five cards are drawn successively with replacement from a well shuffled pack of 52 cards. what is the probability that out of five cards 0, 1, 2,3,4,5 cards are diamond?

Answer:

18x+7

Step-by-step explanation:

3(2x + 5) + 4(3x - 2)

6x+15 + 12x - 8.........distribute

18x+7..........................combine like terms

18x+7

\(Hiya!\)

Sokka is here to help!!

Here's a explanation!

\(3(2x + 5) + 4(3x - 2)\)

You have to distribute:

\(=(3)(2x)+(3)(5)+(4)(3x)+(4)(-2)\)

\(=6x+15+12x+-8\)

You must combine like terms:

\(=6x+15+12x+-8\)

\(=(6x+12x)+(15+-8)\)

\(=18x+7\)

ANSWER:

\(=18x+7\)

Hopefully, this helps you!!

\(Sokka\)

Toshi is correct with the value of 1. 7 × 10^1 times

Owen made a mistake of multiplying the values instead of dividing.

Ratio can be described as the comparison of two or more numbers or elements indicating their their sizes in relation to each other.

It is used to shows how many times one number contains another.

From the information given, we have that;

Mass of Earth = 5.97 x 10^24 kg.

Mass of Neptune = 1.024 x 10^26 kg

To determine the number of times greater, we have;

Mass of Neptune/Mass of Earth

1.024 x 10^26/5.97 x 10^24

Divide the values

0. 17 × 10 ^2

1. 7 × 10^1 times

Toshi is correct with the value 1. 7 × 10^1 times

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Answer:

800

Step-by-step explanation:

20 x 40 = 800

If the tire's radius is changed from 25 cm to 24 inches, the function representing the tire's rotation would require adjustment, incorporating the new radius in its equation. The graph would also change, displaying a slightly different shape and scale due to the alteration in units and resulting adjustments in the function.

When the tire's radius is changed from 25 cm to 24 inches, the function representing the tire's rotation would need to be modified. The original function, which might have been something like f(x) = 2π(25x), where x represents the number of rotations, would now need to incorporate the new radius. Using the conversion factor of 1 inch = 2.54 cm, the adjusted function would become f(x) = 2π(24x/2.54).

The graph representing the function would also be affected by this change. With the new radius, the graph would display a slightly different shape and scale compared to the original one. The x-axis, which represents the number of rotations, would remain the same, but the y-axis, representing the distance traveled, would be altered due to the change in units. The graph's curvature and overall appearance might be slightly different, reflecting the adjustment made to the function.

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If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Answer:

Interquartile Range

The interquartile range of an observation variable is the difference of its upper and lower quartiles. It is a measure of how far apart the middle portion of data spreads in value.

Interquartile Range = U pper Quartile − Lower Quartile

Problem

Find the interquartile range of eruption duration in the data set faithful.

Solution

We apply the IQR function to compute the interquartile range of eruptions.

> duration = faithful$eruptions     # the eruption durations

> IQR(duration)                     # apply the IQR function

[1] 2.2915

Answer

The interquartile range of eruption duration is 2.2915 minutes.

Exercise

Find the interquartile range of eruption waiting periods in faithful.

Step-by-step explanation:

Question:

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)

B) The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth.

Answer:

A) 16.64 Feets

B) 7.65 feets

Step-by-step explanation:

Given the following :

The question above can be solved by applying Pythagoras rule :

A^2 = B^2 + C^2

PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

PR = 16.64feet

Now if PR is adjusted to 16 Feets, the New height of the scaffold will be:

QR² = PR² - PQ²

QR² = 16² - 14²

QR² = 256 - 196

QR² = 60

Take the Square root of both sides

QR = √60

QR = 7.7459666 Feets

Answer:

4

Step-by-step explanation:

For this, you need to find the scale factor of two sides that are already given to you.

So, we will have to use the hypotenuse and one of the legs to make sure there is an accurate scale factor.

Hypotenuse:

15 / 5 = 3

Leg:

6 / 2 = 3

____________

So the scale factor is 3.

Using the leg (with the x) we need to divide 12 by the scale factor (3) to give us what x is equal to.

12 / 3 = 4

So, the answer is 4.

Assuming the question is : "how much does 1 box of blueberries cost?"

After he bought 5 boxes of blueberries and 3 watermelons, he was left with $16.50

Therefore, 5 boxes of blueberries and 3 watermelons cost $60.50 - $16.50 = $44

We are given the cost of 1 watermelon is $8.30

Therefore, 3 watermelons cost $8.30 x 3 = $24.90.

-> 5 boxes of blueberries cost $44 - $24.90 = $19.10

-> 1 box of blueberries cost $19.10 : 5 = $3.82

Answer:

If your trying to find the total of the 5 boxes of blue berries the answer is

$19.10

Step-by-step explanation:

60.50 - 16.50 = 44$ meaning he spent that much.

8.30 x 3 = 24.9

19.10 + 24.9 = 44

hope this helps

Answer:

9in

Step-by-step explanation:

I´m telling you I just got it Right

Answer:

It’s A

Step-by-step explanation:

GOT IT RIGHT

The inverse of the function f(x) = (1/2)x is f^(-1)(x) = 2x.

To find the inverse of a function, we need to switch the roles of x and y and solve for y. Let's follow the steps to find the inverse of the function f(x) = (1/2)x:

Step 1: Replace f(x) with y: y = (1/2)x.

Step 2: Swap x and y: x = (1/2)y.

Step 3: Solve for y: Multiply both sides of the equation by 2 to isolate y: 2x = y.

Step 4: Replace y with f^(-1)(x): f^(-1)(x) = 2x.

Therefore, the inverse of the function f(x) = (1/2)x is f^(-1)(x) = 2x.

We can verify this by composing the function and its inverse. If we apply f(x) followed by f^(-1)(x), we should get the original value of x. Let's check:

f(f^(-1)(x)) = f(2x) = (1/2)(2x) = x.

As expected, the composition of the function and its inverse gives us the original value of x, indicating that we have found the correct inverse.

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To apply the Alternating Series Test, we need to check two conditions:

The terms of the series must alternate in sign.

The absolute values of the terms must decrease as n increases.

Let's analyze the given series: ∑ (-1)^n (n - 6) from n = 7 to infinity.

Alternating Signs: The series has alternating signs because of the (-1)^n term. When n is even, (-1)^n becomes positive, and when n is odd, (-1)^n becomes negative.

Decreasing Absolute Values: Let's examine the absolute values of the terms: |(-1)^n (n - 6)| = |n - 6|.

As n increases, the absolute value |n - 6| also increases. Therefore, the absolute values of the terms do not decrease.

Since the terms do not meet the decreasing absolute values condition, we cannot conclude convergence or divergence using the Alternating Series Test. The Alternating Series Test does not apply in this case.

To determine the convergence or divergence of the series, we need to use other convergence tests, such as the Ratio Test or the Comparison Test.

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Answer:

the answer is g(x) = 1 - x²

Since the intercept of g(x) are :

for x intercept , g(x) =0 (1-x)×(1+x) =0

and for y intercept y= 1

hence then its should be g(x) = 1- x²

The equation of red graph that is g(x) = 1 - x²

Given,

f(x) = 4 - x²

g(x)

Now,

Since the intercept of g(x) are :

for x intercept , g(x) =0 (1-x)×(1+x) =0

and for y intercept y= 1

Thus the equation of graph will be :

g(x) = 1- x²

The coefficient of x² is negative which indicates that the graph is concave down in nature .

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The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .

As given in the question,

Total number of voters in California = 7525

x₁ = Number of voters of central valley residents approved California legislature

   = 68

n₁ = Total number of voters of central valley residents

   = 200

x₂ = Number of voters of bay area residents approved California legislature

   = 156

n₂= Total number of voters of bay area residents

   = 300

p₁ = proportion of voters of central valley

p₂= proportion of voters of bay area

p₁ = x₁/ n₁

   = 68/200

   = 0.34

p₂ = x₂/n₂

    = 156/300

    = 0.52

Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂

                        = √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300

                        = √0.001122 + 0.000832

                        = 0.044

\(p_{w}\) = (68 + 156 )/ (200 + 300)

   = 0.448

\(q_{w} = 1- p_{w}\)

    = 1 - 0.448

    = 0.552

null hypothesis p₁ - p₂ = 0

z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)

  = 4

Tabular value for confidence interval 95% = 1.96

4 > 1.96

We reject the null hypothesis.

Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.

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The solution of the system of equations is (x, y) = (1/3, 1/3).

To solve the given system of equations, we can use any of the following three methods; the substitution method, the elimination method (also known as the addition/subtraction method), and the graphical method. Below, we will solve it using each of these methods.

1. Substitution method:

We will use the substitution method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2) From equation (1), we have

Y + 2x = 3y ...(3)Now substitute equation (3) into equation

(2)2y = 3x - 2 ...(2)Y + 2x = 3y ...(3)2(3y - 2x) = 3x - 2

Multiplying both sides by 2:

6y - 4x = 3x - 2 Grouping like terms:

6y - 3x = 2 Adding 3x to both sides:

6y = 3x + 2Dividing both sides by 6:

y = (3/6)x + 2/6y = (1/2)x + 1/3

Therefore, the solution of the system of equations is (x, y) = (1/3, 1/3).

2. Elimination method:

We will use the elimination method to solve the system of equations. Step-by-step solution is shown below; Given equations are

Y = 3y - 2x ...(1)2y = 3x - 2 ...(2)Multiplying equation (1) by 2,

we get;2Y = 6y - 4x ...(3)Multiplying equation (2)

by -3, we get;-6y = -9x + 6 ...(4) Adding equations (3) and (4),

we get;-4x = -9x + 8

Simplifying;-4x + 9x = 8x = -8x = -2

Therefore, we found the value of x, which is -2.

Substitute the value of x in either equation (1) or (2);

If we substitute x = -2 in equation (1), we get;

Y = 3y - 2(-2)Y = 3y + 4Y - 3y = 4Y = 4/2Y = 2Substitute the value of y in equation (1)

;Y = 3y - 2xY = 3(2) - 2(-2)Y = 6 + 4Y = 10

Therefore, the solution of the system of equations is (x, y) = (-2, 10/2).3.

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The correct answer is option (b): increases, i.e., if the variability (p times q) increases and the sample size remains the same, then the standard error increases.

The standard error measures the variability of sample means around the true population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size. The formula for standard error is:

SE = s / √n, where s is the standard deviation and n is the sample size.

When the variability (p times q) increases, it means that there is more dispersion or spread of values in the population. This increased variability leads to a larger standard deviation (s) in the sample, assuming the sample size remains the same.

Since the standard error is calculated by dividing the standard deviation by the square root of the sample size, an increase in the standard deviation will result in a larger standard error. Therefore, if the variability increases and the sample size remains constant, the standard error will increase.

In summary, the standard error increases when the variability increases and the sample size remains the same. This is because a larger standard deviation implies more uncertainty in the sample mean estimate, resulting in a larger standard error.

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Answer:

  96

Step-by-step explanation:

The loan duration is for 8 years, a total of 12·8 = 96 monthly payments. The 96th payment is the balloon payment.

Answer:

\(y = -x^{2} +4x-10\)

Step-by-step explanation:

I used a graphing calculator to calculate the points so I'm not sure how to do it without, but I hope this helped!

(a)The unit vector that gives the direction of the steepest ascent is (1/√2, -1/√2).

The unit vector that gives the direction of the steepest ascent at P is the gradient vector evaluated at P divided by its magnitude. The gradient of the function f(x, y) is given by (∂f/∂x, ∂f/∂y) = (2x+2, 4y+4). At P(1,-2), the gradient vector is (4,-4), and its magnitude is √(4^2 + (-4)^2) = 4√2.

Therefore, the unit vector in the direction of steepest ascent is (4/4√2, -4/4√2) = (1/√2, -1/√2).

The unit vector that gives the direction of the steepest descent at P is the negative of the unit vector that gives the direction of the steepest ascent. Therefore, the unit vector in the direction of steepest descent is (-1/√2, 1/√2).

