What is the set of independent variables of a function called?; What do you call the set of all possible values of the dependent variable?; What do you call the set of all possible values for the function?

The probability that the sample mean is in between 50 minutes and 51 minutes is 0.345.

n = sample size = 39

σ = standard deviation =4.2

μ = population mean = 49.8

Probability is the chance that an event can occur, in this case probability is used to measure the chance sample mean is between 50 minutes and 51 minutes. So,

P(50 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])

= P([tex]\frac{50-49.8}{\frac{4.2}{\sqrt{39}}}[/tex] ≤ z ≤ [tex]\frac{51-49.8}{\frac{4.2}{\sqrt{39}}}[/tex])

= P(0.30 ≤ z ≤ 1.78)

= P(z ≤ 1.78) - P(z ≤ 0.3)

using z table and we get,

= 0.9625 - 0.6179

= 0.3446

= 0.345

Thus, the probability is 0.345 for the sample mean is within 50 and 51.

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The inequality to buy an apple can be given as 2x ≤ 16

The number of apples we can buy is 8

What is an inequality?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

We are given that we have only$16 dollar to buy apples and each costs $2

Let the number of apples we can buy be x

Hence the inequality can be given as

2x ≤ 16

Now dividing both sides by 2 we get,

x ≤ 8

Hence we can buy at most 8 apples

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The sections of the function that are decreasing, defined by the ordered pairs are;

Section 2; (-1, 4) to (1, 0)

Section 4; (3, 2), to (5, -2)

The part of the second function that is decreasing is; (2, -2) to (3, -5)

A function is a definition of the mapping of the set of input variables unto the set of the output variables.

The points in the specified functions are;

Section 1 line ; (-3, 4) to (-1, 4)

Section 2 line ; (-1, 4) to (1, 0)

Section 3 line ; (1, 0) to (3, 2)

Section 4 line ; (3, 2) to (5, -2)

The points through which the function goes through are; (-4, -2.5), (3, -5), (-2, -2), (0, 5), (2, -2), (3, -5), (4, 2.5) and (5, -2)

A function is decreasing when the positive increase in the x-value of the function is accompanied by a decrease in the y-value.

The sections of the functions that are decreasing are;

Section 2 line ; (-1, 4) to (1, 0),

Section 4; (3, 2) to (5, -2)

Parts of the function that is decreasing is; (2, -2), (3, -5)

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The coordinate pair of D that will make AB perpendicular to CD is ( 4,7)

The slopes of perpendicular lines are opposite reciprocals of each other. Their product is -1.

The slope of a line is given as ( y1-y2)/(x1-x2)

for AB and CD to be perpendicular

( y2-y1)/(x2-x1) × ( y4-y3)/(x4-x3) = -1

therefore (5-4)/-2-1 = ( y4-y3)/(x4-x3)

1/-3 ×(y4-4)/(x4-3) = -1

(y4-4)/(x4-3) = 3/1

therefore 3= y4-4 and 1 = x4-3

therefore y4 = 3+4= 7

and x4 = 1+3= 4

therefore the coordinate of D = (x4,y4) for AB perpendicular to CD = (4,7)

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The additional information is required in order that the triangles are congruent for the SSS congruent theorem is IW = IH

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

Triangles = IWO, and IHO

Given theorem = SSS

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles have the same mark

W O and H O

A O and A O

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

IW must be congruent to IH

Hence, the additional information on the congruency of the triangles is IW = IH

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The graph of the point of intersection is given below.

The point of intersection.

(5/√17, 20/√17) and (-5/√17, 20/√17)

A circle is a two-dimensional figure with a radius and circumference of

2πr.

The equation of a circle is x² + y² = r²

We have,

The equation of a circle

x² + y² = r²

r = 5

x² + y² = 25 ______(1)

The line.

y = 4x _____(2)

Now,

The line intersects the circle.

The point of intersection.

x² + (4x)² = 25

x² + 16x² = 25

17x² = 25

x = √(25/17)

x = ± 5/√17

x = 5/√17 and x = -5/√17

Now,

At x = 5/√17,

y = 4 x 5/√17

y = 20/√17

At x = -5/√17,

y = 4 x 5/√17

y = 20/√17

Thus,

The point of intersection.

(5/√17, 20/√17) and (-5/√17, 20/√17)

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Answer:A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

On solving the derivatives we got - 6x5-15 , 4x² - 98x  , x-5)²-9,  -3x²-16x+9  , -2

Differentiation is the rate at which a function changes with regard to a variable in mathematics (in mathematics, the rate of change of a function with respect to a variable). The usage of derivatives is necessary while solving calculus and differential equation problems.

1. f(x) = 6x5-15 DERIVATIVE

2.f(x) = 4x² - 98x DERIVATIVE

3. f(x) = (x-5)²-9

4.f(x)= -3x²-16x+9 DERIVATIVE

5.f(x)=-2 DERIVATIVE

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From the given question, relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} does not represent the function.

In mathematics, a connection between one variable (the independent variable, x) and another variable is defined as an expression (the dependent variable, y).For example - f(x) = 4x + 6

The collection of ordered pairs from the question is presented.

It is evident that the relation set exists.

{(9, 1), (6,2), (3, 3), (6,4), (9,5)}

It not accurately depict the function since for x = 6, [y] has two potential values, none of which is possible.

so that's why relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} can not represent a function.

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1. The equation of the line is:

y=-2x/3 + 5

2. The equation of the line in slope intercept form is:

y=3x+5

1. Given:

we have two points:

(-3,7) = (x₁,y₁)

(9,-1) = (x₂,y₂)

equation of the line is:

y - y₁ = m(x-x₁)

₁first calculate slope m = y₂-y₁/x₂-x₁

m = -1-7/9-(-3)

m = -8/12

m = -2/3

now, y - 7 = -2/3 (x-(-3)

y-7=-2/3(x+3)

y-7=-2x/3-2

y=-2x/3-2+7

y=-2x/3 + 5

hence equation of the line is y=-2x/3 + 5

2. Given two points:

(2, 11) and (4, 17)

(2, 11) = (x₁,y₁)

and (4, 17) = (x₂,y₂)

slope intercept form:

y=mx+c

we need to calculate the m value:

m = 17-11/4-2

m = 6/2

m=3

now substitute in the given form:

y - 11 = 3(x-2)

y-11=3x-6

y=3x-6+11

y=3x+5

Hence we get the required answer.

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So option b. x² -1 is the correct option of the given statement Because option b satisfy the requirement of not a polynomial.

An expression for a polynomial can be generated using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables (also known as indeterminates) and coefficients make up a polynomial.

It is possible to identify the polynomials by seeing which formulae only include the operations addition, subtraction, multiplication, and non-negative integer exponents. Expressions that include extra operations are regarded as non-polynomial expressions. Specify the grounds for the expressions' non-polynomial status.

Any function in an equation that uses only positive integer exponents or non-negative integer powers of a variable is known as a polynomial function. These equations include, for instance, the cubic equation, the quadratic equation, and others. A polynomial with an exponent of 1 is, for instance, 2x+5.

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Answer:

Only I

Step-by-step explanation:

I. √36 > 5

√36 = 6

6 > 5

Its true

II. 7 < √10

√10 = 3.16 approximately

Hence, 7 > √10

But 7 < √10 is wrong

III. √(17 - 8) > √(17 + 8)

√(17 - 8) = √9 = 3

√(17 + 8) = √25 = 5

√(17 - 8) < √(17 + 8)

But, √(17 - 8) > √(17 + 8) is wrong

Answer:

1.) √36 > 5

Step-by-step explanation:

1.) √36 > 5

= 6 > 5( it is true because 6 is greater than 5)

2.) 7 < √10

= 7 < 3.16 ( it is false because 7 is greater than 3.16)

3.)√17–√8 > √17 + √8

= 4.12 – 2.82 > 4.12 + 2.82

= 1.3 > 6.94( it is false because 6.94 is greater than 1.3)

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In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.

A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.

α, β, and γ are the three angles of the triangle.

4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)

2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))

2πr²+2area[αβγ]=L(α)+L(β)+L(γ)

At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².

2πr²+2area[αβγ]=2αr²+2βr²+2γr²

2πr²+2area[αβγ]=2r²(α+β+γ)

π+area[αβγ]r²=α+β+γ

At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).

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The value of 2xx ÷ 3yy is 288/1225

In mathematics, simply or simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.

Given that, an expression 2xx ÷ 3yy, where x = 12 and y = 35

2x12x12/3x35x35 = 288/1225

Hence, The value of 2xx ÷ 3yy is 288/1225

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Hence for miles greater than 45, the Company A will charge less than Company B.

Given:

Jina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

we are asked to find for what mileages will Company A charge less than Company B = ?

from the question we frame  the inequality as:

⇒ 91< 55+0.80m

⇒ 36<0.80m

⇒ 45<m

or

m>45

Check answer

55+45(0.8)=91 check

Hence for miles greater than 45, the Company A will charge less than Company B.

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The magnitude of u + v is 6.08 and the direction of the vector u + v is 4.7°.

What is rounded to the nearest tenth?

To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.

Given that vector u is 7 (cos 330°, sin 330°)

Vector v equal to is 4 (cos 90°, sin 90°)

Calculating the value of cos 330° and  sin 330°:

cos 330°

= cos (3×90° + 60°)

= sin 60°

= √3/2

sin 330°

= sin (3×90° + 60°)

= -cos 60°

= -1/2

The vector u can be written as 7 (cos 330°, sin 330°) = 7(√3/2, -1/2) =(7√3/2, -7/2) = 7√3/2 i - 7/2j

The vector v can be written as 4 (cos 90°, sin 90°) = 4(0,1) = (0,4) = 0i + 4j

Add vector u and v:

u + v

= 7√3/2 i - 7/2j +  0i + 4j

= 7√3/2 i + 1/2 j

= 6.06 i + 0.5 j

The magnitude of the vector  u+v is √( 6.06² + .5²) = 6.08

The angle is

tan θ = y/x

tan θ =0.5/6.06

θ = 4.7°

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The equation illustrates that the variable that represents the greatest number is E. This cannot be determined with the given information.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

From the information, the variable is given as 1/2m = 1/3n = 1/4p = 1/5q.

It should be noted that the greatest variable cannot be determined based on the information. In conclusion, the correct option is E.

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The point slope form of the slope of escalator and distance is y-24 = 3/4(x-32).

The general point slope form is given by the equation -

y - y1 = m (x - x1)

Now we are given the slope as 3/4. So, keeping the values of y1 and x1 in the equation. Let us assume the points as (32, 24). As per the points, 32 is x1 and 24 is y1.

y - 24 = 3/4(x - 32)

y - 24 = 3x/4 - 3/4×32

Performing division on Right Hand Side of the equation

y - 24 = 3x/4 - 3×8

y - 24 = 3x/4 - 24

Rewriting the equation

y - 3x/4 = - 24 + 24

Solving the equation on Right Hand Side of the equation

y - 3x/4 = 0

y = 3x/4

Thus, the equation is y - 24 = 3/4(x - 32).

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His bottom line was a gain from selling and 3% commission is $257.50.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The cost price of 200 shares of BUI is (19.50×200) = $3900.

The selling price of 200 shares of BUI is (20.75×200) = $4150.

The net gain is (4150 - 3900) = $250 and with 3% commission it is,

= (103/100)×250.

= $257.50.

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Layla should by not more than 4 outfits in order not to exceed her budget

The inequality expression is n  ≤ 4

price of a new bicycles = $418.55

2 bicycle reflectors = $19.39

a pair of bike gloves = $27.23

new biking outfits = $38.86 each

Nora's total money to spend at a bicycle store = $38.86

Layla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items

We write the expression as;

$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86

where n represents the number of the new biking outfits

$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86

( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) /  $38.86≥ n

( $640 - $484.56 ) /  $38.86 ≥ n

( $155.44) /  $38.86  ≥ n

4  ≥ n

Layla should by not more than 4 outfits in order not to exceed her budget

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Answer: K=10

Step-by-step explanation:

To begin, you should multiply out the terms in front of the parentheses. This results in: 47=2k+6+3k-9

Next, we can combine like terms: 47=5k-3

Add 3 to both sides: 50=5k

Divide both sides by 5: 10=k

k=10

Answer: conic sections

Step-by-step explanation: the other options are a part of conic sections that are named depending on the angle of the plane relative to the cone, and the intersection.

The number of hours that plan A last is 1 hour and the number of hours that plan B last is 1 1/2 hours.

The first step is to form a system of equations using the information in the question:

3a + 8b = 15  equation 1

5a + 2b = 8 equation 2

Where:

The elimination method would be used to determine the required values

In order to determine the value of a, multiply equation 2 by 4

20a + 8b = 32 equation 3

Subtract equation 1 from equation 3 :

17a = 17

Divide both sides of the equation by 17

a = 17/17

a = 1 hour

Substitute for a in equation 1 :

3(1) + 8b = 15

3 + 8b = 15

8b = 15 - 3

8b = 12

b = 12 / 8

b = 1 4/8 = 1 1/2 hours

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Answer:

6 2/3

Step-by-step explanation:

2 1/6 + 4 3/6

6 4/6

6 2/3

Answer:

---------------------------------------------------

We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS.

SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.

The missing bit is the other side of the marked angle B and D:

Since the graph has a line from 0 comma 0 and going through 25 comma 8, C. Yes, it is proportional because it is a line that goes through (0, 0).

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it starts from the origin (0, 0) and as such, it is proportional.

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Answer: Casual sneaker sales = $40,500 & Athletic shoe sales = $28,800

Step-by-step explanation:

If the total store sales are $900,000 and you already have the percentages of the casual sneaker sales and athletic shoe sales, then you move the decimal point in each percentage two digits to the left, or simply multiply the percentage by .01, then take that number and multiply it by the total, $900,000

Ex:

4.5%(0.01) = .045

3.2%(0.01) = .032

.045(900,000) = 40,500

.032(900,000) = 28,800

A true average strain in a way that converys information about precision and reliability  (23.0616, 26.9384)

In this question we have been given:

sample size n = 15

the mean failure strain x(bar) = 25.0

the standard deviation s = 3.5

Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.

A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.

c = 0.95 or 95%

In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.

Here, the degree of freedom :

df = n - 1

df = 15 - 1

df = 14

and the column with α =(1-c)/2

                                   =0.025

To find the t-value:

t_(α/2) = 2.145

Therefore, the error margin is:

E = t_(α/2) × s/√n​

E = 2.145× 3.5/√15​

E ≈1.9384

The confidence interval's outer limits are thus:

x{bar} - E = 25.0 - 1.9384

               = 23.0616

x{bar} + E = 25.0 + 1.9384

                = 26.9384

Therefore, the confidence interval is: (23.0616, 26.9384)

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If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

The formula is 2x + 3y = 3. There are an infinite number of solutions to this equation.

We must first enter any random value for any variable, followed by the matching value for the other variable, in order to find any solution to this equation.

Now, if we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, one of the solutions to this equation is (0,1).

Hence, If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.

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Complete question-

Find the one of the solution of 2x + 3y = 3?

For the  given  quadratic function, the  highest  point  that the object  reaches is  (5, 768).

Since we are given with the quadratic function of h(t)=−16t2+160t+368, where  Let a = -16, b = 160, and c = 368, so the vertex for the equation will be  :t = -b/2a = -(160)/2(-16) = -160/(-32) = 5, so substituting this value  in the equation for the value of t is

h(5) = -16(5)2 + 160(5) + 368 = -400 + 800 + 368 = 768

Here the highest point that the object reaches is (5, 768), which means that  at a time of 5 seconds, the object reaches the building after being launched at the height of  768 feet  

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We are standing on the top of a 368 feet tall building and launching a small object upward. The object's vertical position, measured in feet, after t seconds is

We are standing on the top of a 1200 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is  What is the highest point that the object reaches?