Answer:
B) Its final coordinates are (8,-6)
Step-by-step explanation:
1. Translated 1 unit up and 4 units left
(-2,7) becomes (-6, 8)
2. Reflected about the x-axis
(-6,8) becomes (-6, -8)
3. Rotated 90° anticlockwise about the origin
(-6, -8) becomes (8, -6) because when rotating 90 degrees anticlockwise about the origin, point A (x,y) becomes point A' (-y,x). In other words, switch the x and y and make y negative.
f(x) = x - 1. Find the inverse of f(x).
Answer:
f^-1 (x) = x+1
Step-by-step explanation:
f(x) = x-1
y = x-1
Exchange x and y
x = y-1
Solve for y
Add 1 to each side
x+1 = y-1+1
x+1 = y
The inverse is x+1
f^-1 (x) = x+1
2. Solve for z and express your answer in interval notation: 10 – 4z<20
Answer:
I belive its z > -5/2
Step-by-step explanation:
First subtract 10 from both sides.
Then simplify
Then multiply both sides by -1 because you're reversing the inequality
simplify again
Then divide both sides by 4
Finally you simplify to get
z > -5/2
:)
Find the area of the shaded regions.
Answer:
around 22, or 21.98
Step-by-step explanation:
[tex]s1 = {r}^{2} \times \pi = 9 \times 3.14 = 28.26[/tex]
[tex]s2 = 1 \times 3.14 = 3.14[/tex]
[tex]s3 = 28.26 - (3.14 \times 2) = 28.26 - 6.28 = 21.98[/tex]
Which graph represents the equation x2 = 8y? On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 8), and a directrix at y = negative 8. On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 2), and a directrix at y = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (2, 0), and a directrix at x = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (8, 0), and a directrix at x = negative 8.
Answer:
The parabola x²=8y has,
vertex: (0,0)
focus: (0,2)
directrix: y=-2
so that option is the answer,
btw, the parabola opens up to the top and axis of symmetry is x=0
Answer:
It's A!
Step-by-step explanation:
Got it correct on my test! :)
a special window in the shape of a rectangle with semicircles at each end is to be constructed so that the outside perimeter is 100 feet. find the dimensions of the rectangle tha tmaximizes the total area of the window
Answer:
The dimensions of the rectangle are length 25 feet and width 15.92 feet
Step-by-step explanation:
Let L be the length of the rectangle and w be the width.
The area of the rectangular part of the shape is Lw while the area of the two semi-circular ends which have a diameter which equals the width of the rectangle is 2 × πw²/8 = πw²/4. The area of each semi-circle is πw²/4 ÷ 2 = πw²/8
So, the area of the shape A = Lw + πw²/4.
The perimeter of the shape, P equals the length of the semi-circular sides plus twice its length. The length of a semi-circular side is πw/2. So, both sides is 2 × πw/2 = πw
P = πw + 2L
Since the perimeter, P = 100 feet, we have
πw + 2L = 100
From this L = (100 - πw)/2
Substituting L into A, we have
A = Lw + πw²/4.
A = [(100 - πw)/2]w + πw²/4.
A = 50w - πw²/2 + πw²/4.
A = 50w - πw²/2
Now differentiating A with respect to w and equating it to zero to find the value of w which maximizes A.
So
dA/dw = d[50w - πw²/2]/dw
dA/dw = 50 - πw
50 - πw = 0
πw = 50
w = 50/π = 15.92 feet
differentiating A twice to get d²A/dw² = - π indicating that w = 50/π is a value at which A is maximum since d²A/dw² < 0.
So, substituting w = 50/π into L, we have
L = (100 - πw)/2
L = 50 - π(50/π)/2
L = 50 - 50/2
L = 50 - 25
L = 25 feet
So, the dimensions of the rectangle are length 25 feet and width 15.92 feet
 In one of the examples he is working on, he knows that the two coordinates (0,6) and
(8, 10) are on the function that he is deriving. Using the information from these two
coordinates, determine the slope and y-intercept of the function Mike is looking for, and
then write out the correct function.
