Joe’s distance from the start of the path can also be modeled by D = 4s^2/5s+ 10
where D is measured in yards and s is the total number of steps Joe has taken. If Joe jogs at a constant rate of 100 steps per minute, find the rate that Joe’s distance from the start of the path is changing with respect to time, in yards per minute, when s= 200.

The balance of the account at the end of 21 years, given the deposit amount and the interest rate is $10, 351. 41

The balance on the account at the end of 21 years is the future value of the amount in the account today. This means that this balance can be found by the formula:
= Amount deposited x ( 1 + rate) ^ number of years

The balance on the Credit union client's account after 21 years is therefore:
= 2, 500 x ( 1 + 7%) ²¹

= $10, 351. 41

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The measure of the missing length of the triangle is 16 units.

According to the question,

We have the following information:

We have a figure of right-angled triangle where two sides are given.

In order to find the third side of this triangle, we will use the Pythagoras theorem.

So, we have the following expression:

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]

[tex](20)^{2} = AB^{2} + (12)^{2}[/tex]

400 = [tex]AB^{2}[/tex] + 144

Subtracting 144 from both sides of the equation:

[tex]AB^{2}[/tex] = 400-144

[tex]AB^{2}[/tex] = 256

We know that the square root of 256 is 16 or in other words, the square of 16 is 256.

AB = 16 units

Hence, the measure of the missing length of the triangle is 16 units.

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The first guitar lesson will cost (E $80

The cost of the first lesson is solved by comparing the costs

Since the cost of the first lesson is twice the cost of each additional lessons, double counting the first lesson makes the total number of lesson to be 9

if 9 lessons costs $360 then 1 lesson will cost

9 = 360

1 = ?

cross multiplying

8 * ? = 360 * 1

? = 360 / 9

? = 40

The unit cost is 40 taking the double counts makes the first lesson to be 2 * 40 = $80 then other lessons are 40

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a) The claim is given as follows:

[tex]\mu < 122[/tex]

b) The null and the alternative hypothesis are given as follows:

The claim in this problem is given as follows:

The mean systolic blood pressure of all healthy adults is less than 122 mm Hg.

Symbolically, the claim is given as follows:

[tex]\mu < 122[/tex].

As:

At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_0: \mu \geq 122[/tex].

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, that is, enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_1: \mu < 122[/tex].

The questions are given by the image at the end of the answer.

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Proved that ΔXYW ≅ ΔZYW

Consider the two triangles triangle XYW and triangle ZYW

According to SAS congruent rule if 2 sides and one angle of the one triangle is equal to the 2 sides and one angles of the another triangle, then both the triangles are congruent

The length of the side XY = The length of the side ZY

The line YW bisect the angle XYZ

Then the measure of angle XYW = The measure of angle ZYW

The length of the YW is common

Therefore the 2 sides and one angle of the triangle XYW is equal to the 2 sides and one angle of the triangle ZYW

Then the  triangles XYW and triangle ZYW are congruent

Hence, proved that ΔXYW ≅ ΔZYW

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Answer:

A and C = 13 and D and E = 24

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x-20

Answer:

Answer: 4 ∙ 3x - 4 ∙ 5

Step-by-step explanation:

The value of the given limits [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e.

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

Because the value of that function at that point doesn't define.

a)

[tex]\lim_{x \to \infty} 1/x^2[/tex] by substitute limit 1/∞² = 0

b)

[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] here (x² - 4)/(x - 2) = (x - 2)(x + 2)/(x - 2) = (x + 2)

Putting x = 2 will give the limit as 2 + 2 = 4.

c)

[tex]\lim_{x \to \pi} sinx\\[/tex] herer put x to π so sinπ = 0.

c)

[tex]\lim_{x \to \55} e[/tex] here no variable thus e will be the answer.

Hence "The value of [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e".

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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, the statement that could be true for g is: D. g(-13) = 20.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

From the information provided, the domain and range of this function g(x) in interval notation is given by:

Function g(0) = 2 is false because it was stated that g(0) = -2. Also, g(-4) = -11 is outside the scope of the given range for this function.

