You are in charge of drinks for a community barbecue. You need to supply at least 120 cups of
beverage to provide enough for the projected number of people that will attend. So far, you have
received the following donations:
o Enough mix to make 4 gallons of lemonade
o 7 bottles of fruit juice that each contain 64 fl. oz.
How many cups of beverage do you have?
Will you have enough for the barbecue?
O no
O yes

The piecewise linear function that models the situation is given as follows:

A linear function is modeled by:

y = mx + b

In which:

A piecewise function is a function that has different definitions based on the input.

For x between -9 and -3, the function decreases by 8 when x increases by 6, hence the slope is given by:

m = -8/6 = -4/3, hence:

y = -4/3x + b.

When x = -9, y = 9, hence we use it to find b as follows:

9 = -4/3(-9) + b

9 = 12 + b

b = -3.

Thus the first definition is:

y = -4/3x + b, −9 ≤ x ≤ −3

For x between -3 and 4, the function decreases by 8 when x increases by 7, hence the slope is given by:

m = -8/7

y = -8/7x + b.

When x = -3, y = 1, hence we use it to find b as follows:

1 = -8/7(-3) + b

1 = 24/7 + b

b = -17/7

Thus the second definition is:

y = -8/7x - 17/7, −3 < x ≤ 4.

For x between 4 and 10, the function increases by 17 when x increases by 6, hence the slope is given by:

m = 17/6

y = 17/6x + b.

When x = 10, y = 10, hence we use it to find b as follows:

10 = 17/6(10) + b

b = 10 - 170/6

b = -110/6

Thus the third definition is:

y = 17/6x - 110/6, 4 < x ≤ 10

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The conditional statement is that; If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.

First, we will calculate how much is one percent of your height and then subtract that percentage from the total height to get your" height in the evening".

For example:

If my height is 1.64 m, then;

0.01 * 1.64 m = 0.0164 m

Step 2 is;

1.64m - 0.0164m = 1.62326 m

​

Now, using these height, let's write a conditional that uses the described fact:

Conditional:

If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.

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Answer:

The slope would be [tex]-\frac{4}{3}[/tex]

Step-by-step explanation:

A member of the senate will serve for (h+4) years.

An expression, in mathematics, is a finite set of combinations and/ or numbers and variables that accurately represents the the context in question. When two or more expressions are connected using the equality sign then an equation is formed.

Here, we are given that in the US government a member of the senate serves for 4 years longer than a member of the House of Representatives.

Also the House of Representatives serves for- h years

Thus, the number of years a member of the Senate will serve will be 4 more than the number h

= h + 4

Thus, a member of the senate serves for (h+4) years.

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Answer:

I legit don't remember lol

Answer: 303.002

Step-by-step explanation:

The Area of the given composite shape is; 40 square units

We can breakdown the shape into triangle and rectangle and as such we know that;

Formula for area of triangle is;

Area = ¹/₂ * base * height

Formula for area of rectangle is;

Area = Length * Width

Thus;

Area of composite shape = (10 * 3) + (¹/₂ * 10 * 2)

Area of composite shape = 30 + 10

Area of composite shape = 40 square units

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Answer:

1.002, -0.02

Step-by-step explanation:

Probabilities range between 0 and 1.

The answer of part a is y = 8

The answer of part b is RS = 69, ST = 28

Step-by-step explanation:

a. Since RT = RS + RT, subsitute values of RS and RT in the equation

    97 = (8y + 5) + (3y + 4)

    97 = 11y + 9

    97 - 9 = 11y

    88 = 11y

     y = 8

b. Subsitute the value of y in RS and ST just like done in part a

Answer:

22 divided by 2.630= 8 remainder 0.96

Answer: 22/2.630 is 8, remainder is 0.365 or 73/200

The correct answer is option A that is 74.

First, we need to put the expression in the form of mathematical equation. A mathematical equation may be defined as the combination of numbers and arithmetic symbols which are related to each other according to the expression given. The expression in the form of mathematical expression can be written as:

(9 - 2/3×√9)² + (1-6)²

Solving the brackets separately.

(9 - 2/3×3)² + (-5)²

Now in the next step, simplify the equation.

=>(9 - 2)² + 25

=>(7)² + 25

=>49 + 25

=>74.

Therefore, the required answer is 74.

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Answer:5.1,5.2,5.3,5.4,5.6,5.7,5.8,5.9,

Step-by-step explanation:

The cordinates of the turning point of the graph of y=f(x) occurs at (1.1) and (5/3, 23/27)

2

(x−2)+1

Now, differentiating w.r.t. x, we get

f

′

(x)=2(x−1)(x−2)+(x−1)

2

=(x−1)[2(x−2)+x−1]

=(x−1)[3x−5]

Hence,

f

′

(x)=0 implies x=1 and x=

3

5

​

Corresponding values of y are y=1 and y=

27

23

​

 respectively.

∴ Co-ordinates of turning point of the graph of f(x) occurs at (1,1) and (

3

5

​

,

27

23

​

)

Now,

f(x)=(x−1)

2

(x−2)+1

=(x

2

−2x+1)(x−2)+1

=x

3

−2x

2

−2x

2

+4x+x−2+1

=x

3

−4x

2

+5x−1

The value of p for which the equation f(x)=p has 3 distinct solutions lies in interval (

27

23

​

,1)

Area enclosed by f(x),x=0,y=1 and x=1 is

A=∫

0

1

​

(1−f(x))dx

⇒∫

0

1

​

(4x

2

−x

3

−5x+2) dx

⇒A=

12

7\

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The liquidity premium for the corporate bond is 0.25%.

Any additional compensation needed to stimulate investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. For instance, due to its relative illiquidity, a long-term bond will have a higher interest rate than a short-term bond.

Liquidity premium for corporate bond will be:

= 5.25 - 3.5 - 1.5

= Interest - Treasury - Default risk

= 0.25%.

Therefore, the liquidity is 1.25%.

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Answer: $252

Step-by-step explanation:

21$ an hour x 12 hours = $252 total :)

Answer:

She earned $252 thsi month.

Step-by-step explanation:

1  hour = $21

12 hours = $?

21*12 = 252

Answer:

Step-by-step explanation:

you can't really solve for x because there is no equal sign to determine how much x needs to be in order to get the sum.

Step-by-step explanation:

the average change rate for a function g(x) is defined for an interval of x values as

(g(interval end) - g(interval begin))/(interval end - interval begin)

in our case that is

(g(2013) - g(2008))/(2013 - 2008) =

= (24 mil. - 186 mil)/5 = -162 mil./5 =

= -162,000,000 / 5 = -32,400,000

that means that as a mean value there were 32,400,000 digital cameras shipped less every year.

in other words, fewer and fewer digital cameras are sold. the demand is strongly declining.

actually, following the mean values and their trend, there should have been no new digital cameras shipped in 2014 anymore (as 24 mil. - 32.4 mil is less than 0).

66) The number of feet of fencing that Ms. Hamilton needs to buy is 75 feet.

67) The distance around a rectangle is called a perimeter.

The use of Mathematics skills is all-encompassing. Every activity involves some mathematical calculations and the use of mathematical operations, like additions, subtractions, divisions, and multiplication.

When you visit a Merchandise Store, you undertake some mathematical activities by computing how much is needed and the balance you will get. Future projections depend on maths skills.

For instance, budgeting how much it costs you weekly to maintain your hairstyle also involves maths skills.

As you return to school after the summer breaks, you decide how much savings you must spend. It is maths.  Any time calculations are involved, it requires maths.

Length of the yard = 24.75 feet

Width of the yard = 12.75 feet

Perimeter of the yard = 75 feet (24.75 + 12.75)2

Charges for a yard of iron fencing = $50 per yard

3 feet = 1 yard

75 feet = 25 yards (75/3)

The cost of 25 yards = $1,250

Thus, Ms. Hamilton will need to spend $1,250 on this decorative iron fence project.

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Domain: (−∞,∞) , {x|x ∈ R}

Range: [0,∞) , {y|y ≥ 0}

Continuity: y=3x^2 is a parabola opening upwards, the vertex is at (0,0) and the focus is (0,1/12)

Max's and Min's: the minimum and maximum x value goes to infinity while for the y value the minimum is 0 and goes up to infinity.

Intervals: both x and y start to increase from the origin

Symmetry: the axis of symmetry is x=0 so therefore there the parabola is symmetrical

Answer:

Step-by-step explanation:

Given function:

[tex]y=3x^2[/tex]

The domain is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

Therefore, the domain is (-∞, ∞).

The range is the set of all possible output values (y-values).

As x² ≥ 0, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Therefore, the function is continuous on its domain (-∞, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & = 3x^2\\\implies \dfrac{\text{d}y}{\text{d}x} & = 6x\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies 6x & = 0\\x & = 0\end{aligned}[/tex]

[tex]\textsf{When} \:x = 0 \implies y=3(0)^2=0[/tex]

Therefore, the stationary point of the given function is (0, 0).

To determine if a stationary point is minimum or maximum, differentiate the function again and substitute the x-value of the stationary point:

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 6x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6 \end{aligned}[/tex]

As the second derivative is positive regardless of the x-value of the stationary point, the stationary point is a minimum.

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies 6x & > 0 \\ x & > 0\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies 6x & < 0 \\ x & < 0\end{aligned}[/tex]

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As x² ≥ 0 and there is symmetry about the y-axis,

[tex]\textsf{then $f(x)=f-x)$ for all $x$,}[/tex]
so the function is even.

