sat math scores are approximately normally distributed, with a mean of 508 and a standard deviation of 120. skye decides to take the sat exam, and scores 920. what is the probability someone scored less than her on the sat math test?

Answer:

the answer is 20 my guy hope this helps

Answer:

x < - 4

Step-by-step explanation:

7(x + 3) < 5x + 13 ← distribute parenthesis on left side

7x + 21 < 5x + 13 ( subtract 5x from both sides )

2x + 21 < 13 ( subtract 21 from both sides )

2x < - 8 ( divide both sides by 2 )

x < - 4

By solving the given initial value the value of x(t) is [tex]\frac{F_0}{2 \omega^2}[/tex] (sinωt - ωt cosωt)

As per the data given in the question the given differential equation will be:

[tex]\frac{d^{2} x}{dt^{2} }[/tex] + [tex]\omega^2 x=f_0[/tex] sin ωt,

x(0) = 0, x'(0) = 0

Now we have to determine the value of x(t).

Consider the differential equation:

x'' + [tex]\omega^2 x=f_0[/tex] sin ωt, x(0) = 0, x'(0) = 0.

In order to translate a given derivative function with a real variable t into a complex function with a variable s, one uses the Laplace transformation.

Laplace transformation is important in the design of control systems. It is necessary to perform Laplace transforms on several functions in order to analyze the control system.

Apply Laplace transformation on both sides,

[tex]&\left(s^2 L\{x(t)\}\right.\left.-s y(0)-y^{\prime}(0)\right)+\omega^2 \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{s^2+\omega^2} \\[/tex]

[tex]&\left(s^2+\omega^2\right) \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{s^2+\omega^2} \\[/tex]

[tex]& \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{\left(s^2+\omega^2\right)^2} \\[/tex]

[tex]& x(t)=F_0 \omega \mathcal{L}^{-1}\left\{\frac{1}{\left(s^2+\omega^2\right)^2}\right\} \\[/tex]

[tex]& \Rightarrow x(t)=\frac{F_0 \omega}{2 \omega^3}[/tex] (sin ωt -ωt cos ωt)

[tex]& \Rightarrow x(t)\left.=\frac{F_0}{2 \omega^2}[/tex] (sin ωt -ωt cos ωt)

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Solve the given initial-value problem. [tex]\frac{d^{2} x}{dt^{2} }[/tex] + [tex]\omega^2 x=f_0[/tex] sin ωt, x(0) = 0, x'(0) = 0 and x(t)=?

Answer:

I think there are 4 separate terms in that algerbric equation

R-squared is an important statistic in regression, it measures how well the model fits the data.

What is regression ?

Regression is a statistical method used to analyze the relationship between one or more independent variables and a dependent variable. It is used to predict the value of the dependent variable based on the values of the independent variables.

One important statistic from the regression outputs is R-squared, it measures how well the model fits the data. It ranges from 0 to 1, and a higher R-squared value indicates a better fit. In other words, it represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It can provide an overall measure of how well the model is able to explain the variation in the dependent variable based on the independent variable(s).

The statistic that can be hardest to interpret and why can vary depending on the complexity of the model and the user's level of understanding of statistics. But one statistic that can be challenging for some people to interpret is the p-value, which is used to determine the statistical significance of the coefficients of the model.

R-squared is an important statistic in regression, it measures how well the model fits the data.

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The equation of the transaction of friend 1 is; y = 0.12x + 30

The equation of the transaction of friend 2 is; y = 0.15x + 15

The general form if the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Friend 1;

Cost of the new phone including monthly fee = $30

Cost per 100 minutes = $12

Thus, cost per minute = 12/100 = $0.12 per minute

The cost per minute is simply the slope here while $30 is the y-intercept and as such the equation is;

y = 0.12x + 30

Friend 2;

Cost of the new phone including monthly fee = $15

Cost per 100 minutes = $15

Thus, cost per minute = 15/100 = $0.15 per minute

The cost per minute is simply the slope here while $15 is the y-intercept and as such the equation is;

y = 0.15x + 15

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A triangle with the lengths of the sides 6cm , 8cm , and 10cm is a right angled triangle using Pythagoras theorem.

As given in the question,

In the given triangle,

lengths of the sides of the triangle is given by :

6cm , 8cm , and 10cm

In the given measurement longest side is 10cm.

