Which expression is equivalent to (StartFraction (2 a Superscript negative 3 Baseline b Superscript 4 Baseline) squared Over (3 a Superscript 5 Baseline b) Superscript negative 2 Baseline EndFraction) Superscript negative 1?

Answer:

   6 miles

Step-by-step explanation:

The time Johnny rode was ...

  1 h 11 min = (60 min) +(11 min) = 71 min = 71 × (60 sec) = 4260 sec

The distance of one revolution of the bike tire is ...

 C = πd = 3.14(30 in) = 94.2 in

So, the total distance Johnny rode was ...

 (4260 sec)×(94.2 in/sec) = 401,292 in

__

We know there are 5280 feet in a mile, and each of those is 12 inches. So, the number of inches in a mile is ...

  5280 ft = 5280×(12 in) = 63,360 in

__

The number of miles Johnny rode can be found by dividing the total distance by the distance in 1 mile:

  (401,292 in)/(63,360 in/mile) = 6.33 mile

Johnny rode about 6 miles in 1 hour 11 minutes.

Answer:

18.75 meters

Step-by-step explanation:

Final answer:

To find 15 meters increased by 25%, multiply 15 by 0.25 to get 3.75 meters, then add this to the original length to obtain 18.75 meters.

Explanation:

To calculate a 15 meters increase by 25%, first determine what 25% of 15 meters is. You do this by multiplying 15 by the percentage in decimal form (25% = 0.25), so: 15 meters * 0.25 = 3.75 meters. Then, to find the new length, you add this to the original 15 meters to get the total.

15 meters + 3.75 meters = 18.75 meters. Therefore, 15 meters increased by 25% is 18.75 meters.

Step-by-step explanation:

Convert the percentage increase to a decimal: 25% → 0.25.

Multiply the original length by this decimal: 15 meters * 0.25 = 3.75 meters.

Add the increase to the original length: 15 meters + 3.75 meters = 18.75 meters.

Answer:

log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x

Step-by-step explanation:

Given:

log Subscript 2 Baseline 9 x cubed?

Required:

Find the equivalent of the above expression.

First, we need to represent it mathematically;

log Subscript 2 Baseline 9 x cubed = [tex]log_{2} 9x^{3}[/tex]

From Laws of logarithm  

[tex]log_{x} AB = log_{x} (A* B)\\log_{x} AB = log_{x}A + log_{x}B[/tex]

Note how the expression is split into two

We'll apply the same logic above, here

First, is to simplify the mathematical expression;

[tex]log_{2} 9x^{3} = log_{2} (9 * x^{3})[/tex]

Then we split into two

[tex]log_{2} 9x^{3} = log_{2}(9) + log_{2}(x^{3})[/tex]

[tex]log_{2} 9x^{3} = log_{2}(3^2) + log_{2}(x^{3})[/tex]

Also from laws of logarithm,

[tex]log_{m}A^{n} = nlog_{m}A[/tex]

We'll apply this law on [tex]log_{2}(x^{3})[/tex] and [tex]log_{2}(3^{2})[/tex]

[tex]log_{2}x^{3} = 3log_{2}x[/tex]

[tex]log_{2}(3^2) = 2log_{2}3[/tex]

So, [tex]log_{2} 9x^{3} = log_{2}(9) + log_{2}(x^{3})[/tex] becomes

[tex]log_{2} 9x^{3} = 2log_{2}3 + 3log_{2}x[/tex]

log Subscript 2 Baseline 9 x cubed is equivalent to [tex]2log_{2}3 + 3log_{2}x[/tex]

[tex]2log_{2}3[/tex] can be represented as 2 log subscript 2 Baseline 3

and

[tex]3log_{2}x[/tex] can be represented as 3 log subscript 2 Baseline x

Hence, log Subscript 2 Baseline 9 x cubed is equivalent to 2 log subscript 2 Baseline 3 + 3 log subscript 2 Baseline x

Answer:

a) log2 9x^3

Step-by-step explanation:

got it right on edg

Answer:

23 1/4

Step-by-step explanation:

Answer:

m = 1/2  point (5, -7)

Step-by-step explanation:

The equation is in point slope from

y - y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y+7 = 1/2(x-5)

Rewriting

y - -7 = 1/2 (x - 5)

We can see that 1/2 is the slope and (5, -7) is a point on the line

Answer:

a)

Step-by-step explanation:

y - y1 = m(x - x1)

m = ½

Point: (5,-7)

Step-by-step explanation:

The total number of guests for lodge to be full = 153

During heavy snow fall, the lodge will be full.

