How can you tell whether a counting problem is a permutation or combination problem? Give examples to support your answer

Answer:

the third side is √11

Step-by-step explanation:

By Pythagoras theorem, we can find the third side

c^2 = a^2 + b^2

if a = √2

b = 3

then,

c^2 = a^2 + b^2

c^2 =(√2)^2 + (3)^2

c^2 = 2+9

c^2 = 11

Taking square root on both sides:

√c^2 = √11

c = √11

So, the third side is √11

Answer:

The correct answer option is C. [tex]f(x)=-2x^3-2x^2+12x[/tex].

Step-by-step explanation:

From the given graph of the polynomial function, we can see that the graph passes through the following points: [tex](-3,0), (0,0)[/tex] and [tex](2,0)[/tex].

So the roots or zeros of this polynomial function are: [tex]-3,0[/tex] and [tex]2[/tex].

Now, we'd graph the equation of the given polynomial and will check for roots and end behavior of the graph.

Therefore, the polynomial function that is represented by the graph is:

[tex]f(x)=-2x^3-2x^2+12x[/tex]

Answer:

B

Step-by-step explanation:

you cannot have to same x

Hence , Option B  set is not a function

A function is an equation which states relation between x and y variable.

a-{(5,2),(4,2),(3,2),(2,2),(1,2)}

Here, x: x>1 ,x∈N, hence function is possible.

b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}

here ,x can't be established as same x has different values.

c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}

Here, every x has it's unique value hence function can be established.

d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}

Here, every x has it's unique value , hence function can be established.

∴option B - {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)} is one from which we can't establish function.

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Answer:

Graph 1: Consistent Dependent

Graph 2: Consistent Independent

Graph 3: Consistent Dependent

Graph 4: Inconsistent

Step-by-step explanation:

Consistent means they have at least one solution.  So lines that intersect once or lines that intersect infinitely many times are both consistent systems.

If they are the system that has one solution they are considered independent.

If they are the system that has infinitely many solutions then are considered dependent.

Inconsistent means they won't intersect at all.

First graph shows the same line graphed onto itself.  That means they have infinitely many solutions and is therefore a consistent dependent system.

Second graph shows the lines intersecting once.  That means they have one solution and therefore is a consistent independent system.

Third graph shows the same description of graph one and is therefore a consistent dependent system.

The last graph shows parallel lines. Parallel lines do not intersect and therefore do not have a solution.  So this system is inconsistent.

Answer:

C. x-5y = 12 and 3x+2y = -15

Step-by-step explanation:

We need to substitute the solution into the equations

A. x-5y = -12 and 3x+2y = -15

    -3 -5(-3) = -12

   -3 +15 = -12

  False

B. x-5y = -12 and 3x+2y = 15

 -3 -5(-3) = -12

   -3 +15 = -12

  False

C. x-5y = 12 and 3x+2y = -15

 -3 -5(3) = 12      3(-3) +2(-3) = -15

   -3 -15 = 12          -9 -6 = -15

  True                     True

D. x-5y = 12 and 3x+2y = 15

-3 -5(3) = 12      3(-3) +2(-3) = 15

   -3 -15 = 12         -9 -6 = 15

  True                       False

Answer:

Part A: OC. 16π square inches

Part B: OC. 36π square inches

Step-by-step explanation:

Part A:

Given

Diameter of circular picture = d = 8 inches

We need to find the radius first to find the area

So,

Rdius = r = d/2 = 8/2 = 4 inches

[tex]Area = \pi r^2\\= \pi *(4)^2\\= 16\pi\ square\ inches[/tex]

Therefore, option C is the correct answer..

Part B:

As two inches frame is added around the picture, the diameter will become 8+4 =12 inches

The new radius will be:

r = 12/2 = 6

So,

[tex]Area\ with\ frame = \pi r^2\\=\pi *(6)^2\\=36\pi\ square inches[/tex]

Therefore, option C is correct ..

Answer:

65 units²

Step-by-step explanation:

The polygon is composed of a trapezium and a triangle

Trapezium QRSU has area (A)

A = 0.5 h (a + b)

where h is the perpendicular height and a, b are the parallel bases.

h = RS = 7 , a = RQ = 6 and b = SU = 8, so

A = 0.5 × 7 × (6 + 8) = 0.5 × 7 × 14 = 49 units²

Triangle STU has area ( A )

A = 0.5 bh ( b is the base and h the perpendicular height )

here b = SU = 8 and h = 4 ( distance from vertex T to the base SU), so

A = 0.5 × 8 × 4 = 16 units²

Total area = 49 + 16 = 65 units²

Answer:

 3 hours

Step-by-step explanation:

Hours/Lawn = (1/5 h)/(1/15 lawn) = 15/5 h/lawn = 3 h/lawn

It will take the sprinkler 3 hours to water the lawn.

