show that the cosine rule shown below can be solved can be rearranged to give..

The equations which give exponential graphs are y = 5ˣ and y = (1/5)ˣ.

What is an exponential graph?

A curve that depicts an exponential function is known as an exponential graph. A curve with a horizontal asymptote and either an increasing slope or a decreasing slope is called an exponential graph. The graph begins as a horizontal line and then grows or decays slowly at first before accelerating.

The general formula for an exponential function is,

           f(x) = aˣ

Where the input values of the function, which is x, appear as the exponent of the function.

The values x can be all real numbers.

The base of the function (a)  should be a constant. It should be greater than 0 and should not be equal to 1.

Following the above prerequisites, the equations which give exponential graphs are y = 5ˣ and y = (1/5)ˣ.

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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:

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

The correct graph is the last one (where the shaded region is on the right side)

Here we have the system of inequalities below:

y ≤ 1/2x+1

y > -2x+4

The first inequality is:

y ≤ 1/2x+1

Here we have a solid line with positive slope, and the shaded region is below that line.

The second inequality is:

y > -2x+4

This time we will have a dashed line with negative slope, and the shaded region must be above the line, then the correct option will be the last option.

(where the shaded region is on the right quadrant)

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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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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:

350

Step-by-step explanation:

calculator

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 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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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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All possible values of 'x' such that the distance between the points is 17 is, x = 19 or x = 3.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, (x₁, y₁) = (11, 6) and (x₂, y₂) = (x,- 9) and the distance between them

is 17 units.

Therefore, The equation can be constructed as,

[tex]17 = \sqrt{(x - 11)^2 + (- 9 - 6)^2[/tex].

[tex]17 = \sqrt{(x - 11)^2 + 225[/tex].

Taking squares on both sides to remove the square root we have,

289 = (x - 11)² + 225.

289 = x² - 22x + 121 + 225.

x² - 22x + 57 = 0.

x² - 19x - 3x + 57 = 0.

x(x - 19) - 3(x + 19) =0.

x = 19 or x = 3 are the two possible points.

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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: Let's call the area of Brad's rectangular backyard "A". The area of the white circle is "C". The area of the gray region, the portion of the yard that the water from the sprinkler does not reach, is "G".

We know that the sum of the areas of the white circle and the gray region is equal to the area of Brad's backyard:

C + G = A

Therefore, the expression to represent the gray region is:

G = A - C

Step-by-step explanation:

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?

Answer:

The current population in Algeria can be calculated by solving the equation P = 38(1+r)^t, where P is the population in millions after t years. Setting t = 0 gives us the current population: P = 38(1+r)^0 = 38, so the current population in Algeria is 38 million.

The 95% confidence interval for mean of the population is CI = (3.81,6.19).

What is confidence interval?

The confidence interval for the population mean can be found when we know the sample mean and the margin of error of the interval. This last value depends on the standard deviation, the sample size and the confidence level of the interval.

The sample size is n = 100.

The sample mean is x' = 5

The sample standard deviation is s = 6

The confidence level is 1 - α = 0.95

Find the Probability Distribution.

Let [tex]x_1,x_2,....,x_n[/tex] be a random sample of size n taken from a normal distribution with unknown mean μ and unknown variance σ².

The random variable t with formula t = (x' - μ) / (s/√n) has a t distribution with (n - 1) degrees of freedom.

[tex]t_\frac{\alpha}{2}[/tex]

1 - α = 0.95

α = 1 - 0.95

α = 0.05

α / 2 = 0.05 / 2

α / 2 = 0.025

The degree of freedom is -

d.f = n - 1

d.f = 100 - 1

d.f = 99

So, [tex]t_\frac{\alpha}{2}[/tex] using the t-distribution table is -

[tex]t_\frac{\alpha}{2} = 1.984[/tex]

To illustrate the use of the table, note that the t-value with 99 degrees of freedom having an area of 0.025 to the right is [tex]t_\frac{\alpha}{2} = 1.984[/tex].

Then the Confidence interval is -

CI = x' ± [tex]t_{\frac{\alpha}{2},n-1}[/tex] × s/√n

CI = 5 ± 1.984 × 6/√100

CI = 5 ± 1.984 × 6/10

CI = 5 ± 1.984 × 0.6

CI = (5 - 1.19) (5 + 1.19)

CI = (3.81,6.19)

Therefore, the confidence interval is CI = (3.81,6.19).

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A random sample of 100 observations from a population yields a mean equal to 5 and a standard deviation equal to 6. What is the 95% confidence interval for the mean of the population?

Answer:

1 4

2 c³,c²,c,-11

3 1/3

4 -1

5 3/4

Answer:

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

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Answer:

16 is correct

Step-by-step explanation:

Your welcome

Answer:

Step-by-step explanation:

To calculate the value of Andrea's savings account after 8 years, we need to find the balance after compounding the interest for 96 months (8 years x 12 months per year). We can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the balance after t years,

P is the initial balance ($1700),

r is the annual interest rate (2.5%),

n is the number of times interest is compounded in a year (12),

t is the number of years (8).

Converting the interest rate to a decimal and dividing by the number of times compounded per year:

r/n = 2.5% / 12 = 0.021

Plugging in the values into the formula:

A = 1700 * (1 + 0.021)^(12 * 8) = 1700 * (1.021)^96

Calculating the value:

A = 1700 * 2.8412 = 4860.80

So, the value of Andrea's account after 8 years would be $4860.80.

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:

(3^2*2h^4)

Step-by-step explanation:

The Residual is 0.944 kg.

The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.

Given:

Residual is typically defined as actuals minus predicted.

The prediction is calculated from

W = −6.07 + 0.1693L

W = −6.07 + 0.1693(48)

W = 2.0564 kg

And, The actual was 3 kg

So, the residual

= 3 - 2.0564

= 0.9436

= 0.944 kg

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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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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.

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 12th term of the sequence with a first term of -9 and common difference of 2 is 13

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

An nth term of arithmetic term is given as:

[tex]a_n=a+(n-1)d[/tex]

where a is the first term and d is the common difference and n is the term.

Given that a = -9, d = 2

The 12th term of the sequence is:

a₁₂ = -9 + (12 - 1)2

a₁₂ = -9 + 22

a₁₁ = 13

The 12th term of the sequence is 13

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Step-by-step explanation:

x÷12

2/3/12

2×12/3

24/3

8

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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