exponential and logarithmic functions

An item is regularly priced at 70. Shen bought it on sale for 20% off the regular price. Shen paid 56 for the item on sale.

To determine how much Shen paid for the item on sale, follow these steps:

Find the discount amount

Subtract the discount amount from the regular price.

Calculate the discount amount.

Discount amount = Regular price × Discount percentage

Discount amount = 70 × 20%

Discount amount = 70 × 0.20

Discount amount = 14

Calculate the sale price.

Sale price = Regular price - Discount amount

Sale price = 70 - 14

Sale price = 56

Shen paid 56 for the item on sale.

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The coordinates of point P are(0,1)

A part of line which has 2 end points and it is also can be measured

example:

the objects which has starting and the ending point can be taken for consideration

pencil: which is straight and has a fixed length of about 16-22 cm

The intersection of points in a grid system

example the points(25,10) is 25 units long and 10 units up

A(-4,-1) B(6,4) in the ratio 2:3

x1=-4, x2=6,y1=-1,y2=4,m=2,n=3

x=(mx2+nx1)/m+n

=2*6+3*(-4)/2+3

=12-12/5

=0/5

=0

y=my2=ny1/m+n

=2*4+3(-1)/2+3

=8-3/5

=5/5

=1

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For the standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.

The amount of cardboard needed to make a banner depends on the size of the banner. If we know the dimensions of the banner, we can calculate the area of cardboard needed.

Assuming that the banner is a rectangle, let's say its width is w inches and its height is h inches.

Then, the area of the banner can be calculated as:

Area = width x height

Area = w x h

To find out how many square inches of cardboard are needed, we need to add a margin to the dimensions of the banner to account for the thickness of the cardboard. Let's say the margin is m inches.

Then, the width of the cardboard needed is (w + 2m) inches, and the height of the cardboard needed is (h + 2m) inches.

The area of the cardboard needed can be calculated as:

Area of cardboard = (width of cardboard) x (height of cardboard)

Area of cardboard = (w + 2m) x (h + 2m)

So, the total area of cardboard needed for one banner is:

Total area of cardboard = Area of cardboard + Area of margin

Total area of cardboard = (w + 2m) x (h + 2m) + 4m(w + h + 2m)

if we assume that the banner is 2 feet wide (24 inches) and 4 feet long (48 inches), and we add a margin of 1 inch on each side, then we can calculate the total area of cardboard needed as follows:

Total area of cardboard = (24 + 2) x (48 + 2) + 4(1)(24 + 48 + 2)

Total area of cardboard = 26 x 50 + 4(74)

Total area of cardboard = 1300 + 296

Total area of cardboard = 1596 square inches

So, for this standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.

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Add "Spade" to the Card column, with branches to "Even" and "Odd" in the Die column. Thus, option 3 is correct.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο cοmplete the tree diagram, we need tο add the missing branch fοr the spades suit in the card cοlumn.

Here is the cοmpleted tree diagram:

We have added the missing branch fοr the spades suit, which alsο branches intο even and οdd fοr the die rοll. We have alsο filled in the οutcοmes fοr each branch οf the tree, which include the pοssible values fοr the card (2, 3, 4, 5, 6, οr 1 fοr Ace) and the die rοll (even οr οdd).

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The expression of the dimensions are 3w - 2 by w

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

The length of a rectangle is 2 less than 3 times as long as the width

Using the following variable definitions, we have

Based on the given information, we can express the length (l) in terms of the width (w):

l = 3w - 2

Hence, the dimensions are 3w - 2 by w

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Answer:

E

Step-by-step explanation:

My answer

[tex] \frac{2}{5} [/tex]

So, the volume of big cone is 226.08 cu ft for this we have to know about volume.

The area occupied within any three-dimensional solid's borders is known as its volume.

Given, radius of small cone, r = 2 ft

Volume of small cone 25.12 cu ft

[tex]So\ Volume\ of\ small\ cone = \pi rl[/tex]

[tex]25.12 = 3.14 * 2*l[/tex]

[tex]l=\frac{25.12}{3.14\ *\ 2}[/tex]

[tex]l = 4ft[/tex]

Since, cones are similar and bai cone radius is 3 times of small cones then ,

Slant height of big cone = 3 * Slant height of small cone

= 3*4 ft

= 12 ft.

