A square's diagonal (hypotenuse) is 28V2. What is the length of each side?
Answers
In a square, all four sides are the same length. Imagine a square that has been cut by a diagonal. We have two triangles, each with the same length hypotenuse (diagonal length) and two equal side lengths. To find the length of each side, we can use the Pythagorean theorem.
I used x in place of a and b, as both side lengths are equal.
x^2 + x^2 = (28 [tex]\sqrt{2}[/tex])^2
2x^2 = 1568
x^2 = 784
x = 28
The length of each side is 28 units.
Hope this helps!! :)
Answer:
Once it is a square, the lengths are the same. Considering that
a square's diagonal is [tex]s\sqrt{2}[/tex], thus, each length measures 28.
You may use the pythagorean theorem:
[tex](28\sqrt{2} )^2=s^2+s^2\\28\sqrt{2} =\sqrt{s^2+s^2} \\28\sqrt{2} =s\sqrt{2} \\[/tex]
Related Questions
the probability distribution for a game is shown in the table below.
what is the probability of NOT winning a cash prize if the game is played on time?
A) 7/10
B) 1/5
C) 4/5
D) 3/10
Answers
Given:
It is given that
Probability of winning $ 0 = [tex]\frac{3}{10}[/tex]
Probability of winning $ 100 = [tex]\frac{1}{5}[/tex]
Probability of winning $ 200 = [tex]\frac{1}{10}[/tex]
Probability of winning $ 500 = [tex]\frac{2}{5}[/tex]
To find the probability of not winning a cash prize.
Explanation:
Not winning cash prize = winning $ 0
So,
Probability of not winning a cash prize
= Probability of winning $ 0
= [tex]\frac{3}{10}[/tex]
Therefore,
The probability of not winning a cash prize is [tex]\frac{3}{10}[/tex]. Option D.
The correct option is D. 3 / 10.The probability of not winning a cash prize when playing the game is 3/10. This is found by subtracting the total probability of winning (7/10) from 1.
To determine the probability of NOT winning a cash prize, we need to find the combined probability of all outcomes except those with a cash prize ($100, $200, $500). According to the table:
→ The probability of winning $100 is 1/5.
→ The probability of winning $200 is 1/10.
→ The probability of winning $500 is 2/5.
→ First, we calculate the total probability of winning a cash prize:
= 1/5 + 1/10 + 2/5
= 2/10 + 1/10 + 4/10
= 7/10
→ Now, the probability of NOT winning a cash prize is:
= 1 - 7/10
= 3/10
Therefore, the probability of not winning a cash prize when the game is played is Option D) 3/10.
The complete question is:
the probability distribution for a game is shown in the table below.
what is the probability of NOT winning a cash prize if the game is played on time?
Outcome :
$0
$100
$200
$500
Probability:
3/10
1/5
1/10
2/5
A) 7/10
B) 1/5
C) 4/5
D) 3/10
A cylindrical block of cheese has a 6-inch diameter and is 2 inches thick. After a party, only a sector remains that has a central angle of 45 degrees. Find the volume of the cheese that remains. Show all work
Answers
Answer: The volume of cheese remaining is 7 cubic inches (7 in³)
Step-by-step explanation: The cheese is in the shape of a cylinder. The volume of a cylinder is given as follows;
Volume = πr²h
Where r = radius of the top of the cylinder and h = the height of the cylinder.
In this case, the cheese has its radius as 3 inches (that is diameter divided by 2). Also the height is given as the thickness of the cheese which is 2 inches. Note also that part of the cylindrical cheese has been eaten leaving only a potion which has an angle of 45 degrees.
The volume of the left over portion therefore can be calculated as follows;
Volume = (∅/360) x πr²h
Volume = (45/360) x 3.14 x 3² x 2
Volume = (1/8) x 3.14 x 9 x 2
Volume = (1/8) x 56.52
Volume = 7.065
Volume ≈ 7
Therefore the volume of cheese that remains is 7 cubic inches (7 inches³) approximately.
Geomtry east pls help
Answers
CAN SOMEONE PLEASE HELP ME??!!!
PLZ HURRY!!!
Answers
Answer:
It's the first one
19. Find the area of a circle with a
circumference of 18.84 yards.
Answers
Answer:
28.25
Step-by-step explanation:
Final answer:
The area of a circle with a circumference of 18.84 yards is approximately 28.274 square yards, found by first calculating the radius from the circumference and then using the area formula πr².
Explanation:
To find the area of a circle with a given circumference, we first need to determine the radius of the circle using the circumference. The formula to find the circumference C is C = 2πr, where r is the radius of the circle and π (pi) is approximately 3.14159. Since we are given that the circumference C is 18.84 yards, we solve for the radius r as follows:
r = C / (2π)
r = 18.84 yd / (2 × 3.14159)
r = 3 yards (approximately)
Once we have the radius, we can calculate the area of the circle using the formula:
A = πr²
A = π × (3 yd)²
A = 3.14159 × 9 yd²
A = 28.274 yards² (approximately)
Therefore, the area of the circle with a circumference of 18.84 yards is roughly 28.274 square yards.
The length of the diagonal of a rectangle is 181 inches.
Which statement describes the length of the diagonal?
Answers
Answer:
181 is the thing is what it says it is just find the volum
Step-by-step explanation:
Answer:
13 and 14 inches
Step-by-step explanation:
On a coordinate plane, line A goes through points (negative 3, 0) and (0, 4), and line B goes through points (0, negative 4) and (2, 0). Which line has the steeper slope? Line has a steeper slope
Answers
Answer:
Line B
Step-by-step explanation:
I got it right
Line B has a steeper slope than line A because its slope is greater than the slope of line A.
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
For line A, the two points are (-3, 0) and (0, 4).
Plugging these values into the formula, we get:
slope = (4 - 0) / (0 - (-3)) = 4 / 3
For line B, the two points are (0, -4) and (2, 0).
Plugging these values into the formula, we get:
slope = (0 - (-4)) / (2 - 0) = 4 / 2 = 2
Therefore, line B has a steeper slope than line A, because its slope is greater than the slope of line A. Line A has a slope of 4/3, while line B has a slope of 2.
We can also visualize this by drawing the lines on a coordinate plane. Line B will have a more steeply inclined slope than line A, as it will rise more quickly as it moves from left to right.
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On Monday a team of street sweepers cleaned 2 1/2 city blocks Tuesday the team cleaned 1/4 as many blocks as on Monday how many city blocks did the streets sweepers clean on tuesday
Answers
On Tuesday, the street sweepers cleaned [tex]\( \frac{5}{8} \)[/tex] city blocks.
On Tuesday, the team of street sweepers cleaned [tex]\( \frac{1}{4} \)[/tex] as many blocks as they did on Monday.
Given that they cleaned [tex]\( 2\frac{1}{2} \)[/tex] city blocks on Monday, we need to find [tex]\( \frac{1}{4} \)[/tex] of this amount to determine how many blocks they cleaned on Tuesday.
To find [tex]\( \frac{1}{4} \)[/tex] of [tex]\( 2\frac{1}{2} \),[/tex] we multiply [tex]\( 2\frac{1}{2} \)[/tex] by [tex]\( \frac{1}{4} \)[/tex]:
[tex]\[ 2\frac{1}{2} \times \frac{1}{4} = \frac{5}{2} \times \frac{1}{4} = \frac{5}{8} \][/tex]
So, the street sweepers cleaned [tex]\( \frac{5}{8} \)[/tex] city blocks on Tuesday.
The graphic shows the average number of points scored per game for ten players in the NBA.
What is the range value of the data set?
A) 3.45
B) 3.5
C) 6.9
D) 7
Answers
Answer:
C) 6.9
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Which of the following have a frequency factor of b=1? A sine function whose period is 2pi radians. A sine function whose x-coefficient is 2pi. A cosine function with no phase shift whose x-coefficient is 1. A sine function whose graph shows 2 cycles from -4pi radians to 0. A sine function whose graph shows 2 cycles from 0 to 2pi radians. A cosine function whose graph shows 4 cycles from 0 to 4pi radians. A cosine function whose graph shows 1 cycle from 3pi radians to 5pi radians.
Answers
A) A sine function whose period is 2pi radians.
C) A cosine function with no phase shift whose x-coefficient is 1.
D) A sine function whose graph shows 2 cycles from -4pi radians to 0.
G) A cosine function whose graph shows 1 cycle from 3pi radians to 5pi radians.
The solution is,
A) A sine function whose period is 2pi radians.
C) A cosine function with no phase shift whose x-coefficient is 1.
D) A sine function whose graph shows 2 cycles from -4pi radians to 0.
