Which expression is equivalent to 3^8 ?

Answer:

10 hours

Step-by-step explanation:

49kilograms/7hours = 7 kilograms per hour

70 kilograms ÷ 7 kilograms per hour = 10 hours

The distance between two cyclists after 45 minutes as described in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.

It follows from the task content that the distance between the two cyclists after 45 minutes is to be determined from the given parameters.

Given; the speed of the first cyclist is; 12 miles per hour, while the speed of the second cyclist is b miles per hour greater than that of the first.

The speed of the second cyclist is therefore; (b + 12).

On this note, since the distance covered by each cyclist is given by;

Distance = Speed × Time where, Time = 45 minutes = 0.75 hours.

Therefore, the total distance between the two cyclists can be determined from the expression as follows;

7 + 0.75 (12) + 0.75 (b + 12).

Therefore, the distance between the two cyclists as required in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.

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The equation of the plane through point P₀(-2, 3, 9) perpendicular to the line x = -2 - t, y = -3 + 5t, z = 4t is x + 5y + 4z = 49.

To find the equation for the plane through point P₀(-2, 3, 9) perpendicular to the line x = -2 - t, y = -3 + 5t, z = 4t, we need to find the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in the parametric equations, which is (1, 5, 4).

Since the plane is perpendicular to the line, the normal vector of the plane is parallel to the direction vector of the line. Therefore, the normal vector is (1, 5, 4).

Using the normal vector and the coordinates of the point P₀(-2, 3, 9), we can write the equation of the plane in the form Ax + By + Cz = D:

(1)(x - (-2)) + (5)(y - 3) + (4)(z - 9) = 0

Simplifying:

x + 2 + 5y - 15 + 4z - 36 = 0

x + 5y + 4z - 49 = 0

Therefore, the equation of the plane through point P₀(-2, 3, 9) perpendicular to the line x = -2 - t, y = -3 + 5t, z = 4t is:

x + 5y + 4z = 49.

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The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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Answer:

x = 7

Step-by-step explanation:

Δ JUT is similar to Δ JKL (AA postulate ) , then the ratios of corresponding sides are in proportion, that is

\(\frac{JU}{JK}\) = \(\frac{UT}{KL}\) ( substitute values )

\(\frac{-4+4x}{64}\) = \(\frac{36}{96}\) = \(\frac{3}{8}\) ( cross- multiply )

8(- 4 + 4x) = 3 × 64 = 192 ( divide both sides by 8 )

- 4 + 4x = 24 ( add 4 to both sides )

4x = 28 ( divide both sides by 4 )

x = 7

Answer:

=1 and 3 over 41

=1.75

Step-by-step explanation:

If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.

Then the perimeter of the preimage, the original triangle, before its

dilation will be

Let c be the perimeter of the original triangle.

Then we have

\(\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67\)

Then the perimeter of the original triangle is 66.67 units.

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Answer:

36 servings

Step-by-step explanation:

1/4p = 6s

6(1/4p) = 6(6s)

1 1/2p = 36s

Answer:

n=-3

Step-by-step explanation:

                                Let's solve your equation step-by-step.

2−2n=3n+17

Step 1: Simplify both sides of the equation.

2−2n=3n+17

2+−2n=3n+17

−2n+2=3n+17

Step 2: Subtract 3n from both sides.

−2n+2−3n=3n+17−3n

−5n+2=17

Step 3: Subtract 2 from both sides.

−5n+2−2=17−2

−5n=15

Step 4: Divide both sides by -5.

\(\frac{-5n}{-5}\)=\(\frac{15}{-5}\)

n=−3

Answer: A. -18.75x + 600 = 150

Clarissa's sister will have $150 left to pay after 24 weeks.

Step-by-step explanation:

Given, Clarissa's sister makes weekly installment payments for a motorized scooter she purchased from a friend.

Cost of scooter = $600

Weekly installment = $18.75

Clarissa's sister wants to know when she has $150 left to pay for the motorized scooter.

