Answer:
y = 1/4
Step-by-step explanation:
substitute the given value of x = -1 into the equation.
y^2^2 (^-1) =2^-2 = 1/2^2 = 1/4
Ms. King wants to add a triangular deck in
the yard behind her house. Each side is to be
18 feet long. Find the length of the railing
that will fit completely around the deck.
Then find the area of the deck.
The length of the railing that will fit completely around the deck is 54 feet. The area of the triangular deck is approximately 164.25 square feet.
To find the length of the railing that will fit completely around the triangular deck, we need to calculate the perimeter of the triangle. The perimeter of a triangle is the sum of the lengths of all three sides.
Since each side of the triangular deck is 18 feet long, the perimeter (P) can be calculated as:
P = 18 feet + 18 feet + 18 feet
P = 54 feet
So, the length of the railing that will fit completely around the deck is 54 feet.
Next, let's find the area of the triangular deck. The area of a triangle can be calculated using the following formula:
Area (A) = (1/2) * base * height
Since the triangle is equilateral (all sides have the same length), any side can be considered as the base, and the height can be drawn from any vertex to the midpoint of the opposite side.
Let's consider one of the sides (18 feet) as the base. Now, to find the height, we can draw a perpendicular line from the vertex to the midpoint of the base, creating two right-angled triangles.
The height (h) of one right-angled triangle can be found using the Pythagorean theorem:
[tex]h^2 = (18 feet / 2)^2 + (18 feet)^2\\h^2 = 9 feet^2 + 324 feet^2\\h^2 = 333 feet^2\\[/tex]
h ≈ √333 feet
h ≈ 18.25 feet (rounded to two decimal places)
Now, we can find the area (A) of the triangular deck:
A = (1/2) * base * height
A = (1/2) * 18 feet * 18.25 feet
A ≈ 164.25 square feet (rounded to two decimal places)
So, the area of the triangular deck is approximately 164.25 square feet.
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Change the following fraction to a mixed number with the fraction part reduced to lowest terms. 83/42
Answer:
1 [tex]\frac{41}{42}[/tex]
Step-by-step explanation:
[tex]\frac{83}{42}[/tex] = 83 ÷ 42 = 1 remainder 41 , then
[tex]\frac{83}{42}[/tex] = 1 [tex]\frac{41}{42}[/tex]
PLSSSS HELPPPPPPPPPPPPPPPPPP
Answer:
[tex]\huge\boxed{\sf Option \ 1}[/tex]
Step-by-step explanation:
People surveyed = 42
People who approved = 25
So, the sample is:
25 residents who approve.
And population:
42 residents surveyed.
[tex]\rule[225]{225}{2}[/tex]
Given: r(x) = x3 - 7, k(x) = 5 ln (2x) Find: (k ○ r) (x)
The value of (k ○ r) (x) from the given parameters in the task content is; 5 ln(2x³ -14)
What is (k ○ r) (x) from the task content?If follows from the task content that;
r(x) = x³ - 7 and k(x) = 5 ln (2x)It therefore follows that;
(k ○ r) (x) = k(r(x)) = 5 ln (2(x³-7)).
On this note, the expression which represents (k ○ r) (x) is; 5 ln(2x³ -14).
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Help Me On This!!
[tex] \\ \\ \\ [/tex]
Answer:
First Find the Radius of Cake by dividing 40/2
Now Find Area of the cake of Bottom
And Then Use the Formula to calculate volume of Circle
Cross Section Area=π Square
Bole of Circle 4/3π× radius cube
Answer:
24,727.5 cm³
Step-by-step explanation:
Information to keep in mind
r₁ = 20 cm (bottom layer)r₂ = 20/2 = 10 cm (middle layer)r₃ = 10/2 = 5 cm (top layer)h (of each layer) = 15 cmFormula of a cylinder
V = πr²hVolume (total)
V = πr₁²h + πr₂²h + πr₃²hV = πh (r₁² + r₂² + r₃²)V = 3.14 x 15 ([20]² + [10]² + [5]²)V = 47.1 (400 + 100 + 25)V = 47.1 (525)V = 24,727.5 cm³On Saturday, the fruit and juice bar was selling 21 glasses of fruit punch an hour. By 4 p.m., they had sold 126 glasses. If their goal was to sell more than 252 glasses of fruit punch, find the number of hours, h, they must stay open to make their goal.
