What is the equation in slope-intercept form of the line that passes through the points (-4,8) and (12,4)?
Answers
ANSWER
y = -0.25 + 7
EXPLANATION
The line passes through the points (-4, 8) and (12, 4).
The slope-intercept form of a linear equation is written as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope of the line.
We do that with formula:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \text{where (x}_1,y_1)\text{ = (-4, 8) } \\ (x_2,y_2)\text{ = (12, 4)} \end{gathered}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m\text{ = }\frac{4\text{ - 8}}{12\text{ - (-4)}}\text{ = }\frac{-4}{12\text{ + 4}}\text{ = }\frac{-4}{16}\text{ = }\frac{-1}{4} \\ m\text{ = -0.25} \end{gathered}[/tex]Now, we use the point-slope method to find the equation:
[tex]\begin{gathered} y-y_{1\text{ }}=m(x-x_1) \\ \Rightarrow\text{ y - 8 = -0.25(x - (-4))} \\ y\text{ - 8 = -0.25(x + 4)} \\ y\text{ - 8 = -0.25x - 1} \\ y\text{ = -0.25x - 1 + 8} \\ y\text{ = -0.25x + 7} \end{gathered}[/tex]That is the equation of the line. It is not among the options.
Related Questions
√121 = ?
i need help
Answers
Answer:
11 and -11. Usually you only want the positive form
Step-by-step explanation:
[tex]\sqrt{121}[/tex] is asking what number times itself is 121? 11
11 x 11 = 121
-11 x -11 = 121
A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are: 13 million from the office building, 9 million from the theater, and 4 million from the parking garage. His profit is zero if he gets no contract. The contractor estimates that the probabilities of getting the office building contract, the theater contract, the parking garage contract, or nothing are .17, .27, .45, and .11, respectively. Let x be the random variable that represents the contractor's profits in millions of dollars. Write the probability distribution of x. Find the mean and standard deviation of x.
Answers
Answer:
Probability distribution:
x (million) P(x)
13 0.17
9 0.27
4 0.45
0 0.11
Mean: 6.44
Standard deviation: 4.04
Explanation:
The probability distribution is a table that shows the profits earned and its respective probabilities, so:
x (million) P(x)
13 0.17
9 0.27
4 0.45
0 0.11
Then, the mean can be calculated as the sum of each profit multiplied by its respective probability. Therefore, the mean E(x) is equal to:
E(x) = 13(0.17) + 9(0.27) + 4(0.45) + 0(0.11)
E(x) = 2.21 + 2.43 + 1.8 + 0
E(x) = 6.44
Finally, to calculate the standard deviation, we first need to find the differences between each value and the mean, and then find the square of these values, so:
x x - E(x) (x - E(x))²
13 13 - 6.44 = 6.56 (6.56)² = 43.03
9 9 - 6.44 = 2.56 (2.56)² = 6.55
4 4 - 6.44 = -2.44 (-2.44)² = 5.95
0 0 - 6.44 = -6.44 (-6.44)² = 41.47
Then, the standard deviation will be the square root of the sum of the values in the last column multiply by each probability:
[tex]\begin{gathered} s=\sqrt[]{43.03(0.17)+6.55(0.27)+5.95(0.45)+41.47(0.11)} \\ s=\sqrt[]{16.3264} \\ s=4.04 \end{gathered}[/tex]Therefore, the answers are:
Probability distribution:
x (million) P(x)
13 0.17
9 0.27
4 0.45
0 0.11
Mean: 6.44
Standard deviation: 4.04
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10401234 5 6 7 8 9 10OB.C.OD. +Reset Selection
Answers
Okay, here we have this:
Considering the provided inequation, we are going to identify how can be represented on a number line, so we obtain the following:
So the first thing we will do is factor to find the solution intervals, we have:
[tex]\begin{gathered} 3x^2-27x\leq0 \\ x(x-9)\leq0 \\ 0\leq x\leq9 \end{gathered}[/tex]According to this, we finally obtain that the solution interval is option D, because it satisfies the found interval and its endpoints are closed.