G) A cosine function whose graph shows 1 cycle from 3pi radians to 5pi radians.
which have a frequency factor of b=1.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
we have to find the functions which have a frequency factor of b=1.
so, we get,
from the given options, that,
A) A sine function whose period is 2pi radians.
C) A cosine function with no phase shift whose x-coefficient is 1.
D) A sine function whose graph shows 2 cycles from -4pi radians to 0.
G) A cosine function whose graph shows 1 cycle from 3pi radians to 5pi radians.
are the functions which have a frequency factor of b=1.
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If x+y=10 and x - y = 11, what is the value of x - 72
Answers
Answer:
[tex]x+y=10\\\\x-y=11\\-y=11-x\\y=-11+x\\\\x+(-11+x)=10\\x-11+x=10\\2x=21\\x=10.5[/tex]
[tex]x-72\\10.5-72\\-61.5[/tex]
The answer is -61.5
Line AB is parallel to line CD. Which statement is true?
A)
Angle d is congruent to angle b.
B)
Angle d is congruent to angle c.
Angle d is congruent to angle e.
Angle d is congruent to angle f.
Answers
Angle D is congruent to angle E
Answer:
c
Step-by-step explanation:
The government published the following stem-and-leaf plot showing the number of tigers at each major zoo in the country:
Answers
Answer: 2 zoos
Step-by-step explanation: Hope this helped!☺️
A stem-and-leaf plot is a graphical representation of numerical data showing the distribution. In the context of the question, it is visualizing the distribution of the number of tigers in each major zoo in the country.
Explanation:A stem-and-leaf plot is a type of graph used to represent numerical data. The stem of the plot represents the first digit or digits of the data points, while the leaves represent the last digit. This form of data representation is commonly used in statistics to visualize the distribution of a set of data.
In this case, the stem-and-leaf plot that the government published is showing the distribution of the number of tigers in each major zoo in the country. Each 'stem' represents the tens place of the number of tigers and each 'leaf' represents the ones place. For example, if there is an entry of 3|4 in the plot, it means that there is a major zoo in the country that houses 34 tigers.
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Which coordinate pair identifies a point in the third quadrant of the coordinate plane?
A) (8, 12)
B) (7, −9)
C) (−10, 6)
D) (−6, −8)
DO NOT GUESS
Answers
Answer:
The answer is D) (-6,-8) because in order to have a coordinate in the III quadrant you need two negatives.
Step-by-step explanation:
Answer:
The correct answer is D) (-6,-8)
Step-by-step explanation:
All points in the third quadrant have two negative numbers.
3 + x + x = 15
Just need a simple answer and explanation thank you
Answers
Answer:
6
Step-by-step explanation:
3+x+x=15
3+2x=15
2x=15-3
2x=12
x=12/2
x=6
Answer:
x=6
Step-by-step explanation:
x=6 because if you simplify this equation you get 3 + 2x = 15. The first step to solving a equation is having the x value on one side of the equation and the number value on one side. to do this we can subtract 3 from both sides of the equation and get the equation 2x=12. which would mean x=6.
For which function is the domain
-6 _< x _< -1 not appropriate?
A. y=x^2
B. y=2x
C. y=2^x
D. y=square root of x
Answers
Answer:
D. [tex]y=\sqrt{x}[/tex]
Step-by-step explanation:
A square root can't be evaluated if the number we want to find the square of is nagative.
Analyze the diagram below and complete the instructions that follow. Find the surface area of the rectangular prism. Round your answer to the nearest hundredth. A. 157.89 cm^2 B. 306.95 cm^2 C. 346.16 cm^2 D. 347.45 cm^2
Answers
Answer: OPTION D.
Step-by-step explanation:
The missing figure is attached.
For this exercise you need to use the formula to find the surface area of a Rectangular prism. This is:
[tex]SA = 2wl + 2lh + 2hw[/tex]
Where "w" is the width, "l" is the length, and "h" is the height.
In this case you can identify in the figure given in the exercise that the length, the width and the height of this rectangular prism are the following:
[tex]l=11.73\ cm\\w=9.08\ cm\\h=3.23\ cm[/tex]
Then, knowing these values you can substitute them into the formula given above and then evaluate, in order to calculate the surface area of this Rectangular prism.