Answer:use demos cauculator

Step-by-step explanation:

A linear pair is formed of ∠1 and ∠2. The measures of the angle ∠1 is 20 and ∠2 is 160.

Given that,

A linear pair is formed of ∠1 and ∠2.

We have to find the measurements of both angles if m∠1 is eight more than m∠2.

When they refer to something as "linear," they mean that two angles create a straight line (or, 180 degrees). In other words, the two angles add up to 180.

Let us take the ∠1 as x

Then ∠2 will be 8x.

Now, we can write as

x+8x=180

9x=180

x=180/9

x=20

Therefore, the measures of the angle ∠1 is 20 and ∠2 is 8×20=160.

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Answer:

[tex]\sf (A' \cap B) \cup (A' \cap C') =\{1,6,7\}[/tex]

Step-by-step explanation:

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Given sets:

Therefore, the complement sets are:

[tex]\begin{aligned}\sf A' & = \text{U}-\sf A\\& = \{1,2,3,4,5,6,7,8 \}- \{2,4,5,8 \}\\& = \{1,3,6,7 \}\end{aligned}[/tex]

[tex]\begin{aligned}\sf B' & = \text{U}-\sf B\\& = \{1,2,3,4,5,6,7,8 \}- \{1,4,6 \}\\& = \{2,3,5,7,8 \}\end{aligned}[/tex]

[tex]\begin{aligned}\sf C' & = \text{U}-\sf C\\& = \{1,2,3,4,5,6,7,8 \}- \{1,2,3,4,5 \}\\& = \{6,7,8 \}\end{aligned}[/tex]

Solution

[tex]\begin{aligned}\sf (A' \cap B) \cup (A' \cap C') & = \sf \left(\{1,3,6,7 \} \cap \{1,4,6\} \right) \cup \left(\{1,3,6,7 \} \cap \{6, 7, 8 \} \right)\\\\& = \sf \{1,6\} \cup \{6,7 \} \\\\& = \sf \{1,6,7\} \end{aligned}[/tex]

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The value of 9 - √7 is between 6 and 7:

4 < 7 < 9

⇒   √4 < √7 < √9

⇒   2 < √7 < 3

⇒   -3 < -√7 < -2

⇒   9 - 3 < 9 - √7 < 9 - 2

⇒   6 < 9 - √7 < 7

The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.

According to the statement

We have to find that the constant of proportionality.

So, For this purpose, we know that the

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

From the given information:

each equation represents a proportional relationship.

Then

We know that the A proportional relationship is one in which two quantities vary directly with each other

That's why

An equation has a proportional relationship if it can be written in the form y=kx where k is the constant of proportionality.

A linear function of x is given as y = 0.5x - 2.

Yes, this function of x represents a proportional relationship between x and y.

The constant of proportionality is given to be 0.5 provided that the dependent variable y has an initial value of - 2 at x = 0.

The graph of this equation will be a straight line and that means that the equation consists of a proportional relationship.

So, The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Determine whether each equation represents a proportional relationship. if it does identify the constant of proportionality. y = 0.5 x -2

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The figure KLMN is being rotated by 90°, which is a rigid transformation, the true statements are therefore;

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

The given parameters are;

In KLMN, KN||LM

The transformation applied to figure KLMN = A 90° clockwise rotation about point P.

The image of KLMN following the rotation transformation is Figure RSTU.

Please find attached a drawing of the possible diagram in the question obtained from a similar question online.

The options from the question are;

(A) [tex] \overline{ST}[/tex] is parallel to [tex] \overline{RU}[/tex]

(B) [tex] \angle R[/tex] is the same measure as [tex] \angle N[/tex]

(C) [tex] \overline{RS} [/tex] is the same length as \overline{MN}

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

A rotation transformation is a rigid transformation, therefore;

The distances between any two points on the pre–image is the same as the distance between corresponding points on the image, which gives;

Figure KLMN [tex] is congruent to [/tex] Figure RSTU

Figure KLMN [tex] \cong [/tex] Figure RSTU

According to the postulate, Corresponding Angles of Congruent Figures are Congruent, we have;

[tex] \angle T \cong \angle M[/tex]

Which gives;

[tex] \angle T[/tex] = [tex] \angle M[/tex]

[tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

The correct options are therefore;

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

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The four numbers are: -4, -2 ,0, 2 Answer.

How do you solve this: the sum of four consecutive even integers is equal to least of the integer

Solution: Let the numbers be n, n+2, n+4 and n+6.

Their sum = 4n+12 = n or

3n+12 = , or

3n = -12,

n= -4

therefore we get -4, -2, 0, 2

The four numbers are: -4, -2 ,0, 2 . Answer.

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Step-by-step explanation:

80.3÷9.4

80/3÷9/4

80/3×4/9

26.6×4/9

=17.733

This means that Kenna will get 18 pieces from one lenght of pipe