which of these two expressions are equivalent to 5^-3

The Least Common Multiplier of [tex]$q(2-4), r(-6-8), s(-102), t(-26)$[/tex] is [tex]$-9282 q r s t$[/tex].

What is Least Common Multiplier ?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Lowest Common Multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor [tex]$q(2-4): \quad-2 q$[/tex]

Factor [tex]$r(-6-8): \quad-2 \cdot 7 r$[/tex]

Factor [tex]$s(-102): \quad-17 \cdot 2 \cdot 3 s$[/tex]

Factor [tex]$t(-26): \quad-13 \cdot 2 t$[/tex]

Multiply each factor with the highest power:

[tex]$$-13 \cdot 17 \cdot 2 \cdot 3 \cdot 7 \cdot q \cdot r \cdot s \cdot t$$[/tex]

Simplify

[tex]$-9282 q r s t$[/tex]

Complete question: Find the Least Common Multiplier  of Q(2, -4), R(-6, -8), S(-10, 2), T(-2, 6) is:

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Answer:

sorry I don't know now how to read

Answer:

x = 13

Step-by-step explanation:

vertical angles are congruent , then

∠ B = ∠ A , that is

6x - 8 = 5x + 5 ( subtract 5x from both sides )

x - 8 = 5 ( add 8 to both sides )

x = 13

Fred's pay for the specified week, with a rate of $11.25 for regular hours and time and a half for overtime, and number of hours worked of 48.5 hours is presented by completing the attached table as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

A payment rate is the amount of payment or money that is received in a unit of time.

The amount Fred earns per hour = $11.25

The number of regular hours Fred works per week = 40

The rate at which he is paid for overtime = Time and a half

The number of hours Fred works in the specified week = 48.5 hours

Therefore, the amount Fred earns for working overtime = 1.5 × $11.25 = $16.875

The amount Fred earns for regular hours during the specified week = 40 × $11.25 = $450

The number of overtime hours Fred works for during the week = 48.5 - 40 = 8.5

The amount Fred earns for the overtime work = 8.5 × $16.875 = $143.4375

Fred's gross payment for the week is therefore; $450 + $143.4375 = $593.4375

The table can therefore be completed by plugging in the above values as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

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Answer:

The slope of the line is = 3/2

Answer:

Equation in Point Slope Form: y= 3/2x - 3

Step-by-step explanation:

Point slope form is y=mx+b

where m is the slope of the line (rise over run) which in this case is 3/2

b is the y intercept (where the line crosses the y axis) which in this case is at point (0,-3)

The [tex]\vec{v}[/tex] as an ordered triplet of values, separated by commas is ( 0 , 0 , 10 )

The magnitude of V is 10 units.

The sine of the angle between  [tex]\vec{T}[/tex] and [tex]\vec{U}[/tex] is [tex]45^{\circ}[/tex].

As per the given data the value of [tex]\vec{T}[/tex] is ( 3, 1, 0 ) and [tex]\vec{U}[/tex] is ( 2, 4, 0 )

Firstly we have to determine the value of [tex]\vec{v}[/tex].

The value of [tex]\vec{v}[/tex] is given by [tex]\vec T \times \vec U[/tex]

[tex]& v=\left|\begin{array}{lll}\hat{i} & j & \hat{k} \\3 & 1 & 0\\2 & 4 & 0\end{array}\right|[/tex]

[tex]=\hat{k}(12-2)[/tex]

[tex]=10 \hat{k}[/tex]

Therefore [tex]\vec{v}[/tex] = ( 0 , 0 , 10 )

Now we have to determine the value of magnitude of V.

Magnitude of V is represented by [tex]$|\vec{v}|[/tex]

[tex]$|\vec{v}|=\sqrt{100}[/tex]

[tex]$|\vec{v}|[/tex] = 10 units

Therefore the magnitude of V is 10 units.

Now we have to determine the value of sine of the angle between  [tex]\vec{T}[/tex] and [tex]\vec{U}[/tex].

[tex]|\vec{v}|=|\tilde{T}||\tilde{U}| \sin \theta_{T U}[/tex]

[tex]\Rightarrow \theta_{T U}=\sin ^{-1}\left(\frac{|\vec{v}|}{|\vec{T}| |\vec{U}|}\right)[/tex]

[tex]=\sin ^{-1}\left(\frac{10}{\sqrt{200}}\right)[/tex]

[tex]=45^{\circ}[/tex]

Therefore value of sine of the angle between  [tex]\vec{T}[/tex] and [tex]\vec{U}[/tex] is [tex]45^{\circ}[/tex]

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Answer:

3

Step-by-step explanation:

His total doubles 73 and he already has 13 doubles. So, 73-13 = 60.He needs 60 doubles. His current age is 12. So, 17-12 = 5 yrs. 1 yr has 4 season. For 5 yrs 20 season. 60/20 = 3. Hence 3 doubles/season

by sethus1981.

