The length of the remaining two equal sides is 17.3 millimeters.
What is Triangle ?
A triangle is a geometric shape that consists of three line segments or sides and three angles. Triangles are one of the basic shapes in geometry, and they are used extensively in many fields of mathematics, science, engineering, and art.
Let's denote the length of the remaining two equal sides by "x".
Since the trapezoid is isosceles, the two equal sides have the same length.
The perimeter of a trapezoid is the sum of the lengths of all its sides. Therefore, we can set up an equation based on the information given:
shorter base + longer base + 2(equal sides) = perimeter
Substituting the values we know, we get:
9.2 + 12.4 + 2x = 56.2
Simplifying the equation:
21.6 + 2x = 56.2
2x = 34.6
x = 17.3
Therefore, the length of the remaining two equal sides is 17.3 millimeters.
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Kristen’s job is to drive to sites for a construction company. Each month she is paid the same salary. She is also paid extra money for the number of miles she drives her car each month.
In March, Kristen drove 58 miles and was paid a total of $7,748.00.
In April, Kristen drove 72 miles and was paid a total of $8,532.00.
Write an equation in slope intercept form (y=mx+b) that can be used to find y, the total amount she is paid in a month if she drives x miles.
y = (46.5 - (0.5b / 58))x + b This equation allows us to plug in any value for x (the number of miles driven) and calculate Kristen's total pay for that month.
To write an equation in slope intercept form to find Kristen's total pay, we need to first determine the variable values for the equation. In this case, we know that Kristen is paid the same salary each month, so we can assign a constant value to represent her base pay. Let's call this value "b" for simplicity.
Next, we need to determine the relationship between the number of miles Kristen drives and the extra pay she receives. We can do this by calculating the rate at which she is paid per mile. To do this, we can use the formula:
Pay per mile = (Total pay - Base pay) / Number of miles driven
Using the values given in the problem, we can calculate the pay per mile for March and April as follows:
March:
Pay per mile = ($7,748.00 - b) / 58 miles
April:
Pay per mile = ($8,532.00 - b) / 72 miles
To find the overall slope of the equation, we can calculate the difference in pay per mile between March and April:
Slope = (Pay per mile for April - Pay per mile for March) / (Number of miles driven in April - Number of miles driven in March)
Slope = (($8,532.00 - b) / 72 miles) - (($7,748.00 - b) / 58 miles)) / (72 miles - 58 miles)
Simplify the equation and solve for the slope:
Slope = 46.5 - (0.5b / 58)
Now that we have the value of the slope, we can write the equation in slope intercept form:
y = mx + b
y represents Kristen's total pay, m represents the slope we just calculated, x represents the number of miles she drives, and b represents her base pay.
Putting it all together, the final equation for Kristen's total pay in a month given the number of miles she drives is:
y = (46.5 - (0.5b / 58))x + b
This equation allows us to plug in any value for x (the number of miles driven) and calculate Kristen's total pay for that month.
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Given a function f(x) = x+y, 0≤x+2y≤2 , otherwise = 0 (a) Show that f is a PDF. (b) Find the marginal of X and Y . (c) Find the Cov(X, Y ).
a) f(x) is a PDF. b) the marginal of X and Y is (y/2 + 1) / 2 c) the covariance of X and Y is: -1/18
What is meant by PDF?
In probability theory, a probability density function (PDF) is a function that describes the relative likelihood for a continuous random variable to take on a given value.
What is covariance?
Covariance is a statistical measure that quantifies the degree to which two random variables are linearly associated.
According to given information:(a) To show that f(x) is a probability density function (PDF), we need to show that it satisfies the following two conditions:
Non-negativity: f(x) is non-negative for all x in its domain.
Normalization: The integral of f(x) over its domain is equal to 1.
The domain of f(x) is given by the inequality 0 ≤ x + 2y ≤ 2. To find the integral of f(x) over its domain, we need to integrate it with respect to y from (0-x/2) to (2-x/2), and then integrate the result with respect to x from 0 to 2:
∫(0 to 2) ∫(0-x/2 to 2-x/2) (x+y) dy dx
Solving the inner integral with respect to y, we get:
∫(0 to 2) [xy + [tex]y^2[/tex]/2] |_0-x/[tex]2^{(2-x/2)[/tex] dx
= ∫(0 to 2) ([tex]x^2[/tex]/4 - [tex]x^3[/tex]/12 + 1) dx
= [[tex]x^3[/tex]/12 - [tex]x^4[/tex]/48 + x] |_[tex]0^2[/tex]
= 2 - 2/3 + 2 = 8/3
Since the integral is finite and positive, the first condition of non-negativity is satisfied. To satisfy the normalization condition, we divide the function by the integral:
f(x) = (x+y) / (8/3)
Therefore, f(x) is a PDF.
(b) To find the marginal of X, we integrate f(x,y) over the range of y:
f(x) = ∫(0-x/2 to 2-x/2) (x+y) / (8/3) dy
= (x/2 + 1) / 2
Similarly, to find the marginal of Y, we integrate f(x,y) over the range of x:
f(y) = ∫(0 to 2) (x+y) / (8/3) dx
= (y/2 + 1) / 2
(c) To find the covariance of X and Y, we use the formula:
Cov(X, Y) = E[XY] - E[X]E[Y]
To find E[XY], we integrate xy*f(x,y) over the range of x and y:
E[XY] = ∫(0 to 2) ∫(0-x/2 to 2-x/2) xy*(x+y)/(8/3) dy dx
= ∫(0 to 2) [[tex]x^3[/tex]/6 - [tex]x^4[/tex]/24 + [tex]x^2[/tex]/4] dx
= 2/3
To find E[X] and E[Y], we integrate xf(x) and yf(y) over their respective ranges:
E[X] = ∫(0 to 2) x*(x/2+1)/2 dx
= 7/3
E[Y] = ∫(0 to 2) y*(y/2+1)/2 dy
= 7/6
Therefore, the covariance of X and Y is:
Cov(X, Y) = E[XY] - E[X]E[Y] = 2/3 - (7/3)*(7/6) = -1/18
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the four vertices of a regular tetrahedron are snipped off, leaving a triangular face in place of each corner and a hexagonal face in place of each original face of the tetrahedron. how many edges will the new polyhedron have?
If 4 vertices of a "regular-tetrahedron" are snipped off which leaves a "triangular-face" in place of each corner, then there will be 18 edges in the new polyhedron.
If we snip off the 4 vertices of a "regular-tetrahedron", leaving a triangular face in place of each corner and a hexagonal-face in place of each original face of the tetrahedron,
We get a truncated tetrahedron.
we know that a truncated-tetrahedron has ⇒ four regular "hexagonal-faces", four equilateral "triangular-faces", 12 vertices and 18 edges.
Therefore, the new polyhedron will have 18 edges.
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Michael is paid $450 per week and receives a 4% commission on sales in excess of $1000. What was Michaels sales in a week if he paid $570?
Which of the points shown on the unit circle below is on the terminal side of angle θ such that cos θ= 1/2?
a
b
c
d
Answer:
b
Step-by-step explanation:
ITS THE LAST DAY OF THE SEMESTER AND IF I DONT GET THIS RIGHT IM GONNA FAIL PLEASE HELP ASAPPP!!!!
According to the puzzle the specified values are;
1. TU = 156.15m
2. Area of rectangle = 12335.85 m²
3. GH = 182.33m
4. Area of triangle = 8934.17 m²
What is a triangle?Three line segments meet at three non-collinear points to form a triangle, a geometric shape. The three points where the line segments meet are referred to as the vertices of the triangle, while the three line segments themselves are referred to as the sides of the triangle.
1. Given triangle TUV apply Pythagoras theorem,
175² = 79² + TU² after simplification,
TU = 156.15m (option A is correct)
2. Area of rectangle = length × width
Area of rectangle = TU × UV = 156.15 × 79
Area of rectangle = 12335.85 m² (option G is correct)
3. Given triangle GHI apply Pythagoras theorem,
207² = 98² + GH² after simplification,
GH = 182.33m (option I is correct)
4. Area of triangle = [tex]\frac{1}{2}[/tex] × base × height
Area of triangle = [tex]\frac{1}{2}[/tex] × HI × GH
Area of triangle = [tex]\frac{1}{2}[/tex] × 98m × 182.33m
Area of triangle = 8934.17 m²
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PLEASE HELP!!!!!!!!! ITS OVERDUE!!!!!!
ΔDEF is graphed on the coordinate plane.
