Lauren’s age is half of Joe’s age. Emma is four years old than Joe. The sum of Lauren, Emma, and Joe’ age is 54. How old is Joe?

The probability of the maximum number of black hats that could be present in the group is 2.

Since the probability of selecting a student with a green hat is the highest, it is likely that there are more green hats than any other color. Let's assume that there are 7 green hats. If there are 7 green hats, then there are only 5 hats left for the remaining colors. However, we know that there are only 2 red hats and 1 blue hat, leaving a maximum of 2 hats for the black color. Therefore, the greatest possible number of black hats in the group is 2, which would give a total of 2 red hats, 1 blue hat, 7 green hats, and 2 black hats. In conclusion, if the probability of selecting a student with a green hat is the highest, then the greatest possible number of black hats in the group is 2.

To learn more about probability follow the link:

https://brainly.com/question/30034780

#SPJ1

The probability that Angela gets to go to the meeting is 2/5 or 0.4.

What is probability?

There are a total of 5 people in the club, and they need to pick 2 people to go to the meeting. The number of ways to pick 2 people out of 5 is given by the binomial coefficient:

C(5,2) = 5! / (2! (5-2)!) = 10

This means there are 10 equally likely outcomes, which can be represented by the following probability model:

Outcome            Angela goes to meeting?                 Probability

A,B                                    Yes                                              1/10

A,C                                    Yes                                              1/10

A,D                                    Yes                                              1/10

A,E                                     Yes                                              1/10

B,C                                      No                                              1/10

B,D                                      No                                              1/10

B,E                                       No                                              1/10

C,D                                      No                                               1/10

C,E                                       No                                               1/10

D,E                                       No                                               1/10

The probability that Angela gets to go to the meeting is the sum of the probabilities of the outcomes where Angela goes to the meeting:

P(Angela goes to meeting) = P(A,B) + P(A,C) + P(A,D) + P(A,E)

= 1/10 + 1/10 + 1/10 + 1/10

= 4/10

= 2/5

Therefore, the probability that Angela gets to go to the meeting is 2/5 or 0.4.

To know more about the probability, visit:

https://brainly.com/question/11234923

#SPJ1

5 miles each day so 5×7=35 miles a week

Answer:

24328.49 cm

Step-by-step explanation:

as (A = π r²). r is 88 so and is 24328.49cm

The matching word are as follows:- center of dilation - C,corresponding angles - D,dilation - E,scale factor (of a dilation) - A,similar polygons - B respectively.

Corresponding angles are a pair of angles that have the same relative position at the intersection of two lines when one line is crossed by a transversal.

They are located in corresponding (matching) positions in congruent or similar figures, and are congruent if the figures are similar.

center of dilation: C.The fixed point that is parallel to each point on the pre-image and the corresponding point on the picture during a dilatation

corresponding angles: D.a pair of angles in two congruent or similar figures that are in the same relative position

dilation: E. The transformation in which each point on the image lies on the same line as the corresponding point on pre-image and a fixed point called the center of dilation.

scale factor (of a dilation): in a dilation, the constant  rate between the distance from the center of dilation and a point on the image and the distance from the center of dilation and the  matching point on thepre-image

similar polygons: B.two or  further polygons in which corresponding angles are  harmonious and the lengths of corresponding sides are in proportion.

To know more about scale factor visit:

https://brainly.com/question/30314658

#SPJ1

Answer:

24x - 6y + 21

Step-by-step explanation:

3( 8x - 2y + 7 )

Multiply each term in the bracket by 3

= (3 x 8x) - ( 3 x 2y) + (3 x 7)

= 24x - 6y + 21

Rolling a number higher than 3 has a 2/6 or 1/3 chance of happening. Another way to say this is to round a decimal to the closest millionth, which is  [tex]0.333333[/tex]  .

A standard die has 6 sides, labelled with the numbers 1 through 6. When the die is rolled, each side has an equal probability of landing face up.

Since we want to find the probability of rolling a number greater than 3, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.

When you roll a standard die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Since we want to find the probability of rolling a number greater than 3, we need to count how many of these outcomes satisfy that condition.

Therefore, the probability of rolling a number greater than 3 is 2/6 or 1/3. Alternatively, we could express this as a decimal rounded to the nearest millionth, which would be  [tex]0.333333[/tex] .

Learn more about fraction here:

https://brainly.com/question/29156749

#SPJ1

The distance the plane traveled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians, and they are used to describe the amount of rotation or turning between two lines or planes. In a two-dimensional plane, angles are usually measured as the amount of rotation required to move one line or plane to coincide with the other line or plane.

Let's first draw a diagram to visualize the problem:

                    /  |

                  /     |

                 /       |P (plane)

                /        |

               /         |

              /          | h = 6900 ft

            /            

           / θ2.        |  

         /                |

       /                  |

   B ___/θ1__  _|___ A

           d

We need to find the distance the plane traveled from point A to point B, which we'll call d. We can use trigonometry to solve for d.

