Answer: The required simplified form is 20 × 10.
Step-by-step explanation: We are given to find the simplified form of the following radical expression :
[tex]E=\sqrt{400\times 100}.[/tex]
We will be using the following property of radicals :
[tex](i)~\sqrt{x}=x^\frac{1}{2}\\\\(ii)~\sqrt{a\times b}=\sqrt a\times\sqrt b.[/tex]
Therefore, we have
[tex]E\\\\=\sqrt{400\times 100}\\\\=\sqrt{400}\times\sqrt{100}\\\\=\sqrt{20^2}\times\sqrt{10^2}\\\\=((20)^2)^\frac{1}{2}\times(10^2)^\frac{1}{2}\\\\=20^{2\times\frac{1}{2}}\times(10)^{2\times\frac{1}{2}}\\\\=20\times10.[/tex]
Thus, the required simplified form is 20 × 10.
what is the volume , in cubic units , of a pyramid of height 8 and a square base of length 15?
For an angle Θ with the point (12, −5) on its terminating side, what is the value of cosine?
−5
12
negative 5 over 13
12 over 13
A distribution of numbers has the following five-number summary:
20.2, 22.4, 30.0, 37.6, 39.8
True or False? These numbers can be used to calculate the standard deviation of the distribution.
Please Answer quickly! I need this done ASAP! Please.
The correct answer is:
False.
Explanation:
Using the five number summary, we can estimate the standard deviation.
The quartiles are about 0.67 standard deviations from the mean; this could be used to estimate the standard deviation.
However, we cannot accurately calculate the standard deviation using only the fie number summary.
Need help to write equations for 5, 6 & 7
Please explain “ write the equation of the perpendicular bisector of rs point r is located at (-1,3) and point s is located at (3,1) “
HELPPPPPPPPPPPPP and explain
In a certain population, 95% of the people have rh-positive blood. suppose that two people from this population get married. what is the probability that they are both rh-negative, thus making it inevitable that their children will be rh-negative? web assign answer
Final answer:
The probability that both partners in a marriage are Rh-negative in a predominantly Rh-positive population is 0.25% or 1 in 400, critical for understanding the risk of hemolytic disease of the newborn in subsequent pregnancies.
Explanation:
The probability that both people in a marriage are Rh-negative in a population where 95% of the people are Rh-positive is calculated using the complement. Assuming that 5% of the population is Rh-negative, we would calculate the probability that both parents are Rh-negative by multiplying the individual probabilities:
P(both Rh-negative) = P(one Rh-negative) × P(other Rh-negative) = 0.05 × 0.05 = 0.0025
Therefore, the probability that both people are Rh-negative, and thus all of their children would also be Rh-negative, is 0.25% or 1 in 400.
Rh factor and blood type compatibility are crucial in reproduction and transfusion medicine. Understanding these concepts can help prevent complications such as hemolytic disease of the newborn, which occurs during second or subsequent pregnancies due to sensitization of the Rh-negative mother's immune system to Rh-positive fetal cells from a previous pregnancy.
A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for soccer or volleyball. Out of the total 80 people who liked soccer, 30 also liked volleyball. There were 45 people who liked volleyball.
Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)
Like soccer
Do not like soccer
Total
Like volleyball
A
D
G
Do not like volleyball
B
E
H
Total
C
F
I
Part B: What percentage of the survey respondents did not like either soccer or volleyball? (3 points)
Part C: Do the survey results reveal a greater dislike for soccer or volleyball? Justify your answer. (2 points)
There is a ratio of 5 girls to 3 boys in the class in the chorus.there are 24 boys in the chorus how many girls are in the chorus
If ΔGET≅ΔMAP, then what corresponding parts are congruent? segment TG and segment AM ∠T and ∠P segment MP and segment ET ∠E and ∠M
Answer:
2nd Option is correct that is ∠T and ∠P.
Step-by-step explanation:
We are given that ΔGET ≅ ΔMAP
We need to find Congruent part from the given options.
Since, we are given the figure of the congruent triangles with marking not any instruction with which vertex is congruent to which vertex.
So, The Given Name of the Congruent triangle.
We deduce that
G ↔ M
E ↔ A
T ↔ P
Using this we get following congruent parts,
GE ≅ MA , GT ≅ MP and ET ≅ AP
∠G ≅ ∠M , ∠E ≅ ∠A and ∠T ≅ ∠P.
Therefore, 2nd Option is correct that is ∠T and ∠P.
Answer:
∠T and ∠P
Step-by-step explanation:
92.4 is 150% of what number?
Answer:
Number is 61.6
Step-by-step explanation:
Given : 92.4 is 150%.
To find : what number.
Solution : We have given 92.4 is 150%.
Let the number = x
According to question :
150% of x = 92.4
[tex]\frac{150}{100} *x[/tex] = 92.4
On multiplying both sides by 100
150 x = 92.4 * 100.
150 x = 9240
On dividing both sides by 150 .
x = [tex]\frac{9240}{150}[/tex].
x = 61. 6
Therefore, Number is 61.6
Write the standard equation for a circle with center (−6, −8), that passes through (0, 0)
What is the sum os the interior angles of the polygon?
