Write the equation of a line perpendicular to y = 2x + 5 and passing through the point (8,2).
1. y = -1/2 x + 2
2. y = -1/2 x + 6
3. y = -1/2 x - 2
4. y = 1/2 x - 2

The expressions -4(3e+4) is equivalent to  -7+3(-4e-3)

Given expression:

[tex]-7+3(-4e-3)[/tex]

Expand expression:

[tex]-7-12e-9[/tex]

Regroup like terms:

[tex]-12e-9-7[/tex]

= [tex]-12e-16[/tex]

Factor -4 to get:

[tex]-4(3e+4)[/tex]

A mathematical expression is a combination of numbers, symbols, and/or variables that represent a mathematical statement. It can be a simple expression like "2 + 3," or a more complex one like "sin(x) + 3y^2 - 7."

Expressions can be used to perform calculations, represent relationships between different quantities, or describe geometric shapes and structures. They are an essential tool in mathematics and are used in a wide range of fields, including science, engineering, finance, and economics.

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Complete question:

Which expressions are equivalent to -7+3(-4e-3)?

Choose all answers that apply:

(Choice A)

-4(3e+4)

(Choice B)

12e

(Choice C)

None of the above

a. Correct answer is C as sample contains more pink marbles than red marbles, so it's predicted that the bowl has more pink marbles.

b. With 750 marbles in the bowl and proportion of pink marbles being 0.7, there are approximately 525 pink marbles and 225 red marbles, thus you are more likely to pick a pink marble.

a. The correct answer is C. Yes. Because the representative sample contains more pink marbles than red marbles, you can predict that the bowl contains more pink marbles than red marbles.

b. If there are 56 pink marbles and 24 red marbles in a sample of 80 marbles, then the proportion of pink marbles in the sample is 56/80 = 0.7, and the proportion of red marbles in the sample is 24/80 = 0.3. If there are 750 marbles in the bowl, then there are about 0.7750 = 525 pink marbles and 0.3750 = 225 red marbles. So, you are more likely to pick a pink marble.

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The life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year. The solution has been obtained by using the simple interest.

What is simple interest?

A way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time is by using simple interest. The principal amount in a basic interest calculation is constant.

We are given that Jeff has to put $2,225,000 into a bank account if it ever had to make payments on the policy and the company also expects interest rates to be at 1.4% at that time.

So, from this we get,

⇒ Total Interest = $2225000 × 1.4% × 1

⇒ Total Interest = $31,150

Amount payable by company = $2225000 + $31,150

Amount payable by company = $2,256,150

Hence, the life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year.

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The probability of getting a red king card from the deck of cards is 1/26.

The probability formula can be used to determine the likelihood of an event by only dividing the favourable number of possibilities by the entire number of possible outcomes.

As there can never be more favourable outcomes than there are possible outcomes, the probability of an event happening can range from 0 to 1. As a result, 0 cannot represent the percentage of successful outcomes.

Given,

We have a deck of cards.

So, total no of cards = 52

Now, no of red cards = 26.

Now total no. of kings = 4.

Total no. of red kings = 2

Probability of picking a red king from the deck =

2/52

=1/26

Therefore, the probability of getting a red king card from the deck of cards is 1/26.

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The simplification of the logarithm is determined as [tex]\log_32 - 11[/tex].

To solve the problem, we can first convert all the logarithms into the same base, which will be base 3. Using the logarithmic identity that

[tex]\log_a b = \frac{\log_c b}{\log_c a}[/tex]

where;

we get:

[tex]3\log_9(18) + \log_3\left(\sqrt{\frac{8}{27}}\right) - \log_{\frac{1}{27}}(81) - \log_{\sqrt{3}}(2\sqrt{2}) &\\\\= 3\frac{\log_3(18)}{\log_3(9)} + \frac{1}{2}\log_3\left(\frac{8}{27}\right) - \frac{\log_{3}(81)}{\log_{3}(1/27)} - \frac{\log_{3}(2\sqrt{2})}{\log_{3}(\sqrt{3})}[/tex]

