Here is my question. It's for my 6th Grade ALEKS.

Answer: 5.49 × 10-4

Step-by-step explanation:

When you move the decimal over move it over to the right by 4 units.

When you move right it is (-) negative. So you get 5.49 x 10-4.

The solution is Option A.

The sum of the infinite geometric progression is S = -( 9/5 )

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the sum of the geometric progression be represented as S

Now , the equation will be

∑ n = 1 to ∝ ( -3 ( 3/8 )ⁿ )   be equation (1)

The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio

Substituting the values in the equation , we get

when n = 1

a₁ = -3 ( 3/8 )

a₁ = -9/8

when n = 2

a₂ = -3 ( 3/8 )²

a₂ = -27/64

So , the common ratio r = a₂ / a₁

The common ratio r = 3/8

Substituting the values in the equation , we get

The sum of the infinite GP is S = a / ( 1 - r )

The sum of the infinite GP is S = ( -9/8 ) / ( 1 - 3/8 )

The sum of the infinite GP is S = ( -9/8 ) / ( 5/8 )

The sum of the infinite GP is S = - ( 9/5 )

Hence , the sum of GP is - ( 9/5 )

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This simplified form of given expression is: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.

Here,

Now, we can multiply this result by the original expression raised to the power of 3:

(4s⁵t⁻⁷/−2s⁻²t⁴)³ * (1/(-8s⁶t¹²)) = (4s⁵t⁻⁷)³ / (-8s⁶t¹²)

Finally, we'll simplify the numerator by raising 4s⁵t-7 to the power of 3:

(4s⁵t-7)³ = (4s⁵t)³ * (-7)³ = 64s¹⁵t³ * 343 = 21952s¹⁵t³

Putting it all together, we get the abbreviated version of the given expression: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹

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The circle graph for the given table is as mentioned.

In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.

Given is a data as shown in the table.

The circle graph for the given table is attached with the answer.

Therefore, the circle graph for the given table is as mentioned.

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Answe

Step-by-step explanation:

answer is 9

The student would consume 1,095/24, or 45.625 cases of Mt. Dew per year.

Consume is an action or process of buying or using goods or services. It is the use of a resource, typically money or time, for a specific purpose. It is the purchase of goods or services for personal use or for the use of a family, business or organization. Consumption of goods and services is the basic activity of any economy.

Assuming that there are 365 days in a year, the student would consume 1,095 cases of Mt. Dew per year. This can be calculated by multiplying 3 cans per day by 365 days, resulting in a total of 1,095 cans. Since there are 24 cans per case, the student would consume 1,095/24, or 45.625 cases of Mt. Dew per year.

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Step-by-step explanation:

geometric mean theorem for right-angled triangles :

height = sqrt(pq)

where p and q are the parts of side as split by the height of that side.

19.

x = sqrt(4×16) = sqrt(64) = 8

20.

y = sqrt(5×8) = sqrt(40) = 6.32455532...

21.

18 = sqrt(12y)

18² = 12y

324 = 12y

y = 27

22.

10 = sqrt(25x)

10² = 25x

100 = 25x

x = 4

23.

Pythagoras

x² = 5² + height² = 25 + 4×5 = 25 + 20 = 45

x = sqrt(45) = 6.708203932...

24.

Pythagoras

b² = 16² + height² = 256 + 6×16 = 256 + 96 = 352

b = sqrt(352) = 18.76166304...

25.

Pythagoras

27² = 16² + height² = 256 + 16(z - 16) =

= 256 + 16z - 256 = 16z

729 = 16z

z = 729/16 = 45.5625

26.

Pythagoras

x² = (8 - 2)² + height² = 6² + (8 - 2)×2 =

= 36 + 12 = 48

x = sqrt(48) = 6.92820323...

The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

Given here: A force acting on an object.

We know, The formula for force states that the force is equal to mass that is multiplied by the acceleration.

