The null hypothesis in symbolic form is H0: p ≥ 0.0007
The alternative hypothesis in symbolic form is Ha: p < 0.0007
We have,
The null hypothesis in symbolic form is H0: p ≥ 0.0007
This means that the true proportion of male fireflies unable to produce light is greater than or equal to 7 in ten thousand.
The alternative hypothesis in symbolic form is Ha: p < 0.0007
This means that the true proportion of male fireflies unable to produce light is less than 7 in ten thousand.
Thus,
The null hypothesis in symbolic form is H0: p ≥ 0.0007
The alternative hypothesis in symbolic form is Ha: p < 0.0007
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Consider functions fand g.
f(x)= log (x-1)
g(x)= 1/3x2 - 4
Which statement gives the best approximation of the solutions of the equation f(x) = g(x)?
=
OA.
The solutions are where the graphs of the functions cross the x-axis at ≈ -3.464and ≈ 3.642.
OB. The solutions are where the graphs of the functions intersect at
-3.464and ≈ 3.464.
OC. The solutions are where the graphs of the functions intersect at
land ≈ 3.642.
OD. The solutions are where the graphs of the functions cross the x-axis at ≈ -4and ≈ 0.422.
d
The solutions are where the graphs of the functions intersect at x = 1 and the value at x ≈ 3.642
Given data ,
Let the first function be f ( x )
Now , the value of f ( x ) = log ( x - 1 )
Let the second function be g ( x )
g ( x ) = ( 1/3 )x² - 4
On simplifying the equation , we get
f ( x ) = g ( x )
On plotting the graph , we get the point of intersection at x = 1 and x = 3.642
Hence , the solution of equations are x = 1 and x = 3.642
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Answer:
x = 1 and x = 3.642
Step-by-step explanation:
Plato/Edmentum
Write the equation of the line that passes through the points (-2, -1) and (2, 11)
The equation of the line that passes through the points (-2, -1) and (2, 11) will be y = 3x + 5.
Given that:
Points, (-2, -1) and (2, 11)
Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The equation that passes through (-2, -1) and (2, 11) is calculated as,
(y + 1) = [(11 + 1) / (2 + 2)](x + 2)
y + 1 = 3x + 6
y = 3x + 5
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The following data were used in a regression study.
Observation 1 2 3 4 5 6 7 8 9
xi
2 3 4 5 7 7 7 8 9
yi
4 5 4 6 4 6 9 6 11
(a)
Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.)
ŷ =
The estimated regression equation for these data is ŷ = 0.69x + 2.15
Developing an estimated regression equation for these dataFrom the question, we have the following parameters that can be used in our computation:
Observation 1 2 3 4 5 6 7 8 9
xi 2 3 4 5 7 7 7 8 9
yi 4 5 4 6 4 6 9 6 11
Using a graphing tool, we have the following calculation summary
Sum of X = 52Sum of Y = 55Mean X = 5.7778Mean Y = 6.1111Sum of squares (SSX) = 45.5556Sum of products (SP) = 31.2222Regression Equation: ŷ = bX + a
Where
b = SP/SSX = 31.22/45.56 = 0.68537
a = MY - bMX = 6.11 - (0.69*5.78) = 2.15122
So, we have
ŷ = 0.68537x + 2.15122
Rounding the numerical values to two decimal places, we have
ŷ = 0.69x + 2.15
Hence, the estimated regression equation for these data is ŷ = 0.69x + 2.15
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Professor Dorsey is grading papers in the teachers' lounge. She has already finished grading 21 assignments, and is grading 2 more assignments per hour. Her teaching assistant just came in to help her. She can grade at a rate of 9 assignments every hour. At some point, they will be finished and will have graded the same number of papers. How many assignments will they each have graded? How long will that take?
