which function below is the inverse of f(x)= 7x-1/2

The probability of being dealt a card that helps improve your hand is approximately 0.7083 or 70.83%.

To determine the probability of being dealt a card that helps you, we need to consider two factors: the number of favorable cards remaining in the deck and the total number of cards remaining.

At the beginning of the game, a standard deck of 52 cards is used. After the initial deal, you and the dealer have each received two cards, so there are 52 - 4 = 48 cards remaining in the deck.

To determine the favorable cards that can improve your hand, we need to consider the possible outcomes. In this case, you have a four and a jack, and you're looking to improve your hand. Let's analyze the possibilities:

To improve your hand to a better total without exceeding 21, you would want to draw a card between 5 and 9, inclusive. In this case, you know that the dealer's one visible card is a five, so there are three more fives left in the deck. Additionally, there are four cards each of 6, 7, 8, and 9, making a total of 16 favorable cards for improving your hand.

Lastly, if you're hoping to improve your hand to a total of 20, you would need an ace, 2, 3, or 6. As we assumed earlier, there are three aces remaining, and there are four cards each of 2, 3, and 6. So there are a total of 3 + 4 + 4 + 4 = 15 favorable cards for achieving a total of 20.

In total, the number of favorable cards for improving your hand is 3 (blackjack) + 16 (improve to a better total) + 15 (improve to a total of 20) = 34.

To calculate the probability, we divide the number of favorable cards by the total number of cards remaining in the deck:

Probability = Number of Favorable Cards / Total Number of Cards Remaining

Probability = 34 / 48

Simplifying the fraction, the probability is 17 / 24 or approximately 0.7083 (rounded to four decimal places).

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the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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The time when the rocket will be 10 feet from the ground after when it was launched is 10.8 seconds

From the question, we are to determine how long after the rocket was launched will it be at the given height from the ground.

The given equation that represents the height of the rocket after t seconds is

h = -16t² + 170t + 40

The given height is 10 feet.

Now,

Substitute h = 10 into the equation

That is,

10 = -16t² + 170t + 40

16t² - 170t + 10 - 40 = 0

16t² - 170t - 30 = 0

Solve the quadratic equation

Using the quadratic formula,

t = [-b ±√(b² - 4ac)]/2a

a = 16, b = -170, and c = -30

t = [-(-170) ±√((-170)² - 4(16)(-30))]/2(16)

t = [170 ±√(28900 + 1920)]/32

t = [170 ±√(30820)]/32

t = [170 ± 175.556]/32

t = [170+ 175.556]/32 OR [170 - 175.556]/32

t = 345.556/32 OR -5.556/32

t ≈ 10.8 OR -0.17

Since t is time and cannot be negative, t is 10.8 seconds

Hence,

The time is 10.8 seconds

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Answer:

There is No solution

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12x−1=9+12x

12x+−1=9+12x

12x−1=12x+9

Step 2: Subtract 12x from both sides.

12x−1−12x=12x+9−12x

−1=9

Step 3: Add 1 to both sides.

−1+1=9+1

0=10

Hope I helped -

Sleepy~

Answer:

100 is correct answer

Step-by-step explanation:

\( {10}^{2} \\ = 10 \times 10 \\ = 100\)

when ever anything ² , it means that number is multiplied by itself.

in above we multiple 10 with 10 and we get 100.

hope it helped you:)

Answer:

6.63

Step-by-step explanation:

Since you are using a right triangle, you  are  going to be doing the pythagorean theorem. \(a^{2} +b^{2} =c^{2}\) where a  and  b are the legs and c is the slanted side/hypotunse. Let plug it in.

\(a^{2} +10^{2} =12^{2}\)

\(a^{2}\)+100=144

\(a^{2}\)=44

sqr root of 44 is \(2\sqrt{11}\) which is about 6.63

The solution to the recurrence relation is: aₙ = a(1)ⁿ + b * n * (1)ⁿ

= a + bⁿ

The solution to the recurrence relation with initial condition of a₁ = 2 is: aₙ  = 2

A recurrence relation is defined as an equation that recursively defines a sequence in which the next term is a function of the previous term.

The given recurrence relation is:

aₙ = 2aₙ₋₁ - aₙ₋₂

n ≥ 2

a₀ = a₁ = 2

Rewrite the recurrence relation to get:

aₙ - 2aₙ₋₁ + aₙ₋₂ = 0

Now form the characteristic equation:

x² − 2x + 1 = 0

x = 1

We therefore know that the solution to the recurrence relation will have the form:

aₙ = a(1)ⁿ + b * n * (1)ⁿ

= a + bⁿ

To find a and b , plug in n = 0 and n = 1 to get a system of two equations with two unknowns:

2 = a + b*0

2 = a

2 = a + b*1

2 = a + b

Thus:

a = 2 and b = 0

aₙ  = 2 + 0 * n = 2

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Complete question is:

a) Find all solutions of the recurrence relation aₙ = 2aₙ₋₁ - aₙ₋₂.

b. find the solution of the recurrence relation in part (a) with initial condition a₁ = 2

The correct answer is 2 (C) - 2 days is the total slack for activity F. To determine the total slack for activity F, we need to calculate the slack for each activity in the network. Slack refers to the amount of time an activity can be delayed without affecting the project completion time.