From point A, we have an angle of elevation of 16° to the plane. This means that the angle between the horizontal and the line from point A to the plane is 90° - 16° = 74°. Similarly, from point B, we have an angle of elevation of 27° to the plane, so the angle between the horizontal and the line from point B to the plane is 90° - 27° = 63°.

Let's use the tangent function to solve for d:

x = h / tan(74°) = 19906.5 ft

d - x = h / tan(63°) = 23205.2 ft

So,

d = x + h / tan(63°) ≈ 43111.7 ft ≈ 8.15 miles.

Therefore, the distance the plane travelled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

To know more about Angles visit:-

brainly.com/question/25770607

#SPJ1

Answer:

Equation: y= -3/4x+15/2

Step-by-step explanation:

The points given: (-2,9) and (2,6)

Slope ,m=y2-y1/x2-x1=6-9/2-(-2)= -3/(2+2)

slope ,m= -3/4

Equation: y-y1=m(x-x1)

Equation: y-6= -3/4(x-2)

y-6= -3/4x+3/2

y= -3/4x+3/2+6

y= -3/4x+15/2

Learn more about equation of a line

here:

Brainly.com/question/23087740

#SPJ2

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

To learn more about Pythagorean please click on below link        

https://brainly.com/question/29069676

#SPJ1

The value of the limit of the expression Limit x tend to π 1-sinx/2(π-x) ² is infinity (∝)

Given that

Limit x tend to π 1-sinx/2(π-x) ²

To solve this expression, we make use of

If limit of x to a+ of f(x) = limit of x to a- = L, then limit of x to a+ of f(x) = L

The interpretation is that we solve the expression by direct substitution

So, we have

Limit = 1 - sin(π)/2(π - π) ²

Evaluate the difference

Limit = 1 - sin(π)/2(0)²

Evaluate the exponent and the bracket

Limit = 1 - sin(π)/0

Divide

Limit = ∝

Hence, the limit of the expression is ∝

Read more about derivatives at

https://brainly.com/question/5313449

#SPJ1

By rewritting the exponential equation, we can see that the correct options are B and C.

We know that the balance is modeled by the exponential equation below:

[tex]A = 328.23\times e^{0.045*(t - 2)}[/tex]

Now we want to see which of the other equations are equivalent to this one, so we need to rewrite this equation, so let's do that.

First we can rewrite the second part to get:

[tex]A = 328.23\times e^{0.045\times(t - 2)}\\\\A = 328.23\times(e^{-2*0.045*}\times e^{0.045\times t})\\\\A = 300\times e^{0.045\times t}[/tex]

So that is an equivalent equation.

We also can keep rewritting this to get:

[tex]A = 300\times e^{0.045\times t}\\\\A = 300\times(e^{0.045})^t\\\\A = 300\times(1.046)^t[/tex]

The correct options are B and C.

Learn more about exponential equation at:

https://brainly.com/question/11832081

#SPJ1

Answer: m=1/-7

Step-by-step explanation:

2-1/-3-4=1/-7

I don't know if it can be simplified or not

The total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

The interest you receive is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

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

A is the total amount

P is the principal (initial amount borrowed), which is $1,000 in this case

r is the annual interest rate expressed as a decimal, which is 0.08 (8%)

n is the number of times the interest is compounded per year, which is usually 12 (monthly compounding) or 1 (annual compounding)

t is the time in years, which is 4 in this case

Assuming that the interest is compounded annually (n=1), we can plug in the values and simplify:

A = 1000*(1 + 0.08/1)¹⁴

= 1000(1.08)⁴

= 1000*1.3605

= $1,360.50

the total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

To know more about Compound interest  visit:

https://brainly.com/question/26457073

#SPJ1

Answer:

We can solve this expression using the order of operations, also known as PEMDAS:

2 + 77 + 2 + 4 + 18 + (9/4) + 5 + 23 + 78 + 33 - 76 - 4 + 12

First, we can simplify the fraction by adding the whole number and fraction parts:

2 + 77 + 2 + 4 + 18 + 2.25 + 5 + 23 + 78 + 33 - 76 - 4 + 12

Next, we can perform addition and subtraction from left to right:

= 187 + 2.25 + 68

= 257.25

Therefore, the value of the expression 2+77+2+4+18+9/4+5+23+78+33-76-4+12 is 257.25.

LOL the answer is 176.25

The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

To learn more on quadratic equations in vertex form: https://brainly.com/question/29260906

#SPJ1

Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.

The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.

Here,

=>  A = L x W,

where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.

Inputting the numbers provided yields:

=>  A = (7/4) x (1/3)

These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.

The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:

=>  A = (7 x 1) / (4 x 3)

When we multiply the numerator by the remainder, we obtain:

=> A = 7/12

The rectangle's size is 7/12 square inches as a result.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know which set of equations could be combined in such a way as to result in the equation 3x = 18.