Answer:

3 hours 100%

Step-by-step explanation:

Answer:

y = 5x - 39

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 = 5, hence

y = 5x + c ← is the partial equation

To find c substitute (8, 1) into the partial equation

1 = 40 + c ⇒ c = 1 - 40 = - 39

y = 5x - 39 ← equation of line

To write the equation of a line, we will use the slope-intercept form of the equation of a line, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept of the line.
Given the point (8, 1) through which the line passes, and the slope \( m = 5 \), we will plug these values into the equation to find \( b \).
The coordinates of the point give us values for \( x \) and \( y \); specifically, \( x = 8 \) and \( y = 1 \). Using these, we can substitute into the slope-intercept formula:
\[ 1 = 5(8) + b \]
This simplifies to:
\[ 1 = 40 + b \]
To find \( b \), we'll isolate it on one side:
\[ b = 1 - 40 \]
\[ b = -39 \]
Now that we have \( b \), we can write the equation of the line with the given slope \( m \) and y-intercept \( b \):
\[ y = 5x - 39 \]
So the equation of the line that passes through the point (8, 1) with a slope of 5 is:
\[ y = 5x - 39 \]

Answer:

x < -3

Step-by-step explanation:

using the distributive property, distribute 9(2x +1) so it's 18x + 9, subtract 9x from 18x, subtract 9 from -18, divide both sides by 9, x < -3

Inequality is a relationship between two numbers or two expressions.

The value of x in the solution set of 9(2x + 1) < 9x – 18 is

x < -3

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

9(2x + 1) < 9x – 18

Remove the parenthesis.

9 x (2x) + 9 x 1 < 9x - 18

18x + 9 < 9x - 18

Subtract 9x on both sides.

18x + 9 - 9x < 9x - 18 - 9x

9x + 9 < -18

Subtract 9 on both sides.

9x + 9 - 9 < -18 - 9

9x < -27

Divide both sides by 9.

9x/9 < -27/9

x < -3

This means x is less than -3.

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

Thus,

The value of x in the solution set is x < -3.

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

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Answer:

B. 10.5 units

Step-by-step explanation:

The radius of a circle is a segment that has the center of the circle as one endpoint and a point on the circle as the other endpoint. The length of a radius is also called radius.

The figure shows two radii: segments MR and MS.

The lengths of all radii of a circle are equal.

MR = MS = 10.5 units

Answer:

10.5 units

Step-by-step explanation:

The radius of Circle M is the distance from the center M to the circle

That is 10.5 units

Answer:

There will be 96 lemmings in 7 years

Step-by-step explanation:

we have

[tex]f(x)=200(0.901)^{x}[/tex]

This is a exponential function

where

x ------> the time in years

f(x) ----> lemming population

so

For x=7 years

substitute in the function

[tex]f(7)=200(0.901)^{7}[/tex]

[tex]f(7)=96.4[/tex]

There will be 96 lemmings in 7 years

Answer: B

Step-by-step explanation:

Because m<7 and m<6 share a vertex and doesn’t share any common sides and they are across from each other which means they are vertical and vertical angles are congruent

The missing reason for the 3rd step will be vertical angles are congruent. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The diagram is given below.

Then the missing reason for the 3rd step will be vertical angles are congruent.

Thus, the correct option is B.

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Answer: The base of the square is 52.67

Step-by-step explanation:

256=1/2bh

b=base

h=height

256=1/2(12)b

256=6b

52.67=b

Answer:

A

Step-by-step explanation:

The graphs of two functions y=f(x) and y=g(x) intersect at one point. The coordinates of this point are (0,-2). This means

f(0)=-2

g(0)=-2

Thus,

f(0)=g(0)

Note that the blue line passes through the point (-2,4), so

f(-2)=4

and the red line passes through the point (-2,-4), so

g(-2)=-4

Hence,

f(-2)≠g(-2)

and f(0)≠g(-2)

Answer:

First Option

Step-by-step explanation:

It can be seen in the graph that the two plotted functions are linear, which means that if the lines are not parallel or not lying on each other, then the lines will intersect at most one point in the plane. It can be clearly seen that both the lines intersect at the point (0,-2). As far as the functions are concerned, there is an input and an associated output. The term f(0) means that 0 is the input and f(0) is the functional value, which is the output. In the graph, both lines have the y-intercept of -2. Y-intercept is the point where the value of the input (i.e. the value of x) is 0. Since both lines are intersecting at (0,-2), this implies that f(0) = g(0). This essentially means that the the functional value of f, which is -2, is equal to the functional value of g!!!

Answer:

125-135

Step-by-step explanation:

The standard deviation is 7. This implies that the IQ scorings can be between 123 and 137. With a 90% confidence in these numbers, 125-135 is the closest interval to 90% confidence.

Answer: (129.04,130.96)

Step-by-step explanation:

Given : Sample size : n= 145

Mean IQ in the sample : [tex]\overline{x}=130[/tex]

Standard deviation : [tex]\sigma=7[/tex]

Significance level : [tex]\alpha=1-0.9=0.1[/tex]

Critical value : [tex]z_{\alpha/2}=1.645[/tex]

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=130\pm(1.645)\dfrac{7}{\sqrt{145}}\\\\=130\pm0.96\\\\=(129.04,\ 130.96)[/tex]

Hence, the 90% confidence interval for the students' mean IQ score is (129.04,130.96)

Answer:

Part 1) The algebraic expression is equal to [tex]1.10(n-1)[/tex]  or [tex]1.10n-1.10[/tex]

Part 2) The algebraic expression is equal to [tex]\frac{1.10}{n}[/tex]

Step-by-step explanation:

Part 1) Algebraic expression of (n-1) increased by 110%

we know that

110%=110/100=1.10

so

The algebraic expression of (n-1) increased by 110% is equal to multiply 1.10 by (n-1)

[tex]1.10(n-1)[/tex]

Distributed

[tex]1.10n-1.10[/tex]

Part 2) Algebraic expression of n^(-1) increased by 110%

we know that

110%=110/100=1.10

so

The algebraic expression of n^(-1) increased by 110% is equal to multiply 1.10 by n^(-1)

Remember that

[tex]n^{-1}=\frac{1}{n}[/tex]

so

[tex]1.10(n^{-1})=1.10\frac{1}{n}=\frac{1.10}{n}[/tex]

The algebraic expression is 2.1n - 2.1

The expression is given as:

n - 1

When it increases by 110%, the expression becomes

(n - 1) * (1 + 110%)

Express as decimal

(n - 1) * (1 + 1.10)

Evaluate the sum

(n - 1) * 2.10

Expand

2.1n - 2.1

Hence, the algebraic expression is 2.1n - 2.1

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Answer:

D.)  240 miles.

Step-by-step explanation:

By proportion the distance between the 2 cities

= (3 / 1/8) * 10

= 3*8*10

= 240 miles.

The 2 cities are D.) 240 miles away.

By proportion of the distance between the 2 cities

= (3 / 1/8) * 10

= 3*8*10

= 240 miles.

This means that in case your journey is twice as lengthy, you will move two times as a long way. in case you journey three times as long, you will pass 3 instances as a ways. At the same time as in case you tour half as long, you may go 1/2 as far. By something ratio the time adjustments, the distance will alternate proportionally, that is, within the identical ratio.

The made of approach within the ratio is identical to the made from extremes. Two ratios are stated to be identical if their cross products are identical. The sharing formula is given as, a : b :: c : d ⇒ a b = c d.

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Answer:

250

Step-by-step explanation:

If Bulan's team rows their boat at a rate of

2

minutes per

500

meters, they row at a rate of

1

minute per

250

meters. We know this because

1

minute is

1

2

of

2

minutes, and in this time, they will have to have rowed

1

2

the distance they would row in

2

minutes (

500

m).

1

2

of

500

is

250

.

So, we now have the rate in min/m.

If, every

1

minute, Bulan's team rows

250

meters, this means that every

250

meters, they have rowed for

1

minute.

Bulan's team's rowing rate in m/min is

250

m/

1

min.

Answer with explanation:

Speed of rowing boat by Bulan is given as:

→ 2 Minute = 500 meter

→ 1 Minute = 250 Meter

So, Bulan Rowing rate is equal to

  [tex]250 \frac{\text{meter}}{\text{minute}}[/tex]

Final answer:

The missing term in the polynomial 36x³ - 22x + ___ that ensures a GCF of 2x must be ax, where 'a' is an even number. Possible terms could be 4x, -8x, or any other term with an even coefficient and an x factor.

Explanation:

The student's question asks which term can be used in place of the blank in the polynomial 36x³- 22x + ___ so that the greatest common factor (GCF) of the resulting polynomial is 2x. To determine the missing term, we need to look at the existing terms of the polynomial. The first term, 36x³, has a GCF of 2x because 36 is divisible by 2 and x³ has x as a factor. Similarly, the second term, -22x, also has a GCF of 2x since 22 is divisible by 2 and there's already an x present. To ensure that the GCF of the final term with the others is 2x, the term must have both a coefficient divisible by 2 and at least one factor of x.

Let's say the missing term is ax, where 'a' is an even number to keep the common factor of 2x. Therefore, a term like 4x or -8x could work. If the resulting polynomial had a term without x, then the GCF would just be 2, not 2x. Hence, adding a term with a factor of 2 and x not only completes the polynomial but also ensures that the GCF is 2x.

Answer:

1) false

2) true

3) true

4) false

5) -0.75 > - 0.5 false

6) 0.625 < 0.875 true

Step-by-step explanation:

7) July 10, 1913 - - > 134°

January 23, 1971 - - > - 80°

134 ___ - 80

134 > - 80

-80 represents the smaller value

Answer:

d. y = 0.1x+ 200

Step-by-step explanation:

His weekly salary is 200, that is the y intercept

He makes 10%   (.10 in decimal form) of his weekly sales, that is the slope

y= mx+b

y = .1x+200

Net pay is the gross pay after all the deductions.

1. Net pay = 980 - 156.00 - 60.76 - 14.21 = 749.03

The answer is A.

2. Total deductions = Gross pay - Net Pay:

980 - 749.03 = 230.97

The answer is A.

Answer:

A. $749.03

A. $230.97

Step-by-step explanation:

Jones's total deductions are :

[tex]156+60.76+14.21=230.97[/tex] dollars

His gross pay = $980

Net pay = gross pay - deductions

Net pay = [tex]980-230.97=749.03[/tex] dollars

Part A: Net pay is : A. $749.03

Part B : total deductions are : A. $230.97

ANSWER

a. 12 units

EXPLANATION

According to the altitude theorem, RT which is the altitude, is equal to the geometric mean of TQ and TS, the segments created by the foot of the altitude on the hypotenuse.

This implies that:

[tex]x = \sqrt{TQ \times TS} [/tex]

From the diagram, TQ=16 and TS=9.

We substitute these values and solve for x.

[tex]x = \sqrt{9 \times 16} [/tex]

[tex]x = \sqrt{144} [/tex]

[tex]x = 12[/tex]

Therefore x is 12 units.

The correct answer is A

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}12x=76-20y&\text{change the signs}\\8x=84-20y\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x=-76+20y\\8x=84-20y\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-4x=8\qquad\text{divide both sides by (-4)}\\.\qquad x=-2\\\\\text{put the value of x to the second equation}\\\\8(-2)=84-20y\\-16=84-20y\qquad\text{subtract 84 from both sides}\\-100=-20y\qquad\text{divide both sides by (-20)}\\5=y\to y=5[/tex]

[tex]\huge{\boxed{y=\frac{1}{2} x+1}}[/tex]

First, we must find the slope of the graphed line. We can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are known points on the line.

Plug in the values. [tex]\frac{4-2}{-1-0}[/tex]

Subtract. [tex]\frac{2}{-1}[/tex]

Simplify. [tex]-2[/tex]

To find the slope of the perpendicular line, we must find the opposite inverse slope. This means we first need to multiply it by [tex]-1[/tex], then we need to swap the numerator and denominator.

[tex]-2*-1=2[/tex]

Now, swap the numerator and denominator. The numerator is [tex]2[/tex], and the denominator is [tex]1[/tex] by default.

[tex]\frac{1}{2}[/tex]

The only answer choice with a slope of [tex]\frac{1}{2}[/tex] is [tex]\boxed{y=\frac{1}{2} x+1}[/tex]

Answer:

f (x) = (x+5) is linear

Step-by-step explanation:

We are given the following function and we are to determine if it is a linear function or not:

[tex] f ( x ) = ( x + 5 ) [/tex]

For a function to be linear, it must be written in the standard form [tex]y=mx+c[/tex] and its graph gives a straight line.

Whereas, when an equation is squared, its graph becomes a curved one which is not linear.

Therefore, the given function f (x) = (x+5) is linear.

Answer: No, it is not a linear function. It is a Quadratic function.

Step-by-step explanation:

Given the following function:

 [tex]f(x)=x(x+5)[/tex]

You need to apply Distributive property:

[tex]f(x)=(x)(x)+(x)(5)[/tex]

[tex]f(x)=x^2+5x[/tex]

You can observe that the highest exponent of the function is "2", therefore, it is not a Linear function, but a Quadratic function in the form:

[tex]f(x) = ax^2 + bx + c[/tex]

Where a, b, and c are numbers ([tex]a\neq 0[/tex])