a scuba diver plans to go on two dives in one day. in the first, she will descend to feet, and in the second she plans to descend to feet. estimate the difference between the depth of the two dives by first rounding to the nearest ten.

Answer:

The statements that are true about the ordered pair (1, 2) and the system of equations are:

When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.

So, the correct options are:

When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.

Step-by-step explanation:

The integral ∫₁/₁₀¹⁰[㏒₁₀(10x)/x]dx = 2㏑10

Integration is the process of finding the antiderivative of a fuinction.

Given the integral

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]

We evaluate the integral as follows

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]

Now, using the properties of the laws of logarithms, we have ㏒ab = ㏒a + ㏒b

So, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10 + log_{10}x }{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx\\[/tex]

So, using the property of change of base of logarithm, we have that

logx = lnx/ln10

, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{\frac{lnx}{ln10} }{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {\frac{lnx}{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {{lnx} \, dlnx[/tex]

[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = {[lnx]_{\frac{1}{10}}^{10} } + {\frac{[lnx]^{2}}{2} }_{\frac{1}{10}}^{10} } \\= ln10 - ln\frac{1}{10} + \frac{1}{2}[[ln10]^{2} - [ln\frac{1}{10}]^{2} ] \\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [-ln10}]^{2} ]\\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [ln10}]^{2} ]\\= 2ln10 + 0\\= 2ln10[/tex]

So, the we see that the integral [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = 2ln10[/tex]

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Answer: £3136

Step-by-step explanation:

First you want to find 28% of 800 to find out how much it increases by every year.

So 800*0.28= 224

And then you want to multiply 224 to 14 years to see how much he has to pay in 14 years

224*14=3136

Your answer: £3136

The actual balance is $36,400.68 which lower than the goal of $150,000. The Option D is correct.

The Formula to use to derive the actual balance is: P[((1 + r/n)^(n*t)) - 1) / (r/n)] where: FV = future value, P = monthly deposits, r = interest rate, t = time in years, n = number of compound in a year

From the given:

P = 200

r = 2.85% 0.0285

t = 30 years

n = 12 (compounded monthly)

Future value = 200((1 + 0.0285/12)^(12(30)) - 1) / (0.0285 / 12)

Future value = $113,599.32

The difference between the actual balance and the employee's goal is:

= $150,000 - $113,599.32

= $36,400.86

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Answer: A

Step-by-step explanation:

Convert the equation into quadratic form (y=ax^2+bx+c)

y=-3(x-4)(x+6)   =  y=-3x^2-6x+72

Calculate -b/2a

which is 6/-6=-1

then put the value -1 into the equation for x.  

-3+6+72=75

The answer is therefore A.

Answer:

Step-by-step explanation:

You want to find the slopes of the lines shown in the attached graphs.

The slope of a line is its "rise" divided by its "run":

  m = rise/run

To determine slope from a graph, start at an identified point on the left, and count the grid squares up (+) or down (-) to the same horizontal line as the identified point on the right. This is the "rise". Then count the grid squares horizontally to the identified point. This is the "run". The slope is the ratio of these numbers.

1. rise 4, run 6, slope 4/6 = 2/3

2. rise -3, run 4, slope -3/4

3. rise -6, run 3, slope -6/3 = -2

4. run = 0; division by 0 is "undefined", so the slope is "undefined"

5. rise 4, run 1, slope 4/1 = 4

6. rise 0, run (anything), slope 0/1 = 0

__

Additional comment

It is helpful to remember that a horizontal line has a slope of 0, and a vertical line has a slope that is "undefined." Slope is positive if the line goes up to the right. It is negative if the slope goes down to the right.

Because the slope of a vertical line is "undefined," its equation cannot be written in "slope-intercept" form.

Here, points are marked on the lines. When that is not the case, it usually works well to identify points where the line crosses an intersection of grid lines.

You can also use grid crossings to check your answer for the slope. For example, the line on graph 3 crosses grid intersections that are 2 down and 1 over from the marked points (and other grid intersections), confirming a slope of -2.

The value of a and b are -179/171 and -20/171 respectively.

Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. In more complex cases, it is useful to multiply the denominator by its conjugate to cancel out the surds in the denominator.

(2+5√7)/(2-5√7)

by rationalization

(2+5√7)/(2-5√7) × (2+5√7)/(2+5√7)

=( 4+10√7 + 10√7 + 175)/4+10√7 - 10√7- 175

= (20√7+179)/-171

= -20/171 √7 -179/171

therefore the value of a = -179/171 and b = -20/171

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The process of converting individual raw scores in a distribution to a set of scores for which we know the percentiles is known as "normalizing the data" or "standardizing the data."

The steps for standardizing the data are as follows:

Order the raw scores in the distribution from smallest to largest.

Assign each score a percentile rank. This is the percentage of scores in the distribution that are equal to or lower than the score. For example, if a score has a percentile rank of 75, it means that 75% of the scores in the distribution are equal to or lower than that score.

Convert the raw scores to standardized scores (also known as z-scores). This is done by subtracting the mean of the distribution from each score and then dividing by the standard deviation of the distribution. The resulting standardized score represents the number of standard deviations above or below the mean that the raw score falls.

The process of standardizing the data helps to put the raw scores into a common context, which makes it easier to compare scores from different distributions and to draw meaningful conclusions about the data. Additionally, standardized scores can be used to determine the probability of a score falling within a particular range.

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Step-by-step explanation:

cot(θ) = 1/tan(θ)

tan(θ) = sin(θ) / cos(θ)

Given cos(θ) = 15/17, we can find sin(θ) using the Pythagorean identity:

sin(θ) = sqrt(1 - (cos(θ))^2) = sqrt(1 - (15/17)^2) = 4/17

So, tan(θ) = 4/15

And, cot(θ) = 1/tan(θ) = 15/4

Answer: 15/8

Step-by-step explanation: We know that sin(0) will equal 8 by the 8,15,17 triangle. We using the restricted domain value for theta and using the pythagorean identities to get cot(0) as cos(0)/sin(0) and substitute the values. The denominators cancel and the result is 15/8.

The width of the rectangular will be x+4.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.

Area of the rectangle is A = a*b

Given Length is = x+7

And  the area is x² +11x+28

So the width is = x² +11x+28 / x+7

x² +7x+4x+28/x+7

=(x+7)(x+4)/x+7

=x+4

Hence the width of the rectangular will be x+4.

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Answer:

16.2m^2

16.2*20=324

324 rupees

Step-by-step explanation:

Answer:

2[tex]\sqrt{13x^{2} }[/tex]

Step-by-step explanation:

To simplify the expression √52x^4, we can break it down as follows:

√(52x^4) = √(4 * 13 * x^4)

Since the square root of a product is equal to the product of the square roots, we can simplify further:

√(4 * 13 * x^4) = √4 * √13 * √(x^4)

The square root of 4 is 2, and the square root of x^4 is x^2:

2 * √13 * x^2

Therefore, the simplified expression is 2√13x^2.

Answer:

[tex]\large\text{$2\sqrt{13}\;x^2$}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt{52x^4}[/tex]

Prime factorization is the process of representing a positive integer as a product of its prime factors.

The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:

[tex]\sqrt{2^2 \cdot 13 \cdot x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{abc}=\sqrt{\vphantom{b}a}\sqrt{b}\sqrt{c}[/tex]

[tex]\sqrt{2^2} \sqrt{13} \sqrt{x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]2\sqrt{13} \sqrt{x^4}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}},\quad \textsf{assuming} \;a\geq 0[/tex]

[tex]2\sqrt{13} \;x^{\frac{4}{2}}[/tex]

[tex]2\sqrt{13} \;x^2[/tex]

Therefore, the simplified expression is:

[tex]\large\boxed{2\sqrt{13}\;x^2}[/tex]

Using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out via the arithmetic operators.

So, we know that:

Fish: 75kg + 75/4

75 + 18.75

93.75

Fisherman: 100kg + 100/5

100 + 20

120

Positive difference: 120 - 93.75 = 26.25

Therefore, using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.

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Answer:

m = -2

b = -3

Step-by-step explanation:

Point slope formula of a line = [tex]y-y_{1} = M(x-x_{1} )[/tex]

Where x1 and y1 are the coordinates of the point and M is the slope.

Given slope = -2

Point = (-7,11)

So x1 = -7 and y1 = 11

Substituting the values in the point-slope formula, we get:

[tex]y-11 = -2(x - (-7))[/tex]

[tex]= > y = -2x -14 + 11[/tex]

Or

[tex]y = -2x -3[/tex]

Thus, m = -2 and b = -3

(a) The equation to find x is 4x + 22 = 90.

(b) The degree of each angle:

The sum of angle 1 and 2 is equal to right angle.

The value of a right angle is equal to 90°.

In the figure, we have a right angle and one line in it. It makes two angles 1 and 2 with

(a) Find an equation to find x!

(b) Find the degree measure of each angle!

The sum of angle 1 and 2 is equal to 90°. So,

m∠1 + m∠2 = 90

3x + x + 22 = 90

4x + 22 = 90

This is the equation to find x. Then, we find x.

4x + 22 = 90

4x = 90 - 22

4x = 68

x = 68/4

x = 17°

The degree measure of each angle will be

m∠1 = 3x

m∠1 = 3(17)

m∠1 = 51°

m∠2 = x + 22

m∠2 = 17 + 22

m∠2 = 39°

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Let's start by setting up a system of equations to represent the given information:

3r = m - 7

9r = m + 11

where r is the cost of one rose, and m is the total amount of money that Masha has.

We can solve this system of equations using the elimination method:

Multiplying the first equation by 3, we get:

9r = 3m - 21

Subtracting the second equation from this, we get:

0 = -4m - 32

Simplifying, we get:

m = -8

Therefore, Masha has $-8, which means she owes money. This indicates that there may be an error in the problem statement or data provided.

Answer:

Masha has 16 dollars.

Step-by-step explanation:

3x + 7 = Masha's total money

9x = Masha's total money + 11 (after borrowing)

We can use the first equation to find the value of 3x, which is Masha's total money if she buys three roses:

3x + 7 = Masha's total money

3x + 7 = Masha's total money

3x = Masha's total money - 7

We can substitute the second equation to solve for Masha's total money:

9x = Masha's total money + 11

9x = (3x + 7) + 11

9x = 3x + 18

6x = 18

x = 3

Now we know that one rose costs 3 dollars. We can use the first equation to find Masha's total money if she buys three roses:

3x + 7 = Masha's total money

3(3) + 7 = Masha's total money

9 + 7 = Masha's total money

Masha's total money = 16

Answer:

Green

Step-by-step explanation:

All you have to do is retrace retrace Alison’s steps. Note that there are 10 beads in the pattern, the 10th bead black. 210, 200, 190, 180, 170, 160, 150, 140. The 140th bead is black, because it is a multiple of 10. The 139 bead is black as well, because the end of Alison’s pattern contained 2 black beads. The next bead, bead 138, is green. So your answer would be green.

The probability of more heads than tails is 1/2 since the number of tails is divisible by 3.

A fair coin is one that has equal chances of being heads or tails when it is tossed. When a fair coin is tossed four times, the probability of getting more heads than tails is 1/2. This is because for each toss, the probability of getting a head or a tail is equal (1/2). This means that the probability of getting more heads than tails is the same as the probability of getting more tails than heads, which is 1/2.

Since the number of tails is divisible by 3, this means that in the four tosses, there must either be 0, 3, or 6 tails. Since there are no other possibilities, the probability of more heads than tails is 1/2 since it is equally likely to get more heads than tails or more tails than heads.

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The average distance between the Earth and the Moon is about 238,855 miles or 1.28 light-seconds.

To convert miles to feet, multiply by 5,280, giving us approximately 1.27 million feet. A rocket traveling at a speed of 1,540,000 ft/min would take approximately 82.5 minutes to travel to the Moon. The round trip to the Moon and back would take approximately 165 minutes, or about 2 hours and 45 minutes.

It's important to note that this is an estimate and the actual time it takes may vary due to various factors such as the rocket's trajectory, speed, and other environmental conditions. Also, it's worth noting that this speed is significantly faster than current spacecraft speeds, so the actual time it would take a rocket to travel to the Moon and back is likely to be much longer.

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Answer:

Step-by-step explanation:

First you would take .75n = .75 * 12 shirts

.75 * 12 = 9

You then would take 9 + 9.99 which obviously is 18.99$

Answer = 18.99$ per 12 T-shirts

Answer:

-193

Step-by-step explanation:

x+52+67+75=1

x+119+75=1

x+194=1

-194.    -194

x=-193

If the acceleration of the object becomes 2 m/s², the value of force is,

⇒ 18 N

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

For a moving object, the force acting on the object varies directly with the object's acceleration.

Hence, We get;

⇒ F = k × a

Where, F is force of the object and 'a' is acceleration of the object.

Here, When a force of 27 N acts on a certain object, the acceleration of the object is 3 m/s².