Professor Dorsey and her assistant both will have graded ___ assignments in
___hours.
HELPPP
Find the value of X for the following
Answer:
x = 8.1
Step-by-step explanation:
According to Euclidean theorem:
10² = 12 × (2x - 8)
Multiply inside the parenthesis with 12.10² = 24x - 96
Find the second power of 10.100 = 24x - 96
Add 96 to both sides.100 + 96 = 24x
Add the expressions.196 = 24x
Divide both sides by 24.8.1 = x approximately
The average GPA of a random sample of 31 college students who take evening classes was calculated to be
2.74 with a standard deviation of 0.07. The average GPA of a random sample of 18 college students who
take daytime classes was calculated to be 2.73 with a standard deviation of 0.03. Test the claim that the
mean GPA of night students is larger than the mean GPA of day students at the .05 significance level.
Claim: Select an answer which corresponds to [Select an answer
Opposite: [Select an answer which corresponds to [Select an answer
The test is: Select an answer
The test statistic is: t-
The P-value is: Select an answer
Based on this we: Select an answer
(to 2 decimals)
Conclusion There Select an answer appear to be enough evidence to support the claim that the mean
GPA of night students is larger than the mean GPA of day students.
The results of the two-sample t-test, there does not appear to be enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students.
To test the claim that the mean GPA of night students is larger than the mean GPA of day students, we can perform a two-sample t-test. The null hypothesis is that there is no difference in the mean GPAs between the two groups, while the alternative hypothesis is that the mean GPA of night students is larger than the mean GPA of day students.
Using the given data, we can calculate the test statistic as follows:
t = (2.74 - 2.73) / sqrt((0.07^2 / 31) + (0.03^2 / 18)) = 0.45
The degrees of freedom for this test are 31 + 18 - 2 = 47. Using a t-table or calculator, we can find that the p-value for this test is approximately 0.326.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.05 significance level.
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how do i find the sample size of x-bar chart in order to find A2 from upper control limit and lower control limit formulas?
(i hope this makes sense)
It should be noted that to discover the required sample size for an x-bar chart, you must first determine the values of the upper and lower control limit (UCL & LCL) based on the process descriptions and the desired level of restriction.
How to determine the sampleThe equations for UCL and LCL are:
UCL = x + A2R
LCL = x - A2R
Where x denotes the average of the mean samples, R represents the ambit of the means, and A2 stands for a constant value rooted in the amount of the sample..
Utilizing these values, then one can apply the formulas of UCL & LCL to solve for the constant A2, which is utilized to calculate the boundaries of the chart.
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Last week, the price of oranges at the farmer's market was $2.00 per pound. This week,
the price has decreased by 20%. What is the price of oranges this week?
Find the area of the following colored regions.
Step-by-step explanation:
r = 4 m
d = 2 × r
d = 2 × 4
d = 8 m = s
Area of square = s × s
= 8 × 8
= 64 m²
Area of circle = πr²
= 3.14 × 4 × 4
= 50.24²
Area of colored region = A. Square - A. Circle
= 64 - 50.24
= 13.76 m²
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What is the net income from the following income statement? Income Statement Sales Returns $12,800 ($360) Net Sales COGS Gross Profit Overhead ($2,500) Net Income ($8,000) net income = $ [?]
The net income from the given income statement is $7,440. This is calculated by subtracting the overhead expenses from the gross profit.
To calculate the net income, we need to subtract all expenses from the gross profit.
First, we need to calculate the Net Sales by subtracting the Sales Returns of $360 from the Sales of $12,800
Net Sales = Sales - Sales Returns
Net Sales = $12,800 - $360
Net Sales = $12,440
Next, we can calculate the Gross Profit by subtracting the Cost of Goods Sold (COGS) from the Net Sales
Gross Profit = Net Sales - COGS
Gross Profit = $12,440 - $2,500
Gross Profit = $9,940
Now, we can calculate the Net Income by subtracting the Overhead expenses from the Gross Profit
Net Income = Gross Profit - Overhead
Net Income = $9,940 - $2,500
Net Income = $7,440
Therefore, the net income from the given income statement is $7,440.
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Rita draws an angle with a measure of 20 degrees. Which statement about Rita's angle
is true?
A It turns through 20 one-degree angles.
B
It turns through 20 360-degree angles.
C
It turns through one-twentieth of a circle.
D
It turns through one-twentieth of a protractor.
The statement "It turns through one-twentieth of a circle" is accurate. Then the correct option is C.
Given that:
Rita draws an angle with a measure of 20 degrees.
An angle is a unit of rotation created when two rays share the same vertex or endpoint. Since an angle is a measurement of rotation, it may also be measured in degrees. A circle has 360 degrees of arc.
360 degrees is the length of a circle's complete rotation. The rotation of one-twentieth (1/20) of a full revolution, or one-twentieth of a circle, is equivalent to a measurement of 20 degrees.
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120 was divided by a particular number, then 7 was taken from the quotient. afterwards, this difference was multiplied by 5. giving a product of 25. find the particular number.
The particular number from the given equation is 10.
Given that, 120 was divided by a particular number.
Let the particular number be x.
Here, 120/x
7 was taken from the quotient
120/x -7
The difference was multiplied by 5.
5(120/x -7)
Giving a product of 25
5(120/x -7)=25
120/x -7=5
120/x=12
120=12x
x=120/12
x=10
Therefore, the particular number from the given equation is 10.
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What’s 80% of $500 worth items
Answer:
$400
Step-by-step explanation:
80% = 80/100 = 8/10 = 0.8
0.8(500)=400
The population of a town is modeled by the function f(x) = 465(1 + 0.003) x, where x is the time in years. What type of change does this function represent?
The function represents an exponential growth.
What type of change does this function represent?A general exponential function can be written as:
y = A*(1 + r)^x
Where A is the initial value and r is the rate of change, and if r > 0 we have a growth, if -1 < r < 0 we have a decay.
Here f(x) = 465(1 + 0.003)^x is the population function, we can see that the value of r is positive, thus, the function is an exponential growth.
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We have a right prism whose base is a pentagon. Its height is 10ft. The area of the base is [tex]20ft^{2}[/tex]. Solve for LSA and TSA.
The LSA of prism is 157 square feet.
The TSA of prism is 169.738 square feet
We have,
Height = 10 feet
Area of base = 20 square feet
So, area of pentagonal base = 1/4 √5 (5 + 2√5) a²
20 = 1/4 √5 (5 + 2√5) a²
a = 3.14
Now, LSA of prism
= 5bh
= 5(3.14)(10)
= 157 square feet
and, TSA of prism
= 5 x 2(20)/ 15.7 + 157
= 169.738 square feet
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1. Fill in the balance sheet below with each of Rosa's assets and liabilities. Calculate (add up) her total assets and total liabilities. Then calculate her net worth. (15 points) Cash Assets ($) Checking account Liabilities ($) Student loans Credit card(s) balance(s) Net Worth ($) TOTAL ASSETS - TOTAL LIABILITIES
Answer:
Balance Sheet:
Cash Assets ($)
Checking account: $2,000
Liabilities ($)
Student loans: $10,000
Credit card(s) balance(s): $500
Total Assets: $2,000
Total Liabilities: $10,500
Net Worth: Total Assets - Total Liabilities
Net Worth: $2,000 - $10,500
Net Worth: -$8,500
Therefore, Rosa's total assets are $2,000, her total liabilities are $10,500, and her net worth is -$8,500. This indicates that her liabilities exceed her assets, and she has a negative net worth.
Tessa puts 50 marbles in a bag. The number of marbles of each color is shown in the table
below.
Tessa reaches into the bag and randomly selects one marble. What is the probability that the
marble Tessa selects is green?
50
20
2
2/3
Red
15
NUMBER OF MARBLES
Green
20
Blue
10
Yellow
5
A1/50
B1/20
C2/5
D2/3
____________________________________
Green Marbles: 20Blue Marbles: 10Yellow Marbles: 5Red Marbles: 15Total Marbles: 50= 20 ÷ 50 × 100 = 40% There Is A 40% Chance That Tessa Will Select A Green Marble.____________________________________
Help me!!!!!! I have to turn this in in a few min
1. A probability experiment which outputs a single number is a(n) _______________ ________________.
(two words)
2. A discrete random variable can output either a finite or a(n) ______________(countably, uncountably)
infinite number of values.
3. A continuous random variable has its values in one or more __________________. An example is the __________________ distribution whose density function is the horizontal line from X=a to X=b.
4. The _________________ __________________ (two words) of a discrete random variable lists every possible value that the variable can assume and the corresponding probabilities.
5. For a(n) _________________ random variable, a sample is drawn with replacement, or there is a large population size. Successive trials are independent of each other. There is a categorical variable with 2 possible values. The ________________(population, sample) is of a fixed size n.
6. For a ____________________ random variable, a sample is drawn without replacement. Successive trials are dependent on each other. There is a ____________________ (population, sample) of finite size N and a categorical variable with 2 possible values. The sample is of a fixed size _______ (N, n, p, q, r).
7. For each blank, include both the formula and the exact answer; do not use a calculator.
Given a uniform distribution with the sample space [1, 4], the height of its density function is ________________ and it has mean ________________ and standard deviation __________________.
8. The ___________________ ____________________ (two words) distribution has a density function that is bell shaped and symmetric. Its mean is 0 and its standard deviation is 1.
9. The ___________________ is also known as the average, expectation and expected value.
10. The ___________________of a discrete random variable can be found by taking the product of each outcome and its probability and then summing.
11. The ______________________ (one word!) of a discrete random variable can be found by subtracting the square of its mean from the expectation of the square of the random variable.
A truck Can be rented from company A for $60 a day plus $0.30 per mile. Company B charges $40 a day plus $0.70 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for company A a better deal than company B’s?
Which of the following new vehicle borrowers is likely to be offered the lowest APR?
A. Tyler who is buying a used vehicle and has a FICO score of 780
B. Daniel who is buying a used vehicle and has a FICO score of 600
C. Stephanie who is buying a new vehicle and has a FICO score of 780
D. Emily who is buying a new vehicle and has a FICO score of 600
Answer: C. Stephanie who is buying a new vehicle and has a FICO score of 780.
Step-by-step explanation: The Annual Percentage Rate (APR) is the interest rate charged on a loan. Lenders consider various factors when determining the APR, including the borrower's credit score and the type of vehicle being financed.
In this scenario, Stephanie has a FICO score of 780, which indicates a strong credit history and responsible financial behavior. Lenders generally view higher credit scores as an indication of lower credit risk. As Stephanie is buying a new vehicle, lenders may consider this a lower-risk loan compared to financing a used vehicle.
Lower credit risk and the lower risk associated with financing a new vehicle are factors that could result in Stephanie being offered a lower APR compared to Tyler (option A), who is buying a used vehicle, and Daniel (option B), who has a lower FICO score of 600.
It's important to note that other factors, such as the lender's policies, market conditions, and individual loan terms, can also influence the APR offered to borrowers.
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Use (SH)RATEY to graph the given rational function. H(x)=2x/x^2-2x+1
The graph of the rational function is attached in the solution.
Given is a rational function we need to graph it,
h(x) = [tex]\frac{2x}{x^2-2x+1}[/tex]
So,
Finding the coordinates by putting the values of x and finding the corresponding values of h(x), the plot them on the graph and join, the curve obtained will be the graph of the function.
Hence, the graph is attached.
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Eli has 38 in cash and 72 on gift card he says that when he rounds to the nearest 10 tickets he has about a $100 is he correct explain
Eli's statement is incorrect. Since $10 is greater than $5, we cannot round $110 to $100 when rounding to the nearest 10.
To determine if Eli is correct, we need to add the amount of cash he has with the value of his gift card;
$38 + $72 = $110
Since Eli says that he has about a $100 when he rounds to the nearest 10, we need to check whether $110 rounds to $100 or not. To round to the nearest 10, we look at the last digit of the number, which is 0 in this case. If the last digit is 5 or greater, we round up to the next multiple of 10. If the last digit is less than 5, we round down to the previous multiple of 10.
Since the last digit of $110 is 0, we don't need to round up or down. $110 is already a multiple of 10. Therefore, Eli is incorrect in saying that he has about a $100 when he rounds to the nearest 10. He actually has $110.
Alternatively, we can check if $110 is within $5 of $100, which is the threshold for rounding to the nearest 10.
$110 - $100 = $10
Therefore, Eli's statement is incorrect.
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Find the area of the composite figure below.
