4.
STEM In 10 minutes, a heart can beat 700 times. At this rate,
in how many minutes will a heart beat 140 times? At what rate.
can a heart beat? (Example 4)

The mean number of bikes sold by the company from January to June was 146.17.

The mean, also called average refers to data set found by adding all numbers in the data set and then dividing by the number of values in the set.

Given data:​ 110 ​ 158 ​ 112 ​ 176 ​ 119 ​ 202

The total number of bikes sold is:

= 110 + 158 + 112 + 176 + 119 + 202

= 877

The number of months (Jan - Jun) = 6

The mean number of bikes sold will be:

= Ef/x

= 877 / 6

= 146.166666667

= 146.17

Full question "The table shows the number of bikes sold by a company from January to June of last year.​

​Find the mean number of bikes sold by the company from January to June.

​January ​February ​March April​ May​ ​June

​ 110 ​ 158 ​ 112 ​ 176 ​ 119 ​ 202"

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Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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Answer:

  -4, -6

Step-by-step explanation:

You want the constants that go into the binomial factors of x² -10x +24.

The binomial constants used in the factors must have ...

  a product of +24

  a sum of -10.

The positive product means the two factors have the same sign. The negative sum tells you both signs are negative. The negative answer choices are -2, -4, -6. The only pair with a sum of -10 and a product of +24 is -4 and -6.

  = (x -4)(x -6)

Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two: , the raw score is relatively lower than the mean.

If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.

A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two:

If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.

To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.

In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.

By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.

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The value of k that makes the statement true is k = 4.

Value is relative worth,merit of importance of something.if can refer to an intangible concept such as a person principal of a tangible object such as a rare coin.value vary widely across cultures, society and individual and can even vary within the same individual over time.

To show this, we can expand both sides of the equation and compare the terms. The left side of the equation becomes:

x⁴y⁸ + 7x³y¹²

The right side of the equation becomes:

2x⁴y⁸ + 7x³y¹²

Since both sides of the equation are identical, we can conclude that the value of k that makes the statement true is k = 4.

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Answer:

0.020405

Step-by-step explanation:

We solve this question, using z score formula.

z-score formula =

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the above question:

x = 1400, μ = 950, σ = 220

z = 1400 - 950/220

z = 2.04545

Determining the probability from Z-Table:

P(z = 2.04545) = P(x<1400) = 0.97959

P(x>1400) = 1 - P(x<1400)

= 1 - 0.97959

= 0.020405

Therefore, the probability of a student reading at more than 1400 words per minute after finishing the course is 0.020405

Answer:

4

Step-by-step explanation:

\(12/3=4\\x/t=r\\\)

(x is input, t is time, r is rate of change)

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

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Answer:

–6x + 15 < 10 – 5x

A number line from negative 3 to 7 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Step-by-step explanation:

\(-3(2x-5) < 5(2-x)\)

Expand the brackets:

\(\implies -6x+15 < 10-5x\)

Add 6x to both sides:

\(\implies 15 < 10+x\)

Subtract 10 from both sides:

\(\implies 5 < x\)

\(\implies x > 5\)

Therefore, x is bigger than 5.

When graphing inequalities on a number line:

To graph the given inequality on a number line:

Therefore, the correct representations of the given inequality are:

\(\\ \rm\leadsto -3(2x-5)<5(2-x)\)

\(\\ \rm\leadsto -6x+15<10-5x\)

Option C

\(\\ \rm\leadsto -x<-5\)

\(\\ \rm\leadsto x>5\)

Rest are wrong

Answer:

7 movie tickets 59.5

Step-by-step explanation:

divide 34 by 4 and then you get 8.5 then multiply that by 7

For this question, we assume that 2.5% of the thermometers are rejected at both sides of the distribution because they have readings that are too low or too high.

Answer:

The "two readings that are cutoff values separating the rejected thermometers from the others" are -1.96 Celsius degrees (below which 2.5% of the readings are too low) and 1.96 Celsius degrees (above which 2.5% of the readings are too high).

Step-by-step explanation:

We can solve this question using the standard normal distribution. This is a normal distribution with mean that equals 0, \( \\ \mu = 0\), and standard deviation that equals 1, \( \\ \sigma = 1\).

And because of using the standard normal distribution, we are going to take into account the following relevant concepts:

\( \\ Z = \frac{X - \mu}{\sigma}\) [1]

A positive value indicates that the possible raw value X is above \( \\ \mu\), and a negative that the possible raw value X is below the mean.

From the question, we have the following information about the readings on the thermometers, which is a normally distributed random variable:

It coincides with the parameters of the standard normal distribution, and we can find probabilities accordingly.

It is important to mention that the readings that are too low or too high in the normal distribution are at both extremes of it, one of them with values below the mean, \( \\ \mu\), and the other with values above it.

In this case, we need to find:

Here, we can take advantage of the symmetry of the normal or Gaussian distributions. In this case, the value for the 2.5% of the lowest and highest values is the same in absolute value, but one is negative (that one below the mean, \( \\ \mu\)) and the other is positive (that above the mean).

Solving the Question

The value below (and above) which are the 2.5% of the lowest (the highest) values of the distribution

Because \( \\ \mu = 0\) and \( \\ \sigma = 1\) (and the reasons above explained), we need to find a z-score with a corresponding probability of 2.5% or 0.025.

As we know that this value is below \( \\ \mu\), it is negative (the z-score is negative). Then, we can consult the standard normal table and find the probability 0.025 that corresponds to this specific z-score.

For this, we first find the probability of 0.025 and then look at the first row and the first column of the table, and these values are (-0.06, -1.9), respectively. Therefore, the value for the z-score = -1.96, \( \\ z = -1.96\).

As we said before, the distribution in the question has \( \\ \mu = 0\) and \( \\ \sigma = 1\), the same than the standard normal distribution (of course the units are in Celsius degrees in our case).

Thus, one of the cutoff value that separates the rejected thermometers is -1.96 Celsius degrees for that 2.5% of the thermometers rejected because they have readings that are too low.

And because of the symmetry of the normal distribution, z = 1.96 is the other cutoff value, that is, the other lecture is 1.96 Celsius degrees, but in this case for that 2.5% of the thermometers rejected because they have readings that are too high. That is, in the standard normal distribution, above z = 1.96, the probability is 0.025 or \( \\ P(z>1.96) = 0.025\) because \( \\ P(z<1.96) = 0.975\).

Remember that

\( \\ P(z>1.96) + P(z<1.96) = 1\)

\( \\ P(z>1.96) = 1 - P(z<1.96)\)

\( \\ P(z>1.96) = 1 - 0.975\)

\( \\ P(z>1.96) = 0.025\)

Therefore, the "two readings that are cutoff values separating the rejected thermometers from the others" are -1.96 Celsius degrees and 1.96 Celsius degrees.

The below graph shows the areas that correspond to the values below -1.96 Celsius degrees (red) (2.5% or 0.025) and the values above 1.96 Celsius degrees (blue) (2.5% or 0.025).

Answer:

140 square inches

Step-by-step explanation:

10 times 6 is 60

and 10 times 80 is 80

and add that equals 140

9514 1404 393

Answer:

  70 square inches

Step-by-step explanation:

Forget the coloring and look at the outline of the figure. You see it is a trapezoid with bases 6 in (top) and 8 in (bottom). The height is given as 10 in.

The area formula for a trapezoid is ...

  A = (1/2)(b1 +b2)h

  A = (1/2)(6 in +8 in)(10 in) = (1/2)(14)(10) in²

  A = 70 in²

The area of the figure is 70 square inches.

_____

Alternate solution

You can add the areas of the two triangles. The area of each is ...

  A = (1/2)bh

Gray triangle: A = (1/2)(8 in)(10 in) = 40 in²

Brown triangle: A = (1/2)(6 in)(10 in) = 30 in²

Total area = 40 in² + 30 in² = 70 in²

__

If you're paying attention to the formulas, you see that the "alternate solution" computes ...

  A = (1/2)(b1)h + (1/2)(b2)h = (1/2)(b1 +b2)h . . . . . trapezoid formula

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer:

It would be a diagnol line.

Answer:

See explanation. (I just sumbitted this exact assignment this morning, and i submitted something very similar to the example below!)

Step-by-step explanation:

The contrapositive of a conditional is the same as the converse of the inverse of the conditional.

The best way to prove/support this statement is to create an example. You should start by creating a conditional; you can then form the conditional's converse, inverse, and contrapositive. Here is an example:

Conditional: If C, then D. (starting statement)

Converse: If D, then C. (conditional reversed)

Inverse: If not C, then not D. (opposite of the conditional)

Contrapositive: If not D, then not C. (reversed opposite of the conditional)

Based on the information from the example you gave, you can conclude:

The converse of the inverse: If not D, then not C. (reversed opposite of the conditional)

Because: The converse is the conditional reversed (If D, then C). The inverse of the converse, in this case, would then make it the opposite (If not D, then not C).

I have not yet received a grade on this assignment, but I know the information is correct; the amount of explanation you need to give really depends on how your teacher grades. Personally, I just submitted an example (similar to the one above) that was color-coded to help show the different parts of each statement.

I hope this helps! :)

In the differential equation

\(\dfrac{dy}{dx} + 12y = \cos\left(\dfrac{\pi x}{12}\right)\)

multiply on both sides by the integrating factor

\(\mu = \exp\left(\displaystyle\int12\,dx\right) = e^{12x}\)

Then the left side condenses to the derivative of a product.

\(e^{12x} \dfrac{dy}{dx} + 12 e^{12x} y = e^{12x} \cos\left(\dfrac{\pi x}{12}\right)\)

\(\dfrac{d}{dx}\left[e^{12x}y\right] = e^{12x}\cos\left(\dfrac{\pi x}{12}\right)\)

Integrate both sides with respect to \(x\), and use the initial condition \(y(0)=0\) to solve for the constant \(C\).

\(\displaystyle \int \frac{d}{dx} \left[e^{12x}y\right] \, dx = \int e^{12x} \cos\left(\dfrac{\pi x}{12}\right) \, dx\)

As an alternative to integration by parts, recall

\(e^{ix} = \cos(x) + i \sin(x)\)

Now

\(e^{12x} \cos\left(\dfrac{\pi x}{12}\right) = e^{12x} \mathrm{Re}\left(e^{i\pi x/12}\right) = \mathrm{Re}\left(e^{(12+i\pi/12)x}\right)\)

\(\displaystyle \int \mathrm{Re}\left(e^{(12+i\pi/12)x}\right) \, dx = \mathrm{Re}\left(\int e^{(12+i\pi/12)x} \, dx\right)\)

\(\displaystyle. ~~~~~~~~ = \mathrm{Re}\left(\frac1{12+i\frac\pi{12}} e^{(12+i\pi/12)x}\right) + C\)

\(\displaystyle. ~~~~~~~~ = \mathrm{Re}\left(\frac{12 - i\frac\pi{12}}{12^2 + \frac{\pi^2}{12^2}} e^{12x} \left(\cos\left(\frac{\pi x}{12}\right) + i \sin\left(\frac{\pi x}{12}\right)\right)\right) + C\)

\(\displaystyle. ~~~~~~~~ = \frac{12}{12^2 + \frac{\pi^2}{12^2}} e^{12x} \cos\left(\frac{\pi x}{12}\right) + \frac\pi{12} e^{12x} \sin\left(\frac{\pi x}{12}\right) + C\)

\(\displaystyle. ~~~~~~~~ = \frac1{12(12^4+\pi^2)} e^{12x} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) + C\)

Solve for \(y\).

\(\displaystyle e^{12x} y = \frac1{12(12^4+\pi^2)} e^{12x} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) + C\)

\(\displaystyle y = \frac1{12(12^4+\pi^2)} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) + C\)

Solve for \(C\).

\(y(0)=0 \implies 0 = \dfrac1{12(12^4+\pi^2)} \left(12^4 + 0\right) + C \implies C = -\dfrac{12^3}{12^4+\pi^2}\)

So, the particular solution to the initial value problem is

\(\displaystyle y = \frac1{12(12^4+\pi^2)} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) - \frac{12^3}{12^4+\pi^2}\)

Recall that

\(R\cos(\alpha-\beta) = R\cos(\alpha)\cos(\beta) + R\sin(\alpha)\sin(\beta)\)

Let \(\alpha=\frac{\pi x}{12}\). Then

\(\begin{cases} R\cos(\beta) = 12^4 \\ R\sin(\beta) = 12^4\pi+\pi^3 \end{cases} \\\\ \implies \begin{cases} (R\cos(\beta))^2 + (R\sin(\beta))^2 = R^2 = 12^8 + (12^4\pi + \pi^3)^2 \\ \frac{R\sin(\beta)}{R\cos(\beta)}=\tan(\beta)=\pi+\frac{\pi^3}{12^4}\end{cases}\)

Whatever \(R\) and \(\beta\) may actually be, the point here is that we can condense \(y\) into a single cosine expression, so choice (D) is correct, since \(\cos(x)\) is periodic. This also means choice (C) is also correct, since \(\beta=\cos(x)\implies\beta=\cos(x+2n\pi)\) for infinitely many integers \(n\). This simultaneously eliminates (A) and (B).

\(57=\cfrac{5}{8}z+7\implies 57=\cfrac{5z}{8}+7\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8(57)=8\left( \cfrac{5z}{8}+7 \right)} \\\\\\ 456=5z+56\implies 400=5z\implies \cfrac{400}{5}=z\implies 80=z\)

Interest earned on first investment in year 1 is $6,183.13

Interest earned on second  investment in year 1 is $6,167.68

Annual yield on first investment is 6.18%

Annual yield on second investment is 6.17%

What is daily compounding?

Daily compounding means that the interest on the investment is computed on daily basis, 365 days a year.

In a bid to determine the total interest earned in one year on the investment whose interest is compounded daily, we can make use of the future value below to determine its worth after 1 year, from which the initial investment can be deducted to determine the interest in year 1.

FV=PV*(1+r/n)^(n*t)

PV=initial investment=$100,000

r=rate of return=6%

n=365 days a year

t=1 year

FV=$100,000*(1+6%/365)^(365*1)

FV=$106,183.13

Interest=$106,183.13 -$100,000

interest=$6,183.13

Annual yield=effective annual interest

EAR=(1+6%/365)^(365)-1

EAR=6.18%

What is monthly compounding?

It means interest is compounded or computed every month, 12 months a year

FV=PV*(1+r/n)^(n*t)

PV=initial investment=$100,000

r=rate of return=6%

n=12 months a year

t=1 year

FV=$100,000*(1+6%/12)^(12*1)

FV=$ 106,167.78  

Interest=$ 106,167.78  -$100,000

interest=$6,167.68

Annual yield=effective annual interest

EAR=(1+6%/12)^(12)-1

EAR=6.17%

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answer: 28561^2in the area involves multiplying by the 4 sides of the shaded square and the shaded is the colored square.

Answer:

the answer is 37 i believe

37

Step-by-step explanation:

First start with parenthesis 3 + 2=5. Next the brackets

8 - 5=3. Next 15 ÷ 3 = 5. Then Finally, 8 × 4 = 32, and add 5, which 37

We have to calculate a 95% confidence interval for the mean.

The data is: [111, 115, 120, 103, 106].

We can calculate the sample mean as:

and the sample standard deviation as:

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

The degrees of freedom for this sample size are:

The t-value for a 95% confidence interval and 4 degrees of freedom is t=2.776.

The margin of error (MOE) can be calculated as:

Then, we can express the confidence interval as:

Answer:

The 95% confidence interval for the weights of all baby giraffes is 111 ± 8.5.

The 95% confidence interval for the weights of all baby giraffes is 111 ± 8.5.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given:

The data is: [111, 115, 120, 103, 106].

We can calculate the sample mean as:

Mean = ( 111 + 115 + 120 + 103 + 106 )5

Mean = 111

and, Sample Standard Deviation

= √( 1/4 (( 111- 111)² + ( 115- 111)² + ( 120- 111)² + ( 103- 111)² + ( 106- 111)²)

= √186 /4

= 6.82

Now, When σ is not known, s divided by the square root of N is used as an estimate of σM:

= 6.82 / √5

= 3.05

and, The degrees of freedom for this sample size are:

df = 5-1 = 4

Now, The t-value for a 95% confidence and 4 degrees of freedom is t=2.776.

Then, Margin of Error

= t value x  σM

= 2.776 x 3.05

= 8.5

Thus, the confidence interval expressed as 111 ± 8.5.

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Answer:

A. 2^20/3^8

Step-by-step explanation:

Hope this helped, have a good day <3

Answer:

2 20

3 8

Step-by-step explanation:

you times the exponent on the inside to the exponent on the outside

Answer:

x=17

Step-by-step explanation:

See attached.

Because of the Triangle Proportionality Theorem,

24: (2x-4)+6

20: 2x-4

Cross multiply these two ratios

48x-96 = 40x-80+120

Isolate variable: 8x = 96-80+120

Solve: 8x = 136

x=17

Answer:

\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)

Answer:

y = -4/3 x + 5

Step-by-step explanation:

The line crosses y-intercept at 5 gown does 4 units and then left 3 units.

Answer:

\(5.625\pi\) m³.

Step-by-step explanation:

The volume of a cylinder is found by calculating pi * r^2 * h.

In this case, h = 2.5, and r = 1.5.

pi * 1.5^2 * 2.5

= pi * 2.25 * 2.5

= pi * 5.625

So, the exact volume of the cylinder is \(5.625\pi\) m³.

Hope this helps!

Answer: Volume of Cylinder: \(\pi r^{2} *h\)

               5.625π  m.

Step-by-step explanation:

\(\pi r^{2} *h\)   Cylinder Area Formula

\(\pi *1.5^{2} *2.5\)   Substitution

\(\pi * 2.25 *2.5\)   Exponent

\(\pi *5.625\)   Multiply

\(5.625\pi\) Answer

Answer:

Associative

Step-by-step explanation:

The associate property for multiplication states that \(a\times(b\times c)=(a\times b)\times c\), thus, \((2\times 6)\times 4 = 2\times (6\times 4)\). The way factors are grouped does not change the product, essentially.