Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

The component vectors to a linear combination is given by the equation

A = 20 i^ + 14 j^ - 23 k^

The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by

u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃

An equivalent definition, typically used in physics, is

u ⋅ v = ∣u∣ ∣v∣ cos θ,

where θ is the angle between u and v

Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero

Given data ,

Let the component vectors be represented as A

The value of A is

< 20 , 14 , -23 >   be equation (1)

On simplifying the equation to the linear combination , we get

< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^

So , the linear combination of the vectors is given by the equation ,

A = 20 i^ + 14 j^ - 23 k^

Hence , the equation is 20 i^ + 14 j^ - 23 k^

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Therefore , the solution of the given problem of population is . Sample - The 400 clients that the insurance company included in this study

In common parlance, a population is a distinct group of people who share a common citizenship, identity, or set of traits. A population is a sampling that is typical of a broader group of individuals (or even objects) that share one or more variables characteristics.

Here,

A party promises to reimburse another party in exchange for a fee in the case of a certain loss, damage, or injury as a way of financial loss protection. It is a method of risk management that is primarily employed to protect against the risk of a potential loss.

a. Parameter - The average health care cost each year for all of the insurance company's clients

b. Population - All of the insurance company's clients

c. Sample - The 400 clients that the insurance company included in this study

d. Statistic - The average health care costs each year for the 400 clients that the insurance company included in this study

e. Data - The list of the 400 annual health care costs for the clients that the insurance company includes in the study

f. Variable - The cost each year for health care

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40 minutes of 8 hours as a fraction is 1/12.

Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).

Given are 40 minutes to 8 hours.

We can write -

(40 minutes/8 hours)

{40 minutes/(8 x 60)}

(40/480)

1/12

Therefore, 40 minutes of 8 hours as a fraction is 1/12.

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The value of c obtained from the linear inequality (3/5)·c + 7 ≤ 2/5 is the option;

c ≤ -11

An inequality is a (non equal) comparison between two expressions that have different values.

The specified inequality can be expressed as follows;

[tex]\dfrac{3}{5} \times c + 7 \leq \dfrac{2}{5}[/tex]

Simplifying the above inequality by subtracting  7 from both sides, we get;

[tex]\dfrac{3}{5} \times c + 7 - 7 \leq \dfrac{2}{5} - 7[/tex]

Evaluating and simplifying the right hand side into a fraction, we get;

[tex]\dfrac{3}{5} \times c + 0 \leq \dfrac{2}{5} - 7 = \dfrac{2 - 35}{5} = \dfrac{-33}{5}[/tex]

[tex]\dfrac{3}{5} \times c \leq \dfrac{-33}{5}[/tex]

Multiplying both sides by 5, we get;

[tex]5\times \dfrac{3}{5} \times c \leq 5 \times \dfrac{-33}{5}[/tex]

[tex]\dfrac{5}{5} = 1[/tex], therefore;

3·c ≤ -33

Dividing both sides of the above inequality by 3, we get;

3·c ÷ 3 ≤ -33 ÷ 3

c ≤ -11

The correct option is; c ≤ -11

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Answer:

Step-by-step explanation:

$4.50 + $4.50(0.15) = $5.18

$2.25 + $2.25(0.15) = $2.59

$3.00 + $3.00(0.15) = $3.45

When convert it into rectangular form we get x=-1/2 and y=0.

To convert a point in polar coordinates (r, θ) to rectangular coordinates (x, y), you can use the following formulas:

[tex]x = r * cos(θ) \\y = r * sin(θ)[/tex]

Where r is the distance from the origin to the point, and θ is the angle in radians between the positive x-axis and the line connecting the point to the origin.

Alternatively, you can also convert from rectangular to polar coordinates using the following formulas:

[tex]r = sqrt(x^2 + y^2)\\θ = atan2(y, x)[/tex]

Where x, y are the rectangular coordinates and atan2 is a function that computes the angle of a point in a cartesian plane.

In general, it's worth noting that the polar coordinates are often used in some physics and engineering problems, while the rectangular coordinates are often used in computer graphics, analytic geometry and other fields.

The angle of 1's inverse tangent is 45°. This is the outcome of translating to polar coordinates in the form (r,theta).

