There is a local maximum at the point (-1,6), therefore, for x = -1
option D is correct
What do we mean by local maximum point?A local maximum point on a function is described as a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We see that the function adopts values smaller than 6 to the left of x = -1, and to the right of it:
(-3, -2), (-2, 0) to the left of x = -1 where the function's value is 6
and (0, 0), and (1, -2) to the right of x = -1
Therefore, we can say that the pints (-1, 6) is a maximum, that is for x = -1, where the function renders a value of 6.
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find 15x2 2/3 using the distributive property
PLEASE HELP!!!
A cylinder has a height of 15 inches. A similar cylinder has a height of 20 inches.
What is the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder?
Enter your answer by filling in the boxes.
The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 4:3, or 4/3.
How do you find the ratio of the surface area of the larger cylinder to the the smaller cylinder?To find the ratio of the surface areas of the two similar cylinders, we need to consider the ratio of their corresponding dimensions. Since the two cylinders are similar, their radii are proportional to their heights. Let's denote the height of the smaller cylinder as h1, the height of the larger cylinder as h2, the radius of the smaller cylinder as r1, and the radius of the larger cylinder as r2.
Given:
h1 = 15 inches
h2 = 20 inches
The ratio of the heights is:
h2 / h1 = 20 / 15 = 4 / 3
Since the cylinders are similar, the ratio of their radii is the same as the ratio of their heights:
r2 / r1 = 4 / 3
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In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 40,000 dollars. Otherwise, they lose $1.
To find the probability of winning the lottery game, we can use the formula for combinations:
nCk = n! / (k! * (n - k)!)
where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).
So, the number of possible combinations of six numbers from 22 is:
22C6 = 22! / (6! * 16!) = 13,983,816
Therefore, the probability of winning the lottery game is 1 in 13,983,816.
The expected value of playing the lottery game can be calculated as follows:
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)
Expected value = $0.5709
This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.
What is the output for x = -1
Answer:
f(-1) = 16
Step-by-step explanation:
"output" and the f(x) setup just means to plug in -1 in place of x and calculate.
For the function f(x) = 12(3/4)ˣ you have to already know that once you put that -1 in place of x that the -1 power only goes to the 3/4, not the 12 and also what to do with a negative exponent.
Exponent rules are just shortcuts. The shortcut to know here is that the -1 exponent will flip the 3/4 over and make it 4/3 (there are math reasons for this, it's not random. But that's how it works)
So now you have
f(-1) = 12(3/4)⁻¹ which becomes
f(-1) = 12(4/3)
Now you need to know how to multiply with fractions. Here you have a whole, big number times a fraction, which is:
"big num×top all over bottom"
So multiply the 12 times the 4 and put it over the 3
f(-1) = 48/3 = 16
(or you can "cancel" the 12 with the 3 and get 4×4, which is 16, so it comes out the same)
[SKIP TO HERE IF YOU DON'T CARE WHY]
f(x) = 12(3/4)ˣ
f(-1) = 12(3/4)⁻¹
f(-1) = 12(4/3)
f(-1) = 16
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 106, and the sample
standard deviation, s, is found to be 10.
(a) Construct a 95% confidence interval about u if the sample size, n, is 16.
(b) Construct a 95% confidence interval about u if the sample size, n, is 11.
(c) Construct a 90% confidence interval about μ if the sample size, n, is 16.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
what is standard deviation ?A collection of information's values' standard deviation serves as a gauge for how much variance or dispersion there is. It is a statistical word used to describe the degree to which the individual data points depart as from mean or average value that is contained in the data set. By taking taking square root of the variance—the sum of the squared deviations amongst each point in the data and the mean—we can determine the standard deviation. While a high standard deviation suggests that the data points are widely dispersed, a modest standard deviation suggests that the statistics are close to the mean.
given
(a) When the sample size, n, is 16, we can apply the following formula to create a 95% confidence interval regarding the population mean, :
x ± tα/2 * (s/√n)
where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.
We determine that t0.025,15 = 2.131 using a t-distribution table or calculator.
When we enter the values, we obtain:
106 ± 2.131 * (10/√16)
which is equivalent to:
106 ± 5.33
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
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Please help quickly I'm begging!
Assignment details: In this assignment, you will create two graphs and answer questions about Bond's Gym, the business you are supporting.
The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments
Creating the functions of the Bond's GymFrom the question, we have the following parameters that can be used in our computation:
The table of values
For the membership application, we have the following features
Initial value = 600Constant rate of change = (450 - 600)/(15 - 0) = -10So, the function is
f(x) = 600 - 10x
For the membership available, we have the following features
Initial value = 0Constant rate of change = (100 - 0)/(15 - 0) = 20/3So, the function is
g(x) = 20/3x
So, the functions are f(x) = 600 - 10x & g(x) = 20/3x
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The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
40 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A. Mean for both coffee shops because the data distribution is symmetric
B. Median for both coffee shops because the data distribution is not symmetric
C. Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
D. Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric
Why is the median better ?It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.
The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.
The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.
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Question is in the image. Please help me solve these
Answer:
Step-by-step explanation:
write the opposite of loss of 700
Answer:
gain of 700 or 700
Step-by-step explanation:
A loss of 700 would be -700 and the opposite of that is 700.
Helping in the name of Jesus.
In a shipment of 1,750 seeds of each type, how many more defective bean seeds would be expected than pumpkin seeds?
There would be 35 more defective bean seeds than pumpkin seeds in the shipment.
How to solveCalculate the number of defective bean seeds:
Defective bean seeds = Total bean seeds * Defect rate for bean seeds
Defective bean seeds = 1,750 * 0.05 = 87.5
Since we can't have half a seed, we'll round it up to the nearest whole number.
Defective bean seeds = 88
Calculate the number of defective pumpkin seeds:
Defective pumpkin seeds = Total pumpkin seeds * Defect rate for pumpkin seeds
Defective pumpkin seeds = 1,750 * 0.03 = 52.5
Similarly, we'll round it up to the nearest whole number.
Defective pumpkin seeds = 53
Calculate the difference in defective seeds:
Difference in defective seeds = Defective bean seeds - Defective pumpkin seeds
Difference in defective seeds = 88 - 53 = 35
So, there would be 35 more defective bean seeds than pumpkin seeds in the shipment.
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In a shipment of 1,750 seeds of each type, with a defect rate of 5% for bean seeds and 3% for pumpkin seeds, how many more defective bean seeds would be expected than pumpkin seeds?
Can someone help me with this pls
Find the missing value on the table below:
x y
2 4
? 6
4 8
If cos(x) = -5/6, x in quadrant II, then find exact values (without finding x):
sin(2x)= ?
cos(2x)=?
tan (2x)=?
If cos(x) = -5/6, and x lies in quadrant"II", then exact values are:
sin(2x) = (-5√11)/(18);
cos(2x) = 7/18;
tan (2x) = -5√11/7.
We know that, Cos(x) = -5/6 and "x" is in quadrant II, so, we can use the Pythagorean identity to find sin(x):
sin(x) = √(1 - cos²(x)) = √(1 - (-5/6)²) = √(1 - 25/36) = √(11/36) = √11/6
Using the double angle trigonometry identities for sine and cosine, we find sin(2x) and cos(2x):
Substituting the value of Sin(x) and Cos(x),
We get,
sin(2x) = 2sin(x)cos(x) = 2(√11/6)(-5/6) = (-5√11)/(18);
cos(2x) = cos²(x) - sin²(x) = (-5/6)² - (11/6) = 25/36 - 11/36 = 14/36 = 7/18;
Finally, we find tan(2x) by using the identity:
tan(2x) = sin(2x)/cos(2x) = (-5√11/18) / (7/18) = -5√11/7.
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Julie was testing how far two new electric cars—model A and model B—could drive on a full charge. She obtained a sample of 5 55 new cars of each model, charged them fully, and drove them as far as she could along a controlled route. Here is a summary of the distances: Distance Model A Model B Mean 168 km 168 km168, start text, space, k, m, end text 172 km 172 km172, start text, space, k, m, end text Standard deviation 5.4 km 5.4 km5, point, 4, start text, space, k, m, end text 7.5 km 7.5 km7, point, 5, start text, space, k, m, end text Number of cars 5 55 5 55 Julie wants to use these results to test H 0 : μ A − μ B = 0 H 0 : μ A −μ B =0start text, H, end text, start subscript, 0, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, equals, 0 versus H a : μ A − μ B ≠ 0 H a : μ A −μ B =0start text, H, end text, start subscript, start text, a, end text, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, does not equal, 0. Assume that these are representative samples and all other conditions have been met. What is the P-value associated with these sample results? Choose 1 answer: Choose 1 answer: (Choice A) P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 A P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 (Choice B) 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 B 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 (Choice C) 0.05 ≤ P -value < 0.10 0.05≤P-value<0.100, point, 05, is le
The p value based on the information will be E. P - value ≥ 0.20
How to compute the valueOpen Minitab 17. Select 'Stat' -> 'Basic Statistics' -> '2 - Sample t... Select 'Summarized data' from the dropdown menu.
Enter 5 in both Sample size of sample 1 and sample 2, 168 and 172 in Sample mean of Sample 1 and Sample 2. 5.4 and 7.5 in Standard deviation of Sample 1 and Sample 2.
Click on 'Options' and Enter 'Confidence level' 95.0(or the given Cofidence level) , 'Hypothesized difference' 0.0 , 'Alternative hypothesis' 'Difference \\neq Hypothesized difference'. Also the box 'Assume equal variance' can be ticked as requirement.
Click on 'Ok' -> 'Ok'.
Output: -
P - value = 0.361 i.e., P - value ≥ 0.20
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PLEASE HELP I DON'T UNDERSTAND
Ten cards are numbered from 1 to 10 and placed in a box. One card is selected at random and replaced. Another card is randomly selected. What is the probability of selecting two even numbers?
P(two even numbers) _________
Answer:
30%
Step-by-step explanation:
Suppose you have a 4 foot sub and you have to feed 10 people ,how many cuts will you make?
Answer: Cut 3 inch per person
Step-by-step explanation:
there is a 4 foot sub you take the quadrilatiral and divide it by 10 and you get 3 inches per person remember to multiply the reciprocal by 12 as there are 12 inches in a foot and you have 4 foot so the product of that reciprocal will be equal to 4 divided by your sum from adding the recriptorcal into the quadrilateral remember a quadrilateral not a duolateral or a triolatiral as there is 4 feet in the sub. >:)
Answer:
7 Cuts
Step-by-step explanation:
This is because if you do 48 inches / 6 inches = 8 sections Since each cut will create two sections, you need to make 7 cuts (one fewer than the number of sections) to get 8 equal portions.
inverse statement of M implies N
The inverse statement of M implies N is a negation of both the conclusion and the hypothesis.
What is an inverse statement?An inverse statement is one in which both the hypothesis and the conclusion are negated. Let us assume a statement with the hypothesis and conclusion as follows: If they annul the law, we will drive carelessly.
The inverse of this statement will be: If they do not annul the law, we will not drive carelessly. So, both the hypothesis and the conclusion are rewritten in negative terms.
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Write the equation of a line that is perpendicular and passes through the midpoint of AB with A(-3, 5) and B(1, -1).
The given line AB is having endpoints A(-3,5) & B(1,-1).
To find the equation of line AB it can be written as[tex]y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\[/tex]
Substituting the given points
[tex]y-(-1)=(x-1){(5-(-1))/(-3-1)}\\[/tex]
y=-(3/2)x+1/2
For two perpendicular lines [tex]m_1*m_2=-1[/tex]
Therefore, (-3/2)*[tex]m_2[/tex]=-1
or [tex]m_2[/tex] = 2/3
Also, the midpoint of AB will be [tex]{1-(-3)}/2, {5-(-1)}/2[/tex] = (2,3).
The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows
(y-3)=(2/3)(x-2)
3y-9=2x-4
3y=2x+5 is the required equation of the line.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Can someone help me please
The row operation is given as follows:
Division by 7 = multiplication by 1/7.
The matrix after the row operation is then given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
The element at row 1 and column 1 is given as follows:
7.
An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
The first row is given as follows:
7, -4 and 8.
Dividing every element of the first row by 7, the resulting matrix is then given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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Which of these are statistical questions? Select ALL that Apply Question 1: How many minutes does it usually take each teacher to get from home to work? Question 2: During the past year did you work for more than 50 weeks? Question 3: During the past year how many hours did each teacher usually work each week? Question 4: How many extra hours did each doctor work each week?
The statistical questions are:
Question 1: How many minutes does it usually take each teacher to get from home to work?Question 3: During the past year how many hours did each teacher usually work each week?Question 4: How many extra hours did each doctor work each week?What is a statistical question?
A statistical question is a question that can be answered by collecting and analyzing data. It is a question that expects a variability in the response, meaning different individuals may give different answers. Statistical questions usually ask about a population, a group of individuals or objects that share a common characteristic or feature, and seek to understand a pattern or trend within that population.
In general, a statistical question is open-ended, does not have a single correct answer, and requires data analysis to arrive at a reasonable conclusion.
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Which one of the following examples represents a proper
fraction?
A. 15/22
B. 12/9
C. 3/2
O D. 8/8
A.15/22 is the correct answer.
The correct answer is:
A. 15/22, represents a proper fraction.
Here, we have,
A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).
Out of the given options, only option A,
15/22, represents a proper fraction because 15 is smaller than 22.
Therefore, the correct answer is:
A. 15/22, represents a proper fraction.
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34 Points! Multiple choice algebra question. Photo attached. Solve e^x>2.7. Thank you!
Answer:
B
Step-by-step explanation:
not good at explaining this concept but keep the signal its X|X and its near the square root so tadaaa
What is the numerical expression that represents the sun of eight squared and thirty two
The numerical expression that represents the sum of eight squared and thirty two will be 96.
A numerical expression is a mathematical expression that consists of numbers and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
The numerical expression that represents the sum of eight squared and thirty two is
= 8² + 32
= 64 + 32
= 96.
The question is incomplete and the complete question is '' What is the numerical expression that represents the sum of eight squared and thirty two''.
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How many triangles exist with the given side lengths?
3in , 4in , 2in
Step-by-step explanation:
Only ONE .....there are three sides to a triangle and you supplied 3 sides.
if you increase your current quality score of 85% by 7%, you will have a score of?
Answer:
90.95%
Step-by-step explanation:
85 * 0.07 = 5.95 5.95 + 85= 90.95
Answer:
The answer to your problem is, 90.95%
Step-by-step explanation:
Calculation:
In order to find the answer we need to
= Old score + New Score
= 85 + 7% of 85
= 85 + ( [tex]\frac{7}{100}[/tex] x 85 )
= 85 + ( 0.07 x 85 )
= 85 + 5.95
= 90.95
Which 90.95% is our answer.
Thus the answer to your problem is, 90.95%
Can the sides of a right triangle have lengths 7,9 and the square Root of 155
Answer:
No
Step-by-step explanation:
In order for a triangle to be a right angle, the sum of the squares of the two legs (a and b) must be equal the square of the longest side, known as the hypotenuse (c):
[tex]a^2+b^2=c^2[/tex]
The square root of 155 is the longest side as it is approximately 12.45. Thus, if the triangle is a right triangle, the square root of 155 must be the hypotenuse.
We can now check to see whether the sum of the squares of 7 and 9 equal the square of the square root of 155:
[tex]7^2+9^2=(\sqrt{155})^2\\ 49+81=155\\130=155[/tex]
The equation is not true since 130 is less than and not equal to 155. Therefore, a triangle with side lengths 7, 9, and the square root of 155 cannot be a right triangle.
I arrived home to discover that my 50-foot by 40-foot basement has 18 inches of water in it! There are about 7.5 gallons in 1 cubic foot of water. How much water is in the basement?
Calculate using the most appropriate units to describe the amount of water, and state your answer in a meaningful sentence.
The amount of water in the basement is V = 22,500 gallons
Given data ,
To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.
First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:
50 feet x 40 feet x 1.5 feet = 3,000 cubic feet
There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:
3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons
Hence , there are 22,500 gallons of water in the basement
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NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The trigonometry functions when evaluated are shown below
Evaluating the trigonometry functionsIn trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.
They are defined as follows:
sin A = opposite side/hypotenuse.
cos A = adjacent side/hypotenuse.
tan A = opposite side/adjacent side.
So, we have
Figure 1
sin A = 6/9cos A = √5/3tan A = 6/√5Figure 2
sin A = √2/2cos A = √2/2tan A = 1Figure 3
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Solve for the missing side in each triangle
Answer:
6[tex]\sqrt{13}[/tex]
Step-by-step explanation:
a^2+b^2=c^2 c is hypotenuse, which is what we're looking for
12^2+18^2=c^2
144+324=c^2
c=[tex]\sqrt{468}[/tex]=[tex]\sqrt{36*13}[/tex]=6[tex]\sqrt{13}[/tex]