The 20 members of the photography club are trying to raise at least $1,400 for
new photography equipment. They have already raised $540.
Let m represent the amount of money each member must raise, on average, to meet
their goal. Write an expression for the total amount of money going to be raised.
b Write an equation that represents the club raising all the money.
с
Solve the equation. What does the solution mean in context of the scenario?
d Write an inequality representing the amount of money each member must raise,
on average, to meet or exceed their goal.
Write an inequality showing the possible average amount of money each club member
needs to raise.

Step-by-step explanation:

Standard form of circle with    center  (h.k) and radius r :

( x-h)^2 + (y-k)^2 = r^2

FOr the data given:

(x + 4)^2  + ( y-3)^2 = 81             (81 is the radius, 9, squared)

Area = 4b² + 16b + 16 square centimeters

The side length of the larger square, L, is equal to the side length of the smaller square plus twice the width of the border:

L = 4 + 2b

Now, we want to find the total area of the decorative tile, which is the area of the larger square. The area of a square is given by the side length squared:

Area = L²

Substitute the expression for L from above:

Area = (4 + 2b)²

Now, we can expand this expression:

Area = (4 + 2b)(4 + 2b)

Area = 16 + 8b + 8b + 4b²

Area = 16 + 16b + 4b²

So, the total area of the decorative tile in terms of b is:

Area = 4b² + 16b + 16 square centimeters

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Answer:

V ≈ 1809 ft^3

Step-by-step explanation:

Given:

r (radius) = 6ft

h (height) = 16ft

π = 3,14

Find: V (volume) - ?

[tex]v = \pi {r }^{2} \times h[/tex]

[tex]v = 3.14 \times {6}^{2} \times 16 ≈1809 \: {ft}^{3} [/tex]

a) The coordinates of the vertex C' are C'(x, y) = (5, 5).

b) The length of the side A'B' is equal to 4.

In this problem we find the case of a right triangle, whose image must be found by a kind of rigid transformation known as dilation. The dilation formula for a vertex is introduced below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

k - Dilation factor

O(x, y) - Center of dilation

P(x, y) - Original vertex

P'(x, y) - Resulting vertex

And the dilation formula for a formula is:

L' = k · L

Where:

L - Original length.

L' - Resulting length.

Please notice that side lengths can be found by Pythagorean theorem.

we know that O(x, y) = (2, 9), k = 1 / 2, A(x, y) = (6, 7), B(x, y) = (10, 7) and C(x, y) = (6, 1), then the resulting vertices and sides are:

C'(x, y) = (2, 9) + (1 / 2) · [(6, 1) - (0, 9)]

C'(x, y) = (2, 9) + (1 / 2) · (6, - 8)

C'(x, y) = (2, 9) + (3, - 4)

C'(x, y) = (5, 5)

And the length of the side A'B' is:

AB = 8

A'B' = (1 / 2) · AB

A'B' = 4

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The correct equation for the following sentence is 24 = 31.4n + (–8.4) . Option C

Algebraic expressions are simply described as those expressions that are made up of factors, coefficients, constants, terms and variables.

Additionally, algebraic expressions are made up of arithmetic or mathematical operations, such as;

From the information given, we have that;

24 is the constant

Let the number be represented as n

Then, the expression is given as;

24 = 31.4(n) - 8.4

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Answer:

the average amount Mrs. Gordon pays in interest each month, we need to determine the total interest paid over the six-month period and divide it by the number of months.

The total interest paid can be found by subtracting the cost of the stove from the total amount paid over six months:

Total interest paid = Total amount paid - Cost of the stove

The total amount paid over six months is calculated by adding the monthly payments:

Total amount paid = $160/month * 6 months

Let's perform the calculations:

Total amount paid = $160/month * 6 months = $960

Total interest paid = Total amount paid - Cost of the stove

= $960 - $850

= $110

Now, to find the average amount Mrs. Gordon pays in interest each month, we divide the total interest paid by the number of months:

The average amount paid in interest each month = Total interest paid / Number of months

= $110 / 6 months

≈ $18.33

Therefore, Mrs. Gordon pays an average of approximately $18.33 in interest each month.

