 10 red marbles and 30 blue marbles. What is the probability of randomly selecting a red marble from the jar?B. 10/40After every score in a sample is multiplied by 3, the mean is calculated and found to be M = 21. What was the mean for the original scores?A. 7John drives to work each morning and the trip takes an average of μ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John's drive to work will take less than 35 minutes?D. 0.2743Scores on the SAT form a normal distribution with a mean of μ = 500 with σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?A. X=475Which of the following symbols identifies the population standard deviation?C. σA sample of n = 100 scores is selected from a population with μ = 80 with σ = 20. On average, how much error is expected between the sample mean and the population mean?C. 2 pointsWhat happens to the standard error of M as sample size increases?B. it decreasesIf all the possible random samples with n = 36 scores are selected from a normal population with μ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means?C. 80A sample of n = 4 scores has a standard error of 10 points. For the same population, what is the standard error for a sample of n = 16 scores?C. 5A population has μ = 50. What value of σ would make X = 55 a more central, representative score in the population?D. σ = 20A researcher measures eye color for a sample of n = 50 people. Which measure of central tendency would be appropriate to summarize the measurements?C. modeA distribution is positively skewed. Which is the most probable order, from smallest to largest, for the three measures of central tendency?B. mode, median, meanFor the population of scores shown in the frequency distribution table, the mean is ____.


X f
5 2
4 1
3 3
2 2
1 2D. 29/10 = 2.90Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the standard error for the distribution of sample means?C. 6For a particular population, a sample of n = 9 scores has a standard error of 8. For the same population, a sample of n = 16 scores would have a standard error of ____.B. 6For a sample with M = 80, a score of X = 88 corresponds to z = 2.00. What is the sample standard deviation?B. 4You have a score of X = 65 on a math exam. The mean score for the class on the exam is μ = 70. Which of the following values for the standard deviation would give you the most favorable position within the class?D. σ = 10A true/false test has 100 questions. Using the normal approximation to the binomial distribution, what is the probability of getting more than 55 correct by just guessing?B. p(X > 55.5)What term is used to describe the shape of a distribution in which the scores pile up on the left-hand side of the graph and taper off to the right?B. positively skewedFor a population with μ = 80 and σ = 10, what is the X value corresponding to z = -0.50?C. 75What is the value of SS (sum of squared deviations) for the following population? 
Population: 2, 3, 0, 5A. 13

The statement "a sample of n = 9 scores is randomly selected from a population with m = 80 and s = 9 is false.

What is a normal distribution?

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

It is given that:

A sample of n = 9 scores is randomly selected from a population with m = 80 and s = 9.

As we know,

Z = (x - u)/s

Z = 3

x = 83

s = 9

3 = (83 - u)/9

27 = 83 - u

u = 83 - 27 = 56

Thus, the statement "a sample of n = 9 scores is randomly selected from a population with m = 80 and s = 9 is false.

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x = height of original triangle

0.4x = 2
x = 2 / 0.4
x = 5 <==

Answer:

The height of the original triangle is [tex]5\ inches[/tex]

Step-by-step explanation:

we know that

The scale factor is equal to divide the length of the corresponding side of the reduced triangle by the length of the corresponding side of the original triangle

Let

z-----> the scale factor

x----->  the length of the corresponding side of the reduced triangle

y-----> the length of the corresponding side of the original triangle

so

[tex]z=\frac{x}{y}[/tex]

in this problem we have

[tex]z=0.4[/tex]

[tex]x=2\ in[/tex] -----> the height of the reduced triangle

substitute and solve for y

[tex]0.4=\frac{2}{y}[/tex]

[tex]y=2/0.4=5\ in[/tex]

[tex]\displaystyle\sum_{n=1}^\infty(-1)^{n-1}\tan^{2n}\theta=1-\sum_{n=0}^\infty(-\tan^2\theta)^n=1-\dfrac1{1+\tan^2\theta}[/tex]

where [tex]|-\tan^2\theta|=\tan^2\theta<1[/tex] in order that the series converges, which is to say the series converges for

[tex]\tan^2\theta<1\implies|\tan\theta|<1\implies|\theta|<\dfrac\pi4[/tex]

We can simplify the sum a bit further, noting that [tex]1+\tan^2\theta=\sec^2\theta[/tex], giving

[tex]\displaystyle\sum_{n=1}^\infty(-1)^{n-1}\tan^{2n}\theta=1-\cos^2\theta=\sin^2\theta[/tex]

10 is the initial value, found when x=0.  I don't know what you are measuring by "0" and "10" here, so can't be more specific.

