Select the correct aver from each drop-down menu

Among these figures, figure (A or C or E) and figure (B or D) have the same volume

The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

Learn more about volume of prism at

https://brainly.com/question/23766958

#SPJ1

Answer:

Systems by Graphing

Step-by-step explanation:

The equation of line in slope intercept form is y = -0.5x -3.

What is slope intercept form?

The graph of the equation y = mx + b is a line with slope m and y-intercept b. The slope-intercept method is used to depict the linear equation, where m and b are real numbers.

We are given a line on the graph.

Taking two points as (2, -4) and (-2, -2), we get the slope as

⇒m = \(\frac{-2 +4 }{-2-2}\)

⇒m = \(\frac{2 }{-4}\)

⇒m = \(\frac{-1 }{2}\)

⇒m = -0.5

Similarly,

b = -3

We know that slope intercept form is given by

y = mx + b

On substituting, we get

y = -0.5x -3

Hence, the equation of line in slope intercept form is y = -0.5x -3.

Learn more about slope-intercept form from the given link

https://brainly.com/question/1884491

#SPJ1

The transformed function would have a value of -5 when the parent root function has a value of 4.

The function that transforms the parent root function with a horizontal compression by a factor of 2 and a downward shift of 6 units can be represented as follows:

\(f(x) = \frac{1}{2} \times \sqrt{x} - 6\)

This function takes the parent root function, which is represented as \(\sqrt{x}\), and applies a horizontal compression by a factor of 2 by dividing the function by 2. It then applies a downward shift of 6 units by subtracting 6 from the function.

For example, if we input the value x = 4 into the function, we would get the following result:

\(f(4) =\frac{1}{2} \times \sqrt{4} - 6 = \frac{1}{2} \times 2 - 6 = 1 - 6 = -5\)

This means that the transformed function would have a value of -5 when the parent root function has a value of 4.

To learn more about root function, visit:

brainly.com/question/16684818

#SPJ4

Answer:

after step 2 the student made mistake because (-)(minus) will turn into +(plus)

The correct value of x is 3 and student done mistakes in second and fourth steps.

Two or more expressions with an Equal sign is called as Equation.

The given equation is (-6x+15) = -8(-x-3)

The steps solved by student are

Step 1: -6x +15 = 8x + 24

Step 2:15 = 2x + 24

Step 3: -9 = 2x

Step 4: x==3

In the first step there is no error.

In step 2, the RHS Right hand side should be 14x+24 but the student has written 2x which is error.

Step 3 is correct

Step 4 has the error when nine is divided by 2 then the result will be 4.5 but not three

So the value of x should be 3.

Hence, the correct value of x is 3 and student done misakes in second and fourth steps.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.

What is volume ?

Let each side of  he square that's cut-off from each corner be represented by x.

This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.

Thus;

Volume of box is:

V = (15 − 2x)(15 − 2x)x

V = (15 − 2x)²x

V = (4x² - 60x + 225)x

V = 4x³ - 60x² + 225x

Let's differentiate with respect to x to get;

dV/dx = 12x² - 120x + 225

Maximum value of x is at dV/dx = 0

12x² - 120x + 225 = 0

Using quadratic formula, we arrive at;

x = 2.5 or 7.5

Now, let's find the second derivative of the volume;

d²V/dx² = 24x - 120

Putting x = 2.5 gives;

d²V/dx² = 24(2.5) - 120

d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative

At x = 7.5;

d²V/dx² = 24(7.5) - 120

d²V/dx² = 60

Thus, V is minimum at x = 7.5, since d²V/dx² is negative

Thus,we will use x = 2.5

Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)

V = 10 × 10 × 2.5

V = 250 Sq.inches

Dimensions are;

(15 − 2x) = 15 - 2(2.5) = 10 inches

(15 − 2x) = 15 - 2(2.5) = 10 inches

x = 2.5 inches

Learn more about volume

brainly.com/question/1578538

#SPJ4

Answer:

y + 7 = -5/4(x - 4)

Step-by-step explanation:

The formula for point slope form is [ y - y1 = m(x - x1) ].

