draw a quadratic function that only has one root at 3
The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2
What is quadratic equation?A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:
ax^2 + bx + c = 0
If a quadratic function has only one root at 3, then it must be of the form:
f(x) = a(x - 3)^2
where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.
To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:
4 = a(0 - 3)^2
4 = 9a
a = 4/9
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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]
Why is it called a quadratic equation?A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.
A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:
[tex]ax^2+bx+c=0[/tex]
If the quadratic function has only one root at 3, it must have the following form:
[tex]f(x)=a(x-3)^2[/tex]
This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.
We know that f(0) = 4, so we can plug these numbers into the equation to get:
[tex]4=a(0-3)^2[/tex]
simplify the above equation
4 = 9a
The value is,
a = 4/9
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Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content
The expression represents the constraint that the amount of fat in the cookie should not deviate from the target fat content by more than 1.8 grams per cookie is |f - 5| ≤ 1.8
To express the difference between the fat in a cookie from the new recipe and the target fat content, we can use an expression. Let's represent the amount of fat in a cookie from the new recipe as f. Then, the difference between the fat in the cookie and the target fat content of 5 grams per cookie can be expressed as:
|f - 5|
The vertical bars around the expression indicate the absolute value, which means that we want the difference to be positive, regardless of whether f is greater or less than 5.
Now, we also know that the company will accept a difference of up to 1.8 grams per cookie. This means that the expression above should be less than or equal to 1.8:
|f - 5| ≤ 1.8
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Complete Question:
The Billing sly Cookie Company is experimenting with a new low-fat cookie recipe. The management wants the bakers to come up with a cookie that is low in fat but still has good taste. The company decides on a target fat content of 5 grams per cookie. In order to be labeled low-fat, a difference of 1.8 grams per cookie is acceptable. This means the amount of fat should be no more than 1.8 grams above 5 or no more than 1.8 grams below 5.
Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content. Use f to represent the amount of fat in a cookie from the new recipe.
suppose the data on natural birth weights (collected by the world health organization (who)) is normally distributed with the mean equal to 7.25 pound for a full-term birth and standard deviation of 1.0 pounds. what is the probability that a randomly selected baby will weigh more than 9.75 pounds at birth? 0.0062
The probability that a randomly selected baby will weigh more than 9.75 pounds at birth is 0.0062, or about 0.62%. This means that the vast majority of babies will weigh less than 9.75 pounds at birth, as this value is more than two standard deviations above the mean.
We can use the standard normal distribution to solve this problem by first standardizing the value of 9.75 pounds using the formula:
z = (x - mu) / sigma
where x is the value of 9.75 pounds, mu is the mean of 7.25 pounds, and sigma is the standard deviation of 1.0 pound.
Substituting the values, we get:
z = (9.75 - 7.25) / 1.0 = 2.5
We can then use a standard normal distribution table or calculator to find the probability of a z-score greater than 2.5. From the table or calculator, we find that this probability is approximately 0.0062.
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Find the critical t-value that corresponds to 90% confidence. Assume 16 degrees of freedom. (Round to three decimal places as needed.)
1.746 is the critical t value that corresponds to 90% confidence.
To find the critical t-value that corresponds to 90% confidence with 16 degrees of freedom, follow these steps:
1. Determine the desired confidence level: 90%
2. Calculate the corresponding significance level (alpha) by subtracting the confidence level from 100%: 100% - 90% = 10%
3. Divide the significance level by 2 to get the value for a two-tailed test: 10% / 2 = 5%
4. Look up the critical t-value in a t-distribution table using the degrees of freedom (16) and the 5% value.
From the t-distribution table, the critical t-value for 16 degrees of freedom and 90% confidence is approximately 1.746.
So, the CRITICAL T VALUE that corresponds to a 90% CONFIDENCE level with 16 DEGREES FREEDOM is 1.746, rounded to three decimal places.
