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3 years ago

One third 1 3 as a decimal rounded to the nearest hundredth.

1 answer:

7 0

4.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333repeating

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Paul has 2/3 as many postcards as Shawn. The number of postcards Shawn has is 4/5 of the number of postcards Tim has. If the thr

ahrayia [7]

Tim has 56 more postcards than Paul.

Step-by-step explanation:

Total postcards boys have = 280

Let,

x = Paul's postcards

y = Shawn's postcards

z = Tim's postcards

According to given statement;

x + y + z = 280 Eqn 1

$x=\frac{2}{3}y$ Eqn 2

$y = \frac{4}{5}z$ Eqn 3

Putting value of y from Eqn 3 in Eqn 2

$x=\frac{2}{3}*\frac{4}{5}z\\\\x=\frac{8}{15}z$ Eqn 4

Putting value of x and y from Eqn 4 and Eqn 3 in Eqn 1

$\frac{8}{15}z+\frac{4}{5}z+z=280\\\\\frac{8z+12z+15z}{15}=280\\\\\frac{35z}{15}=280\\\\$

Multiplying both sides by $\frac{15}{35}$

$\frac{15}{35}*\frac{35}{15}z=280*\frac{15}{35}\\z=120$

Putting z=120 in Eqn 3

$y=\frac{4}{5}*120\\y=96$

Putting y=96 in Eqn 2

$x=\frac{2}{3}*96\\x=64$

Difference of Tim and Paul = 120-64 = 56

Tim has 56 more postcards than Paul.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

7 0

3 years ago

An engineer wants to know if the average amount of energy used in his factory per day has changed since last year. The factory u

m_a_m_a [10]

Answer:

The calculated value Z = 1.8823 <1.96 at 0.05 level of significance

The average amount of energy used in his factory per day has changed since last year.

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 2000 (MWH)

Given that size of the sample 'n' = 400

Given that mean of sample x⁻ = 2040 MWH

Given that the standard deviation = 425 MWH per day

Step(ii):-

Null hypothesis:H₀: μ = 2000 (MWH)

Alternative Hypothesis:H₁: μ≠ 2000( MWH)

Test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{2040-2000}{\frac{425}{\sqrt{400} } }$

Z = 1.8823

The calculated value Z = 1.8823 <1.96 at 0.05 level of significance

Final answer:-

The calculated value Z = 1.8823 <1.96 at 0.05 level of significance

The average amount of energy used in his factory per day has changed since last year.

3 0

3 years ago

U and V are mutually exclusive events. P(U) = 0.27; P(V) = 0.56. Find:

Alisiya [41]

Answer:

(a) P (U and V) = 0.

(b) P (U|V) = 0.

Step-by-step explanation:

Mutually exclusive events are those events that cannot occur at the same time. That is, if events A and B are mutually exclusive then,

$P (A\cap B) = 0$

Given:

Events U and V are mutually exclusive.

P (U) = 0.27 and P (V) = 0.56

(a)

As events U and V are mutually exclusive, the probability of their intersection will be 0.

That is,

$P(U\ and\ V) = P (U\cap V) = 0$

Thus, the value of P (U and V) is 0.

(b)

The conditional probability of event B given A is:

$P(B|A) =\frac{P(A\cap B)}{P(B)}$

Compute the value of P (U|V) as follows:

$P(U|V) =\frac{P(U\cap V)}{P(V)}\\=\frac{0}{0.56}\\ =0$

Thus, the value of P (U|V) is 0.

(c)

The probability of the union of two events, say A and B, is

$P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Compute the value of P (U or V) as follows:

$P(U\ or\ V)=P(U\cup V)\\=P(U)+P(V)-P(U\cap V)\\=0.27+0.56-0\\=0.83$

Thus, the value of P (U or V) is 0.83.

7 0

3 years ago

Read 2 more answers

To avoid dehydration, a person should drink 8 ounces of water for every 15 minutes of exercise. How much water should Hahn drink

Lostsunrise [7]

Answer:

Step-by-step explanation:

1. Proportion:

8/15=x/135

2. Answer is 72

7 0

3 years ago

(3x^4-x^3-4x^2-2x-20)÷(x^2+2) using long division

rosijanka [135]

Answer is below..............

7 0

3 years ago