If a person draws three cards from a standard deck (without replacing them), what is the probability that at least one of the cards is a face card? (Round your answer to one decimal place.)

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

Step-by-step explanation:

:On hand she has a 20% acid solution and a 50% acid solution. How many ml of each solution should sheStep-by-step explanation:this is the answer

A chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.

The percentage is the ratio of number expressed as a fraction of 100.

Assume chemist needs x mL of 20% of acidic solution and y mL of 50% acidic solution.

A total of 100mL solution is to be created.

x+y=100

x=100-y

The concentration of 20% acidic solution will be 0.2x, concentration of 50% acidic solution will be 0.5x and the sum of their concentrations should be 0.38(100).

0.2x+0.5y=0.38(100)

0.2x+0.5y=38

Substitute x=100-y into the obtained equation.

0.2(100-y)+0.5y=38

20-0.2y+0.5y=38

20+0.3y=38

0.3y=18

y=18/0.3

y=60

Substitute y=60 into x=100-y.

x=100-60

=40

So, the chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.

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Answer:

plug n and r into the equation for the answers.

Step-by-step explanation:

Answer:

(0, -14)

Step-by-step explanation:

Midpoint formula: \((x_m, y_m) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\)

Answer:

a. Variables:

Let's define the variables for the problem:

t: time in minutes (the variable we are solving for)

h1: altitude of the descending airplane in feet

h2: altitude of the ascending airplane in feet

b. System of Equations:

Based on the given information, we can create a system of equations:

Equation 1: h1 = 59,400 - 3,000t (altitude of descending airplane)

Equation 2: h2 = 0 + 2,400t (altitude of ascending airplane)

c. Solving the System using Graphing:

To solve the system using graphing, we need to plot the two equations on a graph and find the point of intersection. Here's the graph:

[Graph]

From the graph, we can see that the two lines intersect at a point. The x-coordinate of the point of intersection represents the time (t), and the y-coordinate represents the altitude (h) where the two airplanes are at the same altitude.

d. Solving the System using Substitution or Elimination:

To check our graphing work, we can solve the system using either substitution or elimination. Let's use substitution:

From Equation 1: h1 = 59,400 - 3,000t

Substitute h1 into Equation 2:

59,400 - 3,000t = 2,400t

Add 3,000t to both sides:

59,400 = 5,400t

Divide both sides by 5,400:

t = 11

Now, substitute the value of t back into either Equation 1 or Equation 2 to find the altitude (h) at that time:

h1 = 59,400 - 3,000 * 11

h1 = 59,400 - 33,000

h1 = 26,400 feet

Therefore, the two airplanes will be at the same altitude of 26,400 feet after approximately 11 minutes.

Explanation of Methods:

Graphing: Graphing the equations provides a visual representation of the problem and helps identify the point of intersection. However, it may not provide an exact value, and the precision depends on the accuracy of the graph.

Substitution or Elimination: These algebraic methods allow for precise calculations and the exact determination of the time and altitude at which the airplanes meet. They require more steps and calculations but offer a more accurate solution.

In the context of the problem, the solution means that after approximately 11 minutes, both airplanes will be at the altitude of 26,400 feet. At this moment, the descending airplane will have descended to the same altitude as the ascending airplane is ascending, resulting in the two airplanes being at the same height above the ground.

Step-by-step explanation:

Answer:

v=(-4w)/(-w+2)

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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Answer:

B, -25

Step-by-step explanation:

3-4 = -1

-1(3 + 3^2 + 13) = -1(25), the answer is -25

Answer:

-25

Step-by-step explanation:

-25 is the answer...........

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Answer:

I'm guessing 401 tickets. lol

Number of tickets Alicia sold is equals to 401 .

" Linear equation is defined as the algebraic expression with one or more variables with highest power of the variable equals to one."

According to the question,

x represents the number of tickets Alicia sold

As per the data given,

Number of tickets Jenna and Matt sold together = 282 + 178

                                                                                 = 460 tickets

Substitute the given values in the condition we get linear equation,

   x + 59 = 460

⇒ x = 460 - 59

⇒ x = 401 tickets

Hence, number of tickets Alicia sold is equals to 401 .

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Answer:

3

Step-by-step explanation:

Let's write the statement as an equation and solve for that number.

x+7=10

x=3

Step-by-step explanation:

\(\bold{x + 7 = 10}\)

\( \longmapsto \: x = 10 - 7\)

\( \longmapsto \: 10 - 7 = 3\)

\(\bold{Hope}\)\(\bold{It}\) \(\bold{Helps!}\)

\(\bold{Study}\)\(\bold{Well}\)~

Answer:

Event a has the probablitity of 50% that it will happen and event b has the same. you have the probability of 50% of choosing a or b

Step-by-step explanation:

Answer:

1.) A

2.) D

3.) A

Step-by-step explanation:

The missing quantities are

Social Security= $217

Medicare = $‭50.75‬

Net Pay is $‭2,633.67‬

First, Taxable income is therefore;

= 3,500 - (76.90 x 4 )

= $‭3,192.4‬0

Federal Income Tax (FIT).

With taxable income of $‭3,192.4‬0, the tax is $565.15 plus 28% of anything above $‭3,073.

= 565.15 + (28% x (‭3,192.4‬0 - 3,073))

= 565.15 + 33.43

= $‭598.58

and, Social Security

= Gross pay x 6.2%

= 3,500 x 6.2%

= $‭217‬

and, Medicare

= 3,500 x 1.45%

= $‭50.75‬

Then, the Net Pay

= 3,500 - 598.58 - 217 - 50.75

= $‭2,633.67‬

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Answer:

neither

Step-by-step explanation:

parallel lines will have the same number next to the x

perpendicular lines will have the negative reciprocal number next to the x

(for example 2 and -1/2 are negative reciprocals)

y−4=3(x+5)

parenthesis first

y−4=3x+15

y=3x+19

y+3= −13(x+1)

y+3= −13x−13

y= −13x−16

3x and −13x are neither the same nor negative reciprocals of each other so

the answer is neither

Answer:

it is the first one

Step-by-step explanation:

The perimeter of PQRS would depend on the lengths of the tangent segments and the lengths of the intercepted arcs. Without specific measurements, we cannot determine the precise perimeter.

To determine the perimeter of quadrilateral PQRS, we need more information about the lengths of the sides or the relationship between the sides and angles. Without specific measurements or additional details, we cannot calculate the exact perimeter of the quadrilateral.

However, we can provide some general information.Since PQ¯ is tangent to circle R at point Q, it is perpendicular to the radius drawn from the center of the circle to point Q. Similarly, PS¯ is tangent to circle R at point S, so it is perpendicular to the radius drawn to point S.

The quadrilateral PQRS is formed by the tangents PQ¯ and PS¯ along with the two arcs intercepted by these tangents on the circle R.

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Answer:

EF = 36

Step-by-step explanation:

FE and GD are congruent

2u - 36 = u

subtract 2u from both sides (-36 = -u)

divide each side by -1 ( u = 36)

now that you know the value of u plug it into the equation 2u -36

the equation is now 2(36)-36

2 times 36 equals 72

now do 72 - 36 and you get 36

that is the value of line segment EF

Answer:

36

Step-by-step explanation:

Ef is equal to gd

so 2u－36＝u

＋36 ＋36

so 2u＝u＋36

－u －u

so u＝36

hope this helps

Answer:

The perimeter of this rectangle is 10 cm.

Answer:

For the first 40 hours that Mr. Ed works, he earns his regular rate of pay, which is $15.50 per hour. So, his regular pay for the week is:

40 hours x $15.50 per hour = $620

For the additional 5 hours he works, he earns overtime pay at a rate of time-and-a-half, which is 1.5 times his regular pay rate. So, his overtime pay for the week is:

5 hours x $15.50 per hour x 1.5 = $116.25

Therefore, Mr. Ed's total pay for the week in which he works 45 hours is:

$620 (regular pay) + $116.25 (overtime pay) = $736.25.

Answer:

5.75.

Step-by-step explanation:

The mean = (8+5+7+10+3+4+31+12)/ 8

= 80/8

= 10.

Now we calculate the difference of each value from the mean We take the absolute ( positive) differences

10 - 8 = 2

10 - 5 = 5

10 - 7 = 3

10 - 10 = 0

10-3 = 7

10 = 4 = 6

10 - 31 = 21

10 - 12 = 2

Sum of the differences = 46

and the mean deviation  is 46/8 = 5.75.

Answer:

260x+127

Step-by-step explanation:

i think its right

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:

Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:

(x^3 - 12x^2) + (-2x + 24)

Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:

x^2(x - 12) - 2(x - 12)

Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:

(x - 12)(x^2 - 2)

Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

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The equation is y(t) = yo) e^-kt =

1058 = 1088e^-3k and yes my answer is reasonable , the number of store decreases as t increases

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

using the formula;

p(t) = p(o) e^-kt

1058 = 1088e^-3k

e^-3k = 1058/1088

e^-3k = 0.972

-3k = ln 0.972

k = -0.03/-3

k = 0.01

when t = 8

p(t) = 1088e^-kt

= 1088e^-0.08

p(t) = 1088× 0.923

p(t) = 1044

in 10 years

p(t) = 1088e^-0.1

p(t) = 984

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Answer:

\(2 \times 3 \times 12 \\ 72 {m}^{2} \)

Answer:

C. 72

Step-by-step explanation:

Triangular Area: 1/2 (b) (h)

12x3=36

36/2=18

18x4=72

I also did the test. Have a great day/night! <3

the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.