A family rents a truck to move from Buffalo to Chicago. The rental has a base cost of $49.95, plus, an additional cost of $1.19 per mile driven. The family also pays for gas, which costs $3.89 per gallon. The truck’s average gas mileage is 18 miles per gallon. The family decided to take a rest in Cleveland, what would be the distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85?

(X=60,Y=47,Z=73),  the measures of the three angles.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question

x+y+z=180

The second and third angles' combined measurements equal twice the first angle's combined measurement, therefore

y+z−2x+y+z=2=0

Third angle has 26 more degrees than second angle, therefore

z−y+z=y+26=26

As a result, we obtain the equation system.

x+y+z=180−2x+y+z=0−y+z=26

(1)(2)(3)

By removing y and z, use equations (1) and (2) to determine x. To get rid of y and z, multiply equation (2) by one before adding it to equation (1).

x+y+z2x−y−z3xx=180=0=180=60(4)

To get rid of z, use equations (1) and 3). To get rid of z, multiply equation (3) by 1 and then add it to equation (1).

x+y+zy−zx+2y=180=−26=154(5)

To determine, substitute x=60 into equation (5).

x+2y(60)+2y2yy=154=154=94=47

In order to find, we can now change x=60 and y=47 in equation (1).

x+y+z(60)+(47)+zz+107z=180=180=180=73

Therefore, there is a solution.

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The inequality of the  graph is  x > -3, and Negated inequality of the graph is x ≤ -3

How to solve inequality?

The inequality is represented as negative one-fifth is greater than or equal to the product of negative two-thirds and a number.

We have,

Given the graph line,

Write both an inequality and a negated inequality that describe this graph:

Let

The inequality of the  graph is  x > -3

Negated inequality of the graph is x ≤ -3

Hence, the inequality of the  graph is  x > -3, and Negated inequality of the graph is x ≤ -3

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(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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Answer:

10:7

Step-by-step explanation:

40:28 are both divisible by 4. 40/4 is 10. 28/4 is 7. So the ratio would be 10:7 since neither is divisible by both the same number, this is the final ratio.

Throughout a hypothesis test, the alternative hypothesis is assumed to be true.

Answer :-FALSE

What is hypothesis test ?

in hypothesis test we compare p-value with level of significance and conclude our null hypothesis is true or not true.

p-value decided null hypothesis is true or not true.

p-value <= level of significance then null hypothesis is true.

We do not say alternative hypothesis is assumed to be true.

Therefore Correct Options

FALASE

No matter what the conclusion of a hypothesis test is, neither the null or alternative hypothesis has been proven to be true.

Answer :- TRUE.

Because,

Yes, no matter what was the conclusion of hypothesis test.

We set always our claim in alternative hypothesis and conclude about the null hypothesis.

We check null hypothesis is true or do not true.

That's reason Correct Options TRUE.

When drawing a conclusion to a hypothesis test, compare the calculated p-value to the calculated test statistic.  

Answer :- FALSE

Because,

We Calculate the test statistic.

Using this test Statistic we calculate p-value

We compare p-value with level of significance and conclude it.

That's reason statement is false. We do to compare p-value and test statistic.

As a p-value approaches 0 it is more likely the hypothesis test conclusion will be "reject the null hypothesis.".

Answer :- TRUE

Because,

p-value is the probability that test hypothesis is accepted or rejected.

We compare always p-value with level of significance.

p-value < 0.05

We reject the null hypothesis.

In given problem p-value = 0

That is we reject the null hypothesis.

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0.26 is  probability that a graduating senior receives two or three job offers.

What is probability in math?

Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.              

                                             Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.

P(2 or 3 jobs)=P(2 jobs)+P(3 jobs)-P(2 jobs and 3 jobs)=P(2 jobs) + P(3 jobs) since a student can not have 2 jobs as well as three jobs at a time.

So,

P(2 or 3 jobs)=0.15+0.11 = 0.26

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Answer:

[tex]a=4, b=-8, c=-12[/tex]

Step-by-step explanation:

Compare the given equation with the general form [tex]y=ax^2 + bx+c[/tex].

The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output is true.

