The length of the side of the square with the same area as the trapezoid is [tex]$12\sqrt{2}$[/tex] cm.
What is the area of a trapezoid?The area of a trapezoid is given by the formula:
[tex]$A = \frac{1}{2}(b_1 + b_2)h$[/tex]
where [tex]$b_1$[/tex] and [tex]$b_2$[/tex] are the lengths of the bases and h is the altitude.
Substituting the given values, we have:
[tex]$A = \frac{1}{2}(12+36)(12) = 288\text{ cm}^2$[/tex]
Since a square has all sides equal in length, the area of a square is given by:
[tex]$A = s^2$[/tex]
where s is the length of each side.
Substituting the area of the trapezoid, we get:
[tex]$s^2 = 288$[/tex]
Taking the square root of both sides, we have:
[tex]$s = \sqrt{288} = 12\sqrt{2}$[/tex]
Therefore, the length of the side of the square with the same area as the trapezoid is [tex]$12\sqrt{2}$[/tex] cm.
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Ejercicio 2.- La temperatura ambiente a las 8 am era de 61 grados Farenheit. Fue aumentando de forma lineal hasta la 1 pm en que el termómetro marcó 81 grados. a) Escriba una ecuación lineal que muestre la temperatura en función de la hora en ese intervalo. b) Calcule con esa ecuación la temperatura a las 11:15 am. Aproxime a la décima de grado Farenheit si fuera necesario. oprondamos a hacer ecuaciones y resolver
a)Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es T(h) = 4h + 29
b) Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
what is aproximadamente ?
"Aproximadamente" is a Spanish word that means "approximately" or "roughly" in English. It is often used to indicate that a value or measurement is not exact, but rather an estimation or approximation.
In the given question,
a) La ecuación lineal que relaciona la temperatura con la hora en ese intervalo es:
T(h) = m*h + b
donde T es la temperatura en grados Farenheit, h es la hora en formato de 24 horas, m es la pendiente de la recta y b es el término independiente.
Primero encontramos la pendiente m:
m = (81 - 61) / (13 - 8) = 4
Luego, encontramos el término independiente b utilizando uno de los puntos:
61 = 4*8 + b
b = 29
Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es:
T(h) = 4h + 29
b) Para encontrar la temperatura a las 11:15 am, primero convertimos el tiempo a horas decimales:
11:15 am = 11 + 15/60 = 11.25 horas
Luego, sustituimos este valor en la ecuación lineal:
T(11.25) = 4(11.25) + 29 = 75.25
Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
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If w = 10 units, x = 5 units, and y = 6 units, what is the surface area of the figure? Round your answer to the nearest tenth. (1 point) Figure is composed of a right square pyramid on top of a square prism. The sides of the square pyramid are equal to the sides of the square prism, the length and width of the square prism is w, the height of the square prism is x, and the height of the square pyramid, which forms a right angle with the center, is y.
The surface area of the figure is 456.2 units²,
How to determine the surface area?The area of the square base is:
base area = w² = (10 units)² = 100 units²
The lateral area is 4 times the area of one rectangular face:
lateral area = 4wx = 4(10 units)(5 units) = 200 units²
The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:
h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²
h = √61 units
So, the area of 4 triangles is ...
area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²
Now we have the areas of the parts, so we can add them together to get the total surface area:
surface area = base area + lateral area + area of triangular faces
= 100 units² + 200 units² + 156.2 units²
therefore, surface area = 456.2 units²
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C. The table below shows the ages in years of 42 children at a birthday party. AGE(YEARS) NO OF CHIDREN 7 2x 8 3x 9 4x-1 10 X 11 X-2 (i). Find the value of x. (ii). Calculate, correct to the nearest whole number the mean age. (iii). Find the probability of selecting at random a child whose age is less than 9 years. 12 x-3 CURT
(1) The value of X is equal to 4 (2) The mean age is 3. (3) The probability of randomly selecting a child under the age of 9 is approximately 0.83.
How to calculate the average?