The members of a chorus agree to buy at least 250 tickets for and outside concert. They buy 20 fewer ow tickets that balcony tickets. What is the lowest number of balcony tickets bought
A boy flies a kite with a 100-foot-long string. The angle of elevation of the string is 48°. Find the vertical distance between the kite and the point at which the boy is holding the string.
Using the sine function of trigonometry, the vertical distance between the kite and the point where the boy is holding the string is calculated to be approximately 74.31 feet when the string's angle of elevation is 48 degrees.
To find the vertical distance between the kite and the point at which the boy is holding the string, we can use trigonometric functions, specifically the sine function which is defined as the ratio of the opposite side to the hypotenuse in a right triangle. Since we know the length of the string, which acts as the hypotenuse of the triangle, and the angle of elevation, we can set up our equation as follows:s
sin(48°) = opposite/hypotenuse
sin(48°) = vertical distance/100 feet
W then multiply both sides by the hypotenuse (100 feet) to solve for the vertical distance:
vertical distance = 100 feet \sin(48°)
To get the numerical value, we use a calculator to find:
vertical distance ≈ 100 feet * 0.7431
vertical distance ≈ 74.31 feet
Therefore, the vertical distance between the kite and the point where the boy is holding the string is approximately 74.31 feet.
You buy a new yoga ball. The ball has a diameter of 26 inches. What is the volume of the ball? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer:
The volume of the ball is [tex]9,198.11\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere (yoga ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]r=26/2=13\ in[/tex] -----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}(3.14)(13^{3})=9,198.11\ in^{3}[/tex]
Multiply the binomial and find the coefficients
(X+y)^1=__×+__y
(×+y)^2=__x^2+__xy+__y^2
(X+y)^3=__×^3+__×^2y+__y^3
(×+y)^4=__×^4+__x^3y+__x^2y^2+__xy^3+__y4
the perimeter of this figure is 42.5 cm. Find the area of this figure.
Answer:
72.25
Step-by-step explanation:
I just took the test and got it correct
Ellen needs to buy 180 inches of ribbon to wrap a present. The store sells ribbon only in whole yards. How many yards does Ellen need to buy to have enough ribbion
A teacher asked her students to divide a large number by 50.
• Aslan divided the number by 50.
• Lucy divided the number by 5 and then divided the answer she got by 10.
• Jack divided the number by 10 and then divided the answer he got by 40.
Who among these got the correct answer assuming they did NOT make mistakes in division?
Answer:
c
Step-by-step explanation:
Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.
Explanation:To find out who got the correct answer, we need to evaluate the division calculations of each student. Let's assume the large number is 'x'.
Aslan divided the number by 50, so his answer is x/50.
Lucy divided the number by 5 and then divided the answer by 10, so her answer is (x/5)/10 = x/50.
Jack divided the number by 10 and then divided the answer by 40, so his answer is (x/10)/40 = x/400.
Therefore, both Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.
Learn more about Division here:https://brainly.com/question/37843448
#SPJ3
What is the sum or difference 6x^7+8x^7
The sum of the expressions 6x^7 and 8x^7 is 14x^7. This follows the simple rule of addition with similar terms, where the coefficients are added together while the variable remains the same.
Explanation:The sum of 6x7 and 8x7 follows the usual rules of addition, it treats similar terms in a similar way to ordinary numbers. To combine these expressions, you simply add or subtract the coefficients (the number parts), while keeping the variables (the letter parts) the same. In this case, the variable is x7. Thus, adding the coefficients 6 and 8 gives you 14, and you keep the x7 the same. The sum is therefore 14x7.
Learn more about Adding Polynomials here:https://brainly.com/question/30136851
#SPJ3
"when the population standard deviation is unknown, sample size is less than 30, and the population has a normal or near-normal distribution"
Henry can write 5 pages of his novel in 3 hours. at this rate, how many pages can henry write in 888 hours?
Need help on this question
If the surface area of a sphere is 256π cm2, what is the radius?
4 cm
8 cm
12 cm
16 cm
The formula for surface area of the sphere is -
Surface area of sphere = 4πr²
Now, the surface area of sphere is given to us as = 256π cm²
Thus,
4πr² = 256π cm²
While equating the equations, we will get
4r² = 256 cm²
r² = 64 cm²
64 is the square of 8, thus the radius of sphere will be = 8 cm.
The correct answer will be = 8 cm radius
Write a formula for the sum of the first n terms in this series.
PLEASE HELP!!!!!!!!!!!!!!!!! What is the simplified form of the expression k^3(k^7/5)^-5
A. k^4
B. 1/k^1/4
C. k^1/4
D. 1/k^4
Javier is comparing two checking accounts. One has a monthly fee of $10 and a per-check fee of $0.10, and the other has a monthly fee of $12 and a per-check fee of $0.05. What is the minimum number of checks Javier needs to write for the second bank to be a better option?
Answer:
41 is the answer for this question. Hope this helps.
Step-by-step explanation:
(apex)
A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
Which number supports the given conjecture?
If a number is divisible by both 3 and 4, then the number is also divisible by 6.
A.
18
B.
42
C.
48
D.
64