1. First, let's draw the network using the information provided:
  - A is the start node and G is the stop node.
  - Activity A has a duration of 5 days and has no predecessor.
  - Activities B, C, and D have durations of 8, 7, and 6 days respectively, and their predecessors are A.
  - Activity E has a duration of 9 days and its predecessors are B, C, and D.
  - Activity F has a duration of 10 days and its predecessors are B, C, and D.
  - Activity G has a duration of 5 days and its predecessors are E and F.

                 A
                /|\
               / | \
              /  |  \
             B   C   D
              \  |  /
               \ | /
                \|/
                 E
                 |
                 F
                 |
                 G

2. Now, let's calculate the slack for each activity:
  - Slack is calculated by subtracting the earliest start time of an activity from the latest start time without delaying the project completion time.
  - The earliest start time for activity F is 17 days.
  - The latest start time for activity F is 19 days (project completion time is 22 days).
  - Total slack for activity F = latest start time - earliest start time = 19 - 17 = 2 days.

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Answer:The idea is to multiply by some number (10, 100, 1000, etc.) so that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2

Step-by-step explanation: sorry if its wrong thats all i remember

Answer:

A. \( y_1 = -m(x_2 - x_1) + y_2 \)

Step-by-step explanation:

Given, slope formula = \( m = \frac{y_2 - y_1}{x_2 - x_1} \)

To find an equivalent equation, let's make \( y_1 \) the subject of the formula.

\( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Cross multiply

\( 1(y_2 - y_1) = m(x_2 -x_1) \)

\( y_2 - y_1 = m(x_2 - x_1) \)

Subtract \( y_2 \) from both sides

\( y_2 - y_1 - y_2 = m(x_2 -x_1) - y_2 \)

\( - y_1 = m(x_2 - x_1) - y_2 \)

Divide both sides by -1

\( \frac{- y_1}{-1} = \frac{m(x_2 -x_1) - y_2}{-1} \)

\( y_1 = -m(x_2 - x_1) + y_2 \)

The velocity of the oxygen molecule at room temperature is 482 m/s.

The kinetic energy of an oxygen molecule at room temperature (300 K) is determined.

The mass of an oxygen molecule is 5.31 × 10-26 kg. As per the statement, the kinetic energy of the oxygen molecule at room temperature is 6.21 × 10-21 J.Kinetic energy

The kinetic energy of an object is the energy that it possesses because of its motion. It is a scalar quantity and has units of joules (J) in the SI system.

The formula for the kinetic energy of an object is given by 1/2mv²,

where m is the mass of the object, and v is its velocity.

The kinetic energy of a gas is calculated using the root mean square velocity of the molecules. RMS velocityRMS velocity is the square root of the average of the square of the velocities of the gas molecules.

It is calculated using the formula vrms = √(3RT/M)

where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. We can obtain the velocity of a single molecule of gas by dividing the RMS velocity by the square root of Avogadro's number.

Here, we have a single oxygen molecule, so we can directly calculate its velocity from the RMS velocity. From the kinetic energy formula, we can get the velocity of the molecule, which is given by √(2KE/m)

Substitute the given values, we get,

Velocity of the molecule = √(2 × 6.21 × 10-21/5.31 × 10-26)= 482 m/s

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Answer:

I think so

Step-by-step explanation:

Im kinda cunfused too

If the function x(t) = cos(2π100t + π/3) is sampled at the minimum sampling rate to avoid aliasing for 10 seconds, 2000 points are generated.

The function x(t) = cos(2π100t + π/3) is sampled at the minimum sampling rate to avoid aliasing for 10 seconds.

To avoid aliasing, we need to use the Nyquist-Shannon Sampling Theorem, which states that the minimum sampling rate should be twice the highest frequency in the signal. In this case, the highest frequency is 100 Hz.

Step 1: Calculate the minimum sampling rate.
Minimum sampling rate = 2 * highest frequency = 2 * 100 Hz = 200 Hz.

Step 2: Calculate the total number of points generated in 10 seconds.
A number of points = sampling rate * time duration = 200 Hz * 10 s = 2000 points.

So, 2000 points are generated when the function x(t) = cos(2π100t + π/3) is sampled at the minimum sampling rate to avoid aliasing for 10 seconds.

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The experimental probability of winning a prize in the contest, based on the given information, is 5/52.

To calculate the experimental probability, we divide the number of favorable outcomes (winning caps) by the total number of possible outcomes (total number of bottles). In this case, out of the 52 bottles purchased, 5 of them have winning caps. Therefore, the number of favorable outcomes is 5, and the total number of possible outcomes is 52.

Hence, the experimental probability is given by:

Experimental Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Experimental Probability = 5/52

Therefore, the experimental probability of winning a prize in the contest is 5/52, which is the simplified fraction form of the answer.

