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3 years ago

A glass is 2/3 full. Then 40cm^3 of orange juice is poured in. The glass is now 4/5 full What is the total volume of the glass?

Mathematics

1 answer:

aev [14]3 years ago

3 0

Answer:

The total volume of the glass is 300 cm^3.

Step-by-step explanation:

Let V represent the total glass volume.

Then (4/5)V - (2/3)V = 40 cm^3. The LCD here is 15, so we rewrite this equation as

(12/15)V - (10/15)V = 40 cm^3, or

(2/15)V = 40 cm^3.

Solve for V by multiplying both sides of this equation by (15/2):

(15/2)(2/15)V = (15/2)(40 = 300 cm^3

The total volume of the glass is 300 cm^3.

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1) Which expression is equivalent to 8x - 2y + x + x

andrey2020 [161]

Step-by-step explanation:

8x - 2y + x + x

8x - 2y + 2x

10x - 2y

D 10x - 2y

So D Option is the correct answer

5 0

3 years ago

what is the surface area of a square pyramid with base side lengths of 10 inches and a slant height of 14 inches

Pavlova-9 [17]

Answer:

The surface area is $380\ in^{2}$

Step-by-step explanation:

we know that

The surface area of the square pyramid is equal to the area of the square base plus the area of its four lateral triangular faces

$SA=b^{2}+4[\frac{1}{2}(b)(l)]$

where

$b=10\ in$

$l=14\ in$ -----> the slant height

substitute the values

$SA=10^{2}+4[\frac{1}{2}(10)(14)]$

$SA=380\ in^{2}$

5 0

2 years ago

A manufacturer of coffee vending machines has designed a new, less expensive machine. The current machine is known to dispense (

cupoosta [38]

Answer:

$t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864$

$p_v = 2*P(\chi^2_{14}>16.786)=0.5355$

And the 2 is because we are conducting a bilateral test.

$\alpha=0.05$ since the the $p_v >0.05$ we fail to reject the null hypothesis.

$\alpha=0.01$ since the the $p_v >0.01$ we fail to reject the null hypothesis.

Step-by-step explanation:

Data given

$\mu=7$ population mean (variable of interest)

$\sigma=0.2$ represent the population standard deviation

$s=0.219$ represent the sample deviation

n=15 represent the sample size

$\alpha=0.05,0.01$ represent the values for the significance level

Hypothesis test

On this case we want to check if the population standard deviation is equal or not to 0.2, so the system of hypothesis are:

H0: $\sigma = 0.2$

H1: $\sigma \neq 0.2$

In order to check the hypothesis we need to calculate the statistic given by the following formula:

$t=(n-1) [\frac{s}{\sigma_o}]^2$

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

$t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864$

P value

We know the degrees of freedom of the distribution 14 on this case and we can find the p value like this:

$p_v = 2*P(\chi^2_{14}>16.786)=0.5355$

And the 2 is because we are conducting a bilateral test.

$\alpha=0.05$ since the the $p_v >0.05$ we fail to reject the null hypothesis.

$\alpha=0.01$ since the the $p_v >0.01$ we fail to reject the null hypothesis.

3 0

3 years ago

What is the simplified form of x+3/x^2-x-12 times x-4/x^2-8x+16?

Alenkinab [10]

$\frac{x+3}{x^2-x-12} * \frac{x-4}{x^2-8x+16} \\= \frac{x+3}{(x-4)(x+3)}* \frac{x-4}{(x-4)(x-4)} = \frac{1}{x-4}* \frac{1}{x-4} = \frac{1}{(x-4)^2}$ * x-4/x^2-8x+16

Hope that helps

3 0

3 years ago

Question Solve the equation. Check your solutions. ∣2x+1∣=∣3x−11∣

kirill [66]

Answer:

x=2 and x=12

Step-by-step explanation:

|2x+1| = |3x-11|

2x+1 = 3x-11

2x = 3x-12

-x = -12

x = 12

2x+1 = -(3x-11)

2x+1 = -3x+11

5x+1 = 11

5x = 10

x = 2

6 0

2 years ago