Thus we have the equation as F=m.a

Now in case 1 we have  

20=m×5

m=4 kg

Again in case 2 we have

16 = 4×a

a=4 ms⁻²

Hence, The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

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Answer: 588π = 1846.32

Step-by-step explanation:

Volume of cylinder = πr²h

Volume = (7)²*12*π = 588π = 1846.32

Answer:-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

-5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

Step-by-step explanation:

a) The leash is 12.2 ft long.

b) The diagonal is 7.1m

c) The altitude is 6.1 in

We can see a right triangle here, where the leash is the hypotenuse of that triangle.

Using the Pythagorean's theorem we can write:

leash = √( (10ft)² + (7ft)²)

leash = 12,2 ft

8) Remember that for a square of side length S, we have:

perimeter = 4*S

diagonal = √2*S

We know that the perimeter is 20 meters, then:

20m = 4*S

S = 20m/4 = 5m

Then the diagonal is:

D = √2*5m = 7.1m

9) For an equilateral triangle of sidelength S, the altitude is:

A = √( S² - (S/2)²)

In this case the side length is 7 inches, then:

A = √( (7in)² - (7in/2)²)

A = 6.1 in

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The expression 48s represents the number of scarves (s) and its per unit  (48).

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given that, Emiko makes shibori scarves and sells them for $48 each on a website for handmade goods.

Here, the expression 48s represents the total price of buying s scarves

We need to tell what 48s mean,

So,

48s here is the total cost for buying s scarves,

That mean, if we buy s scarves we will have to pay $48s

Similarly, if we will buy 4 scarves, we will pay = 48 × 4 = $192

For 10 scarves, we will pay = 48 × 10 = $480

Therefore, we can say $48 is the unit price of the scarf.

Hence, the expression 48s represents the number of scarves (s) and its per unit  (48).

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The question was incomplete, so I answered for the question :-

Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves what do the parts of the expression 48s represents.

Answer:

Step-by-step explanation:

number of scarves

Price of scarves

Let's let w = the width of the rectangle.  If the length is 10 yards less than 3 times the width, then the length is 3w - 10.

How do we find the area?  Length times width, right?

So, we have w(3w - 10) = 77.  Distributing, we get 3w2 - 10w = 77.

We need to put it all on one side, so we subtract 77 from both sides.

3w2 - 10w - 77 = 0

Now, we have to factor the left side. To do this, we multiply 3(-77) = -231.  What are two factors of -231 that add up to -10? How about -21 and 11?  -21(11) = -231 and -21 + 11 = -10.

This may not be how you are taught, but we are now going to split -10w into -21w + 11w and plug that into our equation.

Sooooo, now we have 3w2 - 21w + 11w - 77 = 0

Next, we are going to look at the first two terms, 3w2 - 21w.  What is common between the two? 3w. Factoring out 3w, we get 3w(w - 7).

Now, the second two terms, 11w - 77. What is common? 11. Factoring out 11, we get 11(w - 7).

Putting all of that together, we now have 3w(w - 7) + 11(w - 7) = 0.

I can explain why and make it more confusing, so I'll just tell you that, since the w - 7 is the same in both parentheses, we keep that as one set of parentheses and combine what's in front into a second set of parentheses.

So, we have (w - 7)(3w + 11) = 0

Lastly, for the left side to equal 0, then either w - 7 and/or 3w + 11 has to equal 0, right?

We pull each out and set them equal to 0.

w - 7 = 0

     w = 7

If we plug in 7, we get (7-7)(3(7) + 11) = (0)(21+11) = 0(32) = 0, which is what we want.

3w + 11 = 0

        3w = -11

          w = -11/3

If we plug -11/3 into the same equation, we'd get 0, again what we want.  However, we can't have a negative length!  Therefore, -11/3 is out as an answer.

Our width is 7.  Since the length is 3w - 10, we plug in 7 and get 3(7) - 10 = 21 - 10 = 11.

Let's check. Length times width = 7(11) = 77. Check!

All of three statements about addition, multiplication and division of rational numbers are true.

The square root of any nonperfect square number is an irrational number.

                                   Complex numbers (a + ib)

Real numbers                                                                 Imaginary numbers.

(a + i0)                                                                                      (0 + ib)

Rational numbers               Irrational numbers

(perfect squares)              (non-perfects squares)

Fractions.  

(p/q, q ≠ 0)            

Integers.

(whole nos. -: 0 to ∞)

(negative integers -: - ∞ to - 1)

(positive integers -: 1 to ∞)

The statement adding two rational numbers is a rational number is true.

The statement multiplying two rational numbers is a rational number is true.

The statement if you divide two rational numbers, you’ll always get a rational number is also true.

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Worker B has the higher variance and standard deviation than Worker A.

Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ.

Given,

The number of parts produced per hour by the workers are as follows:

Worker A: 5, 4, 4, 6, 7, 5, 6, 3

Worker B: 4, 8, 1, 9, 2, 9, 4, 3

Average μ = 5

Variance = σ² = Σ(xi - μ)²/N

Variance for first worker

= [(5 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (5 - 5)² + (6 - 5)² + (3 - 5)²]/8

= [0² + -1² + -1² + 1² + 2² + 0² + 1² + -2²]/8

= [1 + 1 + 1 + 4 + 1 + 4]/8

= 12/8

= 1.5

Standard deviation σ = √1.5

 = 1.2247448713916

Variance for second worker

= [(4 - 5)² + (8 - 5)² + (1 - 5)² + (9 - 5)² + (2 - 5)² + (9 - 5)² + (4 - 5)² + (3 - 5)²]/8

= [-1² + 3² + -4² + 4² + -3² + 4² + -1² + -2²]/8

= [1 + 9 + 16 + 16 + 9 + 16 + 1 + 4]/8

= 72/8

= 9

Standard deviation σ = √9

= 3

Hence, Variance and Standard deviation of worker B are higher than worker A.

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Answer:If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.

Step-by-step explanation:

If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.

Answer:

hey, what are you asking

Step-by-step explanation:

The value of x are:

2) x = 18.87

3) x = 26.68

5) x = 35.52

6) x = 13.75

9) x = 3.69

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

2)

Tan 48 = x / 17

1.11 = x / 17

x = 17 x 1.11

x = 18.87

3)

Sin 67 = x / 29

0.92 = x / 29

x = 0.92 x 29

x = 26.68

5)

Cos 16 = x / 37

0.96 = x / 37

x = 0.96 x 37

x = 35.52

6)

Tan 58 = 22/x

1.6 = 22 / x

x = 22/1.6

x = 13.75

9)

Sin 24 = x / 9

0.41 = x / 9

x = 0.41 x 9

x = 3.69

Thus,

The value of x is given above.

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Answer:

2483 in 8yrs means you multiply the two first

2483

× 8

_____

19864

so 8% of 19864

you have to divide the number by the percentage

o. 8÷ 19864= 2483

The value of the angle Z will be 56 degrees.

The angles that the same arc subtends at its circumference are equal. At the circle's centre, two equal chords subtend two equal angles.

The triangle in the centre is an isosceles triangle so the two angles will be 34°.

The third angle will be calculated as:-

Central angle = 180 - 34 - 34

Central angle = 112

The measure of the angle Z will be:-

Z = 112 / 2

Z = 56°

Therefore, the measure of the angle Z suspended outside will be 56 degrees.

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The vertices of triangle J'K'L' after a reflection of the triangle JKL over the x-axis is given as follows:

The original vertices of the figure are given as follows:

J(-5,5), K(5,7) and L(2,3).

For a reflection over the x-axis, the reflection rule is defined as follows:

(x,y) -> (x,-y).

Meaning that the x-coordinate remains constant while the y-coordinate has the sign exchanged.

