The probability that the next contestant will win a prize is 2/5.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
probability that the next contestant will win a prize = number of contestants that won in the last games / total number of contestants in the last games
=> 8/20
To transform to the simplest form. divide both the numerator and the denominator by 4
=> 2/5
Hence the probability that the next contestant will win a prize is 2/5.
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How is the quotient 7^18/7^-9 expressed as a power of 7
The quotient of the expression (7¹⁸/7⁻⁹) expressed as a power of 7 is 7 ²⁷.
What is the quotient of the expression?The quotient of the expression is calculated as follows;
When you divide two numbers with the same base, you subtract the exponents of the base. Using this rule, we can simplify the expression as follows;
7¹⁸ / 7⁻⁹
= 7 ⁽¹⁸ ⁻ ⁻⁹⁾
= 7 ⁽¹⁸ ⁺ ⁹⁾
= 7 ²⁷
Therefore, the quotient of the expression (7¹⁸/7⁻⁹) is 7 ²⁷.
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Math is not my best subject
The values are,
x = 15[tex]\sqrt{2}[/tex]([tex]\sqrt{2}[/tex] -1)/2
y = 15([tex]\sqrt{2}[/tex] -1)/2
z = 15
Labelling the given figure;
In ΔABC
Cos 60 = (y + z)/15[tex]\sqrt{2}[/tex]
⇒y + z = 15[tex]\sqrt{2}[/tex]/2 ....(i) (since cos 60 = 1/2)
In ΔADC
sin 45 = z/15[tex]\sqrt{2}[/tex]
⇒ z = 15 ....(ii) (since sin45 = 1/[tex]\sqrt{2}[/tex])
Now from (i) and (ii)
y = 15([tex]\sqrt{2}[/tex] -1)/2
In ΔABD
Sin 45 = y/x
⇒ 1/[tex]\sqrt{2}[/tex] = (15([tex]\sqrt{2}[/tex] -1)/2)/x
⇒ x = 15[tex]\sqrt{2}[/tex]([tex]\sqrt{2}[/tex] -1)/2
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A solid is made by a hemisphere and cylinder having equal radii. The volume of the solid is 2707 cm'. If the height of the cylinder is 80 cm, find the total surface area of the solid
The total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex]. Let's call the radius of the hemisphere and cylinder "r".
The volume of the solid is the sum of the volumes of the hemisphere and cylinder: V = (2/3)π[tex]r^{3}[/tex] + π[tex]r^{2}[/tex]h. Substituting in the given values, we get: 2707 = (2/3)π [tex]r^{3}[/tex] + π[tex]r^{2}[/tex](80)
To solve for r, we can rearrange the equation and use a numerical method or calculator. We get: r ≈ 11.6 cm
Now, we can use the radius to find the surface area of the solid. The surface area is the sum of the curved surface areas of the hemisphere and cylinder, plus the area of the circular base of the cylinder: A = 2π[tex]r^{2}[/tex] + 2πrh + π[tex]r^{2}[/tex].
Substituting in the given values and solving for A, we get: A ≈ 1818 [tex]cm^{2}[/tex]. Therefore, the total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex].
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You want to know the approximate height of a tall oak tree. You place a mirror on the ground and stand where you can see the top of the tree in the mirror. How tall is the tree? The mirror is 24 feet from the base of the tree. You are 36 inches from the mirror and your eyes are 5 feet above the ground. Round your answer to the nearest tenth
The approximate height of the tall oak tree is 60.0 feet.
To find the height of the tree, follow these steps:
1. Convert the distance between you and the mirror from inches to feet: 36 inches = 3 feet.
2. Create a proportion using similar triangles, where the height of the tree (h) divided by the distance from the tree to the mirror (24 feet) equals your eye height (5 feet) divided by the distance from your eyes to the mirror (3 feet).
3. Set up the proportion: h / 24 = 5 / 3.
4. Solve for h: h = (5 / 3) * 24.
5. Calculate h: h = 40 feet (height of tree above your eye level).
6. Add your eye height (5 feet) to the height of the tree above your eye level: 40 + 5 = 60 feet.
7. Round the answer to the nearest tenth: 60.0 feet.
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25 points! if 1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize, what is the expected value of a ticket?
The expected value of a ticket in this raffle is $12.50.