9514 1404 393
Answer:
y = 1/2x + 6
Step-by-step explanation:
The slope m is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (10 -6)/(8 -0) = 4/8 = 1/2
The y-intercept is given by the formula ...
b = y -mx
b = 6 -(1/2)(0) = 6
Then the slope-intercept equation is ...
y = mx +b
y = 1/2x +6
giả sử tỷ lẹ bệnh nhân tại 1 thành phố là a%
khám ngẫu nhiên b người tại thành phố này tính khả năng 2B + A người có bệnh
Answer:
ask in English then I can help u
Hector's Position:
Hector was standing halfway between first and second base, at the grass line. The
grass line is 95 feet from the pitcher's mound.
6. Calculate the coordinates for Hector's position. [Note: We can assume that 95
feet is an approximately horizontal distance from the pitcher's mound to the grass
line.] (2 points: 1 for x, 1 for y)
Hector was standing at the coordinate ( __, _).
Calculate Hector's Throw:
Answer:
(137.78, 47.72)
Step-by-step explanation:
(I just finished this assignment.)
Tre's position at the pitcher's mound as the point (42.78, 42.78).
( x , y )
Hector is about 95 feet away from the pitcher's mound horizontal, (x axis).
Since we already have the correct y-coordinate, we need to solve for the correct x-coordinate.
x = 95 + 42.78
↓ ↓ ↓
95 + 42.78 = 137.72
Now all you need to do is write out the coordinates.
Hector's coordinates are (137.72, 47.78 )
2.
The reflector of a satellite dish is in the shape of a parabola with a diameter of 4 feet and a depth of 2 feet. To get the maximum reception we need to place the antenna at the focus.
a. Write the equation of the parabola of the cross section of the dish, placing the vertex of the parabola at the origin. Convert the equation into standard form, if necessary. What is the defining feature of the equation that tells us it is a parabola?
b. Describe the graph of the parabola. Find the vertex, directrix, and focus.
c. Use the endpoints of the latus rectum to find the focal width.
d. How far above the vertex should the receiving antenna be placed?
Answer:
Step-by-step explanation:
Assume the dish opens upwards. The cross-section through the vertex is a parabola. You know three points on the parabola: (0,0), (2,2), and (-2,2). Plug the points into y = ax² + bx + c to get a system of three equations where a=0.5, b=c=0.
Equation of parabola: y = 0.5x²
:::::
Vertex (0,0)
Focal length = 1/(4×0.5) = 0.5
Focus (0,0+0.5) = (0, 0.5)
Directrix y = 0-0.5 = -0.5
:::::
At endpoints of latus rectum, y = 0.5
x = ±√0.5 = ±√2/2
Focal width = 2×√2/2 = √2
:::::
Place antenna at focus, (9,2)
I NEED HELP PLEASE! Can someone help me with the last two red boxes please? The rest of the question is for reference. Thank you for your time!
Answer:
I think you can go with:
The margin of error is equal to half the width of the entire confidence interval.
so try .74 ± [tex]\frac{.032}{2}[/tex] = [ .724 , .756] as the confidence interval
Step-by-step explanation:
I need help ASAP thank you
9514 1404 393
Answer:
C
Step-by-step explanation:
The graph shows two vertical asymptotes, so the relevant function will be zero in the denominator for two different x-values. The only possibility is ...
[tex]F(x)=\dfrac{1}{(x-1)(x+1)}[/tex]
Hi I need help this is a FOIL problem
Answer:
you should be able to find the mistake if you know FOIL well
Step-by-step explanation:
F: first digit in both binomials
O: outermost digits in both binomials
I: two most innermost digits
L: last two digits in both binomials
Find the absolute maximum and absolute minimum for f (x )equals x cubed minus 2 x squared minus 4 x plus 2 on the interval 0 less or equal than x less or equal than 3.
9514 1404 393
Answer:
maximum: 2minimum: -6Step-by-step explanation:
The extrema will be at the ends of the interval or at a critical point within the interval.
The derivative of the function is ...
f'(x) = 3x² -4x -4 = (x -2)(3x +2)
It is zero at x=-2/3 and at x=2. Only the latter critical point is in the interval. Since the leading coefficient of this cubic is positive, the right-most critical point is a local minimum. The coordinates of interest in this interval are ...
f(0) = 2
f(2) = ((2 -2)(2) -4)(2) +2 = -8 +2 = -6
f(3) = ((3 -2)(3) -4)(3) +2 = -3 +2 = -1
The absolute maximum on the interval is f(0) = 2.
The absolute minimum on the interval is f(2) = -6.
Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
[infinity]Σ n =1 (-1)^n - 1/n√n
Answer: hello your question is poorly written attached below is the complete question
answer:
The series is absolutely convergent
Step-by-step explanation:
To determine whether the series is absolutely or conditionally convergent or divergent. apply the Root Test
The series is absolutely convergent
attached below is the solution
What is 3a to the power of 4 times a to the power of 2
Answer:ldk
Applying exponential property,
Comparing the base,
Step-by-step explanation:
44y + 321x = 0 biết x=30000
Answer:
y= -240750/11
Step-by-step explanation:
44y + 321. 30000 = 0
44y = - 963000
y= -240750/11
constant of proportionality
Answer:
4.2
Step-by-step explanation:
Constant of proportionality = y/x = 8.4 / 2 = 4.2
It has been claimed from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm. Based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? Perform a hypothesis test for the population mean at alpha = 0.01.
a. Define the null and alternative hypotheses in mathematical terms as well as in words.
b. Identify the level of significance.
c. Include the test statistic and the P-value.
d. Provide your conclusion and interpretation of the results. Should the null hypothesis be rejected? Why or why not?
Diameters data frame of the first sample (showing only the first five observations)
diameters
0 3.46
1 2.64
2 1.89
3 2.56
4 2.09
Diameters data frame of the second sample (showing only the first five observations)
diameters
0 3.10
1 2.04
2 2.18
3 2.60
4 2.76
test-statistic = 2.06
two tailed p-value = 0.0394
Data for all 50 samples cannot be obtained, however, the solution below uses the 10 samples below to show how the hypothesis can be tested.
Answer:
Step-by-step explanation:
Average diameter, μ = 2.30
H0 : Average diameter is equal to 2.30cm
H1 : Average diameter is greater than 2.30 cm
The hypothesis :
H0 : μ = 2.30
H1 : μ > 2.30
Using the readings from the data above :
3.46, 2.64, 1.89, 2.56, 2.09, 3.10, 2.04, 2.18, 2.60, 2.76
Sample size, n = 10
Mean, xbar = ΣX/ n = 25.32 / 10 = 2.532
Sample standard deviation, s = 0.4973 (from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.532 - 2.30) ÷ (0.4973/√(10))
T = 1.475
The Pvalue :
Degree of freedom, df = n - 1 ; 10 - 1 = 9
Pvalue(1.475, 9) = 0.087
Decision region :
Reject H0 ; If Pvalue < α;
Since 0.087 > 0.01 ; we fail to reject the Null and conclude that there is no evidence to suggest that the average diameter is greater than 2.30 cm
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
Step-by-step explanation:
It's geometric. The nth term differs by -5 when compared to the n+1 term.
Sum 0 to n a(-5)^n-1 where a = 2
I think this is what you want, but there is also a formula. See below.
Sum = a (r^n - 1)/(r - 1)
There are 160 pages in a book.15% of the pages having pictures on them. How many
Pages do not have pictures on them?
Answer:
136
Step-by-step explanation:
15/100×160
=24
pages that doesn't have pictures=160-24
=136
A silo is built in the shape of a cylinder with a cone for a roof. If the height of the
cylinder is 5 m, the radius is 2.8 m and the slant height of the cone is 6,6 m,
determine the amount of material needed to create the rounded sides and conical
roof, Round to the nearest tenth of a cubic m.
