Answer:
C. 2
Step-by-step explanation:
A polynomial function has one or more real numbers as roots or zeros. These roots correspond to the values of x for which the function takes on the value of zero.
In this case, y = (x-2)(x+3)², we can factor the equation to find its zeros. The expression (x-2)(x+3)² can be factored into two terms: (x-2) and (x+3)².
The first term, (x-2), is equal to zero when x = 2, meaning that x = 2 is a root of the function.
The second term, (x+3)², is equal to zero when x = -3, meaning that x = -3 is another root of the function.
So, the function y = (x-2)(x+3)² has two roots, or zeros, at x = 2 and x = -3.
Ten thousand marbles were produced on a production line. The first 100 marbles off the line were taken and tested for roundness. Does this sampling result in a simple random sample? Yes, because each group of n items has an equal chance of being selected. No, because each group of n items does not have an equal chance of being selected. Yes, because each item has an equal chance of being selected. No, because each item does not have an equal chance of being selected.
No, because each item does not have an equal chance of being selected. That is option D.
What is a simple random sample?A simple random sample is defined as the type of random sampling where by a particular amount of data (subset) is being selected from the total population of data that is under study.
The simple random sampling method which is used by researchers has the following disadvantages such as:
It relies on the quality of the researchers performing the work.It can require a sample size that is too large.It must have a significant population or demographic at the beginning of the process.It does not provide a guarantee that the data conclusions will be accurate because not all the data have equal chance to be selected.Learn more about random sampling here:
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What is the value of x? enter your answer, as a decimal, in the box. Do not round your answer. X= a right triangle with vertices labeled as a, b, and c. Side c b is the base and the top vertex is a. Side a b contains a midpoint d. A line segment drawn from c to d bisects angle a c b into two parts labeled as a c d and b c d. Angles a c d and b c d are marked with single arc. Side a c is labeled as 4. Base c b is labeled as 7. 5. Segment a d is labeled as 3. Segment b d is labeled as x.
In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.
In right triangle ABC,
BC is the base.
Midpoint of AB is D.
CD bisects ACB.
Measure of ∠ACD = Measure of ∠BCD
AC = 4
BC = 7.5
AD = 3
BD = x
CD bisects angle ACB and intersect at midpoint of AB at point D.
This implies
BD / AD = BC / AC
⇒x / 3 = 7.5 / 4
⇒ x = ( 7.5 × 3 ) / 4
⇒ x = 22.5 / 4
⇒ x = 5.625
Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.
The above question is incomplete , the complete question is :
What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.
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A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place . Texts sent yesterday 29 211 130 21 21 19 67 60 O Help Copy to Clipboard Open Provide your answer below: Standard Deviation Variance- FEEDBACK Content attribution
Using a TI-83, TI-83 Plus, or TI-84 Population standard deviation is 56.4 and Population variance is 3178.5 .
To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the following steps:
Enter the data into a list on the calculator. To do this, press the STAT key, then select Edit. Enter the data into L1.
Calculate the sample mean by pressing STAT, then CALC, then 1-Var Stats. Make sure L1 is selected as the list, then press ENTER.
Find the population variance by pressing STAT, then CALC, then 2-Var Stats. Make sure L1 is selected as the list, then press ENTER. The variance will be displayed as sX².
Take the square root of the population variance to find the population standard deviation. To do this, press the MATH key, then select PRB, then select 5:√(. Enter the population variance, then press ENTER.
Using this method, we find that the population standard deviation is approximately 56.4 and the population variance is approximately 3178.5.
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Complete question is:
A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place .
Texts sent yesterday: 29 211 130 21 5 21 19 67 60 95
A company is making T shirts. They know that the probability of a shirt being defective is (.02).
The company makes a profit of $20 for every shirt they sell. However, each defective shirt costs
the company $35 in replacement costs. How much money does the company really make per
Shirt?
The amount of money the company makes per shirt $18.90
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The chances that event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes
= X/n
To calculate the expected profit per shirt, we need to consider the two possible outcomes:
the shirt is defective or not defective.
If the shirt is not defective, the company makes a profit of $20.
If the shirt is defective, the company incurs a cost of $35 and no profit.
The probability of a shirt being defective is 0.02, so the probability of a shirt not being defective is:
= 1 - 0.02
= 0.98.
Therefore, the expected profit per shirt can be calculated as:
Expected profit = (probability of not defective) x (profit per non-defective shirt)
+ (probability of defective) x (cost per defective shirt)
Expected profit = 0.98 x $20 + 0.02 x (-$35)
Expected profit = $19.60 - $0.70
Expected profit = $18.90
So the company really makes $18.90 per shirt, taking into account the cost of defective shirts.
