Solve the equation for exact solutions. 6 cos^(-1) x = pi
I got √3/2

The probability that the next number pointing north is between 2 and 7 is 13/18 .

1) The circle is divided into 9 parts.

Now the parts are uneven.

So the data about the spins is required to calculate the probability .

The total number of items in the box = 18

favorable outcomes (between 2 and 7) = 13 possible outcome.

Required probability

= favorable outcome / total outcome

= 13 / 18

2) Using the Venn diagram we can calculate the various parts of the problem:

Shoppers at big-box store or online or local store = sum of all the shoppers = 109+57+107+18+17+38+34 = 380 shoppers

3) Shoppers made purchase online or locally owned shop but not at a big box store = 107 + 38 + 34 = 179 shoppers.

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The given sequence160,80,40,20 is the geometric sequence.

In an Arithmetic sequence, the difference between the two consecutive terms is equal.

In a Geometric sequence, the common ratio of the two consecutive terms is equal.

The given sequence is 160, 80, 40, 20

Now,

[tex]T_{1} = 160\\T_{2} = 80\\T_{3} = 40\\T_{4} =20[/tex]

Subtracting the consecutive terms to calculate the common difference,

[tex]d = T_{2} -T_{1} = 80 -160 = -80[/tex]

[tex]T_{3} -T_{4} = 40 -80 = -40[/tex]

So, [tex]T_{2} -T_{1} \neq T_{3} -T_{4}[/tex]

So, the given sequence is not an arithmetic sequence.

Now, Calculating the common ratios,

[tex]r = \frac{T_{2} }{T_{1} } = \frac{80}{160} = \frac{1}{2}[/tex]

and, [tex]r =\frac{T_{3} }{T_{2} } = \frac{40}{80} = \frac{1}{2}[/tex]

Hence, the ratio is the same for consecutive terms.

So, the given sequence is the geometric sequence.

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The ratio of dollars to paintbrushes is 7:4

A ratio expresses the number of times one value is contained in another value.

The number of paintbrushes Jane bought for $7 is 4

From the question, 4 paintbrushes can be bought with $7 (7 Dollars), therefore, seven dollars gives 4 paintbrushes

The ratio of dollars to paintbrushes is therefore 7 to 4, while the ratio of paintbrushes to dollars is 4 to 7

The expression for ratio is the colon symbol ':'

Ratios can also be expressed using the word 'to'.

A ratio can also be expressed using the hyphen '-'

The ratio of paintbrushes to dollars can be expressed as 4:7 or 4 to 7 or 4-7.

The correct option is therefore;

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Answer:

The ratio of paintbrushes to dollars is 4 to 7.

 The ratio of dollars to paintbrushes is 7:4.

 The ratio of paintbrushes to dollars is 4:7.

Step-by-step explanation:

it just is

After 2 hours the plan needs to be changed, and purchase solar for the cost effect.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh.

Total cost = 6x100 = 600 pounds

Total cost for 2 hours = 200 pounds

Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW.

Total cost for this:

From 8 AM to 12 PM = Number of hours 4 hours

4.5 GW = 4500 MW

= 105 pounds/MWh

Total cost for  4 hours = 630 pounds for 4500 MW per hour

Thus, after 2 hours the plan needs to be changed, and purchase solar for the cost effect.

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Answer:

12 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

substitute the given values for p and q into the expression

p² + 3q²

= (- [tex]\frac{1}{2}[/tex] )² + 3(- 2)²

= [tex]\frac{1}{4}[/tex] + 3(4)

= [tex]\frac{1}{4}[/tex] + 12

= 12 [tex]\frac{1}{4}[/tex]

Answer:

$55.71

Step-by-step explanation:

$320/7=$45.71 per day

45.71/8=5.71 per hour

45.71+10=$55.71 for 9 hours of work

45.71+ 45.71+55.71 =$147.13 for 3days +1 hour overtime

The solutions of the equations are x = 1 and y = 2

The system of equations are

4x + 3y = 10

-4x + 5y = 6

Here we have to use the elimination method. Eliminate the x term and find the value of y term

