given the plot of normal distributions a and b below, which of the following statements is true? select all correct answers.Select all correct answers Select all that apply: A has the larger mean. B has the larger mean The means of A and B are equal A has the larger standard deviation. B has the larger standard deviation. The standard deviations of A and B are equal.

Answer:

a) 191.3 students

b) 433.8 students

Step-by-step explanation:

a) Since x represents years since 1998, on the graph, the number of student in 2005 is represented at x = 7.

So, to solve for the number of students studying abroad in 2005, find the approximate y-coordinate of the point on the graph at x = 2005 - 1998 = 7:

(7, 191.296)

         ↓

   191.296

Finally, round this to the nearest tenth.

192.296 ≈ 191.3 students

See the attached images for a graph and an algebraic solution for the coordinate.

b) Since x represents years since 1998, on the graph, the number of student in 2018 is represented at x = 2018 - 1998 = 20.

So, to solve for the number of students studying abroad in 2018, find the approximate y-coordinate of the point on the graph at x = 20:

(20, 433.761)

         ↓

   433.761

Finally, round this to the nearest tenth.

433.761 ≈ 433.8 students

SAS triangle congruence theorem can be used to prove the triangle are congruent.

A triangle is a simple polygon with three sides and three interior angles. It is one of the basic forms of geometry in which three vertices are connected, and is represented by the symbol △. There are different types of triangles, classified based on their sides and angles. Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other. The congruence symbol is "≅".

Angle is the space between two intersecting lines or surface at or close to the point where they meet.

The SAS Postulate says that is the  triangles are congruent if any pair of the  corresponding sides and I their included angles are be congruent.

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The formula for estimating the population variance from the sample requires calculating the sum of squared deviations and dividing it by the number of observations. This is true for both the t-test for dependent means and the t-test for independent means.

This formula is referred to as the "variance sum of squares"or the t-test for dependent means, the formula is:

Where:

x1 = observation 1

x2 = observation 2

N = number of observations

For the t-test for independent means, the formula is:

Sample Variance = [(Σx12)/N + (Σx22)/N]/2

Where:

x1 = observation 1

x2 = observation 2

N = number of observation

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The measure of side BC is 12 units in a right  ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.

A right angle is defined as an angle that is exactly 90 degrees in geometry and trigonometry. If a ray is positioned so that its terminal is on a line and the angles are also equal, the angles are said to be at right angles. The phrase derives from the Latin angulus rectus, where rectus denotes the upright vertical line that is perpendicular to a horizontal base line.

Perpendicular lines—defined as lines that meet at right angles—and orthogonality—defined as the ability to intersect at right angles—are closely connected and crucial geometrical notions.

Given,

m∠CAL = m∠BAL

m∠C = 90°

AD = 8 cm

DH = 4 cm

We have to apply sine rule for ΔADH,

sinθ=opposite side/hypotenuse

sin(∠DAH)=DH/AD

=4/8

=1/2

∠DAH=sin⁻¹(1/2)

∠DAH=30°

Therefore, ∠CAB=2(∠DAH)

=2(30°)

=60°

Now, we have to apply tangent rule in  ∆AHD

tan( ∠DAH)=DH/AH

tan(30°)=4/AH

1/√3=4/AH

AH=4√3

Now, we have to apply cosine rule in ∆AHC

cos(60°)=AH/AC

1/2=4√3/AC

AC=8√3

Now, we have to apply tangent rule in ∆ACB

tan(∠CAB)=opposite side/adjacent side

tan(60°)=BC/AC

√3=BC/8√3

BC=8√3(√3)

BC=24units.

Therefore, the measure of side BC is 12 units in a right  ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.

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Tiles are needed = 90

The number of tiles measuring 40cm by 40cm  that are needed to completely cover a wall 4m by 3.6m is 90.

Squares

Square,  a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).

Number of tiles needed

Convert the Meters to Centimeters

4m = 400cm

3.6m = 360 cm

Then

4m by 3.6m = 400 cm × 360 cm

4m by 3.6m = 144000 cm²

Tiles are needed

Number of needed tiles =  144000 cm² / ( 40 cm × 40 cm)

Number of needed tiles =  144,000 cm² /1600 cm²

Number of needed tiles =  90

Tiles are needed = 90

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The given two triangles are congruent by  Side Side Side congruency.

