5. Which equation's line is steeper and explain how you know

A. y = 3x + 7
B. y=x+9

"The ratio of the number of male staff to the number of female staff is 2:3."

This means if [tex]x[/tex] is the number of male staff, and [tex]y[/tex] is the number of female staff, then these numbers occur in a fixed ratio such that

[tex]\dfrac xy = \dfrac23[/tex]

The sentence does not say anything about the actual number of staff members. There's no reason to believe that there are 50 people working.

What it does say is that 2/5 = 40% of the team is made of males and 3/5 = 60% is made of females.

(a) Of the males, 20% = 1/5 of them are under the age of 20. This means that 20% of 40% of the entire staff is made up of males under 20, or

2/5 × 1/5 = 2/25 = 8%

Of the females, 40% = 2/5 are under the age of 20. So 40% of 60% are females under 20, which comes out to

3/5 × 2/5 = 6/25 = 24%

Adding these up, we get a total of 8% + 24% = 32%.

(b) Yes, any change to the team would adjust this percentage.

Consider a smaller example of a team of 4, 1 each of male/female and under/over 20. 1/4 = 25% of this team is female and under 20. If we add one more under-20 female, the new ratio is 2/5 = 40%. If we add one more member to any other group, the new ratio is 1/5 = 20%.

Answer: y=-1.5x-1

Step-by-step explanation:

A(-8,-2)   B(4,6)    C(x,y) - the midpoint of the line

1. Calculate the coordinates of the midpoint of the segment using the formula:

[tex]\displaystyle\\C(x,y)=(\frac{x_A+x_B}{2} ,\frac{y_A+y_B}{2})\\\\ C(x,y)=(\frac{-8+4}{2},\frac{-2+6}{2})\\\\ C(x,y)=(\frac{-4}{2} ,\frac{4}{2})\\ C(x,y)=(-2,2)\\Thus,\ C(-2,2)[/tex]

2. Find the slope of the line AB using the formula:

[tex]\displaystyle\\The\ slope=\frac{y_B-y_A}{x_B-x_A} \\\\The\ slope=\frac{6-(-2)}{4-(-8)} \\\\The\ slope=\frac{6+2}{4+8} \\\\The\ slope=\frac{8}{12} \\\\The\ slope=\frac{2}{3}[/tex]

3. Find the slope of the line perpendicular to the line AB:

[tex]\displaystyle\\The \ \perp slope=-\frac{1}{the\ slope} \\\\The \ \perp slope=-\frac{1}{\frac{2}{3} } \\\\The \ \perp slope=-\frac{3}{2}[/tex]

4. Find an equation for the perpendicular bisector of the line segment:

[tex]\displaystyle\\The \perp\ slope=\frac{y-y_C}{x-x_C} \\\\-\frac{3}{2}=\frac{y-2}{x-(-2)} \\-\frac{3}{2} =\frac{y-2}{x+2} \\[/tex]

Multiply both parts of the equation by (x+2):

[tex]\displaystyle\\y-2=(-\frac{3}{2} )(x+2)\\\\y-2=-\frac{3}{2}x+(-\frac{3}{2})(2)} \\\\y-2=-\frac{3}{2}x-3 \\\\y-2+2=-\frac{3}{2}x-3+2\\\\ y=-\frac{3}{2}x-1\\\\ y=-1.5x-1[/tex]

Cutting a cake into 8 pieces is a chemical change.

Now,

When the cake is cut, the pieces cannot be joined again and form a cake.

Hence, Cutting a cake into 8 pieces is a chemical change.

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Answer:

The distance between both numbers is 3.2.

Step-by-step explanation:

How to find the answer is to:

1. Subtract the 9 and 7 to get 2.

2. Place your decimal point behind the 2 to make .2

3. Do 5 minus 2 to get 3.

Your answer is 3.2.