1. Complete the algebraic rule for each kind of rotation. (2 points)
Rotation
Algebraic rule
90° clockwise about the origin
(x, y)→
180° about the origin
(x, y) →
270° clockwise about the origin
(x, y) →
2. Draw the image of ΔDEF after a 90° clockwise rotation. (2 points)
3. Draw the image of ΔDEF after a 180° rotation. (2 points)
4. Draw the image of ΔDEF after a 270° clockwise rotation. (2 points)
5. Without drawing a 360° rotation, describe how it would appear. (2 points)
The algebraic rule for each kind of rotation is completed below and a 360° rotation would appear as if the shape didn't rotate at all.
Completing the algebraic rule for each kind of rotationAs a general rule of rotation, the algebraic rule for each kind of rotation are
Rotation Algebraic rule
90° clockwise about the origin (x, y)→ (y, -x)
180° about the origin (x, y) → (-x, -y)
270° clockwise about the origin (x, y) → (-y, x)
The images of the triangles cannot be drawn because they are not given
The description of a 360 degreesA 360° rotation about the origin would result in the original shape returning to its starting position.
It would appear as if the shape didn't rotate at all.
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I NEED HELP ON 16 PLEASEE ASAPP
The measures of the angles in the unit circles are 53 degrees, 138 degrees, 300 degrees and 214 degrees
The question is an illustration of unit circles and the angles would be solved using
(x, y) = (cos(∅), sin(∅))
Figure (a)
Here, we have
(x, y) = (3, 4)
This means that
tan(∅) = y/x
So, we have
tan(∅) = 4/3
Take the arc tan of both sides
∅ = 53 degrees
Figure (b)
Here, we have
(x, y) = (-√5, 2)
This means that
tan(∅) = y/x
So, we have
tan(∅) = 2/-√5
Take the arc tan of both sides
∅ = 138 degrees
Figure (c)
Here, we have
(x, y) = (1, -√3)
This means that
tan(∅) = y/x
So, we have
tan(∅) = -√3/1
Take the arc tan of both sides
∅ = 300 degrees
Figure (d)
Here, we have
(x, y) = (-3, -2)
This means that
tan(∅) = y/x
So, we have
tan(∅) = -2/-3
Take the arc tan of both sides
∅ = 214 degrees
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HELP PLSS
Which student's method was not correct? Explain why that method was not correct.
Give an example of why that student's method doesn't work.
I DESPERATE AND I'LL GIVE LOTS OF POINTS PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Step-by-step explanation:
Top floor is x next floor is 2 x then the bottom is 4 x
= 7x
7x = 245 x = 35
then 35 ft 70 ft 140 ft = 245 ft total
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 5.
Event B: The sum is an odd number.
Write your answers as fractions.
The probability of event A, the sum being greater than 5, is 11/36. The probability of event B, the sum being an odd number, is 1/2.
Explanation:To calculate the probability of each event, we need to determine the total number of possible outcomes and the number of favorable outcomes for each event.
Event A: The sum is greater than 5. There are 11 favorable outcomes (6,5), (6,4), (6,3), (6,2), (6,1), (5,6), (4,6), (3,6), (2,6), (1,6), and (5,5). The total number of possible outcomes is 36. So, the probability of event A is 11/36.
Event B: The sum is an odd number. There are 18 favorable outcomes (1,3), (1,5), (1,5), (2,1), (2,3), (2,5), (2,3), (3,1), (3,3), (3,5), (4,1), (4,3), (4,5), (5,1), (5,3), (5,5), (6,1), (6,3), and (6,5). The probability of event B is 18/36 or 1/2.
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Stella has a bag that contains orange chews, apple chews, and lime chews. She performs an experiment. Stella randomly removes a chew from the bag, records the result, and returns the chew to the bag. Stella performs the experiment 21 times. The results are shown below: A orange chew was selected 12 times. A apple chew was selected 7 times. A lime chew was selected 2 times. If the experiment is repeated 1100 more times, about how many times would you expect Stella to remove a apple chew from the bag? Round your answer to the nearest whole number.
By Probability , You expect Stella to remove a apple chew from the bag
For apple , Pₐ = 7/21
For lime , Pi = 2/21
What is probability with and example?
Probability is a measure of how likely or likely-possible something is to happen. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 potential outcomes overall (a head or tail). P(heads) = 12 is what we write.
