Evaluate : cosec2 45° + tan2 45° – 3sin2 90°

Answer:

Substitute y = 12x + 7

12x+7=-6+25

Simplify

12x+7=19

Solve

19-7=12

12x=12

x=1

Answer:

JCI is the angle :p

Step-by-step explanation:

Answer:

t=2

Step-by-step explanation:

We have the equation:

[tex]t+\frac{1}{4} = \frac{27}{12}[/tex]

And the main thing here is if we do one thing to an equation we do it to both sides. So if we subtract 1/4 from one side, we do it to both sides. If we subtract 1/4 from the left side it cancels out with the 1/4 leaving us just with the "t" unknown, giving us a solution:

[tex]t=\frac{27}{12} - \frac{1}{4}[/tex]

Now from here we can just multiply the 1/4 by 3/3 so we get the same denominator and combine them into one fraction:

[tex]t=\frac{27}{12} - \frac{3}{12}[/tex]

Now subtract the numerators:

[tex]t=\frac{24}{12}[/tex]

Simplify:

t=2

We compute the functions as follows

1. g(f(0)) = -3

2. f(f(2)) = 5

3. f(g(x)) = 6x - 1

4. g(h(x)) = 3x² + 3

5. g(f(x)) = 6x - 3

6.  f(f(x)) = 4x - 3

7. g(g(x)) = 9x

A function is a  mathematical equation that shows the relationship between two variables.

Given that

Let's compute the given functions.

To compute the function g(f(0)), we first compute g(f(x)).

So, g(f(x)) = 3f(x)

= 3(2x - 1)

= 6x - 3

So, g(f(0)) = 6(0) - 3

= 0 - 3

= -3

So, g(f(0)) = -3

To compute the function f(f(2)), we first compute f(f(x)).

So, f(f(x)) = 2(f(x)) - 1

= 2(2x - 1) - 1

= 4x - 2 - 1

= 4x - 3

So, f(f(2)) = 4(2) - 3

= 8 - 3

= 5

So, f(f(2)) = 5

To compute the function f(g(x)), since we have

So, f(g(x)) = 2(g(x)) - 1

= 2(3x) - 1

= 6x - 1

So, f(g(x)) = 6x - 1

To compute the function g(h(x)), Since

So, g(h(x)) = 3(h(x))

= 3(x² + 1)

= 3x² + 3

So, g(h(x)) = 3x² + 3

To compute the function g(f(x)), Since

So, g(f(x)) = 3(f(x))

= 3(2x - 1)

= 6x - 3

So, g(f(x)) = 6x - 3

To compute the function f(f(x)), Since f(x) = 2x - 1,

So, f(f(x)) = 2(f(x)) - 1

= 2(2x - 1) - 1

= 4x - 2 - 1

= 4x - 3

So, f(f(x)) = 4x - 3

To compute the function g(g(x)), Since g(x) = 3x

So, g(g(x)) = 3(g(x))

= 3(3x)

= 9x

So, g(g(x)) = 9x

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Answer:

Step-by-step explanation:

The number of ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties, is calculated using the combination formula. The combination formula is:

C(n, r) = n! / (r! (n-r)!)

Where n is the total number of items, and r is the number of items to choose. In this case, n = 10 and r = 3.

So, the number of ways to choose 3 students out of 10 is:

C(10, 3) = 10! / (3! (10-3)!) = 10! / (3! 7!) = 10 x 9 x 8 / (3 x 2 x 1) = 120.

Therefore, there are 120 different ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties.

The cheapest alternative that Valentino can select is to make the computation and discover which is less expensive when compared to others.

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

Given that the info is incomplete, Valentino needs to analyze the three options and make additions for extra charges or deductions for discount and make a purchase of the cheapest alternative.

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Annual percentage rate (APR) for mortgages differs from a

more traditional interest rate as APR includes other charges and fees while interest rates do not include it.

The annual cost of a loan to a borrower is referred to as interest rate, and it is indicated as a percentage.

APR represents the total yearly cost of a loan to the borrower, including all fees. The APR is stated as a percentage, just like an interest rate. It does, however, contain other costs or fees such mortgage insurance, the majority of closing costs, discount points, and loan origination fees, unlike an interest rate.

Hence, Annual percentage rate (APR) for mortgages differs from a

more traditional interest rate as APR includes other charges and fees while interest rates do not include it.

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The expected value of x is (m+1)/2, and m must be a positive integer.

The expected value of x is the average value of x that we would expect to get if we selected an integer from the set {1, 2, ..., m} many times. To find the expected value of x, we multiply each possible value of x by its probability of being selected and then sum these products. In this case, each integer in the set {1, 2, ..., m} has an equal probability of being selected, so the expected value is (1 + 2 + ... + m) / m = (m(m+1)) / 2m = (m+1) / 2. So the expected value of x is (m+1)/2, and m must be a positive integer.

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The average  largest five-digit number which leaves remainders of 3, 6, 18 and 39 when divided by 9, 12, 24 and 45 respectively is 99741. This can be found by starting at the highest possible number (99999) and subtracting until the remainders of each division are obtained.

To find the largest five-digit number which leaves remainders of 3, 6, 18 and 39 when divided by 9, 12, 24 and 45 respectively, begin by setting the highest possible number (99999). Then, subtract until the remainders of each division become 3, 6, 18 and 39 respectively. This can be done by subtracting 3 from the initial number and then 6, 18, and 39 in order to get the correct remainders. This process can be repeated until the number reaches 99741, which is the largest five-digit number that leaves the given remainders. This number can also be found by using the formula (9x + 3)(12x + 6)(24x + 18)(45x + 39). By plugging in x = 999, the answer of 99741 is obtained.

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Answer: 108

Step-by-step explanation:

5+7 = 12

They split it into 12 parts.

Kunle gets 5/12, Peter gets 7/12

7/12 of 180

Divide by the bottom, multiply by the top

180/12 = 15

15x7 = 105

Therefore, Peter gets 108 marbles.

Please make me brainliest!

Answer:

k:p 5+7=7/12×180=15×7=105

Mr. Doyle washed most of the laundry. And the amount of the laundry that still needs to be washed will be 1/2.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Mr. Doyle washed 2/5 of his laundry. His son washed 1/4 of it. The laundry done by the son is given as,

⇒ (1/4) x (2/5)

⇒ 1 / 10

The amount of the laundry that still needs to be washed is given as,

⇒ 1 - 1/10 - 2/5

⇒ 1 - 1/10 - 4/10

⇒ (10 - 1 - 4) / 10

⇒ 5 / 10

⇒ 1/2

Mr. Doyle washed most of the laundry. And the amount of the laundry that still needs to be washed will be 1/2.

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The conversion of the units gives:

NUMBER 1: 75 mi/hr = 36.957 m/s

NUMBER 2: 5d = 432000 seconds

Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement. For example, converting a distance measured in meters to feet, or converting a weight measured in kilograms to pounds.

NUMBER 1

1 mile = 5820 feet, 1 feet = 0.3048 meter.

1 hour = 60 minutes = 60 * 60 seconds = 3600 seconds

To convert 75 mi/hr to m/s, we have:
75 mi/hr = (75 * 5820 * 0.3048)m / (60 * 60)s = 36.957 m/s

NUMBER 2

Since we have 24 hours in a day, 60 minutes in 1 hour and 60 seconds in a minute. Thus, 5 days can be written as:

5d = 5 * 24 * 60 * 60 = 432000 seconds

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Step-by-step explanation:

A. To find the profit-maximizing level of price and output, we need to find the equilibrium point where the marginal revenue equals marginal cost.

The marginal cost of production is the derivative of the total cost function: MC = dC/dQ = 3.

The marginal revenue is the derivative of the inverse demand function: MR = dP/dQ = -1.

So at the profit-maximizing level of output, MC = MR.

3 = -1

Q = 6

Then we can substitute Q = 6 back into the inverse demand function to find the price:

P (Q) = 12 - Q

P (6) = 12 - 6

P = 6

So the profit-maximizing level of output is 6 units at a price of $6.

B. To find the maximum profit of the firm, we need to calculate the total revenue and the total cost at the profit-maximizing level of output.

The total revenue is the product of the price and the quantity:

TR = P * Q

TR = 6 * 6

TR = 36

The total cost is given by the total cost function:

TC = C (Q)

TC = 3 * Q

TC = 3 * 6

TC = 18

So the maximum profit is the difference between the total revenue and the total cost:

Profit = TR - TC

Profit = 36 - 18

Profit = 18

The maximum profit of the firm is $18 at an equilibrium price level of $6 and an output level of 6 units.

The number of tennis ball mat have is 33.

What is an equation?

a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

We are given that zak has 18 tennis ball and this is 3 times as many as joe have

That means joe has 18/3 = 6 tennis balls

Matt has 9 more tennis ball that matt and joe combined

The combined tennis ball of matt and joe is 18 + 6 =24

Now we add 9 to it so that we have the number of tennis ball matt has

Which is 24+ 9 = 33

Hence matt has 33 balls

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Answer:

a) $0.05 per ounce

b) $0.06 per ounce

c)The best buy would be 1lb for .80

Step-by-step explanation:

.80/16 = .05   16 ounces in a pound

1.95/32 = .06  32 ounces in 2 pounds

Answer:

Step-by-step explanation:

Let x be the cost of the bench. Then the cost of the garden table is 3x.

The combined cost of the bench and the table is 1000, so x + 3x = 1000.

Combining like terms, we get 4x = 1000.

Dividing both sides by 4, we get x = 250.

The cost of the bench is 250.

Answer:

250.

Step-by-step explanation:

Let's call the cost of the bench "x".

The cost of the garden table is then 3x.

So the combined cost of both is x + 3x = 4x = 1000

So x = 250, and the cost of the bench is 250.

The number of starting points a ray has is one.

Option B is the correct answer.

A ray is a line that has a starting point and no end.

We have,

A ray is a line that has one fixed point and the other point is endless.

So,

A ray has one starting point.

Thus,

A ray has one starting point.

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The frequency of each drink in the statistics class can be found to be :

The frequency of something refers to the number of times that thing happens. In this case, it therefore means the number of students who prefer a certain drink over the other ones.

From the table, the number of students who chose Sprite was 6 students. 5 students chose Dr Pepper and 11 students chose Coke. Then only a single student chose Mtn Dew while 7 students chose Pepsi.

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Answer:

(a)  Choice A  + everywhere in (π/2, 3π/4)

(b)  Choice A  - everywhere in (π/2, 3π/4)

(c) Choice A    - everywhere in (π/2, 3π/4)

Step-by-step explanation:

This can be answered by knowing that the interval (π/2, 3π/4) lies in the second quadrant which lies between π/2 and π

π/2 = 90° and 3π/4 = 135° which lies in the second quadrant

If an angle  θ lies in the first quadrant, we have the following facts:
sin(θ) is positive

cos(θ) is negative

tan(θ) = sin(θ)/cos(θ) is also negative (+ve divided by -ve is negative)

Therefore sin(t) is positive in the interval (π/2, 3π/4).
Correct choice is A

(b)

cos(t) is negative in the interval (π/2, 3π/4).
Choice A

(c) tan(t) is negative in the interval (π/2, 3π/4).
Choice A

At t = π/2 tan(t) is undefined

The number of euros with Richard in the beginning is 2.5 euros.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the money with Richard at the beginning be $x.

Richard gambled and doubled his money.

Now, the money is 2x.

He gave one euro to his friend and gambled again.

Here, 2x-1

This time he tripled his money.

So, the money is 3(2x-1)

After this he bought a hamburger for two euro.

Now, 6x-3-2

6x-5

Now he had four times the euros in his wallet that he gambled the first time.

Here, 6x-5=4x

6x-4x=5

2x=5

x=2.5

Therefore, the number of euros with Richard in the beginning is 2.5 euros.

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Answer: The equation that can be solved for t to find the time (in seconds) when the diver hits the water is:

h(t) = 25 - 16e^(-ft) = 0

Where h(t) is the height of the diver in feet at time t, and f is a positive constant related to the speed of the fall.

To find the time when the diver hits the water, we set h(t) equal to zero and solve for t. This gives us the time when the height of the diver is equal to the water surface.

25 - 16e^(-ft) = 0

25 = 16e^(-ft)

e^(-ft) = 25/16

-ft = ln(25/16)

t = -ln(25/16)/f

Note that the negative sign in the equation for t indicates that the time is counted from the moment the diver starts falling. The constant f can be determined from the physical characteristics of the diver and the conditions of the fall, but it is not necessary to know the exact value of f to find the time when the diver hits the water.

Step-by-step explanation:

Answer:

17/30

Step-by-step explanation:

Number of students = 30

Number of girls and A students = 13+4 = 17

Probability of a student being chosen at random being either a girl or an A student = Total Number of girls and A students/Total No of students = 17/30

Probably of a student chosen at random being either a girl or an A student would be 17/30

The probability of choosing a girl or an A student is 17/30 or 0.567.

There are a couple of ways to approach this problem, but one common method is to use the formula:

                  P(girl or A) = P(girl) + P(A) - P(girl and A)

where P(girl) is the probability of choosing a girl, P(A) is the probability of choosing an A student, and P(girl and A) is the probability of choosing a student who is both a girl and an A student.

To calculate each of these probabilities, we first need to find the total number of girls and A students in the class:

                 Total number of girls: 13

                 Total number of A students: 4 boys + 5 girls = 9

Now we can calculate each probability:

                  P(girl) = number of girls / total number of students = 13 / 30

                  P(A) = number of A students / total number of students = 9 / 30

                  P(girl and A) = number of girls who made an A / total number of students = 5 / 30

Plugging in the values, we get:

                  P(girl or A) = P(girl) + P(A) - P(girl and A)

                  = 13/30 + 9/30 - 5/30

                  = 17/30

Therefore, the probability of choosing a girl or an A student at random from the class is 17/30, or about 0.567.

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The demand equation, by assuming it is linear. The equation expresses price p in terms of quantity q, q  =  -10000/3p + 52000

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

An album is downloaded 12000 times per week when its price is $12

It is downloaded 22000 times per week when the price drops to $9

The demand equation = ?

Suppose, price is expressed as p and quantity as q

Formula of linear relationship,

y = mx + c

So,

q  = mp + c

when,  p = 12 then q = 12000

12000 = 12m + c  _________(i)

when, p = 9 then q = 22000

22000 = 9m + c  _________ (ii)

Now by using elimination method solve equation i & ii

12m + c    =   12000

- 9m + (-c) =  -22000

3m  = -10000

m  = -10000/3

12m + c = 12000

c  = 12000 - 12 x (-10000/3)

c  =  12000 + 40000

c  =   52000

q  = -10000/3p + 52000

The equation is q  =  -10000/3p + 52000

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Answer: To find the time it takes Victoria to make one necklace, we can divide the total time by the number of necklaces she can make in that time. If it takes her 4 days to make 8 necklaces, it takes her 4/8 = 0.5 days to make one necklace.

Next, we can convert 0.5 days into hours to find the time it takes her to make one necklace. Since there are 24 hours in a day, it takes her 0.5 * 24 = 12 hours to make one necklace.

So, it takes Victoria 12 hours to make one necklace.

Step-by-step explanation:

Answer:

60 years old

Step-by-step explanation:

-First multiply 24 and 5.   →    24×5=120

-Then divide it by 2.         →.   120÷2=60

The standard form is 6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(3x−1) (2x³ +4x² −5)

Simplifying

3x (2x³ +4x² −5) - 1 (2x³ +4x² −5)

6[tex]x^4[/tex] + 12x³ - 15x - 2x³ - 4x² + 5

Adding the like terms.

6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5

Thus,

6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5

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