Which expression can be used to represent the volume of this prism? 10 × 4 units³ 7 × 7 units³ 3 × 11 units³ 21 × 4 units³

The range from 1-6 has 3 even numbers and 3 odd numbers.

The difference between a collection of numbers' highest and lowest values is known as the range. Subtract the distribution's lowest number from its greatest number to determine it. Range is a statistical measure of dispersion in mathematics, or how widely spaced a given data collection is from smallest to largest. The range in a piece of data is the distinction between the highest and lowest value. You must collect your data, sort it from least to greatest, and then subtract the smallest value from the largest value to get the range in a set of integers. A variety of positive and negative numbers are available.

Given,

A die is rolled 36 times and the number of even numbers is counted.

1) The range from 1-6 has 3 even numbers and 3 odd numbers.

2) Each time the die is rolled, there are 36 draws.

3) 0-1 box average = 0.5

To learn more about range, visit:

https://brainly.com/question/28135761

#SPJ4

The magic ratio for muffins in 2:2:1:1.

The magic muffin ratio is 2:2:1:1. This equates to 2 parts flour, 2 parts liquid, 1 part fat, and 1 part eggs. The most crucial aspect is to remember to utilize the same unit of weight for each component!

Rinse frozen blueberries many times in cold water until the water turns lighter in color to prevent your batter and baked items from developing a purple-blue tint. Then, blot them dry with a paper towel and gently fold them into the batter. The goal of this procedure is to maintain fast breads light and delicate by limiting the quantity of gluten produced during the mixing process. To do this, the dry components are mixed in a one bowl, the wet ingredients are combined in a separate bowl, and then the two mixtures are combined together.

To know more about muffins visit:

brainly.com/question/28950026

#SPJ1

Answer:

y=-3.5

Step-by-step explanation

Answer:

y = -3.5

Step-by-step explanation:

This is a horizontal line ( the y value does not change)

Horizontal lines are of the form

y=   constant

y = -3.5

Answer:

It would be 30 mph

Step-by-step explanation:

45/6=7.5

7.5*4=30

Answer:

30 minutes

Step-by-step explanation:

Each mile takes him 7 minutes 30 seconds. So you will do 7.5 x 4 to get 30 minutes

The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

For more question on equation

https://brainly.com/question/17145398

#SPJ8

The possible roots of the given polynomial function are 5, -2 and -1/2 which are obtained by using the Rational Root Theorem.

To determine the possible rational roots of the polynomial function F(x) = 4\(x^3\) - 6\(x^2\) + 9x + 10, we can apply the Rational Root Theorem. The possible rational roots are all the factors of the constant term (10) divided by all the factors of the leading coefficient (4).

For the given polynomial function F(x) = 4\(x^3\) - 6\(x^2\) + 9x + 10, the constant term is 10 and the leading coefficient is 4.

The factors of 10 are ±1, ±2, ±5, and ±10. The factors of 4 are ±1 and ±2.

Therefore, the possible rational roots of the polynomial function are all the combinations of the factors of 10 divided by the factors of 4. These include ±1/1, ±2/1, ±5/1, ±10/1, ±1/2, ±2/2, ±5/2, and ±10/2.

Simplifying these fractions, we find that the possible rational roots of the polynomial function are ±1, ±2, ±5, ±10, ±1/2, ±5/2, and ±10/2.

Hence, these are the possible rational roots of the given polynomial function.

Learn more about functions here:

https://brainly.com/question/11624077

#SPJ11

The complete question is:

According to the rational root theorem, which of the following are possible roots of the polynomial function below?

F(x) = 4\(x^3\) - 6\(x^2\) + 9x + 10

A. 6

B. 5

C. -1/2

D. 5/4

E. 1/3

F. -2

The final point after reflecting (-4, -7) twice across the x-axis is (-4, 7).To reflect a point across the x-axis, we change the sign of its y-coordinate while keeping the x-coordinate the same.

Given the initial point (-4, -7), let's perform the first reflection across the x-axis. By changing the sign of the y-coordinate, we get (-4, 7). Now, to perform the second reflection across the x-axis, we once again change the sign of the y-coordinate. In this case, the y-coordinate of the previously reflected point (-4, 7) is already positive, so changing its sign results in (-4, -7). Therefore, after reflecting the point (-4, -7) across the x-axis twice, the final point is (-4, 7). The reflection process can be visualized as flipping the point across the x-axis. Initially, the point (-4, -7) lies below the x-axis. The first reflection across the x-axis brings it to the upper side of the x-axis, resulting in (-4, 7). The second reflection flips it back down below the x-axis, yielding the final point (-4, -7).It's worth noting that reflecting a point across the x-axis twice essentially cancels out the reflections, resulting in the point returning to its original position. In this case, the original point (-4, -7) and the final point (-4, -7) have the same coordinates, indicating that the double reflection has brought the point back to its starting location.

learn more about reflecting here:

https://brainly.com/question/15487308

#SPJ11

Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.

There are five number cards on the table.

2- digit 1 card

1- digit 0 card

2- digit 2 card

There is a possibility of putting 1 or 2 in the hundredth place.

If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2

If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place

If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place

If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.

So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.

Similarly, there will be 7 possibilities that the hundredth place is filled by 2.

Hence, there are 14 possibilities as required by the problem.

So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.

Learn more about permutation here-

brainly.com/question/1216161

#SPJ10

4.727273

Step-by-step explanation:

There will be 38 elk in the herd one year from now, rounded to a whole number.

To solve the given problem, we must use the formula for exponential growth or decay.

We'll use the following formula:

N = N0ert

Where,N is the final population;

N0 is the initial population;

r is the intrinsic growth rate;

e is the base of the natural logarithm; and

t is the time (in years).

According to the problem, the carrying capacity for a population of elk is 52, and there are currently 33 elk in the population.

The intrinsic growth rate of elk is 0.2 per year. We need to find out how many elk will be in the herd one year from now, rounded to a whole number.

Using the formula above, we can write:

N = 33e0.2 × 1= 37.98 ≈ 38

Therefore, there will be 38 elk in the herd one year from now, rounded to a whole number. Answer: 38.

for such more question on  whole number

https://brainly.com/question/9879870

#SPJ11

In LR2 (two-dimensional Euclidean space), a line passing through the origin is closed under vector addition, meaning that if you take any two vectors on that line, their sum will also lie on the same line.

However, a line not passing through the origin is not closed under vector addition.

To illustrate this, let's consider a line L in LR2 that does not pass through the origin. We can represent this line as a straight line segment starting from a point A and ending at a point B. The line segment AB represents the line L.

Now, consider two vectors represented by two line segments starting from the origin O and ending at points C and D, respectively. These vectors can be represented as OC and OD. Since the line L does not pass through the origin, OC and OD will not lie on line L.

If we try to add these two vectors, we construct the parallelogram OBCD, where BC represents the vector addition OC + OD. Since OC and OD do not lie on line L, their sum BC will also not lie on line L. This violates the closure property, where the sum of two vectors on a line should also be on the same line.

the geometric figure, in this case, would consist of a line L not passing through the origin, two vectors OC and OD not lying on line L, and the resulting vector BC (sum of OC and OD) not lying on line L. This figure demonstrates that a line in LR2 not passing through the origin is not closed under vector addition.

to more about Euclidean visit:

brainly.com/question/31120908

#SPJ11

Answer:

The answer is B)

\(y = - \frac{1}{2}x + 8\)

Answer:

B.  y = -\(\frac{1}{2}\)x + 8

Step-by-step explanation:

The line is perpendicular to line whose equation is:

y = 2x + 4 and;

passes through point (4,6) .

The product slopes of two perpendicular lines is -1.

The slope of the line whose equation is y = 2x + 4 is; 2

Let the slope of the perpendicular line (l2) be \(m_{l2}\)

\(m_{l2} * 2 = -1\)

\(m_{l2}\) = \(-\frac{1}{2}\)

Taking another point xy on line l2;

\(\frac{y - 6}{x - 4} = -\frac{1}{2}\)

Cross multiplying this gives;

y = -\(\frac{1}{2}\)x + 8 which is the equation of the perpendicular line!

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

To learn more about independent events link is here

brainly.com/question/13488890

#SPJ4

A term is a constant, a variable, or a product of numbers and variables.

A symbol (typically a letter) used in algebra to represent an unknowable numerical value in an equation or algebraic expression. A variable can be defined as a quantity that is changeable and not fixed. A variable in mathematics is an alphabet or term that stands in for an unknowable quantity, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are used. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

Here,

A term can be a number, a constant, a variable, or the product of a number and a variable.

To know more about variable,

https://brainly.com/question/2466865

#SPJ4

According to the given statement the probability that the hand contain exactly 2 face card is \(\frac{1}{221}\).

Calculating a result or perhaps the probability that an event would ever occur is known as simple probability. Probability statistics are used by insurance firms to calculate the probability that they'll have to give out a claimed. By dividing one possible outcome by all other possible possibilities, one may determine a basic probability.

A regular 52-card deck is used to deal a poker hand, which consists of 4 cards.

The total number of cards in a deck 52

Number of faces cards in a deck = 2

Number of cards not face cards = 50

The total number of combinations of drawing 4 cards out of 52 cards = \(={ }^{52} C_4\)

Now , the combination of 4 cards such that exactly 2 of them are face cards =  \({ }^{2} C_2 \times{ }^{50} C_2\)

That probability that perhaps the collection will comprise exactly six face cards is as follows:

= \(\frac{{ }^{2} C_2 \times{ }^{50} C_2}{{ }^{52} C_4}\)

\(=\frac{\frac{2 !}{2 ! 0 !} \times \frac{50 !}{2 ! 48 !}}{\frac{52 !}{4 ! \times 48 !}}\)

=\(\frac{1}{221}\)

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ4

Jerry needed to drive for approximately 20.37 hours more to arrive at his destination

a. The function that represents the distance remaining to Jerry's destination based on the number of hours he has driven is:

f(h) = -65h + 1324

b. The domain of this function is all real numbers greater than or equal to zero, since Jerry cannot drive for a negative amount of time and can potentially drive any positive amount of time.

c. The range of this function is all real numbers less than or equal to 1324, since Jerry cannot drive more miles than the total distance to his destination (which is 1324 miles).

d. To determine how much longer Jerry needed to drive to arrive at his destination, we can set the distance remaining to zero and solve for h:

0 = -65h + 1324

65h = 1324

h ≈ 20.37

Therefore, Jerry needed to drive for approximately 20.37 hours more to arrive at his destination.

Learn more about Distance

brainly.com/question/26550516

#SPJ11

Answer:

q=2,6

r=8,6

s=8,10

t=2,10

Answer:

Q= (-2, -6)

R= (-8, -6)

S= (-8, -10)

T= (-2, -10)

Step-by-step explanation:

Since the rotation is 180 degrees, change all of the numbers to the opposites/negatives.

Then, since the rotation is counterclockwise, switch all of the x and y values.

I hope this helps!

pls ❤ and mark brainiest pls!

The answer to the question is True. This can be answered by the concept of Trigonometry.

First, let's recall the definitions of the asymptotic notations used in the question

f(n) = O(n²) means that there exists a positive constant c and a positive integer N such that f(n) <= c × n² for all n >= N.

g(n) = Theta(n²) means that there exist positive constants c1, c2, and a positive integer N such that c1 × n² <= g(n) <= c2 × n² for all n >= N.

