The perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.
Given that, an isosceles right triangle whose short sides have that length 0.75 units.
Let the longest side be x.
Here, x²=0.75²+0.75²
x²=1.125
x=√1.125
x=1.06 units
Now, the perimeter = 0.75+0.75+1.06
= 2.56 units
Therefore, the perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.
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.the function f(x) = 5^x is stretched vertically by a scale factor
of 2, shifted 3 units to the left and down 1 unit to produce the
function g(x). find g(x).
please help :d
The transformation of the function g(x) is g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, a shift of 3 units to the left, and a downward shift of 1 unit applied to the original function f(x) = 5^x.
- Vertical stretch by a scale factor of 2: Multiply the output by 2.
- Shift 3 units to the left: Replace x with x + 3.
- Shift 1 unit down: Subtract 1 from the output.
Thus, the function g(x) can be written as:
g(x) = 2 * f(x + 3) - 1
Substituting f(x) = 5^x, we get:
g(x) = 2 * 5^(x + 3) - 1
Simplifying:
g(x) = 2 * 125 * 5^x - 1
g(x) = 250 * 5^x - 1
The function g(x) is given by g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, followed by a shift of 3 units to the left, and a downward shift of 1 unit, applied to the original function f(x) = 5^x.
The transformation increases the steepness of the graph, shifts it to the left, and shifts it downward. The expression 250 * 5^x represents the vertical scaling, and the -1 accounts for the vertical shift downward. Overall, g(x) is a modified version of f(x) with these transformations applied.
Therefore, the function g(x) is g(x) = 250 * 5^x - 1.
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Given that abcd is a rhombus, determine the length of each diagonal, ac, and bd if m∠ade=20° and ad = 8cm. please help and show me how you did it
The length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
Rhombus is a special type of parallelogram in which all four sides are congruent. The opposite angles of a rhombus are also congruent, and the diagonals bisect each other at right angles.
Now, let's consider the given rhombus abcd, where ad = 8cm and m∠ade=20°. We need to determine the length of diagonals ac and bd.
First, let's use the law of cosines to find the length of side ae. We know that ad = 8cm, and m∠ade=20°, so we can use the formula:
ae² = ad² + de² - 2ad(de)cos(m∠ade)
Substituting the values, we get:
ae² = 8² + de² - 2(8)(de)cos(20°)
Next, we can use the fact that a rhombus has all sides congruent to find the length of side de. Since abcd is a rhombus, we know that ac and bd are also congruent diagonals that bisect each other at right angles. Therefore, we can draw diagonal ac and use the Pythagorean theorem to find the length of ac:
ac² = (ae/2)² + (de/2)²
Substituting ae² from the previous equation, we get:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Simplifying the equation and using the fact that ac and bd are congruent, we get:
bd² = ac² = (8² + de² - 2(8)(de)cos(20°))/2
Finally, we can use the Pythagorean theorem to find the length of diagonal bd:
bd² = ab² + ad²
Substituting ab = ac/2 and ad = 8cm, we get:
bd² = (ac/2)² + 8²
Substituting ac² from the previous equation, we get:
bd² = ((8² + de² - 2(8)(de)cos(20°))/8)² + 8²
Simplifying the equation, we get:
bd ≈ 12.22 cm
Similarly, we can solve for ac using the equation we derived earlier:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Substituting de ≈ 9.84cm (which we can solve for from the equation ae² = 8² + de² - 2ad(de)cos(m∠ade)), we get:
ac ≈ 15.58 cm
Therefore, the length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
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Question 10(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 11(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12(Multiple Choice Worth 2 points)
The answer to the first question is: Burger Quick, because it has a larger median.
The answer to the second question is: Histogram, because it can show the frequency distribution of the continuous variable "number of carbohydrates" and group the data into intervals.
What is a histogram?A histogram is a graphical representation of a distribution of numerical data. It consists of a series of bars, where each bar represents a range of values of the data and the height of the bar indicates the frequency or count of data points falling within that range.
In a histogram, the horizontal axis represents the range of values or intervals of the data, called bins, and the vertical axis represents the frequency or count of data points falling within each bin. The bins can be of equal or unequal width depending on the nature of the data.
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Suppose you are doing a 5000 piece puzzle. you have already placed 175 pieces. every minute you place 10 more pieces. after 50 minutes, how many pieces will you have placed
After 50 minutes, you will have placed 675 pieces
Given, you are doing a 5000 piece puzzle. You have already placed 175 pieces, and every minute you place 10 more pieces. After 50 minutes, we need to find how many pieces you will have placed.
We can start by finding the number of pieces you place in 50 minutes.
Every minute, you place 10 more pieces, so in 50 minutes, you will place:
10 x 50 = 500 pieces
Adding the pieces you have already placed, we get:
175 + 500 = 675 pieces
Therefore, after 50 minutes, you will have placed 675 pieces
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It has been reported that 48% of teenagers play video games on their phones. A
random sample of 60 teenages is drawn. Find the probability that the proportion of
teenagers in the sample who play videos games on their phone is less than 0. 489
The probability is less than 0.489 is approximately 0.8980 or 89.80% that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489
First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:
Mean = p = 0.48
Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071
Next, we need to standardize the sample proportion using the formula:
z = (sample proportion - population proportion) / standard deviation
z = (0.489 - 0.48) / 0.071 = 1.27
Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.
Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.
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7. For the function f(x) = -5.5 sin x + 5.5 cos x on a. Find the intervals for which f is concave up and concave down on [0,2π]. CCUP_________ CC DOWN______
b. Identify the coordinates of any points of inflection for fon [0,2π].
a. For the function, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).
CCUP: (0, π/4) and (5π/4, 2π)
CCDOWN: (π/4, 5π/4)
b. The coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).
a. To find the intervals for which f is concave up and concave down on [0,2π], we need to determine the second derivative of the function f(x):
f(x) = -5.5 sin x + 5.5 cos x
f'(x) = -5.5 cos x - 5.5 sin x
f''(x) = 5.5 sin x - 5.5 cos x
To find where f is concave up (CCUP), we need to find where f''(x) > 0. Thus, we solve the inequality:
5.5 sin x - 5.5 cos x > 0
sin x > cos x
This inequality holds for 0 < x < π/4 and 5π/4 < x < 2π. Therefore, the intervals for which f is concave up on [0,2π] are (0, π/4) and (5π/4, 2π).
To find where f is concave down (CCDOWN), we need to find where f''(x) < 0. Thus, we solve the inequality:
5.5 sin x - 5.5 cos x < 0
sin x < cos x
This inequality holds for π/4 < x < 5π/4. Therefore, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).
Thus, we have:
CCUP: (0, π/4) and (5π/4, 2π)
CCDOWN: (π/4, 5π/4)
b. To find the coordinates of any points of inflection for f on [0,2π], we need to find where the concavity changes, i.e., where f''(x) = 0 or is undefined. Thus, we solve the equation:
5.5 sin x - 5.5 cos x = 0
sin x = cos x
This equation holds for x = π/4 and x = 5π/4.
To determine the concavity at these points, we can examine the sign of f''(x) in the intervals surrounding these points:
For x in (0, π/4), f''(x) < 0, so f is concave down.
For x in (π/4, 5π/4), f''(x) > 0, so f is concave up.
For x in (5π/4, 2π), f''(x) < 0, so f is concave down.
Therefore, the points of inflection for f on [0,2π] are (π/4, f(π/4)) and (5π/4, f(5π/4)).
To find the coordinates of these points, we can substitute π/4 and 5π/4 into the original function:
f(π/4) = -5.5 sin(π/4) + 5.5 cos(π/4) = -2.75 + 5.5/√2 ≈ 2.45
f(5π/4) = -5.5 sin(5π/4) + 5.5 cos(5π/4) = -2.75 - 5.5/√2 ≈ -5.95
Therefore, the coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).
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Mike calculated the net sales for his company using the following figures:
Gross sales = $50,000
Discounts = $1,800
Freight in = $2,750
Sales returns and allowances = $4,380
The net sales of the company are __________.
a. )
$46,570
b. )
$49,830
c. )
$43,820
d. )
$41,070
To calculate the net sales, we need to subtract the discounts, sales returns and allowances, and freight in from the gross sales.
Therefore, we have:
Net sales = Gross sales - Discounts - Sales returns and allowances - Freight in
Substituting the given values, we get:
Net sales = $50,000 - $1,800 - $4,380 - $2,750 = $41,070
Therefore, the net sales of the company are $41,070. Answer: (d).
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Please help me on this!
The correct point which is solution of equation of line is,
⇒ (1, 2)
We have to given that;
Equation of line is,
⇒ 3x - y = 1
Take a point 2,
⇒ (1, 2) = (x, y)
Plug into above equation of line is,
⇒ 3x - y = 1
⇒ 3 x 1 - 2 = 1
⇒ 3 - 2 = 1
⇒ 1 = 1
Thus, The correct point which is solution of equation of line is,
⇒ (1, 2)
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What is the area of EFG
Answer:
A = 28 units²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = FG = 8 and h = FE = 7 , then
A = [tex]\frac{1}{2}[/tex] × 8 × 7 = 4 × 7 = 28 units²
During one week, Sheila made several changes to her bank account. She made four withdrawals of 40$ each from an ATM she also used her check card for a 156$ purchase then she deposited her paycheck of $375
The amount change in her bank account during that week after withdrawals and deposit is equal to $59.
Total number of withdrawals made by Sheila = 4
Amount made at the time withdrawals using ATM = $40
Amount withdraw using check card to purchase = $156
Amount deposited using paycheck = #375
Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,
4 withdrawals of $40 each
= 4 x $40
= $160
So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,
= $160 + $156
= $316
Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,
$375 - $316 = $59
Therefore, the amount in Sheila's account increased by $59 during that week.
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The above question is incomplete, the complete question is:
During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?
Y – 84 = -11(x – 6)
What is the point and slope
Pyramid A (shown below) has a volume of 20 cubic units and a height of 4 units. What is the area of its base? Rectangular pyramid Group of answer choices 80 square units 5 square units 45 square units 15 square units
The base area of the pyramid is 5 units squared.
How to find the base area?The pyramid has a volume of 20 cubic units and the height of the pyramid is 4 units.
Therefore, the area of the base can be calculated as follows:
Hence,
volume of the pyramid = base area × height of the prism
20 = base area × 4
Therefore,
base area of the pyramid = 20 / 4
base area of the pyramid = 5 units squared.
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Dolly went to the Walmart and he buy 14 teddy bears and 3 dolls for 158 $ and her sister went to the Gwinnett place mall and she buy 8 teddy bears and 12 dolls for 296 $. If they both buy same brand bears and dolls, then what is price of one teddy bear and one doll? (use matrices multiplication to solve system of equations. ) (Show work)
According to formed equations, the price of one teddy bear and one doll is $7 and $20 respectively.
Let us represent the teddy bear as x and dolls as y. Now, framing the equation for Dolly and Gwinnett.
Cost of teddy bear × number + cost of dolls × number = total expenditure
14x + 3y = 158 : equation 1
8x + 12y = 296 : equation 2
Divide the equation by 4
2x + 3y = 74 : equation 3
Subtraction equation 3 from equation 1
14x + 3y = 158
- 2x + 3y = 74
12x = 84
x = 84/12
x = $7
So, the cost of teddy bear = $7
keep the value of x in equation 3 to find the cost of y
2×7 + 3y = 74
14 + 3y = 74
3y = 74 - 14
3y = 60
y = 60/3
y = $20
Thus, the cost of teddy bear and dolls are $7 and $20.
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Help me with this assignment please yall lifesavers
Answer: I think you can easily do this yourself :)
Look up the definition of all the answers, and it'll lead you straight to the answer :D
I remember doing algebra, and it seemed really hard, but once it's all over you'll be like "oooh it makes so much sense looking back on it"
Step-by-step explanation:
Three stages at a music festival are arranged in a triangle. The distances between the centers of each stage are given: Stage A and Stage B: 100 yards Stage B and Stage C: 135 yards Stage C and Stage A: 210 yards List the interior angle measures formed at the center of each stage in descending order (largest to smallest). â
Answer:
BCA
Step-by-step explanation:
The interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.
Let's label the stages A, B, and C. To find the interior angles at each stage, we can use the Law of Cosines:
cos(A) = (b^2 + c^2 - a^2) / 2bc
cos(B) = (c^2 + a^2 - b^2) / 2ca
cos(C) = (a^2 + b^2 - c^2) / 2ab
where a, b, and c are the distances between the centers of the stages.
