How do you find the measure of the side of a triangle using the law of cosines?.

At random a baby born in the united states in 2014 is 3.

Part - A:

All probabilities are between 0 and 1. The probabilities also add to 1 and therefore account for all possible birth orders (9th or higher birth order being included in the "g" group)

Probability of event - "A woman gives birth in 2014 to her third child":

P(X = 3) = 0.168

Part - B:

P(X ≤ 2) = P(X = 1) + P(X = 2)

= P(X ≤ 2) = 0.391 + 0.319

= P(X < 2) = 0.710

P(X > 5) = P(X = 6) + P(X = 7) + P(X = 8)

= P(X > 5) = 0.012 + 0.005 + 0.005

= P(X ≤ 2) = 0.022

Therefore, the correct expression is: X = 3.

Hence the answer is, at random a baby born in the united states in 2014 is 3.

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Using the exponential function given y = 7.1(1.03)ˣ, the amount produced in 2006 was 7.8 billion pounds and the estimated amount in 2014 is 9.8 billion pounds

An exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

In the function given;

y = 7.1(1.03)ˣ

a) What is the estimated number in 2006

We can find the value of x in 2006 as

2006 - 2003 = 3

x = 3

Let's substitute the values into the formula above;

y = 7.1(1.03)³

y = 7.76 ≅ 7.8 billion pounds

b)

The cheese produced in 2014

x = 2014 - 2003 = 11

Plug in the value

y = 7.1(1.03)¹¹

y = 9.83 ≅ 9.8 billion pounds

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The estimate of the total cheese production in 2006 is 7.8 billions of pounds.

The estimate of the total cheese production in 2014 is 9.8 billions of pounds.

[tex]y =7 .1( {1.03})^{x} [/tex]

Where,

The total cheese production in 2006;

x = 3 years

[tex]y =7 .1( {1.03})^{x} [/tex]

[tex]y =7 .1( {1.03})^{3} [/tex]

[tex]y =7 .1(1.092727)[/tex]

y = 7.7583617 billions of pounds

Approximately,

y = 7.8 billions of pounds

The total amount of cheese produced in 2014;

x = 11

[tex]y =7 .1( {1.03})^{x} [/tex]

[tex]y =7 .1( {1.03})^{11} [/tex]

[tex]y =7 .1(1.3842338707244)[/tex]

y = 9.8280604821435

y = 9.8 billions of pounds

In conclusion, the estimated production of cheese in 2006 and 2014 are 7.8 and 9.8 billions of pounds respectively.

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Answer: ∠1= 60° ∠2=120° ∠3=60° ∠4=60° ∠5=120° ∠6=120° ∠7=60°

Step-by-step explanation: hope this helps!

please give brainliest!

Answer:

1. 60°

2. 120°

3. 60°

4. same as 1. 60°

5. same as 2. 120°

6. same as 2 and 5, and the angle given of 120°

7. same as 1. and 3. 60°

Step-by-step explanation:

You are given an angle of 120°

The lines are parallel, and the transversal gives you all the answers. All have to add up to 360°.

The average number of credit hours per semester for all students at the local college is 9.2.

It is given that,

at the local college a study sound that students earned an average of 9.2 credit hours per semester.

⇒ x = 9.2 credit hours per semester

Therefore by the central limit theorem,

x = μ  = 9.2 credit hours per semester

The central limit theorem states that the distribution of a sample variable approximates a normal distribution as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.

Therefore the average number is 9.2 credit hours per semester for all students at the local college.

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The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

Given that,

The lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

We have to find identify the container's dimensions and maximum volume.

We know that,

2(x+y)=4

x+y=2

Now,

Volume is π(x/2)²y

=π(x²/4)(2-x)

=π(f(x))

Now, volume will be maximum when f(x) will be max,

f(x)=x²/4(2-x)

f'(x)=2x(2-x)-x²

f'(x)=4x-3x²

We get,

f'(x)=0

4x-3x²=0

x(4-3x)=0

x=0, 4-3x=0

x=4/3

y value is 2-4/3=6-4/3=2/3

Therefore, The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.

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D'(5) is the expression that gives the rate of change at which the depth is changing at 5 minutes

A rate of change describes the rate at which one quantity changes in relation to another quantity.

Also, the derivative of a function can be found by determining the average rate of change of the function. Thus, these two terms are used interchangeably.

Given: The depth of a rain puddle D(t) is given in inches, and t is given in minutes.

The rate of change of D(t) is the derivative of D(t) which is written as D'(t).

Therefore, the expression that gives the rate of change at which the depth is changing at 5 minutes will be D'(5)

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The result of subtracting and simplifying the rational expression in its fully factored form is [tex]\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}[/tex]

From the question, we are to subtract the rational expressions and express in the factored form

The given expression is

[tex]\frac{n^{2} + 5n - 36 }{n^{2} -25} - \frac{n^{2} +8n +15 }{5n^{2} -125}[/tex]

Factor 5n² - 125

[tex]\frac{n^{2} +5n - 36 }{n^{2} -25} - \frac{n^{2} +8n +15 }{5(n^{2} -25)}[/tex]

[tex]\frac{5(n^{2} +5n - 36) - (n^{2} +8n +15) }{5(n^{2} -25)}[/tex]

[tex]\frac{5n^{2} +25n - 180 - n^{2} -8n -15 }{5(n^{2} -25)}[/tex]

Simplify

[tex]\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}[/tex]

Hence, the expression is [tex]\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}[/tex]

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The combined thickness is 7/8 inches.

The installation over the pad indicates they are joined vertically. So, the combined thickness will be sum of individual thickness of carpet and pad. Hence, calculating the thickness now.

The thickness of the carpet and pad = thickness of carpet + thickness of pad

Keep the values in equation

The thickness of the carpet and pad = 3/8 + 1/2

Taking LCM on Right Hand Side, we get 8

Adding the fractions

The thickness of the carpet and pad = (3 + (1×4))/8

The thickness of the carpet and pad = (3 + 4)/8

The thickness of the carpet and pad = 7/8

Hence, the thickness of the carpet and pad is 7/8 inches.

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The correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3

The two given graphs are isomorphic in nature

In the firsts graph, the serial order is u1, u2, u3, u4, u5

wherease in the second graph the order is v1, v2, v4, v5, v3

Upon analysis, it can be seen that  the correct mapping (an isomorphism) between the sets of vertices of the two graphs is

f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3

Then the correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3.

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Using Conditional Probability,

the probability that the sum of the numbers appearing on the two dice is 8, if 3 appears on the first is 1/5.

We have given that,

Two dice are thrown. Let S be the sample space S={1,2,3,4,5,6×{1,2,3,4,5,6}

Total number of possible outcomes (n(S)) =36

Let A ≡ the event that the sum of the numbers coming up is 8

and B ≡ the event of occurrence of 3 on the first die.

A ≡{(3,5),(6,2),(4,4),(5,3),(2,6)}

favourable cases for A (n(A) )= 5

B≡{(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)}

favourable cases for B (n(B)) = 6

Now, A int B = { (3,5 ) } = 1

favourable cases for AnB (n(An B) )= 1

Probability of event A occur (P(A)) = 5/36

Probability of event B occur (P(B)) = 6/36

Probability of event B occur (P(AnB)) = 1/36

we have to calculate probability the sum of the numbers appearing on the two dice is 8, if 3 appears on the first i.e., P(A/B) --> Conditional Probability

Required probability, P(A/B) = P(ANB)/ P(B)

=> P(A/B) = 1/36/5/36 = 1/5

Hence, the required probability is 1/5.

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The value of x for the given geometric figure by similar triangle property will be 4.67.

If two figures look an exact shape but their size could be small or big then both figures are called similar figures.

For example, a square with a side of 10 cm and another with a side of 20 cm both square will be similar.

When anything has identical pieces facing one another or revolving around an axis, it is said to be symmetrical.

The given figure has three parallel lines and two transversals.

By similar triangle property

x/3.5 = 4/3

x = (4/3)3.5 = 4.67

Hence "The value of x by similar triangle property will be 4.67".

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With a one-way ANOVA, you are comparing the T Statistic with the T critical value.

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z-test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

The critical value should be compared to the test statistic. The alternative hypothesis should be accepted in place of the null hypothesis if the test statistic is more extreme in the alternative's favor than the critical value. The null hypothesis should not be rejected if the test statistic is less extreme than the critical value.

Thus, with a one-way ANOVA, you are comparing the T Statistic with the T critical value.

The question is incomplete, the complete question is"

With a one-way ANOVA, you are comparing the _____ with the _____.

A. T Statistic with the T critical value

B. F Statistic with the F critical value

C. Correlation coefficient with the confidence interval

D. Outlier with the 4th quartile outer-most limit

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It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.  

A quadrilateral that has two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

Here we have proof of Parallelogram

To get correct statement 6 let's rewrite the whole process from the start

Given that GHIK is a parallelogram, m ∠GHJ = 60° and JKL is a line

Here we need to prove m∠LKG = 120°  

   Statement                                  - Reason

1. GHIK is a parallelogram              -  Given  

2. m ∠GHJ = 60°                             -  Given

3. JKL is a line                                 -  Given

4. m ∠JKL = m∠LKG + m∠JKG       -  On line-segment, ∠JKL is equal to the

                                                           the sum of Non-overlapping parts

                                                            m∠LKG and m∠JKG  

5. m ∠JKL = 180°                            - Angle formed by a straight line is 180°  

6. 180°= m∠LKG + 60°                   - In a parallelogram opposite angles are

                                                         equal i.e m∠JKG = m∠GHJ = 60°

7. m∠JKG = m∠GHJ                       - Transitive/ Substitution

9. m∠LKG =  180° - 60°      

10. m∠LKG =  120°                          - from statement 6

Therefore,

It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.    

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The possible key design is 262144.

Algebra is a branch of mathematics that uses mathematical expressions to aid in the representation of problems or situations. In algebra, we use numbers with definite or fixed values, such as 2, -1, 0.5, and so on. In algebra, variables such as x, y, and z are used in addition to numbers.

Given that keys for antique cars had nine parts, with four patterns for each part

We have to determine how many different key designs are possible for these cars

Number of designs possible

= 4x4x4x4x4x4x4x4x4

= 4^9

= 262144

Therefore the possible key design is 262144

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The answer to the poition will be t²/2 which is the displacement of the car.

What is displacement?

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

The given acceleration is given in the function of velocity, v(t) = t

Let, be the function of velocity v(t) and position is x(t).

So the poition will be ∫v(t) dt = ∫t dt

=t²/2

Hence, the position of the given function will be t²/2

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Linear velocity of a person riding is 5.6 ft/s and time for one revolution of ferries wheel is 31.8 sec.

What is linear velocity?

Linear velocity, v, is defined as the rate of change of linear displacement, s, with respect to time, t.

On a ferries wheel, displacement = circumference of the wheel = 2πr

Hence linear velocity, v = 2πr/T

According to the given question:

Diameter of the wheel is 80 feet

So, radius of wheel = 40 feet

If Ferris wheel makes one revolution is 45 seconds

Then linear velocity

v = 2πr/T = 2 x 3.14 x 40/45

v = 5.6 ft/s

If linear velocity of a person riding on wheel is 8 ft/s then time for one revolution

T = 2πr/v = 2 x 3.14 x 40/ 8

T = 31.8 sec

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The value of x is 11

What is supplementary angle ?

Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.

Angles ∠1 and ∠7 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.

∠ 1 = ∠ 7

∴2x + 5 = 4x - 17

4x - 2x =17+5

 2x = 22

   x = [tex]\frac{22}{2}[/tex]

   x = 11

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By using the cross multiplication, we can determine the solutions to the equation  w=2 , w=6.

By multiplying the numerator of one side by the denominator of other side and equating the resulting two products, cross multiplying can be used to solve a fractional equation when each side has a fraction with a single denominator.

Given the expression [tex]\frac{w}{2w-4} = \frac{4}{w}[/tex]

By using cross multiplication, we have

[tex]w^{2} = 4(2w-3)\\ w^{2} = 8w-12\\w^{2}-8w+12=0\\(w-2)(w-6)=0\\w=2 and w=6[/tex]

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Answer:

Step-by-step explanation: 20% to 50%

In the samples, the percent of students that bike to school varies from 20% to 50%.

In the data plot, 10 is the minimum and 25 is the maximum so 10/50= 0.2 or 20%. 25/50= 0.5 or 50%. Meaning it should vary from 20% to 50%.

10 units is the length of the line segment

Given that: the graph of the line segment from negative 6 comma negative 5 to 0 comma 3. Thus:

point 1 (-6, -5) => x1 = -6, y1 = -5

point 2 (0, 3) => x2 = 0, y2 = 3

Length of x-axis (x): x2 -x1 = 0-(-6) = 6

Length of y-axis (y): y2 -y1 = 3-(-5) = 8

Let the length of the line segment be L

Using Pythagorean Theorem:

L² = x² + y²

L² = 6² + 8²

L² = 36 + 64

L² = 100

L = √100 = 10 units

Therefore, the length of the line segment is 10 units. The 3rd option is the answer

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The volume and the surface area of the right cylinder are equal to 175π cubic inches and 120π square inches.

In order to determine the volume (V) in cubic inches and the surface area (A) in square inches of the solid, we must know the dimensions of a right cylinder, whose height (h) in inches and radius (r) in inches are shown in the figure. Below is a description of the formulas:

Here Volume of the cylinder,

V = π · r² · h

Surface area of the cylinder,

A = 2π · r² + 2π · r · h

If we know that r = 5 in and h = 7 in, then the volume and the surface area of the cylinder are, respectively:

Volume is,

V = π · ( 5 in )² · ( 7 in )

V = 175 π in³

Surface area is,

A = 2π · (5 in)² + 2π · (5 in) · (7 in)

A = 120π in²

Therefore volume and surface area of cylinder is 175 π in³ and 120π in².

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There is a total of 190 ways to share apples between them.

What is a ball-and-urn method?

The ball-and-urn method often referred to as stars-and-bars, sticks-and-stones, or dots-and-dividers is a typical combinatorial method.

It is used to resolve issues of the following type: in how many different ways can one divide 'k' undifferentiable items into 'n' distinct bins?

Use the ball-and-urn method,  Let Alice get 'x' apples, Becky get 'y' apples, and Chris get 'z' apples.

⇒x + y + z = 24

We can manipulate this into an equation that can be solved using the ball-and-urn method

All of them get at least 2 apples, so we can subtract 2 from x, 2 from y, and 2 from z.

⇒(x - 2) + (y - 2) + (z - 2) = 18

Let x' = x - 2, y' = y - 2, z' = z - 2.

⇒ x' + y' + z' = 18

We can allow either of them to equal 0, hence this can be solved by the ball-and-urn method.

By the ball-and-urn method, we get

 [tex]$\binom{18 + 3 - 1}{3 - 1} = \binom{20}{2} = \ 190}$.[/tex]

Hence, there are 190 ways to split the apples among them.

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By using completing the square method, the value of x in the given equation (x - 12)(x + 4) = 9 is: D. x - 4 = ±√73

In Mathematics, the standard form of a quadratic equation is given by:

ax² + bx + c = 0.

In this exercise, you're required to determine the value of x in the given equation by using completing the square method. Therefore, we would expand the equation as follows:

(x - 12)(x + 4) = 9

x² - 8x - 48 = 9

Adding 48 to both sides of the equation, we have:

x² - 8x - 48 + 48 = 9 + 48

x² - 8x = 57

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 8x + (8/2)² = 19 + (8/2)²

x² - 8x + 16 = 57 + 16

x² - 8x + 16 = 73

Factorizing the quadratic equation, we have:

(x - 4)² = 73

Taking the square root of both sides of the quadratic equation, we have:

x - 4 = ±√73

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Complete Question:

Use completing the square to solve for x in the equation (x - 12)(x + 4) = 9.

A. x = -1 or 15

B. x = 1 or 7

C. x - 4 = ±√41.

D. x - 4 = ±√73

The half life for this radioactive substance is 40.76 years

As we know that radioactive decay is a first order reaction

For first order reaction, we can write

N = [tex]N^{0}[/tex][tex]e^{-kt}[/tex]

Where N = Amount of substance at time ‘t’

N0 = Initial amount of substance

K = rate constant for first order reaction

t = time in years

Now, as per the question,

This substance is decaying at a rate of 1.7% that means 98.3% will remain after decaying.

For time t = 1 years , N/[tex]N^{0}[/tex] = 0.983

Therefore, we have

N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]

0.983 = [tex]e^{-k }[/tex]

-k = ln(0.983)

-k = -0.017

K = 0.017 [tex]year^{-1}[/tex]

Now for half life, We can write N/[tex]N^{0}[/tex] = 0.5

Therefore, N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]

              0.5 = [tex]e^{-0.017t}[/tex]

ln(0.5) = -0.017t

-0.693 = -0.017t

t = 0.693/0.017 = 40.76 years

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Using linear functions, the inequality for the times when Valente is closer than Chiamaka to the university is:

170 + 110t < 149 + 95t

What is a linear function?

Linear functions have a straight line as their graph. The following is the form of a linear function. y = f(x) + a+bx There is one independent variable and one dependent variable in a linear function.

Solution:

Considering the initial distance as the intercept and the velocity as the slope, the linear functions for the distances of each Chiamaka and Valente are given as follows:

C(t) = 149 + 95t

V(t) = 170 + 110t

Valente is closer when:

V(t) < C(t)

Hence the inequality is:

170 + 110t < 149 + 95t

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Answer:

Step-by-step explanation:

C=1.75m+10.50

Answer:

Step-by-step explanation:

The answer is D

The solutions are,

1. True

2. False

3. True

4. False

For all the given statements the true or false are,

A, X and D are n X n matrices.

1. A is diagonalizable if A XDX⁻¹ for some diagonal matrix D and some invertible matrix X.

→ True

2. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities.

→ False, It always has n eigenvalues, counting multiplicity.

3. If A is diagonalizable, then A is invertible.

→ True, In this case, we can construct a P which will be invertible. And a D.

4. If there exists a basis for R" consisting entirely of eigenvectors of A, then is diagonalizable.

→ False, It's invertible if it doesn't have zero an eigenvector but this doesn't affect diagonalizability.

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To prove the sum of all the intercepts = k^2

xi + yj +zk = k^2

The gradient of the function f(x,y,z) = s

f(x,y,z = 1/2sxi + 1/2 syj =1/2 szk

And the tangent plane at the point (xo,yo,zo) is

sx/x +  sy/y +  sz/z

=  sxo/xo +   syo/yo +  szo/zo

=>  sxo/xo +   syo/yo +  szo/zo = k       ........(1)

To find the x intercept , we set y =z=0 and obtain x = ksxo/sx. similarly, y = ksyo/yo and z= kszo/zo. their sum is

ksxo/xo + ksyo/yo + kszo/zo

=k( sx0/xo + syo/yo + szo/zo)

=k.k = k^2   ...from eqn 1

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Answer:

f-(9-2)

f-7

Step-by-step explanation: