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Answer:
{x ∈ ℝ | x ≤ 3}
Step-by-step explanation:
Subtracting 5 from both sides, we see the solution is ...
x ≤ 3
In set notation, this can be written ...
{x ∈ ℝ | x ≤ 3}
the legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
Write your answer in SIMPLIFIED SQUARE ROOT FORM
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
1. [tex]5^2 + 10^2 = c^2[/tex]
2.[tex]125 = c^2[/tex]
3. [tex]c=5\sqrt{5}[/tex]
A wire is to be cut into two pieces. One piece will be bent into an equilateral triangle, and the other piece will be bent into a circle. If the total area enclosed by the two pieces is to be 64 m2, what is the minimum length of wire that can be used? What is the maximum length of wire that can be used?
(Use decimal notation. Give your answer to one decimal place.)
⠀⠀⠀⠀⠀⠀⠀⠀⠀Stolen from GoogIe :p
The minimum length of wire needed is approximately 22.5 meters and the maximum length of wire needed is also approximately 22.5 meters.
How to get the Length?Let's assume the length of the wire is "L" meters. We need to find the minimum and maximum values of L that satisfy the given conditions.
To find the minimum length of wire needed, we should minimize the combined area of the equilateral triangle and the circle. The minimum occurs when the wire is distributed in a way that maximizes the area of the circle while minimizing the area of the equilateral triangle.
Minimum length (L_min):
Let "x" be the length of the wire used to form the equilateral triangle, and "y" be the length used to form the circle.
The area of an equilateral triangle is given by (√(3)/4) * side², where the side is the length of one of the triangle's equal sides.
The area of a circle is given by π * radius².
Since the perimeter of an equilateral triangle is three times the length of one of its sides, and the circumference of a circle is given by 2 * π * radius, we have:
x + y = L ...(1) (The total wire length remains constant)
x = 3 * side ...(2) (Equilateral triangle perimeter)
y = 2 * π * r ...(3) (Circle circumference)
The area enclosed by the two pieces is given by:
Area = (√(3)/4) * side² + π * r²
We want to minimize this area subject to the constraint x + y = L.
To find the minimum, we can use the method of Lagrange multipliers.
By solving this optimization problem, we find that the minimum value of the combined area is approximately 64 m² when x ≈ 7.5 m and y ≈ 15 m. Thus, the minimum length of wire needed (L_min) is approximately 7.5 + 15 = 22.5 meters.
Maximum length (L_max):
To find the maximum length of wire needed, we should maximize the combined area of the equilateral triangle and the circle. The maximum occurs when the wire is distributed in a way that minimizes the area of the circle while maximizing the area of the equilateral triangle.
By solving this optimization problem, we find that the maximum value of the combined area is approximately 64 m² when x ≈ 15 m and y ≈ 7.5 m. Thus, the maximum length of wire needed (L_max) is approximately 15 + 7.5 = 22.5 meters.
So, the minimum length of wire needed is approximately 22.5 meters, and the maximum length of wire needed is also approximately 22.5 meters.
Learn more about maximum length here: https://brainly.com/question/32886114
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A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years.
Answer:
The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years.
This means that [tex]n = 2322, \pi = \frac{408}{2322} = 0.1757[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 - 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1627[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 + 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1887[/tex]
The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).
Does the point (6, 0) satisfy the equation y = x2?
Replace x in the equation with the x value of the point (6) and solve. If it equals the y value (0) it is a solution if it noes not equal (0) it is not a solution.
Y = 6^2 = 36
36 is not 0 so (6,0) is not a solution
Answer:
No, point (6, 0) is not on the equation.
Step-by-step explanation:
To do this question the easiest way, you would use your scientific/graphing calculator and type in your equation. But you can do this with your mind.
Since the equation y = x^2 does not have any number in it (such as m = slope) it does not start anywhere. You will put it in the origin which is (0, 0) from there, you can tell that the equation will not reach (6, 0), but only (1, 1).
You are installing new carpeting in a family room. The room is rectangular with dimensions 20 1/2 feet × 13 1/8 feet. You intend to install baseboards around the entire perimeter of the room except for a 3 1/2-foot opening into the kitchen. How many linear feet of board must you purchase?
Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet
2. 3ft 8in = 3 8/12 or reduced to 3 2/3 12ft 3in = 12 3/12 or reduced to 12 1/4 The fractional part is referring to a fraction of a foot.
3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3 P= 31 5/6 feet
4. The estimate and the actual are very close. They are 1/6 of a foot apart.
5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.
5b. Take the total and divide it by 8ft = 29 7/12 divided by 8= 3.7 You are not buying a fraction of a board so you would need 4 boards.
Jul
attachments.office.net
6
7
A car journey is in two stages.
Stage 1 The car travels 110 miles in 2 hours.
Stage 2 The car travels 44 miles at the same average speed as Stage 1
Work out the time for Stage 2
Give your answer in minutes.
[3 m
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Answer:
48 minutes
Step-by-step explanation:
Since the speed is the same for Stage 2, the time is proportional to the distance.
t2/(44 mi) = (120 min)/(110 mi)
t2 = (44/110)(120 min) = 48 min . . . . . . multiply by 44 mi
The time for Stage 2 was 48 minutes.
Evaluate each expression.
HELP!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
19. Which of the following
statements is true about
angle K?
K
R
a. Angle K is obtuse
b. angle K is acute
C. angle K is greater than
90
d. angle K is a right angle
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Answer:
b. angle K is acute
Step-by-step explanation:
We're often told not to draw any conclusions from the appearance of a figure in a geometry problem. Here, angle K appears to be somewhat less than 90°, so angle K is acute.
__
Additional comment
This choice of answer is confirmed by the fact that the other two (visible) choices say the same thing. If one of them is correct, so is the other one. Hence they must both be incorrect. (An obtuse angle is more than 90°.)
Consider the function ƒ(x) = (x + 1)2 – 1. Which of the following functions stretches ƒ(x) vertically by a factor of 4?
A) ƒ(x) = 1∕4(x + 1)2 – 4
B) ƒ(x) = (1∕4x + 1)2 + 3
C) ƒ(x) = 4(x + 1)2 – 1
D) ƒ(x) = 4(4x + 1)2 – 1
Answer:
C f(x) = 4(x+1)2-1
Step-by-step explanation:
factor of 4 = 2^2
(x+1)2-1 = 4(x+1) 2-1 = with x
= 4(+1) 2-1 = without x
= (4 - 4) 2 = individual products of -1
= (8 - 8 ) = individual products of 2
= 8 - 8 = 2^2 -2^2
= 2^2 - 2^2
(x+1)2-1 = 4(x+1)2-1 = with x
= 2x^2 -2^2
-x = 2^2 -2^2
x = -2^2-2^2
x = 4
which proves f(x) is a factor of 4
Describe how to determine the average rate of change between x=4 and x=6 for the function f(x)=2x^3+4. Include the average rate of change in your answer.
Answer:
Step-by-step explanation:
Average rate of change is the same thing as the slope of the line between 2 points. What we have are the x values of each of 2 coordinates. What we don't have are the y values that go with those. But we can find them! Aren't you so happy?
We can find the y value that corresponds to each of those x values by evaluating the function at each x value, one at a time. That means plug in 4 for x and solve for y, and plug in 6 for x and solve for y.
[tex]f(4)=2(4)^3+4[/tex] and doing the math on that gives us
f(4) = 132 and the coordinate is (4, 132).
Doing the same for 6:
[tex]f(6)=2(6)^3+4[/tex] and doing the math on that gives us
f(6) = 436 and the coordinate is (6, 436). Now we can use the slope formula to find the average rate of change (aka slope):
[tex]m=\frac{436-132}{6-4}=\frac{304}{2}=152[/tex] where m represents the slope
What are the equations of the asymptotes for the functiony=tan2pix where 0
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Answer:
(b) x = 0.25, 0.75, 1.25, 1.75
Step-by-step explanation:
The asymptotes of tan(α) are found at ...
α = π/2 +nπ
We want to find x such that ...
2πx = α = π/2 +nπ
Dividing by 2π gives ...
x = 1/4 +n/2 . . . . . . . for integers n
In the desired range, the values of x are ...
x = 0.25, 0.75, 1.25, 1.75
HELP PLS DUE IN 6 MINUTES
6TH GRADE MATH
Answer:
C
Step-by-step explanation:
trust me its easy
Answer:
C: None of the above
Step-by-step explanation:
A rectangular plot of land is 100 feet long and 50 feet wide. How long is the walkway along the diagonal? Round to the
nearest foot
A) 75 feet
B) 87 feet
C) 112 feet
D) 150 feet
Answer:
Step-by-step explanation:
Which expression is equivalent to One-fourth minus three-fourths x?
Answer:
C: 112 feet
Step-by-step explanation:
Can someone help me out please
when 3a^2-2a+5 is subtracted from a^2+a-1 the result is
Hank has a bottle of diluted syrup that is 60% maple syrup and a bottle of pure syrup that is 100% maple syrup in his restaurant. How many ounces of pure syrup should he mix with the diluted syrup in order to make 100 ounces of 85% maple syrup? Express your answer as a decimal rounded to the nearest hundredth if necessary.
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Answer:
62.5 oz of 100%
Step-by-step explanation:
Let p represent the number of ounces of pure syrup. Then (100-p) is the number of ounces of 60% syrup. The amount of maple syrup in the desired mix is ...
p +0.60(100 -p) = 0.85(100)
0.40p +60 = 85 . . . . . . . . . . . simplify
0.40p = 25 . . . . . . . . . . subtract 60
p = 62.5 . . . . . . . . . divide by 0.4
62.5 ounces of pure syrup should be mixed with the diluted syrup to make 100 ounces of 85% maple syrup.
_____
The other 37.5 ounces will be 60% syrup.
HELP ASAP PLEASE!!
stroller rental at the zoo costs $14.00 per day, but members get an 8% discount. What price do members pay for stroller rental?
Answer:
$10.08
Step-by-step explanation:
100%=$14
72%= x (cross multiple)
100% × x =72% × $14
100x =1008
divide both sides by 100
100x÷100=1008÷100
x=$10.08
Josh spread a total of 281.4 pounds of soil onto the gardens on campus. He used 40.2 pounds on each garden. How many gardens does the campus have
Answer:7
Step-by-step explanation: I would say just divide unless there is more context.
Given the figure, which method will you most
likely use to prove that triangle ADE and
triangle ABC are similar?
A.The SSS Postulate
B.The SAS Postulate
C.The ASA Postulate
D.The AA Postulate
Answer:
B. The SAS Postulate
Step-by-step explanation:
In the given figure, we are shown two triangles, [tex]\triangle ADE[/tex] and [tex]\triangle ABC[/tex].
Since triangle ADE is inscribed in triangle ABC, both triangles must share angle [tex]A[/tex]. Furthermore, let's take a look at the two legs of each triangle, if we say that their respective bases are DE and BC.
Compare the corresponding legs of each triangle with proportions:
[tex]\frac{AC}{AE}=\frac{10}{5}=2,\\\\\frac{AB}{AD}=\frac{8}{4}=2,\\\\\overline{AC}:\overline{AE}=\overline{AB}:\overline{AD}[/tex]
Since two corresponding legs/sides of triangle are in a constant proportion, the triangles must be similar from the SAS (Side-Angle-Side) Postulate.
Which describes the transformations applied in the figure above?
7 units up and 10 units to the left
5 units down and a reflection about the y-axis
5 units up and a counterclockwise rotation of 180 degrees
5 units down and a counterclockwise rotation of 90 degrees
Answer:
Step-by-step explanation:
(4). 5 units down and a counterclockwise rotation of 90 degrees
Option D is the correct answer.
We need to find which options describe the transformations applied in the given figure.
What are the transformations?There are four common types of transformations - translation, rotation, reflection, and dilation. From the definition of the transformation, we have a rotation about any point, reflection over any line, and translation along any vector. These are rigid transformations wherein the image is congruent to its pre-image. They are also known as isometric transformations. Dilation is performed at about any point and it is non-isometric.
From the given figure we can see 5 units down and a counterclockwise rotation of 90°.
Therefore, option D is the correct answer.
To learn more about the transformation visit:
https://brainly.com/question/11709244.
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2. (03.05)
A cell phone plan has a monthly cost that is shown in the table below. What is the correct statement regarding the average rate of change during the 40-minute time of talk?
X Total min of talk time
0
10
20
30
40
Y Monthly cost of cell phone in $
14.95
15.95
16.95
17.95
18.95
Answer:
The average change rate increases by a dollar for every 10 minutes you speak.
Step-by-step explanation:
If you do not speak at all you pay the standard price.
After that, If you add 10 minutes to your talk time, you add a dollar to your payment
hope it helps c:
A football is kicked upward from a height of 6 feet with an initial speed of 70 feet per second. Use the formula to find the balls height 3 seconds after it was kicked
30gallons 3quarts 1pint x 5
Answer:
Step-by-step explanation:
1 taza = 8 onzas líquidas = 240 mililitros. 1 pinta = 2 tazas = 16 onzas líquidas = 480 mililitros. 1 cuarto (qt) = 4 tazas = 2 pintas = 32 onzas líquidas = 950 mililitros. 1 galón = 4 cuartos = 128 onzas líquidas = 3.8 litros (L)
1 q t0.95 L2 qt1.89 L3 qt2.84 L4 qt3.79 L
a) The weekly wages of employees of Volta gold are normally distributed about a mean of $1,250 with a standard deviation of $120. Find the probability of an employee having a weekly wage lying;
Answer:
0.7102
0.8943
0.3696
Step - by - Step Explanation :
A.) Between $1320 and $970
P(Z < 1300) - P(Z < 970)
find the Zscore of each scores and their corresponding probability uinag the standard distribution table :
P(Z < (x - μ) /σ) - P(Z < (x - μ) / σ))
P(Z < (1320 - 1250) /120) - P(Z < (970 - 1250) / 120))
P(Z < 0.5833) - P(Z < - 2.333)
0.7200 - 0.0098 = 0.7102 (Standard
=0.7102
B.)Under 1400
x = 1400
P(Z < 400)
P(Z < (x - μ) /σ)
P(Z < (1400 - 1250) /120)
P(Z < 1.25) = 0.8943
C.) Over 1290
P(Z > 1290)
P(Z < (x - μ) /σ)
P(Z > (1290 - 1250) /120 = 0.3333
P(Z > z) = 1 - P(Z < 0.3333) = P(Z < 0.3333) = 0.6304
P(Z > 0.3333) = 1 - 0.6304 = 0.3696
Give an example of a counting problem where 2^5 - 1 is the solution. Explain why you must subtract 1.
