Answers
Given:
The expressions are:
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]
To find:
The simplified form of the given expressions.
Solution:
We have,
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]
It can be written as:
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{12a^{2+1}bc^3}{40b^4c^2}[/tex]
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{3-2}}{10b^{4-1}}[/tex]
[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{1}}{10b^3}[/tex]
Therefore, the value of the given expression is [tex]\dfrac{3a^{3}c}{10b^3}[/tex].
We have,
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]
It can be written as:
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{(x+y)(x-y)}{4(x+y)}\cdot \dfrac{x+y}{x-y}[/tex]
[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{x+y}{4}[/tex]
Therefore, the value of the given expression is [tex]\dfrac{x+y}{4}[/tex].
Related Questions
can someone plz help me wit dis plz
Answers
Answer:
b = 6.1 ft
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here A = 10.98 and h = 3.6 , then
[tex]\frac{1}{2}[/tex] × b × 3.6 = 10.98
1.8b = 10.98 ( divide both sides by 1.8 )
b = 6.1
Tim is making 30 sundaes with mint, chocolate, and vanilla ice cream.
1/5
of the sundaes are mint ice cream and
1/2
of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla?
Answers
Answer:
12
Step-by-step explanation:
1/5 mint = 6
30 - 6 = 24
Half of 24 is 12
12 is chocolate
so 12 must be vanilla
calculate the solubility (in g/l) of caso4(s) in 0.250 m na2so4(aq) at 25°c . the sp of caso4 is 4.93×10−5 .
Answers
The given values are: Ksp of CaSO4 = 4.93 × 10⁻⁵, Molarity of Na2SO4 = 0.250(m). Molar mass of CaSO4 = 136.14 g/mol. We can write the equation for the dissolution of CaSO4 in water as:CaSO4(s) ⇌ Ca²⁺(aq) + SO₄²⁻(aq). Let's consider that "x" grams of CaSO4 dissolves in "1 L" of 0.250 M Na2SO4. Since the CaSO4 dissolves according to the following equation:CaSO4(s) ⇌ Ca²⁺(aq) + SO₄²⁻(aq). The concentration of Ca²⁺ ions in the solution will be "x" moles / 1 L. The concentration of SO₄²⁻ ions in the solution will be "x" moles / 1 L. Since the concentration of Na2SO4 in the solution is 0.250 M or 0.250 moles / L, the concentration of SO₄²⁻ ions contributed by Na2SO4 will be (2 × 0.250) M or 0.500 M. In order to determine the value of "x" or the amount of CaSO4 that dissolves, we need to consider the equilibrium of the solution. The Ksp expression for the dissolution of CaSO4 can be written as: Ksp = [Ca²⁺][SO₄²⁻], Ksp = (x)(x) = x². As the dissociation is very small compared to the concentration of Na2SO4, we can consider "0.250" moles of Na2SO4 in "1 L" of the solution completely dissociated. Thus, the final concentrations of Ca²⁺ and SO₄²⁻ ions in the solution will be:[Ca²⁺] = x moles / L[SO₄²⁻] = (x + 0.500) moles /L. Therefore, we can write the expression for the ion product: IP = [Ca²⁺][SO₄²⁻]IP = (x)(x + 0.500)As the value of Ksp is equal to the IP, we can write the expression for Ksp as: Ksp = x² + 0.500xWe can substitute the value of Ksp as 4.93 × 10⁻⁵M:4.93 × 10⁻⁵ = x² + 0.500x. Solving for "x", we get the following quadratic equation: x² + 0.500x - 4.93 × 10⁻⁵ = 0. Solving for "x" using the quadratic formula: x = 0.00796 g/L. Therefore, the solubility of CaSO4(s) in 0.250 M Na2SO4 solution at 25°C is 0.00796 g/L.
To know more about Concentration, click here:
https://brainly.com/question/3045247
#SPJ11
Use iteration to guess an explicit formula for the following sequence - dx = 2dx-1 + 3k2 , for all integers k> 1 and do = 3 You must show your work.
Answers
By using iteration, we can guess the explicit formula for the given sequence. It is found that the sequence follows a quadratic pattern, and the explicit formula is dx = 3([tex]2^{k-1}[/tex]) + 3[tex]k^2[/tex] - 6k + 3.
Let's start by analyzing the given sequence: dx = 2dx-1 + 3[tex]k^2[/tex]. We are given that d1 = 3. We can use this initial value to find d2, d3, and so on.
