the shorter diagonal of a rhombus with 70 degrees is 122 cm long, how long is the longer diagonal

The probability that a data value is less than two standard deviations from the mean is 95.45%.

In a normal distribution, approximately 68% of the data values fall within one standard deviation from the mean. This means that about 68% of the data values lie between the mean minus one standard deviation and the mean plus one standard deviation.

If we extend this to two standard deviations from the mean, we find that approximately 95.45% of the data values fall within two standard deviations from the mean. This means that about 95.45% of the data values lie between the mean minus two standard deviations and the mean plus two standard deviations.

Therefore, the probability that a data value is less than two standard deviations from the mean is 95.45%.

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The probability that a data value is less than two standard deviations from the mean is 95.45%.

In a normal distribution, approximately 68% of the data values fall within one standard deviation from the mean. This means that about 68% of the data values lie between the mean minus one standard deviation and the mean plus one standard deviation.

If we extend this to two standard deviations from the mean, we find that approximately 95.45% of the data values fall within two standard deviations from the mean. This means that about 95.45% of the data values lie between the mean minus two standard deviations and the mean plus two standard deviations.

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Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

Let's start defining the random variable X.

X : '' SAT critical reading scores from the 2019 school year for high school students in the United States ''

We know that X ~ N (μ,σ)

Where μ is the mean and σ is the standard deviation.

⇒ X ~ N (497,115)

If we want to calculate probabilities related to X we need to standardized the random variable. We do this by subtracting the mean to X and then dividing by the standard deviation. This new random variable will be ''Z'' and Z ~ N (0,1)

We can find the probabilities of ''Z'' in any standard normal table.

The cumulative distribution of ''Z'' is the function Φ where  :

P ( Z ≤ a ) = Φ (a)

Now, we need to calculate the following probability :

= P ( 120 < [tex]X[/tex] < 513 )

If we standardized this :

= P ( [tex]\frac{120-497}{115}[/tex] < [tex]\frac{X-497}{115}[/tex] <  [tex]\frac{513-497}{115}[/tex] )

We know that [tex]\frac{X-497}{115}[/tex]≅ Z ⇒

= P ( [tex]\frac{120-497}{115}[/tex] < [tex]Z[/tex] <  [tex]\frac{513-497}{115}[/tex] )

= P ( [tex]\frac{120-497}{115}[/tex] < [tex]Z[/tex] <  [tex]\frac{513-497}{115}[/tex] )

= P ( -3.27 < [tex]Z[/tex] <  0.139 )

= Φ(-3.27) - Φ(0.139)

= 0.9898 - 0.4509

= 0.5389

= 53.89% ≅ 53.8%

Therefore,

Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

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Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

Let's start defining the random variable, X.

X: '' SAT critical reading scores from the 2019 school year for high school students in the United States ''

We know that X ~ N (μ,σ)

Where μ is the mean and σ is the standard deviation.

⇒ X ~ N (497,115)

If we want to calculate probabilities related to X we need to standardize the random variable. We do this by subtracting the mean from X and then dividing by the standard deviation. This new random variable will be ''Z'' and Z ~ N (0,1)

We can find the probabilities of ''Z'' in any standard normal table.

The cumulative distribution of ''Z'' is the function Φ where  :

P ( Z ≤ a ) = Φ (a)

Now, we need to calculate the following probability :

= P ( 120 <  < 513 )

If we standardized this :

= P (  <  <   )

We know that ≅ Z ⇒

= P (  <  <   )

= P (  <  <   )

= P ( -3.27 <  <  0.139 )

= Φ(-3.27) - Φ(0.139)

= 0.9898 - 0.4509

= 0.5389

= 53.89% ≅ 53.8%

Therefore,

Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

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Answer: The last graph

Step-by-step explanation:

i did the test on flvs .

The last graph shows the relationship given in the table

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope = 11.50-8.5/4-2

=1.5

Let us take a point (5, 13), let us check this point which correctly matches the graph

Hence, the last graph shows the relationship given in the table

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Hello!

