Answers
First make the bottom number the same
6•15=90
Bottom number is 90
But what ever you do to the bottom number you do to the top number
So 4•6=24
7•15=105
(24/90-105/90)•4/5
24/90-105/90=-81/90
-81/90•4/5
When multiplying two fractions you times both the top numbers and then the bottom numbers
-324/450
Simplest form=-162/225
Answer is -162/225
Related Questions
According to USA Today, the average cost of a private university is $50,000 with a population standard deviation of $2,500. 100 universities are randomly selected and the average income of those 100 universities was $49,450. Using the 5 step hypothesis testing process, can you support the claim that the average cost of private universities are decreasing? Use a .01 significance level. (Use the z or t value of -2.2) What is your conclusion based on p-value?
Answers
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
What are the hypothesis tested?At the null hypothesis, it is tested if the average cost is still of $50,000, that is:
[tex]H_0: \mu = 50000[/tex]
At the alternative hypothesis, it is tested if the average cost is decreasing, that is:
[tex]H_1: \mu < 50000[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are:
[tex]\overline{x} = 49450, \mu = 50000, \sigma = 2500, n = 100[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{49450 - 50000}{\frac{2500}{\sqrt{100}}}[/tex]
z = -2.2.
What is the p-value and the conclusion?Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.
Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
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The model of a trinomial is shown.
An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x, the 2 tiles below + x squared are labeled + x, and the 14 tiles below the negative x tiles are labeled negative.
What are the factors of the trinomial? Select two options.
x – 14
x + 7
x – 7
x – 2
x + 2
Answers
The factors of the trinomial based on the information given include:
C. x – 7
E. x + 2
What is a trinomial?It should be noted that a trinomial is an algebraic expression that has three non-zero terms. Here, the examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z. Also, 2a² + 5a + 7 is a trinomial in one variables.
In this case, the algebra tile configuration has 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x. Here, the trinomial is x² - 5x - 14.
The factors will be:
x² - 5x - 14.
x² + 2x - 7x - 14
x(x + 2) - 7(x + 2)
= (x + 2)(x - 7)
A polynomial with three terms is called a trinomial.
In conclusion, the correct options are C and E.
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A 2 gallon container of disinfectant costs 22.72. What is the price per cup
Answers
Answer:
$0.71/cup
Step-by-step explanation:
1 gallon = 16 cups
2 gallons = 2 × 1 gallon = 2 × 16 cups = 32 cups
$22.72/(2 gal) = $22.72/(32 cups) = $0.71/cup
The table represents the amount of storage space, in megabytes, used by music files on Zayd’s computer.
A 2-column table with 5 rows titled Zayd's Music Storage. The first column is labeled Number of Files with entries 10, 20, 30, 40, 50. The second column is labeled Space Used (Megabits) with entries 15, 30, 45, 60, 75.
Which statement best describes the relationship between storage space and number of music files?
As the number of files remains constant, the storage space used decreases.
As the number of files remains constant, the storage space used increases.
As the number of files increases, the storage space used decreases.
As the number of files increases, the storage space used increases.
Answers
Answer:
As the number of files increases, the storage space used increases.
Amanda increased the amount of protein she eats every day from 48 g to 54 g. what percentage did Amanda increase the amount of protein she eats
Answers
Step-by-step explanation:
I just answered this. how often did you post that question ?
she added 54-48 = 6g.
how many % of 48g are these 6g ?
100% = 48
1% = 100%/100 = 48/100 = 0.48g
how many % are 6g ?
as many as how often 1% (0.48g) fits into 6g :
6 / 0.48 = 12.5%
400 people were surveyed for this grab how many more people prefer vanilla than do strawberry
Answers
Using proportions, it is found that 68 more people prefer vanilla than do strawberry.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, it is found that, out of 400 people:
35% preferred vanilla.18% preferred strawberry.Hence the amounts are:
V = 0.35 x 400 = 140.S = 0.18 x 400 = 72.The difference is:
140 - 72 = 68.
68 more people prefer vanilla than do strawberry.