The value of side length c is 13.55 units.

The length of side c is calculated by applying sine rule as shown below;

The formula for sine rule is given as;

a/sinC = b/sinA

For the given question, we will have the following equation,

c/sin (34) = 11 / sin (27)

The value of c in the triangle is calculated as follows;

c = (sin 34 / sin 27 ) x 11

c = 13.55 units

Thus, the value of side length c is determined by applying sine rules.

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the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.

what is  rounded to the nearest  ?

"Rounded to the nearest" means finding the nearest value of a specified degree of accuracy. For example, rounding a number to the nearest whole number means finding the closest whole number to that number. If the number is equally close to two whole numbers, it is rounded up to the higher number.

In the given question,

The trajectory of the package can be modeled using the equation:

y = -0.5 * g * x² / v² + tan(∅) * x + h

where:

y = height of the package above the ground at horizontal distance x

g = acceleration due to gravity (9.8 m/s²)

v = horizontal velocity of the drone (100 m/s)

theta = angle at which the package is released

h = initial height of the package above the ground (4500 meters)

To hit the target, we want the package to land on the ground, which means its final height should be zero. So, we can set y = 0 and solve for x to find the horizontal distance at which the package should be released. This gives:

0 = -0.5 * 9.8 * x² / 100² + tan(∅) * x + 4500

Simplifying and rearranging, we get:

0.049 * x² + tan(∅) * x - 4500 = 0

Using the quadratic formula, we can solve for x:

x = (-tan(∅) ± √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)

Since we want the package to land in front of the target, we take the positive root of the equation:

x = (-tan(∅) + √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)

Now, we need to find the value of theta that will make the package hit the target. Since the drone is traveling horizontally, the package will also have a horizontal velocity of 100 m/s when it is released. So, we can use trigonometry to find the angle at which the package should be released. This gives:

tan(∅) = 4500 / x

Substituting this into the equation for x, we get:

x = (-4500 / x + √((4500 / x)²+ 0.049 * 4500 * 4)) / (0.098)

Simplifying and rearranging, we get:

x² = 4500 * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x) / 0.098

Squaring both sides, we get:

x⁴ = 4500² * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x)² / 0.009604

Expanding and simplifying, we get:

x⁴ = 900000000 * (1 + 0.00012345679 * x² - 0.00012345679 * 4500 * x / √(x² + 202500)) / 0.009604

We can solve for x using numerical methods, such as using a graphing calculator or an online solver. Using such a method, we find that:

x ≈ 9,932 meters

Therefore, the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.

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The statement that "if you took a true "if-then' statement and reversed the clauses, the new statement would also be true" is False.

By reversing the clauses within an accurate "if-then", one will manifest a new statement known as the "converse" of the initial formula. Though, it is not inevidably true.

For instance, if the original expression was "If it rains, then the ground gets wet", its converse is "If the ground gets wet, then it rains". Unfortunately, that specific converse has the potential to be incorrect since there are several other methodologies from which the land can gain moisture beside rain (e.g. sprinkler system, someone unintentionally pouring water, etc.).

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Answer:

x²+14x+49

Step-by-step explanation:

(a+b)²=a²+2ab+b²

(x+7)²=x²+2×7×x+7²=x²+14x+49

The cubic polynomial is given as y = 0.25(x³ - 12x + 16). Then the value of y when x = 6 will be 40.

Therefore the option  C is correct.

A polynomial expression is described as an algebraic expression with variables and coefficients.

If the zeroes of the polynomial are negative 4, 2, and 2.

Then the factors will be (x + 4), (x - 2), and (x - 2).

Then the cubic polynomial will be

we can write the polynomial equation as:

y = C(x³ - 12x + 16)

Then the polynomial is maximum at (-2, 8) then the value of C will be 0.25.

y = 0.25 (x³ - 12x + 16)

y = 0.25 (6³ - 12 × 6 + 16)

y = 0.25 (216 - 72 + 16)

y = 0.25 (160)

y = 40

Note that there was no  diagram provides, i solved a similar question

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Answer:

Set your calculator to degree mode.

2) tan(43°) = x/8.2

x = 8.2tan(43°) = 7.6

3) sin(29°) = 3.5/x

x sin(29°) = 3.5

x = 3.5/sin(29°) = 7.2

The effect Lola's  mass decreasing has on the the mean and median

Given  values :  

5 African elephants

The mean mass of the elephants was  3800 kg

The median mass of the elephants was  3600 kg

The smallest elephant, named Lola, weighed 2700 kg

Lola then got very sick and lost weight until her mass reached 1800 kg

2700  ,    A    ,  3600 ,   B    ,  C      

as Median is 3600 and lowest is 2700

now 2700 becomes 1800

1800  ,  A  , 3600  , B , C

so Median remains the same as 3600

So we notice no change in Median

The mean mass of the elephants =  3800 kg

=> total weight = 5 x 3800 = 19000 kg

2700 kg becomes 1800 kg

total mass = 19000 - 2700 + 1800

= 181000 kg

The following can be inferred :

New Mean = 18100/5   = 3620  kg

Mean reduced by 3800 - 3620  = 180 kg

No change in Median weight

Mean reduced by 180 kg

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Answer:

36 °

Step-by-step explanation:

The markings imply equal sides*

So both of the angles are 27° there

To find angle a we do 180 - (27+27) and obtain 126°

Then to find angle y, we do 180-angle a which is 180-126 and we get 54°

We now have reached the triangle where you're supposed to find x right?

So x is equal to 180 - both other angles, which is 180 - (90 and angle y) = 180- (90+54) = 180 - 144 = 36 which is your final answer

Answer:

[tex]A_{\text{red}} = 1766.25 \text{ in}^2[/tex]

Step-by-step explanation:

We can see that there are four bands total on the target, two of which are red bands. With this information, we can solve for the radius of the circle within each band, since we know that each band is the same width:

[tex]r_1 = \dfrac{1}{4} \cdot 30 = 7.5\\[/tex]

[tex]r_2 = \dfrac{2}{4} \cdot 30 = 15\\[/tex]

[tex]r_3 = \dfrac{3}{4} \cdot 30 = 22.5\\[/tex]

[tex]r_4 = 30[/tex]

We can now find the area of each red band by subtracting:

the area of the circle within the white band just inward of the red band

-- from --

the area of the circle within the red band.

Finding the area of the outer red band:

[tex]A_{\text{outer red}} = A(\text{circle within outer red}) - A(\text{circle within outer white})[/tex]

[tex]A_{\text{outer red}} = A(\odot \text{ with radius }r_4) - A(\odot \text{ with radius } r_3)[/tex]

↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])

[tex]A_{\text{outer red}} = (\pi \cdot 30^2) - (\pi \cdot 22.5^2)[/tex]

↓ using 3.14 for [tex]\pi[/tex]

[tex]A_{\text{outer red}} = (3.14 \cdot 30^2) - (3.14 \cdot 22.5^2)[/tex]

↓ evaluating the right side

[tex]A_{\text{outer red}} = 2826 - 1589.625[/tex]

[tex]A_{\text{outer red}} = 1236.375 \text{ in}^2[/tex]

Finding the area of the inner red band:

[tex]A_{\text{inner red}} = A(\text{circle within inner red}) - A(\text{circle within inner white})[/tex]

[tex]A_{\text{inner red}} = A(\odot \text{ with radius }r_2) - A(\odot \text{ with radius } r_1)[/tex]

↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])

[tex]A_{\text{inner red}} = (\pi \cdot 15^2) - (\pi \cdot 7.5^2)[/tex]

↓ using 3.14 for π

[tex]A_{\text{inner red}} = (3.14 \cdot 15^2) - (3.14 \cdot 7.5^2)[/tex]

↓ evaluating the right side

[tex]A_{\text{inner red}} = 706.5 - 176.625[/tex]

[tex]A_{\text{inner red}} = 529.875 \text{ in}^2[/tex]

Finally, we can find the area of all of the red on the target by adding the area of the outer and inner red bands.