We are already given all the information needed so fill it in into the formula.

y - (-7) = -5/4(x - 4)

y + 7 = -5/4(x - 4)

Best of Luck!

Answer:

No

Step-by-step explanation:

The height in which the weight is lifted is given as h = (P x δt) / m

The work done in lifting a weight is given by:

W = F x d

where F is the force required to lift the weight and d is the distance through which the weight is lifted.

The force required to lift the weight is equal to its weight, which is given by:

F = m x g

where m is the mass of the weight and g is the acceleration due to gravity.

The distance through which the weight can be lifted is given by:

d = h

where h is the height to which the weight is lifted.

If the energy used to lift the weight is given by p, and δt is the time taken to lift the weight, then the power used is given by:

P = p / δt

We can use the formula for power to express the force in terms of p and δt:

P = F x v = F x d / δt

F = P x δt / d

Substituting the expressions for F and d into the formula for work, we get:

W = (m x g x h) = (P x δt x h) / d

Solving for h, we get:

h = (P x δt x d) / (m x g)

Substituting the expression for d (d = h), we get:

h = (P x δt x h) / (m x g)

Multiplying both sides by (m x g), we get:

h x m x g = P x δt x h

Dividing both sides by (m x g), we get the final equation:

h = (P x δt) / m

Therefore, the height to which the weight can be lifted (h) in terms of p, δt, and m is given by:

h = (P x δt) / m

where P is the power used to lift the weight, δt is the time taken to lift the weight, and m is the mass of the weight.

Learn more on energy here;

https://brainly.com/question/18128982

#SPJ1

0.46

Step-by-step explanation:

23÷50= 0.46

.

.

.

.

.

.

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

To learn more about slope - point form of the line, visit:

https://brainly.com/question/24907633

#SPJ1

Answer:

Angle 2: 110 degrees, 1 and 2 would have to be the same for the lines to be parallel

Angle 3: 70 degrees angle 3 would have to be the complement to angle 1, so 1+3=180 and 70*3=180, so 3=70 degrees

Angle 4: 70 degrees, 3 and 4 have to be the same opposite angles for the lines to be parallel

Answer:

angle 2: 110

angle 3: 70

angle 4: 70

To prove that n^3 + 2n is divisible by 3 for all integers n using mathematical induction, we need to show that it holds for the base case (n = 0) and then demonstrate that if it holds for any arbitrary integer k, it also holds for k + 1.

**Base Case (n = 0):**

When n = 0, we have 0^3 + 2(0) = 0 + 0 = 0. Since 0 is divisible by any integer, including 3, the base case is satisfied.

**Inductive Step:**

Assume that for some arbitrary integer k, k^3 + 2k is divisible by 3.

Now, we need to prove that it holds for k + 1, which means showing that (k + 1)^3 + 2(k + 1) is also divisible by 3.

Expanding (k + 1)^3 using the binomial theorem, we get:

(k + 1)^3 = k^3 + 3k^2 + 3k + 1

Substituting this back into (k + 1)^3 + 2(k + 1), we have:

(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2

                               = k^3 + 3k^2 + 5k + 3

Now, we can rewrite this expression as:

k^3 + 2k + 3k^2 + 3k + 3

Using the assumption that k^3 + 2k is divisible by 3 (inductive hypothesis), we can express this as a multiple of 3:

3m + 3k^2 + 3k + 3 = 3(m + k^2 + k + 1)

Since (m + k^2 + k + 1) is an integer, we have shown that (k + 1)^3 + 2(k + 1) is divisible by 3.

By satisfying the base case and demonstrating the inductive step, we have proven that n^3 + 2n is divisible by 3 for all integers n using mathematical induction.

we have proven that n³ + 2n is divisible by 3 for all integers n by mathematical induction.

