I’m not sure how to do question 5.

The area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

To get the area of the shaded region, we subtract the area of the sector from the area of the triangle as follows:

The angle m∠AOB = 180° - (34 + 90) {sum of interior angles of a triangle}

m∠AOB = 56°

area of sector = 56/360 × 22/7 × 26 cm × 26 cm

area of sector =14872/45 cm²

area of sector = 330.4888 cm²

area of the triangle = 1/2 × 26 cm × 39 cm

area of the triangle = 507 cm²

area of the shaded region = 507 cm² - 330.4888 cm²

area of the shaded region = 176.5111 cm²

Therefore, the area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

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Subtracting -2y² from -4y² + 5d will give us -2y² + 5d.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

To subtract the two polynomials, we first need to distribute the negative sign to the second polynomial.

So, (-4y² + 5d) - (-2y²) becomes -4y² + 5d + 2y².

Now, combine the like terms, which are the terms that contain y²:

-4y² + 5d + 2y² = (-4 + 2)y² + 5d

So, our final answer is:

-2y² + 5d.

Since our answer is in simplest terms, the final answer is -2y² + 5d.

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Answer:

212,500

Step-by-step explanation:

One number that rounds to 213,000 when rounded to the nearest thousands is 212,500.

Step-by-step explanation:

remember, sine is the up/down leg, cosine is the left/right leg.

the Hypotenuse is the radius of the circle around the trigonometric triangle.

so,

sin(R) = 5/13

cos(R) = 12/13

tan(R) = sin(R)/cos(R) = 5/13 / 12/13 = (5×13)/(13×12) =

= 5/12

Answer:

see explanation

Step-by-step explanation:

using the property of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

given

3x²[tex]y^{5}[/tex] × 4x³[tex]y^{7}[/tex] ( separate like parts in the product )

= 3 × 4 × x² × x³ × [tex]y^{5}[/tex] × [tex]y^{7}[/tex]

= 12 × [tex]x^{(2+3)}[/tex] × [tex]y^{(5+7)}[/tex]

= 12[tex]x^{5}[/tex][tex]y^{12}[/tex]

The height of the cone is approximately 28.867 units and the radius is approximately 21.65 units.

Let's denote the height of the cone as "h" and the radius as "r".

From the problem statement, we know that:

r = (3/4)h ...(1) (given)

The surface area of the cone is given as 3750 square units. The formula for the surface area of a cone is:

Surface Area of Cone = πr(r + l),

where "l" is the slant height of the cone. Since the slant height is not given in the problem, we need to express "l" in terms of "r" and "h" using the Pythagorean theorem:

l² = r² + h²

l² = (3/4)² h² + h²

l² = (9/16)h² + h²

l² = (25/16)h²

l = (5/4)h

Substituting this expression for "l" and the expression for "r" from equation (1) into the surface area formula, we get:

3750 = πr(r + l)

3750 = π[(3/4)h] [(3/4)h + (5/4)h]

3750 = π (9/16 + 15/16) h²

3750 = π (24/16) h²

3750 = (3/2) π h²

h² = (2500/3π)

h ≈ 28.867

Substituting this value of "h" into equation (1), we get:

r = (3/4)h

r ≈ 21.65

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Answer: Radius 37.5    &      height 50

Step-by-step explanation: correct in edmuntum/plato

[tex]\left \{ {{2y-x=-9} \atop {y=2x-3}} \right. \iff \left \{ {{2(2x-3)-x=-9} \atop {y=2x-3}} \right. \iff \{ {{4x-6-x=-9} \atop {y=2x-3}} \right. \\[/tex]

[tex]\{ {{3x=-9+6} \atop {y=2x-3}} \right. \iff \{ {{3x=-3} \atop {y=2x-3}} \right. \iff \{ {{x=-1} \atop {y=2x-3}} \right. \\[/tex]

[tex]\{ {{x=-1} \atop {y=2(-1)-3}} \right \iff \{ {{x=-1} \atop {y=-2-3}} \right \implies \bf \{ {{x=-1} \atop {y=-5}}[/tex]

[tex]\implies (x, \ y) = (-1, \ -5)[/tex]

Answer: C

8x+6/-x^2+1

Step-by-step explanation:

a) Initially, when t = 0, the volume of oil in the tank is given by:

V(0) = 0.5(10 - 0)^3

V(0) = 0.5(1000)

V(0) = 500

So, initially there are 500 litres of oil in the tank.

b) The average rate of change of volume in the first 1 minute is given by:

ΔV/Δt = (V(1) - V(0))/(1 - 0)

ΔV/Δt = (0.5(10 - 1)^3 - 500)/1

ΔV/Δt = (0.5(729) - 500)/1

ΔV/Δt = -285.5

So, the average rate of change of volume in the first 1 minute is -285.5 litres/minute.

c) To estimate the instantaneous rate of change of volume at 5 minutes, we can use the average rate of change over a small interval around 5 minutes. For example, we can use the average rate of change from 4.9 minutes to 5.1 minutes:

ΔV/Δt = (V(5.1) - V(4.9))/(5.1 - 4.9)

ΔV/Δt = (0.5(10 - 5.1)^3 - 0.5(10 - 4.9)^3)/0.2

ΔV/Δt = (-61.4455 - (-62.985))/0.2

ΔV/Δt = 7.6975

So, the estimated instantaneous rate of change of volume at 5 minutes is 7.6975 litres/minute.

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The experimental probability of choosing a nickel based on the 13 trials is 4/13.

What is probability ?

Probability can be defined as ratio number of favourable outcomes, total number of outcomes.

Based on the experimental probabilities shown in the table, we can calculate the probability of choosing a nickel on the 13th trial using the following steps:

Calculate the total number of trials: 12 + 1 = 13

Calculate the total number of times a nickel was chosen in the 12 trials: 12 * 1/4 = 3

Add 1 to the total number of times a nickel was chosen to account for the 13th trial: 3 + 1 = 4

Calculate the experimental probability of choosing a nickel based on the 13 trials: 4/13

Therefore, the experimental probability of choosing a nickel based on the 13 trials is 4/13.

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Answer:

First, we need to convert the mixed number to an improper fraction:

6 3/4 = (4 x 6 + 3)/4 = 27/4

Now we can divide:

45 ÷ 27/4 = 45 x 4/27 = 6.6666666...

Rounding to the nearest hundredth, we get:

6.67

Therefore, 45 divided by 6 3/4 is approximately 6.67.

Answer:6.67

Step-by-step explanation:

The resulting matrix is \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \).

we notice is that the resulting matrix is the zero matrix, which means that all of its elements are zero. This is because the matrices \( A \) and \( B \) are inverses of each other.

To calculate \( A B \), we multiply the elements in each row of \( A \) with the corresponding elements in each column of \( B \) and then add them together. This gives us the elements in the resulting matrix.

So, the first element in the resulting matrix is \( (4 * 1) + (2 * -2) = 4 - 4 = 0 \). The second element is \( (4 * -3) + (2 * 6) = -12 + 12 = 0 \). The third element is \( (2 * 1) + (1 * -2) = 2 - 2 = 0 \). And the fourth element is \( (2 * -3) + (1 * 6) = -6 + 6 = 0 \).

Therefore, the resulting matrix is \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \).

What we notice is that the resulting matrix is the zero matrix, which means that all of its elements are zero. This is because the matrices \( A \) and \( B \) are inverses of each other. When we multiply a matrix by its inverse, we get the identity matrix, which has ones on the main diagonal and zeros everywhere else. But in this case, since the matrices are 2x2, the identity matrix is just the zero matrix.

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Answer:

Step-by-step explanation:

The binomial 121y8z2 - 256x6 can be factored using the difference of two squares rule.

To factor the binomial 121y8z2 - 256x6, use the special factoring methods. Notice that the binomial has a difference of two squares, where the first term is a perfect square and the second term is the square of a binomial. This means that you can factor this binomial using the difference of two squares rule:

[tex]121y8z^2 - 256x^6 = (11y4z^2 - 16x^3) * (11y4z^2 + 16x^3)[/tex]

Therefore, the binomial 121y8z2 - 256x6 can be factored using the difference of two squares rule.

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Answer:

Let's call the total number of people who will attend the movie "x". We know that 95% of these people have yet to arrive, which means that only 5% have already arrived.

We can set up an equation to represent this situation:

5% of x = 170

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 5% (or 0.05, which is the decimal equivalent of 5%):

5% of x / 5% = 170 / 5%

Simplifying the left side of the equation gives:

x = 170 / 0.05

Evaluating the right side of the equation gives:

x = 3400

Therefore, there were 3400 tickets sold for the movie.

First step is wrong (x-2) × 3x³ should be 3x⁴ - 6x³

not 6x²

Answer:

Step-by-step explanation:

16 is diameter so r= 16/2= 8

area of circle = 3.14*r^2

therefore 3.14*8^2

which is 3.14*64=200.96cm sq

Enjoy :)

Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1.

