Answer:
19/3 (6 1/3)
Step-by-step explanation:
(3) A framed print measures 36 in by 22 in. If the print is enclosed by a 2-inch matting, what is the length of the diagonal of the print? Round to the nearest tenth. See illustration. 2 in 12 in 36 in a. 36.7 in b. 39.4 in c. 26.5 in d. 50 in 22 in
The length of the diagonal of the print would be = 36.7 in . That is option A (to the nearest tenth).
How to calculate the diagonal length of the print?The print has the shape of a rectangle which is a type of a quadrilateral that has four sides with two sides parallel to each other.
The diagonal length of the print can be calculated by the use of the Pythagorean formula;
That is c² = a² + b²
C = hypothenuse = ?
a = 22 - 4 = 18in
b = 36 - 4 = 32 in
c² = 18² + 32²
c² = 324 + 1024
c² = 1348
C= √1348
C = 36.7 in ( nearest tenth)
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Henry deposits $6000 into an account that pays simple Interest at an annual rate of 6%. He does not make any more deposits. He makes no withdrawals until
the end of 5 years when he withdraws all the money.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Henry earn?
$
(b) What will the total amount in the account be (including interest)?
$
Answer:
1800
7800
Step-by-step explanation:
6000x0.06 = 360 x 5 for years since its annual then you get 1800 add that to the additional 6000 add those together and you get 7800.
I need a answer and explaination.
Answer:
x = 33°
Step-by-step explanation:
Vertically opposite angles:Vertically opposite angles are congruent.
∠AOB = ∠DOC
4x - 6 = 2x + 60
Add 6 to both sides,
4x = 2x + 60 + 6
4x = 2x + 66
Subtract 2x from both sides,
4x - 2x = 66
2x = 66
Divide both sides by 2
x = 66 ÷ 2
[tex]\boxed{x = 33}[/tex]
∠AOB = 4x - 6
= 4*33 -6
= 132 - 6
∠AOB = 126°
∠DOC = 126°
Mr. Adams divides 223 markers equally among the 26 students in his
class. He puts the
extra markers in a box. What is the least number of
markers he puts in the box?
Answer: 15
Step-by-step explanation:
223 / 26
8 reminder 15
he has to put the remainder in the box
Compute the linear correlation coefficient between the length of the right humerus in the length of the right tibia
The linear correlation coefficient between the length of the right humerus and the length of the right tibia is 0.517.
To compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia, we will use the formula: r = (n∑xy - (∑x)(∑y)) / sqrt([(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)])
Where r is the correlation coefficient, n is the number of observations, x is the length of the right humerus, and y is the length of the right tibia.
First, we will calculate the sum of x, y, xy, x^2, and y^2:
∑x = 24.8 + 24.59 + 24.59 + 24.29 + 23.81 + 24.87 + 25.90 + 26.11 + 26.63 + 26.31 + 26.84 = 278.74
∑y = 65.05 + 35.57 + 35.57 + 34.58 + 34.20 + 34.73 + 37.38 + 37.96 + 37.46 + 37.75 + 38.50 = 428.75
∑xy = (24.8)(65.05) + (24.59)(35.57) + (24.59)(35.57) + (24.29)(34.58) + (23.81)(34.20) + (24.87)(34.73) + (25.90)(37.38) + (26.11)(37.96) + (26.63)(37.46) + (26.31)(37.75) + (26.84)(38.50) = 10659.01
∑x^2 = (24.8)^2 + (24.59)^2 + (24.59)^2 + (24.29)^2 + (23.81)^2 + (24.87)^2 + (25.90)^2 + (26.11)^2 + (26.63)^2 + (26.31)^2 + (26.84)^2 = 7221.47
∑y^2 = (65.05)^2 + (35.57)^2 + (35.57)^2 + (34.58)^2 + (34.20)^2 + (34.73)^2 + (37.38)^2 + (37.96)^2 + (37.46)^2 + (37.75)^2 + (38.50)^2 = 15738.39
Now we can plug these values into the formula and calculate the correlation coefficient:
r = (11)(10659.01) - (278.74)(428.75) / sqrt([(11)(7221.47) - (278.74)^2][(11)(15738.39) - (428.75)^2])r = 117249.11 - 119475.235 / sqrt([79436.17 - 77691.79][173122.29 - 183744.56])r = -2226.125 / sqrt([1744.38][-10622.27])r = -2226.125 / sqrt(-18525838.35)r = -2226.125 / (-4304.18)r = 0.517
Therefore, the linear correlation coefficient between the length of the right humerus and the length of the right tibia is 0.517.
