What are the step to the Quadratic Formula?

The logarithmic form of  13² = 169 is ㏒₁₃ 169 = 2

Using the logarithmic rule , we have that

㏒ₙn = bⁿ

Given 13² = 169

It is important to  note that it can be written either in the logarithmic form or in the index form.

In this case, we have written in the index form as .

㏒₁₃ 169 = 2

Thus, the logarithmic form of  13² = 169 is ㏒₁₃ 169 = 2

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Answer:

you have to add at least one of the animals price in order for it to be solved

Step-by-step explanation:

By using the formula of perimeter of rectangle, it can be calculated that

Length of the fencing required = 2274 feet

What is perimeter of a rectangle?

Perimeter of a rectangle is the length of the boundary of the rectangle.

If the length of the rectangle is l and breadth of the rectangle is b, then perimeter of a rectangle is 2(l + b)

Length of the parking lot = 752 feet

Breadth of the parking lot = 385 feet

Perimeter of the parking lot = 2(752 + 385) feet

                                              = 2 \(\times\) 1137 feet

                                              = 2274 feet

Length of the fencing required = 2274 feet

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Answer:

8

Step-by-step explanation:

(2 + x) (10) = 36 + 8x

20 + 10x = 36 + 8x

10x - 8x = 36 - 20

2x = 16

x = 8

The value of the middle of the three is 25.

Let x be the first odd integer, then the next two consecutive odd integers are x+2 and x+4. The sum of these three consecutive odd integers is given as 75, so we can write the equation:

x + (x+2) + (x+4) = 75

Simplifying the left side of this equation gives:

3x + 6 = 75

Subtracting 6 from both sides gives:

3x = 69

Dividing by 3 gives:

x = 23

So the first odd integer is 23, and the next two consecutive odd integers are 25 and 27. The middle of these three is the second consecutive odd integer, which is 25. Therefore, the value of the middle of the three is 25.

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Answer: Read below!

Step-by-step explanation:

You would want to start off by dividing 75 by 1,400. That will get you your answer.

Answer:

I got a, so sorry if I'm wrong. math isnt my strongest subject. if I am right please mark brainliest

The independent variable of interest in an ANOVA procedure is called a factor. Hence (d).

The independent variable of interest in an ANOVA procedure is referred to as the factor. The factor represents the different categories or levels being compared to assess their impact on a dependent variable. It is the variable that is manipulated or controlled by the researcher to determine its effect on the outcome. In the context of ANOVA, the factor is typically a categorical variable that divides the data into distinct groups or treatments. These groups are compared to evaluate if there are statistically significant differences in the means of the dependent variable across the different levels of the factor. Therefore, the correct answer is factor(d).

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The equation of the circle is (x + 3)² + (y + 5)² = 34.

To write the equation of a circle, we need the coordinates of its center and the radius. Given that the center of the circle is (-3, -5) and it passes through the point (0, 0), we can find the radius by calculating the distance between these two points.

Using the distance formula, the radius can be found as follows:

radius = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-5 - 0)²]

= √[9 + 25]

= √34

Now that we have the center (-3, -5) and the radius √34, we can write the equation of the circle in the standard form (x - h)² + (y - k)² = r², where (h, k) represents the center and r represents the radius.

Substituting the values, the equation of the circle becomes:

(x + 3)² + (y + 5)² = 34

This equation represents a circle with its center at (-3, -5) and a radius of √34, which passes through the point (0, 0).

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Answer:724

Step-by-step explanation: Let us go through trail and error method.

Question: Need to find N, so that 2020+ N should be a perfect cube, as well as a multiple of 56.

2744 is the first number we get after 2020 and it is a cube of 14. ___ equation -01

Let us divide, 2744 with 56.

i.e., 2744/56= 49. ___ equation -02

As per 1st and 2nd equation 2744 meets with the condition. And we can consider it as 2020+ N.

i.e., 2020+N= 2744

N= 2744-2020

Therefore; N= 724.

Answer:

724,

Step-by-step explanation:

14^3 = 2744 is the next perfect cube > 2020.

2744 / 56 = 49.

So that fits the requirements in the question.

So N = 2744 - 2020

= 724,

Answer:

The Probability is 63.7%

Step-by-step explanation:

We need to calculate the area of the circle and the area of the square

From the question, we can see that the square is of side 4 √2 cm

The area of the square is simply the square of its side length

We have this as 4√2 * 4√2 = 16 * 2 = 32 cm^2

The area of the circle can be calculated using the formula for the area of a circle, with the radius being 4 cm

So, we have the area of the circle as;

Pi * r^2

= 22/7 * 4 * 4 = 50.3 cm^2

so, to find the probability, we need to divide the area of the circle by the area of the square

we have this as;

32/50.3 = 0.6366

In percentage, we simply multiply by 100% to give

0.6366 * 100% = 63.66%

To the nearest tenth, this is 63.7%

Answer:

13/20 of a mile

Step-by-step explanation:

2/5 x 4 = 8/20

1/4 x 5 = 5/20

8/20 + 5/20 = 13/20

Step-by-step explanation:

a)

Fill in the table:

b)

The score of 4 is obtained in 2 cases out of 12 as per above table.

The probability is:

c)

The score of 10 is obtained once in 12 cases as per table.

The probability is:

Out of 60 times he can score 10:

Answer:

1) 45

2) 52

3) 48

4) 121

5) (30÷100)×50= 15

6) 60= (20÷100)×(x)

x= 60÷ (20÷100)= 300

7) 0.375

8) 37.5%

9) 0.45

10) 9/20

Hope this helps!!

the answers are in the picture

The tangent line can be represented by any of the equivalent forms of the equation above. Therefore, the correct answer is a) x = 1 + 3t, y = 1 + 10t, z = 1 + 12t.

The tangent line to a curve at a specific point can be found by taking the derivative of the parametric equations and evaluating it at the given point. Let's find the derivative of the given parametric equations:

x = 3t

y = 5t²

z = 4t³

Taking the derivative with respect to t:

dx/dt = 3

dy/dt = 10t

dz/dt = 12t²

Now, we can evaluate these derivatives at t = 1, since that's the point at which we want to find the tangent line:

dx/dt = 3

dy/dt = 10(1) = 10

dz/dt = 12(1)² = 12

So, the direction vector of the tangent line is given by (3, 10, 12). Now, we need a point on the curve to determine the equation of the line. Using the given parametric equations, when t = 1, we have:

x = 3(1) = 3

y = 5(1)² = 5

z = 4(1)³ = 4

Therefore, the point on the curve is (3, 5, 4). We can use the point-direction form of a line to obtain the equation of the tangent line:

(x - x0)/a = (y - y0)/b = (z - z0)/c

where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector. Substituting the values:

(x - 3)/3 = (y - 5)/10 = (z - 4)/12

Multiplying both sides by 3:

x - 3 = (3/10)(y - 5) = (3/12)(z - 4)

Simplifying:

10x - 30 = 3(y - 5) = (5/2)(z - 4)

The tangent line can be represented by any of the equivalent forms of the equation above. Therefore, the correct answer is a) x = 1 + 3t, y = 1 + 10t, z = 1 + 12t.

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Complete Question:

Find parametric equations for the tangent line to the curve with parametric equations x = 3t, y = 5t², z = 4t³ at the point with t = 1.

a.  x = 1 + 3t, y = 1 + 10t, z = 1 + 12t

b. x = 3 + 3t, y = 5 + 10t, z = 4 + 12t

c. x = 1 + 3t, y = 1 + 5t, z = 1 + 4t

d.  x = 3 + 3t, y = 5 + 5t, z = 4 + 4t

\(-13x+8=-8x-7\\\\8=5x-7\\\\15=5x\\\\3=x\)

the value of x is 3.

Answer: X=3

Step-by-step explanation:

Answer:

3<n+5

Step-by-step explanation:

...................

Answer:

n+5-3

Step-by-step explanation:

"Less then" means subtraction and it is less than a number (marked as "n" in this example) plus 5 (+5). If you translate this into an equation, you would get n+5-3.

Monetarists believe that velocity changes in a predictable way, and they also believe that aggregate supply depends on the money supply and velocity.

Monetarists, who follow the economic theories of monetarism, hold several key beliefs about the relationship between money and the economy. Firstly, they argue that velocity, which represents the speed at which money circulates in the economy, changes in a predictable manner. Monetarists believe that changes in the money supply and velocity directly affect economic output and price levels.

Secondly, monetarists assert that aggregate supply, which represents the total quantity of goods and services produced in an economy, depends on both the money supply and velocity. According to this viewpoint, changes in the money supply and velocity can impact the productive capacity of an economy, leading to shifts in aggregate supply.

Lastly, monetarists contend that the short-run aggregate supply (SRAS) curve is upward sloping. This means that in the short run, an increase in the price level will result in a higher level of output supplied by firms. Monetarists argue that this relationship is influenced by the behavior of firms and workers, who adjust their production and wage expectations based on changes in the price level.

In summary, monetarists believe that velocity changes in a predictable manner, and they argue that both the money supply and velocity affect aggregate supply. They also assert that the short-run aggregate supply curve is upward sloping, implying that price level changes can impact output levels in the short term.

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The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

(a) Mean The mean (or average) of a dataset is calculated by summing up all the values and dividing by the total number of values.

The formula for calculating the mean is: `mean = (sum of values) / (total number of values)`For the given dataset, we have:20, 50, 22, 14, 23, 10

Sum of values = 20 + 50 + 22 + 14 + 23 + 10 = 139

Total number of values = 6Therefore, the mean is given by: `mean = 139 / 6 = 23.17`Answer: 23.17 (rounded to two decimal places)

(b) Median To find the median, we need to arrange the dataset in increasing order:10, 14, 20, 22, 23, 50The median is the middle value of the dataset. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values. Here, we have 6 values, so the median is the average of the two middle values: `median = (20 + 22) / 2 = 21` Answer: 21(e)

Sample variance s²The sample variance is calculated by finding the mean of the squared differences between each value and the mean of the dataset.

The formula for calculating the sample variance is: `s² = ∑(x - mean)² / (n - 1)`where `∑` means "sum of", `x` is each individual value in the dataset, `mean` is the mean of the dataset, and `n` is the total number of values.For the given dataset, we have already calculated the mean to be 23.17.

Now, we need to calculate the squared differences between each value and the mean:

20 - 23.17 = -3.1722 - 23.17

= -1.170 - 23.17

= -13 - 23.17

= -9.1723 - 23.17

= -0.1710 - 23.17

= -13.17

The sum of the squared differences is given by:

∑(x - mean)² = (-3.17)² + (-1.17)² + (-13.17)² + (-9.17)² + (-0.17)² + (-13.17)²

= 867.7959

Therefore, the sample variance is given by: `s² = 867.7959 / (6 - 1) = 173.5592`Answer: 173.5592 (rounded to four decimal places)

The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

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Answer:

8.1

Step-by-step explanation:

8.1 is the highest as you would look at the first number before the decimal and is the highest in this equation.

Answer:

the answer is 8.1 to 8 1/2 to 8 7/8

Maximum = n/n+1 and Minimum = 1/n+1

What is the uniform distribution?

Probability distributions with uniform distributions have outcomes that are all equitably likely. Results are discrete and have the same probability in a discrete uniform distribution. Results are continuous and infinite in a continuous uniform distribution. Data near the mean occur more frequently in a normal distribution.

Here, we have

Given: X1, X2,..., Xn is independent and identically distributed random variables having uniform distributions over (0,1).

a) Z = max{X₁, X₂....Xₙ}

Since Z is maximum so it is greater than X1, X2...Xn so cdf of Z will be

F(Z) = P(Z≤z) = P(X₁, X₂....Xₙ≤z) = P(X₁≤z, X₂≤z.....Xₙ≤z)

= P(X₁≤z)P(X₂≤z)....P(Xₙ≤z) = Fₓ(z)Fₓ(z).....Fₓ(z)

F(Z) = zⁿ

So pdf of Z is

F(z) = F'(z) = nzⁿ⁻¹

Expectation of Z is

F(Z) = \(\int\limits^0_1 {zf_Z(z)} \, dz\) = \(n\int\limits^0_1 {} \,\)zⁿdz

= n[zⁿ⁺¹/n+1]₀¹ = n/n+1

b) Let Y = min{X₁, X₂....Xₙ}

Since Y is the minimum so it is less than X1, X2...Xn so the cdf of Y will be

F(Y) = P(Y≤y) = 1 - P(Y>y) = 1- P(X₁, X₂....Xₙ≤z) = 1- P(X₁≤z, X₂≤z.....Xₙ>y)

= 1- P(X₁>y)P(X₂>y)....P(Xₙ>y) = 1- Fₓ(y)Fₓ(y).....Fₓ(y)

= 1 - [1-y]ⁿ

So pdf of Y is

F(y) = F'(y) = n[1-y]ⁿ⁻¹

The expectation of Y is

E(Y) = \(\int\limits^0_1 {yf_Y(y)} \, dy\) = ∫₀¹ yn(1-y)ⁿ⁻¹dy = 1/n+1

Hence, Maximum = n/n+1 and Minimum = 1/n+1

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The derivative of f(x) = | -x³ + 4 | is f'(x) = (-3x²) * (d/dx|-x³ + 4|).

To find the derivative of the function f(x) = | -x³ + 4 |, we will first need to examine the expression inside the absolute value function and then use the chain rule.



1. Identify the inner function: g(x) = -x³ + 4
2. Find its derivative: g'(x) = -3x²
3. Determine the sign of g(x) to know how to differentiate the absolute value:
  - If g(x) > 0, the derivative of |g(x)| is g'(x).
  - If g(x) < 0, the derivative of |g(x)| is -g'(x).
  - If g(x) = 0, the derivative is undefined.

4. Apply the chain rule to find the derivative of the function: f'(x) = (d/dx |g(x)|) * g'(x)

Hence, the derivative of f(x) = | -x³ + 4 | is f'(x) = (-3x²) * (d/dx | -x³ + 4 |) in an unsimplified form. Further simplification requires knowing the sign of g(x).

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The formula relating the monetary multiplier and the reserve ratio shows that as the monetary multiplier increases, the reserve ratio decreases. If the monetary multiplier is 6, the reserve ratio must be 0.167.

To determine the reserve ratio given the monetary multiplier, we can use the formula:

Monetary Multiplier = 1 / Reserve Ratio

Given that the monetary multiplier is 6, we can substitute this value into the formula:

6 = 1 / Reserve Ratio

To isolate the reserve ratio, we can take the reciprocal of both sides of the equation:

1 / 6 = 1 / (1 / Reserve Ratio)

1 / 6 = Reserve Ratio

Therefore, the reserve ratio must be 1/6 or approximately 0.167.

Among the given options, b) 0.167 represents the correct answer.

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The expression  x²-6x+9 is equal to the expression (x-3)², option A is correct.

The given expression is x²-6x+9

x is the variable in the expression

Plus and minus are the operators

We have to factor the expression

x²-6x+9

x²-3x-3x+9

x(x-3)-3(x-3)

(x-3)(x-3)

x²-6x+9 is equal to (x-3)²

(x-3)²

Hence, the expression  x²-6x+9 is equal to the expression (x-3)², option A is correct.

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Answer:

14

Step-by-step explanation:

count the amount of squares inside the shape.

The area of this polygon is 14 units on a coordinate plane.

Area of rectangle is defined as product of the length and width.

Length of large rectangle = 5 units

width of large rectangle = 4 units

Length of small rectangle = 3 units

width of small rectangle = 1 unit

Required area of polygon = large rectangle - 2 × small rectangles

Required area of polygon = 5×4 - 2×(3×1)

Required area of polygon = 20-6

Required area of polygon = 14 units

Hnece, the area of this polygon is 14 units on a coordinate plane.

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The number of people attending affects how much food is prepared for a catered event. The number of people attending is the explanatory variable in this scenario.

One kind of independent variable is an explanatory variable. Both words are frequently used interchangeably. This is the variable that changes as we change it or watch it change. In other words, it is a factor that a researcher has changed in an experiment.

In the given situation, the number of people attending is an explanatory variable and the amount of food prepared is a dependent variable. As the number of people attending increases, the amount of food prepared also increases. This means the effect of one variable alters the effect of another variable. The change of one variable is called an independent variable while the change that occurs because of the independent variable is a dependent variable.

Therefore, the required answer is the number of people attending.

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The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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