In a group of 42 students, 9 study both Art and Biology.
10 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Answer:

Only the second equation is an identity

Step-by-step explanation:

1)

[tex]1+\dfrac{\cos^2\theta}{\cot^2\theta(1-\sin^2\theta)}= \\\\\\1+\dfrac{\cos^2\theta}{\cot^2\theta(\cos^2\theta)}= \\\\\\1+\dfrac{1}{\cot^2 \theta}= \\\\\\1+\tan^2\theta=\sec^2\theta\neq 2\sec^2 \theta[/tex]

This one is not an identity.

2)

[tex]19\cos \theta\left( \dfrac{1}{\cos \theta}-\dfrac{\tan \theta}{\csc \theta} \right)= \\\\\\19\cos \theta \left( \dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta} \right)= \\\\\\19\cos \theta \left( \dfrac{1-\sin^2 \theta}{\cos \theta}\right)= \\\\\\19\cos \theta \left( \dfrac{\cos^2 \theta}{\cos \theta}\right)= \\\\\\19\cos \theta (\cos \theta)= \\\\\\19\cos^2 \theta = 19\cos^2 \theta[/tex]

This one is an identity. Therefore, only the second equation is an identity. Hope this helps!

Answer:

the person above me is right :)

Step-by-step explanation:

Complete Question:

sierrac3000

06/28/2019

Select the correct answer from each drop-down menu.

Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the account after t years can be calculated using the expression below.

250(1+0.018/2)^2t

Use the given expression to complete the statements below.

The expression is the *blank* of the amount initially deposited and the *blank* of one and the rate of increase raised to the number of *blank*

1st Blank:

Product

Sum

Quotient

Square

2nd Blank:

Quotient

Product

Difference

Sum

3rd Blank:

Compounding Periods

Years

Months

Answer:

1st blank = product

2nd blank = sum

3rd blank = years

Step-by-step explanation:

The expression given above is :

250(1+0.018/2)^2t

The expression can thus be explained as:

The *product* of the amount initially deposited and the *sum* of one and the rate of increase raised to the number of *years*

Answer:

15

17

Step-by-step explanation:

x/5=3 ⇒ x=5*3=15

x/2=8.5 ⇒ x= 2*8.5=17

Answer:

See explanation for answers

Step-by-step explanation:

prism = 12*4 + 5*4 + 12*4 + 5*4 + 12*5 + 12*5 = 256 ft²

lateral surface area of pyramid = 4*1/2*5*5 = 50 ft²

area of square base of the pyramid = 5*5 = 25 ft²

total exposed surface area of the figure = 256 + 50 - 25 = 281 ft²

Answer:

Yes.

Step-by-step explanation:

Because the terms inside the parentheses are fully simplified, we can just add up the terms:

(5x - 6) + (x + 2) =

5x - 6 + x + 2 =

5x + x - 6 + 2  =

6x - 4

Answer:

2.5 hours

Step-by-step explanation:

To solve this question we can use the exponencial function:

P = Po * (1 + r)^t

Where P is the final value, Po is the inicial value, r is the rate and t is the time.

In this case, we have Po = 8, P = 7 and r = -5% = -0.05. So, we can solve for t:

7 = 8 * (0.95)^t

0.95^t = 0.875

log(0.95^t) = log(0.875)

t * log(0.95) = -0.1335

t * (-0.0513) = -0.1335

t = -0.1335 / (-0.0513) = 2.6023 hours

Rounding to the nearest half-hour, we have t = 2.5 hours

Answer:

2.5

Step-by-step explanation:

I had this question and got it right

Answer:

24 years

Step-by-step explanation:

James Age = 9 years

Rose's Age = 15 years

Sum of their Ages = 9+15

Sum of their Ages = 24 years

Answer:

y = 8-3x and y = -11/3 + x/3

For the first equation you have to subtract 3x from both sides of the equation. for the second equation you have to move all terms that doesn't contain y to the right side and solve

Answer:

Rational

Step-by-step explanation:

Can convert it to a ratio (-415/1)

Answer:

Rational

Step-by-step explanation:

-415 is an integer. All integers are rational. It can be written as a fraction p/q, where p and q are integers and q is not equal to zero.

-415 can be written as [tex]-\frac{415}{1}[/tex].

