The value of k given the absolute value functions is (a) k = -5
Given that
graph = f(x)
table = g(x)
Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.
Also, from the given table, we have g(0) = -4.
Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.
But we also know that g(0) = -4. Thus, we have:
1 + k = -4
Solving for k, we get:
k = -5
Therefore, the value of k is -5.
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Simplify [tex]\frac{\sqrt 7 + \sqrt 3}{2\sqrt 3 - \sqrt 7}[/tex]
The simplified rational expression for this problem is given as follows:
[tex]\frac{3\sqrt{21} + 13}{12}[/tex]
How to simplify the rational expression?The rational expression in the context of this problem is defined as follows:
[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]
The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:
[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]
Applying the subtraction of perfect squares, the denominator is given as follows:
2² x 3 - 7 = 12.
The numerator is:
[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]
Thus the simplified expression is:
[tex]\frac{3\sqrt{21} + 13}{12}[/tex]
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a bin of 10 light bulbs contains 4 that are defective, if 3 bulbs are chosen with replacement from the bin, what is the chane that exactly 2 fo bulbs in the sample are defective
The probability of exactly 2 defective bulbs in a sample of 3 bulbs chosen with replacement from the bin is 0.288 or approximately 28.8%.
To solve this problem, we can use the binomial probability distribution formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where P(X=k) is the probability of getting exactly k successes, n is the total number of trials, p is the probability of success in each trial, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
In this case, n = 3 (because we are choosing 3 bulbs), p = 4/10 = 0.4 (because the probability of choosing a defective bulb is 4 out of 10), and we want to find P(X=2) (the probability of getting exactly 2 defective bulbs).
Substituting these values into the formula gives:\
P(X=2) = (3 choose 2) * 0.4^2 * (1-0.4)^(3-2)
= 3 * 0.16 * 0.6
= 0.288
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Help please !
I need the answer I’m stuck
Answer: I think it might be A.
Step-by-step explanation:
What is the sum of the polynomials?
The sum of the given polynomial [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]is [tex]9x^{3} - 8x^{2}[/tex].
How to add the polynomials?
Polynomials can be added or subtracted when they contain like terms, which are the same alphabets with the same powers.
Whereas there are no such rules for multiplication, any phrase with any power can be multiplied. The powers of the terms are then modified in accordance with exponentiation principles.
The following polynomial equation is [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]
Polynomial addition is accomplished by combining 'like terms'.
As a result, sorting and adding
= [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]
= [tex]7x^{3} + 2x^{3} - 4x^{2} - 4x^{2}[/tex]
= [tex]9x^{3} - 8x^{2}[/tex]
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Complete question:
What is the sum of the polynomials? (7x3 - 4x2) + (2x3 - 4x2)
Weights of the Pacific yellowfin tuna follow a normal distribution with mean weight 68 pounds and standard deviation 12 pounds. For a randomly caught Pacific yellowfin tuna, what is the probability that the weight is less than 50 pounds
The probability that the weight of a randomly caught Pacific yellowfin tuna is less than 50 pounds is approximately 0.0668 or 6.68%.
The weights of the Pacific yellow fin tuna follow a normal distribution with a mean weight of 68 pounds and a standard deviation of 12 pounds. To find the probability that a randomly caught Pacific yellow fin tuna weighs less than 50 pounds, we can follow these steps:
1. Calculate the z-score for the weight of 50 pounds using the formula:
z = (X - μ) / σ
where X is the weight, μ is the mean, and σ is the standard deviation.
2. Find the probability associated with the z-score using a z-table or calculator.
Let's calculate the z-score:
z = (50 - 68) / 12
z = -18 / 12
z = -1.5
Now, we can use a z-table or calculator to find the probability associated with the z-score of -1.5. The probability that a randomly caught Pacific yellow fin tuna weighs less than 50 pounds is approximately 0.0668, or 6.68%.
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A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online. Results are shown in the table below, but some values are missing. Fill in the missing values.
Answer:
Step-by-step explanation:
Women row is 24 20 44
men row is 64 32 96
total row is 64 32 96
Your school is choosing new school colors. Which group should you ask to get a random sample of student opinion?
since critical values of t vary by sample size, before using the t table we must first calculate
Critical values of t, which are used for hypothesis testing and confidence interval calculations, vary depending on the sample size and the degrees of freedom.
b) degrees of freedom.
Degrees of freedom (df) are calculated based on the sample size and represent the number of independent pieces of information available in the data. It is an important parameter in determining the appropriate critical value to use from the t-distribution table. Therefore, before using the t-table, it is essential to calculate the degrees of freedom of the data set in question.
Options a, c, and d are not correct answers as they do not pertain to the calculation needed before using the t-table.
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Complete Question
Since critical values of t vary by sample size, before using the t table we must first calculate:
a) the Z score.
b) degrees of freedom.
c) the population standard deviation.
d) the sample size.
The degrees of freedom will then determine the critical values of t that should be used in calculating confidence intervals or conducting hypothesis tests. Therefore, it is important to consider the sample size when working with t statistics and using the t table.
To answer your question, before using the t-table, you must first calculate the degrees of freedom. The degrees of freedom are important as they determine the critical values of t based on your sample size. Here's a step-by-step explanation:
1. Obtain your sample data.
2. Determine the sample size (n) by counting the number of data points in your sample.
3. Calculate the degrees of freedom (df) by subtracting 1 from the sample size: df = n - 1.
4. Refer to the t-table with the calculated degrees of freedom to find the critical values of t for your desired level of confidence or significance.
By following these steps, you'll be able to find the appropriate critical values of t based on your sample size before using the t-table.
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In Rodger's state, unemployment compensation is calculated by finding the total of the quarterly wages of two consecutive quarters and dividing by 26. The weekly
unemployment is 65% of that amount. In the quarter including January, February, and March, Rodger made a total of $13,950.80. In the quarter including April, May, and
June, he made a total of $14,250.10. Find Rodger's weekly unemployment amount.
Rodger's weekly unemployment amount will be $ 705.0225
Given that the total of the quarterly wages of two consecutive quarters and divided by 26.
The weekly unemployment is 65% of that amount.
Rodger made a total of $13,950.80.
Then he made a total of $14,250.10
Step 1: the total of the quarterly wages of two consecutive quarters.
= $ 13,950.80 + $ 14,250.10
= $28,200.90
Now Divide the total by 26
= $28,200.90 / 26
= 1,084.65
Then, = 1,084.65 x 65%
= 1,084.65 x 65/100
= 705.0225
Hence, Rodger's weekly unemployment amount is; $ 705.0225
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need help ASAP!!! Please help! I’m having trouble!
The Surface Area of wooden box is 432 inch².
We have,
length = 12 inch
width = 8 inch
Height = 6 inch
So, Surface Area of wooden box
= 2 (lw + wh + lh)
= 2 (96 + 48 + 72)
= 2 x 216
= 432 inch²
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Find the discriminate y=-x^2-6x19
Answer: 112
Step-by-step explanation:
To find the discriminant of a quadratic equation in the form of y = ax^2 + bx + c, where a, b, and c are constants, we can use the formula:
Discriminant = b^2 - 4ac
In this case, the quadratic equation is y = -x^2 - 6x + 19. So, we can identify the coefficients:
a = -1
b = -6
c = 19
Then, we can substitute these values into the formula for the discriminant:
Discriminant = b^2 - 4ac
= (-6)^2 - 4(-1)(19)
= 36 + 76
= 112
Therefore, the discriminant of the quadratic equation y = -x^2 - 6x + 19 is 112.
Steve wants to start his own T-shirt business. His initial costs to get the business going are $1,500. It also costs on average $3 per shirt. Steve charges $10 for each shirt he sells. Which of the following systems is correct for this model to find the break-even point if "x" = the number of shirts sold and "y" = the number of dollars of expense or income?
