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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The table shows the number of turkey and ham sandwiches sold by Derby’s Deli for several days in one week Sandwiches Sold at Derby’s Deli Day Turkey Ham Monday 7 9 Tuesday 13 11 Wednesday 8 8 Thursday 15 6 Friday 12 16 What is the difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold?
The difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold is 3.
First, let's find the median number of turkey and ham sandwiches sold.
To find the median:
1. Arrange the data in ascending order.
2. If there's an odd number of data points, the median is the middle value. If there's an even number of data points, the median is the average of the two middle values.
Turkey sandwiches sold: 7, 8, 12, 13, 15
Ham sandwiches sold: 6, 8, 9, 11, 16
Now let's find the medians:
Turkey median: There are 5 data points, which is odd, so the median is the middle value, 12.
Ham median: There are 5 data points, which is odd, so the median is the middle value, 9.
Finally, let's find the difference between the medians:
Difference = Turkey median - Ham median
Difference = 12 - 9
Difference = 3
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Y – 84 = -11(x – 6)
What is the point and slope
A 2-column table with 6 rows. the first column is labeled years with entries 1, 2, 3, 4, 5, 6. the second column is labeled value(dollar sign) with entries 5,250; 5,512.50; 5,788.13; 6,077.54; 6,381.42; 6,700.49. the data in the table represents the value of a savings account at the end of each year for 6 years. the relationship between the increasing years and the increasing value of the account is exponential. there is rate of change in an exponential relationship. after each year, the value of the account is times as large as the previous year.
The value of the account is 1.05 times as large as the previous year
There is a 2-column table with 6 rows representing the value of a savings account at the end of each year for 6 years. The relationship between the years and the value of the account is exponential, and there is a rate of change in this exponential relationship.
To find the rate of change in this exponential relationship, you can follow these steps:
1. Divide the value of the account in the second year by the value of the account in the first year: 5,512.50 / 5,250 = 1.05.
2. Since the relationship is exponential and the rate of change is constant, the account's value will increase by the same factor every year. In this case, the rate of change is 1.05, which means that after each year, the value of the account is 1.05 times as large as the previous year.
In summary, the rate of change in the exponential relationship between the increasing years and the increasing value of the account is 1.05, meaning that after each year, the value of the account is 1.05 times as large as the previous year.
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If the mean weight of 4 backfield members on the football team is 234 lb and the mean weight of the 7 other players is 192 lb, what is the mean weight of the 11-person team?
The mean weight of the team is approximately ___ pounds.
(Round to the nearest tenth.)
Answer: The mean weight of the 11-person team is 207.3 pounds
Step-by-step explanation:
According to the question,
The mean weight of 4 backfield members = 234 lb
Therefore, the total weight of 4 backfield members = 4 × 234 = 936 lb
Similarly,
The mean weight of the 7 players = 192 lb
And the total weight of 7 players = 7 × 192 = 1344 lb
∴ Total weight of 11 players = (936 + 1344) lb = 2280 lb
We know that,
Mean = [tex]\frac{Total Sum}{Total number of variables}[/tex]
∴ To find the mean weight of the 11 players we need to divide the total weight by 11 :
Mean = [tex]\frac{2280}{11} = 207.27[/tex]
Rounding off to the nearest tenth we get,
Mean = 207.3
Hence, the mean weight of the team is approximately 207.3 pounds
How do I find the answer to this problem The period of y = sin3 is _____
The period of the function y = sin(3x) is (2π/3).
I assume you meant to write "y = sin(3x)".
The period of the function y = sin(3x) can be found using the formula:
period = 2π / b
where "b" is the coefficient of x in the function.
In this case, b = 3, so:
period = 2π / 3
Therefore, the period of the function y = sin(3x) is (2π/3).
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PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!
Answer:
75°
Step-by-step explanation:
Arc length LM is 108°, meaning that angle <K is half of the arc length, 54°.
*REMEMBER* all 3 angles inside a triangle must add up to 180° to make it a triangle.
We have angle <L, <K, and we are looking for angle <M.
51+54+?=180
105+?=180
?=75
Angle <M is 75°
Hope this helps :)
Makayla win the 26 foot ladder against the wall so that it forms a angle of 69° with the ground what’s the horizontal distance between the base of the ladder in the wall round your answer to the nearest 10th of a foot if necessary
Answer:
9.32
Step-by-step explanation:
cos 69 = x/26
x= 26 cos 69
x= 9.317 ~= 9.32
Answer:
Step-by-step explanation:
La familia de una de tus compañeras, que disponía de un terreno con 7 lotes colindantes, y se vieron en la necesidad de venderlos. Establecieron un precio por metro cuadrado de 800 pesos y tienen que calcular el costo, con base en los metros cuadrados que tiene cada lote. Determina el área de cada terreno, así como su precio
The area and cost of each of the lots is given below
What is the area?The area and cost of each of the lots is calculated below
To calculate the rectangle trapezoid, it will be:
B = 140m
h = 50m
b = 70m
Note that Area of Lot 1 : A =(B+b)h/2
Hence Height will be:
A= (140m+ 70m) 50m/2
A = 5250 m²
Cost: C = 5250m² *800 pesos = $4,200,000
Lot 2 is another rectangle trapezoid:
B = 150m
b = 80m
h = 50m
Area: A= (150m+ 80m)50m/2
A = 5750 m²
Cost: C = 5750m² x 800 pesos = $4,600,000
So, for Lot 3 which is a rectangle:
b = 70m
to = 50m
Area: A =a x b
W=50m x 70m
A = 3500 m²
Cost: C = 3500m² x 800 pesos = $2,800,000
Lot 4 is a right triangle:
b = 70m
h = 50m
Area: A =b x h/2
A= (50m x 70m)/2
A = 1750 m²
Cost: C = 1750 m² x 800 pesos = $1,400,000
So for Lot 5 that is a rhomboid:
b = 150 base meters
h=50m
Area: A=b x h
A= (150m x 50m
H = 7500 m²
Cost: C = 7500m² x 800 pesos = $6,000,000
So, for Lot 6 that is an isosceles triangle:
b = 140m
h= 50m
Area: A =b x h/2
A= (140m x 50m)/2
A = 3500 m²
Lastly, the Cost: C = 3500m² x 800 pesos = $2,800,000
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See transcribed text below
The family of one of your colleagues, who had a piece of land with 7 adjoining lots, and they found themselves in need of selling them. They established a price per square meter of 800 pesos and they have to calculate the cost, based on the square meters that each lot has. Before continuing, review the terrain sketch and answer the questions
What is the area and cost of each of the lots?
Tell which measure of central tendency best describes the data.
Weights of books (oz):
12 10 9 15 16 10
Mean
Median
Mode
if a slope is when xincome in thousands of dollars, then what is the slope when income in dollars? (hint: a one-dollar change has only 1/1000 of the impact of a one-thousand-dollar change.)
If the slope is defined as the change in the dependent variable (y) divided by the change in the independent variable (x), then the slope would depend on how the dependent variable and independent variable are measured.
Assuming that the dependent variable y is some form of economic outcome (e.g., consumption, savings, investment) and the independent variable x is income, then the slope of the relationship would depend on the units in which income is measured.
If income is measured in thousands of dollars, then a one-unit change in income would correspond to a $1,000 change. Therefore, the slope would reflect the change in the economic outcome associated with a $1,000 change in income.
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In a recent poll six hundred adults were asked a series of questions about the state of the economy and their children's future. One question was, "do you expect your children to have a better life than you have had, a worse life, or a life about the same as yours?" Suppose the responses showed 245 better, 311 worse, and 44 about the same. Use the sign test and ???? = 0. 05 to determine whether there is a difference between the number of adults who feel their children will have a better life compared to a worse life. State the null and alternative hypotheses. (Let p = the proportion of adults who feel their children will have a better life. ) H0: p ≠ 0. 50
Null Hypothesis (H0): The proportion of adults who feel their children will have a better life is equal to 0.5.
Alternative Hypothesis (HA): The proportion of adults who feel their children will have a better life is not equal to 0.5.
How to explain the hypothesisThe sign test is a non-parametric statistical test used to test the hypothesis that the median of a population is equal to a specified value.
The critical value is 1.96.