Add both equation

3y + 5y = 10 +6

Add the like terms

8y = 16

y = 16 / 8

Divide  the terms

y = 2

Substitute the value of x in the first equation

4x + 3y = 10

4x + 3×2 =  10

Multiply the terms

4x + 6  = 10

4x = 10 - 6

4x = 4

x = 4 / 4

Divide the terms

x = 1

Hence, the solutions of the equations are x = 1 and y = 2

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Answer:

Step-by-step explanation:

2

Answer:

The leading coefficient is 2.

Step-by-step explanation:

Leading coefficients are the numbers with the highest degree or exponent.

Total time taken by Bethany to make a round trip of NY to Pittsburgh as per  given conditions is equal to 1 (7/ 20)hours.

As given in the question,

Time taken by Bethany to flew from NY to Pittsburgh is equal to 3/4 hours

Now using jet stream ,

Time taken by airlines from Pittsburgh to NY is (4/5) th of (3/4) hours

= (4/5) × (3/4) hours

= 3/5 hours

Total time taken by airlines to make a round trip from NY to Pittsburgh is given by:

= [(3/4) + (3/5)] hours

= [(15 +12)/20] hours

= 27/20 hours

= 1 7/20 hours

Therefore, total time taken by Bethany to make a round trip of NY to Pittsburgh as per  given conditions is equal to  1 (7/ 20)hours.

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Answer:

x=9 (9,25)

Step-by-step explanation:

9*7=27

27-2=25

Answer:  2(x+4) >3(x+7)-4

Step-by-step explanation:

Hope this helps

Answer:

2(n+4)≤3(n+7)-4

Step-by-step explanation:

The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.

We need to find the inequality of the statement given;

"Two times the sum of a number and four is no more; than three times the sum of the number and seven decreased by four"

Let n be the unknown number

Then it would be;

2(n+4) ≤ 3(n+ 7) - 4

Hence, The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4

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By Computing the Logarithmic Relation, we calculate that the time between injections is 5.1 hours or 5 hours and 6 minutes.

The given formula is

[tex]D = 5e^{-0.1h}[/tex]

where D is the amount of drug in milligrams in the patient's bloodstream and h is the number of hours after the drug was administered.

So, it is given that D = 3 and we need to evaluate the number of hours it took between the injections,

So, We have,

[tex]D = 5e^{-0.1h}[/tex]

[tex]\frac{D}{5} = e^{-0.1h}[/tex]

Taking Natural log on both sides, we have :

[tex]ln\frac{D}{5} =ln e^{-0.1h}\\\\ln\frac{D}{5} = -0.1h\\[/tex]

We have D = 3, putting it in the formula, we get

[tex]\ln\frac{3}{5} = -0.1h\\\\ln(0.6) = -0.1h\\\\-0.5108 = -0.1 h\\\\h = \frac{0.5108}{0.1} = 5.1[/tex]

Hence, the time between injections is 5.1 hours or 5 hours and 6 minutes.

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The probability of more than 5 people using the emergency room is 0.4729

Since 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. To find the probability of more than 5 people use the emergency room, we use binomial probability.

We find that the binomial probability of x is   P(X = x) = ⁿCₓpˣ(1 - p)ⁿ⁻ˣ

where

Since

Let us now find the probability of x ≤ 5.