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Name the rule for this sequence.
27, 21, 15, 9, 3,...
A) divide the previous term by 0.06
B) divide the previous term by 0.6
C) add 6 from the previous term
D) subtract 6 from the previous term
Answers
Answer:
D) subtract 6 from the previous term
Step-by-step explanation:
27-6=21, 21-6=15, 15-6=9, and 9-6=3
The number 20 is multiplied either by 4 or by 5, then the product is increased either by 3 or by 5, and then the sum is divided either by 6 or by 7. What is the final quotient, if it is a natural number?
Answers
The area of a circle is 25л ft². What is the circumference, in feet? Express your answer in terms of π.
Answers
Answer:
C = 10π ft
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = 2πr ( r is the radius )
to find r use the area formula, that is
A = πr² = 25π ( divide both sides by π )
r² = 25 ( take square root of both sides )
r = [tex]\sqrt{25}[/tex] = 5
then
C = 2π × 5 = 10π ft
please explain how to do this
Answers
The length of arc AB is 3π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°. This can be obtained using the formula to find arc length.
Find the length of the arc AB:Formula used for finding arc length:
If the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,⇒ L = 2 π r (θ/360°)
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
If the angle made by the arc at the center of the circle is in radians, the formula to find the length of the arc is,⇒ L = r × θ
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
Here in the question it is given that,
r = 27 units
θ = 20°
Since the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,
⇒ L = 2 π r (θ/360°)
L = 2 π (27) (20°/360°)
L = π (27) (20°/180°)
⇒ L = 3 π
Hence the length of arc AB is 3 π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°.
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Consider the quadratic equation x² 20x + 13 = 0.
-
Completing the square leads to the equivalent equation (x-
—)² = —
Answers
x^2 + 20x = -13
(B/2)^2 = (20/2)^2 = 10^2 = 100
x^2 + 20x + 100 = -13 + 100
(x + 10)^2 = 87
The analogous equation for the square will be; (x-10)²=87.
What is Equivalent equation?Algebraic equations with equivalent solutions or roots are called equivalent equations.
Based on information provided, an equivalent equation is created by adding or deleting the same quantity or expression from both sides of a given equation;
Using the original equation as a starting point as;
-20x+ x² + 13 = 0
Now x² - 20x = -13.
We need to take the "x" term's coefficient, or b, to complete the square.
Then Divide by 2 and write the equation in the quadratic formula (ax² + bx + c = 0).Then,
B = -20
b/2 = -10
(b/2)² = 100
x² - 20x +100 = -13 + 100
On the left side,
LHS: (x + b/2)² = (x-10)2
RHS: -13 + 100 = 87
(x-10)² = 87
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Can you please answer this question
Answers
Answer:
look above
Step-by-step explanation:
hope it helps
Build Your Math Skills 2B, Round decimals to the nearest hundredth (0.01): 1223.075
Answers
Answer: 1223.07
Step-by-step explanation: you don't round up
Evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration. ) ds s2(s − 1)2
Answers
Solution of integral [tex]\int \frac{ds}{s^{2}(s-1)^{2} }[/tex] is [tex]2ln|\frac{s}{s-1}|-\frac{1}{s}-\frac{1}{s-1}+c[/tex].
We have to evaluate [tex]\int \frac{ds}{s^{2}(s-1)^{2} }[/tex]
By using partial fractions, evaluate the integral
Let [tex]\frac{1}{s^{2}(s-1)^{2} } =\frac{A}{s} +\frac{B}{s^{2}} +\frac{c}{s-1} +\frac{D}{(s-1)^{2} }[/tex]
[tex]1=As(s-1)^{2} +B(s-1)^{2} +Cs^{2}(s-1)+Ds^{2}[/tex]
Put s = 0, 1 = B.1 ⇒ B = 1
Put s= 1, 1 = D ⇒ D = 1
Put s = -1, [tex]1=A(-1)(-2)^{2} +B(-2)^{2} +C(-1)^{2} (-2)+D(-1)^{2}[/tex]
1 = -4A + 4B -2C + D
1 = -4A + 4 -2C + 1
-4 = -4A -2C
2 = 2A + C----------------(1)
Put s = 2, 1 = A(2) + B +C(4) +D(4)
1 = 2A + 1 + 4C +4
-4 = 2A + 4C
-2 = A + 2C---------------(2)
From(1),
C = 2 -2A ---------------(3)
From (2),
⇒ -2 = A + 4 -4A
⇒ -6 = -3A ⇒ A = 2
From (3)
C = 2 - 2(2)
⇒ C = -2
Thus [tex]\int \frac{ds}{s^{2}(s-1)^{2} }= \int (\frac{2}{s} +\frac{1}{s^{2} }- \frac{2}{s-1} +\frac{1}{(s-1)^{2} } )ds[/tex]
= [tex]2 ln|s|-\frac{1}{s} -2ln|s-1|-\frac{1}{s-1}+c[/tex]
= [tex]2ln|\frac{s}{s-1}|-\frac{1}{s}-\frac{1}{s-1}+c[/tex]
Thus,
Solution of integral [tex]\int \frac{ds}{s^{2}(s-1)^{2} }[/tex] is [tex]2ln|\frac{s}{s-1}|-\frac{1}{s}-\frac{1}{s-1}+c[/tex].
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assuming that no denominator equals zero, what is the simplest form of x+2/ x^2 +5x+6 divided by 3x+1/x^2-9
Answers
Answer:
Step-by-step explanation:
What type of quadrilateral is created by the points:
L (-5,4), M (2,2), N (0,-3), S (-7,-1)
Answers
Given same lengths and slopes of the opposite sides and nature of the angle between adjacent sides, we have;
The type of quadrilateral is a parallelogram How can the type of quadrilateral be found?The given points are;
L(-5, 4), M(2, 2), N(0, -3), S(-7, -1)
Lengths of the sides are;
Length of LM = √((2-(-5))²+(2-4)²) ≈ √(53)
Length of MN = √((2-0)²+(2-(-3))²) ≈ √(29)
Length of NS = √((0-(-7))²+((-3)-(-1))²) ≈ √(53)
Length of LS = √(((-7)-(-5))²+((-1)-4)²) ≈ √(29)
Therefore;
The lengths of opposite sides are the same.Slope of LM = (2-4)/(2-(-5)) = -2/7
Slope of MN = (2-(-3))/(0-2) = 5/2
Slope of NS = ((-3)-(-1))/(0-(-7)) = -2/7
Slope of LS = ((-1)-4)/(-7-(-5)) = 5/2
Therefore;
The opposite sides are parallel, and The the adjacent sides are not perpendicularThe quadrilateral created by the points L(-5, 4), M(2, 2), N(0, -3), S(-7, -1) is therefore;
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Sasha solved an equation, as shown below:
Step 1: 8x = 56
Step 2: x = 56 – 8
Step 3: x = 48
Part A: Is Sasha's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (6 points)
Part B: How many solutions does this equation have? (4 points)
I know part A, but what about Part B?
Answers
Part A: Sasha's solution of the equation incorrect. The solution x = 7.
Part B: The equation have They are unique solutions.
According to the question,
Sasha solved an equation, as shown below:
Step 1: 8x = 56
Step 2: x = 56 – 8
Step 3: x = 48
Step 2 is incorrect, the correct steps to find x, we would divide both sides by 8 so,
8 / 8x = 8 / 56
x = 7.
An equation can have infinitely many solutions only if the system of an equation has infinitely many solutions when the two lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. Then the have infinitely many solutions.
But, the given equation have unique solutions. Thus, x=7.
Hence, Part A: Sasha's solution incorrect. The solution x = 7.
Part B: They are unique solutions solutions.
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Help me, 50 pts, I'll give brainliest, *take your time answering if you need *
1. how many groups of 5/7 are in 1
2. 8 divided by 5/7
3. The tape diagram shows that Ehecatl's hair, which is now 12cm long is 60% as long as it was before his haircut.
Complete the table to show different percentages of Ehecatl's hair length before the haircut. (table is the file)
Answers
There are 1.40 groups of 5/7 in 1.