(b) A vector that points in the direction of no change in the function at P is perpendicular to the gradient vector.

Therefore, the vector (-4, -2) is perpendicular to the gradient vector (4, -4) and points in the direction of no change in the function at P. Note that there are infinitely many vectors perpendicular to the gradient vector, but this particular vector is chosen because it has the smallest possible magnitude.

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Answer:

\(y = \frac{c-ax}{b}\)

Step-by-step explanation:

ax + by = c

subtract ax from both sides

ax + by = c

-ax             -ax

=

by = c- ax

divide b on both sides

\(\frac{by}{b}\) = \(\frac{c- ax}{b}\)

=

\(y = \frac{c-ax}{b}\)

Answer:

9/10

Step-by-step explanation:

Requried, it takes 6.15 years for the number of insects in the population to double.

We know that the number of insects at the start of the year (n+1) is P+1, where \(P_n+1 = kP_n\)

So, we can write:

\(P1 = kP_0\\P_2 = kP_1 = k(kP_0) = k^2 P_0\\P_3 = kP_2 = k(k^2 P_0) = k^3 P_0\\P_4 = kP_3 = k(k^3 P_0) = k^4 P_0\\\)

\(Pn = k^n P_0\)

To find out how many years it takes for the number of insects in the population to double, we need to find the value of n such that Pn = 2P0.

So, we have:

\(2P_0 = k^n P_0\)

Dividing both sides by P_0, we get:

\(2 = k^n\)

Taking the natural logarithm of both sides, we get:

\(ln 2 = n ln k\\n = ln 2 / ln k\)

Substituting the value of k as 1.13, we get:

n = ln 2 / ln 1.13

n ≈ 6.15

Therefore, it takes 6.15 years for the number of insects in the population to double.

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Let's denote the radius of the circle by r. The radius of the circle is 5 meters.

The central angle of 2 radians means that it cuts off an arc whose length is equal to 2 times the radius, or 2r. The formula for the area of a sector is:

A = (1/2) r^2 θ

where A is the area of the sector, r is the radius, and θ is the central angle in radians. We can use this formula to find the radius of the circle:

25 = (1/2) r^2 (2)

25 = r^2

r = ±√25

Since the radius of a circle can't be negative, we take the positive square root:

r = 5 m

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\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

we're given that Angela formerly had 8 computer games.

★ She got 3 more video games on her birthday.

★ Then she gave away 4 video games.

_____________________________

_____________________________

\(\huge\red{ Solution -}\)

\(8 + 3 - 4 \\ \dashrightarrow \: 11 - 4 \\ \dashrightarrow \: 7\)

hope helpful :D

Total 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

In the given question, we have to find how many "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

The given word is INQUISITIVE.

The total alphabets in the word INQUISITIVE is 11.

Let us first count the words without U and then insert U wherever applicable.

Now without U we have total 10 alphabets and the alphabet I is repeated by 4 times.

So permutations is 10!/4! = 151,200

Now we need to put U, we can see its 11 alphabets but U should not follow Q so it becomes 10 alphabets.

Hence, Total number of words = 151,200*10

Total number of words = 1,512,000

Hence, 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

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a^4+b^4=(a^2)^2+(b^2)^2

=(a^2+b^2)^2–2a^2b^2

=(a^2+b^2)^2—(√ 2ab)^2

=(a^2+√ 2ab+b^2)(a^2-√ 2ab+b^2)

Must click thanks and mark brainliest

Answer:

100,000,000 . B

Step-by-step explanation:

10 to the 8th power or 10^8 = 100,000,000 (7 extra zeroes)

Answer:

(B) 100,000,000

Step-by-step explanation:

I used a calculator

10x10x10x10x10x10x10x10= 100,000,000

hope it helps :)

Answer:

between 4 and 5

Step-by-step explanation:

consider perfect cubes either side of 81 , that is

64 < 81 < 125 , then

\(\sqrt[3]{64}\) < \(\sqrt[3]{81}\) < \(\sqrt[3]{125}\) , that is

4 < \(\sqrt[3]{81}\) < 5

Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.