What is the value of cosine (startfraction x over 2 endfraction) if tangent x = one-half and x is in quadrant iii? negative startstartroot startfraction 5 minus 2 startroot 5 endroot over 10 endfraction endendroot negative startstartroot startfraction 5 + 2 startroot 5 endroot over 10 endfraction endendroot startstartroot startfraction 5 minus 2 startroot 5 endroot over 10 endfraction endendroot startstartroot startfraction 5 + 2 startroot 5 endroot over 10 endfraction endendroot.

Answer: w=14

Step-by-step explanation: The way I solve it is if you take 27 and subtract 13 from it, you'll get 14. Hope this helps!

Answer:

w=14

Step-by-step explanation:

hope this helps...

Answer:

x = -0.5

Step-by-step explanation:

[tex]factors \: of \: 25 \\ 25 = 5 {}^{2} \\ 5 {}^{(2)x} = 5 {}^{4x + 1} \\ since \: bases \: are \: equal \: \\ hence \: exponents \: are \: equal \\ 2x = 4x + 1 \\ collect \: like \: term \\ 2x - 4x = 1 \\ - 2x = 1 \\ divide \: by \: - 2 \: both \: sides \\ x = - 0.5[/tex]

Answer:

The width of the patio is 3/2 feet.

Step-by-step explanation:

following equation to solve for w:

(20+2w) * (35+2w) = 1350

Expanding the equation, we get:

700 + 140w + 70w^2 = 1350

Subtracting 700 from both sides, we get:

140w + 70w^2 = 650

Dividing both sides by 10, we get:

14w + 7w^2 = 65

We can now solve for w using the quadratic formula:

w = (-b +/- sqrt(b^2-4ac)) / 2a

where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:

w = (-14 +/- sqrt(14^2-47(-65))) / 2*7

w = (-14 +/- sqrt(196+1820)) / 14

w = (-14 +/- sqrt(2016)) / 14

w = (-14 +/- 44) / 14

To find the width of the patio, we need to find the area of the pool and the area of the patio. Let's call the width of the patio "w". The area of the pool is 20 * 35 = <<20*35=700>>700 square feet. The area of the patio is (20+2w) * (35+2w) = 1350 sqr feet. We can set up the following equation to solve for w:

(20+2w) * (35+2w) = 1350

Expanding the equation, we get:

700 + 140w + 70w^2 = 1350

Subtracting 700 from both sides, we get:

140w + 70w^2 = 650

Dividing both sides by 10, we get:

14w + 7w^2 = 65

We can now solve for w using the quadratic formula:

w = (-b +/- sqrt(b^2-4ac)) / 2a

where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:

w = (-14 +/- sqrt(14^2-47(-65))) / 2*7

w = (-14 +/- sqrt(196+1820)) / 14

w = (-14 +/- sqrt(2016)) / 14

w = (-14 +/- 44) / 14

This means that the width of the patio is either 3/2 or -5/2 feet. Since the width cannot be negative, the width of the patio must be 3/2 feet.

The quadratic equation we can use to solve this problem is:

w^2 + 14w - 65 = 0

The relation that is a function is the graph (d)

From the question, we have the graphs to represent the given parameters that can be used in our computation

We are to find out which of them represents a function

For a graph to represent a function, the graph must pass the vertical line test

This means that a line drawn from the x-axis must touch the graph at most once

So, we draw these lines  and attach the graphs (see attachment)

The graph that pass the vertical line test is graph d

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The way to simplify radical expressions include:

Any expression with the radical symbol is referred to as a radical expression. This symbol, which is frequently used to calculate the square root of a number, is frequently called the "square root" symbol by mistake.

But it can also refer to a cube root, a fourth root, or something higher. Radical equations are equations that contain radicals.

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Answer:

1. Identify the unit of measure to be converted.

2. Determine the conversion factor between the original and desired units.

3. Multiply the original measure by the conversion factor to obtain the new unit measure.

4. Check the new unit measure to ensure accuracy.

Step-by-step explanation:

Answer:

D. p = -6

Step-by-step explanation:

1. combine like terms

5/6 P + 7 = 7/6 P + 9

2. subtract 7/6 P from both sides

-2/6 P + 7 = 9

3. subtract 7 from both sides

-2/6 P = 2

4. multiply both sides by -6/2

Answer:

p = -6

Answer: D

Step-by-step explanation:

The analysis of the logical statement from among the  options indicates that the inference that is not true is the option;

A logical statement is one which draws a conclusion based on an hypothesis.

