The radius of a sphere is 6 units. which expression represents the volume of the sphere, in cubic units? three-fourthsπ(6)2 four-thirdsπ(6)3 three-fourthsπ(12)2 four-thirdsπ(12)3

Answer:

Doing this would be impossible

Step-by-step explanation:

Doing this would be impossible. This is because the final digit and the first digit in the 6-digit number would always be a 5 or an 8. This means that the entire 6-digit number will either be completely divisible by both 5 and 15 or neither. Therefore not meeting the requirements that have been set. So in conclusion, this would be impossible to do by using only 5's and 8's as the single digits.

The correct choice for the second set in the pyramiding method of dynamic resistance training would typically be a weight that allows the client to perform fewer repetitions than in the first set, typically around 6 to 8 repetitions of their 12-RM weight.

In the pyramiding method, the goal is to gradually increase the weight lifted while decreasing the number of repetitions. This helps to progressively overload the muscles and stimulate strength gains. Starting with a weight that allows the client to perform 10 to 12 repetitions of their 12-RM weight in the first set ensures that they are working at an appropriate intensity to promote muscle adaptation.

For the second set, the weight should be increased to a level that challenges the client's muscles further. By reducing the number of repetitions to 6 to 8, the load becomes more challenging, leading to greater muscle recruitment and strength development. This gradual increase in intensity and decrease in repetitions can help to maximize the benefits of the training session.

It's important to note that the specific recommendations for sets, repetitions, and weights may vary depending on the individual's fitness level, goals, and training program. Working with a qualified fitness professional can help ensure that the pyramiding method is tailored to the client's needs and abilities for safe and effective training.

Learn more about probability here:

brainly.com/question/32117953

#SPJ11

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

To learn more about interest click here: https://brainly.com/question/31907854

#SPJ11

The principal amount was invested for 8 Years.

In the given question, it is stated that when $314 was invested as the Principal amount, it got an Interest of $175.84 at an interest rate of 7%. We have to find out the total period of time the principal amount was kept and got interested in in order to complete the interest amount of $175.84.

To calculate the Interest, we know that the formula for Simple Interest is:

=> S.I. = (P*R*T)/100, where P = Principal amount, R = Rate of Interest, and T is the Time period. Now, putting values in the formula we get:

=> S.I. = (P*R*T)/100

=> 175.84 = (314*7*T)/100

=> T = 17584/2198

=> T = 8

Hence, we get Invested Time for 8 years.

To know more about Simple Interest, Click here:

https://brainly.com/question/25845758

#SPJ9

An F-curve has df (9,3), so the number of degrees of freedom for the numerator is 9 and the number of degrees of freedom for the denominator is 3.

The degrees of freedom in a statistical calculation describe how many values in a computation can change. The degrees of freedom of chi-square tests, t-tests, and even more complex f-tests may be computed to assist confirm their statistical validity. These tests are frequently used to compare observed data with data that would be expected to be produced if a given hypothesis were followed.

We have F-curve with df = (9, 3)

So The degrees of freedom for the numerator is the first number mentioned in df:

df (numerator) = dfn = 9

The degrees of freedom for the denominator is the second number mentioned in df:

df (denominator) = dfd = 3.

Learn more about Degrees of Freedom:

https://brainly.com/question/30403653

#SPJ4

Answer:

-2/1

Down 2 over 1

The meand and variance are 13.75 cm and 17.52 respectively.

Each possible outcome is equally likely when there is a uniform probability.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

M = ( a + b ) / 2

The variance of the uniform distribution is given by:

V = ( b - a )² / 12

Uniform distribution on the interval ( 6.5, 21 )

Therefore, a = 6.5 and b = 21

Hence, the mean will be:

M = ( 6.5 + 21 )/ 2

M = 27.5 / 2

M = 13.75

The mean of depth is 13.75 cm.

The variance will be:

V = ( b - a )² / 12

V = ( 21 - 6.5 )² / 12

V = 210.25 / 12

V = 17.52

The variance of depth is of 17.52 cm².

Learn more about variance here:

brainly.com/question/25639778

#SPJ4

Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

Learn more about Debt-to-equity ratio here: https://brainly.com/question/27993089

#SPJ11

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Considering the data:

Dilation by a scale factor of 4 from the origin in the form of an A'B'C' reflection over x = 1

<=> The two triangles are comparable to one another since triangles can have the same shape but differ in size, so A′′B′′C′′ is 4 times larger than ABC.

=> the connection between "ABC" and "A"B"C" .

\(\frac{AB}{A"B"} = \frac{1}{4}\)

We settle on C.

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

To know more about equation visit:-

https://brainly.com/question/29657992

#SPJ1

Silver Screen Cinemas has sold a total of 11.9×10^6 ounces of soda.

To find the total amount of soda sold by Silver Screen Cinemas, we need to calculate the sum of the large sodas and the small sodas.

The number of large sodas sold is given as 2.1×10^5, and each large soda has a volume of 30 ounces. Therefore, the total volume of the large sodas is calculated by multiplying the number of large sodas by the volume of each soda: 2.1×10^5 × 30 = 6.3×10^6 ounces.

Similarly, the number of small sodas sold is given as 3.5×10^5, and each small soda has a volume of 16 ounces. So, the total volume of the small sodas is calculated by multiplying the number of small sodas by the volume of each soda: 3.5×10^5 × 16 = 5.6×10^6 ounces.

To find the total amount of soda sold, we add the total volume of the large sodas to the total volume of the small sodas: 6.3×10^6 + 5.6×10^6 = 11.9×10^6 ounces.

Learn more about Cinemas here :-

https://brainly.com/question/20532986

#SPJ11

Answer:

B = 90

Step-by-step explanation:

cause math lol.

Answer:

a = 5 / 4

b = 0

Step-by-step explanation:

3/4√5 - √3 + 2/4√5 + √3 = b√3 + a√5

3/4√5 + 2/4√5 + √3 - √3 = b√3 + a√5

5/4√5 + 0 = b√3 + a√5

0 + 5/4√5 = b√3 + a√5

b√3 = 0

b = 0 / √3

b = 0

a√5 = 5/4√5

a = 5/4√5 / √5

a = 5 / 4

Answer:

257/16

Step-by-step explanation:

Given :

Then :

Answer:

30%

Step-by-step explanation:

a) If and are even integers, then is an even integer. True

b)  If is an even integer, then and are both even integers. True

c) A counterexample is. We have, but. Therefore, the statement is false.

(a) True. Let and be even integers. Then there exist integers and such that and . Then,

Since and are even, they can be written as for some integer . Then, we have

= 2(2k1 + 2k2) = 2(2(k1 + k2))

which shows that is even. Therefore, the statement is true.

(b) True. Let be an even integer. Then, by definition, there exists an integer such that . This implies that is divisible by 2. Since is divisible by 2, we can write as for some integer . Then, we have

\(= (2k)^2 = 4k^2\)

which is an even integer. Therefore, and are both even integers. Therefore, the statement is true.

(c) False. A counterexample is. We have, but. Therefore, the statement is false.

Learn more about integers,

https://brainly.com/question/15276410

#SPJ4

Answer:

9 is c

10 is b

i think the last one is a but not too sure

Step-by-step explanation:

The null and alternative hypotheses are:

H0: β1 = 0 (The slope is not significant.)

H1: β1 ≠ 0 (The slope is significant.)

Here,β1=0.0943seβ1=0.107α=0.05

Test the slope significance and find the t-test statistic.

We need to find the t-test statistic so that we can compare it with the t-distribution, whose distributional properties we know, to determine if we can reject or fail to reject the null hypothesis.t-test statistic is calculated by dividing the value of β1 by its standard error (seβ1) and taking the absolute value of this quotient.

t-test statistic = | β1/seβ1 | = |0.0943/0.107| = 0.881

The degrees of freedom (df) associated with this t-test are df = n - 2, where n is the sample size for the explanatory variable x.

In this problem, the decision rule and conclusion are as follows:

Decision Rule: Reject the null hypothesis if |t-test statistic| > tc where tc is the critical value obtained from the t-distribution with df degrees of freedom and a significance level of α/2 in each tail.

Conclusion: The slope is not significant if we fail to reject the null hypothesis, but the slope is significant if we reject the null hypothesis. Since the t-test statistic (0.881) is less than the critical value (1.987), we fail to reject the null hypothesis. Therefore, we conclude that the slope is not significant.

To know more about null and alternative hypotheses:

https://brainly.com/question/33444525

#SPJ11

Answer:

We can simplify the expression as follows: 1/3 * (6x + 15) - 3 = - 2x - 5

Therefore, the answer is: D. - 2x - 8

Answer:

1.3

Step-by-step explanation:

To find what x equals, you need to first divide by 48 and 37.

This is because that x is being multiplied by 37.

48 ÷ 37 = 1.297.......

The 97 in 1.297 is repeating and goes on forever.

Rounding the the nearest tenth would create the number 1.3 as the correct answer.

The relation accepts reflexive, symmetry, and transitive.

Recall that a relation R is reflexive if the element (x, x) belongs to R for all elements X in the domain of R.

If (x, y) belongs to R, then follows that (y, x) must likewise belong to R, making the situation symmetric.

And it is transitive if (x, y) and (y, z) belongs to R necessarily implies that (x, z) belongs to R.

Given r is a relation on the set of all nonnegative integers R(a,b)

Reflexive - YES. A given number a will always have the same remainder when divided by 5.

Symmetric - YES. If a and b have the same remainder when divided by 5, then b and a are the same pair, so again they will have the same remainder.

Transitive - YES. If a and b as well as b and c have the same remainder when divided by 5, this is possible if both a and c also have the same remainder when divided by 5.

Therefore the relation accepts reflexive, symmetry, and transitive.

To learn more about reflexive & symmetry visit

https://brainly.com/question/3014815

#SPJ4

Correct answer is B. prefer

The correct answer is B, as stated in the line. Millenials, who reached adulthood around the turn of the century and now outnumber baby boomers, prefer cities over suburbs and are far more willing to ride public transportation than their parents. This brings prefer closer to favor because favor is followed by the word "over" in favor and prefer is also followed by "over" in prefer.

This states that according to the survey, if we believe the figures, using local transportation is more convenient and safe for a variety of reasons such as easy access to I Pads, MP3 players, and other electronic devices.

Only in this passage is it explained that on this planet, people in cities like New York and Toronto do not own private cars because they believe they are unsafe. They are also more time consuming than local transportation. The experience of European and Asian cities demonstrates that if buses, subways, and trains are made convenient, comfortable, fast, and safe, a surprisingly large percentage of citizens will choose to ride rather than drive.

To learn more about passages from given link

https://brainly.com/question/12555695

#SPJ4

Step-by-step explanation:

draw a rectangle with width 98 and height 55 there are two of each side, so 98 + 98 + 55 +55 = 306

Answer:

306m

Step-by-step explanation:

You need to find the perimeter of the rectangle. To do that, you just add the side lenghts. So, this is your lawn with the side lengths:

                      55m
           _____________
           |                           |
           |                           |
           |                           |
98m    |                           |     98m
           |                           |
           |                           |
           |                           |
           _____________
                      55m

You just add them together!

55 + 55 + 98 + 98 = 306

so you need 306 meters of fencing

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

\((1-xy)y'=y^2\\\\\\\\\)

\((1-xy) \frac{dy}{dx} = y^2\)

\(\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }\)

It is form of  \(\frac{dx}{dy} + Px = Qy\),

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = \(e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y\)

The solution is;

\(x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c\)

\(xy = lny + c\)

Take c = 0, we get;

\(xy = lny\\\\y = e^{xy}\)

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Learn more about the differential equation visit:

https://brainly.com/question/1164377

#SPJ4

Answer:2 7/8              Simplified version=23/8

Step-by-step explanation:3 1/8-1/4=2 7/8

Answer:

2 7/8

Step-by-step explanation:

Ok first lets make them have the same denominator...

so it would be 3 1/8 for Tony and for his brother would be 2/8

now you would subtract 2/8 from 3 1/8 which would be 2 7/8

Hope this helps

On solving the provide question, we can say that Area of the triangle, \(A = \sqrt{s( s - a )( s - b )( s - c )} \\\) =  34.98 sq units

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in this triangle

\(A = \sqrt{s( s - a )( s - b )( s - c )} \\\)

and here

s = a+b+c/3

a = 10

b = 7

c =12

s = 10+7+12 / 3

s = 14.5

A = 34.98 sq units

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ4

Answer:

16.483 sit-ups

The r-value indicates a strong negative correlation

Explanation:

The equation y = ax + b relates the number of hours of TV watched per day and the number of sit-ups a person can do. Replacing a = -1.341 and b = 32.234, we can rewrite the equation as:

y = -1.341x + 32.234

Replacing x by 11, we can predict the number of sit-ups that a person who watches 11 hours can do, so:

y = -1.341(11) + 32.234

y = -14.751 + 32.234

y = 17.483

Therefore, a person who watches 11 hours of TV can do 17.483 sit-ups.

On the other hand, the value of r shows the correlation between the variables. This value is a number between -1 and 1.

When it is closer to 0, we can say that there is a weak correlation.

When it is closer to 1, the correlation is positive and strong

When it is closer to -1, the correlation is negative and strong

Since r = -0.896, we can say that there is a strong negative correlation.

So, the answers are:

16.483 sit-ups

The r-value indicates a strong negative correlation

In triangle JKL, the measure of angle J is given as (4x-10) degrees, the measure of angle K is given as (3x-7) degrees, and the measure of angle L is given as (4x-1) degrees. We need to find the measure of angle K.

To find the measure of angle K, we can equate it to the given expression (3x-7):

m∠K = (3x-7) degrees.

This equation represents the measure of angle K in terms of x. To determine the specific value of x, we would need additional information or equations related to the angles or sides of triangle JKL.

Without any additional information or constraints, we cannot determine the exact measure of angle K. The measure of angle K will depend on the value of x, which is not provided in the given problem.

To learn more about triangle click here:

brainly.com/question/2773823

#SPJ11

The surface area of the regular four-sided pyramid is 9/2 + 9√(2) square centimeters, and the volume is  9√(2) / 8 cubic centimeters.

To calculate the surface area, we first need to find the area of the base. Since the base of the pyramid is a square, and we are given the diagonal of the base, we can determine the side length of the square using the Pythagorean theorem. The diagonal of a square divides it into two congruent right triangles.

Let's denote the side length of the square base as "s." The diagonal of the base (also known as the hypotenuse of the right triangle) is given as 3 cm. Since the diagonal bisects the square, each leg of the right triangle is s/2. Applying the Pythagorean theorem, we have:

(s/2)^2 + (s/2)^2 = (3/2)^2

s^2/4 + s^2/4 = 9/4

2s^2/4 = 9/4

s^2 = (9/4) × (4/2)

s^2 = 9/2

s = √(9/2)

s = √(9) / √(2)

s = 3/√(2)

s = 3√(2) / 2

Now that we know the side length of the base (s), we can find the area of the base (A_base) by squaring the side length:

A_base = s^2

A_base = (3√(2) / 2)^2

A_base = (9 × 2) / 4

A_base = 18 / 4

A_base = 9/2

To calculate the area of each triangular face, we can use the formula for the area of an isosceles triangle:

A_triangular_face = (1/2) × base × height

In this case, the base is the side length of the square (s), and the height can be found by drawing an altitude from the apex of the pyramid to the midpoint of one side of the base. This height is equal to half the diagonal of the base.

height = (1/2) × diagonal of base

height = (1/2) × 3 cm

height = 3/2 cm

Now we can calculate the area of each triangular face:

A_triangular_face = (1/2) × s × (3/2)

A_triangular_face = (1/2) × (3√(2) / 2) × (3/2)

A_triangular_face = (9√(2) / 4)

Since the pyramid has four triangular faces, the total surface area (A_total) can be calculated by summing the areas of the base and the four triangular faces:

A_total = A_base + 4 × A_triangular_face

A_total = 9/2 + 4 × (9√(2) / 4)

A_total = 9/2 + 9√(2)

A_total = 9/2 + 9√(2) / 1

Simplifying the expression by finding a common denominator:

A_total = (9 + 18√(2)) / 2

A_total = 9/2 + 9√(2)

Therefore, the surface area of the regular four-sided pyramid is 9/2 + 9√(2) square centimeters.

To calculate the volume of the pyramid, we need to find the height (h). The height can be determined using trigonometry, as we are given that the side edges of the pyramid form a 45° angle with the diagonal of the base. Since the diagonal divides the square base into two congruent right triangles, the angle formed between the height and the side edge is also 45°.

By using trigonometric functions, we can find the value of h:

sin(45°) = h / (3/2)

√(2) / 2 = h / (3/2)

h = (√(2) / 2) × (3/2)

h = 3√(2) / 4

Now we can calculate the volume (V) using the formula for the volume of a pyramid:

V = (1/3) × A_base × h

V = (1/3) × (9/2) * (3√(2) / 4)

V = (27√(2) / 8) / 3

V = 9√(2) / 8

Therefore, the volume of the regular four-sided pyramid is 9√(2) / 8 cubic centimeters.

For more questions on surface area

https://brainly.com/question/27950508

#SPJ8