The answer to your question is that she can make 17 trains of 10 cubes so the answer is 17 

Use the sine law: sinB/b = sinA/a

SinB = b*sinA/a

sinB = 3*sin120° /8

∠ B = 18.94° ≈ 19°

Answer:

∠B = 19°

Step-by-step explanation:

Given : In triangle ABC, if ∠A = 120°, a = 8, and b = 3

We have to find the measure of B that is ∠B

Consider the given triangle ABC,

Using Sine rule ,

For a triangle with measure of angle A, B and C and side  a faces angle A,  

side b faces angle B and  side c faces angle C

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]

we have, a = 8 , b = 3 and ∠A = 120°

Consider first two ratios,

[tex]\frac{8}{\sin 120^{\circ}}=\frac{3}{\sin B}[/tex]

Solve for B, we have,

[tex]\sin \left(120^{\circ \:}\right)=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{8}{\frac{\sqrt{3}}{2}}=\frac{3}{\sin \left(B\right)}[/tex]

[tex]\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c[/tex]

[tex]8\sin \left(B\right)=\frac{\sqrt{3}}{2}\cdot \:3[/tex]

Simplify, we have,

[tex]\sin \left(B\right)=\frac{3\sqrt{3}}{16}[/tex]

Taking sine inverse both side, we have,

[tex]B=\sin^{-1}\left(\frac{3\sqrt{3}}{16}\right)[/tex]

We have, [tex]B=18.95^{\circ \:}[/tex]

Thus, ∠B = 19°

Final answer:

Mathematics uses numbers, variables, and operations, particularly in algebraic expressions. An example of this is the equation 5x + 2 = 12, where '5' and '2' are numbers, 'x' is variable, and '+' and '=' are operation symbols.

Explanation:

The subject that uses numbers, variables, and operations is Mathematics. This combination is commonly seen in algebraic expressions. For example, in the equation 5x + 2 = 12, '5' and '2' are numbers, 'x' is a variable, and '+' and '=' are operation symbols. The numbers are used as constants or coefficients, the variable represents an unknown value, and the operations symbols dictate how these elements should interact. Through algebra, we can solve this equation and find the value of the variable 'x'.

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Final answer:

In Mathematics, particularly Algebra, numbers, variables and operation symbols are frequently used. This language is evident in forms like scientific and exponential notation, which are methods to represent large quantities using powers of ten.

Explanation:

The system of using numbers, variables, and operation symbols is commonly seen in Mathematics. In particular, this is prominent in Algebra, where numbers are often represented by variables, and operations like multiplication, division, addition, or subtraction involve these variables. One form of this language includes scientific notation. Scientific notation is a mathematical expression used to represent very large numbers using powers of ten. For instance, 500,000,000 can be written as 5 × 10^8 in scientific notation. Another way to express large quantities is through exponential notation, where the number is represented as a product of two numbers, one of which is a power of ten. Learning and practicing how to use these forms becomes essential for further scientific studies.

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She will pack 1 crate that holds 1,000 and 25 stacks that hold 10.
1,250-1,000=250
250÷10=25

Shawna can pack an order of 1,250 blocks using 1 crate for the thousands and 25 stacks for the tens.

To pack 1,250 blocks using crates and stacks, we need to break down the total number of blocks into thousands and tens:

Step 1: Determine the number of crates (each crate holds 1,000 blocks). 1,250 blocks divided by 1,000 equals 1 crate (1,000 blocks).Step 2: Subtract the blocks already packed in crates: 1,250 - 1,000 = 250 blocks.Step 3: Determine the number of stacks (each stack holds 10 blocks). 250 blocks divided by 10 equals 25 stacks (250 blocks).Therefore, Shawna can pack the order with 1 crate and 25 stacks.

We need to find the rolls whose sum is greater than 10. By looking at the outcomes, we see that (5,6), (6,5), and (6,6) all have a sum greater than 10. Therefore, there are 3 chances to get a sum greater than 10. Since there are 36 chances overall, the probability of rolling greater than 10 are 3/36 = 1/12.

Answer:

Step-by-step explanation:

1/12

1 and 3/4 would be the mixed number that represents the length of each piece. You would get this number by dividing 7 by 4 :)

Final answer:

When a 7-foot board is divided into 4 equal pieces, each piece will be 1.75 feet, or, as a mixed number, 1 3/4 feet.

Explanation:

To figure out the length of each piece when a 7-foot board is divided into 4 equal parts, we perform division. We divide the total length of the board by the number of pieces. That is, 7 ÷ 4 = 1.75.

This is a decimal number. To express it as a mixed number, we remember that '.75' is the same as '75/100', and this fraction can be simplified to '3/4'. So, 1.75 feet is the same as 1 3/4 feet. Therefore, each piece of board will be 1 3/4 feet long.

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Hello!
So the following would be your equation.
3(x+5)-10= 29
Your first step would be to use the Distributive Property based upon PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction). Since we have Parenthesis, we distribute first.
3(x+5)-10=29
^ ^
——————
So, your new equation would be—
3x+15-10=29
Now, you need to combine like terms—
15-10=29
3x+5=29
——————
Therefore your new equation is—
3x+5=29.
Now you need to move the constants (5,29) to one side of the equal sign. To do this, you would use the Subtraction Property of Equality and rid the 5–
3x+5=29
-5 -5
——————
Your equation is now—
3x=24.
Finally, you need to remove the 3 from x. This means you must use the Division Property of Equality, and rid the 3.
3x=24
— —
3 3
Your solved equation is—
X=8

Hope this helped!
~KayEmQue

neeed moldes plz would help a lot

Final answer:

To find points where the tangent plane to an ellipsoid is parallel to a plane, calculate the gradient vector of the ellipsoid and set it proportional to the normal vector of the given plane, then solve the resulting system for  (x, y, z).

Explanation:

To find all the points where the tangent plane to an ellipsoid is parallel to a given plane, you first need to consider the equation of the ellipsoid and the equation of the tangent plane.

The ellipsoid can be described by the general equation  f(x, y, z) = 0, while the tangent plane at a point on the ellipsoid can be described by the gradient of f at that point, given as  ∇f.

The gradient, which is a vector, gives us the normal to the tangent plane at the given point.

For a tangent plane to be parallel to another plane, their normal vectors must be proportional.

So, if we have the normal vector of the given plane, we can set up an equation with the gradient of the ellipsoid, and solve for the points (x, y, z) that satisfy this condition.

It requires solving a system of equations where the coefficients of the normals to both planes are proportional.

These points  (x, y, z) will be the points of tangency where the ellipsoid's tangent plane is parallel to the given plane.

We use the calculus concepts of partial derivatives to find the gradient vector and algebra to solve for the unknowns corresponding to the points of tangency.

Distance to travel = 20 m.
Let us determine the time, t, that each participant took to complete 20 m.

Barbara:
Average speed = (3 m)/(2 s) = 1.5 m/s
t = 20/1.5 = 13.3 s

Mark:
t =  5 s

Carlos:
y = x + 1
where
y = 20 m
x = time, t
Therefore
t =x = y - 1 = 20 - 1 = 19 s

Summary:
Barbara:  13.3 s
Mark:       5 s
Carlos:     19 s

Answer:
The winner is Mark

Final answer:

In a 20 meter race, Mark would win.

Explanation:

In a 20 meter race, Mark would win. Mark finished the race in 5 seconds, while Barbara took 2 seconds to pedal every 3 meters. Carlos' distance from the starting line can be represented by the equation y = x + 1, where x is the time in seconds. When x = 5, Carlos' distance would be 5 + 1 = 6 meters, which is less than 20 meters.

Learn more about race winner here:

https://brainly.com/question/26675090

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