The following common fractions converted into percentages...

[tex]\frac{5}{8}=[/tex] 62.5%

[tex]\frac{8}{9} =[/tex] 88.8% repeating

Step-by-step explanation:

To convert a common fraction into a percentage you must first convert the fraction to a decimal and then multiply by 100

Hope this helps!

Cosecant, Secant, and Cotangent are the three trigonometric functions that are, respectively, abbreviated as Csc sec cot.

The three trigonometric functions for cosecant, secant, and cotangent are, respectively, denoted as Csc sec cot. Due to the fact that these functions are the reciprocals of the sine, cosine, and tangent functions, respectively, they are also known as the reciprocal trigonometric functions.

Secant or sec is expressed as 1/cos, cotangent or cot is represented as 1/tan, or cos/sin, and cosecants or Csc are represented as 1/sin, [tex]$$Cos^{-1[/tex] and 1/cos should not be mistaken with one another because they are significantly different. The reciprocal of cos is 1/cos, and inverse cos is used to find angles.

The relationship between the sides and angles of a right-angled triangle is known as a trigonometric ratio. The ratio of the neighboring side to the opposite side is known as a cotangent.

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The value of the angle is ∠MLN = 21°

What is an angle? In-Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex. The angle that lies in the plane does not have to be in Euclidean space. In case the angles are formed by the intersection of two planes in Euclidean or other space, the angles are considered dihedral angles. The angle is represented using the symbol “∠”. The angle measurement between the two rays can be denoted using the Greek letter θ, α, β etc. If the angles are measured from a line, we can find two different types of angles, such as a positive angle and a negative angle.

Positive Angle: If the angle goes in counterclockwise, then it is called a positive angle.

Negative Angle: If the angle goes clockwise direction, then it is called a negative angle.

∠MLN = ∠MLO - ∠OLN

= 52° - 31°

= 21°

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The rate of return on the $10,000 bond purchased at $8750 with a 10% coupon is 24.29%. The answer closest to this value is option C, 11.43%.

The rate of return on a bond is determined by the coupon rate and the difference between the purchase price and face value of the bond.

The coupon rate is the amount of interest paid annually on a bond expressed as a percentage of the face value of the bond.

In this case, the coupon rate is 10%, and the bond was purchased at $8750.

The face value of the bond is $10,000,

So the difference between the purchase price and face value is $1250.

The rate of return can be calculated as follows:

rate of return = (coupon rate + (face value - purchase price) / purchase price) * 100

rate of return = (0.10 + ($10,000 - $8750) / $8750) * 100

rate of return = (0.10 + ($1250 / $8750)) * 100

rate of return = (0.10 + 0.1429) * 100

rate of return = 0.2429 * 100

rate of return = 24.29%

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P ( A or B ) ≠ P(A) + P(B) Hence, A and B are not mutually exclusive. hence  is not true for events

therefore the given condition is not true and hence statement is not true for the given events

Two events are called mutually exclusive they are independent to each other.

Also, If A and B are any two events,

Then they are called mutually exclusive,

If P(A ∪ B ) = P(A) + P(B)

Or P ( A or B ) = P(A) + P(B)

Here, P(A) = 0.37, P(B) = 0.38 and P(A or B) = 0.27

Since,

0.27 ≠ 0.37 + 0.38

⇒  P ( A or B ) ≠ P(A) + P(B)

Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true

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Answer:

Step-by-step explanation:

x^2+(x-12)^2=144

x=0 or x=12

y=0-12  or 12-12

replace the values in the equation given, and you get

Intersection points are :

(x1,y1) = (0,-12)

(x2,y2) = (12,0)

Elena's total score for the two games is 478, with her score in the first game being 224 and her score in the second game being 254.

Let 'x' be Elena's score in the first game and 'y' be Elena's score in the second game.

