Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than 1/3 the distance from the first city to the second city. The distance from the second city to the third city was 10 miles less than 5/4 the distance from the first city to the second city. If the distance from his original location to the first city and the distance from the second city to the third city were the same, what was the total distance Eric traveled?

Answer:

root 61

Step-by-step explanation:

You can use the distance formula or draw a triangle with sides 5 and 6

Answer:

Present value is $993.47

Step-by-step explanation:

PV = present value

Fv = future value = $1,600

Discount (i) = 10%

N = Years = 5

The formula for this is given by:

PV = FV/(1 + i)^N

PV = $1600/(1 + 0.10)^5

PV = $1600/1.1^5

PV = $1600/1.61051

PV = $993.47

Answer:

The mean is M=0.17 defective bulbs.

The standard deviation is s=0.165 defective bulbs.

Step-by-step explanation:

We can calculate the mean as the sum of the product between the number of defective bulbs and its proportion:

[tex]M=\sum_i p_i\cdot X_i=0.9\cdot0+0.05\cdot 1+0.03\cdot2+0.02\cdot3\\\\M=0+0.05+0.06+0.06\\\\M=0.17[/tex]

The standard deviation can be calculated  as the sum of the product between the deviation from the mean for each number of defective bulbs and its proportion:

[tex]s=\sqrt{\sum_i p_i\cdot (X_i-M)^2}\\\\s=\sqrt{0.9\cdot(0-0.17)^2+0.05\cdot (1-0.17)^2+0.03\cdot(2-0.17)^2+0.02\cdot(3-0.17)2}\\\\s=\sqrt{0.02601+0.00072+0.000363+0.000242}\\\\s=\sqrt{0.027335}\\\\s\approx0.165[/tex]

Answer:

Test statistic z = 2.3839.

P-value = 0.0086.

At a signficance level of 0.05, there is enough evidence to support the claim that the percentage of residents who favor construction is above 56%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of residents who favor construction is above 56%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.56\\\\H_a:\pi>0.56[/tex]

The significance level is 0.05.

The sample has a size n=900.

The sample proportion is p=0.6.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.56*0.44}{900}}\\\\\\ \sigma_p=\sqrt{0.000274}=0.017[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.6-0.56-0.5/900}{0.017}=\dfrac{0.039}{0.017}=2.3839[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.3839)=0.0086[/tex]

As the P-value (0.0086) 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 percentage of residents who favor construction is above 56%.

Answer:

[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]

[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]

Step-by-step explanation:

Notation

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

For this case the 9% confidence interval is given by:

[tex] 8.8104 \leq \mu \leq 11.1248[/tex]

We can calculate the mean with the following:

[tex]\bar X = \frac{8.8104 +11.1248}{2}= 9.9676[/tex]

And we can find the margin of error with:

[tex] ME= \frac{11.1248- 8.8104}{2}= 1.1572[/tex]

The margin of error for this case is given by:

[tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE[/tex]

And we can solve for the standard error:

[tex] SE = \frac{ME}{t_{\alpha/2}}[/tex]

The critical value for 95% confidence using the normal standard distribution is approximately 1.96 and replacing we got:

[tex] SE = \frac{1.1572}{1.96}= 0.5904[/tex]

Now for the 98% confidence interval the significance is [tex]\alpha=1-0.98= 0.02[/tex] and [tex]\alpha/2 = 0.01[/tex] the critical value would be 2.326 and then the confidence interval would be:

[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]

[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]

Answer:

I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]

Step-by-step explanation:

Answer:

-8 * 5 = -40

a⁵ * a = a⁶

b⁶ * b³ = b⁹

Answer is -40a⁶b⁹

Answer:

[tex]c_n=9\,n-1[/tex]

Step-by-step explanation:

Recall that the general formula for the nth term of an arithmetic sequence is given by:

[tex]c_n=c_1+(n-1)\,d[/tex]

where  [tex]c_1[/tex]  is the first term of the sequence (in our case 8), and [tex]d[/tex] is the common difference for the sequence (the number that is added to a term in order to get the term that follows. In our case, "9" is the common difference (you can check this by subtraction between any two consecutive terms.