Using Pythagoras theorem :

( Hypotenuse ) ² = (Base)² + ( Altitude)²

Here

( 6 )² + ( 8 )²

= 36 + 64

= 100

= 10²

It satisfy the condition of Pythagoras theorem.

It is a right angled triangle with hypotenuse = 6cm.

Therefore, the given lengths of the sides of the triangle represents it is a right angled triangle.

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Brand A's mean absolute deviation is 2.02, whereas brand B's is 1.905, showing that the two brands' mean absolute deviations ARE comparable.

A group of at least two numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for one given collection of numbers, including as the arithmetic mean approach, which utilizes the sum of the series' values, and the root - mean - square method, which takes the average of a group of products.

For every dot plot, determine the mean absolute deviation.

Deviation from the mean for Brand A:

The points are, 1,1,2,2,2,3,4,4,5,5,5,5,6,6,7,7,8,8,8,9

Mean = (1 + 1 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9)/20 = 98/20

Mean = 4.9

Mean Absolute Deviation = [(1 - 4.9) + (1 - 4.9) + (2 - 4.9) + (2 - 4.9) + (2 - 4.9) + (3 - 4.9) + (4 - 4.9) + (4 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (6 - 4.9) + (6 - 4.9) + (7 - 4.9) + (7 - 4.9) + (8 - 4.9) + (8 - 4.9) + (8 - 4.9) + (9 - 4.9)] / 20

= [(3.9) + (3.9) + (2.9) + (2.9) + (2.9) + (1.9) + (0.9) + (0.9) + (0.1) + (0.1) + (0.1) + (0.1) + (1.1) + (1.1) + (2.1) + (2.1) + (3.1) + (3.1) + (3.1) + (4.1)] / 20

= 40.4/20

Brand A's mean absolute deviation was 2.02, while Brand B's was:

The points are, 1,3,3,4,4,4,4,4,5,5,5,6,6,6,6,8,8,9,10,10

Mean = (1 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 8 + 8 + 9 + 10 + 10)/20

Mean = 111/20 = 5.55

Mean Absolute Deviation = [(1 - 5.55) + (3 - 5.55) + (3 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (5 - 5.55) + (5 - 5.55) + (5 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (8 - 5.55) + (8 - 5.55) + (9 - 5.55) + (10 - 5.55) + (10 - 5.55)] / 20

Deviation from the mean is 38.1/20.

Brand B's mean absolute deviation is 1.905.

As a result, the following judgment is made regarding the outcomes illustrated by the determine the exact location:

For brand A, the average absolute deviation is 2.02

For brand A, the average square deviation is 1.905.

For the two brands, the Average Absolute Deviation IS comparable.

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The complete question is-

Martin and Clara decide to keep track of the number of different colors in two brands of tennis shoes, brand A and brand B. Their results are represented by the dot plots. The mean absolute deviation for brand A is____ The mean absolute deviation for brand B is__ The mean absolute deviations for the two brands ___ similar.

Most accurate statement is "The plane clears the tower with about 6 yards to spare". So the option c is correct.

In the given question, a plane travels 1500 yard before lifting off the ground.

If the plane continues on the runway, it is 600 more yard to the control tower, which is 198 feet high.

Instead, the plane takes flight and travels 603 yards.

Initial distance traveled = 1500

Yards to control tower = 600

Height of control tower = 198 feet

Height of control tower = 198×3 yards

Height of control tower = 594 yards

If the airplane's rate of ascent is proportionate to the distance flown, then 1 yard of length equals 1 yard of height achieved.

The height of the plane would be 600 yards after flying 600 yards to the location of the control tower.

So, Difference in height = Height of plane - Height of tower

Difference in height = 600 yards - 594 yards

Difference in height = 6 yards

Hence, most accurate statement is "The plane clears the tower with about 6 yards to spare". So the option c is correct.

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if the density of the metal cube is 2.3 x 10⁻³ kilograms/micro liters, 2968 cm. is the length of one side of a cube if the mass is 88 milligrams

The amount of digits that contribute to the correctness of a value—often a measurement—are known as significant figures. The first digit that is non-zero is where we begin counting significant figures.

The number of significant single digits (0 through 9 inclusive) in an expression's coefficient is referred to as the significant figures in scientific notation. The amount of accuracy or assurance an expert or scientist uses to state a quantity is indicated by the number of significant figures in a statement.