Out of 21 times that the experiment was performed
A orange chew was selected 12 times
A orange chew was selected 7 times
A lime chew was selected 2 times
then for the orange ones we have a relative frequency (that can be thought as the probability ) of
P₀ = 12/21
For apple , Pₐ = 7/21
For lime , Pi = 2/21
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Kathleen bought a used 2017 Honda Civic for
$18,000. The car will depreciate at a rate of 11% per
year.
Write an equation that can be used to predict the
value of Kathleen's Honda Civic over the next few
years by typing values into the blank spaces.
y =
).x
(
Answer: y = 18000(0.89)^x, where x represents the number of years in the future.
Step-by-step explanation:
Answer:
Y= 18,000 X (0.11x)
Step-by-step explanation:
x being years y being car
how would i write the x and y values
Anyone help in number 2
Answer:
see explanation
Step-by-step explanation:
(a)
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 7 , then
sum = 180° × (7 - 2) = 180° × 5 = 900°
(b)
since the polygon is regular then the 7 interior angles are congruent
each interior angle = 900° ÷ 7 ≈ 128.6° ( to 1 decimal place )
(c)
the sum of the exterior angles of a polygon is 360°
since the polygon is regular then the 7 exterior angles are congruent
each exterior angle = 360° ÷ 7 ≈ 51.4° ( to 1 decimal place )
Answer:
a) 900°
b) ≈ 128,6°
c) ≈ 51,4°
Step-by-step explanation:
a) s = (n - 2) × 180°
n - the number of sides (in this case, it's 7)
s - the sum of interior angles
s = (7 - 2) × 180° = 5 × 180° = 900°
.
b) In order to find the size of each angle, we have to divide the sum by the number of sides:
900° / 7 ≈ 128,6°
.
c) Since the sum of exterior angles of a polygon is 360°, we can find the size of one exterior angle by dividing this sum by the number of sides:
360° / 7 ≈ 51,4°
10. Kyle has a container in a shape of a cone. The container has a radius of 5 inches and a height
of 8 inches.
a) What is the volume of the container? (Leave in terms of pi.)
Answer:
Volume= 66.7π
Step-by-step explanation:
Volume = 1/3 ×π×h×r^2
V = 1/3 ×π ×8× 5 ^2
V = 66.7πinches^ 3
Which expression is the equivalent
The expression that is equivalent to 5[4+3(x−6)] is 15x - 70
How to find the equivalent expression?To simplify the expression 5[4+3(x−6)] , we can first simplify the expression inside the square brackets, which is (x-6) multiplied by 3 and then added to 4. This gives us:4 + 3(x - 6) = 4 + 3x - 18 = 3x -
this expression back into the original equation, we get:5[4+3(x−6)] = 5(4 + 3x - 18) = 5(3x - 14) = 15x - 70
Therefore, the expression 15x - 70 is equivalent to 5[4+3(x−6)] as seen here.
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Missing parts;
Which expression is the equivalent to 5[4+3(x−6)]
I NEED HELP PLEASE!!!
Surface area of rectangular prism is 280/9yd²
Define rectangular prismA rectangular prism, also known as a rectangular cuboid, is a three-dimensional geometric shape that has six rectangular faces, where each face is perpendicular to the adjacent faces. It is a special type of cuboid where all the faces are rectangles.
The rectangular prism has eight vertices, 12 edges, and six faces, where each face has a pair of congruent and parallel rectangular sides. The opposite faces of the rectangular prism are congruent and parallel, which means that it has a uniform cross-section throughout its length.
Sides of rectangular prism are
l=3yd
b=1 1/3yd=4/3yd
h=2 2/3yd=8/3yd
Surface area of rectangular prism=2(lb+bh+lh)
=2(3×4/3+4/3×8/3+8/3×3)
=2(4+8+32/9)
=280/9yd²
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Shown below is a circle inside of a square, ABCD.
The circle touches the 4 sides of the square.
The area of the circle is 105cm²
Find the area of the square, ABCD.
The area of the square ABCD is approximately 420/π cm².
To find the area of the square, follow these steps:
1. Calculate the radius of the circle:
Since the area of the circle is 105 cm², you can use the formula for the area of a circle,
which is A = πr²,
where A is the area and r is the radius.