This confidence interval suggests that we are 90% confident that the population mean lies between $273 and $658.

This confidence interval provides us with an estimate of the population mean with 90% confidence. This confidence interval suggests that we are 90% confident that the population mean lies between $273 and In other words, we can be 90% sure that the population mean falls within this range. This confidence interval does not tell us the actual population mean, but it provides us with an estimate of where the population mean is likely to lie. Furthermore, it also provides us with an indication of the degree of uncertainty associated with our estimate.

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Answer:

4/13

Step-by-step explanation:

The question asking to find P(jack or heart)

You have to use the formula below:

P(A or B) = P(A) + P(B) - P(A and B)

Event A here is jack and event B is heart, now let's find the three probabilities on the right side to be able to find the left side.

P(jack) =4/52 because there are 4 jacks in a standard deck of cards

P(heart) =13/52 because there are 13 heart cards

P(jack and heart) =1/52 because there is only one jack card with a heart symbol

Now, plug in the three answers in the above formula:

P(jack or heart) = 4/52 + 13/52 - 1/52

this equal to 16/52

Last step, reduce the result by dividing the top and the bottom numbers by 4

The final answer is 4/13

Answer:207.24 and 483.56

Step-by-step explanation:

The formula for the surface area of a cylinder is:

A=2πrh+2πr2

Meaning that we only have to plug the values in.

2π(3)(8)+2π(3)²

=48π+18π

=66π

=66(3.14)

=207.24

Second Cylinder:

2π(7)(4)+2π(7)²

=56π+98π

=154π

=154(3.14)

=483.56

The hypothesis of the conditional statement is "if an angle measures 130 degrees," and the conclusion is "the angle is obtuse."

A conditional statement is a statement in the form "if X, then Y," where X is the hypothesis and Y is the conclusion. In this case, the hypothesis is that the angle measures 130 degrees, and the conclusion is that the angle is obtuse.

An angle is obtuse if it measures more than 90 degrees but less than 180 degrees. Since 130 degrees is greater than 90 degrees but less than 180 degrees, the conclusion that the angle is obtuse follows logically from the hypothesis that the angle measures 130 degrees.

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Answer:

To find the minimum number of lawns Jacob will need to mow, we can set up the following inequality:

12x + 150 >= 380

To solve this inequality, we need to get x by itself on one side of the inequality. We can do this by subtracting 150 from both sides of the inequality:

12x >= 230

Then, we can divide both sides of the inequality by 12 to get the value of x:

x >= 19.17

Since x represents the number of lawns Jacob needs to mow, it must be an integer. Therefore, the minimum number of lawns Jacob will need to mow is 20.

This means that Jacob needs to mow at least 20 lawns in order to earn enough money to buy the electronic tablet. If he mows more than 20 lawns, he will have more than enough money to buy the tablet.

The rate of interest  for the given data can be found as 6%.

Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time. The amount can be calculated by adding the interest to the principal.

The given data as per the question is as below,

P = $4000, t = 6 years and Interest = $1440.

Suppose the rate of interest be r% per annum.

Substitute all the values in the expression for simple interest (P × r × t)/100 as follows,

1440 = (4000 × 6 × r)/100

⇒ r = 6%

Hence, the rate of interest is obtained as 6%.

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Answer:

2x-2y-3z

Step-by-step explanation:

8x+-6x

=8x-6x

=2x

-9y+7y

=-2y

2z+-5z

= 2z-5z

=-3z

2x-2y-3z

8x - 9y + 2z

-6x + 7y - 5z

On adding these two equation :

8x + ( -6x) = 2x

-9y + 7y = -2y

2z + (-5z) = -3z

we will get :

2x - 2y -3z

.

In the addition/subtraction method, the two equations in the system are added or subtracted to create a new equation with only one variable. In order for the new equation to have only one variable, the other variable must cancel out. In other words, we must first perform operations on each equation until one term has an equal and opposite coefficient as the corresponding term in the other equation.

.

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y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

Kenji and Ramon are at a distance of 750 m after a time interval of 1 hour from each other.

Kenji runs for a total time of 60 minutes + 15 minutes = 75 minutes.

Ramon runs for a total of 60 minutes.

Now, we find the total distance covered by Kenji and Ramon in the time intervals of 75 minutes and 60 minutes respectively.

Kenji runs a total distance of 150 meters/minute * 75 minutes = 11250 meters.

Ramon runs a total distance of 200 meters/minute * 60 minutes = 12000 meters.

Now, we find the difference in their distances.

The distance between Kenji and Ramon is 12000 meters - 11250 meters = 750 meters.

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Complete Question:

Kenji and Ramon are running cross country. Kenji run at a rate of 150 meter per minute and Ramon runs at a rate of 200 meters per minute. If Kenji starts 15 minutes before Ramon, how far apart are they after one hour?

Answer:

Your answer is -13x + 20

Step-by-step explanation:

2x - 5*(3x - 4)

Discribute the -5.

2x + [ (-5)(3x) + (-5)(-4) ]

2x + [ (-15x +20) ]

2x - 15x + 20

- 13x + 20

Answer:

y = 4x - 2

Step-by-step explanation:

y = 4x + b

-6 = 4(-1) + b

-6 = -4 + b

b = -2

y = 4x - 2

Answer:

[tex]y - (-6) = 4(x - (-1))[/tex] or [tex]y = 4x - 2[/tex]

Step-by-step explanation:

We can use point slope form: [tex]y - y_{1} = m(x - x_{1})[/tex], where [tex](x_1, y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.

We plug in (-1, -6) and 4 to get:  which simplifies to [tex]y + 6 = 4(x + 1)[/tex]

If we want to express this in the form y = mx + b, we have to do a little rearranging. [tex]y + 6 = 4(x + 1)[/tex] becomes [tex]y + 6 = 4x + 4[/tex] and then we subtract 6 from both sides to get: [tex]y = 4x - 2[/tex]

Two triangles are similar when their corresponding angles are congruent, and the corresponding sides are proportional. Hence, option C s the most appropriate answer to the given question.

When we are given triangles, we can prove that two triangles are similar to the given conditions by applying various tests of similarity.

Similar triangles are triangles that have the same shape, but they may have different sizes.

Hence, to prove them to be similar, we have to prove the corresponding angles are congruent and the corresponding sides are proportional. Hence, option C is the only right choice for the given question.

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For the scientific method , the true statement about the hypothesis is  (b) research studies are designed to prove a hypothesis.

The term Hypothesis is defined as the observation which is proposed as the possible outcome or results of an experiment .

we know that ; in order to prove a hypothesis, the experiments are designed and after that they are performed based on given hypothesis.

That is how the experiments are designed based on a previous idea which may result in a particular outcome.

So , any hypothesis is dependent on a specific experiment( research studies) .

Therefore , the correct option is (b) .

The given question is incomplete , the complete question is

In the scientific method, which of the following is true about a hypothesis?

(a) the same hypothesis may not be tested more than once.

(b) research studies are designed to prove a hypothesis.

(c) a specific hypothesis is generated based on an established theory.

(d) a hypothesis both explains and predicts a phenomenon.

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The line integral of the vector field in the figure is zero. This is due to the fact that the vector field is perpendicular to the curve c, and therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.

1. The line integral of a vector field is the integral of the dot product of the vector field and the tangent vector of the curve along the curve.

2. The vector field in the figure is perpendicular to the curve c.

3. The dot product of two perpendicular vectors is zero.

4. Therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.

5. Hence, the line integral of the vector field in the figure is zero.

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The two sequence A and sequence B both are correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that triangle UVW and Triangle ABC are congruent.

A transformation is a way of changing the size or position of a shape.

Every point in the image is the same distance from the mirror line as the original shape.

Triangle UVW made a 180 degrees of rotation about point V and then a triangle along the directed line segment VB.

This is same as translation along the directed line segment UA then about 180 degrees rotation about point A.

Hence, the two sequence A and sequence B both are correct.

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The function that models the data in the given table is: D. y = -2x + 10.

The function that models the data of a table can be expressed in the slope-intercept form as y = mx + b, where:

Find the slope of the function using two pairs of values from the table, (6, -2) and (10, -10):

Slope (m) = change in y / change in x = (-10 - (-2)) / (10 - 6)

Slope (m) = -8 / 4

Slope (m) = -2

Find the y-intercept (b) by substituting m = -2 and (x, y) = (6, -2) into y = mx + b:

-2 = -2(6) + b

-2 = -12 + b

-2 + 12 = b

10 = b

b = 10

To write the function, substitute m = -2 and b = 10 into y = mx + b:

y = -2x + 10

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The rate of current in the stream on that​ day is; 2 miles per hour

When dealing with relative velocity, we can say that;

When the motorboat travels downstream, then it means the total velocity will be;

Total velocity = Velocity of the motorboat in still water + Velocity of the stream.

If the motorboat travels upstream, the total velocity will be;

Total velocity = Velocity of the motorboat in still water - Velocity of the stream.

Thus,

Upstream speed = (14 mi/h - S)

Downstream speed = (14 mi/h + S)

Where;

S is the rate of current in the stream.

We are told that going downstream, it takes 15 minutes more to travel 12 miles, then we can write the system of equations as;

(14 mi/h + S)*T = 12 mi

(14 mi/h - S)*(T - 15 min) = 12 mi

Making T the subject in the first equation gives;

T = (12 mi)/(14 mi/h + S)

Plugging in (12 mi)/(14 mi/h + S) for T in the second equation gives;

(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi

Multiply both sides by (14 mi/h + S) to get;

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)

Since the speeds are in miles per hours, we can rewrite as:

- 15 min = -0.25 h

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)

168 mi²/h - 12mi*S  + 49mi²/h + 0.25h*S² = 168mi²/h + 12mi*S

- 12mi*S  + 49mi²/h - 0.25h*S² = 12mi*S

-24mi*S -  0.25h*S²  + 49mi²/h = 0

Solving this quadratic equation with online quadratic equation solver gives us; S = 2 mph

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Answer:

{ No SIMPLIFIED: [tex]\frac{9}{12} inches[/tex] }
{ SIMPLIFIED: [tex]\frac{3}{4} inches[/tex] }

Step-by-step explanation:

If we want to know about the plant grows, we need to add the fractions in 3 weeks with this solution:
[ The inch of the plant 1st week ] + [ The inch of the plant 2nd week ] + [ The inch of the plant 3rd week ] = [ The inch of the plant in 3 weeks ]

Look at the denominator of 3 weeks, it is 12 and the numerators are 1,3,5
To plus the fraction we remain the denominator and plus the numerators together which we can result in this equation:
[tex]\frac{1}{12}[/tex] + [tex]\frac{3}{12}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{1 + 3 + 5}{12}[/tex] = [tex]\frac{9}{12}[/tex] { SIMPLIFIED: [tex]\frac{9 : 3 }{12 : 3} = \frac{3}{4}[/tex] }
So then we see that if you choose no simplified then: Michael's plant grow  [tex]\frac{9}{12}[/tex] inches in 3 weeks or you could choose the simpliflied one then: Michael's plant grow [tex]\frac{3}{4}[/tex] inches in 3 weeks.

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Answer:

Solution in picture.

Step-by-step explanation:

A triangle has three angles which adds up to 180°.

First do the easy ones such as 90°. Then the Triangle. Then the vertical angles. Then the two angles of supplementary angles which adds up to 180°. Etc.

Answer:

3.75 Hours or 225 Minutes

Step-by-step explanation:

5/4 = 1.25 So it takes 1.25 hours to do an assignment

1.25 x 3 = 3.75

Which equals 225 Minutes

Answer: 3.75 or 3 3/4

Step-by-step explanation:

This is a unit rate problem

A unit rate is a rate for one of something. (i.e, 1 pencil for 4 notebooks)

So first, to find the time needed for one assignment, we divided 5 hours by 4 hours.

5/4 = 1.25 (1 and 1/4)

Now we multiply the unit rate by 3.

1.25 times 3 = 3.75, or 3 3/4.

Answer:

4

Step-by-step explanation:

gradient = slope = m = rise / run

  from the origin (0,0) this line rises '12' and has a run of '3'

             12/3 = 4

The value of the double integral ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3] is  0.677

In this question we need to calculate the double integral. 3x sin(x + y) dA, R = [0, π/6] × [0, π/3]

i.e., to find ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3]

First we integrate the function 3x sin(x+y) as a function of y, treating the variable x as a constant.

G(x) = ∫_[0, π/6] (3x sin(x+y)) dy

G(x) = 0.402 xcos(x) + (3x sin(x) / 2)

Now we calculate the integral of the previous result as a function of x.

i.e., ∫_[0, π/3] G(x) dx

= ∫_[0, π/3] [0.402 xcos(x) + (3x sin(x) / 2)] dx

= 0.677

Therefore, the solution to the double integral. 3x sin(x + y) da, r = [0, π/6] × [0, π/3] is  0.677

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Answer:

Step-by-step explanation: To find the measure of angle ACB, we can use the Pythagorean Theorem: AB^2 + AC^2 = BC^2.

Substituting in the given values for AB and AC, we get: 10.2^2 + 4.9^2 = BC^2

Solving for BC, we get: BC = √(10.2^2 + 4.9^2)

Substituting this value back into the equation for the Pythagorean Theorem, we get:

AB^2 + AC^2 = (√(10.2^2 + 4.9^2))^2

Simplifying this equation, we get:

AB^2 + AC^2 = 10.2^2 + 4.9^2

This equation is already in the correct form, so we can solve for ∠ACB directly:

∠ACB = tan^-1(AC/AB)

Substituting in the given values for AC and AB, we get:

∠ACB = tan^-1(4.9/10.2)

Using a calculator, we find that tan^-1(4.9/10.2) is approximately equal to 26.7°.

Rounded to 3 significant figures, this value is 26.7°.