Substituting k = 2 into the given equation, we get d2 = 2d1 + 3([tex]2^2[/tex]) = 2(3) + 3(4) = 6 + 12 = 18.
Similarly, substituting k = 3, we get d3 = 2d2 + 3[tex](3^2)[/tex] = 2(18) + 3(9) = 36 + 27 = 63.
Based on these calculations, we observe that each term in the sequence is related to the previous term by multiplying it by 2 and adding 3[tex]k^2[/tex]. Moreover, we notice a quadratic pattern in the sequence.
To find the explicit formula, we can express dx in terms of k:
dx = 2dx-1 + 3[tex]k^2[/tex]
= 2(2dx-2 + 3[tex](k-1)^2[/tex]) + 3[tex]k^2[/tex]
= 4dx-2 + 6[tex](k-1)^2[/tex][tex](k-1)^2[/tex] + 3[tex]k^2[/tex].
We can continue this iteration process, expanding dx-2 in terms of dx-3, and so on. By continuing this process and simplifying the equation, we find that the explicit formula for the sequence is dx = 3([tex]2^{k-1}[/tex]) + 3[tex]k^2[/tex] - 6k + 3.
In conclusion, by using iteration, we have determined that the explicit formula for the given sequence dx = 2dx-1 + 3[tex]k^2[/tex], with d1 = 3, is dx = 3([tex]2^{k-1}[/tex]) + 3[tex]k^2[/tex] - 6k + 3.
Learn more about quadratic here:
https://brainly.com/question/22364785
#SPJ11
Mia is working two summer jobs, making $11 per hour babysitting and making $20 per hour lifeguarding. In a given week, she can work a maximum of 15 total hours and must earn no less than $220. If x represents the number of hours babysitting and y represents the number of hours lifeguarding, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Answer: 11x + 20y ≥ 220
x + y ≤ 15
Hope this helps
9514 1404 393
Answer:
x + y ≤ 1511x +20y ≥ 2203 hours babysitting and 11 hours lifeguardingStep-by-step explanation:
The two inequalities represent the two relations described in the problem statement.
x + y ≤ 15 . . . . . . . Mia works a maximum of 15 hours
11x + 20y ≥ 220 . . . . Mia makes at least $220
These are graphed in the attachment. The solution area is the doubly-shaded area with vertices at (9, 6), (0, 11) and (0, 15). One possible solution is shown at (3, 11), which represents ...
3 hours babysitting
11 hours lifeguarding . . . . . . . . total 14 hours for $253
Question Help
One taco supreme and two pan pizzas provide 3200 calories. Two taco supremes and one pan pizza
provide 3280 calories. Find the caloric content of each item.
Answers
Answer:
4324eqW
Step-by-step explanation:
3 + 5 =7
Work out the size of angle x.
42°
Х
123°
Answers
Answer:
42+123+x=180
x=180-165
x=15 degrees
Step-by-step explanation:
Given f(x)= 5 (6) x for rexeh 1 o elsewhere for a continuous veidon variable z. (a) Compute p(2.4 x <3). (6) Compite Elx)
Answers
a. the value of P(2.4 < x < 3) is 8.1.
b. the value of E(X) is 10.
Given function is f(x) = 5(6)x for x≥1 and elsewhere for a continuous random variable z.
a. Compute P(2.4 < x < 3)
For continuous random variable, P(a < x < b) = ∫f(x)dx, where f(x) is the probability density function (PDF).
Here, f(x) = 5(6)x for x≥1 and elsewhere
So, P(2.4 < x < 3) = ∫f(x)dx = ∫2.4^35(6)xdx= 5 ∫2.4^36xdx= 5 [(3^2 - 2.4^2)/2] = 5 [(9 - 5.76)/2] = 5 [1.62] = 8.1
Hence, the value of P(2.4 < x < 3) is 8.1.
b. Compute E(X)Expected value of X is given by E(X) = ∫xf(x)dxFor continuous random variable, E(X) = ∫xf(x)dx, where f(x) is the probability density function (PDF).Here, f(x) = 5(6)x for x≥1 and elsewhereSo, E(X) = ∫xf(x)dx = ∫1∞5(6)x.xdx+ ∫-∞0 0dx= 5 ∫1∞6x^2dx+ 0 = 5 [(6) (x^3)/3]1∞= 5 [(6) (1^3)/3] = 10
Hence, the value of E(X) is 10.
