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4 years ago

8×4-5×(3⅕-2½)+(4-1)²

Mathematics

2 answers:

Anna35 [415]4 years ago

7 0

Answer:

101/2

Step-by-step explanation:

choli [55]4 years ago

7 0

Answer:

75/2

Step-by-step explanation:

Simplify the following:

8×4 - 5 (3 + 1/5 - (2 + 1/2)) + (4 - 1)^2

Put 2 + 1/2 over the common denominator 2. 2 + 1/2 = (2×2)/2 + 1/2:

8×4 - 5 (3 + 1/5 - (2×2)/2 + 1/2) + (4 - 1)^2

2×2 = 4:

8×4 - 5 (3 + 1/5 - (4/2 + 1/2)) + (4 - 1)^2

4/2 + 1/2 = (4 + 1)/2:

8×4 - 5 (3 + 1/5 - (4 + 1)/2) + (4 - 1)^2

4 + 1 = 5:

8×4 - 5 (3 + 1/5 - 5/2) + (4 - 1)^2

Put 3 + 1/5 - 5/2 over the common denominator 10. 3 + 1/5 - 5/2 = (10×3)/10 + 2/10 + (5 (-5))/10:

8×4 - 5(10×3)/10 + 2/10 + (5 (-5))/10 + (4 - 1)^2

10×3 = 30:

8×4 - 5 (30/10 + 2/10 + (5 (-5))/10) + (4 - 1)^2

5 (-5) = -25:

8×4 - 5 (30/10 + 2/10 + (-25)/10) + (4 - 1)^2

30/10 + 2/10 - 25/10 = (30 + 2 - 25)/10:

8×4 - 5(30 + 2 - 25)/10 + (4 - 1)^2

30 + 2 = 32:

8×4 - 5 (32 - 25)/10 + (4 - 1)^2

| 2 | 12

| 3 | 2

- | 2 | 5

| 0 | 7:

8×4 - 5×7/10 + (4 - 1)^2

-5×7/10 = (-5×7)/10:

8×4 + (-5×7)/10 + (4 - 1)^2

The gcd of -5 and 10 is 5, so (-5×7)/10 = ((5 (-1)) 7)/(5×2) = 5/5×(-7)/2 = (-7)/2:

8×4 + (-1×7)/2 + (4 - 1)^2

4 - 1 = 3:

8×4 - 7/2 + 3^2

8×4 = 32:

32 - 7/2 + 3^2

3^2 = 9:

32 - 7/2 + 9

Put 32 - 7/2 + 9 over the common denominator 2. 32 - 7/2 + 9 = (2×32)/2 - 7/2 + (2×9)/2:

(2×32)/2 - 7/2 + (2×9)/2

2×32 = 64:

64/2 - 7/2 + (2×9)/2

2×9 = 18:

64/2 - 7/2 + 18/2

64/2 - 7/2 + 18/2 = (64 - 7 + 18)/2:

(64 - 7 + 18)/2

| 1 |

| 6 | 4

+ | 1 | 8

| 8 | 2:

(82 - 7)/2

| 7 | 12

| 8 | 2

- | | 7

| 7 | 5:

Answer: 75/2

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Step-by-step explanation:

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3 years ago

Two candidates face each other in an election. The Democratic candidate is supported by 46% of the population, and the Republica

7nadin3 [17]

Answer:

27.98% probability that less than half of them (3 or fewer) would support the Republican candidate

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they support the Republican candidate, or they do not. The people are chosen at random, which means that the probability of them supporting the republican candidate is independent from other people. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

The Republican candidate is supported by 54%. This means that $p = 0.54$

Suppose you run a poll of 8 people (randomly choose 8 people). What is the probability that less than half of them (3 or fewer) would support the Republican candidate?

This is $P(X \leq 3)$ when $n = 8$ .

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

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

$P(X = 0) = C_{8,0}.(0.54)^{0}.(0.46)^{8} = 0.0020$

$P(X = 1) = C_{8,1}.(0.54)^{1}.(0.46)^{7} = 0.0188$

$P(X = 2) = C_{8,2}.(0.54)^{2}.(0.46)^{6} = 0.0774$

$P(X = 3) = C_{8,3}.(0.54)^{3}.(0.46)^{5} = 0.1816$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0020 + 0.0188 + 0.0774 + 0.1816 = 0.2798$

27.98% probability that less than half of them (3 or fewer) would support the Republican candidate

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3 years ago

The length of a rectangular poster is 7 inches more than twice its width. Find the length of the poster if its perimeter is 110

lakkis [162]

Let W = width of poster
Since the length is 7 inches longer than the width, the length is represented by W + 7.
We know the perimeter is equal to twice the length + twice the width and that is 110 inches. Mathematically that looks like:
2(W + 7) + 2(W) = 110
Now let's solve for W:

2(w+7)+2w=110

Step 1: Simplify both sides of the equation.

2(w+7)+2w=110

Simplify: (see simplify steps down below)

4w+14=110

Step 2: Subtract 14 from both sides.

4w+14−14=110−14

4w=96

Step 3: Divide both sides by 4.

4w4=964

w=24

Answer:

w=24

Simplify Steps:
(2)(w)+(2)(7)+2w=110(Distribute)

2w+14+2w=110

(2w+2w)+(14)=110(Combine Like Terms)

4w+14=110

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4 years ago

Select the proper placement for parentheses to speed up the addition for the expression 4 + 6 + 5

nata0808 [166]

Im guessing that by making 10 it will speed up the addition process so it should be
B since (6+4) = 10 then +5 =15

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