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Answer:

To calculate Tom's new average, you need to know the total number of runs he scored in the three matches and the total number of runs he scored in the recent two matches.

You can use the following formula to calculate the new average:

New Average = (Total Runs + Recent Runs) / Total Matches

First you need to find the total runs he scored in the first 3 matches:

74 (average) * 3 (number of matches) = 222 runs

Then you need to find the total runs he scored in the recent two matches:

42 (runs in match 1) + 31 (runs in match 2) = 73 runs

Now you can find the new average by adding the total runs in recent two matches and total runs in the first 3 matches and divide it by the total number of matches:

(222 + 73) / 5 = 295 / 5 = 59

So, Tom's new average is 59 runs.

Answer: 59

Step-by-step explanation:

Please refer to the image below:

Answer:

-5.255

Step-by-step explanation:

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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The angle is 45 degrees between the trajectories the ball takes before and after hitting the rail.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.  To determine the value

To determine the value A statement is not an equation if it has no "equal to" sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Hence, The angle is 45 degrees between the trajectories the ball takes before and after hitting the rail.

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Answer:

i don't know ok thank you bye

Answer:

\(\mu=-4\)

Step-by-step explanation:

We know that \(\overline{PR} \perp \overline{QR}\).

Since \(\overline{PR}\) is horizontal, \(\overline{QR}\) is vertical. Therefore, \(\mu=-4\).

If Trudy deposited $1260 in a savings account that pays 5.5% interest compounded daily, then the amount of interest he will earn in 60 days is $32850.32

The deposited amount = $1260

Interest is compounded daily.

The interest rate = 5.5%

The time period = 60 days

The compound interest equation

A = \(P(1+\frac{r}{n})^{nt}\)

Where A is the final amount

P is the principal amount

r is the interest rate

n is the number of times interest applied

t is the time period

Substitute the values in the equation

A = \(1260(1+\frac{0.055}{60})^{(60)(60)}\)

A = 1260 × 27.07

A = $34110.32

The interest = Final amount - Deposited amount

= 34110.32 - 1260

= $32850.32

Hence, if Trudy deposited $1260 in a savings account that pays 5.5% interest compounded daily, then the amount of interest he will earn in 60 days is $32850.32.

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The Half of a number minus seven is one and five-tenths is

x/2-7=1.5

We have given that,

Half of a number minus seven is one and five-tenths

Suppose consider number is x

half of number is x/2 -7.........(1)

Now next we have 1 and 5 tenths

1+5/10

=1+0.5

=1.5

Now,

x/2-7=1.5

Therefore,

The answer is x/2-7=1.5

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Answer:

Move all terms not containing d

to the right side of the inequality.

Inequality Form:

d<7

Step-by-step explanation:

Sorry no graph

Answer:

d < 7

Step-by-step explanation:

d + 12 < 19

1. Subtract 12 from both sides

d + 12 - 12 < 19 - 12

d < 7

Answer:

Step-by-step explanation:

The solution is the coordinates of the point (p,n) of intercept of lines described by given equations.

Answer:

Vertex is (-8, 4)  not one of the answers offered!

Step-by-step explanation:

Factor -1/8 out of the first two terms. Leave a space inside parentheses in which to add a number.

\(y=-\frac{1}{8}(x^2 + 16x + \text{-----})-4\)

Complete the square by squaring half the coefficient of x and adding it in the space.

\((\frac{16}{2})^2=64\)

Add 64 in the space you made, then compensate for that at the end of the expression by subtracting  \(-\frac{1}{8}(64)=-8\)

\(y=-\frac{1}{8}(x^2+16x+64)-4+8\\y=-\frac{1}{8}(x+8)^2+4\)

The x-coordinate of the vertex is the opposite of +8, the number inside the parentheses.  The y-coordinate of the vertex is the number at the end of the expression.

V(-8, 4)

Answer:

The fraction is 3/10 = .3

Answer:

-4

Step-by-step explanation:

Compute the slope of the line through the following points:

p_1 = (-7, -2) and p_2 = (-2, -22)

The slope of the line through (x_1, y_1) and (x_2, y_2) is:

(y_2 - y_1)/(x_2 - x_1)

Substitute (x_1, y_1) = (-7, -2) and (x_2, y_2) = (-2, -22):

= (-22 - -2)/(-2 - -7)

-(-7) = 7:

= (-22 - -2)/(-2 + 7)

-2 + 7 = 5:

= (-22 - -2)/5

-(-2) = 2:

= (-22 + 2)/5

-22 + 2 = -20:

= (-20)/5

The gcd of -20 and 5 is 5, so (-20)/5 = (5 (-4))/(5×1) = 5/5×-4 = -4:

Answer:  = -4

Answer: B

Step-by-step explanation:

multiply all the the sales by 11% and you will get the answers in option b

ex: 1300*0.11=143

Answer:

Step-by-step explanation:

cos(∠X) = adj./hyp.

arccos(adj./hyp.) = ∠X

arccos(13/18) = 43.761...≈ 43°