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what is e and in
calculus for business
Question 10 of 20
What is the domain of the exponential function f(x)=3*-5?
O A. (-∞0, +00)
O B. (3,+00)
O C. (-∞0,-5)
O D. (-5,+00)
Answer: The answer is A. (-∞0, +00)
What benefits came from the collapse of communism in eastern europe? select three answers.
Greater freedom of movement, growing entrepreneurship, more contact with Western Europe.
three benefits came from the collapse of communism in eastern europe
Entrepreneurship is the creation or receipt of financial rewards. Under this definition, entrepreneurship is generally viewed as a change that involves more risk than is normally incurred when starting a business, and that may also involve value beyond its actual economic value.
An entrepreneur is a person who creates and/or invests in one or more groups while taking maximum risk and enjoying maximum return. [citation needed] The way to start a business is known as entrepreneurship. Entrepreneurs are usually seen as innovators, sources of new ideas, objects, offerings and ventures/technologies.
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What is the vertex for the graph below?
Answer:B
Step-by-step explanation: the graph moves x vertically -1 while y is moved vertically to 4
Help me with this question…..
The volume of the cone shown can be described to be A. 513 π cubic units
How to find the volume of a cone ?The volume of a cone can be found by the formula :
= π x radius ² x height / 3
The radius of this cone is 9 units and the height is 19 units.
The volume of this cone then is :
= π x radius ² x height / 3
= π x 9 ² x 19/ 3
= π x 81 x 19/ 3
= π x 513
= 513 π cubic units
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Finance. A person wishes to have $22,500 cash for a new car 3 years from now. How much should be placed in an
account now, if the account pays 4.8% annual interest rate, compounded weekly?
(Round to the nearest dollar.)
Answer:
$20,907
Step-by-step explanation:
To calculate the amount that needs to be placed in an account now to have $22,500 in 3 years, you can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = principal (the initial amount placed in the account)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = number of years
In this case, r = 0.048, n = 52 (since the interest is compounded weekly), and t = 3.
So, we have:
A = 22,500
P = ?
r = 0.048
n = 52
t = 3
Plugging these values into the formula:
22,500 = P * (1 + 0.048/52)^(52 * 3)
Solving for P, we get:
P = 22,500 / (1 + 0.048/52)^(52 * 3)
P = 22,500 / (1 + 0.048/52)^(156)
Rounding to the nearest dollar, we get:
P = $20,907
So, a person should place $20,907 in the account now, if the account pays 4.8% annual interest rate, compounded weekly, to have $22,500 in 3 years.
This net will be folded to form a prism.
A net of a rectangular prism. From top to bottom, the rectangles are labeled B, D, E, F. The left side is labeled A and the right side is labeled C.
Which pairs of faces will be opposite one another when the prism is created? Check all that apply.
D and F
A and C
A and B
B and F
B and E
B and C
E and F
A and F
Answer:
i think the answer is A and C, B and E
Answer:
D and F
A and C
B and E
Step-by-step explanation:
Triangle adb, point c lies on segment ab and forms segment cd, angle acd measures 90 degrees. Point a is labeled jungle gym and point b is labeled monkey bars. Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars?.
To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.
Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.
Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:
ad^2 + cd^2 = ac^2
We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:
bd^2 + cd^2 = ac^2
We also know that c lies on ab, so we can write:
ac = ab - bc
Substituting this into our equation, we get:
bd^2 + cd^2 = ab^2 - 2abbc + bc^2
Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:
bd^2 + y^2 = (x + y)^2 - 2xy + x^2
Simplifying, we get:
bd^2 - x^2 = 2xy - y^2
Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.
To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.
Since angle adb = angle bad, we can write:
2 angle adb + angle acd = 180 degrees
Substituting in the values of our angles, we get:
2 angle adb + 90 degrees = 180 degrees
Solving for angle adb, we get:
angle adb = 45 degrees
Now, we can use the fact that triangle adb is isosceles to write:
angle bad = (180 - 45)/2 = 67.5 degrees
Finally, we can use the law of sines to relate bd and x:
bd/sin(67.5) = x/sin(45)
Simplifying, we get:
bd = x
Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.
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find the vertical asymptotes
Answer: Vertical asymptotes are = [tex]-4, 1,4[/tex]
Horizontal asymptote = [tex]y=0[/tex]
Step-by-step explanation:
If you need explanation just say you want...
You purchase 5 action figures per week. You have 30 action figures, which is 40% of the total number of action figures you need to complete your collection. How many weeks until your collection is complete?
Answer: Let's call the total number of action figures you need to complete your collection "x". Based on the information given, we know that 30 action figures is 40% of x, so we can write the equation:
30 = 0.40x
To solve for x, we'll divide both sides of the equation by 0.40:
x = 30 / 0.40
x = 75
So, the total number of action figures you need to complete your collection is 75. Since you purchase 5 action figures per week, it will take you 75 / 5 = 15 weeks to complete your collection.
Step-by-step explanation:
When an accountant records on hand, they are noting a company’s
A. human resources; total liquid assets
B. cash; total of amount dollars, money orders, checks, and other forms of
money
W
C. supplies; materials that need to be purchased soon
D. inventory; number of employees on payroll
Answer:
The correct answer is D. inventory; number of employees on payroll. An accountant records on hand to note a company's inventory, which is the stock of goods available for sale or use in the production process. The number of employees on payroll refers to the human resources aspect of a company, which is separate from the inventory.
Suppose you deposit $1,000 into a
savings account that earns simple
interest. After 4 years, the savings
account balance is $1,200. Determine
the annual interest rate.
100
1000
The annual interest rate on the saving account is 5%.
What does an annual interest rate refers to?Also known as annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. Its represents the actual yearly cost of funds over the life of a loan or the income earned on an investment.
To determine our annual interest rate, we can use the formula for simple interest: I = Prt. We need to find "r" which is our interest rate.
Now, we know the interest earned (I = $200) and the principal (P = $1,000), we can substitute those values into the formula:
$200 = $1,000 * r * 4
r = $200 / ($1,000 * 4)
r = 0.05. Therefore, the annual interest rate is 0.05 or 5%.
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If the number x² y is a negative integer, then -y is a positive number
Answer: Yes, this statement is true. If the number x² y is a negative integer, it means that x² is a positive integer and y is a negative integer. Therefore, -y would be a positive number.
Step-by-step explanation:
Given the following observation for ortime serie X
t=1,2,3,4,5,6,7,8,9,10
Xt=47,64,23,71,38,64,55,41,59,48
Find
r(2)
Answer:t he autocorrelation of the time series X at lag 2 is approximately -0.018.
Step-by-step explanation:
To find the autocorrelation of the time series X at lag 2, we need to calculate the covariance between X(t) and X(t-2). This can be done using the following formula:
r(2) = cov(X(t), X(t-2)) / var(X(t))
where cov(X(t), X(t-2)) is the covariance between X(t) and X(t-2), and var(X(t)) is the variance of X(t).
To calculate the covariance, we'll use the following formula:
cov(X(t), X(t-2)) = sum((X(t) - mean(X(t))) * (X(t-2) - mean(X(t-2)))) / (n - 1)
where n is the number of observations in the time series. To calculate the variance, we'll use the following formula:
var(X(t)) = sum((X(t) - mean(X(t)))^2) / (n - 1)
First, let's calculate the mean of X(t):
mean(X(t)) = (47 + 64 + 23 + 71 + 38 + 64 + 55 + 41 + 59 + 48) / 10 = 51
Next, let's calculate the covariance between X(t) and X(t-2):
cov(X(t), X(t-2)) = sum((X(t) - 51) * (X(t-2) - 49)) / (10 - 1) = -10.3
Finally, let's calculate the variance of X(t):
var(X(t)) = sum((X(t) - 51)^2) / (10 - 1) = 563.7
Plugging in these values, we can find the autocorrelation at lag 2:
r(2) = cov(X(t), X(t-2)) / var(X(t)) = -10.3 / 563.7 = -0.018
So the autocorrelation of the time series X at lag 2 is approximately -0.018.
Expand and simplify (x + 2)(x + 1)
Answer:
x^2 + 3x + 2
Step-by-step explanation:
(x + 2) * (x + 1) =
= x * x + x * 1 + 2 * x + 2 * 1 =
= x^2 + x + 2x + 2 =
= x^2 + 3x + 2
Mark bought 4 pounds of bananas for $2.36 this week. Last week he paid $1.83 for 3 pounds of bananas. Which was the lower unit price?
Answer:
4 pounds
Step-by-step explanation:
2.36/4 = 0.59 cents a banana
1.83/3 = 0.61 cents a banana
Can anyone please solve this
The answers include the following:
61324318111566What is Addition?This is referred to as a mathematical operation in which two or more numbers or quantities are added together to form a sum.
3x = 18
x = 18/3 = 6
x+9 =22
x = 22-9 = 13
x/4 = 6
x = 6 × 4 = 24
x-12 =19
x = 19+12 =31
2x + 9 = 25
2x = 25-9 =16
x=16/2 = 8
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identify all the linear functions with a rate of change greater than or equal to 1.5
A student is trying to prove that the triangle XAB is similar to triangle XYZ.