A.
h > 12
B.
h > 8
C.
h > 6
D.
h > 14
Answer:
option C, 6
Step-by-step explanation:
If we subtract 252 - 126
we get 126 then divide by 21 to get 6.
therefore 6 hours
edit: If you liked my answer Brainlist Please.
Show the number on a number line:
-12 ÷ 4 =
Answer:
well if we take -12 and divide it by four we will get -3.
Step-by-step explanation:
If we have a total of negative 12, just divide it by 4 and the difference between each division is the sum.
Your answer will be -3 on the number line.
:)
Answer:
Step-by-step explanation:
-12/4 = -3
3. Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to
the nearest hundredth.
Answer:
20% probability
Step-by-step explanation:
First, we need to calculate the area of all the figures inside the rectangle.
Area of triangle= 1/2 BH
So, 3x2=(6)
Area of Square= L^2
3x3=(9)
Area of rectangle= LxW
=60.
60+9+6= 75.
75 is the total area.
Now, lets find the added area of only the triangle and square.
9+6= 15
The probability will be 15/75=
Convert into percent form
= 20%
Hope this helps and please mark me brainliest :)
Answer:
20% probability
Step-by-step explanation:
20% probability
20% probability
20% probability
20% probability
The speed of the jet Alyssa flew on from Boston to London was 480 mph. On her return flight, the speed of the jet was 600 mph with a tail wind. What was Alyssa's average speed on the round trip? Round your answer to one decimal place.
Answer:
533.3mph
Step-by-step explanation:
The graph of g(x) = f(x + 2) + 3 is the graph of y = f(x) shifted
Answer:
The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
Step-by-step explanation:
The cost of buying a small piece of land in a remote village since the year 1990 is represented by the following table: Time (years) Cost (thousands of dollars) 0. 30 36.9 44.1 51.1 57.9 65.1 21 4 6 8 10
which modle for C(t), the cost of the piece of land t years since 1990, best fits the data?
C(t) = 30 × (1.23)^t
C(t) = 30 + 7t
C(t) = 30 + 3.5t
C(t) = 30 × (1.12)^t
Answer:
Step-by-step explanation:
C(t)=30+3.5t
hope this help yw and can i get brainly pls
The step function f(x) is graphed.
5
4+
3+
2+
1+
-5-4-3-2-1 1
-2+
-3
-4
-5
92
O
3 4
5 x
What is the value of f(1)?
0
O 1
02
O 4
Answer:
f(1) = 0
Step-by-step explanation:
PLEASE HELP!!! WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER
In circle k(O), AC is a diameter, AB is a chord, and MA is tangent to the circle. Angle MAB is acute. Prove that mMAB=mACB.
Let's call C the point on K(O) and segment AO. I assume you're aware of a 'secant tangent angle theorem', where if you know the measure of arc BC you can solve for angle BAD. Since CD is a diameter of the circle, the measure of arc CD is 180 degrees - with this you can easily find the measure of all arcs of the circle then apply the theorem
Please Help!!!!
Using the slope formula, find the slope of the line through the given points. (12,0) and (2,-5)
Answer: The slope is 1/2
Step-by-step explanation:
Calculate the rise (change in y-component) divided by the run (change in x-component).
rise = 0 - (-5) = 5
run = 12 - 2 = 10
slope = 5/10 = 1/2
1.3 as a mixed number
Answer: 1 3/10
Step-by-step explanation:
first turn it into a fraction 13/10 then how many times does 13 fit into 10. It fits once with 3 remaining. So you get 1 and 3/10
Answer:
1 3/10
Step-by-step explanation:
When you read the decimal number, it reads the same as the equivalent mixed number:
1.3 = "one and three tenths" = 1 3/10
__
Additional comment
This will generally be the case. Some mixed numbers found this way can have their fractions reduced:
1.2 = "one and two tenths" = 1 2/10 = 1 1/5
Find the determinant of this matrix:
[tex]\left[\begin{array}{ccc}0&1\\1&0\end{array}\right][/tex]
Answer:
-1
Step-by-step explanation:
Formula to the determinant is:
[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc[/tex]
0(0)–1(1)
0-1
-1
Answer:
-1
Step-by-step explanation:
Formula: ad-bc
0(0) - 1(1)
0-1
-1
you build a two-person tent, as shown. How many square feet of material is needed to make the tent, assuming the tent has a floor?
The material is needed to make the tent, assuming the tent has a floor would be equal to 36/√3.
What is a triangular prism?Connect three rectangles edge to edge. Now close their triangular mouths from both ends. That shape is called a triangular prism.
Let the tent width be w and the given Length is 6 feet.
[tex]tan\theta = \dfrac{opposite }{adjecent} \\\\tan60 = \dfrac{h}{w/2} \\\\\sqrt{3} = \dfrac{6}{w/2} \\\\\sqrt{3} = \dfrac{12}{w} \\\\w = \dfrac{12}{\sqrt{3} }[/tex]
[tex]sin60 = \dfrac{opposite }{hypotenuse} \\\\sin60 = \dfrac{6}{x}\\\\x = \dfrac{6}{\sqrt{3}/2 }\\\\x = \dfrac{12}{\sqrt{3} }[/tex]
The area of the front tent =
[tex]\dfrac{1}{2} \times base \times height\\\\\dfrac{1}{2} \times w\times h\\\\\\\dfrac{1}{2} \times 12/\sqrt{3} \times 6\\\\\dfrac{36}{\sqrt{3} }[/tex]
The area of the back tent is also the same.
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Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
Answer:
the answer is in the picture
50 points each question. Please help. How do I solve?
Answer:
[tex]\dfrac{dy}{dx}=-y\left(4+\dfrac{1}{x}\right)[/tex]
or written in rational form:
[tex]\dfrac{dy}{dx}=\dfrac{-4xy-y}{x}[/tex]
Step-by-step explanation:
[tex]\ln(xy)+4x=45[/tex]
[tex]\textsf{Apply the product log law}\quad\ln(ab)=\ln(a)+\ln(b):[/tex]
[tex]\implies \ln(x)+\ln(y)+4x=45[/tex]
[tex]\textsf{Add}\:\dfrac{d}{dx}\:\textsf{in front of each term}:[/tex]
[tex]\implies \dfrac{d}{dx}\ln(x)+\dfrac{d}{dx}\ln(y)+\dfrac{d}{dx}4x=\dfrac{d}{dx}45[/tex]
[tex]\textsf{Differentiate the}\: x \: \textsf{terms and constant terms first}:[/tex]
[tex]\implies \dfrac{1}{x}+\dfrac{d}{dx}\ln(y)+4=0[/tex]
[tex]\textsf{When differentiating with respect to}\:y,\: \textsf{differentiate and add}\: \dfrac{dy}{dx}:[/tex]
[tex]\implies \dfrac{1}{x}+\dfrac{1}{y}\dfrac{dy}{dx}+4=0[/tex]
[tex]\textsf{Rearrange to make}\:\dfrac{dy}{dx}\:\textsf{the subject}:[/tex]
[tex]\implies \dfrac{1}{y}\dfrac{dy}{dx}=-4-\dfrac{1}{x}[/tex]
[tex]\implies \dfrac{dy}{dx}=y\left(-4-\dfrac{1}{x}\right)[/tex]
[tex]\implies \dfrac{dy}{dx}=-y\left(4+\dfrac{1}{x}\right)[/tex]
If you want it in rational form, then:
[tex]\implies \dfrac{dy}{dx}=-4y-\dfrac{y}{x}[/tex]
[tex]\implies \dfrac{dy}{dx}=\dfrac{-4xy-y}{x}[/tex]
[tex]~~~~~\ln(xy) +4x = 45\\\\\\\implies \dfrac{d}{dx} \left[\ln(xy) +4x \right] = \dfrac{d}{dx} ( 45)\\\\\\\implies \dfrac{1}{xy} \cdot \dfrac{d}{dx} (xy) + 4 = 0\\\\\\\implies \dfrac 1{xy} \left( x\dfrac{dy}{dx} + y \right) +4 =0\\\\\\\implies x\dfrac{dy}{dx} + y + 4xy=0\\\\\\\implies x \dfrac{dy}{dx} =-y-4xy\\\\\\\implies \dfrac{dy}{dx} = \dfrac{-y-4xy}x[/tex]
Which of the following scenarios MUST represent two independent events?
P(blue) = 20%, P(green) = 60%, P(blue and green) = 13%
P(blue) = 40%, P(green) = 30%, P(blue and green) = 13%
P(blue) = 70%, P(green) = 30%, P(blue and green) = 21%
P(blue) = 80%, P(green) = 20%, P(blue and green) = 18%
Answer: C) P(blue) = 70%, P(green) = 30%, P(blue and green) = 21%
Step-by-step explanation:
Given probabilities P(A) AND P(B) are independent, the probability that both events to occur is given by:
P(A)∩P(B)
thus from the example, independent events will be:
P(blue)=70%, P(green)=30%, P(blue and green)=21%
Because:
P(blue)∩P(green)=0.7×0.3=0.21=21%
What is the radius of a sphere with a volume of 320 ft 3 , to the nearest tenth of a foot?
Answer:
A=10240033.0/pift /ft
Step-by-step explanation:
Calculate the area of circle:
Round the number: A=10240033.0/pift /ft
Answer: A=10240033.0/pift /ft
The radius of the sphere is 4.2 feet.
What is a Sphere?A sphere is a geometrical shape in three dimension which has every point on the surface of it at an equal distance from a common point called the center of the sphere.
Volume of a sphere is given by the equation,
Volume = [tex]\frac{4}{3}[/tex]πr³, where r is the radius.
We have volume of the given sphere = 320 feet³
Substituting this value in the main equation, we get,
320 = [tex]\frac{4}{3}[/tex]πr³
320 × 3 = 4πr³
960 / 4π = r³
960 / (4 × 3.14) = r³
r³ = 76.43
r = 4.24 ≈ 4.2
Hence, the radius of the sphere with a volume of 320 feet³ has a radius of 4.2 feet, to the nearest tenth of a foot.
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(10 : 2) • 3 = 10 · (2 - 3)
O A. True
O B. False
Answer:
I have got an answer it is false for explanation go to picture
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEWhat is the measure of XYZ?
A. 56.5
Answer:
it is 113*
Step-by-step explanation:
hat is the measure of XYZ?
BRAINLIEST +STARSS!!!
Question 1 (6 points) Retake question ✓ Saved
Anthony's sink is shaped like a half-sphere, and it has a volume of 512n cubic inches.
It is completely full of water, and he has two different cylindrical cups he can use to
scoop it out.
The blue cup has a diameter of 4 in. and a height of 8 in., and the green cup has a
diameter of 8 in. and a height of 8 in.. How many cupfuls of water will it take for him
to empty his sink using each cup?
In your answer, give the number of cupfuls it will take to empty the sink using each
cup, and then explain how you calculated it.
