PLEASE HELP!
Jenny likes to paint. She estimates the number of paintings she completes using the function P of w equals one half times w plus one, where w is the number of weeks she spends painting. The function J(y) represents how many weeks per year she spends painting. Which composite function would represent how many paintings Jenny completes in a year?
Options:

Answer:

I believe the answer is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle. The correct option is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

To find the measure of angle A, we need to use the tangent trigonometric function this is because except for the hypotenuse of the triangle the other two sides of the equation are known.

Therefore, the equation of the tangent function of trigonometry for angle A can be written as,

tan(A) = Perpendicular /Base

tan(A) = 9.4 / 6.7

Hence, the equations below that can be used to find the measure of ∠A is tanA=9.4/6.7.

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Answer:

4p + 1 > −15 or 6p + 3 < 45

has solution any number.

The graph looks like this

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

     ---------(-4)---------(7)-------------

The shading is everywhere from left to right.

Step-by-step explanation:

Let's solve this first:

4p+1>-15

Subtract 1 on both sides:

4p>-16

Divide both sides by 4:

p>-4

or

6p+3<45

Subtract 3 on both sides:

6p<42

Divide both sides by 6:

p<7

So our solution is p>-4 or p<7

So let's graph that

~~~~~~~~~~~~~~~~~~~~~~~~~~~~O

                         O~~~~~~~~~~~~~~~~~~~~~~~~~~~~ p>-4

---------------------(-4)---------------------(7)--------------------

or is a key word! or means wherever the shading exist for either is a solution.

So this shading is everywhere.

The answer is all real numbers.

The final graph looks like this:

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

     ---------(-4)---------(7)-------------

The shading is everywhere from left to right.

Answer:

Solution is (-∞,∞)

Step-by-step explanation:

[tex]4p + 1 > -15 \ or \ 6p + 3 < 45[/tex]

Solve each inequality separately

[tex]4p + 1 > -15[/tex]

Subtract 1 from both sides

[tex]4p> -16[/tex]

Divide both sides by 4

[tex]p> -4[/tex]

Solve the second inequality

[tex]6p + 3 < 45[/tex]

Subtract 3 from both sides

[tex]6p< 42[/tex]

Divide both sides by 6

[tex]p< 7[/tex]

[tex]p> -4 \ or \p< 7[/tex]

Solution is (-∞,∞)

Answer:

-3,3.1, 3 2/10

Step-by-step explanation:

When you are putting different numbers from least to greatest, you need to put them in the same form...

First things first we should put -3 wayy up front. negative numbers are worth less than positive numbers.

Then we need to turn 3 2/10 into a decimal.

3 2/10 -------> 3.2

3.2 is more than 3.1

Thus, the order is

-3,3.1, 3 2/10

Hope this helps and have a nice day.

Answer:

-3, 3.1, 3 2/10

Step-by-step explanation:

3 2/10, 3.1, -3

Negative numbers are smaller than positive numbers

-3

Then we need to compare fractions and decimals.

Lets change the fraction to a decimal

2/10 = .2

3.2 and 3.1

3.1 < 3.2

So in order from least to greatest

-3, 3.1, 3 2/10

Answer:

B and C cannot be points on the unit circle

Step-by-step explanation:

This like asking which of the points does not satisfy x^2+y^2=1.

Let's look at (-2/3 , sqrt(5)/3)

x=-2/3

y=sqrt(5)/3

We have x^2=4/9 while y^2=5/9, and x^2+y^2=4/9+5/9=9/9=1.

This first one looks great and is on the unit circle.

Let's look at (sqrt(3)/2 , 1/3)

x=sqrt(3)/2

y=1/3

We have x^2=3/4 and y^2=1/9 , and x^2+y^2=3/4+1/9=31/36 (this is not 1).

This point is not on the unit circle.

Let's look at (1,1)

x=1

y=1

We have x^2=1 and y^2=1, and x^2+y^2=1+1=2 (this is not 1).

This point is not on the unit circle.

Let's look at (0.8,-0.6)

x=0.8

y=-0.6

We have x^2=.64 and y^2=.36, and x^2+y^2=.64+.36=1

This point is on the unit circle.

Answer:

B and C

Step-by-step explanation:

FreckledSpots is correct.

Answer:

Increasing on it's domain [tex](-\infty,\infty)[/tex] because the slope is positive.

The domain and range are both all real numbers, also known as

[tex](-\infty,\infty)[/tex].

Step-by-step explanation:

All domain really means is what numbers can you plug in and you get number back from your function.

