Simplify the ratio 15:9:6

Answer:

Step-by-step explanation:

15/27 - 5/9

5:9

5 to 9 ratio

Answer:

Step-by-step explanation:

It’s is a because if you divide 4.41 divide by 3 you will get 1.47

Step-by-step explanation:

1 yard = 3 feet

So 3 yards = 9 feet

$4.41 / 9 feet = $0.49 per foot

$1.05 / 3 feet = $0.35 per foot

The second one is cheaper, so that's the better buy.

Answer:

151

Step-by-step explanation:

because 225-74 =151

151 books

There are 225 books, and 74 have already been placed on the shelf. Subtract 225 minus 74 to find that Ivan needs to place 151 more books on the shelf.

Answer:

135 degrees

Step-by-step explanation:

Coterminal means it ends at the same spot around the circle.

To calculate the resulting angle we need to reduce/increase the started value to arrive to a value between 0 and 359 degrees.  

If the starting angle is greater or equal to 360, we subtract 360 until we get below 360.

If the starting angle is below 0, we add 360 until we get equal or greater than 0.

So, starting with 495, we subtract 360 a first time....

A = 495 - 360 = 135

We're already in the desired range (0-359)... so we have our answer.

the length of DE is 9/2 units and m<CAB is 45

The measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.

A triangle is a polygon with three angles and sides.

Given that, a right triangle ABC, right-angled at B,  

Here D and E are midpoints of AB and BC, and also AB = AC, CB = 9 units.

We need to find the measurements of DE and angle CAB in the given triangle ABC,

Since, the two sides are equal in the triangle then it is a right-isosceles triangle,

In a right-isosceles triangle, the two acutes angles are measured 45°

Therefore, ∠ CAB = ∠ ACB = 45°

Hence, ∠ CAB = 45°

Now, using the midpoint theorem, we will get. CB = 2DE

Therefore,

9 = 2DE

DE = 4.5 units

Hence, the measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.

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Answer:

2. The correct answer option is 25%.

3. The experimental probability is 3% greater than the theoretical probability.

Step-by-step explanation:

2. We are given that a number cube is rolled 20 times out of which 5 times it lands on the number 2.

We are to find the experimental probability of getting the number 2.

P (2) = [tex]\frac{5}{20} \times 100 =\frac{1}{4} \times 100[/tex] = 25%

3. The theoretical Outcomes are: HH HT TH TT

So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%

Total number of outcomes = [tex]28+22+34+16[/tex] = 100

So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%

Therefore, the experimental probability is 3% greater than the theoretical probability.

For this case we have that the total of the balls is 86. We know there are 8 footballs then:

Basketball: Two more than twice the number of footballs are basketballs, that is:

[tex]2 + 2 (8) = 2 + 16 = 18[/tex]

There are 18 Basketballs.

Baseballs: Four less than 5 times the number of footballs are baseballs, that is:

[tex]5 (8) -4 = 40-4 = 36[/tex]

There are 36 Baseballs.

Softballs: Six more than half of baseballs are softballs. That is to say:

[tex]6+ \frac {36} {2} = 6 + 18 = 24[/tex]

There are 24 Softballs

If we add we must get 86.

[tex]8 + 18 + 36 + 24 = 86[/tex]

ANswer:

There are 8 Footballs

There are 18 Basketballs.

There are 36 Baseballs.

There are 24 Softballs

Answer:

Step-by-step explanation:

The sum of the two shorter sides must be greater than the longest side.

5 + 8 = 13

13 is not greater than 14, so the three segments cannot form a triangle.

Answer: No

Step-by-step explanation:

A triangle can be formed only if the sum of 2 sides of the triangle is bigger than the length of the third side of this triangle.

In this case we have AB = 5, BC = 8 and AC = 14.

AB + AC > BC → 5 + 14 > 8 →1 9 > 8 ok!

AB + BC > AC → 5 + 8 > 14 → 13 > 14 false!

BC + AC > AB → 8 + 14 > 5 → 22 > 8 ok!

As we have that AB + BC > AC FALSE, this segments cannot form a triangle.

Answer: 500 dollars

You just plug in 100 to the x’s in the equation

The company's profit be if 100 games are sold is $41100

The profit function is given as:

[tex]p(x) = -0.3x^2 + 45x - 1000[/tex]

When the number of games is 100, it means that

x = 100

So, we substitute 100 for x in the profit function

[tex]p(x) = -0.3x^2 + 45x - 1000[/tex] becomes

[tex]p(100) = -0.3(100)^2 + 45(100) - 1000[/tex]

Evaluate the exponents

[tex]p(100) = -0.3(10000) + 45(100) - 1000[/tex]

Open all brackets

[tex]p(100) = -3000 + 45100 - 1000[/tex]

Evaluate like terms

[tex]p(100) = 41100[/tex]

Hence, the company's profit be if 100 games are sold is $41100

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Answer:

11 units

Step-by-step explanation:

Since ∆ABC is isosceles, it means that at least two sides are congruent/equal in length.

