For safety reasons, the angle a ladder makes with the ground should be no greater than 67°. Find the length to the nearest foot of the shortest ladder that will safely reach a roof that is 25 feet high.

Round to the nearest foot.

The length of the ladder is ______________

Answer:

= 9

Step-by-step explanation:

100% corresponds to the original number.

21% = 21/100 = 0.21

7% = 7/100 = 0.07

100% = 100/100 = 1

Then:

27 ⇒ 0.21

A ⇒ 1

A = 27*1/0.21

A = 128.57

The original number is:

128.58

7% of 128.58:

128.58*0.07 = 9

= 9

(6, -4) is the missing value in the solution to the equation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that the value of y = -4 and find the value of x

6x+7y=4x+4y

6x - 4x = 4y -7y

2x = -3y

Putting the value of y in the above equation.

2x = -3y

2x = -3(-4)

2x = 12

x = 6

Therefore, the Missing value in the solution to the equation is (6,-4).

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Complete question:

6x + 7y = 4x + 4y

Complete the missing value in the solution to the equation.

(__,-4)

The quadrant in which the point (-11, -22) lies is the third (3rd) quadrant.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate in a graph.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Generally speaking, the coordinates of the third (3rd) quadrant are all negative, which simply means that both the x-values and y-values are negative e.g (-11, -22).

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Answer:

1.25% chance of finding exactly 4 left-handers

Step-by-step explanation:

About 10% of people are left-handed. So in a class with 32 students:

1 / 10 * 4/32 = 1/10 * 1/8

1/10 * 1/8 = 1/80 = 0.0125 = 1.25%

The probability of getting at least 6 heads is3/256 or 0.0117

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

Given that,

A fair coin is tossed = 8 time.

We have to find the probability of getting at least 6 heads.

Since, the probability of getting head, when one coin is tossed = 1/2

And the probability of getting tale = 1/2  

The probability of getting head at least  6 times when coin is tossed 8 times can be given as,

The head can come 6 times, then probability = [tex](1/2)\x^{6} (1/2)\x^{2}[/tex] =  (1/2)⁸

The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸

The head can come 8 times, then probability = (1/2)⁸

The probability of getting head at least 6 times

= (1/2)⁸ + (1/2)⁸ +  (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117

The probability of getting at least 6 heads is3/256 or 0.0117

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Therefore ,When Sebastian needs to buy coffee If he buys from the warehouse, this should cost $240 even by end of the year of annual year.

An entry fee is a yet another charge that must be paid each year when you apply for a particular credit card. Special benefits usually cover these expenditures, that ranged from $95 to $500. These benefits include the possibility of earning air miles, tickets, or cash back.

Here,

Given :

If he continues to buy his coffee from of the nearby shop, this should cost $300 by the conclusion of the year.

If he buys from the warehouse, this should cost $240 even by end of the year.

Therefore ,When Sebastian needs to buy coffee, the best financial advise is to buy it at a warehouse shop since he will save money at the end of every year.

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The intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

Option (D) is correct.

What is the intersection of two sets?

The intersection of two sets, A and B, is the set of elements that are common to both sets. It is often represented by A ∩ B.

In this case, Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 4, 5, 6, 7, 8}. The set that represents A ∩ B is {2, 4, 6, 8} because these are the elements that are common to both sets A and B.

So the correct answer is {2, 4, 6, 8}

Hence, the intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

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Therefore , the solution of the given problem of expression comes out to be area of diagram of given by expression = 12x².

Mathematicians must be able to multiply, division, add, and remove. An expression would look like this when put together: Data, a mathematical operator, and an equation The elements of a statement of fact, like additions, subtractions, multiplications, divisions, etc., comprise values, variables, and functions. It is feasible to compare and contrast phrases and expressions.

Here,

Given :

A diagram with 13 square

Let us consider it to be x unit each side of square .

So ,

If we want to find the area of this diagram,

We can write an expression as follows:

=> 12*x²

Thus ,

Area of diagram of given by expression = 12x²

Therefore , the solution of the given problem of expression comes out to be area of diagram of given by expression = 12x².

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The correct option D Quadratic, model best portrays provided data in the chart.

The relation for the height reached by the ball with time is given as:

Time (seconds): 1 2 3 4 5 6 7 8

Height(feet): 4 11 16 19 20 19 16 11

Plot the graph for the given values.

As it is seen from the graph that the line forms parabola.

Thus, the Quadratic model best portrays provided data in the chart.

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Answer:

Step-by-step explanation:

second one because he can bike faster than the can swim and walk and the first increase is the biggest

The change Δf is 0.462, value of the estimate is 0.4 and the approximation error is 0.062.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given function is,

f(x) = 2x³ - 2x

x₀ = 1 and dx = 0.1

(a) f(x₀) = f(1) = 2 - 2 = 0

f(x₀ + dx) = f(1.1) = 2 (1.1)³ - (2 × 1.1) = 0.462

Δf = f(x₀ + dx) - f(x₀) = 0.462 - 0 = 0.462

(b) Value of the estimate is,

f'(x) = 6x² - 2

f'(x₀) = f'(1) = 6 - 2 = 4

df = f'(x₀) dx = 4 × 0.1 = 0.4

(c) Approximation error is,

| Δf - df | = | 0.462 - 0.4 | = 0.062

Hence the change, value of the estimate and the approximation error are  0.462, 0.4 and 0.062 respectively.

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For the 21% of a number is 27, the value of 7% of that number is 7.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

⇒ 21% of a number is 27

Let a number is = x

So, We can formulate;

⇒ 27% of x = 27

Solve for x as;

⇒ 27/100 × x = 27

⇒ 27x = 27 × 100

⇒ 27x = 2,700

⇒ x = 2,700 / 27

⇒ x = 100

So, 7% of 100 is,

⇒ 7% of 100

⇒ 7/100 × 100

⇒ 7

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The value of the co-terminal angle in the range [ 0 , 360° ] is 308° , located in the fourth quadrant

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

In the third quadrant going anti-clockwise, only tan is positive.

In the fourth quadrant going anti-clockwise, only cos is positive

Given data ,

Let the co-terminal angle be represented as A

Now , it is the angle that share the terminal side of an angle occupying the standard position

Positive co-terminal angles: 308°, 668°, 1028°, 1388°, 1748°

Negative co-terminal angles: -52°, -412°, -772°, -1132°

Now , the trigonometric relations in the fourth quadrant going anti-clockwise, only cos is positive

Hence , the positive angle in the co-terminal angle is 308°

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Jason is purchasing hot dogs and wings for a party. The price of one set of wings is $8. [tex]7 x+4 y \leq 40[/tex] is the equation system.

x = pounds of wings, y = pounds of dogs that aren't

[tex]$\begin{array}{rl}7 x+4 y \leq 40 \Rightarrow 4 y & \leq-7 x+40 \\ x \geq 5 & y \leq-\frac{7}{4} x+10\end{array}$[/tex]

The inequality's sign will indicate which half-plane to shade, unless you are graphing a vertical line. Shade above the line if either the or > symbol is present. Shade below the line if the symbol "or" is used. When a linear inequality contains the symbols "less than" or "less than or equal to," you should shade below the boundary line. In a linear inequality, you will shade above the boundary line if the symbol is > (greater than) or (greater than or equal to). The approach used to resolve linear inequalities in two variables is the same as that used to resolve linear equations.

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Answer:

(-1,-2)

because the inverse of (-4,-2) is (-2,-4) so when we simplify both number or when we divide by both numbers by 2 we get (-1,-2)

so the inverse of f(x) _ (-4,-2) is (-1,-2)

y is directly proportional to x and the constant of proportionality is 13.8.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

From the graph, the coordinate points are (2, 27.60) and (6, 82.80).

Here, slope m=(82.80-27.60)/(6-2)

= 55.2/4

m=13.8

Substitute m=13.8 and (x, y)=(2, 27.60) in y=mx+c, we get

27.60=13.8(2)+c

27.60=27.6+c

c=0

Substitute m=13.8 and c=0 in y=mx+c, we get

y=13.8x

y/x=13.8

Hence, y is directly proportional to x and the constant of proportionality is 13.8.

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[tex]57=\cfrac{5}{8}z+7\implies 57=\cfrac{5z}{8}+7\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8(57)=8\left( \cfrac{5z}{8}+7 \right)} \\\\\\ 456=5z+56\implies 400=5z\implies \cfrac{400}{5}=z\implies 80=z[/tex]

Answer:

B. 5

Step-by-step explanation:

the mean value is of course the sum of all data points divided by the number of data points, but when the data points are distributed like here (left and right from the middle equally balanced, and the middle has the most entries), you can read it off the chart right away : it is the middle value.

How likely something is to occur is known as its probability.Consequently, 16.7% of people are likely to choose a hot dog.

How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.The probability of anything occurring is known as probability.

To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur. 16.7% of people will select a hot dog.Relevant frequency and likelihood

The likelihood or chance that an event will occur is known as probability.Expected outcome divided by total outcome is the formula for probability.

based on the figure

Total result equals 4 + 6 + 2

Total result: 12

Given that there are two hot dogs, the likelihood of selecting one is as follows:

Hot dog: Pr = 2/12

Hot dog: Pr = 0.1667

Consequently, 16.7% of people are likely to choose a hot dog.

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The term refers to a thorough count, often known as a comprehensive enumeration.

Every unit, whether it be an individual or the entire population, is studied during a census. A comprehensive enumeration, which refers to an exhaustive count, is what is meant by the term.

A census is a survey that is carried out on the entire collection of observational objects that are a part of a certain population or universe. A census is a thorough count of a population or groups at a particular period in relation to clearly specified qualities, such as population, production, or traffic on specific roadways.

The population of a nation is counted during a census. It also provides information about those individuals, including their histories, possessions, and way of life. Censuses are a key decision-making tool for both governments and enterprises.

The correct answer is option C. A study of the durability of earthquake-proof building materials.

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Answer:

31.01

Step-by-step explanation:

A= πr^2= π · 3.142 ≈31.01432

The correct domain for the set, D = { -2, -4, 2}.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

We have the set = {(-2,5), (-4, 1)(2, 12)}

We know that the domain is usually the input value

as, the the x values in the set is also considered as the domain.

Now, from the set {(-2,5), (-4, 1)(2, 12)} the domain value is

D = { -2, -4, 2}

Hence, the domain is D = { -2, -4, 2}.

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The Probability of (Sophomore | Girl) is 0.4.

The study of potential outcomes of events, along with their relative probabilities and distributions, is done in the area of mathematics known as probability. A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% are both acceptable ways to express the likelihood that a specific event (or set of events) will occur in everyday speech. Statistics is the study of events with a probability component.

Given

Probability of sophomore is P(A) = 12/30

                                              = 0.4

Probability of sophomore being girl is P(A) = 7/18

                                              = 0.38

P(Sophomore | Girl) = [tex]\dfrac{A \cap B}{B}[/tex]

                                 = P(A/B) × P(B)

                                  = 0.4/0.38 × 0.38

                                  = 0.4

Thus, Probability of (Sophomore | Girl) is 0.4.

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The fraction of time Vincent was able to play basketball today is 2/3 of the usual amount of time Vincent plays basketball everyday.

Fraction of time Vincent plays basketball everyday = 4/5 of an hour

1 hour = 60 minutes

Time Vincent plays basketball everyday = 4/5 of 60

= 4/5 × 60

= 48 minutes

Vincent played basketball today for 32 minutes

Fraction of time Vincent plays basketball everyday = x of 38 minutes

32 = x × 48

32 = 48x

x = 32/48

x = 4/6

x = 2/3

Therefore, Vincent was able to play basketball for 2/3 of 48 minutes today.

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[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{(-4)}}} \implies \cfrac{4 +4}{-6 +4} \implies \cfrac{ 8 }{ -2 } \implies - 4[/tex]

Answer:

Step-by-step explanation:

To find the equation of a line passing through two points, we can use the slope-point form:

y - y1 = m(x - x1)

where (x1, y1) is one of the points on the line, m is the slope of the line and can be calculated as

m = (y2 - y1) / (x2 - x1)

where (x2, y2) is the second point on the line.

Given the points (-6, -5) and (4, -3), we can substitute the values into the slope formula to find m:

m = (-3 - (-5)) / (4 - (-6)) = 2 / 10 = 1/5

Next, we can substitute the point (-6, -5) and the slope 1/5 into the slope-point form to find the equation of the line:

y - (-5) = 1/5 (x - (-6))

y + 5 = 1/5 x + 6

5y + 25 = x + 30

5y = x + 5

y = (x + 5) / 5

Thus, the equation of the line passing through the points (-6, -5) and (4, -3) is y = (x + 5) / 5.