Customers at a restaurant were surveyed to see which type of service they had during their visit (table service, assisted service, or self-service) and their age (18 years or younger or over 18 years old). The results of the survey were displayed in a segmented bar chart.

Which of the following describes this data set?

Categorical and univariate
Numerical and univariate
Categorical and bivariate
Numerical and bivariate

Using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

ABC refers to a triangle with vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

So, the triangles PRE and POC appear to be comparable triangles in the diagram.

Utilizing the similarity theorem:

PR/RE = PR+RO/OC

x/135 = (x+140)/230

By cross-multiply:
230x = 135(x+ 140)

230x = 135x + 18,900

230x - 135x = 18,900

95x = 18900

x =18900/95

x = 198.94

Therefore, using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.

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Correct question:
To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

f(x) = Area = (length)(width)

width = x

The length is 16 yards greater than 3 times x

length = 3x+16

f(x) = (3x+16)(x) = 3x^2 + 16x

Answer:

Step-by-step explanation:

We have been given that -- The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards

Length of parking lot is 16 + 3x

Width of parking lot is x

We have to write the function f(x) that describes the area, in square yards, as a function of the width, x

Area of rectangle is Length × width

[tex] \sf Area = f(x) [/tex]

put value of length and width here,

[tex] \sf f(x) = (16 + 3x)(x )[/tex]

[tex] \sf f(x) = 3x^2 + 16x [/tex]

Therefore, f(x) = 3x² + 16x

The rule of reflection for the triangle △JKL to △J'K'L' is x = -4.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the vertices of △JKL are J(1, 0), K(-5, 2), L(4, -4).

The vertices of △J'K'L' are J'(-9, 0), K'(-3, 2), L'(-12, -4).

The formula of midpoint of (x₁, y₁) and (x₂, y₂) is

((x₁+x₂)/2,  (y₁+y₂)/2)

The midpoint of J(1, 0) and J'(-9, 0) is ((1+(-9)/2,(0+0)/2) = (-8/2,0) = (-4,0)

The midpoint of K(-5, 2) and K'(-3, 2) is ((-5+(-3)/2,(2+2)/2) = (-8/2,4/2) = (-4,2)

The midpoint of L(4, -4) and L'(-12, -4) is ((4+(-12)/2,(-4+(-4))/2) = (-8/2,-8/2) = (-4,-4)

Thus the x-coordinate of the midpoint is the same.

Thus the line of reflection is x = -4.

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Answer: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `

Step-by-step explanation: Straight lines `2x + y = 5` and `x-2y = 3` intersect at point `A`. Points `B` and `C` are chosen on these two lines such that `AB = AC`. Then the equation of a line `BC` passing through the point `(2.3)` is: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `

I hope this helps :)

Answer:

30 ft

Step-by-step explanation:

Answer:

122 ft

Step-by-step explanation:

The 100 ft and the 70 ft are two legs of a right triangle....their distance apart is the hypotenuse of this triangle ....use Pythagorean theorem

d^2 = 100^2 + 70 ^2

  d = 122 ft

Answer:

m4 - 11 = 1

Step-by-step explanation:

Given information,

→ m4 - 11

→ m = 3

Now the value of expression is,

→ m4 - 11

→ (3)4 - 11

→ 12 - 11 = 1

Hence, value of expression is 1.

Answer:

The probability for the green one is 6/10

and for the next one, it is 4/10  

Step-by-step explanation:

The given function is  x² - 7x + 5 and the most general antiderivative of the function  is F(x) = x³/3 - 7x²/2 + 5x + c.

The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;

F(x) = ∫f(x)dx

From the question, f(x) = x² - 7x + 5

Therefore,

F(x) = ∫x² - 7x + 5

F(x) = x³/3 - 7x²/2 + 5x + c

Where c is the constant of the integration (antiderivative).

The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.

Therefore,  F(x) = x³/3 - 7x²/2 + 5x + c is the most general antiderivative of the function.

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Answer:

two or four

Step-by-step explanation:

Any degree-X polynomial can have up to 8 zeros (some of them can have multiciplity higher than 1).

The polynomial can be written as:

f(x) = (x-a)(x-b)(x-c)(x-d)(x-e)(x-f)(x-g)(x-h)

and we're already told that there are 2 x-intercepts, one with multiplicity 1. Let's assign those x-intercepts a and b=c=d (multiplicity 3).

We're left with (x-e)(x-f)(x-g)(x-h), where e, f, g and h need to be non-real complex numbers (otherwise they'd provide x-intercepts).

The complex zeros (more accurate term than imaginary) must come in pairs - if a number c is a zero of the function, its conjugate is a zero too. That means that we need to have an even number of complex zeros.

We can either have 4 distinct complex zeros, or 2 complex zeros, each with multiplicity of 2.

Answer:

  (c)  ∠acb ≅ ∠dcb

Step-by-step explanation:

You want to know what additional information is required to show ∆abc ≅ ∆dbc by SAS, given ac ≅ dc.

This postulate tells you triangles are congruent if two corresponding sides are congruent, and the angles between them are congruent.

In the given geometry, the corresponding sides are given as congruent, so the additional information required is that the angles between them are congruent.

The angle between sides ac and bc is ∠acb.

The angle between sides dc and bc is ∠dbc.

The additional information required is ...

  ∠acb ≅ ∠dcb . . . . . matches choice C

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By evaluating the function graphically ,  f (4) = -4

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

The x-axis is indicated with the input values. The vertical displacement from the x-axis is the appropriate output value for any input value. For instance, the output is identical to f when x = a. (a).

According to the Given information

f( x ) = y

where x is an input and y is an output

We need to find the value for f(4)

f( 4 ) = y

For x = 4 we have a corresponding value at y axis as -4 in fourth quadrant

f (4) = -4

By evaluating the function graphically ,  f (4) = -4

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Answer: 248

Step-by-step explanation: First, you add 4 + 6 to get 10, then you multiply that by 5 to get 50. Then you multiply 50 by 5 to get 250, so 250-2 = 248. I hoped this solved your problem.

Answer:

248

Step-by-step explanation:

(4+6)x5x5-2

10x5x5-2

50x5-2

250-2

248

(if wrong sorry)

The number of supervisors for baby unicorns is 9 times the number of unicorns.

Let 'n' be the number of supervisors.

Let there be u number of unicorns.

A unicorn daycare center needs two supervisors for every 18 unicorns, according to the question.

As a result, mathematically, it is stated as

9/u = 2/18

9n = u

As a result, the relationship between the number of supervisors and unicorns was established.

Hence, there are nine times as many supervisors as unicorns.

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The slope of a line perpendicular to Y =-7 is 7. We may use this as a substitution in the inverse slope formula because the slope of Y = -7 is -1.

To find the slope of a line perpendicular to Y = -7, we need to use the inverse slope formula.

The inverse slope formula is m = -1/m1

where m1 represents the original line's slope.

We may use this as a substitution in the inverse slope formula because the slope of Y = -7 is -1.

m = -1/-1

This simplifies to m = 1.

As a result, a line's slope that is perpendicular to Y = -7 is 7.

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the solution to the equation is x=12

The distributive property is defined as

Let us now solve the equation.

5(x - 6) = 2(x + 3)

Using the distributive property, simplify the parentheses on both sides.

5(x - 6) = 2(x + 3)

5x - 30 = 2x + 6

The parenthesis was simplified. However, we have one x term on one side and another x term on the other.

5x - 30 - 2x = 2x + 6 - 2x

3x - 30 = 6

We only have an x term on one side of the equation now.

To begin, reverse the subtraction by adding 30 to either side of the equation.

To keep an equation balanced or true, we do the identical operation on both sides.

3x - 30 + 30 = 6 + 30

3x = 36

We're getting close to an answer. Only one more step.

The x term is multiplied by 3.

We can undo the multiplication operation by dividing both sides by 3.

3x / 3 = 36 / 3

x = 12

So, x is equal to 12.

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The graph of y = f(x) has end behavior as x ⇒ ∞, y ⇒ - ∞ and

as x ⇒ - ∞, y ⇒ ∞.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

The given function f(x) has end behavior as x approaches infinity y approaches negative infinity and as x approaches negative infinity y approaches infinity.

As when x value is positive y value is negative and when y value is negative x value is positive.

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This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).

Given that,

The statement is a confidence interval is the rejection region of a two-sided test.

We have to say if the statement is true or false.

We know that,

In statistics, a confidence interval describes the probability that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of predicted observations are frequently used by analysts.

Therefore, This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).

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The graph is given below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = 1.5x - 2

We can have the following coordinates on the graph.

x = 1, y = 1.5 - 2 = -0.5

(1, -0.5)

x = 2, y = 3 - 2 = 1

(2, 1)

x = 3, y = 4.5 - 2 = 2.5

(3, 2.5)

x = 4, y = 6 - 2 = 4

(4, 4)

And so on.

The graph of y = 1.5x - 2 is given below.

Thus,

Some of the coordinates on the graph are:

(1, -0.5), (2, 1), (3, 25), (4, 4), and so on.

The graph is given below.

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Answer:

a

Step-by-step explanation:

Answer:

The answer is: A. Hope it helps.

By using algebra (5, 4) is not a solution of the inequality.

Boundary does not contain in the given graph this is the error was made when graphed.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

x + 2y ≤ 12

Here the inequality contain ≤ .

Since, if there is ≤  sign then graph must contain boundary line.

The boundary line is solid line need to use in the graph.

But in the given graph the boundary line is dotted.

Boundary does not contain in the graph.

Hence, this is the error was made when graphed.

Also from graph we can see that the point (5, 4) is not contain in the graph.

Hence, (5, 4) is not a solution of the inequality.

Now prove by using algebra.

Plug x = 5, y = 4 in the given inequality

⇒  5 + 2(4) ≤ 12

         5 + 8 ≤  12

             13 ≤  12

It is not possible that 13 ≤  12.

Hence, (5, 4) is not a solution of the inequality.

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Answer:

1 hour and 20 minutes I think

Step-by-step explanation:

add all of them up then divide by 60

The number which is less than that of -2.67 are -2.8, -2.9, -3.0.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Which numbers are less than –8/3 = -2.67

So given in the option which is less than -2.67

Numberless -2.7 are

-2.8, -2.9, -3.0.

Hence the number is less than that of -2.67 are -2.8, -2.9, -3.0.

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Complete Question.
Which numbers are less than-8/3 Select all that apply.
A. -2.6 (repeating)
B.-2.76
C.-2 1/4
D. -11/4
E. -2

The value of all the given expression are as follow:

a. Absolute value of -3 / 2 is equal to 3 /2.

b. The value of 32^4 is equal to 1048576.

c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.

d. Value of 4^2 is 16

As given in the question,

Simplification of the given expressions are :

a. The absolute value of ( -3 / 2 )is

| - 3 / 2 | = ( 3/2 )

b. The value of the expression 32^4  is:

32^4

= 32 × 32 × 32 × 32

=  1048576

c. The value of the given expression ( 32 ) ^ 1/4 :

( 32 ) ^ 1/4

= ( 2⁵) ^ 1/4

= 2^(5/4)

d. Value of 4^2 is

4^2

= 4 × 4

= 16

Therefore, the value of the given expression is given by :

a. Absolute value of -3 / 2 is equal to 3 /2.

b. The value of 32^4 is equal to 1048576.

c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.

d. Value of 4^2 is 16

The complete question is:

What is the absolute value of -3/2 ?

what is the value of 32^4?

what is the value of 32 to the one - fourth power?

what is the value of 4^2?

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By using testing of hypothesis, it can be concluded that-

The correct set of hypotheses is

[tex]H_0 : \mu \geq 85[/tex]

[tex]H_a : \mu < 85[/tex]

What is testing of hypothesis?

Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.

A student believes that the average grade on the final examination in statistics is at least 85.

The null hypothesis is [tex]\mu \geq 85[/tex]

The alternative hypothesis is [tex]\mu < 85[/tex]

So, the correct set of hypotheses is

[tex]H_0 : \mu \geq 85[/tex]

[tex]H_a : \mu < 85[/tex]

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The percentage of all customers prefer port drink and tea is 17.55%. The result is obtained by multiplying the two percentages of the data.

We have a number of customers.

Of all customers, find the percentage that they prefer port drink and tea!

If 55% prefer soda over port drink, then the ones who prefer port drink is

100% - 55% = 45%

Of the customers who prefer port drink, 61% prefer coffee over tea. So, the ones who prefer tea is

100% - 61% = 39%

From that information, we can get the ones who prefer port drink and tea. Let's say pt = port drink and tea.

pt = 39% × 45%

pt = 0.39 × 0.45

pt = 0.1755

pt = 17.55%

Hence, of all customers, the percentage who prefer port drink and tea is 17.55%.

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Answer:

l and lll

Step-by-step explanation:

228.32 + 48.16 - 28.16 = 248.32

The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.

The slope-intercept form is expressed as;

y  = mx + b

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

Given the data in the question;

First, determine the slope of the line q using the slope intercept-form.

y = mx + b

3x + 5y = 10

5y = -3x + 10

y = (-3/5)x + 10/5

y = (-3/5)x + 2

Hence;

Slope of line q m = -3/5

Since, line r is parallel to line q, they both have the same slope.

Therefore, slope of line r will be m  = -3/5

Now, plug the point  (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.

y - y₁ = m( x - x₁ )

y - (-4) = (-3/5)( x - 5 )

y + 4 = (-3/5)x + 3

y = (-3/5)x + 3 - 4

y = (-3/5)x - 1

Therefore, the equation of line r is  y = (-3/5)x - 1.

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The whole numbers are closed under subtraction only by distributive property else they are not closed under subtraction.

Whole numbers constitute natural numbers including zero. The subset is given by {0, 1, 2, 3, 4, 5, …}, the set does not include fractions, decimals, and negative integers. The set of whole numbers is represented by ‘W’={0, 1, 2, 3, 4, 5, …...}

To check if the whole numbers are closed under subtraction or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.

Let us consider each property one by one -

1. The closure property-

let's take two whole numbers say 5 and 2.

now 5-2=3, but 2-5= -3 which is not a whole number.

Thus, whole numbers are not closed under subtraction by closure property.

2. The commutative property-

let's take two whole numbers say 5 and 2.

now 5-2=3 and 2-5=-3

hence, we get 2-5 ≠ 5-2.

Thus, whole numbers are not closed under subtraction by commutative property.

3. The associative property-

let's take three whole numbers say 5, 3, and 2.

now (5-3)-2 = 0 and 5-(3-2)= 4

hence, we get (5-3)-2 ≠ 5-(3-2).

Thus, whole numbers are not closed under subtraction by associative property.

4. The distributive property-

let's take three whole numbers say 20, 6, and 5.

now, 20 × ( 6 – 5 ) =  20 × 6 – 20 × 5  = 20

         and 20 × ( 6 – 5 ) = 20 × 1 = 20

Hence, 20=20.

Thus, whole numbers are closed under subtraction only by distributive property.

Hence, we can conclude that whole numbers are closed under subtraction only by distributive property.

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Answer:

Step-by-step explanation:

slope=-5/4

b=5

y=-5/4x+5

Answer:

Here

Step-by-step explanation:

The vertex of the parabola is at (0.5, 8.5).