[tex]= 6\frac{\log_3(2)+\log_3(3)}{2\log_3(3)} + \frac{1}{2}\left(\log_3(2^3)-\log_3(3^3)\right) - \frac{\log_{3}(3^4)}{\log_{3}(3^{-3})} - \frac{\log_{3}(2\sqrt{2})}{1/2}\\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) + \frac{3\log_3(2)-9\log_3(3)}{6} - \frac{12}{3} - 2\log_{3}(2\sqrt{2})[/tex]

[tex]= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) - \frac{3}{2} + \frac{\log_3(2) }{2} - 4 - \log_3(8) \\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{\log_3(2) }{2} - \log_3(2^3)\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{1}{2} (\log_3(2) )- \log_38\\\\= 6\left (\frac{\log_3(2)}{\log_3(3)}\right) -5+ \log_3(2) - 2\log_3(8)\\\\= 6\log_32 \ - \ 6\log_33 - 5 + \log_32-2\log_38\\\\= \log_3\left (\frac{2^6\times 2 }{3^6\times 8^2}\right) - 5\\\\[/tex]

[tex]= \log_3\left (\frac{2^7 }{3^6\times 2^6}\right) - 5\\\\= \log_3\left (\frac{2 }{3^6}\right) - 5\\\\= \log_32 - \log_33^6 - 5\\\\= \log_32 - 6 - 5\\\\=\log _32 \ - 11[/tex]

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Answer:

  25 cm

Step-by-step explanation:

You want to know the length of the hypotenuse in a right triangle with legs 15 cm and 20 cm.

The given leg lengths have the ratio ...

  15 : 20 = 3 : 4 . . . . . . . scale factor of 5

This means they are part of a 3 : 4 : 5 right triangle.

The length "t cm" is 5·5 cm = 25 cm.

The value of t is 25.

__

Additional comment

In case you've never heard of a {3, 4, 5} right triangle, you can figure the missing hypotenuse from the Pythagorean theorem:

  c² = a² +b²

  t² = 15² +20² = 225 +400 = 625

  t = √625 = 25

The {3, 4, 5} Pythagorean triple is used repeatedly in algebra, geometry, and trig problems, along with some others: {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. These can appear as multiples of the basic triple, as here, where the multiple is 5 × {3, 4, 5} = {15, 20, 25}.

The exponential function in the graph can be written as:

h(x) = 3*2^x

We can see that h(x) is an exponential function, so we can write this in a general form as:

h(x) = a*b^x

Where a is the initial value and b is the base of the exponential.

First, we can see that it passes through the ponit (0, 3), replacing these values we will get:

3 = a*b^0

3 = a

So the equation is:

h(x) = 3*b^x

We also can see that it passes through (1, 6), replacing these values we will geT:

6 = 3*b^1

6 = 3*b

6/3 = b

2 =b

The exponential function is:

h(x) =3*2^x

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Answer:

put 5 units up

Brody bought 2 drinks and 10 pretzels.  Let's use algebra to solve this problem. Let d be the number of drinks that Brody bought, and let p be the number of pretzels that he bought. We know that he bought a total of 12 drinks and pretzels, so:

d + p = 12

We also know that each drink costs $6 and each pretzel costs $3.25, and he spent a total of $44.10 on drinks and pretzels. So:

6d + 3.25p = 44.10

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:

p = 12 - d

Substituting this into the second equation, we get:

6d + 3.25(12 - d) = 44.10

Simplifying:

6d + 39 - 3.25d = 44.10

2.75d = 5.10

d = 1.85 (rounded to two decimal places)

Since d represents the number of drinks, we can't have a fractional value for it. However, we can round it to the nearest whole number and use that to solve for p:

d ≈ 2

p = 12 - d = 12 - 2 = 10

Therefore, Brody bought 2 drinks and 10 pretzels. We can check that this solution satisfies both equations:

2 + 10 = 12 (first equation)

6(2) + 3.25(10) = 44.10 (second equation)

Therefore, our solution is correct

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Brody and his children went into a movie theater and he bought $44.50 worth

of drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He

bought a total of 12 drinks and pretzels altogether. Determine the number of

drinks and the number of pretzels that Brody bought

The ramp will rise 16.8 inches from the ground at its highest end, when the angle of elevation is 19 degrees and the length of the fiberboard is 27 inches.

