9. A player is dealt some cards from a 52-card deck. a. What is the probability that the 4th card dealt was the first ace? b. In a different hand with 8 cards, what is the probability that the 4th car

Answer:

390cm³

Step-by-step explanation:

6cm×5cm×13cm= 30cm²×13cm= 390cm³

Answer:

x > 4

Step-by-step explanation:

Flip the equation.

24<8+4x

4x+8>24

Subtract 8 from both sides.

4x+8-8>24-8

4x>16

Divide both sides by 4.

4x/4>16/4

x > 4

All the required relationship is given below.

Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.

Given:

A linear function: y = mx + b,

and an exponential function : y = a(b)ˣ

In a linear function,

y = mx + b.

m is the slope or rate of change and b is the y-intercept.

In an exponential function: y = a(b)ˣ,

a is the initial value and r is the rate of change.

When the x-values rise by a certain amount, the y-values change in different ways for linear and exponential relationships:

The y-values in a linear connection differ by an equal amount.

The y-values have identical ratios in an exponential relationship.

Because both linear and exponential equations must rise at the same pace as they began, they are similar.

Therefore, the required relationship is given above.

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The annual growth rate written as a decimal is 0.97.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

Based on the graph, we would calculate the value of a and b as follows;

\(f(x) = a(b)^x\)

0.9 = a(b)⁰

a = 0.9

Next, we would determine value of b as follows;

0.927 = 0.9(b)⁻¹

0.927 = 0.9/b

b = 0.9/0.927

b = 0.9709 ≈ 0.97

Therefore, the required exponential function is given by;

\(f(x) = y = 0.9(0.97)^x\)

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The magnitude of vector Q is approximately |Q| = 1890.07.To determine the magnitude of vectors P and Q, you can use the Pythagorean theorem. Let's calculate the magnitudes:

For vector P: Px = 840,Py = -1870. The magnitude of vector P, |P|, can be calculated as follows:

|P| = \(sqrt(Px^2 + Py^2)\)

|P| = sqrt\((840^2 + (-1870)^2)\)

|P| = sqrt(705600 + 3496900)

|P| = sqrt(4202500)

|P| ≈ 2050.01

Therefore, the magnitude of vector P is approximately |P| = 2050.01.

For vector Q: Qx = -1860 ,Qy = -341

The magnitude of vector Q, |Q|, can be calculated similarly:

|Q| = \(sqrt(Qx^2 + Qy^2)\)

|Q| =\(sqrt((-1860)^2 + (-341)^2)\)

|Q| = sqrt(3459600 + 116281)

|Q| = sqrt(3575881)

|Q| ≈ 1890.07

Therefore, the magnitude of vector Q is approximately |Q| = 1890.07.

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Answer:

48\(\pi\) cubic feet

Step-by-step explanation:

Have a good day :)

Answer:

Tom drove 282 miles.

Step-by-step explanation:

x = number of miles driven

220.81 = 14.95 + 0.73x

-14.95       -14.93

205.86 = 0.73x

/0.73        /0.73

282 = x

Hope this helps!

Step-by-step explanation:

so, the time to answer questions has to be added to the speaking time to get the total time of the meeting.

the speaking time is constant (25 minutes).

q = 1 means t = 25 + q = 25 + 1 = 26

q = 2 means t = 25 + q = 25 + 2 = 27

q = 3 means t = 25 + q = 25 + 3 = 28

q = 8 means t = 25 + q = 25 + 8 = 33

The unit rate in teaspoons per pound would be 1/2 teaspoons per pound.

What is the unit rate?

A unit rate means a rate for one or something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

The number of teaspoons:

                                      \(=1\frac{3}{4}\\\\=\frac{4+3}{4}\\\\=\frac{7}{4}\)

Amount of pasta:

                              \(=3\frac{1}{2}\\\\=\frac{6+1}{2}\\\\=\frac{7}{2}\)

Now the unit rate = number of teaspoons/ amount of pasta

                             \(=\frac{7/4}{7/2}\\\\=\frac{1}{2}\\\)

Hence, the unit rate in teaspoons per pound would be 1/2 teaspoons per pound.

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Answer:

Step-by-step explanation:

1/2

Answer:

i think a but not sure

Step-by-step explanation:

i always second guess myself but a was first answer for me

Answer:

The 3rd one (7+3)a^4

Step-by-step explanation:

This is because you have to distribute everything in the parentheses to (a) to the fourth power.

Hope this helps.

Jill needs to invest approximately $40,816.33 at a 7% annual interest rate compounded yearly to achieve her goal of $50,000 for a round-the-world holiday in 3 years.

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where

We can rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

Now we can substitute the given values into the formula and calculate:

P = 50000 / (1 + 0.07/1)^(1*3)

P = 50000 / (1 + 0.07)^3

P = 50000 / (1.07)^3

P = 50000 / 1.2250431

P ≈ $40,816.33

Therefore, Jill needs to invest approximately $40,816.33 at a 7% annual interest rate compounded yearly to achieve her goal of $50,000 for a round-the-world holiday in 3 years.

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1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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Answer:

6/5

Step-by-step explanation:

(a) To calculate the estimated standard error of the mean of the difference scores, we need to first find the mean of the difference scores and the sample standard deviation of the difference scores.

The difference scores are obtained by subtracting the baseline appetite for fatty foods (x) from the appetite for fatty foods in the mildly stressful environment (y). So, the difference scores are:

-3, 10, 8, -3, 7, 11, -3, 6, 4, 4, 3, 4

The mean of the difference scores is:

(−3+10+8−3+7+11−3+6+4+4+3+4)/12 = 4.0/12 = 0.33

The sample standard deviation of the difference scores is:

s = √[Σ(y-x-0.33)²/(n-1)] = √[Σ(y-x-0.33)²/11] = √[232.67/11] = 4.06

Therefore, the estimated standard error of the mean of the difference scores is:

SE = s/√n = 4.06/√12 = 1.17

(b) To calculate t-obtained, we need to use the formula:

t = (M - μ) / (SE)

where M is the mean of the difference scores, μ is the hypothesized population mean (which is 0, since we are testing for a significant difference), and SE is the estimated standard error of the mean of the difference scores.

So, t-obtained is:

t = (0.33 - 0) / 1.17 = 0.28

The absolute value of t-obtained is:

|t-obtained| = |0.28| = 0.28

Therefore, the absolute value of t-obtained is 0.28.

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The difference between a set of data's upper quartile (75th percentile) and lower quartile (25th percentile) is known as the interquartile range. It is a dispersion metric that specifies a range within which half the data is contained.

The interquartile range is a measure of dispersion that is used to show how variable the data is. It is figured out by taking the lower quartile of a set of data the 25th percentile and subtracting it from the upper quartile the 75th percentile. The middle 50% of the data are represented by this range, which shows how variable the data set is. Then, sort the data in numerical order before calculating the interquartile range. Next, determine the data set's median, or its middle value.  Find the median of the lower half of the data set to compute the lower quartile, and the median of the upper half of the data set to calculate the upper quartile. The interquartile range can then be calculated by deducting the lower quartile from the upper quartile. To better understand the distribution of data points within a set, the interquartile range is frequently used in conjunction with the median. It is a helpful tool for figuring out how much variation there is in a data set.

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Answer:

Rise over Run is another term for the slope

Step-by-step explanation:

to find the slope, (y2 - y1)/(x2 - x1)

Answer:

If you look at a graph, you see 2 lines forming a "plus" shape. The horizontal line is called the x-axis, and the verticle line is called the y-axis. Rise over run is how much the y changes when the x changes. So if the graph increases its y value by 2 each time the x increases by 1, then rise over run is 2.