Answer:
Below
Step-by-step explanation:
To find the break-even point, we need to determine the point at which the total revenue equals the total cost. Let's call the number of shirts sold "x".
The total cost includes the initial costs of $1,500 and the cost per shirt of $3x, so the total cost is:
y = 1500 + 3x
The total revenue is the price per shirt of $10 multiplied by the number of shirts sold, so the total revenue is:
y = 10x
To find the break-even point, we need to set the total cost equal to the total revenue and solve for x:
1500 + 3x = 10x
Simplifying this equation, we get:
1500 = 7x
Dividing both sides by 7, we get:
x = 214.29
Therefore, Steve needs to sell 215 shirts to break even.So the correct system to find the break-even point is:
y = 1500 + 3x (total cost)
y = 10x (total revenue)
suppose lengths of text messages are normally distributed and have a known population standard deviation of 3 characters and an unknown population mean. a random sample of 22 text messages is taken and gives a sample mean of 31 characters. what is the correct interpretation of the 90% confidence interval?
Answer: The 90% confidence interval for the population mean of the length of text messages is a range of values that is likely to contain the true population mean with a probability of 0.90 (or 90%). Based on the given information, we can calculate the confidence interval as follows:
Standard error of the mean (SE) = σ / sqrt(n)
where σ is the population standard deviation, n is the sample size, and sqrt denotes the square root.
SE = 3 / sqrt(22) ≈ 0.639
Margin of error (ME) = t(α/2, df) × SE
where t(α/2, df) is the critical value from the t-distribution with df degrees of freedom, and α is the level of significance (1 - confidence level).
For a 90% confidence level and 21 degrees of freedom (df = n - 1), the critical value is approximately 1.717.
ME = 1.717 × 0.639 ≈ 1.098
The confidence interval can be calculated as:
CI = sample mean ± ME
= 31 ± 1.098
= (29.902, 32.098)
Therefore, we can say that we are 90% confident that the true population mean of the length of text messages falls between 29.902 and 32.098 characters. In other words, if we were to repeat the sampling process many times and construct a 90% confidence interval for each sample, we would expect 90% of the intervals to contain the true population mean. Additionally, we can interpret the margin of error as the maximum amount that the sample mean is expected to differ from the true population mean, with a probability of 90%.
Step-by-step explanation:
A suitcase measures 24 inches long and 18 inches high what is the diagonal length of the suitcase to the nearest 10th of a foot
Answer: Split it in half to turn it into a triangle! The hypotenuse if the triangle will give you the diagonal length of the suitcase, because it’s a rectangle. Hope this helps :D
Step-by-step explanation:
HELP ASAP !!!!Subtract.
(9h² + 5h + 6) − (3h² + 5h + 2)
Answer:
2(3h^2+2)
Step-by-step explanation:
Each input value, x, is squared and then 3 is added to
the result. The domain of the function is [0, ∞).
make a graph or equation
The equation of the function is f(x) = x² + 3, where x represents the input value and f(x) represents the output value. Graph is in below figure.
What is a domain of the function?The domain of a function is the set of all possible input values (also called the independent variable) for which the function is defined. In other words, it is the set of values that can be plugged into the function to produce a valid output value (also called the dependent variable).
The equation of the function is f(x) = x² + 3, where x represents the input value and f(x) represents the output value.
To graph this function, we can plot points by choosing values of x and computing the corresponding values of f(x). Since the domain of the function is [0, ∞), we will only consider non-negative values of x.
x f(x)
0 3
1 4
2 7
3 12
4 19
We can plot these points on a coordinate plane and connect them with a smooth curve to obtain the graph of the function:
Note that the graph is a parabola that opens upwards and passes through the point (0, 3).
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he diameter of a semicircle is 23 centimeters. What is the semicircle's area?
