Use the permutation formula below to find the number of outcomes when n = 5 and r = 2.

Answer:

they are the same line

Step-by-step explanation:

if you divide the first line by 2 you'll get:

2(3x)+2y=2(23)===> 3x+y=23

Answer:Rules for rotating points about the origin

1. The point (a,b) rotated 90° counterclockwise about the origin

becomes (-b,a).

A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)

A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)

B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)

C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)

D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)

Step-by-step explanation:

Answer:

71.4% ( i think)

Step-by-step explanation:

If we translate 1 in 1.4 using what is described, it turns into (1/1.4)

Putting this into a calculator, we get 0.714286. Translated into a percent, that becomes 71.4286%

The probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.

When the odds are given as "1 in 1.4," it means that there is 1 chance of success (having a law degree) for every 1.4 chances of failure (not having a law degree).

To find the probability that a member of the Senate (selected randomly) has a law degree, you can use the formula:

Probability = 1 / (1 + Odds)

In this case, the odds are 1 in 1.4, so the probability is:

Probability = 1 / (1 + 1.4) ≈ 1 / 2.4 ≈ 0.4167

So, the probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.

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Answer: Choice B

[tex]2 = \log_{8}(64)[/tex]

======================================================

Explanation:

The original equation is [tex]8^2 = 64[/tex] with 8 as the base. That is also the base of the log when we get the final answer shown above. Logs are useful to isolate the exponent.

The general rule is that [tex]\text{y} = b^{\text{x}}[/tex] is equivalent to the log form of [tex]\text{x} = \log_{b}(\text{y})[/tex] where b is the base of each.

2 = log Subscript 64 Baseline 8 is the  logarithmic equation which is equivalent to 82 = 64.

Two or more expressions with an Equal sign is called as Equation.

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.

The logarithmic equation equivalent to 82 = 64 is:

2 = log Subscript 64 Baseline 8

This is because the logarithmic equation relates the base (64) to the result of the exponentiation (8), which in this case is 2.

Hence, 2 = log Subscript 64 Baseline 8 is the  logarithmic equation which is equivalent to 82 = 64.

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Step-by-step explanation:

b1) Any line parallel to the x-axis is horizontal. If we look at the graph of a horizontal line, we see that for any x-value you give, the y-value will be the same. In this case, the y-value is -1. Hence, the equation for the line is [tex]y=-1[/tex], as y will be -1 no matter the x.

The gradient for a horizontal line is 0, as the "rise" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would have 0 on the top, which makes the whole fraction 0.

b2) Any line parallel to the y-axis is vertical. If we look at the graph of a vertical line, we see that for any y-value, the x-value will be the same. In this case, the x-value is -1. Hence, the equation for the line is [tex]x=-1[/tex], as x will be -1 no matter the y.

The gradient for a vertical line is undefined, as the "run" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would be dividing by 0, which is undefined.

Answer:

Step-by-step explanation:

Let the epicenter be E(x, y).

Use the distance formula for each given distance:

Use the first and third equations, considering both have same term for x, and solve for y:

Substitute y into one of equations and solve for x:

The epicenter is E( - 2, 3)

Answer:

(-2, 3)

Step-by-step explanation:

Given:

Model each given point as the center of a circle and the distance the epicenter is away from the point as the circle's radius.

The epicenter's location will be the point of intersection of the three circles.

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where (a, b) is the center and r is the radius

Circle A

[tex]\implies (x+2)^2+(y-5)^2=4[/tex]

[tex]\implies x^2+4x+4+y^2-10y+25=4[/tex]

[tex]\implies x^2+4x+y^2-10y+25=0[/tex]

Circle B

[tex]\implies (x-2)^2+(y-3)^2=16[/tex]

[tex]\implies x^2-4x+4+y^2-6y+9=16[/tex]

[tex]\implies x^2-4x+y^2-6y-3=0[/tex]

Circle C

[tex]\implies (x+2)^2+(y+4)^2=49[/tex]

[tex]\implies x^2+4x+4+y^2+8y+16=49[/tex]

[tex]\implies x^2+4x+y^2+8y-29=0[/tex]

To find the point of intersection of the three circles, solve simultaneously.

