25 points!!!
using the 30° 60° 90° Triangle Theorem solve for x
(leave it in simplest radical form)

b) Scatter plot chart would indicate a positive correlation

c) Candidate D would be the most cost-effective choice, as their expected salary would increase the most. Candidate F would also be a good choice, as their expected salary would increase by £1,000.

A scatter plot chart can be used to plot the data of the two variables on a two-dimensional graph, and the data points can be connected with a line or a curve.

a) The weights of the attributes in this case seem to be appropriate for the purpose of selecting a Regional Officer for the Western Region.

This data shows that the charity is placing a greater emphasis on the candidate's commitment, managerial experience and ideas, as these are likely to be the most important factors in selecting a successful Regional Officer.

Additionally, Education has the lowest weight at 10, indicating that this is not a major factor in consideration.

Overall, the weight of each criteria reflects the importance of the criteria to the charity and is appropriate for this case.

b) The scatter plot chart would indicate a positive correlation between the two variables, with the higher aggregate score corresponding to the higher expected salary.

Based on this chart, candidates A, D and F would be the best 2-3 candidates, with the highest aggregate scores of 50, 90 and 62 respectively.

c) If the charity is prepared to pay £1,000 for each additional aggregate score, then candidate D would be the most cost-effective choice, as their expected salary would increase the most (from £60,000 to £61,000). Candidate F would also be a good choice, as their expected salary would increase by £1,000 (from £52,000 to £53,000).

Candidate A would not be recommended, as their expected salary would increase by only £500 (from £46,000 to £46,500).

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As a result, whereas the latter two expressions are not polynomials, the first two and last one are polynomial.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or any expression . For instance, the first two terms of the polynomial with the variables x and y have coefficients of 7 and -3, respectively. The constant coefficient is the third term of 1.5.

An expression made up of variables and coefficients and utilizing solely the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables is referred to as a polynomial.

Let's examine each phrase separately:

Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "3X² -5x⁴+2x-12" is a polynomial.

Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x⁵-5x⁴+4x³-3x²+2x-1" is a polynomial.

- Since it contains negative exponents of variables, which are not permitted in polynomials, "x⁻⁵-5x⁻⁴+4x⁻³+2x⁻¹ - 1" is not a polynomial.

- Because it contains division, which is not permitted in polynomials, "4/x⁴+3/x³-2/x²-1" is not a polynomial.

-Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x³-7x²+9x-5x⁴-20" is a polynomial.

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Answer:196 possible committees

Step-by-step explanation:

Part (a): Three cases:

Case 1: 3 men and 5 women: (7 C 3) * (5 C 5) = 35 * 1 = 35; or

Case 2: 4 men and 4 women: (7 C 4) * (5 C 4) = 35 * 5 = 175; or

Case 3: 5 men and 3 women: (7 C 5) * (5 C 3) = 21 * 10 = 210

35 + 175 + 210 = 420 possible committees

Part (b): Six cases:

Cases 1–3: Oldest man included (but not oldest woman):

Case 1: 3 men and 5 women: Not possible**; therefore, 0; or

Case 2: 4 men and 4 women: 1 * (6 C 3) * (4 C 4) = 20 * 1 = 20; or

Case 3: 5 men and 3 women: 1 * (6 C 4) * (4 C 3) = 15 * 4 = 60; or

Cases 4–6: Oldest woman included (but not oldest man):

Case 4: 3 men and 5 women: (6 C 3) * (5 C 5) = 20 * 1 = 20; or

Case 5: 4 men and 4 women: (6 C 4) * 1 * (4 C 3) = 15 * 4 = 60; or

Case 6: 5 men and 3 women: (6 C 5) * 1 * (4 C 2) = 6 * 6 = 36

0 + 20 + 60 + 20 + 60 + 36 = 196 possible committees

Answer:

6+20

Step-by-step explanation:

The cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents.

The given equation is 24b = t, where b is the cost of one bottle of water and t is the price of a case of 24 bottles.

We are given that the price of the case is $7.50. Substituting this value in the equation, we get:

24b = 7.50

To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides by 24:

b = 7.50/24

Simplifying this expression, we get:

b = 0.3125

Therefore, the cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents. In other words, if you were to buy a case of 24 bottles of water for $7.50, each bottle of water would cost you about 31.25 cents.