Answer: in2
Step-by-step explanation:
answerd
A percent is a way of a expressing a part out of 100. Remember learning about ratios and how they compare quantities? A part-to-whole ratio is a ratio that compares a part of a whole to another part of a whole. A percent is a part-to-whole ratio where the whole is 100. 40%, or 40 out of 100, is a ratio that compares 40, the part, to 100, the whole.
Which of these could you express as a percent?
A
how many of the 100 yogurts in the refrigerator are strawberry
B
the average size of the 100 yogurts in the refrigerator
C
the maximum number of yogurts the refrigerator can hold
D
how many grams of sugar the 100 yogurts in the refrigerator have altogether
A statement that could be expressed as a percent : 'how many of the 100 yogurts in the refrigerator are strawberry'
The correct answer is an option(A)
We know that a part-to-whole ratio is nothing but a ratio that compares a part of a whole to another part of a whole.
And the percent is nothing but a part-to-whole ratio where the whole is 100.
Consider the case 'how many of the 100 yogurts in the refrigerator are strawberry.'
Let us assume that x represents the number of strawberry yogurts out of total 100 yogurts in the refrigerator'
So, a part-to-whole ratio would be x/100
We can observ ethat here whole = 100
So, we could express the number of strawberry yogurts as a percent.
The correct answer is an option(A)
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URGENT! Will give brainliest :)
A line of best fit was drawn for 16 data points. What is the maximum number of these data points that mav not actually be on the line?
O A. 15
O B. 16
O C. 14
O D. 13
Answer:
The maximum number of data points that may not actually be on the line of best fit for 16 data points is 15 (Option A). This is because a line of best fit is an approximation of the relationship between the variables being studied, and it is unlikely that all data points will fall exactly on the line.
Step-by-step explanation:
To determine the line of best fit, a regression analysis can be performed. This involves finding the equation of the line that best represents the relationship between the variables. The line of best fit minimizes the distance between each data point and the line.
However, even with a perfect line of best fit, there may still be some data points that do not fall exactly on the line. This is due to natural variability in the data and measurement error.
Therefore, it is possible for all 16 data points to fall on the line of best fit, but it is more likely that some points will deviate slightly from the line. The maximum number of data points that may not actually be on the line is 15.
(I NEED THIS ASAP)
3. Select all the transformations that produce congruent images.
(A.) dilation
(B.) horizontal stretch
(C.) reflection
(D.) rotation
(E.) translation
(C.) reflection and (D.) rotation produce congruent images.
What three transformations are congruent?
We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.
(A) Dilation, (B) horizontal stretch, and (E) translation do not produce congruent images because they change the size, shape, and/or orientation of the original object.
(C) Reflection produces congruent images because the resulting image is a mirror image of the original object, and therefore has the same size and shape.
(D) Rotation produces congruent images because the resulting image is the same shape and size as the original object, just rotated to a different orientation.
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Given the triangle below...
30°
B
79
A
What is the measure of angle B?
Answer: 71
Step-by-step explanation: to get the answer you have to know that all the angles of a triangle have to add up to 180 so therefore you add the angles they gave you and then you minus them from 180 and you get 71
I am really stuck on this question please help!!!
substitute 140 for 'y', because 'y' is the amount of available cabinets (they need to be available in order for it to be installed).
you have;
140 = 8x + 40
solve for x from here
Answer:
Step-by-step explanation:
To find out how many weeks it will take to fill the high school's order, we need to solve the equation for the number of weeks (x). We can start by plugging in the given value of 104 for y since y represents the number of cabinets, and then solving for x:
y = 8x + 40
104 = 8x + 40
-40 -40
64 = 8x
x = 8
Therefore, it will take 8 weeks to produce enough cabinets to fill the high school's order.
a newsletter publisher believes that more than 51% of their readers own a personal computer. is there sufficient evidence at the 0.05 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
Answer: The null hypothesis for this scenario is that the proportion of readers who own a personal computer is 0.51 or less:
H0: p <= 0.51
The alternative hypothesis is that the proportion of readers who own a personal computer is greater than 0.51:
Ha: p > 0.51
To test this hypothesis, we would need to collect a random sample of readers and determine the proportion of readers who own a personal computer in the sample. We could then use a one-sample proportion test to determine whether the proportion in the sample is significantly different from the null hypothesis value of 0.51. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is sufficient evidence to substantiate the publisher's claim that more than 51% of their readers own a personal computer. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is not sufficient evidence to substantiate the publisher's claim.