Answer:

20

Step-by-step explanation:

The height of the platform is when t=0

h(0) = -4(0)^2 + 75(0) +20

        =20

The height of the platform is 20

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers. Irrational numbers can also be expressed as non-terminating continued fractions and many other ways.

The answer is True

The statement that all irrational numbers are real numbers is true.

Real number is a union of rational number and irrational numbers.

An irrational number is a number that cannot be expressed as a fraction or ratio of two integers. All the root values, repeating values, comes under irrational numbers.

Since irrational numbers can still be plotted on the number line, they are considered real numbers. Therefore, all irrational numbers are also real numbers.

Thus, all irrational numbers are also real numbers.

Yes, the given statement is true.

Learn more about irrational numbers here:

https://brainly.com/question/17450097

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Answer: 2/3xy^-2z

Step-by-step explanation:

18/27 = 2/3

x^2 / x = x

y / y^3 = y^-2

z isn’t changed

Put the variables together after dividing and you get 2/3xy^-2z.

Step-by-step explanation:

do you mean like this?

18x²y/27xy³z =

if yes the answer is like this

18/27 = 2/3

x²/x = x

y/y³ = 1/y²

1/z = 1/z

multiply all and that's the answer

⅔ * x * 1/y² * 1/z =

[tex] \frac{2x}{3 {y}^{2} z} [/tex]

Answer: 4 feet < Length < 21 feet

Step-by-step explanation:

From the question, the length of the rectangular fence is 4 feet more than its width and the perimeter of the fence is less than 42 feet. The range of the lengths of the fence will be:

Length is greater than 4 feet (4 feet more than the width. This means that the length must be at least 4 feet) and less than 21 feet i.e the length must be less than 1/2 of the perimeter which is 42/2 = 21. Therefore, the answer will be:

4 feet < Length < 21 feet

Answer:

12.5

its right

Step-by-step explanation:

Answer:

Step-by-step explanation:

6--6 = 12

4-1 = 3

12/3 = 4

y=4x

-6-4 = -10

y=4x-10

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through (1, -6) and (4, 6).

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

Now,

(1, -6) = (a, b) and (4, 6) = (c, d)

Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4

m = 4

The equation of a line is given as y = mx + c.

(1, -6) = (x, y)

-6 = 4 x 1 + c

-6 = 4 + c

-6 - 4 = c

c = -10

Now,

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

Learn more about equation of a line here:

https://brainly.com/question/23087740

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Answer:

14^2/15

Step-by-step explanation:

70/15 simplifies to 14/3

14/3 X 14/5

= 14^2/15

Answer:

Solution set:  (3, 4) and (4, 3)

Step-by-step explanation:

Please, to indicate exponentiation, use " ^ ":  a^2 and b^2

Then you have:

a + b = 7 and a^2 + b^2 = 25.

Let's eliminate b:  Solve a + b = 7 for b, obtaining b = 7 - a.

Then we have:

a^2 + (7 - a)^2 = 25, or

a^2 + 49 - 14a + a^2 - 25 = 0, or

2a^2 - 14a + 24 = 0, or

a^2 - 7a + 12 = 0, which factors as follows:

(a - 3)(a - 4) = 0

This results in a = 3 and a = 4, in which case the equation a + b = 7 tells us that the b values are 4 and 3 respectively.

Solution set:  (3, 4) and (4, 3)

answer:

Solution,

diameter of tank=1.4 m

Height of tank=1.9 m

Given tank has top and bottom

Now, The total surface area of cylinder tank is given by:

[tex]tsa = 2\pi \: {r}^{2} + (2\pi \: r \: ) \times h[/tex]

r( radius of tank)=

[tex] \frac{diameter}{2} = \frac{1.4}{2} = 0.7 \: m[/tex]

h(height of tank)=1.9 m

TSA of 1 tank

=

[tex]2 \times 3.14 \times {(0.7)}^{2} + 2 \times 3.14 \times 0.7 \times 1.9 \\ = 11.435 \: {m}^{2} [/tex]

TSA Of 3 tanks

=

[tex]3 \times 11.435 \: {m}^{2} \\ = 34.3 \: {m}^{2} [/tex]

Given a tin of plate covers 5m^2 area.

No.of tins required:

1 tin 5m^2

x tin 34.3 m^2

[tex]5x = 34.3(cross \: multiplication) \\ or \: x = \frac{34.3}{5} \\ x = 6.86 \\ x = 7 \: tins[/tex]

therefore 7 tins are required.

Hope this helps...

Good luck on your assignment....

Answer:

there are 62 prime numbers with squares

Answer:

i believe it is 3...?

11, 13, and 17

Step-by-step explanation:

11 = 121

13= 169

17 = 289

these are prime numbers

Answer:

343 cubic inches

Step-by-step explanation:

7 times 7 times 7 is 343

Answer:

3h−3k

Step-by-step explanation:

Answer:

x = 12, y = 16

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{AD}{PS}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values

[tex]\frac{20}{2x+6}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )

18(2x + 6) = 540 ( divide both sides by 18 )

2x + 6 = 30 ( subtract 6 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

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

and

[tex]\frac{AB}{PQ}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values

[tex]\frac{y}{24}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )

27y = 432 ( divide both sides by 27 )

y = 16

Complete Question

Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the accoutnt after t years can be calculated using the expression below.

[tex]250(1+\frac{0.018}{2})^{2t}[/tex]

Use the given expression to complete the statements below.

The expression is the___(Product , Sum  , Quotient , Square) of the amount initially deposited and the____(Quotient , Product , Difference , Sum)  of one and the rate of increase raised to the number of ___.(Compounding Periods , Years, Months)

Answer:

Step-by-step explanation:

For an amount invested at compound interest at a rate of r% with period for t years,

Amount [tex]=P(1+\frac{r}{k})^{tk}[/tex]

Comparing with the given expression: [tex]250(1+\frac{0.018}{2})^{2t}[/tex]

Period =2

Rate =0.018

Total Compounding Period =2 X t, where t=Number of years

Therefore:

The expression is the Product of the amount initially deposited and the Sum of one and the rate of increase raised to the number of Compounding Periods .

(b+1)/2b

quotient = divided by

we're dividing a number that is 1 more than b (b + 1), with a number twice as large as b (2b).

Answer:

185 -> Spent on new CD's

$ 555 -> Savings Account

Steps:

37*20 = 740/4 = 185 -> Spent on new CD's

740 - 185 = $ 555 -> Savings Account

Description:

The 2 question is asking that how much money did she spend on her CD. We times 37 and 20 = that will equal 740 then we divide 740 by 4 = 185. Meaning we just solved for question 2. Answer is 185 spent on new CD.

For question 3 this time we get 740 again we do it by 37 times 20 equal 740. we minus it by 185 the spent on new CD answer. so 740-185= $555. So answer for question 3 is $555 to her saving account.

Please mark brainliest

Hope this helps.

Answer:

" Expected Payoff " ⇒ $ 1.80 ; Type in 1.80

Step-by-step explanation:

Take the probability of winning into consideration;

[tex]Total Number of Tickets - 500,\\Tickets 1 Person Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 500,\\Money Won - 900 Dollars,\\\\Proportionality - 1 / 500 = x / 900 - where, x = " Expected Payoff "\\1 / 500 = x / 900 - CrossMultiplication,\\\\500 * x = 900,\\x = 900 / 500,\\x = 1.80 Dollars Won!\\\\Conclusion ; x = 1.80 Dollars[/tex]

Solution ; " Expected Payoff " ⇒ $ 1.80

Answer:

1, 2, 4, 6 are true statements

Answer:

[tex]y=-5/8x+6[/tex]

Step-by-step explanation:

[tex]m=\frac{7/2 - 11}{4--8}[/tex]

[tex]m=\frac{-15/2}{12}[/tex]

[tex]m=-5/8[/tex]

[tex]y=-5/8x+b[/tex]

[tex](-8,11)[/tex]

[tex]11=-5/8 \times -8+b[/tex]

[tex]b=11-(-5/8)(-8)[/tex]

[tex]b=6[/tex]

Answer:

Step-by-step explanation:

a = 22 cm

b = 12 cm

h = 8 cm

[tex]Area=\frac{(a+b)*h}{2}\\\\=\frac{(22+12)*8}{2}\\\\=\frac{34*8}{2}\\\\=34*4[/tex]

= 136 cm²

Answer:

-2

Step-by-step explanation:

To find the slope we use the formula

m = (y2-y1)/(x2-x1)

   = (-3-1)/(0- -2)

  = -4 / (+2)

  = -2