The absolute value of the test statistic is greater than 1.96. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the number of adults who feel their children will have a better life compared to a worse life.
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Triangle abc lies on the plane such that point b is at b(-8,-4). the midpoint of side ac is m with coordinates m(7,5). if a segment from a was drawn to the midpoint of side bc then where would it intersect bm
If a segment from a was drawn to the midpoint of side AB then where would it intersect BM is AN = 2.5cm and MN = 3.5cm.
A midpoint is a point in the midway of a line connecting two locations. The two reference points are the line's ends, and the midpoint is located between the two. The midway splits the line connecting these two places in half. Furthermore, a line drawn to bisect the line connecting these two points passes through the midpoint.
The midpoint formula is used to locate the midway between two places with known coordinates. If we know the coordinates of the other endpoint and the midpoint, we can apply the midpoint formula to obtain the coordinates of the endpoint.
ΔAMN = ΔABC (Corresponding angles)
ΔANM = ΔACB (Corresponding angles)
ΔAMN ≈ ΔABC (By AA similarity test)
[tex]\frac{AM}{AB} =\frac{AN}{AC} =\frac{MN}{BC}[/tex] (CPST)
Since, M is mid-point of AB,
AM = 1/2AB, or, AM/AB = 1/2
AM/AB = AN/AC = 1/2.
AN/AC = 1/2
AN/5 =1/2 [AC = 5cm]
MN/7 =1/2 [BC = 7cm]
MN = 7/2 = 3.5
AN = 2.5cm and MN = 3.5cm.
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Using the equation of the line of best fit, estimate the number of coffee drinks sold on a day that 32 ice cream treats
were sold.
write an explanation that justifies your conclusion.
The number of coffee drinks sold on a day that 32 ice cream treats were sold using the equation of line of best fit is y = 32m + b, where y represents the number of coffee drinks sold and ice cream treats that were sold = 32.
To estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold, we would need to use the equation of the line of best fit. This equation represents the trend of the data collected and can be used to make predictions based on that trend.
Assuming that the data collected shows a positive correlation between the number of ice cream treats sold and the number of coffee drinks sold, we can use the equation of the line of best fit to estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold.
Let's say that the equation of the line of best fit is y = mx + b, where y represents the number of coffee drinks sold and x represents the number of ice cream treats sold. Using the data collected, we can find the values of m and b that best fit the trend.
Once we have the equation, we can substitute x = 32 into the equation and solve for y. This will give us an estimate of the number of coffee drinks sold on a day that 32 ice cream treats were sold.
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You have $20 to spend. You go to the store and buy a bouncy ball for an unknown amount of money and then you buy a glider airplane for $3. If you have $15 left over, how much did you spend on the bouncy ball?
Answer: Let's start by subtracting the cost of the glider airplane from the total amount of money you started with:
$20 - $3 = $17
We know that you spent $15 of that $17 on the bouncy ball, since you had $15 left over after buying both items:
$17 - $15 = $2
Therefore, you spent $2 on the bouncy ball.
Answer: $2.
Step-by-step explanation:
Hello im new to brainly and i needed some help becuase i dont understand the question.
The number of customers surveyed were 15 customers.
The greatest number of items purchased by a customer was 11 items.
The customers purchased 9 items is 2 customers.
The customers purchased at least 5 items was 7 customers.
The median number of items purchased was 3.
How to interpret the line plots?How many customers were surveyed?
1 (0 items) + 1 (1 item) + 2 (2 items) + 4 (3 items) + 0 (4 items) + 2 (5 items) + 0 (6 items) + 2 (7 items) + 0 (8 items) + 2 (9 items) + 0 (10 items) + 1 (11 items) = 15 customers
The greatest number of items purchased by a customer is 11 items. 2 customers purchased 9 items.
How many customers purchased at least 5 items?
2 (5 items) + 0 (6 items) + 2 (7 items) + 0 (8 items) + 2 (9 items) + 0 (10 items) + 1 (11 items) = 7 customers
To find the median, we need to find the middle value of the data. Since there are 15 customers, the median will be the 8th value when the data is ordered.
0, 1, 2, 2, 3, 3, 3, 3, 5, 5, 7, 7, 9, 9, 11
The median number of items purchased is 3.