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Kim's hourly wage is $14. She works 37 hours per week. What is her monthly income?
Answer:
2072
Step-by-step explanation:
Multiply 14 x 37
518 x 4
2072
Answer: $2,072 a month
Step-by-step explanation:
multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply 518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072
What 25% of 140? Question 8 options: 25 35 45 50
Answer:
35
Step-by-step explanation:
Change the percent to decimal form and of means multiply.
25% of 140
.25 * 140
35
Answer:
35
Step-by-step explanation:
A random survey of enrollment at 35 community colleges across the United States yielded the following figures:
6,414; 1,550; 2,109; 9,350; 21,828; 4,300; 5,944; 5,722; 2,825; 2,044; 5,481; 5,200; 5,853; 2,750; 10,012; 6,357; 27,000; 9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080; 11,622.
Assume the underlying population is normal.
a.
i. = __________
ii. sx = __________
iii. n = __________
iv. n – 1 = __________
b. Define the random variables X and in words.
c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United States.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
e. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?
The larger sample size also reduces the impact of individual outliers, which could potentially skew the results. Therefore, increasing the sample size will result in more reliable results, and a smaller error bound and confidence interval.
The error bound (E) for the sample size of 35 community colleges is calculated using the formula: E =[tex]1.96 * √[p*(1-p)/n].[/tex]
With n = 35, p = 0.5 (assuming the mean of the enrollment figures is 0.5), the error bound is calculated to be E = 0.823.
If the sample size is increased to 500 community colleges, the error bound would be reduced to 0.338. This is because the larger the sample size, the smaller the error bound. The confidence interval would also be reduced, since it is directly proportional to the error bound.
In practical terms, a larger sample size means more reliable results. This is because when the sample size is increased, the results tend to be more representative of the entire population, leading to more accurate conclusions.
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the medians of a triangle intersect at the ___
Answer:
orthocentre
Step-by-step explanation:
this is the answer to your question
when the finite population correction factor is applied to the sample mean, the resulting standard error for the sample mean is equal to
The finite population correction factor (FPC) is a factor used when the sample size is more than 5% of the population size. It corrects for the bias that can occur when taking a sample from a finite population.
Applying the FPC to the sample mean results in the standard error for the sample mean being equal to the population standard deviation divided by the square root of the sample size times the FPC.
In other words, the standard error for the sample mean is equal to:
Standard Error = Population Standard Deviation/√(Sample Size*FPC)
The FPC is calculated by taking the reciprocal of the following formula:
FPC = (N-n)/(N-1), where N is the population size and n is the sample size.
In conclusion, applying the FPC to the sample mean reduces the bias that can occur when taking a sample from a finite population, and the resulting standard error for the sample mean is equal to the population standard deviation divided by the square root of the sample size times the FPC.
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1. Representar en GeoGebra las funciones dadas y determinar comprobando analíticamente: a. Tipo de función b. Dominio y rango c. Asíntotas, tanto vertical y horizontal, si las tiene: [tex]f(x)=\frac{2x^{2}-4}{x^{2}-4 }[/tex]
The given functions in GeoGebra and determine by analytically checking:
a. function type is [tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]
b. Domain and range Range (-2, +2).
c. Asymptotes is HA = 2 and VA = ±2
The function y = f( x) is classified into different types of functions, grounded on factors similar as the sphere and range of a function, and the function expression. The functions have a sphere x value that's appertained as input. The sphere value can be a number, angle, numeric, bit.
[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]
Functions in mathematics can be compared to the operations of a dealing (soda pop) machine. When you put in a certain quantum of plutocrat, you can elect different types of tonics. also, for functions, we input different figures and we get new figures as the result. sphere and range are the main aspects of functions.
[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]
x² = 4
x = ± 2
Range (-2, +2).
