Jeff purchased 5 items at the same price and 1 item for $2.95. What was the individual price of the 5 items if Jeff's total was $18.90 before tax?

When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is E. Pi.

The area of a circle is given by the formula A = π\(r^2\), where A is the area and r is the radius. If the area of the circle is increasing twice as fast as its radius, we can express this relationship as:

dA/dt = 2(dr/dt)

Here, dA/dt represents the rate of change of the area with respect to time, and dr/dt represents the rate of change of the radius with respect to time.

Since we are considering an expanding circle, both dA/dt and dr/dt are positive.

Now, let's solve for the relationship between dA/dt and dr/dt:

dA/dt = 2(dr/dt)

π\(r^2\) = 2(dr/dt)

Dividing both sides by \(r^2\):

π = 2(dr/dt) / \(r^2\)

Simplifying further:

π = 2(dr/dt) / \(r^2\)

π = 2/r

Therefore, the relationship between the rate of change of the area and the rate of change of the radius is π = 2/r.

To find the value of r, we rearrange the equation:

r = 2/π

Thus, the radius is 2/π, which is approximately 0.6366.

To know more about area, refer here:

https://brainly.com/question/15906335

#SPJ4

The required probability that the total number of spots showing is less than 7 is 9.26%

The probability of an event is found by considering all possibilities that follow the given condition. The probability value cannot exceed the interval [0,1].

Three six-sided dice are rolled at the same time.

It is asked to calculate the probability that the total number of spots showing is less than 7.

If the die is rolled, possible outcomes are as given below.

S: {1, 2, 3, 4, 5, 6}

Number of elements in sample space, n(S) = 6.

Probability of any specific outcome from S = 1/6

If the three dice are rolled together, the total number of elements in the sample space will be \((6^3)\)

Then, the probability of getting any of any specific outcome from this sample will be given by: \(\frac{1}{6^3} =\frac{1}{216}\)

Find the total possibilities for which the total of outcomes of all three dice is less than 7. It is possible when we get the following outcomes.

The minimum total that we get is 3 with outcomes (1,1,1) on three dice.

For a total of 3:

Possible outcomes: [1, 1, 1]

The number of possibilities \(A_1=1\)

For total 4:

Possible outcomes: [1,1,2], [1,2,1], [2, 1, 1]

Number of possibilities \(A_2=3\)

For a total of 5:

Possible outcomes:  [1,1,3], [1,3,1], [3, 1, 1],  [1,2,2], [2,2,1], [2, 1, 2]

The number of possibilities \(A_3=6\)

For a total of 6:

Possible outcomes :  [1,1,4], [1,4,1], [4, 1, 1],[1, 2, 3] ,[1,3,2],[2, 3, 1], [3,2,1], [3, 1, 2],[2,1,3], [2, ,2 ,2]

The number of possibilities : \(A_4=10\)

The number of possibilities for which the total number of spots showing is less than 7 is given by,

\(A_1+A_2+A_3+A_4\)

=> 1+ 3+ 6+ 10

=> 20

The probability that the total number of spots showing are less than 7 is calculated below.

P = 20/216

P = 0.0926

P = 9.26%

Learn more about Probability at:

https://brainly.com/question/30034780

#SPJ4

The given question is incomplete, complete question is:

Explain how to solve this problem:

You have three six-sided dice. When all three dice are rolled at the same time, calculate the probability of the following outcomes:

a. The total number of spots showing is less than 7

Answer:

Value of 10z = 8

Step-by-step explanation:

Given:

Equation of variable;

10z

and value of z = 0.8

Find:

Value of 10z

Computation:

We know that in given equation 10z

10 is constant(fixed value) and z is variable(changeable value)

where value of variable z is given 0.8

So,

By putting value of variable z in given equation

⇒ 10z

⇒ 10(0.8)

by multiplying variable and constant

Value of 10z = 8

For this problem, we are given the coordinates of the endpoint on the diameter of a circle. We need to write the equation in standard form and graph the circle.

To write the equation we need to know the coordinates of the center and the size of the radius. We will first find the center, which is the midpoint of the diameter:

The center is located at (-10, 6). The radius is the distance between the center and one of the given points.

The equation of the circle is:

Now we need to graph the circle, we need to find the center (-10,6) and trace the circle in a way that passes through (-7,2) and (-13, 10).

Answer:

Yes because there are still only two possible outcomes

Step-by-step explanation:

I think it’s this one cause I’m on it too

The apprοximate number οf students enrοlled in public schοοls in the United States is 7.68 × 10⁷, which cοrrespοnds tο chοice (C).

Unitary method widely used ease, already-present variables, οr all impοrtant elements frοm the οriginal Bishοp custοmizable questiοn can all be used tο achieve the gοal. If sο, a secοnd chance tο engage with the οbject will present itself. Otherwise, every crucial element that affects hοw well a prοοf οf an expressiοn wοrks will be gοne.

Here,

Tο sοlve this prοblem, we can start by multiplying the number οf students in the lοcal schοοl system by 480, since there are 480 times mοre students in public schοοls in the United States.

1.6 × 10⁵ × 480

= 7.68 × 10⁷

Therefοre, the apprοximate number οf students enrοlled in public schοοls in the United States is 7.68 × 10⁷, which cοrrespοnds tο chοice (C).

To know more about unitary method  visit:

brainly.com/question/28276953

#SPJ1  

say Steve is x ,then jenny will be x + 12

five years ago Steve's age was x - 5 and Jenny's age was x + 12 - 5= x + 7

since jenny was four times Steve's age 5 years ago the equation will be

x + 7 = 4(x - 5)

= x + 7 = 4x - 20

putting like terms together, we will have

4x - x = 20 + 7

= 3x = 27

this means 3x ÷ 3= 27 ÷ 3

x = 9

this means Steve is 9 years old and Jenny is 21 years old

(a) The standard deviation of the required distribution for vitamin C is approximately 7.98 mg/d.
(B) The plot should show a bell-shaped curve centered at 60 mg/d, with the RDA located slightly to the right of the center.

(a) To determine the standard deviation of the required distribution for vitamin C, we can use the information provided about the estimated average requirement (EAR) and the recommended dietary allowance (RDA). The EAR is the mean of the distribution (60 mg/d), and the RDA (75 mg/d) is assumed to be the 97.72 percentile.

We can use the Z-score formula to find the standard deviation:

Z = (X - μ) / σ

Where Z is the Z-score, X is the value of the RDA, μ is the mean (EAR), and σ is the standard deviation.

First, find the Z-score corresponding to the 97.72 percentile. Using a standard normal table or calculator, we find that Z ≈ 2.0.

Now, plug in the values into the Z-score formula:

2.0 = (75 - 60) / σ
σ = (75 - 60) / 2.0
σ = 15 / 2.0
σ = 7.5 mg/d
Plugging in the values, we get:
1.88 = (75 - 60) / σ

Solving for σ, we get:
σ = (75 - 60) / 1.88 = 7.98

The standard deviation of the required distribution is 7.5 mg/d.

(b) To sketch the distribution of vitamin C requirements for 19- to 30-year-old women, follow these steps:

1. Draw a normal distribution curve.
2. Mark the mean (EAR) at 60 mg/d on the horizontal axis.
3. Mark the RDA at 75 mg/d and the UL at 2000 mg/d on the horizontal axis.
4. Indicate that the standard deviation is 7.5 mg/d.

The distribution of vitamin C requirements for 19- to 30-year-old women is Normal, with a mean of 60 mg/d and a standard deviation of 7.98 mg/d. The EAR, RDA, and UL can be marked on the plot as follows:

- EAR: 60 mg/d, located at the center of the distribution
- RDA: 75 mg/d, located at the 97.72 percentile of the distribution
- UL: 2000 mg/d, located at the far right end of the distribution (beyond the range of the plot)

Learn more about Standard Deviation:

brainly.com/question/23907081

#SPJ11

Answer:

m^2-2m-3

Step-by-step explanation:

\( \frac{6m \times (m - + 1)}{(m - 3)(m + 1)} + \frac{m \times (m - 3)}{(m - 3)(m + 1)} \\ \frac{ {6m}^{2} + 6m}{ {m}^{2}- 2m - 3} + \frac{ {m}^{2} - 3m }{ {m}^{2} - 2m - 3 } \\ \frac{ {7m}^{2} + 3m}{ {m}^{2} - 2m - 3} \)

The slope of the line passing through the points (0, 30) and (8, 18) is -1.5.

Given is a graph of a line passing through the points (0, 30) and (8, 18).

To find the slope of the line passing through two points, you can use the formula:

slope = (y2 - y1) / (x2 - x1)

Let's use the points (0, 30) and (8, 18) to calculate the slope:

x1 = 0

y1 = 30

x2 = 8

y2 = 18

slope = (18 - 30) / (8 - 0)

= -12 / 8

= -1.5

Therefore, the slope of the line passing through the points (0, 30) and (8, 18) is -1.5.

Learn more about slope click;

https://brainly.com/question/3605446

#SPJ1

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

About quadratic equation here:

https://brainly.com/question/30098550

#SPJ11

To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

To know more about quadratic equation visit:

https://brainly.com/question/30164833

#SPJ11

Answer:

fx/gx=10

Step-by-step explanation:

fx= (36x5)-(44x4)-(28x3)

fx=80

gx= 4x2

gx=8

To work out fx/gx:

fx/gx=80/8

fx/gx=10

Answer:

0.750 kg

Step-by-step explanation:

Hi there ,

As you know 1 kg = 1000g

So when we convert g to kg then we divide the given value of grams by 1000.

So in this case we have 750 grams, changing it we have :

\(\frac{750}{1000}\)

Since there are 3 zeroes in 1000 we move the decimal point by 3 places to the left leaving the answer as : 0.750 kg or \(\frac{750}{1000}\) kg

Please mark me as brainliest if you found the above answer helpful

The function f can be implemented using a single 4-to-1 multiplexer and two inverters.

A 4-to-1 multiplexer is a digital logic component that selects one of four input signals based on the select lines. It has four data inputs (D0, D1, D2, D3), two select lines (S0, S1), and one output (Y). By properly connecting the inputs and select lines, we can realize the desired function f.

To implement the function f using a single 4-to-1 multiplexer and two inverters, we need to carefully assign the input signals and select lines to achieve the desired behavior. The truth table of the function f will guide us in determining the appropriate connections.

First, we can use the inverters to complement the required inputs if needed. Then, we can connect the complemented and uncomplemented inputs to the select lines of the multiplexer. The output of the multiplexer will be the result of the function f.

By carefully selecting the input assignments and connections, we can effectively implement the function f using a single 4-to-1 multiplexer and two inverters. This approach offers a compact and efficient solution for realizing the desired logic function.

Learn more about lines here: https://brainly.com/question/31454782

#SPJ11

Two possible solutions to the equation W = 250 + 132.5T are:

T = 2, W = 515

T = 5, W = 912.5

To find possible solutions to the equation W = 250 + 132.5T, we need to substitute values for T and calculate the corresponding value of W.

Let's consider two possible values for T:

Solution 1: T = 2 (indicating 2 T-shirts in the box)

W = 250 + 132.5 * 2

W = 250 + 265

W = 515

So, one possible solution is T = 2 and W = 515.

Solution 2: T = 5 (indicating 5 T-shirts in the box)

W = 250 + 132.5 * 5

W = 250 + 662.5

W = 912.5

Therefore, another possible solution is T = 5 and W = 912.5.

Hence, two possible solutions to the equation W = 250 + 132.5T are:

T = 2, W = 515

T = 5, W = 912.5

Learn more about equation from

https://brainly.com/question/29174899

#SPJ11

Answer:

x = 300.5

Step-by-step explanation:

5x + 2x + 3x - 5 = 3000

Combine like terms

10x - 5 = 3000

Add 5 to both sides

10x = 3005

Divide both sides by 10 to get x alone

x = 300.5

Answer:

17.75

Step-by-step explanation:

Therefore, we should draw a ring around the numbers 113 and 124.

A number is a mathematical object used to count, measure, and label. It is an abstract concept that represents a quantity or value. Numbers can be represented using symbols or words and can be classified into different types such as natural numbers, integers, rational numbers, real numbers, and complex numbers, among others. Numbers are used in a wide range of mathematical operations, including addition, subtraction, multiplication, division, and more complex calculations, and are an essential part of everyday life.

Here,

101 102 103 104 105

106 107 108 109 110

111 112 113 114 116

117 118 119 115 120

121 122 123 124 125

After dividing each number by 9, we get:

11 11 11 11 11

11 11 12 12 12

12 12 12 12 13

13 13 13 12 13

13 13 13 13 14

The numbers with a remainder of 4 when divided by 9 are: 13 and 4.

To know more about number,

https://brainly.com/question/28210925

#SPJ1

The general solution of the differential equation is \(\(y(x) = c_1 + c_2{e^{-4x}} + 16{x^2} - \frac{1}{2}\)\) Where, \(\(c_1\)\) and \(\(c_2\)\) are constants of integration.

Given differential equation is \(\( \left(D^{2}+4 D\right) y=96 x^{2}+2 \).\)

We can solve this second-order differential equation as:

Step-by-step solution:

Let the auxiliary equation be :

\(\({m^2} + 4m = 0\)\)

We get the roots of this equation by solving it:

\(\(m(m+4)=0\)\)

Therefore, \(\(m_1 = 0\)\) and \(\(m_2 = -4\)\)

As these roots are real and different, we can write the general solution of the differential equation as:

\(\({\rm{General\ solution}} = {c_1}{{\rm{e}}^{m_1x}} + {c_2}{{\rm{e}}^{m_2x}}\)\)

Therefore, the general solution of the differential equation is \(\(y(x) = c_1 + c_2{e^{-4x}} + 16{x^2} - \frac{1}{2}\)\) Where, \(\(c_1\)\) and \(\(c_2\)\) are constants of integration.

Learn more about differential equation visit:

brainly.com/question/32645495

#SPJ11

Answer:

23446

76532

12839

09192

29292

a. If we had an extremely magnified view of the solution, to the atomic-molecular level, the following species would be observed (including charges, if any) :2 Na+, NO3-, Ag+, and Cl-.b. The balanced net ionic equation for the reaction that produces the solid is: Ag+ + Cl- → AgCl↓c. Calculate the percent sodium chloride in the original unknown mixture:

1. Calculate the amount of AgCl precipitated. According to the balanced chemical reaction, 1 mol of AgNO3 reacts with 1 mol of NaCl to produce 1 mol of AgCl. A 0.542 M AgNO3 solution contains 0.542 mol/L of AgNO3.0.542 mol/L × 0.135 L = 0.07317 mol AgNO3 reacted with NaCl.0.07317 mol AgNO3 × (1 mol NaCl / 1 mol AgNO3)

= 0.07317 mol NaCl precipitated.2. Calculate the number of moles of NaCl and NaNO3 in the original sample.Mass of sample = 1.41 gMass of AgCl produced = 1.464 g Subtracting the mass of AgCl from the mass of the sample gives us the mass of NaCl and NaNO3 in the original sample:

Mass of NaCl and NaNO3 = 1.464 g − 1.41 g = 0.054 g.The percent of NaCl in the sample is given by: Mass of NaCl in the sample / Mass of the sample × 100 %= 0.067 g / 1.41 g × 100 %= 4.7%.Therefore, the percent of NaCl in the original mixture is 4.7%.

To know more about magnified visit:

https://brainly.com/question/32284838

#SPJ11

Answer:

182 cubic feet

Step-by-step explanation:

(7 x 4)/2 to get the area of triangle

than times 13 to get the volume

Answer:

3/10

Step-by-step explanation:

4/15+x=17/30

x=17/30-4/15

x=17/30-8/30

x=9/30

simplify

x=3/10

Using the central angle theorem, we can find that the value of the angle:

∠ BOC = 130°.

An inscribed angle is the angle formed inside the circle when two chords intersect it. It can also be defined as the angle made by two specific points at a given location on a circle. Instead, an inscribed angle is defined by two circle chords that share an endpoint.

In the given question,

O is the centre of the circle.

OC, OD, OE, OA and OB are all radius of the circle.

AC and BD are the diameters of the circle.

As BD intersects AC and the angles are given as:

∠COD = 50°

∠DOE = 60°

So, ∠ AOE = 180 - 50 - 60

= 70°

Similarly, ∠AOB = 50°.

Now, ∠ BOC = 360° - 50° - 60° - 70° - 50°

= 130°

Therefore, ∠ BOC = 130°.

To know more about central angle, visit:

https://brainly.com/question/29545066

#SPJ9

Answer:

12000

Step-by-step explanation:

sqrt144*1000000= sqrt144*sqrt10^6= 12*10^3=12000

Answer:

7

Step-by-step explanation:

The Linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

The point-slope equation for a line is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point-slope equation y - 5 = 3(x - 2),

we can see that the slope of the line is 3 and it passes through the point (2, 5).

To find the linear function for the line, we need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line intersects the y-axis).

To get the equation in slope-intercept form, we need to isolate y on one side of the equation.

We can do this by distributing the 3 to the x term:y - 5 = 3(x - 2)  y - 5 = 3x - 6  y = 3x - 6 + 5  y = 3x - 1

Therefore, the linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

For more questions on Linear .

https://brainly.com/question/2030026

#SPJ8

Answer:

The answer is 36

Step-by-step explanation:

=16-4(-5)

=16-(-20)

=36