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2 years ago

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Mathematics

2 answers:

skelet666 [1.2K]2 years ago

6 0

It would be 30 because with the 2 tablespoons and 12 ounces of water to get the amount of water you had to divide 12 divided by 2 which equals 6. So that means you would do 5x6 which equals 30

mestny [16]2 years ago

3 0

30 ounces of water for 5 teaspoons of lemon

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Evaluate: 2|x-4|+6 for x=2

Lina20 [59]

<h3>Answer:</h3>

$10$

<h3>Step-by-step explanation:</h3>

$2|x -4| +6 \text{ for } x = 2 \\ 2|2 -4| +6 \\ 2|-2| +6 \\ 2(2) +6 \\ 4 +6 \\ 10$

6 0

3 years ago

There are 12 inches in one foot, creating the equation y=12x If a door frame is 5.75 feet tall, how many inches tall is it?

Neko [114]

There are 69 inches in 5.75 feet.

8 0

2 years ago

How to solve using substitution<br> y=3/4X+5<br> 4x-3y=-1

Pachacha [2.7K]

Please, use parentheses to enclose each fraction:
y=3/4X+5 should be written as <span>y=(3/4)X+5

Let's eliminate the fraction 3/4 by multiplying the above equation through by 4:

4[y] = 4[(3/4)x + 5]
Then 4y = 3x + 20
(no fraction here)

Let 's now solve the system

4y=3x + 20
4x-3y=-1

We are to solve this system using subtraction. To accomplish this, multiply the first equation by 3 and the second equation by 4. Here's what happens:

12y = 9x + 60 (first equation)
16x-12y = -4, or -12y = -4 - 16x (second equation)

Then we have

12y = 9x + 60
-12y =-16x - 4

If we add here, 12y-12y becomes zero and we then have 0 = -7x + 56.
Solving this for x: 7x = 56; x=8

We were given equations
</span><span>y=3/4X+5
4x-3y=-1

We can subst. x=8 into either of these eqn's to find y. Let's try the first one:

y = (3/4)(8)+5 = 6+5=11

Then x=8 and y=11.

You should check this result. Subst. x=8 and y=11 into the second given equation. Is this equation now true?</span>

5 0

3 years ago

Huilan is 15 years younger than Thomas. The sum of their ages is 33 . What is Thomas's age?

Sphinxa [80]

h = t - 15

h + t = 33

Because we have a value of h, we can plug it into the second equation to solve for t.

t - 15 + t = 33

Add 15 to both sides.

t + t = 48

Combine like terms.

2t = 48

Divide both sides by 2.

t = 24

<h3>Thomas's age is 24.</h3>

6 0

3 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

3 years ago