To obtain a term of 3x, the second equation must be subtracted from the first. That will result in 3x +2y = 18, not the equation of interest.

A term of 3x can be obtained by adding twice the first equation to the second:

  2(x +y) +(x -2y) = 2(4) +(10)

  3x = 18 . . . . . as required

A term of 3x can be obtained by subtracting the second equation from the first. That will result in 3x +2y = 18, not the equation of interest.

These equations are dependent. The second is the opposite of the first. They have an infinite number of solutions, not the single solution of the system of equations of interest.

Therefore, the value of x is 9.

A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with three-line segments. The three line segments that connect the three points are called sides of the triangle, and the points themselves are called vertices. The angle formed between any two adjacent sides of a triangle is called an interior angle of the triangle. The sum of the interior angles of a triangle is always 180 degrees.

There are many different types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles. An equilateral triangle is a triangle in which all three sides are equal, an isosceles triangle is a triangle in which two of the sides are equal, and a scalene triangle is a triangle in which none of the sides are equal. An acute triangle is a triangle in which all three interior angles are less than 90 degrees, an obtuse triangle is a triangle in which one of the interior angles is greater than 90 degrees, and a right triangle is a triangle in which one of the interior angles is exactly 90 degrees.

Given by the question.

According to Thel's theorems

[tex]\frac{5}{3} =\frac{15}{x}[/tex]

5x=45

x=9

To learn more about acute:

https://brainly.com/question/1311149

#SPJ1

Answer: decrease in the GDP by 2.5%.

Step-by-step explanation:

As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a) where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°. Plugging those values into the formula, we get d = 300 * tan(15°) = 517.4 feet. Rounding this to the nearest whole number, we get 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a). This equation is derived from the Pythagorean Theorem, where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°, so we can plug these values into the equation. When we do this, we get d = 300 * tan(15°) = 517.4 feet. As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

Learn more about distance here

https://brainly.com/question/28956738

#SPJ1

Answer:

Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:

tan(1) = 2tan(1/2) / (1 - tan^2(1/2))

To find tan(1/2), we can use the half-angle formula for tangent:

tan(1/2) = sin(1) / (1 + cos(1))

We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:

tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)

Again, we cannot simplify this expression any further without a calculator.

For the second expression, we are asked to find the value of:

tan(arctan(6/4))

By definition, tan(arctan(x)) = x for all x, so we have:

tan(arctan(6/4)) = 6/4 = 3/2

Therefore, the exact value of the expression tan(6/4) is 3/2.

Evaluating the linear equation in x = 19 we can see that the temperature was 5.76 degrees, so your answer is correct.

Here we have a linear equation that relates the wind temperature with the wind's velocity.

The linear equation is:

y = -0.36*x + 12.6

Where y is the temperature and x is the wind speed. We want to find the temperature when the speed is 19 miles per hour, to get it, just replace x by 19 in the linear equation above, then we will get:

y = -0.36*19 + 12.6

y = -6.84 + 12.6

y = 5.76

So your answer is correct.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

The product is decreased by a factor of 16.

What is a factor?

In mathematics, a factor is a number or quantity that, when multiplied with another number or quantity, produces a given result. For example, in the expression 3 x 4 = 12, 3 and 4 are factors of 12. Factors can also refer to algebraic expressions, where they are the expressions that are multiplied together to obtain a larger expression.

Let's say we have two numbers, A and B, and we want to find the product of A and B.

The product of A and B is AB.

If we decrease A by a factor of 2, the new value of A becomes A/2. If we decrease B by a factor of 8, the new value of B becomes B/8.

So the new product of A/2 and B/8 is:

(A/2)(B/8) = AB/16

Therefore, the product is decreased by a factor of 16.

To learn more about factors, visit the link:

https://brainly.com/question/25829061

#SPJ1

Answer:

a_2 = 16

a_3 = -32

a_4 = 64

Step-by-step explanation:

Multiply each term by r to get the next term.

a_1 = -8

a_2 = -8 × (-2) = 16

a_3 = 16 × (-2) = -32

a_4 = -32 × (-2) = 64

Answer:

Rusty Raspberry's total earnings last year would be the sum of his earnings from playing baseball and his earnings from book royalties.

Earnings from playing baseball = $1,715,000

To calculate earnings from book royalties, we need to find out how much Rusty received in royalties for the 300,000 copies sold.

Royalties per book = 10% of $24 = $2.40

Total royalties for 300,000 books = $2.40 x 300,000 = $720,000

Therefore, Rusty Raspberry's earnings from book royalties last year = $720,000

Total earnings = Earnings from playing baseball + Earnings from book royalties

= $1,715,000 + $720,000

= $2,435,000

Therefore, Rusty Raspberry's total salary last year from the book and his baseball career was $2,435,000.

Answer:37

Step-by-step explanation:

<UYW=<UYV+<VYW=36+2x=110

2x=110-36=74

x=74/2=37