Answer:
Below
Step-by-step explanation:
See image
L side goes from 3 units to 6 units so scale factor is 2
Answers for this photo?
The slope for:
1 = 1/2 (Option E)
2 = 2 (Option C)
3 = -1/2 (Option H)
4 = -2 (Option A)
What is slope in Maths?The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
The formula for slope (m) is given as:
m = Rise/Run = y2-y1/x2-x1
(x1,y1) = Coordinates of the first point in the line
(x2,y2) = Coordinates of the second point in the line.
1) The points are:
x1= -2
y1 = 2
x2 =2
y2 = 4
m = (4 - 2) / (2 - (-2))
m = 2 / 4
m = 1/2
Thus, Δy/Δx = 1/2
2) The points are:
x1= -1
y1 = -12
x2 =5
yx = 0
m = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
m = (0 - (-12)) / (5 - (-1))
m = 12 / 6
m = 2
Thus, Δy/Δx = 2
3) Where the points are:
x1= 2
y1 = -6
x2 = - 4
y2 = -3
Substituting the given values, we get:
m = (-3 - (-6)) / (-4 - 2)
m = 3 / (-6)
m = -1/2
Thus, Δy/Δx = -1/2
4) Where the points are:
x1= 0
y1 = 3
x2 = 1.5
y2 = 0
Substituting the given values, we get:
m = (0 - 3) / (1.5 - 0)
m = -3 / 1.5
m = -2
Thus, Δy/Δx = -2
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6-90. Evaluate the expression 10-2x for the x-values given below.
(show work)
a. x=2
b. x = 1/2
c. x = -2
Answer:
Step-by-step explanation:
Evaluate the expression 10 - 2x for the x-values given below.
a. x = 2 \quad b. x = \frac {1}{2}\quad c. x = -2
a.x=2b.x=
2
1
a.x=-2
RECAP NEED HELP PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
The required measure of angle x in the triangle is 35°.
What are trigonometric equations?
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
From triangle,
Sin x = perpendicular/hypotenuse
Sin x = 4/7
Sin x = 0.57
X =sin⁻¹(0.57)
X = 34.9
x = 35°
Thus, the required measure of angle x in the triangle is 35°.
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A young channel catfish weighs about 0. 1 pound. During the next 8 weeks, its weight increases by about 23% each week.
Weight is 0.229 pounds after 4 weeks.
As a young channel catfish only weights 0.1 pounds,
It gains weight over the following 8 weeks at a rate of roughly 23% every week.
In this case, the exponential growth function is as follows:
Exponential formulas are provided by.
[tex]y=a(1+r)^{x}[/tex]
where an is the starting amount, r is the growth rate, x is the duration, and y is the weight at the end of "x" weeks.
Our values are a = 0.1, r = 0.23 (or 23%), and t = 4.
As a result,
[tex]y=0.1(1+0.23)^{4} \\[/tex]
y = 0.1(2.289)
y = 0.229
Consequently, the weight at 4 weeks is 0.229 pound.
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Complete question:
A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.
A number, k, truncated to 2 d.p. is 47.00
Write an inequality to show the lower and
upper bounds of k. help quickly please!!!!!
MARK ME BRAINLIEST TOO!! :)
The lower and upper bounds of h - k are 42.31 and 42.49 respectively.
Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.
The upper and lower bounds can be written using error intervals
The lowest value of h is 47.15
The greatest value of h is 47.24
The greatest value of k is 4.84
The lowest value of k is 4.75
Thus upper bound of h -k = 47.24 - 4.75 = 42.49
Thus lower bound of h -k = 47.15 - 4.84 = 42.31
Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively. dont forget mark me brainliest
Write down all of the options which are true of
similar shapes.
They must be the same shape
They can be different shapes
They must be the same size
They can be different sizes
All of the options which are true of similar shapes include the following:
A. They must be the same shape.
D. They can be different sizes.
What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied.
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Phythagorean inequality
The Pythagorean inequality is given below.
Statement of Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
[tex]AC^{2}=AB^{2} +BC^{2}[/tex]
Let ABC be a triangle with the longest side opposite B
If the square of the longest side is greater than the sum of the squares of the two shorter sides, then the triangle is obtuse at BIf the square of the longest side is less than the sum of the squares of the two shorter sides, then the triangle is acute.If the square of the longest side is equal to the sum of the squares of the two shorter sides, then the triangle is right angled at B.We can also write as follows:
If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.
If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.
If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.
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