As from the question we get to know that ΔRST and Δ UTS  

and

RS = UT

RT = US

The proof for the above claim

RS = UT    {given}

RT = US    {given}

ST = TS     {Common}

Therefore, we can say that by SSS theorem ΔRST and Δ UTS  is congruent to each other.

ΔRST  ≅ Δ UTS    by SSS Theorem

If two geometric figures are identical in every way, they are said to be congruent.

For example, two squares having the same side-length are congruent.

Similarly, two circles with the same radius are congruent.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. ’ ≅’ is the congruence symbol.

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The properties of the unique solution of the system AX=B depend on the matrix of the system. That is, it depends only on the coefficients on the left side. RHS configuration is not the issue.

The method of least squares is an important statistical technique practiced to find the regression line or the best fit line for a particular pattern. This procedure is described by an equation with specific parameters. The method of least squares is used liberally in analysis and regression. In regression analysis, this method is a standard approach to approximating a system of equations using more equations than unknowns.

The least squares method actually defines a solution to minimize the resulting sum of squares or error for each equation. Find the formula for the sum of squared errors to help find the variation in the observed data.

The least squares method is often used in data fitting. A best fit result is assumed to reduce the sum of squared errors or residuals reported as the difference between the observed or experimental values ​​and the corresponding fitted values ​​in the model.

Linear System of Equation:

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

A linear system of three variables determines the collection of levels. Intersection is the solution.

For example,

3x + 2y -z =1 , 2x - 2y + 4z =-2

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Answer:

13

Step-by-step explanation:

-11+2/3x(-12)+4/1/8 Identify the sign

-11-\\\2/3x12+4/1/8 multiplying and inverting

-11-2/3x12+4x8 Simplify

-11 -2x4+4x8

-11-8+32

13

Answer: 1

Step-by-step explanation:

Using substitution method, the system of linear equations showed that there 27 and 35 quarters and nickel respectively

System of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

To solve this problem, we have to write a system of linear equations which consist of two linear equations.

Let;

x + y = 62...eq(i)

0.25x + 0.05y = 8.50 ...eq(ii)

Using substitution method

From equation (i)

x + y = 62

x = 62 - y ...eq(iii)

Put equ(iii) into eq(ii)

0.25( 62 - y) + 0.05y = 8.50

y = 35

Put y = 35 in equation (i)

x + 35 = 62

x = 27

The number of quarters and nickels are 27 and 35 respectively

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The value of the equation 4 is multiplied by the difference of 5 and a number is A = 20 - 4n

where n is the number

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as n

Let the equation be A

Now , the value of A is

4 is multiplied by the difference of 5 and a number is

Substituting the values in the equation , we get

A = 4 ( 5 - n )

where n is the number

On simplifying the equation , we get

The value of A = 4 ( 5 ) - 4 ( n )

The value of A = 20 - 4n

Therefore , the value of equation A is A = 20 - 4n

Hence , The value of the equation 4 is multiplied by the difference of 5 and a number is A = 20 - 4n , where n is the number

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Answer:

3K

Step-by-step explanation:

So option b. x² + x is the correct option of the given statement Because option b satisfy the requirement of polynomial.

A polynomial is a mathematical equation made up of variables (sometimes called indeterminates) and coefficients, and can be expressed using just the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials can be located. Expressions with additional operations are considered non-polynomial expressions. Describe the reasons why the expressions are not polynomials.

A polynomial function is a function in an equation that exclusively employs positive integer exponents or non-negative integer powers of a variable. Examples of such equations include the cubic equation, the quadratic equation, and others. For example, 2x+5 is a polynomial with an exponent of 1.

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Answer: 325

Step-by-step explanation:

723 -73 =650 divided by 2

Hope this helps

The multiplication of polynomial in descending powers is,

32x^2 + 68x + 21.

What is polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Consider, the given polynomials

(8x + 3)(4x + 7)

Taking multiplication,

8x(4x + 7) + 3(4x + 7)

Simplifying,

32x^2 + 56x + 12x + 21

32x^2 + 68x + 21

Hence, the multiplication of polynomial in descending powers is,

32x^2 + 68x + 21.

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Answer:

(x - 3)² + (y + 3)² = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

the radius r is the distance from the centre to a point on the circle.

given (3, - 3 ) is the centre and (3, 0 ) is a point on the circle

since the x- coordinates of both points are 3 then r is the absolute value of the difference of the y- coordinates, that is

r = | - 3 - 0 | = | - 3 | = 3

then equation of circle is

(x - 3)² + (y - (- 3) )² = 3² , that is

(x - 3)² + (y + 3)² = 9

The degrees of freedom (df): For a chi-square test of independence, the df is (number of variable 1 groups − 1) * (number of variable 2 groups − 1).

Under the null speculation and sure conditions (mentioned below), the check statistic follows a Chi-Square distribution with stages of freedom identical to ( r − 1 ) ( c − 1 ) , wherein is the quantity of rows and is the quantity of columns.

The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated. The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated minus one.

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Complete question:

what degrees of freedom should be used to conduct a chi-squared test of independence using this table?

After solving, the surface integral S is [tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14.

In the given question, we have to evaluate the surface integral.

(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.

Now the surface integral is:

[tex]\int\int_{S}(x + y + z) dS[/tex]

x = u+v, y = u−v, z = 1+2u+v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6

The parametric curve is

r(u,v) = <u+v, u−v, 1+2u+v>

Then surface integral is calculated as

[tex]\int\int_{S}(x + y + z) dS=\int\int_{A}f(x(u,v), y(u,v), z(u,v))|r_{u}\times r_{v}| dudv[/tex]

Now find partial derivatives of parametric curve with respect to u and v

[tex]r_{u}[/tex](u,v) = <1, 1, 2>

[tex]r_{v}[/tex](u,v) = <1, -1, 1>

Now find cross product

[tex]r_{u}\times r_{u}[/tex] = <1, 1, 2> × <1, -1, 1>

[tex]r_{u}\times r_{u}[/tex] = <1+2, 2-1, -1-1>

[tex]r_{u}\times r_{u}[/tex] = <3, 1, -2>

Now parametric function is

x+y+z = u+v+u-v+1+2u+v

x+y+z = 4u+v+1

Then the surface integral is:

[tex]\int\int_{S}(x + y + z) dS=\int^{6}_{0}\int^{8}_{0}(4u+v+1)\sqrt{14}dudv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(4\frac{u^2}{2}+uv+u)^{8}_{0}dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}[(4\frac{(8)^2}{2}+8v+8)-(4\frac{(0)^2}{2}+0\cdotv+0)]dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(128+8v+8)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(136+8v)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}(136v+8\frac{v^2}{2})^{6}_{0}[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}[(136\times6+8\frac{6^2}{2})-(136\times0+8\frac{0^2}{2})][/tex]

[tex]\int\int_{S}(x + y + z) dS[/tex] = √14×(816+144)

[tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14

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The value of 'b' obtained for the given exponential function is 0.055.

The stated exponential function is-

y = 5832(b)ˣ

This, function contains the point (3, 1).

Put the value in the r function;

1 = 5832(b)³

(b)³ = 1/5832

b = ∛1/5832

b = 0.055

Thus, the value of 'b' obtained for the given exponential function is 0.055.

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Therefore,  the speed is  792/5 ft/sec  and distance covered during 15 second free fall is 1,584 ft.

The rate at which something or someone is moving is known as their speed. If you are aware of the distance traveled and the time required to get there, you can calculate the average speed of an object. The equation speed = distance * time is used to calculate speed.

Here,

Given:

The maximum free fall speed for a parachutist is 108 miles per hour.

5280 feet make up a mile.

Thus,

The speed is given by

=> 108 x 5280 x 1/3600 sec

=> 792/5 = 792/5 ft/sec  

and the distance of the parachutist fall during 15 seconds of free fall is given  by

=> 792/5 ft/sec x 10 sec = 1,584 ft

Therefore,  the speed is  792/5 ft/sec  and distance covered during 15 second free fall is 1,584 ft.

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Answer:

  D.  70°32'

Step-by-step explanation:

You want the angle represented by arccos(0.333) to the nearest minute.

The attached calculator shows the angle in degrees (70.54903521713) and in degrees, minutes, and seconds (70°32'56.53"). There are 60 seconds in a minute, so the number of seconds being more than 30 means the minutes should be rounded up to ...

  70°33'

The closest answer choice is D. 70°32'.

The system of equations is  0.05n+0.10d=1.90  and n=d+2

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The calculation is as follows:

We know that

One nickel = $0.05,

So n nickels are worth 0.05n.

One dime = $0.10,

so dd dimes are worth 0.10d.