The formula for calculating the average of given numbers is equal to the sum of all values divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.
(i). Given that there are a total of 42 children on the birthday, finding the value of x:
2x + 3x (4x-1) + x + (x-2) + (x-3) = 42
11x - 6 = 42
11x = 48
x = 4
Therefore, the value of x is equal to 4.
(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:
Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42
= (14 + 24 + 27 + 40 + 22 +12) / 42
= 139/42
= 3.31
Rounded to the nearest whole number, the average age is 3.
(iii). The probability of randomly selecting a child under 9 is obtained by adding the number of children aged 7, 8 or 9 (because we want children under 9) and dividing by the total number of children:
Number of children under 9 years = 2x + 3x + (4x-1)
Number of children under 9 years = 9x - 1
Number of children under 9 = 9(4)–1
Number of children under 9 years = 35
Probability of choosing a child under 9 = number of children under 9 / total number of children
Probability of choosing a child under 9 = 35/42
The probability of choosing a child under 9 years old is ≈ 0.83
Thus, the probability of randomly selecting a child under the age of 9 is approximately 0.83.
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Find the range of the relationship
Answer:
The range is {-7, -4, -1, 2, 5}.
Find the probability of drawing a green, then yellow, with replacement.
A bag has 4 green blocks, 6 red blocks, 7 blue and 3 yellow.
P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of science, such as statistics, physics, and engineering, as well as in everyday life to make informed decisions based on the likelihood of various outcomes.
The probability of drawing a green block on the first draw is 4/20 (since there are 4 green blocks out of a total of 20 blocks in the bag).
Since the block is being replaced back into the bag after each draw, the probability of drawing a yellow block on the second draw is still 3/20.
Therefore, the probability of drawing a green block followed by a yellow block is:
P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%
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For #1 - 6, use the information given to write the equation of the line in slope intercept form.
1. Line where slope is -32 and y-intercept is 7
1. Line where slope is 5 and x -intercept is 2
1. Line going through the points (-1, -5) and (4, -2)
1. Line going through the points (0, 1) and (2, -2)
1. Line where m = 4 and and b = -76
1. Line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0
An equation of a line where slope is -32 and y-intercept is 7 is y = -32x + 7.
An equation of a line where slope is 5 and x-intercept is 2 is y = 5x - 10.
An equation of a line that is going through the points (-1, -5) and (4, -2) is y = 3x/5 - 22/5
An equation of a line that is going through the points (0, 1) and (2, -2) is y = -x/2 + 1
An equation of a line where m = 4 and and b = -76 is y = 4x - 76.
An equation of a line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0 is y = 3x + 0.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 5)/(4 + 1)
Slope (m) = 3/5
At data point (-1, -5) and a slope of 3/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 5 = 3/5(x + 1)
y = 3x/5 + 3/5 - 5
y = 3x/5 - 22/5
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A recliner is discounted by $190. If the original price is $800, estimate the sale price by first rounding each number to the nearest hundreds
all u got to do is subtract
Miranda is standing at the corner of a 7 m by 11 m field. She needs to go to the corner diagonally opposite from where she is standing. How much shorter is it if she cuts across the diagonal instead of walking around the perimeter of the field? Round your answer to the nearest hundredth of a meter.
Therefore, Miranda saves approximately 22.96 meters by cutting across the diagonal instead of walking around the perimeter of the field.
What is perimeter?Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a square, rectangle, triangle, or circle. It is the distance around the shape, and is measured in units such as centimeters, meters, feet, or inches. To find the perimeter of a shape, you simply add up the lengths of all its sides. For example, the perimeter of a square with sides of length 5 cm would be 4 × 5 cm = 20 cm. The perimeter of a rectangle with length 6 cm and width 4 cm would be 2 × (6 cm + 4 cm) = 20 cm.