Answer:
The green would take 4 and the blue would take 16 times respectivly. I did it by finding the volumes of the cups in terms of pi, then dividing it by the volume of the sink.
Step-by-step explanation:
So the volume of the whole half sphere is 512pi.
Now we have to find the volumes of the cup.
Equation: [tex]\pi r^2h[/tex]
Blue cup:
[tex]\pi 2^2(8)\\\pi 4(8)\\\pi 32[/tex]
It would take 16 times to drain it completly.
Green cup:
[tex]\pi 4^2(8)\\\pi 16(8)\\\pi 128[/tex]
It would take 4 times to drain it completly.
Forty pounds of candy is distributed in 5/7 lb bags. How many bags can be filled?
_______ bags can be filled.
Answer:56 bags
Step-by-step explanation:
you are dividing 40 into 5/7 so its technically 40*7 divided by 5, which equals 56. double check by doing 56*5 divided by 7 and you get 40 pounds,
[tex]\frac{40(7)}{5}[/tex]Answer:
To find out how many can be filled, divide the number of pounds of candy by the number of pounds a single bag can hold.
40 can be considered 40/1.
So,
40/1 ÷ 5/7
Make 5/7 a reciprocal(basically flipping the fraction upside down):
40/1 ÷ 7/5
Convert the division symbol into a multiplication symbol:
40/1 × 7/5
Solve!
[tex]\frac{40(7)}{5}[/tex]
Cancel:
[tex]\frac{8(7)}{1}[/tex]
= 56 bags can be filled.
On a camping trip you bring 12 items for 4 dinners. For each dinner you use 3 items. In how many ways can you choose items for the first dinner? for the second? for the third? for the fourth?
Answer:
220 options, 84 options, 20 options, 1 optionStep-by-step explanation:
The first dinnerCombinations of 3 out of 12 items
12C3 = 12!/(12-3)!3! = 12!/9!3! = 12*11*10/2*3 = 220The second dinnerCombinations 3 out of remaining 9 items
9C3 = 9!/(9 - 3)!3! = 9!/6!3! = 9*8*7/2*3 = 84The third dinnerCombinations of 3 out of remaining 6 items
6C3 = 6!/(6 - 3)!3! = 6!/3!3! = 6*5*4/2*3 = 20 The fourth dinnerCombinations of 3 out of 3 remaining items
3C3 = 3!/(3 - 3)!3! = 3!/0!3! = 1
Solve cos 0 = 1 for 0, where 0º = 0 < 90°.
A) 60°
B) 0°
C)90
D)30
Answer:
to you in 1980 is the lol in lol1234in lol to you in the kids in the lero girl
At a Harare swimming club, there are 35 girls and 25 boys. . In a Bulawayo swimming club, there are 22 girls and 14 boys. Which swimming club has the greatest proportion of girls? Explain how you worked out your answer.
Answer:
Bulawayo
Step-by-step explanation:
Proportions can be compared numerous ways. Here, we find it convenient to look at the difference between girls and boys relative to the number of boys.
__
HarareWith 35 girls and 25 boys, there are 10 more girls than boys. 10 is less than half of the number of boys, so the ratio of girls to boys is less than 1.5.
BulawayoWith 35 girls and 15 boys, there are 8 more girls than boys. 8 is more than half of the number of boys, so the ratio of girls to boys is more than 1.5.
Comparision"More than 1.5" is greater than "less than 1.5", so Bulawayo has the greatest proportion of girls.
_____
Additional comment
As a fraction of the total, the proportions of girls are ...
Harare: 35/(35+25) = 35/60 = 7/12 = 21/36
Bulawayo: 22/(22+14) = 22/36 . . . . . . greater than 21/36.
What is the following product?
3 StartRoot 2 EndRoot (5 StartRoot 6 EndRoot minus 7 StartRoot 3 EndRoot
What is the surface area of this design?
400in
256in
640in
384in
Answer:
I don’t know
Step-by-step explanation: