What is 8/15 simplyfied??

Answer: A, B, C, E

Step-by-step explanation:

Answer: B.180

Step-by-step explanation:

number of acres = 60

area required for one goat = 1/3 of an acre

number of goats one acre can hold =  3

number of goats her land can support = 60*3 = 180

Answer:

see explanation

Step-by-step explanation:

since both AB and CD are at right angles to AE then

AB and CD are parallel lines.

since AB and AE are at right angles to each other then

AB and AE are perpendicular lines

no LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

Answer:

log_20(35)= 1.5372435736805

Step-by-step explanation:

Applying the AA similarity theorem, the length of DF is: 15 units.

When two angles in one triangle are congruent to the corresponding two angles in another triangle, both are said to be similar to one another. This means that, the corresponding sides of these two triangles would be proportional or have the same ratio.

In the image attached bellow, triangle DEF and triangle DBC are similar to each other because they have two pairs of corresponding angles that are congruent which are:

<DFE ≅ <DCB [right angles are equal]

<EDF ≅ <BDC [reflexive property of congruence]

Therefore, their corresponding sides will have equal ratios such as:

DC/DF = BC/EF

Substitute:

27/DF = 49.5/27.5

Cross multiply:

DF = (27.5 * 27) / 49.5

DF = 15

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The value of the equation after the evaluation is 35

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

The distributive property is straightforward to recall. Numerous mathematical features allow us to make algebraic expressions as well as arithmetic calculations simpler.

Using the distributive property we can rewrite this expression as:

[tex]15(2\frac{1}{3} )= (15*2)+(15*\frac{1}{3} )[/tex]→[tex]30[/tex]→[tex]\frac{15}{3}[/tex]→[tex]30+5[/tex]→[tex]35[/tex]

Evaluating the equation:

[tex]15(2\frac{1}{3} )=15*(\frac{7}{3} )=35[/tex]

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The percent decrease in the number of people who went to the pool over these four weeks is 30%.

From the information given, in the the first week of July, a record 1060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 348 fewer people went to the pool than in the third week

The total number of people at the end of the week will be:

= 1060 - 100 + 130 - 348

= 742

The percentage decrease will be:

Decrease / Original value × 100

= (1060 - 742) / 1060 × 100

= 30%

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it takes 2.25 seconds

oh, and it's 18 seconds for the next question assuming we had the same test.

Answer: 73.74

Step-by-step explanation: I just used a calculator. I hope it's right. Check me if I'm wrong.

Function f'(X) is increasing for x< - 1.260   because f ′(x) > 0 for x < −1.260

Describe function using an example?

A unique relationship where each input only has one output. Where x is the input value, it is frequently expressed as function "f(x)".

                             Example: "f of x equals x divided by 2" (f(x) = x/2). This expression is a function because each input "x" has a single output "x/2": • f(2) = 1.

Given,

              f'(X) = 2x² + 4/x

              f'(x) =  2x³ + 4/x

So, here f'(X) is positive for x< 1.260 .

f'(X) is increasing for x< - 1.260   because f ′(x) > 0 for x < −1.260

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Answer:

the rate of change is 3x(slope)

Answer:

where is your circle graph

Step-by-step explanation:

i need the graph in order to solve this

Since, there are 08 students in the class, among 02 of  them should be selected as the best students in the class. In 28 different ways this can be done.

Use the formula of combinations given as ⁿ[tex]C_{r}[/tex] to find the numbers of possible ways to select r things out of a total of n things. Let n be the total number of students in the class and r as the number of students required to be selected as best students in the class. Now, use the formula

ⁿ[tex]C_{r}[/tex] = [tex]\frac{r!}{(n- r)!}[/tex] to simplify the expression .

Given that a class has 8 students in which 2 students will be selected for a best students in the class. .

Therefore, n = 08 and r = 02, substituting these values in the formula we get,

Number of possible ways of selection = ⁿ [tex]C_{r}[/tex] = ⁸C₂

Now,

Number of possible ways of selection = [tex]\frac{8!}{2! ( 8 - 2)!}[/tex]

Or, Number of possible ways of selection = [tex]\frac{8!}{2! 6!}[/tex]

Solving further,

Number of possible ways of selection = 8 × 7× 6!/ 2× 1 ×6!

Number of possible ways of selection = 4 × 7 = 28

Hence, the total number of ways to select the required number of students is 28.

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Answer:

Step-by-step explanation:

Are you after a solution for y?

quotient of y and 3 is a fancy word for division

y/3+9=10

To solve for y subtract 9 from both sides

y/3+9-9=10-9

y/3=1

To solve for y

multiply both sides by 3

3(y/3)=1*3

y=3

Answer:

[tex]y = \frac{1}{10}x[/tex]

Step-by-step explanation:

⭐ What is slope-intercept form?

First, we need to find the value of "m" using the slope formula.

⭐ What is the slope formula?

Substitute the two coordinates you are given into the slope formula.

[tex]m = \frac{1-2}{10-20}[/tex]

[tex]m = \frac{-1}{-10}[/tex]

[tex]m = \frac{1}{10}[/tex]

Substitute the value of "m" into the slope-intercept form equation.

[tex]y = \frac{1}{10}x + b[/tex]

Next, we need to find the value of "b". To do so, substitute a coordinate that you are given into the equation and solve for "b".

I am going to use (10,1), but you can also use (20,2).

[tex]1 = \frac{1}{10} (10) + b[/tex]

[tex]1 = 1 + b[/tex]

[tex]0 = b[/tex]

Substitute the value of "b" into the slope-intercept form equation.

[tex]y = \frac{1}{10}x[/tex]

Step-by-step explanation:

as percent means per 100

So we can say 0.54 or 54100 is the same as 54%.

hope understand

The probability of drawing three aces in a row without replacement is  0.00018 from a deck of 52 cards.

We know that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.

We are given that cards are drawn without replacement, it means counts of cards after drawing a single card will change.

We know very well that in a deck of 52 cards, count of aces is 4.

So,probability of drawing a single ace from 52 cards is =4/52.

Now,after drawing a single ace total number of cards reduce to 51 and number of aces counts reduce to 3

So, probability of drawing a single ace from 51 cards = 3/51

Similarly probability of drawing of single ace from 50 cards is =2/50

So, total probability of drawing of three aces is =(4/52) × (3/51) × (2/50)

or P(E)=(1/13) × (1/17) × (1/25) =1 / 5525 =0.00018

Hence, required probability is 0.00018 .

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Answer: 7x-2=10x+x+6x

Step-by-step explanation:

sub in and solve

or solve the equation

7x-2=17x

10x=-2

x=-2/10

x=-1/5

7x-2=10x+x+6x is true

Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.

What is independent events?

Winning a hockey game and scoring a goal is dependent because if we score a goal then only we can win the game.

Hence, Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.

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1. The equation of the straight line is y = -x -1.

2. The equation of the point-gradient form is 3x -y - 10.

3. The equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.

What is a straight line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things. In daily language, a line segment with two points designating its endpoints is also referred to as a "line."

Here, we have

1. The slope-intercept form of the equation of a line is:

y = mx + b

We are fortunate to be given the y-intercept, the point(0,-1) therefore, the value, b, in the slope-intercept form is -1:

y = mx - 1

Substitute the other point(-1,0) into the equation and then solve for the value of m:

0 = -m - 1

m = -1

y = -x -1

Hence, the equation of the straight line is y = -x -1.

2. We know that the equation of a line passing through the point (x₀, y₀  ) whose slope is m is (y -  y₀) = m(x -x₀)

The equation of a line passing through the point(2,-4) and the slope is 3.

(y+4) = 3(x-2)

y + 4 = 3x - 6

3x -y - 10

Hence, the equation of the point-gradient form is 3x -y - 10.

3. Consider the given equation: y = x-2

Since, the line is parallel to given line. so slope will be same.

slope = 1

We know that the second line will also have a slope of 1, and we are given the point (0,1). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

1 = b

Now, we put the value of b in the equation and we get

y = x + 1

Hence, the equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.

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Answer: 8 + i

Step-by-step explanation:

The complex number 8/1+i can be written in standard form as 8 + i. In standard form, a complex number is written as a+bi, where a is the real part and bi is the imaginary part. In this case, the real part is 8 and the imaginary part is i. Therefore, the standard form of the complex number 8/1+i is 8 + i.

Answer: 4-4i

Step-by-step explanation:

[tex]\displaystyle\\\frac{8}{1+i} =\\\\\frac{8(1-i)}{(1+i)(1-i)}=\\\\\frac{8(1-i)}{1^2-i^2} =\\\\\frac{8(1-i)}{1-(\sqrt{-1})^2 }=\\\\\frac{8(1-i)}{1-(-1)}=\\\\\frac{8(1-i)}{1+1} =\\\\\frac{8(1-i)}{2} =\\\\4(1-i)=\\\\4-4i[/tex]

Option A is correct.

For testing, if x is a significant predictor of y in simple linear regression, we need to determine if the slope is significantly different from zero.

What is linear regression?

A statistical technique known as linear regression is used to represent the connection between a scalar answer and one or more explanatory factors. When there is just one explanatory variable, simple linear regression is employed; when there are numerous explanatory variables, multiple linear regression is utilized.

Based on the value of another variable, linear regression analysis makes predictions about the value of the first variable. The dependent variable is the one you're trying to forecast. The independent variable is the one you are utilizing to make a prediction about the value of the other variable.

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Therefore the answer to when math classroom of 30. the students affected by the disease is modeled by the logistic function is first case : 6 , second case : 15.68  and third case : 5.18

A function is a particular relation that transfers every element in set A to exactly one element in set B. There cannot be an empty set in either A or B. For a specific input, a function defines a specific output.

