Find the slope of a line that passes through the following points (3,2) (5,-3)

A. 2/5
B. 5/8
C. -5/2
B. -5/8

Answer:

8 1/12 boxes

Step-by-step explanation:

Your first step to solve this problem is to convert those fractions to a common denominator. I would choose 12. So your first would be 4 4/12 and your second would be 3 9/12. You would then add those up and get 8 1/12 boxes of muffins bought at the bake sale.

(a)

[tex]\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}[/tex]

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

[tex]\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt[/tex]

[tex]=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}[/tex]

(b) The series

[tex]\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}[/tex]

converges by comparison to the convergent p-series,

[tex]\displaystyle\sum_{n=3}^\infty\frac1{n^2}[/tex]

(c) The series

[tex]\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}[/tex]

converges absolutely, since

[tex]\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}[/tex]

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

Answer:

40%

Step-by-step explanation:

Because there are 5 rectangle total, we can dive 100% into 5 parts.

Each part is then 20%, there are 2 shaded rectangles thus the answer is 40%.

The distance that the car has left to drive can be represented as option (D) 4(0.5t) is the correct answer.

The speed is the rate of change of position of an object in any direction. Speed tells us how fast or slow an object travels and describes the distance traveled divided by the time taken to cover the distance.

For the given situation,

The speed of the car,S = 0.5 miles per minute

Let the time be t.

Let the distance be D.

The distance between the car and the home = 4 miles.

The formula that relates speed, distance and time is

[tex]Speed=\frac{Distance}{time}[/tex]

⇒ [tex]Distance=(Speed)(time)[/tex]

Here initially at t=0, the car is 4 miles apart from the home and it travels at 0.5 miles per minute, so the equation can be represented as

⇒ [tex]D=4(0.5t)[/tex]

Hence we can conclude that the distance that the car has left to drive can be represented as option (D) 4(0.5t) is the correct answer.

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Answer:

Part A:

I would multiply the length, width, and depth of the pool to find the volume of it. That would be how much water can fit inside. 25 ft x 15 ft x 10 ft = 3750 ft

Part B:

a. 3750 ft

Answer:

m=3/2 or m=1.5

Step-by-step explanation:

slope formula:

m=(y1-y2)/(x1-x2)

in order to get this we need two points such as (3,0) and (1,-3) which are points on this line. So:

m=(0-(-3))/(3-1)

m=3/2 or m=1.5

Answer:

a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future us 0.58.

b) The margin of error is of 0.03.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Point estimate:

The point estimate is [tex]\pi[/tex].

Margin of error:

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

(a) What is the point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future.

579 out of 1007 adults. So

[tex]\pi = \frac{579}{1007} = 0.575[/tex]

Rounding to two decimal places, 0.58

The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future us 0.58.

(b) At 90% confidence, what is the margin of error

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.645\sqrt{\frac{0.58*0.42}{1007}}[/tex]

[tex]M = 0.03[/tex]

The margin of error is of 0.03.

Answer:

a) 0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers

b) 0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers

c) 1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Standard deviation of 500 kilometers

This means that [tex]\sigma = 500[/tex]

a. Assuming the mean is 1500 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

Mean of 1500 km means that [tex]\mu = 500[/tex]

The probability is the pvalue of Z when X = 500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 1500}{500}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers.

b. Assuming the mean is 1200 kilometers, what is the probability of a northward displacement of less than 500 kilometers?

Now [tex]\mu = 1200[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 1200}{500}[/tex]

[tex]Z = -1.4[/tex]

[tex]Z = -1.4[/tex] has a pvalue of 0.0808

0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers.

c. If, in fact, the northward displacement is less than 500 kilometers, which is the more plausible mean, 1200 or 1500 kilometers?

1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.

Answer:

c. 80,360

Step-by-step explanation: multiply the number of cases they make each day by the amount of pastries each case contains

Answer:

b

Step-by-step explanation:

Answer:

2/8 is the median

Step-by-step explanation:

Answer: The median is 2/8

Step-by-step explanation:

Because the median is the middle number, and 2/8 is at the middle.

Answer:

A

Step-by-step explanation:

When finding out which number is the greatest, I would convert these numbers to numerals with decimals for easier comparison.

3[tex]\sqrt{5}[/tex] is approximately 6.71.

