A vending machine automatically pours coffee into cups. The amount dispensed is normally distributed with a mean of 7.4 oz and a standard deviation of0.26 oz. Find the probability the machine will overflow an 8-oz cup.

Answer:

main number

Step-by-step explanation:

Final answer:

A base number in mathematics is the number raised to a power, where in scientific notation it is always 10, whereas in economic terms, a base year is a reference year for economic measurements.

Explanation:

The definition of a base number in mathematics generally refers to the number that is being raised to a certain power. In the context of scientific notation, the base number is always 10. This is used to succinctly represent very large or very small numbers in the form N x 10^n, where N is a number greater than or equal to 1 and less than 10, and n is a positive or negative integer; for example, 10^0 = 1. However, the concept of a base extends beyond just the number 10; any number can act as a base in different mathematical contexts.

When discussing numbers in a positional numeral system, the base determines the value of each digit in the number and how those digits are combined to represent the overall number. For instance, in the base-10 system, the digits 0 through 9 are used, and the position of each digit indicates how many multiples of powers of 10 it represents. Finally, in the context of economic indexes, a base year is a reference year against which economic growth or inflation is measured.

Check the picture below, that enclosed area is pretty much our "washer".

now, to get the outer radius, or "farther" radius from the axis of rotation, what I usually do is, use the f(x) - g(x) to get the area under the curve, using the axis of rotation for g(x).

[tex]\bf \stackrel{\textit{top, f(x)}}{4\sqrt{x}}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{farthest radius}}{4\sqrt{x}-0\implies 4\sqrt{x}} \\\\\\ \stackrel{\textit{top, f(x)}}{x}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{closest radius}}{x-0\implies x} \\\\[-0.35em] ~\dotfill\\\\ 4\sqrt{x}=x\implies \stackrel{\textit{squaring both sides}}{16x=x^2\implies }16x-x^2=0[/tex]

[tex]\bf x(16-x)=0\implies x= \begin{cases} 0\\ 16 \end{cases}\qquad \qquad \impliedby \textit{these are the bounds} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int\limits_{0}^{16}~\pi [(4\sqrt{x})^2-(x)^2]dx\implies \pi \int\limits_{0}^{16}[16x-x^2]dx\implies \pi \int\limits_{0}^{16}16x~~-~~\pi \int\limits_{0}^{16}x^2[/tex]

[tex]\bf \pi \left. 16\cdot \cfrac{x^2}{2} \right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16}\implies \left. \pi 8x^2 \cfrac{}{}\right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16} \\\\\\ \left( \pi [2048]-\pi [0] \right)-\left(\left[ \cfrac{4096\pi }{3} \right]-[0] \right)\implies 2048\pi -\cfrac{4096\pi }{3} \implies \cfrac{2048\pi }{3}[/tex]

Answer:

[tex]\large\boxed{V=288\pi}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{W have the radius}\ R=6.\ \text{Substitute:}\\\\V=\dfrac{4}{3}\pi(6^3)=\dfrac{4}{3}\pi(216)=4\pi(72)=288\pi[/tex]

Answer:

40 square units

Step-by-step explanation:

The surface area is given by

LA = 2(wh+lh)

where h is the height l is the length and w is the width

We do not include the top or bottom

We know l=6 w=4 and h=2

LA = 2 ( 4*2 + 6*2)

lA = 2( 8+12)

    = 2 (20)

    = 40

Step-by-step explanation:

(700 4/7) ÷ (1 2/5)

Write the fractions in improper form:

(4904/7) ÷ (7/5)

To divide by a fraction, multiply by the reciprocal:

(4904/7) × (5/7)

24520/49

500 20/49

There are 500 pieces.

Answer:

(700 4/7) ÷ (1 2/5)

Write the fractions in improper form:

(4904/7) ÷ (7/5)

To divide by a fraction, multiply by the reciprocal:

(4904/7) × (5/7)

24520/49

500 20/49

There are 500 pieces.

Answer:

B

Step-by-step explanation:

Circumference of a circle is:

C = 2πr

Area of a circle is:

A = πr²

The circumference of the well is 47 ft and the area of the well in the drawing is 0.641 cm².  If we say r is the radius of the circle on the drawing in centimeters and R is the actual radius of the well in feet, then:

47 = 2πR

0.641 = πr²

Solving for each:

R = 47 / (2π) ≈ 7.48 feet

r = √(0.641 / π) ≈ 0.452 cm

The scale is the ratio of R / r:

R / r = (7.48 ft) / (0.452 cm) = 16.6 ft/cm

So 1 cm = 16.6 ft.

This isn't one of the options.  Are you sure you copied the problem correctly?

Maybe you meant that the circumference is 4π feet, and the area is 0.64π cm².  If so:

R = 4π / (2π) = 2 feet

r = √(0.64π / π) = 0.8 cm

R / r = (2 feet) / (0.8 cm) = 2.5 ft/cm

So 1 cm = 2.5 ft.

Answer:

B

Step-by-step explanation:

And arithmetic sequence is a sequence in which the difference between each of the numbers are constant.

It is not A, because the difference between 3 and 9 is positive 6, and the difference between 9 and 81 is positive 72.

It is not C, because the difference between 4 and 1 is -3, and the difference between 1 and 4 is positive 3.

It is not D, because the difference between 2 and -2 is -4, and the difference between -2 and 2 is positive 4.

And it is B because the numbers maintain a constant difference between each other, which is -3.

Answer:

B

Step-by-step explanation:

An arithmetic sequence has a common difference (d) between consecutive terms.

The only sequence with a common difference is B

1 = 4 = - 3

- 2 - 1 = - 3

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

Answer:

99x +84 ≤ 1,150

Step-by-step explanation:

Her budget is $1,150, this means that the price of all her purchases cannot exceed it. In other words, the sum of all her purchases must be less or equal to 1,150.

To find how many watches she can buy, you need to multiply it by the price of the watches, which is $99, so it will be 99x.

As for the shirts, she spent $84.

So the inequality equation you will need will be the sum of the price of watches and shirts is less than or equal to 1,150.

99x + 84 ≤ 1,150

Answer:

log₄ 10 = log₁₀ 10 / log₁₀ 4

Step-by-step explanation:

Taking the x to be a power then;

[tex]4^x +2 =12[/tex]

[tex]4^x = 12-2[/tex]

[tex]4^x=10[/tex]

Introduce log on both sides

x log 4= log 10

x= log 10/log 4

log₄ 10 = log₁₀ 10 / log₁₀ 4

Answer: x = log₄(3/4)  = -0.207

Step-by-step explanation:

when you have the equation:

n^x = b

whe have that:

Logₙ(b) = x

in this case we have the equation:

4^(x+2) = 12

(4^x)*(4^2) = 12

16*4^x = 12

4^x = 12/16 = 3/4

x = log₄(3/4)  = -0.207

Answer:

[tex]y - 7 = \frac{1}{4}(x + 2)[/tex]

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are. Plus, perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES] so −4 becomes ¼.

I am joyous to assist you anytime.

Konichiwa~! My name is Zalgo and I am here to help you out today. If f were to equal -3, first we need to put -3 into the equation. It would look like "f(-3)=x^2". The answer to that equation is 9.

I hope that this helps! :T

"Stay Brainly and stay proud!" - Zalgo

Answer:

D) 120pi yd2

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

6 times 6 is 36 and 36 plus 4 is 40 not 42

Jeff can make his choices independently so there are a total of

[tex] 2 \times 14 \times 4[/tex]

different sundaes.  

Answer: D. 112

Answer:

D 112

Step-by-step explanation:

Just multiply the number of different ways to choose things to come up with all your possibilities.

That is you just do 2(14)(4)=28(4)=112

When it asks for descending order of the polynomial it wants you to put the exponents in order from largest to smallest like so...

C. [tex]x^{12} +3x^{7} + 4x^{3}  -9x[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option C

Step-by-step explanation:

In this question the given polynomial is 4x³ + 3x⁷ - 9x + x¹²

If we rewrite it in the descending order of the powers then the polynomial will be

x¹² + 3x⁷ +4x³ + 9x

This polynomial matches with option C.

Option C is the answer.

Final answer:

To find the coordinates of point C when given the midpoint M and point D, we find the average of the endpoints' coordinates. Solving the equations, we find that the coordinates of point C are (2, 8).

Explanation:

The student is asking to find the coordinates of point C given that the midpoint M of line segment CD is at (6, 6), and point D is at (10, 4). To find point C, we use the concept that the midpoint's coordinates are the average of the coordinates of the endpoints of the segment. That means:

The x-coordinate of C can be found by the equation 6 = (xC + 10) / 2 which leads to xC = 2(6) - 10,

The y-coordinate of C can be found by the equation 6 = (yC + 4) / 2 which leads to yC = 2(6) - 4.

Solving for xC and yC, we find:

xC = 12 - 10 = 2,

yC = 12 - 4 = 8.

Therefore, the coordinates of point C are (2, 8).

Answer:

x = -5/2 y +4

Step-by-step explanation:

2x+5y = 8

Subtract 5y from each side

2x+5y -5y = -5y+8

2x = -5y+8

Divide each side by 2

2x/2 = -5y/2 +8/2

x = -5/2 y +4

Answer:

4x + y = - 2

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = - 4x - 2 ( add 4x to both sides )

4x + y = - 2 ← in standard form

Answer:

4x + y = -2

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

6 3/4 (2/9)

(27/4)(2/9)

4 divided by 2 is 2.

27 divided by 9 is 3.

Answer: 3/2

Answer:

6ft 3in

Step-by-step explanation:

4ft + 1ft = 5ft

4in +11in= 15in

15in =1ft and 3in

5ft+ 1ft 3in= 6ft 3in

Answer:

So ordered pair a is (2,11)

Step-by-step explanation:

We are given

a = b+c

and ordered pair b =(6,3) and ordered pair c =(-4,8)

Putting values of b and c in the given equation and adding x and y coordinates of b and c we can find ordered pair a.

a=(6,3)+(-4,8)

a =(6-4,3+8)

a =(2,11)

So ordered pair a is (2,11)

Answer:

2 1/2

Step-by-step explanation:

5 is 2 more than 2 so the the first part would be 2.

[tex]\dfrac{5}{2}=\dfrac{2\cdot2+1}{2}=2\dfrac{1}{2}[/tex]

[tex]\bf (-3yz)(-3yz)(-3yz)(-3yz)\implies (-3yz)^1(-3yz)^1(-3yz)^1(-3yz)^1 \\\\\\ (-3yz)^{1+1+1+1}\implies (-3yz)^4\implies (-3)^4 y^4 z^4\implies 81y^4 z^4[/tex]

The expression (-3yz) (-3yz) (-3yz) (-3yz) is  (-3yz) ⁴

  ⇒(-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹=(-3yz)¹⁺¹⁺¹⁺¹

   ⇒ (-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹ = (-3yz)⁴

Learn more about multiplication here:-https://brainly.com/question/1087373

#SPJ2

The answer is:

The volume of the sand is approximately 0.015605 m3

To solve the problem, and find the volume of the sand that Zed purchased, we need to use the formula to calculate the density and isolate the volume from it.

So, solving we have:

[tex]density=\frac{mass}{volume}[/tex]

From the statement we know that:

The mass of the sand is 25 kg

The density of the dry sand is 1,602 kg/m3

So, substituting and solving we have:

[tex]density=\frac{mass}{volume}\\\\volume=\frac{mass}{density}\\\\volume=\frac{25kg}{1,602\frac{kg}{m^{3}}}=0.015605m^{3}[/tex]

Hence, the volume of the sand is approximately 0.015605 m3

Have a nice day!

Answer: no

Step-by-step explanation:

Linear functions are straight lines and are also written in the form y=mx+b

The linearity of 3[g(x)] = x depends on the form of g(x). If g(x) is linear, such as g(x) = ax, then the equation is linear. Otherwise, if g(x) involves non-linear operations, the overall equation will not represent a linear function.

Whether or not the equation 3[g(x)] = x represents a linear function depends on the form of g(x). If g(x) is a linear function, then the equation represents a linear transformation. If g(x) is nonlinear, then the overall function is not linear.

For example, if g(x) = exp(3x), the relationship is non-linear due to the exponential function. However, if the g(x) function is a simple linear function like g(x) = a₁x, with a constant coefficient, the equation maintains its linearity. In this scenario, the function could even represent a constant multiple of the identity function, where g(x) = x/3.

It is important to note that in the context of mathematics, understanding whether a function is linear involves recognizing if it can be written in the form of g(x) = mx + b, where m and b are constants, and the function results in a straight line on a graph.

Answer:

He needs 0.075 lbs of sugar and 4.925 lbs of water.

Step-by-step explanation:

Let x lbs be the amount of sugar in the syrup. Then 5-x lbs is the amount of water in this syrup.

Note

5 lbs - 100%

x lbs - 1.5%

Write a proportion:

[tex]\dfrac{5}{x}=\dfrac{100}{1.5}[/tex]

Cross multiply:

[tex]100x=5\cdot 1.5\\ \\100x=7.5\\ \\x=\dfrac{7.5}{100}=0.075[/tex]

So, he needs 0.075 lbs of sugar and 5 - 0.075 = 4.925 lbs of water.

Answer: 1 x 10^27 m

Step-by-step explanation:

Answer:

1st and 3rd options

Step-by-step explanation:

We have been given three scatter plots. We are asked to choose the plots with cluster.

We know that cluster in a dot plot is formed when many data points lie in a small interval.

We can see that graphs represented by 1st option and 3rd option have many data points in a small interval, therefore, 1st and 3rd options are correct choice.

Answer:

Step-by-step explanation:

Answer:

[tex]area = base \times hight 36 \times 18 \: ad perimeter \: base \times base \times hight \times hight36 \times 36 \times 18 \times 18[/tex]

Area is given by base * the Hight which gives the area of the pool