Deep learning is part of machine learning methods and is based on artificial neural networks with representation learning. It is a machine learning technique that teaches computers to carry out operations that comes naturally to humans: learn by example. Deep learning is a key technology behind driverless cars, enabling them to recognize a stop sign, or to distinguish a pedestrian from a lamppost. Deep learning networks learn by identifying intricate data structures in the data they experience. By developing computational models that are composed of multiple processing layers, the networks can create multiple levels of abstraction to represent the data. A layer is the highest-level building block in deep learning. A layer is a container that usually receives weighted input, transforms it with a set of functions through data processing and passes these values as output to the next layer.

Note: The question is incomplete. The complete question probably is: The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output. select one: true false.

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Solution:

60

Step-by-step explanation:

60 is divisible by 2 -> 60 / 2 = 30

60 is divisible by 3 -> 60 / 3 = 20

60 is divisible by 5 -> 60 / 5 = 12

Answer: 60

Step-by-step explanation:

60 has all prime factors of 2,3 and 5. :)

The option A is correct

In other words, the amount of heat entering the system must be greater than the amount of mechanical effort leaving the system.

Recall the first law of thermodynamics' ideas in order to comprehend this.

dQ = dU + dW

Assuming perfect conditions. There is no heat loss outside. No matter how much heat we give the gas dQ , some of it will be utilised to boost the gas's internal energy while the rest will be used to produce work. This must be less than dQ in turn.

Because of this extremely fundamental characteristic of all engines, none of them can operate at 100% efficiency. Even the "Carnot engine," the most ideal engine, is not entirely efficient.

The option A is correct

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The answer is 0.1657

Solution:

Given: [tex]\frac{1}{2*6}[/tex]+[tex]\frac{1}{4*8}[/tex]+ .. . . . . . . . +[tex]\frac{1}{20*24}[/tex]

∴ [tex]\frac{1}{12}[/tex] + [tex]\frac{1}{32}[/tex] + [tex]\frac{1}{60}[/tex] + [tex]\frac{1}{96}[/tex] + . . . . . .  + [tex]\frac{1}{480}[/tex]

∴ [tex]\frac{40}{480}[/tex] + [tex]\frac{15}{480}[/tex] + [tex]\frac{8}{480}[/tex] + . . . . . . +[tex]\frac{1}{480}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)

∴[tex]\frac{79.54}{480}[/tex]

= 0.1657

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After carefully calculating the sequence we have come to find that The answer of the given equation is 0.1657

What is a sequence?

A sequence is an ordered collection of enumerated objects in mathematics where repetitions are permitted. It has members, just like a set (also called elements, or terms). The length of the sequence refers to the total (possibly infinite) number of elements.

Contrary to a set, the same elements may appear more than once at various points in a sequence, and in contrast to a set, the order is important. The formal definition of a sequence is a function from natural numbers (the positions of the sequence's elements) to the elements at each position. A function from any index set is what is meant by an indexed family, which is a generalisation of the idea of a sequence.

[tex]\frac{1}{2\times6} + \frac{1}{4\times8} + \frac{1}{6\times10}.....\frac{1}{20\times24}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)= 0.1657

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The jumper is in free fall for 7.07 s if the parachute is opens at 1000 ft

The jumper is in free fall for 7.29 s if the parachute is opens at 950 ft

The reasonable domain for the function h is

0 ≤ t ≤ 10

The reasonable range for the function h is

0 ≤ h ≤ 1800

The duration of free fall is calculated using the given function

h = -16t² + 1800

the parachute is opens at 1000 ft

h = -16t² + 1800

1000 = -16t² + 1800

16t² = 1800 - 1000

16t² = 800

t² = 800 / 16

t² = 50

t = √50

t = 7.07 s

the time at this situation is 7.07s

the parachute is opens at 950 ft

h = -16t² + 1800

950 = -16t² + 1800

16t² = 1800 - 950

16t² = 850

t² = 850 / 16

t² = 53.125

t = √53.125

t = 7.2887 s

the time at this situation is 7.29s

reasonable domain

minimum t = 0

for maximum t, h = -16t² + 1800 = 0

16t² = 1800

t = 10.61

0 ≤ t ≤ 10

the reasonable domain is 0 ≤ t ≤ 10

reasonable range

h = -16t² + 1800

at t = 0, h = 1800

at t = 10.606, h = 0

0 ≤ h ≤ 1800

the reasonable range is 0 ≤ h ≤ 1800

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The value of x, in dollars, so that they have equal weekly pay is $18,000.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is a set of values that have the potential of coming out as outputs of a function.

We are given that Guy and Jim earn the same weekly pay.

Then g(x) = f(x)

So, 185 + .03x = 275 + .025x

Rearranging terms so that the x's are together and the constants are together:

0.005x = 90

∴ x =  18,000

Thus, the value of x, in dollars, so that they have equal weekly pay is $18,000.

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A company's balance sheet is its financial statement at a given point in time and lists its assets, liabilities, equity capital, total debt, and other items.

A balance sheet is a list of all your capital, obligations, and assets. The assets and liabilities of a firm are described in detail on a balance sheet, which is a financial statement.

The Equity Section of the Nortech Corporation's Balance Sheet exists as follows:

Common Stock:

500,000 shares, Authorized at $1 par value

200,000 Issued Shares at $1 = $200,000

Additional Paid-in Capital          4,143,000

3,000 shares, Treasury stock        (3,000)

Retained Earnings                       253,500

Total Equity                           $4,593,500

1c. Shares Outstanding = 197,000 (200,000 - 3,000)

2. Balance in Additional Paid-in Capital = $4,143,000

3. Earnings per share = $0.75 ($147,750/197,000)

4. Dividend per share = $0.25 ($49,250/197,000)

5. The Treasury stock is reported as $3,000 on the balance sheet.

6. With a 2-for-1 stock split, the par value becomes $0.50 ($1/2)

Data and Calculations:

Par value of Common Stock = $1

Authorized Shares = 500,000 shares

Issue price per share = $22

Common Stock Account = $200,000

Issued Shares = 200,000 shares ($200,000/$1)

Treasury Stock = $3,000 (3,000 x $1)

Additional Paid-in Capital = $4,200,000 (200,000 x $21)

Additional Paid-in Capital (Treasury Stock) = $57,000 ($19 x 3,000)

Balance of Additional Paid-in Capital = $4,143,000 ($4,200,000 - $57,000)

Retained earnings for the year:

Beginning Balance $155,000

Net income                147,750

Dividends paid         (49,250)

Ending Balance    $253,500

The complete question is:

At December 31, the records of Nortech Corporation provided the following selected and incomplete data: Common stock (par $1; no changes during the current year).Shares authorized, 500,000.Shares issued, ?; issue price $22 per share. Common Stock account, $200,000.Shares held as treasury stock, 3,000 shares, cost $20 per share. Net income for the current year, $147,750.Dividends declared and paid during the current year, $49,250.Retained Earnings balance, beginning of the year, $155,000.Required: Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par value per share. (Round "per share" answers to 2 decimal places.)

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8x-20

Step-by-step explanation:

12x-18-4x-2

8x-20

The required money that should have been invested to earn $55 is $1024.84.

Given that,
How much should you invest at 4.6% simple interest in order to earn $55 interest in 14 months is to be determined.

When some apply for their money on something so that they can get higher value in returns of their money.

Here,
SI = [p × r  ×t]/100
55 × 100 = p × 4.6 / 12 × 14
p = $1024.84

Thus, the required money that should have been invested to earn $55 is $1024.84.

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Answer:

62.16

Step-by-step explanation:

994.01 - 200.00 / 12

The rate of interest monthly is 0.55%.

What is rate of interest?

An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the total loan amount.

Given that,

The deposit amount is $4,200.

The future value is $5,994.74

The number of months = 7(12) = 84.

The payment i.e. PMT = $0

Based on the above information, the calculation is as follows:

The formula is

= RATE(NPER,PMT,-PV,FV,TYPE)

After applying the above formula, the rate of interest monthly is 0.55%.