Substitute equation B into equation A to eliminate x² and y²:

[tex]\implies x^2-4x+y^2-6y-3=x^2+4x+y^2-10y+25[/tex]

[tex]\implies -4x-6y-3=4x-10y+25[/tex]

Rearrange to isolate y:

[tex]\implies -6y-3=8x-10y+25[/tex]

[tex]\implies 4y-3=8x+25[/tex]

[tex]\implies 4y=8x+28[/tex]

[tex]\implies y=2x+7[/tex]

Substitute the expression for y into equation C and simplify:

[tex]\implies x^2+4x+(2x+7)^2+8(2x+7)-29=0[/tex]

[tex]\implies x^2+4x+4x^2+28x+49+16x+56-29=0[/tex]

[tex]\implies 5x^2+48x+76=0[/tex]

Substitute the expression for y into equation B and simplify:

[tex]\implies x^2-4x+(2x+7)^2-6(2x+7)-3=0[/tex]

[tex]\implies x^2-4x+4x^2+28x+49-12x-42-3=0[/tex]

[tex]\implies 5x^2+12x+4=0[/tex]

Equate the equations to eliminate 5x² and solve for x:

[tex]\implies 5x^2+48x+76=5x^2+12x+4[/tex]

[tex]\implies 48x+76=12x+4[/tex]

[tex]\implies 36x+76=4[/tex]

[tex]\implies 36x=-72[/tex]

[tex]\implies x=-2[/tex]

Substitute the found value of x into the found expression for y:

[tex]\implies y=2(-2)+7[/tex]

[tex]\implies y=-4+7[/tex]

[tex]\implies y=3[/tex]

Therefore, the point of intersection of the three circles if (-2, 3) and hence the location of the earthquake's epicenter is (-2, 3).

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The volumes of the right prisms are listed below:

In this problem we have six cases of right prisms with rectangular bases, the volume of right prisms (V), in cubic length units, is equal to the product of the area of the base (A), in square length units, and the height (h), in length units. The equation of the volume of the right prism is shown below:

V = w · l · h     (1)

Where:

Now we proceed to calculate each volume:

Prism 1 (w = 2 / 3 ft, l = 1 / 3 ft, h = 1 / 2 ft)

V = (2 / 3 ft) · (1 / 3 ft) · (1 / 2 ft)

V = 1 / 9 ft³

Prism 2 (w = 1 / 8 in, l = 3 / 4 in, h = 13 / 16 in)

V = (1 / 8 in) · (3 / 4 in) · (13 / 16 in)

V = 39 / 512 in ³

Prism 3 (w = 7 / 8 cm, l = 1 / 4 cm, h = 1 / 12 cm)

V = (7 / 8 cm) · (1 / 4 cm) · (1 / 12 cm)

V = 7 / 384 cm³

Prism 4 (w = 1 / 7 cm, l = 7 / 8 cm, h = 2 / 3 cm)

V = (1 / 7 cm) · (7 / 8 cm) · (2 / 3 cm)

V = 1 / 12 cm³

Prism 5 (w = 9 / 10 m, l = 2 / 3 m, h = 1 / 5 m)

V = (9 / 10 m) · (2 / 3 m) · (1 / 5 m)

V = 3 / 25 m³

Prism 6 (w = 7 / 8 yd, l = 6 / 7 yd, h = 1 / 2 yd)

V = (7 / 8 yd) · (6 / 7 yd) · (1 / 2 yd)

V = 3 / 8 yd³

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The attached graph represents the piecewise function.

The piecewise function is given as:

f(x) = 3x - 5, x ≤ -1

      = -2x + 3, -1 < x < 4

      = 2, x ≥ 4

To plot the graph, we simply plot the equations together with their domains

i.e.

3x - 5 with the domain of x ≤ -1,  -2x + 3 with the domain of -1 < x < 4 and 2 with the domain of x ≥ 4

See attachment for the graph of the function

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Answer:

the third option, x = –3, –1, 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

If (x, 68, 85) form a Pythagorean Triple, what is the value of x?

to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse

x = √(85²- 68²)

x = (7225 - 4624)

x = √2601

x = 51

Answer:

  x = 51

Step-by-step explanation:

The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.

A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:

  a² +b² = c²

The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...

  {5, 12, 13}, {7, 24, 25}, {8, 15, 17}

There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.

The given values of the triple have the ratio ...

  68/85 = (4·17)/(5·17) = 4/5

Only the values in the {3, 4, 5} triple and its multiples will have this ratio.

The value of x is 3·17 = 51, so the triple is {51, 68, 85}.

  x = 51

__

Additional comments

Any primitive triple will have two odd numbers.

The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.

For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.

__

The above triple can be verified using the Pythagorean theorem:

  51² +68² = 2601 +4624 = 7225 = 85²

A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².

The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.

This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:

x⁴

x - a

(x - b)²

In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².

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Answer:

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

The volume of the rectangular prism is of 28.6875 mm³.

The volume of rectangular prism of length l, width w and height h is given by:

V = lwh.

For this problem, the dimensions are:

Hence the volume is:

V = 2.125 x 6.75 x 2 = 28.6875 mm³.

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The expression of v = (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0) is [tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

To express v= (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0), it will be written as:

[tex](2,1,5)=x(1,2,1)+y(1,0,2)+z(1,1,0)[/tex]

This will yield the following equations:

x + y + z = 2........(1)

2x + z = 1..........(2)

x + 2y = 5........(3)

The solution to the system of equations above is:

x = 1, y = 2, z = -1

Therefore, the linear combination is:

[tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

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Answer:

70

Step-by-step explanation:

45+90=135

180-45=45

q=45

45+65=110

180-110=70

70-45=25

p=25

45+25=70

Answer: 70°

Step-by-step explanation:

We know that the sum of all 3 angles in a triangle is 180°. Hence, we can just set all measures to be equal to 180° and solve for the variables.

[tex]p+65+90=180\\p+155=180\\p=25[/tex]

[tex]45+90+q=180\\135+q=180\\q=45[/tex]

[tex]p+q=25+45=70[/tex]

The sum of p and q is 70°.

The function g(x) is g(x)= (3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

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The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.

Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).

(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get

P(t)=40

(50(1+0.05t))/(2+0.01t)=40

Cross multiply both sides, we get

50(1+0.05t)=40(2+0.01t)

Apply the distributive property a(b+c)=ab+ac, we get

50+2.5t=80+0.4t

Subtract 0.4t and 50 from both sides, we get

50+2.5t-0.4t-50=80+0.4t-0.4t-50

2.1t=30

Divide both sides with 2.1, we get

t=14.29 months

(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get

[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]

(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.

Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.

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The secant in the diagram is [tex]\overline{AD}[/tex]

Segment AD intersect the circle at two points. So it can be a secant.

We have been given that a circle of center O. We have to find the segment that is secant.

Secant : If a line which intersect the circle at two points.Then the line segment  is called  secant.

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)

Segment OB intersect the circle at one point B only. so OB cannot be a Secant.

Segment AD intersect the circle at two points. So it can be a secant.

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Step-by-step explanation:

3 answer.....

......dkdkdk

Answer:

10 hours

Step-by-step explanation:

The rate x time of the first day + the rate x time of the second day equal the distance of 180 miles.

Let t = time

10t + 8t = 180

18t = 180

t = 10

Answer:

68

Step-by-step explanation:

Lets first find the quantity of tape the computing center is purchasing/month.

3/5 Of their 1600 dollar spending is on the heavy duty tapes, meaning they are spending 960 dollars/month on heavy duty tape, if we divide that by the original price, 40, it will give us the original quantity of heavy tape they are purchasing, 24/month.

The other 2/5 of their money, 640 dollars, are spent on regular tape, meaning they purchase 20 rolls of regular tape/month.

Given they are purchasing 24 rolls of heavy tape and 20 rolls of regular tape every month, we can simply multiple those by the new prices and sum the results.

24*38=912

20*31=620

912+620=1532

Then to find the money they are saving we subtract the new price from the original price.

1600-1532=68

The solution of the equations y=[tex]x^{2}[/tex]-x-22 and y=x-7 is that x=-3,5 and y=-10,-2.

Given equations y=[tex]x^{2} -x-22[/tex], y=x-7.

We are required to solve these equations for the value of x and y.

Equation is relationship between two or more variables expressed in equal to form.Equations of two variables look like ax+by=c.It may be a linear equation, quadratic equation and cubic equations.

The given equations are:

y=[tex]x^{2}[/tex]-x-22-----------1

y=x-7----------------2

Put the value of y from second equation in first equation.

x-7=[tex]x^{2}[/tex]-x-22

Solving

[tex]x^{2}[/tex]-x-x-22+7=0

[tex]x^{2}[/tex]-2x-15=0

[tex]x^{2}[/tex]-5x+3x-15=0

x(x-5)+3(x-5)=0

(x+3)(x-5)=0

x=-3,5

Put the values of x=-3 and 5 one by one to get the two values of y in second equation.

y=x-7

x=-3

y=-3-7

=-10

x=5

y=5-7

=-2

Values of y are -10 and -2.

Hence the values of x are-3 and 5 and values of y are -10,-2.

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answer : 2 1/2

divide y by x

divide  2 1/2 by 1

its 2 1/2

10 divided by 4 is also

2 1/2

17 1/2 divided by 7 is also

2 1/2

Answer:

1 - 100 primes numbers

Step-by-step explanation:

2,3,5,7,11,13,17,19,23,29,31,37,41,47,57,59,61,67,71,79,83,8797

Answer:

C. 0.12

Step-by-step explanation:

Let's use a sample number of 100

Out of 100 members, 50 are in the brass section

Out of those 50, 24% play the trombone. This means that 12 people total play the trombone.

12/100 is .12.. That is the final answer

The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex]  the result of the division is [tex]30.8666667[/tex] in decimal form.

When a large number is distributed into small numbers of equal parts is called division.

The number [tex]1.5[/tex] is not a factor of [tex]46.3[/tex] ,  on dividing them the remainder is not zero.

Therefore,  first convert [tex]1.5[/tex] it into a whole number by multiplying it  [tex]10[/tex] so it becomes [tex]15[/tex] .

Then convert [tex]46.3[/tex]  it into a whole number by multiplying it by [tex]10[/tex] so it becomes [tex]463[/tex]

Here,  [tex]\dfrac{463 \times 10}{15 \times 10}[/tex] which results in [tex]\dfrac{463}{15}[/tex].

Now, divide [tex]\dfrac{463}{15}[/tex] ,  the result will be [tex]30.8666667[/tex].

The solution to the problem when [tex]46.3[/tex] divided by  [tex]1.5[/tex] the result is [tex]30.8666667[/tex].

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The maximum value of the objective function is 26 and the minimum is -10

The objective function is given as:

z=−3x+5y

The constraints are

x+y≥−2

3x−y≤2

x−y≥−4

Start by plotting the constraints on a graph (see attachment)

From the attached graph, the vertices of the feasible region are

(3, 7), (0, -2), (-3, 1)

Substitute these values in the objective function

So, we have

z= −3 * 3 + 5 * 7 = 26

z= −3 * 0 + 5 * -2 = -10

z= −3 * -3 + 5 * 1 =14

Using the above values, we have:

The maximum value of the objective function is 26 and the minimum is -10

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The previous tax rate was 20%

What is tax rate?

Tax rate is the percentage of the earnings tax payers would pay to the government from their earnings as taxes.

It should be borne in mind that the new tax rate is 25% which has increased by 25% compared to the previous tax rate, which is the unknown.

The mathematical relationship between the current and prior tax rates is as shown below:

Current tax rate=previous tax rate*(1+% increase in tax rate)

Current tax rate=25%

previous tax rate=X

% increase in tax rate=25%

25%=X*(1+25%)

25%=X*1.25

X=25%/1.25

X=previous tax rate=20%

Technically speaking, an increase of 25% in 20% is 5%(i.e. 20%*25%=5%), which when added to the original 20% would give a tax rate of 25%.That the shortcut to affirming that the new tax rate of 25% is correct

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Using derivatives, the equation of the tangent line is: y + 2= -(x + 2)

The equation is:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the derivative at point [tex](x_0, y_0)[/tex].

The function is:

[tex]x^2 + y^2 = 8[/tex].

Applying implicit differentiation, the derivative is:

[tex]2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0[/tex]

[tex]2ym = -2x[/tex]

[tex]m = -\frac{x}{y}[/tex]

We have that x = y = -2, hence m = -1 and the equation is:

y + 2= -(x + 2)

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