We know that the total score for the two games is 478, so we can write the following equation:

x + y = 478

We also know that the score in the second game is 30 more than 3/4 of Elena's score in the first game. We can write this as:

y = x + 30

Substituting this into the first equation gives:

x + x + 30 = 478

Simplifying gives:

2x + 30 = 478

Subtracting 30 from both sides gives:

2x = 448

Dividing both sides by 2 gives:

x = 224

So, Elena's score in the first game is 224. Substituting this value into the equation for the second game gives:

y = 224 + 30

So, Elena's score in the second game is 254.

In summary, Elena's total score for the two games is 478, with her score in the first game being 224 and her score in the second game being 254.

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An experimental unit treats a person (also known as a subject), an object, or another clearly defined object.

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Answer:

Last option: 4a³

Step-by-step explanation:

Adding up the terms in the a³ column we get

12a³ -6a³ -2a³ = B

B = 12a³ -6a³ -2a³

B = (12 - 6 -2)a³

B = 4a³ ANSWER

Last choice in the answer choices

Using the concept of sine rule and cosine rule, the value of angle ACB is

36.64°

The sine rule is a mathematical formula used in trigonometry to find the relationship between the sides and angles of a triangle. It states that the sine of one of the angles in a triangle is equal to the ratio of the length of the side opposite that angle, divided by the length of the hypotenuse. The formula can be written as:

sin(A) = a / c

where A is one of the angles in the triangle, a is the length of the side opposite angle A, and c is the length of the hypotenuse. The sine rule is commonly used to find the length of one side of a triangle when the lengths of the other two sides and one angle are known. Another form of the sine rule is the "ambiguous case" formula, which can be used to find one of the angles in a triangle when the lengths of all three sides are known:

a / sin(A) = b / sin(B) = c / sin(C)

where A, B, and C are the angles in the triangle, and a, b, and c are the lengths of the sides.

In the given problem, we can simply substitute the values into the formula and then solve for the unknown angle.

a / sin A = b / sin B = c / sin C

But since we don't know the value of BC, we can find that first using cosine rule.

a² = b² + c² - 2(bc) cos A

a² = 9² + 6² -2(9)(6)cos80

a² = 98.23

a = √98.23

a = 9.9

Going back to using sine rule;

a / sin A = b / sin B = c / sin C

9.9 / sin 80 = 6 / sin C

sin C = (6 sin 80) / 9.9

sin C = 0.5968

C = sin⁻¹(0.5968)

C = 36.64°

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The probabilities of the individual outcomes are the same.

The probability model for this situation is uniform.

A mathematical illustration of a random event is a probability model. Its sample space, occurrences therein, and associated probability for each event serve as its definition.

The collection of all potential outcomes is the sample space S for a probability model.

Hence, it can be seen that there is 2 of each number so there is an equal chance. when there is an equal chance that is uniform.

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The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 30%.

The probability that a randomly selected school or district uses digital content is 72%. To find the probability that a randomly selected school uses digital content and uses it as part of their curriculum, we need to divide the number of schools that use digital content and use it as part of their curriculum (6) by the total number of schools (20). This gives us 6/20 or 30%. Therefore, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 30%.

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The equivalent fractions, with a common numerator of 6, are given as follows:

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

Equivalent fractions are fractions for which the ratio of the numerator and the denominator is the same.

For fraction 2/5, the numerator is of 2, hence 6/2 = 3 and the equivalent fraction is obtained as follows:

(2 x 3)/(5 x 3) = 6/15.

For fraction 3/10, the numerator is of 3, hence 6/3 = 2 and the equivalent fraction is obtained as follows:

(2 x 3)/(2 x 10) = 6/20.

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Answer:

0.29

Step-by-step explanation:

Answer:

0.285714

Step-by-step explanation:

The correct expression for the given scenario is,

⇒ y = 6 × 4³

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A population has a beginning number is 6.

