using partial quotients 5,166 divide by 42

Answer:

solution given;

let

AB=a

AC=b=30ft

AB=c=20ft

<A=115°

By using Cosine rule.

a²=b²+c²-2bc cos angle

a²=30²+20²-2*30*20 Cos 115°

a²=1807.1419

a=√[1807.1419]

a=42.51

Side A is 42.51ft.

Again

Cos B=\( \frac{a²+c²-b²}{2ac} \)

Cos B=\( \frac{42.51²+20²-30²}{2*42.51*20} \)

Cos B=0.7687

<B=Cos -¹(0.7687)

<B=39.46°

Angle B is 39.46

___________________________________

\(\quad\quad\quad\quad\tt{ \angle{A = 115° }}\)

\( \tt{\overline{A}²=b²+c²-2bc \cos( \angle{a}) }\)

\( \tt{\overline{A}²=(30)²+(20)²-2(30)(20) \cos( \angle{115°}) }\)

\( \tt{\overline{A}²=900+400-2(600) \cos( \angle{115°}) }\)

\( \tt{\overline{A}²=1300-1200 \cos( \angle{115°}) }\)

\( \tt{\overline{A} ²=1807.1419}\)

\( \tt{\overline{A}= \sqrt{ 1807.1419}}\)

\( \pink {\boxed{ \tt{ \overline{A}=42.51}}}\)

\( \tt{ cos\;B = \frac{ {a}^{2} + {c}^{2} - {b}^{2} }{2ac} }\)

\( \tt{ cos\:B = \frac{ {42.51}^{2} + {20}^{2} - {30}^{2} }{2(42.51)(20)} }\)

\( \tt{ cos\:B = 0.7687}\)

\( \tt{ \angle{B} = { \cos}^{ - 1} (0.7687)}\)

\(\pink{\boxed{\tt{ \angle{B} = {39.46°}}}}\)

___________________________________

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✍︎ C.Rose❀

The value of the angle θ is approximately 24.2 degrees to 1 decimal place.

In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Given that tan θ = 23/52, we can find the value of the angle θ.

To find the value of θ, we can use the inverse tangent or arctan function. Taking the inverse tangent of both sides of the equation, we have:

θ = arctan(23/52)

Using a calculator or trigonometric tables, we can evaluate the inverse tangent of 23/52. The result is approximately 24.2 degrees.

Note that in the context of a right-angled triangle, the tangent function is defined for acute angles (less than 90 degrees). Since 0 degrees is the smallest possible angle, it is considered an acute angle in this case.

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Answer:

64 ft

Step-by-step explanation:

square root of 256 is 16. so each side is 16 ft.  16*4=64

The total length of wood is 16 feet

Area of a Square = Side × Side.

Therefore, the area of square = Side2 square units.

Given:

Area of square = 256 square feet

Now,

Area of square = 4*side

256 = side * side

side ²= 256

side = √256

side =16

Hence, the length of wood is 16 feet.

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The width of the river is 43.3 m.

Given that a scene in which we need to find the width of the river,

The surveyor looks around and discovers the specified measurements. In order to obtain the solution, she used a pair of similar triangles.

Using the definition of similar triangles,

Similar triangles are geometric figures that have the same shape but not necessarily the same size.

They have corresponding angles that are congruent and corresponding sides that are proportional.

So,

AB / DE = AC / CD

AB / 18.6 = 79.6 / 34.2

AB = 43.3

Hence the width of the river is 43.3 m.

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Answer:

4 Pieces

Step-by-step explanation:

8 ÷ 2 = 4

Answer:

Step-by-step explanation:

Hello there!

He has 8 ft of wood, and he needs each peice to be 2 ft long. To solve this, we divide 8 ft by 2 ft (this will determine how many 2 ft peices can be cut from 8 ft). 8 ÷ 2 = 4, so this means he can cut four peices of wood to build the doghouse for Chester!

I hope this answer helped you! If it did, please rate it and give it a Thanks!