We have to given that;
1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize.
Now, For the expected value of a ticket, we need to multiply the probability of winning each prize by the amount of each prize, and then add up those values.
Hence, In this case, there are a total of 16 prizes as,
⇒ (10 $20 prizes, 5 $50 prizes, and 1 $100 prize),
Thus, the probability of winning any one prize is,
⇒ 1/16
So, the expected value of a ticket would be:
= (10/16) $20 + (5/16) $50 + (1/16) x $100
= $12.50
Therefore, the expected value of a ticket in this raffle is $12.50.
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Sylvia’s car trunk measures 4.25 ft wide by 4 ft deep and 4 1 thirdft high. she has cubic boxes 16 inches wide and smaller rectangular boxes 3 inches wide by 6 inches long and 4 inches high. she has to get as many of the large boxes into her trunk as she can, and after that, she can fill the space up with the smaller boxes. how many large and small boxes can she fit into her trunk?
Sylvia can fit 9 large cubic boxes and 240 small rectangular boxes into her car trunk.
How many boxes can fit in Sylvia's car trunk?We first need to convert all measurements to the same unit. Since the large cubic boxes are given in inches, we need to convert the dimensions of the trunk to inches as well.
The trunk measures 51 inches wide (4.25 ft x 12 in/ft), 48 inches deep (4 ft x 12 in/ft), and 53.33 inches high (4*1/3 ft x 12 in/ft).
Next, we need to determine how many large boxes can fit in the trunk. Since each large box is 16 inches wide,
we can fit 3 boxes across the width of the trunk:
(51 inches ÷ 16 inches = 3.19)
Similarly, we can fit 3 boxes deep and 3 boxes high.
Therefore, the maximum number of large boxes Sylvia can fit in her trunk is:
27 (3 x 3 x 3 = 27)
After fitting as many large boxes as possible, we can calculate the remaining volume of the trunk and use this to determine how many small boxes can fit.
The remaining volume is approximately 59,712 cubic inches (51 in x 48 in x 20 in).
Dividing this by the volume of each small box:
(3 in x 6 in x 4 in = 72 cubic inches)
We can fit 829 small boxes in the remaining space.
Therefore, Sylvia can fit a total of 27 large boxes and 829 small boxes in her trunk.
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Muriel and Ramon bought school supplies at the same store.
Muriel bought 2 boxes of pencils and 4 erasers for a total of $11.
Ramon bought 1 box of pencils and 3 erasers for a total of $7.
Which of the following systems of equations can be used to find p, the price in dollars of one box of pencils, and e, the
price in dollars of one eraser?
.
2p+ 4e = 11
p+3e = 7
2p+4e = 7
p+ 3e = 11
4p + 2e = 11
3p+e=7
4p +2e=7
3p+e=11
This system represents the purchase made by Muriel (2 boxes of pencils and 4 erasers for $11) and Ramon (1 box of pencils and 3 erasers for $7).
How to solveThe correct system of equations to find the price of one box of pencils (p) and one eraser (e) is:
2p + 4e = 11
p + 3e = 7
This system represents the purchase made by Muriel (2 boxes of pencils and 4 erasers for $11) and Ramon (1 box of pencils and 3 erasers for $7).
By solving this system of equations, you can determine the individual prices for a box of pencils and an eraser.
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in a survey of some people, it was found that the ratio of the people who liked pop songs and rap songs is 7:9. out of which, 60 people liked both songs, 30 liked rap songs only and 40 liked none of the songs. find the number of people who did not like pop songs.
Solve with steps.
The number of people who did not like pop songs is 175.
Given data :
In a survey, the ratio of people who liked pop songs and rap songs is 7: 9.
The number of people who liked both songs = 60.
The number of people who liked only rap songs = 30.
The number of people who liked none of the songs = 40
First of all, we will find the number of people who only like pop songs. We are given a ratio of 7:9 for the people who liked pop songs and rap songs. Let us assume that the number of people who liked pop songs is x and those who liked rap songs is y. According to the ratio given,
[tex]\frac{x}{y} = \frac{7}{9}[/tex] .....(1)
As we know the number of people who only liked rap songs are 30. Therefore, y - x = 30
x = y - 30
We will substitute the value of x in equation 1.