Sides CA and AB are congruent, since BC is the base. So, CA = 4.

That means the perimeter is 4 + 4 + 3 = 11 un

Answer:

13 min 40 sec

Step-by-step explanation:

656 copies *(1 min/48 copies)= 656 /48 min = 13  32/48 min = 13 2/3 min

2/3 min = 2/3 min * 60 sec/1 min = 40 sec

13 2/3 min = 13 min 40 sec

For this case we have that by definition, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees.

Now, according to the figure we have that from V to S there are 180 degrees, like this:

[tex]5x + 25x + 30 = 180[/tex]

We add similar terms:

[tex]30x + 30 = 180[/tex]

Subtracting 30 from both sides of the equation:

[tex]30x = 150[/tex]

Divide by 30 on both sides of the equation:

[tex]x = \frac {150} {30}\\x = 5[/tex]

Answer:

[tex]x = 5[/tex]

Answer:

The t-shirt cost $23.33.

Step-by-step explanation:

Answer:

$140

Step-by-step explanation:

If x was the amount of money Mr. Green had remaining, and y was the amount of money Mrs. Green had remaining, then:

x / y = 3 / 2

And, since they spent the same amount of money:

200 - x = 180 - y

We can solve this system of equations through substitution.

x = 3/2 y

200 - 3/2 y = 180 - y

20 = 1/2 y

y = 40

So Mrs. Green had $40 remaining.  Since she started with $180, she must have spent $140.  So that was the cost of the shirt.  Let's check our answer by seeing how much Mr. Green had remaining and how it compares.

$200 - $140 = $60

$60 / $40 = 3 / 2

Yep, it checks out.

The answer is:

The piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]

To find the correct option, we need to look for the piecewise function that contains the following functioncs existing in the determined domains (inputs).

From the graph, we know that we need the following functions:

- A horizontal line, which exists from -∞ to -1, givind as input 8.

The function will be:

[tex]y=8[/tex]

Then, the piecewise function it will be:

[tex]8; x\leq -1[/tex]

- A quadratic function (convex parabola) which y-intercept is equal to 1, exists from -1 to 5, and it vertex (lowest point for this case) is located at (2,-3)

The function will be:

[tex]y=x^{2}-4x+1[/tex]

Finding the y-intercept, we have:

[tex]y=0^{2}-4*80)+1[/tex]

[tex]y=1[/tex]

Finding the vertex of the parabola, we have:

[tex]x_{vertex}=\frac{-b}{2}\\\\x_{vertex}=\frac{-(-4)}{2}=\frac{4}{2}=2[/tex]

[tex]y_{vertex}=x_{vertex}^{2}-4x_{vertex}+1[/tex]

[tex]y_{vertex}=2^{2}-4*2+1=4-8+1=-3[/tex]

The vertex of the parabola is located at the point (2,-3).

Then, for the piecewise function it will be:

[tex]x^{2} -4x+1;-1<x<5[/tex]

- A negative slope function, which evaluated at x equal to 5 (input), gives as output -4.

The function will be:

[tex]y=-x+1[/tex]

Proving that it's the correct equation by evaluating "x" equal to 5, we have:

[tex]y=-5+1[/tex]

[tex]y=-4[/tex]

It proves that the equation is correct.

Then, for the piecewise function it will be:

[tex]-x+1\geq 5[/tex]

Hence, we have that the piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]

Have a nice day!

Answer:

Step-by-step explanation:

In the form ...

  ax^2 +bx +c = 0

the sum of the roots is -b/a. Here, that is -k/3. You want that value to be 3, so we have ...

  -k/3 = 3

  k = -9

__

The solution can be found by completing the square. We choose to start by making the leading coefficient be 1.

  x^2 -3x +4/3 = 0

  (x^2 -3x +9/4) + (4/3 -9/4) = 0 . . . . . . . add and subtract (3/2)^2

  (x -3/2)^2 = 11/12 . . . . . . . . . . . . . . . . . . add 11/12, write as square

  x = 3/2 ± √(11/12) = (9±√33)/6 . . . . . . . .simplify

Answer: -8 square root of 3 (choice a)

Step-by-step explanation:

You have to find 2 numbers that multiply to 48 and in the same time, 1 of these numbers is a perfect square. In this case, the numbers are 16 and 3. So -2√16*3

Then since 16 is. A perfect square, and the square root is 4, you take out the 4 and multiply it by -2 so that is -8 and now you are left with -8√3. Hopefully that helped.

ANSWER

[tex] - 8 \sqrt{3} [/tex]

EXPLANATION

We want to simplify:

[tex] - 2 \sqrt{48} [/tex]

Remove the perfect square under the radical sign.

[tex] - 2 \sqrt{16 \times 3} [/tex]

Split the radical sign for the factors under it.

[tex] - 2 \sqrt{16} \times \sqrt{3} [/tex]

Simplify:

[tex] - 2 \times 4\times \sqrt{3} [/tex]

This finally gives us:

[tex] - 8 \sqrt{3} [/tex]

The first choice is correct.

Use the fact that the co/sine functions are [tex]2\pi[/tex]-periodic and that the tangent function is [tex]\pi[/tex]-periodic. Also, recall that [tex]\cos x[/tex] is even (so that [tex]\cos(-x)=\cos x[/tex]) and [tex]\sin x[/tex] is odd (so that [tex]\sin(-x)=-\sin x[/tex].

15.

[tex]\cos\left(-\dfrac{13\pi}3\right)=\cos\dfrac{13\pi}3=\cos\left(\dfrac\pi3+4\pi\right)=\cos\dfrac\pi3=\boxed{\dfrac12}[/tex]

16.

[tex]\sin\dfrac{23\pi}4=\sin\left(\dfrac{3\pi}4+5\pi\right)=\sin\left(\dfrac{3\pi}4+\pi\right)=\sin\dfrac{7\pi}4=-\dfrac1{\sqrt2}[/tex]

[tex]\implies\csc\dfrac{23\pi}4=\boxed{-\sqrt2}[/tex]

17.

[tex]\cos\left(-\dfrac{7\pi}2\right)=\cos\dfrac{7\pi}2=\cos\left(\dfrac\pi2+3\pi\right)=\cos\left(\dfrac\pi2+\pi\right)=\cos\dfrac{3\pi}2=0[/tex]

[tex]\implies\sec\left(-\dfrac{7\pi}2\right)=\boxed{\text{undefined}}[/tex]

18.

[tex]\tan\left(-\dfrac{29\pi}6\right)=\dfrac{\sin\left(-\frac{29\pi}6\right)}{\cos\left(-\frac{29\pi}6\right)}=-\dfrac{\sin\frac{29\pi}6}{\cos\frac{29\pi}6}[/tex]

[tex]\sin\dfrac{29\pi}6=\sin\left(\dfrac{5\pi}6+4\pi\right)=\sin\dfrac{5\pi}6=-\dfrac12[/tex]

[tex]\cos\dfrac{29\pi}6=\cos\dfrac{5\pi}6=\dfrac{\sqrt3}2[/tex]

[tex]\implies\tan\left(-\dfrac{29\pi}6\right)=-\dfrac{-\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}[/tex]

[tex]\implies\cot\left(-\dfrac{29\pi}6\right)=\boxed{\sqrt3}[/tex]

Answer:

The function has a maximum

The maximum value of the function is

[tex]f (-1) = 11[/tex]

Step-by-step explanation:

For a quadratic function of the form:

[tex]ax ^ 2 + bx + c[/tex] where a, b and c are the coefficients of the function, then:

If [tex]a <0[/tex] the function has a maximum

If [tex]a> 0[/tex] the function has a minimum value

The minimum or maximum value will always be at the point:

[tex]x=-\frac{b}{2a}\\\y=f(-\frac{b}{2a})[/tex]

In this case the function is: [tex]f(x) = -5x^2 - 10x + 6[/tex]

Note that

[tex]a = -5,\ a <0[/tex]

The function has a maximum

The maximum is at the point:

[tex]x=-\frac{-10}{2(-5)}[/tex]

[tex]x=-1[/tex]

[tex]y=f(-1)[/tex]

[tex]y= -5(-1)^2 - 10(-1) + 6[/tex]

[tex]y= 11[/tex]

The maximum value of the function is

[tex]f (-1) = 11[/tex]

The function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum value at the vertex of its parabola. The maximum value is f(x) = 11 when x = -1.

To determine whether the quadratic function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum or a minimum value, we need to examine the coefficient of the [tex]x^2[/tex]term. The general form of a quadratic function is [tex]f(x) = ax^2 + bx + c.[/tex] If 'a' is negative, the parabola opens downwards, and the function has a maximum value at its vertex. In this case, 'a' is -5, which is negative, so the function has a maximum value.

To find the vertex of the parabola, we use the formula for the x-coordinate of the vertex, which is given by -b/(2a). Here, a = -5 and b = -10. Plugging these values into the formula gives us:

x = -(-10) / (2 * (-5))

x = 10 / -10

x = -1

Now that we have the x-coordinate of the vertex, we can find the y-coordinate (the maximum value) by substituting x = -1 into the original function:

[tex]f(-1) = -5(-1)^2 - 10(-1) + 6[/tex]

f(-1) = -5(1) + 10 + 6

f(-1) = -5 + 10 + 6

f(-1) = 5 + 6

f(-1) = 11

Therefore, the maximum value of the function [tex]f(x) = -5x^2 - 10x + 6[/tex] is 11 when x = -1. This is the value at the vertex of the parabola, confirming that it is the maximum value since the parabola opens downwards.

It’s the first one and the third one

Answer: A and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The equation of a proportional relation is of the form

y = kx,

where k is a number.

Here you have

3 - 6x = y,

which can be rewritten as

y = -6x + 3

Because of the +3, your equation is not for the form y = kx, and it is not a proportional relation.

X^2-4x+4 is the answer, to save you points next time, use an app called M8thw8y

First you want to drop the parenthesis. If there is a “+” sign, you do not have to change anything. If there is a “-“ sign, you have to distribute the negative in order to simplify, so imagine you are distributing -1 to 7x + 3 to make it -7x -3.

So, you now have x^2 + 3x - 4 + 16 -5 - 7x -3. (I evaluated the 4^2 to 16)

Now, what you want to do now is to combine like terms. Notice that there is only one x^2, so it is the same. There are two terms that have “x”. 3x and -7x react like normal numbers and they form -4x. The numbers who don’t have x on them you combine like terms.

Answer is x^2 - 4x - 12

Answer:

1000 runners

Step-by-step explanation:

Take total number of runners to be -----------x

90% of x managed to complete the marathon= 90/100 × x =0.9x

30% of those who completed the marathon were men= 30% × 0.9x

=0.3×0.9x= 0.27x

=270 men completed the marathon; this means

0.27x=270--------------------------------find x by dividing both sides by 0.27

x= 270/0.27

x=1000 runners

Answer:

1000

Step-by-step explanation:

Given : In a marathon 90% runner were managed to complete it and 30% were men.

To Find: If 270 men completed it how many total runner began the marathon.

Solution:

Let x be the number of total runners

Now we are given that 90% runner were managed to complete it

So, number of runners managed to complete = [tex]90\% \times x =\frac{90}{100}x=0.9x[/tex]

Now we are given that out of 90% , 30% were men

So, Numbers of men runners = [tex]30\% \times 0.9x=\frac{30}{100} \times 0.9x =0.27x[/tex]

Now we are given that 270 men completed it

So, [tex]0.27x=270[/tex]

[tex]x=\frac{270}{0.27}[/tex]

[tex]x=1000/tex]

Hence 1000 runners began the marathon.

Answer:

[tex]\large\boxed{5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}}[/tex]

Step-by-step explanation:

[tex]5(x+y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5x+5x\\\\3\left(\dfrac{y}{x}\right)=\dfrac{3y}{x}\\\\5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}[/tex]

Answer:

44

Step-by-step explanation:

0.5 m - 0.75 n = 16

Substitute n = 8 into the equation  

0.5 m - ( 0.75 × 8 )  = 16

0.5 m - 6  = 16

( Add 6 to both sides )

0.5 m = 26

( Divide by 0.5 )

m = 52

There are 50 degrees in angle c

Answer: A. 50°

Step-by-step explanation:

Since the measure angles of a triangle add up to 180° and the right triangle=90°, therefore when you subtract 180-90-40, you get 90-40, which then equals to 50°.

Answer:

C. 3.3 • 10^-7

Step-by-step explanation:

(1.1•10^-5)(3 •10^-2)

Multiply the numbers out front of the powers of ten, then add the exponents on the powers of 10

1.1 * 3   * 10 ^(-5+-2)

3.3 ^ (-7)

Answer:

C

Step-by-step explanation:

Answer: he spends 2.5 hours in the weight room each week.

Step-by-step explanation: 2.5 multiplied by 2 (which is the twice amount of time spent working out in the pool) is 5.

So the answer is 2.5

Answer:

22/25

Step-by-step explanation:

The overlap between the 61% and the 75% is the 48%, which means that 13% of the people are married and have no kids (61-48=13)

The 75% includes the people who have one or more kids, and the people who have one or more kids and are married.

Now all we have to do is 13% + 75% = 88% = 22/25

Using Venn probabilities, it is found that there is a 0.88 = 88% probability that a person in a survey is married or has a child.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In this question, the events are:

The probabilities are given by:

[tex]P(A) = 0.61, P(B) = 0.75, P(A \cap B) = 0.48[/tex]

Hence:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

[tex]P(A \cup B) = 0.61 + 0.75 - 0.48[/tex]

[tex]P(A \cup B) = 0.88[/tex]

0.88 = 88% probability that a person in a survey is married or has a child.

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(540 + 540 + 900 + 900) + (2160) = (Surface area of Lateral faces) + (Top) = 5040 sq cm.

5040 / 720 = dishes of craft paint = 7 dishes

Answer:

7 dishes

Step-by-step explanation:

Answer:

x+7

Step-by-step explanation:

let x= the amount of money he got that day

he gains $7/day

x+7