[tex]Volume\ of\ big\ cone = \pi rl[/tex]

[tex]= 3.14*6*12[/tex]

[tex]= 226.08\ cu ft[/tex]

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Answer:

-137

Step-by-step explanation:

23, 15, 7, -1, -9,-17...........

    -8  -8   -8  -8.....

∴ -8n+23

if n = 20

-8(20)+23=-137

Answer:

-137

Step-by-step explanation:

The pattern is -8 every term so

15 + (-8(20-1)) = -137

its pretty much multiplying the rate by what term you want. you subtract the 1 because you started with the first term.

Answer:

14

Step-by-step explanation:

6/9 = x+2/24

Cross multiply to expand

9( x + 2) = 24x 6

9x + 18 = 144

Subract 18 from both sides

9x = 126 Divide both sides by 9

X = 14

10/ 2x-9 = 20/9

Cross multiply

20( 2x - 9) = 10 x 9

40x - 180 = 90

Add 180 to both sides

40x = 270

Divide both sides by 40

X = 6.75

Scale question

Convert 240miles to inches

240 x 63, 660 = 15,206,400

Ratio is 3:15,206,400

Reduce to lowest term by divide both sides by 3

Scale is 1: 5068800

Answer:

Option C) is the correct answer.

The value of the stock needs to go up by 42.86% to be equal to what the investor first paid for it.

Let's say the investor initially paid $100 for the stock. A 30% decrease in the value of the stock would mean it is now worth $70. To bring the value of the stock back up to $100, it needs to increase by $30, which is 42.86% of the current value ($30/$70).

Therefore, the value of the stock needs to go up by 42.86% from its current value for the investor to break even.

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The length of MN is equal to: 32.2 ft.

In Mathematics, Pythagorean's theorem is modeled by the following mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the length of sides of a right-angled triangle.

In order to determine the length of MN in right-angled triangle LNM, we would have to apply Pythagorean's theorem.

LN² + MN² = LM²

16² + MN² = 36²

256 + MN² = 1,296

MN² = 1,296 - 256

MN² = 1,040

MN = √1,040

MN = 32.2 ft.

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The correct response, based on the facts provided, is 625.

What does a math power mean?

When a base number is raised to an exponent in mathematics, the exponent represents how many times the base number has been multiplied, and the base amount is the factor that is multiplied by itself.

What do you call 5 to the power of?

In mathematics and mathematics, the fifth power, or subsolid, of a number, n, is obtained by multiplying five occurrences of n around each other:[tex]n⁵ = n × n × n × n × n.[/tex]The fourth power of a number or the squares of a number of times its cube can also be used to create fifth powers.

5 to the fourth power (also written as 5⁴) is:

[tex]5 × 5 × 5 × 5 = 625[/tex]

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The volume of a cylinder is πr²h.

Given, that H = 2 ft and R = 6 Feet.

So V = πr²h = 3.14 x 6 x 6 x 2

                   = 3.14 * 72

                   = 226.08 ft³

Answer:

The volume of the cylinder is 226.08 feet^3

Step-by-step explanation:

The volume of a 3-d shape with sides straight up is

BaseArea × height.

For a cylinder the base is a circle. Area of a circle is pi•r^2

So the Volume of your cylinder is:

V = pi•r^2 • h

Fill in the info given.

V = 3.14 • 6^2 • 2

= 226.08

The units for volume are cubed, that is, 3rd power.

So 226.08 cubed ft

or 226.08 ft^3

Hope this helps!

The diagonal of the square bisect the angles. Therefore, the angle x in the square is 60 degrees.

A square is a quadrilateral with each angles equal to 90 degrees. The sum of angles in a square is 360 degrees.

The diagonal of a square is perpendicular to each other. It divided the square into two congruent isosceles triangle.

The diagonal of a square bisects the angles of a square. Therefore, the angles are 45 degrees each after bisection.

Hence, let's find the angle x in the square.

Therefore,

180 - 105 + x + 45  = 180

75 + x + 45 = 180

x + 120 = 180

subtract  120 from both sides of the equation

x + 120 - 120 = 180 - 120

x = 60 degrees

Therefore,

x = 60 degrees

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At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Therefore the probability density function has inflection points at x = μ ± σ.

The probability density function (PDF) of a normally distributed random variable is defined as:

f(x) = 1/(σ√2π) e-(x - μ)²/2σ²

where μ is the mean,

σ is the standard deviation.

This equation has two inflection points at x = μ ± σ. To show this, we differentiate the equation twice with respect to x.

f'(x) = -(x - μ) / σ² e-(x - μ)²/2σ²

f''(x) = [-(x - μ)² / σ³ - 1] e-(x - μ)²/2σ²

At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Thus, we have proved that the PDF of a normally distributed random variable has inflection points at x = μ ± σ.

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The value of z can be determined by solving the equation 7z-94 = 2z+76, which yields z=35.

To determine the value of z in the given equation, it is necessary to solve the equation 7z-94 = 2z+76. Begin by subtracting 2z from both sides of the equation, which yields 7z-2z-94 = 76. Simplifying this yields 5z-94 = 76. To solve for z, add 94 to both sides of the equation, which yields 5z = 170. Dividing both sides by 5 yields z = 34. Since the equation is not asking for an exact value, it can be rounded to the nearest whole number, which is 35. Therefore, the value of z is 35.

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√3/2  and √3x / x.

The value of sin (cos-1 (1/2)) and tan (sec-1 (x/3)) are:Sin (cos-1 (1/2)):In the trigonometry section, the cosine inverse (or arccosine) is used to find the angle whose cosine value is equal to a given number.The cosine inverse (or arccosine) of a number is the angle whose cosine is equal to that number (cos-1). Therefore, cos-1 (1/2) represents the angle that has a cosine of 1/2.The sine is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.Sin (cos-1 (1/2)) = sqrt (1 - cos2 (cos-1 (1/2)))Since cos (cos-1 (1/2)) = 1/2, we can substitute it.Sin (cos-1 (1/2)) = sqrt (1 - (1/2)2) = sqrt (3/4) = √3/2Tan (sec-1 (x/3)):The secant inverse (or arcsecant) is used to find the angle whose secant value is equal to a given number.The secant inverse (or arcsecant) of a number is the angle whose secant is equal to that number (sec-1). Therefore, sec-1 (x/3) represents the angle that has a secant of x/3.The tangent is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.Tan (sec-1 (x/3)) = sqrt (sec2 (sec-1 (x/3)))Since sec (sec-1 (x/3)) = 3/x, we can substitute it.Tan (sec-1 (x/3)) = sqrt (3/x) = √3 /√x = (√3 /√x) × (√x /√x) = √3x / xTherefore, sin (cos-1 (1/2)) = √3/2 and tan (sec-1 (x/3)) = √3x / x.

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Answer:

C

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 36 square feet.

Because the rectangle has a gap on the left side in the shape of a semicircle, we can first solve for the area of that semicircle.

if you know the radius of a semicircle, you can use the formula:

[tex]A = \frac{\pi r^{2} }{2}[/tex]

But first, we need to solve for the radius.

Because the diameter is twice the size of the radius, we can use this expression:

So, the radius of the semicircle is 2ft.

Inserting 2 into the formula for r:

First, we need to evaluate the exponent:

Dividing 4 by 2 gives:

This simplifies to:

Subtracting that from the area of the rectangle:

36 - 6.28319 = 29.71681 = [tex]29.7ft^{2}[/tex] (Rounded to the nearest tenth)

Therefore, the answer is C.

The area of Circle B could be about 300 in², about 900 in², or about 2,700 in² depending on its radius.

To determine which one is correct, you would need to know the radius or diameter of the circle.

Use the formula for the area of a circle, which is

A = πr²,

where A is the area and

r is the radius.

If you have the radius, plug it into the formula and calculate the area.

Compare the calculated area to the options provided (300 in², 900 in², or 2,700 in²)

to determine which one is closest to the area of Circle B.

Without more information about Circle B's radius or diameter, it is impossible to determine the exact area from the

options given.

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The value of cos C is 3/5

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

In a right angle triangle, the longest side is called the hypotenuse and the other two sides are called opposite and adjacent. The line facing the acute angle( tetha) is the opposite. The ratio of the sides with the acute angle are called trigonometric ratio.

sin(tetha) = opp/ hyp

cos( tetha) = adj/ hyp

tan(tetha) = opp/adj

In the triangle, using angle C,

opposite = 4

adjascent = 3 and hypotenuse = 5

cos (C) = 3/5

therefore the value of cos (C) = 3/5

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Answer:

1/3

Step-by-step explanation:

The exponent -1 indicates that we need to take the reciprocal of the base 3.

So, 3^(-1) = 1/3

Therefore, the answer is 1/3.

Answer:

1/3

Step-by-step explanation:

Rewrite the expression using the negative exponent rule [tex]b^{-n}[/tex] = [tex]\frac{1}{b^{n} }[/tex]

The answer is 1/3

The domain of the given function H (t) is 0 ≤ t ≤ 40.

What is the domain of a function?

The collection of all the values for which a function is defined is known as the domain of that function.

We are given that the height of a model rocket, H (t) is a function of time since it was launched, t.

From the graph, we can see that the value of t is represented on the x- axis is ranging from 0 to 40.

Hence, the domain of the given function H (t) is 0 ≤ t ≤ 40.

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The probability that exactly 5 of the invoices will be paid within ten working days is 19.34% or 0.1934.

This is a binomial distribution problem, with n = 12 (the sample size) and p = 0.5 (the probability of success, which is an invoice being paid within ten working days). We want to find the probability that exactly 5 of the invoices will be paid within ten working days.

Using the binomial probability formula, the probability of exactly 5 invoices being paid within ten working days is:

P(X = 5) = (12 choose 5) * (0.5)^5 * (1-0.5)^(12-5) = 0.1934

Where (12 choose 5) is the binomial coefficient, which represents the number of ways to choose 5 invoices from a sample of 12.

Therefore, the correct answer is 0.1934 rounded to four decimal places.

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If BG=BE, we can conclude that triangle BGE is an isosceles triangle.

In a circle, the radius is a line segment that connects the center of the circle to any point on the circle. Therefore, BG and BE are both radii of the circle. In an isosceles triangle, two sides have the same length, and the third side is a different length. In this case, the two sides with the same length are BG and BE, and the third side is GE. Since BG and BE are radii of the circle and therefore have the same length, we can conclude that triangle BGE is isosceles, and the angles opposite BG and BE are congruent.

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Answer:

width is 3 inches, length is 11 inches.

Step-by-step explanation:

Let l be the length and w be the width.

We have:

[tex]l = 2w + 5[/tex]

[tex](2w + 5)(w) = 33[/tex]

[tex]2 {w}^{2} + 5w = 33[/tex]

[tex]2 {w}^{2} + 5w - 33 = 0[/tex]

[tex](w - 3)(2w + 11) = 0[/tex]

[tex]w = 3[/tex]

[tex]l = 2(3) + 5 = 11[/tex]

The mathematical equation f(w) = w² - 6w provides a representation of the remaining surface area, measured in square meters, of the field following the construction of the basketball court.

The rectangular field has an area of length x width, which can be expressed as (2w)(w) = 2w² square meters.

The basketball court has an area of length x width, which can be expressed as (w)(w+6) = w² + 6w square meters.

To find the remaining area of the field after the basketball court is built, we need to subtract the area of the basketball court from the area of the rectangular field.

So the function f(w) representing the remaining area, in square meters, is:

f(w) = 2w² - (w² + 6w)

f(w) = 2w² - w² - 6w

f(w) = w² - 6w

Therefore, the function f(w) = w² - 6w represents the area, in square meters, remaining of the field once the basketball court is built.

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Complete question:

A grounds committee of a housing community plans to build a basketball court in an empty rectangular field.

1. The rectangular field-has a width of 2w meters and a length that is 13 meters longer than its width.

2. The basketball court has a width of w meters and a length that is 6 meters longer than its width.

Which function, f(w), represents the area, in square meters, remaining of the field once the basketball court is built?

It is not possible to determine the relationship between the two variables based on this scatterplot.

The scatterplot below does not show a good candidate for linear regression because the points do not follow a clear pattern. There is no consistent trend that shows a correlation between the X and Y variables. Therefore, it is not possible to determine the relationship between the two variables based on this scatterplot.The linear regression is a statistical technique that enables the analysis of relationships between two or more continuous variables. The method attempts to find the line of best fit, which represents the overall relationship between the two variables. A scatterplot, which is a graphical display of a dataset, can be used to determine whether two variables are good candidates for linear regression.In order for two variables to be a good candidate for linear regression, they must have a strong positive or negative correlation. In other words, the points on the scatterplot must follow a clear pattern that shows a linear relationship between the X and Y variables. If there is no clear pattern or the points are randomly scattered, then it is not possible to determine the relationship between the two variables based on a linear regression model.

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