If Miranda walks around the perimeter of the field, she will travel a distance equal to the perimeter of a rectangle, which can be calculated as follows:
[tex]Perimeter = 2(Length + Width) = 2(7m + 11m) = 2(18m) = 36m[/tex]
To cut across the diagonal of the field, Miranda will travel a distance equal to the length of the diagonal of the rectangle. This can be found using the Pythagorean theorem:
[tex]Diagonal = \sqrt(Length^2 + Width^2) = \sqrt(7m^2 + 11m^2) = \sqrt(170m^2) \approx 13.04m[/tex]
So, the distance Miranda saves by cutting across the diagonal is:
[tex]36m - 13.04m \approx 22.96m[/tex]
Rounding to the nearest hundredth of a meter gives:
≈ 22.96m to 2 decimal places
Therefore, Miranda saves approximately 22.96 meters by cutting across the diagonal instead of walking around the perimeter of the field.
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An electronics store bought a flat-
screen television from its supplier
for $699 and marked up its price
by 15%. Richard makes an 8%
commission on his sales. If Richard
sells the flat-screen television at full
price, how much commission will he
earn (rounded to the nearest cent)?
The markup price of the flat-screen television is:
$699 + ($699 x 0.15) = $803.85
The commission that Richard will earn on the sale is:
$803.85 x 0.08 = $64.31
Therefore, Richard will earn a commission of $64.31 (rounded to the nearest cent).
In 2014, Michelle's annual base salary was $87,000. She also earned 3% commission of her annual sales of $500,000. What was Michelle's income during 2014?
Answer: Michelle's income during 2014 was her base salary plus her commission.
Her commission was 3% of $500,000, which is 0.03 x $500,000 = $15,000.
So her total income for 2014 was $87,000 + $15,000 = $102,000.
Step-by-step explanation:
Determine the domain of the graph above
The domain of the graph in this problem is given as follows:
C) -3 ≤ x ≤ 4.
How to obtain the domain of the graph?To determine the domain of a graph, you need to identify the set of all possible input values (also known as the independent variable) that produce a valid output (also known as the dependent variable) on the graph.
On a graph, the input values are represented by the values of x of the graph.
On the graph in this problem, we have that it assumes values of x between -3 and 4, with closed intervals, hence the domain is given as follows:
-3 ≤ x ≤ 4.
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In an election, suppose that 40% of voters support a new tax on fast food. If we poll 165 of these voters at
random, the probability distribution for the proportion of the polled voters that support a new tax on fast food
can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal
places.
The values accurate to two decimal places for -2 standard deviation, mean, and +2 standard deviation are 0.30, 0.40, and 0.49, respectively.
What are the values of the mean and the standard deviation?We can use the following formulas to calculate the mean and standard deviation of the sampling distribution:
Mean: μ = p = 0.40 (since the population proportion is 0.40)
Standard deviation: σ = √((p(1-p))/n)
σ = √((0.40(1-0.40))/165)
σ = 0.049
Now we can calculate the values for -2SD, mean, and +2SD as follows:
-2SD: μ - 2σ = 0.40 - 2(0.049) = 0.30
Mean: μ = 0.40
+2SD: μ + 2σ = 0.40 + 2(0.049) = 0.49
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Explain what the constant of proportionality means in the equation y = 5/2 x
Answer:
[tex]y = \frac{5}{2} x[/tex]
[tex] \frac{y}{x} = \frac{5}{2} [/tex]
The constant of proportionality is the ratio of y to x. Here, the ratio of y to x is 5 to 2. We see that y is directly proportional to x.
The number is less than 9,000.
The number is even.
50% of the digits are even.
The digits in the thousand's place and the hundred's place are odd.
The digit in the thousand's place is the number of nickels in a quarter.
The difference between the digit in the thousand's
place and the hundred's place is four.
The digit in the hundred's place is the identity element for multiplication.
The digit in the ten's place is the number of sides on a quadrilateral.
The digital root of the number is seven.
Answer:
5146
Explanation:
There are 5 nickels in a quarter,
5 - 1 = 4,
There are 4 sides in a quadrilateral,
and 6 would make the digital root 7.
5146 -> 5 + 1 + 4 + 6 = 16
16 -> 1 + 6 = 7
A bus traveled on a level road for 2 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 3 hours. Find the average speed on the level road if the entire trip was 225 miles.
By answering the presented question, we may conclude that As a result, the average speed on the flat road is 57 miles per hour.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
Let's apply the formula:
distance = time speed
The bus went for 2 hours on the level road, hence the distance travelled is:
1 distance = x 2
The bus went for 3 hours on the twisting route, hence the distance travelled is:
3 distance2 = (x - 20)
Because the bus's total distance travelled is 225 miles, we may write:
distance1 plus distance2 equals 225
Substituting distance1 and distance2 expressions yields:
x × 2 + (x - 20) × 3 = 225
When we simplify this equation, we get:
2x + 3x - 60 = 225
5x = 285\sx = 57
As a result, the average speed on the flat road is 57 miles per hour.
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HELP PLEASE !
Using the table given in the photo, please help me understand and answer these questions. any help would be very appreciated!!!
The average rate is given as 0.2895 gallons per hour
What is gallons per hour?Gallons per hour (GPH) is a unit of measurement used to express the rate of flow of a liquid, typically fuel.
It represents the number of gallons of fuel that can flow through a particular system or device in one hour.
For example, the GPH of a car's fuel pump indicates how many gallons of fuel it can deliver to the engine in one hour. This unit is commonly used in the context of measuring the fuel efficiency of vehicles or other machinery.
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change 52 out of 97 to a percentage? give your answer to one decimal place
radical form of a^2/5
help please
Answer:
The answer is ⁵√a²
Step-by-step explanation:
a⅖=⁵√a²
Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 2.7, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 1.6, 1.4
Determine the scale factor used.
2
3
one third
one half
The scale factor is 1/3.
What is the scale factor?
The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Here, we have
Given: Triangle D has been dilated to create triangle D′.
To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:
4.8 / 1.6 = 3
4.2 / 1.4 = 3
2.7 / x = 3
Knowing that the scaling for each edge is 3, we can solve for x.
2.7 / 3 = x
0.9 = x
The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.
So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.
Hence, the scale factor is 1/3.
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Which pair does not represent the probabilities of complementary events?
4/7 and 3/7
16% and 84%
0.25 and 0.50
0 and 1
0 and 1 are the numbers that do not represent the probabilities of complementary events.
What is probability?Probability is a measure of the possibility or chance that an event will occur.It is a value between 0 and 1, with 0 indicating that the event will not happen and 1 indicating that the event will almost likely happen. The number of favourable outcomes divided by the total number of possible outcomes is the probability of an event. Probability is utilised extensively in a wide range of professions, including mathematics, statistics, science, economics, and engineering.
According to the given information:In probability theory, complementary events are two events that together encompass all possible outcomes, and their probabilities add up to 1. The complement of an event A is the absence of A, indicated by A'. Therefore, the probability of the complement of A is 1 minus the probability of A, or P(A') = 1 - P(A).
In the given pair, 0 represents the probability of an impossible event, and 1 represents the probability of a certain event. These events are not complementary, as there is no other event that can occur apart from a certain event, and their probabilities do not add up to 1. Therefore, this pair does not represent the probabilities of complementary events.
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Find the value of x please.
choices are..
16
19
18
15
Answer:
We have supplementary angles.
123 + 3x = 180
3x = 57
x = 19
Answer:
x = 19
Step-by-step explanation:
Angle on a straight line add up to 180
123 + 3x = 180
3x = 180 - 123
3x = 57
3x/3 = 57/3
x = 19
Each tile is 3/4 of inch by 3/4 of an inch what is the area of each tile
Answer:
9/16 of a square inch
Step-by-step explanation:
[tex] \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} [/tex]
Answer:
9 /16 inches^2
Step-by-step explanation:
To find the area of the tile, multiply the length by the width
A = 3/4 * 3/4
A = 9 /16 inches^2
Use π = \frac{22}{7}: Henry bought exactly the right amount of fencing to put around his circular herb garden, which has a diameter of 14 feet. Then he decides to make the garden larger by doubling the diameter. How much more fencing does Henry need to purchase to enclose the new garden?