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Based on the given information, Trey can fit 160 plastic cubes inside the box.

What is volume of cube?

The volume of a cube is calculated by cubing the length of any one side of the cube. In other words, if a cube has sides of length "s", then its volume "V" is V = s³

To calculate the number of plastic cubes that can fit inside the box, we need to first calculate the volume of the box and the volume of each plastic cube. Then, we can divide the volume of the box by the volume of each plastic cube to get the total number of cubes that can fit inside.

The volume of the box is:

4 ft x 2.5 ft x 2 ft = 20 cubic feet

The volume of each plastic cube is:

(1/2 ft) x (1/2 ft) x (1/2 ft) = 1/8 cubic feet

To find out how many plastic cubes can fit inside the box, we can divide the volume of the box by the volume of each plastic cube:

20 cubic feet ÷ (1/8 cubic feet) = 160

Therefore, Trey can fit 160 plastic cubes inside the box.

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Answer:

The correct answer is 36π

Step-by-step explanation:

Answer:

if the mass of 16cm3 of a metal is 20g what is the mass of 30cm3

44°+107°+x°=180

151°+x°=180°

x°=180°-151°

x°=29°

After the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s.

In a perfectly elastic collision, the total momentum of the system is conserved, as well as the total kinetic energy. This means that the sum of the momenta of the carts before the collision is equal to the sum of the momenta after the collision. In this case, since cart b is initially at rest, its initial momentum is zero.

We can use conservation of momentum to determine the final velocities of the carts. Let the velocity of cart b after the collision be v, then the velocity of cart a after the collision is -4 m/s. The momentum of cart a before the collision is m(4 m/s) = 4m, and the momentum of cart b after the collision is 3mv.

Using conservation of momentum, we have:

m(4 m/s) + 0 = m(-4 m/s) + 3mv

Simplifying this equation, we get:

8m = 3mv + 4m

Dividing both sides by 3m, we get:

v = (8/3) - (4/3)v

Solving for v, we get:

v = 2 m/s

So after the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s. We can verify that this satisfies conservation of momentum:

m(4 m/s) + 0 = m(-4 m/s) + 3m(2 m/s)

4m = 4m

This result shows that in a perfectly elastic collision, even though the carts exchange momentum, the total momentum of the system is conserved.

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Answer : 10.5

Explanation: Divide 168/16

The probability of getting a '1' on the first roll and '2' on the second roll for the given expression is [tex]\frac{1}{18}[/tex] .

What about probability?

In mathematics and statistics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

The probability of an event A is denoted by P(A) and is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In other words, it is the number of ways that event A can occur divided by the total number of possible outcomes.

For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6, since there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

Probability is used in many different fields, such as gambling, statistics, and science, to make predictions about the likelihood of different outcomes. It is also used to model complex systems and to test hypotheses in scientific experiments.

According to the given information:

When a die is rolled 2 times, the output we get

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Total no of getting '1' on first roll and '2' on second roll = 2

Total outcomes = 36

⇒ [tex]\frac{2}{36}[/tex]

⇒ [tex]\frac{1}{18}[/tex]

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Recording the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting is as follows:

Customer Billing:

Debit Accounts Receivable $3,200

Credit Service Revenue $3,200

(To record the performance of services for customers during the month.)

Customer Billing:

No Record during the current month.

Cash-basis accounting recognizes expenses and revenues when cash exchange takes place.

Accrual-basis accounting matches expenses and revenues to the month or period when the transaction occurs, whether there is a cash exchange or not.

For instance, the accrual-basis will recognize the receipt of cash as follows:

Next Month:

Debit Cash $3,200

Credit Accounts Receivable $3,200

On the other hand, the cash-basis will recognize revenue with the receipt of cash as follows:

Next Month:

Debit Cash $3,200

Credit Service Revenue $3,200

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We can conclude after answering the presented question that As a equation result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's name the first car's fuel efficiency (miles per gallon) x and the second car's fuel efficiency y. We are aware of the following:

The first automobile used 25 gallons of gas and covered 25 miles.

