If a fraction between 0 and 1 is multiplied by another fl fraction between 0 and 1, the product is greater than 1

Answer:

-6

Step-by-step explanation:

4a-3b

Plug in a b

4(-3)-3(-2)

-12+6=-6

Then the terminal point of 5pi/4 will be the pair of negatives of the terminal point od pi/4, it will be:

which is the option B in the list.

Winning the jackpot in a certain lottery requires you to pick two correct numbers between 1 and 59, and in a separate drawing, you also have a 7.32397915e-8 chance of winning when you also pick one correct number between 1 and 30.

A number of ways to select r items from n, nCr = n!/(r! x (n - r)!)

Number of possible methods to choose 4 winning numbers from 59 = 59C4

= 59!/(55! x 4!)

= 455,126

The number of possible ways to choose a single accurate number from 30 = 30.

The odds of winning the jackpot are 1/(probability) (Number of ways in which 4 winning numbers can be selected from 59 x Number of ways in which the correct single number can be selected from 30)

= 1/(455,126 x 30)

= 1/13653780

= \(7.32397915^{8}\)

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Answer:

Hello,

Answer: B   : y=(m-3)*(x+1)²3

Step-by-step explanation:

The parabola with vertex (-1,3)

is y=k(x+1)²+3

(0,m) is a point of the parabola:

m=k*(0+1)²+3 ==> k=m-3

So, y=(m-3)*(x+1)²+3 is the correct equation.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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The number written on the board will be negative 27. This can be solved by using the concept of algebra.

Algebra is the study of mathematical symbols, while logic is the manipulation of those symbols.

Let x be the number.

There is a number written on the board. One student increased the number by 23. Then the first number will be

⇒ x + 23

But another student decreased the same number by 1. Then the second number will be

⇒ x - 1

The first student's result was 7 times greater than the result of the second student.

7 first number = second number

or, 7(x + 23) = x - 1

or, 7x + 161 = x - 1

or, 6x = - 162

or, x = - 27

The number written on the board will be negative 27.

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25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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Answer:

The $52 jacket by 60(0.60) cents.

Step-by-step explanation:

To find how much percent off is each item. We would need to multiply 52 by 0.85 and 56 by 0.80. The work is below:

52*0.85=44.2

56*0.80=44.8

We can say that the $52 jacket costs less than the $56 jacket by a difference of 60(0.60) cents.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

(i) The smallest angular speeds that cause the toast to hit and then topple to be butter-side down 3.84 rad / s

(ii) The largest angular speeds that cause the toast to hit and then topple to be butter-side down 11.51 rad / 5

The distance from the counter to the floor, d = 82 cm = 0.82 m

Rotation is less than 1 rev.

The toast rotates at a constant angular speed as it falls, and the toast is falling with a constant acceleration (gravitational acceleration).

Using the kinematic equations of motion to calculate the time taken by the toast to hit the floor

\($d & =v_i t+\frac{1}{2} g t^2 \\\)

\($d & =0+\frac{1}{2} g t^2 \\\)

Therefore \($t & =\sqrt{\frac{2 d}{g}}=\sqrt{\frac{2 \times 0. 82}{9.8}\)

= 0.409 s

Where

\($v_i$\) is the initial speed of the toast, \($v_i=0$\) because the toast is falling from rest.

t the time that the toast takes to hit the floor.

g is the gravitational acceleration.

d is the distance between the counter and the floor.

Part (a)The toast is accidentally pushed over the edge of the counter with the butter side up, then the toast rotates as it falls. If the toast hits the ground and then topples to be butter-side down, it has to land on one of its edges. The smallest angle, in this case, is \($\frac{1}{4}$\) revolution and corresponds to the smallest angular speed

\($\omega_{\min } & =\frac{\Delta \theta}{\Delta t} \\\)

\($\omega_{\min } & =\frac{0.25 \mathrm{rev}}{\Delta t}=\frac{0.25 \times 2 \pi}{\Delta t} \\\)

Therefore \($ \omega_{\min } & =\frac{0.5 \pi}{0.409}\)

= 3.84 rad/s

Where

\($\omega_{\min }$\) is the minimum angular speed for the toast to land butter-side down. \($\Delta \theta$\) is the smallest angle for the toast to land butter-side down in radians.

\($\omega_{\min }$\) = 3.84 rad / s

Part b:

The toast is accidentally pushed over the edge of the counter with the butter side up, then the toast rotates as it falls. If the toast hits the ground and then topples to be butter-side down, it has to land on one of its edges. The largest angle, in this case, is \($\frac{3}{4}$\) revolution and corresponds to the largest angular speed

\($\omega_{\max } & =\frac{\Delta \theta}{\Delta t} \\\)

\($\omega_{\max } & =\frac{0.75 \mathrm{rev}}{\Delta t}=\frac{0.75 \times 2 \pi}{\Delta t} \\\)

Therefore \($ \omega_{\max } & =\frac{1.5 \pi}{0.409}\)

= 11.51 rad / s

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When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 82 cm and for rotation less than 1 rev, what are the (i) smallest and (ii) largest angular speeds that cause the toast to hit and then topple to be butter-side down?

Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

The nearest foot is 19

Answer:

2,240

Step-by-step explanation:

6% of 2,000 is 120 so times that by 2

Answer:

$240.00

Step-by-step explanation:

2000(.06)(2)=240

The number of years of employment is A. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

The system of equations given is:

x = 4y

x = 8 + 2y

You can solve the system by setting the two expressions for x equal to each other:

4y = 8 + 2y

2y = 8

2y / 2 = 8 / 2

y = 4

Substitute y = 4 into the first equation to solve for x:

x = 4 x 4

= 16

So, Mae (y) has been at the company for 4 years and Nikhil (x) has been at the company for 16 years.

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Answer:

AB = 10.398

Step-by-step explanation:

By cosine rule, we have:

AB² = AC² + BC² - 2(AC)(BC)cos(ACB)

⇒ AB² = 7² + 10² - 2(7)(10)cos(73)

⇒ AB² = 49 + 100 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140(0.292)

⇒ AB² = 149 - 40.88

⇒ AB² = 108.12

⇒ AB = √(108.12)

⇒ AB = 10.398

The expanded and simplified form of the expression (x + 5)(x - 1) is  x² - x + 5x - 5.

Given the expression in the question;

(x + 5)(x - 1)

To expand and simplify the expression (x+5)(x-1),

we use the distributive property:

(x + 5)(x - 1)

x(x - 1) + 5(x - 1)

Now we can simplify each term by using the distributive property again:

x(x - 1) = x² - x

5(x - 1) = 5x - 5

Putting these terms back together, we have:

(x+5)(x-1) = x² - x + 5x - 5

Combining like terms, we get:

(x+5)(x-1) = x² + 4x - 5

Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.

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=========================================================

Explanation:

The changes of this number are

The overall net change is -0.4+0.008+20 = 19.608

We'll be adding this net change to the original number

143.351 + 19.608 = 162.959

This value is exact and hasn't been rounded.

Answer:

20%

Step-by-step explanation:

The theoretical probability of drawing a red marble can be found by dividing the number of red marbles by the total number of marbles in the bag:

P(red) = number of red marbles / total number of marbles

P(red) = 5 / (5 + 8 + 12)

P(red) = 5 / 25

P(red) = 0.2

So the theoretical probability of randomly drawing a red marble is 20%, which corresponds to option (C).

The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get

A = x * (6-x)/2

A = 3x - x2/2

To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:

A' = 3 - x = 0

x = 3

So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:

y = (6 - 3)/2 = 3/2

So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

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Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Answer:

There were 89 retail stores in 1997.

Step-by-step explanation:

You know:

y =  11*x + 12

where y is the total number of stores and x is the number of years after 1990.

Being this a linear function (Linear functions are those functions that have the form y = mx + b as it happens in this case), to know the total number of stores and, then you must know the value of x, that is, the number of years after 1990, and replace that value in the given function.

To find out how many retail stores there were in 1997, then since 1990 7 years have passed, calculated by subtracting: 1997 - 1990 = 7

So, 7 is the number of years after 1990, then x=7

Replacing in the function y=11*x + 12 you get:

y=11*7+12

Solving:

y=77+12

y=89

There were 89 retail stores in 1997.

Yes she will be left with 0 grapes

Step-by-step explanation:

14-8=6 6-6=0

Answer:

5

Step-by-step explanation:

3(2x+1)=7x-2

6x + 3 = 7x - 2

6x - 7x = -2 - 3

-x = -5 /(-1)

x = 5

Answer:

5

Step-by-step explanation:

3 ( 2x + 1 ) = 7x - 2

Step 1 : Remove the parentheses

6x + 3 = 7x - 2

Step 2 : Move the variable to the left-hand side and move extra number the right-hand side

6x + 3 = 7x - 2

-7x  -3   -7x  -3

6x - 7x = -2 - 3

Step 3 : Combine like terms

-x = -5

Step 4 : Change the sign to make x positive

x = 5

SOLUTION : x = 5

Hope this helps :)

Answer:

please provide the diagram

Step-by-step explanation:

for the solution figure is necessary so provides us to solve this problem

Answer:

\(5.24\mathrm{cm}\)

Step-by-step explanation:

\(\mathrm{Solution:}\\\mathrm{Given:}\\\mathrm{Angle\ subtented\ by\ arc\ MT}(\theta)=100^o=\frac{5}{9}\pi^c\\\mathrm{Length\ of\ arc\ MT}(l)=?\\\mathrm{Radius\ of\ circle}(r)=3cm\\\mathrm{Now,}\\\mathrm{\theta=}\frac{l}{r}\\\mathrm{or,\ }l=\theta r=\frac{5}{9}\pi\times3=\frac{5}{3}\pi=5.24\mathrm{cm}\)

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer:

\(y=\displaystyle\frac{2}{3}x\)

Step-by-step explanation:

Hi there!

The given linear equations are organized in slope-intercept form: \(y=mx+b\) where m is the slope of the line and b is the y-intercept (the value of y when x=0)

First, we can determine the slope using the following formula:

\(m=\displaystyle\frac{y_2-y_1}{x_2-x_1}\) where two given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in any two points from the graph that falls on the line (you can see below that I've used (3,2) and (0,0):

\(m=\displaystyle\frac{2-0}{3-0}\\\\m=\displaystyle\frac{2}{3}\)

Therefore, the slope of the line is \(\displaystyle\frac{2}{3}\). Plug this into \(y=mx+b\) as m:

\(y=\displaystyle\frac{2}{3}x+b\)

We know that the point (0,0) falls on the line. Because y=0 when x=0, we know that the y-intercept (b) is 0:

\(y=\displaystyle\frac{2}{3}x+0\\\\y=\displaystyle\frac{2}{3}x\)

I hope this helps!

Let x and y represent the two numbers that add up to 24.

x + y = 24

=> y = 24 - x

The product of the two numbers is P = x*y = x*(24 - x) = 24x - x^2.

To maximize the product P, solve P' = 0 for x.

P' = 24 - 2x

24 - 2x = 0

=> x = 12

Also P'' = -2 which is negative

for x = 12

The product when x = 12 is 12*12 = 144

hope it helps!

Answer:

y > Two-thirds x + 1     /c