[tex]A_{\text{red}} = A_{\text{outer red}} + A_{\text{inner red}}[/tex]

[tex]A_{\text{red}} = 1236.375 \text{ in}^2 + 529.875 \text{ in}^2[/tex]

[tex]\boxed{A_{\text{red}} = 1766.25 \text{ in}^2}[/tex]

Let h be the altitude of the balloon in feet and t be the time in minutes. At time t = 0, the balloon is at an altitude of h = 0. Since the balloon rises at a rate of 440 feet per minute, the equation that gives the altitude of the balloon as a function of time is:

h(t) = 440t

To find out how long it took the balloon to reach its final altitude of 92400 feet, we can set h(t) equal to 92400 and solve for t:

440t = 92400

t = 210

Therefore, it took the balloon 210 minutes to reach its final altitude.

Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.

To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:

Time spent on videos = 10% of 40 hours = 4 hours

Time spent on homework = 15% of 40 hours = 6 hours

Time spent on games = 20% of 40 hours = 8 hours

Time spent on social media = 25% of 40 hours = 10 hours

Time spent on shopping online = 20% of 40 hours = 8 hours

Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.

The difference between these two amounts is:

6 hours - 8 hours = -2 hours

This means that Heracio spent 2 hours more on shopping online than on doing homework.

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses:

4v - w = 4(4i - i) - (-9i) = 16i - 4i + 9i = 21i

Now, we can substitute the values of u, v, and w into the expression:

5u - (4v - w) = 5(-7i + 7j) - (21i) = -35i + 35j - 21i = -56i + 35j

Therefore, the final result is -56i + 35j.

Answer:

  -60i +39j

Step-by-step explanation:

You want the value of 5u -(4v -w) given ...

These are added the way any polynomials are added. Like terms can be combined.

  5u -(4v -w)

  = 5(-7i +7j) -(4(4i -j) -(-9i))

  = -35i +35j -(16i -4j +9i)

  = -35i +35j -25i +4j

  = -60i +39j

__

Additional comment

We have assumed a typo in the definition of v, that 4i-j was wanted instead of 4i-i.

<95141404393>

Answer

Construction Model Stats

User

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

ChatGPT

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

User

The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.

ChatGPT

We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:

tan(18 degrees) = h / d

Solving for h, we get:

h = d * tan(18 degrees)

Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:

h = 510 feet * tan(18 degrees)

h ≈ 157.3 feet

Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.

User

The following regular polygon has 15 sides. This distance from its center to any given vertex is 12 inches.

Which of the following is the best approximation for its perimeter?

(1) 68 inches

(3) 84 inches

(2) 75 inches

(4) 180 inches

ChatGPT

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

Answer:

To find the percentage of Virginia's gross pay that she took home after deductions, we need to first calculate her gross pay and then subtract the total amount of deductions to find her net pay. Then, we can divide her net pay by her gross pay and multiply by 100 to find the percentage.

Virginia earns $69,500 per year, so her gross pay per paycheck (assuming she is paid every two weeks) is:

$69,500 / 26 = $2,673.08

Her total deductions from her most recent paycheck were:

$200.20 + $180.65 + $72.00 + $110.00 + $250.00 = $812.85

So her net pay was:

$2,673.08 - $812.85 = $1,860.23

To find the percentage of her gross pay that she took home, we can divide her net pay by her gross pay and multiply by 100:

($1,860.23 / $2,673.08) x 100 ≈ 69.59%

Therefore, the closest option is (3) 69.59%.

Answer:

Step-by-step explanation:

Answer:    x=a/3      x=a/5

Step-by-step explanation:

15x²-2ax = a²          subtract a² from both sides

15x²- 2ax - a² = 0

You would solve this like you would any quadratic.  Factor.