The second automobile used 20 gallons of petrol and drove 20 miles.

The two automobiles went a total of 1075 miles, thus 25x + 20y = 1075.

Their combined fuel economy was 50 miles per gallon, thus x + y = 50/1 = 50.

[tex]25x + 20y = 1075\\x + y = 50\\25x + 20y = 1075\\-20x - 20y = -1000\\5x = 75x = 15\\x + y = 50\\15 + y = 50\\y = 35\\[/tex]

As a result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.

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Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.

Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for Eric's guests. The first part of the expression (326 + 37g) represents the cost of the hotel room for all g guests, while the second part of the expression (287 + 23g) represents the cost of food and beverage for all g guests. To calculate the total cost of the hotel room and food and beverage, we can use the following formula: (326 + 37g) - (287 + 23g) = 39 + 14g.Expression 2, on the other hand, represents the difference in cost between the hotel room and the cost of food and beverage for a single guest. The first part of the expression (38 + 14g) represents the cost of the hotel room for one guest, while the second part of the expression (287 + 23g) represents the cost of food and beverage for one guest. To calculate the total cost of the hotel room and food and beverage for one guest, we can use the following formula: 38 + 14g.In conclusion, Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.

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Answer: 6 songs.

Step-by-step explanation:

Each song is $2 dollars. $12 divided by $2 equals 6.

So he can download 6 songs.

Answer:

Step-by-step explanation:

Formula for the sum of interior angle of an n-gon is S = (n-2)x180°.

So for our 5 sided polygon we get:

             S = (5-2)x180° = 540°          

Now we can solve:

             [tex]100+4x+(3x+3)+(5x-2)+103=540[/tex]

                                                        [tex]12x+204=540[/tex]

                                                                  [tex]12x=336[/tex]

                                                                      [tex]x=28[/tex]°

Solution:   [tex]x=28[/tex]°

Answer: x=43

Step-by-step explanation:

We know The interior angles in a hexagon sum to 720°.

so we can add all the angles and equal them to 720

100 + 4x + (3x + 3) + (5x-2) + 103 = 720

Simplify by combining like terms

(100 + 3 -2 + 103) and (4x + 3x +5x)

204 + 12x = 720

Subtract 204 from both sides to isolate x

204 - 204 + 12x = 720 - 204

12x = 516

Divide both sides by 12 to solve for x

12/12 x = 516/12

Simplify

x = 43

to check your work, substitute the value of x into your equation and solve

100 + 4x + 3x + 3 + 5x-2 + 103 = 720

100 + 4(43) + (3)(43) + 3 + (5)(43) -2 + 103 = 720

100 + 172 + 129 + 3 + 215 -2 + 103 = 720

720 = 720

They equal so your solution is correct

Statement (A) is true, Statement (B) is false, Statement (C) is true, Statement (D) is true and Statement (E) is false.

The given information is that P(odd) = 1/3

where odd numbers are 3 and 5, and there are two odd-numbered sections out of six equal sections.

(A) The probability of landing on an odd-numbered section is not exactly 33.33%, but approximately equal to 33.33% or 1/3.

So, statement (A) is true.

(B) The probability of landing on an even-numbered section is not exactly 66.67%, but approximately equal to 66.67% or 2/3.

So, statement (B) is false.

(C) The probability of landing on an odd-numbered section is given as 1/3, which is less than the probability of landing on an even-numbered section, which is 2/3. Therefore, statement (C) is true.

(D) It is given that one of the sections is numbered 6. So, it is not impossible to land on 6. Therefore, statement (D) is false.

(E) To determine if the spinner is fair, we need to know the probability of each outcome, which is not provided in the given information. Therefore, we cannot determine if the spinner is fair or not based on the information given. So, statement (E) is uncertain.

Therefore, the true statements about this game are (A), (C), and (D).

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Answer:

the answer to the question is B

Step-by-step explanation:

no need for explanation just trust the source

(a) The probability of rain on January 1st is 0.614. (b) The probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083. (c) the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053. (d) They wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days. (e) The distribution of X is a geometric distribution.

a) The probability that it will rain on January 1st can be estimated using the information provided by komonews.com, which states that the chances of rain on any day in the first week of January in Seattle is about 0.614. Assuming that the probability of rain is constant across all days of the week, the probability of rain on January 1st is also 0.614.

b) The probability that it will rain for the first time in the New Year on January 3rd can be calculated by considering the probability of no rain for the first two days, followed by rain on the third day. The probability of no rain for the first two days is [tex](1-0.614)^2[/tex] = 0.136, and the probability of rain on the third day is 0.614. Therefore, the probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083.

c) The probability that the people of Seattle get to wait at least 3 days until it rains for the first time in the New Year can be calculated by considering the probability of no rain for the first three days. The probability of no rain for the first three days is [tex](1-0.614)^3[/tex] = 0.053. Therefore, the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053.

d) The expected value or average of the number of days people in Seattle wait for the first day of rain in the New Year can be calculated by using the formula E(X) = 1/p, where p is the probability of rain on any given day. Therefore, the expected value or average number of days people in Seattle wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days.

e) The number of days until it rains for the first time in the New Year, X, is a geometric random variable since it represents the number of trials until the first success (rain). The probability of success (rain) remains constant over time, and the trials (days) are independent of each other. Therefore, the distribution of X is a geometric distribution.

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Answer:

12 L 500 mL

Step-by-step explanation:

The length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

we shall represent the unknown leg of the right triangle with the letter "x" so that by Pythagoras rule we can evaluate for x as follows:

8² = 5² + x²

x = √(8² - 5²) {make TV the subject}

x = √(64 - 25)

x = √39

x = 6.2450

Therefore, the length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.

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The sum given to the kindergarten was reduced by 15%.

Let's first find out how much money the kindergarten spent in March:

So, in April, the kindergarten spent the same amount on books, which was $200. It also reduced its spending on food by $240, which means it spent:

Food: $1400 - $240 = $1160

The remaining 20% of the sum given in April was spent on cleaning services, which means:

Cleaning services: 20% of sum given in April = 0.2 x $x (where x is the sum given in April)

We can set up an equation based on the above information:

$200 + $1160 + 0.2x = x

Simplifying and solving for "x":

$1360 + 0.2x = x

0.8x = $1360

x = $1700

Therefore, the sum given to the kindergarten in April was $1700, which means it was reduced by:

($2000 - $1700) / $2000 x 100% = 15%

So, the sum given to the kindergarten was reduced by 15%.

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Using mensuration, we can find that the mass of male is greater than that of the female's by 63.507kg.

Mensuration can be defined as a measurement action. Our world is three dimensional. Both elementary school mathematics and secondary school mathematics heavily rely on the idea of measurement. Also, measuring is directly related to our daily life. When we learn to measure items, we practise measuring both 2D and 3D shapes. Both conventional and nonconventional units of measurement can be used to determine the size of objects or quantities.

In the given table,

Height of male = 1.68m.

Mass of male = 158.757kg.

Height of female = 1.448m.

Mass of female = 95.25kg.

Difference between mass of male and female,

= 158.757 - 95.25

= 63.507kg.

The mass of male is greater than that of the female's by 63.507kg.

So, 2nd statement is true.

Rest of the statements are not true.

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We can conclude by answering the provided question that expression As a result, b = 1 is not a valid substitute for b in the equation because it would set the denominator to zero and render the expression undefined.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical association or routine. A real integer, a mutable, or a mix of the two can be used as an equation. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and geometry. They are used in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

The expression is as follows:

[tex]b^2 / (-7b + 7)\\-7b + 7 = 0\\b = 1\\[/tex]

As a result, b = 1 is not a valid substitute for b in the equation because it would set the denominator to zero and render the expression undefined.

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a is 15 days

b is 20%

hope this helps you

Answer:

a is 15 daysb is 20%

Step-by-step explanation:

The equation of the tangent line is y = -x/3 + 1/3 where

The equation of a tangent line to a curve is the equation of the line that touches the curve at that point and tangent to it.

