Michael is building a skateboard
ramp. The ramp needs to include a
right angle to be safe. If the side
lengths are 10 feet, 2.5 feet, and 10.5
feet, will the ramp be safe? Prove
your answer with an inequality.

answer : 26

steps

get hypotenuse

a² + b² = c²

7² + 8² = c²

49 + 64 = c²

113 = c²

square root of c is √113 which 10.63

7 + 8 + 10.63 = 25.63

Calculation the variance and standard deviation of the discrete random variable is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation is the square root of Variance 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].

As given in the question,

Therefore , the variance and standard deviation of the discrete random variable is calculated with the help of the following formulas:

Variance 'σ²' = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex]  and standard deviation  'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].

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The relative frequencies for the following number set is 10 30 40 50 60 70 10 30 40 60 60 80 20 30 50 60 70 90 20 30 50 60 70 90

How do you find the relative frequency in a frequency distribution?

Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency. Divide the total number of occurrences of the result you're interested in by the total number of occurrences if your data are observational. This may be expressed mathematically as relative frequency = frequency of the desired result / all occurrences.

There are 24 items.

Relative Frequency:

10 - (2) - 8.33%

20 - (1) - 4.17%

30 - (4) - 16.67%

40 - (2) - 8.33%

50 - (3) - 12.5%

60 - (5) - 20.83%

70 - (3) - 12.5%

80 - (1) - 4.17%

90 - (2) - 8.33%

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The integers are -47, -11, -6, 12, 20 in order of least to greatest.

A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.

Positive numbers, negative numbers, and zero make up integers. Thus, integers include 0 through 3, as well as -1, -2, and -3. No further parts, such as fractions or decimals, are allowed in integers. Therefore, fractional and decimal numbers like 3 1/2 and -7.5 are NOT integers.

Integer is derived from the Latin integer, which means whole or untouched, from the prefix in (for "not") with tangere ("to touch"). The words "entire" and "integer" are both derived from the same root, which is the French word entire.

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The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6

g(x) = 4x +9.

An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.

The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.

Given,

f(x) = x²+x-6

g(x) = 4x +9

f(g(x))=f(4x+9)

g(f(x))=4(x²+x-6)+9

g(f(x))=4x²+4x-24+9

g(f(x))=4x²+4x-15

Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6

g(x) = 4x +9.

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The denominator of function is -x/2 - 1 and vertical asymptote  x = -2.

A vertical line that is not a part of the function's graph but serves as a guide is known as a vertical asymptote. Because it occurs at an x-value outside of the function's domain, the graph cannot cross it. There may be more than one vertical asymptote for a function.

Given graph

the function of graph is F(x) = [tex]2\frac{\left(-\frac{x}{2}\ +\ 1\right)}{\left(\frac{x^{2\ }}{4}-1\right)}[/tex] = 2(1- x/2)/(x²/4 - 1)

reducing the equation

F(x) = 2/(-x/2 - 1)

denominator is -x/2 - 1

for  vertical asymptote -x/2 - 1 = 0

x  = -2

Therefore for function is -x/2 - 1 and  vertical asymptote at x  = -2.

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The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is

(x-4)^ 2+k = 0 using quadratic equation properties .

What is quadratic equation ?

A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Properties of graph of quadratic equation :

1. The shape of curve y = f(x) is a parabola.

2. If a>0, the parabola opens upwards.

3. If a<0, the parabola opens downwards.

4.The coordinates of vertex of parabola in all these cases is

(-b/2a , -D/4a).

The given equation is x^ 2-8x+19=0

a  = 1,

b = -8,

c = 19.

As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.

So, the vertex = (4,3)

The minimum value = 3 at 4.

So, the value of k = 3,

Given equation can be written as x^ 2-8x+16+3 = 0.

                                                      = (x-4)^ 2 +3 = 0.

The option A is correct.

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The equation of the line is  f(X)=(-1/6)x—(19/6)

What is equation?

In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

first linear functions have their general form as y= mx + c, where y belongs to the range and X belongs to the domain, m is the slope, and c is the y-intercept.

So using f(x) =y

Given that f(—5)=-4 , X=—5 and y=-4, hence by substituting into the general eqn y= mx+c, You get

-4= -5m+c ------(1)

Also given that f(1)=—3, X=1 and y=—3, hence by substituting into the general eqn y= mx+c, You get

-3= m+c --—-(2)

Solve equation (1) and (2), simultaneously to find the value of m and c. After which you will substitute into y=mx+c or f(X)=mx+c to get your f(X).

Note: you will get m=—1/6 and c=-19/6, from the simultaneous equations.

Hence f(X)=(-1/6)x—(19/6) and correct option is D.

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                               ......................................................................                                      

Answer:

Step-by-step explanation:

You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...

The attached calculator display shows the result:

Answer:

2,228

Step-by-step explanation:

Each unit will make 13.25 in profit before incorporating the one time cost. This means that 29,521/13.25= the amount needed to break even.

Answer:

$103

Step-by-step explanation:

In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:

Now we can solve the equation for x.

We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.

We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.

Answer: 12

Step-by-step explanation:

The x−intercept is 6 and the y-intercept is 5.

What is an equation of a line?

In high school algebra, "the equation of a line" is a crucial concept. This refers to an equation in the (x,y) plane with a line as its solution set. The "slope-intercept" form is the most widely used form in algebra. y = mx + b. In essence, x is used as a parameter in this formula, and y is written as a function of x: y = f(x) = mx+b.

Here, we have

The given equation of a line is:

−10x − 12y = −60

10x + 12y = 60

x/6 = y/5 = 1

Hence, the x−intercept is 6 and the y-intercept is 5.

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Answer:

No because x-coordinate 17 appears twice.

Step-by-step explanation:

In a function, no two ordered pairs can have the same x-coordinate.

Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.

The absolute error and the percent error of the police officer’s estimate will be 4.29%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.

The absolute error and the percent error of the police officer’s estimate are calculated as,

%error = [(14 - 13.4) / 14] x 100

%error = (0.60 / 14) x 100

%error = 4.29%

The outright mistake and the percent blunder of the cop's gauge will be 4.29%.

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Answer:

  (a)  For every day that passes, a person drives 54 miles

Step-by-step explanation:

You want to know the situation in which one quantity changes relative to another at a constant rate.

The rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.

We assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.

If the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.

As with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.

The situation with a constant rate of change is ...

  For every day that passes, a person drives 54 miles.

__

Additional comment

When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.

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Answer:

This is an irrational number.

Step-by-step explanation:

If you see the decimal, it has the values of 1 and 0, but are not constant.

If it were to be 0.010101010... it would be rational.

But this decimal does not look like that, so its irrational.

Hope this helps.

Answer: 9.8

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

When the 2 equations are graphed the point (13, 17) is not

a solution to the system of linear equations.

So the answer is no.

If you want to look for the solution**- the solution to the equation is (12, 18)

There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.

A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.

A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this

Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.

Given that,

Total number voters = 80,000

Total number of votes polled = 90%

Thus,

= (90/100) × 80,000

= 72,000

So, total percent of votes received by B if A gets 60% of polled votes.

= 100% - 60%

= 40%

Hence, total number of votes received by B

= (40/100) × 72,000

= 28,800

Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.

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The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

What is the right triangle is triangle?

A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using this information, we can determine which of the given sets of side measures could form a right triangle:

A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:

(61 m)² = (60 m)² + (11 m)²

61² = 60² + 11²

61² ≠ 60² + 11²

Since the left side does not equal the right side, these sides cannot form a right triangle.

B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(34 in)² = (24 in)² + (28 in)²

34² = 24² + 28²

34² = 24² + 28²

The left side equals the right side, so these sides could form a right triangle.

C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(55 ft)² = (45 ft)² + (35 ft)²

55² = 45² + 35²

55² = 45² + 35²

The left side equals the right side, so these sides could form a right triangle.

D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:

(48 cm)² ≠ (46 cm)² + (15 cm)²

48² ≠ 46² + 15²

Since the left side does not equal the right side, these sides cannot form a right triangle.

Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

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Answer: (x+1)(x+4)

Step-by-step explanation:

Step 1: Use the sum-product pattern

x^2 + 5x + 4

x^2 + 4x + x + 4

Step 2: Common factor from the two pairs

x(x+4) + x+4

Step 3: Rewrite in factored form

(x+1)(x+4)

There are $21.5 money was spent on a pass and lunch for each student.

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

Given that:

The amount spent by school on pass of 40 students and 3 teachers = $546.53

And, the amount spent for the lunch only for students = $351.60

Now,

The money spent for pass of 43 person = $546.53

Then, The amount of pass for each person  = 546.53/43

                                = $12.71

Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40

⇒ $8.79

Therefore, amount of pass and lunch for each student = 12.71 + 8.79

                              = $21.5

Thus, $21.5 is the required answer.

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The area of the floor in the scale drawing will be equal to 150 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Length of the classroom, l = 30 feet and,

The width of the classroom, w = 20 feet.

As per the scale drawing, the length of the classroom, l' = 15 feet

Let the scale width, w' = x feet

As we can see that the original length is twice the scale drawing.

Then, the original width also is twice the scale drawing.

So, w' = 20/2 = 10 feet.

Now, the area of the floor in the scale drawing will be,

A = wl

A = (15)(10)

A = 150 in².  

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Answer: x = 14/5 or x = 2.8

Step-by-step explanation:

Step 1: Divide both sides of the equation by five: a common nonzero real number.

(5x)/5= 14/5

Step 2: Simplify

x = 14/5

Answer:

Step-by-step explanation:

The expected value for the given problem is E(x) = 1.4.

What is expected value?

The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

A projected average value for an investment at some point in the future is known as the expected value (EV).

Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.

The formula for to find the expected value is given as,

E ( X ) = μ = ∑ x P ( x ) .

E(x) =  0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05

E(x) = 1.4

Hence, the expected value for the given problem is E(x) = 1.4.

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Answer:

27.6•\• is the answer from me