The smallest number such that when it is divided by 8 has a remainder of 6 and when it is divided by 9, has a remainder of 7

Answer: The value of sin(2x) can be found using the identity:

sin(2x) = 2sin(x)cos(x)

Since tan(x) = -1/5, we can use the tangent definition to find the sine and cosine values:

tan(x) = sin(x) / cos(x) = -1/5

Cross multiplying and solving for sin(x), we get:

sin(x) = -5 / sqrt(26)

And using the Pythagorean identity:

cos^2(x) + sin^2(x) = 1

We can find cos(x):

cos(x) = sqrt(1 - sin^2(x)) = sqrt(1 - (-5/sqrt(26))^2) = sqrt(26) / sqrt(26) = sqrt(26) / sqrt(26) = sqrt(26) / 5

Finally, substituting the values of sin(x) and cos(x) into the formula for sin(2x), we get:

sin(2x) = 2sin(x)cos(x) = 2 * (-5 / sqrt(26)) * (sqrt(26) / 5) = -2 sqrt(26) / 5 = -2 sqrt(26) / 5 = -2 sqrt(26) / 5

So the exact value of sin(2x) is -2 sqrt(26) / 5.

Step-by-step explanation:

For the given condition the correct inequality is,

⇒ x ≥ 20

Where, x represent the number of questions.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

A student decides to solve at least 20 math problems every day to better their grade if they self and math problems every day.

Let number of questions done by a student = x

So, The inequality for the given condition is,

⇒ x ≥ 20

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Answer:489

Step-by-step explanation:just divide 42,543 by 87

Answer489 I hope this helps

Step-by-step explanation:

The answer is 489 use a calculator

There is not enough information to determine the rates of change which is therefore denoted as option C in the table and graph given.

This is referred to as a pictorial representation or a diagram that represents data or values in an organized manner.

In the graph and table there was no clear representation of the variables in the x and y coordinates which is therefore the reason why there won't be enough information to determine the rate of change which is therefore the correct choice.

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The full question:

Compare the rates of change of the following table and graph. x y 1 -4 2 -8 3 -12 4 -16 A. The rate of change of the table is greater than the rate of change of the graph. B. There is not enough information to determine the rates of change. C. The rate of change of the table is equal to the rate of change of the graph. D. The rate of change of the graph is greater than the rate of change of the table.

Answer:

solution

we assume the negative part because their is no squares of negative number.

10²-2(-10)-100

we get answer which is 20

Answer:

∠ Y = 60° , WY = 7 in

Step-by-step explanation:

the sides WX and YX are congruent then the triangle is isosceles with base angles congruent, that is

∠ Y = ∠ W = (180 - 60)° ÷ 2 = 120° ÷ 2 = 60°

Since all 3 angles in the triangle are congruent , all 60° then the triangle is equilateral with 3 congruent sides, then

WY = 7 in

A car is through internet is better to buy.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In the fall of 2014,

1 U.S. dollar =  1.10 Canadian dollars.

Here, An automobile in Toronto sells for 26,000 Canadian dollars.

And, The same car on sale for 23,000 U.S. dollars on the internet.

Thus, The cost of car on internet is,

⇒ 23,000 U.S. dollars

⇒ 23,000 × 1.10 Canadian dollars.

⇒ 25,300 Canadian dollars.

Thus, A car is buy through internet is better to buy.

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Answer:

no real factors

Step-by-step explanation:

-2x² - 11x - 20

try use the first 3 answers as factor, you'll see non works.

Force is required to make an object move, and force acts differently on objects depending on the type of motion it exhibits. In the case of curvilinear motion, a special force comes into the picture, i.e., centripetal force – literally meaning “centre seeking.” Centripetal force is the force acting towards the centre of the circular path. In this article, let us discuss what centripetal force is and how it is different from centrifugal force.

if a total of 480 were sold then the number of each type of vehicle sold is,

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,

A car dealership sells SUVs and passenger cars

the number of each type of vehicle sold = ?

Let x be the number of passenger cars sold.

Then, the number of SUVs sold = x + 20

The combined total of the two types of vehicles sold was 480, so we can write an equation:

x + (x + 20) = 480

Expanding the right side:

2x + 20 = 480

Subtracting 20 from both sides:

2x = 460

Dividing both sides by 2:

x = 230

The number of SUVs sold =  230 + 20

                                           = 250

So, 230 passenger cars were sold and 250 SUVs were sold.

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Least number of uniform = 45

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Given,

Curtis wears a uniform number that rounds to 50 to the nearest ten and 0 to the nearest hundred.

Whole numbers, that can be rounded to 50 to the nearest ten are

45, 46, 47, 48, 49, 50, 51, 52, 53, 54

Smallest number is 45

Hence, 45 is the least uniform number Curtis can have.

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more information needed. no graphs to choose.

no multiple choice given..

Answer:

[tex] \frac{1}{16} [/tex]

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Answer:

16 is correct

Step-by-step explanation:

Your welcome

The rate of change of the function y=3x+3 is 3

From the question, we have the following parameters that can be used in our computation:

y = 3x + 3

The above function is a linear function

A linear function is represented as

y = mx + c

Where

m = slope = rate of change

Using the above as a guide, we have the following:

rate of change = 3

Hence, the rate of change is 3

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Aidan and Bella will have the exact same amount of savings in 5 months.

We know two simultaneous equations have a unique solution when they intersect at a point,

when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.

From the given information, Let the number of months be 'm'.

And, The two equations are 90 + 20x and 15 + 35x.

Therefore, The number of months in which they will have the same amount of savings would be,

90 + 20x = 15 + 35x.

75 = 15x.

x = 5.

So, In 5 months they will have the same amount of savings.

Q. Aidan and Bella each plan to open a savings account. Aidan starts with $90 and plans to save $20 every month. Bella starts with $15 and plans to save $35 every month, in which month they will have the same amount of savings?

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The value of x is 2 so that the volume is 48 m³

The area of a rectangle is the region occupied within the boundary of the rectangle.

The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. The area of a rectangle is obtained by multiplying its length and width (breadth).

Area of a Rectangle = Length × Width

Volume of a rectangular solid is the product of the length, width, and height.

Volume of a rectangular solid in terms of the area of the base. The area of the base B is equal to Length × Width

Base = Length × Width

Volume of rectangular solid = Base × Height

Given:

Length of rectangular piece of metal = 10 - 2x

Breadth of rectangular piece of metal = 8 - 2x

Area of rectangle = Length × Width

(10 - 2x) (8 - 2x) = 24

80 - 20x - 16x + 4x² = 24

4x² - 36x + 56 = 0

x² - 9x + 14 = 0

x² - 7x - 2x + 14 = 0

x(x - 7) -2(x - 7) = 0

(x - 2)(x - 7) = 0

x = 2 and x = 7(Not possible)

when x = 2 cm (height)

Volume = Area of Base × height

Volume = 24 × 2

Volume = 48 cm³

So, the value of x is 2.

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The volume of the concrete required to be poured for a rectangular prism floor slab are;

11. 5 1/3 cubic yards

12. 74 2/27 cubic yards

A rectangular prism is a polyhedron that consists of six rectangular faces, in which the adjacent faces are perpendicular and opposite faces are parallel.

11. The dimensions of the floor slab = 18' × 24' × 4''

Where the shape of the slab is a rectangular prism, we get;

Width of the floor slab = 24 feet

Length of the floor slab = 18 feet

Height of the floor slab = 4 inches

4 inches = (1/3) ft

The volume of the cement is therefore;

V = 24 ft × 18 ft × (1/3) ft = 144 ft³

The volume of the concrete required to pour a floor slab of the dimensions: 18' × 24' × 4'' is 144 cubic feet

1 yard = 3 feet

The dimensions of the slab are therefore;

Length = 24/3 yards = 8 yards

Width = 18/3 yards = 6 yards

Height = (1/3)/3 yards = (1/9) yards

The volume of the slab = 8 yards × 6 yards× 1/9 yard = 16/3 cubic yards

12. The dimensions of the slab are;

Length of the slab = 80 feet = 80/3 yards

Width of the slab = 60 feet = 60/3 yards = 20 yards

Height of the slab = 5 inches = 5/12 ft = 5/(12 × 3) yard = 5/36 yard

The volume of the concrete slab is therefore;

(80/3) yards × 20 yards × (5/36) yard = 74 2/27 cubic yards

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Answer:

So, about 2.28% of men in the country are no more than 64 inches tall.

Step-by-step explanation:

First, we need to standardize the value of 64 inches to a z-score:

z = (64 - 68) / 2 = -2

We can use a standard normal distribution table or a calculator to find the percentage of men who are no more than 64 inches tall:

P(Z ≤ -2) = 0.0228

Answer:

Step-by-step explanation:

I took your points looooser hahahaha

Answer:

  (c)  Low Price Rentals, because it will charge $68.20 for the trip, while Easy Rental will charge $85.00.

Step-by-step explanation:

You want to compare two car rental options for a 120-mile trip. Low Price charges $49 and $0.16 per mile; Easy charges $25 and $0.50 per mile.

We find it convenient to use a graphing calculator to plot the rental charges versus mileage. We find the charges to be ...

You can also evaluate the charges by adding the fixed fee to the mileage cost for each option, as in the second attachment.

Answer:

If the angle between two unit vectors u and v is 3.14/3, then using the law of cosines, ||u + v||^2 = 2 + 2cos(3.14/3) = 2 + 2(0.5) = 3. Hence ||u + v|| = sqrt(3).

To find the value of k such that the system has a unique solution, no solution, or an infinite number of solutions, we can use the determinant of the coefficient matrix. If the determinant is nonzero, then the system has a unique solution. If the determinant is zero and the system of equations is inconsistent, then the system has no solution. If the determinant is zero and the system of equations is consistent, then the system has an infinite number of solutions. In this case, the determinant of the coefficient matrix is zero, which implies that the system has an infinite number of solutions.

The eigen values and eigen vectors of the matrix can be found by solving the characteristic equation, which is obtained by det(A - λI) = 0, where A is the matrix and I is the identity matrix.

For the matrix

2 1 -1

3 2 -3

3 1 -2

the characteristic equation is

(2 - λ)(3 - λ) - 3 = 0

which gives us λ = 1 and λ = 3 as the eigen values.

The corresponding eigen vectors can be found by solving the system of equations (A - λI)x = 0, where x is the eigen vector.

For λ = 1, the eigen vector is (1, -1, 1).

For λ = 3, the eigen vector is (-1, 2, 1).

If f(x) is a polynomial of degree 4 with roots 1, 2, 3, 4 and leading coefficient 1, and g(x) is a polynomial of degree 4 with roots 1, 1/2, 1/3, 1/4 and leading coefficient 1, then the limit of 1/f(x)/g(x) as x approaches infinity does not exist. This can be seen by noting that f(x) and g(x) both grow without bound as x grows without bound, so the ratio of the two polynomials also grows without bound.

The velocity of the rock after one second is v(1)=13.28 m/s.

The given equation is

H(t) = 17t - 1.86t² ------(1)

velicity=17 m/s.

(a) the velocity of the rock after one second will be:

v(t) = dH/dt = 17-3.72t

v(1) = 17 - 3.72(1)

v(1)= 13.28 m/s

(b)the velocity of the rock when t=a

v(a) = 17 - 3.72a.

(c)

The rock hits the surface when H(t) = 0

17t - 1.86t² = t(17-1.86t)=0

⇒ t= 0 or 17-1.86t = 0

The first case is launch, the second is returning to the ground.

17 - 1.86t = 0

17= 1.86t

t = 17/1.86

t ≅9.139s

(d)

v at surface = v at the time from part (c).

v(9.139) = 17- 3.72(9.139)

v(9.139) ≅ -17 m/s

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Full question:

if a rock is thrown upward on the planet mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H=17t-1.86t²

(a) find the velocity of the rock after one second

(b) find the velocity of the rock when t=a

(c) when will the rock hit the surface

(d) with what velocity will the rock hit the surface?

The monthly principal and interest payment is $916.6.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

From the given information SI = (75000×8×15)/100.

SI = 750×8×15.

SI = $90000.

Therefore, A = P + SI = 75000 + 90000 = $165000.

In 15 years there is 15×12 = 180 months.

Therefore, the monthly payment is,

= $(165000/180).

= $916.6

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a. probability of neither a math major nor an engineering major is: 0.1783

b. probability is only an engineering major: 0.5167

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Given that,

n(S) = 60

n(math) = n(M) = 183 ⇒ P(M) = n(M)/ n(S) = 183/600

n(engineering) = n(E) = 366 ⇒ P(E) = n(E)/ n(S) = 366/600

n(M∩E) = 56

P (M∩E) = n(M∩E) / n(S) = 56/600

a) probability of neither a math major nor an engineering major is:

P (M' ∩ E') = P (M∪E)'

P (M' ∩ E') = 1 - P (M∪E)

P (M' ∩ E') = 1 - [P(M) + P(E) - P(M∩E)]

P (M' ∩ E') = 1 - [183/600 + 366/600 - 56/600]

P (M' ∩ E') = 0.1783

b)

probability is only an engineering major:

P(E - M) = P(E) - P(M∩E)

P(E - M) = 366/600 - 56/600

P(E - M) = 0.5167

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Answer:

5x linear monomial



-7 constant monomial

x^2+4 quadratic binomial

x^2-3x+11 quadratic trinomial

2x-9 linear binomial

Step-by-step explanation:

Linear indicates a line, the power of x in the equation is 1 (which we never write the power one, so it looks like just x)



Quadratics have an x to the power of 2

A constant is a plain number with no variable.

The prefixes mono-, bi-, and tri- can help you with these. Mono- means one. Monomials have one term, such as 5x or -7

Bi- means two. Binomials have two terms such as x^2+4 or 2x-9.

Tri- means three. Trinomials have three terms such as x^2-3x+11.

The question is:

How many Syrian citizens choose to leave the country every year for better opportunities?

A survey that is collected through the facts and numbers from the data is a quantitative survey.

We have to write a quantitative survey or simulation question(s)?

For that,

we will form the variable and target group.

The question:

How many Syrian citizens choose to leave the country every year for better opportunities?

Variable: Number of citizens looking for better opportunities

Target Group: Syrian citizens.

Hence, the question is given above.

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The probability that a cat, jumping on 7 keys in sequence and at random (possibly with repetition), will strike the first seven notes of Beethoven's Fifth Symphony is; P = 2.45 * 10⁻¹⁴

The parameters expressed are;

Number of Piano Keyboard keys = 88

The following steps can be used in order to determine the probability that a cat, jumping on 7 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony:

Step 1 - The four notes of the piano are 3 LA's and 1 REb.

Step 2 - The probability that the first key is LA is 1/88.

Step 3 - The probability that the second key is LA is 1/88.

Step 4 - The probability that the third key is LA is 1/88.

Step 5 - The probability that the key is REb is 1/88.

Step 6 - So, the probability that a cat, jumping on 4 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony is:

P = 1/88 * 1/88 * 1/88 * 1/88 * 1/88 * 1/88 * 1/88

P = 2.45 * 10⁻¹⁴

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The volume of the rectangular prism is 400 cubic centimeters which we can calculate using formula: Volume = L * W * H

The volume of rectangular prism can be computed by simply multiplying their dimensions. If the rectangular prism was built with cubes that each have a volume of one cubic centimeter, then the volume of the rectangular prism can be calculated by multiplying the number of cubes in each dimension.

Let's assume that the rectangular prism has a length of "L" cubes, a width of "W" cubes, and a height of "H" cubes. Then, the volume of the rectangular prism can be calculated as follows:

Volume = L * W * H

Each cube has a volume of one cubic centimeter, so the volume of the rectangular prism is equal to the number of cubes it contains. In other words, if the rectangular prism has 10 cubes along its length, 5 cubes along its width, and 8 cubes along its height, then its volume would be:

Volume = 10 * 5 * 8 = 400 cubic centimeters

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Answer:

1,500 beds

Step-by-step explanation:

Occupancy rate  shelter A = 300 x 20/100 = 60

Let capacity of shelter B be X

60% occupancy ==> 60/100 x X = 0.6X

Occupancy rate of A to rate of B is 1: 15 can be expressed as fraction 1/15

Therefore
60/0.6X = 1/15

1 x 0.6X = 60 x 15

0.6X = 900

X = 900/0.6 = 1,500 beds