To find the equation of the tangent line to the curve y = 1/(3sinx + 3cosx) at (0, 1/3), we know that the value of the tangent at that point is the derivative of the curve at that point.

so, differentiating y wiith respect to x, we have

y =  1/(3sinx + 3cosx)

= (3sinx + 3cosx)⁻¹

Let u = 3sinx + 3cosx

y = u⁻¹

dy/dx = du⁻¹/du du/dx

= -u⁻² du/dx

Now du/dx = d(3sinx + 3cosx)/dx

= d3sinx/dx + d3cosx/dx

= 3cosx - 3sinx

So, dy/dx = -u⁻² du/dx

= -(3sinx + 3cosx)⁻²(3cosx - 3sinx)

= -(3cosx - 3sinx)/3sinx + 3cosx)²

Now, at (0, 1/3)

dy/dx = -(3cosx - 3sinx)/3sinx + 3cosx)²

= -(3cos0 - 3sin0)/3sin0 + 3cos0)²

= -[3(1) - 3(0)]/[3(0) + 3(1))²

= -[3 - 0]/[0 + 3)²

= -3/3²

= -1/3

Now, the equation of a line in slope form passing through the point (x', y') is

(y - y')/(x - x') = m where m = slope

For the tangent line

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

(y - y')/(x - x') = m

(y - 1/3)/(x - 0) = -1/3

(y - 1/3)/x = -1/3

y - 1/3 = -x/3

y = -x/3 + 1/3

Comparing this with the equation of a line in slope-intercept form y = mx + b where m = slope and b = y-intercept

So, the equation of the tangent line is y = -x/3 + 1/3 where

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Answer:

x=3, y=2

Step-by-step explanation:

First Add both equations

3x-y=7                     ---1

x+y=5                      ---2

----------

so we get, 4x=12

so x=3

Now plug x back into equation 2 so we get y=2

Step-by-step explanation:

that means we optionally multiply one or both equations with some factors, so that one variable term has the same coefficient in both equations but with different signs.

and then we add both equations giving us one equation in the other variable, which we can solve.

and then we use that with any of the original equations to solve for the first variable.

in this case we don't need the multiplication step, as the terms in y have already the same coefficient (1) with different signs.

so, we add both equations

3x - y = 7

+ x + y = 5

------------------

4x 0 = 12

4x = 12

x = 12/4 = 3

x + y = 5

3 + y = 5

y = 5 - 3 = 2

Answer: Kayla sold 1/12 gallons more than Ethan.

Step-by-step explanation:

Let's start by finding out how much lemonade Kayla sold. We know that together, Ethan and Kayla sold 1 1/4 gallons, which is the same as 5/4 gallons. We also know that Ethan sold 2/3 gallons. Therefore, we can find how much Kayla sold by subtracting Ethan's sales from the total sales:

Kayla's sales = Total sales - Ethan's sales

Kayla's sales = 5/4 - 2/3

To subtract these fractions, we need to find a common denominator. The smallest common multiple of 4 and 3 is 12, so we can rewrite the fractions with 12 as the denominator:

Kayla's sales = (5/4)(3/3) - (2/3)(4/4)

Kayla's sales = 15/12 - 8/12

Kayla's sales = 7/12

Therefore, Kayla sold 7/12 gallons of lemonade. Now, we need to compare this to Ethan's sales. We can convert Ethan's sales to twelfths to make it easier to compare:

Ethan's sales = (2/3)(4/4) = 8/12

Now we can see that Kayla sold more lemonade than Ethan. The difference in sales is:

Kayla's sales - Ethan's sales = 7/12 - 8/12

Kayla's sales - Ethan's sales = -1/12

The result is negative, which means that Ethan sold 1/12 gallons less than Kayla. Therefore, Kayla sold 1/12 gallons more than Ethan.

Answer:

To work out the probability that Caroline buys fruit or buys a CD or both, you can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are events.

In this case, A is the event that Caroline buys fruit and B is the event that Caroline buys a CD.

The probability that Caroline buys fruit is 0.4 and the probability that Caroline buys a CD is 0.6.

To find the probability that Caroline buys fruit and a CD, you can multiply the probabilities of the two events:

P(A and B) = P(A) x P(B) = 0.4 x 0.6 = 0.24

Therefore, the probability that Caroline buys fruit or buys a CD or both is:

P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.6 - 0.24 = 0.76

So, the probability that Caroline buys fruit or buys a CD or both is 0.76 .