Answer: 5 & 12
Step-by-step explanation: The formula for the Pythagorean theorem is a^2 + b^2 = c^2. So if 5^2 + 12^ = 13^, 5 & 12 must be the side lengths that form the right angle.
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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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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1. Find the square root of each of the following numbers: (i) 152.7696
What is y - 4 = -2(x - 1) in Slope-Intercept Form y = -2x - 6 y = -2x + 6 y = -2x - 2 y = -2x + 2
The equation y - 4 = -2(x - 1) in slope-intercept form include the following: C. y = -2x - 2.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.By making the variable "y" the subject of formula, we have the following:
y - 4 = -2(x - 1)
y = -2x + 2 - 4
y = -2x - 2
Therefore, the slope (m) is equal to -2.
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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
hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.
The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.
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25. Which is the solution set of the equation
2x² + 3x - 2 = 0?
(1) (-1/2,2}
(2) {1/2,-2}
(3) {1/2,2}
(4) {-1/2,-2}
Answer:
(2) {1/2,-2}
Step-by-step explanation:
2x² + 3x - 2 = 0
Delta = b² - 4ac
= 3² - 4 (2)(-2)
= 9 + 16
Delta = 25
[tex] \sqrt{25} = 5[/tex]
X= -3-5÷4 = -2
X'= -3+5÷4 = 2/4 = 1/2
S = { 1/2 ; -2 }
Answer:
Step-by-step explanation:
2x² + 3x - 2 = 0
2x² -x +4x - 2 = 0
(2x² -x) +(4x - 2) = 0
x(2x -1) +2(2x -1) = 0
(x +2)(2x-1) =0
(x +2) =0
x = -2
OR
(2x-1) =0
x = 1/2
ans: (2) (1/2, -2)
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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(co 5) a textbook company claims that their book is so engaging that more than 55% of students read it. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g
If a hypothesis test rejects the null hypothesis in the context of the claim made by the textbook company, it means that the observed proportion of students who read the book is statistically significantly greater than 55%, suggesting that their book may indeed be more engaging.
If a hypothesis test is performed that rejects the null hypothesis, it means that the observed results are unlikely to have occurred by chance if the null hypothesis were true. In the context of the claim made by the textbook company, the null hypothesis would be that the proportion of students who read the book is equal to or less than 55%.
If the hypothesis test rejects the null hypothesis at a certain level of significance (such as α = 0.05), it means that the observed proportion of students who read the book is statistically significantly greater than 55% at that level of significance.
However, it is important to note that statistical significance does not necessarily imply practical significance. Even if the hypothesis test rejects the null hypothesis, the difference between the observed proportion and 55% may be small, and the practical significance of the result may be limited.
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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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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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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
A cone with a radius of 3 inches and a height of 18 inches is shown
What is the volume, in a cubic inches, of the cone. Round your answer to the nearest integer
Answer: about 169.65
Step-by-step explanation:
You do pi r squared multiplied by height over 3.
28.27 is the area of the circle and you multiply is by six because 18/3=6. 28.27x6 = about 169.65
Fill in the blanks with the appropriate justifications (reasons) for the steps used in solving the equation. Statements
statements:
1. x/2-9=-4 given
2. x/2=-13
3.x=-26
what are the justifications for 2 and 3
The justifications for 2 and 3 are;
Addition property of equality and
Multiplication property of equality
What are the justifications for the steps used in solving the equation?1. x/2 - 9 = -4 given
Add 9 to both sides
2. x/2 = -13 (Addition property of equality)
cross product
3.x = -26 (Multiplication property of equality)
Therefore, x/2 - 9 = -4 where x Is -26 is justified by addition and multiplication property of equality.
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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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what is the 4th term/number of (a+b)^9, pascal’s triangle?
Step-by-step explanation:
hope this will help you Thanks
Can someone help me asap? It’s due tomorrow.
Answer: I’m pretty sure it’s B
Step-by-step explanation:
Tonya is making a circle graph of the data shown in the table. How many degrees will the section for piano have?
Guitar: 1/4
Piano: 1/6
Drums 13/45
Flute 1/10
Trumpet 7/36
The section for piano will have 60 degrees in the circle graph.
How to solveTo find out how many degrees the section for piano will have in the circle graph, we first need to find the fraction of the circle that the piano represents.
The total degrees in a circle is 360 degrees. We can use the given fraction of piano (1/6) and multiply it by 360 degrees to find out the degrees of the section for piano.
Degrees for piano = (Fraction of piano) × 360
Degrees for piano = (1/6) × 360
Now, multiply the fraction by 360:
Degrees for piano = 60
So, the section for piano will have 60 degrees in the circle graph.
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→ 60° ( btw, ° means degrees )
— if a WHOLE circle is 360° and the piano is 1/6 of the circle, then all you have to do is multiply 1/6 by 360° which gives you 60 OR 60°
HEY- you look hungry, eat up !! →
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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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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if you flip a fair coin 10 times, what is the probability of obtaining as many heads as you did or less? 0.0107 0.9453 0.0321 0.7769
To calculate this probability, we need to use the cumulative binomial probability formula:
P(X ≤ k) = Σ(i=0 to k) (n choose i) p^i (1-p)^(n-i)
Where:
- X is the number of heads obtained
- k is the number of heads we want to calculate the probability for (in this case, the same number of heads obtained)
- n is the total number of coin flips (10 in this case)
- p is the probability of getting heads on a single flip (0.5 for a fair coin)
- (n choose i) is the binomial coefficient, which represents the number of ways to choose i heads out of n flips
For this problem, we want to calculate P(X ≤ 10), since we're interested in the probability of obtaining as many heads as we did or less. Plugging in the values, we get:
P(X ≤ 10) = Σ(i=0 to 10) (10 choose i) 0.5^i 0.5^(10-i)
= (10 choose 0) 0.5^0 0.5^10 + (10 choose 1) 0.5^1 0.5^9 + ... + (10 choose 10) 0.5^10 0.5^0
= 0.00098 + 0.00977 + 0.04395 + 0.11719 + 0.20508 + 0.24609 + 0.20508 + 0.11719 + 0.04395 + 0.00977 + 0.00098
= 0.9453
Therefore, the probability of obtaining as many heads as we did or less when flipping a fair coin 10 times is 0.9453.
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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?
solve -3(x-3)≤ 5(1-x)
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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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.
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]
A(n) _____________ volume is similar to a primary partition, but in fact, is not a primary partition.1. mirrored2. simple3. spanned4. striped
A(n) "spanned" volume is similar to a primary partition, but in fact, is not a primary partition.
A spanned volume is similar to a primary partition, but in fact, is not a primary partition. In a spanned volume, you can combine free space from multiple disks to create a larger logical storage unit, while a primary partition is a segment of a hard disk drive that the operating system recognizes as a separate logical storage unit. A volume can span multiple partitions depending on how it is configured, or it can encompass a single partition. Different operating systems have different ways of configuring and managing volumes.
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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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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
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: