Answer
sqrt 544 feet
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
12^2 + 20^2= c^2
144+400=c^2
544=c^2
c= sqrt 544
3. Sarah is ready to buy her first car and will need to finance $32,000. She is currently considering two different loan options through Capital One Auto and Chase Auto. Each of the loan options is for a 72 month term.
Capital One Auto is offering a 6.9% interest rate compounded annually
Chase Auto is offering a 7.8% simple interest rate
Using a full sentence, explain which of the two loans you believe
Sarah should choose and why.
Answer:
Capital One Auto
Step-by-step explanation:
Based on the provided information, Sarah should go for the loan option offered by Capital One Auto with a 6.9% interest rate compounded annually because it is a lower interest rate than that of Chase Auto and compounded annually is more beneficial in the long term as opposed to simple interest rate offered by Chase Auto.
Answer the following questions, please
8. The volume of the right cylinder is
Area of base of the cylinder * height9. The height of a slice is h/10
10. The approximate volume of the slice when divided into 10 is
Area of base of the cylinder * h / 1011. The approximate volume of the oblique cylinder by summing up the slices is
Area of base of the cylinder * height12. Cavalieri's principle tells us that if we have two three-dimensional objects that have the same cross-sectional area at every level, then they will have the same volume.
What is the base of the cylinder?The base of the cylinder is a circle, hence area of the base which is area of a circle is given by the formula
= πr^2
Since the two cylinders, have same cross-sectional area at all points. then the area of the base = πr^2
With a common height, h we have the volume
= Area of base of the cylinder * height
= πr^2 * h
Cavalieri's principle let us know that if the solid object have equal cross-sectional area at same points then the volume at a particular point is equal
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A tourist from Mexico is vacationing in the U.S. One day, he notices that gasoline costs 2.97 dollars per gallon. On that same day, 1 peso is worth 0.053 dollars. How much does the gas cost in pesos per liter?
Answer: 3.71
Step-by-step explanation:
how do i solve this problem
The coordinates of the image of the triangle and the rules that can be used to transform the triangle are;
1. A' is located at (-3, 3)
B' is located at (-2, -1)
C' is located at (2, 1)
Second part; The rules are;
(x, y) → (x + 5, -y)
(x, y) → (5·x, 5·y)
What is a transformation of a geometric figure?A transformation of a figure is the reorientation of the figure to change the size and position of the figure.
1. The coordinates of the triangle ABC following the transformation (x, y) → (-x, y) are;
A(3, 3) (x, y) → (-x, y) A'(-3, 3)
B(2, -1) (x, y) → (-x, y) B'(-2, -1)
C(-2, 1) (x, y) → (-x, y) C'(2, 1)
2. The coordinates of the vertices of the triangle are; (1, 1), (4, 1), and (0, 4)
Translating the triangle five units right, we get;
(1 + 5, 1) = (6, 1), (4 + 5, 1) = (9, 1), and (0 + 5, 4) = (5, 4)
The coordinates of the triangle following a translation 5 units right are therefore; (6, 1), (9, 1), and (5, 4)
The coordinates of the image of the point (x, y) following a reflection across the x-axis is the point (x, -y), therefore;'
The coordinates of the image of the triangle obtained from the previous transformation following a reflection across the x-axis is therefore;
(6, 1) reflection across the x-axis → (6, -1)
(9, 1) reflection across the x-axis → (9, -1)
(5, 4) reflection across the x-axis → (5, -4)
A rule that takes the triangle to a congruent triangle right five units and reflected over the x-axis is therefore;
(x, y) → (x + 5, -y)The transformation of a triangle by a dilation by a scale factor of five, such that the triangle is five times larger can be obtained by the expression for a dilation transformation as follows;
(x, y) → (a·x, a·y)
Therefore, we get;
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4 consecutive odd integers with a sum of 3048
Answer:
The integers you seek are:
759, 761, 763, 765
since
759 + 761 + 763 + 765 = 3048.
Hope this helps!
The regular price of a cell phone is $150 during a weekend sell all cell phones were 35% off how much will Colin save if he buys his cell phone during the sale
Answer:
Step-by-step explanation:
cost of the phone = 150
sale is 35% off
Multiply the original cost $150.00 time the percent off as a decimal.
35% = . 35 (drop the sign and move the decimal two places left.)
150 X .35 = 52.50 off the price
He will save $52.50 off the cell phone during the sale.
suppose that the distance a car travels varies directly with the amount of gasoline it uses. a certain car uses 28 gallons of gasoline to travel 924 miles. how many miles can the car travel if it has 19 gallons of gasoline? miles
The distance a car travels varies directly with the amount of gasoline it uses. If a car uses 28 gallons of gasoline to travel 924 miles, the car can travel 627 miles with 19 gallons of gasoline.
We can set up a proportion to solve the problem:
distance / gasoline = constant
Let's use x to represent the distance the car can travel with 19 gallons of gasoline:
924 / 28 = x / 19
Simplifying and solving for x:
x = (924 / 28) * 19 = 627 miles
Therefore, the car can travel 627 miles with 19 gallons of gasoline.
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In cyclic quadrilateral PQRS,
[tex]\frac{\ \textless \ P}{3} =\frac{\ \textless \ Q}{4} =\frac{\ \textless \ R}{5}[/tex]
Find the largest angle in quadrilateral PQRS, in degrees. ("<" =angle and the answer isn't 120)
The largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.
what is quadrilateral?
A quadrilateral is a four-sided polygon, which is a two-dimensional closed shape with straight sides. In other words, a quadrilateral is a geometric figure that has four sides, four vertices, and four angles. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.
From the given information, we have:
angle P = 3p
angle Q = 4q
angle R = 5r
Since PQRS is a cyclic quadrilateral, the sum of opposite angles is equal to 180 degrees. Therefore, we have:
angle P + angle R = 180 degrees
3p + 5r = 180 degrees
Similarly, we have:
angle Q + angle S = 180 degrees
4q + S = 180 degrees
S = 180 - 4q
To find the largest angle, we need to find the largest angle measure among angles P, Q, R, and S.
Let's substitute the expression for S in terms of q into the equation for angle Q and simplify:
angle Q = 4q
angle Q + angle S = 180 degrees
4q + (180 - 4q) = 180 degrees
4q - 4q + 180 = 180 degrees
180 = 180 degrees
This equation is true, but it does not provide any information about the largest angle in PQRS.
Let's now substitute the expressions for angles P, Q, and R in terms of p and r into the equation for angle P + angle R = 180 degrees:
3p + 5r = 180 degrees
We want to find the largest angle, so we need to find the largest value of p or r that satisfies this equation. One way to do this is to try different values of p and r that satisfy the equation and see which one yields the largest value for angle P or angle R.
Let's try p = 10 and r = 30:
3p + 5r = 3(10) + 5(30) = 150
This satisfies the equation, so we can calculate angle P and angle R:
angle P = 3p = 30 degrees
angle R = 5r = 150 degrees
Therefore, the largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.
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if $x$ and $y$ are positive integers for which $3x + 2y + xy = 115 + 7x + 6y$, then what is $x + y$?
The value of x + y is (xy -115)/4 .
What is Equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
given expression is ,
3x + 2y + xy = 115 + 7x + 6y
so, we have to find the value of x + y
take the value of x and y at one side ,
xy = 7x + 6y - 3x - 2y +115
xy = 4x + 4y + 115
take the integer on other side,
4x + 4y = xy -115
take 4 common from left hand side,
4( x + y) = xy - 115
x + y = (xy -115)/4
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How do u do this???? :)
Answer:
If I did this right it should be: A)720g flour B)(i) 480g (ii) 2
Step-by-step explanation:
I need some help pretty please
Answer:
[tex]y - ( - 20) = 9(x - ( - 2))[/tex]
[tex]y + 20 = 9(x + 2)[/tex]
Step-by-step explanation:
[tex]m = \frac{79 - ( - 20)}{9 - ( - 2)} = \frac{99}{11} = 9[/tex]
[tex]y - ( - 20) = 9(x - ( - 2))[/tex]
[tex]y + 20 = 9(x + 2)[/tex]
If a bird flies at a rate of 28 miles in 2 hrs, how many miles does it travel in 40 minutes?
Answer: 9 and 1/3
Step-by-step explanation:
First of all, you have to find the unit rate. So 28 divided by 2 = 14.
The bird flies at a unit rate of 14 miles in 1 hour.
Next, we need to find out what fraction of an hour is 40 minutes.
How many minutes in an hour? 60... so 40 would be 40/60 of an hour or 4/6 or 2/3 of an hour.
Next, remember the formula D=rt which is distance= rate multiplied by time
We can use this formula here: 14 times 2/3 = 9 and 1/3
samantha needs to mix a 40% alcohol solution with a 60% alcohol solution to create 100 milliliters of a 58% solution. how many milliliters of each solution must samantha use?
Samantha needs to mix 10 milliliters of the 40% alcohol solution with 90 milliliters of the 60% alcohol solution to create 100 milliliters of a 58% solution.
Let x be the number of milliliters of the 40% alcohol solution that Samantha needs to mix, and let y be the number of milliliters of the 60% alcohol solution. Since Samantha needs to create 100 milliliters of a 58% solution, we can write the following system of equations:
x + y = 100 (equation 1: total volume)
0.4x + 0.6y = 0.58(100) (equation 2: alcohol concentration)
In equation 1, we see that the total volume of the resulting mixture must be 100 milliliters. In equation 2, we convert the concentration of the 58% solution into a decimal and set it equal to the weighted average of the concentrations of the two solutions.
We can solve this system of equations to find the values of x and y:
x + y = 100
0.4x + 0.6y = 58
Multiplying the first equation by 0.4, we get:
0.4x + 0.4y = 40
Subtracting this equation from the second equation, we get:
0.2y = 18
y = 90
Substituting y = 90 into equation 1, we get:
x + 90 = 100
x = 10
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a grab bag contains 2 football cards and 8 basketball cards. an experiment consists of taking one card out of the bag, replacing it, and then selecting another card. what is the probability of selecting a football card and then a basketball card? express your answer as a decimal.
The probability of selecting a football card and then a basketball card is 0.16 or 16%. The probability of selecting a football card and then a basketball card can be calculated by multiplying the probability of selecting a football card on the first draw and the probability of selecting a basketball card on the second draw.
Since the first card is replaced before the second draw, the probability of selecting a football card or a basketball card remains the same on both draws.
The probability of selecting a football card on the first draw is 2/10, or 0.2, since there are 2 football cards in a total of 10 cards in the bag. The probability of selecting a basketball card on the second draw is 8/10, or 0.8, since there are 8 basketball cards left after the first draw.
Therefore, the probability of selecting a football card and then a basketball card can be calculated as follows:
P(Football and Basketball) = P(Football on 1st draw) x P(Basketball on 2nd draw)
= (2/10) x (8/10)
= 0.16
So, the probability of selecting a football card and then a basketball card is 0.16 or 16%.
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Is 0.999
A) Likely
B) Unlikely
C)Neither unlikely or likely
D)Impossible
Answer: A) Likely
Step-by-step explanation: Without further context, it's hard to tell what 0.999 represents.
Answer: The number 0.999 is a valid number that exists between the values of 0 and 1 on the number line. Therefore, it is possible and not unlikely or impossible. The correct answer is option C, which is "Neither unlikely nor likely".
Step-by-step explanation: The number 0.999 is the decimal representation of a fraction that is very close to 1 but not relatively equal to 1. However, it is still an important number found between 0 and 1 on the number line and is commonly used in math and science.
The statement "0.999 is probable" or "0.999 is unlikely” suggests that the number is somehow unique or rare, which it is not. In fact, 0.999 is a standard number used in many calculations and applications.
So the correct answer is option C, which means that 0.999 is neither particularly probable nor improbable. It only exists as a valid number between 0 and 1.
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What is the sum of 12 - 5i and -3 + 4i? a. -16 + 63ib. 9 - i c. 9 - 9i d. 15 - 9i
Answer: 9 - i
Step-by-step explanation:
The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)
We have to give that,
The sum of numbers 12 - 5i and - 3 + 4i.
Now, we can find the sum of complex numbers as,
(12 - 5i) + (- 3 + 4i)
12 - 5i - 3 + 4i
Combine like terms,
12 - 3 - 5i + 4i
9 - i
Therefore, The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)
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Answer of the second question with explanation.
1 + 1/(1 + 1/(1 - 1/2)) =
a quality control expert at life batteries wants to test their new batteries. the design engineer claims they have a variance of 8100 with a mean life of 1192 minutes. if the claim is true, in a sample of 72 batteries, what is the probability that the mean battery life would be greater than 1173.8 minutes? round your answer to four decimal places.
The probability that the mean battery life would be greater than 1173.8 minutes is 0.9588
We can solve this problem using the central limit theorem, which tells us that the distribution of sample means from a population with a known variance becomes approximately normal as the sample size increases.
The standard error of the mean can be calculated as
SE = σ / sqrt(n)
where σ is the population standard deviation, n is the sample size
Here, we are given that the population variance is 8100, so the population standard deviation is the square root of 8100, which is 90.
SE = 90 / sqrt(72) = 10.6066
Next, we need to standardize the sample mean using the z-score formula
z = (X - μ) / SE
where X is the sample mean, μ is the population mean.
Here, the population mean is given as 1192 minutes and the sample mean we are interested in is 1173.8 minutes.
z = (1173.8 - 1192) / 10.6066 = -1.7356
We want to find the probability that the sample mean is greater than 1173.8 minutes. Since we have a negative z-score, we need to find the area to the right of this value on a standard normal distribution. We can use a z-table or a calculator to find this probability.
Using a standard normal distribution table, we find that the area to the right of z = -1.7356 is 0.9588.
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Please help me answer the equation of the area of triangles as attached below.
Answer:15
You multiply 6 and 5. That equals 30 then divide the 30 by 2 and that equals 15
PLS HELPPPPPPPPPP i need this completed today
The given measure of ∠ DEC = 80 degrees
How to solve for the angleWe have the following details
m ∠BAC = 46 degrees
m ∠ CBA = 54 degrees
We are to find the measure of angle DEC
This is a question that shows us two similar triangles
We have ∠BAC = DCE
∠ CBA = ∠ EDC
then ∠ DEC = ∠ BCA
The angle sum propertyThe measure of the angles that are in a triangle is given as 180 degrees
we have ∠BAC + ∠ CBA + ∠ BCA = 180
46 + 54 + ∠ BCA = 180 degrees
∠ BCA = 180 - 100
∠ BCA = 80 degrees
We know that corresponding angles are equal when we have parallel lines
since ∠ DEC = ∠ BCA
∠ DEC = 80 degrees
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what changes the width of a confidence interval? a marketing director wants a 95% confidence interval for the mean cost of running shoes. she randomly
The width of the confidence interval increases as the sample size increases and decreases as the confidence interval decreases. The confidence interval decreases as the sample size increases and increases as the confidence level increases.
Sample size is defined as the number of observations used to determine
an estimate of a particular population. The size of the model is drawn by people. Sampling is the process of selecting a group of individuals from a population to estimate the characteristics of the entire population. Select the number of establishments in a population group for analysis.
The sample size increases with the square of the standard deviation and decreases with the square of the difference between the mean under the alternative hypothesis and the mean under the null hypothesis.
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Find the perimeter of a polygon. Assume that lines which appear to be tangent are tangent A. 32.1 B. 39 C. 45.2 D. 59.7
Check the picture below.
Pls answer fast!!! Whoever gets it correct first gets a brainly!!!!
Answer: B
Step-by-step explanation:
The answer is 9x^2 + 14xy -19y^2
Which sign makes the statement true?
-2/5 ? -4/10
< > =
The fractions [tex]\frac{-2}{5}[/tex] and the fraction [tex]\frac{-4}{10}[/tex] , both are equal [tex]\frac{-2}{5} =\frac{-4}{10}[/tex], which means the "=" sign makes the statement true.
What are inequality signs?A mathematical relationship between two expressions is called inequality, and it is expressed using one of the following:
"less than or equal to": [tex]\leq[/tex]
"greater than" :>
"greater than or equal to" : [tex]\geq[/tex]
"less than": <
"not equal to": [tex]\neq[/tex]
To compare the fraction, make the denominator of both fractions the same.
Given:
Fraction 1 = [tex]\frac{-2}{5}[/tex]
Fraction 2 = [tex]\frac{-4}{10}[/tex]
To make the same denominator we can multiply by 2 to the numerator and denominator of the fraction 1.
[tex]\frac{-2}{5} =\frac{-2 * 2}{ 5*2}[/tex]
[tex]\frac{-2}{5} =\frac{-4}{10}[/tex]
Hence from the above calculation, the given fractions are equal.
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find m<7 if m<8 =110
180º-110º = 70º
m∠7 = 70°
solve each system by substitution
The solution to the system of equations is p = 4 and q = 2
What do you mean by Substitution method ?The substitution method is a way to solve a system of linear equations. In this method, we solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. This produces a new equation with one variable, which we can then solve for its value. Once we know the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.
To solve the system of equations using the method of substitution, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. We can start by solving the second equation for p:
p + 2q = 8
p = 8 - 2q
Now we can substitute this expression for p in the first equation:
2p - 3q = 2
2(8 - 2q) - 3q = 2
16 - 4q - 3q = 2
16 - 7q = 2
-7q = -14
q = 2
We can now substitute q = 2 into the expression we found for p:
p = 8 - 2q
p = 8 - 2(2)
p = 4
Therefore, the solution to the system of equations is p = 4 and q = 2.
correct question Solve the equations 2p – 3q = 2 and p + 2q = 8, using the method of substitution.
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Find the volume of the cylinder rounded to the nearest tenth.
PLSSSSSSS HELP!!
To calculate the volume, you'll need to use the formula V = πr²h, where V represents the volume, r is the radius of the circular base, h is the height of the cylinder,
and π (pi) is a mathematical constant approximately equal to 3.14159.
Hi there! I understand you need help finding the volume of a cylinder
To apply this formula, you'll first need to know the values of the radius and the height of the cylinder. Once you have these values, follow these steps:
1. Square the radius (r²).
2. Multiply the squared radius by the height (r²h).
3. Multiply the result by π (V = πr²h).
Lastly, round the calculated volume to the nearest tenth as requested. Remember that I cannot provide you with the exact volume without the radius and height of the cylinder. Please provide the values, and I'll be glad to assist you with the calculation.
Keep in mind that the answer should be concise, so providing an answer in 180 words is not necessary. The information above should be sufficient to help you understand how to calculate the volume of a cylinder.
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Which value is NOT greater than [-4.2] A [-4.2]
B [3.5]
C [4.1]
D [-4.5]
The value that is NOT greater than [-4.2] is D. [-4.5]
The values [-4.2], [3.5], and [4.1] are all greater than [-4.5]. To determine which value is the greatest, we can use a number line or compare the numbers directly. On a number line, we can see that [-4.5] is located to the left of [-4.2], [3.5], and [4.1]. This means that [-4.2], [3.5], and [4.1] are all greater than [-4.5].
Alternatively, we can compare the values directly. We know that -4.5 is less than -4.2 since -4.5 is farther to the left on the number line. We also know that 3.5 and 4.1 are positive values, which are greater than any negative value. Therefore, the answer is [-4.5] is not greater than [-4.2]. Hence, option D is correct.
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I need help finding the product to these algebra problems.
7. The simplified expression is 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex], 8. The simplified expression is 5(m - 2)/(m - 1), 9. The simplified expression is 3/5,
10. The simplified expression is -(p + 10)/(p(9 - p)).
What is an expression?
7. To simplify the expression, we can cancel out common factors in the numerator and denominator:
(32x³ * y)/(5x * y²) * (15y)/(8x² *[tex]y^{4}[/tex] )
= (32/5) * (x³/x²) * (1/y²) * (3/2) * (1/x²) * (1/y³)
= 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex]
Therefore, the simplified expression is 96[tex]x^{-1}[/tex][tex]y^{-5}[/tex].
8. The simplified expression is 5(m - 2)/(m - 1).
To simplify the expression, we can factor the numerator:
(m² - 6m + 8)/(2m - 2) = (m - 4)(m - 2)/(2(m - 1))
We can then cancel out common factors:
(m - 4)(m - 2)/(2(m - 1)) * 10/(m - 4)
= 5(m - 2)/(m - 1)
Therefore, the simplified expression is 5(m - 2)/(m - 1).
9. The simplified expression is 3/5.
To simplify the expression, we can first simplify the fractions within the parentheses:
28n + 40/35n + 50 = (4n + 8)/(5n + 10)
12n + 24/8n + 16 = (3n + 6)/(2n + 4)
We can then simplify the expression by multiplying the two fractions:
(4n + 8)/(5n + 10) * (3n + 6)/(2n + 4)
= 2(2n + 4)/(5n + 10) * 3(n + 2)/(2(n + 2))
= 3/5
Therefore, the simplified expression is 3/5.
10. The simplified expression is -(p + 10)/(p(9 - p)).
To simplify the expression, we can factor the second fraction in the numerator and then cancel out common factors:
(p + 10)/(9 - p) * (p² - 5p - 36)/(4p² + 16p)
= (p + 10)/(9 - p) * ((p - 9)(p + 4))/(4p(p + 4))
= -(p + 10)/(p(9 - p))
Therefore, the simplified expression is -(p + 10)/(p(9 - p)).
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−3x − 8y = 20
−5x + y = 19
Answer:
x = -4,
y = -1
Step-by-step explanation:
{-3x - 8y = 20,
{-5x + y = 19;
Make x or y the subject from either the 1st or the 2nd equation (I chose to make x the subject from the 2nd equation, because after division, the numbers can be written as a finite decimal fraction):
-5x = 19 - y / : (-5)
x = -3,8 + 0,2y
Replace x in the 1st equation with its value from the 2nd one (the underlined expression):
-3(-3,8 + 0,2y) - 8y = 20
Multiply every term inside the bracket by the term on the outside:
11,4 - 0,6y - 8y = 20
Collect like terms and add them together:
-8,6y = 20 - 11,4
-8,6y = 8,6 / : (-8,6)
y = -1
y = -1x = -3,8 + 0,2 × (-1) = -4