The logical statement which is incorrect can be found by examining the specified statements as follows;

If p then q,

The converse statement , found by switching the positions of the hypothesis and the conclusion is therefore;

q therefore p

The inference is correct

The statement, if not p, not q . q therefore not not p

According to the law of contraposition, a conditional statement is true when the contrapositive statement is also true.

The statement if not p, not q. which is the contrapositive of the statement if q then p

The inference, q, therefore not not q is incorrect

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Answer:

b is the y-intercept.

Step-by-step explanation:

The equation is in the y = mx + b form.

b is the y-intercept.

Answer:

13/15

Step-by-step explanation:

Step 1) Convert to -5/15 - (-18/15)

Step 2) -5/15 - (-18/15)= 13/15

If the interest rate on your loan is lowered from 3.5% to 3%:

A) The percentage change is 14.28%

B) The percentage point of change is 0.5%

A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe. An interest rate is the percentage of a loan, deposit, or borrowing that must be paid in interest each period (called the principal sum). The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.

Let the capital will be 100

For interest rate 3.5% then the loan amount will be:

100×(3.5/100)=3.5

For interest rate 3% then the loan amount will be:

100×(3/100)=3

A) Percentage change=((-3.5+3)/3.5)×100

=(-0.5/3.5)×100

=14.28%

B) Percentage point of change=3.5%-3.0%

=0.5%

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t = 3.750 and t = 0.070 are, the following x- values, between A) 0 and 1 and D) 3 and 4

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable (x) using the formula  ax² + bx + c = 0 and a≠0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

According to question.

y = -16t² + 56t+ 4

⇒ -16t² + 56t + 4

⇒ -4t² + 14t + 1

⇒ t = [-14 ±√((14)² - 4*(-4)*1)]/-8

⇒ t = [-14 ±√(212)]/-8

⇒ t = [-14 ± 14.560]/-8

⇒ t = [-14 ± 14.560]/-8

⇒ t = -(28.56)/-8 and t = 0.560/-8

⇒ t = 3.750 and t = 0.070

hence, t = 3.750 and t = 0.070 are, the following x- values, between A) 0 and 1 and D) 3 and 4

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The new coordinate for point B is (0,2). Hence option B is the correct option.

What is coordinate of a point?

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x,y) the x-value and y-value.

Given that the coordinate of point A and B are (3,0) and (0,4).

The line AB is dilated by 1/2.

This means the scale factor is 1/2.

The x coordinate of point B is 0.

The y coordinate of point B is 4.

Multiply 1/2 with the x coordinate and y coordinate of point B to find the new coordinate of point B:

The new  x coordinate of point B is (0 × 1/2) = 0

The new  y coordinate of point B is (4 × 1/2) = 2.

The new coordinate of point B is (0,2).

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x+y=4 is most likely the equation for line K so the set of equations has infinitely many solutions.

Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.

Given

There must be identical lines made up of the same points for there to be an endless number of solutions. This implies that when expressed in the simplest terms, their equations are also identical.

As a result, x+y Equals 4. Equation here corresponds to B.

2x + 2y = 8

Dividing equation by 2

x + y = 4

As a result, x+y Equals 4. Equation here corresponds to B.
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i) The amount of work that Mrs. Maharjan did in 2 days is; ¹/₃ parts

ii) The amount of work that was left to do is; ²/₃ parts

iii) The amount of work that was done by Mrs. Rai is; ²/₃ parts

We are told that Mrs. Maharjan can do ¹/₆ part of a work in 1 day.

Thus;

i) Amount of work done in two days = ¹/₆ + ¹/₆ = ¹/₃ part

This represents the amount of work that Mrs. Maharjan did in 2 days.

(ii) Since Mrs. Maharjan did ¹/₃ part of the work in 2 days, then it means that the amount of work that was left to do is;

1 - ¹/₃ = ²/₃ parts

(iii) Since we are told that Mrs. Rai did the remaining works, the the amount of work that was done by Mrs. Rai is as calculated in ii above.

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Complete question is;

Mrs. Maharjan can do ¹/₆ part of a work in 1 day. She worked for 2 days and left. The remaining parts of the work is done by Mrs. Rai.

(i) How much work did Mrs. Maharjan do in 2 days?

(ii) How much work was left to do?

(iii) How much work was done by Mrs. Rai?​

When we reject the null and the null is true, we have a made a type I error

The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.

null hypothesis is denoted as H₀

Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. When you can reject the null hypothesis, your results are statistically significant.

when the p-value is greater than your significance level, you fail to reject the null hypothesis.

Sometimes , we reject our null hypothesis even when its true

there we made a type I error in hypothesis

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The function's domain is (a) all real numbers.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set. A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

The formula for the function is: f(x) = Negative 5/6. X in superscript?

