The given y = 2(x – 3)² – 6 is a function because one x-value maps to only one y-value.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
We are given y = 2(x – 3)² – 6.
Part A: Yes, the given is a function because one x-value maps to only one y-value.
As the function is not one-to-one due to one y-value sometimes can map to two x-values.
For the domain (3, + ∝), the relation is a one-to-one function.
Part B:
y = 2(x – 3)² – 6
y + 6 = 2(x – 3)²
(x – 3)² = y/2 + 3
x - 3 = ± √y/2 + 3
Thus, x = 3 ± √y/2 + 3
Hence y and [tex]y ^{-1}[/tex] are an inverse function
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3 comic books for $6.75FInd the unit rate
Answer:
$2.25 per comic book
Explanation:
To find the unit rate we need to divide the total cost of the comic books by the number of comic books. So,
$6.75/3 = $2.25 per comic book
Therefore, the unit rate is $2.25 per comic book
95 times 10 to the 4 power
There's a lack of info regarding the question, however if you are looking for the answer in scientific notation and expanded form, here you go.
Scientific Notation:
[tex]95[/tex] × [tex]10^4[/tex]
Expanded Form:
[tex]950,000[/tex]
Not what you're looking for? Feel free to comment on the matter and we'll see what else we can do to assist you further.
Suppose that scores on a recent statistics exam were normally distributed, that students in the 80th percentile of scores earned 85 points, and that students in the 30th percentile of scores earned 65 points. What was the mean of all exam scores in the class?.
The mean of all exam scores in the class is 72.67 ~ 73 . Mean is ratio of sum of score in all exam to the total numbers of all exams.
The exam scores are normally distributed , normally distributed is an arrangement in which most of values in middle and rest are symmetrically distributed at the ends 80th percentile of scores earned 85 it implies that 80% of students score is 85 or less and 30th percentile of scores earned 65 means 30% of students score is 65 or less .
Z-score value for 80th percentile is 0.841
Z-score value for 30th percentile is – 0.524
Formula for normally distributed,
Z =( X – μ) / σ
where μ is mean of scores , σ is standard deviations of scores ,X is sample mean
For 80th percentile , X= 85 , Z= 0.841
0.841=( 85- μ) /σ ----(1)
-0.524= (65-μ) / σ ----(2)
Solving equations (1) and (2)
- (841/524)= (85-μ )/( 65-μ) => 841μ – 841(65) = -524μ +85(524)
⇒ 1365μ= 99,205 => μ= 72.67
So, the value of mean of scores obtained by students in a class is 72.67 ~ 73
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Question is in image and you don’t have to show work if you don’t want to
1) Since that angle is a central angle, then we can tell that the measure of the arc is the same as the measure of the central angle.
2) So now, let's write out the following formula:
[tex]A=\frac{\alpha}{360}\times\pi r^2[/tex]Note that this formula is valid for angles given in degrees.
3) We can plug into alpha the measure of the central angle as well as the radius:
[tex]\begin{gathered} A=\frac{135}{360}\times\pi(6)^2 \\ A=\frac{3}{8}\times36\pi \\ A=\frac{27}{2}\pi \end{gathered}[/tex]Thus, the answer is:
[tex]\frac{27}{2}\pi\:m²[/tex]6. a boat is being pulled into a dock by a rope attached to the bow of a boat and passing through a pulley on the dock that is 5 meters higher than the bow of the boat. if the boat is being pulled in at a rate of 4 meters per second, how fast is the boat approaching the dock when it is 10 meters from the dock?
When the boat is 10 m from the dock, it is approaching the dock at the rate of √125/10 m/s.
What is differential equation ?In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions. Applications frequently involve a differential equation that provides a connection between the three, functions that reflect physical quantities, derivatives that show the rates at which those values change, and derivatives that represent the rates of change.
CalculationLet x = distance of the boat from the dock at time t
y = length of rope at time t
Draw a right triangle with horizontal leg x, vertical leg 5, and hypotenuse y.