To prove that the expression n³ + 2n is divisible by 3 for all integers n, we will use mathematical induction.

Let's first verify the statement for the base case, which is n = 0.

When n = 0, we have

0³ + 2(0) = 0 + 0 = 0,

which is divisible by 3 since 0 divided by any non-zero number is always 0 with no remainder.

Assume that the statement holds true for some arbitrary integer \(k\), where k is a non-negative integer. That is, assume that \(k^3 + 2k\) is divisible by 3.

We need to prove that the statement also holds true for k+1. That is, we need to show that (k+1)³ + 2(k+1) is divisible by 3.

Expanding (k+1)³ + 2(k+1), we get:

(k+1)³ + 2(k+1) = k³ + 3k² + 3k + 1 + 2k + 2

= k³ + 3k² + 5k + 3.

Now, let's express (k+1)³ + 2(k+1) in terms of our inductive hypothesis:

k³ + 3k² + 5k + 3 = (k³ + 2k) + (3k² + 3k + 3).

By our inductive hypothesis, we know that k³ + 2k is divisible by 3. Therefore, we can write k^3 + 2k as 3m for some integer m.

Substituting this back into our expression, we have:

(k³ + 2k) + (3k² + 3k + 3) = 3m + 3(k² + k + 1)

= 3(m + k² + k + 1)

The expression 3(m + k² + k + 1) is a multiple of 3 since it can be written as 3(m + k² + k + 1). Therefore, we have shown that (k+1)³ + 2(k+1) is divisible by 3.

By completing the base case and the inductive step, we have proven that n³ + 2n is divisible by 3 for all integers n by mathematical induction.

Learn more about mathematical induction here

https://brainly.com/question/29503103

#SPJ4

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

To know more about point , visit:

https://brainly.com/question/26310043

#SPJ1

The equation for determining the probability of two independent events occurring at the same time is,                       P(A and B) = P(A) * P(B). The probability that at least one of the two independent events occurs is,                                  P(A or B) = 1 - (P(not A) * P(not B)).

The equation for determining the probability of two independent events occurring at the same time is the product of their individual probabilities. For independent events A and B, the equation is:
P(A and B) = P(A) * P(B)

To find the probability that at least one of the two independent events occurs, you can use the complement rule. First, calculate the probability that neither event occurs (i.e., both events don't occur), and then subtract that from 1:
P(A or B) = 1 - P(not A and not B)

Since A and B are independent, the equation for the probability of neither event occurring is:
P(not A and not B) = P(not A) * P(not B)

So the final equation for the probability that at least one of the two independent events occurs is:
P(A or B) = 1 - (P(not A) * P(not B))

Know more about probability here:

https://brainly.com/question/13604758

#SPJ11

The sum of angle in a triangle is 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angle A, B and C is 180 i.e A+B +C = 180°

Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180

How do we prove that the sum of angle in a triangle is 180°?

Since triangle is 3 sided, n= 3, because n denote the number if sides

therefore the sum of angle = (n-2) 180 = (3-2)×180

= 180°

therefore the sum of angle In a triangle is 180°

learn more about sum of angle In a triangle from

https://brainly.com/question/25215131

#SPJ1

Answer:

1135.38

Step-by-step explanation:

Original amount  = 1015;

First decrease = 6%

Followed by an increase  = 19%

Unknown:

Final amount:

Solution:

If 100% of a value implies multiplying by 1;

        6% decrease  = 0.94

        19% increase  = 1.19

Now;

Final amount  = 1015 x 0.94 x 1.19  = 1135.38

The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.

The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.

On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.

Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.

Graph A has a slope of -1/3 and the shaded part is above the boundary line.

Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.

Learn more about inequality graph on:

https://brainly.com/question/24372553

#SPJ1

The class boundaries for the given frequency distribution are:

515.5-209.5, 209.5-214.5, 214.5-219.5, 219.5-224.5, 224.5-229.5, 229.5-234.5, and 234.5-239.5.

Class boundaries are the values that define the intervals or classes for a frequency distribution. To find the class boundaries for the given distribution, we need to subtract 0.5 from the lower class limit and add 0.5 to the upper class limit for each class interval.

For example, the lower limit of the first interval is 205, so we subtract 0.5 to get 204.5, and the upper limit is 209, so we add 0.5 to get 209.5. Similarly, we can find the class boundaries for each interval using the same method.

The resulting class boundaries are 515.5-209.5, 209.5-214.5, 214.5-219.5, 219.5-224.5, 224.5-229.5, 229.5-234.5, and 234.5-239.5.

For more questions like Boundaries click the link below:

https://brainly.com/question/30267084

#SPJ11

The proportion of the meals ordered that exceeded the recommended daily allowance of 2400 mg of sodium is 0.2119.

z = (x-μ)/σ,

where

x is the raw score = 2400mg

μ is the population mean = 2000mg

σ is the population standard deviation = 500mg

z = 2400 - 2000/500

z = 0.8

Probability value from Z-Table:

P(x<2400) = 0.78814

P(x>2400) = 1 - P(x<2400) = 0.21186

Converting to percentage:

0.21186 × 100

= 21.186%

= 0.2119

Learn more about research on:

brainly.com/question/18296452

#SPJ1

Answer:

Christmas Party

Step-by-step explanation:

Christmas Eve party :

Youngest = 15

Oldest = 29

Therefore , range = 29 - 15 = 14

Christmas Party :

Youngest = 27

Oldest = 42

Therefore, range = 42 - 27 = 15

Christmas Day party has a larger age range of visitors.

Given that: The youngest person to attend the Christmas Eve party is 15 and the oldest is 29. So the range is = 29 - 15 = 14.

Given that: The youngest person to attend the Christmas Day party is 27 and the oldest is 42. So, the range is  = 42 - 27 = 15.

Since 15 > 14, so Christmas Day party has a larger age range of visitors.

Learn more: https://brainly.com/question/22739156

The important difference to note for the scales of measurement and how they are analyzed is whether they involve ratios, intervals, categories or numbers. The scales of measurement can be divided into four types: nominal, ordinal, interval, and ratio.

Nominal scales use categories or numbers to group data, but these categories or numbers have no inherent order or value. Examples of nominal scales include gender, race, or eye color. Ordinal scales use categories or numbers to group data, but these categories or numbers have a specific order or rank. Examples of ordinal scales include educational attainment, income, or level of agreement on a survey question.

Interval scales use numbers as responses on the scale, but the distance between the numbers is not meaningful. Examples of interval scales include temperature measured in Celsius or Fahrenheit, or IQ scores. Ratio scales use numbers as responses on the scale, but the distance between the numbers is meaningful and there is a true zero point. Examples of ratio scales include height, weight, or income.

In summary, the important difference to note for the scales of measurement and how they are analyzed is whether they involve categories or numbers, and whether the numbers have a specific order or rank, a meaningful distance between them, or a true zero point.

Know more about scales of measurement here:

https://brainly.com/question/13086959

#SPJ11

Answer:

-12,27

Step-by-step explanation:

Answer: To find the value of (f - g)(2), we need to first evaluate f(2) and g(2), and then subtract g(2) from f(2).

Starting with f(x), we substitute x = 2:

f(2) = 3(2^2) + 1 = 3(4) + 1 = 12 + 1 = 13

Next, we evaluate g(x) at x = 2:

g(2) = 1 - 2 = -1

Now we can calculate (f - g)(2) by subtracting g(2) from f(2):

(f - g)(2) = f(2) - g(2) = 13 - (-1) = 14

Therefore, the value of (f - g)(2) is 14.

Step-by-step explanation:

Answer:

the answer is 13/103

Step-by-step explanation: