IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
Out of a randomly selected 3700 people from the population, how many of them
would have an IQ less than 66, to the nearest whole number?

The type of conic section that is represented in the provided equation form is ellipse.

To identify the type of conic section from an equation whether it is circle or ellipse.

Let us  suppose the equation as,

\(Ax^{2} +By^{2}+Cx+Dy+E=0\)

In this equation,

We have to identify the type of conic section that has the equation,

\(4x^{2} +25y^{2}=100\)

By comparing this equation with the above equation, we get,

\(A=4\\B=25\)

Here neither \(A\) or \(B\) is equal to \(0\) and the sign of both are

similar(positive), so the equation form is ellipse.

Therefore, the type of conic section which is represented in the provided equation form is ellipse.

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The correct option for the given relation is option C. Using a voltmeter and an ammeter connected in series with battery, emf and terminal voltage.

The serial connection of an ammeter Option A and B are incorrect because the voltmeter is connected in parallel to the circuit. Without causing a buildup, charged particles in a conductor. If it happens otherwise, it generates its own electric field, which cancels out the electric field from the outside, ultimately causing the current to step in the wrong direction choice D. We can measure the terminal voltage, or emf, of the battery X in option C using a voltmeter and an ammeter connected in series. R allows us to measure current.

Therefore appropriate choice is option C.

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Answer:

Solution given:

length of arc LM={angle}/360*2*π*r

=here π=180 for angle and π for length

=(3π/4)/360*2*π *6

=(3*180/4)/360*2*π*6

=9/2π

option C

9/2π is a required answer.

Answer:

6.29

Step-by-step explanation:

so you know that the unknown side which is 7x + 27 equals 71.

You can begin by subtracting 27 from 71 which will give you 44.

you then know that 44 = 7x

then you just have to do 44 divided by 7 to find x which isss...

look above at answer  

Answer:

12* ( 4+5)

Step-by-step explanation:

48 = 12 * 4

60 = 12 * 5

48 + 60 = 12*4 + 12*5

             = 12*( 4 + 5)

            = 12* 9

            = 108

The solution to the equation 2x⁴ * x³ is 2x⁷

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Inequalities shows the non equal comparison between two or more numbers and variables.

The system of inequalities y ≥ 3x - 1 and x + 3y ≤ 6 is represented by the graph shown

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Answer:

The third answer is correct

when you plug 1 into the equation

4(1)-9= -5

4(2)-9 = -1

4(3)-9= 3

Step-by-step explanation:

The sigma notation of the given series is \(\sum _{j=1}^5\:\left(4j-9\right)\), option C is correct.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given series is -5+(-1)+3+7+11

The sigma notation of the given series is \(\sum _{j=1}^5\:\left(4j-9\right)\)

Now let us check by plugging j values from 1 to 5

When j =1,

4(1)-9= -5

When j =2

4(2)-9 = -1

when j=3

4(3)-9= 3

Hence, the sigma notation of the given series is \(\sum _{j=1}^5\:\left(4j-9\right)\), option C is correct.

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To find the matrix B = [b11 b12; b21 b22] that corresponds to the identification of complex numbers (a+ib) with vectors (a, b) in R^2, we can use the following mapping:

b11 = 1, b12 = 0, b21 = 0, b22 = 1

The matrix B above is a 2x2 identity matrix. This means that the mapping between complex numbers and vectors in R^2 is simply a one-to-one correspondence, where the real part of the complex number corresponds to the first component of the vector, and the imaginary part corresponds to the second component. The identity matrix preserves the vector representation, indicating that there is no transformation or rotation applied.

The complex numbers can be represented in the form (a+ib), where 'a' is the real part and 'b' is the imaginary part. On the other hand, vectors in R^2 can be represented as (a, b), where the first component represents the x-coordinate and the second component represents the y-coordinate.

To establish a connection between complex numbers and vectors in R^2, we can define an identification mapping. By identifying the real part of the complex number with the first component of the vector and the imaginary part with the second component, we establish a one-to-one correspondence.

The matrix B = [b11 b12; b21 b22] represents the transformation between complex numbers and vectors. In this case, the matrix B is simply the 2x2 identity matrix, where all diagonal elements are 1 and all off-diagonal elements are 0. This means that the mapping does not involve any transformation or rotation.

By using this identification, we can now treat complex numbers as vectors in R^2 and perform operations on them using vector arithmetic. This mapping is particularly useful in applications where complex numbers can be interpreted geometrically, such as in electrical engineering and signal processing, where complex numbers represent phasors or vectors in the complex plane.

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Answer:

Step-by-step explanation:

\(H(t) = 14000(0.8)^{t +3}\\\\ = 14000*(0.8)^{t}*(0.8)^{3}\\\\=14000*(0.8)^{t}*0.512\\\\=7168(0.8)^{t}\)

Answer:

it is 7168(0.8)t

Step-by-step explanation:

hope this helped

Answer:

12x8x10=960

Step-by-step explanation:

The statement "a point estimate consists of a single sample statistic that is used to estimate the true population parameter" is False as it is not used to estimate the true population parameter.

A point estimate is used to provide an estimate or approximation of the population parameter.

The true population parameter refers to the exact value of the characteristic being measured in the entire population.

However, since it is usually not feasible or practical to measure or observe the entire population, we often rely on taking a sample from the population.

By collecting data from a sample, we can calculate sample statistics such as the sample mean or sample proportion.

These sample statistics serve as point estimates, providing an estimate or best guess of the population parameter based on the available sample information.

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Answer:

\(slope = \frac{4}{1} = 1 \\ y - intercept = 3 \\ \therefore \: \: y = 4x + 3\)

Answer: -4 and 9

Step-by-step explanation:

If two right triangles have congruent acute angles, then the triangles are similar.

Right Triangle Similarity Theorems are a set of geometric principles that relate to the similarity of right triangles.

Here are two examples of these theorems:

Angle-Angle (AA) Similarity Theorem:

According to the Angle-Angle Similarity Theorem, if two right triangles have two corresponding angles that are congruent, then the triangles are similar.

In other words, if the angles of one right triangle are congruent to the corresponding angles of another right triangle, the triangles are similar.

For example, if triangle ABC is a right triangle with a right angle at vertex C, and triangle DEF is another right triangle with a right angle at vertex F, if angle A is congruent to angle D and angle B is congruent to angle E, then triangle ABC is similar to triangle DEF.

Side-Angle-Side (SAS) Similarity Theorem:

According to the Side-Angle-Side Similarity Theorem, if two right triangles have one pair of congruent angles and the lengths of the sides including those angles are proportional, then the triangles are similar.

For example, if triangle ABC is a right triangle with a right angle at vertex C, and triangle DEF is another right triangle with a right angle at vertex F, if angle A is congruent to angle D and the ratio of the lengths of the sides AB to DE is equal to the ratio of the lengths of BC to EF, then triangle ABC is similar to triangle DEF.

These theorems are fundamental in establishing the similarity of right triangles, which is important in various geometric and trigonometric applications.

They provide a foundation for solving problems involving proportions, ratios, and other geometric relationships between right triangles.

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Answer:

x = 1

Step-by-step explanation:

Given

3(x - 2) + 2 = 5(x - 3) + 9 ← distribute and simplify both sides

3x - 6 + 2 = 5x - 15 + 9

3x - 4 = 5x - 6 ( subtract 5x from both sides )

- 2x - 4 = - 6 ( add 4 to both sides )

- 2x = - 2 ( divide both sides by - 2 )

x = 1

For every 1 km = there are 1,000 meters. Therefore:

15,000 m to km is:

For every 1 decimeter, there are 100 millimeters.

Answer:

\(11 \div 3 \times 15 \\ 11 \div 1 \times 5 \\ 11 \times 5 \\ = 55\)

Answer:

Is there a picture to go with it?

Answer:

i think 1

Step-by-step explanation:

Answer: zero, hope it helps!! tell if there’s an error

Answer:

Audrey needs to collect 3 more coins.

Step-by-step explanation:

Since she already scored 53 points, we have to find out how many more points she needs to score 97.

So, 97-53=45 points.

The problem says that each coin Audrey collects is worth 22 points. Therefore, 45 divided by 22= 2 remainder 1. However, if she only collects two more coins, Audrey will only have 96 points in total, not 97.

So, add another coin to make 3.