Note: The question is incomplete. The complete question probably is: Research performed at NASA and led by Emily Horton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2.
Right Humerus (mm) Right Tibia (mm)
24.8 65.05
24.59 35.57
24.59 35.57
24.29 34.58
23.81 34.20
24.87 34.73
25.90 37.38
26.11 37.96
26.63 37.46
26.31 37.75
26.84 38.50
Compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia.
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help!!!!!!!!!!!!!!!!
Answer:
2 3/7
Step-by-step explanation:
Answer:
2^[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
2^3·1/2 = 2^[tex]\frac{3}{2}[/tex]
the image you posted is very blurry, but it looks like the answer is the last choice
how much is 55000 a year per hour
Assuming a 40-hour workweek, 55000 per year would be approximately 26.44per hour.
Subtract 55000 from 52, the number of weeks in a year, and you get 1057.69. Subtract 1057.69 from 40, the number of hours in a workweek, to get 26.44.To the nearest dollar, round up: 26.44 = 27 Calculating how much an individual would make per hour with a yearly salary of $55,000 is a fairly straightforward process. Divide the annual income of $55,000 by the 52 weeks that make up a year. As a result, we get a score of 1057.69. After that, divide this number by the 40 hours that make up a workweek. As a result, we get a score of 26.44. The final step is to round this result up to the nearest dollar, which gives us an hourly wage of $27. 55,000 dollars a year is therefore equal to about 27 dollars per hour.
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Harry needs wood pieces to complete a project in woodshop class. He needs two pieces of wood that have a length of two and three eighths feet and four pieces of wood that are one and one third feet. What is the total amount of wood that Harry will need for the project?
three and four elevenths feet
three and seventeen twenty fourths feet
four and one third feet
ten and one twelfth feet
Thx!
The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A
Addition of Fraction
Wood 1:
Length of each = 2 5/8 feet
Number of pieces = 6
Total = Length of each × Number of pieces
= 2 5/8 × 6
= 21/8 × 6
= 126 / 8
= 15 3/4 meters
Wood 2:
Length of each = 1 1/5 feet
Number of pieces = 3
Total = Length of each × Number of pieces
= 1 1/5 × 3
= 6/5 × 3
= 18/5
= 3 3/5 meters
Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters
= 126/8 + 18/5
= (630+144) / 40
= 774/40
= 19 14/40
= 19 7/20 meters
Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A
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A is the point (-1, 5). Let (x, y) be any point on the line y = 3x.
(3 marks)
a Write an equation in terms of x for the distance between (x, y) and A(-1, 5).
b Find the coordinates of the two points, B and C, on the line y = 3x which are a distance
of √74 from (-1, 5).
(3 marks)
e Find the equation of the line that is perpendicular to y = 3x and goes through the
point (-1, 5).
Find the coordinates of the point of intersection between ₁ and y = 3.x.
e Find the area of triangle ABC.
(2 marks)
The distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).
What is Distance?The length along a line or line segment between two points on the line or line segment.
The distance formula is Distance=√(x₂-x₁)²+(y₂-y₁)²
Equation in terms of x for the distance between (x, y) and A(-1, 5) and y = 3x. be any point on the line
Distance=√(x+1)²+(3x-5)²
b. We need to find coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1, 5).
√(x₁+1)²+(3x₁-5)² =√74
√(x₂+1)²+(3x₂-5)² =√74
Simplifying each equation and solving for x, we get:
x₁ = -4/3 or x₁ = -2
x₂ = 2/3 or x₂ = -4
Simplifying each equation and solving for x, we get:
x₁ = -4/3 or x₁ = -2
x₂ = 2/3 or x₂ = -4
Substituting each value of x into y = 3x, we get the coordinates of B and C:
B: (-4/3, -4)
C: (2/3, 2)
The slope of y = 3x is 3,
Slope of any line perpendicular to it is -1/3.
Using the point-slope form of a line, we get the equation of the line passing through (-1, 5) with slope -1/3:
y-5=-1/3(x+1)
The point of intersection between y = 3x and the line y = (-1/3)x + (14/3), we can set the two equations equal to each other and solve for x:
3x = (-1/3)x + (14/3)
x = 14/10 = 7/5
y = 3(7/5) = 21/5
So the point of intersection is (7/5, 21/5).
To find the area of triangle ABC, we can use the distance formula between the points B and C:
d = √2/3 - (-4/3))² + (2 - (-4))²)
d=2√10
The base of the triangle is the distance between the x-coordinates of B and C, which is 2.
The area of the triangle is:1/2×b×h
=2√10
Hence, the distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).
