Alexander is building a rectangular pen in his backyard for his dog. The pen will have a length of 13 feet and a width of 2x feet.

The volume of the described solid is V = 16r³/3

Given,

A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)

Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = \(\int\limits^b_a {A(x)} \, dx\)

The equation of circle x² + y² = r² where r is the radius of the circle.

Equation of upper semicircle yu= √(r²-x²)  and

Equation of lower semicircle yl = -√(r²-x²)

Area of cross-section A(x) = (yu² - yl²)

Substitute yu and yl values

A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²)        (1)

The limit for volume v varies from -r to r

Thus Volume v = ₋\(\int\limits^r_r {A(x)} \, dx\)

Substitute A(x) from (1)

V = ₋\(\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx\)

⇒V = 4[r²x - x³/3 ]

⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3

The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3

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Answer:

The relationship between n and k represent by 8n+7k=73 (option B) when 100 ounces of fuel are used in total

11 more units of energy were produced by the type A generator than by the type B generator

Step-by-step explanation:

Type A generate produces n units of energy so,f(n)=10+8n

Type B generate produces k units of energy so,g(k)=17+7k

f(x) and g(x) represent amounts of fuel used.

Total ounces of fuel used = 100

f(x)+g(x) = 100

f(n)+g(k)=100

10+8n+17+7k=100

8n+7k=100-10-17

8n+7k=73

The relationship between n and k represent by 8n+7k=73(option B)

Total ounces of fuel used = 216

f(x)+g(x) = 216

f(n)+g(k)=216

10+8n+17+7k=216

8n+7k=216-10-17

8n+7k=189

n+7n+7k=189

n+7(n+k)=189

Total energy produced = n + k = 25

n+7(n+k)=189

n=189-7(n+k)

n=189-(7 ✕ 25)

n=189-175

n=14 units

Total energy produced = n + k = 25

Substitute n = 14 in n + k = 25,we get

14+k =25

k=25-14=11

k=11 units

11 more units of energy were produced by the type A generator than by the type B generator

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Answer:

in 20 miles she would have taken her 100 minutes (or 1 hour and 40 mins)

Step-by-step explanation:

Divide 10 by 2 to see how many mins its takes to travel 1 mile which is 5 mins, then multiply 20 by 5 to get 100 minutes

2:10

1:5

2.5/1

your welcome

Answer:

The result can be shown in multiple forms.

Exact Form:

x

=

e

4

3

x

=

e

4

3

Decimal Form:

x

=

18.19938334

…

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

x/5=3-7

x/5=-4

x=-4×5

x=-20

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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Answer:

select the first one, the 4th one, and 5th one

The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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Answer:

Step-by-step explanation:

12 in = 12 x 2.45

= 29.4cm

29.4cm

Step-by-step explanation:

Answer:

(a) 12.5%

(b) 20%

(c) 96th

Step-by-step explanation:

Let X denote the results of the 2018 SAT math exam.

It is provided that the mean of exam was, μ = 531 and standard deviation of σ  114.

Assume that X follows a normal distribution.

(a)

Compute the probability of test takers who scored lower than 400 on the math SAT as follows:

\(P(X<400)=P(\frac{X-\mu}{\sigma}<\frac{400-531}{114})\)

                   \(=P(Z<-1.15)\\\\=0.12507\\\\\approx 0.125\)

Thus, the percentage of test takers who scored lower than 400 on the math SAT is 12.5%.

(b)

Compute the probability of test takers who scored between 600 and 700 points as follows:

\(P(600<X<700)=P(\frac{600-531}{114}<\frac{X-\mu}{\sigma}<\frac{700-531}{114})\)

                             \(=P(0.61<Z<1.48)\\\\=P(Z<1.48)-P(Z<0.61)\\\\=0.93056-0.72907\\\\=0.20149\\\\\approx 0.20\)

Thus, the percentage of test takers who scored between 600 and 700 points is 20%.

(c)

Compute the value of P (Z < 725) as follows:

\(P(X<725)=P(\frac{X-\mu}{\sigma}<\frac{725-531}{114})\)

                   \(=P(Z<1.70)\\\\=0.95543\\\\\approx 0.96\)

Thus, a student who scores 725 has a 96th percentile rank.

Answer:

Slope (m): 1/2

Step-by-step explanation:

The rise is 1. As you can see on (-6,0), it goes up one and goes to the right 2 times. ( rise/run). This pattern continues as you can see on your graph.

Answer:

8m=10m

Step-by-step explanation:

Answer: A quotient is the the number resulting from the division of one number by another.

Step-by-step explanation:

24/4 the quotient (answer) is 6

Answer:

La suma de los cuatro ángulos de un cuadrilátero es igual a 360 grados. Entonces, si dos ángulos miden 60° y 80°, la suma de esos ángulos es de 140 grados.

Los otros dos ángulos están en una proporción de 2:9, lo que significa que la suma de sus medidas es de 11 partes. Si representamos las medidas de estos ángulos como 2x y 9x, respectivamente, entonces podemos escribir la ecuación:

2x + 9x = 11 partes

11x = 11 partes

x = 1 parte

Por lo tanto, el ángulo más pequeño mide 2x = 2 partes o 2 × 1 = 2 grados, y el ángulo más grande mide 9x = 9 partes o 9 × 1 = 9 grados.

En resumen, los dos ángulos faltantes miden 2° y 9°.

Step-by-step explanation:

The sample space for this experiment is the one in the last option.

The sample space is the set of the possible outputs that we can have for selecting two marbles.

For example, if first you get a yellow marble, and then a red one, the output will be:

yellow red,

And that is different to the output:

red yellow

Where in the second one you draw the red one first.