To know more about variable visit:
https://brainly.com/question/28248724
#SPJ11
Given f(x)= 5 (6) x for rexeh 1 o elsewhere for a continuous veidon variable z. We are required to compute p(2.4 < x <3) and E(x).
Compute p(2.4 < x <3)For the given function, f(x) = 5 (6) x for 1 ≤ x ≤ 3 and 0 elsewhere.
So, the total area under the curve will be equal to 5 (6) 2 = 60.
And the required probability is given by the area under the curve from 2.4 to 3. [Illustration is provided below]
Hence, p(2.4 < x <3) = 3.6
(b)Compute E(x)Expected value of x, E(x) is given by E(x) = ∫xf(x) dx,
which is equal to the area under the curve multiplied by the distance over which the function is spread.
Let's calculate the area under the curve, which is equal to 60, as we have calculated earlier.
Now, we calculate the distance over which the function is spread.
Distance = 3 - 1 = 2 unitsHence, E(x) = 60/2 = 30.
Answer:Therefore, p(2.4 < x <3) = 3.6 and E(x) = 30.
To know more about variable, visit:
https://brainly.com/question/15078630
#SPJ11
Please help these are just practice problems before my test tomorrow and I need help!
Answers
Answer:
x²=20² -14²
x²=400-196
x²=204
x=√204
Assuming the sample was taken from a normal population, test at ů. = 0.05 and state the decision. Họ: H = 13 HA: U < 13 ř= 10 S= 0.7 n = 9
Answers
the test statistic (t = -12.857) is smaller than the critical value (-1.860), we have enough evidence to reject the null hypothesis.
To test the hypothesis regarding the population mean, we can perform a one-sample t-test.
Given:
- Null hypothesis (H₀): μ = 13
- Alternative hypothesis (Hₐ): μ < 13
- Sample mean ([tex]\bar{X}[/tex]) = 10
- Sample standard deviation (s) = 0.7
- Sample size (n) = 9
- Significance level (α) = 0.05
To conduct the t-test, we can calculate the test statistic and compare it with the critical value from the t-distribution.
The test statistic (t-score) is calculated as:
t = ([tex]\bar{X}[/tex] - μ) / (s / √n)
Plugging in the values:
t = (10 - 13) / (0.7 / √9)
t = -3 / (0.7 / 3)
t = -3 / 0.233
t ≈ -12.857
To determine the critical value, we need to find the appropriate degrees of freedom (df) for a one-sample t-test. In this case, df = n - 1 = 9 - 1 = 8.
Using a significance level of α = 0.05 and looking up the critical value for df = 8 in the t-distribution table, we find the critical value to be approximately -1.860.
Since the test statistic (t = -12.857) is smaller than the critical value (-1.860), we have enough evidence to reject the null hypothesis.
Decision: Based on the test results, at α = 0.05, we reject the null hypothesis (H₀: μ = 13). There is sufficient evidence to support the alternative hypothesis (Hₐ: μ < 13), suggesting that the population mean is less than 13.
Learn more about test statistic here
https://brainly.com/question/31746962
#SPJ4
Given question is incomplete, the complete question is below
Assuming the sample was taken from a normal population, test at α = 0.05 and state the decision. Họ: μ = 13 HA: μ < 13 [tex]\bar{X}[/tex]= 10 s= 0.7 n = 9
A fair die is tossed twice and let X1 and X2 denote the scores obtained for the two tosses, respectively
Calculate E[X1] and show that var (X1) =
Determine and tabulate the probability distribution of Y = | X1 – X2 | and show that E[Y] =
The random variable Z is defined by Z = X1 – X2. Comment with reasons (quantities concerned need not be evaluated) if each of the following statements is true or false
E(Z2) = E(Y2)
Var(Z) = Var(Y)
Answers
1. When a fair die is tossed the expected value E[X1] = 3.5 and the variance var(X1) = 35/12.
When a fair die is tossed, each of the six possible outcomes has an equal probability of 1/6. Let X1 denote the score obtained in the first toss.
