Q5.
120 cm
The circle has a radius of 120 cm. Find the area of this circle.
Diagram NOT
accurately drawn

Given:

2x + 4y = 14

4x + y = 20

Required:

We need to find the equivalent to the given system.

Explanation:

Consider the equation

Multiply both sides of the equation by -4, it will not affect the equations of the system

Final answer:

The equivalent system of the equation is

\(\\ \bull\tt\dashrightarrow Diameter=2(Radius)\)

\(\\ \bull\tt\dashrightarrow Diameter=2(4.2)\)

\(\\ \bull\tt\dashrightarrow Diameter=8.2m\)

Answer:

Solution given:

radius [r]=4.2m

since

diameter is twice of radius

so

diameter=2*radius=2*4.2=8.4m

option B.8.4m

The given values into the equation of the least squares regression line: 0.6 * 520 + 10.0 = 322 hot dogs were sold that day. 357 hot dogs were sold on the day when 520 people attended the fair.

In this problem, we have data collected on the number of hot dogs sold (h) and the number of people attending a fair (p) over a two-week period. The least squares regression line is a line that best fits the data points and represents the relationship between the variables.

The equation of the least squares regression line is given as 0.6p + 10.0. This equation indicates that the number of hot dogs sold (h) can be estimated by multiplying the number of people attending (p) by 0.6 and adding 10.0.

We are given that the residual for the day when 520 people attended the fair is 35. A residual is the difference between the actual observed value and the predicted value on the regression line. In this case, the predicted value is 0.6 * 520 + 10.0 = 322 hot dogs. The actual value is the number of hot dogs sold on that day. The residual is calculated as the actual value minus the predicted value, which gives us 35.

To find the number of hot dogs sold on that day, we can set up an equation using the residual: h - 322 = 35. Solving this equation, we find that h = 322 + 35 = 357. Therefore, 357 hot dogs were sold on the day when 520 people attended the fair.

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QUESTION:

Data was collected on h, the number of hot dogs sold, and p, the number of people attending a fair over a two week period. The least squares regression line has equation y = 0.6p + 100. The residual for the day when 520 people attended was 35. How many hot dogs were sold that day? OA. 322 OB. 287 OC. 220 OD. 555 O E. 357 The salaries of a random sample of a company's employees are summarized in the frequency distribution below. Approximate the sample mean using the grouped data formulas O A. $17,500.00 OB. $19,663.05 O C. $16,087.95 OD. $17,875.50 Employees Salary (5) 5.001 - 10,000 10,001 - 15,000 15,001 - 20,000 20,001 - 25,000 25,001 - 30,000

Answer:

72

Step-by-step explanation:

12x6=72

Answer:

Add the whole anwser

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

5 is rational

1/4 is rational

the product of the two is 5/4 which is also rational

The closure property refers to the mathematical law that states that if we perform a certain operation (addition, multiplication) on any two numbers in a set, the result is still within that set.In the expression (2x3 x2 - 4x) - (9x3 - 3x2), we are simply subtracting one polynomial from the other.

To simplify it, we'll start by combining like terms. So, we'll add all the coefficients of x3, x2, and x, separately.The given expression becomes: (2x3 x2 - 4x) - (9x3 - 3x2) = 2x3 x2 - 4x - 9x3 + 3x2We will then combine like terms as follows:2x3 x2 - 4x - 9x3 + 3x2 = 2x3 x2 - 9x3 + 3x2 - 4x= -7x3 + 5x2 - 4x

Therefore, the correct simplification of the expression is -7x3 + 5x2 - 4x. The demonstration of the closure property is shown as follows:The subtraction of two polynomials (2x3 x2 - 4x) and (9x3 - 3x2) results in a polynomial -7x3 + 5x2 - 4x. This polynomial is still a polynomial of degree 3 and thus, still belongs to the set of polynomials. Thus, the closure property holds for the subtraction of the given polynomials.

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Answer:

You will receive $21.69, assuming there's no tax ;).

I added the 24.49 to the 3.82 and got 28.31, then subtracted that from 50.

Answer:

Step-by-step explanation:

3/4 and 8/9 both lie between 0 and 1.  Their LCD is 36.

Thus, 3/4 = 27/36 and 8/9 = 32/36.

Dividing the number line between 0 and 1 into 36 equal lengths, plot a dot at the 27th such mark and then another dot at the 32nd mark.