To calculate the height of the ramp at its highest end:

1. First, calculate the length of the hypotenuse of the triangle formed by the ramp, using the Pythagorean Theorem. This can be done by squaring the length of the ramp (27 inches) and the angle of elevation (19 degrees) and adding them together. The result is 750.41 inches.

2. Next, take the square root of the result from step 1. This gives us 27.45 inches, which is the length of the hypotenuse.

3. Then, subtract the length of the ramp from the length of the hypotenuse. This gives us 8.45 inches.

4. Finally, divide the result from step 3 by 2. This gives us the height of the ramp at its highest end, which is 16.8 inches.

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The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:

9 x 4 + (3 − 2)

First, we need to calculate the difference of 3 and 2, which is 1. Then, we add it to the product of 9 and 4, which is 36. So the final expression is:

36 + 1 = 37

Therefore, the correct numerical expression is 9 x 4 + (3 − 2) = 37.

Option D : The equation that demonstrates the inverse property is D. 3/4 x 4/3= 1, which shows that the multiplication of the reciprocal of a number equals 1.

According to the multiplicative property known as the inverse property, the result of multiplying any non-zero number by its inverse or reciprocal will equal the multiplicative identity, which is 1.

The inverse property of multiplication states that for any non-zero number a, its inverse or reciprocal, when multiplied by a, will result in 1. The reciprocal of a number is the number that when multiplied by the original number results in 1.

For example, the reciprocal of 3 is 1/3 because 3 x 1/3 = 1.

Similarly, the reciprocal of 4/3 is 3/4 because (4/3) x (3/4) = 1.

So, if we multiply 3/4 by its reciprocal 4/3, we get:

(3/4) x (4/3) = (3 x 4) / (4 x 3) = 12 / 12 = 1

This shows that the product of 3/4 and 4/3 is 1, which is the multiplicative identity. Hence, this equation demonstrates the inverse property of multiplication.

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Which equation would demonstrate the inverse property?

A. (3x4) + (3x5) = 3(4+5)

B. 3x5 = 5x3

C. 3x4x5= (3x4)x5

D. 3/4 x 4/3= 1

A parabola is a U-shaped curve that can open upwards or downwards. Its equation is typically in the form y = ax^2 + bx + c, where a, b, and c are constants. The properties of a parabola are determined by these constants.

Description about vertex,max/min,axis of

Description about vertex,max/min,axis ofsymmetry,zero(s),direction of opening,y-intercept of parabola:

Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards. The vertex is located at the point (-b/2a, f(-b/2a)), where f(x) is the

function that defines the parabola.

Max/min: The maximum or minimum value of the parabola is the y-coordinate of the vertex. If the parabola opens downwards, the maximum value occurs at the vertex. If the parabola opens upwards, the minimum value occurs at the vertex.

Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two mirror-image halves. The equation of the axis of symmetry is x = -b/2a.

Zero(s): The zero(s) of the parabola are the x-values where the parabola intersects the x-axis. These are also called roots or solutions of the quadratic equation. If the discriminant (b² - 4ac) is positive, the parabola intersects the x-axis at two points. If the discriminant is zero, the parabola intersects the x-axis at one point (which is also the vertex). If the discriminant is negative, the parabola does not intersect the x-axis and has no real roots.

Direction of Opening: The direction of opening of the parabola is determined by the sign of the coefficient a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.

y-intercept: The y-intercept is the point where the parabola intersects the y-axis. It is located at the point (0, c), where c is the constant term in the quadratic equation.

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Correct question is "For each parabolas, describe the following properties:

Vertex

Max/min

Axis of

Symmetry

Zero(s)

Direction of

Opening

y-intercept."

