Use the given conditions to find the exact values of
sin(2u),
cos(2u),
and
tan(2u)
using the double-angle formulas.
sin(u) = −3/5, 3????/2 < u < 2????
Use the given conditions to find the exact values of
sin(2u),
cos(2u),
and
tan(2u)
using the double-angle formulas.
tan(u) = 5/3, 0 < u < ????/2
Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.
75°
Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.
????/8

Computing a one-sample t-test is appropriate when d) all of the above

A statistical hypothesis test called the one-sample t-test is used to examine whether an unknown population mean differs from a given value. The test is applicable to continuous data. When doing a t-test, it is typical to make the following assumptions: the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and equality of variance in standard deviation.

When performing a one-sample t-test, the data should be collected at random from a population that is generally healthy. When each participant is put into a single group and is present on time, it is suitable. Additionally, it is suitable when the population variance is unknown.

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In an acute triangle, all the three angles are less than 90°.

How do triangles work?

The definition of an acute triangle?

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The answer is regression equation.

What is  regression equation?

The regression of y on x is that the algebraic expression of the regression lines. it's accustomed predict the values of the variable quantity from the given values of freelance variables.

Main Body:

When there is a relation between 2 variables , regression equation is used to describe the relation .

Hence regression equation is the result.

The actual question is like:

Given a collection of paired sample​ data, the​ ____________________ y with caret=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

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The true statements are:

The function is given as D(x) = 2x

The function D(x) is a linear function, and it is also a proportional function

Proportional functions represent direct variation

This means that (b) and (e) are true

Also set x = 5, 6 and -2

D(5) = 2 x 5 = 10

D(6) = 2 x 6 = 12

D(-2) = 2 x -2 = -4

This means that (a) is true

Lastly, the function D(x) is dependent on x for its value

This means that x is the dependent variable.

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Answer:

D. -1,1, -1/7,1/7

Step-by-step explanation:

Use all the factors of the leading coefficient, 7. And also, all the factors of the constant, 1.

Put the factors of the constant on top (numerator). Put the factors of the leading coefficient on the bottom (denominator).

+- 1/1 and +- 1/7

Simplifying:

-1, 1, -1/7, 1/7

That's it. Just list of possibilities of the rational zeroes.

All the Options (1, 2, 3) are correct i.e., A is always similar to A. and  If A is most similar to B, then we can say B is similar to A. and at last If A is most similar to B and B is also similar to C, then A must be similar to C matrix.

Properties of Similar square Matrices : Similar matrices percentage many residences and it's miles those theorems that justify the selection of the word ``similar.'' First we can display that similarity is an equivalence relation. Equivalence members of the family are essential withinside the have a look at of diverse algebras and might continually be seemed as a sort of susceptible model of equality.

Sort of alike, however now no longer pretty equal. The perception of matrices being row-equal is an instance of an equivalence relation we were operating with on account. Row-equal matrices aren't equal, however they may be lots alike. For instance, row-equal matrices have the identical rank. Formally, an equivalence relation calls for 3 situations hold: reflexive, symmetric and transitive. We will illustrate those as we show that similarity is an equivalence relation.

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The equivalent resistance of the circuit is d)11.5 ohms. So, correct option is d.

We know very well that net resistance when resistors are connected in parallel and net resistance when resistors are connected in series is different.

So, we can see that three 4.7kΩ are connected in parallel.

So, using formula of net resistance in parallel

=>1/Rₙ=(1/R₁)+(1/R₂)+(1/R₃)

Therefore,1/Rₙ=1/4.7+(1/4.7)+(1/4.7)

=>1/Rₙ=3/4.7kΩ

=>Rₙ=4.7/3kΩ

=>Rₙ=1.5kΩ

Now, we have net resistance of three resistors.

Now, remaining three resistors are now connected in series

So, using formula of net resistance when resistors are connected in series=Rₙ=R₁+R₂+R₃

So, three resistors have resistance 4.7kΩ,1.5kΩ,5.2kΩ respectively

Therefore, Rₙ=4.7+1.5+5.2=11.5kΩ.

Hence, equivalent resistance is d)11.5kΩ.

