what is the graph of 5x+3y=13

Answer:

[tex]\lim_{x \to \infty} \frac{x}{x}=1[/tex]

Calculating the limit by product rule is WRONG

Step-by-step explanation:

Indeterminate forms is an expression involving 2 functions whose limit cannot be determined by limits of individual functions. If we calculate the limits by general rules used for calculating the limits, we will not have a clear answer.

Examples of indeterminate forms are:

[tex]\frac{0}{0}, \frac{\infty}{\infty} , 0\cdot\infty, 1^{\infty},\infty-\infty, 0^0,\infty^0[/tex]

To find the limits of such forms, we have to use L'hospital rule, which states that if:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = Indeterminate form \\ Then\\\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}[/tex]

[tex]\lim_{x \to \infty} \frac{x}{x}= \lim_{x \to \infty} x\cdot \lim_{x \to \infty} \frac{1}{x} \\ \lim_{x \to \infty} \frac{x}{x}= =\infty\cdot\frac{1}{\infty} \\ \lim_{x \to \infty} \frac{x}{x}=\infty\cdot0[/tex]

As it is an INDETERMINATE FORM, we cannot calculate its limit by product rule. We have to use L'Hospital Rule:

[tex]\lim_{x \to \infty} \frac{x}{x}= \lim_{x \to \infty} \frac{d(x)/dx}{d(x)/dx}\\\lim_{x \to \infty} \frac{x}{x}=\lim_{x \to \infty} \frac{1}{1}\\\lim_{x \to \infty} \frac{x}{x}=1[/tex]

Answer:

  distributive property

Step-by-step explanation:

The distributive property tells you ...

  a(b+c) = ab +ac

  5(4+2) = 5·4 +5·2 = 20 +10

[tex]\text{It would most likely be the distributive property}\\\\\text{In the equation:}\\\\5(4+2)=20+10\\\\\text{You would see that you can distribute the 5 into the variables inside }\\\text{the parenthesis}\\\\\text{In which it is set up in that particular way in order to do so}[/tex]

Answer:

[tex] \frac{3}{5}[/tex]

Step-by-step explanation:

The adjacent sides are 3 and 4. Thus the hypotenuse is: (by Pythagoras Theorem)

$=\sqrt{3^2+4^2}$

$=\sqrt{25}$

$=5$

Now by definition of $\sin$, we get:

$\sin \theta= \frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5}$

Answer:

The probability that the next customer will request mid-grade gas and fill the tank is 0.1800

Step-by-step explanation:

In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:

probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks

probability that the next customer will request mid-grade gas and fill the tank=  30%*60%

probability that the next customer will request mid-grade gas and fill the tank= 0.1800

The probability that the next customer will request mid-grade gas and fill the tank is 0.1800

Answer:

7/30

Step-by-step explanation:

Answer:

(A) Interpretation is below

(B) The slope in the new units is now 60.45

The intercept in the new units is 38.634

(C) yes

(D) yes

Step-by-step explanation:

(A) The intercept here is 47. This means that the minimum response or payment is 47 (thousand dollars).

The slope is 650. This means that the change in Y due to a change in X is 650. In other words, if there is a change of 1(thousand square feet), there will be a resulting increase of 650(thousand dollars). It will result in an increase instead of decrease because the slope is positive or bearing a + sign.

(B) The new units are EUROS and SQUARE METRES.

$1 = €0.822

1s.f. = 0.093s.m.

The new fitted line would be:

0.822Y = 47(0.822) + (0.093)(650)X

0.822Y = 38.634 + 60.45X

The slope in the new units is 60.45 and the intercept on the y-axis is 38.634.

Answer:

2.17% of students who received a merit scholarship did not receive enough to cover full tuition

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this question, we have that:

[tex]\mu = 3464, \sigma = 489[/tex]

If the cost of full tuition was $4450 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?