Now

The total 0.05n+0.10d =  $1.90

i.e.  

0.05n+0.10d=1.90

And,  

n=d+2

Therefore we can conclude that The system of equations is  0.05n+0.10d=1.90  and n=d+2

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Answer:

[tex]\sqrt[4]{256}[/tex]

Step-by-step explanation:

1. simplify the expression

4^4 = 256

2.  calculate the fourth root of 256 because we used the power of 4

[tex]\sqrt[4]{256}[/tex] = 4

Equivalent expression is (x-1)/2x for ((1 -1/x)/2), So Option 1 is correct.

If two expressions can be written similarly or can be combined into a single, simpler phrase, then those two expressions are comparable. Additionally, you can tell if two expressions are equal if you substitute values for the variable in both and they get the same result. The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.

This is the rationale for why these fractions simplify to the same number. Equivalent ratios are two ratios that have identical values. Divide or multiply both amounts by the same number to arrive at an equivalent ratio. The method is the same as determining equivalent fractions.

Here expression is ((1 -1/x)/2)

take x as lcm then (x-1)/2x

correct option is (A).

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Correct Question:

Which expression is equivalent to the following complex fraction?

(1-1/x)/2

A) x-1/2x

B) -1/2

C) 2x-2/x

D) 2x/x-1

Both abbreviations are correct:

PEMDAS stands for:

BODMAS stands for:

PEMDAS and BODMAS are both mathematical acronyms that are used to help people remember the order of operations when solving a math problem.

The order of operations should be followed when solving an equation because it ensures that the problem is solved correctly and accurately. It is important to remember that both acronyms represent the same order of operations, and that each step should be followed in the order given.

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PEMDAS stands for

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

BODMAS stands for

Bracket

Orders

Division and Multiplication

Addition and Subtraction

Both of these are the same, just a different acronym and way of representing them.

The functions that model a mountain with steeper sides are (c) g(x) = -|3x - 1| +2 and (d) g(x) = -|4x-2| +1​

From the question, we have the following parameters that can be used in our computation:

f(x) = -|x - 2| + 1

The above function is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where

Slope = a

So, the slope of f(x) = -|x - 2| + 1 is

Slope = -1

Take the absolute value of this slope

Steep = 1

This means that the slopes of the functions in the options are

Slope (a) = -1/4

Slope (b) = -1/3

Slope (c) = -3

Slope (d) = -4

Take the absolute values of the above slope

Steep (a) = 1/4

Steep (b) = 1/3

Steep (c) = 3

Steep (d) = 4

A slope with a greater absolute value means a steeper line

3 and 4 are greater than 1

This means that the equations (c) and (d) are steeper than the given equation

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Answer:

The table that represents g(x) is

x         g(x)

1           1

2          5

3          9

Step-by-step explanation:

From the given information, we have that

f(x) = 2x - 3 and

g(x) = f(2x)

Then,

g(x) = f(2x) becomes

g(x) = f(2x) = 2(2x) -3

g(x) = 4x - 3

Now, we will put the values of x from 1 to 3 into the equation

When x = 1

g(x) = 4x - 3 becomes

g(x) = 4(1) - 3

g(x) = 4 - 3

g(x) = 1

When x = 2

g(x) = 4x - 3 becomes

g(x) = 4(2) - 3

g(x) = 8 - 3

g(x) = 5

When x = 3

g(x) = 4x - 3 becomes

g(x) = 4(3) - 3

g(x) = 12 - 3

g(x) = 9

Hence, the table that represents g(x) is

x         g(x)

1           1

2          5

3          9

Answer:

1,229

Step-by-step explanation:

100 + 100 = 200

1,000 + 200 = 1,200

9 + 9 = 18

1,200 + 18 = 1,218

1,218 + 11 = 1,229

The probability distribution of rolling a die is

P(1) = 1/6, P(2) = 1/6, P(3) = 1/6, P(4) = 1/6, P(5) = 1/6, P(6) = 1/6

Given that,

Let T be the outcome of a roll with a fair die.

Then

T = {1, 2, 3, 4, 5, 6}

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability of getting 1 P(1) = 1/6

The probability of getting 2 P(2) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 4 P(4) = 1/6

The probability of getting 5 P(5) = 1/6

The probability of getting 6 P(6) = 1/6

Therefore, the probability distribution of rolling a die has been found

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