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(Complete question) is:

Calculate the equivalent resistance in ohms of the following circuit : a)18100kΩ

b)11470kΩ

c)18.1kΩ

d)11.5kΩ

After solving, the probability that we select a gold marble is 2/31.

In the given question,

A bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles.

So, Total marbles = 2+8+21

Total marbles = 31

As we know that, probability refers to the likelihood that an event will occur. If we don't know how such an event will end out, we can analyze the probability or likelihood of various outcomes. Statistic is the analysis of events that follow a probability distribution.

We have to randomly select one marble from the bag then we have to find the probability that we select a gold marble is

P(G) = Total number of gold marble/Total marbles

P(G) = 2/31

Hence, the probability that we select a gold marble is 2/31.

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The polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on. The standard form of polynomial is given by, f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² .....a₁x + a0, where x is the variable and ai are coefficients.

In the given options, when we analyse

x2 + 3x + 2 is given in standard form that is x2 + 3x + 2

15q 12q2 is not present in standard form

3t3 + 3t2 + 2t 14  is given in standard form

Therefore, the polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14

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The amount of money that Erica owes at the end of 6 years is $8,551.56.

The amount of money that  has in his account would increase at a compound rate each month. Compound growth is when both the amount that was invested and the interest that has already been earned increases at each compounding time.

The formula that can be used to determine the future value with monthly compounding is:

A = P(1 + r/n)^nt

Where:

A = $5300 x (1 + 0.0067)^(6 x 12)

A = $5300 x 1.0067^72 = $8,551.56

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The index value for 5 years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, Year 5: 1,414.74 as it starts at 1000 index points.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement. Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Here,

Market value of the stocks:

Year 1: 2,645 million

Year 2: 2,957 million

Year 3: 3,318 million

Year 4: 3,193 million

Year 5: 3,742 million

Value of Index in 5 years:

Year 1: 1,000

Year 2: 1,117.96

Year 3: 1,254.44

Year 4: 1,207.18

Year 5: 1,414.74

Calculations:

Year 1: 2,645 million / 2,645 million × 1,000 = 1,000.00

Year 2: 2,957 million / 2,645 million × 1,000 = 1,117.96

Year 3: 3,318 million / 2,645 million × 1,000 = 1,254.44

Year 4: 3,193 million / 2,645 million × 1,000 = 1,207.18

Year 2: 3,742 million / 2,645 million × 1,000 = 1,414.74

Since the index starts at 1,000 points, the values for the subsequent years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, and Year 5: 1,414.74.

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Answer:

3 tiles

because 1/4+1/4+1/4=3/4

I hope this helps you!

None of the options are commutative for the given binary operations.

commutative property:

a*b = b*a

* is any binary operation.

Consider option a: subtraction of integers

Let a = 2,  b = 3

a - b = b - a (commutative property)

But

2 - 3  ≠ 3 - 2

-1  ≠ 1 not commutative

Option b: . division of nonzero real numbers

Let a = 2,  b = 3

a/b = b/ a (commutative property)

But

2/3  ≠ 3/2  not commutative

Option c. function composition of polynomials.

Let polynomial be a - b

Let a = 2,  b = 3

a - b = b - a (commutative property)

But

2 - 3  ≠ 3 - 2

-1  ≠ 1 not commutative

Thus, none of the options are commutative for the given binary operations.

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The service life that appear to be out of control is 0.0456 as per the given sample service life.

The sample standard deviation is the root-mean square of the discrepancies between observations and the sample mean: A large divergence is defined as two or more standard deviations from the mean.

The sample standard deviation (s) is the square root of the sample variance and a measure of the deviation from expected values.

It is given that,

Rationale:

UCL=520

LCL=480

Mean [tex]\bar{x}[/tex]=500

The standard deviation of sample([tex]S_{n}[/tex])=11.55

Z(for UCL)=(UCL-Mean)/[tex]S_{n}[/tex]

=(520-500)/10

=2

Similarly, Z(for LCL)=(LCL-Mean)/[tex]S_{n}[/tex]

==(480=500)/10

=-2

Now, by using the z table for finding the confidence level between the Z value of -2 and 2.

Therefore, confidence level=0.4772+0.4772

=0.9544

Risk(alpha)=1-confidence level

=1-0.9544

=0.0456

The service life that appear to be out of control is 0.0456 as per the given sample service life.

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For a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.

It is given to us that -

There is 95% confidence

The margin of error is 0.04

We have to do the estimation of the population proportion.

We know that in case of unknown population proportion, we can assume that the value of population proportion can be regarded as 0.5.

It is known that the formula of sample size is given by -

[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }[/tex] ----- (1)

where,

n = sample size

Z = critical value of Z-value

p = population proportion

E = margin of error

Also, we know that for a 95% confidence interval, Z = 1.960

From the given information, we have

p = 0.5

and E = 0.04

Substituting the values in equation (1), we have

[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }\\= > n = \frac{(1.960)^{2}*0.5(1-0.5) }{(0.04)^{2} }\\= > n = \frac{3.8416*0.25}{0.0016}\\ = > n = 600.25[/tex]

Since this is the value of minimum sample size, rounding up, we have the sample size as 601.

Therefore, for a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.

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By evaluating the exponential equation, we will see that the amount that Erica owes after 6 years is $8551.56

Here we just need to use the exponential equation:

A = P*(1 + r/n)^(n*t)

Where A represents the amount owed t years after, and the other letters represent:

Replacing all that in the given quadratic equation we will get:

A = $5,300*(1 + 0.08/12)^(12*6) = $8551.56

Then the amount that Erica owes is $8551.56

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The vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

Given, an isosceles triangle

and we are asked that is vertex angle congruent to the base angles,

Let suppose ABC is an isosceles triangle with AB = AC

as we know that the angles opposite to the equal sides are also equal.

so, ∠ABC = ∠ACB

now, if ∠ABC = ∠ACB = x

then, on using angle sum property, we get

∠ABC + ∠ACB + ∠BAC = 180°

x + x + ∠BAC = 180°

∠BAC = 180° - 2x

as, x ≠ 180° - 2x

therefore, ∠BAC ≠ ∠ABC

So, the vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

Hence, the vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

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Answer Desisonw 2

Step-by-step explanation:

The Average proportional failure of the instructors is 0.10

From the question  we are told that

Sample size 100  

Instructor    Number of Failures  

Prof. A         13

Prof. B         0

Prof. C         11

Prof. D         16

Confidence level= 0.95

From Z table

Z=1.96

Generally proportion for failure is mathematically given as

proportion of failure = number of failure/ sample size

Prof A

Pa = 13/100

Pa = 0.13

Prof B

Pb = 0/100 = 0

Prof c

Pc = 11/100 = 0.11

Prof D

Pd = 16/100 = 0.16

Average proportional failure = (0.13 + 0.16 + 0.11 +0)/4 = 0.10

Therefore the Range is 0.0412 to 0.1588

Given the range 0.0412 to 0.1588 Prof B and Prof D are outside the Range making them the correct options

Therefore, the Average proportional failure of the instructors is 0.10

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If W(t) denotes the sumo wrestler's weight then the Function's formula will be w(t) = 5.5t + 79.5

Function formula: This relationship is often represented as y = f(x), or "f of x," and y and x are related in such a way that there is a unique value of y for every x; consequently, f(x) cannot have multiple values for the same x.

if we take y = mx + b,

the slope, m = 5.5, we need to find b,

at x = 11 and y = 14

14 = (5.5) (11) + b

b = 79.5

We plug in the qualities for x, y, and m. Then, we rearrange and deduct 60.5 from the two sides.

This makes the equation,

y = 5.5x + 79.5

or we can write as

w(t) = 5.5t + 79.5

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(complete question)

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms.Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).

Write the function's formula.

W(t)=?

Perpendicular lines (or segments) really structure four right points, regardless of whether only one of the right points is set apart with a case.

Let m and n be lines that converge line a. Let m be perpendicular to a. This implies that every one 4 of the points framed by the convergence of m and an are 90°.

Allow n to be opposite to a. This implies that every one 4 of the points framed by the convergence of n and an are likewise 90°.

Since the points are all consistent, this implies that the equivalent side inside points (between lines m and n) are harmonious. In the event that two same-side inside points are harmonious, the lines are equal. In a direction plane, two particular nonvertical lines are equal if and provided that they have a similar slant. Any two vertical lines are equal.

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The fraction of Jonas age represent the age of nick after 6 years is 7/10.

Given that, present age of nick is 8 years and Jonas age is 14 years.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

After 6 years

Nick's age =14 years and Joan's age =20 years

So, the fraction =14/20

= 7/10

Therefore, the fraction of Jonas age represent the age of nick after 6 years is 7/10.

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Answer: neither

What we know:

Process:

Slope of line 1

Set up equation                                                                    y2-y1/x2-x1

Substitute                                                                              9-(-3)/3-(-1)

Simplify                                                                                  12/4

Solve                                                                                      slope = 3

Slope of line 2

Set up equation                                                                   y2-y1/x2-x1

Substitute                                                                             11-1/5-0

Simplify                                                                                 10/5

Solve                                                                                     slope = 2

Relationship

3 is not equal to 2, so they are not parallel

The opposite reciprocal of 3 is -1/3, which is not equal to 2, so they are not perpendicular

Total weight the bowl including the water and fih is 9.22 pound

What does math add mean?

To add is to integrate or bring two things together. The ability to add more than two numbers is then taught to students by building on this understanding. The foundational concept for understanding more complex operations like multiplication and division in higher grades is addition.

Given that :

An empty bowl weighted = 3.4 pound

A water that weighted = 5.12 pound

A fih that weighted = 0.7 pound

Total weight = A bowl + water + fih = 3.4 + 5.12 + 0.7 = 9.22 pound

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There is not enough money left to buy a card for $3.25 but they spend $ 5.88 to buy a gift.

What are combined earnings?

The term "Combined Earnings" refers to the total (without repetition) of (a) the aggregate (without repetition) Dividend Capacity of the Regulated Subsidiaries, (b) EBITDA, and (c) the aggregate (without repetition) tax provision, created in accordance with GAAP, for the Regulated Subsidiaries.

Here, we have

The earnings from Wednesday of Samuel and Jason are:

Samuel earnings = 12.5 x 0.40 = $5

Jason earnings = 7.1 x 0.40 = $2.84

The combined earnings from Wednesday are as follows:

Combined earnings = Samuel's earnings + Jason's earnings

Combined earnings = $5 + $ 2.84 = $ 7.84

The spended earnings are:

Spended earnings = combined earnings x ¾

Spended earnings = 7.84 x ¾ = $ 5.88

The leftover is:

 Leftover = combined earnings – spended earnings

 Leftover = 7.84 – 5.88 = $ 1.96

Hence, they spend $ 5.88 to buy a gift but not enough money to buy a card for $3.25.

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Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L

According to our question-

Qin = 4 000m3/day

Cin = 25mg/L

V = 20 000m3

k = 0.25/day

Find: Count = ?

outStarting from the mass balance equation for steady state 0 = QCin - QCount - kCountV

manipulate the equation to get:

\(Count=Cin(Q/Q+kV)\)  

Then simple plug in your givens:

Count = (25mg/L)((4000m3/day)/(4000m3/day + 0.25/day(20000m3))

Count = 11mg/L

Hence, Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L.

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The monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75 is 64

Z-score gives you an idea of how far from the mean a data point is.

it’s a measure of how many standard deviations below or above the population mean a raw score is. A z-score can be placed on a normal distribution curve. Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve).

The basic z score formula for a sample is:

z = (x – μ) / σ

According of the question,

Monthly utility bills in a city follows normal distribution

Mean of the monthly utility bills in a city : μ = $70

A standard deviation of monthly utility bills in a city : σ = $8

Z-score of utility bill = -0.75

z - score = x - μ / σ

=> - 0.75 = x - 70 / 8

=> -6 = x - 70

=> x = 70 - 6

=> x = 64

Hence , the x-value is 64

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A rectangle's area of 28cm2 (measured in cm2) is numerically equal to 4 times the rectangle's circumference (measured in cm). The rectangle's length to width ratio is 5:2.

Given,

l/b = 5/2

l = 5b/2

area = 4 times the rectangle's perimeter,

which equals 4*2(l+b)

= 8(l+b)

= 8(5b/2 + b)

= 28b cm2.

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