Riley could have read any fraction between 1/2 and 4/5 of the book.
We must determine the range of potential fractions of the book that Riley may have read in order to determine what portion Riley may have read.
Riley must have read less than 4/5 of the book because we know she read less than Mariette. Riley read more than Erika, and because we also know that Riley read more, Riley must have read more than 0.5 of the book.
Therefore, the fraction of the book that Riley could have read is between 0.5 and 4/5, or:
0.5 < Riley's fraction < 4/5
To express this range as a single fraction, we can find a common denominator for 0.5 and 4/5:
0.5 = 2/4
4/5 = 4/4 * 1/5 = 5/5 × 4/25 = 20/25
So the range of possible fractions for Riley is:
2/4 < Riley's fraction < 20/25
We can simplify this range by finding the lowest common denominator of 4 and 25, which is 100:
2/4 = 25/50
20/25 = 80/100
So the range of possible fractions for Riley is:
25/50 < Riley's fraction < 80/100
We can simplify this range by dividing both sides by 50:
1/2 < Riley's fraction < 4/5
Therefore, Riley could have read any fraction between 1/2 and 4/5 of the book.
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Ariel wants to join the volleyball team in the fall, so she went to an overnight volleyball camp last weekend to practice her skills. Before she left, she packed a shower caddy shaped like a rectangular prism with a volume of 420 cubic inches. The caddy is 10
1
2
inches long and 5 inches tall.
How wide is the shower caddy?
The width of the shower caddy is 8 inches.
What is Volume?
Volume is a measure of the total amount of material that an object contains. In mathematical terms, volume is calculated by multiplying the length, width, and height of an object.
We can use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.
We know that the volume of the caddy is 420 cubic inches, the length is 10.5 inches, and the height is 5 inches. Let's substitute these values into the formula and solve for the width:
420 = 10.5w × 5
Divide both sides by 52.5:
8 = w
Therefore, the width of the shower caddy is 8 inches.
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Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax using the following expression, where c
represents the original cost of the coffee pot.
c−0.2c
Which other expression could Kelly use to calculate her cost before sales tax?
A. 0.8c
B. 1.2c
C.1.8c
D.80c
Use the times and corresponding closing prices of the stock to create coordinate pairs. Let x represent the number of weeks since the first data point, and let y represent the closing price at each time. So, x = 0 represents the data point from 5 years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since 5 years ago, when x = 0. Fill in the table to represent your data as coordinate pairs.
x (Weeks Since 5 Years Ago) y (Closing Price, in $)
most recent 260
7 days ago 259
1 month ago 256
6 months ago 234
1 year ago 208
3 years ago 104
5 years ago 0
The complete table is:
x (weeks since 5 years ago) y (in $)
260 150.01
259 150.06
256 149.42
234 142.03
208 152.79
104 97.65
0 70.43
The coordinates are given by (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).
The X axis suggests the weeks since 5 years ago and Y axis suggests the closing price at each time.
Number of weeks in a year is 52 weeks.
Most recent time suggests, x = 52*5 = 260
when x = 260, then y = 150.01
7 days ago that is 1 weeks ago, x = 260 -1 = 259
The value of y then = $ 150.06
1 months ago that is 4 weeks ago, x = 260 - 4 = 256
The closing price then is, y = 149.42
6 months ago, x = 260 - 52/2 = 260 - 26 = 234
The closing price then is, y = 142.03
1 year ago that is 52 years ago, x = 260 - 52 = 208
The closing price was then, y = 152.79
3 years ago, x = 260 - 52*3 = 260 - 156 = 104
The closing price was then, y = 97.65
5 years ago, x = 260 - 52*5 = 260 - 260 = 0
The closing price was then, y = 70.43.
Then the coordinates are (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).
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Which statement is true?
The only true statement is 2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4.
option A.
What is the rule of BODMAS?BODMAS is an acronym that stands for "Brackets, Orders, Division, Multiplication, Addition and Subtraction".
The rule of BODMAS states that when you have a mathematical expression that involves multiple arithmetic operations, you need to perform them in a certain order. You should start by evaluating anything inside brackets or parentheses first. Then, you should work out any exponents or square roots. After that, you should perform any division or multiplication from left to right, and finally, you should perform any addition or subtraction from left to right.
If we apply the rule of BODMAS to all the given options, we would notice that only option 1 is true.
2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4
L.H.S ⇒ 2 x (6) - 6
= 12 - 6
= 6
R.H.S ⇒ 14 ÷ (3.5 x 2 ) + 4
= 14 ÷ (7) + 4
= 2 + 4
= 6
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PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL
SHOW WORK
The Number of atoms ≈ 5.119 x 10^24 atoms
The Mass ≈ 248.0 g
Mass ≈ 248.0 g
How many atoms are present in 8.500 mole of chlorine atoms?To find the number of atoms, we use Avogadro's number, which is 6.022 x 10^23 atoms/mole.
Number of atoms = (8.500 moles) * (6.022 x 10^23 atoms/mole)
Number of atoms ≈ 5.119 x 10^24 atoms
Determine the mass (g) of 15.50 mole of oxygen.To find the mass, we need the molar mass of oxygen, which is 16.00 g/mole.
Mass = (15.50 moles) * (16.00 g/mole)
Mass ≈ 248.0 g
Determine the number of moles of helium in 1.953 x 10^8 g of helium.
To find the number of moles, we need the molar mass of helium, which is 4.00 g/mole.
Number of moles = (1.953 x 10^8 g) / (4.00 g/mole)
Number of moles ≈ 4.883 x 10^7 moles
Calculate the number of atoms in 147.82 g of sulfur.
To find the number of atoms, we first need to find the number of moles of sulfur, and then use Avogadro's number. The molar mass of sulfur is 32.07 g/mole.
Number of moles = (147.82 g) / (32.07 g/mole)
Number of moles ≈ 4.609 moles
Number of atoms = (4.609 moles) * (6.022 x 10^23 atoms/mole)
Number of atoms ≈ 2.772 x 10^24 atoms
Determine the molar mass of Co.
The molar mass of cobalt (Co) is 58.93 g/mole.
Determine the formula mass of Ca3(PO4)2.
To find the formula mass, we need to add up the molar masses of all the elements in the compound.
Ca3(PO4)2 contains 3 calcium (Ca) atoms, 2 phosphorus (P) atoms, and 8 oxygen (O) atoms.
Molar mass of Ca = 40.08 g/mole
Molar mass of P = 30.97 g/mole
Molar mass of O = 16.00 g/mole
Formula mass = (3 * 40.08) + (2 * 30.97) + (8 * 16.00)
Formula mass = 120.24 + 61.94 + 128.00
Formula mass ≈ 310.18 g/mole
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John buys new baseball equipment for $2000. The purchase made is with a credit card that has a 19% APR. John makes a $150 payment monthly. How many months will it take John to pay off the balance?
It will take John approximately 17 months to pay off the balance.
What is simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Assuming that John does not use the credit card for any other purchases and that the credit card company uses a simple interest calculation method, we can use the following steps to calculate the number of months it will take John to pay off the balance:
Calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:
Monthly interest rate = 19% / 12 = 0.01583
Calculate the monthly finance charge by multiplying the outstanding balance by the monthly interest rate:
Monthly finance charge = $2000 x 0.01583 = $31.66
Subtract the monthly payment from the monthly finance charge to get the amount that will be applied to the outstanding balance:
Payment applied to balance = $150 - $31.66 = $118.34
Divide the outstanding balance by the payment applied to balance to get the number of months it will take to pay off the balance:
Number of months to pay off balance = $2000 / $118.34 = 16.9
(rounded up to the nearest whole number)
Therefore, it will take John approximately 17 months to pay off the balance.
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A parking space has an area of 209 ft.² and a height of 19 feet. A custom truck has rectangle dimensions of 13.5 x 8.5 feet. Can the truck fit in the parking space?
Yes, the truck fit in the parking space for the given rectangle dimensions through which 13.5ft<19ft or 11ft>8.5ft
What about rectangle dimensions?
The dimensions of a rectangle refer to its length and width, which are the two perpendicular sides of the rectangle. The length is the longer side of the rectangle, while the width is the shorter side. The dimensions are usually denoted by the letters "l" and "w", with the length written first.
For example, if a rectangle has a length of 6 units and a width of 4 units, its dimensions would be written as "6 x 4", or "l = 6, w = 4". The area of a rectangle can be calculated by multiplying its length by its width, while its perimeter is given by the sum of twice its length and twice its width.
According to the given information:
We know the are of parking space = [tex]209ft^{2}[/tex]
So, 19 x b = 209
b = 11
13.5 ft < 19 ft and 11 ft > 8.5 ft
So, the truck fit in the parking space (parallelogram area formula)
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What is the reason for Statement 3 of the two-column proof?
O Linear Pair Postulate
O Angle Addition Postulate
O Definition of complementary angles
Definition of angle
k
Given: mzJMK = 52"
m2KML = 38
Prove: ZJML is a right angle.
Statements
1. m/JMK = 52"
2 m/KML = 38"
3.
M
m/JMK+m/KML = m/JML
4.52 +38 = m/JML
5.90 = m/JML
6 /JML is a right angle
Reasons
Given
Given
Substitution
Property of Equality
Simplification
Definition of right
angle
The measure of ∠JMK =52° and ∠KML = 38°.
Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.
To Prove: is a right angle.
Proof:
Statements Reasons
1. m∠JMK = 52° Given
2. m∠KML = 38° Given
3. m∠JMK + m∠KML = m∠JML
The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.
4. 52° + 38° =m∠JML Substitution property of equality
5. 90° = m∠JML Simplification
6. ∠JML is a right angle. Definition of right angle
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the coefficient of determination resulting from a particular regression analysis was 0.85. what was the slope of the regression line?
The slope of the regression line is 0.922. Option C is correct.
The coefficient of determination (R-squared) is defined as the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a linear regression model. It can be calculated as the square of the correlation coefficient (r) between the dependent and independent variables.
If we assume a simple linear regression model with a single independent variable (x) and a single dependent variable (y), the slope of the regression line (b) can be calculated as:
b = r * (Sy / Sx)
where r is the correlation coefficient between x and y, Sy is the standard deviation of y, and Sx is the standard deviation of x.
If the coefficient of determination is 0.85, then the correlation coefficient is the square root of 0.85, which is approximately 0.922. Assuming the standard deviations of x and y are known, we could use the formula above to calculate the slope of the regression line as:
b = 0.922 * (Sy / Sx)
Therefore, 0.922, could be the slope of the regression line in this case, if the assumptions of a simple linear regression model with known standard deviations are met. Option C is correct.
The complete question is
The coefficient of determination resulting from a particular regression analysis was 0.85. What was the slope of the regression line?
a. 0.85
b. -0.85
c. 0.922
d. There is insufficient information to answer the question.
e. None of the above
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what is the constant of proportionality in the equation y=6/5x
Step-by-step explanation:
The only number there : 6/5 is the constant of proportionality
which of the following questions does a test of significance answer?a) is the sample or experiment properly designed?b) is the observed effect due to chance?c) is the observed value correct?d) is the observed effect important?
The significance test is a test that claim on the basis of p-value and cannot check if the observed effect and it is the observed effect due to chance. So, the right choice for the answer is option(b).
We have to determine the statement that reflects the test of significance in a number of statements. We check the each option one by one. A significance test tests the claim made. This test used to investigate the claim by considering the null and alternate hypothesis. It cannot used to check about the sample or the experiment are properly design or not. Now, the significance test determines that the observed effect is due to chance. Because it measures the observed difference between the group using the p-value ( probability or chance).
If the p-value<α, then accept the null hypothesis.If the p-value ≥α then reject null hypothesis.A significance test, tests the claim. It cannot say if the observed effect is important or not. It is only based on test the claim on the basis of p-value and cannot check if the observed effect is important. Hence, option( b) is right.
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a blanket measures 1 1/4 yards on each side. how many square yards does the blanket cover?
Answer:
Add 1 1/4 x 1 1/4
Step-by-step explanation:
what is the 4th term/number of (a+b)^9, pascal’s triangle?
Step-by-step explanation:
hope this will help you Thanks
in testing a hypothesis from a random sample involving three or more means, the appropriate test would be a one-way anova. True or false?
3x - 1 <_ 2x what is the answer
Answer:
x<-1/5
Step-by-step explanation:
Imma assume the _ is a - soo
3x-1<-2x
5x<-1
x<-1/5
Graph the image of square JKLM after a dilation with a scale factor of 1/5, centered at the origin.
The image of square JKLM after a dilation with a scale factor of 1/5 centered at the origin is a smaller square with vertices J'(-0.4, 0.4), K'(0.4, 0.4), L'(-0.4, -0.4), and M'(0.4, -0.4).
What is graph?A graph is a visual representation of data, relationships or functions, typically consisting of points, lines, and curves plotted on a coordinate system.
To graph the image of square JKLM after a dilation with a scale factor of 1/5 centered at the origin, we need to perform the following steps:
Plot the vertices of the square JKLM.
Draw lines connecting the vertices to form the square.
Find the coordinates of the image vertices after dilation with a scale factor of 1/5 centered at the origin.
Plot the image vertices and connect them to form the image square.
Here's a step-by-step guide to performing each of these steps:
Plot the vertices of square JKLM:
J(-2, 2) K(2, 2)
+------+
| |
| |
+------+
L(-2, -2) M(2, -2)
Draw lines connecting the vertices to form the square:
J(-2, 2) K(2, 2)
+------+
| |
| |
+------+
L(-2, -2) M(2, -2)
Find the coordinates of the image vertices after dilation with a scale factor of 1/5 centered at the origin:
To find the coordinates of the image vertices, we need to multiply the coordinates of each vertex by the scale factor of 1/5:
[tex]J' = (-2 * 1/5, 2 * 1/5) = (-0.4, 0.4)\\K' = (2 * 1/5, 2 * 1/5) = (0.4, 0.4)\\L' = (-2 * 1/5, -2 * 1/5) = (-0.4, -0.4)\\M' = (2 * 1/5, -2 * 1/5) = (0.4, -0.4)\\[/tex]
Plot the image vertices and connect them to form the image square:
J'(-0.4, 0.4) K'(0.4, 0.4)
+------+
| |
| |
+------+
L'(-0.4, -0.4) M'(0.4, -0.4)
The image of square JKLM after a dilation with a scale factor of 1/5 centered at the origin is a smaller square with vertices J'(-0.4, 0.4), K'(0.4, 0.4), L'(-0.4, -0.4), and M'(0.4, -0.4).
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The image of square JKLM after a dilation with a scale factor of 1/5, centered at the origin, is a smaller square centered at the origin.
To graph the image of square JKLM after a dilation with a scale factor of 1/5, centered at the origin, we can follow these steps:
Draw the original square JKLM.
Draw a line segment from the origin to each vertex of the square.
Multiply the length of each line segment by 1/5.
Draw a new square centered at the origin, with side lengths equal to the lengths of the new line segments.
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Can someone help me asap? It’s due tomorrow.
Answer: I’m pretty sure it’s B
Step-by-step explanation:
How many seconds will it take the model rocket to reach its maximum height?
The answers to the following prompts are give as follows:
9 (c) the time taken for rocket to hit the ground is 5
10 (c) the maximum height is 4
11 (b) the solutions of 16x² - 64 = 0 are -4 and 4
9) To find the time it takes the rocket to hit the ground, we need to find the value of s when h(s) = 0 since h(s) represents the height of the rocket.
So we need to solve the equation: -3s^2 + 6s + 45 = 0.
Factoring, we get -3(s - 5)(s + 3) = 0. So s = 5 or s = -3. Since time cannot be negative, we take s = 5.
Therefore, the answer is (c) 5.
10 ) The maximum height of the rocket occurs at the vertex of the parabola given by the function h(s) = -3s^2 + 6s + 45. The s-coordinate of the vertex is given by s = -b/2a, where a = -3 and b = 6. So s = -6/-6 = 1. Therefore, the answer is (a) 1.
11) We can solve the equation 16x² - 64 = 0 by factoring out the greatest common factor, which is 16: 16(x² - 4) = 0.
Then, we can factor the quadratic expression as a difference of squares: 16(x + 2)(x - 2) = 0. Therefore, the solutions are x = -2 and x = 2, and the answer is (b) -4 and 4.
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on september 23, 2013, president obama had an approval rating of 46% (according to a gallup poll). suppose a sample of 100 americans is taken that same week. what is the probability that the sample proportion has between a 42% and a 47% approval rating? (use 4 or more decimal places in your computations!)
If a sample of 100 Americans is taken that same week, then the probability that "sample-proportion" has between a 42% and a 47% approval rating is 0.7693 or 76.93%.
To calculate the probability that the sample-proportion falls between 42% and 47% for a sample of 100 Americans, we use the standard normal distribution.
The Sample size (n) is = 100,
The Sample proportion (p) = 46% or 0.46,
The "Standard-deviation" (σ) = √(p×(1-p)/n) = √(0.46×(1-0.46)/100) ≈ 0.0497,
We now calculate the "z-scores" corresponding to the lower and upper bounds of the desired range,
We know that, the value of "z" is (x - μ)/σ,
where x = desired proportion, μ = mean proportion, and σ = standard deviation,
So, The probability that the sample proportion has between a 42% and a 47% "approval-rating", is written as :
⇒ P(0.42 < x < 0.47) = P[(0.42 - 0.46)/0.0497 < z < (0.47 - 0.46)/0.0497],
⇒ P(0.42 < x < 0.47) = P[-0.807 < z < 2.015],
⇒ P(0.42 < x < 0.47) = 0.9783 - 0.209,
⇒ P(0.42 < x < 0.47) = 0.7693,
Therefore, the required probability is 0.7693 or 76.93%.
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Theorem: A line parallel to one side of a triangle divides the other two proportionately.
In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:
Which statement can be proved true using the given theorem?
Group of answer choices
Segment BD = 12
Segment BD = 4
Segment BF = 16
Segment BF = 9
Since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.
What is triangle?A triangle is a three-sided polygon that is one of the basic shapes in geometry. It is defined by three points that are connected by three line segments. Triangles have three angles, which add up to 180 degrees, and three sides, which add up to the sum of the lengths of the other two sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. Triangles come in a variety of forms, from the equilateral triangle, which has three sides of equal length, to the isosceles triangle, which has two sides of equal length, to the scalene triangle, which has three sides of different lengths.
The correct answer is: Segment BF = 9. This can be proved true using the given theorem, since segment DE is parallel to segment BC and segment EF is parallel to AB. Therefore, since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.
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Fill in the blanks with the appropriate justifications (reasons) for the steps used in solving the equation. Statements 1.x/2-9=-4 given 2. x/2=-13 3 x=-26 what are the justifications for 2 and 3
Therefore, the justification for step 2 is "Addition Property of Equality" and the justification for step 3 is "Multiplication Property of Equality".
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually separated by an equal sign. It means that the expressions on both sides of the equal sign represent the same value or quantity. Equations can involve one or more variables and may have different degrees of complexity. They are commonly used to model various real-world situations and to solve problems in mathematics, science, engineering, and other fields.
Here,
2. To isolate the variable term, add 9 to both sides. This yields:
x/2 - 9 + 9 = -4 + 9
Simplifying the left side, we get:
x/2 = 5
3. To solve for x, multiply both sides by 2. This yields:
x/2 * 2 = 5 * 2
Simplifying both sides, we get:
x = -10
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1. Find the square root of each of the following numbers: (i) 152.7696
can someone please help me with these 3 there due tomorrow!!
Answer:
mean= 56.9
median= 55.5
mode= 64
Homework 18.1.-trigonometric ratios
Find the 3 trigonometric ratios. If needed, reduce fractions.
The 3 trigonometric ratios of the right triangle with respect to angle A are as follows:
sin A = 12 / 13
cos A = 5 / 13
tan A = 12 / 5
How to find angles of a right triangle using trigonometric ratios?The side of a right angle triangle can be found using trigonometric ratios as follows:
Therefore, let's find the 3 trigonometric ratios with respect to angle A.
sin A = opposite / hypotenuse
sin A = 36 / 39
sin A = 12 / 13
cos A = adjacent / hypotenuse
cos A = 15 / 39
cos A = 5 / 13
tan A = opposite / adjacent
tan A = 36 / 15
tan A = 12 / 5
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Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answer:
C
Step-by-step explanation:
3x - 9y = 9 → (1)
- 2x +2y = 8 ( subtract 2y from both sides )
- 2x = - 2y + 8 ( divide through by - 2 )
x = y - 4
substitute x = y - 4 into (1)
3(y - 4) - 9y = 9
3y - 12 - 9y = 9
- 6y - 12 = 9 ( add 12 to both sides )
- 6y = 21 ( divide both sides by - 6 )
y = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex]
Your cousin bought a used car. He paid a total of $12,755 for the car. The total cost includes: • The list price of the car, x • A 7% sales tax on the list price . Plus $450 in additional fees.
What is the price of the car your cousin bought?
List price:
Let's use the variable x to represent the list price of the car.
The total cost your cousin paid for the car is the list price plus a 7% sales tax on the list price, plus $450 in additional fees.
We can write this as an equation:
Total cost = List price + 0.07(List price) + 450
We know that the total cost your cousin paid was $12,755, so we can substitute that into the equation:
12,755 = x + 0.07x + 450
Simplifying the right side:
12,755 = 1.07x + 450
Subtracting 450 from both sides:
12,305 = 1.07x
Dividing both sides by 1.07:
x = 11,500
Therefore, the list price of the car your cousin bought was $11,500.
The list price of the car your cousin bought was $11,500.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's start by setting up an equation to represent the total cost of the car:
Total cost = List price + 7% of List price + $450
We know that the total cost is $12,755, so we can substitute that in:
$12,755 = List price + 0.07(List price) + $450
Simplifying this equation, we get:
$12,755 = 1.07(List price) + $450
Subtracting $450 from both sides, we get:
$12,305 = 1.07(List price)
Dividing both sides by 1.07, we get:
List price = $11,500
Therefore,
The list price of the car your cousin bought was $11,500.
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The figure shown is created by joining two rectangles..
3 ft
10 ft
3 ft
3. ft
Enter the area of the figure, in square feet. Need help please
The area of the figure is 39ft²
What is area of a rectangle?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
Area of a rectangle is expressed as ;
A = l × w
where l is the length and w is the width.
Dividing the shape into two;
The area of shape 1 = l× w
= 3× 7 = 21ft²
The area of shape 2 = l× w
= 6 × 3 = 18 ft²
therefore the total area = 21+18 = 39 ft²
therefore the area of the figure is 39ft²
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Hungry Harry is a giant ogre with an appetite that fluctuates throughout the day. H(t) models the weight
of sheep (in kg) that Harry would like to swallow t hours after he wakes up. Here, t is entered in radians.
H (t) = 12 sin (2/24t) +15
What is the second time after Harry wakes up that he feels like consuming 17 kg of sheep?
Round your final answer to the nearest tenth of an hour.
The second time when harry feel like consuming 17 kg of sheep after he wakes up is equal to 39.7 hours ( round to nearest tenth of an hour).
Function is equal to
H (t) = 12 sin (2/24t) +15
Where H(t) models the weight of sheep in kg that Harry like to swallow in 't' hours after wakes up.
't' in radians.
Harry wants to consumes 17kg
⇒ H(t) = 17 for t.
Substituting the given expression for H(t), we get,
⇒ 12 sin(2/24 t) + 15 = 17
⇒ 12 sin(2/24 t) = 2
⇒ sin(2/24 t) = 1/6
⇒ 2/24 t = sin^(-1)(1/6)
We know that sin^(-1)(1/6) = 0.167
Substitute the value we get,
⇒ t = 12 × 0.167
⇒ t = 2.004 radians
This gives us the first time after Harry wakes up that he feels like consuming 17 kg of sheep.
For the second time,
Add one full period to the first time, since the function H(t) has a period of 12π/2 = 6π.
The second time is,
t = 2.004 + 6π
= 2.004 + 6×3.14
= 20.844 radians
To round to the nearest tenth of an hour,
Since there are 12 hours in a full revolution.
Convert radians to hours by dividing by 2π and then multiplying by 12.
t = 20.844/(2π) × 12
= 3.31 × 12 hours
= 39.69
= 39.7 (rounded to the nearest tenth)
Attached graph.
Therefore, the second time after Harry wakes up that he feels like consuming 17 kg of sheep is approximately 39.7 hours after he wakes up.
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A box of chocolates contains five milk chocolates, three dark chocolates, and four white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is white chocolate, and the third is milk chocolate. Find the probability of this occuring.
A. 28/165
B. 1/8
C. 180/1331
D. 2/33
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0. 07 and the probability that the flight will be delayed is 0. 16. The probability that it will not rain and the flight will leave on time is 0. 83. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth. How would you figure this out?
The probability that it is raining and the flight is delayed is equal to the probability of it raining multiplied by the probability of the flight being delayed.
Therefore, the probability that it is raining and the flight is delayed is 0.07 * 0.16 = 0.0112. Rounded to the nearest thousandth, this is 0.011.