Step-by-step explanation:
order the measurements from greatest to least 45 inches, 6 yards, and 2 and1/4 feet
Answer:
2.25 feet, 45 inches, and 6 yards
Step-by-step explanation:
first, convert all to the same unit of measurement
I will use inches
45 inches = 45 inches
6 yards, 1 yard = 3 feet so 6 yards are equal to 18 feet and 1 foot is equal to 12 inches so 12*18 is 216 inches so 6 yards = 216 inches
Next 1 foot equals 12 inches so 2.25 * 12 = 27 so 2.25 feet = 27 inches.
Now let's look at the complete conversion
45 inches
6 yards = 216 inches
2.25 feet = 27 inches
looking at the inches we can see that 27 is the least then 45 then 216 therefore
2.25 feet < 45 inches < 6 yards so the order is
2.25 feet, 45 inches, and 6 yards
please help me with this question
Answer:
Step-by-step explanation:
The answer is attached below. There isn't much explanation for this. You just translate the word problem into a mathematical inequality.
A paper company produces 4,000 notebooks in 4 days.How many notebooks can it produce in 12 days
Answer:
12000 In 12 days
Step-by-step explanation:
12÷4=3
4000×3=12000
Draw a dot plot (line plot) to show how many movies Shane watched in a four week period. (from weeks 1-4 he watched 2, 4, 0, and 5)
Answer:
The analysis is given below :
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The expedition has a 28 gallon tank and gets 17 mpg. It can drive miles before running out of gas
On solving the provided question we can say that equation As a result, the expedition can go 476 kilometres before running out of fuel.
What is equation?A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 equals 2, for instance.
To calculate how far the expedition can travel before running out of gas, apply the following formula:
Miles = (Gallons of gas) x (Miles per gallon)
Plugging in the given values, we get:
Miles = 28 gallons x 17 mpg
Miles = 476 miles
As a result, the expedition can go 476 kilometres before running out of fuel.
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Calculate the size of angle edc
Answer:
64 degrees
Step-by-step explanation:
Corresponding angles are equal so angle BAF = 133 degrees. Supplementary angles add to 180 degrees so angle AFC = 47 degrees.
Angles on a straight line add to 180 degrees so angle CFE = 180 - 47 = 133 degrees.
Angles in a quadrilateral add to 360 degrees so angle EDC = 360 - (133 + 101 + 62) = 64 degrees.
Therefore angle EDC = 64 degrees
Select one or more expressions that together represent all solutions to the
equation. Your answer should be in radians.
Assume n is any integer.
-4 cos(5x)+1=1
The solutions for the given equation be written as: x = (2n + 1)π/10, where n is any integer.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It usually contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.
According to given information:Starting from the given equation:
-4cos(5x) + 1 = 1
Simplifying the equation, we get:
-4cos(5x) = 0
Dividing both sides by -4, we get:
cos(5x) = 0
Now, we need to find the values of x that satisfy this equation. Recall that the cosine function is equal to 0 at odd multiples of π/2, i.e.,
cos(θ) = 0 for θ = (2n + 1)π/2, where n is an integer.
So, substituting θ = 5x, we get:
cos(5x) = 0 for 5x = (2n + 1)π/2
Dividing both sides by 5, we get:
x = (2n + 1)π/10
So, the solutions for the given equation are:
x = π/10, 3π/10, 5π/10, 7π/10, 9π/10, 11π/10, 13π/10, 15π/10, 17π/10, ...
which can be written as:
x = (2n + 1)π/10, where n is any integer.
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