(05. 05 MC)


A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:



Likes hamburgers Does not like hamburgers Total

Likes burritos 49 92

Does not like burritos 75 38

Total 81 205



Part A: What percentage of the survey respondents did not like either hamburgers or burritos? (2 points)


Part B: Create a relative frequency table and determine what percentage of students who like hamburgers also like burritos. (3 points)


Part C: Use the conditional relative frequencies to determine which two data point has strongest association of its two factors. Use complete sentences to explain your answer. (5 points)

The number of workdays that will allow Liliana to prepare enough paintings for the exhibit are 10 days, 5 days and 8 days (2nd - 4th option).

The first step is to determine the inequality sign that would be used in the inequality that represents the information in the question.

Here are inequality signs and what they mean:

The form of the equation is:

number of painting already made + (new paintings per day x number of days) > 26

10 + (4 x n) > 26

10 + 4n > 26

4n > 26 - 10

4n > 16

n > 16 / 4

n > 4

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The estimated amount he paid at the other store is $5.5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The amount(A₁) Gabe spent in dollars at one store is

A₁ = 13.09d + 28, where 'd' is the number of items he bought.

Then he spent 22 dollars at another store.

let, A₂ = 22 and he bought 4 items.

Therefore, The estimated amount he paid at the other store is,

= 22/4.

= $5.5

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The rate of interest be required in order for Deondra to end up with $201,000 is 14.88%

percentage, a relative value indicating hundredth parts of any quantity.

Given that Deondra is going to invest $90,000 and leave it in an account for 15 years.

We have o find the interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $201,000

A=PRT

201000=90000×R×15

201000=1350000R

Divide both sides by 1350000

R=0.1488×100

R=14.88

Hence, the rate of interest be required in order for Deondra to end up with $201,000 is 14.88%

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The construction manager will need 6 more workers  to complete the project

To determine how many more workers are needed to complete the project in 36 days, the construction manager would need to determine the rate of work per worker and then calculate how many more workers are needed to achieve the desired rate.

If 12 workers to complete a building project in 54 days. Then 1 work will complete work in:

12 × 54 days = 648 days /worker

If the building project needs to be completed in 36 days, you need:

648 / 36 = 18 workers

Number of workers left = 18 - 12 = 6 workers

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The value of the unknown variable {t} is equal to 3/4.

        [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given is the equation as -

- 2 = (t/3) - 3t

The given equation is -

- 2 = (t/3) - 3t

Solving further , we get -

(t/3) - 3t = - 2

t/3 - 3t = - 2

t(1/3 - 3) = - 2

t(1 - 9)/3 = - 2

-8t/3 = -2

t = 2 x 3/8

t = 3/4

Therefore, the value of the unknown variable {t} is equal to 3/4.

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Answer: Choose A my smart self just knew

The two real solutions to this quadratic equation are -2 and 3/2.

The Quadratic Formula is the most popular method for solving quadratic equations of the form ax²+bx+c=0. It is derived from the quadratic equation which states that if a, b, and c are real numbers, and a is not equal to zero, then the roots of the quadratic equation ax²+bx+c=0 can be determined by the following equation:

x = (-b ± √(b² - 4ac))/(2a)

The quadratic formula can be used to solve for the two real solutions of any quadratic equation. It works by determining the discriminant, which is the number under the square root in the equation. The discriminant is calculated by subtracting 4ac from b². The ± symbol indicates that there are two solutions, one with the plus sign and one with the minus sign.

For example, if we have a quadratic equation 2x²+5x-3=0, the discriminant can be calculated as follows:

b² - 4ac = (5)² - 4(2)(-3) = 25 + 24 = 49

The two solutions can then be found using the formula:

x = (-5 ± √49)/(2(2))

x = (-5 ± 7)/(4)

x = -2 or 3/2

Therefore, the two real solutions to this quadratic equation are -2 and 3/2.

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Complete question:

Which of the following methods can be used in solving quadratic equation of the form ax²+bx+c=0?​

A) Factoring

B) Completing the Square

C) Quadratic Formula

D) Graphing

The area of the circle equation is shown below

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

Area of radius 1 = π

The area of a circle is proportional to the square of its radius.

When the radius is multiplied by a scale factor of "r," the area is multiplied by the square of that factor: r^2.

So, the area of a circle of radius "r" is given by π * r^2 square units.

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Answer: 12x ft

Step-by-step explanation:

12 times x

           .    .

            ω

Answer:

Step-by-step explanation:

213

The length of MA with the endpoints at M(7, -2) and A(2, -6) is √41 units.