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Answer this Question
The missing numbers on the grids are given as follows:
2 and -6.
How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
x and y.
The top grid represents the sum of the measures, hence:
x + y = -4.
The bottom grid represents the subtraction of the measures, hence:
x - y = 8.
Adding the two equations, the value of x, representing the left grid, is given as follows:
2x = 4
x = 2.
Then the value of y, representing the right grid, is given as follows:
2 + y = -4
y = -6.
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Use the first three non-zero terms of a Maclaurin series to estimate the integral from 0 to 1 of the cosine of x squared, dx.
0. 905
0. 904
0. 806
1. 16
Using the first three non-zero terms of a Maclaurin series, the estimated value of the integral from 0 to 1 of the cosine of x squared, dx is 0.905
To estimate the integral from 0 to 1 of the cosine of x squared, dx using the first three non-zero terms of a Maclaurin series, we first need to find the Maclaurin series for cosine of x squared:
cos(x^2) = 1 - x^4/2! + x^8/4! - x^12/6! + ...
The first three non-zero terms are 1, -x^4/2!, and x^8/4!.
Now we can use these terms to estimate the integral from 0 to 1:
∫₀¹ cos(x²) dx ≈ ∫₀¹ [1 - x^4/2! + x^8/4!] dx
Integrating term by term, we get:
∫₀¹ [1 - x^4/2! + x^8/4!] dx ≈ [x - x^5/5! + x^9/9!] from 0 to 1
Plugging in 1 and 0, respectively, and simplifying, we get:
[x - x^5/5! + x^9/9!] evaluated at x=1 - [x - x^5/5! + x^9/9!] evaluated at x=0
= [1 - 1/120 + 1/6561] - [0 - 0 + 0]
≈ 0.905
Therefore, the estimated value of the integral from 0 to 1 of the cosine of x squared, dx using the first three non-zero terms of a Maclaurin series is 0.905.
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420 g of fl our is to be divided into a ratio of 7 : 3 for two different recipes. Find the smaller amount.
Can somebody check if 8 and 9 are correct?
Answer:
Yes, they are totally correct, I've checked with a calculator
3 /12 cups of flour for every 3/4 of a cup of milk. How much flour for 1 cup of milk
The amount of cup of flour for 1 cup of milk is 1/3 cup
What is proportion?Proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 4 girls you could write the ratio as: 1 : 4 (for every one boy there are 4 girls).
Another example is if 5 mangoes cost $250, the price of mango will 250 × 1/5 = $50
Similarly, 3/12 cups of flour is for every 3/4 cups of milk
therefore,
1 cup of milk will need 3/12 × 4/3
= 12/36
= 1/3
therefore for 1 cup of milk 1/3 of flour will be needed.
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a small plane leaves an airport and flies north at 240 mi/hr. a jet leaves the airport 30 minutes later and follows the small plane at 360 mi/hr. how long does it take the jet to overtake the small place?
According to the distance, it will take the jet 1 hour to overtake the small plane.
Let's first calculate the distance traveled by the small plane in the time it takes for the jet to overtake it. Since the small plane is flying for an extra 30 minutes, its travel time is "t + 0.5" hours. Therefore, the distance traveled by the small plane is:
Distance of small plane = Speed of small plane x Time of small plane
Distance of small plane = 240 x (t + 0.5)
Now, let's calculate the distance traveled by the jet in "t" hours:
Distance of jet = Speed of jet x Time of jet
Distance of jet = 360 x t
Since both planes are at the same point at the time of overtaking, we can set the distances traveled by both planes equal to each other:
240 x (t + 0.5) = 360 x t
We can solve for "t" using algebra:
240t + 120 = 360t
120 = 120t
t = 1
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I need help with these questions pls
Volumes of the cylinder are given by:
(A) (1) Volume = 2486.88 cubic in.
(2) Volume = 108518.4 cubic ft.
(3) Volume = 47608.68 cubic yd.
(B) (4) Volume = 508.68 cubic ft.
(5) Volume = 8490.56 cubic yd.
(6) Volume = 43407.36 cubic in.
