Terry's mother combines 1.5 liter bottles of juice with two 0.25 liter cans of sparkling water to make punch. what is the total amount of punch that Terry's mother make?

The term ((fx - fa)/(x-a)) represents the slope of a secant line between two points on a function. This slope can be used to approximate the derivative of the function at point A.

To use the expression ((fx - fa)/(x-a)), you need to understand that it represents the average rate of change of a function f(x) over the interval [a, x]. In this context, f(x) and f(a) are the function's values at the points x and a, respectively. The expression helps in finding the slope of the secant line that connects the two points on the graph of the function. Simply plug in the values for f(x), f(a), x, and an into the expression to calculate the average rate of change over the given interval.

The term ((fx - fa)/(x-a)) represents the slope of a secant line between two points on a function. To use it, you would first choose two points on a function, let's call them to point A and point B. Point A has coordinates (a, fa) and point B has coordinates (x, fx). Then, you would substitute these values into the formula ((fx - fa)/(x-a)) to find the slope of the secant line between these two points. This slope can be used to approximate the derivative of the function at point A.

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Answer:

it s b) 4 2 the power of 7

Step-by-step explanation:

The geometry term that each statement represent is option D. Statement 1: postulate; Statement 2: theorem

A statement serves as a  declarative sentence which can be  true or false and it is been referred to as proposition.

A statement can be seen as to be correct when there is approved mathematical arguments and operations hence, statement 1 is a theorem and statement 2 is a postulate.

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Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer:

Step-by-step explanation:

The correct statement is: h(1) = h(2-1)

The statement "h(x) = h(2-x)" implies that the function h is symmetric about the line x = 1. Based on this symmetry, the following statements must be true:

h(1) = h(2-1) = h(1) - This means that the value of the function at x = 1 is equal to the value of the function at x = 1.

h'(1) = -h'(1) - This means that the derivative of the function at x = 1 is equal to the negative of the derivative of the function at x = 1.

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Answer:

B

Step-by-step explanation:

The rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83

What is the Volume of a Sphere?

The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements of a sphere's volume include m3, cm3, in3, etc. The sphere has a circular, three-dimensional form. Its form is determined by three axes: the x, y, and z axes. Sports like basketball and football are all instances of spheres with volume.

Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We may use the following formula to get the volume of a sphere whose radius is "r":

Here, In the question, It is given that:

Radius = 4inch.

Rate of increase = 569 cubic inches;

So, using the Volume of Sphere, formula:

\(\begin{aligned}v=\frac{4}{3} \pi r^3 \\\frac{d v}{d t} &=\frac{d}{d t}\left[\frac{4}{3} \pi r^3\right] \\&=\frac{4 \pi}{3}\left(3 r^2\right) \frac{d r}{d t} \\\frac{d v}{d t} &=4 \pi r^2 \frac{d r}{d t}\end{aligned}\)

\(\begin{aligned}&\frac{d r}{d t}=\frac{\frac{d v}{d t}}{4 \pi r^2}\\&\left.\frac{d r}{d t}=\frac{569}{(4 \pi)(4)^2}=\frac{d}{d t}_{r=4}^{d r^2}=569\right]\\&\frac{d v}{d t}=\frac{569}{64 \pi} \sim 2.83\end{aligned}\)

Hence,  the rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83

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Answer:

HT = 17 cm

<T = 58°

<H = 32°

Step-by-step explanation:

✔️Find HT:

Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²

Where,

a = HW = 15 cm

b = WT = 8 cm

c = HT

Plug in the values:

HT² = 15² + 8²

HT² = 289

HT = √289

HT = 17 cm

✔️Find <T by applying trigonometric ratio formula:

Recall: SOH CAH TOA

Reference angle (θ) = <T

HW = 15 cm = Opposite side length

WT = 8 cm = Adjacent side length

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos T = 8/15

T = \( cos^{-1}(0.5333) \)

T ≈ 58°

✔️Find <H:

Sun of interior angles of a triangle = 180°

Therefore,

m<H + m<T + m<W = 180°

Substitute

m<H + 58° + 90° = 180°

m<H + 148° = 180°

m<H = 180° - 148°

m<H = 32°

a) It is like winning a free entry ticket raffle.

b) The probability that you will win something (either a free raffle entry or a cash prize -  \(\frac{1}{3}\) .

c) The probability that you win nothing at all is - \(\frac{2}{3}\)

a)  One of every five people plays and gets a free entry in a raffle.

  P(Free entry)= \(\frac{1}{5}\)

Two of every fifteen people play and win a small cash prize.

   P( Small prize)= \(\frac{2}{15}\)

  P(Free entry) = \(\frac{1}{5}\)

                        = \(\frac{1 . 3}{5 . 3}\) = \(\frac{3}{15}\)

​                 \(\frac{3}{15}\) > \(\frac{2}{15}\)

​    P(Free entry) > P( Small prize)

b)  P(Win something)   =P(Free entry)  +  P(Small prize)

                                     = \(\frac{1}{5} + \frac{2}{15}\)

                                     = \(\frac{3}{15} + \frac{2}{15}\)      ( use addition)

                                     = \(\frac{3 + 2}{15}\)

                                     = \(\frac{5}{15}\) = \(\frac{1}{3}\)

c) P(Win nothing)  +  P(Win something) = 1

  P(Win nothing) = 1 - P(Win something)

   P(Win nothing)  = 1 - \(\frac{1}{3}\)         (use subtraction)

   P(Win nothing) = \(\frac{3}{3} - \frac{1}{3}\)

   P(Win nothing) = \(\frac{2}{3}\)

So,

a) It is like winning a free entry ticket raffle.

b) The probability that you will win something (either a free raffle entry or a cash prize -  \(\frac{1}{3}\) .

c) The probability that wins nothing at all is - \(\frac{2}{3}\)

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The complete question is :

The city has created a new contest to raise funds for a big Fourth of July fireworks celebration. People buy tickets and scratch off a special section on the ticket to reveal whether they have won a prize. One out of every five people who play gets a free entry in a raffle. Two out of every fifteen people who play win a small cash prize. a. If you buy a scratch-off ticket, is it more likely that you will win a free raffle ticket or a cash prize? Explain your answer. b. What is the probability that you will win something (either a free raffle entry or a cash prize)? c. What is the probability that you will win nothing at all? To justify your thinking, write an expression to find the complement of winning something.

​

​

Answer:

A. Pr(8)   = 1/10

B.  Pr(odd)  = 1/2

C.  Pr(even)  = 1/2

D. Pr(less than 6)  = 1/2

E.  Pr(prime) = 2/5

F. Pr(3 or 8)  = 1 / 5

G. Pr(8, 9 or 10) = 3/10

H. Pr(greater than 9)  = P(10) = 1/10

Step-by-step explanation:

We assume a FAIR 10-faced die, meaning there is an equal probability of throwing any one of the ten numbers.

With 10 possible outcomes each with equal probability, the probability of throwing any number is 1/10.

(It is preferable to work with fractions in probability because fractions are exact numbers, while decimals can often be rounded, or truncated).

A. Pr(8)   means probability of throwing an 8,  therefore Pr(8) = 1/10

B. Pr(odd)  there are 5 odd number from 1 to 10, so Pr(odd) = 5/10 = 1/2

C. Pr(even)  there are 5 even number from 1 to 10, so Pr(even) = 5/10 = 1/2

D. Pr(less than 6)  there are 5 numbers less than 6 (between1 to 10),

       so Pr(less than 6) = 5/10 = 1/2

E. Pr(prime) (remember that 1 is not prime)

   A prime number is an integer not divisible by any number except one and itself.

   Between 1 to 10, the four prime numbers are 2,3,5,7

   therefore Pr(prime) = 4/10 = 2/5

F. Pr(3 or 8)  

(3 or 8) make 2 successful outcomes out of 10, so Pr(3 or 8) = 2/10 = 1 / 5

G. Pr(8, 9 or 10)

similarly, (8,9 or 10) make three successful possible outcomes out of 10, so

P(8,9 or 10) = 3/10

H. Pr(greater than 9)

there is only one successful outcome, namely "10" out of 10 possible outcomes.  So

P(greater than 9) = P(10) = 1/10

1. please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?

A die is singular for dice, which can take up any number of faces.  With a 10-faced solid, we can make a 10-faced die numbered 1 to 10.

2. and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you

See solutions above.

Answer:

Remember that standard probabilities are defined as the ratio between the number of favorable cases, and the total number of possible events.

In this case, we have a 10-sided die, which means its faces are numbered from 1 to 10, which gives us 10 total number of possible events. In other words, the denominator of the ratio is going to be 10.

Now we're able to find each probability.

\(P_{8} =\frac{1}{10}=0.10\)

The numerator is 1 because there's only one number 8 in the die, that means the number of favorable cases is 1, and, as we said before, the total number of possible events is 10.

\(P_{odd} =\frac{5}{10}=0.5\)

The numerator is 5 because there are 5 odd numbers from 1 to 10. In other words, there are 5 favorable cases to this probability.

\(P_{even}=\frac{5}{10}=0.5\)

There are 5 even numbers from 1 to 10, that's why we had the same probability.

We know that there are only 5 numbers less than 6 for this die.

\(P_{<6}=\frac{5}{10}=0.5\)

A prime number is such that it can be divided only by itself and the unit. So, there are four prime numbers from 1 to 10, which are 2, 3, 5, 7.

\(P_{prime}=\frac{4}{10}=0.4\)

When we are going to find the probability of an event "or" another, we must sum those favorable cases.

\(P_{3 \ or \ 8} =\frac{1+1}{10}=\frac{2}{10}=0.2\)

In this case, we need to some all three favorable cases. The die has only one 8, one 9 and one 10. So, the probability is

\(P_{8,9,10}=\frac{1+1+1}{10}=\frac{3}{10} =0.3\)

We know that there's only one number greater than 10 on such die.

\(P_{>10}=\frac{1}{10}=0.1\)

Lastly, "die" refers to this special 10-sided dice. In other problems, you can find "a die" with more faces even. But, in general, "die" refers to a dice.

It is required to solve the equation:

To do this, subtract 2 1/4 from both sides of the equation:

Subtract the mixed fractions on the right:

The answer is x=3.

Answer:

what is the question tho you didn't post it

have a good day :)

Step-by-step explanation:

Using the equation, it is found that it will take 2.4 hours for the airplane to travel 1200 miles.

An airliner moves at a consistent pace from New York to London.

The equation that relates the time in hours needed to travel d miles is given by:

\(t = \frac{1}{500} d\)

In this problem, we want the time needed to travel 1200 miles, thus, and:

\(t = \frac{1}{500} * 1200 = 2.4\)

Hence, it will take 2.4 hours to travel 1200 miles.

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The leading coefficient and the degree are 7 and 5

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

-6 - 12x^2 + 7x^5 + 5x

The degree is the highest power in the expression

So, we have

Degree = 5

The leading coefficient is the coefficient of the term with highest power in the expression

So, we have

leading coefficient = 7

Hence, the leading coefficient is 7

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The chief of security for the Mall of the Dakotas directed a study of theft. He selected a sample of 200 boxes that had been tampered with and ascertained that for 80 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 45 boxes, employees had stolen the goods, and for the remaining 75 boxes, he blamed poor inventory control.

In his report to the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the 0.10 significance level. H0: The proportions are as stated. H1: The proportions are not as stated. The decision rule using a 0.10 significance level is: Reject H0 if the computed chi-square value is greater than 4.605. Compute the value of chi-square as follows: Observed Frequencies: Shoplifting: 80 Employee theft: 45 Poor inventory control: 75 Total: 200 Expected Frequencies: Shoplifting: (80+45+75) x (80/200) = 80. Employee theft: (80+45+75) x (45/200) = 36. Poor inventory control: (80+45+75) x (75/200) = 84. Total: 200The formula for chi-square is: χ2=∑((Oi−Ei)2/Ei). Using the observed and expected frequencies from above, we get: χ2 = [(80 - 80)²/80] + [(45 - 36)²/36] + [(75 - 84)²/84] = 2.4. The value of chi-square is 2.4, which is less than 4.605. Therefore, we fail to reject H0. Hence, the chief of security for the Mall of the Dakotas cannot say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely at a 0.10 significance level.

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Answer:

23. y = 47

Step-by-step explanation:

40 + 5x =180 (angls on a straight line add up to 180 degrees)

5x=140 (minus 40 from both sides)

x = 28 (divide both sides by 5)

3y - 1 = 140

3y =141 (add 1 to both sides)

y = 47 (divide both sides by 3)

Answer:

y=47

Step-by-step explanation:

Answer:

distribution

Step-by-step explanation:

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

Answer:

Step-by-step explanation:

Since ∠S and ∠Y are complementary, we have:

∠S + ∠Y = 90°

We also know that:

m∠S = 2(m∠Y) − 30°

Substituting the second equation into the first equation, we get:

2(m∠Y) − 30° + ∠Y = 90°

Combining like terms:

3(m∠Y) = 120°

Dividing both sides by 3:

m∠Y = 40°

Therefore, m∠Y is 40 degrees.

Answer:

the daily balance of Elliott's account for the month of June is $1497.37.

Step-by-step explanation:

Day 1: 1223

Day 10: 1838 (1223+615)

Day 15: 1775 (1838 - 63)

Day 22: 1655 (1775 - 120)

To find the average daily balance, we add up the balances for each day and divide by the number of days in June:

Answer: D) 59°

Step-by-step explanation:

As per the density the probability that a density measurement of the post-1982 pennies is 0.3565 g/cm3.

Density is an important physical property that can help identify materials. In this case, we are interested in the density of zinc and how it relates to the post-1982 pennies.

To calculate the probability of a density measurement within 5% of the density of zinc, we need to first determine the range of densities that fall within 5% of the zinc density.

The 5% range of the zinc density is calculated by multiplying the zinc density (7.13 g/cm3) by 5% (0.05), which gives us 0.3565 g/cm3.

The upper and lower limits of this range are then calculated by adding and subtracting this value from the zinc density, respectively.

The upper limit is 7.4865 g/cm3 (7.13 + 0.3565),

while the lower limit is 6.7735 g/cm3 (7.13 - 0.3565).

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Answer:

15

Step-by-step explanation:

Distance between two points is = √(x2 - x1)² + (y2 - y1)²

x1 = -5, y1 = 4; x2 = 7, y2 = -5

|PQ| = √(7 - (-5))² + (-5 - 4)²

|PQ| = √(7 + 5)² + (-9)²

|PQ| = √(12)² + 81

|PQ| = √144 + 81

|PQ| = √225

|PQ| = 15

Answer:

The average change in balance each day during his time $41

Step-by-step explanation:

Here, we want to write an integer to represent the average balance change in the 30 days period.

First, let’s find difference between opening and closing balance= (1800-570) = 1230

We shall now divide this by 30 = 1230/30 = $41

Answer:

The average chang in his time is 41

Step-by-step explanation:

The probability of having a flip flop is 4/9.

In the question, we can see from the data that we have that Xavier's mother has a large collection of shoes. the table shows flip flop 8, boots 4, and clogs 6.

Recall that probability deals with the possibility that an event may occur or not occur under a given circumstance. We know that;

Total number of the shoes = 4 + 6 + 8 = 18

Probability of a flip flop = 8/18 = 4/9

This is the possibility that what would be picked is a flip flop.

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Answer: ? = 42

Step-by-step explanation:

 (a-b)² = a² - 2ab + b².   From 9p² -?p + 49   we see  

9p² = (3p)² and  49 = 7²   Then Middle term is  -2·(3p)·7 = -42p

The formula for the average cost per shirt, A, in terms of x is:

A = 400/x + 8 + 0.04x

To find the formula for the average cost per shirt, A, we need to divide the total cost by the number of shirts produced, which is represented by x in this case.

The cost of producing x shirts is given by the equation:

C = 400 + 8x + 0.04x²

To find the average cost per shirt, we divide the total cost (C) by the number of shirts (x):

A = C / x

A = (400 + 8x + 0.04x²) / x

Simplifying the expression:

A = 400/x + 8 + 0.04x

Therefore, the formula for the average cost per shirt, A, in terms of x is:

A = 400/x + 8 + 0.04x

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===============================================================

Explanation:

The first step is to locate point M. It is at (-3, -5). Ignore the other points as your teacher is not asking to transform them.

Reflecting point M over the line y = -3 will have us move 2 units up to arrive at the line of reflection, and then we move 2 more additional units up to get to N = (-3, -1).

Now reflecting point N over the line y = 2 will have us move (-3,-1) three units up to get to the line of reflection, and then we move up another 3 units to get to P = (-3,2) which is the last stop. This is also the location of point M'.

See diagram below.

--------

Extra info: Overall, those two reflections combine to a translation of shifting 10 units up. Algebraically, we can write the translation rule \((x,y) \to (x,y+10)\). Two reflections only turn into a translation if and only if the lines of reflection are parallel.

Answer:

The y-intercept is (0,-3

Step-by-step explanation:

Step-by-step explanation:

to find the y intercept you simply equate x to 0. therefore, the y intercept is -4.5

and its coordinate is:

(0, -4.5)

The statements that are true are:

π is the area of a circle of radius 1.

π is the circumference of a circle of diameter 1.

π is the constant of proportionality relating the diameter of a circle to its circumference.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

We have,

Circumference of a circle = 2πr

Area of a circle = πr²

π is the area of a circle of radius 1.

Area = πr² = π x 1 = π

π is the area of diameter 1.

2r = 1

r = 1/2

Area = πr² = π x 1/4 = π/4

π is the circumference of a circle of radius 1.

Circumference of a circle = 2πr = 2 x π x 1 = 2π.

π is the circumference of a circle of diameter 1.

Circumference of a circle = 2πr = 2 x π x 1/2 = π.

π is the constant of proportionality relating the diameter of a circle to its circumference.

Diameter ∝ Circumference

2r = 2πr

2r = π (2r)

π is the constant of proportionality relating the radius of a circle to its area.

r = (πr)r

Thus,

π is the area of a circle of radius 1 is true.

π is the circumference of a circle of diameter 1 is true.

π is the constant of proportionality relating the diameter of a circle to its circumference is true.

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