So, P(X ≤ 5) = ¹¹C₀p⁰(1 - p)¹¹⁻⁰ + ¹¹C₁p¹(1 - p)¹¹⁻¹ + ¹¹C₂p²(1 - p)¹¹⁻² + ¹¹C₃p³(1 - p)¹¹⁻³

+ ¹¹C₄p²(1 - p)¹¹⁻⁴ + ¹¹C₅p⁵(1 - p)¹¹⁻⁵

So, substituting the values of the variables into the equation, we have

= ¹¹C₀(0.49)⁰(1 - 0.49)¹¹ + ¹¹C₁(0.49)¹(1 - 0.49)¹⁰ + ¹¹C₂(0.49)²(1 - 0.49)⁹ + ¹¹C₃(0.49)³(1 - 0.49)⁸

+ ¹¹C₄(0.49)⁴(1 - p)⁷ + ¹¹C₅(0.49)⁵(1 - 0.49)⁶

= (1)(1)(0.51)¹¹ + (11)(0.49)(0.51)¹⁰ + (55)(0.49)²(0.51)⁹ + (165)(0.49)³(0.51)⁸

+ (330)(0.49)⁴(0.51)⁷ + (462)(0.49)⁵(0.51)⁶

= 0.0006071 + (11)(0.49)(0.0011904) + (55)(0.2401)(0.0023341) + (165)(0.117649)(0.0045768)

+ (330)(0.0576480)(0.0089741) + (462)(0.0282475)(0.0175963)

= 0.0006071 + 0.0064163 + 0.0308230 + 0.0888452

+ 0.1707218 + 0.2296378

= 0.5270512

≅ 0.5271

So, P(X ≤ 5) = 0.5271, we see that the binomial probability of more than 5 people is P(X ≥ 5) = 1 - P(X ≤ 5)

So, substituting the value of the variable into the equation, we have

= 1 - 0.5271

= 0.4729

The probability is 0.4729

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The measure of the Largest angle using the angle sum property of a triangle is: 80°

What is the Angle sum property of a triangle?

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

In the given figure, we have:

Measure of 1st angle = 64°

Measure of 2nd angle = (2x + 14)°

Measure of 3rd angle = (6x + 14)°

and we know the angle of the property,

using the  angle of property,

64° + (2x + 14)° + (6x + 14)° = 180°

⇒64° + 8x + 14° + 14° = 180°

⇒92°  + 8x = 180°

⇒ 8x = 180° - 92°

⇒8x = 88°

⇒ x = 11°

So,

Measure of 2nd angle = (2x11 + 14)°

Measure of 2nd angle = (36)°

Measure of 3rdangle = (6x11 + 14)°

Measure of 2nd angle = (80)°

Hence,

The measure of the Largest angle using the angle sum property of a triangle is: 80°

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The volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

Given, water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches.

We have to express the volume V of the water in the cone as a function of the height h of the water.

Now, at any instant let the height of the water in the cone be h and radius of the water in the cone be r,

So, using the concept of similarity in triangles

we get, r/4 = h/16

r = h/4

Now, the volume of the water in the cone be,

V = (1/3)πr²h

V = (1/3)π(h/4)²h

V = (1/48)πh³

So, the function expressing the volume of the water in the cone be,

V = (1/48)πh³

Hence, the volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

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The scalene right triangle RGH is given by the image shown at the end of the answer.

There are two classifications of triangles, either regarding the side lengths or the angles.

Regarding the side lengths, the classifications are given as follows:

Regarding the measure of the greatest angle, the classifications are given as follows:

In this problem, RGH is a scalene right triangle, hence:

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The Isosceles obtuse triangle in which the obtuse vertex is angle T is represented with the attached diagram.

An isosceles obtuse triangle is a type of triangle which is formed by two equal sides of the triangle.

As long as the measures of the angles add up to 180°, it is an isosceles obtuse triangle.

An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.

A triangle is a polygon with three sides and three angles. There are different types of triangle, which includes:

So therefore, an isosceles obtuse triangle is formed by having two equal sides of a triangle.

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Answer:

11

Step-by-step explanation:

Find the difference using subtraction:

18 - 7 = 11

So, the numbers are 11 units apart.

The solution of the composite function (f/g)(x) is [tex]\frac{-4x+3}{6+7x}[/tex]

Composite functions are when the output of one function is used as the input of another.

In other words, a composite function is generally a function that is written inside another function.

Composite function involves the composition of functions is combining two or more functions as a single function.

