Multiply:
(2sin B+cos B)by 3cosec B.secB​

Answer:

a.8

Step-by-step explanation:

y=-16

-16=-2x

16=2x

x=16/2=8

The recursive formula for this problem is given as follows:

\(P_n = 1.05 \times P_{n - 1}\)

The explicit formula for this problem is given as follows:

\(P_n = 150(1.05)^n\)

The number of tickets in 2026 is given as follows:

297 tickets.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number which is defined as the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n}\)

In which \(a_1\) is the first term.

The parameter values for this problem are given as follows:

\(a_1 = 150, q = 1.05\)

Hence the function is given as follows:

\(P_n = 150(1.05)^n\)

2026 is 14 years after 2012, hence the number of tickets is given as follows:

\(P_{14} = 150(1.05)^{14} = 297\)

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The required simplified expression is given as  -12h² + 5g - 4. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expressions
y = –10g – 4h²  + 15g – 8h²  – 4
y = -4h²  - 8h²  -10g + 15g - 4
y = -12h² +5g -4

Thus, the required simplified expression is given as  -12h² + 5g - 4. Option C is correct.

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Given that the polynomials p(x) = 5x²-x+ 4 and q(x) = 3x² + 7x-1,

a. The polynomial  p(x) + q(x) =  8x² + 6x + 3.

b. The polynomial  2p(x) - q(x) =  7x² - 9x + 9.

c. The polynomial p(x)q(x) = 15x⁴ - 3x³ + 35x² + 27x - 4

A polynomial is a mathematical function in which the power of the unknown is greater than or equal to 2.

1. Given the polynomials p(x) = 5x²-x+ 4 and q(x) = 3x² + 7x-1, we desire to find p(x) + q(x), we proceed as follows.

To find  p(x) + q(x), we add both polynomials. so, we have that

p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

So,   p(x) + q(x) = 5x²- x + 4 + 3x² + 7x - 1.

Collecting like terms, we have that the equation

p(x) + q(x) = 5x² + 3x² + 7x - x + 4 - 1.

= 8x² + 6x + 3.

So, p(x) + q(x) =  8x² + 6x + 3.

b. To find  2p(x) + q(x), we add both polynomials. so, we have that

p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

We multiply p(x) by 2 to obtain 2p(x). so,

2p(x) = 2(5x²- x + 4)

= 10x²- 2x + 8

So,   2p(x) + q(x) = 10x²- 2x + 8 - (3x² + 7x - 1)

= 10x²- 2x + 8 - 3x² - 7x + 1)

Collecting like terms, we have that the equation

2p(x) + q(x) = 10x² - 3x² - 7x - 2x + 8 + 1.

= 7x² - 9x + 9.

So, 2p(x) - q(x) =  7x² - 9x + 9.

c. To find  p(x)q(x), we multiply both polynomials. so, we have that p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

p(x)q(x) = (5x²- x + 4)(3x² + 7x - 1)

= 5x²×3x² + 5x² × 7x + 5x²(-1) - x × 3x² - x × 7x - x × ×(-1) + 4 × 3x² + 4 × 7x  + 4 × (-1)

= 15x⁴ + 35x² - 5x² - 3x³ - 7x² - x + 12x² + 28x - 4

Colecting like terms, we have that

= 15x⁴ - 3x³ + 35x² - 5x²  - 7x² + 12x² - x + 28x - 4

= 15x⁴ - 3x³ + 35x² + 27x - 4

So, p(x)q(x) = 15x⁴ - 3x³ + 35x² + 27x - 4

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\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000e^{0.08\cdot 4}\implies A=2000e^{0.32}\implies \boxed{A\approx 2754.26}\)

Step-by-step explanation:

I am not sure but i think is this

Answer:

D. \( x^2 + 3x - 88 \)

Step-by-step explanation:

Area of rectangle = \( length (l) * width (w) \)

Length of rectangle = (x - 8)

Width = (x + 11)

Area of rectangle = \( (x - 8)(x + 11) \)

Expand the expression

\( x(x + 11) -8(x + 11) \) (distributive property of multiplication)

\( x^2 + 11x - 8x - 88 \)

Combine like terms

\( x^2 + 3x - 88 \)

Expression for the area of the rectangle = \( x^2 + 3x - 88 \)

Answer:

x2 + 3x - 88

Step-by-step explanation:

Plato/Edmentum

Answer:

two is the number

Step-by-step explanation:

i think that

The required number is 1.786.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the number is x,

According to given condition,

3×x²= 2×x+6

⇒3x²= 2x+6

⇒3x²-2x-6=0

There are two values of x, -1.12 and 1.786

Neglect negative value,

By solving the equation, the value of x is 1.786.

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Step-by-step explanation:

Nothing further can be done with this topic. Please check the expression entered or try another topic.

More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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An

Step-by-step explanation:

Answer:

\(-6\leq x\leq 16\)

Step-by-step explanation:

So we have the inequality:

\(|x-5|\leq 11\)

Definition of Absolute Value:

\(x-5\leq 11\text{ or } x-5\geq -11\)

Note that the sign is flipped in the second case because we multiplied by a negative.

Add 5 to both sides to both equations:

\(x\leq 16\text{ or } x\geq -6\)

Merge:

\(-6\leq x\leq 16\)

And we're done!

According to the normal distribution, the percentages are as follows:

3.59% of the grades will be A.

9.98% of the grades will be B.

74.92% of the grades will be C.

8.64% of the grades will be D.

2.87% of the grades will be F.

Given a normally distributed variable with a mean and standard deviation, the z-score of a measure X is calculated as follows:

The z-score calculates the number of standard deviations above or below the mean for a given measure.

The p-value, which is the percentile of X, is discovered by looking at the z-score table and is related with this z-score.

The proportion of students who receive an A = 1 - p-value of Z = 1.8.

By the z-table, Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359.

3.59% of the grades will be A.

For B= p-value of Z = 1.8 - p-value of Z = 1.1,

Hence 0.9641 - 0.8643 = 0.0998.

9.98% of the grades will be B.

For C = p-value of Z = 1.1 - p-value of Z = -1.2,

Hence 0.8643 - 0.1151 = 0.7492.

74.92% of the grades will be C.

For D= p-value of Z = -1.2 -p-value of Z = -1.9,

Hence 0.1151 - 0.0287 = 0.0864.

8.64% of the grades will be D.

For F= p-value of Z = -1.9,

Hence 2.87% of the grades will be F.

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Step-by-step explanation:

Question 1:

In the expression 4y - 6x² + 5 + 9x, there are

4 terms. (4y/6x²/5/9x) A term consists of a coefficient and a variable, or otherwise a constant term like 5.

Question 2:

4(6x - 5) - 7x

= (24x - 20) - 7x

= 17x - 20.

Therefore the correct answers are

the 1st and 2nd options.

Question 3:

3x - 8y + 11x - 4 + 5y

= (3x + 11x) + (5y - 8y) - 4

= 14x - 3y - 4.

The 4th option is correct.

Question 1

There are 4 terms.

They are 4y, 6x^2, 5, and 9x.

Terms are separated by operation signs (+, -, ×, ÷).

Even if a constant is multiplied by a variable, if there isn't a multiplication sign, it's one single term.

Question 2

Use the distributive property. Multiply the term outside the variable by the terms inside.

4×6x = 24x

4×(-5)=-20 (there's a negative sign incase you don't see it)

24x-20-7x

Since 24x and 7x are like terms, you can subtract them.

24x-7x=17x

17x-20

You can see the first and second choices are correct.

Question 3

Combine the like terms.

The like terms are

3x and 11x

-8y and 5y

-4

Add them all.

3x+11x=14x

-8y+5y=-3y

-4

So the expression simplified is...

14x-3y-4

It's the third choice.

The interest earned after 3 months is $75

What is simple interest?

The simple interest on a deposit is the principal deposited multiplied by the interest and the time the deposit lasted

I=PRT

I=interest=unknown

P=principal=$6000

R=interest rate=5%

T= 3 months=0.25 year

I=$6000*5%*0.25

I=$75

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Answer:

75 dollars

Step-by-step explanation:

i got it right

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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The points that must lie on the same graph of the quadratic function is given as follows:

(1,6).

The quadratic function in the context of this problem is defined as follows:

y = (x - 3)² + k.

When x = 5, y = 6, hence the value of the constant k is obtained as follows:

6 = (5 - 3)² + k

6 = 4 + k

k = 2.

Hence the equation is:

y = (x - 3)² + 2.

The other point also has a numeric value of y = 6, hence:

(x - 3)² + 2 = 6

(x - 3)² = 4.

Hence the two options are:

Hence the point is (1,6).

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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Answer:

24 for being able to not have one, 6 for having one of each

Step-by-step explanation:

multiplication

with the option of none

4*2*3=24

without the option of none

3*1*2=6

Answer:

The correct answer is B. 5.45%.

The rate of return built into the annuity is equal to the present value of the annuity divided by the initial amount, $3,000,000.

The present value of an annuity can be calculated using the formula PV = PMT [(1 - (1 / (1 + i)^n)) / i], where PMT is the payment amount, i is the rate of return, and n is the number of payments.

In this case, the PMT is $250,000, i is 5.45%, and n is 20, yielding a present value of $3,000,000.

Therefore, the rate of return is 5.45%.

Answer:

it is 5 feet squared

Step-by-step explanation:

multiply them all

Answer:

9x + 8y

Step-by-step explanation:

Answer:

should be C

Step-by-step explanation:

They are congruent

In the picture, the angle diagnoly across from the 4th angle is congruent (or equal to) the angle making 5 and that angle congruent.

Answer:

The answer is below

Step-by-step explanation:

Let t1 be the arrival times between a packet and its immediate predecessor and t2 be the arrival times between a packet and successor. Let L1 be the lengths of the predecessor packet and L2 the length of the packet itself. Therefore:

P(no collision between packet and predecessor or successor) = \(P(t_1>L_1)P(t_2>L_2)\)

If P1 is the probability that there is no collision with preceding packets, hence:

P(no collision with other packets) = \(P_1*P(t_2>L_2)\)

λ = 10 packets/s, fixed packet length = 20 ms = 0.02 s. Hence:

\(P(t_1>L_1)=P(t_2>L_2)=e^{-\lambda *0.02}=e^{-10*0.02}=e^{-0.2}\)

P(no collision between packet and predecessor or successor) = \(P(t_1>L_1)P(t_2>L_2)\) = \(e^{-0.2}*e^{-0.2}=e^{-0.4}\)

P(packet collides with either its predecessor or its successor) = 1 - P(no collision between packet and predecessor or successor) = \(1-e^{-0.4}=0.33\)

If the transmission times change, the answer would also change.

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

m∠14 = 80°

Step-by-step explanation:

Angles m∠13 and m∠14 lies on a straight line. Angles on a straight line sums up to 180°.

Hence we can say that,

m∠13 + m∠14 = 180

100 + m∠14 = 180

m∠14 = 180 - 100

m∠14 = 80