I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.

The domain is all real numbers.

In interval notation that is [tex](-\infty,\infty)[/tex].

Now the range is the set of numbers that get hit by y=3x+2.

Well y=3x+2 is a linear function that is increasing.  I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.

If slope is positive, then the line is increasing.

If slope is negative, then the line is decreasing.

So y=3x+2 hits all values of y because it is increasing forever.  The range is all real numbers. In interval notation that is [tex](-\infty,\infty)[/tex].

Answer:

17/25

Step-by-step explanation:

First, convert the decimal into a fraction. To do so, move the decimal point to the right two place values and place over 100.

0.68 = 68/100

Next, simplify. Divide common factors. Remember, what you do to one side, you do to the other. Divide 4 from both sides:

(68/100)/4 = (17/25)

17/25 is your answer.

~

0.68 can be expressed as the fraction 17/25 in the lowest terms.

Step 1: Let x be the decimal representation of the fraction.

x = 0.68

Step 2: Since there are two digits after the decimal point, we can multiply both sides of the equation by 100 to eliminate the decimal.

100x = 68

Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 4.

100 ÷ 4 = 25

68 ÷ 4 = 17

The simplified fraction is:

0.68 = 17/25

Therefore, 0.68 can be expressed as the fraction 17/25 in the lowest terms.

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Answer:

[tex]18\sqrt{2}[/tex]

Step-by-step explanation:

We need to simplify the following expression: [tex]2\sqrt{18} + 3\sqrt{2} + \sqrt{162}[/tex]

Then:

[tex]6\sqrt{2} + 3\sqrt{2} + 9\sqrt{2}[/tex]

[tex]18\sqrt{2}[/tex]

Therefore, the result is: [tex]18\sqrt{2}[/tex]

Answer:

y = 2x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2, so

y = 2x + c ← is the partial equation

To find c substitute (- 2, 3 ) into the partial equation

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = 2x + 7 ← equation of line

Answer:

Statement 1, 2 and 4 are true where as statement 3 is not true.

Step-by-step explanation:

Statement 1: The y-intercept is -1

Point (3/8, 1/2)

Slope = m = 4

y = mx + c

1/2 = 4(3/8) + c

1/2 = 3/2 + c

1/2 = 3/2 + 2c/2

-2 = 2c

c = -1

This statement is true as the y-intercept is -1.

Statement 2: The slope intercept equation is y= 4x - 1

slope = m = 4

y-intercept = c = -1

y = mx + c

y = 4x - 1

This statement is true as the slope intercept equation is y= 4x -1

Statement 3: The point slope equation is y - 3/8 = 4 (x - 1/2)

Point slope equation: y - y1 = m (x - x1)

Points: (x, y) (3/8, 1/2)

y1 = 1/2

x1 = 3/8

Slope = m = 4

y - 1/2 = 4 (x - 3/8)

This statement is not true as the slope intercept equation is y - 1/2 = 4 (x - 3/8) instead of y - 3/8 = 4 (x - 1/2).

Statement 4: The point (3/8, 1/2) corresponds to (x1, y1) in the point slope form of the equation

This statement is true as shown in statement 3's explanation where x1 = 3/8 and y1 = 1/2

!!

Step-by-step explanation:

Triangles can be solved if you know either of three pieces of information:

You can solve for the remaining sides and angles using law of sine and law of cosine.

Law of sine:

(sin A) / a = (sin B) / b = (sin C) / c

Law of cosine:

c² = a² + b² − 2ab cos C

Here, A is the angle opposite side a, B is the angle opposite side b, and C is the angle opposite side c.

Law of cosine can also be written as:

b² = a² + c² − 2ac cos B

a² = b² + c² − 2bc cos A

And law of sine can also be written as:

a / (sin A) = b / (sin B) = c / (sin C)

(Notice that when C = 90°, law of cosine becomes Pythagorean theorem.)

Triangle theorems, like the Pythagorean theorem, are used to establish relationships between the sides of triangles and solve problems. These theorems are used to find unknown sides of triangles when other sides are known. Understanding and applying these theorems can enhance your problem-solving skills in several disciplines.

Theorems about triangles, such as the Pythagorean Theorem, can be used to solve various types of mathematical and real-life problems. The Pythagorean Theorem establishes a relationship between the sides of a right-angled triangle. It states that the square of the hypotenuse (side opposite the right angle, labeled 'c') is equal to the sum of the squares of the other two sides (labeled 'a' and 'b'). This relationship is represented by the equation: a² + b² = c².

To use this theorem in solving problems, usually, two sides of a right triangle are known, and the other side is what we need to find out. For example, if the lengths of a and b are known, then c can be found using the formula c = √a² + b². Similarly, if c and one of the other sides are known, the unknown side can be found by rearranging the Pythagorean theorem equation.

Equipped with the understanding of the Pythagorean theorem and other triangle theorems, you can combine various problem-solving strategies to tackle a vast array of problems. This reasoning skill is useful not only in mathematics but also in science disciplines and in everyday life.

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Answer:

D year 15

Step-by-step explanation:

Given:

y= 8x^2-40x+6

year is the best prediction for when 1206

Finding value of x for y=1206

8x^2-40x+6= 1206

8x^2-40x+6-1206=0

8x^2-40x-1200=0

Solving the above by quadratic formula:

x= [tex]\frac{-b\sqrt{b^{2}-4ac } }{2a}[/tex]

 = [tex]\frac{40\sqrt{40^{2}-4(8)(-1200) } }{2(8)}[/tex]

x= 15 and x= -10

As year can not be negative, hence correct answer is

D: year 15!

To find the probability of drawing certain colour of balls, we first need to find the total number of balls:

5 + 7 +5 = 17

For the number of red balls that need to be added

The original probability of drawing a red ball:

red ball/ total number of balls

= 5/17

To find the number of balls required, we can set an equation.

Let the number of red balls that need to be added be x.

5+x / 17+x = 5/6

(5+x) x 6 = (17+ x) x5

30 +  6x = 85 + 5x

6x - 5x = 85 - 30

x = 55

Therefore, 55 red balls need to be added.

For the number of black balls that need to be added

The original probability of drawing a white ball:

white ball/ total number of balls

=5/17

To find the probability required, we can set an equation.

Let the number of black balls that need to be added be y.

5/ 17 + y = 1/6

5 x 6 = 17 + y

30 = 17 + y

30 - 17 = y

y = 13

Therefore, 13 black balls need to be added.

Hope it helps!

Answer:

JM ≈ 12.9 miles

Step-by-step explanation:

The length of the arc is calculated as

arc = circumference × fraction of circle

     = πd × [tex]\frac{90}{360}[/tex]

JM = π × 16.4  × [tex]\frac{1}{4}[/tex]

     = [tex]\frac{16.4\pi }{4}[/tex] ≈ 12.9

The length of the arc JM will be 12.88 miles.

Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/360) 2πr

The diameter is 16.4 miles. Then the radius will be

r = d / 2

r = 16.4 / 2

r = 8.2 miles.

And angle (θ) will be 90 degrees.

Then the length of the arc JM will be

Arc = (90/360) 2π x 8.2

Arc = 12.88 miles

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Answer:

C. She paid $30 for the table.

Step-by-step explanation:

y = 35x+ 30

This is in slope intercept form

y =mx+b

where m is the slope, which tells us the change

and b is the y intercept, which tells us how much the initial value was (when x=0)

Since x is the number of chairs, and letting x=0

y= 0 chairs +30

Since y= cost of the chairs and the table

y= 30, which is the cost of the table since we bought 0 chairs

Answer:

280

Step-by-step explanation:

If a square has sides of length 70 meters, the perimeter is 280.

Formula: P=4a

P = 4a = 4·70 = 280

Answer:

9

Step-by-step explanation:

70% of 30 is 21, so to find the number of boys, take the original 30, and subtract 21, leaving you with 9, hope this helps and good luck bud :)

There are 9 boys in the class.

To determine the number of boys in a class where 70% are girls, multiply the total number of students by the percentage of boys in the class.

Given:

Answer: There are 9 boys in the class.

Answer: C. [tex]126\pi \text{units}^2[/tex]

Step-by-step explanation:

The surface area of right cylinder is given by :-

[tex]S.A.=2\pi r(r+h)[/tex]

Given : Height : h=2 units

Radius : r= 7 units

The the surface area of the given right cylinder will be :-

[tex]S.A.=2(\pi) (7)(2+7)\ \ \ \text{Put }\pi=3.14[/tex]

i.e. [tex]S.A.=126\pi \text{units}^2[/tex]

Hence, the surface area of the right cylinder = [tex]126\pi \text{units}^2[/tex]

Answer:

C

Step-by-step explanation:

Answer:

a) increases b) decreases

Step-by-step explanation:

Typically, descriptions of trends are indicated as the change of the dependent (y) variable with respect to the increase of the independent (x) variable. In this case, age is the x variable and hours of sleep is the y variable.

Answer:

The data shown on the scatter plot below demonstrates the relationship between a young boy’s age (in months) and the average number of hours that he sleeps each night.

Step-by-step explanation:

The slope of the best fit line shows that as the boy’s age  

increases

the average number of hours that he sleeps each night  

decreases

.

For this case we must simplify the following expression:

[tex]-3 (x + 3) ^ 2-3 + 3x[/tex]

We solve the parenthesis:

[tex]-3 (x ^ 2 + 2 (x) (3) + 3 ^ 2) -3 + 3x =\\-3 (x ^ 2 + 6x + 9) -3 + 3x =[/tex]

We apply distributive property to the terms within parentheses:

[tex]-3x ^ 2-18x-27-3 + 3x =[/tex]

We add similar terms:

[tex]-3x ^ 2-18x + 3x-27-3 =\\-3x ^ 2-15x-30[/tex]

Answer:

[tex]-3x ^ 2-15x-30[/tex]

Answer: [tex]-3x^2-15x-30[/tex]

Step-by-step explanation:

We need to remember that [tex](a\±b)^2=a^2\±2ab+b^2[/tex]

Knowing this, we can simplify  the expression:

[tex]-3(x + 3)^2 - 3 + 3x=-3[x^2+2(x)(3)+3^2]-3+3x=-3[x^2+6x+9]-3+3x[/tex]

Apply Distributive property:

[tex]=-3x^2-18x-27-3+3x[/tex]

Add like like terms:

[tex]=-3x^2-15x-30[/tex]

Since it has the form [tex]ax^2+bx+c[/tex], it is already expressed in Standad form.

To calculate the mileage, you divide the total miles driven (973.50 miles in this case) by the total gallons used (29.5 gallons in this case). Doing so would give you how far the motorcyclist can travel on a single gallon of gasoline, which is the mileage in miles per gallon.

To calculate the mileage in miles per gallon (mpg) of a motorcyclist, we need to divide the total amount of miles driven by the total amount of gallons used. In this case, the motorcyclist has ridden 973.50 miles and used 29.5 gallons.

So, the formula would be: Mileage = Total Miles / Total Gallons

Applying the values from the question to the formula gives: Mileage = 973.50 miles / 29.5 gallons

This would provide you with your miles per gallon, indicating how far the motorcyclist can travel on a single gallon of gasoline.

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the motorcyclist got an average of 33 miles per gallon on their trip.

To calculate the mileage in miles per gallon for the motorcyclist who rode 973.50 miles using 29.5 gallons of gasoline, you divide the total miles traveled by the gallons of gas used:

Therefore, the motorcyclist got an average of 33 miles per gallon on their trip.

Answer:

The cost of each candy bar is $3....

Step-by-step explanation:

Let:

x= $4 (soft drink)

z= price of each candy bar

y=5z(Total price of 5 candy bars)

C= $19(spent money)

The equation is:

C= x+y

$19=$4+5z

Subtract 4 from both sides:

$15=5z

Divide both sides by 5

z=$3

Hence the cost of each candy bar is $3....

Answer:

C) Lateral Area

Step-by-step explanation:

A) Base Area

The formula for base area of of a cylinder is pir^2.

B) Aread

The formula for surface area or area of a cylinder is 2pirh x 2pir^2 = 2pir (h + r)

C) Lateral Area

The formula for lateral area of a cylinder is 2pirh

D) Volume

The formula for volume of a cylinder is base area x h or pir^2h

!!

Answer:

C. Lateral area.

Step-by-step explanation:

We have been given that a right cylinder where h is the height and r is the radius. We are asked to determine the meaning of our given expression [tex]2\pi rh[/tex].

We know that lateral surface area of cylinder is equal to the circumference of base of cylinder times the height of the cylinder.

We know that base of cylinder is circular and circumference of circle is [tex]2\pi r[/tex], therefore, the expression [tex]2\pi rh[/tex] represents lateral area of cylinder.

Answer:

Her income increase by 27.5% from 2004 to 2007

Step-by-step explanation:

Step 1 : Kieya's income in 2004 was $40,000

Step 2 : Kieya's income in 2007 was $51,000

Step 3 : Calculate difference in $

Income in 2007 - Income in 2004 = Increase (+ve) or decrease (-ve) in income

51000 - 40000 = 11000 increase in income

Step 4 : Calculate difference in terms of percentage

Income of 2007-Income of 2004  x 100

          Income of 2004

51000-40000 x 100

    40000

