Every student in the senior class is taking history or science and 85 of them are taking both. If there are 106 seniors taking history and 109 seniors taking science, how many students are in the senior class?

The shaded area's Fraction= 21/100 and Decimal = 0.21.

Step-by-step explanation:

When an area is divided into multiple smaller regions ( smaller squares ) is called parts.

In case of Squares, it can be divided into either rows or columns, sometimes both.  

Form the given diagram, the square consists of 10 rows and 10 columns which makes 100 (10×10) parts in it.

One fraction is obtained by dividing it by the total number of parts.

In this square, 21 shaded fractions are given.

∴ The fraction of shaded Area = 21/100.

Decimal of shaded Area=0.21.

Answer:

The correct answer is 15.72 or  6 ∛18

Step-by-step explanation:

Let's calculate the cube root of 216 * 18

∛(216 * 18)

216 = 8 * 27

8 = 2³; 27 = 3³

18 = 9 * 2 or 3² * 2

∛(8 * 27 * 18)

Simplifying:

∛(2³ * 3³ * 3² * 2)

∛(2³ * 3³ * 3² * 2)

2 * 3 ∛(3² * 2

6 * 2.62 = 15.72 or 6 ∛18

Answer:

the answer would be A

Step-by-step explanation:

Answer:

[tex]\cos\theta=\pm0.5[/tex]

Step-by-step explanation:

Given:

[tex]\sin^2\theta=0.75[/tex]

To find [tex]\cos\theta[/tex]

Using trigonometric relations for sums and differences of squares of the ratios.

We know:

[tex]\sin^2\theta+\cos^2\theta =1[/tex]

Plugging in  [tex]\sin^2\theta=0.75[/tex] in the above relation.

[tex]0.75+\cos^2\theta =1[/tex]

Subtracting both sides by 0.75.

[tex]0.75+\cos^2\theta-0.75 =1-0.75[/tex]

[tex]\cos^2\theta =0.25[/tex]

Taking square root both sides.

[tex]\sqrt{\cos^2\theta} =\sqrt{0.25}[/tex]

∴ [tex]\cos\theta=\pm0.5[/tex]  (Answer)

Answer: the answer would be c

Step-by-step explanation:

-> 40 hours per week, 52 weeks a year

shop and save grocers

monthly wages: $3,800

hourly wages: $3800 / 160 = $23.75 per hour

yearly wages: $23.75 per hour x 40 hours per week x 52 weeks a year

= $49,400

unbelievable toys

yearly wages: $43,000

convenience store

$16.50 per hour x 40 hours per week x 52 weeks a year

= $34,320

49,400 - 34,320 = 15,080

..? that's not even an answer choice what-

Answer:

We will buy it at $9.95 plus  5% tax because it is slightly cheaper than other price

Step-by-step explanation:

$9.95 x 18 = 179.10 + 5% sales tax(8.95) = 188.055

$9.75 x 18 = 175.50 + 15 = 190.50

hence sales tax can be get back by submitting monthly return file. so the first method is cheaper than second one,

The first shop offers a better price for 18 rolls of film. You will pay [tex]$179.10[/tex]for 18 rolls of film at the first shop.

Let's calculate the total cost for each shop:

For the first shop:

- The price per roll is [tex]$9.95[/tex].

- There is a 5% sales tax.

- The total cost without tax for 18 rolls is [tex]18 rolls * $9.95/roll = $179.10[/tex].

- The sales tax on this amount is 5% of [tex]$179.10[/tex], which is [tex]0.05 = $8.955.[/tex]

- The total cost including tax is [tex]$179.10[/tex][tex]+ $8.955[/tex] [tex]=$188.055.[/tex]

 For the second shop:

- The price per roll is [tex]$9.75.[/tex]

- There is no sales tax.

- The shipping cost is a flat rate of [tex]$15.00.[/tex]

- The total cost for 18 rolls, excluding shipping, is 18 rolls *[tex]$9.75/roll[/tex] [tex]= $175.50.[/tex]

- Adding the shipping cost, the total cost is [tex]$175.50[/tex][tex]+ $15.00 = $190.50[/tex].

 Comparing the two total costs:

- First shop: [tex]$188.055[/tex] (approximately [tex]$179.10[/tex] without rounding the tax)

- Second shop: [tex]$190.50[/tex]

 The first shop offers a better price for 18 rolls of film. You will pay approximately [tex]$179.10[/tex] for 18 rolls of film at the first shop, which is less than the [tex]$190.50[/tex] you would pay at the second shop.

Answer: 3/5 * 3/1 is 9/5 I think

Step-by-step explanation: Go to a calculator and type it but I think it’s KCF so yeah

Answer:

9/5 or 1.8

Step-by-step explanation:

3/5 * 3/1 = 9/5 or 9 divided by 5 gets 1.8

Answer:

For 0 hours = $40

For 1 hours = $75

For 2 hours = $110

For 3 hours = $145

For 4 hours = $180

For 5 hours = $215

Step-by-step explanation:

Given equation is:- [tex]C=35n+40[/tex]

where, C=Cost in dollars, n=hours.

Now, Amy charge $40 for service call and $35 for per hour service.

So,

For 0 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 0)+40[/tex]

[tex]C=0+40[/tex]

[tex]C=40[/tex]

Therefore for 0 hours Amy charge $40.

For 1 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 1)+40[/tex]

[tex]C=35+40[/tex]

[tex]C=75[/tex]

Therefore for 1 hours Amy charge $75.

For 2 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 2)+40[/tex]

[tex]C=70+40[/tex]

[tex]C=110[/tex]

Therefore for 2 hours Amy charge $110.

For 3 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 3)+40[/tex]

[tex]C=105+40[/tex]

[tex]C=145[/tex]

Therefore for 3 hours Amy charge $145.

For 4 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 4)+40[/tex]

[tex]C=140+40[/tex]

[tex]C=180[/tex]

Therefore for 4 hours Amy charge $180.

For 5 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 5)+40[/tex]

[tex]C=175+40[/tex]

[tex]C=215[/tex]

Therefore for 5 hours Amy charge $215.

Answer:

v= -0.61445783132

Step-by-step explanation:

Divide both sides by 8.3

-5.1 ÷ 8.3= -0.61445783132

8.3v ÷ 8.3= v

So, v=-0.61445783132

8.3v ÷ 8.3= v

Answer:

I think is d I need help please

Answer:

6.40=$12.60

Step-by-step explanation:

First, make the equation following the problem.

$7.50 + $0.85 = $12.60

Then, find the number of miles.

$7.50 * $0.85 = $6.40

$6.40=$12.60

Don't need to solve it because it is asking for the equation.

This is a linear equation problem in Mathematics. The equation to find out the number of miles for the given total charge would be 7.50 + 0.85m = 12.60. Through algebraic manipulation, it is found that the shuttle travelled 6 miles.

The subject of this question is in the field of Mathematics, specifically under linear equations in algebra. In this problem, the customer is charged a flat fee of $7.50 and then an additional $0.85 per mile. The total charge for this trip was $12.60, and we're tasked with finding the number of miles covered for this charge.

The equation to solve this problem would be 7.50 + 0.85m = 12.60, where 'm' represents the miles. We subtract 7.50 from both sides, then we get: 0.85m = 5.1. To solve for 'm', we divide both sides by 0.85, and we receive m = 6 miles.

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Answer:

$0.25 per ticket

Step-by-step explanation:

$3 for 12 tickets so divided the number of tickets by amount of money spent to find price per ticket.

3/12 = $0.25 per ticket

Answer:

0.25

Step-by-step explanation:

beacuse  it is 0.25 because 0.25 times 12 = $3.00

Kyle will have more time to play video games

Solution:

From given question,

Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games.

5 hours of homework = 3 hours of video games

Victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed.

1 hour of homework = 30 minutes of playtime

Suppose if victor spends 5 hours doing homework or reading, then he could play,

5 hours of victor homework = 30 minutes x 5 = 150 minutes of play

That is,

150 minutes = 120 + 30 = 2 hours 30 minutes

This 2 hours 30 minutes playtime of victor is less than kyle playtime (which is 3 hours )

So Kyle gets more play time

The correct ordered pair for the given equation is D. (3,4).

To find the correct ordered pair, we substitute the x-value from each pair into the equation and check if the resulting y-value matches the one in the ordered pair.

Substituting x = 5 into the equation gives us 52 - 2(5) + 1 = 25 - 10 + 1 = 16, which does not match the y-value of 10 in the ordered pair (5,10), so A is not correct.

Substituting x = -1 gives us (-1)2 - 2(-1) + 1 = 1 + 2 + 1 = 4, which does not match the y-value of 3 in (-1,3), so B is not correct.

Substituting x = 1 gives us 12 - 2(1) + 1 = 1 - 2 + 1 = 0, which does not match the y-value of 2 in (1,2), so C is not correct.

Finally, substituting x = 3 into the equation gives us 32 - 2(3) + 1 = 9 - 6 + 1 = 4, which matches the y-value in the ordered pair (3,4), making D the correct answer.

Therefore, the correct ordered pair is D. (3,4).

Evaluate.

12.25 - 7 2/3 = 12 1/4 - 7 2/3 = 12 3/12 - 7 8/12 = 4 7/12

answer: B

Answer:

The 2 expressions are:

1) −2.6x−(−5.9x) = −2.6x + 5.9x

2) −2.6x+(−5.9x) = −2.6x - 5.9x

Options:

−2.6x−5.9x  -> equivalent to 2nd expression

5.9x+(−2.6x)  = −2.6x) + 5.9x -> equivalent to 1st expression

5.9x−(−2.6x)  = 5.9x + 2.6x = 2.6x + 5.9x ->  equivalent to neither expression

−5.9x+(−2.6x)  = −5.9x − 2.6x =  − 2.6x − 5.9x -> equivalent to 2nd expression

−2.6x+5.9x  -> equivalent to 1st expression

−5.9x+2.6x = 2.6x − 5.9x ->  equivalent to neither expression

Explanation:

We started with x = 1 and ended up with y = -2. So the point (x,y) = (1,-2) is on the diagonal line. In other words, point P is located at (1,-2).

Answer:

Domain: (-∞,∞) or  -∞ <[tex]x[/tex]<∞

Range: [1,∞) or [tex]y\geq 1[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2-2x+2[/tex]

To find range and domain of the function.

Solution:

The given function is a second degree function as the highest exponent of the variable is 2. Thus, it is a quadratic function.

For all quadratic functions the domain is a set of all real numbers. So, the domain can be given as: (-∞,∞) or  -∞ <[tex]x[/tex]<∞

In order to find the range of the quadratic function, we will first determine if the function has a minimum point or the maximum point.

For a quadratic equation : [tex]ax^2+bx+c[/tex]

1) If [tex]a>0[/tex] the function will have a minimum point.

2) If  [tex]a<0[/tex] the function will have a maximum point.

For the given function: [tex]f(x)=x^2-2x+2[/tex]

[tex]a=1[/tex] which is greater than 0, and hence it will have a minimum point.

To find the range we will find the coordinates of the minimum point or the vertex of the function.

The x-coordinate [tex]h[/tex] of the vertex of a quadratic function is given by :

[tex]h=\frac{-b}{2a}[/tex]

Thus, for the function:

[tex]h=\frac{-(-2)}{2(1)}[/tex]

[tex]h=\frac{2}{2}[/tex]  [Two negatives multiply to get a positive]

[tex]h=1[/tex]

To find y-coordinate of the vertex can be found out by evaluating [tex]f(h)[/tex].

[tex]k=f(h)[/tex]

Thus, for the function:

[tex]k=f(1)=(1)^2-2(1)+2[/tex]

[tex]k=f(1)=1-2+2[/tex]

[tex]k=f(1)=1[/tex]

Thus, the minimum point of the function is at (1,1).

thus, range of the function is:

[1,∞) or [tex]y\geq 1[/tex]

Answer:

Step-by-step explanation:

The cyclist's speed is 0.35 kilometers per minute. She will travel 0.7 kilometers in 2 minutes.

The question deals with converting speed from kilometers per hour to kilometers per minute, and also calculating distance given a certain time and speed.

First, we convert speed from kilometers per hour to kilometers per minute. There are 60 minutes in an hour, so we divide the speed of the cyclist (21 kilometers per hour) by 60: 21/60 = 0.35 kilometers per minute.

Next, we calculate the distance the cyclist will travel in 2 minutes. Distance equals rate times time, so we multiply the cyclist's speed by the time: 0.35 kilometers per minute * 2 minutes = 0.7 kilometers.

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[tex]\bf G(\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad H(\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}}\implies \cfrac{-9}{4+3}\implies -\cfrac{9}{7}[/tex]

Answer:

3 1/4 + 2 7/8= 6 1/8

Step-by-step explanation:

1.  Cross multiply 1/4 and 7/8 which equals 1  1/8.

2. 3+2+1(from cross multiplying)= 6

Answer: 6 1/8

Using fraction strips, the result of 3 1/4 + 2 7/8 is 6 1/8.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given, Jane is adding 3 1/4 + 2 7/8 using fraction strips.

Fraction strips are rectangular pieces (electronic or copied on paper strips) to represent different parts of the same whole. They can be cut apart and manipulated to see how various parts can be added together to make the whole or compare different fractional amounts for equivalency.

First, we will add fraction parts

=> 1/4 + 7 / 8

We can write 1/4 as 2/8 since they have the same values

=> 2/8 + 7/8

Since now the denominators are the same, therefore we can add the numerators directly. Hence, the sum of 2/8 and 7/8

=> 9/8

=> 8/8 +1/8

=> 1 + 1/8

Thus the sum = 3 + 2 + 1 + 1/8

Sum = 6 + 1/8

therefore, the sum of 3 1/4 + 2 7/8 using fraction strips is 6 1/8.

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Answer:

[tex]([7]x+[2])^2[/tex]

Step-by-step explanation:

Given:

[tex]49x^2+28x+4[/tex]

We need to factorize the given trinomial.

To solve the above expression we will Split the product of first term and third term to get the second term by either adding or subtracting.

So we get;

[tex]49x^2+14x+14x+4\\\\7x(7x+2)+2(7x+2)\\\\(7x+2)(7x+2)\\\\(7x+2)^2[/tex]

Hence Final Answer is:

[tex]([7]x+[2])^2[/tex]

The required number of costume is 8 and remaining fabric is 2 yards.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The total length of fabric is 26 yards.

And, the requirement for each costume is 3 yards.

Now, the number of costumes to be made and the remaining fabric are the quotient and remainder of the following expression,

26 ÷ 3

It gives the quotient and remainder as 8 and 2 respectively.

Hence, the number of costumes and the fabric left are given as 8 and 2 yards respectively.

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You would spend $63.58 on gas per week.

Step-by-step explanation:

Given,

Distance per day = 117 km

Distance in a week = 117*7 = 819 km

1 km = 0.6214 mile

819 km = 819*0.6214 = 508.93 miles

Car's mileage = 42.0 mi/gallons

Let,

x be the gallons for 508.93 miles

x gallons = [tex]\frac{508.93}{42}=12.12[/tex]

Therefore,

12.12 gallons of gas is needed for one week.

1 US gallon = 3.785 liters

12.12 gallons = 12.12*3.785

12.12 gallons = 45.87 liters

Cost of gas per liter = 1.10 euro

Cost of 45.87 liters = 1.10*45.87 = 50.457 euros

1 euro = $1.26

50.457 euros = 1.26*50.457 = $63.58

You would spend $63.58 on gas per week.

Keywords: multiplication, division

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Answer: 29.25

Step-by-step explanation:

3(9.75)

Answer:

A

Step-by-step explanation:

12f means 12 x f

+24 means you add 24

Because of pedmas, you do the multiply first so its (12xf)+24

(Also twelve four isn't a number, so B and C don't make sense)

Answer:

He can cook 52 or less than 52 batches of lasagna.

Step-by-step explanation:

0.9L+0.3S≤60

Putting the value of s = 44

0.9L+0.3 (44) ≤ 60

0.9L+ 13.2 ≤ 60

0.9L ≤ 60 -13.2

L ≤ 46.8/0.9

L ≤ 52

Answer:

Eldar can cook 555 batches of lasagna at most.

Step-by-step explanation:

3 3/4 is the answer

10 3/4 --- 43/4

6 4/4--- 7 or  28/4

43/4- 28/4=  15/4

15/4 simplified is 3 3/4

Answer:

43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4

Step-by-step explanation:

10 3/4 - 6 4/4 . The expression means we should find the difference between 10 3/4 and 6 4/4. The best approach to find the difference of this kind of fractions with whole number is by turning each to an improper fraction.

10 3/4 . This whole number fraction can be turn to an improper fraction as follows

10 × 4 + 3 = 43 then 43/4

6 4/4.   4 × 6 + 4 = 28/4.

Now , let's find the difference

The denominator is same, which is 4

43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4

Answer:

[tex]\frac{24}{25}[/tex]

Step-by-step explanation:

Given

cosA = [tex]\frac{3}{5}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]

Then the opposite side using Pythagorean triple is 4, thus

sinA = [tex]\frac{4}{5}[/tex]

Using the trigonometric identity

sin2A = 2 sinAcosA, then

sin2A = 2 × [tex]\frac{4}{5}[/tex] × [tex]\frac{3}{5}[/tex]

         = [tex]\frac{2(4)(3)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]

Answer:

[tex]\sin(2A)=\frac{24}{25}[/tex]

Step-by-step explanation:

Double angle identity for sine is

[tex]\sin(2A)=2\sin(A)\cos(A)[/tex].

We know [tex]\cos(A)[/tex]. We now need to find [tex]\sin(A)[/tex] to find our answer.

Recall the following [tex]Pythagorean Identity[/tex]:

[tex]\sin^2(A)+\cos^2(A)=1[/tex].

Replace [tex]\cos(A)[/tex] with [tex]\frac{3}{5}[/tex]:

[tex]\sin^2(A)+(\frac{3}{5})^2=1[/tex]

[tex]\sin^2(A)+\frac{9}{25}=1[/tex]

Subtract [tex]\frac{9}{25}[/tex] on both sides:

[tex]\sin^2(A)=1-\frac{9}{25}[/tex]

[tex]\sin^2(A)=\frac{25}{25}-\frac{9}{25}[/tex]

[tex]\sin^2(A)=\frac{25-9}{25}[/tex]

[tex]\sin^2(A)=\frac{16}{25}[/tex]

Now to finally get the value of [tex]\sin(A)[/tex] take the square of both sides:

[tex]\sin(A)=\pm \sqrt{\frac{16}{25}}[/tex]

Since [tex]A[/tex] is in the interval [tex](0,90)[/tex], then [tex]\sin(A)>0[/tex].

[tex]\sin(A)=\sqrt{\frac{16}{25}}[/tex]

[tex]\sin(A)=\frac{\sqrt{16}}{\sqrt{25}}[/tex]

[tex]\sin(A)=\frac{4}{5}[/tex]

So let's finally find the numerical value of [tex]\sin(2A)[/tex].

[tex]\sin(2A)=2\sin(A)\cos(A)[/tex]

[tex]\sin(2A)=2\cdot \frac{4}{5} \cdot \frac{3}{5}[/tex]

[tex]\sin(2A)=\frac{2(4)(3)}{5(5)}[/tex]

[tex]\sin(2A)=\frac{24}{25}[/tex]

Side note:

If [tex]A[/tex] is between 0 and 90 degrees, then we are in the first quadrant.

If we are in the first quadrant, both [tex]x=\cos(A)[/tex] and [tex]y=\sin(A)[/tex] are positive.