-8.25x + 12 – 1.75x = 10.5x + 1.75
-
=

As a result of answering the question, we may state that equation In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.

A mathematical equation is a process that links two statements and indicates equality using the equals symbol (=). A theoretical statement that proves the equality of two formulas is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14.

A. With n=10 and p=4/52, the binomial distribution of the number of kings seen in the 10 trials, K, is followed (since there are 4 kings in a standard deck of 52 cards). K's average is:

mean(K) is equal to\(n * p (10 * 4/52 = 0.7692).\)

Meaning: On average, we anticipate seeing 0.77 kings per 10 trials.

B. This is the variance of K:

The formula for var(K) is \(n * p * (1 - p) = 10 * 4/52 * (1 - 4/52) = 0.7255.\)

K's standard deviation:

\(\sqrt(var(K)) = \sqrt(0.7255) = 0.8524\) where sd(K) =

D. The binomial distribution can be used to calculate the likelihood of receiving more than four kings:

P(K > 4) = 1 - P(K 4) = 1 - 0.0407 for binom.cdf(4, 10, 4/52).

Interpretation: In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.

D. The binomial distribution can be used to get P(K 3):

Binom.cdf(3, 10, 4/52) = P(K 3) = 0.8789

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Answer:

140

Step-by-step explanation:

72/3.6*7

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the formula for finding the perimeter of a triangle

STEP 2: Write the given sides

STEP 3: Substitute the values into the formula

STEP 4: Choose the equation that could not be used to find the third side

The equation in option B can be seen in equation 1 in Step 3

The equation in option C can be seen in equation 3 in Step 3

The equation in option D can be seen in equation 2 in Step 3

Hence, the equation that could not be used to find the third side is the equation in option A

x - 14.8 = 2.94 + 7.3

Answer:

58%

Step-by-step explanation:

50/86 is approximately equal to 0.58, and when you convert that into percentage you get 58%

Based on the information, the incorrect step is C. step 3.

Step 1: 4(3x – 3y = 6) –3(4x – 7y = 2)

Step 2: 12x – 12y = 24 –12x + 21y = –6

Step 3: 9y = 18

Step 4: y equals 1 over 2

Correct calculation:

3x – 3y = 6 (1)

4x – 7y = 2 (2)

make x the subject in ....(1)

3x - 3y = 6

3x = 6 + 3y

x = 6 + 3y/ 3

x = 2 + y

substitute x = 2 + y into (2)

4x – 7y = 2 (2)

4(2 + y) - 7y = 2

8 + 4y - 7y = 2

8 - 3y = 2

8 + 2 = -3y

10 = -3y

y = 10/-3

y = -3 1/3

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Michael solved the system of linear equations and provided the solution. 3x – 3y = 6 4x – 7y = 2 Step 1 4(3x – 3y = 6) –3(4x – 7y = 2) Step 2 12x – 12y = 24 –12x + 21y = –6 Step 3 9y = 18 Step 4 y equals 1 over 2 In which step did Michael show his first error? Step 2 Step 3 Step 4

Given equation of the Circle is ,

\(\sf\implies x^2 + y^2 = 25 \)

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

\(\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2\)

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

\(\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }\)

Hence the point lies within the circle .

Answer:

inside the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 25 ← is in this form

with r = \(\sqrt{25\) = 5

Calculate the distance d from the centre to the point (- 4, 2 ) using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 4, 2)

d= \(\sqrt{(-4-0)^2+(2-0)^2}\)

   = \(\sqrt{(-4)^2+2^2}\)

   = \(\sqrt{16+4}\)

    = \(\sqrt{20}\)

    ≈ 4.5 ( to 1 dec. place )

Since 4.5 is less than the radius of 5

Then (- 4, 2 ) lies inside the circle

We are asked to find the measure of angle 5 in the image.

Analysing the image, we see that it consists of two parallel lines that are being intercepted by another line. In the points at which the slant line intercepts the parallel pair of lines, we know that the angles formed are equal in the following fashion:

angle 1 equals angle 5 (alternate angles between parallel lines)

angle 7 equals the angle marked with measure 70 degrees (again because by construction they are alternate angles among parallel lines)

of course it also happens that angle 2 equals angle 6, and angle 4 equals angle 8, but we don't need in oarticular these las pairs of angles to answer the question. we just need the first two pairs mentioned above that I am marking as bold now.

we also recall that the angles that added form a straight line, are called "supplementary angles", and added must give 180 degrees (the straight line).

Then, we know that angle 1 plus angle 70 degrees (in the upper portion of the drawing), must add to 180 degrees.

SInce one is 70 degrees, then angle 1 must be 180 - 70 = 110 degrees

So we know that angle 1 measures 110 degrees.

We now recall that we have mentioned that angles 1 and 5 must be equal for being alternate angles between parallel lines, so we conclude that angle 5 is 110 degrees.

The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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√(3x + 1) - 5 = 0

The first step is to collect like terms and that involves moving the constant to one side of the equation. The 5 moves to the right and becomes a positive, (when a negative value crosses to the other side of an equation it becomes a positive and vice versa).

√(3x + 1) = 5

Square both sides (to eliminate the square root sign on the left side of the equation)

3x + 1 = 25

Subtract 1 from both sides of the equation

3x + 1 - 1 = 25 - 1

3x = 24

Divide both sides of the equation by 3

x = 8

(x + 3)^2/3 - 5 = - 1

Add 5 to both sides of the equation

(x + 3)^2/3 - 5 + 5 = - 1 + 5

(x + 3)^2/3 = 4

∛(x + 3)^2 = 4

Find the cube of both sides (to eliminate the cube root sign on the left hand side)

(x + 3)^2 = 4^3

(x + 3)^2 = 64

Add the square root to both sides of the equation to eliminate the square on the left of the equation

x + 3 = √64

x + 3 = 8

Subtract 3 from both sides of the equation

x = 5

Profitability ratios is a type of financial ratio shows the combined effects of liquidity, asset management and debt management of a business. So the statement is true.

Financial ratios are calculations used to assess various data to evaluate the company's performance. It is calculated using quantitative data from financial statements. There are mainly four financial ratios

So the statement given is true.

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Answer:

195.205998 years

Step-by-step explanation:

P=P0(1.046)^t   P=future population   P0=initial population  t=years passed

38,000,000,000 = 5,849,000(1.046)^t

1.046^t = 38,000,000,000/5,849,000

1.046^t = 38,000,000/5,849

plug in log on both sides

log 1.046^t = log (38,000,000/5,849)

t[log 1.046] = log (38,000,000/5,849)

t = In (38,000,000/5,849)/ In 1.046

t ≈ 195.205998 (hope this helps)

Answer:

The blue box

Step-by-step explanation:

Youre talking about range which takes place on the y-axis (domain is the x-axis).

The top point is an open circle which indicates in the math world the parentheses and the bottom point 1 in a bracket as its a closed circle.

Answer: The initial volume is 593.76mL

Step-by-step explanation:

As you do not say anithing about the pressure, i guess that the pressure remains constant.

If the gas is an ideal gas, we have:

P*V = n*R*T

where P is pressure, n is number of moles and R is a constant.

Now, initially we have:

P*Vi = n*R*315°C

finally we have:

P*825mL = n*R*452°C

Now we can take the quiotient of those two equations and get:

(P*Vi)/(P*852mL) = (n*R*315°C)/( n*R*452°C)

Now we have:

Vi/852mL = 315/452

Vi =  (315/452)*852mL = 593.76mL

So when we expand the gas at constant pressure, we increase the temperature.  

Answer:

691 mL

Step-by-step explanation:

Let's use Gaussian elimination. Consider the augmented matrix,

\(\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]\)

• Add row 1 to row 2, and add -1 (row 1) to row 3:

\(\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]\)

• Add -2 (row 2) to row 3:

\(\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]\)

• Add -2 (row 3) to row 2:

\(\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]\)

• Add row 2 and row 3 to row 1:

\(\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]\)

So the inverse is

\(\begin{bmatrix}1&-1&-1\\-1&2&3\\1&1&4\end{bmatrix}^{-1} = \boxed{\begin{bmatrix}5&3&-1\\7&5&-2\\-3&-2&1\end{bmatrix}}\)

Answer:

The answer is C

Step-by-step explanation:

PLATO

Answer:

pretty sure it's 360 :)

Step-by-step explanation:

...

Area = ( 1/2 × 4 × 3 ) + ( 1/2 × 5 × 6 )

Area = 6 + 15

Area = 21 ft^2

Answer:

No

Step-by-step explanation:

f(x) = x²

f(3) = 3²

     = 3 × 3

     =  9    Not 16

also

√16 = 4

Answer:

\(2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25\)

The function resulting from composition of functions f(x) = 3 · x + 4 and g(x) = 4 · x² + 5 · x is equal to f ° g (x) = 12 · x² + 20 · x.

In this problem we find the definition of two functions:

f(x) = 3 · x + 4, g(x) = 4 · x² + 5 · x

With these functions we need to make an operation known as compostion, which is defined below:

f ° g (x) = f [g (x)]

Where the independent variable of function f is substituted by function g. Now we determine the composite function below:

3 · (4 · x² + 5 · x) + 5 · x

12 · x² + 15 · x + 5 · x

12 · x² + 20 · x

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Answer:

(B) 0.7%

Step-by-step explanation:

X = Land Elevation (in ,000 feet)

Y = Unidentified Artifacts (in %)

The hypothetical theory says that:

The higher the elevation, the higher the percentage of unidentified artifacts in the location.

To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.

Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.

Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%

Answer:

Ok, the EZ plan can be written as:

C1(x) = $0.15*x

where x is the number of minutes used in the whole Month.

The 40 to Go Plan can be written as:

C2(x) = $0.05*x + $40.

So we have two linear relationships.

The Ez plan has a larger slope, but has no y-intercept.

So we now can find the number of minutes needed to have the exact monthly cost in each plan:

C1(x) = C2(x)

$0.15*x = $0.05*x + $40

($0.15 - $0.05)*x = $40

$0.10*x = $40

x = $40/$0.10 = 400.

So if in one month, you use exactly 400 minutes, you will pay exactly the same wich each plan.

Now, if you speak less than 400 minutes, is better to use the EZ Pay Plan, because it has o y-intercept, and is more efficient for lower values of x.

If you will use more than 400 minutes per month, then the 40 to Go Plan is better, because the slope is smaller.

We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways

Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

The value of the thickness of each record if the volume of the carton is 100π is,

⇒ 2.78 inches

We have to given that;

Karen can fit 25 vinyl records of diameter 12 in. inside a cylindrical carton with the same diameter.

We know that;

Volume of cylinder is,

⇒ V = πr²h

Hence, We get;

100π = π × (12/2)² × h

100 = 36h

h = 100 / 36

h = 50/18

h = 2.78 inches

Thus, The value of the thickness of each record if the volume of the carton is 100π is,

⇒ 2.78 inches

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Answer:

8 cm^2

Step-by-step explanation:

If the triangle is isosceles the sides are the same

Let the sides be x

We know that we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse

x^2+x^2 = (4 sqrt(2))^2

2x^2 =16(2)

2x^2 = 32

Divide by 2

2x^2/ 32/2

x^2 = 16

Taking the square root of each side

sqrt(x^2) = sqrt(16)

x = 4

The area of the triangle is

A =1/2 bh

A = 1/2 (4) (4)

A = 1/2(16)

A = 8

Answer:

8

Step-by-step explanation:

a^2 + b^2 = c^2

c = \(4\sqrt{2}\)

\(c^{2} = 32\)

a^2 + b^2 = 32

a=b (isosceles triangle)

a=b=4

base = 4

height = 4

area = 1/2 bh = 1/2(4)(4) = 8

Answer:

534.54

Step-by-step explanation:

750.92 - 216.38 = 534.54 hope this helps   :)