= 0.275 x 100

= 27.5 %

!!

Option A. 11,000 :)

hope this helps!

Answer:

748 mm^2.

Step-by-step explanation:

We can split it up into 2 congruent triangles whose common base is 44 mm. and who have the same height 17 mm.

Area of a triangle= 1/2 * base * height.

So the area of the whole figure = 2 * 1/2 * 44 * 17.

=  44 *17

= 748 mm^2.

Answer:

It's 78 when you round it to nearest 10

flooring a value, simply means, dropping it to the closest integer, so for the floor function or ⌊x⌋, that means

⌊ 2.5 ⌋ = 2

⌊ 2.00000001 ⌋ = 2

⌊ 2.999999999999⌋ = 2

⌊ -2.0000000001⌋ = -3

⌊ -2.999999999999⌋ = -3

let's recall that on the negative side of the number line, the farther from 0, the smaller, so -1,000,000 is a tiny number compared to the much larger -1.

⌊ -5.2 ⌋ = -6.

The notation [[x]] is not standard in typical mathematics; however, it seems that you are looking for a function that represents the floor of x. The floor function, often denoted as ⌊x⌋, is defined as the greatest integer that is less than or equal to x.
To find the floor of -5.2:
1. Identify the integer part of -5.2 without rounding. The integer part is -5 since this is the whole number component of -5.2.
2. Determine if the decimal part (.2 in this case) would cause the number to round up or down. Since the floor function requires us to find the greatest integer less than or equal to the number, we ignore the positive decimal part because it doesn't change the floor for negative numbers.
3. For positive numbers, the floor is the same as stripping away the decimal part without rounding. However, for negative numbers, if the number is not already an integer, the floor is actually one less than the integer part.
4. In the case of -5.2, because the number is negative and not an integer (due to the decimal part), the floor value is -6.
So, f(-5.2) = ⌊-5.2⌋ = -6.

For this case we must find the domain of the following function:

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

By definition, the domain of a function is given by all the values for which the function is defined. The given function is not defined when the denominator is equal to zero, that is:

[tex]x-3 = 0\\x = 3[/tex]

Thus, the domain of the function is given by all real numbers except 3.

Answer:

x other than 3

Answer:

[tex]\large\boxed{h=\dfrac{3V}{\pi r^2}}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cone:}\ V=\dfrac{1}{3}\pi r^2h.\\\\\text{Solve for}\ h:\\\\\dfrac{1}{3}\pi r^2h=V\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}\pi r^2h=3V\qquad\text{divide both sides by}\ \pi r^2\\\\h=\dfrac{3V}{\pi r^2}[/tex]

Answer:

27/20

Step-by-step explanation:

7+1=8

5*4=20

5*1=5

8/20+5/20+14/20

Add numbers from left to right to find the answer.

8+5=13+14=27

27/20 is the correct answer.

Answer:

Option D

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle B is formed by the intersection of the lines a and c. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

b^2 = a^2 + c^2 - 2*a*c*cos(B).

The question specifies that c=71, B=123°, and a=65. Plugging in the values:

b^2 = 65^2 + 71^2 - 2(65)(71)*cos(123°).

Simplifying gives:

b^2 = 14293.0182932.

Taking square root on the both sides gives b = 119.6 (rounded to the one decimal place).

This means that the Option D is the correct choice!!!

Answer:

Option A) 121.73

Step-by-step explanation:

The given scenario can be represented by a Triangle ABC attached in the image below.

We have 3 sides of the triangle ABC, using the measure of these sides we can find the angle opposite to side c which will help us in finding the measure of bearing.

Law of cosine relates the 3 sides of the triangle and angle opposite to one side by following equation:

[tex]c^{2}=a^{2}+b^{2}-2abcos(C)[/tex]

Using the values of a,b, and c we get:

[tex]230^{2}=200^{2}+260^{2}-2(200)(260)cos(C)\\\\2(200)(260)cos(C)=200^{2}+260^{2}-230^{2}\\\\ cos(C)=\frac{200^{2}+260^{2}-230^{2}}{2(200)(260)}\\\\ cos(C)=\frac{547}{1040}\\\\ C=cos^{-1}(\frac{547}{1040})\\\\ C=58.267[/tex]

Thus, the measure of angle C comes out to be 58.267 degrees. The angle with which the boat will have to turn will be:

180 - 58.267 = 121.733 degrees.

Therefore, option A is the correct answer

Answer:

A.) 121.73

Step-by-step explanation:

I got it correct on founders edtell