Answer:

2.64

Step-by-step explanation:

b*h=5.28

5.28/2=2.64

Answer:

Quadratic

Step-by-step explanation:

I have no idea how to explain it except that it follows the standard               ax² + bx + c format

Quadratic is the answer to your question! :)

Answer:

1. =2.5759 ; 2. =0.8290 ;  3. =2  ; 4. =1.7959 ; 5. = 3.9138

Step-by-step explanation:

1. Taking logarithm with base 3 on both sides, we get:

b = log₃(17)

b ≈ 2.5759

2. Taking logarithm with base 12 on both sides, we get:

r = log₁₂(13)

r ≈ 0.8290

3. Taking logarithm with base 9 on both sides, we get:

n = log₉(49)

n = 2

4.Taking logarithm with base 16 on both sides, we get:

v = log₁₆(67)

v ≈ 1.7959

5.Taking logarithm with base 3 on both sides, we get:

a = log₃(69)

a ≈ 3.9138

The number of sacks of trash that Jorge's brother picked up is given as follows:

3.75 sacks.

The number of sacks of trash that Jorge's brother picked up is obtained applying the proportions in the context of the problem.

Jorge picks up 2 1/2 sacks of trash, which is a mixed number, hence the decimal number that represents this amount is given as follows:

2 + 1/2 = 2 + 0.5 = 2.5 sacks.

His brother picks up 1 1/2 times as much as Jorge, which is 1 + 1/2 = 1.5 times the amount picked by Jorge, hence the number of sacks of trash that Jorge's brother picked up is obtained as follows:

2.5 x 1.5 = 3.75 sacks.

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Answer:

[tex]90 { \: cm}^{2} [/tex]

Step-by-step explanation:

First, we can find one triangle's area (they are all the same and isosceles):

h = XY = 6 cm, a = BC = 5 cm

[tex]s(triangle) = \frac{1}{2} \times h \times a = \frac{1}{2} \times 6 \times 5 = 15[/tex]

And now, multiply this number by 6 (since there are 6 of these identical triangles):

S(hexagon) = 15 × 6 = 90 cm^2

Answer:

a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:

Circumference = 2π × radius; but diameter = 2 × radius. Hence:

Circumference = π * diameter.

Given that diameter of the tire = 2.5 ft:

Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft

b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.

1 mile = 5280 ft

The number of rotation required to cover 1 mile (5280 ft) is:

number of rotation =

Step-by-step explanation:

Thats the best i can find.

Answer:

Your answer is correct and you showed all the necessary steps to find the circumference and the number of times the tire would have to rotate to travel one mile. Well done!

Answer:

1. is the distance from the center of the circle to any point on it's circumference

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601 (rounded to four decimal places).

The probability of an event is defined as the number of ways the event can occur divided by the total number of possible outcomes. To solve the given problem, we will use the binomial distribution formula.

The formula for the probability of less than 4 successes in n trials, given the probability of success p, is:P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)Where X is a binomial random variable with n = 50 trials and p = 0.03 probability of success, i.e., taking general education courses on a pass/fail basis.

Now, let's calculate each term:

P(X = 0) = C(50, 0) (0.03)⁰ (0.97)⁵⁰P(X = 0) = 1 × 1 × 0.97⁵⁰ ≈ 0.3669P(X = 1) = C(50, 1) (0.03)¹ (0.97)⁴⁹P(X = 1) = 50 × 0.03 × 0.97⁴⁹ ≈ 0.3937P(X = 2) = C(50, 2) (0.03)² (0.97)⁴⁸P(X = 2) = 1225 × 0.0009 × 0.97⁴⁸ ≈ 0.1872P(X = 3) = C(50, 3) (0.03)³ (0.97)⁴⁷P(X = 3) = 19600 × 0.000027 × 0.97⁴⁷ ≈ 0.0123P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)P(X < 4) = 0.3669 + 0.3937 + 0.1872 + 0.0123P(X < 4) ≈ 0.9601

Hence, the probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601.

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In set-builder nοtatiοn, we can write:

Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }

Range οf h(x): { y ∈ R | y ≥ 0 }

In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο a unique element in anοther set, called the range. It is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput.

The dοmain οf h(x) is the set οf all values οf x that make the functiοn well-defined, i.e., there shοuld be nο negative number inside the square rοοt.