Thus, a basis for s⊥ is the set {(-2, 2, 0)}.

What is a basis for s ⊥?

The question involving the terms "subspace," "containing," and "spanned."

If s is the subspace of R³ containing only the zero vector, s⊥ (the orthogonal complement of s) is the entire R³ space. This is because all vectors in R³ are orthogonal to the zero vector.

If s is spanned by (1, 1, 1), to find s⊥, we need a vector that is orthogonal to (1, 1, 1). We can use the dot product to determine orthogonality. For a vector (x, y, z), the dot product with (1, 1, 1) should be zero:

(1, 1, 1) · (x, y, z) = 0
x + y + z = 0

One possible vector that satisfies this equation is (-1, 1, 0). So, s⊥ is the subspace spanned by (-1, 1, 0).

If s is spanned by (1, 1, 1) and (1, 1, -1), to find a basis for s⊥, we need a vector orthogonal to both given vectors. We can use the cross product of the given vectors to find the orthogonal vector:

(1, 1, 1) × (1, 1, -1) = (-2, 2, 0)

Thus, a basis for s⊥ is the set {(-2, 2, 0)}.

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High clouds are those that form at altitudes of at least 20,000 ft (6000 m).

At high altitudes, ice crystals form due to which cloud formation occurs.   Cirrus, cirrostratus, and cirrocumulus clouds are a few types of clouds. Cirrostratus clouds frequently form a thin, white layer that resembles a veil and covers the entire sky. Small, spherical, white clouds called cirrocumulus develop in long rows. Because they can provide information about changes in atmospheric pressure, temperature, and moisture levels in the upper atmosphere, these high clouds are crucial for meteorologists to investigate.

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Using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.

It basically consists of a variable, perhaps with an additional numerical constant.

To easily understand this concept, consider the example below. 3x – 4 = 5. It is a straightforward class 7 equation.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

So, we have the following algebraic expression after converting the word problem:

To Geraldine:

g = t - 4

To Steven:
s = 2g

Inputting Tom's age into equation 1 results in:

g = t - 4

To determine Steven's age:

s = 2(t-4)

s = 2t - 8

Therefore, using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.

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a)  The volume of paint left in the can is:

.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

b)  the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

(a) To convert gallons to cubic meters, we need to know the conversion factor between the two units. One U.S. gallon is equal to 0.00378541 cubic meters. Therefore, the volume of paint left in the can is:

0.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

(b) We can use the formula for the volume of a rectangular solid to find the volume of wet paint needed to coat the wall evenly:

Volume = area * thickness

We want to solve for the thickness, so we rearrange the formula to get:

Thickness = Volume / area

The volume of wet paint needed is equal to the volume of dry paint needed since they both occupy the same space when the paint dries. Therefore, the volume of wet paint needed is:

0.003321 m^3

The area of the wall is given as:

13.7 m^2

So the thickness of the layer of wet paint is:

0.003321 m^3 / 13.7 m^2 = 0.000242 m

Therefore, the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

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Answer:

To find the direction of the bird's resultant vector, we need to use the vector addition method.

If we draw a vector diagram, we can see that the bird's velocity vector is directed towards the south and has a magnitude of 45 mph. The wind's velocity vector is directed towards the east and has a magnitude of 12 mph.

To add these vectors, we can draw them tail-to-head and then draw a line from the tail of the first vector (bird's velocity) to the head of the second vector (wind's velocity). This line represents the resultant vector.

Using the Pythagorean theorem, we can find the magnitude of the resultant vector:

Resultant velocity = √(45² + 12²) = √(2025 + 144) = √2169 = 46.55 mph

To find the direction of the resultant vector, we use trigonometry. The angle between the resultant vector and the south direction is given by:

θ = tan⁻¹(12/45) = 15.94°

Therefore, the direction of the bird's resultant vector is 0 + 15.94 = 15.94°, rounded to the nearest hundredth.

Step-by-step explanation:

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The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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Answer:The race is 111.6

Step-by-step explanation:The race is 111.6 m long.

8 hurdles spaced 12.3 m apart means 7 spaces that are 12.3 m in length; 7*12.3 = 86.1

Add to this the distance to the first hurdle and the distance from the last hurdle:

86.1+15+10.5 = 111.6 m

Step-by-step explanation:

Answer:

If I am incorrect, please let me know.

Step-by-step explanation:

This is the work I did.

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Answer:

2.720 : 16 : 2 = 85

Step-by-step explanation:

Dado que, en caso de no funcionar la tecla del 3 en la calculadora para tipear el número 32, no se podrá realizar el calculo de 2.720 : 32, que tiene como resultado 85, se puede realizar otro cálculo sin tipear dicho número para llegar al mismo resultado.

La mitad de 32 es 16, osea que, dividiendo 2.720 por 16, estaremos obteniendo un resultado que será el doble de lo pretendido, es decir, 170. Por lo tanto, dividiendo dicho resultado por 2, obtendremos el número 85, realizando así el mismo cálculo que el deseado inicialmente.

Answer:

A scale factor is a number which scales, or multiplies, some quantity.

Answer:

The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

Step-by-step explanation:

x is present in the algebraic expression, therefore, option A is correct.- x is present in the expression, therefore, option B is correct.- x + y is present in the expression, therefore, option D is correct.

The given expression is: 3x[3(x + y)]^3x[3(x + y)]^3 × (x + 3)(x + y)

To simplify the given expression, we will first solve the expression within the brackets as follows:

(3(x + y))^3 = (3)³(x + y)³ = 27(x + y)³

Now, we will substitute the above value in the expression:

3x[3(x + y)]^3 = 3

x × 27(x + y)³ = 81x(x + y)³

Multiplying both terms of (x + 3)(x + y), we get:

(x + 3)(x + y)

= x(x + y) + 3(x + y) + 3y

= x² + xy + 3x + 3y + yx + 3y

= x² + 4xy + 6y + 3x

The final expression after substituting the value of 3x[3(x + y)]^3 and (x + 3)(x + y) is:

81x(x + y)³ × (x² + 4xy + 6y + 3x)

= 81x(x + y)³x² + 81xy(x + y) + 6xy + 27x(x + y)

= 81x³ + 189xy² + 81x²y + 6xy + 27x² + 81xy

Now, let's check which options are correct:- 3x is present in the expression, therefore, option A is correct.- x is present in the expression, therefore, option B is correct.- x + y is present in the expression, therefore, option D is correct.

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Answer:

Option C; 3x - y = -27 and x + 2y = 16

Step-by-step explanation:

1. Let us consider the equation 21x - y = 9. In this case it would be best to keep the equation in this form, in order to find the x and y intercept. Let us first find to y - intercept, for the simplicity ⇒ 21 * ( 0 ) - y = 9 ⇒ y = - 9 when x = 0. Now if we take a look at the first plot of line q, we can see that the x value is -9 rather than the y value, so this equation doesn't match that of line q. This would eliminate the first two options being a possibility.

2. Now let us consider the equation 3x - y = -27. Let us consider the x-intercept in this case. That being said, ⇒ 3x - ( 0 ) = -27 ⇒ 3x = -27 ⇒ x = -9 when y = 0. As we can see, this coordinate matches with one of the coordinates of line q, which might mean that the second equation could match with the equation for line v.

3. To see whether Option 3 is applicable, we must take a look at the 2nd equation x + 2y = 16. Let us calculate the y - intercept here: ( 0 ) + 2y = 16 ⇒ 2y = 16 ⇒ y = 8 when x = 0. Here we can see that this coordinate matches with that of the second coordinate provided as one of the points in line v. That means that ~ Answer: Option C

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}} \implies \cfrac{-14}{3 +4}\implies \cfrac{-14}{7}\implies -2\)