Therefore, let's solve the function below:

f(x) = -4x + 3

g(x) = 6 + 7x

Hence,

(f/g)(x) = f(x) / g(x)

Therefore,

f(x) / g(x) = [tex]\frac{-4x+3}{6+7x}[/tex]

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The approximate of √59 is 7.7 when rounded off to the nearest tenth place.

Given,  √59

we are asked to determine the approximation without using a square root button.

√59 is a decimal number since it is not a perfect square. Therefore, rather than finding a precise value, we will need to obtain a near approximation of 59 in decimal form.

the square root of the number 59 is:

7.6811

You rounded to the nearest tenths place. The 6 in the tenths place rounds up to 7 because the digit to the right in the hundredths place is 8.

= 7.7

When the digit to the right is 5 or greater we round away from 0.

7.6811 was rounded up and away from zero to 7.7

Hence we get the required approximation.

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Michael was assigned a total of 98 task which a fraction of 2/7 is 28

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Data;

We can find the number of problem as

28 = 2/7 * x

7 * 28 = 2x

x = 98

The number of task assigned is 98.

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Answer:

75

Step-by-step explanation:

1 minute=15

2 minutes=30

3 minutes=45

4 minutes=60

5 minutes=75

Answer:

4.25 minutes

Step-by-step explanation:

[tex]\frac{32 \:copies}{1\:min} = \frac{136\: copies}{x \: min} \\\\x\: min = \frac{136 \: copies}{32 \: copies} \\\\x=4.25 \: min[/tex]

Answer: 4 mins 15 seconds (4.25 mins)

Step-by-step explanation:

136 copies/32 copies per minute = 4.25 minutes

So we know it will take 4.25 mins. 4.25 mins is equal to 4 mins and 15 seconds.

The surface area of a cube that has a width of 25 centimeters is 3750 cm².

It should be noted that surface area simply implies the measure of the total area that the surface of an object occupies.

In this case, the surface area of a cube is measured as 6a² where a = side

In this case, the side is 25. Therefore, the surface area will be:

= 6a²

= 6 × 25²

= 3750 cm²

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If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2  .

In the question ,

it is given that ,

In the rectangle ABCD , the coordinate of the point A is (3,4) and the coordinate of the point B is (7,6) .

since the sides of the rectangle are at 90° , that means they are perpendicular .

which means AB⊥BC ,

the slope of AB = (6-4)/(7-3)

slope = 2/4

slope = 1/2

Since , AB⊥BC ,

(slope of AB)×(slope of BC) = -1

substituting the values , we get

(1/2)×(slope of BC) = -1

slope of BC = -1/(1/2)

slope of BC = -2 .

Therefore , If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2  .

The given question is incomplete , the complete question is

On rectangle ABCD, if A is located at (3,4) and B is located at (7, 6), what is the slope of BC ?

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Answer: e) 6.7

Step-by-step explanation:

This is a Similarity of Triangles problem (geometry)

if x is the height of the lamp post, then:

x/5 = (3 + 9) / 9

x (9) = (12) (9)

x = 60/9 = 6.7

Answer:

They should pay AED 180 as interest.

Step-by-step explanation:

Simple interest:

        P = The amount borrowed = AED 3000

        R = rate of interest = 3% per year

       t = time = 24 months = 24 ÷ 12 = 2 years

          [tex]\sf \boxed{Interest = PRt}[/tex]

Substitute the values,

                            [tex]\sf = 3000 * \dfrac{3}{100}*2\\\\ = 30*3*2\\\\=AED \ 180[/tex]

A disadvantage of using a questionnaire is that B. The respondent controls the validity.

Questionnaires are a means of gathering data in research in order to find out more about a certain phenomenon. They involve writing questions and giving them to a respondent to fill out the answers.

Questionnaires are inexpensive to administer and can lead to confidential results which is good. However, they have the disadvantage that respondents control the validity of questionnaire results and can decide to lie if they feel it would make them look better, which would confuse the research results.

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