We know that dy/dt = -1 and want to find dx/dt when x = 10.
By the Pythagorean Theorem, x^2 + 5^2 = y^2.
2x(dx/dt) = 2y(dy/dt)
dx/dt = y(dy/dt) / x When x = 10, y2 = 100 + 25 = 125
So, y = √125
dx/dt = -√125 / 10
When the boat is 10 m from the dock, it is approaching the dock at the rate of √125/10 m/se
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URGENT!! HOMEWORK DUE TONIGHT!!
A dilation of a linear function will have a slope that is steeper or less steep than the slope of a parent function.
True or False
Step-by-step explanation: Stretches and compression change the slope of a linear function.
If the line becomes steeper, the function has been stretched vertically or compressed horizontally.
If the line becomes flatter, the function has been stretched horizontally or compressed vertically.
Horizontal Stretch/Compression by a factor of b
f(x)→ f(1• f(x→f(1 bx) • b > 1 stretches away from the y-axis.
• 0 < |b| < 1 compresses toward the y-axis.
• y-intercepts remain the same.
Vertical Stretch/Compression by a factor of a
• f(x) → a f(x) • a > 1 stretches away from the x-axis.
• 0 < |a| < 1 compresses toward the x-axis.
• x-intercepts remain the same.Stretches and compression's change the slope of a linear function.
If the line becomes steeper, the function has been stretched vertically or compressed horizontally.
If the line becomes flatter, the function has been stretched horizontally or compressed vertically.
Horizontal Stretch/Compression by a factor of b
• f(x)→f(1 bx) • b > 1 stretches away from the y-axis.
• 0 < |b| < 1 compresses toward the y-axis.
• y-intercepts remain the same.
Vertical Stretch/Compression by a factor of a
• f(x) → a f(x) • a > 1 stretches away from the x-axis.
• 0 < |a| < 1 compresses toward the x-axis.
• x-intercepts remain the same.Stretches and compression change the slope of a linear function.
If the line becomes steeper, the function has been stretched vertically or compressed horizontally.
If the line becomes flatter, the function has been stretched horizontally or compressed vertically.
Horizontal Stretch/Compression by a factor of b
• f(x)→f(1 bx) • b > 1 stretches away from the y-axis.
• 0 < |b| < 1 compresses toward the y-axis.
• y-intercepts remain the same.
Vertical Stretch/Compression by a factor of a
• f(x) → a f(x) • a > 1 stretches away from the x-axis.
• 0 < |a| < 1 compresses toward the x-axis.
• x-intercepts remain the same.
A boat takes off from the dock at 2.5 m/s and speeds up at 4.2 m/s2 for 6.0 s. How far has the boat traveled? Round your answer to the nearest whole number
The displacement of the boat is 91 meters approximately.
What are equations of motion?Three equations of motion can be used when the motion of the object is under constant acceleration and on a straight path.
They are listed below as:
[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]
Given the following data;
Initial velocity = 2.5 m/s
Acceleration = 4.2 m/s sq.
Time = 6.0 seconds
To determine the displacement of the boat, we will use the second equation of motion.
Mathematically, the second equation of motion is ;
[tex]s = ut + \dfrac{1}{2} at^2[/tex]
Where:
S is the displacement or distance.
u is the initial velocity.
a is the acceleration.
t is the time measured in seconds.
Now Substituting the values into the formula;
[tex]s = 2.5(6) + \dfrac{1}{2} (4.2) (6)^2\\\\\\s = 15+ 75.6 = 90.6[/tex]
Displacement, S = 91 meters approx.
Therefore, the displacement of the boat is 91 meters approximately.
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i need help with my homewrok PLEASE CHECK WORK number 3
Mr. Welsh
has a stating production of
f(1)=70
from the statement
He has determined that the production of eggs will increase each year to be the square of 60 eggs less than the previous year
previous year =fn
then
[tex](f_n-60)^2[/tex][tex]f_{n+1}=(f_n-60)^2[/tex]where
f(1)=70
then the correct answer is
option C
Please help me!! I seriously need an answer and a right one. 80 points. A pyramid has a square base that measures 20 inches on each side and 30 inches high. Find the volume of the pyramid.
Answer:
4000
Step-by-step explanation:
the formula for volume of pyramid is Base LX Base WXH divide by 3 so the base length is 20 inches and since it's a square the base width should also be 20 inches and the height is 30 inches so 20X20X30 divide by 3 would be the volume.
Evaluate the Expression: a(b-c) if a=-6, b=14, and c=7
Substitute -6 for a, 14 for b and 7 for c in the exprerssion a(b-c) to ontain the value of expression.
[tex]\begin{gathered} a(b-c)=-6(14-7) \\ =-6\cdot7 \\ =-42 \end{gathered}[/tex]So answer is -42.
The commercial jet that travels from Miami to New York averages about 300 mi/h. The air distance fromMiami to New York is 1092 miles. Write a function to represent the distance d remaining on the trip thours after takeoff.
1) We can write the following as a function to describe this distance remaining.
2) As time goes by the distance between Miami and NY decreases. So, we can write a decreasing linear function for that. Note that at t=0 there are 1092 miles between them.
3) Thus, the answer is:
[tex]d=1092-300t[/tex]A test tube is cylindrical in shape with a length of 152 mm and a radius of 6.5 mm. What is the volume of the test tube?Report your answer in mm' but do not include the unit mm in your answer box. Round your answer to the nearest wholenumber and do not include commas in your answer. The formula for volume of a cylinder is V = ar?h.
The formula for the volume of a cylinder is
[tex]V=\pi r^2h[/tex]Where
V is the volume of the cylinder
r is the radius of the cylinder
h is the height (or length) of the cylinder
Now,
Given,
r = 6.5 mm
h = 152 mm
Let's substitute the given values into the formula and figure out the volume of the cylinder. This is shown below:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(6.5)^2(152) \\ V=6422\pi \end{gathered}[/tex]Using a calculator and rounding the answer to the nearest whole number, we have:
[tex]\begin{gathered} V=6422\pi \\ V\approx20175.31 \\ V=20,175 \end{gathered}[/tex]AnswerVolume = 20,175 cubic millimeters
CB = 2x, BD = 4x and CD = 12. What is the value for x and BC if B is between C and D?
We can pose this question in the following way:
The value for x and BC are:
[tex]2x+4x=12\Rightarrow6x=12\Rightarrow\frac{6}{6}\cdot x=\frac{12}{6}\Rightarrow x=2[/tex]Then, x = 2. And BC is :
[tex]BC=2\cdot x=2\cdot2\Rightarrow BC=4[/tex]Which choices are equations for the line shown below? Check all that apply.(-2,5)(2-3)A. y + 3 = -2(x - 2)B. y-5=-2(x + 2)C. y = 2x+1D. y=-0.5x + 1Ey- 5 = -2(x - 2)
Given the points on the line:
(x1, y1) ==> (-2, 5)
(x2, y2) ==> (2, -3)
Let's find the equations that represent the line.
Apply the point-slope form:
y - y1 = m(x - x1)
Where m represents the slope, x1 and y1 represents the values of one point on the line.
To find the slope of the line apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Substitute values into the formula and solve for m:
[tex]\begin{gathered} m=\frac{-3-5}{2-(-2)} \\ \\ m=\frac{-3-5}{2+2} \\ \\ m=\frac{-8}{4} \\ \\ m=-2 \end{gathered}[/tex]Substitute -2 for m in the point-slope equation:
y - y1 = -2(x - x1)
Substitute the coordinates of each point for x1 and y1
At (-2, 5):
y - 5 = -2(x - (-2)) ==> y - 5 = -2(x + 2)
At (2, -3):
y - (-3) = -2(x - 2) ==> y + 3 = -2(x - 2)
The possible equations for line are:
• y - 5 = -2(x + 2)
• y + 3 = -2(x - 2)
ANSWER:
• A. y + 3= -2(x - 2)
• B. y - 5 = -2(x + 2)
g does a correlation of -0.7 or 0.8 give a larger coefficient or determination? we say that the linear relationship that has the larger coefficient of determination is more strongly correlated. which of the values shows a stronger correlation?