Now, since f and g are non-decreasing positive functions, we can assume without loss of generality that N > 0 and c1 > 0. Then, for all n >= N, we have:

f(n) <= c × n² (by the definition of O notation)

c1 × n² <= g(n) <= c2 × n² (by the definition of Theta notation)

Multiplying the first inequality by c1, we get:

c1 × f(n) <= c × c1 × n²

Since c1 and n^2 are positive, we can divide both sides by n² to obtain:

c1 × (f(n) / n²) <= c × c1

Now, let's define a new function h(n) = f(n) / n². Since f(n) and n² are both non-decreasing positive functions, h(n) is also non-decreasing and positive. Moreover, for all n >= N, we have:

h(n) <= (c × c1) / c1 = c

Therefore, we have shown that there exists a positive constant c and a positive integer N such that h(n) <= c for all n >= N. This means that h(n) = O(1).

Using this result, we can conclude that:

f(n) = h(n) × n² = O(1) × n² = O(n²)

Therefore, we have:

f(n) = O(n²) and g(n) = Theta(n²) => f(n) = O(g(n))

Therefore, the answer to the question is True.

To learn more about Trigonometry here:

brainly.com/question/28863906#

#SPJ11

The Laplace transform of te²t sin(7t) is given by: L\{te^{2t}sin(7t)\} = -\frac{49(s-4)e^{2s} + 7(s-2)e^{2s} + 14e^{2s}}{[(s-2)^2 + 49]^2}

The Laplace transform of te²t sin(7t) is given by: L\{te^{2t}sin(7t)\} = -\frac{d}{ds} L\{e^{2t}sin(7t)\}

The first step is to determine the Laplace transform of e²t sin(7t).

We can use the product rule to simplify it. $$\frac{d}{dt}(e^{2t}sin(7t)) = e^{2t}sin(7t) + 7e^{2t}cos(7t)

Taking the Laplace transform of both sides, we get: L\{\frac{d}{dt}(e^{2t}sin(7t))\} = L\{e^{2t}sin(7t)\} + L\{7e^{2t}cos(7t)\} sL\{e^{2t}sin(7t)\} - e^0sin(7(0)) = L\{e^{2t}sin(7t)\} + \frac{7}{s-2}

Now solving for L\{e^{2t}sin(7t)\}: L\{e^{2t}sin(7t)\} = \frac{s-2}{(s-2)^2 + 49}

Substituting into the initial formula: L\{te^{2t}sin(7t)\} = -\frac{d}{ds}\Big(\frac{s-2}{(s-2)^2 + 49}\Big)

L\{te^{2t}sin(7t)\} = -\frac{49(s-4)e^{2s} + 7(s-2)e^{2s} + 14e^{2s}}{[(s-2)^2 + 49]^2}
Therefore, the Laplace transform of te²t sin(7t) is given by:$$L\{te^{2t}sin(7t)\} = -\frac{49(s-4)e^{2s} + 7(s-2)e^{2s} + 14e^{2s}}{[(s-2)^2 + 49]^2}

Know more about Laplace transform here:

https://brainly.com/question/29583725

#SPJ11

Answer:

To determine Martha's monthly pension, we need to use the formula provided by the Merrick Oaks School District for calculating the annual pension benefit:

Annual Pension Benefit = (Years of Service x Average of Last Three Annual Salaries) / 55

where 55 is the "pension factor" used by the district.

Using this formula, we can calculate Martha's annual pension benefit as follows:

Annual Pension Benefit = (18 x $100,000) / 55

Annual Pension Benefit = $32,727.27

Therefore, Martha's annual pension benefit is $32,727.27.

To calculate her monthly pension, we simply divide the annual pension benefit by 12:

Monthly Pension Benefit = $32,727.27 / 12

Monthly Pension Benefit ≈ $2,727.27

Therefore, Martha's monthly pension benefit would be approximately $2,727.27 if she retires after 18 years of service.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the angles of quadrilateral be

x, 2x, 3x , 4x

sum of all angles of quadrilateral = 360°

x + 2x + 3x + 4x = 360°

10x = 360°

x = 360/10 = 36°

Ans. the four angles are :-

x = 36°

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

Answer:

Step-by-step explanation:

Let the angles of quadrilateral be

x, 2x, 3x , 4x

sum of all angles of quadrilateral = 360°

x + 2x + 3x + 4x = 360°

10x = 360°

x = 360/10 = 36°

Ans. the four angles are :-

x = 36°

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

Answer:

\(\boxed{\tt a=9}\)

Step-by-step explanation:

We are given the equation:

\(-5a+7= -38\)

We want to solve for a, so we must isolate a on one side of the equation.

7 is being added to -5a. The inverse of addition is subtraction. Subtract 7 from both sides of the equation.

\(-5a+7-7=-38-7\)

\(-5a=-38-7\)

\(-5a=-45\)

a is being multiplied by -5. The inverse of multiplication is division. Divide both sides of the equation by -5.

\(\frac{-5a}{-5} =\frac{-45}{-5}\)

\(a=\frac{-45}{-5}\)

\(a=9\)

Let's check our solution. Plug 9 in for a.

\(-5a+7=-38\)

\(-5(9)+7=-38\)

\(-45+7=-38\)

\(-38=-38\)

This checks out, so we know our solution a=9 is correct.

-5a +7 =-38

-5a +7 (-7) = -38 (-7)

-5a= -45

-5a (÷-5)= -45 (÷-5)

a= 9

Hey there!

(3^4)^(5) ÷ 3^5

3^4(5)

= 3^20

= 3,486,784,401

3^5

= 3 * 3 * 3 * 3 * 3

= 9 * 9 * 3

= 81 * 3

= 243

= 3,486,784,401 ÷ 243

= 14,348,907

SIMPLIFY IT!

= 14,348,907

≈ 3^15

Therefore, your answer is: 3^15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Explanation:

Let's review three examples of product of exponent rule and dividing of exponent rule before solving the problem.

Looking at these examples, we can tell that we can multiply exponents and subtract exponents. These rules are applied in this question. Now, let's solve the question to obtain our answer.

Solution:

Final Answer:

The possible length of rectangle can be represented by linear inequality   20 ≤ x ≤ 50.

What are linear inequalities?

Linear inequalities are mathematical statements that compare two algebraic expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), or ">=" (greater than or equal to). A linear inequality can be represented graphically as a shaded region on a coordinate plane.

A linear inequality typically involves a variable, usually represented by a letter such as "x" or "y", and constants, which are numbers. The variable is usually on one side of the inequality symbol, and the constants are on the other side.

Now,

Let's use the formula for the perimeter of a rectangle, which is given by:

Perimeter = 2(length + width)

We know that the width of the rectangle is 30 cm, so we can substitute that into the formula:

Perimeter = 2(length + 30)

We also know that the perimeter is between 100 cm and 160 cm, so

100 ≤ 2(length + 30) ≤ 160

To solve for the possible lengths of the rectangle,

50 ≤ length + 30 ≤ 80

20 ≤ length ≤ 50

20 ≤ x ≤ 50, where x=length.

Therefore, the possible lengths of the rectangle are between 20 cm and 50 cm.

To know more about linear inequalities visit the link

brainly.com/question/11897796

#SPJ1

Answer:

39

Step-by-step explanation:

3/17 of 221

= 3/17 x 221

= 663/17

=39

The equation can be used to solve for b is b = 5 / tan30°

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a triangle, ∠ BCA = 90°, ∠ CAB = 30°, we need to find the equation for AC,

The equation for AC(b) =

tan30° = 5/b

b = 5 / tan30°

Hence, the equation can be used to solve for b is b = 5 / tan30°

Learn more about equation, click;

https://brainly.com/question/29657992

#SPJ1