Have a wonderful day!

The cost per ounce of the premium walnut is $0. 23

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

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Answer:

  5/10

Step-by-step explanation:

An equivalent fraction will have the numerator and denominator multiplied by the same value.

The denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...

  \(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)

The value of the rational expression when x is equal to 4 is 2. The correct answer is option C: 2.

To find the value of the rational expression (x - 12)/(x - 8) when x is equal to 4, we substitute x = 4 into the expression:

[(4) - 12]/[(4) - 8]

Simplifying the numerator and denominator:

(4 - 12)/(-4)

Further simplifying the numerator:

(-8)/(-4)

Now, we can divide -8 by -4:

(-8)/(-4) = 2

So, when x is equal to 4, the value of the rational expression is 2.

Therefore, C is the right response.

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When the relation between two variables is a linear relation, the rate of change between any two pairs of values for those two variables is the same. That is why we get the same answer no matter if we use consecutive rows from the table or not.

Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

Answer:

C

Step-by-step explanation:

Answer:13

Step-by-step explanation:

A company's income tax liability is referred to as "deferred tax liability" when it is not paid in full during the fiscal year. This record is accounted for on the accounting report of the organization as an obligation.

Taxable income is the sum of the following: pre-tax financial income, insurance costs, depreciation, and 154,000 dollars. Taxable income is $148,000.

A listing on a company's balance sheet known as a "deferred tax liability" records taxes that are owed but will not be paid until a later date.

It varies. There are two kinds of deferred tax items: a liability and an asset. The first one is the money that the company owes (the deferred tax liability), and the second one is the money that the company is owed (the deferred tax asset).

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According to the trigonometric relations in a right triangle, the following relation is valid:

the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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Answer:

The answer is D.

Step-by-step explanation:

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

B

NNzbbxhsnjajajbajajajajakakkakajabsbd

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

The total cash due at signing is $3,700 at the local dealership..

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

The total cash due is calculated as:

Down payment: $1,800

Security deposit: $400

Acquisition fee: $300

Total: $1,800 + $400 + $300

Apply the addition operation, and we get

= $3,700

Thus, the total cash due at signing is $3,700.

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ANSWER:

15.71 inches

STEP-BY-STEP EXPLANATION:

Given:

Radius: 6 inches

Angle: 150°

We are asked to calculate the length of the long run. We can calculate this distance by multiplying the ratio of the angles by the circumference, just like this:

The distance traveled is 15.71 inches

The experimental probability of the computer generating a 3 or a 4 will be 28%.

Experimental probability can be found in the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event;

\(P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}\)

We are given that a computer generates 75 integers from 1 to 8 at random. The results are recorded in this table.

Outcome;

1 2 3 4 5 6 7 8

Number of times outcome occurred;

12 16 9 12 4 7 5 10

Therefore,

P_e(E) = 9 + 12 /2

P_e(E) =28%

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Answer:28%

Step-by-step explanation:
i took the quiz<33

Total earnings for an 8-year period is - 378520 dollars.

The salaries, year by year, can be written in a sequence

           40000,  40000 + 2090 , 40000 + 2(2090)......

which is an arithmetic sequence, with

                         a=40,000  , d=2090

and the general term

                        \(a_{n}\) = 40000 + 2090 (n - 1)

gives the salary at the beginning of year n.

Recall that for the arithmetic sequence,

              \(a_{n}\) = \(a + (n - 1 )d\)

the nth partial sum is given by either of the equivalent formulas:

              \(S_{n} = \frac{n}{2} [2a + (n - 1 )d ]\)

we find \(S_{8}\) = the sum of the first 8 salaries:

            \(S_{n} = \frac{8}{2} [2. 40000 + (8 - 1 )2090 ]\)

                 = 4 [ 80000 + 7 × 2090 ]

                 = 4 [ 80000 ++ 14630 ]

                 = 4 × 94630

                 = 378520

So, total earnings for an 8-year period is - 378520 dollars.

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Answer:

Step-by-step explanation: !!DISCLAIMER IM NOT ALWAYS THE SMARTEST BUT IM PRETTY SURE THIS IS RIGHT!

!well what I did. You know that 60 minutes=one hour. So I put 2 & 1/2 over 60.

Make 2 & 1/2 a improper fraction=5/2.

So 5/2 over 60

Then divide. 5/2 divided by 60 ( which is 60/1)

Then leave change flip, meaning leave the 5/2 change the division sign to multiplication, and flip, which you would flip 60/1 to 1/60

So we have 5/2 times 1/60. Multiply across. 5 times 1= 5. 2 times 60=120

So we have 5/120

Now we simplify 120 divided by 5 = 24. And 5 divided by 5 = 1

So 1/24

That’s all I know.. I know it didn’t have the answers but I hoped it help a bit

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In option (c) A boxplot of the data has a large outlier, we would not be safe constructing the interval based on an SRS of size 24 from the population.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Constructing a one-sample t interval for a population mean is generally safe when the population is not Normal, as long as the sample size is large enough (usually at least 30) or the sample is taken from a population that is not too skewed or has outliers.

Therefore, options (a), (b), and (e) suggest that the sample may come from a population that is roughly Normal or can be transformed to be Normal, and so constructing the interval based on an SRS of size 24 would be safe.

Option (d) suggests that the sample standard deviation is large, but this does not necessarily mean that constructing the interval would not be safe.

It may reduce the precision of the interval, but as long as the sample size is sufficient, the interval can still be constructed.

Option (c) suggests that the sample has a large outlier, which may significantly affect the distribution of the sample and the calculation of the interval.

Therefore, in this circumstance, constructing the interval based on an SRS of size 24 would not be safe.

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Answer:

x*y+2

Step-by-step explanation:

The number of roots in the equation x² - 6x + 9 = 0 is two, ( x = 3 ) double roots.

A quadratic equation in its standard form is expressed as;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the quadratic equation in the question;

x² - 6x + 9 = 0

Compared to the standard form ax² + bx + c = 0

Plug a, b and c into the quadratic formula and solve for x.

x = ( -(-6) ±√((-6)² - 4×1×9 )) / (2×1)

x = ( 6 ±√(36 - 36 )) / (2×1)

x = ( 6 ±√(0 )) / (2)

x = ( 6 ± 0 )/ 2

x = (6-0/)2, x = (6+0)/2

x = 6/2, x = 6/2

x = 3, x = 3.

Therefore, the value of x is 3 ( double root ).

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Answer:

dy/dx = 6x(x²-3)cos2x - 2(x²-3)³sin2x

Step-by-step explanation:

We use the Product Rule:

y= (x²-3)³cos2x

dy/dx =   (x²-3)³ d(cos2x)/dx + cos2x * d ((x²-3)³)/dx

=   (x²-3)³ * -2sin2x + cos2x * 3(x²-3)*2x

= -2sin2x*(x²-3)³ + 6xcos2x*(x²-3)

=  6x(x²-3)cos2x - 2(x²-3)³sin2x

Yes, all of the conditions for inference have been met to carry out a t-test for a difference in means.

Three main conditions need to be satisfied: the random condition, the 10% condition, and the Normal/large sample condition.

The random condition is met because the real-estate agent randomly assigned the homes to be staged or empty. This ensures that the sample is representative of the population of comparable homes.

The 10% condition is met because the agent selected 10 comparable homes, and the sample of 5 staged and 5 empty homes represents less than 10% of the population of comparable homes.

The Normal/large sample condition is met because the dot plot of each sample shows no strong skewness and no outliers. Additionally, with a sample size of 5 for each group, the t-test can still be valid even if the population distributions are not exactly normal.

Therefore, all the conditions for inference have been met, allowing the real-estate agent to carry out a t-test for a difference in means and test the hypothesis regarding the selling prices of staged and empty homes.

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