Here ,

Given:

P(t) =  [tex]\frac{180}{5 + 25e^{-0.45t} }[/tex]

First case :how many students understand exponential functions initially is

Where t is number of days

t=0

P(0)= [tex]\frac{180}{5 + 25e^{-0.45(0)} }[/tex]

P(0)=180/(25+5)

P(0)=6

Second case: how many students will understand exponential functions after 3 days

t=3

P(3)=[tex]\frac{180}{5 + 25e^{-0.45(3)} }[/tex]

P(3) ≈ 15.68

Third case: how many days will it take for 24 students to understand exponential functions

t=24

P(24)=[tex]\frac{180}{5 + 25e^{-0.45(24)} }[/tex]

P(24)  ≈ 5.18

Therefore the answer to when math classroom of 30. the students affected by the disease is modeled by the logistic function is first case : 6 , second case : 15.68  and third case : 5.18

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Based on the line of best fit that models the data points, the y-value when x = 24 is equal to 20.

In order to determine a linear equation for the line of best fit that models the data points described above, we would have to calculate the slope of the trend line.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided, we have the following points:

Points on x-axis = (4, 8).

Points on y-axis = (5, 8).

Substituting the given points into the formula, we have;

Slope, m = (8 - 5)/(8 - 4)

Slope, m = 3/4

Slope, m = 0.75

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + c

Where:

Note: The y-intercept is equal to 2 based on the ordered pair (0, 2).

A linear equation for the line of best fit in slope-intercept form is given by:

y = 0.75x + 2

When x = 24, the value of y is;

y = 0.75(24) + 2

y = 18 + 2

y = 20.

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The value of the definite integral is [tex]\frac{\pi }{4} - \frac{1}{2}[/tex]

Using microscopic slivers or stripes of the region, a definite integral is a formal estimate of the area beneath a function. Integrals can reflect a region's (signed) area, the total value of a function that changes over time, or the amount of a given thing given its density.

Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.

Given,

[tex]\int\limits^\frac{1}{2} _0 {\frac{\sqrt{x} }{\sqrt{1-x} } } \, dx = \int\limits^\frac{\pi }{4} _0 {2sin^{2}y } \, dy[/tex]

[tex]\int\limits^\frac{1}{2} _0 {\frac{\sqrt{x} }{\sqrt{1-x} } } \, dx = \frac{\pi }{4} - \frac{1}{2}[/tex]

[tex]\int\limits^\frac{\pi }{4} _0 {2sin^{2}y } \, dy = \frac{\pi }{4} -\frac{1}{2}[/tex]

∴[tex]\frac{\pi }{4} - \frac{1}{2}[/tex] = [tex](\frac{\pi }{4} - \frac{1}{2})[/tex]

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Answer:

/x/=3 then x value has 3 and -3

Answer:

The required equation has only two solution x = 3 and x = -3 is x2 -9

Step-by-step explanation:

At a = √25/π^2 - 0.04 revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

In the given question, we have to find how many revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

r = acosti + asintj + 0.2tk, length = 10 unit

So |r| = [tex]\int^{2\pi}_{0}\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt[/tex]

From the given equation,

x = acost, y = asint, z = 0.2t

dx/dt = -asint, dy/dt = acost, dz/dt = 0.2

10 = [tex]\int^{2\pi}_{0}\sqrt{(-a\sin t)^2+(a\cos t)^2+(0.2)^2}dt[/tex]

10 = [tex]\int^{2\pi}_{0}\sqrt{a^2\sin^2 t+a^2\cos^2t+0.04}dt[/tex]

As we know that sin^2x+cos^2x = 1. So

10 = [tex]\int^{2\pi}_{0}\sqrt{a^2+0.04}dt[/tex]

10 = [tex]\sqrt{a^2+0.04}\int^{2\pi}_{0}dt[/tex]

10 = [tex]\sqrt{a^2+0.04}\cdot[t]^{2\pi}_{0}[/tex]

10 = √(a^2+0.04)∙[2π-0]

2π√(a^2+0.04) = 10

Divide by 2π on both side, we get

√(a^2+0.04) = 5/π

Taking square on both side, we get

a^2+0.04 = 25/π^2

Subtract 0.04 on both side, we get

a^2 = 25/π^2 - 0.04

taking square root on both side, we get

a = √25/π^2 - 0.04

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The right question is:

How many revolutions will the circular helix

r = acosti + asintj + 0.2tk

make in a distance of 10 units measured along the z-axis?

Answer:

80+60+3x+4=180

140+3x+4=180

144+3x=180

3x=180-144

3x=36

x=12

Answer:

x = 12

Step-by-step explanation:

All triangles equal to 180 degrees so, we can set up this expression:

180 = (3x + 4) + 80 + 60

All we have to do is solve:

180 = (3x + 4) + 80 + 60

180 = 3x + 4 + 140

180 = 3x + 144

-144        -144

36 = 3x

/3     /3

12 = x

The numbers are 10 and 10. And the sum of their squares will be 200.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

The sum of the two numbers is 20.

Let the first number be 'x'. Then the other number is (20 - x). Then the equation is given as,

y = x² + (20 - x)²

Differentiate the function, then we have

y' = 0

2x + 2(20 - x)(-1) = 0

x - 20 + x = 0

2x = 20

x = 10

Then the other number is given as,

⇒ 20 - 10

⇒ 10

The sum of their squares is given as,

⇒ 10² + 10²

⇒ 100 + 100

⇒ 200

The numbers are 10 and 10. And the sum of their squares will be 200.

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