Furthermore, function g(7) = -1 is not within the domain for the given function. However, g(-13) = 20 is within the domain for the given function and produces an output that is within the scope of the given range for this function.

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The conversion of 230.2 g to metric ton is given by 0.0002302 metric tons.

Grams (g) and metric ton (MT) are the SI units of mass. Scientist measure various things with different units. The following are measures and their units;

Convert metric ton to grams:

1 metric ton = 1,000,000 grams

230.2 g = 230.2 ÷ 1,000,000

= 0.0002302 metric tons

Therefore, it can be said that 230.2 g is equivalent to 0.0002302 metric tons

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The probability that Jordan will win in three or fewer matches if they play 5 matches using binomial probability distribution is; 0.95636

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula for binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring

x = the number of expected successful outcomes

n = the number of trials you perform

nCx = the number of different combinations for x items you test in n trials

We are given probability that Jordan wins the match as 1/3. Thus;

p = 1/3 = 0.333

Thus, probability that Jordan will win in three or fewer matches if they play 5 matches is;

P(X ≤ 3) = P(0) + P(1) + P(2) + P(3)

From online binomial probability calculator, we have;

P(X ≤ 3) = 0.95636

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[tex]\stackrel{\textit{\LARGE arithmetic mean}}{\cfrac{14+7+10+5}{\underset{\textit{number of data elements}}{4}}\implies \cfrac{36}{4}\implies \text{\LARGE 9}}[/tex]

Answer:

the mean is 9 .

Step-by-step explanation:

i did this & got it correct .

Answer: 1/5

Step-by-step explanation:

Answer: 5/10

Step-by-step explanation:5/10 is the smallest answer here you et get to 0 concluding your answer to 5/10

Answer:

-9

Step-by-step explanation:

From the scores on the diagram we can tell that the arrow first stand on the point -3 and then on the point -6.

If we add -6 to -3 the product will be:

(-3) + (-6) = -9

The answer in blocks will be (-3) and (-6)

If we add -6 to -3 the product will be:

(-3) + (-6) = -9

Given,

In the question:

Fill in the blanks to complete the equation that describes the diagram.

Now, According to the question:

From the scores on the diagram we can tell that the arrow first stand on the point -3 and then on the point -6.

If we add -6 to -3 the product will be:

(-3) + (-6) = -9

What is Number line ?

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Hence, The answer in blocks will be (-3) and (-6)

If we add -6 to -3 the product will be:

(-3) + (-6) = -9.

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The points that must be on the graph for the quantities to be proportional to each other are (2, 44), (3, 66) and (4, 88)

From the question, we have the following parameters that can be used in our computation:

Championship T-shirts sell for $22 each.

The above parameter means that

The unit rate of a T-shirt = $22

This can be represented as

Unit rate = 22

The interpretation of the above rate is that:

The number of n T-shirts is the unit rate multiplied by n

So, we have the following equation

Cost of n shirts = Unit Rate * n

When the number of shirts is 2, we have

Cost of 2 shirts = 22 * 2

Cost of 2 shirts = 44

When the number of shirts is 3, we have

Cost of 3 shirts = 22 * 3

Cost of 3 shirts = 66

When the number of shirts is 4, we have

Cost of 8 shirts = 22 * 4

Cost of 4 shirts = 88

So, the points are (2, 44), (3, 66) and (4, 88)

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The solutions to the trigonometric equation sin(2x) = sin(x) on the first quadrant is given as follows:

The trigonometric equation in this problem is defined as follows:

sin(2x) = sin(x).

To verify the solutions, we replace each possible solution into each side of the equation, and verify if they are equal, as follows:

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The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

Given that, the nth term of a series represented by [tex]a_n=\frac{4^n}{5^{n+1}.n}[/tex].

A convergent series is a series whose partial sums tend to a specific number, also called a limit. A divergent series is a series whose partial sums, by contrast, don't approach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Next term in the series is [tex]a_{n+1}=\frac{4^{n+1}}{5^{n+2}.(n+1)}[/tex]

Now, the ratio is [tex]|\frac{a_{n+1}}{a_n}| =|\frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} | \frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |\frac{4^{n+1}}{4^n}.\frac{5^{n+2}}{5^{n+1}} .\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |4.\frac{1}{5}} .\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |\frac{(n+1)}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+\frac{1}{n} |[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+0|[/tex]

⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= 0.8[/tex]

Since 0.8 < 1 so the series converges.

The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.

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Answer:

From the ratio test, r = 0.8. The series converges.

Step-by-step explanation:

TTT

The quadratic function of the given graph is y = (x + 3)² + 8.

Quadratic function:

Basically, the standard form of the quadratic function is written as,

f(x) = a(x - h)² + k,

And a not equal to zero.

Here if a is positive, the graph opens upward, and if a is negative, then it opens downward. And the line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Given,

Here we have the graph and we have to find the quadratic function of the graph.

While we looking in to the given graph,

We have identified then the graph is opening the upward direction, So, the value of a is positive.

Now, we have to find the value of a which is 1.

And the vertex of the graph is (-3, 8).

So, the standard form of the quadratic function of the graph is written as,

=> y = (x + 3)² + 8.

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Answer:

f(3)=13

Step-by-step explanation:

f(x)=5x-2

f(3)=5(3)-2

 =15-2

 =13

Answer:

to be real i don´t think you can do anything because they´re not like terms. you can´t combine them (add) because they don´t have anything in common

Step-by-step explanation:

The test statistics that reject the null hypothesis are given as follows:

t such that |t| > 1.6766.

The null hypothesis is rejected when the test statistic is out of the accept done, defined by the critical value.

The critical value is obtained considering these three features are follows:

These parameters in this problem are given as follows:

Using a t-distribution calculator, the critical value is given as follows:

t = 1.6766.

Hence, as we have a two-tailed test, test statistics with absolute value greater than the critical value reject the null hypothesis.

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Answer:

  True

Step-by-step explanation:

You want to know if My-Lien has enough room in a truck with a capacity of 3.385 tons to move 3 5/16 tons of gravel.

The empty space can be found by subtracting the load from the capacity of the truck. The attached calculator output shows there is room for an addition 0.0725 tons.

My-Lien will have enough room to move the gravel.

__

Alternate solution

You can convert 3 5/16 to a decimal: 3.3125. Clearly, this amount is less than 3.3850.

The given exponential function is increasing so it will be growth and the percentage increase is 97%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given function,

y = 7000(1.97)^x

As x increase the 1.97^x will be increased thus, y will be increased so it will be growth.

Suppose x = 0

y = 7000

Suppose x = 1

y = 1.97 x 7000

% increase = (1.97 x 7000 - 7000)/7000

% increase = 97 %

Hence "The given exponential function is increasing so it will be growth and the percentage increase is 97%".

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The unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

Given that, Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

The cost of each fork of brand A

= 2.17/42

= $0.0517

The cost of each fork of brand B

= 3.97/48

= $0.0828

Therefore, the unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

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The value of 198.02 percent of £83.02 is £164.40

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

The value will be illustrated thus:

198.02% × £83.02

= 1.9802 × £83.02

= £164.3962

= £164.40

The value is £164.40.

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The graph of g(x) = f(x - 5) has a slope of 1 and the y-intercept is -5

A graph is a pictorial representation of data and the graph presented represents g(x) = f(x - 5) is attached

The graph shows a linear function written in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Comparing the equation with the above we can see that

m = 1

y intercept, c

this is a point where the graph cuts the y axis

c = -5

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The amount of raisins that Ben will mix if he wants to make a larger batch is 21 ounces of raisins

The amount is determined by comparing the trial mix used

Initially, 8 ounces of peanuts, 6 ounces of raisins, and 10 ounces of chocolate candies. This has a ratio of

peanut : raisins : chocolate

8 : 6 : 10

If 8 ounces of peanuts was used with 6 ounces of raisins, 28 ounces of peanuts wall be mixed with ? raisins

8 peanuts  = 6 raisins

28 peanuts = ? raisins

? = 28 * 6 / 8

? = 21 ounces of raisins

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