Using the given distances, we have:
a = 100, b = 135, c = 210
cos(A) = (135^2 + 210^2 - 100^2) / (2*135*210) ≈ 0.309
cos(B) = (210^2 + 100^2 - 135^2) / (2*210*100) ≈ -0.692
cos(C) = (100^2 + 135^2 - 210^2) / (2*100*135) ≈ -0.905
To find the interior angles, we can take the inverse cosine (also known as arccosine) of each value:
A ≈ 71.7 degrees
B ≈ 133.4 degrees
C ≈ 175.0 degrees
So the interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.
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Find f'(-2) for f(x) = ln(5x² + 20x + 1). Round to 3 decimal places, if necessary.
To find f'(-2), we need to first find the derivative of f(x) using the chain rule.
f'(x) = (1/(5x² + 20x + 1)) * (10x + 20)
Then, we can plug in x = -2 to get f'(-2):
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = 0
Therefore, f'(-2) is equal to 0.
To find f'(-2) for f(x) = ln(5x² + 20x + 1), we first need to find the derivative of f(x) using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
1. Let u = 5x² + 20x + 1. Then, f(x) = ln(u).
2. Find the derivative of f(x) with respect to u: f'(x) = d[ln(u)]/du = 1/u.
3. Find the derivative of u with respect to x: du/dx = d(5x² + 20x + 1)/dx = 10x + 20.
4. Apply the chain rule: f'(x) = (1/u) * (du/dx) = (1/(5x² + 20x + 1)) * (10x + 20).
Now, to find f'(-2), simply substitute -2 for x in the derivative:
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = (1/(-19)) * 0
Since any number multiplied by 0 is 0, we have:
f'(-2) = 0.000
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Select all the correct answers.
Isosceles trapezoid ABCD is shown.
Which three statements are correct?
In the given Isosceles trapezoid ABCD, the following three statements are correct:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths. Non-parallel sides on isosceles trapezoids have the same lengths. Hence, AD ≅ BC
A triangle with two equal sides is said to be isosceles. The two angles facing the two equal sides are also equal. Hence, ∠ADC ≅ ∠BCD.
The diagonals of the isosceles trapezoid are also equal. Hence, AC ≅ BD.
Thus, three correct statements in the given question are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
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Which of the following tables represents a linear relationship that is also proportional?
Answer:
Step-by-step explanation:
proportional means the graph passes through the origin, also known as (0,0). In this case, the only table with both 0’s in the x and y is the second one from the top.
A triangular frame is being built as the support for a ramp. The longest part of the
frame will sit on the ground. The second longest side is 2'3" and forms an 18°
angle with ground. The smallest side is 10" long. Determine the angle the
smallest side will make with the ground.
The smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
To determine the angle the smallest side will make with the ground, we can use the law of sines. The law of sines states that for any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.
Let's label the sides of our triangle as follows:
The longest side (sitting on the ground) is side c
The second longest side is side b
The smallest side is side a
We know that side b is 2'3" long, which is equivalent to 27 inches. We also know that side a is 10 inches long. We can use the law of sines to solve for the angle opposite side a:
sin(A) = (a/c) * sin(C)
We can solve for sin(C) by using the fact that the sum of the angles in any triangle is 180 degrees:
C = 180 - A - B
We know that angle B is 18 degrees, so we can substitute that into our equation for C:
C = 180 - A - 18
C = 162 - A
Substituting this expression for C into our equation for sin(A), we get:
sin(A) = (a/c) * sin(162 - A)
We know that c is the longest side of the triangle and therefore opposite the largest angle. Since we are interested in the angle opposite side a, we can assume that angle A is the smallest angle in the triangle. We can use this assumption to simplify our equation for sin(A):
sin(A) = (a/c) * sin(162)
Plugging in the values for a, c, and sin(162), we get:
sin(A) = (10/27) * 0.951
sin(A) = 0.352
Taking the inverse sine of both sides, we get:
A = sin^-1(0.352)
A ≈ 20.6 degrees
Therefore, the smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
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After Paul and Marlena got married, they decided they wanted to take a
Caribbean cruise to celebrate their ten year anniversary. The cruise will cost them
$5,800. How much should they deposit into an account now that pays 5.3%
interest, compounded daily, in order to have enough for their cruise in ten years?