[tex]\frac{y - 30}{y} = \frac{7}{9}[/tex]
9y - 270 = 7y
2y = 270
y = 135
Now, x = 135 -30
x = 105
Total number of people in survey = x + y + 40
105 + 135 + 40 = 280
Out of 280, the number of people who liked pop songs is 105. So, the number of those who did not like pop songs is ( 280 - 105) = 175.
Therefore, the number of people who did not like pop songs are 175.
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At a mountain village in papúa new guinea it rains on average 6 days a week. Determine the probability of rains on two successive days
Answer:
36/49.
Step-by-step explanation:
Probability if rains on one day = (6/7)
Probabiilty it rains the next day also
= 6/7 * 6/7
= 36/49.
Draw a triangle with one side length of 5 units and another side length
of 7 units. What additional piece of information will guarantee that only
one triangle can be drawn?
It should be noted that to craft a triangle with an edge measuring 5 units of length, another side 7 units in magnitude, we can get underway by sketching an uninterrupted line of 7-units duration.
How to explain the informationSubsequently, draw an additional segment arriving at a peak of 5-units from the starting point of the former line. From the end-point of the line calculated as 7 units, draw a joined line towards the conclusion of the 5 unit-length section. This enables two distinctive triangles:
Also, to guarantee that just a single triangle can be drawn, it is imperative to recognize the angle resting between the two assigned sides. In case we are endowed with the inclination between both varying lengths of five and seven units, then only an original composition of triangle can be constructed.
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For a triangle ABC , the length of AC and BC are given and is acute. Justify if it is possible to have BC<ACsin angle A
PLEASE EXPLAIN USING WORKING AND CALCULATIONS AND NOT AN EXAMPLE. Thank you in advance!
The required answer is a possible scenario where BC (c) is less than AC * sin(angle A)
To justify if it is possible to have BC < AC sin(angle A) for an acute triangle ABC, let's consider the sine formula for a triangle.
The sine formula for a triangle states that:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite to those sides, respectively.
Now let's isolate side BC (b) in the equation:
b = c * sin(B) / sin(C)
Since triangle ABC is acute, all angles A, B, and C are less than 90°. Therefore, sin(B) and sin(C) will be positive values between 0 and 1.
Let's now compare BC (b) to ACsin(angle A):
b < AC * sin(A)
c * sin(B) / sin(C) < AC * sin(A)
We can rewrite the inequality in terms of angle C:
sin(B) / sin(C) < (AC * sin(A)) / c
Now let's recall that angle C is the angle opposite to side AC (c), and angle B is the angle opposite to side BC (b). Since sine is a positive increasing function for acute angles (0° to 90°), it follows that the sine of a larger angle will result in a larger value.
As angle C is opposite to the longer side (AC), angle C > angle B. Therefore, sin(C) > sin(B), and their reciprocals will have the opposite relationship:
1 / sin(C) < 1 / sin(B)
Now, let's multiply both sides of the inequality by c * sin(B):
c < AC * sin(A)
This inequality represents a possible scenario where BC (c) is less than AC * sin(angle A), justifying the initial claim. So, yes, it is possible to have BC < AC sin(angle A) for an acute triangle ABC.
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A cylindrical can without a top is made to contain 181 in^3 of liquid. Find the dimensions that will minimize the cost of the metal to make the can.
The dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.
How to find the dimensions that will minimize the cost of the metal to make the cylindrical can without a top?We can use the following steps:
Step 1: Write the volume formula for the cylinder.
The volume (V) of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since the volume is given as 181 in³, we have:
181 = πr²h
Step 2: Solve for h in terms of r.
Divide both sides by πr²:
h = 181 / (πr²)
Step 3: Write the surface area formula for the cylinder without a top.
The surface area (S) of a cylinder without a top is given by the formula S = 2πrh + πr², where r is the radius and h is the height.
Step 4: Substitute h from step 2 into the surface area formula.
Replace h with 181 / (πr²) in the surface area formula:
S = 2πr(181 / (πr²)) + πr²
Step 5: Simplify the surface area formula.
After simplifying the surface area formula, we get:
S = (362 / r) + πr²
Step 6: Minimize the surface area.
To minimize the surface area, differentiate S with respect to r and set the derivative equal to 0:
dS/dr = -362/r² + 2πr = 0
Step 7: Solve for r.