To convert it into rectangle equation we have

[tex]x=rcos(theta)\\y=rsin(theta)\\r=1\\theta= 3*pi/2\\x= cos(3*pi/2)\\x= -1/2\\y=sin(3*pi/2)\\y=0[/tex]

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Answer:

k=4

Step-by-step explanation:

[tex] \frac{1}{2} k - \frac{4}{1} k = - 8 - 6[/tex]

[tex] \frac{(1 \times 1) - (4 \times 2)}{(2 \times 1)} k = - 14[/tex]

[tex] \frac{1 - 8}{2}k = - 14[/tex]

[tex] - \frac{7}{2} k = - 14[/tex]

[tex] \frac{ - \frac {7}{2} }{ - \frac{7}{2} }k = \frac{ - 14}{ - \frac{7}{2} } [/tex]

[tex]k = 4[/tex]

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.

Here,

A cylinder has a volume of V = r2h.

As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.

The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.

Thus, you would receive one-third of the initial mass.

What would occur if you increased the radius by 1/3 in contrast to this?

Next, you would have

=> V = π[(1/3)r]2h

=> V = π(1/9)r2h

=> V = (1/9)πr2h

You would then possess 1/9 of the volume.

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

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The probability of P(B and C) is 1/6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. It is more likely that an event will occur if its probability is higher.

For e.g., A straightforward illustration is tossing a fair (impartial) coin.

Given that, the probabilities, P(A) = 1/8, P(C) = 1/4, and P(A and B) = 1/12

P(A and B) = P(A)×P(B)

Therefore,

1/12 = 1/8 × P(B)

P(B) = 8/12 = 2/3

Now,

P(B and C) = P(C)×P(B)

P(B and C) = 1/4×2/3

P(B and C) = 1/6

Hence, P(B and C) = 1/6

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We calculated length of model bird in the picture = 2 ¹⁵₁₆ inch and scale factor =1/2

It is expressed as the ratio of the dimension of a model object and dimension of an actual object.

A scale factor is a number which is multiplied by an object in order to form a proportional enlarged or reduced object.

Given, the length of an actual bird = 5⁷₈ inch = 47/8 inch

also given, 1 inch = 0.5 inch

   1 inch = 1/2 inch

we need to determine the length of model bird by multiplying the above factor.

now, length of model bird = 47/8 × 0.5 inch = 47/16 inch = 2¹⁵₁₆ inch

scale factor = length of model bird/ length of actual bird = 47/16 /47/8

scale factor = 1/2

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The solution of the system of equations:

y = 3x - 4

y = (-1/2)*x + 3

Is (2, 2).

Here we have the following system of equations:

y = 3x - 4

y = (-1/2)*x + 3

To solve this graphically, we just need to graph both equations on the same coordinate axis, and find a point where these two graphs intercept.

Below you can see the graph of the system, and there you can see that the lines intercept at the point (2, 2), so that is the solution of the system.

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From the classification angles, it was possible to find the arcs:

UL=40, UY= 90, TY=50, YLE =270, LE=140 and UET=220.

If UE= 180 and TE=40, you have:

UET=UE+TE

UET=180+40

UET=220

They are a lot of classifications for angles like complementary angles, supplementary angles, right angles, and others. See below:

The question gives mTE=40, and it asks:

UL is opposite the arc TE, therefore its value is also 40.

The figure shows a right angle, then UY is equal to 90.

If UY is equal 90, YE is equal to 90 too, because they are supplementary. If YE=90 and TE=40, you have:

TE+TY=90

40+TY=90

TY=90-40

TY=50

YLE = YE+UE. The figure shows YE=90 and UE represents a semicircle (180). Thus,

YLE= 90+180=270

If UE= 180 and UL=40, you have:

UE=UL+LE

180=40+LE

LE=180-40

LE=140

If UE= 180 and TE=40, you have:

UET=UE+TE

UET=180+40

UET=220

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Answer: The sum of the numbers from 1 to 400 that are divisible by 11 is equal to $11 \cdot 666 = 7326$.

Step-by-step explanation:

To find the sum of all the natural numbers from 1 to 400 that are not divisible by 11, we can first find the sum of all the natural numbers from 1 to 400, and then subtract the sum of all the natural numbers from 1 to 400 that are divisible by 11.

The sum of the natural numbers from 1 to 400 is equal to $\frac{400 \cdot 401}{2} = 80150$.

There are 400/11 = 36 numbers that are divisible by 11 between 1 and 400, inclusive. The sum of these numbers is equal to $11 + 22 + 33 + \dots + 396 = 11(1 + 2 + 3 + \dots + 36)$. The sum of the first 36 natural numbers is equal to $\frac{36 \cdot 37}{2} = 666$. Therefore, the sum of the numbers from 1 to 400 that are divisible by 11 is equal to $11 \cdot 666 = 7326$.

Subtracting the sum of the numbers that are divisible by 11 from the sum of all the numbers from 1 to 400 gives us a final answer of $80150 - 7326 = 72824$. This is not equal to 35840, as stated in the problem.

Answer:

--------------------------------

Use the sum of the first n terms formula for an AP:

The sum of all natural numbers from 1 to 400:

The greatest natural number less than 400 but divisible by 11:

Sum of the numbers divisible by 11:

Sum of the numbers not divisible by 11:

Answer:A two-way table, also known as a contingency table, is a way to organize and present categorical data in a tabular format. It can be used to show the relationship between two categorical variables, such as whether a student lives with a grandparent and the number of people who live in their home.

Based on the information you provided, the two-way table would look like this:

More than 4 people | 6 | 10

4 or fewer people | 4 | 30

It should be noted that the information you provided does not add up to 50 students.

Total for students living with grandparents: 10,

Total for students with more than 4 people: 6+10 =16.

Let me know if this table is incorrect and I'll provide you with more information

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

9+2+4+6+123=

11+10+123
21+123
144

Answer:

which one is correct about HRM?

The cost of the order can be expressed as 7x + 5, where x is the number of t-shirts ordered.

In this expression, "7x" represents the cost of the t-shirts, where each shirt is $7 and the number of shirts is represented by "x". The "$5" represents the flat shipping fee for the entire order, which does not change regardless of the number of shirts being ordered.

By adding the cost of the shirts and the shipping fee, we can find the total cost of the order. It's important to understand that the value of "x" must be specified to evaluate the expression.

For example, if 3 shirts are ordered, then x = 3 and the expression becomes:

So the total cost of the order would be $26.

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Answer:

Step-by-step

Closure property is true for division except for zero.

Answer:

2/15 6/15 8/15 9/15 12/15

Step-by-step explanation:

Answer: 2/15, 6/15, 8/15, 9/15, 12/15.

Step-by-step explanation:

Just treat the denominators like they are not there for now, and treat the numerators like they are whole numbers and then rearrange:

8, 2, 9, 6, 12

Now rearrange from smallest to largest:

2, 6, 8, 9, 12

Now just put the denominators back in under the arranged numbers:

2/15, 6/15, 8/15, 9/15, 12/15

Words and their definitions:

Numerator: Top part of the fraction

Denominator: Bottom part of the fraction

The transformation of f (x) exists g (x) = f (x) - 4.

A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

A function that has a positive constant increased to a variable exponent, other than 1, is referred to as an exponential function. By solving at a certain input value, a function is assessed. When the beginning value and growth rate are known, an exponential model can be discovered.

We observed that:

f (0) = 2

For the function g (x) we have:

g (0) = -2

Therefore,

g (x) = f (x) - 4

Looking for intersection with axis and we have:

g (0) = f (0) - 4

g (0) = 2 - 4

g (0) = -2 (correct demonstration)

The transformation of f (x) is: A. g (x) = f (x) - 4

Therefore, the correct answer is option A. g (x) = f (x) - 4.

The complete question is;

Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.

Which of the rules given below shows the transformation of f?

A. g(x) = f(x) - 4

B. g(x) = f(x - 4)

C. g(x) = f(x) + 4

D. g(x) = f(x + 4)

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The building in the drawing is 700 centimeters or 7 meters.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Given 3 meters on real is equal to 7 centimeters on drawing

i.e. 3 meters=7 centimeters

or, 1 meter = 7/3 centimeters

We need to find reading for 300 meters so,

or, 300 meters=7/3*300 centimeters

                        =700 centimeters or 7  meters

Therefore the building in the drawing is 700 centimeters or 7 meters.

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Tracy gets $1299.375 interest after 8 years and 3 months for an investment of  $3,500 at a 4.5% annual interest rate.

What is Simple Interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

The formula for calculating Simple Interest is -

S.I. = (P×R×T)/100

where, P = initial principal balance, R = annual interest rate and T = time (in years)

So, the principal rate, P = $3,500, the interest value, R = 4.5%, and the Time is T= 8.25 years.

Applying the formula for Simple Interest -

S.I. = (P×R×T)/100

S.I. = (3500×4.5×8.25)/100

S.I. = 1299.375

Therefore, the interest amount obtained is $1299.375.

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If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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Answer:

(8, -2)

Step-by-step explanation:

Given:

[tex]\textsf{If P = (8, 2), Find $\sf R_{x-axis}(P)$}[/tex]

[tex]\sf R_{x-axis}(P)[/tex] means to reflect the given point P in the x-axis.

When a point is reflected in the x-axis, the x-value is unchanged, but the y-value becomes negative:

Therefore:

[tex]\sf R_{x-axis}(P)=(8,-2)[/tex]

It will take 9 seconds a pendulum that is 9 meters long to swing back and forth.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE are Given the expression of length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth modeled as;

T = 2√L

Given

Length of the pendulum = 9 meters

Required Time (period)

Substitute the given value into the formula

T =  2√L

T =  2√9

T = 2  x 3

T = 6 seconds

Hence the period is 6 seconds

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Answer:

(3,18)

Step-by-step explanation:

You do not give the center of dilation, so I am using the origin (0,0)

You multiply the x and y by 3

(1,6)

1 x 3 = 3

(1,6)

6 x 3 = 18

(3,18)

One possible set of perimeters for the two figures is 4x and 16x.

Dilation is one of the type of transformation where the size of the object is made smaller or larger without affecting the shape.

Let A be the area of the original figure.

New area after dilation = 16A

Suppose that the figure is a square.

Area of a square is the square of it's side length and perimeter is four times the length of one side.

Let 'x' be the length of a side of the original figure.

Area of the original figure, A = x²

Perimeter of original figure = 4x

New area = 16 A = 16 x² = (4x)²

So the side length of new figure = 4x

Perimeter of new figure = 4 (4x) = 16x

Hence one of the possible set of perimeters for the two figures given is 4x and 16x.

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Step-by-step explanation:

TRY WITH SOME Trigonometric FUNCTION.

IF SOMETHING IS Wrong . I AM STILL A STUDENT

a) Probability of student passed in English and Accounting [tex]= \frac{21}{50}[/tex]

b)  Probability of  Number of Student passed Accounting [tex]=\frac{3}{5}[/tex]

c)  Given that student passed Accounting. Probability that they passed English = [tex]\frac{9}{125}[/tex]

The ratio of favorable outcomes to all possible outcomes of an event is known as the probability.

Here let us assume the Total Number of students is 100.

Students who passes in English = 60% of total number of students  

                                                   =  [tex]60*100/100=60[/tex]

Students who passes in English = 60.

Out of 60 students , 70% of 60 pass in Accounting = [tex]70/100*60=42[/tex]

So Student who passed in both English and Accounting = 42.

Also Number of student that do not passed in English = 100 - 60 = 40.

Out of these 40 students , 45% passes in Accounting = [tex]45/100*40=18[/tex]

So Number of student pass in Accounting but not in English = 18.

Total Number of student pass in Accounting = 42 + 18 = 60.

A) Number of student passed in English and Accounting = 42

   Total Number of student = 100

   Probability of student passed in English and Accounting= [tex]\frac{42}{100} = \frac{21}{50}[/tex]

B) Total Number of Student passed Accounting = 60

    Total Number of student = 100

    Probability of  Number of Student passed Accounting = [tex]\frac{60}{100} = \frac{3}{5}[/tex]

C) Probability that student passed Accounting = 60/100.

    Probability that student passed English = 60/100.

Given that student passed Accounting. Probability that they passed

 English = [tex]\frac{60}{100} * \frac{60}{100} = \frac{3600}{10000} = \frac{9}{125}[/tex]

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The maximum allowable pipe diameter is given as : 0.501. Option B

From the question the interior diameter of the pipe is said to be 0.49

The pipe is said to have the thickness of 0.005 inches.

The exterior diameter of the pipe would be solved as 0.49 + 2 * 0.005

= 0.49 + 0.01

= 0.5

The questions said the variance in the diameter of this pipe is 0.001

Then the maximum allowable pipe diameter would be solved as: 0.001 + 0.5 = 0.501

The diameter of the pipe that is allowable is 0.501

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