From the options, the one that shows the complete sample space is the last one:

"Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow

Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red

Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear

Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green

Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue"

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130.3

85×(23/15) = (X/85) × 85

85×(23/15) = X

X =130.3

The height of the chalkboard is 55.4 in.

A ratio is a relationship between two things when it is expressed in numbers or amounts.

Given that, the aspect ratio in width to height  of a chalkboard is 23:15 and the width is 85 inches,

Let the height be y,

Establishing the ratio,

23/15 = 85/y

y = 15/23x85

y = 55.4

Hence, the height is 55.4 inches.

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Answer:3.8

Step-by-step explanation:

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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The equation of line FG is given as follows:

y = -0.5x - 5.5.

The circle has a center of (1, -1), hence the equation is given as follows:

(x - 1)² + (y + 1)² = r².

Point (-1, -5) is on the circumference of the circle, hence the radius is obtained as follows:

(-1 - 1)² + (-5 + 1)² = r²

r² = 40.

Hence:

(x - 1)² + (y + 1)² = 40.

Applying implicit differentiation, the derivative is given as follows:

2(x - 1) + 2(y + 1)m = 0

2x - 2 +2m(y + 1) = 0

m = (x - 1)/(y + 1)

At x = -1 and y = -5, hence the slope is given as follows:

m = -2/4

m = -0.5.

Hence the equation is given as follows:

y + 5 = -0.5(x + 1).

y = -0.5x - 5.5.

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The answer of 3200 divided by 100 by three different ways is 32.

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.

Now the given division is,  3200 divided by 100.

Since we know that division can be represented in three different way that is,

a) Factoring

b) Long division

c) Synthetic division

So,

a) Factoring 3200 divided by 100 we get,

(2x2x2x2x2x2x2x5x5)/(2x2x5x5)

= 2x2x2x2x2

= 32

b) Long division 3200 divided by 100

      32      

100| 3200

    -  300

         200

       - 200

          000

So,Quotient is 32

remainder is 0.

c) Synthetic division 3200 divided by 100

Let x = 100

Therefore, 3200 = 32x

now to divide 32x/x syntehtic division is given as,

1 |  32  

    1

Hence 32x/x  by synthetic division we get 32 R 0.

Therefore, the required answer is 32.

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Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

Answer: The best problem solving strategy to solve this problem with is a formula. Additionally Brandon had $12.50 before going to the store.

Step-by-step explanation: Formula and Solving it

He Spent $2.50 on pencils.

Amount left after buying a pencil = x - 2.50

Next, he spent half of the amount left in his pocket.

He spent (x - 2.50)/2 on notebook and paper.

So the total amount he spent = 2.50 + (x -2.50)/2

Amount left when he got home =$ 5.00

That means, x - Total amount spent = 5

=> x - (2.50 + (x -2.50)/2 ) = 5

=> x - 2.50 -x/2 + 2.50/2 = 5

=> x/2 - 2.50/2 = 5

=> x/2 = 5 + 2.50/2

=> x/2 = 6.25

=>x = $12.5

The equation of the line is y = x.

To find the equation of a line given its graph, you need to follow the steps below.

Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.

Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.

Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.

Example:Let's say you are given the graph of a line below: .

Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.

Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.

Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.

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The product is calculated by multiplying each row of matrix A by each column of matrix B and summing the results.The result of the operation is the matrix AB = [9 6; 5 4].

Matrix multiplication is defined as the process of multiplying two matrices together to form a third matrix. The product of two matrices A and B is denoted as AB. To calculate the product, each entry in the resulting matrix is calculated by multiplying each row of matrix A by each column of matrix B and summing the results. In other words, the entry in row i and column j of the product matrix AB is the sum of the products of elements in row i of matrix A and column j of matrix B.In the example given, the product of matrices A and B is AB. The product is calculated by multiplying each row of matrix A by each column of matrix B and summing the results. For example, the first entry in the product matrix, AB, is calculated as (1*2 + 0*3 + 0*4) + (0*2 + 1*3 + 0*4) + (0*2 + 0*3 + 1*4) = 2 + 3 + 4 = 9. The remaining entries are calculated in the same way. The result of the operation is the matrix AB = [9 6; 5 4].

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Answer:

Perimeter is about 12.95 /// Area = 8

Step-by-step explanation:

a) The relationship of the graph is drawn by using the above table is attached below:

b) Since, the time is increasing the pay of increasing is more. By this we have known the graph.

An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph. Though it is frequently helpful to think about functions as mappings, which also include which set is the domain and which set is the codomain, it is also important to note that mappings do not just refer to the relationship between input and output. A codomain should be considered, for instance, while determining if a function is onto (surjective) or not. The codomain is not determined by the graph of a function alone.

Given, equation of pay is:

p=8.25t

Here p represents the pay and t represents the time he works.

The table is:

20          10       0       30         4           5             6

165       82.5     0      247.5    330   412.5         495

a) The relationship of the graph is drawn by using the above table:

b) Since, the time is increasing the pay of increasing is more. By this we have known the graph.

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The logarithm of base 7 of t, as a logarithm of base 2 is given as follows:

log2(t)/log2(7).

A logarithm is defined as follows:

log_a(b).

In which:

To change the logarithm to a new base c, the logarithm is written by the fraction presented as follows:

log_c(b)/log_c(a).

In this problem, the logarithm is defined as follows:

log_7 t.

The new base is given as follows:

2.

(as stated in the problem, since we want the logarithm as a logarithm of base 2).

Hence, applying the change of base, the logarithm of base 2 will be given as follows:

log2(t)/log2(7).

As the term log2 represents the logarithm of base 2 of the term.

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