A correlation of + 0.8 gives a larger coefficient of determination and shows a stronger correlation.
Given that,
We say the linear relationship with the larger coefficient of determination is more strongly correlated when the correlation is greater, such as when it is -0.7 or 0.8.
A coefficient of correlation of +0.8 or -0.8 indicates a strong correlation between the independent variable and the dependent variable. An r of +0.20 or -0.20 indicates a weak correlation between the variables.
Therefore, A stronger correlation can be seen when there is a correlation of +0.8, which has a higher coefficient of determination.
A correlation of + 0.8 gives a larger coefficient of determination and shows a stronger correlation.
Given that,
We say the linear relationship with the larger coefficient of determination is more strongly correlated when the correlation is greater, such as when it is -0.7 or 0.8.
A coefficient of correlation of +0.8 or -0.8 indicates a strong correlation between the independent variable and the dependent variable. An r of +0.20 or -0.20 indicates a weak correlation between the variables.
Therefore, A stronger correlation can be seen when there is a correlation of +0.8, which has a higher coefficient of determination.
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Use the graph of f(x) and the description of g(x) to compare the functions.
The comparison results are as follows -
f(x) has greater y - intercept than that of g(x).g(x) has lesser relative minimum value than f(x)What is a function?A function is a relation between a independent variable and a dependent variable such that the value of dependent variable depends upon the independent one. For example -
f(x) = 4x + 5
h(x) = 7x + 9
Given are two functions such f(x) and g(x).
The y - intercept is a point on the y - axis where the graph of the function cuts the y - axis. It can be seen that the y - intercept[c] of f(x) has a positive value as it is above the origin and that of g(x) has a negative value. Therefore, f(x) has greater y - intercept than that of g(x). Mathematically - c[f(x)] > c[g(x)]
A relative minimum point is a point where the function changes direction from decreasing to increasing. The relative minimum point of f(x) has the coordinates (0.8, - 1.5) and that of g(x) is (-1, -2.25). Therefore, g(x) has lesser relative minimum value as -2.25 < -1.5.
Therefore -
f(x) has greater y - intercept than that of g(x).g(x) has lesser relative minimum value than f(x)To solve more questions on relative max. and min. points, visit the link below-
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I Need Assistance with a Question for my Friend. Thanks! I'll Mark Brainliest ONLY for Complete and Correct Answer, As Well As a Full Step-By-Step Explanation.
Select the equivalent expression. (3².5)³= ?
Only Choose One Of The Following
35.53
35.5
36.5
36.53
The value of the expression (9 × 5)³ given is 91125.
What is an expression?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the expression is illustrated as:
(3².5)³
It's important to solve the values in the parentheses first. This will be:
(3².5)³=
(9 × 5)³
= 45
= 45 × 45 × 45
= 91125
Note that the options you gave are incorrect based on the expression.
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What is the equation of the line that passes through the point (1,−3) and has a slope of -3?
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since the line has a slope of -3, equation of line is y = -3x + c.
Substitute (1,-3) into the equation to find c.
-3 = -3(1) + c
c = 0
Since y-intercept is 0, equation of line is y = -3x.
Equation of the line which passes through the point (1,-3) and the slope of the line is -3 is equal to y = -3x .
As given in the question,
Line passes through the point ( 1, -3) and the slope of the line is equal to -3.
Standard equation of the line passes through the point ( x₁ , y₁) and slope m is given by :
( y -y₁ ) / ( x - x₁ ) = m
Substitute the given value of the point ( x₁ , y₁) = (1, -3 ) and slope m = -3 in the standard form we get,
( y -(-3) ) / ( x - 1) = -3
⇒ ( y +3 ) = -3 ( x -1)
⇒ y = -3x + 3 - 3
⇒ y = -3x
Therefore, equation of the line which passes through the point (1,-3) and the slope of the line is -3 is equal to y = -3x.