So, We get;

⇒ F = k × a

⇒ 27 = k × 3

⇒ k = 9

Thus, If the acceleration of the object becomes 2 m/s², the value of force is,

⇒ F = k × a

⇒ F = 9 × 2

⇒ F = 18 N

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The values of the proportion will be calculated by standardizing the normal distribution and using the Z table to find the values.

Here we are given that the mean distance traveled is 50,000 miles

with a standard deviation of 10,000

Now we need to find the proportion of trucks expected to travel between 34,000 and 50,000

(a)

Now for this, we need to find the area under the given normal curve between 34,000 and 50,000

For this, we need to first find the standard value. Hence we get

(X - μ)/σ

where μ = mean = 50,000

σ = standard deviation = 10,000

Hence we get

(34000 - 50000)/10000

= -1.6

(50000-50000)/10000 = 0

Looking up the value we will get

0.4452

(b)

The percentage of trucks to travel less than 30,000 will be

Z(30,000 - 50,000)/10000

= Z(-2)

looking the value up we will get

0.02275

= 2.275 %

More than 60,00 will be

1 - Z(60000-50000)/10000

= 1 - Z(1)

= 1 - 0.84134

= 0.15866

= 15.866%

Since the question asks "or" it will be a union of the 2 values to get

18.141%

(c)

Now the miles traveled by at least 80% of trucks will have a Z score of  0.8

Now in the Z table, we get the closest to be 0.80234 which has a Z value of 0.85

Now the no. of trucks will be

0.85 X 10000 + 50000

= 8500 + 50000

= 58,500

d)

Now if the standard deviation was 7000 instead of 10,000

The proportion of trucks to travel between 34 and 50 would be

Z(-16000/7000) = Z(-2.29)

0.48713

Percentage of trucks to travel less than 30 or more than 60 thousand miles in a year

is 100[ Z(-20000/7000) + 1 - Z(10000/7000) ]

= 100[Z (-2.86) + 1 - Z(1.43)]

= 100[0.00212 + 1 - 0.92364]

= 100 X 0.07849

= 7.849%

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The sum of a and b is obtained as follows:

a + b = 5.

The function for this problem is defined as follows:

f(x) = ax/[bx - 4]

f(1) = -2 means that when x = 1, y = -2, hence:

-2 = a/(b - 4)

a = -2b + 8

f(2) = 2 means that when x = 2, y = 2, hence:

2 = 2a/(2b - 4)

2a = 4b - 8

a = 2b - 4.

Equaling the two equations, the value of b is obtained as follows:

-2b + 8 = 2b - 4

4b = 12

b = 3.

Hence the value of a is ob:

a = 2b - 4

a = 2(3) - 4

a = 2.

Hence the sum is of:

a + b = 2 + 3

a + b = 5.

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The sum of the 1st and three-term of the GP is 87.75.

What is geometric progression?

A geometric progression often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.

Here, we have

Given:  3rd term is 27 and whose 6th term is 8​

Let the GP terms are a, ar, ar², ar³, ar⁴ and ar⁵,

Given ar² = 27 and ar⁵ = 8

Take the ratio of the sixth term to the third term:

ar⁵ / ar² = 8/27 => r³ = (2/3)³

r = 2/3

We know that

ar² = a(2/3)² = 27

=> a(4/9) = 27

=> a = 27*9/4 = 243/4

So, the terms are 243/4, 243/4*(2/3), 243/4*(4/9), 243/4*(8/27), 243/4*(16/81), 243/4*(32/243)

= 243/4 + 27

= 60.75 + 27

= 87.75

Hence, the sum of the 1st and three-term of the GP is 87.75.

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Answer:

Step-by-step explanation:

What is Joey's total distance run on the first day?

Joey runs 5 laps around the track, which we can assume is 1 mile per lap. So, she runs 5 miles. Additionally, she runs 1.5 miles, so her total distance run on the first day is 5 + 1.5 = 6.5 miles.

What is Joey's total distance run on the second day?

Joey runs 3 laps around the track, which we can assume is 1 mile per lap. So, she runs 3 miles. Additionally, she runs 4 miles, so her total distance run on the second day is 3 + 4 = 7 miles.

Answer:

23.50y+1

Step-by-step explanation:

2(4.25y-7.5+7.5y+8)

2(4.25y+7.5y-7.5+8)

2(11.75y+0.5)

2(11.75y) + 2(0.5)

23.50y + 1

Answer:

y = 1500 * 0.9575^t

Step-by-step explanation:

Where 0.9575 is equal to 1 - 0.0425, which represents a decrease of 4.25% each year.