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3 years ago

Balancing the equations

Mathematics

1 answer:

erastovalidia [21]3 years ago

8 0

The first one is 1, 1, 1. the second one is 3, 4, 1, 4.

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I did 3 over 7 then 8 over x. I'm getting decimals. ‍♀️

julia-pushkina [17]

Answer:

The length of side b is 9.

Step-by-step explanation:

Triangles are similar if they have the same shape, but can be different sizes.

When two figures are similar, the ratios of the lengths of their corresponding sides are equal.

If you know that two objects are similar, you can use proportions and cross products to find the length of an unknown side. We know that the triangle $ABC$ is similar to the triangle $XYZ$ . Therefore the following relation must be true:

$\frac{AB}{AC} =\frac{XY}{XZ}$

We know that side $AB$ is equal to 8, side $AC$ is equal to b, side $XY$ is equal to $2\frac{2}{3}$ , and side $XZ$ is equal to 3.

Substituting these values into the above relation and solving for b we get that:

$\frac{8}{b} =\frac{2\frac{2}{3} }{3}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{2}{3}=\frac{8}{3}\\\\\frac{8}{b}=\frac{\frac{8}{3}}{3}\\\\8\cdot \:3=b\frac{8}{3}\\\\24=b\frac{8}{3}\\\\8b=72\\\\b=9$

5 0

2 years ago

41% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the

lys-0071 [83]

Answer:

a) 0.2087 = 20.82% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.

b) 0.1834 = 18.34% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.

c) 0.3575 = 35.75% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have very little confidence in newspapers, or they do not. The answers of each adult are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

41% of U.S. adults have very little confidence in newspapers.

This means that $p = 0.41$

You randomly select 10 U.S. adults.

This means that $n = 10$

(a) exactly five

This is $P(X = 5)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.41)^{5}.(0.59)^{5} = 0.2087$

0.2087 = 20.82% probability that the number of U.S. adults who have very little confidence in newspapers is exactly five.

(b) at least six

This is:

$P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 6) = C_{10,6}.(0.41)^{6}.(0.59)^{4} = 0.1209$

$P(X = 7) = C_{10,7}.(0.41)^{7}.(0.59)^{3} = 0.0480$

$P(X = 8) = C_{10,8}.(0.41)^{8}.(0.59)^{2} = 0.0125$

$P(X = 9) = C_{10,9}.(0.41)^{9}.(0.59)^{1} = 0.0019$

$P(X = 10) = C_{10,10}.(0.41)^{10}.(0.59)^{0} = 0.0001$

Then

$P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.1209 + 0.0480 + 0.0125 + 0.0019 + 0.0001 = 0.1834$

0.1834 = 18.34% probability that the number of U.S. adults who have very little confidence in newspapers is at least six.

(c) less than four.

This is:

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.41)^{0}.(0.59)^{10} = 0.0051$

$P(X = 1) = C_{10,1}.(0.41)^{1}.(0.59)^{9} = 0.0355$

$P(X = 2) = C_{10,2}.(0.41)^{2}.(0.59)^{8} = 0.1111$

$P(X = 3) = C_{10,3}.(0.41)^{3}.(0.59)^{7} = 0.2058$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0051 + 0.0355 + 0.1111 + 0.2058 = 0.3575$

0.3575 = 35.75% probability that the number of U.S. adults who have very little confidence in newspapers is less than four.

5 0

2 years ago

#5 math homework need help.

makvit [3.9K]

Answer:

y≥5

Step-by-step explanation:

The range is the output values

y is greater than or equal to 5

y≥5

5 0

2 years ago

What is y/3<-1. Please answer!!

enot [183]

Y/3 < -1

y < -1 * 3

y < -3

hope this helped, God bless!

6 0

2 years ago

For the following problem, match the name of the number property that was used to get to each step from the previous step.

Artyom0805 [142]

Answer:

Step-by-step explanation:37 • 2 • (-5+ 5+ 1/2)

37 • 2 • (0 + 1/2 )

37 • 2 • 1/2

37 • 1

identity property of addition

commutative property

inverse property of multiplication

inverse property of addition

identity property of multiplication

6 0

2 years ago