Now, A population has a beginning number is 6.

Hence, The population if it expands at a rate of 4 for 3 years is,

⇒ y = 6 × 4³

Thus, The correct expression for the given scenario is,

⇒ y = 6 × 4³

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Answer:

Step-by-step explanation:

x = -2

F(x)=1.5(2)^x=0.375 , G(x)=-3(1/4)^x=-48

x=0

F(x)=1.5(2)^x=3, G(x)=-3(1/4)^x=-3

x=1/2

F(x)=1.5(2)^x=1.06 , G(x)=-3(1/4)^x=-6

Answer:

70%

Step-by-step explanation:

56 / 80 x 100 = 70%

Answer:

1050 ml ÷1000 = 1.05 liters of water

Step-by-step explanation:

I think this is right!!

Have a good rest of your day please mark brainiest

A graph of the points with its ordered pair to show the number of cereal boxes there are for shipment of 4, 8, 10, 14, and 16 cases is shown in the image attached below.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the x-values and y-values in this table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 144/24

Constant of proportionality, k = 6.

When x= 4, the number of cereal boxes y is given by:

y = 6x

y = 6(4)

y = 24 ⇒ ordered pair (4, 24).

When x= 8, the number of cereal boxes y is given by:

y = 6x

y = 6(8)

y = 48 ⇒ ordered pair (8, 48).

When x= 10, the number of cereal boxes y is given by:

y = 6x

y = 6(10)

y = 60 ⇒ ordered pair (10, 60).

When x = 14, the number of cereal boxes y is given by:

y = 6x

y = 6(14)

y = 84 ⇒ ordered pair (14, 84).

When x = 16, the number of cereal boxes y is given by:

y = 6x

y = 6(16)

y = 96 ⇒ ordered pair (16, 96).

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Answer:

Step-by-step explanation:I don’t know u nerdy boy

The exact interest will be $124.44.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

Katy Perry's bank granted her a single-payment loan of $4,400 at an interest rate of 6% exact interest to buy a new sound system.

The term of the loan is 172 days in years it will be 172/365.

S = 4400*6*172/365*100 = 124.44

Hence the exact interest will be $124.44.

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The equation that can be used to find how much Carmen earns each week is y = 35 + 0.17x

The number of pamphlets she needs to deliver to earn $86 is 300 pamphlets

Base salary of Carmen = $35

Additional earnings per week= $0.17

Number of pamphlet Carmen delivers = x

Total amount Carmen earns = y

y = 35 + 0.17x

Number of pamphlets she needs to deliver to earn $86;

y = 35 + 0.17x

86 = 35 + 0.17x

86 - 35 = 0.17x

51 = 0.17x

x = 51/0.17

x = 300 pamphlet

Hence, Carmen earnings is represented by y = 35 + 0.17x and Carmen needs to deliver 300 pamphlet to earn $86

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A complex number is the product of a real number and an imaginary number in the form of a + bi. Complex numbers are used to solve equations that don't have real solutions, such as [tex]x^{2}[/tex] + 1 = 0.

How to solve a complex number?

Given:

When solving and reasoning with complex numbers, it's important to keep the following properties in mind:

1. The sum of two complex numbers is the sum of their real and imaginary parts.

For example, (a + bi) + (c + di) = (a + c) + (b + d)i

2. The product of two complex numbers is the product of their real and imaginary parts.

For example, (a + bi).(c + di) = (ac - bd) + (ad + bc)i

3. The magnitude (or absolute value) of a complex number is the distance from the origin to the point (a,b) on the complex plane.

For example, |a + bi| = √a^2 + b^2

4. The conjugate of a complex number is its mirror image across the real axis.

For example, the conjugate of (a + bi) is (a - bi).

These properties can be used to solve and reason with complex numbers. For example, to find the quotient of two complex numbers, one could divide the product of their conjugates by the product of their magnitudes.

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Answer:

Step-by-step explanation:

76