MA has the endpoints at M(7, -2) and A(2, -6). The distance of MA can be found as follows:

Using distance formula, the formula follows Pythagorean principle.

d = √(y₂ - y₁)² + (x₂ - x₁)²

x₁ = 7

x₂ = 2

y₁ = -2

y₂ = -6

Applying the formula,

distance of MA = √(-6 + 2)² + (2 - 7)²

distance of MA = √(-4)² + (-5)²

distance of MA = √ 16 + 25

distance of MA = √41

Therefore, distance of MA is √41 units.

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Answer: The value of 2c²d would be 2 * (0.5)² * 3 = 2 * (0.25) * 3 = 0.5 * 3 = 1.5

This is because you first square the value of c (0.5² = 0.25), then you multiply it by 2 (0.25 * 2 = 0.5) and then by d (0.5*3 = 1.5)

Step-by-step explanation:

[tex] \large \underline{ \tt \: \: Given \: : \: } \\ \: \: \: \: \boxed{ \red{\tt c : 0.5}} \\ \: \: \: \: \boxed{ \green{ \tt \: d : 3 \: \: \: }}[/tex]

[tex] \: [/tex]

put the value of c nd d in given eqⁿ ~

[tex] \: [/tex]

[tex] \large \tt \: 2 { \red{c}^{2}}\green{d}[/tex]

[tex] \: [/tex]

[tex]\large \tt \: 2 \times { \red{0.5}^{2}} \times \green{3}[/tex]

[tex] \: [/tex]

[tex]\large \tt \: 2 \times { \red{0.25}} \times \green{3}[/tex]

[tex] \: [/tex]

[tex] \large \tt \: 2 \times { \purple{0.75}}[/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \large \tt \purple{ \: \: 1.5 \: \: }}}[/tex]

[tex] \: [/tex]

hope it helps!:)

Answer:

4/5

Step-by-step explanation:

Answer: x=12

Step-by-step explanation:

The question: 1/4 of ___ = 3

Let's start solving it.

First, let's set ___ as x and rewrite the equation.

1/4 of x = 3

Now, when you say 1/4 of x, you mean that you multiply x by 1/4.

So the equation is:

1/4*x=3

Finally, multiply both sides by 4.

Answer: x = 12

9.44ft-lbs work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.

when force is constant

Work = force x distance

i.e., w= fx

According to the question, force is not constant

Hence, For each infinitely small amount of work equals Force times the infinitely small change in the distance

dW= Fx dx

Total work W=[tex]\int\limits^0.9_0 {Force} \, dx[/tex] ----1

To stretch/compress a spring, we would need to apply a different amount of force, depending on the amount it is stretched/compressed

F=Kx ----2

where K is the spring constant

putting 2 in 1

W=[tex]\int\limits^0.9_0 {Kx} \, dx[/tex] ----3

According to ques F s 7 and x is 0.3

so, K= 7/0.3

K=23.3

Putting this value in 3

W=[tex]\int\limits^0.9_0 {23.3x} \, dx[/tex]

Putting constant out

W=23.3[tex]\int\limits^0.9_0\ {x} \, dx[/tex]

W=23.3 (x∧2)/

W=23.3(0.9∧2-0)

W=9.44

Therefore, 9.44 ft-lbs of work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.

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The solution to this system of equations is (8,1).

An equation is an expression that uses mathematical symbols to represent a relationship between two or more things. Equations are often used to solve problems, describe patterns, and make predictions. Equations can involve numbers, variables, operations, and other mathematical elements.

The solution to this system of equations can be found by solving the two equations for x and y respectively. For the first equation, we can solve for y:

y = √9 - x

For the second equation, we can solve for x:

x = 6 - 2y

Substituting the value of y from the first equation into the second equation, we find that:

6 - 2√9 - x = 0

Solving for x yields the solution:

x = 8

Substituting the value of x into the first equation, we find that:

y = 1

Therefore, the solution to this system of equations is (8,1).

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Answer: 9cm

Step-by-step explanation:

x = - 2 is a vertical line with an undefined slope.

A slope is a measure of how steep a line is when graphed on a coordinate plane. It is the ratio of the change in y-coordinates (rise) to the change in x-coordinates (run) between two points on a line. It is represented by the letter m in the slope-intercept form of a linear equation, y = mx + b.

x = -2 is an equation of a vertical line, which means that for this line, the x-coordinate is always -2. A vertical line does not have a slope because it does not have a change in y-coordinate for a given change in x-coordinate. It is infinitely steep or undefined.

So, x = -2 is not a slope but an equation of a vertical line that has an undefined slope.

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a) The amplitude and period of the function that could model the height of the message in a bottle as a function of time, t are 2 feet and 24 seconds.

b) At t = 0, h(t) = 8 feet , the equation of the function that could represent the situation is h(t) = 2 Cos( π/12( t + 6) + 8.

We have, In a bottle a message is floating on top of the ocean in a periodic manner. The time between periods of maximum heights = 24 sec.

Average height of bottle = 8 feet

The distance from the highest and lowest point = 4 feet

The height at any movement of time can be modelled as a cosine function,

h( t) = A cos(B(t - C)) + D

Where A --> amplitude of wave function

2π/B--> periodicity

C --> phase shift ( right / left)

D --> vertical shift

a) Amplitude, A in feet is defined as the maximum height that bottle reaches from mean sea level. It is calculated by the difference between hightest and lowest point and divided by 2. In this case, the distance from the highest and lowest point is 4 feet. So, amplitude is

A = 4/2 = 2 feet .

Time period, T in seconds is the time taken by bottle to complete one cycle. In this case, it is equal to time taken to reach at maximum height. That is equals to 24 seconds.

b) Period = 2π/ B = 24 seconds , so

B = 2π/24 => B = π/12

Using the part A results, the equation of movement is, h( t) = 2 cos(π/12( t - C) + D

At t = 0 , the message in a bottle is at its average height, i.e., 8 feet and moves upwards after. This implies at t = 0 ,

h(t) = 8 feet

=> 8 = 2 cos(π/12( 0 - C)) + 8

=> 2 cos(π/12( 0 - C) )= 0

=> cos(π/12(-C) )= 0

=> cos( πC/ 12) = 0

=> πC/12 = cos⁻¹ ( 0)

=> πC/12 = π/2

=> C = 12/2 = 6

plugging all known values in cosine function equation to get required equation, h(t) = 2 Cos( π/12( t + 6) + 8

Hence, the required equation is h(t) = 2 Cos( πt/12 + π/2) + 8.

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Complete question :

A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. A cosine function can model the movement of the message in a bottle in relation to the height.

Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points)

Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? (5 points)

The given equation y = -2x + 5 is a linear equation.

The given equation is:

y = -2x + 5

We observe the highest degree of x in a given equation to know whether it is a linear equation or not.

We know that if the highest degree of x in an equation is 1 then it is a linear equation else its a quadratic or non - linear equation.

In the given equation the highest degree of x is 1, hence it is a linear equation.

We can also check the same by graphing the equation.

If the graph of the given equation is a straight line then it is said to be a linear equation. The graph of this equation is also a straight line.

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3 different types of solutions for the quadratic formula are :

1. Factoring

2. Quadratic Formula

3. Completing the square

Quadratic formula/equation has a common formula

f(x) = a[tex]x^{2}[/tex] + bx + c

Where :

a is the coefficient of [tex]x^{2}[/tex]

b is the coefficient of x

c is the constant term

To solve that equation, we can use 3 solutions.

1. Factoring

This solution uses the factor of number and leaves 0 at the right side.

Common formula is ( x + a )( x + b ) = 0

Example :

[tex]x^{2}[/tex] + 6x + 8 = 0

(x + 4)(x + 2) = 0

x = -4 or x = -2

2. Quadratic Formula

The quadratic formula is

x = [tex]\frac{-b +- \sqrt[]{b^{2}-4ac } }{2a}[/tex]

Example :

[tex]x^{2}[/tex] + 6x + 8 = 0

x = [tex]\frac{-6 +- \sqrt{6^{2} -4(1)(8)} }{2(1)}[/tex]

x = [tex]\frac{-6 +- \sqrt{4} }{2}[/tex]

x = [tex]\frac{-6+2}{2}[/tex] or x = [tex]\frac{-6-2}{2}[/tex]

x = -2 or x = -4

3. Completing the square

Example :

[tex]x^{2}[/tex] - 6x + 5 = 0

[tex]x^{2}[/tex] - 6x = -5

because a = -1, add [tex](\frac{-6}{2}) ^{2}[/tex] or 9

[tex]x^{2}[/tex] - 6x + 9 = -5 + 9

[tex]x^{2}[/tex] - 6x + 9 = 4

[tex](x - 3 )^{2}[/tex] = 4

x-3 = ± 2

x -3 = 2 or x - 3 = -2

x = 5 or x = 1

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The extraneous roots of a given rational function occurs when we solve for a rational equations -, when we will multiply this results then the equation to clear the fractions and cancelling a 0/0 term , we will get the extraneous root.

Extraneous means external , these roots are there because when we solve an equation we cannot always get  an equivalent equations when we simplify it.

Extraneous roots are used while solving a  log equations. Extraneous roots occurs every time we apply functions to both sides of an equation that are not invertible. for example , | 2 x − 1 | = ( 2 x − 1) 2 , the two of this equations are totally same.

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The probability that the sum of the two values showing is 5 is 1/9 which is approximately 0.111 or 11.11%.

There are a total of 36 possible outcomes when rolling two fair 6-sided dice. Since the dice are fair, each outcome is equally likely. To find the probability of getting a sum of 5, we need to determine how many of the 36 possible outcomes will result in a sum of 5.

The possible outcomes that add up to 5 are (1,4), (2,3), (3,2) and (4,1). These are 4 possibilities, so the probability of getting a sum of 5 when rolling two fair 6-sided dice is 4/36 or 1/9 which is approximately 0.111 or 11.11%.

In general, the probability of getting a certain sum when rolling two fair dice is determined by the number of ways that the two dice can combine to give that sum.

Therefore, the probability that the sum of the two values showing is 5 is 1/9 which is approximately 0.111 or 11.11%.

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Answer:

The odometer shows that the car has traveled 41,000 miles by January 1, 2020, so we can use this as the starting point (x = 0) for our equation. We also know that the car travels 19,000 miles each year.

We can use this information to write an equation for the number of miles on the car's odometer x years after 2020.

The equation would be : y = 41,000 + (19,000 * x)

Where y represents the number of miles on the car's odometer and x represents the number of years after 2020.

The y is the number of miles at the odometer and x is the number of years passed from 2020.

This equation gives the number of miles on the car's odometer x years after 2020, whenever we have to know the number of miles on the odometer we just need to plug in the number of years passed in the equation.

The numerical coefficient in the expression 5x is 5. 5x denotes a 5 times multiplier applied to the variable x.

A phrase or a number that is multiplied by a variable is referred to as a coefficient. In most cases, the constant word comes before the variable term.

In a polynomial series or an equation, a coefficient is often a multiplicative factor.

Mathematical statements known as expressions are made up of two words, at least one of which must contain either variables, integers, or both. These expressions can either be expressed as numbers, variables, or as a product of numbers and variables. The mathematical operators used to separate the integers in these expressions are a mixture of numbers.

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-11 number represents the yardage for play.

A series of plays that starts with the ball being positioned on the ground with its longest axis perpendicular to the goal line is known as scrimmage.

We know that

The quarterback backups to 5 yards (negative number).

He falls back another 6 yards more (negative number).

To know the total number of yards the quarterback felt back, we just need to sum these negative numbers.

-5-6=-11

-11 number represents the yardage for play.

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The measures of KM, KQ, LK, LR, NK and PM are 2, 2, 4, 4, 6 and 2 respectively.

1) KM: Since N is the midpoint of QR, we know that QN = NR, so QN + NR = QN + QN = 2QN = 26 = 12. Therefore, KM = KR - QN = (PK+KQ) - QN = 4 - 6 = -2.

2) KQ: Since PK = 4 and KM = -2, we have KQ = PK + KM = 4 + (-2) = 2.

3) LK: The median of a triangle connects a vertex to the midpoint of the opposite side, and it's length is 2/3 the length of the hypotenuse of the right triangle formed by the median and the two segments from the vertex to the endpoints of the median.

In this case, LK = (2/3)(PQ) = (2/3)(4+2) = (2/3)*6 =4

4)LR: In this case, LR = LK = 4

5) NK: NK = QN = 6

6) PM: PM = PK - KQ = 4 - 2 = 2

Please note, that in order to be able to calculate all these lengths and measures, it is assumed that the triangle PQR is a valid triangle i.e, the sum of the lengths of any two sides of the triangle is greater than the length of the third side.

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Answer:

The area of the book is 108 square inches.

Step-by-step explanation:

This is calculated by multiplying the base (9 inches) by the height (12 inches). The area of a right triangle is equal to one-half of the base multiplied by the height.

Answer:

108 inches

Step-by-step explanation:

Multiply 12 by 9

All the points on the graph represent the possible solution coordinates of the function y = |x| - 7.

Given is the expression as -

y = |x| - 7

The given function is -

y = |x| - 7

Refer to the graph of the function attached. All the points on the graph represent the possible solution coordinates of the function {y}.

Therefore, all the points on the graph represent the possible solution coordinates of the function {y}.

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