(7) Volume = 9420 cubic ft.
(8) Volume of cylindrical flower vase = 1105.28 cubic in.
Surface Area of the Cylinder are given by:
(1) Surface Area = 113.04 square in.
(2) Surface Area = 1444.4 square ft.
(3) Surface Area = 678.24 square yd.
(4) Surface Area = 1130.4 square yd.
(5) Surface Area = 602.88 square in.
(6) Surface Area = 1055.04 square ft.
(7) Surface Area = 1570 square ft.
(8) Surface Area = 791.28 square yd.
(9) Surface Area = 326.56 square in.
We know that the volume of a cylinder with radius 'r' and height 'h' is given by,
V = 2πr²h
(A) (1) From the figure, radius = 6 in and height = 11 in.
So the volume = 2π(6)²*11 = 2486.88 cubic in.
(2) Radius = 24 ft. and height = 30 ft.
Hence, the volume of cylinder = 2π(24)²*30 = 108518.4 cubic ft.
(3) Radius = 19 yd. and height = 21 yd.
Hence, the volume of cylinder = 2π(19)²*21 = 47608.68 cubic yd.
(B) (4) Radius = 3 ft. and height = 9 ft.
Hence, the volume of cylinder = 2π(3)²*9 = 508.68 cubic ft.
(5) Radius = 13 yd. and height = 8 yd.
Hence, the volume of cylinder = 2π(13)²*8 = 8490.56 cubic yd.
(6) Radius = 16 in. and height = 27 in.
Hence, the volume of cylinder = 2π(16)²*27 = 43407.36 cubic in.
(7) Radius = 10 ft. and height = 15 ft.
Hence, the volume of cylinder = 2π(10)²*15 = 9420 cubic ft.
(8) Cylindrical flower vase is 11 inch tall and radius of vase is 4 inches.
The volume of flower vase = 2π(4)²*11 = 1105.28 cubic in.
Now we know that the surface area of a Cylinder with radius 'r' and height 'h' is given by,
S = 2πrh + 2πr²
(1) Radius = 2 in. and Height = 7 in.
Hence the surface area = 2π*2*7 + 2π(2)² = 113.04 square in.
(2) Radius = 10 ft. and Height = 13 ft.
Hence the surface area = 2π*10*13 + 2π(10)² = 1444.4 square ft.
(3) Radius = 6 yd. and Height = 12 yd.
Hence the surface area = 2π*6*12 + 2π(6)² = 678.24 square yd.
(4) Radius = 9 yd. and Height = 11 yd.
Hence the surface area = 2π*9*11 + 2π*9² = 1130.4 square yd.
(5) Radius = 6 in. and Height = 10 in.
Hence the surface area = 2π*6*10 + 2π(6)² = 602.88 square in.
(6) Radius = 8 ft. and Height = 13 ft.
Hence the surface area = 2π*8*13 + 2π(8)² = 1055.04 square ft.
(7) Radius = 10 ft. and Height = 15 ft.
Hence the surface area = 2π*10*15 + 2π(10)² = 1570 square ft.
(8) Radius = 6 yd. and Height = 15 yd.
Hence the surface area = 2π*6*15 + 2π(6)² = 791.28 square yd.
(9) Radius = 4 in. and Height = 9 in.
Hence the surface area = 2π*4*9 + 2π(4)² = 326.56 square in.
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PLEASE HELP
Nathaniel is moving the dresser in his bedroom so it is against a different wall.
The length of the wall is feet and the dresser is feet long.
Which estimation is best for centering the dresser along the wall?
A.
The dresser should be placed about 6 feet from each end of the wall.
B.
The dresser should be placed about 8 feet from each end of the wall.
C.
The dresser should be placed about 10 feet from each end of the wall.
D.
The dresser should be placed about 12 feet from each end of the wall
To determine the best estimation for centering the dresser along the wall, we need to consider the length of the wall and the length of the dresser. Let's call the length of the wall "W" and the length of the dresser "D".
Since we don't know the actual values of W and D, we'll have to work with the given options.
Option A suggests placing the dresser about 6 feet from each end of the wall. This would leave a space of W - 12 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
Option B suggests placing the dresser about 8 feet from each end of the wall. This would leave a space of W - 16 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
Option C suggests placing the dresser about 10 feet from each end of the wall. This would leave a space of W - 20 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
Option D suggests placing the dresser about 12 feet from each end of the wall. This would leave a space of W - 24 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
To find the best estimation for centering the dresser along the wall, we need to determine which option provides the closest match between the available space in the middle of the wall and the length of the dresser.
Without knowing the actual values of W and D, it's difficult to say for certain which option is best. However, we can make an educated guess by considering the lengths of typical bedroom walls and dressers.
Based on this, option C (placing the dresser about 10 feet from each end of the wall) seems like a reasonable estimation for centering the dresser along the wall. This option provides a space of W - 20 feet in the middle of the wall, which is likely sufficient for most dressers.
Of course, the actual placement of the dresser will depend on other factors as well, such as the layout of the room and the location of other furniture. It's always a good idea to measure carefully and test different arrangements before settling on a final placement for any piece of furniture.
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IN A CLASS OF 100 STUDENTS ,35 LIKE SCIENCE ,45 LIKE MATH , 10 LIKE BOTH. HOW MANY LIKE EITHER OF THEM , HOW MANY LIKE NEITHER OF THEM
Answer: 5 like either, 5 like neither.
Step-by-step explanation: If we add up those who like science, math and both, we get 90. That leaves 10 students, and because all the other numbers end in 5’s or 0’s, I’d say we split this evenly. So 5 like either, and 5 like neither.
Answer:
Like either science or math but not both: 60
Like neither: 30
Step-by-step explanation:
Total: 100
Like science: 35
Like math: 45
Like both: 10
Subtract 10 from "like science" and 10 from "like math"
Like only science: 25
Like only math: 35
Like both science and math: 10
Total who like math, science, or both: 70
Like either science or math but not both: 25 + 35 = 60
Like neither: 100 - 70 = 30
Reema bought pencils for school in August. She gave
now had 3 pencils left.
。 of them to her friends. She used
of what she had left the first month of school. She
How many pencils did she buy in August?
O A 48
O B. 36
O c. 24
OD. 12
O E. 6
By simplification Reema bought 5 boxes of pencils, which is a total of 60 pencils, in August.
Let x be the number of pencils Reema bought in August. According to the problem, she gave away 1/4 of the pencils, which means she kept 3/4 of the pencils. Then, she used 2/3 of what she had left, which means she used:
(2/3)(3/4)x = (1/2)x
So, if she used half of what she had left, she must have started with twice as many pencils. Therefore:
2x = total number of pencils she started with
And we know that she ended up with 3 pencils left, so:
2x - (1/4)(2x) - (1/2)x = 3
Simplifying this equation, we get:
(7/4)x = 3 + (1/2)x
Multiplying both sides by 4/7, we get:
x = (12/7)(3) = 36/7
Since Reema cannot buy a fractional number of pencils, we need to round up to the nearest whole number. Therefore, Reema bought 5 boxes of pencils, or a total of 60 pencils, in August.
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Write a derivative formula for the function.
f(x) = 12.7(4.1^x) / x^2
The answer is:
[tex]f'(x) = 12.7(4.1^x)(ln(4.1)/x - 2/x^2)[/tex]
What is quotient rule?The derivative of f(x), we can use the quotient rule. Let's define
[tex]u(x) = 12.7(4.1^x)[/tex]. [tex]v(x) = x^2[/tex]Then:
[tex]f(x) = u(x)/v(x) = (12.7(4.1^x))/x^2[/tex][tex]f'(x) = [v(x)u'(x) - u(x)v'(x)]/v(x)^2[/tex][tex]f'(x) = [(x^2)(12.7(4.1^x)ln(4.1)) - (12.7(4.1^x))(2x)]/x^4[/tex]Simplifying this expression gives:
[tex]f'(x) = 12.7(4.1^x)(ln(4.1)/x - 2/x^2)[/tex]To find the derivative of f(x), we used the quotient rule, which states that the derivative of a quotient of two functions is equal to (the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator) divided by the denominator squared.