The expected number of guests during heavy snow fall = 153

During partial snow fall, the expected number of guests = 62

The probability of heavy snowfall = 0.4

The probability of partial snow fall = 1 - 0.4 = 0.6

The expected number of guests = [(0.4) (153)] + [(0.6) (62)]

= 61.2 + 37.2

 =  98.4

Answer:

£8.10

Step-by-step explanation:

Since we have to convert Euro to pound we will first find value of one euro in terms of pound.

Given

£3 = €4

=> £3/4 = €1

=> €10.80 = £3/4 * 10.80  ---->multiplying both side by 10.80 as we have have to find value of €10.80  in pounds

= > €10.80 = £8.10

Answer:

£8.10

Step-by-step explanation:

Given,

£3 = €4

Dividing both side by four

€1 = £0.75

We have to convert €10.80 to pounds

Multiplying 10.80 both side

€10.80 = £0.75 x 10.80

€10.80 =£8.10

Hence,  €10.80 is equal to £8.10.

The price of adult ticket is $ 13and child ticket is $12.Hope this will help u.....

The probability of drawing a red marble first and a yellow marble second is 5/21.

To find the probability that the first marble drawn is red and the second one is yellow, we need to consider the total number of marbles and the number of red and yellow marbles in the bag.

Since we are drawing without replacement, the probabilities are dependent.

The probability of drawing a red marble on the first draw is 5/7. After the first marble is drawn, there are now 4 red marbles and 2 yellow marbles left in the bag. The probability of drawing a yellow marble on the second draw is 2/6.

Therefore, the probability of drawing a red marble first and a yellow marble second is (5/7) × (2/6) = 10/42 = 5/21.

Final answer:

The probability of drawing a red marble first and then a yellow marble from a bag with 2 yellow marbles and 5 red marbles is calculated by multiplying the probability of each event, giving a final answer of 5/21.

Explanation:

The calculation of the probability that the first marble is red and the second one is yellow when two marbles are drawn without replacement from a bag containing 2 yellow marbles and 5 red marbles involves step-by-step conditional probabilities.

Step 1: Calculate the probability of drawing a red marble first. Since there are 5 red marbles out of a total of 7 marbles, the probability is 5/7.

Step 2: Now that a red marble has been drawn and not replaced, there are 1 yellow marble less and 1 red marble less in the bag, making a total of 6 marbles. The probability of then drawing a yellow marble is 2/6, or 1/3.

Step 3: To find the combined probability of both events happening in sequence (a red marble first, then a yellow marble), multiply the individual probabilities: (5/7) * (1/3).

The final answer is therefore (5/7) * (1/3) = 5/21.

Answer:

Positive

Step-by-step explanation: When you look at a graph you always look at it like your reading a book. So you read it from left to right and if you read the line shown it is going up meaning it is positive.

Hope this helps :)

Answer:

The Answer is 39/10! I Did The Assignment!

Step-by-step explanation:

The radius is 3.9 units

In geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere. Look at the image of a circle given below showing the relationship between radius and diameter.

given:

As, CB ⊥ AC by the radius-tangent theorem.

In ΔABC, applying the Pythagoras theorem

r² + 8² = (r+ 5)²

r² + 64= r² + 25 + 10 r

64 - 25 = 10 r

39 = 10r

r= 39/10

r= 3.9 units

Hence, the radius is 3.9 units.

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Answer:

4 or 3/2

Step-by-step explanation:

The given equation is 3(x - 4) (2x - 3) =0

When we have 0 on the right hand side of given equation , we can compare two factors with 0 .

we can do this by :

(3×x - 3×4) (2x-3)=0

(3x-12)(2x-3)=0

either , (3x-12)=0

or,3x = 12

or, x = 12/3

or ,x = 4

now , comparing other factor:

(2x -3) =0

or, 2x = 3

or ,x=3/2

Answer:

Step-by-step explanation:

Exact Form:

x=5,−32

Decimal Form:

x=5,−1.5

Mixed Number Form:

x=5,−112

                      ( I tried... )

Answer:

30 units

Step-by-step explanation:

In order to find the side lengths, you can either draw it out, or imagine it in your head. I would recommend drawing it if you're unfamiliar to the topic.

So when you draw it out, you see that AB is the width of the rectangle, and BC is the length.

In order to calculate it, you'd have to keep in mind which direction each line goes. Since AB is horizontal, we would use the x coordinates to find the length. [tex]x_{1}[/tex]-[tex]x_{2}[/tex] is the formula, where A is [tex]x_{2}[/tex], since it is farther left.

width = 2 - (-3)

w = 5

Now, you'd do the same thing, but with BC, and [tex]y_{1}[/tex]-[tex]y_{2}[/tex]. In this case, B is [tex]y_{1}[/tex], since it is further up.

length = 2 - (-4)

l = 6

Now, multiply them to find the area of a rectangle.

5 x 6 = 30

I hope this helps!

Answer: 18°

Step-by-step explanation:

From the question, Miles hs a piece of paper that is 1/4 of a large circle and he cuts the paper into five equal parts from the center of the circle.

The total angle of a circle is 360°. Since Miles caught 1/4 of the circle, this means that he'll have an angle of : 360° × 1/4 = 90°.

Then, he now cuts the paper into five equal parts. This means that we divide 90° by 5 which will give:

= 90° ÷ 5

= 18°

The angle measure of each part is 18°.

Answer:

18°

Step-by-step explanation:

Extracting the key information from the question:

*** Miles has paper that is 1/4 of a large circle.

*** He cut this paper into five equal parts.

*** We are required to calculate the angle measure of each part.

The sum of the angles in a circle is 360°. So I miles has 1/4 of a large circle, it means that the sum of the angles of this paper should be a quarter of 360°

= 1/4 × 360°

= 90°

Again, since he cuts the paper into five equal parts, we will find the angle measure of each part by dividing 90° by 5.

The angle measure of each

= 1/5 × 90°

= 18°

Therefore, each of the five parts of paper had an angle of 18°

Answer: A = $1503.6

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1000

r = 6% = 6/100 = 0.06

n = 1 because it was compounded once in a year.

t = 7 years

Therefore,.

A = 1000(1 + 0.06/1)^1 × 7

A = 1000(1.06)^7

A = $1503.6

Answer:d

Step-by-step explanation: just factor it out

The factorisation of the given polynomial is (x+2)(2x+3). Therefore, option D is the correct answer.

The given polynomial is 2x²+ 7x + 6.

We need to factorise the given polynomial.

In order to factorise a quadratic algebraic expression in the form ax² + bx + c into double brackets:

Now, 2x²+ 7x + 6=2x²+ 4x +3x+ 6

=2x(x+2)+3(x+2)

=(x+2)(2x+3)

Therefore, option D is the correct answer.

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For given equation x^2+6x-15=0, value of x is [tex]-3\pm 2 \sqrt{6}[/tex]

The "solutions" of an equation are referred to as the roots of the equation. Solutions are the numbers that, once the variable has been solved, are equal to it. We can use the discriminant formula to obtain the roots of quadratic equations.

The given equation [tex]x^2+6x-15=0\\[/tex] can be solved using discriminant method.

[tex]d=b^2 -4ac\\[/tex].......................1

[tex]x=-b\pm\sqrt{d}/2a[/tex].....................2

To calculate d,

Substitute a=1,b=6,c=-15 in eq 1.

[tex]d=6^2-4\times 1\times -15\\ d=96[/tex]

[tex]x=-6\pm \sqrt{96}/2\\x=-3\pm 2\sqrt6[/tex]

Thus, value of x is  [tex]-3\pm 2 \sqrt{6}[/tex]

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Final answer:

x = -3 ±√24.

Explanation:

To solve the quadratic equation x²+6x-15=0 by completing the square, follow these steps:

First, move the constant term to the other side of the equation:

x² + 6x = 15.

Add the square of half the coefficient of x to both sides to complete the square: (6/2)² = 9, so add 9 to both sides resulting in x² + 6x + 9 = 24.

Now the equation is a perfect square on the left side:

(x+3)² = 24.

Take the square root of both sides to solve for x:

x+3 = ±√24.

Subtract 3 from both sides to find the values of x:

x = -3 ±√24.

Answer:

The probability is 1/254,251,200

Step-by-step explanation:

We proceed as follows;

Firstly, we are selecting 5 state capitals out of 50. The number of ways we can do this is 50P5 = 50!/5!(50-5)! = 254,251,200 ways

Now, out of this number of ways , only one route is desired in that particular order.

This means the probability of having the route scheduled in that particular order would be;

1/254,251,200

Answer:

0.000000003933

Step-by-step explanation:

As the candidate will visit the capitals of 5 of the 50 states, the probability of each capital being selected is 1/50.

As we want a probability of 5 specific capitals in a specific order, we can calculate the probability of each capital being chosed:

First city being Sacramento: Probability of 1/50

Second city being Albany: Probability of 1/49 (as the first city is not available now)

Third city being Juneau: Probability of 1/48

Fourth city being Hartford: Probability of 1/47

Fifth city being Bismarck: Probability of 1/46

So the final probability is 1/(50*49*48*47*46) = 0.000000003933

Answer:

3x(x-2)

Step-by-step explanation:

1. find out the common factor in each components which is 3x

2. done.

Answer:

4/3 servings or her dish can be made

These are the 2 equations:

Total = 5 and 1/8 pounds + 6 pounds + 4 and 7/8 pounds

N = Total / 10

Step-by-step explanation:

We know 1 serving = 12 pounds

We want the number of servings able to make. call it N

N =  (Total pounds)/ (12 pounds/serving)

P = pasta per serving

S = sauce per serving

O= onions per serving

It appears that  

P*N = 5 and 1/8 pounds

S*N = 6 pounds

O*N  = 4 and 7/8 pounds

5 and 1/8 + 6 + 4 and 7/8 = Total

16 pounds total.

N = 16/12 = 4/3 servings

Total = 5 and 1/8 pounds + 6 pounds + 4 and 7/8 pounds

N = Total / 10

Answer:

Tan x = 125/500= 0.25

so x = arctan (0.25)

=14 degree

The measure of the diving angle is 14°.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

Sea level and 500 ft are parallel.

This means,

x° and end drive angles are alternate angles.

So,

tan x = 125/500

tan x = 0.25

x = [tex]tan^{-1}[/tex] (0.25)

x = 14°

Thus,

The measure of the diving angle is 14°.

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Answer:

Therefore, the number of bundles to be bought is 22 bundles

Step-by-step explanation:

Here we have;

Dimensions of roof

Square pyramid = 4 triangular sides

Base length of triangle = Length of gutter on one side = 18 ft

Height of triangle = Length from the gutter on one side to the top of the roof = 15 ft

∴ Area of one of the four triangles = 0.5 × Base × Height = 0.5 × 15 × 18 = 135 ft²

Total area of four sides of the pyramid = 4 × Area of one of the four triangles

∴ Total area of four sides of the pyramid = 4 × 135 ft² = 540 ft²

Area covered by one bundle of shingle = 25 ft²/bundle

Therefore number of bundles of shingles required = [tex]\frac{Total \, area \ of \, four \ sides \ of \ the \ pyramid}{Area \ covered \ by \ one \ bundle \ of \ shingle} = \frac{540 \ ft^2}{25 \ ft^2/bundle} = 21.6 \ bundles \approx 22 \ bundles[/tex]

Therefore, the number of bundles to be bought = 22 bundles.

Answer:

3.33 can i have brainliest

Step-by-step explanation:

5/3 = 1.6666666666...

1.6666666666..... X 2 = 3.333333.....

Answer:

d

Step-by-step explanation:

D. Rational number, 0.375

I Got it Right

Hope i Helped ❤

Answer:

1/1 x 1/2 x 1/2 = 1/4

One times One-Half times One-Half Equals One-Fourth

The Probability is 1/4 or One-Fourth.

Step-by-step explanation:

There is a One-Half possibility on two of them for choosing D.

Multiply that by each other and than by 1.

Answer:

6 times

Step-by-step explanation:

In order to figure out how many times a number goes into another number we need to divide the numbers:

88/14 ≅ 6.29

Since the answer is 6.29 then 14 fits into 88, 6 full times

Answer:

76.3 millions of people per year

Step-by-step explanation:

Missing text of the question:

"The world population1 , in billions, was approximately

[tex]P=7.17e^{0.01064t}[/tex]

where t is in years since April 20, 2014. At what rate was the world's population increasing on that date? Give your answer in millions of people per year, rounded to one decimal place."

Answer:

The expression that gives us the world population in billions t years after April 20, 2014 is

[tex]P=7.17e^{0.01064t}[/tex]

Where t is expressed in years.

Here we want to find the rate of change of this function at that date.

The rate of change of a function is given by its derivative. Therefore, we have to calculate the derivative of the function P, and the calculate its value at the date indicated.

The derivative of the function is:

[tex]P'(t)=7.17 \cdot 0.01064 e^{0.01064 t}=0.0763 e^{0.01064t}[/tex]

Now we want to find the rate of change at the date April 20, 2014, which means zero years after that date; so we have to substitute t = 0 into the expression of the derivative, and we find:

[tex]P'(0)=0.0763e^0 = 0.0763[/tex]

So, 0.0763 billions, which corresponds to 76.3 millions of people per year.