To calculate the expected value E[X1], we find the sum of all possible values of X1 multiplied by their respective probabilities:
E[X1] = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 3.5
To calculate the variance var(X1), we use the formula:
var(X1) = E[X1^2] - (E[X1])^2
First, we find E[X1^2] by taking the sum of the squares of all possible values of X1 multiplied by their respective probabilities:
E[X1^2] = (1^2 * 1/6) + (2^2 * 1/6) + (3^2 * 1/6) + (4^2 * 1/6) + (5^2 * 1/6) + (6^2 * 1/6) = 91/6
Substituting the values into the formula, we calculate var(X1):
var(X1) = (91/6) - (3.5)^2 = 35/12
Therefore, E[X1] = 3.5 and var(X1) = 35/12.
2. The probability distribution of Y = |X1 - X2| is tabulated as follows:
Y |X1 - X2| P(Y)
0 0 1/6
1 1 2/6
2 2 2/6
3 3 1/6
To calculate E[Y], we find the sum of all possible values of Y multiplied by their respective probabilities:
E[Y] = (0 * 1/6) + (1 * 2/6) + (2 * 2/6) + (3 * 1/6) = 1
Therefore, E[Y] = 1.
3. The statements E(Z^2) = E(Y^2) and Var(Z) = Var(Y) are false.
E(Z^2) and E(Y^2) represent the expected values of the squares of the random variables Z and Y, respectively. Since Z = X1 - X2 and Y = |X1 - X2|, the squares of Z and Y have different probability distributions, leading to different expected values.
Similarly, Var(Z) and Var(Y) represent the variances of Z and Y, respectively. Since Z and Y have different probability distributions, their variances will generally not be equal.
Therefore, E(Z^2) ≠ E(Y^2) and Var(Z) ≠ Var(Y).
To know more about variance refer here:
https://brainly.com/question/31432390
#SPJ11
please help me it's worth 10+ points
Answers
Answer:
10, 12 and 11
Step-by-step explanation:
On each median , the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.
TZ = 2 × ZX = 2 × 5 = 10
UY = UZ + ZY = 8 + 4 = 12
ZW = [tex]\frac{1}{3}[/tex] × VW = [tex]\frac{1}{3}[/tex] × 33 = 11
need help imm struggling
Answers
Answer:
1733.33
Step-by-step explanation:
The volume of a pyramid is (length*width*height) divided by 3
Answer:
1733.33
Step-by-step explanation:
v = (lwh)/3
v = (20 x 20 x 13)/3 = 5200/3 = 1733.33
What should be done to both sides of the equation in order to solve y - 4.5 = 12.2?
Answers
Add 4.5
---
hope it helps
Answer: add 4.5 to both sides
Step-by-step explanation: this will allow the 4.5 to be removed from the y side and since you added it to one side you have to add it to the other side. This will give your y the value of 16.7.
Brainliest plz
I really need help fast and ill do anything just help me plz
Answers
C = pi x diameter
Diameter = 20cm
You times pi by 20cm (diameter) to get the circumference of approx 62.84cm
Then times the circumference by the angle in the circle
62.84 x 70/360 = 12.22cm
simplify the expression: (4 3i)(2 − 8i).
a. 32 – 26i
b. −16 26 i
c. 32 38i
d. −16 38i
Answers
The correct answer should be 32.
To simplify the expression (4 + 3i)(2 - 8i), we can use the distributive property of multiplication.
First, we multiply the real parts of the two complex numbers:
(4)(2) = 8.
Next, we multiply the imaginary parts of the two complex numbers:
(3i)(-8i) = -24i^2.
Remember that i^2 is defined as -1, so we can substitute -1 for i^2:
-24i^2 = -24(-1) = 24.
Now, we combine the real and imaginary parts:
8 + 24 = 32.
Therefore, the simplified expression is 32.
Since none of the given answer choices match the simplified expression, it appears that there may be an error in the options provided. The correct answer should be 32.
Know more about Imaginary here:
https://brainly.com/question/1978187
#SPJ11
A right prism has a volume of 65 cubic inches. The prism is enlarged so its height is increased by a factor of 20, but the other dimensions do not change. What is the new volume? A. 1000in.3 B. 1300in.3 C. 1200in.3 D. 1100in.3
Answers
Answer:
The answer is B, have a wonderful day!
Step-by-step explanation:
Please answer no links!!!!!!!!!!!
Answers
Answer:
2 (4, 14)3 (3, 5)a bag contains 15 red marbles, 15 white beads, 20 green beads, and 25 blue beads. What is the probability of randomly drawing a blue bead?
