Fancy food catering prepares 3696 fluid ounces of fruit punch foe a wedding reception. they plan to divide the punch equally among 4 different punch bowls. each serving of punch 6 ounces. how many servings of fruit punch are available at the reception?

Answer:

Step-by-step explanation:

equation of finding a midpoint is (x2+x1)/2 and (y1+y2)/2

7) (4+12)/2 = 8 and (9+-4)/2= 2.5

hence midpoint is (8,2.5)

8) we are told the midpoint so we can now find the co-ordinates of the other endpoint:

(5+x)/2= -3

rearrange to find x--> 5+x =-6, so x=-11

(-7+y)/2=2

rearrange to find y--> -7+y=4, so y=11

other endpoint: (-11,11)

5) the gradient of the new equation is parallel to y=3x+7 so it will stay the same

y=3x+c

we know that the points this line passes through is: (-4,-8) so we substitute this into our new equation to find c

-8= (3 x -4) +c

-8=-12 +c

so c= 4

Hence our new equation is y=3x+4

6) perpendicular gradient means that our existing gradient needs to be reciprocated (turned into negative and then flipped)

new gradient is -1/3

y=-1/3x+c

we know the value for x and y so we can substitute into our new equation to find c

9=(-1/3 x -6) +c

9=2 + c

c= 7

Hence our new equation is y=-1/3x+7

Hope this helps!

Answer:

A, B, F

Step-by-step explanation:

Well, to do this let's start by simplifying each of the ratios! If they can be simplified to 8:2 then they are a match

A: 16:4

Divide both sides by 2: 8:2 (This is an answer)

B: 40:10

Divide both sides by 5: 8:2 (This is also an answer)

C: 2:8

This one is not possible, because you would have to multiply the 2 by a whole number, and the 8 by a number less than one. Both have to be multiplied/divided by the same number.

D: 10:4

To get the 4 into a 2, we divide by 2. If we divide the 10 by 2 we get 5. Thus, this is not an answer.

E: 1:6

To get the 6 into a 2, we must divide it by 3. If we divide 1 by 3, we get a decimal, not 8.

F: 4:1

Multiply both sides by 2: 8:2 (This is our final answer)

Answer:

see explanation

Step-by-step explanation:

If the ratios of two pairs of corresponding sides of the 2 triangles are equal and the included angles are congruent then the triangles are similar by the

SAS postulate.

[tex]\frac{AC}{DF}[/tex] = [tex]\frac{5.1}{1.7}[/tex] = 3

[tex]\frac{BC}{EF}[/tex] = [tex]\frac{3.3}{1.1}[/tex] = 3

∠ C = 180° - (36 + 67)° = 180° - 103° = 77° , then the included angles

∠ C and ∠ F = 77° are congruent

Then

Δ ABC and Δ DEF are similar by the SAS postulate

We fail to reject the null hypothesis and there is no significant evidence for the manager to conclude that the standard deviation has decreased at the α = 0.01

What is standard deviation?

The standard deviation is a statistic that expresses the degree of variation or dispersion among a group of data. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

The null and alternative hypotheses are:

[tex]H_{0} :[/tex] α = 0.004

[tex]H_{a} :[/tex] α < 0.004

Under null hypothesis, the test statistic is:

[tex]x^{2} = \frac{(n-1)s^{2} }{\alpha ^{2} }[/tex]

   = (29 - 1)0.0036² / 0.004²

   = 22.68

Now the critical value of x² at 0.01 level of significance for

df = n-1

  = 29 - 1

 = 28

[tex]x_{critical} ^{2}[/tex] = 48.278

Since the test statics

x² = 22.68 is less than the critical value

[tex]x_{critical} ^{2}[/tex] = 48.278

∴ we fail to reject the null hypothesis and there is not significant evidence for the manager to conclude that standard deviation has decreased at α = 0.01

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The answer of the given fraction after simplification is 2.11.

To simplify simply means to make anything easier. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common components from the numerator and the denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given fraction is:

= 3 * 3/9 + 2 * 10/18

By simplifying the given fraction, we get

=  3 * 1/3 + 10/9

= 1 + 1.11

= 2.11

The answer of the given fraction after simplification is 2.11.

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Given the graphed equation:

Let's determine the point that represents a negative solution for x.

The solutions are the points where both lines meet.

From the graph, the solution which has a negative solution for x is:

(-2, -3)

In this point of intersection, the value of the x-coordinate is -3 (which is a negative value).

Therefore, the point which represents a negative solution for x is:

(-2, -3)

ANSWER:

(-2, -3)

We are asked to find how many deciliters can be found in 1 mililiter.

To get the solution we have to find the conversion factor. All we need to do is divide the volume by 100.

Here is a formula

This implies,

ANSWER: 0.01

Here, we want to evaluate the expression

We use the order of operations here PEDMAS ( parentheses, exponents (roots and powers) , division, multiplication, addition and subtraction)

We start out with the parentheses, then move on with the terms outside by multiplication

We have this as follows;

The perimeter of the sector is 2cm

The diagram shows a sector of a circle, center O.

The radius of the circle is 6cm.

The angle AOB is 120

We need to find the perimeter of the sector

s = r∅

Where ∅ is the angle subtended by the arc

r is the radius of the circle

s = 6 (120/360)

s = 6 (1/3)

s = 2

Therefore,  the perimeter of the sector is 2cm

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Solution:

The volume of a cylinder is expressed as

Given the cylindrical water tank below:

where

By substitution, we have

Hence, the volume of the cylindrical water tank, to the nearest whole number, is

Answer:

it is half of volume of tube.

tube volume = area of circle (πr)× height of tube (h)

volume of tube = π × r × t

1/2 tube volume = 1/2 × π × r × h

£350 is divided in the ratio 3:11 is £75 and £275.

The given ratio is 3:11.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

We need to divide £350 in the given ratio

Now, 3+11=14

3/14 × 350

= £75

11/14 × 350

= £275

Hence, £350 is divided in the ratio 3:11 is £75 and £275.

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Answer:

Step-by-step explanation:

0 0. 4 0

9 3 3 8. 0 0

 − 0      

   3 8    

 −   0    

   3 8 0  

 − 3 7 2  

       8 0

     −   0

       8 0

0.40

2.45 is the answer to 9.3 divided by 3.8

Given the building that can be modeled as a

right rectangular prism with dimentions

8 * 2 3/4 * 2 3/4

Volume is given by

since we have 850 bricks

the volume occupied by 850 bricks is therefore

then

the cost of the 850 bricks is

cost of bricks is $3085.50

To earn exactly $252, madison needs to work for 21 hours.

Time         money

worked      earned

5                    60

8                    96

12                  144

15                  180

We need to find how many hours should madison work to earn exactly $252

For 5 hours she earns $60

So in 1 hour she earns $ 60/5 = 12

For $1 she needs to work for 1/12 hour

For 252 she need to work for (1/12) 252

For 252 she need to work for 21

Therefore, to earn exactly $252, madison needs to work for 21 hours.

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The relative extrema of the function  f(x) = x³ + 4x² - x - 4 is at

( [tex]-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27}[/tex] )and the graph of the function is attached below.

The given function is f(x) = x³ + 4x² - x - 4

For the relative extrema we will first have to find the first derivative of the function:

f'(x)  = 3x² + 8x - 1

Now for4 the function to have an extremum, f'(x) = 0

3x² + 8x - 1 = 0

Solving we get :

the values of x using the quadratic formula  are [tex](-\frac{4-\sqrt{19}}{3} , -\frac{4+\sqrt{19}}{3} )[/tex] .

Now we will substitute the values of x in the function f(x) to get the local extremum.

The maximum value of f(x) is [tex]\frac{56+38\sqrt19}{27}[/tex].

The minimum value of f(x) is [tex]\frac{56-38\sqrt19}{27}[/tex] .

Now we will use various points to find the values of f in the function.

At x = -3 , y = 8

At x = 0 , y = -4

At x =-1 , y = 0

Hence the relative extremum of the function is at [tex](-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27})[/tex] .

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Answer:

40q7572928254949262618394938282920420

we have

x2 + 9x + 8

Find the factors

Complete the square

(x^2+9x+81/4)-81/4+8=0

Rewrite as perfect squares

(x+9/2)^2=81/4-8

(x+9/2)^2=49/4

square root both sides

(x+9/2)=(+/-)7/2

x=-9/2(+/-)7/2

so

x1=-9/2+7/2=-1

x2=-9/2-7/2=-8

therefore

x2 + 9x + 8=(x+1)(x+8)

answer is

The factors are

(x+1) and (x+8)

The focus of a parabola does not lie on it. Hence, the equation of parabola is given as y² = 2y - x².

The parabola can be defined as a conic section curve, all of whose points are equidistant from a fixed point called as focus and a fixed line called as directrix.

Given that,

The focus of parabola is (0, 1).

The vertex of parabola is (0, 0).

Suppose, there is one more point on parabola as (x, y).

Since focus of a parabola is equidistant from all the points on parabola.

Use distance formula to find the distance between two points (x₁, y₁) and (x₂, y₂) as √((x₂ - x₁)² + (y₂ - y₁)²) to find the equation of parabola as,

√((x - 0)² + (y - 1)²) = √((0- 0)² + (0 - 1)²)

=> x² + (y - 1)² = 1

=>  (y - 1)² = 1 - x²

=> y² - 2y + 1 = 1 - x²

=> y² = 2y - x²

Hence, the equation of the parabola having vertex at origin and focus at  (0, 1) is  y² = 2y - x².

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Using the compound interest formula, we have:

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Regression

A) We can see the graph and through the data that the most indicated form is to find the regression model since there is not much uniformity among the data to describe it as a purely linear model.

Plotting that scatterplot, and generating the equation we know that the equation is:

The given expression is

Terms are the expressions separated by negative or positive signs. In this case, there are 4 terms.

Coefficients are the number multiplying the variable. IN this case, the coefficients are -2, 3, and -1.

The variable is just x because it's the only letter present in the expression.

The powers are x'8 and x'2.

Answer:

D

Step-by-step explanation:

The total commission is the number of laptops times the commission per laptop. Thus, [tex]c=39.95l[/tex].

Setting [tex]l=15[/tex], [tex]c=39.95(15)=599.25[/tex].

Answer:

6(3a+7b+1)

Step-by-step explanation:

36a+42v-18a+6
18a+42b+6
GCF=6
6(3a+7b+1)

The factor of the given expression is 6(3a+7b+1).

A factor is a number that divides another number, leaving no remainder.

Given an expression, 36a + 42b - 18a + 6

On factoring, we get,

36a + 42b - 18a + 6

= 18a+42b+6

= 6(3a+7b+1)

Hence, The factor of the given expression is 6(3a+7b+1).

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Answer:factor of x³ + 343

Step-by-step explanation: Option D is correct. A factor of an expression is usually referred to as a number or an algebraic expression that divides the known expression. The above algebraic expression needs to be expanded to determine its factor; Mathematically; x³ + 343 = (x + 7) (x² - 7x + 49) Therefore, we can conclude that the factors are (x + 7) (x² - 7x + 49)

Answer: 19/24

Explanation:

From the information given,

Number of green marbles = 15

Number of red marbles = 9

Total number of marbles = 15 + 9 = 24

Probability is expressed as

number of favorable outcomes/number of total outcomes

Probability f selecting a greeen marble = 15/24

Even numbers divide 2 without a remainder. The even numbered marbles are

red = 2, 4, 6, 8

green = 2, 4, , 68, 10, 12, 14

Total number of even numbered marbles = 11

Probability of selecing an oevennumber = 10124

The events are not mutually exclusive becuse they can occur together. For two ebvents, A and B that are not mutually exclusive,

P(A U B) = P(A) + P(B) - P(A and B)

Thus,

the probability that the marble is green or even numbered = Probability of selecting a green marble + Probability of selecting an even number - Probability of selecting a green and even numbered marble

Number of green even numbere marble s = 7

Probability of selecting a green and even numbered marble = 7/24

Thus,

the probability that the marble is green or even numbered = 15/24 + 11/24 - 7/24

the probability that the marble is green or even numbered = 19/24

Let the number of professors be x.

If there are 16 times as many students as professors, then the number of students will be:

If the number of students and professors is 42,500, then we have that:

Solving by dividing both sides by 17, we have:

Hence, we can calculate the number of students in the college to be:

Therefore, there are 40,000 students in the college.

Answer:

See below

Step-by-step explanation:

Maximum height will be found at the t value = - b/2a  

  b = 192    a = -16  

      so max height will be at   t = - 192/(2 * -16) = 6 s

Max height will be   h = -16(6^2) + 192(6)   = 576 ft