In our case, we defined u(x) and v(x) as the numerator and denominator, respectively, and used the formula to find the derivative of f(x).The derivative of u(x) is found using the chain rule and the derivative of [tex]4.1^x[/tex], which is [tex]4.1^x[/tex] times the natural logarithm of 4.1.
The derivative of v(x) is simply 2x. We then substitute these values into the quotient rule formula and simplify the resulting expression to get the final derivative formula:
[tex]f'(x) = 12.7(4.1^x)(ln(4.1)/x - 2/x^2)[/tex]This formula tells us the slope of the tangent line to the graph of f(x) at any given point x.
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5. Betty will spend $375. 00 on a new lawnmower. She will use her credit card to withdraw $400
cash to pay for the lawnmower. The credit card company charges a $6. 00 cash-withdrawal
fee and 3% interest on the borrowed amount, but not including the cash-withdrawal fee. How
much will Betty owe after one month?
The amount Betty will owe after one month is $418,
Betty will owe more than $400 after one month because of the cash-withdrawal fee and interest charges. The cash-withdrawal fee is a one-time charge of $6.00, which means Betty's total borrowed amount is $406.00.
The interest on this amount at a rate of 3% for one month is calculated by multiplying the borrowed amount by the interest rate and time, giving $12.18.
Therefore, Betty will owe $418.18 after one month, which is the borrowed amount plus the cash-withdrawal fee and interest charges.
It's important to be aware of the additional fees and charges associated with borrowing on a credit card, as they can significantly increase the amount owed and lead to financial difficulties if not managed properly.
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1. This table représents Ana's check register. Her checking account had a balance of
$1,093. 12 on October 8.
Use the information in the check register to determine the balance of Ana's checking
account after the transaction on October 22.
Ana's Check Register
Date
Description
Deposit
Withdrawal
Balance
10/8
$1,093. 12
10/15
Rent
$525. 50
10/22
Paycheck
$645. 87
The balance of Ana's checking account after the transaction on October 22 is $1,213.49.
To determine the balance of Ana's checking account after the transaction on October 22, we'll follow these steps:
1. Start with the initial balance on October 8: $1,093.12
2. Subtract the withdrawal for rent on October 15: $1,093.12 - $525.50 = $567.62
3. Add the deposit from the paycheck on October 22: $567.62 + $645.87 = $1,213.49
The balance of Ana's checking account after the transaction on October 22 is $1,213.49.
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Melanie knows she needs 5kg of grass seed to make a square lawn 8m by 8m. Grass seed is sold in 3kg boxes. Melanie wants to make a rectangular lawn by 12m by 14m. She has 4 boxes of grass seed. Has Melanie got enough grass seed to make a lawn by 12m by 14. Show your working out
Melanie does not have enough grass seed to make a lawn.
To find out if Melanie has enough grass seed to make a lawn by 12m by 14m, we need to calculate the area of the lawn and compare it to the amount of grass seed she has.
The area of the square lawn is 8m x 8m = 64 square meters. To cover this area with 5kg of grass seed, we can calculate the amount of grass seed needed per square meter: 5kg / 64 square meters = 0.078125 kg/square meter.
The area of the rectangular lawn is 12m x 14m = 168 square meters. To cover this area with the same amount of grass seed per square meter, we can calculate the total amount of grass seed needed: 168 square meters x 0.078125 kg/square meter = 13.125 kg.
Since Melanie only has 4 boxes of grass seed, which is a total of 12kg, she does not have enough to cover the rectangular lawn. She would need at least 1.125 kg more grass seed to cover the area.
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The surface of a workbook is 14 inches tall and 10 inches wide. what is its perimeter?
The perimeter of the workbook is 48 inches when the surface of a workbook is 14 inches tall and 10 inches wide.
Given data:
Height or length = 14 inches
width = 10 inches
The perimeter can be determined by adding up all four side lengths or by adding the length and the width, and then multiplying by two because there are two of each side length.
We need to find the perimeter of the rectangle. we can find it by using the formula,
P = 2L + 2W
where:
L = length
W = width
substuting the W and L values in the equation we get:
P = 2L + 2W
= 2 × (14) + 2 × (10)
= 28 + 20
= 48 inches
Therefore, The perimeter of the workbook is 48 inches.
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