Tο find the dοmain οf h(x), we set the expressiοn inside the square rοοt tο be nοn-negative and sοlve fοr x:

3x² - 5x + 2 ≥ 0

Factοrizing the quadratic expressiοn, we get:

(3x - 2)(x - 1) ≥ 0

The sοlutiοn set fοr this inequality is given by the interval:

x ≤ 1/3 οr x ≥ 2/3

Therefοre, the dοmain οf h(x) is:

{ x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }

The range οf h(x) is the set οf all pοssible values that the functiοn can take. Since the square rοοt is always nοn-negative, the range οf h(x) is:

{ y ∈ R | y ≥ 0 }

In set-builder nοtatiοn, we can write:

Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }

Range οf h(x): { y ∈ R | y ≥ 0 }

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Using the sine's function in the given triangle, the value of x is 75.7 respectively.

What is the triangle?

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.

There are three sides and three angles in every triangle, some of which may be the same.

The angle total of a triangle will always be equal to 180°.

A quadrilateral can be divided in half from corner to corner to form a triangle because the angle total of a quadrilateral is equal to 360°.

A triangle is effectively half of a quadrilateral, therefore it makes sense that its angle measurements are also half. 180° is one-half of 360°.

So, right triangles are used to depict figures like this one, which has a hypotenuse of 85, a base of x, and a top angle of 63°.

The hypotenuse and the side that faces the angle are both present.

The sine function's opposite/hypotenuse ratio is as follows:

sin 63° = x/85

Now, solve as follows:

sin 63° = x/85

85(sin 63°) = x

75.7 = x

Therefore, using the sine's function in the given triangle, the value of x is 75.7 respectively.

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Complete question:

In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box.

The missing length w of the given trapezium with the area of  128.885 cm² is found to be: w = 14.9 cm.

A closed-form, two-dimensional quadrilateral with two parallel, opposite sides is called a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. Four sides as well as four corners make up the trapezium.

The term "isosceles trapezium" refers to a trapezium with equal-length legs, meaning that the 2 non parallel sides are equal.

Area of Trapezium =  ½ (Sum of parallel sides) × (Height between parallel sides)

128.885  =  ½(5.3 + 12) × w

128.885 * 2  =  17.3 w

w = 128.885 * 2 / 17.3

w = 14.9

Thus, the missing length w of the given trapezium with the area of  128.885 cm² is found to be: w = 14.9 cm.

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Answer:

hey kid the answer is twice

the diameter of a circle is twice the length of its radius

Step-by-step explanation:

Answer: (2 times) the length of the radius

Step-by-step explanation:

r= 2D

see attachment

Answer: i don't know what type of answer ur looking for but

the answer for substitution is x=-4, y=7

Step-by-step explanation:

y = 3x + 19

8x + 2y = - 18   ====>   y = -4x - 9

Equate the two expressions of 'y'

3x + 19 = - 4x- 9

7x = -28

x = -4       then y = 3x + 19 = 3(-4) + 19 = 7

(-4, 7)

The formula for the volume of the shaded region is given as follows:

V = π/3[(R² - r²)(H - h)]

The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.

V = πr²h/3.

Hence, for the large cone, the volume is given as follows:

Vl = πR²H/3.

For the smaller cone, the volume is given as follows:

Vs = πr²h/3.

Hence the volume of the shaded region is given as follows:

V = Vl - Vs

V = πR²H/3 - πr²h/3

V = π/3[(R² - r²)(H - h)]

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Answer:

The answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Step-by-step explanation:

Allstars mean height:

= (73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15

= 1007 / 15

= 67.6 inches

Super Stars mean height:

= (66 + 68 + 62 + 63 + 47 + 64 + 65 + 50 + 60 + 64 + 65 + 65 + 58 + 60 + 55) / 15

= 912 / 15

= 60.2 inches

We can see that the Allstars team has a higher mean height than the Super Stars team, with an average of 67.6 inches compared to 60.2 inches. Therefore, the Allstars team typically has the tallest players

Thus the answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad R(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 +3}{2}~~~ ,~~~ \cfrac{ 4 +4}{2} \right) \implies \left(\cfrac{ 10 }{2}~~~ ,~~~ \cfrac{ 8 }{2} \right)\implies \stackrel{ \textit{\LARGE S} }{(5~~,~~4)}[/tex]