The line of reflection used to create the image is the y-axis. The x-axis is the line of reflection utilized to produce the picture of polygon ABCD to A' B' C' D'. The y-coordinates of each vertex.
in A' B' C' D' are the inverse of the corresponding y-coordinates in ABCD, but the x-coordinates stay constant. The x-axis is a horizontal line that goes through the origin and mirrors points that cross it. As a result, when each point in ABCD is mirrored across the x-axis, the point in A' B' C' D' is produced. As a result, the transformation that maps ABCD to A' B' C' D' is an x-axis reflection. the graph to answer the question. Graph of polygon ABCD with vertices at negative 6 comma negative 2, negative 4 comma 5, 1 comma 5, negative 1 comma negative 2.
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Line A passes through the points (-1, 5) and (3, 21).
Line B passes through the points (4, -2) and (-3, 19).
Find the point where line A intersects line B.
Answer:
A line's angle of slope between two points is (5, -4).
Step-by-step explanation:
Explanations are given in attachment!
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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Darlene organizes recycling drives for old cellular phones and other electronics. She is paid
$200 per week plus $25 for each event. This month, she will work four weeks and wants to
earn at least $1,200. Darlene decides to organize four recycling events each week this month.
Enter an inequality for the number of events Darlene needs to organize to reach her goal of
at least $1,200. Solve the inequality and explain whether four events each week are enough
to meet her goal.
(Please help)
If the number of events is taken as x then the inequality is:
[tex](200*4)+(x*25)\geq 1200[/tex] ( as there are only 4 weeks in a month )
If we further solve this inequality we can get the answer:
[tex]800+(x*25)\geq 1200[/tex]
[tex]x*25\geq 400[/tex]
[tex]x\geq \frac{400}{25}[/tex]
[tex]x\geq 16[/tex]
So, as we saw here, the minimum number of events required for Darlene to complete the goal is 16.
But she is planning to organize 4 events which is insufficient. She needs to organize 12 more events in order to satisfy the inequality.
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Let's first calculate how much Darlene will earn in one week by organizing four recycling events:
$200 (base pay) + $25 (per event) x 4 (number of events) = $300
So, if Darlene organizes four recycling events per week, she will earn $300 per week.
To reach her goal of at least $1,200 in four weeks, we can set up the following inequality:
4 x (number of events) x $25 + $200 x 4 ≥ $1,200
100 x (number of events) + $800 ≥ $1,200
100 x (number of events) ≥ $400
(number of events) ≥ 4
Therefore, the number of events Darlene needs to organize to reach her goal of at least $1,200 is at least 4.
Since Darlene plans to organize four recycling events per week, this means she would need to work four weeks to reach her goal. Therefore, organizing four events each week would be enough to meet her goal, as long as she works all four weeks
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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Calculator
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling
in the boxes.
ft²
113
1 2
3 ft
3
4
5
2½ ft
6
7
8
Answer:93 1/3 yards or 280ft
Step-by-step explanation:Step-by-step explanation: first I converted it all into feet. Giving me L=9ft H=8ft and W= 4ft
Then inserted the values into the formula for surface area SA=2lw+2lh+2hw. Then solved it all out in a calculator
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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Mrs. Tinney’s class has the following scores on their most recent test:
100
98 95 88 72 16 0 78 80
85
Calculate the five number summary and use it to draw (and label) your box and whisker plot on a number line. Show your work for all calculations.
If Mrs. Aguiar’s class has a five number summary of: 30, 50, 80, 90, 95, which class’ scores are more consistent? How do you know?
The mean for Mrs. Tinney’s class is 71.2 and the mean for Mrs. Aguiar’s class is 79. What conjecture could we make about symmetry? Explain.
The five number summary for Mrs. Tinney's class is: 0, 72, 85, 96.5, 100. Tinney's class has a smaller IQR. We would need to look at a histogram or box and whisker plot to confirm these conjectures.
Describe Median?The median is a statistical measure that represents the middle value of a dataset. It is the value that separates the lower half of the dataset from the upper half. To find the median, the data must be arranged in order from smallest to largest, and then the middle value is identified.
If the dataset contains an odd number of values, then the median is the middle value. For example, if the dataset is {2, 4, 6, 7, 9}, then the median is 6, which is the middle value.
If the dataset contains an even number of values, then the median is the average of the two middle values. For example, if the dataset is {2, 4, 6, 7, 9, 10}, then the median is (6+7)/2 = 6.5, which is the average of the two middle values, 6 and 7.
To find the five number summary for Mrs. Tinney's class, we first need to order the scores from least to greatest:
0, 16, 72, 78, 80, 85, 88, 95, 98, 100
The minimum score is 0 and the maximum score is 100.
The median is the middle score, which is 85.
To find the first quartile, we split the scores into two halves at the median and find the median of the lower half:
0, 16, 72, 78, 80
The median of the lower half is 72.
To find the third quartile, we find the median of the upper half:
88, 95, 98, 100
The median of the upper half is 96.5.
Therefore, the five number summary for Mrs. Tinney's class is: 0, 72, 85, 96.5, 100.
To compare the consistency of the two classes, we can look at the interquartile ranges (IQRs), which give the range of scores that contain the middle 50% of the data. The IQR for Mrs. Tinney's class is 96.5 - 72 = 24.5, while the IQR for Mrs. Aguiar's class is 90 - 50 = 40. Mrs. Tinney's class has a smaller IQR, which means that their scores are more consistent.
The means for the two classes suggest that the data may not be symmetric. If the data were symmetric, we would expect the means to be roughly in the middle of the data set. However, the mean for Mrs. Aguiar's class is closer to the upper end of the data set, which suggests that the data may be skewed to the right. The mean for Mrs. Tinney's class is closer to the lower end of the data set, which suggests that the data may be skewed to the left. However, we would need to look at a histogram or box and whisker plot to confirm these conjectures.
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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
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:
which of the following is the standard equation of a circle with center (-1,-6) and radius 5?
Answer:
(x + 1)^2 + (y + 6)^2 = 25.
Step-by-step explanation:
The standard equation of a circle with center (h, k) and radius r is given by:(x - h)^2 + (y - k)^2 = r^2In this case, the center of the circle is (-1, -6) and the radius is 5. Substituting these values into the equation, we get:(x - (-1))^2 + (y - (-6))^2 = 5^2Simplifying and rearranging terms, we get:(x + 1)^2 + (y + 6)^2 = 25Therefore, the standard equation of the circle with center (-1, -6) and radius 5 is (x + 1)^2 + (y + 6)^2 = 25.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.
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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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!
Answer of the second question with explanation.
1 + 1/(1 + 1/(1 - 1/2)) =
PLS HELP WILL GIVE BRAINLIEST ALMOST DUE
Which equation could represent the line of best fit for the temperatures based on the altitudes?
Answer:
[tex]y = - \frac{7}{5} x + 59[/tex]
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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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.
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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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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The value of a collectible coin can be represented by the equation y = 2X+ 9.74, where x represents the number of
vears that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the value of the coin when Consuello originally purchased it?
The value of the coin when Consuello originally purchased it was $9.74.
What is the value of coin?
The given equation is y = 2x + 9.74, where x represents the number of years that Consuello has owned the coin and y represents the total value of the coin in dollars.
To find the value of the coin when Consuello originally purchased it, we need to find the value of y when x = 0.
Substituting x = 0 in the equation, we get:
y = 2(0) + 9.74
y = 0 + 9.74
y = 9.74
Therefore, the value of the coin when Consuello originally purchased it was $9.74.
What is coin?
A coin is a small, flat, round piece of metal or other material used as money to buy goods and services. It is typically issued by a government or other authority as legal tender and has a fixed value that is recognized within a specific country or region. Coins can be made from various metals, such as copper, nickel, silver, and gold, and often feature engravings or other designs that are intended to make them difficult to counterfeit.
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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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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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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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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.
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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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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A researcher estimates that a fossil is 3200 years old.Using carbon-14 dating,a procedure used to determine the age of an object,the researcher discovers that the fossil is 3600 years old.
a.Find the percent error
b.what other estimates gives the same percent error?Explain your reasoning
The percentage error between the estimated age and the carbon-14 dating age of the fossil is 12.5% and an estimated age of approximately 2978 years would give the same percent error of 12.5%.
What is the definition of percentage?
Percentage is a way of expressing a fraction or proportion as a part of 100. It is denoted by the symbol "%". The term "percent" means "per hundred". For example, if 50% of a group of people are men, it means that 50 out of every 100 people in the group are men.
Now,
a). To find the percent error between the estimated age and the carbon-14 dating age of the fossil, we can use the formula:
percent error = |(estimated age - carbon-14 dating age) / estimated age| x 100%
Substituting the given values, we get:
percent error = |(3200 - 3600) / 3200| x 100%
= |-400 / 3200| x 100%
= 12.5%
Therefore, the percent error between the estimated age and the carbon-14 dating age of the fossil is 12.5%.
b). To find other estimates that give the same percent error, we can use the formula:
percent error = |(estimated age - carbon-14 dating age) / estimated age| x 100%
If we let x be the estimated age that gives the same percent error, then we can write:
12.5% = |(x - 3600) / x| x 100%
Simplifying, we get:
0.125 = |(x - 3600) / x|
Taking the positive square root of both sides (since percent error cannot be negative), we get:
√0.125 = (x - 3600) / x
Simplifying, we get:
x = 3600 / (1 - √0.125)
x ≈ 2978
Therefore, an estimated age of approximately 2978 years would give the same percent error of 12.5% as the original estimated age of 3200 years. This means that if the fossil were actually 2978 years old, the carbon-14 dating would have given an age estimate of approximately 3299 years, which is 12.5% higher than the true age.
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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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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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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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