Let 'x' be the number of weeks .

Money she left to pay = (Cost of scooter ) - (Weekly installment) x (Number of weeks)

\(\Rightarrow\ 150=600-18.75x\)

\(\Rightarrow\ 18.75x=600-150=450\\\\\Rightarrow\ x=\dfrac{450}{18.75}=\dfrac{45000}{1875}=24\)

i.e. After 24 months when she has $150 left to pay for the motorized scooter.

Hence, the correct answer is :

A. -18.75x + 600 = 150

Clarissa's sister will have $150 left to pay after 24 weeks.

Answer:

B)-18.75x+600=150

Step-by-step explanation:

Got it right on my test!

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

UW = 117 , SR = 24

Step-by-step explanation:

since the pairs of triangles are similar then the ratios of corresponding sides are in proportion.

(1)

Δ UML ≅ Δ UWV

\(\frac{UW}{UM}\) = \(\frac{UV}{UL}\) ( substitute values )

\(\frac{UW}{45}\) = \(\frac{104}{40}\) ( cross- multiply )

40 UW = 45 × 104 = 4680 ( divide both sides by 40 )

UW = 117

(2)

Δ SRT ≅ Δ KRJ

\(\frac{SR}{KR}\) = \(\frac{ST}{KJ}\) ( substitute values )

\(\frac{SR}{12}\) = \(\frac{16}{8}\) = 2 ( multiply both sides by 12 )

SR = 12 × 2 = 24

Answer:

she did better in math

Step-by-step explanation:

she did better in math because

14-17=-3

so she lost 3 marks in math

31-39=-8

she lost 8 marks in English

Answer:

Multiply the first equation by 5 and the second equation by 2. Then add.

Multiply the first equation by 2 and the second equation by 5, then subtract.

Step-by-step explanation:

Given

\(- 2x + 5y = -15\)

\(5x + 2y = -6\)

Required

Steps to solve using elimination method

From the list of given options, option 2 and 3 are correct

This is shown below

Option 2

Multiply the first equation by 5

\(5(- 2x + 5y = -15)\)

\(-10x + 25y = -75\)

Multiply the second equation by 2.

\(2(5x + 2y = -6)\)

\(10x + 4y = -12\)

Add

\((-10x + 25y = -75) + (10x + 4y = -12)\)

\(-10x + 10x + 25y +4y = -75 - 12\)

\(29y = -87\)

Notice that x has been eliminated

Option 3

Multiply the first equation by 2

\(2(- 2x + 5y = -15)\)

\(-4x + 10y = -30\)

Multiply the second equation by 5

\(5(5x + 2y = -6)\)

\(25x + 10y = -30\)

Subtract.

\((-4x + 10y = -30) - (25x + 10y = -30)\)

\(-4x + 25x + 10y - 10y= -30 +30\)

\(21x = 0\)

Notice that y has been eliminated

Answer:

How many solutions does the system have?

✔ exactly one

The solution to the system is

(

⇒ 0,

⇒ -3).

Step-by-step explanation:

the next two parts

Answer:

a) Points A and B are symmetrical over the x-axis. Points A and B are on the same location on the x-axis but opposite directions on the y-axis. Points A and B lie on the same vertical line.

b) A (4,3); B (4,-3); C (3,-5); D (-4,-3); E (-5,3)

1. A point with a positive x-coordinate is to the right of the y-axis. [A,B,C]

2. A point with a negative x-coordinate is to the left of the y-axis. [D,E]

3. A point with a positive y-coordinate is above the x-axis. [A,E]

C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

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To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)

where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.

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you can simplify this expression to obtain the numerical value of dg/dθ at the point (r, θ) = (2√2, π/4).

To evaluate the partial derivative dg/dθ using the Chain Rule, we need to calculate the derivatives of g with respect to x and y, and then multiply them by the partial derivative of x and y with respect to θ. Let's proceed step by step.

