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Sati [7]
3 years ago
8

It takes William 45 minutes to weed the garden. It takes his younger sister May 75 minutes to do the same job. If they work toge

ther, how long will it take them?
A. 25 minutes
B. 28 minutes
C. 36 minutes
D. 60 minutes
Mathematics
1 answer:
marshall27 [118]3 years ago
4 0

Answer:

B. 28 minutes

Step-by-step explanation:

According to the given statement,

William weeds the whole garden in 45 minutes, then in one minute he will weed 1/45 of the garden

and

similarly, 1/75 of the garden in one minute.

When they both will work together, they will weed (1/45+1/75) of the garden in one minute

Solving the equation:

= \frac{1}{45}+ \frac{1}{75}\\= \frac{75+45}{3375}\\ =\frac{120}{3375}\\ = 0.036

Garden weeded in one minute by both = 0.036

So, number of minutes to weed whole garden = 1/0.036

= 27.77 minutes

Rounding off will give us: 28 minutes

So,

Option B is the correct answer ..

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marusya05 [52]

Answer:

Ans 1. x= 7

Ans 2.a.

\overline {AC} \cong \overline {JL} \\\textrm{is the additional information required to prove the triangles are congruent by SAS postulate}

Ans.2.b.

\overline {BC} \cong \overline {KL} \\\textrm{is the additional information required to prove the triangles are congruent by the HL theorem}

Step-by-step explanation:

Solution:

1.

Vertically opposite angles are equal.

\therefore (x+16) = (4x-5)\\\therefore (4x-x) = (16+5)\\\therefore (3x) = (21)\\\therefore x = 7

2.a.

proof for Δ BAC ≅ ΔKJL by SAS postulate.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

\overline{AC} \cong \overline{JL}\ \textrm{additional information require to prove the tangles are congruent by SAS postulate}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Side-Angle-Side postulate...PROVED}

2.b.

proof for Δ BAC ≅ ΔKJL by HL theorem.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

\overline{BC} \cong \overline{KL}\ \textrm{additional information require to prove the tangles are congruent by HL theorem}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Hypotenuse Leg Theorem......PROVED}

5 0
3 years ago
Evaluate the expression for x = - 5 and y = 7 <br><br> 2x+3y-11
jolli1 [7]

Answer:2(-5)+3(7)-11=-10+21=11-11=0

Step-by-step explanation:

4 0
2 years ago
On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees
Ann [662]

Answer:

59.87% probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent

Step-by-step explanation:

For each employee, there are only two possible outcomes. Either they are absent, or they are not. The probability of an employee being absent is independent from other employees. So we use the binomial probability distribution 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.

5% of the production employees at Midland States Steel are absent from work.

This means that p = 0.05

What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent

This is P(X = 0) when n = 10. So

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

P(X = 0) = C_{10,0}.(0.05)^{0}.(0.95)^{10} = 0.5987

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4 0
3 years ago
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Number of 4 m² = 6148 ÷ 4 = 1537

Answer: The zoo can have 1537 plants.
8 0
3 years ago
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4. Bobbie scores m marks in a test. <br> Georgia scores three times as many marks as Bobbie.
xxTIMURxx [149]

Marks of Bobbie = x

Then, marks of Georgia

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= 3 times m

= 3 × m

= 3m

6 0
3 years ago
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