Step-by-step explanation:

7x^×2-16x-15

14x^-16x-15

\(\\ \sf\longmapsto x+4=\sqrt{8-x}\)

\(\\ \sf\longmapsto (x+4)^2=8-x\)

\(\\ \sf\longmapsto x^2+16+8x=8-x\)

\(\\ \sf\longmapsto x^2+8x-x+16-8=0\)

\(\\ \sf\longmapsto x^2+7x+8=0\)

\(\\ \sf\longmapsto x^2-8x+x+8\)

\(\\ \sf\longmapsto (x-8)(x-1)=0\)

\(\\ \sf\longmapsto x=8,-1\)

Option C

Answer:

\({ \rm{x + 4 = \sqrt{8 - x} }} \\ \\ { \rm{ {(x + 4)}^{2} = {( \sqrt{8 - x}) }^{2} }} \\ \\ { \rm{(x + 4)(x + 4) = 8 - x}} \\ \\ { \rm{ {x}^{2} + 8x + 16 = 8 - x}} \\ \\ { \rm{ {x}^{2} + 9x + 8 = 0 }} \\ \\ { \rm{(x + 1)(x + 8) = 0}} \\ \\ { \boxed{ \tt{x _{1} = {}^{ - } 1}}} \: \: { \rm{and}} \: \: { \boxed{ \tt{x _{2} = {}^{ - } 8}}}\)

The possible rational roots of the polynomial are ±1/2, ±1, ±3/2, ±3, ±9/2, ±9 while the actual roots are 1, -3, 3/2

To find the possible rational roots of the polynomial 2x^3 + x^2 - 12x + 9 = 0, we can use the rational root theorem. According to the theorem, if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors other than 1), then p must be a factor of the constant term (in this case, 9) and q must be a factor of the leading coefficient (in this case, 2).

The factors of 9 are ±1, ±3, and ±9, and the factors of 2 are ±1 and ±2. Therefore, the possible rational roots of the polynomial are:

±1/2, ±1, ±3/2, ±3, ±9/2, ±9

We can now use synthetic division or long division to check which of these possible roots are actual roots of the polynomial. After checking, we find that the real rational root of the polynomial are x = 1, -3, 3/2

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The technology I used in helping me solve the problem is using Microsoft Excel. I made one column for the x values which were gathered from the choices, one column for f(x) whose equation is 8^(x-9), and another column for g(x) whose equation is log(3x) + 2.

Inputting this equation into the last two columns yield the values shown in the picture. The 'NUM' means that the equation at that value of x is undefined. From the values, the correct solution would be:

(0,0), (9.2,1.5) and (9.6,3.5) to the f(x) equation

(9.6,3.5) to the g(x) equation.

X                  f(x)                                                g(x)

                 0.0                                             0.0 #NUM!

                 9.2                                              1.5           3.4

                 9.6                                              3.5           3.5

                 5.3                                              0.0          3.2

                 3.5                                              0.0          3.0

An equation is a mathematical statement consisting of two expressions joined by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation gives the value of the variable x as x = 7.

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To use substitution to determine which value of x makes the equation true, we must first have an equation to substitute the values from the set {4, 8, 10} into.

If we don't have an equation, we can't use substitution.

It would be helpful if you could provide an equation to solve with the set {4, 8, 10}

As per the given interest rates, she have to pay $103.95  in fees for her actively managed fund.

Interest:

Interest means the amount to be paid on the borrowed money or the amount received on the money lent.

Given,

Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return.

Here we need to find the fees for her actively managed fund.

First we have to change rate of return percent to decimal form,

That is,

5% = 0.05

Now, we have to multiply the amount and decimal to get Alizeh 's profit,

=> 9000 x 0.05

=> 450

Therefore, the fund's total after 1 year, including initial investment and profit is

=>9000 + 450

=> 9450.

Now, we have to change fee percent  that is the expense ratio into decimal form,

=> 1.1% = 0.011

Therefore, the fees for her fund is,

=> 9450 x 0.011

=> 103.95

Therefore, she have to pay $103.95 for her managed fund.

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Hello!

453 millions

= 453 000 000

Answer:

32

Step-by-step explanation:

we know that the teacher divides a bag of licorice, meaning that the teacher most likely used up all the licorice. We also know that 4 ropes were given to eachstudent and that there are 8 of them so 4 x 8=32

:)