Given:

g(x, y) = 1/(8x + 4y^2)

x = rsin(θ)

y = rcos(θ)

(r, θ) = (2√2, π/4)

Step 1: Find the partial derivatives of g with respect to x and y.

∂g/∂x = -(1/(8x + 4y^2)^2) * (8) = -8/(8x + 4y^2)^2

∂g/∂y = -(1/(8x + 4y^2)^2) * (8y^2) = -8y^2/(8x + 4y^2)^2

Step 2: Find the partial derivatives of x and y with respect to θ.

∂x/∂θ = r*cos(θ)

∂y/∂θ = -r*sin(θ)

Step 3: Evaluate the partial derivative dg/dθ at the given point.

Substituting the values r = 2√2 and θ = π/4 into the partial derivatives, we have:

∂g/∂x = -8/(8x + 4y^2)^2 = -8/(8(2√2) + 4(2√2)^2)^2 = -8/(16√2 + 32)^2

∂g/∂y = -8y^2/(8x + 4y^2)^2 = -8(2√2)^2/(8(2√2) + 4(2√2)^2)^2 = -32/(16√2 + 32)^2

∂x/∂θ = r*cos(θ) = (2√2)*cos(π/4) = 2

∂y/∂θ = -r*sin(θ) = -(2√2)*sin(π/4) = -2

Finally, we can calculate the partial derivative dg/dθ using the Chain Rule:

dg/dθ = (∂g/∂x) * (∂x/∂θ) + (∂g/∂y) * (∂y/∂θ)

Substituting the partial derivatives we calculated earlier:

dg/dθ = (-8/(16√2 + 32)^2) * 2 + (-32/(16√2 + 32)^2) * (-2)

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Answer:

C. $19.65

Step-by-step explanation:

You have to find 20% of $98.25

This is equal to,

20% * $98.25                Because of usually means multiplication

= .20 * 98.25                 Because .20 = 20%

= 19.65!

Answer:

x = 162

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the interior angles of the quadrilateral and equate to 360

90 + 60 + x + 48 = 360 , that is

198 + x = 360 ( subtract 198 from both sides )

x = 162

Answer:

Yes u did thats what i did too XD

Answer:

The equation would be if y is the numbers in the sequence (like 3, 9, 27) and x is the is the number in the order (like 3 is 1, 9 is 2, 81 is 4) the the equation would be y = 3^x.

Step-by-step explanation:

Answer:

---------------------------------

It is assumed the provided numbers are the zero's of the polynomial function.

We know complex zero's come in pairs if function has rational constants.

So we should have zero's: 8, 3, -i and i.

Find the polynomial:

Answer:

(8, -7)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

6x + 7y = -1

x - y = 15

Step 2: Rewrite Systems

x - y = 15

Step 3: Solve for y

Substitution

Step 4: Solve for x

Answer:

(1) y = - 2x - 2

(2) y = 1/3x + 6

Step-by-step explanation:

(Picture 1)

y = mx + b

The line cuts the y axis at -2, meaning b = -2

When y increase s by 1, x decreases by 2, meaning mx = -2x

That makes y = - 2x - 2

(Picture 2)

The line cuts the y axis at 6, meaning b = 6

When y increases by 1, x increases by 3, meaning mx = x/3 or 1/3x

That makes y = 1/3x + 6

There are 4,320 ways to select six of the letters of the word algorithm and write them in a row if the first letter must be "a".

There are 7 letters in the word "algorithm", and we need to select 6 of them and arrange them in a row such that the first letter is "a". We can first choose the remaining 5 letters from the remaining 6 letters (excluding "a") in 6 choose 5 ways

⁶C₅ = 6!/5! = 6

Once we have chosen the 5 letters, we can arrange the 6 selected letters (including "a") in a row in 6! ways. Therefore, the total number of ways to select 6 letters and arrange them in a row with the first letter being "a" is

⁶C₅ × 6! = 6 × 720 = 4,320

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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