The given mass of the metal cube is 2.3 × 10⁻³kg/micro-liters or 2300000 gm/liter

The density of the metal cube is 88 mg or 0.088 gm.

Now, we know that density, d = mass/volume.

So, volume of the metal cube,

V = mass/density

V = (2300000/0.088)

V = 26136363.7 L

Now, we know that volume of a cube is a³ where a is the length of a side of the cube. So, a³ = 26136363.7 L or 26136363.7 dm³.

So, a = 296.8 dm or 2968 cm.

So, the length of one side of the cube is 2968 cm.

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The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 4∛(x¹⁰) + 5x³∛(8x)

Simplify the expression, then we have

⇒ 4∛(x¹⁰) + 5x³∛(8x)

⇒ 4∛[(x³)³ · x] + 5x³∛(2³ · x)

⇒ 4x³ ∛x + 10x³ ∛x

⇒ 14x³ ∛x

The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.

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The value(s) of x will make x² = 16 true are 4 and -4.

B. is the answer

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included

The values of x that will make x² = 16 true are -4 and 4.

x² = 16 can be written as follows:

x² = 16

x = ±√16

x = ± 4

x = 4 or -4

This because the square of 4 is 16 i.e. 4² = 16. Likewise the square of -4 is 16 i.e. (-4)².

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The amounts of each type that should be produced to maximize profit is given as follows:

Hence the maximum profit is of:

birr 710.

A system of inequalities is used to model the situation, for which the variables are given as follows:

The number of products is a countable amount, meaning that it cannot assume negative values, hence the first two constraints are given as follows:

For table A, the constraint is of at most 108 hours, hence:

6x + 4y ≤ 108.

For table B, the constraint is of at most 24 hours, hence:

x + y ≤ 24.

Hence the four constraints are combined to form a system of inequalities, which is solved graphically.

The profit function is given as follows:

P(x,y) = 40x + 30y.

As products of type A contribute more to profit, we must find the vertex on the solution which has the highest value of x, which is of:

(17,1).

Meaning that 17 items of type A are made and one item of type B, and the profit is given as follows:

P(17,1) = 40 x 17 + 30 = birr 710.

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The trainee's z-score is -1.5.

An illustration of a standardized score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Given:

Mean= 77

standard Deviation = 2

x= 74

Using z score formula

Z score = (x - μ)/ σ

Z score = (74 - 77)/ 2

Z score = -1.5

Now, the P-value from Z-Table:

P(x<74) = 0.066807

P(x>74) = 1 - P(x<74)

            = 0.93319

P(74<x<77) = 0.5 - P(x<74)

                  = 0.43319

Hence, the z- score is -1.5.

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The general solution of  dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]

A differential equation is an equation that contains one or more functions with its derivatives.

The given differential equation is  dy over dx equals x times y plus 3 times x question

dy/dx=xy+3x

dy/dx=x(y+3)

dy/dx-x(y+3)=0

Solve seperable ODE

[tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]

Hence, the general solution of dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]

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True solution is a homogeneous mixture of two or more substances in which the particles of solute are dispersed uniformly throughout the solvent. An example of a true solution is a mixture of salt and water.

True solution is a type of homogeneous mixture in which the particles of solute ( the substance that is dissolved ) are dispersed uniformly throughout the solvent (the substance that is doing the dissolving). The particles of solute are too small to be seen with the eye and the mixture appears to be one single substance. An example of a true solution is a mixture of salt and water. The salt molecules are dispersed evenly throughout the water, producing a salty taste throughout the entire solution.

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The cost will be $627,000 for about n = 59 units made.

We know that the polynomial function:

C(n) = 3n^3 - 4n^2 + 250b + 75,000

Gives the cost of producing n products.

We want to find the value of n, such that the cost is $627,000

So we need to solve the cubic equation:

3n^3 - 4n^2 + 250n + 75,000 = 627,000

Now we can subtract 627,000 in both sides to get:

3n^3 - 4n^2 + 250n - 619,500 = 0

And now we can graph that equation and find the intercepts:

There you can see that the intercept is at n = 59, so that is the answer.