To find the value of r that minimizes the surface area, solve the equation for r:
r³ = 181/π
r = (181/π)¹/³
Step 8: Find the height h.
Substitute the value of r back into the equation for h from step 2:
h = 181 / (π((181/π)¹/³)²)
Step 9: Calculate the dimensions.
Calculate the dimensions r and h using the values obtained in step 7 and step 8:
r ≈ 2.82 inches
h ≈ 7.10 inches
So, the dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.
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(3. 5 points) use the given data in problem 33 (page 302) to answer the following questions. Assume that population data follow normal distribution. (a) (1. 5 points) calculate a two-sided 95% confidence interval for true average degree of polymerization. (b) (one points) does the interval suggest that 440 is a plausible value for true average degree of polymerization? explain. (c) (one point) does the interval suggest that 450 is a plausible value for true average degree of polymerization? explain
For items A and B, us this data set of the price, in dollars, of a milkshake at five different restaurants:4,2,9,14,6. If necessary, round your answer to the nearest tenth of a unit. Decimal answers must round to tenth place.
(I need help, quick!)
Answer:
I'm assuming that A and B are two different items, and you want me to work with the same data set for both items. Here are the calculations:
1. Mean price of milkshake:
To find the mean price of a milkshake, you need to add up all the prices and divide by the total number of prices:
(4 + 2 + 9 + 14 + 6) / 5 = 7
Therefore, the mean price of a milkshake is $7.
2. Median price of milkshake:
To find the median price of a milkshake, you need to put the prices in order from lowest to highest:
2, 4, 6, 9, 14
The median is the middle value. Since there are five values, the middle value is the third value, which is 6.
Therefore, the median price of a milkshake is $6.
3. Mode of price of milkshake:
To find the mode of the price of a milkshake, you need to find the price that appears most frequently in the data set. In this case, there is no price that appears more than once, so there is no mode.
Therefore, there is no mode for the price of a milkshake.
I hope that helps! Let me know if you have any further questions.
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Find the height of a skyscraper if you know that its top is 1000 feet
from a point on the ground and its base is 200 feet from the same
point.
The 1,000 feet and 200 feet distances of the top and the base of the skyscraper from the point on the ground, indicates, using Pythagorean Theorem that the height of the skyscraper is 400·√6 feet
What is the Pythagorean Theorem?Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the other two sides.
The distance of the top of the skyscraper from a point on the ground = 1000 feet
The distance of the base of the skyscraper from the same point = 200 feet
Therefore, according to the Pythagorean Theorem, in the right triangle formed by the ray from the top of the skyscraper to the point on the ground, the height, h, of the skyscraper, and the distance of the point on the ground from the skyscraper, we get;
1000² = h² + 200²
h² + 200² = 1000²
h² = 1000² - 200² = 960,000
h = √(960,000) = 400·√6
The height of the skyscraper is 400·√6 feet
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im gonna be sending a lot of problems since i wasnt in my class for the lesson
Answer:
168
Step-by-step explanation:
Volume is the ''area'' of a 3d shape
to find the volume, multiply the length, width, and height of the shape.
6x7x4
=42x4
=168 cubic yards
hope it helps
pls mark brainliest!!!
Answer:
168 cubic yards
Step-by-step explanation:
The formula for a rectangular prism volume is:
[tex]V=lwh[/tex]
Since we have all 3, the length, the width, and the height, we can plug in the numbers to substitute:
V=6·7·4
=168
So, the volume of this rectangular prism is 168 cubic yards.
Hope this helps :)
Peter gets a part-time job cleaning and maintaining his community's swimming pool and spa. 40 Here are some facts about the pool and spa. There is an outlet for a vacuum halfway along the side of the pool. What is the approximate length the hose should be to reach any part of the pool surface from there? Show your work. Answer Between _and _ft.
The length of the hose to reach any part of the pool surface from there will be 22.36 feet.
How to calculate the length:Length of hose = √(L² + W²)
The pool is 20 feet long and 10 feet wide, the length of the hose needed would be approximately:
Length of hose = √(20² + 10²) = √500 = 22.36 feet
Therefore, Peter would need a vacuum hose that is approximately 22.36 feet long to reach any part of the pool surface from the outlet.
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Kira had 3/5 acres land she planted 3/7 of it with corn. How many acres did she plant with corn?
Kira planted 9/35 acres with corn.
If Kira planted corn on 3/7 of her land total of 3/5 acres, what is the area she planted with corn?To find out how many acres planted with corn, we first need to understand that the total amount of land she had was 3/5 acres. Then, we know that she planted 3/7 of her land with corn.
To calculate the area planted with corn, we multiply the total area of her land (3/5 acres) by the fraction that represents the portion she planted with corn (3/7). This gives us:
(3/5) x (3/7) = 9/35 acres
Therefore, Kira planted 9/35 acres of her land with corn.
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 3 in this case. This gives us:
(9/3) / (35/3) = 3/11 acres
So, Kira planted approximately 0.26 acres with corn.
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Mrs. Ross is a librarian at Westside Library. In examining a random sample of the library's book collection, she found the following. 902 books had no damage, 80 books had minor damage, and 43 books had major damage. Based on this sample, how many of the 30,000 books in the collection should Mrs. Ross expect to have no damage? Round your answer to the nearest whol number. Do not round any Intermediate calculations.
Mrs. Ross should expect to have about 26,417 books with no damage in the entire collection. Rounded to the nearest whole number, the answer is 26,417.
Mrs. Ross found 902 out of a sample of books no damage. She wants to estimate number of undamaged books out of total collection of 30,000 books. How many books can she expect to have no damage?
Mrs. Ross found that 902 out of the sample of (902 + 80 + 43) = 1025 books had no damage. This means that the proportion of books with no damage in the sample is 902/1025. We can use this proportion to estimate the number of books with no damage in the entire collection.
Let X be the number of books with no damage in the collection of 30,000 books. Then we can write:
902/1025 = X/30000
To solve for X, we can cross-multiply and simplify:
902 × 30000 = 1025 × X
X = 902 × 30000 / 1025
X ≈ 26,417.07
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0. Jared works as a landscaper. He installs a sprinkler that sprays water in a circle with an 8-foot radius. What is the approximate area covered by the sprinkler? Use 3. 14 for n.
The area covered by a sprinkler that sprays water in a circle of an 8-foot radius is 200.96 square feet.
Circle is a 2-Dimensional shape. It has no vertex and edges. It has a center point which equidistant from any point of boundary or circumference of a circle.
Radius refers to the distance between the center and any point on the boundary or circumference of the circle.
The area of a circle is given as the product of a constant pi and the square of the radius.
A = π[tex]r^2[/tex]
A is the area
r is the radius
r = 8 feet
A = π * 8 * 8
= 3.14 * 8 * 8
= 200.96 square feet
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Identify the volume of a cube with edge length 8 ft.
V = 512 ft^3
V = 256 ft^3
V = 514 ft^3
V = 324 ft^3
The volume of a cube with edge length 8 ft are V = 512 ft³
The volume of a cube is calculated by multiplying the length of one of its sides by itself three times (V = s³). Therefore, for a cube with an edge length of 8 ft, its volume would be V = 8³ = 512 ft³.
Therefore, the correct answer is: V = 512 ft³
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oil spills into the ocean in a circular pattern. the radius increases at the constant rate of 5 meters every 10 minutes. how fast is the area of the spill increasing at the end of an hour?
The area of the spill is increasing at a rate of approximately 94.25 square meters per minute at the end of an hour.
Using the formula for the rate of change of the area, we can calculate the rate at which the area is increasing at the end of an hour:
dA/dt = 2πr(dr/dt) = 2π(30 meters)(0.5 meters per minute) ≈ 94.25 square meters per minute
Area is a mathematical concept that refers to the amount of space contained within a two-dimensional shape or surface. It is typically measured in square units, such as square meters or square feet. The formula for calculating the area of a shape depends on its geometry. For example, the area of a rectangle is calculated by multiplying the length and width, while the area of a circle is calculated by multiplying pi (approximately equal to 3.14) by the square of its radius.
Area is used in a variety of fields, including mathematics, physics, engineering, and architecture. In mathematics, the study of area is a fundamental part of geometry, and is used to solve problems related to shapes and their properties. In physics, the concept of area is used to calculate quantities such as force, pressure, and energy.
