Solve ABC using diagram and the given measurement A=64 a=7.4

A translation 3 units left and 2 units up best describes the graph of  f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x

How to solve this problem?

f(x) = log2(x + 3) + 2 (given)

g(x) = log2x (given)

We need to describe the best statement for the graph

The graph is shown in the image

The following steps are shown to describe the graph.

The general equation of f(x) = log2(x-h)+k

When h > 0 (positive)

The graph of the base of the function shift to the right

When  h < 0 (Negative)

The graph of the base function shifts to the left.

When k > 0 (Positive)

The graph of the base function shifts upward.

When k < 0 (Negative)

The graph of the base function shifts downward

Here h = 3 , k = 2

Hence , a translation 3 units left and 2 units up describes the graph.

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Answer: B & A

Step-by-step explanation: I think?

Answer:

  2x² +5

Step-by-step explanation:

You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.

The area is the product of length and width, so the width will be ...

  A = LW

  W = A/L = (2x³ +6x² +5x +15)/(x +3)

The cubic expression can be factored by grouping, so we have ...

  Area = (2x³ +6x²) +(5x +15)

  = 2x²(x +3) +5(x +3)

  = (2x² +5)(x +3)

Then the width is ...

  [tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]

The width of the rectangle is 2x² +5.

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After 81 minutes of driving the distance to destination is 32.8 miles.

Th function that has two variables with first order term is called linear function.  While plotting on the XY coordinate system we get a straight line.

Why do we use linear equation in this problem?

as per question, distance to destination is a linear function of total driving time so we use the equation of straight-line having slope m and y intercept b for determining unknown values.

given, distance to destination in miles is a linear function of total driving time in minutes.

y=mx+b

in the equation, y denotes the distance to destination in miles

                 x is the total driving time in minutes

         m is the slope of linear equation

      b is the y intercept

Milan has 68 miles to his destination after 37 minutes of driving

68 = mx37+b

he has 45.6 miles to destination after 65 minutes of driving

45.6=mX65+b

solving the two equations by addition method

slope, m= -0.8

from the above two equation

we get b=97.6

now, after 81 minutes of driving the distance to destination, y=mx+b

                                               y= -0.8x81+97.6

                               distance = 32.8 miles

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The equation of the line that has the slope of 7/3 is:  y = (7/3) x - 27/49

Finding the slope and y-intercept is necessary to express the equation of a graphed line in y-intercept (y=mx+c) form, which can then be used to get the equation of the line. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.

Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

Given that,

slope (m) = 7/3

Putting (7,-9) into the equation: y =mx+c

or, -9 = (7/3) × (7) + c

or, -9 = 49 /3 + c

or, c = (-9) × (3/49)

or, c = -27/49

Thus, the equation becomes:

or, y = (7/3) x + -27/49

or, y = (7/3) x - 27/49

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Answer:

Below

Step-by-step explanation:

2^9 possibilities =512

9 possibles with only ONE tails  (9 C 1)

36 possibles with TWO tails     ( 9 C 2)

45 out of 512       45/512 = .088  

Answer:

58

Step-by-step explanation:

There are 5 lines between 50 and 60

60 - 50 = 10

10 / 5 = 2

This means that each increment is 2.

We see the end of the box plot is above the fourth increment above 50.

4 x 2 = 8

50 + 8 = 58

Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;

T = mx + b

Where:

Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;

f(x) = T = 9.25x + 3

When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;

f(1) = T = 9.25(1) + 3

f(1) = T = 9.25 + 3

f(1) = T = $12.25.

In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.

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Complete Question:

The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?

a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]

b.  [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]

a. The derivative of a cubic function

[tex]y=ax^3+bx^2+cx+d[/tex]  is  [tex]y'=3ax^2+2bx+c[/tex].

Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.

b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].

Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]

A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.

A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3

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The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

Given :

emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 %  .

Freshmen = 0.85

sophomores = 0.80

it is clearly visible that the freshmen or sophomores is greater than the 40 % .

Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

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The correct option is b) ii only

From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.

What is meant by distribution?

The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.

What are the 3 types of distribution?

The Three Types of Distribution

What are the 5 factors of distribution?

Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.

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The solution is D = 200 feet

The diameter of the circular store is = 200 feet

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the diameter of the circle be represented as = D

Let the radius of the circular store be = r

D = 2r

Now , the area of the circular store be = A

The value of A = 31,415 feet²

The area of the circular store is given by the formula

Area of the circle = πr²

Substituting the values in the equation , we get

31415 = 3.1415 x r²

Divide by 3.1415 on both sides of the equation , we get

r² = 10000

Taking square roots on both sides of the equation , we get

r = 100 feet

Now , the diameter of the store = 2 x radius of the store

Diameter of the store D = 2 x 100 feet

Therefore , diameter of the store D = 200 feet

Hence , The diameter of the circular store is = 200 feet

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There are 21 days for there to be 150 frogs in the pond.

There are 37 days for there to be 1400 frogs in the pond.

What is exponential growth?

Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.

Given:

There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.

The exponential equation for the given problem is,

[tex]A(t) = Ar^t^/^1^0[/tex]

To find the number of days for there to be 150 frogs in the pond.

Here,

A(t) = 250, A = 25, r = 3

⇒

[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]

t ≈ 21

Hence, there are 21 days for there to be 150 frogs in the pond.

Now to find how long for there to be 1400 frogs in the pond, we solve:

[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]

t ≈ 37

Hence, there are 37 days for there to be 1400 frogs in the pond.

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The complete answer: A domain is a set of input data in a relationship.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

An input value and an output value are matched in a relation.

A relation is a function where each input value yields one and only one output value.

Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,

while the range is the set of output values.

The domain of a function or relation is the set of all possible independent values that it can have.

Therefore,  a domain is a set of input data in a relationship.

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The factor of the expression 8w - 16 will be 8 and (w - 2).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.

The expression is given below.

⇒ 8w - 16

The factor of each term in the expression, then we have

8w = 8 x w

16 = 8 x 2

Then the expression is written as,

⇒ 8w - 16

⇒ 8 × w - 8 × 2

⇒ 8 × (w - 2)

⇒ 8(w - 2)

The component of the articulation 8w - 16 will be 8 and (w - 2).

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The value of the c in the function c = 19m - 15 when m=10 is 175.

A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.

Given the function;

c = 19m - 15,

where m represents the number of months and c represents the total number of car sent to New York.

To find the value of c:

when m = 10,

Substitute the value of m to the function;

c = 19 (10) - 15

c = 190 - 15

c = 175.

Therefore, the value of c is 175.

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A)

A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.

So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414

It is believed that the machine is underfilling the bags.

So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414

Given,

n= 8

Population standard deviation (б) = 18

x= 407

We will use the t-test since n > 8 and we are given the population standard deviation.

t=x-μ / (б/[tex]\sqrt{n-1}[/tex])

t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]

t= -1.028

Use the t table to find p value

p-value = 12.706

Level of significance α = 0.025

p-value>α

It is a two-tailed test.

So, we fail to reject the null hypothesis.

So, its bag-filling machine works correctly at the 414-gram setting.

B)

Let μ be the population mean amount of ozone in the upper atmosphere.

As per the given, we have

[tex]H_{0}[/tex]    : μ = 4.8

[tex]H_{1}[/tex] : μ ≠ 4.8

Sample size: n= 26

Sample mean = 4.6

Standard deviation = 1.2

Since population standard deviation is now given, so we use a t-test.

t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]

t= -0.2/0.24

t= -0.833

It is a two-tailed test.

We are accepting the null hypothesis.

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Answer:

A.[tex] \frac{7}{6} \sqrt{x} [/tex]

Step-by-step explanation:

Solution Given:

[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]

Bye using indices formula

[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]

we get

[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]

[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]

[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]

[tex] \frac{7}{6} \sqrt{x} [/tex]

The lines that carry the rectangle onto itself are x = 0 and y = 1

The graph that completes the question is added as an attachment

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

The rectangular graph

The coordinates of one end of the graph are

(-3, 3) and (-3, -1)

Next, we calculate the midpoint of these ends

So, we have

Midpoint = 1/2(x₁ + x₂, y₁ + y₂)

Substitute the known values in the above equation, so, we have the following representation

Midpoint = 1/2(-3 + 3, -1 + 3)

Evaluate the like terms

Midpoint = 1/2(0, 2)

So, we have

Midpoint = (0, 1)

So, we have

x = 0 and y = 1

Hence, the reflection lines are x = 0 and y = 1

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Interest is the price you pay to borrow money or the cost you charge to lend money.

To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.

310-285 = 25

So, Polly will pay $25 in interest.

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280 is the number which is 16 2/3% more than 240

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.

(1/6) th of 240 = 240/6 = 40

40 more than 240 = 280

So, 280 is the number which is 16 2/3% more than 240

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Answer:

Step-by-step explanation:

Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.

Let s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...

  s +(s -42) = 244

Add 42 and simplify

  2s = 286

  s = 143 . . . . . divide by 2

  hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs

143 sodas and 101 hot dogs were sold.

The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.

The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.

The given statement for the problem is, " 20 divided by 1 plus 4".

It can be written in the form of expression as follows,

The sign of plus is given as '+'.

And, for divide it is '÷'.

Now, 20 divided by 1 plus 4 can be written as,

20 ÷ 1 + 4

Which is evaluated  by BODMAS to give,

20 + 4 = 24.

Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.

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The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.

Given :

Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,

Let g(x) = f(x) − 5.

g(x) = (x−p)(x−q)(x−r)(x−s)h(x)

The condition f(t) > 5 translates to g(t) > 0.

Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :

the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }

The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.

Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have

f(x)=x(x−1)(x−3)(x−4)+5

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Full question ;

Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?

The two inequalities that describe the total cost and no. of guests are

18a + 9c ≤ 2475 and

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let 'a' be the no. of adults and 'c' be the no. of children.

The expense for this event must not exceed $2,475.00.

Therefore, 18a + 9c ≤ 2475...(i)

The venue can hold no more than 150 guests.

Therefore, a + c ≤ 150...(ii)

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The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]

Given that,

Length of the ladder is, [tex]l=9ft[/tex]

Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.

Now, from triangle ABC,

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

[tex]h^{2} +b^{2} =l^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = 81               (Equation-1)

Differentiating the above equation with respect to time, 't'.

So,

We can write,

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0

[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0

[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0                (Equation-2)

In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.

Let us assume,

h = 3 ft and db/dt = 3 ft/s

We can substitute values in equation-1,

[tex]3^{2} +b^{2}[/tex] = 81

9 + [tex]b^{2}[/tex] = 81

[tex]b^{2}[/tex] = 81-9

[tex]b^{2}[/tex] = 72

b = [tex]\sqrt{72}[/tex]

b = 8.48 ft

Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]

3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0

3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0

3*[tex]\frac{dh}{dt}[/tex] = - 25.44

[tex]\frac{dh}{dt}[/tex] = -25.44/3

[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s

Therefore,

The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

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Answer:

[tex]2x^2+7x+C[/tex]

Step-by-step explanation:

Find the antiderivative of f'(x)=4x+7

[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]