You get that this is:
[tex]SA = 2(9.08\ cm)(11.73\ cm) + 2(11.73\ cm)(3.23\ cm) + 2(3.23\ cm)(9.08\ cm)\\\\SA=347.45\ cm^2[/tex]
4. A book club earns $230 for its meetings. They want to divide the money to pay for 7 meetings. When the treasurer types 230 ÷ 7 into a calculator, the number that appears is 32.8571. Where should the treasurer round the answer? Explain. Pls explain
Answers
Answer:
to the tenths place, 32.86
Step-by-step explanation: It is because money is always rounded to the tenths place
Find the value of x.
Answers
Answer:
x = 50
Step-by-step explanation:
The measure of the secant- secant angle is one half the difference of the measures of the intercepted arcs, that is
x = [tex]\frac{1}{2}[/tex] (130 - 30) = 0.5 × 100 = 50
Is the leading coefficient of the function positive or negative?
Answers
Answer:
Negative.
Step-by-step explanation:
To understand the question, you first must understand the slopes of different types of equations.
A linear equation: [tex]y = 2x[/tex] will travel from the third quadrant to the first.
If you plug in 2 for x, y will equal 4. Both values are positive, leading to a positive correlation.
A linear equation: [tex]y = -3x[/tex] will face the other direction, as shown in your attached image. When you plug in a positive number for x, like 5, y will equal -15, making the graph go up and left towards negative values.
How to find the mad of the numbers 3,7,4,2
Answers
Answer:
the mean absolute deviation would be 1.5.
Step-by-step explanation:
Mean: 3 + 7 + 4 + 2 = 16/4 = 4
4 - 3 = 1
4 - 7 = 3
4 - 4 = 0
4 - 2 = 2
(M.A.D) Mean Absolute Deviation: 1 + 3 + 0 + 2 = 6/4 = 1.5
What is the value of n in the equation below?
StartFraction 12 Superscript n Over 12 Superscript 5 EndFraction = 12 Superscript 4
Negative 20
Negative 9
9
20
Answers
Answer:
It's 9
Step-by-step explanation:
I just took the test and got it right.
Answer:
its positive 9
Step-by-step explanation:
please help with this
Answers
Answer:
Arc Length: [tex]S=r\theta[/tex]
[tex]S=3\frac{7\pi}{3}\\S=7\pi in[/tex]
90 points
The table shows the number of bottles of different kinds of juice sold at a cafeteria on Monday.
If the cafeteria has 80 customers on Tuesday, which prediction for Tuesday is NOT supported by the data in the table?
A) The number of bottles of cranberry juice sold will be 6 more than the number of bottles of pineapple juice sold.
B) The number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold.
C) There will be a total of 50 bottles of orange and cranberry juice sold.
Eliminate
D) The difference between the number of bottles of apple juice sold and the number of bottles of pineapple juice sold will be 14.
Answers
Answer:
I would say that the answer is D
Sry if I was wrong
Step-by-step explanation:
Statement (B) the number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold is not supported.
What is an arithmetic operation?Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them. Addition, subtraction, multiplication, and division are the four basic math operations.
There is a total of 80 customers on Tuesday.
Total number of bottles sold on Monday = 11+7+18+4 = 40
We are assuming total customers on Monday = 40
As we can see them on Tuesday the number of customers is doubled of customers on Monday.
Kind of juice Number of bottles sold on Tuesday:
Apple 22
Cranberry 14
Orange 36
Pineapple 8
Total 80 customers on Tuesday
The number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold is not supported.
Thus, statement (B) the number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold is not supported.
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Ina city school, 65% of students have green eyes. 25% have red hair, and 15% have green eyes and
red hair. What is the probability (rounded to the nearest whole percent) that a randomly selected
student will have red hair given that the student has green eyes?
Answers
Answer:
23% of student will have red hair given that the student has green eyes.
Step-by-step explanation:
We are given the following in the question:
Percentage of students that have green eyes = 65%
[tex]P(G) =0.65[/tex]
Percentage of students that have red hairs = 25%
[tex]P(R) =0.25[/tex]
Percentage of students that have green eyes and red hairs = 15%
[tex]P(G\cap R) =0.15[/tex]
We have to find the conditional probability of randomly selected student that will have red hair given that the student has green eyes.
[tex]P(R|G) = \dfrac{P(R\cap G)}{P(G)}[/tex]
Putting values, we get,
[tex]P(R|G)=\dfrac{0.15}{0.65} = 0.2307\approx 23\%[/tex]
Thus, 23% of student will have red hair given that the student has green eyes.
The slope of the line passing through the points (6,2) and (7,3) is
3/5
1
-1
Answers
Answer:
Step-by-step explanation:
hello :
let : A(6,2) and B(7,3)
the slope is : (YB - YA)/(XB -XA)
(3-2)/(7-6) = 1/1
the slope is : 1
A person is carrying a dog that weighs 50 pounds. The person weighs x pounds. Which equation can be used to find w, the total weight of the person and the dog in pounds?
Answers
Answer:
w = x + 50
Step-by-step explanation:
The dog is 50 pounds. The person's weight is x. You are trying to find the total weight of the dog and person. Therefore, you need to combine the two values to get the total, making the equation w = x + 50, or x + 50 = w
Find the Area of the figure below, composed of a rectangle and one semicircle,
with another semicircle removed. Round to the nearest tenths place.
Answers
The Area of the figure below, composed of a rectangle and one semicircle, with another semicircle removed is 150 cm².
Length of the rectangle = 15cm.
Width of the rectangle = 10cm.
Diameter of semicircle = 10cm.
Therefore the radius of semicircle = diameter of semicircle/2
Therefore the radius of semicircle = 10/2 = 5cm.
Area of the given figure = Area of rectangle + Area of semicircle - Area of semicircle.
So, area of the given figure = Area of rectangle.
Area of rectangle = length × width
Area of rectangle = 15 × 10 = 150 cm²
Therefore the area of the figure below, composed of a rectangle and one semicircle, with another semicircle removed is 150cm².
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Rounded to the nearest tenth, the area of the figure is 150.0 square units.
To find the area of the figure composed of a rectangle and two semicircles, with one semicircle removed, you can follow these steps:
Calculate the area of the rectangle.
Calculate the area of the larger semicircle.
Calculate the area of the smaller semicircle (the one that's removed).
Subtract the area of the smaller semicircle from the sum of the area of the rectangle and the larger semicircle.
Given that the dimensions of the rectangle are 15 by 10, the radius of the semicircle is half the width of the rectangle, so it's 10/2 = 5.
Area of Rectangle:
Area_rect = length x width = 15 x 10 = 150 square units
Area of Larger Semicircle:
The radius of the larger semicircle is 5 units (half of the width of the rectangle).
Area_larger_semicircle = (1/2) x π x r^2
Area_larger_semicircle = (1/2) x π x 5^2 = (1/2) x π x 25 = 12.5π square units
Area of Smaller Semicircle (the one that's removed):
This is also a semicircle with a radius of 5 units.
Area_smaller_semicircle = (1/2) x π x 5^2 = (1/2) x π x 25 = 12.5π square units
Subtract the area of the smaller semicircle from the sum of the area of the rectangle and the larger semicircle:
Total Area = Area_rect + Area_larger_semicircle - Area_smaller_semicircle
Total Area = 150 + 12.5π - 12.5π
The "12.5π" terms cancel out when you subtract them, so you're left with:
Total Area = 150 square units
Rounded to the nearest tenth, the area of the figure is 150.0 square units.
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i need help asap pls !!!
Answers
Answer:
100°
Step-by-step explanation:
AB = AC (given)
Therefore, ∆ ABC is an isosceles triangle.
m<B=m< C= 40°
sum of the interior angles of a triangle= 180°
m<A+40°+40°=180°
m<A = 180°-80° = 100°
Answer:
< A is 100
Step-by-step explanation:
<B is 40 <C is also 40
so 40+40= 80 then you have to do 180-80. Which equals 100.
These planets are dense; rocky surface; thin atmosphere; rotate slowly on its axisss
Answers
Answer:
The planet you're describing is Mercury. It fits all the criteria of the question.
Note: If you're looking for another planet, Mars has a thin atmosphere and is rocky, but does not rotate slowly. Venus rotates very slowly and is rocky, but has a thick atmosphere. Earth doesn't have a thin atmosphere or rotate slowly, but it is rocky and dense.
Answer:
The Terrestrial or Inner Planets
Step-by-step explanation:
You are describing the terrestrial or inner planets of our Solar System. All of these planets, Mercury, Venus, Earth, and Mars are rocky and have a dense surface unlike the gas giant or outer planets, Jupiter, Saturn, Uranus and Neptune.