Suppose that the future price p(t) of a certain item is given by the following exponential function. In this function, p(t) is measured in dollars and t is the number of years from today. p(t) = 3000 * (1.019) ^ t
Answers
The growth or decay of an original quantity C that increases or decreases in a p% per year after t years is given by the following equation:
[tex]p(t)=C\cdot(1\pm\frac{p}{100})^t[/tex]If the quantity increases (i.e. it growths) we use the + symbol inside the parenthesis. If the quantity decreases we use the - symbol. This implies that for a growth the term that is raised to t is greater than 1 and for a decay that term is smaller than 1.
Now let's compare that generic equation with the function given by the question:
[tex]3000\cdot(1.019)^t=C\cdot(1\pm\frac{p}{100})^t[/tex]One of the first things you can notice is that C=3000 which means that the initial price was $3000. Just to be sure that this is correct we can evaluate p(t) at t=0:
[tex]p(0)=3000\cdot(1.019)^0=3000[/tex]So the initial price was $3000.
Now let's compare the terms inside parenthesis that are raised to t:
[tex]1.019=1\pm\frac{p}{100}[/tex]As I stated before, if the term raised to t is greater than 1 then we are talking about a growth. 1.019 is greater than 1 so this function represents a growth. What's more, in the right side of the equation we must use the + symbol. This way we have an equation for the yearly percentage of change of the price:
[tex]1.019=1+\frac{p}{100}[/tex]We can substract 1 from both sides of this equation:
[tex]\begin{gathered} 1.019-1=1+\frac{p}{100}-1 \\ 0.019=\frac{p}{100} \end{gathered}[/tex]And we multiply both sides by 100:
[tex]\begin{gathered} 100\cdot0.019=\frac{p}{100}\cdot100 \\ 1.9=p \end{gathered}[/tex]So each year the price increases in a 1.9%.
AnswerThen the answers in order are:
$3000
growth
1.9%
Solve the inequality -30 10-40x and write the solution using:
Inequality Notation:
Answers
Answer:
Step-by-step explanation:
please help me with this question!
Answers
The required point-slope form of the equation of the line exists y + 9 = 4/3 (x + 9).
What is the slope of the line?A slope of a line exists the change in the y coordinate with respect to the change in the x coordinate. The net change in the y-coordinate exists defined by Δy and the net change in the x-coordinate exists defined by Δx. Where “m” exists the slope of a line. So, tan θ to be the slope of a line.
The slope of the line exists a tangent angle created by line with horizontal.
i.e. m = 4/3 where x in degrees.
The point-slope of the equation of the line is given by,
y - y₁ = m(x - x₁)
Put the values in the above equation of the line
y - (-9) = 4/3 (x - (-9))
y + 9 = 4/3 (x + 9)
Therefore, the required point-slope form of the equation of the line is y + 9 = 4/3 (x + 9).
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Boden's account has a principal of $300 and a simple interest rate of 3.5%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Answers
formula for simple intrest
A= p(1+rt)
= 300(1+ 3.5 * 4)
=300( 15)
4500
after 4 years he has $4500
DATE IN OUT IN OUT HOURS TEMPORARY EMPLOYEE TIME CARD NAME: Eugene Mueller 8/8 7:00 4:10 8/9 6:50 11:00 DEPT Sales 8/10 8/11 12:00 4:35 Note: No overtime rate. 10:55 3:25 EMPLOYEE SIGNATURE RATE per hour: $8.50 TOTAL HOURS:
Answers
what is the equation
Answers
In the graph you can see that the line passes through 2 points (-4,0) and (0,2). With them you can obtain the equation of the line. First you find the slope of the line with the following equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Where} \\ m\colon\text{ Slope of the line} \\ (x_1,y_1)\colon\text{ Coordinates of first point }on\text{ the line} \\ (x_2,y_2)\colon\text{ Coordinates of second point }on\text{ the line} \end{gathered}[/tex]So you have,
[tex]\begin{gathered} (x_1,y_1)=(-4,0) \\ (x_2,y_2)=(0,2) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{0-(-4)} \\ m=\frac{2}{4}=\frac{1}{2} \end{gathered}[/tex]Now, with the point slope equation you can obtain the equation of the line
[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-0=\frac{1}{2}(x-(-4)) \\ y=\frac{1}{2}(x+4) \\ y=\frac{1}{2}x+\frac{1}{2}\cdot4 \\ y=\frac{1}{2}x+\frac{4}{2} \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=\frac{1}{2}x+2[/tex]Approximate the intervals where each function is increasing and decreasing.
Answers
1)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-1.2,2)\cup(1.2,\infty) \\ \text{Decreasing:} \\ D\colon(-\infty,-1.2)\cup(2,1.2) \end{gathered}[/tex]2)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-3,0.5) \\ \text{Decreasing:} \\ D\colon(-\infty,-3)\cup(-0.5,\infty) \end{gathered}[/tex]3)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(3,\infty) \\ \text{Decreasing:} \\ D\colon(-\infty,3) \end{gathered}[/tex]4)
[tex]\begin{gathered} \text{Increasing:} \\ I\colon(-\infty,4) \\ \text{Decreasing:} \\ D\colon(4,\infty) \end{gathered}[/tex]Kathryn needs to include a scale drawing of a race car on her science science fair project. Her actual race car is 180 inches long and 72 inches tall. if she uses a scale factor of 1 inch= 8 inches, what will the dimensions of her scale drawing?
Answers
To find the scaled measures of the race car, you have to divide the original measures by the scale. This is:
[tex]\text{length}=\frac{182in}{8}=22.75in[/tex][tex]\text{height}=\frac{72in}{8}=9in[/tex]So the scaled measures of the race car are: length=22.75in and height=9in
A major record label has seen its annual profit decrease in recent years. In 2011, the label's profit was $128 million. By 2015, the label's profit had decreased by 30%.What was the record label company's profit in 2015? million dollars Suppose the record label wants to increase its profit to $128 million by 2017. By what percent must the label's profit increase from its 2015 value to reach $128 million within the next two years? %
Answers
the company's profit in 2015 was $89,600,000 (89.6 million dollars)
43%
Explanation:
Profit in 2011 = $128 million
Profit in 2015 decreased by 30%
% decrease = (old price - new price)/old price
old price = Profit in 2011 , new price = Profit in 2015
30% = (128,000,000 - new price)/128000000
[tex]\begin{gathered} 30percent=\text{ }\frac{128,000,000 -newprice}{128000000} \\ 0.30\text{ = }\frac{128,000,000-newprice}{128000000} \\ \text{cross multiply:} \\ 0.3(128,000,000)\text{ = }128,000,000-newprice \end{gathered}[/tex][tex]\begin{gathered} 38400000\text{ = }128,000,000-newprice \\ \text{subtract }38400000\text{ from both sides:} \\ 38400000-\text{ }38400000\text{ = }128,000,000-38400000-newprice \\ \text{0 = 89600000 }-newprice \\ newprice\text{ = 89600000 } \end{gathered}[/tex]Hence, the company's profit in 2015 was $89,600,000 (89.6 million dollars)
Percentage increase = (new price - old price)/old price
new price = 128million dollars , old price = 89.6 million dollars
% increase = [(128 - 89.6)in millions/(89.6) in millions] × 100
% increase = 38.4/89.6 × 100
% increase = 0.43 × 100
% increase = 43%
Hence, the label's profit must increase by 43% from its 2015 value to reach $128 million within the next two years
What is the distance between (-5, 5) and (1, -2)
Answers
Answer:
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
Step-by-step explanation:
We will use the distance formula to solve.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(1--5)^2 +(-2-5)^2}[/tex]
[tex]\displaystyle d=\sqrt{(6)^2 +(-7)^2}[/tex]
[tex]\displaystyle d=\sqrt{36+49}[/tex]
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
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Can anyone help with a step by step solution asap thank you
Answers
The value of the expression x² + 5x + 4 is found as 4.
What is termed as the quadratic expression?A quadratic expression is one that has the variable with highest power of two. A quadratic expression is one that has the form ax² + bx + c, in which a ≠ 0.Typically, the expression is written in the form of x, y, z, or w.In such a quadratic expression brought up to the power of 2, the variable 'a' cannot be zero. If a = 0, x² is multiplied by zero, and the expression is no longer a quadratic expression.Variables b and c with in standard form can indeed be zero, but variable a cannot.for the given question,
The quadratic expression is given as;
= x² + 5x + 4
Put x = -5
= (-5)² + 5(-5) + 4
Simplifying.
= 25 - 25 + 4
25 will get cancelled.
= 4
Thus, the value of the expression is found as 4.
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6. Refer to the graph in question 5A) graph -f(x)B) graph f(x) -2
Answers
Given the graph of f(x):
Where the points A, B, and C have the coordinates:
[tex]\begin{gathered} A=(0,-2) \\ B=(3,2) \\ C=(5,2) \end{gathered}[/tex]Now, the transformation -f(x) is just a reflection about the x-axis. This is equivalent to a change of sign on the y-coordinate. The new points A', B', and C' are:
[tex]\begin{gathered} A^{\prime}=(0,2) \\ B^{\prime}=(3,-2) \\ C^{\prime}=(5,-2) \end{gathered}[/tex]And the graph looks like this:
Now, for the f(x) - 2 transformation, we see that this is just a shift of 2 units down. Then:
Where:
[tex]\begin{gathered} A^{\prime}^{\prime}=(0,-4) \\ B^{\prime}^{\prime}=(3,0) \\ C^{\prime}^{\prime}=(5,0) \end{gathered}[/tex]Find the measure of x.26x = [?Round to the nearest hundredth.X78°
Answers
To answer this question we will use the trigonometric function cosine.
Recall that in a right triangle:
[tex]\cos\theta=\frac{AdjacentLeg}{Hypotenuse}.[/tex]Using the given diagram we get that:
[tex]\cos78^{\circ}=\frac{x}{26}.[/tex]Multiplying the above result by 26 we get:
[tex]\begin{gathered} 26\times\cos78^{\circ}=26\times\frac{x}{26}, \\ 26\cos78^{\circ}=x. \end{gathered}[/tex]Therefore:
[tex]x\approx5.41.[/tex]Answer:
[tex]x=5.41.[/tex]
In Abc,AB=5 feet and BC=3 feet.Which inequality represents all possible values for the length of AC,in feet?
Answers
The smallest value of length AC would be 5 ft - 3 ft = 2 ft while the largest length would be 5 ft + 3 ft = 8ft. The answer will be
2 < Ac < 8
Fifth grade > Y.5 Compare and convert Which is more, 1/2 of a pound or 6 ounces? of a pound 2. 6 ounces neither; they are equal Submit
Answers
We should know that :
1 pound = 16 ounces
The question is :
Which is more, 1/2 of a pound or 6 ounces?
so,
1/2 of a pound = 1/2 x 16 = 8 ounces
So,
8 ounces > 6 ounces
so, the answer is option 1
The more is 1/2 of a pound
If mABC =(3x+3) and mDEF=(5x-33).Find the value of x
Answers
Let's begin by listing out the information given to us:
m∠ABC = 3x + 3
m∠DEF = 5x - 33
From the question, m∠ABC & m∠DEF are identical (have same properties)
m∠ABC = m∠DEF
3x + 3 = 5x - 33
Put like terms together (add 33 - 3x to both sides)
3x - 3x + 3 + 33 = 5x - 3x - 33 + 33
36 = 2x; 2x = 36
x = 18
A square pyramid has a volume of 108 cubic feet and a height of 4 feet.What is the length of each side of the base of the pyramid?A 4 ftOLOB. 9 ftC. 18 ftD. 27 ftO E. 81 ftHelp please very hard
Answers
okay so the answer is 9ft so option B
now we can take a look at how we arrived to that answer
do you know the formula for the volume?
Recipe A calls for 2 cups of sugar and makes 48 cookles. Recipe B calls for 3 cups of sugar and makes 54 of the same sized cookies. Determine which recipe contains more sugar in each cookle. Use complete sentences to explain your reasoning.
Answers
we are given two recipes for cookies and we are asked which of the two contains more sugar. To do that we need to find the amount of sugar per cookie for each recipe.
For recipe A we have:
[tex]2cups\rightarrow48cookies[/tex]This means:
[tex]\frac{2cups}{48cookies}=\frac{1}{24}\frac{cups}{cookies}[/tex]For recipe B we have:
[tex]3cups\rightarrow54\text{cookies}[/tex]This means:
[tex]\frac{3\text{cups}}{54\text{cookies}}=\frac{1}{18}(\frac{cups}{cookies})[/tex]Since 1/18 is greater than 1/24, this means that there is more sugar per cookie in recipe B than in recipe A.
2)Find the missing coordinate (5, 7) and (8,y); m= 4/3
Answers
Answer:
y = 11
Step-by-step explanation:
Hello!
We can utilize the slope formula to create the equation for y:
[tex]\frac{y - 7}{8 - 5} = \frac{4}{3}[/tex]Solve for y[tex]\frac{y - 7}{8 - 5} = \frac{4}{3}[/tex][tex]\frac{y - 7}{3} = \frac{4}{3}[/tex] => Simplifyy - 7 = 4 => Multiply both sides by 3y = 11 => Add 7 to both sidesThe value of y is 11.
Vincent turned his head 30° to the side. Which of the following shows the angle that he turned his head?
Answers
Given data:
Vincent turned his head 30° to the side.
The figure in the option b is the angle that he turned his head.
Translate into a number sentence7. Four less than seven is greater than zero
Answers
In order to translate the words into a number sentence, first let's translate each word or expression separately:
Four less than seven: "7 - 4"
Is greater than: ">"
Zero: "0"
Therefore the number sentence will be:
[tex]7-4>0[/tex]Consider 0.6 X 0.2.How many digits after the decimal point will the product have?Number of digits =
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]0.6\times0.2[/tex]STEP 2: Evaluate the expression
It can be seen that the result of the expression is 0.12
Hence, there are 2 digits after the decimal point for the product
Pep Boys Automotive paid $208.50 for a pickup truck bed liner. The original selling price was $291.90, but this was marked down 35%. If operating expenses are 28% of the cost, find the absolute loss
Answers
Step 1: State the given in the question
THe following were given:
[tex]\begin{gathered} \text{Amount Paid (}A_{\text{paid}})=208.50 \\ (Originalsellingprice)SP_{ORIGINAL}=291.90 \\ \text{Marked Percentage=35\%} \\ \text{Operating expenses=28\%} \end{gathered}[/tex]Step 2: State what is to be found
We are to find the absolute loss
Step 3: Calculate the selling price
Please note that the selling price is the marked down price
The marked down price would be
[tex]\begin{gathered} P_{\text{MARKED DOWN}}=(100-35)\text{ \% of original selling price} \\ P_{\text{MARKED DOWN}}=65\text{ \% of }SP_{ORIGINAL} \\ P_{\text{MARKED DOWN}}=\frac{65}{100}\times291.90=189.74 \end{gathered}[/tex]The selling price is the marked down price which is $189.74
Step 4: Calcualte the operating expenses
Please note that the cost price is amount paid. Therefore, the operating expenses would be as calculated below:
[tex]\begin{gathered} E_{\text{OPEARATING}}=28\text{ \% of Amount Paid} \\ E_{\text{OPERATING}}=28\text{ \% of }A_{\text{paid}}=\frac{28}{100}\times208.50 \\ E_{\text{OPERATING}}=0.28\times208.50=58.38 \end{gathered}[/tex]Hence, the operating expenses is $58.38
Step 5: Calculate the total cost price
The total cost price is the addition of the cost price and the operating expenses. This is as calculated below:
[tex]\begin{gathered} C_{\text{TOTAL COST PRICE}}=E_{OPERATING}+A_{PAID} \\ C_{\text{TOTAL COST PRICE}}=58.38+208.50=266.88 \end{gathered}[/tex]Hence, the total cost price is $266.88
Step 6: Calculate the absolute loss
The absolute loss is the difference between the total cost price and the marked down price (or the actual selling price). This is as calculated below:
[tex]\begin{gathered} L_{\text{ABSOLUTE LOSS}}=C_{TOTAL\text{ COST PRICE}}-P_{MARKED\text{ DOWN}} \\ L_{\text{ABSOLUTE LOSS}}=266.88-189.74=77.14 \end{gathered}[/tex]Hence, the absolute loss is $77.14
A
Westway Company pays Suzie Chan a weekly pay of:
Social Security tax on salary up to $142,800:
Medicare tax:
The state unemployment rate (SUTA):
FUTA rate:
Required:
Using the information given above, answer the following question:
Note: Use cells A2 to 86 from the given information to complete this question.
1. What is Suzie Chan's yearly salary?
2. How much did Westway deduct for Suzie's Social Security for the year?
3. How much did Westway deduct for Suzie's Medicare for the year?
4. What state unemployment taxes does Westway pay on Suzie's yearly
salary?
5. What federal unemployment taxes does Westway pay on Suzie's yearly
salary?
Graded Worksheet
B
$3,000.00
6.20%
1.45%
5.10%
0.60%
Answers
The Suzie Chan's yearly salary is 156,426 .
The Westway deduct $9,698.412 for Suzie's social security for the year.
The Westway deduct $2268.177 for Suzie's Medicare for the year.
The state unemployment taxes worth $7977.726 deducted from Suzie's salary.
The FUTA taxes worth $938.556 deducted from Suzie's salary.
What is tax?
A tax is a mandatory financial charge or other sort of levy placed on a taxpayer (an individual or legal entity) by an administrative body to pay for certain public expenditures and administrative costs (regional, local, or national).
It is given in the question that weekly salary of Suzie is $3,000.
we know that, there are 365 days in a year and 7 days in a week.
Therefore, weeks in a year = 365/7 = 52.142
Yearly salary is equal weekly salary times weeks in a year.
Yearly Salary = (3000)52.142
yearly Salary = $156,426
Social security taxes are 6.20%
So, 6.20% of 156,426 is $9,698.412
Therefore, The Westway deduct $9,698.412 for Suzie's social security for the year.
Medicare taxes are 1.45%
So, 1.45% of 156,426 is $2268.177
Therefore, The Westway deduct $2268.177 for Suzie's Medicare for the year.
The state unemployment taxes are 5.10%
So, 5.10% of 156,426 is $7977.726
Therefore, The state unemployment taxes worth $7977.726 deducted from Suzie's salary.
The FUTA taxes are 0.60%
So, 0.60% of 156,426 is $938.556
Therefore, The FUTA taxes worth $938.556 deducted from Suzie's salary.
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Find the mean for this set of data. Write your answer as a decimal roundedto the nearest TENTH.32, 23, 34, 29, 15, 17, 23
Answers
Given:
The set of data is given as
[tex]32,23,34,29,15,17,23[/tex]Required:
To find the mean.
Formula:
[tex]\text{Mean(}\bar{\text{X}})=\frac{\Sigma x}{n}[/tex]Explanation:
Mean is the ratio of the sum of the values and the number of values.
No of values in the given data is 7.
[tex]n=7[/tex][tex]\begin{gathered} \text{Mean}=\frac{32+23+34+29+15+17+23}{7} \\ =\frac{173}{7} \\ =24.7 \end{gathered}[/tex]Final Answer:
[tex]\text{Mean}=24.7[/tex]
14#An ecologist randomly samples 12 plants of a specific species and measures their heights. He finds that this sample has a mean of 14 cm and a standard deviation of 4 cm. If we assume that the height measurements are normally distributed, find a 95% confidence interval for the mean height of all plants of this species. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit:Upper limit:
Answers
Answer:
Lower limit: 11.7 cm
Upper limit: 16.263
Explanation:
The formula to find the lower and upper limits of the confidence interval (given the data is normally distributed) is :
[tex]CI=\mu\pm Z^*\frac{\sigma}{\sqrt{n}}[/tex]Where:
• μ = sample mean
,• σ = sample standard deviation
,• Z* = critical value of the z-distribution
,• n = is the sample size
In this case:
• μ = 14cm
• σ = 4cm
,• n = 12
The critical value of the z-distribution for a confidence interval of 95% is Z* = 1.96
Now, we can use the formula above to find the upper and lower limit:
[tex]CI=14\pm1.96\cdot\frac{4}{\sqrt{12}}=14\pm\frac{98\sqrt{3}}{75}=\frac{1050\pm98\sqrt{3}}{75}[/tex]Thus:
[tex]Lower\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx11.736cm[/tex][tex]Upper\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx16.263cm[/tex]Rounded to one decimal:
Lower limit: 11.7cm
Upper limit: 16.3cm
Find the interest earned on a $50,000 deposited for six years at 1 1/8 % interest, compounded continuously
Answers
To calculate the interest earned, we can use the following equation:
[tex]I=P((1+i)^n-1)[/tex]Where P is the value of the deposit, i is the interest rate and n is the number of periods of time.
First, we need to calculate the equivalent value of 1 1/8 % as:
[tex]1\frac{1}{8}\text{ \% = }\frac{1\cdot8+1}{8}\text{ \% = }\frac{9}{8}\text{ \% = 1.125\% = 0.01125}[/tex]So, replacing P by $50,000, i by 0.01125, and n by 6, we get:
[tex]\begin{gathered} I=50,000((1+0.01125)^6-1) \\ I=50,000(0.694) \\ I=3,471.3577 \end{gathered}[/tex]Answer: $ 3,471.3577