An airplane travels at a constant speed of 575 miles per hour write and equation that can be used to determine

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Step 01:

Data

Longs Peak = 30.5 miles N65°W

Pikes Peak = 80.6 miles S13°E

distance between the two peaks = ?

Step 02:

Diagram

Step 03:

Longs Peak = 30.5 miles N65°W

x1:

30.5 * Sen 65 = 27.64

y1:

30.5 * Cos 65 = 12.89

Pikes Peak = 80.6 miles S13°E

x2:

80.6 * Sen 13 = 18.13

y2:

80.6 * Cos 13 = 78.53

Step 04:

DIstance

d = 66.3152

The answer is:

The distance between the two peaks is 66.32 miles

The range of the data is the difference between the highest and lowest values, which is 8 inches. Adding another plant with a height of 14 inches would not change the range, so the range would remain 8 inches.

Data is a collection of facts, figures, or information that can be processed and used to draw conclusions or make decisions. It can be stored in a variety of formats, including numerical, text, images, audio, and video. Data can be collected from a variety of sources, such as surveys, observations, experiments, or transactions. It can be used to inform decisions in areas such as business, health care, education, and research. Data can be analyzed to gain insight, develop strategies, identify trends, and make predictions. Data is a valuable resource and is increasingly important in today's digital age.

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The solution set for the quadratic equation (2x - 7)² = 25 is 6 and 1.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

The solution set for a quadratic equation is the roots of the quadratic equation.

Given, (2x - 7)² = 25.

2x - 7 = ± 5.

2x = ± 5 + 7.

x = (± 5 + 7)/2.

x = 12/2 Or 2/2.

x = 6 or 1.

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Step-by-step explanation:

if you brought this in here correctly, oh, it is a real mystery !

common sense ! we need common sense !

what can I add to e.g. 15 to still keep the 15 ?

this works with any other number as well.

e.g. 1

I have 1.

how much can I add to 1 to still have 1 afterwards ?

1+? = 1

? = 0

right. there is no other solution, as there are also no miracles in math.

whatever is added, is then added. to remain unchanged we can only add 0.

so,

15 + something = 15 can only be true, if that something is 0.

something = |3x|

that means the absolute value of 3x, which will always be +3x even for negative x.

but it does not matter.

|3x| = 0 (has to be 0 to make the main statement true).

therefore, 3x = 0

therefore, x = 0.

so, they're is only one dot (a filled dot) at precisely 0 in the graph that makes this a true statement.

Answer:

Dear user,

Answer to your query is provided below

Water left in the tank is 158 m^3

Step-by-step explanation:

Volume of Rectangular tank = 4.5 x 6 x 8 = 216m^3

Water used = 58m^3

Water left = 216 - 58 = 158m^3

\(\frac{2}{13}\)

Probability is finding the chance that some specific outcome will occur. In this case, we are looking for the probability of one of two outcomes.

Equally Likely Outcomes

When drawing a card from a well-shuffled deck, all outcomes (cards) are equally likely to be drawn. Each card was a 1/52 probability of occurring.

Probability of Two Outcomes

In a deck of cards, there are 4 cards of each number. This means that the probability of drawing a 2 is 4/52, the same for a queen.

So, to find the probability of one of the two desired outcomes is equal to adding the probabilities together.

This fraction can then be simplified further:

Answer:

he would need to mow lawns for 8 hours

Step-by-step explanation:

Answer:

Draw a picture of Angkor Wat

Answer:

Step-by-step explanation:

You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.

David's solution is correct up to Step 4.

At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...

  Step 4: (5 -3)x -4 = 2x -4

David's incorrect solution should have been 2x -4.

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15

Step-by-step explanation:

Answer:

No, Franco's calculation is incorrect.

Step-by-step explanation:

No, Franco's calculation is incorrect. The correct answer is 9.37 x 0.1 = 0.937.

When multiplying a decimal number by a decimal number, the decimal point in the product should be placed so that the number of decimal places in the product is equal to the sum of the number of decimal places in the factors. In this case, the number 9.37 has two decimal places, and the number 0.1 has one decimal place. Therefore, the product of 9.37 x 0.1 should have a total of 2 + 1 = 3 decimal places.

To obtain the correct answer, we need to multiply 9.37 x 0.1 using standard long multiplication:

Copy code

9.37

x 0.1

0.937

Therefore, the correct answer is 0.937, not 93.7 as Franco stated.

Answer:

No. This is incorrect.

Step-by-step explanation:

9.37 × 1 = 9.37

Times by 1 the number stays the same.

If you multiply by 0.1 the decimal will move one place and the 9.37 should get smaller! The sentence in the problem shows 93.7 which is bigger.

9.37 × 10 = 93.7

9.37 × 0.1 = 0.937

The 5 ft by 8 ft dimensions of the car and the (width) 2 ft by (height) 3 ft dimensions of the chair, indicates that the vehicle can haul both chairs in one trip.

The dimensions of rectangularly shaped solid are the height, the width and the length of the solid.

The possible dimensions of the vehicle and the chair obtained from a similar online question are;

Length of the vehicle = 8 feet

Width of the vehicle = 5 feet

The height of one chair = 3 feet

The width of one chair = 2 feet

Therefore;

The width of the vehicle of 5 feet indicates that the vehicle can contain the two chairs placed side by side with their widths of 2 feet each, to get;

Width of  the two chairs = 2 feet + 2 feet = 4 feet < 5 feet

The two chairs placed horizontally, such that we get;

The total length of the horizontally placed chairs = 3 feet + 3 feet = 6 feet

The combined height of the two chaires, of 6 feet is less than the length of the car which is 8 feet, therefore;

The car can haul both chairs placed horizontally in a single trip.

The vehicle could therefore be used to haul both chairs in a single trip.

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Answer:

A. 4 ounces

Step-by-step explanation:

Given that Elana paid $2.50 for 10 ounces of popcorn, let x be the amount popcorn a dollar will buy.

Thus we have:

$2.50 = 10 ounces

$1 = x

Cross multiply

$2.50 × x = 10 ounces × $1

Divide both sides by $2.50

($2.50 × x)/$2.50 = (10 ounces × $1)/$2.50

x = (10 ounces)/2.50

x = 4 ounces

Therefore, you can buy 4 ounces of popcorn per dollar

Answer:

-66

Step-by-step explanation:

- 13, ____, -119

first, find the common difference:

-13 - (-119) = 106

next, divide 106 by 2: \(\frac{106}{2}\) = 53

so, the common difference is 53.

now, subtract 53 from -13:

-13 - 53 = -66

Answer:

-66

Step-by-step explanation:

the sequence goes -13,-66,-119

just subtract with 53

(decreasing arithmetic sequence)

Answer:

-3x+10

Step-by-step explanation:

this is for 2

-3x+7+3

Collect like terms.

-3x+(7+3)

Simplify.

-3x+10

Answer:

From the given information, the value of a is 3 and the measurement of ∠R is 25°

Step-by-step explanation:

For this problem, we have to find the value of a and the measurement of ∠R. We are given some information already in the problem.

ΔJKL ≅ ΔPQR

This means that all of the angles and all of the sides of each triangle are going to be equal to each other.

So, knowing this, let;s find the measurement of ∠R first.

All triangles have a total measurement of 180°. We are already given two angle measurements. We are given that the m∠P is 90° because the small box in the triangle represents a right angle and right angles equal 90°. We are also given that the m∠Q is 65° because ∠Q is equal to ∠K so they have the same measurement. Now, let's set up our equation.

65 + 90 + m∠R = 180

Add 65 to 90.

155 + m∠R = 180

Subtract 155 from 180.

m∠R = 25°

So, the measurement of ∠R is 25°.

Now let's find the value of a.

KL is equal to PQ so we will set up an equation where they are equal to each other.

7a - 10 = 11

Add 10 to 11.

7a = 21

Divide 7 by 21.

a = 3

So, the value of a is 3.

Answer:

The first thing you should do for this case is to graph the data you have in the statement to see the relationship between grapes and blueberries.

The function represented by the table is

y = 0.25x

Then, as Mandie is making 15 glasses of fruit salad, we have:

y + x = 15

We have two equations and two unknowns that we must solve.

y = 0.25x

y + x = 15

Resolving

For x:

0.25x + x = 15

1.25x = 15

x = 15 / 1.25 = 12

For y:

y = 0.25x = 0.25 (12) = 3

Answer

The ratio of grapes to blueberries she should use is 12: 3

1. My Russian is a bit rusty. I think you're asking to find the antiderivatives in the first part:

а) \(\displaystyle \int 2x^n - 5x \, dx = \boxed{\frac2{n+1} x^{n+1} - \frac52 x^2 + C}\)

This follows from the power rule for differentiation,

\(\dfrac d{dx} x^n = n x^{n-1}\)

I'm not sure what the power on the first term is, so I just use a general real number n. This solution is correct as long as n ≠ -1; otherwise we would have

\(\displaystyle \int 2x^{-1} - 5x = 2\ln|x| - \frac52 x^2 + C\)

б) Using the fact that

\(\dfrac d{dx} \sin(x) = \cos(x)\)

as well as the power rule from part (a),

\(\displaystyle \int 3 \cos(x) - x \, dx = \boxed{3 \sin(x) - \frac12 x^2 + C}\)

в) By the chain rule,

\(\dfrac d{dx} \sin(5x) = 5 \cos(5x)\)

\(\dfrac d{dx} \cos(3x) = -3 \sin(3x)\)

Hence

\(\displaystyle \int \cos(5x) - \frac16 \sin(3x) \, dx = \boxed{\frac15 \sin(5x) + \frac1{18} \cos(3x) + C}\)

2. These just look like standard definite integrals. Using the known derivatives mentioned in part (1) in conjunction with the fundamental theorem of calculus, we have

a)

\(\displaystyle \int_0^1 x^2 \, dx = \frac13 x^3 \bigg|_{x=0}^{x=1} = \frac13 (1^3 - 0^3) = \boxed{\frac13}\)

б)

\(\displaystyle \int_0^{\frac\pi2} \sin(x) \, dx = -\cos(x) \bigg|_{x=0}^{x=\frac\pi2} = -\left(\cos\left(\frac\pi2\right) - \cos(0)\right) = \boxed{1}\)

Answer:

84

Step-by-step explanation:

2+1-6+29*3

= 2+1-6+87

= 3-6+87

= -3+87

= 84

The length of line having mid point B ⇒  7x - 2.

Given that,

B is the mid point of AC

And also given that

length of segment AB = 2x+5

And length of segment BC = 5x - 7

A straight path established by linking a group of points in a plane is known as a line. It is a one-dimensional form with only a length and no width or height. A line can extend indefinitely in both ends in opposite directions. To indicate a line, we can use upper case characters.

Now since B is the mid point of AC,

So, The line AC is sum of the line segment AB and line segment BC.

Therefore,

AC = AB+BC

     = (2x+5)+(5x - 7)

     = 7x - 2

Hence,

The length of AC is 7x - 2

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Answer:

I really hope this helps :), 68

The supportive statement regarding the trapezoid based on the information is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

The non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The missing statement to support all other statements would be that m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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Answer:

Substitution means that we need to replace some of the variables by the given values.

1)  t = rs*(s + 1)      (if r=4 and s=5)

So we just need to replace r by 4 and s by 5 in the equation.

t = 4*5*(5 + 1) = 20*6 = 120

t = 120

2)  k = 6 - 5q/2g     (if q=3 and g=8)

We need to replace q by 3, and g by 8.

k = 6 - (5*3)/(2*8) = 6 - 15/16 = 5.167

k = 5.167

3) p = a + b - 2c   (if a = 2, b = -1, c = 5)

Replacing the variables we get:

p = 2 + (-1) - 2*(5)

p = 2 - 1 - 10 = -9

p = -9

4) I = 1/x - 2/y + z   (if x = 4, y = 6, and z = 2/3)

Replacing the variables we get:

I = 1/(4) - 2/(6) + (2/3)

I = 1/4 - 2/6 + 2/3 =  1/4 - 1/3 + 2/3

I = 1/4 + 1/3 = 3/12 + 4/12 = 7/12

I = 7/12 = 0.583

Rational Function: any function that is found by a rational fraction.

Its form: \(\frac{1}{x}\)

Finding Zeros of  a Rational Function:

\(f(x)=\frac{(x-3)(x+2)}{(x-5)(x-3)}\)

   2. Find restrictions by equating the denominator to 0

\(x-5=0\)                \(x-3=0\)      when x=-5 and 3, the function is undefined

\(x=-5\)                   \(x=3\)

  3. Set the numerator equal to zero

\(x-3=0\)              \(x+2=0\)  

\(x=3\)                    \(x=-2\)

Be careful - since we have x-3 on both the numerator and denominator the graph will not intersect the x-axis at that point. This is what is called a removable discontinuity.

Therefore, the only zero occurs at (-2,0)

a) There are 5 grades within one standard deviation of the mean.

b) All of the grades fall within two standard deviations of the mean.

c) There are 4 grades with a z-score less than 0.3.

The standard deviation is the square root of the variance.

We need to first calculate the mean and standard deviation of the grades.

Step 1: Calculate the mean

Mean = (60 + 64 + 75 + 77 + 83 + 86 + 91 + 95 + 98 + 100) / 10

= 811 / 10

= 81.1

Step 2: Calculate the standard deviation

s = √ {Σ(xi - x)²} / (N - 1)

where xi is the individual grade, x is the mean, and N is the total number of grades.

SD = √ {(60 - 81.1)² + (64 - 81.1)² + ... + (100 - 81.1)²} / 9

SD = √ [9746.9] / 9

SD = 10.78

Step 3: Use the mean and standard deviation to answer the questions.

A) One standard deviation from the mean in either direction would be:

81.1 - 10.78 = 70.32

81.1 + 10.78 = 91.88

So, the grades that fall within one standard deviation of the mean are:

(75, 77, 83, 86, 91)

There are 5 grades within one standard deviation of the mean.

B) Two standard deviations from the mean in either direction would be:

81.1 - 2(10.78) = 59.54

81.1 + 2(10.78) = 102.66

So, the grades that fall within two standard deviations of the mean are:

(60, 64, 75, 77, 83, 86, 91, 95, 98, 100)

All of the grades fall within two standard deviations of the mean.

C) To calculate the z-score for each grade, we use the formula:

z = (x - μ) / σ   ; where x is the individual grade, μ is the mean, and σ is the standard deviation.

For a z-score to be less than 0.3, we need to find the grades that satisfy:

(x - μ) / σ < 0.3

Rearranging this inequality, we get:

x < μ + 0.3σ

Substituting the values for μ and σ, we get:

x < 84.86

So, the grades that have a z-score less than 0.3 are (60, 64, 75, 77)

There are 4 grades with a z-score less than 0.3.

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

An appropriate assignment of digits to the outcomes for a simulation of this random process would be:

Option 1: Let 0 and 1 = the student is enrolled in the nursing program. Let 2-5 = the student is not enrolled in the nursing program. Skip the digits 6, 7, 8, 9, and 0.

This option assigns two digits, 0 and 1, to represent the two possible outcomes: a student is either enrolled in the nursing program (outcome 1) or not enrolled (outcome 2-5). The digits 2-5 represent the non-nursing program outcomes, and the digits 6-9 and 0 are skipped.

Option 1 is appropriate because it assigns a unique digit to each possible outcome, and the skipped digits are not relevant to the simulation. Additionally, the proportion of digits assigned to each outcome (2 out of 10) corresponds to the proportion of students in the nursing program (20%).

At a speed of 48 miles per hour, it would take 13 hours.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given:

The amount of time needed to complete a certain road trip, t, varies inversely with the speed of a vehicle, s. At a speed of 52 miles per hour, the trip will be complete in 12 hours.

Distance is constant.

And we know the formula:

Distance = speed x time

              = 52 x 12

              = 624 miles

Now to find the time:

Now for speed = 48 miles per hour

time,

t = distance / speed

 = 624/48

 = 13 hours

Therefore, 13 hours would it take at a speed of 48 miles per hour.

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The solutions to the quadratic equation are [−5/2,1/3]. Option A

Given the inequality;

6x^2≥5−13x

First, convert to quadratic equation

\(6 {x}^{2} - 5 + 13x \geqslant 0 \)

No, let's solve the quadratic equation using the factorization method

\(6 {x}^{2} + 13x - 5 \geqslant 0\)

Multiply 6 by -5 and find two factor that their product equals the number and their sum equal 13. Those two number are + 15 and -2

Substitute as 15x and 5

-2x in the inequality, we have;

\(6 {x}^{2} +15x - 2x - 5 \geqslant 0\)

Factor the common multipliers

\(3x(2x + 5) - 1(2x + 5) \geqslant 0\)

We have two expressions, written as;

\((3x - 1) (2x + 5)\geqslant 0\)

Let's solve to get the roots of x

\(3x+ 1 \geqslant 0 \)

\(x \geqslant 1/3\)

\(2x + 5 \geqslant 0\)

\(x \geqslant \frac{ - 5}{2} \)

Thus, the solutions to the quadratic equation are [−5/2,1/3]. Option A

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