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To calculate the total volume of the solid we will divide it into n shell cyline thickness of [tex]$\Delta y$.[/tex]

The internal shell cylinder circumference C shall be[tex]$2 \pi r_i$[/tex]

where r is the in The shell cylinder internal area A shall be C.

where h is the height

The volume of the shell cylinder[tex]$\Delta v$[/tex] shall be[tex]$A \cdot \Delta y$.[/tex]

Then we will have:

[tex]\Delta v=A \cdot \Delta y=C \cdot h \cdot \Delta y=2 \pi r_i h \cdot \Delta y \Rightarrow d v=2 \pi r_i h \cdot d y$$[/tex]

The total volume of the solid shall be the summation of all n shell cylinders

[tex]\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y$$[/tex]

[tex]\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y[/tex]

[tex]The value $a$ is the value of $y$ at the point where $x=0$ then:For $x=0 \Rightarrow y=0^3 \Rightarrow y=0$ then $a=0$.The value $b$ is the value of $y$ at the point where $x=1$ then:[/tex]

[tex]For $x=1 \Rightarrow y=1^3 \Rightarrow y=1$ then $b=1$.Since the integration will be with variable $y$ we have to express the function $y=x^3$ in terms of $y$ :$$[/tex]

y=x^3 \[tex]Rightarrow x=\sqrt[3]{y}[/tex]

Substituting in V, we will have:

[tex]V= & 2 \pi \int_a^b r_i h d y=2 \pi \int_0^1(1-y)(1-\sqrt[3]{y}) d y=2 \pi[/tex]\[tex]int_0^1(1-y)\left(1-y^{\frac{1}{3}}\right) d y \\[/tex]

&[tex]1-y \\& \frac{1-y^{\frac{1}{3}}}{1-y} \\& \frac{-y^{\frac{1}{3}}+y^{\frac{1}{3}} \cdot y^{\frac{1}{1}}}{} \\[/tex]

[tex]& 1-y-y^{\frac{1}{3}}+y^{\frac{1}{3}+\frac{1}{1}}= \\& =1-y-y^{\frac{1}{3}}+y^{\frac{1+3}{3}}= \\[/tex]

[tex]& =1-y-y^{\frac{1}{3}}+y^{\frac{4}{3}}= \\& =y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1[/tex]

Substituting in V:

[tex]V=2 \pi \int_0^1\left(y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1\right) d y=2[/tex][tex]{1}{3}+1}}{\frac{1}{3}+1}-\frac{y^{1+1}}[/tex]{[tex]1+1}+y\right]_0^1=2[/tex] [tex]\pi\left[\frac{y^{\frac{4+3}{3}}}{\frac{4+3}{3}}[/tex]-[tex]\frac{y^{\frac{1+3}{3}}}{\frac{1+3}{3}}-\frac{y^2}{2}+y\right]_0^1$$[/tex]

Calculating the definite integral:

By definition[tex], $\int_a^b f(x) d x=\left.F(x)\right|_a ^b=F(b)-F(a)$[/tex] then:

[tex]& V=\frac{\pi}{14}\left[\left(12 \cdot 1^{\frac{7}{3}}-21 \cdot 1^{\frac{4}{3}}-14[/tex][tex]\cdot 1^2+28 \cdot 1\right)-\left(12 \cdot 0^{\frac{7}{3}}-21 \cdot[/tex] [tex]0^{\frac{4}{3}}-14 \cdot 0^2+28 \cdot 0\right)\right] \\[/tex]

& V=[tex]\frac{\pi}{14}[(12 \cdot 1-21 \cdot 1-14 \cdot 1+28 \cdot 1)-\underbrace{(12 \cdot 0-21 \cdot 0-14 \cdot 0+28 \cdot 0)}_0][/tex]

[tex]& V=\frac{\pi}{14}(12-21-14+28)=\frac{\pi}{14}(12+28-21-14)=\frac{\pi}{14}(40-35)=\frac{5 \pi}{14} \approx \frac{5 \cdot 3,1416}{14} \approx \frac{15,708}{14} \\& V \approx 1,122[/tex]

Answer:[tex]$V \approx 1,122 u . v$. (units of volume)[/tex]

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Answer:

The theoretical probability of rolling a two with one standard die is 1/6. This can be written as a decimal by dividing 1 by 6, which is approximately 0.167. As a percentage, this is approximately 16.7%. Here are all three forms:As a fraction: 1/6As a decimal: 0.167As a percentage: 16.7%

Step-by-step explanation:

Answer:

Step-by-step explanation:35.5 136.45w = ...

Missing: $309.99. ‎$144.99 ‎PLEASE ‎HURRY ‎$27.50

The probability that everyone gets a red card will be 0.125.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The accompanying cards are managed by three individuals indiscriminately, so everybody gets a similar number of cards. There are three red cards and three blue cards.

Then the probability that everyone gets a red card is given as,

P = (3/6) × (3/6) × (3/6)

P = (1/2) × (1/2) × (1/2)

P = 1/8

P = 0.125

The probability that everyone gets a red card will be 0.125.

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let additive inverse of it is y

So, y + (-9x+3) = 0

y = 9x-3

The measure of angle BCA = The measure of angle C prime A prime B.

Given that

Triangle ABC is transformed to triangle A′B′C′, as shown below:

A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes.

A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0.

A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.

According to the question

Triangle ABC is transformed to triangle A′B′C′, as shown below:

Here the triangle ABC is similar A'B'C' are similar triangles.

For similar triangles angles are congruent.

A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0.

A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.

Therefore,

<BAC = <B'A'C'

<ABC = <A'B'C'

<ACB = <A'C'B'

Hence, The correct relationship between the measures of the angles of the two triangles is the measure of angle BCA = The measure of angle C prime A prime B.

The complete question is : Triangle ABC is transformed to triangle A′B′C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles? The measure of angle CAB = The measure of angle C prime B prime A prime The measure of angle BCA = The measure of angle A prime B prime C The measure of angle CAB = The measure of angle C prime A prime B prime The measure of angle BCA = The measure of angle C prime A prime B prime

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The equation for total amount to be paid represented as y and pounds of potatoes represented as x will be y = 0.64x

Ax + By + C = 0 can be used to express a linear equation in two variables, where x and y are the two variables, and each has a degree of one.

Ex. -2x+3y=8

Total weight of potatoes in pounds Dontrell bought= x

Let total amount Dontrell he pays= $ y

It is given 5.5 pounds are bought by paying $3.52

5.5 pounds = $3.52

1 pound = $ 3.52/5.5

1pound=$0.64(Using Unitary method)

Dontrell buy x pounds potatoes and he pays $y

Therefore,

y=0.64x

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Assume that x and y are both differentiable functions of t and are related by the equation y=cos(5x). The value of dy/dx is 25.

What is  differentiable functions?

Differentiable simply means that the derivative exists at each location within its domain. As a result, the function must also exist (i.e., be continuous) on its domain in order for the derivative to exist. Because of this, a differentiable function can also be continuous.

Given that x, y are both differentiable function of t. and

[tex]y=\cos (5 x)[/tex]

Find [tex]\frac{d y}{d t}=$.[/tex] when [tex]$x=\frac{\pi}{10}$[/tex] given that [tex]$\frac{d x}{d t}=-5$[/tex], when [tex]$x=\frac{\pi}{10}$[/tex]

Given function is

[tex]$ y=\cos 5 x $[/tex]

[tex]$\frac{d y}{d t}=-\sin (5 x) \cdot \frac{d}{d t}(5 x) \text { (By chain } $[/tex]

[tex]$ =-\sin 5 x \cdot 5 \frac{d x}{d t} $[/tex]

[tex]$ \text { at } x=\frac{\pi}{10}$[/tex]

[tex]$ \frac{d y}{d t}=-\sin \left(8 \times \frac{\pi}{10}\right) \times 5 \times-5$[/tex]

[tex]$-\frac{d x}{d t}=-5 $[/tex]

[tex]$2^{20} $[/tex]

[tex]$\text { at } x=\frac{\pi}{10}$[/tex]

[tex]$ =25 \sin \frac{\pi}{2} $[/tex]

[tex]$=25 \times 1 $[/tex]

[tex]$ \frac{d y}{d t}=25 $[/tex]

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The exact value for sin (∅) is √15/4 if  cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

In mathematics, the trigonometric functions—also known as circle, angle, or goniometric functions—are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths.  As some of the most basic periodic functions, they are frequently employed in Fourier analysis to examine periodic phenomena.

The sine, cosine, and tangent are the trigonometric functions that are most commonly utilized in contemporary mathematics. The cotangent, secant, and their less common reciprocals, the cosecant, are each of their reciprocals.

Given, cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

cos²∅+sin²∅=1

sin²∅=1-cos²∅

sin²∅=(1-(-1/4)²)

sin²∅=1-(1/16)

sin²∅=15/16

sin∅=√15/4

Therefore, the exact value for sin (∅) is √15/4 if  cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

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