All categories

3 years ago

100 points

Mathematics

1 answer:

Effectus [21]3 years ago

6 0

Answer:

It will take the first person 12 days and the second person x+12 or 20 days

Step-by-step explanation:

The equation for time to do a job is

1/A + 1/B = 1/C

where A is the time for person A to do the job alone

B is the time for person B to do the job alone

and C is the time for A and B to do the job together

Person A does it in x days and Person B does it in x+8 days and together they do it in 7.5 days

Substituting in

1/ (x) + 1/ (x+8) = 1/ 7.5

Multiply by (x)(x+8)(7.5) to clear the fractions

(x)(x+8)(7.5)(1/ (x) + 1/ (x+8)) = (1/ 7.5)(x)(x+8)(7.5)

Distribute

(x)(x+8)(7.5)(1/ (x)) +(x)(x+8)(7.5)( 1/ (x+8)) = (1/ 7.5)(x)(x+8)(7.5)

Cancel

(x+8)(7.5) + 7.5x = (x)(x+8)

Distribute

7.5x +60 +7.5x = x^2 +8x

Combine like terms

15x +60 = x^2 +8x

Subtract 15x from each side

15x-15x +60 = x^2 +8x-15x

60 = x^2 -7x

Subtract 60 from each side

60-60 = x^2 -7x - 60

0 = x^2 -7x - 60

Factor

0 = (x-12) *(x+5)

Using the zero product property

x-12=0 x+5=0

x=12 x=-5

Since the number of days cannot be zero

It will take the first person 12 days and the second person x+12 or 20 days

You might be interested in

A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports

hichkok12 [17]

Answer:

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

$t = 3.054$

The p-value is $p-value = P(Z > 3.054) = 0.0011291$

The conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 51$

The first sample mean is $\mu_1 = 36$

The second sample size is $n_2 = 41$

The second sample size is $\mu_2 = 25$

The first standard deviation is $\sigma _1 = 21.4 \ g$

The second standard deviation is $\sigma _2 = 12.8 \ g$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 = \mu_ 2$

The alternative hypothesis is $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }$

=> $t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }$

=> $t = 3.054$

The p-value is mathematically represented as

$p-value = P(Z > 3.054)$

Generally from the z table

$P(Z > 3.054) = 0.0011291$

=> $p-value = P(Z > 3.054) = 0.0011291$

From the values obtained we see that $p-value < \alpha$ so the null hypothesis is rejected

Thus the conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

5 0

3 years ago

The relationship between feet and inches is described by the equation y = 12x, where x = a given length in feet and y = the equi

Westkost [7]

The answer is B, 75 inches. This is because for every for there is 12 inches. So, if you plug in 6.25 where the x is, it is saying there are 12 inches per 6.25 feet. So multiply 12 by 6.25 to get 75, your answer, B. Hope this helps

8 0

2 years ago

Which is the biggest number 2.07 2.24 2.4 2 2.04

Temka [501]

Among all these no., see the first no. that lies before or left side of decimal point, here... 2 is common so next check the no. After decimal... 2.0, 2.2, 2.4, 2 is considered as 2.0 and then we have 2.0... Let's not take 2.0s and let's take 2.2 and 2.4 which is greater than 2.0. Next see the second no. That comes after decimal We have 2.24 and 2.4 which can be taken as 2.40... The no.s after decimal, 24 is greater than 40 so 2.4 is greater...

3 0

3 years ago

6 × 2 − 4 × 5 + 12 ÷ 4 insert parentheses

Varvara68 [4.7K]

Answer: (6 x 2) - (4 x 5) + (12 / 4)

6 0

3 years ago

Read 2 more answers

I don’t understand the polynomials

Serhud [2]

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

A polynomial can have:

constants (like 3, −20, or ½)
variables (like x and y)
exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed
that can be combined using addition, subtraction, multiplication and division ...

... except ...

... not division by a variable (so something like 2/x is right out)

So:

A polynomial can have constants, variables and exponents,
but never division by a variable.

Also they can have one or more terms, but not an infinite number of terms.

These are polynomials:

3x
x − 2
−6y2 − ( 79 )x
3xyz + 3xy2z − 0.1xz − 200y + 0.5
512v5 + 99w5
5
(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

These are not polynomials

3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)
2/(x+2) is not, because dividing by a variable is not allowed
1/x is not either
√x is not, because the exponent is "½" (see fractional exponents)

But these are allowed:

x/2 is allowed, because you can divide by a constant
also 3x/8 for the same reason
√2 is allowed, because it is a constant (= 1.4142...etc)

7 0

2 years ago