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Number of students in senior class is 130

Solution:

Given that Every student in the senior class is taking history or science

85 of them taking both history and science

106 seniors takes history

109 seniors takes science

To find: number of students in senior class

Let A be the set of the students of the senior class that take history

Let B be the set of students of senior class that they science

The number of students in senior class is given by:

[tex]|A \cup B|=|A|+|B|-|A \cap B|[/tex]

Where,

A = 106 and B = 109 and |A n B| = 85

[tex]|A \cup B|=106+109-85=130[/tex]

Thus number of students in senior class is 130

Answer:

130

Step-by-step explanation:

Since 106 seniors are taking history and 109 seniors are taking science. If we add those numbers of seniors up we get 215, then we subtract the number of seniors that are taking both history and science because we counted them twice. So the total is 215 - 85 = 130. Therefore there are 130 students in the senior class.

Answer:

what about it?

Step-by-step explanation:

Answer:

372.6

Step-by-step explanation:

Answer: 15

5,10,15,20

3/4 is 15

Cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3

Solution:

Let "a" be the cost of 1 adult ticket

Let "s" be the cost of 1 student ticket

Given that,

4 adult and 10 student tickets cost 58$ overall on the first day

So we can frame a equation as:

4 adult ticket x cost of 1 adult ticket + 10 student ticket x cost of 1 student ticket = $ 58

[tex]4 \times a + 10 \times s = 58[/tex]

4a + 10s = 58 ------ eqn 1

On the second 5 adult and 1 student cost 38$ overall

So we can frame a equation as:

5 adult ticket x cost of 1 adult ticket + 1 student ticket x cost of 1 student ticket = $ 38

[tex]5 \times a + 1 \times s = 38[/tex]

5a + 1s = 38 ------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "s"

Multiply eqn 2 by 10

50a + 10s = 380 ---- eqn 3

Subtract eqn 1 from eqn 3

50a + 10s = 380

4a + 10s = 58

( - ) --------------------

46a = 322

Substitute a = 7 in eqn 1

4a + 10s = 58

4(7) + 10s = 58

28 + 10s = 58

10s = 58 - 28

10s = 30

Thus cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3

Answer:

Step-by-step explanation:

line G :

5y = -2x - 20...put in slope intercept form (y = mx + b)

y = -2/5x - 4....the slope(m) = -2/5

Part A.) slope intercept form for line R...since R is parallel to G, it will have the same slope....so slope(m) = -2/5

(-10,8)...x = -10 and y = 8

slope(m) = -2/5

y = mx + b

8 = -2/5(-10) + b

8 = 4 + b

8 - 4 = b

4 = b

so ur equation is : y = -2/5x + 4 <=== part A answer

since line E is perpendicular to line G, it will have a negative reciprocal slope...all that means is flip the slope and change the sign....so the slope of line E is : (flip -2/5.....-5/2.....change the sign......5/2)

(-10,8)...x = -10 and y = 8

slope(m) = 5/2

y = mx + b

8 = 5/2(-10) + b

8 = -25 + b

8 + 25 = b

33 = b

so ur equation is : y = 5/2x + 33 <== part B answer

The equation for line R is y = -2/5x + 12. The equation for line E is y = 5/2x + 33.

Part A: To write the equation for line R in slope-intercept form, we need to find the slope and the y-intercept. Since line R is parallel to line G, it will have the same slope. The slope of line G can be determined by dividing the coefficient of x by the coefficient of y: -2/5. We can use the point-slope form, y - y1 = m(x - x1), to find the equation. Substituting the coordinates of the point (-10,8), the equation for line R is y - 8 = (-2/5)(x + 10). Simplifying, we get the equation for line R: y = -2/5x + 12.

Part B: To write the equation for line E in slope-intercept form, we need to find the slope and the y-intercept. Since line E is perpendicular to line G, its slope will be the negative reciprocal of the slope of line G. The slope of line G is -2/5, so the slope of line E will be 5/2. Using the point-slope form and substituting the coordinates of the point (-10,8), the equation for line E is y - 8 = (5/2)(x + 10). Simplifying, we get the equation for line E: y = 5/2x + 33.

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Answer:

-46y+48x

Step-by-step explanation:

Answer:

-46y + 48x

Step-by-step explanation:

-12(3y - 4x) -10y

-36y + 48x - 10y

-36y - 10y + 48x

-46y +48x

Answer:

length of rectangle=16 inches

width of rectangle=10.5 inches

Step-by-step explanation:

given ,perimeter of rectangle=53 inches

let ,length of rectangle= l=2b-5

  width of rectangle=b

p=2(l+b)

53=2(2b-5+b)

26.5=3b-5

31.5=3b

b=[tex]\frac{31.5}{3}[/tex]

b=10.5 inches

l=21-5=16 inches

Answer:

see the attached figure

Step-by-step explanation:

we know that

If two triangles are similar, then its corresponding sides are proportional and its corresponding angles are congruent

Corresponding sides are named using pairs of letters in the same position on either side of the similarity statement

Corresponding angles are named using a letter in the same position on either side of the similarity statement.

therefore

Corresponding angles

∠D and ∠R

∠E and ∠S

∠F and ∠T

Corresponding sides

DE and RS

EF and ST

DF and RT

Answer: The equation has No Solution.

Step-by-step explanation:

Given the following equation:

[tex]-3a+3a+6=7[/tex]

You can simplify it by adding the like terms.

It is important to remember the, by definition, the like terms have the same variable and the same exponent.

In this case, you can identify that the term [tex]-3a[/tex] and the term [tex]3a[/tex] are "like terms", because their variables and their exponents are the same.

So, if you add them, you get:

[tex]-3a+3a=0[/tex]

Then:

[tex]0+6=7\\\\6=7\ (FALSE)[/tex]

Therefore, since there is no value that satisfies the equation, you can conclude that the equation has No Solution.

Answer:

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

y - 5 = 0(x - 0)

y - 5 = 0

y = 5

Answ  For Lateral Area : When all the side faces are the same: Multiply the perimeter by the "slant length" and divide by 2. This is because the side faces are always triangles and the triangle formula is "base times height divided by 2"er:

Step-by-step explanation:

Answer:

I do not agree. When the expressions have like terms collected and are factored, they are the same.

Step-by-step explanation:

Make 6x-2x+4 the same as 4(x+1):

6x - 2x + 4      Collect the like terms 6x and -2x

= 4x + 4       Factor. Divide each term by 4 and take it out of a bracket

= 4(x + 1)

4(x+1) = 4(x+1)

They are equivalent expressions, just written differently.

Answer:

No Jamie is incorrect

Step-by-step explanation:

No, because in the expression 4(x+1)  you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.

Also in the expression 6x-2x+4  ,you will first need to subtract 2x from  6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4

Our final answer is:

6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4

Answer:

58 dollars

Step-by-step explanation:

(100% - 65% = 35% or 0.35)  

x(0.35) = 20.30

divide both sides by 0.35

x = 58  

The swimsuit was originally 58 dollars.

Answer:

$58

Step-by-step explanation:

Answer:

-3x^3+74x-5

Step-by-step explanation:

(x+5)(-3x^2+15x-1)

-3x^3+15x^2-x-15x^2+75x-5

-3x^3+15x^2-15x^2+75x-x-5

-3x^3+74x-5

The given expression can be simplified to obtain -3x³ + 74x - 5. The correct option is (a).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given algebraic expression is (x + 5)(-3x² + 15x - 1).

It can be evaluated as follows,

(x + 5)(-3x² + 15x - 1)

⇒ x(-3x² + 15x - 1) + 5(-3x² + 15x - 1)

⇒ -3x³ + 15x² - x - 15x² + 75x - 5

⇒ -3x³ + 74x - 5

Hence, the product of the given expression is -3x³ + 74x - 5.

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Answer:

Expected value would be $ 0.896

Step-by-step explanation:

Given,

The price of the lottery ticket = $44800000,

Also, the probability of winning the grand prize = .000000020,

Thus, the expected value of the lottery ticket = value of the lottery ticket × probability of getting the lottery ticket

= 44800000 × .000000020

= $0.896

Note : value of lottery ticket = prize amount - cost of each ticket,

Here the cost price of a ticket is not given,

That's why we did not consider it.

Final answer:

The expected value of a lottery ticket with a grand prize of $44.8 million and a winning probability of 0.00000002 is $0.896, assuming the ticket has no cost.

Explanation:

To calculate the expected value of a lottery ticket, we need to consider both the payout and the probability of each outcome. Given that the grand prize is $44.8 million with a probability of winning of 0.00000002, we can compute the expected value.

To find the expected value (EV) of the lottery ticket, we use the following formula:

EV = (Payout × Probability of winning) - (Cost of ticket × Probability of losing)

Plugging in the values, we get:

EV = ($44,800,000 × 0.00000002) - ($0 × (1 - 0.00000002))

EV = $0.896.

Since the cost of the ticket is not given, we assume it's $0 for the purpose of this illustration. The expected value of the lottery ticket when rounded to three decimal places is $0.896.

The quantity "q" sold by Catera is 13

Solution:

Given that Catera has found that as she increases her price, p, the quantity she sells q, decreases

The following equation relates q, the quantity she sells, to p, the price she charges:

Where, "p" is the price and "q" is the quantity she sells

Given that Catera price is $ 232

To find: quantity she sells

Substitute p = 232 in given equation

232 = 284 - 4q

4q = 284 - 232

4q = 52

[tex]q = \frac{52}{4} = 13[/tex]

q = 13

Therefore the quantity she sells is 13

Solve for x.

8x=4x-32

Subtract 4x from both sides.

4x=-32

Divide by 4 on both sides.

x=-8

answer: x=-8

Answer:

x=-8

Step-by-step explanation:

8x=4x-32

4x-8x=32

-4x=32

x=32/-4

x=-8

Answer:

Step-by-step explanation:

Cylinder:

d= 6cm;  r =6/2 = 3cm

h =7.5cm

Volume of ice cream in cylinder = πr²h

                                            = π * 3 * 3 * 7.5 = 67.5 π cubic cm

Cone:

h =  6 cm;

d = 3cm ; r = 3/2 = 1.5cm

Volume =(1/3)πr²h

             = (1/3) * π * 1.5 * 1.5 * 6

= π * 1.5*1.5 * 2 = 4.5π cu. cm

Hemisphere on top:

r = 1.5cm

Volume = (2/3)πr³

  =(2/3)* π * 1.5 *1.5 * 1.5

= 2 *π * 0.5*1.5*1.5

= 2.25π cu.cm

Volume of ice cream in each cone =  4.5 π + 2.25π = 6.75π cubic cm

No of cones = volume of cylinder/ Volume of ice cream in each cone

       =π *67.5 / 6.75 * π

 = 67.5 * 100 / 6.75 * 100

= 6750 / 675

= 10

number of cones which can be filled with ice cream = 10 cones

Answer:

Option D. 124°

Step-by-step explanation:

step 1

Find the measure of angle AOC

The triangle AOC is an isosceles triangle, because OA=OC=radius

so

[tex]m\angle OAC=m\angle OCA=28^o[/tex]

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

[tex]m\angle OAC+m\angle OCA+m\angle AOC=180^o[/tex]

substitute the given values

[tex]28^o+28^o+m\angle AOC=180^o[/tex]

[tex]56^o+m\angle AOC=180^o[/tex]

[tex]m\angle AOC=180^o-56^o[/tex]

[tex]m\angle AOC=124^o[/tex]

step 2

Find the measure of arc AC

we know that

[tex]arc\ AC=m\angle AOC[/tex] ----> by central angle

we have

[tex]m\angle AOC=124^o[/tex]

therefore

[tex]arc\ AC=124^o[/tex]

step 3

we know that

The inscribed angle is half that of the arc comprising

[tex]m\angle ABC=\frac{1}{2}[arc\ AC][/tex]

[tex]m\angle ADC=\frac{1}{2}[arc\ AC][/tex]

so

[tex]m\angle ABC=m\angle ADC[/tex]

therefore

[tex]m\angle ABC+m\angle ADC=2m\angle ABC=arc\ AC[/tex]

substitute the value of the arc AC

[tex]m\angle ABC+m\angle ADC=124^o[/tex]

To find the length of the diagonal path on a rectangular lawn, calculate the square root of the sum of the squares of its width and length.

The length of the diagonal path can be found using the Pythagorean theorem.

Given the dimensions of the rectangular lawn (10 m wide and 15 m long),

the length of the diagonal path (d) is calculated as:

d = √(10^2 + 15^2) = √(100 + 225) = √325 = 5√13 m.

Answer:

Yes, A KLP can be reflected across the line containing KP and then translated so that Pis mapped to M.

Step-by-step explanation:

The figure shows two congruent by HA theorem (they have congruent hypotenuses and a pair of congruent angles adjacent to the hypotenuses) triangles KLP and QNM.

A rigid transformation is a transformation which preserves lengths. Reflection, rotation and translation are rigit transformations.

If you reflect triangle KLP across the leg KP and translate it up so that point P coincides with point M , then the image of triangle KLP after these transformations will be triangle QNM.

Triangle KLP can be reflected across the line containing KP and then translated so that P is mapped to M

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

Triangle KLP can be reflected across the line containing KP and then translated so that P is mapped to M

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Answer:

-2.5

Step-by-step explanation:

We are given that a quadratic  function  graph f(x).

We have to find the value of f(6).

The given graph is parabolic .

The vertex of the graph is at (3,-2).

The graph cut the x -axis at point (1,0) and (5,0).

The graph cut the y-axis at point (0,-2.5).

To find the value of f(6) we will find the value of y  corresponding to x=6.

When we draw a vertical line x=6 then we see that it cuts the given graph at point (6,-2.5).

Therefore, the value of f(6)=-2.5

Hence, the f(6) for the quadratic function graph=-2.5

Mrs. clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?

Mrs. Clark bought 17 science kits

Given that Mrs. clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill

To find: number of kits she bought

Cost of one kit = $ 5

Tax amount = $ 4.85

Total amount spend including tax = $ 89.85

Lets first get rid of the tax in the total amount

Amount without tax = Total amount spend including tax - Tax amount

Thus amount without tax = $ 89.85 - $ 4.85 = $ 85

Since we know that each kit costs $5,  we would divide 85 by 5 to see find how many kits she bought

[tex]\begin{array}{l}{\text { number of kits bought }=\frac{\text { amount spent }}{\text { cost of one kit }}} \\\\ {\text { number of kits bought }=\frac{85}{5}=17}\end{array}[/tex]

Thus Mrs. clark has bought 17 science kits

Answer:

Ms. Clark bought 17 science kits

Step-by-step explanation:

The ratio of the time levon spent on the treadmill to the time he spent lifting is 5/7 or 5:7

Step-by-step explanation:

Given

Time spent on treadmill = [tex]T_t = 25\ min[/tex]

Time spent on weight lifting = [tex]T_w = 35\ min[/tex]

We have to find the ratio of the time Levon spent on the treadmill to the time he spent lifting

The ratio will be denoted by r

[tex]r = \frac{T_t}{T_w}\\=\frac{25}{35}\\[/tex]

Simplifying the fractions

[tex]=\frac{5*5}{7*5}\\=\frac{5}{7}[/tex]

The ratio of the time levon spent on the treadmill to the time he spent lifting is 5/7 or 5:7

Keywords: Ratio, fraction

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Answer: 10 and 23

Step-by-step explanation:

Let the first number be x and the second number be y.

Also , let x be the bigger number and y the smaller number.

From the first statement;

x + y = 33 ............................. equation 1

From the second statement

twice the smaller number = 2y

so, if the bigger number is 3 more than two times the smaller number, this means that

x = 2y + 3 .................................... equation 2

Solving the resulting linear equations by substitution method .

substitute x = 2y + 3 into equation 1 , that is

x + y = 33 becomes :

2y + 3 + y = 33

3y + 3 = 33

3y = 30  

y = 10

Substitute y = 10 into equation 2 , that is

x = 2y + 3 becomes

x = 2(10) + 3

x = 20 + 3

x = 23

Answer: The function is EVEN.

Step-by-step explanation:

For this exercise it is important to remember that:

1. A function f(x) is even if and only if:

[tex]f(-x) = f(x)[/tex] for all "x"

2. A function f(x) is odd if and only if:

[tex]f(-x) = -f(x)[/tex] for all "x"

So knowing that, and given the following function k(x):

[tex]k(x)=x^6 - x^2 + 7[/tex]

You can plug [tex]-x[/tex] in for "x", order to know if this is even. Then, you get:

[tex]k(-x)=(-x)^6 - (-x)^2 + 7\\\\k(-x)=x^6-x^2+7[/tex]

Therefore, since:

[tex]f(-x) = f(x)[/tex]

You can determine that that the given function [tex]k(x)=x^6 - x^2 + 7[/tex] is Even.

Answer:

cos θ = 1/2

Step-by-step explanation:

4 cos θ + 4 sin² θ = 5

Use Pythagorean identity.

4 cos θ + 4 (1 − cos² θ) = 5

4 cos θ + 4 − 4 cos² θ = 5

0 = 4 cos² θ − 4 cos θ + 1

0 = (2 cos θ − 1)²

0 = 2 cos θ − 1

cos θ = 1/2

Answer:

60° and 300°

Step-by-step explanation:

Before beginning to answer this question, you'll need a quick formula that will be very helpful trying to answer questions like this one:

You'll see why this formula is useful soon.

Work:

[tex]4cosx+4sinx^2=5[/tex]

[tex]sinx^2+cosx^2=1[/tex]

[tex]sinx^2=-cosx^2+1[/tex]

[tex]4cosx+4(-cosx^2+1)=5[/tex]

[tex]4cosx-4cosx^2+4=5[/tex]

[tex]-4cosx^2+4cosx+4=5[/tex]

[tex]4cosx^2-4cosx-4=-5[/tex]

[tex]4cosx^2-4cosx+1=0[/tex]

[tex]4u^2-4u+1=0[/tex]

[tex](2u-1)^2=0[/tex]

[tex](2cosx-1)^2=0[/tex]

[tex]2cosx-1=0[/tex]

[tex]2cosx=1[/tex]

[tex]cosx=1/2[/tex]

[tex](cos^-^1)cosx=1/2(cos^-^1)[/tex]

[tex]x=60[/tex] [tex]x=300[/tex]

1. Growth came from personal and government spends and other investments.

2. Economy is slowing down and reflects weaker outlook in 2020

1.  Real Gross Domestic Product showed increment at the rate of 1.9% annually by the end of 3rd quarter of 2019. This estimate was released by Bureau of economic analysis. They also had estimated that Real GDP was increased by approximately 2.0% when 2nd quarter of 2019 ended.

Factors that contributed the increase in real GDP by the end of 3rd quarter included expenditures and consumption of the common people for personal use, expenditure of federal government along with local and state governments, investments in fixed residential assets, and also exports.

2. International Monetary Fund estimated and projected a slower growth rate for United States in 2019 and 2020 and revised the growth rate as downward of 0.3% for both 2019 and 2020.  This shows us that GDP will now grow at the rate of 7% and 7.2% , which reflects a very weak outlook for domestic demand, weaker than expected. Global trade tension poses a threat to the economic outlook.