Solve the equation
- 1
- m - 7 = 5
3

Answers

Answer 1

Answer:

1/3m-7=5

One solution was found :

m = 36
Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

1/3*m-7-(5)=0

Step by step solution :

Step 1 :

1
Simplify —
3
Equation at the end of step 1 :

1
((— • m) - 7) - 5 = 0
3
Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

7 7 • 3
7 = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

m - (7 • 3) m - 21
——————————— = ——————
3 3
Equation at the end of step 2 :

(m - 21)
———————— - 5 = 0
3
Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

5 5 • 3
5 = — = —————
1 3
Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

(m-21) - (5 • 3) m - 36
———————————————— = ——————
3 3
Equation at the end of step 3 :

m - 36
—————— = 0
3
Step 4 :

When a fraction equals zero :

4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

m-36
———— • 3 = 0 • 3
3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
m-36 = 0

Solving a Single Variable Equation :

4.2 Solve : m-36 = 0

Add 36 to both sides of the equation :
m = 36

One solution was found :

m = 36

I happen this help

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Answers

Answer:

Step-by-step explanation:

y=4x+30

Answer: y = 30x + 4 (/1)

Step-by-step explanation:

30 is the y intercept because it says its' the startup fee. Therefore it must be the y intercept.

4 must be the gradient. Basically, on a Cartesian plane, the y intercept will be on 30. Move 4 digits up and 1 to the left continually

The taxi driver charges $3.50 just to get in the cab and then $2.50 per mile. If Lisa travels m miles, which equationtells Lisa how much she will have to pay for her taxi ride, r?
A r = 2.5 +3.5
B = 3.5m + 2.5
r= 2.5m + 3.5
Dr= 2.5m - 3.5

Answers

Answer:r=2.5m+3.5

Step-by-step explanation:

the answer is 2.5m + 3.5 because we don't know how many miles the taxi driver drove

Please what is the answer of number 1

Answers

Answer:

-80

Step-by-step explanation:

First you multiply both sides of the equation by 5 to get rid of the fraction, it becomes Y + 30 = -50.

To get rid of the 30 you subtract 30 from each side and that makes it Y = -80.

Your answer does not want the Y=, so your answer is -80.

If this helps, please mark it Brainliest :)

The probability that a person has a certain disease is 0.03. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.92. Of the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.01. a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present

Answers

Answer: 0.74

Step-by-step explanation:

A= "The person is sick"

B= "The test gives a positive result"

P(A)=0.03

P(B|A)=0.92

P(B|A')=0.01

P(A')=1-P(A)=1-0.03=0.97

P(B)=P(B|A)P(A)+P(B|A')P(A')=0.92*0.03+0.01*0.97=0.0373

Based in Bayes Rule

P(A|B)=P(B|A)P(A)/P(B)=0.92*0.03/0.0373=0.74

A true/false test has 90 questions. Suppose a passing grade is 58 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessing. Assume the student gets 58 answers correct out of 90. Use a significance level of 0.05. Steps 1 and 2 of a hypothesis test procedure are given below. Show step 3, finding the test statistic and the p-value and step 4, interpreting the results.

Answers

Answer:

1 and 2) Null hypothesis: $p \leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}$ (1)

3) $z=\frac{0.644 -0.5}{\sqrt{(0.5(1-0.5))/(90)}}=2.732$

4) $p_v =P(z>2.732)=0.0031$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of correct answers is not significantly higher than 0.5

Step-by-step explanation:

Data given and notation

n=90 represent the random sample taken

X=58 represent the number of correct answers

$\hat p=(58)/(90)=0.644$ estimated proportion of correct answers

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Step 1 and 2: Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of correct answers is higher than 0.5.:

Null hypothesis: $p \leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.644 -0.5}{\sqrt{(0.5(1-0.5))/(90)}}=2.732$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>2.732)=0.0031$

Answer:

Step-by-step explanation:

Hello!

The variable of interest is X: the number of correct answers on a true/false test out of 90 questions.

The parameter of interest is p: population proportion of correct answers in a true/false test.

The passing grade is 58/90 correct questions.

The claim is that if the students answer more than half of the answers, then he is not guessing, i.e. if the proportion of correct answers is more than 50%, the student did not guess the answers, symbolically: p>0.5

Then the hypotheses are:

H₀: p ≤ 0.5

H₁: p > 0.5

α: 0.05

since the sample size is large enough, n= 90 questions, you can apply the Central Limit Theorem to approximate the distribution of the sample proportion to normal, p'≈N(p;[p(1-p])/n) and use the standard normal as a statistic:

$Z=\frac{p'-p}{\sqrt{(p(1-p))/(n) } }$ ≈N(0;1)

The sample proportion is the passing grade of the student p': 58/90= 0.64

Then under the null hypothesis the statistic is:

$Z_(H_0)= \frac{0.64-0.5}{\sqrt{(0.5*0.5)/(90) } } = 2.656= 2.66$

This test is one-tailed (right) and so is the p-value, you can calculate it as:

P(Z≥2.66)= 1 - P(Z<2.66)= 1 - 0.996093= 0.003907

With this p-value, the decision is to reject the null hypothesis.

Then at a 5% level, there is significant evidence to conclude that the proportion of correctly answered questions is greater than 50%, this means that the student didn't guess the answers.

I hope this helps!

Sales of Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years. The sales manager has predicted in 2004 and 2005 sales would be 410 VW's. Using exponential smoothing with a alpha = 0.30 develop a forecast for 2006 through 2010. What is the forecast value for 2010?Please answer to one decimal place. (Example: 466.1)Formula: Ft = Ft-1 + alpha(At-1 - Ft-1)Actual sales data:2005 = 4502006 = 4952007 = 5182008 = 5632009 = 584

Answers

Answer:

Step-by-step explanation:

Given the data:

Year___Actual sale (At) ___forecast(Ft)

2005__450_____________410

2006__495____________ 422

2007__518____________ 443.9

2008_ 563____________ 466.1

2009_584____________ 495.2

2010__

Using the formula :

Ft = Ft-1 + alpha(At-1 - Ft-1)

Ft-1 = previous year forecast

At-1 = previous year actual

Alpha = 0.3

Forecast:

2006:

410 + 0.3(450 - 410) = 422.0

2007:

422 + 0.3(495 - 422) = 443.9

2008:

443.9 + 0.3(518 - 443.9) = 466.1

2009:

466.1 + 0.3(563 - 466.1) = 495.2

2010:

495.2 + 0.3(584 - 495.2) = 521.8

Forecasted value for 2010 = 521.8

Final answer:

By utilizing the method of exponential smoothing with alpha=0.3 and applying the forecasting formula iteratively, the forecasted sales of Volkswagen Beetles for 2010 in Nevada is 525.7 units.

Explanation:

The exponential smoothing method is commonly used in business and economics for forecasting future data in situations where historical data is available. The forecast value for 2010 using exponential smoothing with alpha = 0.30 can be obtained by implementing the provided formula in an iterative manner. This formula takes into account the actual data point from the previous year (At-1) and the forecasted data point for that year (Ft-1).

Let us use the forecast value for 2004 and 2005, which was predicted as 410 for each year, as our initial forecast value (F1).

By applying the formula Ft = Ft-1 + alpha * (At-1 - Ft-1) iteratively for each year from 2006 to 2009, we get:

Forecast for 2006 (F_2006) would be 410 + 0.30*(450-410) = 422.
Then, the forecast for 2007 (F_2007) is 422 + 0.30*(495-422) = 443.9.
The forecast for 2008 (F_2008) is 443.9 + 0.30*(518-443.9) = 466.1.
For 2009 (F_2009), the forecast is 466.1 + 0.30*(563-466.1) = 496.37.

Using these forecasted rates, we then forecast for the year 2010. The forecast for 2010 (F_2010) is calculated by 496.37 + 0.30*(584-496.37) giving 525.67 (rounded to one decimal place). Hence the forecast for the year 2010 using exponential smoothing with the alpha as 0.30 is estimated to be 525.7 VolksWagen Beetles.