cos5xcosx-sin5xsinx=??????????????????

Answer:

I-

Step-by-step explanation:

) 5)8%2=80)4)88=5=5=88=9=5)5=

Answer:

Slope of dotted/dashed line: -3

Slope of Reflection line: 0.25

Equation of Reflection line: y = 0.25x - 2

Step-by-step explanation:

Slope of dotted line: rise/run. So 3/1 = 3. It is a negative slop because of the way it is facing ( \ ).

Slope of reflection line: rise/run. So 1/4 = 0.25. It is a positive slope ( / ).

Equation of reflection line: y = mx + b

m = slope

b = y-intercept

y = 0.25x - 2

The volume of the cube as a function of m, the number of minutes elapsed, is V(m) = 4m^3 + 18m^2 + 30m + 27.

The volume of a cube with an edge length of 3 feet is given by V = s^3, where s is the length of a side.

Since the edge is increasing at a rate of 2 feet per minute, the length of the side can be expressed as s = 3 + 2m, where m is the number of minutes elapsed.

Substituting this expression for s into the volume formula, we get:

V(m) = (3 + 2m)^3

Expanding this expression, we have:

V(m) = (3 + 2m)(3 + 2m)(3 + 2m)

= (9 + 6m + 6m + 4m^2)(3 + 2m)

= (9 + 12m + 4m^2)(3 + 2m)

= 27 + 18m + 12m + 8m^2 + 6m^2 + 4m^3

= 4m^3 + 18m^2 + 30m + 27

Therefore, the volume of the cube as a function of m, the number of minutes elapsed, is V(m) = 4m^3 + 18m^2 + 30m + 27.

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Answer:

Assuming you're talking about the angles of a triangle, X would be \(34^{.}\)

Step-by-step explanation:

The sum of the angles in a triangle is 180, 180 - 32 - 80 = 68, \(\frac{68}{2}\) is 34, so X is equal to \(34^{.}\).

The representation of did sign decimal integers in 8-bit binary (two's complement) -16 =  11110000.

The correct option is C.

A maximum of 256 values, or 0 through 255, can be represented by 8 bits. The total number of states that may be represented and the number of bits in a binary number are both listed in Table 5.1. G = gigabits; K = kilobits; M = megabits; 1,048,576 = gigabits; 1,0737,41,824 = kilobits.

The most common number of bits in a byte is eight. A byte is a unit of digital information. The byte is indeed the smallest addressable unit of recollection in many computer architectures because historically, a single character of text was encoded in a computer using a byte's worth of bits.

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What is the 8-bit binary (two's-complement) representation of signed decimal integers -16?

A. 11111011

B. 11010110

C. 11110000

D. 10111000

Answer:

126

Step-by-step explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

\($^9C_4$\)

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

\($^9C_4=\frac{9!}{4!(9-4)!}$\)

      \($=\frac{9!}{5! \ 4!}$\)

     \($=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$\)

    = 126

Answer:

I'm not sure but

Step-by-step explanation: The area is 9.5 feet.

Answer:

c!

Step-by-step explanation:

The expression can be used to find the number of CDs that are not country music is 52-c. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Kayla has 52 CDs in her music collection. Let c represent the number of country music CDs in Kayla's collection.

The expression can be used to find the number of CDs that are not country music is written as below:-

E =  52-c

The correct option is D for the required expression.

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Part A:

Each snowball costs $0.30 to make and is sold for $1.25 each.

The profit per snowball is:

P = $1.25 - $0.30 = $0.95

The profit is $0.95 per snowball

Part B:

Little brother gave away 12 snowballs. The student lost the profit of those 12 snowballs:

12 x $0.95 = $11.40

The student lost $11.40 in profits

Note: The student also lost the $0.30 for the cost to make each snowball, but it's not accounted for.

The dimensions of the box that minimize the amount of material used are:

Sides of the base = 30 cm

Height = 15 cm

To minimize the amount of material used, we need to minimize the surface area. Let's express the surface area of the box in terms of s and h. The total surface area (A_total) is the sum of the area of the base (A_base) and the areas of the four sides (A_sides):

A_total = A_base + A_sides

= s² + 4sh

Now, let's express A_total in terms of a single variable. We can do this by substituting the volume equation, 13,500 = s²h, into the equation for A_total:

A_total = s² + 4sh

= s² + 4s(13,500/s²) [substituting h with 13,500/s²]

= s² + 54,000/s

To find the dimensions that minimize the amount of material used, we need to find the minimum value of A_total. To do this, we can take the derivative of A_total with respect to s, set it to zero, and solve for s.

dA_total/ds = 2s - 54,000/s²

Setting this derivative to zero and solving for s:

2s - 54,000/s² = 0

2s = 54,000/s²

2s³ = 54,000

s³ = 27,000

s = ∛27,000

s ≈ 30 cm

Now that we have the value of s, we can substitute it back into the volume equation to find the value of h:

13,500 = s²h

13,500 = (30 cm)²h

13,500 = 900h

h = 13,500/900

h = 15 cm

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Answer:

A

Step-by-step explanation:

The answer to the first expression is 1.

A =1

B= 7

C=28

D=5/3

Answer:

The value of x in the equation 1.5(x + 4)-3 = 4.5 (x-2) is 4.

Step-by-step explanation:

1.5( x + 4)-3 = 4.5 (x - 2)

Using the distributive property muntiply the term in the equation.

1.5x + 1.5×4-3 = 4x - 4.5 × 2

1.5x + 6-3 = 4.5x - 9

isolate the variable x using transporting method and solve for x

4.5x - 1.5x = 6 - 3 + 9

3x = 12

therefore, x = 12/3 = 4

Hope This Helps You!!!

Answer:

We have 2 rational solutions

0 irrational solutions

0 complex solutions

Step-by-step explanation:

a^2 + 8a + 12 = 0

Using the discriminant

b^2 -4ac where ax^2 + bx+ c

so a =1  b = 8 and c = 12

8^2 -4(1)*12

64 - 48

16

Since the discriminant is greater than 0, we have 2 real solutions

since we can take the square root of 16, we have rational solutions

We have 2 rational solutions

Since this is a quadratic equations, there are only 2 solutions so there are

0 irrational solutions

0 complex solutions

Answer:

2 Rational Solutions

0 Irrational Solutions

0 Complex Solutions

Step-by-step explanation:

The discriminant of the quadratic formula is the name given to the portion underneath the radical (or the square root)"

\(x = \frac{1}{2} (-b\frac{ + }{ - } \sqrt{ {b}^{2} - 4ac })\)

Discriminant = D = b²-4ac

If D is less than 0 you have two complex solutions.

If D is equal to 0 you'll have one real solution.

If D is bigger than 0 you'll get two real solutions.

So here we have:

a=1

b=8

c=12

Which means D=64-4(1)(12)=64-48=16>0

D is bigger than 0, so you'll have two real solutions. And since 16 is a perfect square, they'll both be rational numbers.

The hotel owner needs approximately 2,248 square feet of fabric to make a pool covering for the winter for their regular hexagonal pool with a side-to-side length of 30 feet.

To calculate the area of the pool, we first need to find the apothem (the distance from the center of the hexagon to the midpoint of any side). For a regular hexagon, the apothem is equal to the side length times the square root of 3 divided by 2. So, the apothem of this hexagonal pool is:

apothem = 30 × √3/2 = 25.980762

The area of a regular hexagon is given by the formula:

area = 3 × √3/2 × apothem^2

Substituting the value of the apothem, we get:

area = 3 × √3/2 × 25.980762^2 = 2247.72

Rounding this to the nearest square foot, the hotel owner will need approximately 2,248 square feet of fabric to construct the cover for the pool.

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Answer:

0.125

Step-by-step explanation:

It has not been bar notated unlike all of the other ones. Bar notation is used for repeating decimals. So therefore if it has not been bar notated it is not a repeating decimal, it is a terminating decimal. Meaning it ends at the last digit and does not go any further.

Hope this helps!

The system of equations that represents the number of each type of basket Jake scored is given by:

x + y = 13

2x + 3y = 28

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Jake scored 28 points in his basketball game by shooting only two-point and three-point shots, hence:

2x + 3y = 28.

He scored a total of 13 baskets, hence:

x + y = 13.

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The particle is at the point (-1.112,3.909) after traveling for 20 microseconds.

We have been given a circle,

(x-3)²+(y-4)²=25

whose center is (3,4)

and with a radius of 5 units.

The particle starts at (3,-1) which is the 6 o'clock position in the circle, and ends at (8,4) after 7 microseconds which are at the 3 o'clock position in the circle.

So, the particle traveled 1/4 of the circumference of the circle in 7 microseconds

therefore according to the unitary method it will travel 5/7 of the circumference of the given circle.

so it will subtend 2π×5/7 of the circle from (3,-1)

from the polar form of the circle and the shifting of center of the circle we can conclude

that it's location will be

(5 × cos (10π/7) - 3 , 5 × sin (10π/7) - 4)

= (-1.112,3.909)

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We can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

Based on the line of best fit for the data, we can estimate the number of servings of kakigori Cho will sell on a day when the high temperature is 29° Celsius.

From the scatter plot, we can see that the line of best fit is increasing as the temperature increases.

By estimating the value on the line of best fit for the temperature of 29° Celsius, we can approximate the number of servings sold. Based on the scatter plot, it appears that the number of servings sold is around 100 when the temperature is 29° Celsius.

Therefore, we can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

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Answer:

r=20

Step-by-step explanation:

r/20​​−5=−4

r/20​​=−4+5

r/20=1

r=1×20

r=20

Answer:

20

step by step

Answer:

11

Step-by-step explanation:

there are 12 months in a year

we want to equally split the 130 into 12 equal payments

130/12=10.833 or 11

The probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I can be denoted as P(S|C'). The correct option is (a) P(S'|C').

To represent the probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I, we need to consider the complement of the events.

The complement of event C (grade of B or better in Calculus I) is C' (grade less than B in Calculus I). Similarly, the complement of event S (grade of A in Statistics I) is S' (grade other than A in Statistics I).

Therefore, the probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I is denoted as P(S|C'). This notation indicates the conditional probability of event S occurring given that event C' has occurred.

Among the given options, (a) P(S'|C') correctly represents the desired probability. Option (b) P(CIS) represents the joint probability of events C, I, and S, which is not relevant to the given question.

Option (c) P(SIC) represents the joint probability of events S, I, and C, which is also not relevant. Option (d) P(SIC) is a duplicate of option (c) and does not represent the desired probability.

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Answer:

x=7

Step-by-step explanation:

The initial number of bacteria in the culture was approximately 116. We can solve this using differential equation.

Let N(t) be the number of bacteria present at time t, and let k be the constant of proportionality for the growth rate. Then the differential equation that describes the growth of bacteria is:

dN/dt = kN

We can solve this differential equation to get:

N(t) = N0e\(^({kt)}\)

Where N0 is the initial number of bacteria at time t=0.

Using the given information, we can set up a system of two equations:

500 = N0e\(^{(3k)}\)

5000 = N0e\(^{(10k)}\)

Dividing the second equation by the first equation, we get:

10 = e\(^{(7k)}\)

Taking the natural logarithm of both sides, we get:

ln(10) = 7k

Solving for k, we get:

k = ln(10)/7

Substituting this value of k into either of the two equations above, we can solve for N0:

500 = N0e\(^{(3ln(10)/7)}\)

N0 = 116 (rounded to the nearest integer)

Therefore, the initial number of bacteria in the culture was approximately 116.

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Answer:

11

Step-by-step explanation:

x=2

5*2+1=10+1=11

Answer: g(2) = 11

Step-by-step explanation:

So, you the 2 as x for 5x + 1, and you get 10 + 1. Then you can get an 11 as your answer.

Question:

James has 14,500g of sand in his sandbox. He brings home another 7,400g of sand from the beach to add to his sandbox. How many kilograms of sand does James have in his sandbox now?

Answer:

The quantity of sandbox James has is 21.9kg

Step-by-step explanation:

Given

Initial quantity of sandbox = 14,500 g

Additional quantity = 7,400 g

Required

Total quantity of sandbox in kg

Tp get the total quantity of sandbox, we simply add in the initial and additional quantity of sandbox together;

This is represented mathematically as follows;

Total = Initial Quantity + Additional Quantity

Total = 14,500 g + 7,400 g

Total = 21,900 g

But the question says the answer should be in kg

1000 g is equivalent to 1 kg

21,900 g will be equivalent to \(\frac{21,900}{1,000} kg\)

\(21,900g = \frac{21,900}{1,000} kg\)

\(21,900g = 21.9 kg\)

Hence, the quantity of sandbox James has is 21.9kg

To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.



To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:

1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.

2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.

3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.

Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.

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Answer:

259.21/100 X 30 = 77.763

sale price = $77.76

Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.

It is simple to establish whether the inverse of a function is also a function using the horizontal line test.

Because it fails the vertical line test, a function's inverse might not actually be a function.

Graph of the line

f\left( x \right) = - x + 2

f(x)=−x+2.

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Answer:

The mean would be 82

Step-by-step explanation:

To find the mean you add up all the numbers.

\(68 + 73 + 95 + 81 + 85 + 90 + 77 + 84 + 75 + 92 = 820\)

Then you divide that be the amount of numbers are given to you.

\(820 \div 10 = 82\)

And that is how you find the mean.

Sorry if it is wrong I'm tired.