9514 1404 393
Answer:
146.0 m²
Step-by-step explanation:
The lateral areas of the cylinder and cone are given by the formulas ...
A = πrs . . . . cone area; radius r, slant height s
A = 2πrh . . . . cylinder area; radius r, height h
__
The total area lateral area of the silo is ...
A = π(2.8 m)(6.6 m) +2π(2.8 m)(5 m) = π(2.8 m)(6.6 m +2(5 m)) = 46.48π m²
A ≈ 146.0 m² . . . area of sides and roof of silo
_____
Additional comment
The answer is requested in cubic meters. Area has units of square meters. There is nothing in this problem statement that seems to be requesting a volume, which is what would have units of cubic meters.
If a^2+b^2= 4 and ab = 5, what is the value of
(a+b)^2?
A. 10
B. 12
C. 14
D. 16
Answer:
14
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
FOIL
a^2 + ab+ab + b^2
Combine like terms
a^2 +2ab + b^2
Rearranging
a^2+b^2 +2ab
We know a^2+b^2 = 4 and ab= 5
4 + 2(5)
4+10
14
Answer:
C. 14.
Step-by-step explanation:
We use the identity:-
a^2 + b^2 = (a + b)^2 - 2ab
So 4 = (a + b)^2 - 2(5)
(a + b)^2 = 4 + 2(5)
= 14.
Angles CED and CBD subtend the same arc. Determine the measure of ∠CED.
Question options:
1)
100°
2)
150°
3)
310°
4)
50°
Answer:
[tex]50^{\circ}[/tex]
Step-by-step explanation:
Inscribed angles that form the same arc have the same angle measure, no matter where they lie on the circle. Since the measure of angle CBD forms the same arc as angle CED, the measure of angle CBD must be equal to the measure of angle CED, hence [tex]m\angle CED=\boxed{50^{\circ}}[/tex]
Answer:
the answer is 4)50°
Step-by-step explanation:
because it is same
Hi! I would appreciate if you could solve this for me. The question I need help with is question 41. Thank you. :)
Answer:
Expression: 7+7+9.5+6+9.5
Evaluation: 39 cm
Step-by-step explanation:
Let's write the numerical expression for the figure to the right. The perimeter is the addition of all sides of the figure. Therefore, we write 7+7+9.5+6+9.5 for our expression.
Now, to evaluate the expression, we just add them together. 7+7+9.5+6+9.5=39 cm.
I need the help ASAP please
Answer:
Option B
Answered by GAUTHMATH
1000 randomly selected Americans were asked if they believed the minimum
wage should be raised. 600 said "yes." What is the 99% confidence interval
for the proportion of Americans who believe that the minimum wage should
be raised?
Answer:i dont now
Step-by-step explanation:
Help anyone know this??
Answer:
plug n and r into the equation for the answers.
Step-by-step explanation:
Which confidence level would produce the widest interval when estimating the mean of a population based on the mean and standard deviation of a sample of that population? A. 60% B. 70% C. 80% D. 90%
Answer:
D. 90%
Step-by-step explanation:
it is within the 90th percentile
The confidence level of D. 90% would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population.
What is Confidence Interval?Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.
From the definition of the confidence interval itself, it is clear that the level with the widest interval will be the highest confidence level.
So if you need a wider interval for estimating the mean of a population from the mean and standard deviation, you need to take higher confidence level.
Here the options are 60%, 70%, 80% and 90%.
Here, the highest level is 90% which is the highest among the given levels.
Hence the confidence level is option D. 90%.
To learn more about Confidence Interval, click here :
https://brainly.com/question/22851322
#SPJ7
Choose the correct correspondence
Answer:
The Answer is K.
Step-by-step explanation:
K is the answer because it is the only other point on the line DK
Will give brainliest answer
Answer:
14 hours
Step-by-step explanation:
Take any two consecutive high tides and to find their x coordinatey and sub them..