Then the vertices of the reflected figure are given as follows:

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Answer: 90%

Step-by-step explanation:

Step 1: Calculate the total number of marbles in the bag.

3 red + 3 green + 15 yellow + 9 purple = 30 marbles

Step 2: Calculate the number of marbles that are not red.

3 green + 15 yellow + 9 purple = 27 marbles

Step 3: Calculate P(not red).

27/30 = 0.9

Answer: 90%

Answer:

the answer is answer c

Step-by-step explanation:

The absolute inequality 3/4 * |(1/3)x + 2| < 6 has a solution of (d) x > -30 and x < 18

To solve the inequality, we'll start by isolating the absolute value expression on one side of the inequality.

3/4 * |(1/3)x + 2| < 6

We'll first distribute the 3/4 across the absolute value:

|(1/3)x + 2| < 8

To simplify this, we'll split the inequality into two cases:

(1/3)x + 2 < 8

(1/3)x + 2 > -8

First, let's consider the case where (1/3)x + 2 < 8

(1/3)x < 6

x < 18

Now let's consider the case where (1/3)x + 2 > -8

(1/3)x > -10

x > -30

So, the solution set is x > -30 and x < 18

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Complete question

Solve the inequality three-fourths times the absolute value of the quantity one third times x plus 2 end quantity is less than 6. x > −8 and x < −4 x > −30 and x < 2 x < −30 and x < 18 x > −30 and x < 18

Answer:

1. The unit price for a doll is three dollars. The unit price for a purse is six dollars.

2. One doll costs three. One purse costs six.

3. Polly spends $24 on the 2 dolls and 3 purses.

Step-by-step explanation:

Doing some calculations, 1 doll costs three dollars and 1 purse costs six dollars.

5 x 3 + 6 = 21

7 x 3 + 1  = 27

If Polly buys 2 dolls and 3 purses, that means she spends six dollars on the dolls and eighteen dollars on the purses.

(2 x 3) + (3 x 6) = $24

Polly spends $24 on 2 dolls and 3 purses.

The range of the side of the square is 24 to 31. The interval notation is (24,31).

What is interval notation?

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words.

Given that, the perimeter of a square must be greater than 96 inches but less than 124 inches.

Inequality form is

96 < P < 124

Where P is the perimeter.

The perimeter of a square is P = 4s, where s is the length of the side.

Putting P = 4s in 96 < P < 124

96 < 4s < 124

Divide by 4:

24 < s < 31

The interval notation is (24,31).

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The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The area of the triangle is given as,

A = 1/2 [(x + 4)(x + 7)]

Simplify the equation, then we have

A = [(x + 4)(x + 7)] / 2

A = (x² + 7x + 4x + 28) / 2

A = (x² + 13x + 28) / 2

The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

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The total cost of a meal costing $32 with 7% sales tax and 18% automatic tip is $40

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The sales tax is 7% and the automatic tip is 18%. If the meal costs $32, hence:

Sales tax = 7% of $32 = 0.07 * 32 = $2.24

Automatic tip = 18% of $32 = 0.18 * 32 = $5.76

The total cost = cost of meal + sales tax + automatic tip

Substituting:

Total cost = $32 + $2.24 + $5.76 = $40

The total cost is $40

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The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle θ intersects the unit circle in the first quadrant at x=17/23.

We know that;

The given parameters are represented as;

⇒ (x, y) = ( cos θ , sin θ )

Here, x = 17/23

Hence, We get;

⇒ cos θ = 17/23

Now, Using the following trigonometry identity;

⇒ cos²θ + sin²θ = 1

⇒ (17/23)² + sin²θ = 1

⇒ 289/529 + sin²θ = 1

⇒ sin²θ = 1 - 289/529

⇒ sin²θ = 529 - 289 / 529

⇒ sin²θ = 240/529

⇒ sin θ = √240/529

⇒ sinθ = 15.5 / 23

Thus, The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

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