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The maximum likelihood estimate for p is 1/2, as it maximizes the likelihood of observing the sequence.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include operations such as addition, subtraction, multiplication, and division, as well as the manipulation of equations

The maximum likelihood estimate (MLE) for p is the value that maximizes the likelihood function, which represents the probability of observing a particular sequence of red and white chips given the assumed distribution of reds and whites. In this case, we have two options for the proportion of reds, either 1/3 or 1/2. To calculate the likelihood of observing the sequence red, white, white, red, and white given p = 1/3, we calculate (1/3)(2/3)(2/3)(1/3)(2/3) = 4/243. To calculate the likelihood of observing the sequence given p = 1/2, we calculate (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32. As we can see, the maximum likelihood estimate for p is 1/2, as the likelihood of observing this sequence given p = 1/2 is greater than the likelihood of observing this sequence given p = 1/3.

The maximum likelihood estimate for p is 1/2, as it maximizes the likelihood of observing the sequence.

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The expression that represents the length, in inches, of the third side of the triangle is 5 + 2 = 7 a 3 inches.

A triangle is a three-sided geometric shape that has three angles and three sides. The three sides all join together at the vertices to form a closed shape. Triangles are one of the most basic shapes and can be found in many objects and structures in nature, such as mountains, trees, and the human body. Triangles can also be seen in architecture, artwork, and mathematics.

This can be calculated by subtracting the sum of the two given side lengths (8 a 6 inches) from the given perimeter (9 a 12 inches). The difference of 1 a 6 inches is equal to the third side length of the triangle (7 a 3 inches).

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23/20 students in barbara's class have both a cat and a dog.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Given that,

The number of students in barbara's class having a pet cat = 2/5

The number of students in barbara's class having a pet dog = 3/4

Thus, the fraction of the students in barbara's class have both a cat and a dog = 2/5+3/4 = 8+15/20= 23/20

Hence, 23/20 students in barbara's class have both a cat and a dog.

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James gets 140 pounds.

What is a ratio?

A ratio is a mathematical comparison of two or more values. A ratio can be written in various ways, such as "5 to 3" or "5:3", which means that for every 5 parts, there are 3 parts. Ratios can also be simplified to their lowest form, just like fractions.

In this case, Carly and James share money in a ratio of 5:3, meaning that for every 5 parts of the money that Carly gets, James gets 3 parts. If Carly gets £70 more than James, we can set up the equation as:

x + 70 = 5/8 * x

Where x is the amount James gets.

Solving this equation we get:

x = 140

Hence, James gets 140 pounds.

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The direct relantionship model indicates that variable q is equal to 225 / 19 when r is 45.

In this problem we must derive an equation based on following relationship:

Variable q is directly proportional to r.

In other words, we have the following direct relationship model that describes well the situation:

q = k · r

Where:

First, determine the constant of proportionality:

k = q / r

k = 76 / 20

k = 19 / 5

Second, calculate the variable r is:

q = r / k

q = 45 / (19 / 5)

q = 225 / 19

The statement presents several typing mistakes, correct form is introduced below:

q is directly proportional to r is 76 when r is 20.

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Answer:

-1233

Step-by-step explanation:

Step 1.) Plug in the orresponding number to letter

- |135+ -2| 2- -7.

Step 2.) Find absolute value

-| 137 | 2- -7

Step 3.) Solve

-137 × 9

= -1233

Answer:

see explanation

Step-by-step explanation:

given a system of equations graphically , then the solution is at the point of intersection of the 2 lines.

However, the 2 lines shown are parallel and never intersect and therefore have no solution.

Answer:

to get your answer you have to. Then after that, and finally

Answer:

14/3

Step-by-step explanation:

Cross Multiply 6/7 by 4

6/7 x 4/1

= 28/6

Simplify

=14/3

Pie charts, bar charts, area charts, or bubble charts are the 3 types of graphs we use to compare data

The pie chart is used for relative comparison, which is strongly discouraged by a lot of data visualizers because it takes up too much space but the information value provided is very little unless more visual aids are provided which then is meaningless.

Bar charts are used for precise comparison, Comparing parts of a bigger set of data, highlighting different categories, or showing change over time.

Having a long categories label which offers more space, and If you want to illustrate both positive and negative values in the dataset.

If you want to compare volumes, use an area chart or a bubble chart.

The area chart shows part-to-whole relations and portrays the volume of your data and not just the relation to time.

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