The sum of any number and zero is the original number: Identity property

When two numbers are added, the sum is the same regardless of the order of addends: Commutative property

When three or more numbers are added, the sum is the same regardless of how the addends are grouped: Associative property

A + B = B + A if A and B are any two whole numbers.

In other words, the sum of two whole numbers is true regardless of how the addends—or real numbers—are arranged.

Any order will work for adding the numbers. Even if the numbers are rearranged, the sum of the two numbers remains the same.

When an is a whole number, A + 0 equals 0 + A.

In other words, the number itself is equal to the sum of any whole number and zero. In other words, zero is the only whole number that when added to, does not alter the value (identity) of the original number.

The additive identity or identity element for the addition of whole numbers is the integer 0 (zero).

When zero is added to a number, the result is unchanged.

If any three whole numbers are A, B, and C, then (A + B) + C = A + (B + C)

In other words, whole number addition is associative.

Any group or placement of the numbers has no effect on the sum when three or more are added.

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Answer:

A

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 )

A y = [tex]\frac{1}{2}[/tex] x+ 2 ← has slope m = [tex]\frac{1}{2}[/tex]

B y = - [tex]\frac{1}{2}[/tex] x + 7 ← has slope m = - [tex]\frac{1}{2}[/tex]

C y = 2x + 4 ← has slope m = 2

D y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{4}[/tex] ← has slope m = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

• the product of the slopes of perpendicular lines = - 1

- [tex]\frac{1}{2}[/tex] × 2 = - 1

then lines B and C are perpendicular

The cube root of 27 is 3√t=3, which indicates that 3√t.

Cube root, or the cube root of a number, is simply the square root of that number. It can be used in various mathematical contexts to simplify complicated calculations. For example, when dealing with complex fractions and rational numbers (numbers that have a decimal point), the cube root can be used to solve problems more quickly and accurately.

We are aware that 5×5×5×5 Equals 125. Therefore, 125 is known as the cube of 5. Finding a number's cube root, on the other hand, entails doing the cube operation in reverse and is symbolised by the symbol.

A number x's cube roots are the integers y that answer the equation.

3√t is the cube root of 27,so 3√t=3 .

3√3

3×3×3=27

Hence the correct answer Is option (b) 3√t is the cube root of 27,so 3√t=3 .

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Answer: D because Angle D = Angle L

Answer:

(3/2,1/2)

Step-by-step explanation:

y=2x^2-6x+5

a=2

b=-16

substitute the coefficients into the expression

x= - -6/2x2

x=3/2

y=2x^2-6x+5, x=3/2

calculate the function value for x=3/2

y=1/2

(3/2,1/2)

Answer: the width of the rectangle is 14 units

Let's denote the length of the rectangle to be x and the width to be y.

The first sentence tells us that the length, x , is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. x = 2y - 4.

In the question given that the perimeter of the rectangle is 76 units

Perimeter of a rectangle is 2( length + breadth )

According to the question :

76 = 2(x + y)

76 = 2(2y – 4 + y)

76 = 2(3y – 4 )

76 = 6y – 8

84 = 6y

y = 14 units

putting the value of in x = 2y – 4

x = 2(14) – 4

x = 24 units

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Answer: How do you write a population growth equation?

The annual growth of a population may be shown by the equation: I = rN (K-N / K), where I = the annual increase for the population, r = the annual growth rate, N = the population size, and K = the carrying capacity.

Step-by-step explanation: hope this helps!!!

Answer:

Step-by-step explanation:

The annual growth of a population may be shown by the equation: I = rN (K-N / K), where I = the annual increase for the population, r = the annual growth rate, N = the population size, and K = the carrying capacity.

The angles ∠YWZ and ∠XWY are 36° and 144° respectively.

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The measure of the missing angles are d= 77° , e= 31° ,and f = 72°.

As given in the question,

Angle e is vertically opposite to the given angle 31°

⇒Measure of angle e = 31°

Angle d is vertically opposite to the given angle 77°

⇒Measure of angle d = 77°

Angle e , Angle f and angle d are linear pairs

⇒∠e +∠f +∠d =180°

⇒31° +∠f + 77°=180°

⇒ ∠f =180° -108°

⇒ ∠f =72°

Therefore, the measure of the missing angles are d = 77° , e = 31° and

f = 72°.

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Answer: 0.0000413

Step-by-step explanation:

The -5 exponent is the amount of zeros that go behind 413.

The probability that a randomly selected point of the diagram lies within the circular region as requested in the task content is; π/4.

It follows from the task content that the probability that a randomly selected point of the diagram lies within the circular region is to determined.

This probability in discuss is equal to the ratio of the area of the circle to the area of the rectangle.

Consequently, the area of the circle is equal to;

πr².

However, since the side length of the square, which is the diameter of the circle is; 2r; it follows that it's area is;

2r × 2r = 4r².

Therefore, the probability is; πr²/4r².

When expressed in its simplest exact form, we have;

π/4.

Therefore, The probability that a randomly selected point of the diagram lies within the circular region as requested in the task content is; π/4.

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The total number of blocks is 659.

Given that there is 9 in one's place of the total number of blocks. It is also given that the number in the hundreds place is 1 more than the number in the tens place.

If we assume x as the number on hundreds place and y as the number on tens place, then according to the question:

x=y+1                                                                                                          ......(1)

Also, the sum of hundreds and tens place numbers is 11.

x+y=11                                                                                                       ......(2)

substitute the value of x from equation (1) in equation (2)

y+1+y=11

=>2y=10

=>y=5

Now substitute the value of y in equation (1);

x=5+1

x=6

Therefore, number on the hundreds place is 6 and on the tens place is 5 and the total number is 659.

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Answer:

Step-by-step explanation:

To find the scale factor, take the value of one side length from the scaled copy and divide it by the value of the corresponding side length of the original.

39/13 = 3

Therefore, the scale factor is 3.

Answer:

y≤-1

Step-by-step explanation:

Subtract 9 from both sides

4-9 = -5

Divide the remainding by 5

-5 / 5 = -1

If a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function is "false" statement.

A matrix function can be defined in a variety of ways (or matrix-valued function). One manner is in which the function takes the shape of a matrix, rather than numbers, the matrix contains functions. A(t), for example, is a 2 x 2 matrix function.

Some key features regarding the matrix function are-

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The complete question is-

If a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function. (True/False)

The geometry term represented by the statement "If two points are given, then exactly one line can be drawn through those two points." is "geometric postulate".

Postulates are assertions that are believed to be correct in the absence of evidence.

In this sense, the main feature of the postulate is its widespread acceptance by the scientific community, that is, by the vast majority of scientists who are committed to its investigation.

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Answer: What are the values of sin, cos and tan?

Sin Cos Tan Chart

Angles (in degrees) 0° 60°

Sin θ 0 √3/2

Cos θ 1 1/2

Tan θ 0 √3

Cot θ ∞ 1/√3

Step-by-step explanation:  hope this helps a little!!!!

All statements are true, but if you try to reverse them they won't necessarily be true.

let us start

Square ⇒ Has 4 sides

But if something has 4 sides it doesn't mean it's a square (example: rectangle)

Angle is 80° ⇒ acute angle

But acute angle is any angle below 90°, not just 80° so the reverse isn't true.

x – 17 = 4 ⇒ x = 21

And if we reverse

x = 21 ⇒ x – 17 = 4

we see that it's true for either direction.

x = 7 ⇒ |x| = 7

But |x| = 7 doesn't mean that x has to be 7, x can also be -7, so the reverse isn't true.

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The volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

for given question,

We need to find the volume of the solid whose base is the region bounded between the curve y = x³ and the y-axis from y = 0 to y = 1 and whose cross section taken perpendicular to the y-axis are squares.

Now we rewrite given curve y = x³ in terms of x.

[tex]x=\sqrt[3]{y}[/tex]

Since the length of the side of each cross sectional square is [tex]2\sqrt[3]{y}[/tex], the cross sectional area A(y) can be given by

A(y) = [tex](2\sqrt[3]{y})^2[/tex]

A(y) = [tex]4y^{\frac{2}{3} }[/tex]

The region is bounded from y = 0 to y = 1

so, the volume V can be found by,

[tex]V=\int\limits^1_04y^{\frac{2}{3} }~dy\\\\V=4\int\limits^1_0 y^{\frac{2}{3} }~dy\\\\V=4\times \frac{3}{5} \\\\V=\frac{12}{5}\\\\V=2.4[/tex]

Therefore, the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

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The state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.

We are given that:

The rate of tax on sales for South Salt Lake is = 7.05 %

That is:

Sale tax rate = r = 7.05 %

Now, we are given that the selling price of a car = $ 21,900

Selling price = $ 21,900

Now we need to find the sales tax amount that will be imposed on the car.

For this, we will calculate the percentage.

Sales tax = 7.05 % of $ 21,900

Sales tax = 7.05 % × $ 21,900

Sales tax = 7.05 / 100 × $ 21,900

Sales tax = 7.05 × $ 219

Sales tax = $ 1543.95

Therefore, we get that the state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.

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The error was the use of just a line on each name instead of a line with an arrow head pointing to the right. It should be: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex]are opposite rays.

To name two rays that are opposite each other, start the name of each of the rays with the letter of the endpoint that connects both rays together, then use the letter of the point where each of the rays extend to infinity.

The line on top both of the letters of the rays must have an arrow head, "→" that points to the right.

In problem 26, the letters used in naming the opposite rays were correct, but, the line on each letter that was used had no arrows pointing to the right. They are wrong.

The correct way of naming the opposite rays is: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex].

Therefore, we can conclude that, the error was the use of just a line on each name instead of a line with an arrow head pointing to the right. It should be: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex]are opposite rays.

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Based on the percentage of those who love running and those who don't,  the total percentage of the athletes who do not enjoy cycling is 24.5%.

The percentage who don't enjoy cycling are:

= Percentage who enjoy running and but not cycling + Percentage who don't enjoy running or cycling

Solving gives:

= ((1 - 70%) x 45%) + ( (1 - 45%) x (1 - 80%))

= (30 % x 45%) + (55% x 20%)

= 24.5%

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The total possible ways of arranging 30 students in two groups of sizes 4 and 6 respectively are 6309453150, which is obtained by using the prerequisite knowledge of combinations.

What is the combination?

A combination is a mathematical procedure that deduces the number of feasible selections in a collection of articles in which the order of the selection does not matter. In combinations, you can choose any items in any order. Its formula is given by C(n,r) = n! / (n - r)! r!)

Calculation of the total possible ways of arranging two focus groups of students with sizes 4 and 6 respectively

Given a group of 30 students

Two focus groups are to be arranged in sizes 4 and 6 respectively

Total number of possible ways to arrange the two focus groups = C(30,4) × C(26,6)

Using the formula for combination, we get,

T.F.O = [30! / (26! 4!)] × [26! / (20! 6!)]

T.F.O = 27405 × 230230

         = 6309453150

Hence, the required possible ways to arrange two groups are given by 6309453150.

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Answer: 296 with a remainder of 1 (I'm guessing this by mental math, btw, why not just use a calculator, the calc is your best chance for a right answer anyway)

Edit: Used calc, was close lol, 296.5 is the exact answer

Step-by-step explanation:

P.S: Question, is that supposed to be divided or square rooted?

Anyway, I'll explain it since I can't leave it hanging:

2*2 = 4 so 5-4 = 1 and bring 9 down, after that 2*9 = 18, so it becomes 1, and then bring down 3 for 13, and 6*2 = 12, so 13-12 = 1, and that is 296 with a remainder of 1.

Answer:

6 miles

Step-by-step explanation:

1 1/2 miles x 4 days= 6 miles over 4 days