This clearly shows that 32/36 is larger than 27/36.

The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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Answer:

27

Step-by-step explanation:

Speed is regarded as the rate at which a particular distance is traveled over time. 138.92 miles  has charlotte traveled in feet during this time

From the information given:

The speed at which charlotte is driving = 64.3 ml/h

The time which she took of her eyes from the road = 3.36 s

During the entire journey, the time at which she took her eyes off the road, she is probably not driving.

∴We will have to convert the 64.3 mi/h to m/s

Since 1 mi/hr = 0.44704 m/s

64.3 mi/h will be:

= (64.3 mi/hr × 0.44704 m/s) ÷ 1 mi/hr

= 30.39872 m/s

Now, using the relation:

Speed = distance/ time

30.39872 m/s = (distance)  / 3.36 s

By Cross multiplying

Distance = 30.39872 m/s  × 3.36 s

Distance = 138.92 m

in conclusion, Charlotte traveled by feet for 138.92 m during this time

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Numerical values that appear in the mathematical relationships of a model and are considered known and remain constant over all trials of a simulation are parameters.

Numerical values that appear in the mathematical relationships of a model and are considered known and remain constant over all trials of a simulation are not referred to as events.

In the context of simulations, these constant numerical values are typically known as parameters.

Parameters are fixed values that define the characteristics of a system or model being simulated.

They represent the fixed inputs or conditions that remain constant throughout the simulation.

These values are determined based on prior knowledge, experimental data, or theoretical assumptions.

For example, in a simulation model of a manufacturing process, parameters may include the production rate, the machine capacity, the setup time, or the defect rate.

These values are known and constant throughout the simulation runs.

It is important to distinguish parameters from variables in simulations. While parameters remain constant, variables are the factors or quantities that can change during the simulation and are often the focus of analysis or study.

By incorporating known and constant parameter values into a simulation model, researchers can analyze the behavior and performance of the system under different conditions, explore various scenarios, and make predictions or decisions based on the simulation outcomes.

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(a) The probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013. (b) The expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes

a) The probability that a randomly selected customer spends less than 65 minutes at the gym is calculated using the standard normal distribution formula.

z = (x - μ) / σ

where,μ = 70 minutes, σ = 20 minutes, x = 65 minutes

Substituting the given values, we get

z = (65 - 70) / 20

z = -0.25

Using a standard normal table or calculator, the probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013.

b) The standard deviation (standard error) of the sample mean can be calculated using the formula:

SE = σ/√n

where,σ = 20 minutes, n = 49

Substituting the given values, we get

SE = 20/√49

SE = 2.857 minutes

Therefore, the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes, respectively.

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No, it is not necessarily true that both ABT and ATB are defined for matrices A and B of size m × n.

In order for the matrix product ABT to be defined, the number of columns in A (which is n) must be equal to the number of columns in BT (which is also n). This means that the number of rows in B (which is m) must be equal to the number of rows in A (which is also m). So, if A and B are both square matrices of size n × n, then ABT is defined

On the other hand, in order for the matrix product ATB to be defined, the number of columns in AT (which is m) must be equal to the number of columns in B (which is also n). This means that the number of rows in A (which is m) must be equal to the number of rows in B (which is also m). So, if A and B are both square matrices of size m × m, then ATB is defined.

However, if A and B are not square matrices, then it is possible that only one of ABT or ATB is defined, or neither of them are defined. In general, the product of two matrices is only defined if the number of columns in the first matrix is equal to the number of rows in the second matrix.

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Answer:

kayla and 9968

Step-by-step explanation:

Answer:

Jeff, 9968

Step-by-step explanation:

you can take the tens and ones of the number you are multiplying by and use those number to multiply by the first number

50 is in the tens

6 is in the ones

178×56= 9968

Answer:

u= 2.5

Step-by-step explanation:

Using BIDMAS

Step 1: Expand the bracket

9(u-2) + 1.5u=8.25

9u-18+1.5u=8.25

Step 2: collect like terms

9u+1.5u=8.25+18

10.5u=26.25

Step 3: Divide both sides by 10.5 to get u

u= \(\frac{26.25}{10.5}\)= 2.5

It's equation in point-slope from is -1/6x+5/2.

An equation is a formula that is express the equality of two equation.