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2 US Dollars is equivalent to 38.5 Mexican Pesos. A pair of pants cost 462 Mexican Pesos. How much do they cost in US Dollars?
Answer:
$24
Step-by-step explanation:
462/38.5 = 12
12 * 2 = 24
If the sample mean is 7, the hypothesized population mean is 4, and the standard error of the sample mean is 2, compute the test value needed for the z test.Question 11 options:1.503.00–3.00–1.50
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given values
[tex]\begin{gathered} mean(\mu)=7 \\ H_0=4 \\ Standard\text{ deviation\lparen}\sigma)=2 \end{gathered}[/tex]STEP 2: Write the formula to get the test value for the z test
[tex]z=\frac{\mu-H_0}{\sigma}[/tex]STEP 3: Find the test value n
[tex]\begin{gathered} By\text{ substitution,} \\ z=\frac{7-4}{2}=\frac{3}{2}=1.5 \end{gathered}[/tex]Hence, the tets value needed for the z test is 1.50
given the function f(x)= |x+5| find f(-10)
We have the following function:
[tex]f(x)=|x+5|[/tex]then, evaluating -10 we get:
[tex]f(-10)=|-10+5|=|-5|=5[/tex]therefore, f(-10)=5
the item to the trashcan. Click the trashcan to clear all your answers.Factor completely, then place the factors in the proper location on the grid.10b2 +17b+ 321234567890CDI+1345167NEXT QUESTIONASK FOR HELP
1) Let's factor completely this 2nd-degree polynomial, rewriting that 17b as the sum of two terms.
[tex]\begin{gathered} 10b^2+17b+3 \\ 10b^2+15b+2b+3 \end{gathered}[/tex]2) Now, let's group those factors and rewrite that as a product, placing outside the parentheses the GCD. Grouping the terms whose coefficient share the same
[tex]\begin{gathered} (10b^2+2b)+(15b+3) \\ 2b(5b+1)+3(5b+1) \\ \mathbf{(5b+1)(2b+3)} \end{gathered}[/tex]Thus this is the answer (in bold).
(some zs are something else but come up as z expect last one!) In A ABC, m ZA=62° and m ZB=39° In AXYZ, m ZY=39° and m ZZ = 790 Julie says that the triangles are congruent because all the corresponding angles have the same measure. Ramiro says that there is not enough information given to determine whether the triangles are similar, congruent, or neither. 1. Which student correct? (1 point) Explain your reasoning and include all relevant calculations. (2 points)
Answer
1) Julie is correct.
2) All of the explanation and calculation is provided below.
Ramiro is wrong because the information provided is sufficient to obtain all the other requiired information and determine if the two triangles are similar or not.
Explanation
To answer this question, we need to first note that the sum of angles in a triangle is 180°.
So, we need to first find the third angle for each of the two triangles described before answering the question.
In triangle ABC
Angle A = 62°
Angle B = 39°
Angle A + Angle B + Angle C = 180°
62° + 39° + Angle C = 180°
101° + Angle C = 180°
Angle C = 180° - 101°
Angle C = 79°
In triangle XYZ
Angle Y = 39°
Angle Z = 79°
So,
Angle X + Angle Y + Angle Z = 180°
Angle X + 39° + 79° = 180°
Angle X + 118° = 180°
Angle X = 180° - 118°
Angle X = 62°
So, we can see that the three angles for the two triangles are the same.
And one of the conditions for two triangles to be congruent is for all of their corresponding angles to be the same measures.
1) Hence, Julie is correct.
2) All of the explanation and calculation is provided above.
Ramiro is wrong because the information provided is sufficient to obtain all the other requiired information and determine if the two triangles are similar or not.
Hope this Helps!!!
15.6 cm15.6 cm111111118.10.2 m1C
a We want to obtain the area of a circle of radius 15.6cm.
[tex]A=\pi r^2[/tex]Here, r = 15.6cm so that;
[tex]\begin{gathered} A=15.6^2\pi \\ A=243.4\pi \end{gathered}[/tex]1( If a company's expenses for a month are $35,000 and they earn a profit of $101 550 what was the company's total amount of income?
2( Why was it helpful to solve i first when solving the problem
The company's total amount of income that is earned is $136,500.
What is the total income?Profit is the difference between revenue and expenses. Income is the total revenue that is earned by a company before any deductions. Expenses include all the cost incurred in running a business. Income is the sum of profit and expenses. A venture is profitable only if the revenue is greater than expenses.
Profit = income - expenses
Income = profit + expenses
$35,000 + 101,500 = $136,500
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write down the root of f(x)=0
The root for the function f(x) = 0 is 0.
Given,
The function, f(x) = 0
We have to find the root of the function.
Root of a function;
The values of x for which a function, f(x), equals 0 are called the roots of the function. The only root, in the case of the function f(x)=2x f(x) = 2x, would be x=2, as that number results in f(x)=0 f(x) = 0.
So,
Here; the function f(x) = 0 is f(0)
The value of f(0) = 0
Root of 0 is 0.
Then,
The root for the function f(x) = 0 is 0.
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n a study of 1228 randomly selected medical malpractice lawsuits, 856 were later dropped or dismissed. construct a 99% confidence interval for the true proportion of the medical malpractice that were dropped or dismissed. explain the meaning
The 99% confidence interval for the actual percentage of medical malpractice cases that were either rejected or dropped is |Z|= 13.784
We are open to the alternative theory that
The proportion of medical malpractice cases that are settled or rejected varies from the proportion that proceed to trial.
Our null and alternative hypotheses are initially written down.
H0: No distinction
H1: There is a distinction
n = 1228
P = 856
X = n-p
= 372
Z is equal to (((x+0.5)-1228/2 divided by 1228/2).
= 372.5 - 614/17.52
= -13.784
|Z|= 13.784
Because there is evidence suggesting a lawsuit will be dismissed if the value is greater than 0.5, the choice is made to reject the null hypothesis and embrace the alternative. Therefore, there are distinctions between lawsuits that proceed to trial and those that are dismissed.
The actual percentage of medical malpractice cases that were either rejected or abandoned has a 99% confidence interval of |Z|= 13.784
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I need help with this practice problem solving It is trigonometry I will send an additional pic to you, it’s a graph, use the graph to answer the problem****
we have the function
f(x)=sinx+2
using a graphing tool
see the attached figure
Convert the ordered pairs to points without pi
so
(0,2) ------> (0,2)
(pi/2,3) ----> (1.57,3)
(3pi/2,1) ----> (4.71,1)
(-pi/2,1) ---> (-1.57,1)
(-3pi/2,3) ---> (-4.71,3)
Plot the ordered pairs, and join them to graph the function in your sheet
8) Given m∠ABC is 124 and m∠ABD IS 37, find m∠DBC.
To obtain the measure of the missing angle, subtract the measure of ∠ABD from the measure of ∠ABC. Note that m∠ABD + m∠DBC = m∠ABC.
[tex]m\angle DBC=m\angle ABC-m\angle ABD[/tex]Thus, we have:
[tex]m\angle DBC=124\degree-37\degree=87\degree[/tex]At a fundraising event, Keith is drawing raffle tickets to determine winners. Keith has already drawn a ticket for the 1st prize and will next draw a name for the 2nd prize. Are these 2 events dependent or independent?
ANSWER
Dependent
EXPLANATION
We want to determine if the two events are dependent or independent.
Two events are said to be dependent if the occurrence of the first event affects the probability of the occurrence of the second event.
Two events are said to be independent if the occurrence of the first event does not affect the probability of the occurrence of the second event.
After the ticket for the first prize is drawn from the raffle, the total number of tickets will change and so, the probability of drawing a ticket for the second prize will be different from what it originally was.
This implies that the picking of the first ticket affects the probability of the picking of the second ticket.
Hence, the two events are dependent.
