Is the mass of one pound of lead greater than less than or equal to one pound of feathers?

astraxan [27]

Answer:

x = -8/2

Step-by-step explanation:

To make the equation easier to work with, our first step will be to make all of our fractions have a common denominator. Both 2 and 4 are factors of 8, so that will be our common denominator.

Old Equation: 1/4x - 1/8 = 7/8 + 1/2x

New Equation (with common denominators): 2/8x - 1/8 = 7/8 + 4/8x

Now, we're going to begin to isolate the x variable. First, we're going to subtract 2/8x from both sides, eliminating the first variable term on one side completely.

2/8x - 1/8 = 7/8 + 4/8x

-2/8x -2/8x

__________________

-1/8 = 7/8 + 2/8x

We're one step closer to our x variable being isolated. Next, we're going to move the constants to the left side of the equation. To do this, we must subtract by 7/8 on both sides.

-1/8 = 7/8 + 2/8x

- 7/8 -7/8

______________

-1 = 2/8x

Our last step is to multiply 2/8x by its reciprocal in order to get the x coefficient to be 1. This means multiply both sides by 8/2.

(8/2) -1 = 2/8x (8/2)

The 2/8 and 8/2 cancel out, and you're left with:

-8/2 = x

I hope this helps!

7 0

3 years ago

Sandeep uses 1/5 of a cup of vinegar in his salad dressing recipe. How much vinegar would Sandeep use to make 4/5 of a recipe?

Westkost [7]

Answer:

4 /25

Step-by-step explanation:

Given that :

Cup of vinegar used per recipe = 1/5 cup

Amount of vinegar to be used for 4/5 of a recipe ;

1 cup recipe = 1/5 cup vinegar

4/5 cup recipe = x

Cross multiply :

x = 1/5 * 4/5

x = 4/25 cup

Hence, Sandeep will use 4/25 cup of vinegar

6 0

3 years ago

Condense the following logs into a single log:

mamaluj [8]

QUESTION 1

The given logarithm is

$8\log_g(x)+5\log_g(y)$

We apply the power rule of logarithms; $n\log_a(m)=\log_(m^n)$

$=\log_g(x^8)+\log_g(y^5)$

We now apply the product rule of logarithm;

$\log_a(m)+\log_a(n)=\log_a(mn)$

$=\log_g(x^8y^5)$

QUESTION 2

The given logarithm is

$8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)$

We apply the power rule of logarithm to get;

$=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)$

We apply the product to obtain;

$=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)$

We apply the quotient rule; $\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )$

$=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})$

$=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})$

7 0

3 years ago

Use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothe

omeli [17]

Answer:

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Step-by-step explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.

If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.

(a) Now, we are given alternate hypothesis, $H_1$ : p < 3/5

Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

P-value = P(Z < -1.68) = 1 - P(Z $\leq$ 1.68)

= 1 - 0.95352 = 0.0465

Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which we reject the null hypothesis.

(b) Now, we are given alternate hypothesis, $H_1$ : p > 0.383

Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

P-value = P(Z > 0.41) = 1 - P(Z $\leq$ 0.41)

= 1 - 0.6591 = 0.3409

Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject the null hypothesis.

5 0

2 years ago

What is the value of x?

stiks02 [169]

Answer:

Step-by-step explanation:

Use Pythagoras Theorem

x² + 16² = 34²

x² + 256 = 1156

x² = 1156 - 256

x² = 900

x= √3*3*10*10

x= 3*10

x = 30

4 0

3 years ago

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