105 = πr²
Divide both sides by π:
r² = 105/π
Take the square root of both sides:
r = √(105/π)
2. Calculate the side length of the square:
Since the circle touches all 4 sides of the square, the diameter of the circle is equal to the side length of the square. The diameter is twice the radius (d = 2r), so:
d = 2√(105/π)
3. Calculate the area of the square:
Now, use the formula for the area of a square, which is A = s²,
where A is the area and s is the side length. In this case, s = d:
A = (2√(105/π))²
A = 4 * (105/π)
4. Multiply to find the area:
A = 420/π cm².
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2a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 424 gram setting. it is believed that the machine is underfilling the bags. a 25 bag sample had a mean of 415 grams with a variance of 400 . assume the population is normally distributed. a level of significance of 0.1 will be used. find the p-value of the test statistic.
If a 25 bag-sample has mean of 415 grams and variance of 400, then the p-value of test statistic is 0.0169.
To test whether the bag filling machine is working correctly at the 424 gram setting, we use one-sample t-test.
The null hypothesis is that mean weight of the bags filled by machine is 424 grams, and
The Alternative hypothesis is that the mean weight is less than 424 grams.
The test statistic "t" :
⇒ t = (415 - 424)/√(400/25)) = -2.25,
The degrees of freedom for this test is = 25-1=24.
To find the p-value of the test statistic, we need to determine the probability of observing a t-value less than or equal to -2.25,
Using a t-distribution table with 24 degrees of freedom, the p-value corresponding to t = -2.25 is approximately 0.0169.
Therefore, the p-value of the test statistic is 0.0169.
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Violet owns a small business selling clothing. She knows that in the last week 53 customers paid cash, 3 customers used a debit card, and 2 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.
At the beginning of 2005 there were 670 deer living in a nature reserve. The population is declining by x% each year and after 4 years has reduced to 557. Find the value of x. Give your answer correct to 2 decimal places.
The annual rate of decline is 5.3%.
What is exponential ?
Exponential refers to a mathematical function where the variable is in the exponent. Exponential functions have the general form:
[tex]f(x) = a^{x}[/tex]
here "a" is a constant called the base, and "x" is the variable. When the base "a" is a positive number greater than 1, the function grows exponentially as "x" increases. When the base "a" is a number between 0 and 1, the function decays exponentially as "x" increases.
We can start by using the formula for exponential decay:
[tex]N(t) = N0 * (1 - r)^{t}[/tex]
where N(t) is the population after t years, N0 is the initial population, r is the annual rate of decay (as a decimal), and t is the time in years.
We are given that the initial population is 670, so N0 = 670. After 4 years, the population has reduced to 557, so N(4) = 557. We can plug these values into the formula and solve for r:
[tex]557 = 670 * (1 - r)^{4}[/tex]
[tex](557/670)^{1/4} = 1 - r[/tex]
[tex]0.947 = 1 - r[/tex]
[tex]r = 0.053[/tex]
So the annual rate of decline is 5.3%.
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The area of a circle is 44 cm2.
If its radius is r cm, find r, correct to two decimal places.
Be careful not to round your answer until the very end.
pi r^{2}=
Step-by-step explanation:
Area of a circle = pi r^2
44 cm^2 = pi r^2
r = sqrt (44/pi)
r = 3.74 cm
Answer:
≈ 3,74 cm
Step-by-step explanation:
Given:
A (area) = 44 cm^2
Find: r (radius) - ?
[tex]a = \pi {r}^{2} [/tex]
[tex]\pi {r}^{2} = 44[/tex]
[tex] {r}^{2} = \frac{44}{\pi} [/tex]
[tex]r = \sqrt{ \frac{44}{\pi} } ≈3.74[/tex]
answer the question in the image pls :)....................................
The true statements about the image △A'B'C' include the following:
A. AB is parallel to A'B'.
B. [tex]D_{O, \frac{1}{2} }[/tex] (x, y) = (1/2x, 1/2y)
C. The distance from A' to the origin is half the distance from A to the origin.
What is a dilation?In Mathematics and Geometry, a dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.
Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 0.5 centered at the origin as follows:
Ordered pair A (-4, 3) → Ordered pair A' (-4 × 1/2, 3 × 1/2) = Ordered pair B' (-2, 1.5).
Ordered pair B (4, 4) → Ordered pair B' (4 × 1/2, 4 × 1/2) = Ordered pair B' (2, 2).
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What should be subtracted from -1963 to obtain -9512
Step-by-step explanation:
no calculator at hand ?
-1963 - x = -9512
-x = -9512 + 1963 = -7549
x = 7549
so, 7549 has to be subtracted.
Find the total mass in tones of 2500 books each with a mass of 700 grams
The total mass in tones of the 2500 books is 1.75 tones
What is proportion?A proportion is defined as an equation having two ratios that are set equal to each other.
From the information given, we have that;
There are 2500 books
But then, a book weighs 700 grams
So, we have;
1 book = 700 grams
then, 2500 books = x grams
cross multiply
x = 1, 750, 000 grams
Let's convert the grams to tones , we get;
I gram = 10⁻⁶
Then 1. 75 × 10⁻⁶ = x
cross multiply
x = 1. 75 tones
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There are 6 seats in the front row of an auditorium in how many ways can 6 student arrange themselves to sit in the front row
6 Students can arrange themselves in 720 different ways to sit in the front row of an auditorium.
To determine the number of ways 6 students can arrange themselves to sit in the 6 seats in the front row, you can use
the concept of permutations.
There are 6 seats, so for the first seat, there are 6 choices of students who can sit there.
For the second seat, 5 students remain, so there are 5 choices.
For the third seat, 4 students remain, so there are 4 choices.
For the fourth seat, 3 students remain, so there are 3 choices.
For the fifth seat, 2 students remain, so there are 2 choices.
For the last seat, only 1 student remains, so there is 1 choice.
Now, multiply the number of choices for each seat together to find the total number of arrangements:
6 × 5 × 4 × 3 × 2 × 1 = 720 ways.
So, 6 students can arrange themselves in 720 different ways to sit in the front row of an auditorium.
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How could you correctly rewrite the equation 4(5 + 3) = 2(22 – 6) using the distributive property?
Answer: 20+12=44-12
Step-by-step explanation:
You can distribute the multiplication on both sides of the equation.
Whenever you see a number before parentheses, it means to multiply that number to all terms in the parentheses.
so the new equation will be: (4 * 5) +(4 *3) = (2 *22) - (2*6)
Next, we simplify: 20 + 12 = 44 - 12
If the above equation is what you are looking for then use that but you can simplify further and add the numbers together so it will be
32=32
A golfer measured the speed, in miles per hours (mph) of several drives with the same golf club. The frequency table tells how often each speed occurred. What is the median speed of the drives in miles per hour?
Answer: 90
Step-by-step explanation:
To find the median speed of the drives, list the speeds in order from lowest to highest and find the middle value. If there's an even number of speeds, find the average of the two in the middle.
Explanation:To find the median speed of the drives in miles per hour, you would first arrange the speeds in order from smallest to largest and then identify the speed that sits exactly in the middle of this list. If there is an even number of observations, the median is the average of the two middle speeds.
For instance, if the speed of the drives listed in the table are 50 mph, 60 mph, 70 mph, 80 mph, and 90 mph, the median would be 70 mph. If the speeds were 50 mph, 70 mph, 80 mph, and 90 mph, the median would be the average of 70 and 80 mph, which is 75 mph.
The frequency table is useful in identifying how often each speed occurred, but it won't directly affect your calculation of the median. It's important to understand this concept as part of a broader understanding of statistics and data analysis.
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daniel made a rectangle from 2 congruent trapezoids with bases 11 and 8 and height of 6. give the length, width, and area of the rectangle
Since the rectangle is made up of 2 congruent trapezoids, we can find the length and width of the rectangle by combining the lengths and widths of the trapezoids.
First, let's find the length of the rectangle:
The length of each trapezoid is the average of its bases:
length = (11 + 8) / 2 = 9.5
Since the trapezoids are congruent, the length of the rectangle is twice the length of a trapezoid:
length of rectangle = 2 * 9.5 = 19
Next, let's find the width of the rectangle:
The height of the trapezoids is the same as the height of the rectangle:
height = 6
The width of the rectangle is the same as the width of a trapezoid. To find the width of a trapezoid, we need to use the Pythagorean theorem, since the trapezoid has a height of 6 and bases of 11 and 8:
width = sqrt(6^2 + ((11-8)/2)^2) = sqrt(36 + 0.75) = sqrt(36.75)
So, the width of the rectangle is:
width = sqrt(36.75)
Finally, let's find the area of the rectangle:
area = length * width = 19 * sqrt(36.75) ≈ 87.83
Therefore, the length of the rectangle is 19 units, the width is approximately 6.07 units, and the area is approximately 87.83 square units.
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