This is 1 subtracted by the pvalue of Z when X = 4450. So

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

[tex]Z = \frac{4450 - 3464}{489}[/tex]

[tex]Z = 2.02[/tex]

[tex]Z = 2.02[/tex] has a pvalue of 0.9783.

1 - 0.9783 = 0.0217

2.17% of students who received a merit scholarship did not receive enough to cover full tuition

Answer:

7. [tex]x \leq 5[/tex]

8. [tex]x\geq 4[/tex]

9. x < 5

10. x < -7

11.  x < 45

12. [tex]x\geq -10[/tex]

13. x < -7

14. x < 45

15. [tex]x\leq 50[/tex]

16. [tex]w\geq 16[/tex]

18. q > 4

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

The three angles form a straight line so they add to 180 degrees

x+ 100 +3x = 180

Combine like terms

100+4x= 180

Subtract 100 from each side

100+4x-100= 180-100

4x= 80

Divide each side by 4

4x/4 = 80/4

x = 20

Answer:

[tex]x = 20 \: \: degrees[/tex]

Step-by-step explanation:

Angles in a straight line = 180 degrees

[tex]x + 3x + 100 = 180 \\ 4x + 100 = 180 \\ 4x = 180 - 100 \\ 4x = 80 \\ \frac{4x}{4} = \frac{80}{4} \\ x = 20 \: \: degrees[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

[tex]\tan \theta-\cot \theta[/tex]

Step-by-step explanation:

[tex](\sec \theta - \csc \theta)(\cos \theta + \sin \theta)= \\\\\\\left( \dfrac{1}{\cos \theta}-\dfrac{1}{\sin \theta} \right)(\cos \theta + \sin \theta)= \\\\\\\left( \dfrac{1}{\cos \theta} \cdot \cos \theta \right) + \left( \dfrac{1}{\cos \theta} \cdot \sin \theta \right) - \left( \dfrac{1}{\sin \theta} \cdot \cos \theta \right) - \left( \dfrac{1}{\sin \theta} \cdot \sin \theta \right)= \\\\\\1+\dfrac{\sin \theta}{\cos \theta}-\dfrac{\cos \theta}{\sin \theta} -1= \\\\\\\tan \theta-\cot \theta[/tex]

Hope this helps!

Answer:

a. The 95% confidence interval for the difference between means is (0.071, 0.389).

b. There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.

c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.

In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.

In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.

Step-by-step explanation:

The table with the data is:

Sample 1 Sample 2

0.580    0.382

0.711      0.276

0.571     0.570

0.666    0.366

0.598

The mean and standard deviation for sample 1 are:

[tex]M=\dfrac{1}{5}\sum_{i=1}^{5}(0.58+0.711+0.571+0.666+0.598)\\\\\\ M=\dfrac{3.126}{5}=0.63[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.58-(0.63))^2+...+(0.598-(0.63))^2]}\\\\\\ s=\sqrt{\dfrac{1}{4}\cdot [(0.002)+(0.007)+(0.003)+(0.002)+(0.001)]}\\\\\\ s=\sqrt{\dfrac{0.015}{4}}=\sqrt{0.0037}\\\\\\s=0.061[/tex]

The mean and standard deviation for sample 2 are:

[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(0.382+0.276+0.57+0.366)\\\\\\ M=\dfrac{1.594}{4}=0.4[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(0.382-(0.4))^2+(0.276-(0.4))^2+(0.57-(0.4))^2+(0.366-(0.4))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(0.015)+(0.029)+(0.001)]}\\\\\\ s=\sqrt{\dfrac{0.046}{3}}=\sqrt{0.015}\\\\\\s=0.123[/tex]

Confidence interval

We have to calculate a 95% confidence interval for the difference between means.

The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.

The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.

The difference between sample means is Md=0.23.

[tex]M_d=M_1-M_2=0.63-0.4=0.23[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07[/tex]

The critical t-value for a 95% confidence interval is t=2.365.

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

[tex]MOE=t\cdot s_{M_d}=2.365 \cdot 0.07=0.159[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = 0.23-0.159=0.071\\\\UL=M_d+t \cdot s_{M_d} = 0.23+0.159=0.389[/tex]

The 95% confidence interval for the difference between means is (0.071, 0.389).

Hypothesis test

This is a hypothesis test for the difference between populations means.

The claim is that the fish in this particular polluted lake have signficantly elevated mercury levels.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.

The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.

The difference between sample means is Md=0.23.

[tex]M_d=M_1-M_2=0.63-0.4=0.23[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.23-0}{0.07}=\dfrac{0.23}{0.07}=3.42[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-1=5+4-2=7[/tex]

This test is a right-tailed test, with 7 degrees of freedom and t=3.42, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>3.42)=0.006[/tex]

As the P-value (0.006) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.

c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.

In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.

In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.

Answer:

The answer is 2pix3 or  [tex]2\pi x^3\\[/tex]

Step-by-step explanation:

This problem brothers on the mensuration of solid shapes, a cylinder.

we know that the expression for the volume of a cylinder is

[tex]volume= \pi r^2h\\[/tex]

let the radius r of the base be=  x

and the height h of the cylinder be =  2x

we can now solve the expression that represents the volume of the cylinder, in cubic  units.

[tex]volume= \pi *x^2*2x\\volume= \pi *2x^3\\\\volume= 2\pi x^3\\[/tex]

Answer:

The probability that the sample mean weight of these 400 bags exceeded 10.6 ounces is P(Xs>10.6)=0.

Step-by-step explanation:

When we take samples of size n=400, we have the folllowing parameters for the sampling distribution for the sample means:

[tex]\mu_s=\mu=10.5\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.1}{\sqrt{400}}=\dfrac{0.1}{20}=0.005[/tex]

We can calculate the probability that the sample mean weight of these 400 bags exceeded 10.6 ounces calculating the z-score for Xs=10.6 and then its probability P(Xx>10.6), using the standard normal distribution:

[tex]z=\dfrac{X_s-\mu_s}{\sigma_s}=\dfrac{10.6-10.5}{0.005}=\dfrac{0.1}{0.005}=20\\\\\\P(X_s>10.6)=P(z>20)=0[/tex]

Answer:

I could find out the surface area and it's capacity

Answer:

Step-by-step explanation:

If half of the wine barrels are infected, it means that the proportion of infected wine is 0.5

We would set up the hypothesis test.

For the null hypothesis,

p = 0.5

For the alternative hypothesis,

p < 0.5

Considering the population proportion, probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 28

n = number of samples = 80

P = 28/80 = 0.35

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.35 - 0.5)/√(0.5 × 0.5)/80 = - 2.68

From the normal distribution table, the area below the test z score in the left tail 0.0037

Therefore,

p value = 0.0037

Assuming a significance level of 0.05, therefore,

Since alpha, 0.05 > than the p value, 0.0037, then we would reject the null hypothesis.

Answer:

C and E

Step-by-step explanation:

Focus = (-3,2)

So,

Distance to the focus =

√(x+3)²+(y-2)²

Now

Directrix:

y = 4 and p = -4

Distance from the directrix

= y+p

= y-4

Answer:

30 ≥ 4.65x

Step-by-step explanation:

He cannot purchase more than $30, so the amount that he buys must always be less than 30.

Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.

Answer:

[tex]f(x)=0.2\,(x-2)^2+1[/tex]

Option "B" as per the list of possible answers

Step-by-step explanation:

Notice that the parabola has a minimum at the point (2, 1), therefore first look at which of the options gives you  [tex]f(2) = 1[/tex]. You would be able then the discard the last two functions listed (they render "-1" (not 1) for x = 2.

Now to decide between the first and the second option, notice that the first option has a negative coefficient (-0.2) multiplying the perfect square [tex](x-2)^2[/tex] which means that the branches of such parabolic function would be pointing down. So you discard the first option, and now the only one left is the second option:

[tex]f(x)=0.2\,(x-2)^2+1[/tex]

which you can check briefly by evaluating a couple of easy points  (like what values you get for x = 0, and at x = 4, and confirm it is the correct option.

Answer:

A = 1168.67 cm²

Step-by-step explanation:

[tex]A=2\pi rh+2\pi r^{2}[/tex]           Use this equation to find the surface area

[tex]A=2\pi (6)(25)+2\pi (6)^{2}[/tex]  Multiply    

[tex]A=2\pi (150)+2\pi (36)[/tex]     Multiply

A = 942.48 + 226.19     Add

A = 1168.67 cm²

Answer:

1169.14cm2

Step-by-step explanation:

The surface area is that area which you can feel. Now there are two circles one at the top and one at the bottom.

These areas are expressed as;

π×r2 { remember area of a circle}.

Therefore for the two areas we have twice the area of once since they are the same. Hence we have:

2×π×r2.

Secondly, there is still another area we haven't talked about yet. It's the area you feel at the side and this area curls into a circular fashion.

Now let's assume the two circles are the top and bottom are knocked off , we would have a shape that looks like a rectangle.

Now area of a rectangle is the multiplication of both sides. In this case the side would be the height,h and the circumference of the circle since the rectangle forms into a circle when she try to join both edges together.

Hence the area of this Shape would be;

2πr{circumference} × h=2πrh

Hence the total surface area would be;

2πr2 + 2πrh.

Substituting the giving values we have;

Note: to obtain raduis,r ; we divide the diameter by 2.

2 × 22/7 × 6^2 + 2 × 22/7 × 6× 25

2×22/7(36+150)

44/7(186)= 8184/7

=1169.1429cm2

=1169.14cm2{ to 2 decimal place}

Answer:

C

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

14 green and 14 purple marbles = 28 marbles

P( purple) = purple/ total

                 = 14/28

                  =1/2

Answer:

$71.59

Step-by-step explanation:

[tex]43.25+26.25[/tex]

[tex]=69.5[/tex]

[tex]69.5*\frac{103}{100}[/tex]

[tex]69.5*1.03[/tex]

[tex]=71.585[/tex]

Answer:

62/7

Step-by-step explanation:

The budget illustrates ratios and proportions.

The maximum amount to spend on food each day is $8

The given parameters are:

[tex]\mathbf{Budget = \$62}[/tex]

[tex]\mathbf{Days = 7}[/tex]

So, the daily budget is:

[tex]\mathbf{Daily = \frac{Budget}{Days}}[/tex]

So, we have:

[tex]\mathbf{Daily = \frac{\$62}{7}}[/tex]

[tex]\mathbf{Daily = \$8.85714285714}[/tex]

Remove decimal parts (do not approximate)

[tex]\mathbf{Daily = \$8}[/tex]

Hence, the maximum to spend each day is $8

Read more about ratios and proportions at:

https://brainly.com/question/13114933

Answer:

c

step-by-step explanation:

ok the slope of the line is 2

and so by using the formula y1+y2/x1+x2 we can get the ration of each table

the first table is  -9+-7/-25+-21

this can be simplified to  -16/-46 which is about  0.347

using this formula for each table you can find the answer .

im

too lazy to do the rest

Answer:

It's C

Step-by-step explanation:

I did the quiz, see Arjinoodles for a detailed explanation.

Answer:

The 90​% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 9 - 1 = 8

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595

The margin of error is:

M = T*s = 1.8595*2.7 = 5

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 25.3 - 5 = 20.3 milligrams

The upper end of the interval is the sample mean added to M. So it is 25.3 + 5 = 30.3 milligrams.

The 90​% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.

[tex]the \: answer \: is \: 7 \: square \: units \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

A) 1500 girls

B) 25% are men

Step-by-step explanation:

I hope this helps

Answer:

Hello!

Step-by-step explanation:

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.

So,you have to multiply.

Hope this helps.