An asymptote is a line being approached by a wind but noway touching the wind. i.e., an asymptote is a line to which the graph of a function converges. We generally don't need to draw asymptotes while graphing functions. But graphing them using dotted lines( imaginary lines) makes us take care of the wind not touching the asymptote. Hence, the asymptotes are just imaginary lines.
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Complete question:
Represent the given functions in GeoGebra and determine by analytically checking: a. function type b. Domain and range c. Asymptotes, both vertical and horizontal, if it has them:
g when is welch's t-test used to compare two population means, and what distributional assumptions are needed?
In the following question, Welch's t-test is used to compare the means of two populations with unequal variances. It is a variation of the standard Student's t-test, which is used when the variances are assumed to be equal.
Welch's t-test is generally used when the sample sizes are small and the variances are significantly different.
The distributional assumptions that are needed for Welch's t-test include:
Normality - The data from each population must be normally distributed, although this assumption is not always strictly required for the test to be valid.
Equal variances - The variances of the two populations must be equal. In practice, this assumption is often difficult to satisfy, particularly when the sample sizes are small. Welch's t-test does not require the assumption of equal variances.
Independence - The samples from each population must be independent of each other. This means that the observations in one sample should not be related to the observations in the other sample.
Welch's t-test is a parametric test, which means that it is based on assumptions about the underlying distribution of the data. If the distributional assumptions are not met, then the test may not be valid. In such cases, non-parametric tests may be used instead, such as the Wilcoxon rank-sum test.
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the first pentagon is dilated to form the second pentagon. drag and drop the answer to correctly complete the statement.
Hence, the correct answer to the question is: The second pentagon is either an enlargement or a reduction of the first pentagon, depending on the dilation factor.
The first pentagon is dilated to form the second pentagon. Drag and drop the answer to correctly complete the statement.The dilation is a transformation in which a figure is resized without changing its shape. It is an enlargement or a reduction of a geometric figure that maintains its similarity.
Therefore, if the first pentagon is dilated, the second pentagon will be an enlarged or a reduced form of the original pentagon.Since it is a dilation, the ratio of the corresponding sides of the pentagon will remain the same. Also, the angles of the pentagon will remain the same. Hence, both the pentagons will be similar to each other. The second pentagon will either be an enlargement or a reduction of the first pentagon. It will also have the same number of vertices and edges as the first pentagon.However, the size of the second pentagon will depend on the dilation factor. If the dilation factor is greater than 1, then the second pentagon will be an enlargement of the first pentagon. If the dilation factor is less than 1, then the second pentagon will be a reduction of the first pentagon.
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Which of the following is a cofactor for some enzymes and is a mineral whose primary route of excretion is through the feces and trace amounts in the urine?
A) chloride
B) copper
C) iron
D) manganese
E) calcium
Iron is required for the production of hemoglobin, which carries oxygen in red blood cells. It is also necessary for the functioning of many enzymes involved in energy metabolism.
The correct answer is (B) magnesium. Magnesium is a cofactor for some enzymes and is a mineral whose primary route of excretion is through the feces and trace amounts in the urine.
What is a cofactor?
A cofactor is a non-protein chemical that helps enzymes function correctly. It can be a metal ion or a small organic molecule. Cofactors work in tandem with the enzyme's active site to help catalyze reactions. Enzymes are protein molecules that assist in biochemical reactions, with each enzyme being specific to a certain reaction. Enzymes act as a catalyst by lowering the energy barrier required for a reaction to occur.
Magnesium is a cofactor for many enzymes that help to regulate nerve and muscle function, as well as glucose metabolism. It is needed for the production of proteins, DNA, and RNA, and it is a vital component of bone health. Magnesium is also necessary for the regulation of heart rhythm and blood pressure. Magnesium deficiencies can lead to muscle weakness, tremors, and seizures. The mineral magnesium's primary route of excretion is through the feces, with trace amounts being excreted in the urine.Calcium is an essential mineral that is involved in the formation and maintenance of bones and teeth, as well as blood clotting, nerve function, and muscle contraction.