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The screen of a tablet has dimensions 8 inches by 5 inches. The
border around the screen has thickness z.
a. Write an expression for the total area of the tablet, including the
frame.
8 inches
5 inches
b. Write an equation for which your expression is equal to 50.3125. Explain what a solution to this
equation means in this situation.
c. Try to find the solution to the equation. If you get stuck, try guessing and checking. It may help to
think about tablets that you have seen.
(a) The expression for the total area of the tablet = (8 + 2z)(5 + 2z)
(b) Equation is: (8 + 2z)(5 + 2z) = 50.3125 and the solution to this equation refers to the thickness of frame for which the area of the tablet is 50.3125.
(c) Solution or the thickness of the frame must be 0.375 inches.
The dimensions of the screen of a tablets are 8 inches by 5 inches.
border around the screen has thickness z.
So the length with frame = 8 + 2z
and the width of the screen with frame = 5 + 2z
So the expression for the total area of the tablet = Length* Width = (8 + 2z)(5 + 2z)
Equation for which the expression is equal to 50.3125 is given by,
(8 + 2z)(5 + 2z) = 50.3125
So the solution to this equation refers to the thickness of frame for which the area of the tablet is 50.3125.
Solving the equation we get,
(8 + 2z)(5 + 2z) = 50.3125
40 + 10z + 16z + 4z² = 50.3125
4z² + 26z - 10.3125 = 0
Solving this quadratic equation we get the solutions,
z = -6.875, 0.375
Since the thickness cannot be negative so -6.875 must be neglected.
Hence the thickness of the frame is 0.375 inches.
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El volumen de este prisma rectangular es de 6 centímetros cúbicos. ¿Cuál es el área de superficie?
The surface area of the given volume of the rectangular prism is equal to 13.86 square centimeters.
Volume of the rectangular prism is 6 cubic centimeters.
Let the dimensions of the rectangular prism be length (l), width (w), and height (h).
Volume of the rectangular prism = l x w x h
⇒ l x w x h = 6
Use the given volume to find one of the dimensions .
Then use that information to find the surface area.
To calculate the surface area at least two of the dimensions known.
Let us assume that the height (h) is 1 centimeter.
⇒l x w x 1 = 6
⇒ l x w = 6
Use this equation to solve for one of the dimensions.
⇒ l = 6/w
Substituting this value of l into the surface area formula, we get,
Surface area = 2lw + 2wh + 2lh
⇒Surface area = 2(6/w)w + 2w(1) + 2(6/w)(1)
⇒Surface area = 12/w + 2w + 12/w
⇒Surface area = 2w + 24/w
Value of w that gives the minimum surface area,
Take the derivative of the surface area formula with respect to w and set it equal to 0,
d/dw (2w + 24/w) = 0
⇒ 2 - 24/w^2 = 0
Solving for w, we get,
⇒w = √(12)
Substituting this value of w back into the surface area formula, we get,
⇒ Surface area = 2(√(12)) + 24/√(12)
⇒Surface area = 4√3 + 4√3
⇒Surface area = 8√3
⇒ Surface area = 13.86 square centimeters
Therefore, the surface area of the rectangular prism is approximately 13.86 square centimeters.
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Solve the triangle. Round decimal answers to the nearest tenth.
The measures of the angles A = 81.2, B = 65.2, and C = 33.6 to the nearest tenth using the cosine and sine rule.
What is the cosine and sine rule?In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles. While sine rule is a relationship between the size of an angle in a triangle and the opposing side.
Considering the given triangle, angle C is calculated with cosine rule as follows;
c² = a² + b² - 2(b)(c)cosC
14² = 25² + 23² - 2(25)(23)cosC
196 = 1154 - 1150cosC
C = cos⁻¹(958/1150)
C = 33.6
by sine rule;
14/sin33.6 = 25/sinA
sinA = (25 × sin33.6)/14 {cross multiplication}
A = sin⁻¹(0.9882)
A = 81.2
B = 180 - (33.6 + 81.2) {sum of interior angles of a triangle}
B = 65.2
With proper application of the cosine and sine rule, we have the measures of the angles A = 81.2, B = 65.2, and C = 33.6 to the nearest tenth.
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Find the surface area of this regular pyramid
The surface area be 243 square feet.
Hence option (d) is correct.
In the given regular pyramid
Slant height = l = 6 ft
Edge of base = s = 9ft
Then,
Area of base = a = 9x9 = 81 square ft
Perimeter of base = p = 4x9 = 36 ft
Since surface area of regular pyramid = A = a + (1/2)ps
= 81 + (36x9)/2
= 81 + 162
= 243
Hence, A = 243 square ft.
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Answer:
The surface area be 243 square feet.
Step-by-step explanation:
The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that
the profit can be modeled by the function p= -0. 25x2 +30% +6, where x is the price of each ticket. How
many tickets have to be sold in order to make a profit of $281?
To make a profit of $281, the number of tickets that need to be sold is 150.
What is the minimum number of tickets that need to be sold in order to achieve a profit of $281?The profit from selling local ballet tickets can be determined by using the given function: [tex]p = -0.25x^2 + 0.30x + 6[/tex].
To find the number of tickets required to achieve a profit of $281, we can set p equal to 281 and solve for x. This results in a quadratic equation that can be solved using the quadratic formula.
Once we obtain the two possible values of x, we can select the positive value which represents the ticket price. Using this ticket price, we can then calculate the number of tickets required to achieve a profit of $281, which is 150.
In order to increase the profit, we can try adjusting the ticket price or increasing the number of tickets sold. However, it is important to keep in mind that there may be practical limits to both of these options.
For example, increasing the ticket price too much may deter customers from purchasing tickets, while increasing the number of tickets sold may require additional marketing efforts or larger venues.
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Use the quadratic formula to determine the exact solutions to the equation.
2x2−9x+1=0
I feel like it's either b or d. I keep getting the same answer when I solve it but the thing is, it's not on the answer choices. My answer was (9 ± √ - 89 )/ 4
but it's not thereeeee :((
The exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
To solve the quadratic equation 2x² - 9x + 1 = 0 using the quadratic formula, we first need to identify the values of a, b, and c. From the given equation, we can see that a = 2, b = -9, and c = 1.
The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a, b, and c, we get:
x = (-(-9) ± √((-9)² - 4(2)(1))) / 2(2)
x = (9 ± √(81 - 8)) / 4
x = (9 ± √73) / 4
So, the exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
As for the answer choices, it's possible that the answer key has simplified the solution further. However, your answer is correct and provides the exact solutions to the equation.
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a norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram.what should the dimensions of the rectangular part of the norman window be to allow in as much light as possible if there is only 12 ft of framing material available
The width should be 12 feet and the height should be 6 feet.
Let's assume that the rectangular part of the window has a width of x feet. Since the semi-circle at the top is half the width of the rectangle, its radius will also be x/2 feet. Therefore, the height of the rectangle can be expressed as 12 - x/2, since we have a total of 12 feet of frame material available.
To find the area of the rectangle, we can multiply its length and width together: A = x(12 - x/2) = 12x - x²/2. To maximize this area, we can take its derivative with respect to x and set it equal to 0:
dA/dx = 12 - x = 0
x = 12
So the width of the rectangle should be 12 feet, and its height would be 12 - (12/2) = 6 feet. This would maximize the amount of light entering the rectangular part of the window, given the 12 feet of frame material available.
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Check all that are inequalities.
-3 = y
t > 0
-4. 3 < a
g = 5 and one-half
k less-than Negative StartFraction 5 Over 7 EndFraction
x = 1
Anwer: B C E
The inequalities in the given options are: B) t > 0, C) 3 < a, E) k < -5/7, The correct option is B,C,E.
B) t > 0: This represents an inequality because the symbol ">" indicates "greater than." It states that the variable "t" is greater than zero. In other words, it means that "t" has to be a positive number and cannot be zero or negative.
C) 3 < a: This represents an inequality because the symbol "<" indicates "less than." It states that the number 3 is less than the variable "a." In other words, it means that "a" has to be greater than 3 for the inequality to hold true.
E) k < -5/7: This represents an inequality because the symbol "<" indicates "less than." It states that the variable "k" is less than -5/7. In other words, it means that "k" has to be a value smaller than -5/7 for the inequality to be true.
The other options, such as -3 = y, g = 5 and one-half, and x = 1, do not represent inequalities because they either show an equation (equality) or simply assign values to variables without any comparison.
Therefore the correct option is B,C,E.
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