458 divided by 31 using compatible numbers

Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, [tex]A(10) = 0.7278A(0)[/tex]. We use this to find k.

[tex]A(t) = A(0)e^{-kt}[/tex]

[tex]0.7278A(0) = A(0)e^{-10k}[/tex]

[tex]e^{-10k} = 0.7278[/tex]

[tex]\ln{e^{-10k}} = \ln{0.7278}[/tex]

[tex]-10k = \ln{0.7278}[/tex]

[tex]k = -\frac{\ln{0.7278}}{10}[/tex]

[tex]k = 0.03177289938 [/tex]

Then

[tex]A(t) = A(0)e^{-0.03177289938t}[/tex]

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

[tex]A(5) = A(0)e^{-0.03177289938*5}[/tex]

[tex]A(5) = 0.8531[/tex]

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Your answer iss...

It is 51º

Answer:

B. 35°

Step-by-step explanation:

First, find the two interior angles that are adjacent to angles 90° and 125° respectively.

Thus:

Interior angle 1: 180° - 90° = 90° (linear pair)

Interior angle 2: 180° - 125° = 55° (linear pair)

P + 90° + 55° = 180° (sum of interior angles in a triangle)

P + 145° = 180°

Subtract 145° from each side

P = 180° - 145°

P = 35°

Answer:

44.85

Step-by-step explanation:

There are two ways to do it, you can either multiply 0.3 by 34.5 and then add it to 34.5 to get 44.85, or you can add the 30% to 100% and get 1.3 which you multiply by 34.5 and that gets you 44.85

Answer:

16

Step-by-step explanation:

1) Find out r of the sequence. The first term(a1) is 16384, the second term (a2) is 8192.

8192=16384*r. r= 0.5

2) Use the rule that an=a1*r^(n-1)

a11=a1*r^10

a11= 16384*((0.5)^10)= 16384/ (2^10)=16.

Answer:

378 and 380

Step-by-step explanation:

The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.

Answer:

Step-by-step explanation:

Let the first number = x

Let the second number = x + 2

x + x + 2 = 758                      Collect like terms

2x + 2 = 758                         Subtract 2

2x = 758 - 2                          Combine

2x = 756                                Divide by 2

2x/2 = 756/2

x = 378

The first number is 378

The second number 380

If your teacher is really fussy, you can do it this way.

Let the first number = 2x

Let the second number = 2x + 2

The reason for this is to guarantee that both numbers were even to start with.

2x + 2x+2 = 758                    Combine like terms

4x + 2 = 758                          Subtract 2

4x = 756                                Divide by 4

x = 756/4

x = 189

Therefore 2x = 378

2x + 2 = 380                 Just as before.

No. The F test has a requirement that samples be from the normally distributed populations, regardless of how large the samples are.

The F-test simply shows whether the variances that are in the numerator and the denominator are equal. The F-test can be applied on a large sampled population.

One main assumption of the F test is that the populations where the two samples are drawn are normally distributed.

Regarding the question, it's important to note that when using the F test with these​ data, it's not correct to reason that there is no need to check for "normality".

It should be noted that the F test has a requirement that samples are from the normally distributed populations, regardless of how large such samples are.

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9514 1404 393

Answer:

  A.  1/2

Step-by-step explanation:

The points on a unit circle are (cos(θ), sin(θ)), where θ is the angle from the +x axis to to the ray from the origin through that point.

If the point is (√3/2, 1/2), then sin(θ) = 1/2.

