Simplify
92
97

1. 95
2.1/99
3.1/9-5
4. 1/95

Step 1) Set up a proportion

180 girls / x boys = 4 girls / 3 boys

540 = 4x

x = 135 boys

Step 2) Add the number of boys and girls together

180 + 135 = 315

Answer: 315 total students

\(Your answer it W^2 = 1024/4 = 256.\)

Step-by-step explanation:

Answer:

(f+g)(x) = x - 7

Step-by-step explanation:

it is simple - when adding 2 functions your simply add both expressions. and the result is then the function of the sum.

the same applies also to other arithmetic operations.

-3x -5 + 4x - 2 = x - 7

Answer:

1. x = 4.5

2. x = 0.75 or x = -4.5

Explanation:

The quadratic formula says the solutions of the equation with the form ax² + bx + c are:

So, if the equation is 4x² - 36x + 81, the value of each constant is

a = 4

b = -36

c = 81

Then, the solutions are

It means that this equation has a unique solution x = 4.5

In the same way, if we have the equation 8x² + 30x = 27, we first need to subtract 27 from both sides, so:

8x² + 30x - 27 = 27 - 27

8x² + 30x - 27 = 0

Now, we can identify the values of a, b, and c.

a = 8

b = 30

c = -27

Therefore, the solutions of the equation are

So, the solutions for each quadratic equation are:

1. x = 4.5

2. x = 0.75 or x = -4.5

The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.

The rate of change is $ 0.75 per attraction.

The table on the number of tickets and total cost is:

Number of tickets                 1                        5                 10               15

Total cost                          $ 10. 75             $ 13.75       $17.50        $ 21. 25

The number of tickets that Sam can buy when he has $ 37 is:

= (Amount to spend - Cost of admission ) / Cost per ticket

= ( 37 - 10 ) / 0.75

= 36 tickets

The rate of change is therefore the $ 0.75 charged per ticket per event.

The number of tickets for $ 10. 75 is:

= ( Total cost - Cost of admission ) / cost per ticket

= ( 10. 75 - 10 ) / 0.75

= 1 ticket

The cost of 5 tickets :

= ( Number of tickets x cost per ticket) + cost of admission

= (5 x 0. 75 ) + 10

= $ 13. 75

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Answer:

-8.66666666666666666666666666666666666

-9

Step-by-step explanation:

The equation is separable:

\(\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^2+x}{\sqrt x}\implies \mathrm dy=\left(x^{3/2}+x^{1/2}\right)\,\mathrm dx\)

Integrate both sides to get

\(y=\dfrac25x^{5/2}+\dfrac23x^{3/2}+C\)

Given that \(y(1)=0\), we find

\(0=\dfrac25+\dfrac23+C\implies C=-\dfrac{16}{15}\)

so the IVP has the solution

\(\boxed{y(x)=\dfrac25x^{5/2}+\dfrac23x^{3/2}-\dfrac{16}{15}}\)

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

The sum of the angles of any triangle is 180°,

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

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Answer:

169.188 _\(\geq\)__ 169.098

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Answer:

c) Propability of rolling doubles=6

Propability of rolling a sum grrater then or equal to 8 = 15

(Together add up to 21)

d)6 ->(1,1)(1,2)(1,3)(2,1)(2,2)(3,1)

e)9 ->(1,6)(3,4)(5,2)(3,5)(5,3)(3,6)(5,4)(5,5)(5,6)

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:

48.48%

Step-by-step explanation:

Let's assume that there is a number N of women.

32% of these are smokers, then there are 0.32*N smokers

then 68% of these are non-smokers, then there are 0.68*N non-smokers.

Let's assume that the probability of having a ectopic pregnancy for a non-smoker is p (and the probability for a smoker will be 2*p)

Then the number of women with an ectopic pregnancy that are non-smokers is:

p*0.68*N

The number of women with an ectopic pregnancy that are smokers is:

2*p*0.32*N

Then the total number of women with an ectopic pregnancy will be:

p*0.68*N + 2*p*0.32*N

The percentage of women having an ectopic pregnancy that are smokers is equal to the quotient between the number of women with an ectopic pregnancy that are smokers and the total number of women with an ectopic pregnancy, all that times 100%.

The percentage is:

\(P = \frac{2*p*0.32*N}{p*0.68*N + 2*p*0.32*N} *100\%\)

Taking p and N as common factors, we get:

\(P = \frac{2*p*0.32*N}{p*0.68*N + 2*p*0.32*N} *100\% = \frac{N*p}{N*p} \frac{2*0.32}{0.68 + 2*0.32} *100\%\)

Then we get:

\(\frac{2*0.32}{0.68 + 2*0.32} *100\% = 48.48\%\)

Answer:

1.5

Step-by-step explanation:

6 to the log base of 6 will be one (they essentially cancel each other out, log is the opposite of exponents) and we are left with 1.5.

Answer:

n = 6

Step-by-step explanation:

Distribute 4 in 2n - 5:

\(\displaystyle{4\cdot 2n - 4\cdot 5 = 3n + 10}\\\\\displaystyle{8n-20=3n+10}\)

Subtract both sides by 3n:

\(\displaystyle{8n-20-3n=3n+10-3n}\\\\\displaystyle{5n-20=10}\)

Add both sides by 20:

\(\displaystyle{5n-20+20=10+20}\\\\\displaystyle{5n=30}\)

Divide both sides by 5:

\(\displaystyle{\dfrac{5n}{5}=\dfrac{30}{5}}\\\\\displaystyle{n=6}\)

Therefore, n = 6

Answer:

n=6

Step-by-step explanation:

Original equation: 4(2n-5)=3n+10

Step 1 (Distribute the 4):

4(2n)-4(5)=3n+10

8n-20=3n+10

Step 2 (Subtract 3n from both sides):

8n-20-3n=3n+10-3n

(8n-3n)-20=(3n-3n)+10

5n-20=10

Step 3 (Add 20 to both sides):

5n-20+20=10+20

5n=30

Step 4 (Divide both sides by 5):

5n/5=30/5

n=6

The total amount Holla paid for the shirt is: B. $18.74

Given the following data:

To find the total amount she paid for the shirt:

First of all, we would determine the discount on the shirt:

\(Discount = \frac{20}{100} \times 22\\\\Discount = 0.2 \times 22\)

Discount cost = $4.4

\(Selling\; price = Cost\;price - Discount \\\\Selling\; price = 22 - 4.4\)

Selling price = $17.6

Next, we would determine how much tax is to be paid:

\(Tax \;cost = \frac{6.5}{100} \times 17.6\\\\Tax \;cost = 0.065 \times 17.6\)

Tax cost = $1.444

\(Total\;amount = selling \;price + tax\;cost\\\\Total\;amount = 17.6 + 1.444\)

Total amount = $18.74

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Answer:

12 hours

Step-by-step explanation:

4 / 2

2/2

1

4 = 2²

2² x 3 = 4 x 3 = 12

Answer:

  the ramp must be lowered

Step-by-step explanation:

Use the definition of the sine function to find the height of a ramp that is 8°.

  Sine = Opposite/Hypotenuse

  sin(8°) = height/8

  height = 8×sin(8°) = 1.11

The height Nate's dad allows is 1.11 feet. At 1.5 feet, the ramp is too high.

The ramp must be lowered.

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Answer:

A

Step-by-step explanation:

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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The Cartesian equation will be;

⇒ (x - 3) / 1 = (y - 0)/2

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation is,

⇒ r = 3i + λ (i + 2j)

Where, 'λ' is a parameter.

Now,

Since, The equation is,

⇒ r = 3i + λ (i + 2j)

Where, 'λ' is a parameter.

Hence, The Cartesian equation is find as;

⇒ xi + yj = 3i + λi + 2λj

By compare, we get;

⇒ x = 3 + λ

⇒ y = 2λ

Thus, The Cartesian equation is;

⇒ (x - 3) / 1 = (y - 0)/2 = λ

Therefore, The Cartesian equation will be;

⇒ (x - 3) / 1 = (y - 0)/2

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

1 hour did he drive yesterday

Answer:

796871

Step-by-step explanation:

Based on the given conditions, formulate:

5000 x (1 - (1 + 10%) 10)

-------------------------------                                                                  

           1 - (1 + 10%)                                                                          

Evaluate the equation/expression:

796871.23005

Find the closest integer to

798871.23005

=  796871