Start my multiplying the first and last coefficients

15(-a²)  = -15a²    =>find 2 numbers that multiply to this but add to middle

                                term (-2a)

-5a   and   +3a     multiply to -15a² and adds to -2a

Substitute the middle term with the numbers we just found, keeping the x

15x²- 2ax - a² = 0

15x²- 5ax+3ax - a² = 0         > group the first 2 terms and last 2

(15x²- 5ax)(+3ax - a²)= 0      > this is not your factors, you need to take

                                                 GCF out of each grouping

5x(3x-a)+a(3x-a)=0              >if the parenthesis is same, you did good

                                                now the parenthesis is your GCF and one of

                                                your factors, whatever is left is your other

                                                factor

(3x-a)(5x-a)=0                        > set each factor = 0 and solve for x

(3x-a)=0         and             (5x-a)=0  

x=a/3                                    x=a/5

Step-by-step explanation:

The 'x's '   ( the domain)  are mapped into two values of 'y' (the range)

Range =   1,6

Answer:

[tex]y = -x/5 -4.[/tex]

Step-by-step explanation:

To simplify the line x + 5y = 20 into y = mx + b form:

x + 5y = 20.

5y = -x + 20.

y = -x/5 + 4.

The line parallel to the line y = -x/5 + 4 will have the same slope of -1/5.

We get the equation:

y = -x/5 + b.

To find b, we plug in the point (5, -5).

-5 = -5/5 + b.

-5 = -1 + b.

b = -4.

[tex]y = -x/5 -4.[/tex]

The coordinates of the resulting point, R', are (1,-4).

A translation is a type of transformation in geometry that moves a point or an object from one place to another without changing its size, shape, or orientation.

To translate a point, you need to specify the direction and distance of the movement.

Given that:

The point R(1,-2) is being translated 2 units down, which means that it will move vertically downwards by a distance of 2 units.

The x-coordinate will remain the same, as the movement is only in the y-direction.

So, to find the coordinates of the resulting point, R', we subtract 2 from the y-coordinate of the original point R:

R' = (1, -2 - 2)

R' = (1, -4)

Therefore, resulting coordinates of R' are (1,-4).

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Answer: Let's start by using algebra to represent the problem.

Let X be the amount of money that Kyle started with.

Then we can create the following equations:

And we know that he's out of money, so:

Substitute the first equation into the second equation to get:

Substitute the first two equations into the third equation to get:

Substitute all three equations into the fourth equation to get:

(0.5X + 36.50) + (0.25X + 9.25) + (0.25X + 4.75) = X

Simplify and solve for X:

Therefore, Kyle started with $101.

Answer:

Step-by-step explanation:

C (Wait for another defendant, check with him and write this answer)

The baker should use 24kg amount of flour when making the biscuits. The correct answer is (b) 24kg.

To determine the amount of flour the baker should use when making biscuits, we can use the given ratio of flour to sugar, which is 4:1.

Since the ratio is 4:1, for every 4 parts of flour, there is 1 part of sugar. Therefore, the ratio of flour to sugar can be expressed as 4/1.

If the baker uses 6kg of sugar, we can set up a proportion to find the corresponding amount of flour:

4/1 = x/6

Cross-multiplying, we get:

4 * 6 = 1 * x

24 = x

Therefore, the baker should use 24kg of flour when making the biscuits.

In summary, the correct answer is (b) 24kg.

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Answer:

The equation of the circle with a diameter of 14 and whose center is (-4,6) is  [tex]x^{2}+y^2+8x-12y+3=0[/tex]

Step-by-step explanation:

Given that diameter is 14. So, the radius is 14/2 which is equal to 7.

Also, the center is (-4,6).

We know that the equation of a circle with center (h,k) and radius r units is

[tex](x - h)^2+(y-k)^2=r^2 .[/tex]

Here, h=-4, k=6 and r=7.

Putting these values in the above equation,

[tex](x - (-4))^2+(y-6)^2=7^2 .[/tex]

[tex](x +4)^2+(y-6)^2=49 .[/tex]

On solving, the equation of the circle is

[tex]x^2+y^2+8x+-12y+3=0[/tex].

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