Answer:

Perimeter: 3/4

Area: 9/16

Step-by-step explanation:

The ratio of the perimeters is equal to the ratio of the sides so:

18/24 = 3/4

Ratio of Area = (Ratio of Sides)^2

(3/4)^2 = 9/16

I wasn't sure about the answer so I used Gauthmath

Answer:

option c is the answer for your question

x + 3y -15 = 0

Step-by-step explanation:

let (x,y) be the coordinate of bisector,

so (x,y) should be equal distance from point (8,9) and (4,-3)

(x-8)^2 + (y-9)^2 = (x-4)^2 + (y-(-3))^2

or, (x^2 - 16x + 64) + (y^2 - 18y + 81 )= (x^2 -8x + 16) + (y^2 + 6y + 9)

After cancelling x^2 and y^2 from both side, we get

-16x - 18y +145 = -8x +6y + 25

or, -16x + 8x - 18y - 6y +145 -25 = 0

or, -8x - 24y + 120 = 0

or -8 ( x + 3y - 15) = 0

or, x + 3y - 15 = 0 ------ this is the equation of the perpendicular bisector of line segment with endpoints (8,9) and (4,-3)

Events are said to be INDEPENDENT if the occurence of one does not rest or depend on the outcome of another. Therefore, since the outcome of event A and B does not depend on each other, then both events are INDEPENDENT

Giving a brief description of the options given :

• Dependent events are simply events where the outcome of one event affects the occurence of the other. This is usually related to selection without replacement, where the number of subjects changes after each selection.

• Mutually Exclusive events simply refers to a scenario whereby two events cannot occur simultaneously. For instance, obtaining a head and a tail simultaneously during a single coin throw.

• Complement events describes two exactly opposite events. For instance, the Complement of obtaining a 4 on a 6 - sided die roll is (1, 2, 3, 5, 6)

For the event described above , the occurrence of A does not hinder the occurrence of the other (not a dependent event ) and it is possible to have both events simultaneously (not Mutually exclusive) (If we have 3 in all throws then both events have occurred )

Therefore, the best description for events A and B is that both events are INDEPENDENT.

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Answer: the answer is dependent

Step-by-step explanation:

Events are independent if the knowledge of one event occurring does not affect the chance of the other event occurring. In this case, the chance of Event B occurring is greater if Event A occurs, so these events are dependent. Since the spinner could land on 3, 3, and 3, the events are not mutually exclusive.

Answer:

1/144

Step-by-step explanation:

(-1/12)^2

(-1/12)*(-1/12)

1/144

Step-by-step explanation:

In right angled triangle ABC,

Taking alpha as reference angle,

By pythagoras theorem,

p=BC,h=AB,b=AC

Taking thita as reference angle,

p=AC,h=AB,b=BC

Keep smiling and hope u are satisfied with my answer.Have a good day :)

Answer: there are 100 centimeters in 1 meter. Meters to centimeters multiply by 100. Centimeters to meters divide by 100.

Step-by-step explanation:

Meters to centimeters multiply by 100

(10,000 m ) (100) = 1,000,000 cm.

(100 m) (100) = 10,000 cm.

Centimeters to meters divide by 100.

100 cm / 100 = 1 meter

10,000 cm /100 = 100 m

Answer:

Area of the metal sheet required = 364 square inches

Step-by-step explanation:

Area of the metal sheet required = Surface area of the lateral sides of the vent transition

Since, lateral sides of the vent is in the shape of a trapezoid,

Therefore, surface area of the vent = 4(Surface area of one lateral side)

                                                           = [tex]4[\frac{1}{2}(b_1+b_2)h][/tex]

Here, [tex]b_1[/tex] and [tex]b_2[/tex] are two parallel sides and [tex]h[/tex] is the distance between these parallel sides.

Surface area of the vent = [tex]4[\frac{1}{2}(8+5)14][/tex]

                                         = 364 square inches

Therefore, area of the metal sheet required = 364 square inches

Answer:

Sin X = 12 / 37

Step-by-step explanation:

Given a right angled triangle, we are to obtain the Sin of the angle X ;

Using trigonometry, the sine of the angle X , Sin A is defined as the ratio of the angle opposite X to the hypotenus of the right angle triangle.

In the right angle triangle :

Sin X = opposite / hypotenus

Opposite = 12 ; hypotenus = 37

Sin X = 12 / 37

because it's value will always be same

Answer:

This value doesn't depend on x or y

It'll be the same things always

y=1/2x-2 is perpendicular to y=2x+3

Answer:

$16186.20

Step-by-step explanation:

Assuming that P represents the initial amount, A represents the end amount, r represents the annual interest rate, m represents the amount of times compounded per year, and t represents the amount of years, we can write this as

A = P(1+r/m)^(mt)

Since 12,000 is invested, that is the initial amount. To find the interest rate as a decimal from a percent (as we need it in decimal form for this formula), we can divide the percent by 100 to get 6%/100 = 0.06 as our interest rate. Because there are 12 months in a year, the interest is compounded 12 times a year, and since it takes 5 years, t=5. Our formula is now

A = 12000 * (1+0.06/12)^(12 * 5)

A = 12000 * (1+0.06/12) ^(60)

A = 16186.20 rounded to the nearest cent

Step-by-step explanation:

[tex] \frac{ {c}^{2} - 4 }{c + 3} [/tex]

[tex] \frac{(c - 2)(c + 2)}{(c + 3)} [/tex]

9514 1404 393

Answer:

  (a)  -23

Step-by-step explanation:

The sequence is arithmetic with first term 3 and common difference -2. Then the general term is ...

  an = a1 +d(n -1)

  an = 3 -2(n -1)

and the 14th term is ...

  a14 = 3 -2(14 -1) = 3 -2(13) = 3 -26

  a14 = -23

Answer:

Step-by-step explanation:

Interior angle opposite to each side of the polygon is:

Since the circle is unit circle, its radius is 1 unit.

Let the side is a, then as per definition of sine we have:

The perimeter is:

Answer:

37.5%

Step-by-step explanation:

A=P(1+r)^t

363=192*(1+r)^2

1.375=1+r, r=0.375=37.5%

Notice that the condition x ≠ 2πk for (presumably) integer k means cos(x) ≠ ±1, and in particular cos(x) ≠ 1 so that we could divide both sides by (1 - cos(x)) safely. Doing so lets us separate the variables:

(1 - cos(x)) y' - y sin(x) = 0

==>   (1 - cos(x)) y' = y sin(x)

==>   y'/y = sin(x)/(1 - cos(x))

==>   dy/y = sin(x)/(1 - cos(x)) dx

Integrate both sides and solve for y. On the right, substitute u = 1 - cos(x) and du = sin(x) dx.

∫ dy/y = ∫ sin(x)/(1 - cos(x)) dx

∫ dy/y = ∫ du/u

ln|y| = ln|u| + C

exp(ln|y|) = exp(ln|u| + C )

exp(ln|y|) = exp(ln|u|) exp(C )

y = Cu

y = C (1 - cos(x))

Answer:

[tex]4\sqrt{5}[/tex]

Step-by-step explanation:

Prime factorize 20 and 45

[tex]\sqrt{20}=\sqrt{2*2*5}=2\sqrt{5}\\\\\\\sqrt{45}= \sqrt{5*3*3}=3\sqrt{5}[/tex]

[tex]\sqrt{20}-\sqrt{5}+\sqrt{45}=2\sqrt{5}-\sqrt{5}+3\sqrt{5}[/tex]

                           [tex]=(2-1+3)\sqrt{5}\\\\\\= 4\sqrt{5}\\[/tex]

Answer:

3/4 or 75% or .75

Step-by-step explanation:

You would multiply 3 * .25 because there are three people getting 25% of a pie. All of the answers above are equivalent

Answer: the radius is perpendicular to the chord.

If a radius of a circle bisects a chord which is not diameter, then the radius is perpendicular to the chord.

Answered by Gauthmath must click thanks and mark brainliest

The radius is perpendicular to the chord.

If the radius of the circle is perpendicular to the chord of the circle, the radius bisects the chord. The two strings are congruent only if they are equidistant from the center of the circle.

No, not all strings in a circle are diameters because the diameter passes through the center of the circle. Therefore, all the diameters of a circle are also strings, not all the strings of a circle.

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