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All of the following are correct about the triangles shown, except which?
In △ABE, the sin(A) is the same as the tan(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
In △ABE, the cos(A) is the same as the sin(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
In △ADG, the tan(G) is the same as the tan(A) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
In △ACF, the sin(F) is the same as the sin(E) in △ABE because the triangles are 45-45-90.
The false statement regarding the trigonometric ratios is given as follows:
In △ABE, the sin(A) is the same as the tan(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.For similar triangles, the ratios are equal, as the side lengths are proportional.
In a 45-45-90 triangle, the sine is equals to the cosine.
However, similar triangles have different values of sine and tangent, hence the first statement is false.
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Let [tex]f(x)=-5x+3[/tex] and [tex]g(x)=6x-2[/tex]. Find f times g and its domain.
The result of f times g is; -30x² + 28x - 6 while it's domain as required is the set of all real numbers.
What is the domain of f times g?As evident in the task content;
f(x) = -5x + 3 while g(x) = 6x - 2.
Hence, the result of f times g is; (-5x + 3) (6x - 2).
open parenthesis
f × g = -5x(6x) - 5x(-2) + 3(6x) + 3(-2)
= -30x² + 10x + 18x - 6
f × g = -30x² + 28x -6.
By observation, the function above is a quadratic function and hence, it's domain is the set of all real numbers.
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-6=4+n i need help ASAP
what is 2 quarts to liters?
There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.
Therefore, 2 Quarts is 1.8927059 liters, which is equal to almost 2 liters.
Quart:
A quart is an English unit of volume equal to one quarter of a gallon. Currently, there are three types of quarts: Liquid Quart and Dry Quart of the US Conventional System, and Imperial Quart of the UK Imperial System. All of them are approximately equal to 1 liter. It is subdivided into 2 pints or (in the US) 4 cups. Historically, the exact size of a quart has varied over time and with the value of a gallon across different commodities.
Liter:
A liter or liter is a metric unit of volume. A liter is defined as the volume of a cube with sides measuring 10 centimeters. In the US, it is approximately 3.785 liters gallon.
According to the Question:
The conversion factor from quarts to liters is 0.94635295. To find how many liters are in quarts, multiply the conversion factor or use the volume converter above 2 quarts equals 1.8/10 of 93 liters.
To convert 2 quarts to equivalent liter values, multiply the amount in quarts by 0.94635295 (conversion factor). In this case, you should multiply 2 quarts by 0.94635295 to get the equivalent result in liters:
2 quarts x 0.94635295 = 1. 8927059 liters
Therefore,
2 quarts equals 1.8927059 liters.
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I NEED HELP ASAP HAS TO BE TURNED IN TMR
According to the information, the surface area of the pyramids is as follows: 1.377 inches², 2.208 inches², 3.160 inches².
How to find the surface area of the pyramids?To find the surface area of the pyramids we must perform the following mathematical operations.
A. Find the surface area of the base:
1. 13 * 13 = 169 in²2. 5.2 * 4.5 / 2 = 11.7 in²3. 7 * 10 = 70 in²B. We must find the surface area of the faces:
1.
8 * 13 = 10452 * 4 = 2082.
11.7 * 3 = 35.13.
6*7=4242 / 2 = 2110 * 4.8 = 4848 / 2 = 2421 + 24 = 4545 * 2 = 90 in²How to find the area of the total surface of the figures?To find the total area of the total surface of the figures we must perform the following procedure:
C. Add the area of the base to the area of the faces:
1.
169 + 208 = 377 in²2.
11.7 + 35.1 = 46.8 in²3.
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the most important part of the design cycle is.....
The most important part of the design cycle is the "Iteration" phase.
In this phase, the designer goes back and forth between testing and evaluating the design, making changes, and testing again until the desired outcome is achieved.
In mathematical terms, the iteration phase can be seen as an optimization process, where the designer seeks to minimize the difference between the desired and actual outcomes.
This phase is crucial because it allows the designer to identify and resolve any issues with the design, ensuring that the final product is functional and meets the desired specifications.
In conclusion, the iteration phase of the design cycle is essential for ensuring that the final design is effective, efficient, and meets all the requirements. The designer must repeat this phase multiple times to achieve the desired outcome and ultimately improve the overall design.
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Suppose that nâ¡0 and n â¡ 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equationdv/dx+(1-n)P(x)v(x) = (1 â n)Q(x).
The substitution v = y^1-n transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x) is shown below.
An equation is in the form
dy/dx +P(x)y=Q(x)yⁿ, where P and Q are functions of x alone or constants, is called Bernoulli's equation.