Then, the formula for the nth term of this sequence is

[tex]c_n=8+(n-1)\,9=8+9\,n-9=9\,n-1[/tex]

Answer:

india

Step-by-step explanation:

Answer:

The value of the sample mean resonance frequency is 112Hz

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 111.6

Upper bound: 112.4

Sample mean: (111.6 + 112.4)/2 = 112Hz

The value of the sample mean resonance frequency is 112Hz

The value of the sample mean resonance frequency is 112 Hz.

The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.

The sample mean resonance frequency = (lower limit + upper limit) / 2

(111.6 +112.4) / 2

= 224 / 2

= 112 Hz

To learn more about confidence interval, please check: https://brainly.com/question/15905477

Answer:

Option B

Step-by-step explanation:

Before a researcher specifies the relationship among variables he must have an inventory of propositions/constructs which are mostly stated in a declarative form. These are then tested by examining the relationships between measurable variables of this constructs/propositions.

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

The value of y that would make O P parallel to L N = 36

Step-by-step explanation:

This is a question on similar triangles. Find attached the diagram obtained from the given information.

Given:

The length of O L = 14

the length of O M = 28

the length of M P = y

the length of P N = 18

Length MN = MP + PN = y + 18

Length ML = MO + OL = 28+14 = 42

For OP to be parallel to LN,

MO/ML = MP/PN

MO/ML = 28/42

MP/PN= y/(y+18)

28/42 = y/(y+18)

42y = 28(y+18)

42y = 28y + 18(28)

42y-28y = 504

14y = 504

y = 504/14 = 36

The value of y that would make O P parallel to L N = 36

Answer:

D-36

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500

Solution

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 32500

For the alternative hypothesis,

Ha: µ ≠ 32500

This is a two tailed test.

Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.

Since n = 15,

Degrees of freedom, df = n - 1 = 15 - 1 = 14

t = (x - µ)/(s/√n)

Where

x = sample mean = 35500

µ = population mean = 32500

s = samples standard deviation = 6500

t = (35500 - 32500)/(6500/√15) = 1.79

We would determine the p value using the t test calculator. It becomes

p = 0.095

Assuming alpha = 0.05

Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.

Answer:

Step-by-step explanation:

given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the  given point is

[tex]y-y_0 = m(x-x_0)[/tex] or equivalently

[tex] y = mx+(y_0-mx_0)[/tex].

Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].

So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x  intercept is [tex]\frac{mx_0-y_0}{m}[/tex].

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]

The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get

[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]

Replacing the values in our previous findings we get that the y intercept is

[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]

The x intercept is

[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]

The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is

[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]

So regardless of the point we take on the graph, the area of the triangle is always 2.

Answer:

  0

Step-by-step explanation:

The sorted data set is ...

  1 2 3 3 5 7 8 9

The median is the average of the middle two numbers: (3+5)/2 = 4.

Replacing one of the 3s with a 1 makes the data set be ...

  1 1 2 3 5 7 8 9

The average of the middle two numbers is (3+5)/2 = 4.

The median increases by 4 - 4 = 0.

Answer:

( 3.5 , -2 )

Step-by-step explanation:

Answer:

( 3.5 , -2)

Explanation:

On edge

Answer:

(C)Out of 5,000 randomly chosen children, 250 children carry the virus.

Step-by-step explanation:

[tex]\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%[/tex]

The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.

Option C is the correct option.

Answer:

50%

Step-by-step explanation:

The chances of getting either heads or tails on a coin is 50/50. Convert that to probability and that is 1/2. Convert it to percentage of 100 and it is 50%.

Only time a coin isn't 50/50 is if the coin itself is a weighted coin.

Answer:

The probability that Bronson gets just spinach is;

P = 1/7

or

P = 0.1429

Step-by-step explanation:

There are three possibilities;

- just one topping

- two topping

- three topping

For just one topping, the number of possible outcomes is;

N1 = 3C1 = 3!/(1!2!) = 3 possible outcomes

For two topping, the number of possible outcomes is;

N2 = 3C2 = 3!/(2!1!) = 3 possible outcomes

For three topping, the number of possible outcomes is;

N3 = 3C3 = 3!/3! = 1 possible outcomes

Total number of possible outcomes;

N = N1+N2+N3

N = 3+3+1 = 7

The probability that Bronson gets just spinach is;

Getting spinach is one out of seven possible outcomes, so;

P = 1/N = 1/7

P = 1/7 or 0.1429

Answer:

For a sample size of n = 609.

Step-by-step explanation:

Central limit theorem for proportions:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

We have that p = 0.58.

We have to find n for which s = 0.02. So

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]

[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]

[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]

[tex]n = 609[/tex]

For a sample size of n = 609.

Answer:

No solution

Step-by-step explanation:

Using substitution, we get to the answer 12=0, which is untrue meaning no solution.

Hope this helps! Please give Brainliest!!

Answer:

no solution

Step-by-step explanation:

y= -1/4x+2

3y = - 3/4x-6  ⇒ y= - 1/4x - 2

These are parallel lines as have same slope of -1/4, so there is no solution

Answer:

A reflection and a dialation

Step-by-step explanation:

In this case a rotation is not nessasary, so I would suggest a reflection in the y-axis and a dialation to shrink the triangle to A'B'C'

So for the transformations that could have occurred to map ABC to A'B'C' you should choose the answer

a reflection and a dialation

The transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation

Thus, in the transformation shown, figure ABC was reflected over the y-axis and then dilated to give A'B'C'.

Therefore, the transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation

Learn more about transformation on:

https://brainly.com/question/1462871

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=5-1=4[/tex]

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

Answer: p = 1/25

Step-by-step explanation:

Ok, you know that the probability of rolling a six is p = 1/5

now, if you want to have two sixes, then you have two events with a probability of 1/5.

And as you know the joint probability for two events is equal to the product of the probabilities, then the probability of rolling two sixes is:

p = (1/5)*(1/5) = 1/25.

Answer:

D: 9

Step-by-Step Explanation:

The average rate is synonymous with the slope. Since we want to find the average rate of change from x = 5 to x = 6, we will use the two points (5, 18) and (6, ?). We will need to find ? first.

Since the table represents a quadratic function and we are given the vertex, we can use the vertex form of a quadratic:

[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]

Where (h, k) is the vertex.

The vertex is (1, 2). Hence:

[tex]f(x)=a(x-1)^2+2[/tex]

To determine a, pick a sample point from the table and solve for a. We can use (2, 3). Hence:

[tex](3)=a((2)-1)^2+2[/tex]

Solve for a:

[tex]1=a(1)^2\Rightarrow a=1[/tex]

Hence, our function is:

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

Evaluate the function when x = 6:

[tex]\displaystyle f(6)=(6-1)^2+2=27[/tex]

So, our two points are (5, 18) and (6, 27).

Again, to find the average rate of change between x= 5 and x = 6, find the slope between their two points. Hence:

[tex]\displaystyle m=\frac{27-18}{6-5}=9[/tex]

Our answer is D.

Answer:

the answer is 3

Step-by-step explanation:

i took the test

Answer:

y = 2/3x + 4

Step-by-step explanation:

Step 1: Find slope

m = (4-0)/(0+6)

m = 2/3

Step 2: Write in y-int (0, 4)

y = 2/3x + 4

Answer:

50 teaspoons = 0.246446 liters

0.246446 rounded to the nearest hundredth is 0.25

so your answer is 0.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's A 0.25 I litteraly random guessed it