Based on the given condition the formula

M= -1/6

Substitute {m -1/6

                        { X= 9

                        {Y = 1

(Into y= mx+b)

1=-1/6×9+b

Reduce the expression into the Lowest term

1=-1/2×3+b

Write as a single fraction

1=-3/2+b

Rearrange variables to the left side of the equation.

-b= -3/2-1

Now we have to find the denominator and write the numerators above common denominator

-b=-3-2/2

Calculate the sum or difference

-b=-5/2

b=5/2

Substitute {m=-1/6 b=5/2 into y mx+b

Y=-1/6x+5/2

Rewrite the equation of the line

Y= -1/6x+5/2 in point-slope

Y-1 = -x-9/6

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Answer:

f(a)=3(a+2)-2

f(4)=3(4+2)-2

f(4)=3(6)-2

f(4)=18-2

f(4)=16

Hope  this helps!

Answer:

f(4)= 16

Step-by-step explanation:

f(4)= 3(a + 2) -2

f(4)= 3(4 + 2) -2

f(4) = 3(4) + 3(2) -2

f(4)= 12 + 6 -2

f(4)= 18-2

f(4)= 16

Three different whole numbers whose sum and product are equal are 1, 2, and 3.

1 + 2 + 3 = 6

1 x 2 x 3 = 6

As demonstrated above, the sum and product of 1, 2, and 3 is the same.

Hope this helps!! :)

Answer:

1 2 and 3

Step-by-step explanation:

Answer:4.94*10^5

Step-by-step explanation:

Step-by-step explanation:

Hello there! I think the answer is: 4.94 × 10^5

In scientific notation, you move the decimal point until you get a number between 1 and 10. Then you count the number of digits after.

My reasoning is below-

There are 3 zeros right of the number 494.

Therefore, I got the answer 4.94 x 10^5

Answer:

24

Step-by-step explanation:

You should draw a picture to let everything fall into place:

.................2x.......................

N ----x+7------ O ---10---- P

Then you can easily see that

x+7 + 10 = 2x

17 = 2x - x

so x = 17

NP = 2x = 2*17 = 34

NO = x+7 = 17+7 = 24

OP = 10

NO + OP = 24 + 10 = 34 = NP

Answer:

270

Step-by-step explanation:

used formula LxWxH

Answer:

∠ C = 58°

Step-by-step explanation:

DB is a perpendicular bisector , so

∠ ADC = 2 × 32° = 64°

Since AD = CD then Δ ACD is isosceles with the base angle congruent , then

∠ C = \(\frac{180-64}{2}\) = \(\frac{116}{2}\) = 58°

Answer:b=30

Step-by-step explanation:

Alternate angles are the same so the angle opposite 30=125
125+30=155.but angles on a straight line=180
So we subtract 180-155 which leaves us with 25 for the top angle in the triangle.Angles in a triangle must add to 180 so we do, 125+25=150
180-150=30

The equation for the asymptote of the graphed function is x = 7

The asymptote is a endlessly tendency to a given value. A vertical one is a tendency to infinity.

Here we can see that there is a vertical asymoptote, notice that in one end the function tends to positive infinity and in the other it tends to negative infinity.

The equation of the line where the asymptote is, is:

x = 7

So that is the answer.

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Answer:

3 + 15n = 153

Step-by-step explanation:

More than = + (addition)

Product = x (multiplication)

Product of 15 and n = 15 x n = 15n

Therefore,

3 + 15n = 153.

Answer:

x=-7

Step-by-step explanation:

On squaring both sides of the equation, we will not get answer from the options. Rather, the resultant equation will be 6x² + 84 - 60x - 8✓3x = 0.

Let us square both the sides to find the desired equation.

(✓3x + 4)² = (1 + 3x - 11)²

Solving the Right Hand Side of the equation

(✓3x + 4)² = (3x - 10)²

So, on we have (a+b)² on Left Hand Side of the equation and (a-b)² on Right Hand Side of the equation. We know the expanded form to be used here is -

Left Hand Side = a² + b² + 2ab

Right Hand Side = a² + b² - 2ab

So, finding the square now -

(✓3x)² + 4² + 2×4×✓3x = 3x² + 10² - 2×3x×10

Solving both sides of the equation

3x² + 16 + 8✓3x = 9x² + 100 - 60x

Rewriting the equation

9x² - 3x² + 100 - 16 - 60x - 8✓3x = 0

6x² + 84 - 60x - 8✓3x = 0

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