The substitution using [tex]v = y^{1-n}[/tex]
Differentiate both side with respect to 'x'
[tex]v^{'} = (1-n)y^{-n}y^{'}[/tex]
[tex]\frac{dy}{dx} = \frac{1}{1-n} y^{n}v^{'}[/tex]
we get, [tex]\frac{1}{1-n} y^{n}v^{'}[/tex] + P(x)y = Q(x)yⁿ
= [tex]v^{'} + (1-n)P(x)y^{1-n} = (1-n)Q(x)[/tex]
using [tex]v = y^{1-n}[/tex]
The given equation is well expressed as:
[tex]v^{'} + (1-n)P(x)v = (1-n)Q(x)[/tex]
or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)
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A family went on a cross-country road trip for their summer vacation. The following table shows the number of days and the total amount of miles their car had driven.
Number of Days 2 5 6 8 12
Miles Driven 425 967 1,253 1,253 2,648
Which of the following graphs is most appropriate to construct for the data given in the table to observe how the miles change over a certain number of days? Explain.
A scatter plot, because it would show the association, or relationship, between the two variables
A scatter plot, because it would show how a variable changes over time between each individual data point
A line graph, because it would show the association, or relationship, between the two variables
A line graph, because it would show how a variable changes over time between each individual data point
Thus, a line graph would be more appropriate for this particular data set to observe the changes in the miles driven over a certain number of days.
What is data?Data refers to any collection of facts, figures, or information that can be processed, analyzed, and interpreted to gain insights and knowledge. It can be in various forms such as text, images, audio, video, or numerical values, and can be collected from various sources such as surveys, sensors, social media, or transactions.
Given by the question: -
The most appropriate graph to construct for the given data is a line graph because it would show how the miles driven change over time between each individual data point. A line graph is useful for showing trends or changes over time, and it allows us to see the progression of the miles driven during the trip. This graph would have days on the x-axis and miles driven on the y-axis, with a line connecting the data points. This would help to visualize any patterns or trends in how the miles driven change over time during the trip.
On the other hand, a scatter plot would show the relationship between the two variables, but it would not show the changes over time. While scatter plots are useful for showing relationships between variables, they do not show the order or progression of the data points over time.
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Both Marker Farms and Jackson Farms sell apples at the farmer’s market. Maker offers 23 apples in 2 Baskets. Jackson farms offers 39 apples in 3 baskets. if price were the same for which farm provides a better value for a customer wanting apples
The farmer will make 14 baskets containing each of 5 apples and 7 peaches.
What is CGF?In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.
here, we have,
How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?
Given:
A farmer harvests 70 apples and 98 peaches.
They want to make baskets that have both apples and peaches to sell at the market.
Each basket should contain the same combinations of fruit.
They want to sell all the apples and peaches and as many baskets as possible.
Find:
How many baskets can the farm make having x apples and y peaches in the baskets?
Solution:
So, for solving this kind of question first we have to find the greatest common factor, we get;
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
So, the farmer will make 14 baskets each of 5 apples and 7 peaches.
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Which are the remote interior angles of ∠4?.
The remote interior angles of ∠4 are ∠1 and ∠2.
In a triangle, the remote interior angles are the two angles that are not adjacent to the exterior angle. In this case, ∠4 is the exterior angle, so the two angles that are not adjacent to it are ∠1 and ∠2. These are the remote interior angles of ∠4.
Here is a step-by-step explanation:
1. Identify the exterior angle. In this case, it is ∠4.
2. Find the two angles that are not adjacent to the exterior angle. These are ∠1 and ∠2.
3. These two angles are the remote interior angles of ∠4.
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What is the value of f divided by 13
When f=52
Answer:
4
Step-by-step explanation:
We know
f = 52
What is the value of f divided by 13
52 divided by 13 = 4
So, the value of f divided by 13 is 4.
A campus contains buildings numbered 1 through 70. What is the probability that a student will enter a building that is not a multiple of 12?.
The probability that a student will enter a building that is not a multiple of 12 is 0.914
We can find the probability by finding the number of buildings that are not a multiple of 12 and dividing it by the total number of buildings (70).
The buildings that are multiples of 12 are:
12, 24, 36, 48, 60, and 70
So there are 6 buildings thar are multiple of 12.
So, the number of buildings that are not a multiple of 12 is
70 - 6 = 64
Therefore, the probability that a student will enter a building that is not a multiple of 12 is
= 64/70
= 0.914
= 91.4 %
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Brad has a $27 online gift
card. He plans to buy as many
books as he can. The cost of each
book is $3. How many books can
he buy without spending more
than his gift card amount?
Answer:
Step-by-step explanation:
Just divide the amount of the giftcard between the unit cost of the books.
[tex]\frac{gift-card-amount}{cost-of-books}=\frac{27}{3}=9[/tex]
Brad can buy 9 books with his gift card
Mr. Rideout is in charge of washing the windows on a bus. He washes 25 of the 30 windows before lunch. After lunch he washes 7 of the remaining windows. How many windows does Mr. Rideout still need to wash?
The remaining number of windows is given by the equation A = 11 windows
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of windows that needs to be washed = 30 windows
The number of windows that was washed before lunch = ( 2/5 ) of the total
Substituting the values in the equation , we get
The number of windows that was washed before lunch = ( 2/5 ) x 30
The number of windows that was washed before lunch = 2 x 6
The number of windows that was washed before lunch = 12 windows
So , the remaining number of windows = 30 - 12 = 18 windows
And ,
The number of windows that was washed after lunch = 7 windows
So , the remaining number of windows that needs to be washed A = remaining number of windows - number of windows that was washed after lunch
On simplifying the equation , we get
The remaining number of windows that needs to be washed A = 18 - 7
The remaining number of windows that needs to be washed A = 11 windows
Hence , the equation is A = 11 windows
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How do you calculate orthogonal projection?
The vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b."
So the vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b." The following is the formula for projecting "a" orthogonally onto "b": CSS Copy: p = (dot(a, b) / dot(b, b)) * b, where "dot" stands for the dot product of the two vectors.
The procedures to determine the orthogonal projection of a vector "a" onto a vector "b" are as follows:
Identify the "a" and "b" dot product.
Add "b" to itself and calculate the dot product.
Divide the intersection of "a" and "b" by the intersection of "b" and itself.
Multiply the vector "b" by the step 3 result.
Here is a MATLAB sample that shows the orthogonal projection.
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. Rachel mows a rectangular lawn that is twelve yards-long and eight and two-thirds yards wide. In square yards what is the area of the lawn Rachel mows? Represent your answer using an area model.
The area of the rectangular lawn Rachel mows is 100 square yards
How to determine the area of the lawn
The formula for calculating the area of a rectangle is expressed with the formula;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values as given,
length = 12 yards
Width = 8 1/3 = 25/3 yards
Then,
Area = 12 × 25/3
Divide the factors
Area = 4(25)
Multiply the values
Area = 100 square yards
Hence, the value is 100 square yards
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7. Katarina plans to borrow $600 at 3% over 5 years. What amount of simple interest should
she expect to pay?
A. $15
B. $18
C. $90
D. $180
The amount of simple interest is (c) $90
How to determine the amount of simple interestFrom the question, we have the following parameters that can be used in our computation:
Principal = $600
Rate = 3%
TIme = 5 years
The simple interest is calclated as
Simple interest = PRT
Substitute the known values in the above equation, so, we have the following representation
Simple interest = 600 * 3% * 5
Evaluate
Simple interest = 90
Hence, the amount is $90
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Please help me with this.
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Determine the missing measures for the parallelogram below.
need help on this one
Based on the information in the graph, the angles of the parallelogram would be 68° and 112°, while the length of its sides would be 15 and 8.
How to identify the length and angles of this figure?To identify the length and angles of this figure we must carefully look at the lengths shown and the angles shown. Taking into account the shape of the parallelogram, we can infer that the values that correctly complete the dimensions of the figure are:
A = 112°B = 68°C = 112°basis = 15side = 8This is because the parallelogram has two equal sides and equal bases, so if the upper one measures 15, the lower one must measure the same. Additionally, if the side measures 8 the other side must measure 8. In the case of the angles it would be the same.
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Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the critical value if the hypothesis is to be tested at the 0.05 level of significance?
The critical value for the 0.05 level of significance is k = 21.
To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.
We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.
So, we want to find the smallest k such that:
P(X <= k) >= 1 - 0.05
where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.
The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.
This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.
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Find the equation of the straight lines Parallel to the line y + 8 = 0 and passes through (2; 1).
Answer:
[tex]y = 1[/tex]
Step-by-step explanation:
Rearranging the equation:
[tex]y = -8[/tex]
Three points to be considered:
1. Above is a horizontal line cutting through the y-axis at y value of [tex]-8[/tex].
2. A horizontal line has a slope (or gradient) of 0.
3. Parallel lines have the same slope (or gradient)
∴The straight line passing through (2, 1) will also have a zero slope. In addition, this is a horizontal line, which cuts the y-axis at y value of 1.
The equation of straight line:
y = 1