Answers
Step-by-step explanation:
For right triangles tan B = opposite leg / adjacent leg
tan B = 3/4
arctan (3/4) = B = 36.87 degrees
Related Questions
there are 90 people in the restaurant. the probability of someone ordering a drink with the food is 60%. use normal approximation of binomial distribution to answer the following 6 questions. 1. what is the mean of the normal distribution? 2. what is the standard deviation of the normal distribution? 3. what is the probability that exactly 50 people will order a drink? 4. what the probability that more than 50 people will order a drink? 5. what is the probability that less than 50 people will order a drink? 6. what is the probability that between 52 or more and 56 or less people will order a drink?
Answers
1. Mean = 54
2. Standard Deviation = 6.3
3. Probability = 0.077
4. Probability = 0.845
5. Probability = 0.155
6. Probability = 0.323
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:
Answers
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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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
Answers
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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Help asap Thank you in advance
Answers
The ball will hit the ground after 4 seconds (x2 = 4).
How to solveGiven the formula h(x) = -16x^2 + v0x + h0, we can plug in the values for the initial velocity (v0) and the initial height (h0) to find the equation that describes the ball's height as a function of time.
v0 = 64 ft/s (initial velocity)
h0 = 12 ft (initial height)
Now, we can write the function for the ball's height:
h(x) = -16x^2 + 64x + 12
To find when the ball hits the ground, we need to solve for x when h(x) = 0:
0 = -16x^2 + 64x + 12
This is a quadratic equation, and we can solve it using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = -16, b = 64, and c = 12.
x = (-64 ± √(64^2 - 4*(-16)12)) / 2(-16)
First, we find the discriminant (b^2 - 4ac):
64^2 - 4*(-16)*12 = 4096 + 768 = 4864
Now we can plug the discriminant back into the quadratic formula:
x = (-64 ± √4864) / (-32)
We have two possible solutions:
x1 = (-64 + √4864) / (-32)
x1 = (-64 + 64) / (-32)
x1 = 0
x2 = (-64 - √4864) / (-32)
x2 = (-64 - 64) / (-32)
x2 = 128 / 32
x2 = 4
Since x1 = 0 represents the initial time when the ball is kicked, we discard this solution.
Therefore, the ball will hit the ground after 4 seconds (x2 = 4).
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The height, in feet, after x seconds of an object launched straight up can be found by the function h(x)=−16x2+v0x+h0, where v0 is the initial velocity of the object and h0 is the initial height.
A ball is kicked straight up into the air from a height of 12 ft with an initial velocity of 64 ft/s. After how many seconds does the ball hit the ground?
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
Answers
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 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
Answers
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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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
Answers
1. Find the square root of each of the following numbers: (i) 152.7696
Answers
1. Start by making pairs of digits from the right: 15, 27, 69, 6.
2. Find the largest integer whose square is less than or equal to the first pair, which is 15. Since 3^2 = 9 < 15 and 4^2 = 16 > 15, the integer we are looking for is 3.
3. Write the digit 3 as the first digit of the square root.
4. Subtract the square of 3 from 15 to get 6.
5. Bring down the next pair of digits, 27, and append them to 6 to get 627.
6. Double the first digit of the current root estimate (which is 3) to get 6.
7. Find the largest digit to fill in the blank in "3_ × _ = 6" such that the resulting product is less than or equal to 627. This digit is 7, since 3×7 = 21 < 627 and 3×8 = 24 > 627.
8. Write down the digit 7 as the second digit of the root estimate.
9. Subtract the square of 37 from 627 to get 60.
10. Bring down the next pair of digits, 69, and append them to 60 to get 6069.
11. Double the first digit of the current root estimate (which is 37) to get 74.
12. Find the largest digit to fill in the blank in "37_ × _ = 606" such that the resulting product is less than or equal to 6069. This digit is 1, since 37×1 = 37 < 6069 and 37×2 = 74 > 6069.
13. Write down the digit 1 as the third digit of the root estimate.
14. Subtract the square of 371 from 6069 to get 152.769.
Therefore, the square root of 152.7696 is approximately 12.36 (rounded to two decimal places).
n each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference in two population means. are the conditions for use of a t-model met? in a random sample of 100 university students, the distribution of time spent at university
Answers
libraries is approximately normal
Yes, the conditions for use of a t-model are met. The sample size is large enough (100) and the distribution of time spent at university libraries is approximately normal.
Which statement is true?
Answers
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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The points (2, −4) and (2, 7) are on a
coordinate plane. What is the distance
between the points?
Answers
The distance between the points (2, -4) and (2, 7) is 11 units.
What is distance?
In mathematics, the distance between two points is a numerical value that represents the amount of space between them. The distance between two points is calculated using the Pythagorean theorem, which applies to any two points in a two-dimensional or three-dimensional space.
The two points have the same x-coordinate of 2, so they lie on a vertical line. To find the distance between them, we need to find the difference between their y-coordinates.
The y-coordinate of the first point is -4 and the y-coordinate of the second point is 7. Therefore, the difference between the y-coordinates is:
7 - (-4) = 7 + 4 = 11
So the distance between the two points is 11 units.
Therefore, the distance between the points (2, -4) and (2, 7) is 11 units.
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Homework 18.1.-trigonometric ratios
Find the 3 trigonometric ratios. If needed, reduce fractions.
Answers
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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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.
Answers
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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Can someone help me asap? It’s due tomorrow.
Answers
Answer: I’m pretty sure it’s B
Step-by-step explanation:
explanation
A is has no correlation
B is too broad if a category to determine much
D has no correlation
Therefore the answer is C
a blanket measures 1 1/4 yards on each side. how many square yards does the blanket cover?
Answers
Answer:
Add 1 1/4 x 1 1/4
Step-by-step explanation:
can someone please help me with these 3 there due tomorrow!!
Answers
Answer:
mean= 56.9
median= 55.5
mode= 64
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?
Answers
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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3x - 1 <_ 2x what is the answer
Answers
Answer:
x<-1/5
Step-by-step explanation:
Imma assume the _ is a - soo
3x-1<-2x
5x<-1
x<-1/5
What is the value of the expression?
12.325-(2.24 times 3.9)
Please hurry!
Answers
Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answers
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]
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?
Answers
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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the reason why we need to have leap years is because group of answer choices the year does not contain an exact multiple of 30-day months. the year does not contain an exact multiple of 7-day weeks. the year does not contain an exact multiple of 24-hour days. some years are longer than others because sometimes it just takes a little longer to go once around the sun.
Answers
A year is approximately 365.24 days long, so without leap years, our calendar would slowly become out of sync with
the Earth's orbit around the sun.
The reason why we need to have leap years is because the year does not contain an exact multiple of 24-hour days.
This would eventually cause the seasons to occur at different times of the year.
To keep the calendar aligned, we add an extra day (February 29th) to the calendar every four years, making the year
366 days long.
A year is approximately 365.24 days long, so without leap years, our calendar would slowly become out of sync with
the Earth's orbit around the sun.
This ensures that the calendar year stays in sync with the astronomical year.
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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?
Answers
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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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!)
Answers
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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How many seconds will it take the model rocket to reach its maximum height?
Answers
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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sam has a goal of walking 3 1/2 miles by the end of the day he walks 1 1/8 miles before lunch and 3/4 mile after resting what is the remaining distance in miles that sam needs to walk to reach his goal?
Show your work
Answers
Sam still needs to walk 7/8 of a mile to reach his goal.
How to determine how many miles that sam needs to walk to reach his goalTo find out how many miles Sam has already walked, we add the distance he walked before lunch (1 1/8 miles) to the distance he walked after resting (3/4 mile):
1 1/8 + 3/4 = 9/8 + 3/4 (since we need a common denominator of 8)
= 18/8 + 3/8
= 21/8
So Sam has already walked 2 5/8 miles.
To find out how much further he needs to go to reach his goal of 3 1/2 miles, we subtract what he's already walked from his goal:
3 1/2 - 2 5/8 = 7/2 - 21/8 (again, we need a common denominator of 8)
= 28/8 - 21/8
= 7/8
So Sam still needs to walk 7/8 of a mile to reach his goal.
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help me please with this question what is 11/12 divided by 4
Answers
Answer:
[tex]\frac{11}{8}[/tex]
Step-by-step explanation:
[tex]\frac{11}{2}[/tex] ÷ 4 = [tex]\frac{11}{2}[/tex] x [tex]\frac{1}{4}[/tex] = [tex]\frac{11}{8}[/tex]
So, the answer is [tex]\frac{11}{8}[/tex]
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
Answers
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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Graph the image of square JKLM after a dilation with a scale factor of 1/5, centered at the origin.
Answers
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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Write the absolute value equations in the form lx-bl is greater than or equal to or lx-bl is less than or equal to write an absolute value inequality that has the following solution set x < or equal to -9 or x > or equal to -5
Answers
The final absolute value inequality that represents the solution set x ≤ -9 or x ≥ -5 is |x + 7| ≥ 2.
If the absolute value expression is greater than or equal to a number (e.g. |x| >= 5).
We can write it as two separate inequalities: x >= 5 or x <= -5.
The absolute value expression is less than or equal to a number (e.g. |x| <= 3)
We can write it as the single inequality: -3 <= x <= 3.
Using these rules:
We can write an absolute value inequality that has the solution set x <= -9 or x >= -5200 as follows:
| x + 2604 | >= 5193
To see why this works,
Let's first look at the case where x is less than or equal to -9. In this case, we have:
x + 2604 <= -9
x <= -2613
Plugging this into our inequality:
| -2613 | >= 5193
Which is true, since |-2613| = 2613 >= 5193.
Now let's look at the case where x is greater than or equal to -5200. In this case, we have:
x + 2604 >= -5200
x >= -7804
Plugging this into our inequality, we get:
| -7804 | >= 5193
Which is also true, since |-7804| = 7804 >= 5193.
Therefore, the inequality | x + 2604 | >= 5193 has the solution set x <= -9 or x >= -5200, as desired. I hope this helps! Let me know if you have any other questions.
Midpoint = (-9 + (-5)) / 2 = -7
The absolute value inequality will have the form |x - (-7)|.
|x + 7| ≥ 2, since the distance between -9 and -7 is 2.
|x + 7| ≤ -2, since the distance between -5 and -7 is -2.
However,
An absolute value cannot be negative, so the second inequality doesn't make sense. Therefore, we'll only use the first inequality.
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