A gift box is 4 inches long, 3 inches wide, and 2 inches high. What is the volume of the gift box

The pair of expressions that are equivalent are 6r + 3 and 9r, and 9(3r-4) and 27r - 36.

Let's simplify each expression to see which pairs are equivalent:

Now, let's compare them:

The equivalent pairs are:

So, the correct answer is:

B. 6r + 3 and 9r C. 9(3r-4) and 27r - 36

Answer:

x^5/6 + 2x^7/3.

Step-by-step explanation:

x^1/3 ( x^1/2 + 2x^2 )

= x^(1/3 + 1/2) + 2x^(1/3 + 2)

= x^5/6 + 2x^7/3

The simplified form of the expression  [tex]x^{1/3} ( x^{1/2} + 2x^2 )[/tex] is [tex]x^{5/6}+2x^{7/3}[/tex].

The given expression is [tex]x^{1/3} ( x^{1/2} + 2x^2 )[/tex].

Distribute [tex]x^{1/3}[/tex] to the expression in parenthesis.

[tex]x^{1/3} . x^{1/2} + x^{1/3}.2x^2[/tex]

When the bases are same then the powers will be added.

[tex]x^{1/3+1/2}+2x^{2+1/3}[/tex]

Lets solve the powers by using LCM of the fractions:

[tex]x^{(2+3)/6}+2x^{7/3}[/tex]

Simplify the powers:

[tex]x^{5/6}+2x^{7/3}[/tex]

Hence, the simplified form of the expression  [tex]x^{1/3} ( x^{1/2} + 2x^2 )[/tex] is [tex]x^{5/6}+2x^{7/3}[/tex].

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Answer:

Residual for the week will be $6.

Step-by-step explanation:

Regression equation predicting the per barrel cost of jet fuel is,

[tex]\hat{y}=2+\frac{7}{6}x[/tex]

where, [tex]\hat{y}[/tex] = cost of jet fuel

x = cost of crude oil per week

If the cost of crude oil in any week = $60

Then predicted cost of jet fuel,

[tex]\hat{y}=2+[\frac{7}{6}\times (60)][/tex]

  = 2 + 70

  = $72

Residual price = Actual cost - predicted cost

                        = $78 - $72

                        = $6

Therefore, residual price will be $6.                            

The residual of the week in which a barrel of crude oil costs $60 is $6

The least square regression equation is given as:

[tex]\mathbf{\^y = 2 + \frac 76x}[/tex]

When a barrel of crude oil costs $60, it means that x = 60.

So, we have:

[tex]\mathbf{\^y = 2 + \frac 76 \times 60}[/tex]

[tex]\mathbf{\^y = 2 + 7 \times 10}[/tex]

Multiply

[tex]\mathbf{\^y = 2 + 70}[/tex]

Add

[tex]\mathbf{\^y = 72}[/tex]

So, we have:

Actual Cost = $78

Predicted Cost = $72

The residual is then calculated as:

[tex]\mathbf{Residual = Actual - Predicted }[/tex]

This gives

[tex]\mathbf{Residual = \$78 - \$72}[/tex]

Subtract

[tex]\mathbf{Residual = \$6}[/tex]

Hence, the residual of the week is $6

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The ratio of the surface area of the smaller sphere to the surface area of the larger sphere is,

⇒ 25 : 64

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

The ratio of the lengths of the radii of two spheres is 5 : 8.

Now, We get;

The ratio of the surface area of the smaller sphere to the surface area of the larger sphere is,

⇒ 5² : 8²

⇒ 5² / 8²

⇒ 25 / 64

⇒ 25 : 64

Thus, The ratio of the surface area of the smaller sphere to the surface area of the larger sphere is,

⇒ 25 : 64

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Answer:

He would break the school record by 70 points.

Step-by-step explanation:

22.8*20= 456

456*.25= 114 (how many points he would be getting if he increased his scoring by 25%)

456+114= 570

Answer:

The answer is option 2.

Step-by-step explanation:

You have to use the formula of area of trapezium :

[tex]area = \frac{1}{2} \times (ab + cd) \times bc[/tex]

Let AB be 13 inches,

Let CD be 17 inches,

Let BC be 8 inches,

[tex]A = \frac{1}{2} \times (13 + 17) \times 8[/tex]

[tex] = \frac{1}{2} \times30 \times 8[/tex]

[tex] = \frac{1}{2} \times 240[/tex]

[tex] = 120 \: {inches}^{2} [/tex]

Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 8x - 2y - 17 = 0

Collect the x- terms and the y- terms together and add 17 to both sides

x² - 8x + y² - 2y = 17

Use the method of completing the square on both x and y terms.

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 17 + 16 + 1

(x - 4)² + (y - 1)² = 34 → A

Answer:

(x−4)2+(y−1)2=34

Step-by-step explanation: hope this helps :)

Answer:

Around 1806.42

The correct statements about the graph of the equation y=2x are that as the x-coordinates increase by 1, the y-coordinates increase by 2, and you can get the y-coordinate by substituting the x-coordinate into 2x.

Concerning the equation y=2x, option C is the correct statement about the graph. This is because linear equations like this represent a direct proportionality between variables x and y. When the x-coordinate increases by 1, the y-coordinate increases by the coefficient of x, in this case, 2, reflecting the equation's slope which is the constant rate of change for y in relation to x. Option D is also true because, for any point on the graph, substituting the x-coordinate into the expression 2x will yield the corresponding y-coordinate, as per the definition of a functional relationship in algebra. Thus, solutions to the equation y=2x include an infinite number of points on the graph, not just two as stated in option A, making options A and B incorrect.

Answer:

True

Step-by-step explanation: 1 yard = 3 feet

d

Step-by-step explanation:

Answer:

number 1  + number 2 + number 3 = 15

Number 1 = x + 12

Number 2 = x - 12

Number 3 = x

(x + 12) + (x - 12) + x = 15

x + 12 + x - 12 + x = 15

x + x + x +12 -12 = 15

3x = 15

x = 15/3 = 5

Check:

Number 1 = 17

Number 2 = 5 -12 = -7

Number = 5

number 1  + number 2 + number 3 = 15

17 + (-7) + 5 = 15

10 + 5 = 15

15 = 15

Answer is 5

Step-by-step explanation:

Answer:

y = 1/2x+4

Step-by-step explanation:

First we find the slope

m = (y2-y1)/(x2-x1)

    = (3-6)/(-2-4)

    = -3/-6

   =1/2

The equation of a line in slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

y =1/2x+b

Substitute one of the point into the equation

6 = 1/2(4) +b

6 = 2+b

b=4

y = 1/2x+4

Answer:

D. y = 1/2x + 4

Step-by-step explanation:

Slope: (6-3)/(4--2) = 3/6 = 1/2

y = ½x + c

6 = ½(4) + c

6 = 2 + c

c = 4

y = ½x + 4

Answer:

We conclude that the effectiveness is less than the 85% claim the company is making.

Step-by-step explanation:

We are given that a manufacturer of a new medication on the market for Crohn's disease makes a claim that the medication is effective in 85% of people who have the disease.

One hundred seventy-five individuals with Crohn's disease are given the medication, and 135 of them note the medication was effective.

Let p = percentage of people who have the Crohn's disease.

So, Null Hypothesis, [tex]H_0[/tex] : p = 85%      {means that the effectiveness is equal to the 85% claim the company is making}

Alternate Hypothesis, [tex]H_A[/tex] : p < 85%      {means that the effectiveness is less than the 85% claim the company is making}

The test statistics that would be used here One-sample z proportion statistics;

                        T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of individuals who note the medication was effective = [tex]\frac{135}{175}[/tex] = 0.77

           n = sample of individuals with Crohn's disease taken = 175

So, test statistics  =   [tex]\frac{0.77-0.85}{\sqrt{\frac{0.77(1-0.77)}{175} } }[/tex]

                               =  -2.515

The value of z test statistics is -2.515.

Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

Since our test statistic is less than the critical value of z as -2.515 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the effectiveness is less than the 85% claim the company is making.

The study's findings suggest that the medication is less effective than the manufacturer's claim of 85%.

Step-by-Step Calculation

1. Define the parameter

The parameter we are testing is the population proportion p of people with Crohn's disease for whom the medication is effective. The manufacturer's claim is that [tex]\( p = 0.85 \)[/tex].

2. State the hypotheses

- Null hypothesis [tex]\( H_0 \): \( p = 0.85 \)[/tex]

- Alternative hypothesis [tex]\( H_a \)[/tex] : [tex]\( p < 0.85 \)[/tex]

3. Check conditions for the test

We use a one-sample z-test for proportions. The conditions are:

- Random sample: Assume the sample is random.

- Large enough sample size: Both [tex]\( np \)[/tex] and [tex]\( n(1-p) \)[/tex] should be greater than 10.

Calculations:

- [tex]\( np = 175 \times 0.85 = 148.75 \)[/tex]

- [tex]\( n(1-p) = 175 \times 0.15 = 26.25 \)[/tex]

Both values are greater than 10, so the conditions are met.

4. Perform the calculations

Sample proportion [tex]\( \hat{p} \)[/tex]:

[tex]\[ \hat{p} = \frac{135}{175} = 0.7714 \][/tex]

Standard error (SE) of the sampling distribution:

[tex]\[ SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.85 \times 0.15}{175}} = \sqrt{\frac{0.1275}{175}} = \sqrt{0.000728571} \approx 0.027 \][/tex]

Test statistic (z):

[tex]\[ z = \frac{\hat{p} - p}{SE} = \frac{0.7714 - 0.85}{0.027} = \frac{-0.0786}{0.027} \approx -2.91 \][/tex]

5. Determine the p-value

Using the standard normal distribution, we find the p-value for [tex]\( z = -2.91 \).[/tex]

Looking up this value in a z-table or using a statistical calculator, the p-value for [tex]\( z = -2.91 \)[/tex] is approximately 0.0018.