8 divided by 5/7 is 11 1/5.
Here is the completed table:
Length (cm) Percentage
12 60% of Ehecatl's old hair
4 20% of Ehecatl's old hair
20 100% of Ehecatl's old hair
How do we carry out division?Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
In order to determine how many groups of 5/7 are in 1, divide 1 by 5/7
1 ÷ 5/7
1 x 7/5 = 7/5 = 1.40
8 ÷ 5/7
8 x 7/5
= 56 / 5
= 11 1/5
What are the lengths of Ehecatl's hair ?
The first step is to determine the length of her hair before she cut it
Length of the hair before it was cut = new length / 60%
12 / 0.6 = 20
60% x 20 = 12cm
20% x 20 = 4cm
100% x 20 = 20cm
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Create an equivalent system of equations using the sum of the system and the first equation. x 4y = 8 4x y = 2 x 4y = 8 5x y = 2 x 4y = 8 5x 5y = 2 x 4y = 8 4x 5y = 10 x 4y = 8 5x 5y = 10
Answers
An equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
What are equations?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.[tex]3x+5=14[/tex], for example, is an equation in which [tex]3x+5[/tex] and [tex]14[/tex] are two expressions separated by a '=' sign.Given:
[tex]x+4y=8\\4x+y=2[/tex]
Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]
Therefore, an equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
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The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.
x + 4y = 8
4x + y = 2
x + 4y = 8
5x + y = 2
x + 4y = 8
5x + 5y = 2
x + 4y = 8
4x + 5y = 10
x + 4y = 8
5x + 5y = 10
2x+3≥7 OR 2x+9>1
Please help me
Answers
Answer:
x > -4
Step-by-step explanation:
[tex]2x+3 \geq 7 \\ \\
2x \geq 4 \\ \\
x \geq 2[/tex]
[tex]2x+9>1 \\ \\ 2x>-8 \\ \\ x>-4[/tex]
So, the union of these solutions is x > -4.
PLS HELP ASAP.........
Answers
Answer:
Step-by-step explanation:
Because there is sound and a tune that plays again anytime people are shown having fun at the carnival, the Kit Kat commercial is effective. When the sound is silenced, the commercial's lyrics will come to the viewer's thoughts without any further thought.
Given: y varies directly with x and has a constant rate of change of 7. when the value of y is 12, then the value of x would be _____.
Answers
Answer:X=12/7
Step-by-step explanation:
Y [tex]\alpha[/tex] X
⇒Y=KX
Where K is the constant
From the question,k=7
⇒ When Y=12,
y=KX
12=7X
X=12/7
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. which statements about the two rectangular solids are true? check all that apply.
Answers
The correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.What are solids?Solid geometry or stereometry is the standard name for the geometry of three-dimensional Euclidean spaces in mathematics. Stereometry is concerned with the volume measurements of various solid forms, such as pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones, and balls bordered by spheres.To find which statements are correct:
Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.
The volume of the first triangle is: [tex]2x^{2} h[/tex]
The volume of the second triangle is: [tex]x^{2} h[/tex]
Therefore, the correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.Know more about solids here:
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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
A) The bases are congruent.
B) The solids are similar.
C) The ratio of the volumes of the first solid to the second solid is 8:1.
D)The volume of the first solid is twice as much as the volume of the second solid.
E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more
surface area than the second solid.
How do I do this!!!!!
Answers
The expected values of the binomial distribution are given as follows:
1. 214.
2. 21.
3. 31.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For item 1, the parameters are:
p = 3/7, n = 500.
Hence the expected value is:
E(X) = np = 500 x 3/7 = 1500/7 = 214.
For item 2, the parameters are:
p = 0.083, n = 250.
Hence the expected value is:
E(X) = np = 250 x 0.083 = 21.
For item 3, the parameters are:
p = 1/13, n = 400.
Hence the expected value is:
E(X) = np = 400 x 1/13 = 31.