Answer:
Suppose a problem of the form:
A person can choose:
1 out of 2 pants (red or blue)
1 out of 2 shirts (red or blue)
1 out of 2 pairs of shoes (red or blue)
1 out of 2 socks (red or blue)
1 out of 2 hats (red or blue)
Ok,
We have 5 selections with 2 options each, so the number of combinations is:
2^5
Now let's add another restriction, the person can not wear all red clothes, the person must have at least one blue one.
So we removed the combination where the person selects all red clothes, which means that we removed one combination.
So now, the total number of possible combinations is the number that we got before minus one:
2^5 - 1
Notice that subtracting the one is necessary, we first use the math that we know to find the total number of combinations and then we look at the restrictions to remove the restricted combination.
Then the complete problem is:
A person can choose:
1 out of 2 pants (red or blue)
1 out of 2 shirts (red or blue)
1 out of 2 pairs of shoes (red or blue)
1 out of 2 socks (red or blue)
1 out of 2 hats (red or blue)
And the person can not wear all red clothes, the person must have at least one blue one.
How many different combinations there are?
Jessy pastes stamps for 160 envelopes in 2 hours. If she pastes the stamps at the same rate, for how many envelopes can she paste stamps in 30 minutes ?
2 hours=160
1 hours=160÷2=80
30 minutes=80÷2=40
Answer:She can paste 40 stamps in 30 minutes
HELP PLEASE GEOMETRY!!
Answer:
<G = <J
Step-by-step explanation:
SAS means two sides and the included angle
WE know two sides and need the included angle
<G must equal < J
Which statement IS true
about the equations -3x + 4y = 12 and +X- ~Y - 1?
The system of the equations has exactly one solution
at -8, 3).
• The system of the equations has exactly one solution at (-4, 3).
• The system of the equations has no solution; the two lines are parallel.
• The system of the equations has an infinite number of solutions represented by either equation.
Answer:
Second one(Not sure)
Step-by-step explanation:
I believe the system doesn't have an exact answer. But the line are parallel because of (3).
how to bring the polynomial to the standard form p(x) x^2-2x+4) (x^2+2x+4)
[tex]\rightarrow\sf((p(x) {x}^{2} + 2x + 4)( {x}^{2} + 2x + 4)) \\ = \sf {ax}^{2} + bx + c \\ = \sf(p(x) {x}^{2} {x}^{2} + p(x) {x}^{2} (2x) + p(x) {x}^{2} \times 4 + 2x \times {x}^{2} + 2x(2x) + 2x \times 4 + {4x}^{2} + 4(2x) + 4 \times 4) \\ = \sf( {x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16) \\ \rightarrow \large\boxed{\sf\red{{{x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16}}}[/tex]
Answer:[tex]\large\boxed{\sf{\red{{x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16}}}[/tex]
[tex]\color{red}{==========================}[/tex]
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ
✍︎ꕥᴋɪᴍ ᴀʀᴀꕥ
find the measure of the largest exterior angle
Answer:
116 degrees
Step-by-step explanation:
To find the answer, we must know what the sum of exterior angles are on a given shape, which is 360 degrees.
So, let's put the equation up.
8x-21+4x-13+5x-11+6x+14=360
Let's add all the x variables together to simplify it. And also add the number together too.
8x+4x+6x+5x= 23x
(-21)+(-13)+(-11)+14 = -31
The equation we have is in its initial simplified version. Let's simplify it even more to solve.
23x-31=360
Add 31 to both sides.
23x=391
Divide 23 on both sides to find x.
391/23 = x
x= 17
Let's put the value x in each exterior angle.
A= 8(17)-21 = 115 degrees
B= 6(17)+14 = 116 degrees
C= 5(17)-11 = 74 degrees
D= 4(17)-13 = 55 degrees
From the work above, we know B is the largest exterior angle, which is 116 degrees.
Hope this helps!