The function mentioned above is exponential

There are no input value restrictions for exponential functions

Consequently, the function's domain is (a) all real numbers.

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The exists no solution for which the water depth 14 feet in the ocean near the shore.

We determine the function's period since that is the number of it takes hours for the ocean to return to its original depth of a specific number of feet.

The function's duration is 2π/ (π/6.2) = 12.4 hours.

When t = 0, midnight, or 12:00AM, it is low tide.

As a result, the next low tide will occur at 12:24 PM, or t = 12.4, 12.4 hours from now.

A high tide will occur halfway between those two low tides, at t=6.2 hours after midnight, or at 6:12AM.

Another high tide will occur at t=18.6 hours after midnight, or at 6:36 PM, 12.4 hours later.

If t = 0 is used in the equation, the low tide occurs at that time;

d = 35 - 28cos(pi/6.2)t

d = 35-28cos(pi/6.2)0

d = 35-28cos(0)

d = 35-28(1)

d - 35-28

d = 7

Therefore, there will never be 4 feet there because the lowest depth that may exist is 7 feet.

Thus, the exists no solution for which the water depth 14 feet in the ocean near the shore.

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The volume of the liquid in the bigger flask which is in the shape of the cone is V = 980π.

A cone is a recognizable three-dimensional geometric shape with a smooth and curving surface that is directed upward in mathematics. The

Greek word "konos," which denotes a peak or a wedge, is the source of the English word "cone."

The apex is the pointy end, while the base is the level area.

So, the volume of liquid in the bigger flask:

We know that the radius of the bigger flask is 14cm.

The liquid is filled to a height of 15cm.

The volume of cone formula: V = πr²h/3

Substitute values as follows:

V = πr²h/3

V = π(14)²15/3

V = π196*5

V = 980π

Therefore, the volume of the liquid in the bigger flask which is in the shape of the cone is V = 980π.

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Answer:

You will need to use information from (a)

Answer:

y= 20x+50

Step by Step:

A polynomial function of degree n has at most n real zeros and at most n-1 turning points.

What is polynomial function ?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

What isa Zeros of Polynomials?

Every polynomial will have as many zeros as its degree if we are able to factor it over the entire set of complex numbers, though some of these zeros are repeated and therefore counted more than once. As the function might not be fully factorable over the set of real numbers, if we limit ourselves to the set of real numbers, we might or might not be able to identify this many zeros.

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Step-by-step explanation:

the same as every other individual outcome of a roll of 2 dice : 1/6 × 1/6 = 1/36

The computation of (9 × 20 + 60) ÷ 4 - 16 + 4 × (20 × 5) is 444.

The expression can be simplified using PEMDAS rule.

Therefore,

Hence, we have to simplify the expression according to the operator that comes first in the PEMDAS rule.

Therefore,

(9 × 20 + 60) ÷ 4 - 16 + 4 × (20 × 5)

(180 + 60) ÷ 4 - 16 + 4 × 100

240 ÷ 4 - 16 + 400

60 - 16 + 400 = 444

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The time calculation which involve calculating the time in GMT when it is 1:31:45 PM EDT (Eastern Daylight Savings Time) is

The conversion given in the problem is

Eastern Daylight Savings Time = Greenwich mean time GMT - 4

Eastern Daylight Savings Time + 4 = Greenwich mean time GMT

Solving for the time equivalence in Greenwich mean time

Greenwich mean time GMT = Eastern Daylight Savings Time + 4

substituting known values

Greenwich mean time = 1 : 31 : 45 PM + 4

Greenwich mean time = 5 : 31 : 45 PM

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The relationship between the time it takes to boil a pot of water, T (in seconds), and the amount of water, A (in litres),

T ∝ A,

setting up the equation and solving:

2.96 liters of water will boils in 220 seconds.

An equation is a mathematical statement that shows that two expressions are equal.

A proportionality constant is a coefficient that relates two quantities that are proportional to each other. In other words, if two quantities are proportional, their ratio is always the same, and this constant ratio is the proportionality constant.

This proportionality can be written as an equation by introducing a constant of proportionality, k:

T = k * A

We are given that it takes 200 seconds to boil 2.7 litres of water, so we can set up an equation using this information:

200 = k * 2.7

Solving for k, we find that k = 200/2.7 = 74.07407407407407.

Now that we know the value of the constant of proportionality, we can use it to find the amount of water in the pot if it boils in 220 seconds. We can set up the following equation:

220 = 74.07407407407407 * A

Solving for A, we find that the amount of water in the pot is A = 220 / 74.07407407407407 = 2.962962962962963 litres.

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