6[tex]\frac{1}{4}[/tex] is 6.25

6.55 is, well 6.55.

From here, we can tell that 6.71 is the greatest, followed by 6.55 and 6.25 is the smallest. Thus, the order in descending order should be 3[tex]\sqrt{5}[/tex], 6.55 then 6[tex]\frac{1}{4}[/tex], which is Option A.

Answer:

no

Step-by-step explanation:

Hello There!

We can figure out if the given side lengths form a right triangle using the Pythagorean Theorem

The Pythagorean Theorem states that the hypotenuse (longest side) squared equal to sum of the two legs squared

so if it is a right triangle then

[tex]74^2=71^+24^2[/tex]

[tex]74^2=5476\\71^2=5041\\24^2=576\\5041+576=5617\\5476\neq 5617[/tex]

5617 is not equal to 5476 therefore the given side lengths do not form a right triangle

~TheMathWIz

Answer:3

Step-by-step explanation:

12/4=3, 9/3=3

hope it helps

Answer:

36

Step-by-step explanation:

Answer:

yes and no a.a

Step-by-step explanation:

Car A travels the fastest on 1 gallon of gas.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that car, the magazine reports the numbers of miles driven for different amounts of fas for Three car.

Consider us solving for the miles per gallon of individual cars

A. miles driven =140

A gallons= 5

x= 140/5

x= 28 miles per gallon

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Answer:

Step-by-step explanation:

30

Answer:

Open circle going right. <-- graphed

Step-by-step explanation:

1billion is the correct answerStep-by-step explanation:

Answer:

60% decrease

Step-by-step explanation:

To work out percentage change you takeaway the original number by the new number (New number-Original number) in this case 24-60=(-36), then divide the decreased amount by the original number and multiply the answer by 100 (Decrease amount ÷ Original number x 100) for this question you'd do (-36)÷60=(-0.6) then (-0.6)x100=(-60).

The minus shows its a decrease in percentage by 60%

(I hope this helps srry if it doesn't make sense)

Answer:

A,C,D,F

Step-by-step explanation:

Answer:

umm whats the question-

help you in what man?

there is no question

Answer:

rotational symmetry of 60 degrees around the origin - yes

rotational symmetry of 120 degrees around the origin - yes

Step-by-step explanation:

A regular hexagon has 6 congruent angles

the the angles created on the line of symmetry are equal to 60 so the angle of rotational symmetry is 60 degrees.

The regular hexagon, like stated before, has 6 congruent angles so the order of symmetry is 6

Here is a visual from basic-matematics

Answer:

Step-by-step explanation:

It is easy to see that (-2, 0) and (0, -4) are points on the line.

gradient = (difference of y-coordinates)/(difference of x-coordinates) = (0-(-4))/(-2-0) = 4/(-2) =  -2

Answer:

(x + 6)(x - 4)

Step-by-step explanation:

x² + 2x - 24

(x + 6)(x - 4)

-4 and +6 multiply to 24 and add to +2.

Answer:

Step-by-step explanation:

(5 dollars)/(4 girls) = (5/4 dollars)/girl = (1.25 dollars)/girl

:::::

(5.52 dollars)/(4 girls) = (5.52/4 dollars)/girl = (1.38 dollars)/girl

Answer:

We accept the null hypothesis, that is, that the population mean is not different from 0.7.

Step-by-step explanation:

A brochure claims that the average maximum height a certain type of plant is 0.7 m.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 0.7[/tex]

A gardener suspects that this estimate is not accurate locally due to soil conditions.

Hypothesis test to determine whether the population mean is different from 0.7m, which means that the alternate hypothesis is:

[tex]H_{a}: \mu \neq 0.7[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that [tex]\mu = 0.7[/tex]

A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m.

This means, respectively, that [tex]n = 43, X = 0.65[/tex]

Assume that the population standard deviation is 0.2 m.

This means that [tex]\sigma = 0.2[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.65 - 0.7}{\frac{0.2}{\sqrt{43}}}[/tex]

[tex]z = -1.64[/tex]

Pvalue of the test:

Since we are testing that the mean is different of a value, and z is negative, the pvalue of the test is 2 multiplied by the pvalue of z = -1.64

z = -1.64 has a pvalue of 0.0505

2*0.0505 = 0.101

Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m.

0.101 > 0.01, which means that we accept the null hypothesis, that is, that the population mean is not different from 0.7.