The area of the isosceles trapezoid is 281.25 square cm.
How to solve for the area?Let's denote the length of the base of the trapezoid as "b".
According to the problem statement, the length of each of the equal sides is one-half the length of the base, which means each equal side has length b/2.
The height of the trapezoid is given as one-fourth the length of the base, so we can write it as h = b/4.
To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.
The two parallel sides of length b each contribute b to the perimeter, while the other two sides of length b/2 contribute a total of b to the perimeter.
Therefore, we can write:
Perimeter = 2b + 2(b/2) = 3b
We know that the perimeter of the trapezoid is 45 cm, so we can set up an equation:
3b = 45
Solving for b, we get:
b = 15
Now we can use the formula for the area of a trapezoid to find the area of this isosceles trapezoid. The formula is:
Area = (1/2)h(b1 + b2)
where h is the height, b1 and b2 are the lengths of the two parallel sides. In this case, b1 and b2 are both equal to b (since it's an isosceles trapezoid), and h = b/4.
Substituting these values, we get:
Area = (1/2)(b/4)(b + b) = (1/2)(b/4)(2b) = b^2/8
Substituting b = 15, we get:
Area = 15^2/8 = 281.25 sq cm
Therefore, the area of the isosceles trapezoid is 281.25 square cm.
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In an isosceles trapezoid, the length of the equal sides is one-half the length of the base, while the height is one-fourth the length of the base. If the perimeter of the trapezoid is 45 cm.
Find the areae
Evaluate the expression. (2 + 4)(8 + 3)^0 Responses
Answer: The answer is 6.
Step-by-step explanation:
A regular deck of playing cards is well shuffled. Please answer the following questions. All answers should be in fraction form.
On a single draw, what would be the probability of drawing the Ace of Hearts?
On a single draw, what would be the probability of drawing an Ace?
On a single draw, what would be the probability of drawing a red card?
On a single draw, what would be the probability of drawing a face card? A face card is a Jack, Queen or King.
What would be the probability of not drawing an Ace?
On the first draw, the Ace of Hearts is removed and not replaced. What would the probability be that on the next draw you draw another Ace?
Answer:
1/52
4/52 == 1/13
13/52 == 1/4
12/52 == 6/26 == 3/13
48/52 == 12/13
3/51
In this polygon, all angles are right angles. What is the area of this polygon? 18ft,12ft,21ft,8ft
In the given situation the required area of the polygon is 258ft².
What is a polygon?A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry.
A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.
A polygonal circuit's segments are referred to as its edges or sides.
Like other concepts in geometry that they created, the word "polygon" is Greek in origin. It merely denotes a lot of (poly) angles (gon).
There cannot be any bends, gaps, or openings in the shape of a polygon.
So, an object's area is how much space it takes up in two dimensions.
A rectangle's area is calculated as follows:
Area = length * breadth
Now, calculate the area as follows using the formula:
Area = [18 * (21 - 12)] + (12 * 8) = 258 ft²
Therefore, in the given situation the required area of the polygon is 258ft².
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Correct question:
In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft.
1. The tiles shown are placed in a bag. You randomly select one of the tiles,
return it to the bag, and then randomly select another tile. What is the
probability that the first number divided by the second number is greater
than zero?
the numbers:
-2
-1
2
1
Therefore, the probability that the first number divided by the second number is greater than zero is 1/3.
What is probability?In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.
Here,
Since we are returning the first tile to the bag before selecting the second one, the two selections are independent of each other.
There are two cases to consider:
Case 1: We select a positive number on the first draw.
The probability of selecting a positive number on the first draw is 2/3, since there are two positive numbers (-12 and 1) out of a total of three tiles.
Regardless of what number we select on the first draw, there is only one negative number (-2) in the bag, so the probability of selecting a negative number on the second draw is 1/3.
Therefore, the probability of selecting a positive number on the first draw and a negative number on the second draw (which results in a quotient greater than zero) is:
(2/3) x (1/3) = 2/9
Case 2: We select the negative number (-2) on the first draw.
The probability of selecting the negative number (-2) on the first draw is 1/3.
In this case, we must select the positive number on the second draw in order for the quotient to be greater than zero. There is only one positive number (1) in the bag, so the probability of selecting it on the second draw is 1/3.
Therefore, the probability of selecting the negative number (-2) on the first draw and the positive number on the second draw (which results in a quotient greater than zero) is:
(1/3) x (1/3) = 1/9
Since these are the only two cases that satisfy the condition, the overall probability is the sum of the probabilities of these two cases:
2/9 + 1/9 = 3/9 = 1/3
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a rectangle prism has a base that is 6 centimeters by 11 centimeters and has a height of 5.5 centimeters what is the surface area in square centimeters of the prism
the total area of all four square faces: 4 x 60.5 cm² = 242 cm²
To find the surface area of a rectangular prism, we need to calculate the area of each of its six faces and then add them up.
The two rectangular faces are congruent, so we only need to calculate one of them and multiply by 2.
The area of one rectangular face is:
6 cm x 5.5 cm = 33 cm²
Multiplying by 2 gives us the total area of both rectangular faces:
2 x 33 cm² = 66 cm²
The other four faces are also congruent, so we only need to calculate one of them and multiply by 4.
The area of one of the square faces is:
11 cm x 5.5 cm = 60.5 cm²
Multiplying by 4 gives us the total area of all four square faces:
4 x 60.5 cm² = 242 cm²
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Desmond is curious about how many hours of TV his family watches each week. Upon asking his family members, he found that they watched 30 hours of TV last week versus 17.7 hours of TV this week.
12.3 hours or 12 hours and 18 minutes.
This suggests that Desmond's family has decreased their TV-watching time by 12.3 hours in the past week.
This can be expressed numerically as 12.3 hours, or 12 hours and 18 minutes.
To calculate this, we can subtract 17.7 hours from 30 hours:
Last week: 30 hours of TV
This week: 17.7 hours of TV
30 hours - 17.7 hours = 12.3 hours
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Solve each of the following system of linear equations
x_1+〖3x〗_2=1
2x_1+〖5x〗_2=3
Answer:
To solve the system of linear equations:
x_1 + 3x_2 = 1 ...(1)
2x_1 + 5x_2 = 3 ...(2)
We can use the method of elimination to eliminate one of the variables. To do this, we multiply equation (1) by 2, and subtract it from equation (2), as follows:
2(x_1 + 3x_2 = 1) => 2x_1 + 6x_2 = 2 ...(3)
2x_1 + 5x_2 = 3 ...(2)
(2x_1 + 6x_2 = 2) ...(3)
-x_2 = 1
Thus, we have found that x_2 = -1.
We can substitute this value of x_2 into either equation (1) or (2) to solve for x_1. Let's use equation (1):
x_1 + 3(-1) = 1
x_1 - 3 = 1
x_1 = 4
Therefore, the solution to the system of linear equations is x_1 = 4, x_2 = -1.
So the solution set is {(4, -1)}.
gage stocks two ponds with bass and blue hill. he stocks pond a with 60 fish and pond b with 300 fish. gage stocks pond b with twice the amount of bass and six times the amount of bluegills as pond a. how many bass and bluegills does gage stock in pond w
Finally, we can use the earlier equations to find the number of bass and bluegills in pond B:
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
What is a math equation, exactly?In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.
Let's denote the number of bass in pond A as "x" and the number of bluegills in pond A as "y".
According to the problem, Gage stocks pond B with twice the amount of bass as pond A, so the number of bass in pond B is 2x. He also stocks pond B with six times the amount of bluegills as pond A, so the number of bluegills in pond B is 6y.
We know that Gage stocks pond A with a total of 60 fish, so:
x + y = 60
We also know that Gage stocks pond B with a total of 300 fish, so:
2x + 6y = 300
x + 3y = 150
Now we have two equations:
x + y = 60
x + 3y = 150
We can solve for x in the first equation:
x = 60 - y
Substitute this expression for x into the second equation:
(60 - y) + 3y = 150
2y = 90
y = 45
Now that we know that pond A has 45 bluegills, we can use the equation x + y = 60 to find that pond A has 15 bass (since 45 + 15 = 60).
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
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During the summer, Curran and AJ
started their own business mowing
lawns. Before starting any work, Curran
spent $20 to ! ll up the gas tank for the
lawnmower. The boys agreed that each
person would earn the same amount
after Curran was reimbursed the money
he spent for gas. After a week of work,
the boys were paid a total of $177.
Curran ! lled up the gas tank just once.
How much did each boy earn?
The boys agreed that each person would earn the same amount after Curran was reimbursed the money he spent on gas. After a week of work, the boys were paid a total of $177. thus each boy earned $88.50.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
Let's denote the amount each boy earns by x.
According to the given information, Curran spent $20 for gas, which he should be reimbursed for. This means that the total revenue of the business was $177 + $20 = $197.
Since each person earns the same amount, we can set up an equation:
2x + $20 = $197
Simplifying and solving for x, we get:
2x = $177
x = $88.50
Therefore, each boy earned $88.50.
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Consider the following points.
(−2,−3),(3,3)
and (3,−3)
Step 1 of 2 : Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene.
The perimeter of a triangle is the sum of the lengths of its three sides.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
In the case of triangle HGI, the perimeter is calculated by adding the three side lengths together. For example, if the three sides are labeled a, b, and c, the perimeter would be calculated as a + b + c.
The perimeter of triangle HGI can be calculated by knowing the lengths of its three sides. If the lengths of the three sides are 7, 8, and 9 units respectively, the perimeter of triangle HGI is 7 + 8 + 9 = 24 units.
The perimeter of triangle HGI can also be calculated using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. Using this theorem, the lengths of the other two sides can be calculated if the length of one side and the measure of the included angle is known.
In summary, the perimeter of triangle HGI can be calculated by adding the lengths of its three sides or by using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known.
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Please help 13. Phil works at a department store and gets an employee discount. The price he pays can be modeled by the function d(c) = c - 0.08c , where is the original price of the item. Find d(25) and describe what this means in context.
With the original price at 25 units , he paid 23 units and d(25) means the price he paid when the original price is 25 units.
How to solve a function?Phil works at a department store and gets an employee discount. The price he pays can be modelled by the function d(c) = c - 0.08c , where c is the original price of the item.
Therefore, let's find d(25) and describes what it means.
Hence,
d(c) = c - 0.08c
where
c = original priceTherefore,
d(25) = 25 - 0.08(25)
d(25) = 25 - 2
d(25) = 23
Therefore, d(25) is the price he paid when the original price is 25 units. Therefore, he paid 23 units
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7. Alexis has 145 stickers. She wants to divide the stickers evenly among 5 of her friends. How
many stickers will each friend get?
Write your answer in the box.
stickers.
8. There are 2,472 seats in the school auditorium. The seats are divided into 6 equal sections.
How many seats are in each section? Write your answer in the box.
seats
Explain how you found your answer. Show your work.
Answer: 7: 29 stickers for each friend
8: 412 seats in each section
Step-by-step explanation:
We will have to divide 145 (stickers) by 5 (friends) to get 29
We will have to divide 2472 by 6 to get 412
7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers
8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.
I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.
Solve for x. Round all intermediate values and answers to the nearest tenth . 19 70 61
12.6 is the measure of the value of x
Solving the sides of a right triangleThe given diagram is a right triangle and we need to determine the measure of value of 'x'.
First, we need to determine the measure of the height using the trigonometry identity;
cos55 = h/45
h = 45cos55
h = 25.81
Determine the measure of 'x'
tan 64 = h/x
x = h/tan64
x = 25.81/tan64
x = 12.6
Hence the measure of the value of x from the fiigure is 12.6
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use transformations of f(x)=[tex]x^{2}[/tex] to graph g(x)=[tex]x^{2}[/tex] -3 select all the transformations that are needed to graph the given function
Select all the transformations that are needed to graph the given function using .
A.
Shift the graph to the left.
B.
Stretch the graph vertically by a factor of .
C.
Shift the graph .
D.
Reflect the graph about the y-axis.
E.
Reflect the graph about the x-axis.
F.
Shift the graph to the right.
G.
Stretch the graph horizontally by a factor of .
H.
Shift the graph .
I.
Shrink the graph horizontally by a factor of .
J.
Shrink the graph vertically by a factor of .
The transformations that are needed to graph the given function is
Shrink the graph vertically by a factor of 3.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
f(x) = x²
g(x) = x² - 3
We see that,
f(x) → g(x)
There is a vertical shrink by a factor of 3.
Thus,
There is a shrinking vertically of f(x) by a factor of 3.
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Find the slope of the line. (-5, -4) (1,-3)
Answer: The slope of the line between the points (-5, -4) and (1,-3) is 1/6 = 0.1667.
Step-by-step explanation:
To calculate the slope between two points, we apply the following formula:
[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff \ m=\dfrac{y_2-y_1}{x_2-x_1} }}[/tex]
where m is the slope of the line.
We identify the points:
[tex]\boldsymbol{\sf{\diamond x_1=-5 \ \ \ \ \diamond y_1=-4 \ and \ x_2=1 \ \ \ \ \diamond y_2=-3 }}[/tex]
We substitute these points in the formula and solve:
[tex]\boldsymbol{\sf{m=\dfrac{-3-(-4)}{1-(-5) }=\dfrac{1}{6}=0.1667 }}[/tex]
The slope of the line between the points (-5, -4) and (1,-3) is 1/6 = 0.1667.
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ACB radio is rated at 7.5 watts, and actual measurements show that it delivers 5.1 watts to its antenna. What is its
efficiency?
(Type a whole number or decimal rounded to two decimal places as needed)
Answer:
The efficiency of the ACB radio is 68%.
Step-by-step explanation:
here is a step-by-step explanation of how to calculate the efficiency of the ACB radio:
Recall that the efficiency of a radio is the ratio of the power delivered to the antenna to the input power, expressed as a percentage.
Identify the given values: we are told that the ACB radio is rated at 7.5 watts, and it delivers 5.1 watts to the antenna.
Plug in the values to the efficiency formula: Efficiency = (Power delivered to the antenna / Input power) x 100%. Using the given values, we get: Efficiency = (5.1 / 7.5) x 100%.
Perform the division: 5.1 divided by 7.5 equals 0.68, or 68% when multiplied by 100%.
Round the answer: The prompt asks for the answer to be rounded to two decimal places, so we get 0.68 rounded to two decimal places is 0.68.
State the answer: The efficiency of the ACB radio is 68%.
What does the index value of 99.2 in 1980 mean? Explain your reasoning.
The index value of 99.2 in 1980 mean Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992, the correct option is D.
What is the ratio?
Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
Years, prices, prices as a percentage of 1990 price, price index 1990=100
Now,
The given table shows the average gasoline prices per gallon for various years, as well as the price index for each year, with 1990 being the reference year with a price index of 100. The price index measures the change in the price of gasoline relative to the price in 1990. Therefore, the price index value of 99.2 for 1980 means that the average gasoline price in 1980 was 0.992 times the price of gasoline in 1990.
It is important to note that the gas price index does not directly measure the cost per gallon of gas. Rather, it is a measure of the change in gasoline prices over time, with a reference year (in this case, 1990) used as a baseline.
Therefore, by ratio the answer will be Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992.
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**URGENT**
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $14.69 and the monthly cost for 57 minutes is $17.68 . What is the monthly cost for 39 minutes of calls?
I will give brainliest. Just please help
The monthly cost for 39 minutes of calls is $14.30.
According to given information :Let's start by using the given information to find the slope and y-intercept of the linear function that gives the monthly cost in terms of the total calling time. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Using the points (34, 14.69) and (57, 17.68), we get:
m = (17.68 - 14.69) / (57 - 34) = 0.09
To find the y-intercept, we can use the point-slope form with either of the two points:
y - 14.69 = 0.09(x - 34)
y - 14.69 = 0.09x - 3.06
y = 0.09x + 11.63
So the monthly cost (y) is a linear function of the total calling time (x) with a slope of 0.09 and a y-intercept of 11.63.
To find the monthly cost for 39 minutes of calls, we simply substitute x = 39 into the equation:
y = 0.09(39) + 11.63 = 14.30
Hence, the monthly cost for 39 minutes of calls is $14.30.
What is cost price ?
Cost price refers to the amount of money that is paid to purchase an item or produce a good. It includes all the costs incurred in the production or acquisition of an item, such as the cost of raw materials, labor, and other expenses. Cost price is important for businesses because it helps determine the profit margin on a product, which is the difference between the selling price and the cost price. A business needs to set a selling price that covers the cost of producing or acquiring a product and leaves room for profit.
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Someone help me asap!
The sinusoidal function is y = sin(2/3x) - 5
How to determine the sinusoidal functionThe general form of a sinusoidal function is given by:
y = A sin(Bx + C) + D
where:
A is the amplitudeB is the frequencyC is the phase shiftD is the vertical shiftWe know that the period is 3π and the amplitude is 1.
So, we have
A = 1
B = (2π)/(3π) = 2/3
So, we have
y = sin(2/3x + C) + D
The point (-3π/2, -5) implies that, the function is shifted down by 5 units
So, we have
y = sin(2/3x) - 5
Hence, the function is y = sin(2/3x) - 5
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Spiral Review
8. The temperature in Alaska is -6 °C and drops to -11 °C overnight.
Write and evaluate a subtraction expression to determine the change
in temperature.
Answer:
The subtraction expression to determine the change in temperature is:
-11 °C - (-6 °C)
Simplifying the expression:
-11 °C + 6 °C
The change in temperature is -5 °C.
A nurse administers 25 milligrams of a drug to a patient. The amount of the drug, A, in milligrams, left in the patient after t hours can be modeled by the function A(t) = 25e 0.354 How many hours will it take for the amount of the drug left in the patient to drop to 0.25 milligrams? Round your answer to the nearest tenth of an hour.
As a result, it will take around 4.9 hours for the quantity of medicine remaining in the body to decline to 0.25 milligrams.
What is exponent?In mathematics, an exponent (also known as power or index) is a number that indicates how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number. For example, in the expression 2³, 2 is the base number and 3 is the exponent. The exponent 3 indicates that the base number 2 is multiplied by itself 3 times, resulting in the value 8. Exponents are a shorthand notation for repeated multiplication and are used in many areas of mathematics and science.
Here,
The given model for the amount of the drug left in the patient after t hours is:
A(t) = 25e*(0.354t)
We need to find the time t when the amount of the drug left in the patient is 0.25 milligrams. So we can set A(t) = 0.25 and solve for t:
0.25 = 25e*(0.354t)
Dividing both sides by 25, we get:
0.01 = e*(0.354t)
Taking the natural logarithm of both sides, we get:
ln(0.01) = 0.354t
Simplifying, we get:
t = ln(0.01)/0.354 ≈ 4.9 hours
Therefore, it will take about 4.9 hours for the amount of the drug left in the patient to drop to 0.25 milligrams.
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PLEASE HELP!
Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
Answer:
Step-by-step explanation:
A possible trigonometric function that would model the tide situation for this beach is:
h(t) = -2 + 3sin(πt/12)
where h(t) represents the height of the tide at time t in hours, and πt/12 represents the angle (in radians) corresponding to the time t on a unit circle with a period of 24 hours.
The constant -2 represents the lowest point of the tide (2 feet below sea level), and the coefficient of 3 in front of the sine function determines the amplitude of the tide, which is 3 feet (half the difference between the highest and lowest points of the tide, which is 4 - (-2) = 6 feet). The sine function oscillates between -1 and 1, so the range of the function h(t) is between -2 - 3 = -5 feet (when the sine function takes on its minimum value of -1) and 4 - 2 = 2 feet (when the sine function takes on its maximum value of 1), as expected for the given tidal range.
Because the Earth rotates through two tidal “bulges” every lunar day, coastal areas experience two high and two low tides every 24 hours and 50 minutes. High tides occur 12 hours and 25 minutes apart. It takes six hours and 12.5 minutes for the water at the shore to go from high to low, or from low to high.
time series data of a typical the gap store should show which of the following data patterns? multiple choice a. trend b. cyclical c. seasonal d. all of the options are correct. e. random
The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.
What is time series data:
Time series data refers to a collection of data points that are measured over time at regular intervals. The time series data could refer to various metrics such as sales, revenue, foot traffic, website traffic, inventory levels, and other relevant business metrics that change over time.
By analyzing time series data, businesses can gain insights into trends, patterns, and other factors that can affect their operations.
Time series can be used for forecasting. By analyzing past trends and patterns, businesses can make predictions about future performance and take proactive measures to achieve their goals.
Since the time series will follow the trend, have multiple choices, and will be cyclical and it will analyze the patterns over time periods seasonally.
Therefore,
The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.
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A card is drawn at random from a standard deck. What is the probability that it is a black card and a king?
Answer: 1/52 or 1.923%
Step-by-step explanation:
Due to the fact that the standard deck of 52 cards has 4 Kings then out of 52 is 1 that is going to be a black card. Hence the 1/52 as for the 1.923% is the percentage form of 1/52 for either or you need.
Find the measures of AB and AC
Show all necessary calculations for full credit.
Applying the AA Similarity theorem:
AC = 10
AB = 20
What are Similar Triangles?If two triangles have two corresponding congruent triangles they are similar to each other according to the AA Similarity theorem, which means their corresponding sides are proportional.
Triangles DCE and ACB are similar to each other by AA Similarity theorem, therefore:
AC/CE = BC/CD
Substitute:
AC/8 = 15/12
AC = (15 * 8)/12
AC = 10
Also,
AB/16 = 15/12
AB = (16*15)/12
AB = 20
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A carver begins work on a block of material that has a mass of 1250 g. The block's dimensions are 5 cm by 14 cm by 7 cm. What is the density of the material?
Answer:
Below
Step-by-step explanation:
Definition of density is mass / volume = 1250 g / (5 x14x7) = 2.55 gm/cm^3
Find and interpret the average rate of change illustrated in the following graph
Answer:
Step-by-step explanation:
Average rate of change is the same thing as the slope. Ours here is negative. Our rate of change then goes down $5000 per year, so it is -5 per year. That means that the value of the machine decreases $5000 for every year that goes by.
Solve for x. 6/-4.5=8/4x
The value of x when we solve the equation 6/ -4.5 = 8/4x is x = - 1.5.
What is equation?A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. Another well formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's equivalents in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.
The given equation is:
6/ -4.5 = 8/4x
Using the method of cross multiplication or butterfly method of multiplication we have:
6(4x) = (8)(-4.5)
24x = -36
x = -1.5
Hence, the value of x for the equation 6/ -4.5 = 8/4x is x = - 1.5.
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Find answers to 6,7,8
The solution is, the length of MP = 9.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
from the given figure we get,
MPN is a right angled triangle,
by using Pythagorean theorem, we get,
here, height = 12
hypotenuse = 15
so, base = MP
= √15² - 12²
=√81
=9
Hence, The solution is, the length of MP = 9.
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Select ALL of the solutions of the following system of linear inequalities below.
The solutions of the system of inequalities are:
(0, 3)
(6, 2)
How to find the solutions of the system?Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).
And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.
Then the points that are solutions are:
(0, 3)
(6, 2)
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