To find \( A \), start by multiplying both sides by \( (4A) \). Then, you will have \( (4A)^{-1}(4A)=\left[\begin{array}{ll} 5 & 2 \\ 4 & 2 \end{array}\right] \). This simplifies to \( \left[\begin{array}{ll} 5A & 2A \\ 4A & 2A \end{array}\right] \). Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1. This means that \( 5A=1 \) and \( 2A=1 \). Solving these two equations yields \( A=\frac{1}{5} \).

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The variables to use in a model depend on the type of model being developed and the problem being addressed. In general, variables are the inputs to a model that are used to predict the outputs or dependent variables.

In statistical models, the independent variables, also known as predictors or features, are chosen based on their ability to explain the variability in the dependent variable. For example, in a linear regression model, the independent variables may include factors such as age, income, education, and gender, which are thought to be related to the dependent variable, such as the likelihood of purchasing a product.

In machine learning models, the variables may include a wide range of features, such as text, images, or sensor data, that are used to make predictions or classifications. The process of selecting the most relevant features, also known as feature selection, is an important step in developing effective models that can generalize well to new data.

Ultimately, the choice of variables depends on the specific problem being addressed, and may involve a combination of domain expertise, statistical analysis, and machine learning techniques to identify the most important predictors or features.

P.S: An overview was given as your information is incomplete.

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Any number that has the same ratiο as 1:2 and faIIs between 0 and 6 withοut repeating can be used fοr the divisiοns οf 2 by 4 and 3 by 6.

The basic unit οf mathematics is the number. Numbers are used fοr a variety οf activities, such as measuring, cοunting, and indexing. Accοrding tο their prοperties, numbers can be cIassified intο a variety οf categοries, incIuding naturaI numbers, whοIe numbers, ratiοnaI and irratiοnaI numbers, integers, reaI numbers, cοmpIex numbers, even and οdd numbers, etc. It is pοssibIe tο determine the οutcοme number using simpIe integer arithmetic οperatiοns.

In the given questiοn, we need tο find twο sets οf three distinct numbers between 0 and 6 that have the same ratiο.

One pοssibIe sοIutiοn is:

2 divided by 4.

= 3 divided by 6

Here:

The ratiο οf the first set is 2:4 οr 1:2. When we divide 2 by 4, we get 0.5.

The ratiο οf the secοnd set is 3:6 οr 1:2. When we divide 3 by 6, we aIsο get 0.5.

Therefοre, we have:

2 divided by 4.

= 0.5

3 divided by 6.

= 0.5

Sο, we can say:

2 divided by 4

= __ divided by __

where 3 and 6 can be any numbers that have the same ratiο as 1:2.SimiIarIy,

3 divided by 6

= __ divided by __

where 3 and 6 can be any numbers that have the same ratiο as 1:2.

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Answer:

To simplify the expression, we can combine the like terms.

(3x + 1/2) + (7x - 4 1/2)

= 3x + 7x + 1/2 - 4 1/2 (distributing the addition)

= 10x - 4 (combining the like terms)

Therefore, (3x + 1/2) + (7x - 4 1/2) simplifies to 10x - 4.

Epidemiology would include option (a), (c), and (d).

Epidemiology is the study of the distribution and determinants of health-related states or events in specified populations, and the application of this study to the control of health problems (JM. A Dictionary of Epidemiology, 2001). According to this definition, Epidemiology would include the following activities:

Option (a): Describing the demographic characteristics of persons with acute aflatoxin poisoning in Chittagong: This activity fits with the definition of Epidemiology because it involves studying the characteristics of a specified population, in this case the demographic characteristics of persons with acute aflatoxin poisoning in Chittagong, in order to better understand the determinants and distribution of the health-related state (acute aflatoxin poisoning).

Option (c): Comparing the family history, amount of exercise, and eating habits of those with and without newly diagnosed diabetes: This activity fits with the definition of Epidemiology because it involves studying the determinants of a health-related state, in this case newly diagnosed diabetes, in order to better understand the distribution and control of this health problem.

Option (d): Recommending that 'Kashundi restaurant' in IUB be closed after implicating it as the source of a hepatitis A outbreak: This activity fits with the definition of Epidemiology because it involves applying the study of the distribution and determinants of health-related states to the control of health problems, in this case the control of a hepatitis A outbreak.

In summary, Epidemiology would include option (a), (c), and (d).

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Answer:

AC is about 33 inches.

Step-by-step explanation:

Set your calculator to degree measure.

[tex] \tan(35) = \frac{x}{47} [/tex]

[tex]x = 47 \tan(35) = 32.91[/tex]

Answer:

400

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 400 because you have to solve from left to right because of PEMDAS. So first you mutlipy 5x8 which is 40, and then you do 40x10 which is 400.

Part a) After 30 minutes since the accident, the oil slick has a radius of 15 feet (0.5 * 30 = 15). Therefore, the volume of the oil slick is V(15) = 0.08π * 15 ^ 2 = 705.66 cubic feet. Part b) The function (V∘r)(t) = 0.08π * (0.5t) ^ 2 = 0.02πt ^ 2 is obtained by combining the two functions V(r) and r(t).

Part c) The function (V∘r)(t) = 0.02πt ^ 2 tells us the volume of the oil slick in terms of time t. As time increases, the volume of the oil slick also increases exponentially. Part d) To find out after how many minutes the oil slick will be 705 cubic feet, we can set (V∘r)(t) equal to 705, and solve for t. Therefore, t = (705 / 0.02π) ^ 1/2 ≈ 16.4 minutes. Therefore, after 16 minutes and 24 seconds, the oil slick will be 705 cubic feet.

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Answer:

30 baskets per minute

Step-by-step explanation:

We know

Shaq shot 420 baskets in 14 minutes.

Find his basket rate in baskets per minute.

We take

420 / 14 = 30 baskets per minute

So, the answer is 30 baskets per minute.

The correct answer is B. 3.

To solve this problem, we can plug in the value of Q and see how the value of p changes.
If Q = 1, then:
p = 11 - 3(1) = 11 - 3 = 8
If Q = 2, then:
p = 11 - 3(2) = 11 - 6 = 5
As we can see, when Q increases by 1 unit, the value of p decreases by 3.

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Using the leg rule and the Pythagorean theorem, we have:

x = 4

y ≈ 4.5

The leg rule that can be use to solve the missing measures of the right triangle is given as:

hypotenuse/leg = leg/part

We have the following:

Hypotenuse = 9

Leg = 6

Part = x

Plug in the values:

9/6 = 6/x

9x = 36

x = 36/9

x = 4

Use the Pythagorean theorem to find y:

y = √(6² - 4²)

y ≈ 4.5

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The solution of system of equation is (0, -3).

System A:
Line 1: y = -3x
Line 2: y = -3x + 1

This system of equations is inconsistent. This means the system has no solution. The two lines are parallel and will never intersect, therefore there is no solution to this system of equations.

System B:
Line 1: y = x - 3
Line 2: 2x + 3y = -9

This system of equations is consistent independent. This means the system has a unique solution. The two lines will intersect at one point, which is the solution to this system of equations. We can solve for x and y by using substitution or elimination method.

Using substitution method:
2x + 3(x - 3) = -9
2x + 3x - 9 = -9
5x = 0
x = 0

Substituting x = 0 into Line 1:
y = 0 - 3
y = -3

Solution: (0, -3)

System C:
Line 1: y = -2x - 3
Line 2: y = x + 3

This system of equations is consistent independent. This means the system has a unique solution. The two lines will intersect at one point, which is the solution to this system of equations. We can solve for x and y by using substitution or elimination method.

Using elimination method:
y + 2x = -3
y - x = 3

Adding the two equations:
3x = 0
x = 0

Substituting x = 0 into Line 1:
y = -2(0) - 3
y = -3

Solution: (0, -3)

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The formula for the exponential function that passes through the given points is (a) 3(2ˣ) and (b) g(x) = (2(3)^(1/2))((1/3)^(x/6)).

To find the formula for an exponential function that passes through two points, we can use the formula:
f(x) = abˣ
where a and b are constants. We can use the two points to create a system of equations and solve for the constants.

For part a:
3/4 = ab⁻²
12 = ab²

Dividing the second equation by the first equation gives us:
16 = b⁴

Taking the fourth root of both sides gives us:
b = 2

Plugging this value back into the first equation gives us:
3/4 = a2⁻²
3/4 = a(1/4)
a = 3

So the formula for the exponential function is:
f(x) = 3(2ˣ)

For part b:
6 = ab⁻³
2 = ab³

Dividing the second equation by the first equation gives us:
1/3 = b⁶

Taking the sixth root of both sides gives us:
b = (1/3)^(1/6)

Plugging this value back into the first equation gives us:
6 = a(1/3)^(-1/2)
6 = a(3)^(1/2)
a = 6 / (3)^(1/2)
a = 2(3)^(1/2)

So the formula for the exponential function is:
g(x) = (2(3)^(1/2))((1/3)^(x/6))

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