Answer:
common denominator of 1/a + 1/b is ab
however simplifying the complex fraction gives: (b-a)/(b +a)
Step-by-step explanation:
common denominator of 1/a + 1/b
should be the product of the denominators
a*b
so 1/a + 1/b = (b + a)/ab
ao
( 1/a - 1/b) divided by (1/a + 1/b) = (b - a)/(ab) divided by (b+a)/ab
To find the common denominator for 1/a and 1/b within a complex fraction, we use ab. The complex fraction (1/a - 1/b) divided by (1/a + 1/b) can be simplified by multiplying the numerator and denominator by ab, leading to a simplified form of (b² - a²) / (a² + b²).
When finding the common denominator for complex fractions like 1/a and 1/b, it's similar to dealing with real numbers. Given the complex fraction (1/a - 1/b) divided by (1/a + 1/b), we can identify a and b as the denominators. To combine the fractions within the complex fraction, we need a common denominator, which is ab. Thus, the fractions would become (b/a - a/b) and (a/b + b/a), both with a common denominator of ab.
In the complex fraction ((1/a - 1/b) / (1/a + 1/b)), by finding the common denominator, we then rewrite the equation as (b/a - a/b) / (a/b + b/a), which simplifies to (b² - a²) / (a² + b²) when multiplied by ab in both the numerator and the denominator. This process of finding the common denominator allows us to combine and simplify the complex fraction.
What is the efficiency of a machine that produces 4500 joules of output work for every 4250 joules of input work? (remember to put it in correct units and round to the hundredths place)
Answer:
105.88%
Step-by-step explanation:
Efficiency:
Output/input × 100
4500/4250 × 100
105.8823529%
Subtract 6 from me. Then multiply by 2. If you subtract 40 and then divide by 4, you get 8. What number am I?
Answer:
42
Step-by-step explanation:
Let the number be "x"
We translate the word equation to algebraic equation.
First,
subtract 6 from me, so we have:
x - 6
Now,
Multiply by 2, so we have:
2(x-6)
Now,
Subtract 40, then divide by 4:
[tex]\frac{2(x-6)-40}{4}[/tex]
Now, you get "8", so equate this to 8, we get:
[tex]\frac{2(x-6)-40}{4}=8[/tex]
We now solve using algebra:
[tex]\frac{2(x-6)-40}{4}=8\\2(x-6)-40=4*8\\2(x-6)-40=32\\2x-12-40=32\\2x-52=32\\2x=32+52\\2x=84\\x=42[/tex]
The number is 42
The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. If the scores at this school have the same distribution as national scores.
(a) What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?(b) What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?(c) What is the sampling distribution of the sample mean score for a random sample of 36 students?
Answer:
a. mean=18.6
b. standard deviation=1.0
c. The distribution is a symmetry and mound-shaped but nowhere near normal.
Step-by-step explanation:
a. let [tex]\mu_x[/tex] be the sample mean.
-For a normal distributed sample, the population mean is equal to the sample mean:
[tex]\mu_x=\mu\\\\=18.6[/tex]
Hence, the sample mean is 18.6
b. Let s denote the sample standard deviation.
-For a normally distributed population, the sample standard deviation is calculated using the formula;
[tex]s=\frac{\sigma}{\sqrt{n}}\\\\=\frac{6}{\sqrt{36}}\\\\=1.0[/tex]
Hence, the sample standard deviation is 1.0
c. The sample has a mean of 18.6 and a standard deviation of 1.0
-Since it's derived from a normally distribted population, it will be symmetrical and have an almost normal shape.
-Hence, it is a symmetry and mound-shaped, but Not Normal.
The mean of the sampling distribution is 18.6. The standard deviation of the sampling distribution is 1.0. The sampling distribution of the sample mean score for a random sample of 36 students is normally distributed with a mean of 18.6 and standard deviation of 1.0, according to the central limit theorem.
Explanation:The mean and standard deviation of the population, which are given as 18.6 and 6.0 respectively, are used to calculate the mean and standard deviation of the sampling distribution.
(a) According to the central limit theorem, the mean of the sampling distribution of the sample mean score for a random sample of 36 students (µx-bar) is equal to the mean of the population (µ), so µx-bar = µ = 18.6.
(b) The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students (σx-bar) is the standard deviation of the population (σ) divided by the square root of the sample size (n), so σx-bar = σ/√n = 6.0/√36 = 1.0.
(c) The sampling distribution of the sample mean score for a random sample of 36 students is a normal distribution with mean µx-bar = 18.6 and standard deviation σx-bar = 1.0, according to the central limit theorem, since the sample size is sufficiently large (n > 30).
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PLEASE HELP, ASAP! PLEASE AND THANK YOU!
Answer:
The answer to your question is 6.- B 7.- D
Step-by-step explanation:
Data
Parallelogram ACFG
6.-
m∠GAC = 112°
m∠ACF = ?
Process
These angles are supplementary, they measure the same.
∠GAC + ∠ACF = 180
-Substitution
112 + ∠ACF = 180°
-Solve for ∠ACF
∠ACF = 180° - 112°
-Result
∠ACF = 68°
7.-
m∠AGF = 2a + 10
m∠ACF = a + 20
The angles ∠GAC and ACF are equal, they measure the same.
∠GAC = ∠ACF
-Substitution
a + 20 = 2a + 10
-Solve for a
a - 2a = 10 - 20
-Result
-a = -10
a = 10
-Find ∠AGF
∠AGF = 2(10) + 10
20 + 10
= 30°
A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?
A.
-3x + 4y = 3
B.
-1.5x − 3.5y = -31.5
C.
2x + y = 20
D.
-2.25x + y = -9.75
Please Help!!!!! 25 Points!!!!!!
Answer: 7 yards will be your answer.
Step-by-step explanation: I tried. Sorry if the answer is wrong!
Answer:
8 yards
Step-by-step explanation:
The small triangle is inside the big triangle and shares two of it's legs which means it is similar to the big triangle.
12:15
x:10
4:5
x must be 8
To play basketball with her friends, Evangeline needs to pump air in her ball, which is completely deflated. Before inflating it, the ball weighs 0.615 kilograms. Afterwards, it weighs 0.624 kilograms. The diameter of the ball is 0.24 meters.Assuming the inflated ball is perfectly spherical, what is the air density within it.
Answer:
1.24 kilograms per cubic meter.
Step-by-step explanation:
The air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]"
Air density:The initial weight of 7 ball [tex]= 0.615 \ kg\\\\[/tex]
weight of 7 inflated balls[tex]= 0.624 \ kg\\\\[/tex]
Calculating the mass (weight) of 7 air:
[tex]\to 0.624-0.615\ kg\\\\ \to 0.009\ kg\\\\[/tex]
Calculating the diameter of 7 balls:
[tex]\to 0.24 \ m\\\\[/tex]
Calculating the Radius of the ball:
[tex]\to \frac{\text{diameter}}{2}\\\\ \to \frac{0.24}{2}\\\\ \to 0.12\ m\\\\[/tex]
Calculating the volume of air in the ball:
[tex]\to \frac{4}{3} \pi r^3\\\\\to \frac{4}{3} \pi (0.12)^3 \\\\ \to 1.333333 \times 3.14 \times 0.001728 \\\\ \to 0.00723456\\\\[/tex]
Calculating the density of air:
[tex]\to \text{Air density}=\frac{\text{Mass}}{\text{volume}}\\\\[/tex]
[tex]=\frac{ 0.009}{0.00723456}\ \frac{kg}{m^3}\\\\ =1.244\ \frac{kg}{m^3} \\\\=1.24\ \frac{kg}{m^3}[/tex]
Therefore, the air density is "[tex]1.24\ \frac{kg}{m^3}[/tex]".
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Round to 2 SF
644.8
pleeeeeeeeaaaaaaaaaaasssssssssseeeeeeeeee
Answer:
640
Step-by-step explanation:
the 2nd 4 rounds up making it 640 instead of 650
Elijah wants to know the cross-sectional area of the circular pipe. He measures the diameter which he finds, to the nearest millimeter, to be 5 centimeters. To find the area of the circle, Elijah using the formula A=πr^2, where A is it the area of the circle and r is the radius. he uses 3.14 for π. what value does Elijah get for the area of circle? type is that number. (Hint:3 decimal points!)
Answer:
The area is 0.002m² to 3 dp
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes(I.e cross sectional area of pipe ) , this time the a circle.
It requires us to look for the area of the shape
Given data
Diameter d = 5cm
Converting to mm = 5/100= 0.05m
Radius of circle r=d/2=0.05/2 =0.025mm
Given the area of the circle
A=πr²
A=3.14*0.025²
A=0.0019m²
To 3 dp we have area as 0.002m²
The clocks radius is 10m. What is the circumference of the clock
Answer:
20π or 62.8 roughly
Step-by-step explanation:
Hello!
The formula for finding the circumference of a circle is 2rπ:
In that case, all we have to do is substitute 10m for our r.
2 × 10 = 20.
So circumference will be 20π.
Using 3.14 for π:
We get that 62.8 is a rough estimate for the circumference.
Really, it's 62.831..... going on forever since π is irrational.
Thus, the answer exactly is [tex]\boxed{20\:\pi}}[/tex].
Hope this helps!
Final answer:
The circumference of a clock with a radius of 10m is calculated using the formula C = 2πr, resulting in a circumference of 20π m or approximately 62.83185 m when using the approximate value of π (3.14159).
Explanation:
The circumference of a clock can be calculated using the formula for the circumference of a circle which is C = 2πr, where C is the circumference and r is the radius of the clock. Given that the radius of the clock is 10m, we substitute the value into the formula to get the circumference.
So, the circumference of the clock is C = 2π(10m) = 20π m.
The exact value of π (π is approximately 3.14159) would allow us to find the numerical value for the circumference, which would be approximately C ≈ 62.83185 m.
Students in a club are selling flowerpots to raise money each flowerpot sells for $15. Write an expression that represents the total amount of money in dollars, the students raise from selling x flowerpots.
Answer:
The expression that represents the total amount of money raised from selling [tex]\(x\)[/tex] flowerpots is [tex]\(15x\)[/tex].
Explanation:
The total amount of money raised from selling [tex]\(x\)[/tex] flowerpots can be represented by the expression:
[tex]\[ \text{Total amount of money} = \text{Price per flowerpot} \times \text{Number of flowerpots sold} \][/tex]
Given that each flowerpot sells for $15, and [tex]\(x\)[/tex] represents the number of flowerpots sold, the expression would be
[tex]\[ \text{Total amount of money} = 15x \][/tex]
So, the expression that represents the total amount of money raised from selling [tex]\(x\)[/tex] flowerpots is [tex]\(15x\)[/tex].
Solve the system using substitution.
y = 4x − 5
y = 2x + 1
A. (−2, −3)
B. (1, 3)
C. (−2, −13)
D. (3, 7)
Answer:its D (3,7)
Step-by-step explanation:
A bungee jumper is jumping off the New River Gorge Bridge in West Virginia, which has a height of 876 feet. The cord stretches 850 feet and the jumper rebounds 75 of the distance fallen.
(a) After jumping and rebounding 10 times, how far has the jumper traveled downward? How far has
the jumper traveled upward? What is the total distance traveled downward and upward?
(b) Approximate the total distance, both downward and upward, that the jumper travels before coming to rest.
In this scenario, a bungee jumper's total distance traveled can be calculated using a geometric series. The initial drop is the bridge's total height, and each following jump is 75% of the previous one. Summing this series gives the total downward and upward travel.
Explanation:This problem is a classic example of a geometric series used in mathematics. The first downward travel is the entire height of the bridge, 876 feet. Each consecutive downward travel will be 75% of the previous downward travel, as the question specifies that the jumper rebounds 75% of the distance fallen.
For the downward distance after 10 jumps, you sum the geometric series with first term (a) of 876 feet, common ratio (r) of 0.75, and n terms (n) being 10. The sum S of such a series can be calculated as: S = a * (1 - r^n) / (1 - r). The upward travel distance will be 75% of the total downward distance.
To find out the total distance before the jumper comes to rest, we look at the situation when the sum of the geometric series tends to infinity (i.e., as the number of terms n approaches infinity) which can be calculated as S = a / (1 - r).
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What is the constant of proportionality of 3y = 27x
Answer:
9
Step-by-step explanation:
3y = 27x
We want to find k when y = kx
Divide each side by 3
3y/3 = 27x/3
y = 9x
The constant of proportionality is 9
What is the amplitude of the graph of the equation y=3cos2x?
Many goes bowling, he has 25.00 to spends, he spends 4.25 for rent shoes and spends 2.50 for each game he bowls. Wich inequality can manny use to determine x the greatest number of games he can bowl?
Answer:
Answer: B
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let x represent the greatest number of games he can bowl.
Many goes bowling, he spends 4.25 for rent shoes and spends 2.50 for each game he bowls. It means that the amount that he would spend in bowling x games is
4.25 + 2.5x
If he has 25.00 to spend, then the inequality that Manny can use to determine the greatest number of games he can bowl is
4.25 + 2.5x ≤ 25
Tell if the measures 10, 12, and 16 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
Answer:
Yes, acute
Step-by-step explanation:
Because 10 and 12 add up to more than 16, it is possible to construct an acute triangle with these side lengths. Since 10^2 + 12^2 ≠ 16^2, we know that any triangle so constructed will not be a right triangle.
The measures 10, 12, and 16 can be the side lengths of a triangle because the sum of the two shorter sides must be greater than the longest side for a triangle to exist.
In this case, 10 + 12 is greater than 16, 16 + 10 is greater than 12, and 12 + 16 is greater than 10, satisfying the triangle inequality theorem. Therefore, a triangle can be formed.
Classifying the triangle: Using the Pythagorean theorem, we can determine that the triangle with side lengths 10, 12, and 16 is a scalene triangle, and since 10^2 + 12^2 is less than 16^2, it is an obtuse triangle.
Which is the equation of a line that has a slope of 5 and passes through point (2, -3)?
To all
o y = -x-4
o y = 1/2 X-2
To y = 1/8 x + 3
Answer:
y = 5x - 13
Step-by-step explanation:
Use the formula y = mx + b to solve for b. Then plug in known values.
Answer:
y=5x-13
Step-by-step explanation:
What is 6 times 0 ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Answer:
6 x 0 = 0
Step-by-step explanation:
10) Stephanie spent half of her weekly
allowance buying pizza. To earn more
money her parents let her weed the garden
for $4. What is her weekly allowance if
she ended with $8?
Answer:
$16
Step-by-step explanation:
-Given that her balance after buying one pizza is half her weekly allowance.
#We multiply her balance times 2 to determine her total weekly allowance:
[tex]Total \ Allowance=Balance \times 2\\\\=8\times 2\\\\=\$16[/tex]
Hence, her total weekly allowance is $16
Makayla charges 20 cents per square inch for her frame. How much will she charge for a frame that measures 18 inches on each side and has a width of 3 inches ?
Answer:
The answer is $10.8 (1,080 cents)
Step-by-step explanation:
First of all, let us calculate the area of the frame:
Area = Length × width = 18 × 3 = 54 in²
We are told that she charges 20 cents per square inch, therefore:
1 in² = 20 cents
∴ 54 in² = 20 × 54 = 1,080 cents.
We know that 100 cents = $1
∴ 1,080 cents = 1/100 × 1,080 = $10.8
What are the surface area and volume ratios of a cylinder change if the radius and height are multiplied by 5/4 ?
Answer:
The ratio of the surface areas and volume is 8((5y+5x) /25xy)
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes.
Let us assume that the radius =x
Radius r=5x/4
And the height =y
Height h= 5y/4
We know that the total surface area of a cylinder is
A total = 2πrh+2πr²
We can factor out 2πr
A total = 2πr(h+r)
The volume of a cylinder is given as
v= πr²h
The surface area and volume ratios
Can be expressed as
2πr(h+r)/πr²h= 2(h+r)/rh
= (2h+2r)/rh= 2h/rh + 2r/rh
= 2/r + 2/h
= 2(1/r + 1/h)
Substituting our value of x and y
For radius and height we have
= 2(1/5x/4 + 1/5y/4)
=2(4/5x + 4/5y)
=2*4(1/5x + 1/5y)
= 8 (5y+5x/25xy)
Answer:
Ratio of surface area = 25/16
Ratio of volume = 125/64
Step-by-step explanation:
The surface area and volume of a cylinder are given by the formulas:
Surface area = 2*(pi*r^2 + pi*r*h)
Volume = pi*r^2*h
If we increase the radius and height by 5/4, we have that:
New surface area = 2*(pi*(5/4*r)^2 + pi*(5/4)*r*(5/4)*h) = (5/4)^2 * 2*(pi*r^2 + pi*r*h) = (5/4)^2 * Surface area
New volume = pi*(5/4*r)^2*(5/4)*h = (5/4)^3 * pi*r^2*h = (5/4)^3 * Volume
So the ratios are:
ratio of surface area = New surface area / Surface area = (5/4)^2 = 25/16
ratio of volume = New volume / Volume = (5/4)^3 = 125/64
find the area of a regular octagon with a perimeter of 96 centimeters
Answer:
A≈695.29cm²
Step-by-step explanation:
The area of a regular octagon with a perimeter of 96 cm is calculated by first finding the length of one side, then calculating the area of one of the eight isosceles triangles formed within the octagon, and finally multiplying this area by eight to get the total area, which is 384 cm².
To calculate the area of a regular octagon with a given perimeter, we first need to determine the length of one side. Since a regular octagon has equal sides, we can divide the perimeter by 8. In this case, the perimeter is 96 centimeters, so each side of the octagon is 96 cm / 8 = 12 cm.
We know that a regular octagon can be divided into eight identical isosceles triangles. The area of an isosceles triangle can be found by the formula A = (1/2)bh, where b is the base and h is the height.
To find the height of each triangle, we can draw an altitude from the center of the octagon to the base of one of the triangles, which creates two 90-degree triangles.
By using the Pythagorean theorem on one of these right-angled triangles, with the base of each being half the length of an octagon's side (6 cm), and the Pythagorean triple 6-8-10, we can determine the height to be 8 cm. Thus, the area of each triangle is (1/2) * 12 cm * 8 cm = 48 cm².
Finally, since there are eight triangles, the total area of the octagon is 8 * 48 cm² = 384 cm².
List the sides of the triangle in order from shortest to longest.
Answer:
Angle M = 120 degrees
Shortest side = MN
Middle Side = MO
Longest side = ON
Step-by-step explanation:
Answer:
MN < NO < OM
Step-by-step explanation:
∡ M = 180 -45-75=60°
45° opposite side - MN - shortest side
75° opposite side - OM - longest side
60° opposite side - NO
MN < NO < OM
How high is the toy after 1 second , what is the toy’e maximum height ? , how long is the toy in the air ?
Answer:
i.)12 feet
Step-by-step explanation:
ut+1/2gt^2
7×1+1/2×10×1^2 =12
Consider the system of equations. y = 3x + 2 y = − 2 3 x − 4 Explain why these particular equations can be graphed immediately.
Answer:
These equations are in slope-intercept form. I can use the y-intercept and slope to graph both lines. I plot the y-intercept and use rise over run to locate another point on the line. Then, I can draw a line through the two points.
Step-by-step explanation:
A jar lid has a diameter of 32
millimeters. What is the
circumference of the lid to the
nearest tenth?
Answer:
32pi cm or 100.530964915 mm
Step-by-step explanation:
To find this answer you will need to use the equation 2*pi*r or pi*d.
Your value 32 can be plugged in as your value of d which can then be substituted to make 32 pi or if you use a calculator you get 100.530964915.
hope this helps!
Answer: 100.5 mm
Step-by-step explanation: The formula to find the circumference of a circle is 2(pi)r
Since we know the diameter is 32, divide 32 by 2 to get the radius: 16
2(pi)(16) = 100.5309
To the nearest tenth, that would be 100.5
Can anyone help??????
Answer:
C) 109.5
Step-by-step explanation:
Use cosine of 64°
cos 64° = 48/x
Put x on one side
x = 48/ cos 64°
x = 109.4962576
Answer:
The answer is C or 109.5 units
Step-by-step explanation:
We have to use the trig function cosine to find the answer.
cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
cosine of 64 = 0.438371147
the equation is: cos 64 = [tex]\frac{48}{hypotenuse}[/tex]
So using this equation,
we must divide 48 by the cosine of 64 to get the hypotenuse
this equals 109.5
The hypotenuse is our length that we need to find so the question is solved.
Hope This helps
Branliest is appreciated!
The solution to an inequality is represented by the number line.
*number line below*
How can this same solution be written using set-builder notation?
{x | x > _____}
Answer:
3 maybe
Step-by-step explanation:
Solution shown in the picture is (x | x > 3).
Inequalities on a number line: x > 0 is represented by the arrow starting from 0 with a hollow point moving towards the numbers greater than 0. x < 0 is represented by the arrow starting from 0 with a solid point moving towards the numbers less than 0. Equal to sign (=) represents a solid point on a number line.
Inequality given in the picture shows,
An arrow starting from 3 with a hollow point moving towards the numbers greater than 3.Therefore, inequality shown in the picture will be x > 3.
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PROBLEM 2
Evaluate the expression 9 – z when z = 8.
Answer:
9-8=1
Step-by-step explanation:
Substitute 8 for z and gives you 9-8 which equals 1
You know:
z = 8 so substitute/plug it into the expression
9 - z Plug in 8 into "z" since z = 8
9 - 8
1