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What is the end behavior of the function f of x equals negative 4 times the cube root of x? as x → –[infinity], f(x) → –[infinity], and as x → [infinity], f(x) → [infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0.
Answers
The end behavior of the function is as:
as →∞, f(x)→+∞ and as x→-∞, f(x)→+∞
What is end behavior?The x-axis "endpoints" of a function's graph are referred to as its "end behavior" in this context.
How do determine the end behavior of a function?choosing the polynomial function's greatest degree. The highest degree term will dominate the graph since it will expand more quickly than the other terms as x gets very big or very small.
Function f(x)=2∛x has the following graph:
The behavior of the function at its conclusion is because it leads to infinity.
as x→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
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A sample of disinfecting bleach shows a density of 9.4 lb/gal. If 100 pounds of bleach is required for disinfection, how many gallons must be applied
Answers
the number of gallons that must be applied is 94 gallons.
What is density?Density is simply defined as the ratio of the mass to the volume occupied by an object or substance.
It is denoted with rho, 'ρ'
The formula for density is given as;
Density = mass/ volume
From the information given, we have that
density = 9.4 lb/galmass = 100 pounds volume is unknownTo determine the volume, we need to make it the subject from the formula
Volume = density × mass
Volume = [tex]\frac{9. 4}{100}[/tex]
Volume = 0. 094
The number of gallons is given as;
= Volume × 1000
= 0. 094 × 1000
= 94 gallons
Thus, the number of gallons that must be applied is 94 gallons.
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The age of a father is three times that of his son. In ten year's time their ages will add up to 68 years. If the son is x years old today write down an algebraic expression for: the present age of the father and the son's age in ten year's time and the father's age in 10 year's time.
Answers
Answer:
46 and 22
Step-by-step explanation:
let the father b (f) and d son is (s)
so
f=3s.....(1)
(f+10) +(s+10)=68 .... (2)
substitute f=3s in equation (2)
we have
(3s+10)+(s+10)=68
4s+20=68
4s=68-20
4s=48
s=12 .......(3)
substitute (3) in (1)
f=3*12
which f=36
in 10 year time
f+10 =46
s+10=22
Which choice is equivalent to the expression below?
5x√2-3√2+x√2
Answers
Answer:
You did not list any choices but if you simplify that the answer is 6√2x-3√2
Step-by-step explanation:
If they want you to factor it instead of simplifying the answer is 3√2(2x-1)
Answer:
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]
Step-by-step explanation:
So you haven't provided any options, but I'm assuming they want it in most simplified form.
To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.
So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y
[tex]5xy-3y+xy[/tex]
So in here, think of y as the variable and the 5x, -3, and x as the coefficients.
In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))
[tex](5x-3+x)y[/tex]
Simplify this expression to get
[tex](6x-3)y[/tex]
Now just plug the sqrt(2) back in as y and you get the expression
[tex](6x-3)\sqrt{2}[/tex]
Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]
Which of the following equations have complex roots?
A. 3x^2-1=6x
B. 3x^2+2=0
C. 2x^2-1=5x
D. 2x^x+1=7x
Answers
Answer: B
Step-by-step explanation:
We can rearrange the equation to get [tex]x^2=-\frac{2}{3}[/tex], which clearly has complex roots.
Yes I did it
Help please, also provide work
Answers
Answer:
9) 128
10) 78
11) 31
12) 148
Step-by-step explanation:
9) we know that the segment across from the angle 48° is double the angle.
48 · 2 = 96
The segments around the circle should all add up to 360 so we add the two segments we know to find the unknown segment.
136 + 96 = 232
360 - 232 = 128
The answer for 9 is 128.
10)
61 + 80 = 141
180 - 141 = 39
39 * 2 = 78
The answer for question 10 is 78.
11)
236 + 62 = 298
360 - 298 = 62
62 ÷ 2 = 31
The answer for question 11 is 31.
12)
50 · 2 = 100
100 + 112 = 212
360 - 212 = 148
The answer for question 12 is 148.