Answer:
Step-by-step explanation:
185
A table of values of a linear function is shown below. Find the output when the input is n. Type your answer in the space provided.
input 1 2 3 4 n
output 5 2 −1 −4
The linear function is solved and the output is y = -3n + 8
Given data ,
Let the linear function be represented as A
Now , the value of A is
The table of inputs = { 1 , 2 , 3 , 4 , n }
The table of outputs = { 5 , 2 , -1 , -4 , a }
So , the first point is P ( 1 , 5 ) and second point is Q ( 2 , 2 )
Slope m = ( 5 - 2 ) / ( 1 - 2 )
m = -3
And , the equation of line is y - 5 = -3 ( x - 1 )
Adding 5 on both sides , we get
y = -3x + 8
Now , when the input is n , the output is
y = -3n + 8
Hence , the equation is y = -3n + 8
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What rational number can you multiply by -7/3 in order to get a product of 1? What is the relationship between these rational numbers? Explain your reasoning .
Answer:
-3/7
Step-by-step explanation:
-7/3 × ? = 1
-7/3 × -3/7 = 1
you see how both the three's and Steven's canceled out resulting in one as the answer. also it has to be a negative 3/7 since two negative signs in multiplication result in a positive sign.
write the following using rational exponents
4√5
The numerical expression 4√5 in the rational exponents will be [tex]4\cdot \left ( 5 \right)^\frac{1}{2}[/tex].
Given that:
Numerical expression: 4√5
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The expression is also written as,
[tex]\rightarrow 4 \sqrt5\\\\\rightarrow 4 \cdot \left ( 5 \right)^\frac{1}{2}[/tex]
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Good-afternoon everyone! This past week I've managed to finish up some math work. However, I want to make sure I didn't make any errors in the process of solving and if I did, I want to know how to fix them and make sure I don't make those errors next time. If anyone would be willing to check my work, I would deeply appreciate it! Basically, the question is asking to give the error that the student made and to find the correct area & volume of the cone. For the surface area, I got an answer of 1244.1 meters squared. For the volume, I got an answer of 2787.6 meters squared. Thank you so much for your time and help! :)
you're correct, Jan used the height instead of the slant-height, which is needed for the SA, so hmm well, we really don't know the slant-height, hmmm let's find it, keeping in mind the slant-height is just the hypotenuse of either triangular cross-section
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{L}\\ a=\stackrel{adjacent}{11}\\ o=\stackrel{opposite}{22} \end{cases} \\\\\\ L=\sqrt{ 11^2 + 22^2}\implies L=\sqrt{ 121 + 484 } \implies L=\sqrt{ 605 }\implies L=11\sqrt{5} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{surface area of a cone}\\\\ SA=\pi rL + \pi r^2~~ \begin{cases} r=radius\\ L=slant~height\\[-0.5em] \hrulefill\\ r=11\\ L=11\sqrt{5} \end{cases}\implies SA=\pi (11)(11\sqrt{5})+\pi (11)^2 \\\\\\ SA=121\pi \sqrt{5}+121\pi \implies \boxed{SA\approx 1230.14~m^2} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=11\\ h=22 \end{cases}\implies V=\cfrac{\pi (11)^2(22)}{3}\implies \boxed{V\approx 2787.64~m^3}[/tex]
The mass of one sample of bacteria, in grams, grows according to the expression 8x + 1 , where x is time in hours from now. Another sample of bacteria grows according to the expression 2x − 5 . How long ago did the two samples have the same mass? What was their mass?
The mass of the sample before one hour is negative 7.
Given that:
Mass of the first sample, m₁ = 8x + 1
Mass of the second sample, m₂ = 2x - 5
In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The number of hours when the mass of the samples is the same. Then we have
m₁ = m₂
8x + 1 = 2x - 5
6x = - 6
x = - 1
The mass of the sample before one hour is calculated as,
m₁ = 8(-1) + 1
m₁ = - 8 + 1
m₁ = - 7
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worth 20 points
A net of a rectangular pyramid is shown in the figure.
A net of a triangular prism with base dimensions of 4 inches by 6 inches. The larger triangular face has a height of 4 inches. The smaller triangular face has a height of 4.6 inches.
What is the surface area of the pyramid?
33.2 in2
66.4 in2
90.4 in2
132.8 in2