6. Make a decision

Since the p-value (0.0018) is less than the significance level [tex]\( \alpha = 0.05 \)[/tex], we reject the null hypothesis.

There is statistical evidence at the 0.05 significance level to support the claim that the effectiveness of the medication is less than 85%.

Angles 1 and 3 are vertical angles, so they are congruent.

Answer:

b

Step-by-step explanation:

looked it up

Answer:

i think its b

Answer:

Since Tom got only £50 while Jay got £60 for th same amount invested in the same time, Jay got the better investment.

Step-by-step explanation:

In order to show that Jay got a better investment we first need to calculate how much Tom earnt in simple interest during those two years. In order to do that we must apply the correct formula shown below:

M = c*r*t

Where M is the total of interest, c is the amount invested, r is the rate of interest and t is the time elapsed. Thefore Tom got:

M = 1000*0.025*2

M = £50

Since Tom got only £50 while Jay got £60 for th same amount invested in the same time, Jay got the better investment.

Answer:  height as h and base as 2h.

A = ½(b)(h). Substituting known facts gives 36 =½(2h)(h), which means that 36 = h2

and therefore h = 6 inches, height = 12 in.

Step-by-step explanation: I hope this helps :]

Final answer:

To determine the length of the base of the triangle with an area of 36 square inches and the base being twice the height, we use the area formula for a triangle (A = bh/2). After solving the equation, we find that the height is 6 inches and the base, being twice the height, is 12 inches.

Explanation:

The question asks to find the length of the base of a triangle given the area and a relationship between its base and height. We can use the formula for the area of a triangle, which is A = bh/2, where A is the area, b is the base, and h is the height of the triangle. Given the area of 36 square inches and the base being twice the height (b = 2h), we substitute into the area formula to solve for the base.

Plugging in the values, the equation becomes:

36 = (2h)h/2

Multiplying both sides by 2 to eliminate the fraction gives us:

72 = (2h)(h)

Which simplifies to:

72 = 2h^2

Dividing both sides by 2 gives us:

h^2 = 36

And taking the square root of both sides yields:

h = 6 inches

Knowing that the base is twice the height, we can find the base:

b = 2h = 2(6) = 12 inches

Therefore, the length of the base of the triangle is 12 inches.

Answer:

12.1

Step-by-step explanation:

Answer: 12.1

Because you have to plug in your numbers in the expression d = 7km

Answer:

they are like terms

Step-by-step explanation:

the sign ± is not a matter only veriable and power

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.

Answer:

192

Step-by-step explanation:

3 * 4^3

Using PEMDAS

Exponents first

4^3 = 4*4*4 = 64

Replace into the expression

3 *64

3*64 =192

Answer:

200 laps left

Step-by-step explanation:

50 * 2 = 100

100 miles have been completed

500 - 100 = 400

400 miles left

400 / 2 = 200

200 laps left

Answer:

a. y = negative one-fifth x + 1

Step-by-step explanation:

The linear function of a line that passes through points (–5, 2) and (10, –1) will be y = (-1/5)x + 14.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

The line passes through points  (–5, 2) and (10, –1)

Slope m = (-1 - 2)/(10 + 5)

Slope m = -3/15

m = -1/5

Thus, y = (-1/5)x + c

Put (10, –1)

-1 = (-1/5)10 + c

c = 14

Thus, the linear equation will be as, y = (-1/5)x + 14

Hence "The linear function of a line that passes through points (–5, 2) and (10, –1) will be y = (-1/5)x + 14.".

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The Pythagorean theorem, established by the ancient Greek philosopher Pythagoras, defines the relationship in a right-angled triangle between the squares of the lengths of the legs (a and b) and the hypotenuse (c) with the famous equation: a² + b² = c².

The Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in the field of mathematics, specifically in geometry. It was established by the ancient Greek philosopher, Pythagoras, who made significant contributions to understanding the relationships in geometric figures. The theorem reveals a specific relationship between the sides of a right-angled triangle. It states that the square of the length of the hypotenuse (√), which is the side opposite the right angle, is equal to the sum of the squares of the lengths of the other two sides. This can be elegantly expressed in the formula: a² + b² = c². Here, a and b represent the legs of the triangle, while c represents the hypotenuse.

For example, if a right triangle has legs of lengths 9 units and 5 units, using the Pythagorean theorem, we can calculate the length of the hypotenuse. We would square each of the legs (√9² + 5²), add these together, and take the square root to find that the hypotenuse is approximately 10.3 units long.

This theorem is not only a theoretical concept but is also practical in various real-world scenarios, such as calculating distances in navigation. An old adage suggests that the shortest distance between two points is a straight line. When dealing with the distances on a map or between points in space, a right triangle can often form, and using the Pythagorean theorem allows us to calculate the direct straight-line distance (hypotenuse) easily.

Answer:84

Step-by-step explanation:you have to add 54 plus 3