A. $550.81
B. $2,431.23
C. $2,957.82
D. $3,414.04
PLEASEEE
Paul and Marlena should deposit approximately $2,431.23 into an account now to have enough for their cruise in ten years.
So, the correct answer is B. $2,431.23.
To calculate the amount Paul and Marlena should deposit into an account now in order to have enough for their cruise in ten years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{ (nt)}[/tex]
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is what we need to find.
The future value (A) is given as $5,800.
The interest rate (r) is 5.3% or 0.053 as a decimal.
The interest is compounded daily, so n = 365 (number of days in a year).
Using the formula, we can rearrange it to solve for P:
[tex]P = A / (1 + r/n)^{(nt)[/tex]
Substituting the given values:
[tex]P = 5800 / (1 + 0.053/365)^{(365\times 10)[/tex]
Calculating this expression:
P ≈ 2,431.23
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Select the correct answer. What is the sum of the first five terms in this series? 3 + (-9) + 27 + (-81) + . . .
A. 243
B. -9
C. 61
D. 183
A line shape like a trapezoid has an area of 337. 5ft^2 if the length of the bases are 25 fr and 20 ft then the perpendicular distance between bases would be
The perpendicular distance between the bases of a trapezoid with an area of 337.5 ft² and base lengths of 25 ft and 20 ft is 15 ft.
Area = (1/2) * (Base1 + Base2) * Height
In this case, the area is 337.5 ft², Base1 is 25 ft, and Base2 is 20 ft. We need to solve for the height, which represents the perpendicular distance between the bases.
Plugging in the known values into the formula:
337.5 = (1/2) * (25 + 20) * Height
Simplifying the expression:
337.5 = (1/2) * (45) * Height
Multiplying both sides of the equation by 2 to get rid of the fraction:
675 = 45 * Height
Dividing both sides by 45 to solve for the height:
Height = 675 / 45
Height = 15 ft
Therefore, the perpendicular distance between the bases of the trapezoid is 15 ft.
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in each hand of a card game, there is a 54% chance of winning 3 points and a 46% chance of losing 4 points. is the game a fair game? explain
Answer: yes, the game is fair.
Step-by-step explanation:
The game is fair because:
a. you are playing with multiple players, and they have equal odds
b. the odds of winning are higher, so there is balance since you earn less points.
Give brainliest please!
Customer: "I prepaid 70% of the total cost of $127. 50 last week. "
Employee: "Okay. The total you still owe is
The total amount the customer still owe is $38.25. Customer: "I prepaid 70% of the total cost of $127.50 last week."
Employee: "Okay. The total you still owe is $38.25."
Here the customer prepaid 70% of total cost of $127.50 last week and the employee need to replay how much amount the customer still owe is. To find out the total amount the customer still owes after prepaying 70% of the total cost of $127.50,
Calculate the prepaid amount: 70% of $127.50 = 0.7 * 127.50 = $89.25Subtract the prepaid amount from the total cost: $127.50 - $89.25 = $38.25So the total amount the customer still owe is $38.25.
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Which of the following statements is correct about the value of: 13 + √50
A. 13 + √50 is an irrational number
B. 13 + √50 is an integer
C. 13 + √50 is a rational number
D. 13 + √50 is neither a rational or irrational number
The statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number
The statement that is correct about the value of: 13 + √50From the question, we have the following parameters that can be used in our computation:
13 + √50
When the above expression is evaluated we have
13 + √50 = 20.0710678119
The above result (20.0710678119) is an irrational number
This is because the number 20.0710678119 cannot be expressed as a ratio of two integers
Hence, the statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number
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PLEASE HELP
A survey was done that asked people to indicate whether they prefer saltwater fishing or freshwater fish in the results of the survey are shown in the two way table
complete a relative frequency table from this data.
enter your answer is rounded to the nearest 10th of a percent in the boxes
According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.
To find the percentage of people that make up each group, we must find the total number of people who were surveyed:
228 + 245 + 242 + 285 = 1,000
Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:
Age 30 and younger and Saltwater fishing:
1,000 = 100%
228 = ?%
Hence, We get;
228 x 100 / 1,000 = 22.8%
Age 30 and younger and Freshwater fishing:
1,000 = 100%
245 = ?%
245 x 100 / 1,000 = 24.5%
Over 30 years old and Saltwater fishing:
1,000 = 100%
242 = ?%
242 * 100 / 1,000 = 24.2%
Over 30 years old and Freshwater fishing:
1,000 = 100%
285 = ?%
285 * 100 / 1,000 = 28.5%
To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:
Age ranges
228 + 245 = 473
242 + 285 = 527
1,000 = 100%
473 = ?%
473 * 100 / 1,000 = 47.3%
1,000 = 100%
527 = ?%
527 * 100 / 1,000 = 52.3%
Fishing mode preferences
228 + 242 = 470
245 + 285 = 530
1,000 = 100%
530 = ?%
530 * 100 / 1,000 = 53%
1,000 = 100%
547 = ?%
470 * 100 / 1,000 = 47%
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Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
Point B is the image of point A under a rotation about the origin.
Describe Rotation?Rotation is a transformation in which an object or a point is turned around a fixed point or a fixed axis. The fixed point or axis is called the center of rotation, and the angle of rotation specifies the amount and direction of the turn. When an object is rotated, its orientation changes but its shape and size remain the same.
For example, if you rotate a square by 90 degrees around its center, it will look the same as before, but it will be oriented differently. Similarly, if you rotate a point in a coordinate system around the origin, its position will change, but its distance from the origin will remain the same.
Rotations are commonly used in geometry, physics, and engineering to describe the motion of objects, such as the rotation of the Earth around its axis or the rotation of a wheel on an axle. They are also used in computer graphics to create animations and in robotics to control the movement of robotic arms and other devices.
When point A is rotated about the origin to form point B, the distance between the origin and each point remains the same. The direction from the origin to point A and the direction from the origin to point B are related by the angle of rotation. Specifically, point B is the image of point A under a rotation about the origin.
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The equation The equation y=5,520x -1,091 was given for the line of best fit. What does the slope of the line mean in the context of this problem? was given for the line of best fit. What does the slope of the line mean in the context of this problem?
The slope of the line is 5,520 and it means the price of the diamond increases at a rate of 5,520 per diamond's weight.
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 equation;
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.Based on the information provided about this situation, it can be modeled by this linear equation:
y = mx + c
y = 5,520x - 1,091
By comparison, we have the following:
Slope, m = 5,520.
y-intercept, c = -1,091.
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Complete Question:
The function described by the equation y =5,520x - 1,091 is a model of the relationship between a diamond's weight and its price. What does the slope of the line mean in the context of this problem?
A tennis court in the shape of a rectangle has an area of 7200 square
feet. One pair of sides measures twice the length of the other pair of
sides. What are the dimensions of the tennis court?
Answer:
60 x 120
Step-by-step explanation:
2x(x) = 7200
2[tex]x^{2}[/tex] = 7200 divide both sides by 2
[tex]x^{2}[/tex] = 3600
[tex]\sqrt{x^{2} }[/tex] = [tex]\sqrt{3600}[/tex]
x = 60
This is one of the dimensions. The other dimension is twice 60 or 120.
a = lw
a = (60)(12)
a = 7200
Helping in the name of Jesus.
Sam has a cylindrical storage container 7 inches tall with a radius of 5 inches.
How much cat litter will fit in the container?
Use 3. 14 for π. Round your answer to the nearest tenth.
Answer: _____________ cubic inches
The cylindrical storage container can hold 549.5 cubic inches of cat litter.
To find the volume of the cylindrical storage container, we need to use the formula:
V = πr²h
Where:
π is a constant approximately equal to 3.14
r is the radius of the container
h is the height of the container
Substituting the given values, we get:
V = 3.14 x 5² x 7
V = 549.5 cubic inches
Since we know that the vessel can hold549.5 boxy elevation of cat waste, we can use this value to determine how important cat waste can fit in the vessel in other units. For illustration, if we want to know how numerous liters of cat waste can fit in the vessel, we can convert boxy elevation to liters using the conversion factor 1 liter = 61.02 boxy elevation. boxy elevation61.02 boxy elevation per liter = 8.998 liters thus, the spherical storehouse vessel can hold roughly 9 liters of cat waste.
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