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For what real numbers x is the value of x2
– 6x + 9 negative?
Answer:
Step-by-step explanation:
EZ
its 21
which formula would you use to calculate the total enclosed space of firms 2’s structure?
Answer:
Firm 2's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,
Volume = πr²h
where r = radius of the structure
h = height of the Firm
By substituting the values of 'r' and 'h' in the given formula,
V =
�
(
70
2
)
2
(
60
)
π(
2
70
)
2
(60)
=
�
(
35
)
×
60
π(35)×60
= 6597.345
≈ 6597.35 cubic feet
Total enclosed space of Firm 2 is 6597.35 cubic feet.
g calculate the labor force participation rate if you know that the adult working-age population is 320 million, 114 million of which are not in the labor force. what is the labor force participation rate? (round your answer to the nearest tenth.)
The labor force participation rate is 64.4%.
To calculate the labor force participation rate, we need to know the number of people who are either employed or actively seeking employment. We can calculate this as follows:
Labor force = adult working-age population - not in labor force
Labor force = 320 million - 114 million
Subtract the numbers
Labor force = 206 million
So the labor force participation rate is
Labor force participation rate = (labor force / adult working-age population) x 100%
Substitute the values in the equation
Labor force participation rate = (206 million / 320 million) x 100%
Labor force participation rate = 64.4%
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I need help ASAP please Just looking for an answer
Answer:
B
Step-by-step explanation:
there are 3 soccer games in a month, and 8 are played at night. the season is 4 months. how many games are the season?
There are a total of 48 soccer games in the season.
Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:
Number of day games = Total number of games - Number of night games
= 12 games/month x 4 months - 8 night games/month x 4 months
= 48 games - 32 games
= 16 games
Therefore, the total number of games in the season is:
Total number of games = Number of day games + Number of night games
= 16 games + 32 games
= 48 games
So, there are 48 soccer games in the season.
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20 points and brainly fast please!
Answer:
C
Step-by-step explanation:
Hellppppppppppppppppp
Answer:
Step-by-step explanation:
asdfasdf
I ask you, to solve the system.
y=x2+2x-2
y=x+10
Answer:
y = 22 - x2 or x = 12 - x2
Step-by-step explanation:
Find the value of x.
The value of x is 5
What is a chord?A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. All diameters are chord and but all chords are not diameter.
Since the value of the chords are thesame, the arc length RS and PQ are thesame.
Therefore ;
x+17 = 4x+2
collect like terms
4x -x = 17-2
3x = 15
divide both sides by 3
x = 15/3
x = 5
therefore the value of x is 5
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solve for a "7a = 14"
Answer: a=2
7a=14
a=14/7
a=2
noah sold 30 avocados that were small and large. he sold the small avocados for 35 cents and the large ones for 50 cents. if noah made $13.50, how many of each kind did he sell?
Noah sold 10 small avocados and 20 large avocados.
Let's assume that Noah sold "x" small avocados and "y" large avocados.
From the given information, we can write two equations:
x + y = 30 (since Noah sold a total of 30 avocados)
0.35x + 0.50y = 13.50 (since Noah made $13.50)
Now, we can use any method to solve these equations, such as substitution or elimination. Here, we will use the substitution method:
From the first equation, we can write:
x = 30 - y
Substituting this value of x in the second equation, we get:
0.35(30 - y) + 0.50y = 13.50
Simplifying this equation, we get:
10.50 - 0.35y + 0.50y = 13.50
0.15y = 3
y = 20
Substituting this value of y in the equation x = 30 - y, we get:
x = 30 - 20 = 10
Therefore, Noah sold 10 small avocados and 20 large avocados.
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kevin and micah collect seashells on the beach. the table shows the number of broken and whole seashells each person collects. if kevin collects 200 shells and micah collects 100 shells, who would be expected to have more whole seashells?
Kevin is expected to have more whole seashells, with [tex]75[/tex]% of his collection being whole seashells, compared to Micah's [tex]60[/tex]%.
What is the ratio?To determine who is expected to have more whole seashells, we need to compare the ratio of whole seashells to the total number of seashells collected for each person.
Person Whole Seashells Broken Seashells Total Seashells
Kevin 150 50 200
Micah 60 40 100
To calculate the ratio of whole seashells to total seashells, we divide the number of whole seashells by the total number of seashells, and then multiply by 100 to get a percentage:
Kevin: 150/200 [tex]\times[/tex] 100 = [tex]75[/tex]%
Micah: 60/100 [tex]\times[/tex] 100 = [tex]60[/tex]%
Therefore, Kevin is expected to have more whole seashells, with [tex]75[/tex]% of his collection being whole seashells, compared to Micah's [tex]60[/tex]%.
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The complete question is: Kevin and Micah collected seashells on the beach. The table below shows the number of broken and whole seashells each person collected. If Kevin collected 200 shells and Micah collected 100 shells, who is expected to have collected more whole seashells?
Broken Seashells Whole Seashells
Kevin 70 130
Micah 40 60
what is the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud?
There is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
To find the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud, we need to use the formula for the margin of error:
[tex]$$E = z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$[/tex]
where E is the margin of error, [tex]$z_{\alpha/2}$[/tex] is the critical value for the desired confidence level (let's assume 95%, so [tex]$z_{\alpha/2} = 1.96$[/tex]), p is the population proportion of websites experiencing click fraud, and n is the sample size.
We know that p=0.15, so we can plug in the values:
[tex]$$E = 1.96\sqrt{\frac{0.15(1-0.15)}{400}} = 0.05$$[/tex]
So the margin of error is 0.05. This means that there is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
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1. use the quadratic equation to find the exact solutions to this equation, and simplify your answer: 2x^2 6x 12
As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].
To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.
Substituting these values in the quadratic formula, we get
[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]
Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]
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Please help with 14!! 30 points please give a correct answer
Answer:
r=8
Step-by-step explanation:
a. -3(6-r)=6
-18+3r=6
3r=6+18
3r=24
r=[tex]\frac{24}{3}[/tex]
r=8
b. 3r instead of -3r
Help please Hurry
Brenda throws a dart at this square shaped target: Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)
The probability of hitting the black circle is closer to 0 and the probability of hitting the white portion of the target is closer to 1.
What is probability?
Probability refers to the numerical measure of the likelihood or possibility of a specific event taking place. It is a mathematical concept that involves calculating the ratio of the number of desired outcomes to the total number of possible outcomes. Probability ranges from 0 (representing an impossible event) to 1 (representing a certain event), with values in between indicating the degree of likelihood. Probability is widely used in various fields, including mathematics, statistics, science, engineering, finance, and social sciences, to make predictions, analyze data, and make decisions under uncertainty.
Explanation of the given questions :
Part A: The black circle has a radius of 1 unit and its center is the same as that of the square. Therefore, its diameter is 2 units, which is much smaller than the side length of the square, which is 11 units. This means that the area of the circle is much smaller than the area of the square.
Therefore, the probability of hitting the black circle is closer to 0.
Part B: The white portion of the target is the area of the square minus the area of the black circle. The area of the square is [tex]11 x 11 = 121[/tex] square units.
The area of the circle is [tex]\pi \times r^2 = \pi\times 1^2 = \pi[/tex] square units, which is approximately 3.14 square units. Therefore, the area of the white portion of the target is [tex]121 - 3.14 = 117.86[/tex] square units.
Since this is much larger than the area of the black circle, the probability of hitting the white portion of the target is closer to 1.
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Helen flips a coin and rolls a dice calculate the probability of getting 4 and tails
Answer:
1/12 or 0.0833
Step-by-step explanation:
P(Coin) = 1/2
P(Dice) = 1/6
1/2 × 1/6 = 1/12