The answer of the given question based on the circle is , Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
What is Circumference?Circumference is distance around edge of circular object. It is same as perimeter of circle. The circumference of a circle can be calculated using the radius of the circle, which is half the diameter.
The circumference of circle with diameter d is given :
C = πd
Using the given diameter of 14 feet, the circumference of the original garden is:
C1 = πd1 = (22/7) * 14 = 44 feet
When the diameter is doubled to 28 feet, the circumference of the new garden is:
C2 = πd2 = (22/7) * 28 = 88 feet
To find how much more fencing Henry needs to purchase to enclose the new garden, we need to subtract the original circumference from the new circumference:
C2 - C1 = 88 - 44 = 44 feet
Therefore, Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
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Question 9 (10 points)
A rectangular mattress has a length that is twice it's width. The width is known to be
1 meter across, what is the area of the mattress?
O2 sq. meters
none of these
3 sq. meters
6 sq. meters
1/18 is the area of the mattress. none of these of the option.
What is a quick rectangle answer?
A quadrilateral of the kind represented by a square has equal sides that are equal to one another and four vertices that are equal to 90 degrees. The equiangular quadrilateral is hence another name for it. Since a rectangle's opposite sides are parallel and equal, a parallelogram is another word for a rectangle. With four sides, four corners, and four right angles (90°), a square form is a closed 2-D object. A square's opposing sides are comparable and equal.
Based on the given conditions, formulate = 1/2 * 1/1 + 2 * 1/2 * 2/1+2
= [tex]\frac{2/3}{2 * 3 * 2}[/tex]
= [tex]\frac{2}{3} * \frac{2}{2 * 3 * 2}[/tex]
Cross out the common factor = 1/3 * 1/3 * 2
= 1/3 * 3 * 2
= 1/18
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complete the vector to describe the transformation
The translation vector for the rectangle is described by T(x, y) = (- 3, - 6).
How to derive the translation vector of an entire figure
In this problem we must derive the translation vector between a rectangle and its image set on Cartesian plane (let assume that the origin is on the lower left corner of the square). The translation formula is:
B(x, y) = A(x, y) + T(x, y)
Where:
A(x, y) - Coordinates of the original point.B(x, y) - Coordinates of the image.T(x, y) - Translation vector.If we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:
T(x, y) = B(x, y) - A(x, y)
T(x, y) = (3, 3) - (6, 9)
T(x, y) = (- 3, - 6)
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What is the surface area of this right triangular prism?
Enter your answer in the box.
Answer:
The surface area is 720 in^2
Which is the best estimate of the difference between 67/8 and 1/82
Answer:
8.36
Step-by-step explanation:
67 - 1
8. 82
= 2747 - 4
328
=2743
328
= 8.36
NEED ASAP PLSS
The average weight per adult is 150 pounds, and the average weight per child is 40 pounds. Write an equation for the number of adults A and the number of children C the elevator can hold.
Let's assume that the elevator has a weight capacity of W pounds.
We can set up two equations to represent the number of adults (A) and the number of children (C) the elevator can hold:
Averaged weight per adult * Number of adults + Averaged weight per child * Number of children ≤ Weight capacity of the elevator
Using the given values, we can substitute:
150A + 40C ≤ W
This equation represents the weight limit of the elevator, where the sum of the weight of all adults and children inside the elevator cannot exceed W.
Convert: 83.36m= cm
pls help
Answer: 8,336
Step-by-step explanation:
So 1 meter is equal to 100 centimeters. All you have to do is multiply 83.36 by 100.
83.36 * 100 = 8,336
Hope this helps!!! :)
Name
Date
- Sarah received a coupon for 15% off the total purchase price at a shoe store. Let p be the
original price of the purchase. Use the expression p-0.15p for the new price of the purchase.
Write an equivalent expression by combining like terms.