Answers
Answer:
1/3 or 33%
Step-by-step explanation:
15 + 15 + 20 +25 is equal to 75
25/75 is 1/3
Answer:
1 by 3
Step-by-step explanation:
15 + 15 + 20 + 25 = 75
so,
again,
25 divided by 75 is equal to 1 by 3Ajjwjjwjwjwjsbsbaa shah sash’s
Answers
Answer:
okay then
Step-by-step explanation:
Answer: gtyrehretr
Step-by-step explanation:
NO LINKSS !! I WILL REPORT !! HELPP ME PLSS I I WASTED MOST OF MY POINTSS AND NO ONE ENDS UP HELPING ME PLSSS HELP ME Write the slope-intercept inequality for the graph below. If necessary, use <=
fors or > = for >
Answers
Answer: Y less than -3x – 3
Step-by-step explanation:
Sails come in many shapes and sizes. The sail on the right is a triangle. Is it a right triangle? Explain your reasoning.
Answers
Answer:
not a right triangle
Step-by-step explanation:
you can use the pythagorean theorem to prove whether not this is a right triangle
if this triangle is a right triangle then the following equality should be true
a²+b²=c²
(9.75)²+(3.45)²=(10.24)²
(95.06)+(11.90)=(104.86)
106.96≠104.86
since the following equality is not true, this is not a right triangle.
Translate into an equation: Twenty-six more than the product of a number and
17 is -42.
Answers
“the product of a number and 17” = 17n
“twenty six more than” = + 26
And if the next question has you solve it:
17n + 26 = -42
Subtract 26 from both sides
17n = -68
Divide both sides by 17
n = -4
P(x) = x2 + x +1
How many terms does this polynomial have?
Answers
Answer:
3
Step-by-step explanation:
2. A cow gives 24litre milk each day. If the milkman sells 75% of the milk, how many
liters of milk is left with him?
Answers
Answer: 6 liters
Step-by-step explanation:
24 liters
He sells 75%
24 x 0.75 = 18 liters
24 - 18 = 6
He still has 6 liters left
CAN SOMEONE HELP ME PLEASE
Answers
Answer: 9 x 6 x 6
Step-by-step explanation: 9 x 6=54 54 x 6 = 324 ft
A pump fills a pool at a constant rate. At the end of 1 minute it has filled 6 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
Answers
Answer:
I would need to see the different tables to answer this question.
Please help me someone.!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
[tex]y=-|x|+2[/tex]
Step-by-step explanation:
The y-intercept is 2 and the line of symmetry is the y-axis.
Suppose there is a family with four children. Assume that it is equally probable for a boy or a girl to be born. a. What is the probability of all girls? b. What is the probability of all girls given there is at west one girl? c. What is the probability of at least one boy and one girl?
Answers
a. The probability of all girls in a family with four children is 1/16 or 0.0625.
b. The probability of all girls given there is at least one girl is 1/15 or 0.0667.
c. The probability of having at least one boy and one girl in a family with four children is 15/16 or 0.9375.
a. To calculate the probability of all girls, we need to consider the possible outcomes of each child being a girl. Since each child has an independent probability of being a girl or a boy, the probability of all girls is (1/2) * (1/2) * (1/2) * (1/2) = 1/16 or 0.0625.
b. Given that there is at least one girl, we have three remaining children. The probability of all girls among the three remaining children is (1/2) * (1/2) * (1/2) = 1/8. Therefore, the probability of all girls given there is at least one girl is 1/8 divided by the probability of having at least one girl, which is 1 - (1/2)⁴ = 15/16, resulting in a probability of 1/15 or approximately 0.0667.
c. The probability of having at least one boy and one girl can be calculated by subtracting the probability of having all boys from the total probability space. The probability of having all boys is (1/2)⁴ = 1/16. Therefore, the probability of having at least one boy and one girl is 1 - 1/16 = 15/16 or approximately 0.9375. This probability accounts for all possible combinations of boys and girls in a family with four children, excluding the scenario of having all boys.
To learn more about independent probability click here: brainly.com/question/27987662
#SPJ11
Essie has two identical containers she fell one with milk and the other with water if the first container holds about 10 L of milk how much does the second container holds
Answers
Answer:
10 liters of water
Step-by-step explanation:
Given
[tex]A = 10L\ milk[/tex]
Required
How much the second holds
Since they are both identical, then both containers hold the same volume (even if the quantity they hold are different)
Hence:
[tex]B = 10L\ water[/tex]