Find the volume of a cone with a radius of 4 ½ m. and a height of 10 m.

Step-by-step explanation:

remember the GCF (greatest common factor) ?

every number or term is the product of certain prime numbers (prime factors).

the product of factors that the discussed numbers or terms have in common is the GCF.

1)

12x³ + 8x

12x³ :

12 / 2 = 6

6 / 2 = 3

3 / 2 no

3 / 3 = 1 finished

12 = 2×2×3

x³ = x×x×x

so,

12x³ = 2×2×3×x×x×x

8x :

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1 finished

8 = 2×2×2

x = x

so,

8x = 2×2×2×x

what factors do they have in common ?

2×2×x = 4x

so, the GCF = 4x

that means

12x³ + 8x = 4x×3x² + 4x×2 = 4x(3x² + 2)

2)

18a² + 2a

18a² :

18 / 2 = 9

9 / 2 no

9 / 3 = 3

3 / 3 = 1 finished

18a² = 2×3×3×a×a

2a :

2 / 2 = 1 finished

2a = 2×a

so, they have 2×a = 2a in common.

the GCF = 2a.

that means

18a² + 2a = 2a×9a + 2a×1 = 2a(9a + 1)

3)

25b⁴ + 30b³

25b⁴ :

25 / 2 no

25 / 3 no

25 / 5 = 5

5 / 5 = 1 finished

25b⁴ = 5×5×b×b×b×b

30b³ :

30 / 2 = 15

15 / 2 no

15 / 3 = 5

5 / 3 no

5 / 5 = 1 finished

30b³ = 2×3×5×b×b×b

so, they have 5×b×b×b = 5b³ in common.

the GCF = 5b³

that means

25b⁴ + 30b³ = 5b³×5b + 5b³×6 = 5b³(5b + 6)

Answer: D. 9.68

Step-by-step explanation:

145.2 oz/ 15 cups = 9.68 oz per cup

If the circle is dilated by a factor of 2, the equation of the circle is: C. (x + 3)² + (y - 2)² = 18.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 2)² = 3²

(x + 3)² + (y - 2)² = 9.

By dilating with a scale factor of 2, we have:

(x + 3)² + (y - 2)² = (9 × 2)

(x + 3)² + (y - 2)² = 18

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Answer:

8.345

Step-by-step explanation:

(8.34+8.35)/2 = 16.69/2

= 8.345

We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.

Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.

To get mt = m, substitute u = tk into mt = mu (tk).

Rewrite m(tk) as (mt)k using the associative property of multiplication.

To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.

Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.

Since 1 Equals k, we get u = tk = t(1) = t.

We get mt = mt by substituting u = t into the original equation mt = mu.

As a result, we have demonstrated that mt = mu when t | u.

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Answer:assuming its a rectangle its 13.5

Step-by-step explanation: L x H = Area

Answer:

5.5 or 5 1/2 inches

Step-by-step explanation:

The longest is 12 3/4

The two smallest combined are 3 and 4 1/4 = 7 1/4

12 3/4 - 7 1/4 = 5 1/2

Answer:

32

Step-by-step explanation:

if Leo has provided the coordinates of the jungle gym and the four-square courts, we can use the distance formula to calculate the distance between them.  the four-square courts are approximately   [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).

The distance formula is:

[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where  [tex](x1, y1)[/tex] and [tex](x2, y2)[/tex] are the coordinates of two points, and d is the distance between them.

For example, let's say the jungle gym is located at (3, 4) on the grid, and the four-square courts are located at (9, 8). Using the distance formula, we have:

[tex]d = sqrt((9 - 3)^2 + (8 - 4)^2)[/tex]

[tex]= sqrt(6^2 + 4^2)[/tex]

[tex]= sqrt(36 + 16)[/tex]

[tex]= sqrt(52)[/tex]

[tex]\approx 7.2[/tex]

Therefore, the distance from the jungle gym to the four-square courts is approximately   [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).

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Answer:

Step-by-step explanation:

Para convertir 44 semanas a meses, debemos saber cuántas semanas hay en un mes. El número de semanas en un mes no es exacto, pero generalmente se considera que hay alrededor de 4.33 semanas en un mes (ya que el año tiene aproximadamente 52 semanas y 12 meses).

Entonces, para calcular cuántos meses hay en 44 semanas, podemos dividir 44 por 4.33:

44 semanas / 4.33 semanas por mes = 10.16 meses (aproximadamente)

Por lo tanto, 44 semanas equivalen aproximadamente a 10.16 meses.

The distance of the satellite from station A is approximately 47 miles

The satellite is approximately 911 miles above ground

Let the distance from station A to the satellite be a and the distance from the station B to the satellite be a + 48

Using trigonometry

tan 87 degrees = height of the satellite above the ground, h / a

tan 87 degrees = h / a

h = a * tan 87

while

tan 84 degrees = h / a + 48

h = (a + 48) tan 84

substituting for h

a * tan 87 = (a + 48) tan 84

a (tan 87 - tan 84) = 48 tan 84

a (9.567) = 48 tan 84

a = 48 tan 84 / 9.567

a = 47.436

The distance of the satellite from station A is approximately 47 miles

The height above ground

h = a * tan 87

h = 47.436 * tan 87

h = 910.857 miles

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Accοrding the given expressiοns this is the right answer  (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32

(1/5)³= 1/5 × 1/5 × 1/5 = 1/125

In mathematics, an expressiοn is a cοmbinatiοn οf numbers, variables, and οperatοrs that represents a mathematical relatiοnship οr fοrmula. It can include numbers, variables, and mathematical οperatοrs such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and rοοts. Fοr example, 2x + 3y is an expressiοn that includes the variables x and y, and the οperatοrs additiοn and multiplicatiοn. Expressiοns can be simplified, evaluated, οr used tο represent mathematical relatiοnships.

a) (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32

b) (1/5)³ = 1/5 × 1/5 × 1/5 = 1/125

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The area of the trailer's base is 176 square feet.

Volume is a measure of the amount of space that an object occupies. It is a three-dimensional quantity that is usually measured in cubic units, such as cubic meters, cubic feet, or cubic centimeters.

We have a cargo trailer with a volume of 2,112 cubic feet, a height of 12 feet, and a width of 8 feet. We want to find the area and length of the trailer's base.

Since the volume of the trailer is given by V = lwh, we can write:

2,112 = lw(12)

Simplifying this equation, we get:

l = 2,112 / (w x 12)

l = 2,112 / (8 x 12) [Substituting the value of w as 8 feet]

l = 22

Therefore, the length of the trailer's base is 22 feet.

To find the area of the trailer's base, we can use the formula A = lw:

A = l x w

A = 22 x 8

A = 176 square feet

Therefore, the area of the trailer's base is 176 square feet.

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Step-by-step explanation:

lol sorry for untidy work

The coordinates of B' after the sequence of transformations are given as follows:

B'(3,-4).

The coordinates of B are given as follows:

B(-3,1).

After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:

B'(3, 1).

The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:

B'(1, -3).

The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:

B'(3,-4).

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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).

In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Finally, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

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Answer:

If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.

Given,

Annual deposit = $1000

Rate = 8% compounded annually

Time(n) = 10 year

Amount = ?

As we know the formula ,

Amount = P(1+r/100)ⁿ

Amount = 1000(1+8/100)¹⁰

Amount = 1000(1+0.08)¹⁰

Amount =1000(1.08)¹⁰

Amount = 1000 × 2.15892

Amount = $2158.92

Hence, amount in 10year will be $2158.92

Answer: Click THANKS if you like my answer. have a good day sir/maam #keep safe

D. The x-intercepts cannot be compared because either p or q does not have an x-intercept.

The function q is a constant function and its graph is a horizontal line passing through y = -1. It does not intersect the x-axis, so it does not have an x-intercept.

The function p is a logarithmic function, and its x-intercept is the point at which the graph of p intersects the x-axis. To find the x-intercept of p, we need to set p(x) = 0 and solve for x.

log₂ (x - 1) = 0

2^0 = x - 1

1 = x - 1

x = 2

So the x-intercept of p is x = 2.

Since q does not have an x-intercept, we cannot compare the x-intercepts of p and q. Therefore, the correct answer is D.

Step-by-step explanation:

hope its help <:

The circumference's shortest distance between points A and C is 102.91m.

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle with four equally long sides.

As a result, a square is a particular form of rectangle since it has rectangles with equal-length sides.

So, we know that:

AC = 80 m

CD = 50 m

Apply the Pythagorean theorem to the right triangle using ADC.

AC = √AD² + CD²

AC = √80² + 50²

AC = 94.34m

The shortest path through the park from point A to point C must only follow the lines depicted in the diagram.

Hence, we must deduct AC by 15 meters in diameter.

94.34m - 15m = 79.34m

The shortest distance is 79.34 miles plus one-half a circle's circumference.

As the circle's diameter is 15 meters, the radius is 15/2 = 7.5m.

The circumference would be:

2*π*r = 47.14m

The half circumference would be:

47.14/2 = 23.57m

Then,

79.34m + 23.57m = 102.91m

Therefore, the circumference's shortest distance between points A and C is 102.91m.

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The triangle that would not represent the three sides of a triangles is: {9, 21, 32}

We can determine this through the use of the triangle rule. The rule tells us that the sum of the two sides of the triangle have to be greater than that of the other side.

With this in mind, we have that for each of this

14 + 24 > 37

15 + 30 > 43

9 + 21 < 32

10 + 19 > 26

Hence the third option does not fulfill the rule

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32. g(x) = 4x + 4

This transformation shifts the graph

of f(x) 4 units upward.

33. g(x) = 4x-3

This transformation shifts the graph

of f(x) 3 units downward.

34. g(x)=4(x+2)

This transformation shifts the graph

of f(x) 2 units left.

35. g(x) = 4(x-5)

This transformation shifts the graph

of f(x) 5 units right.

36. g(x) = -4x

This transformation reflects the graph

of f(x) about the x-axis.

37. g(x) = -4x

This transformation reflects the graph

of f(x) about the y-axis.

chatGPT

Answer: 160

Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.

We can claim that after answering the above question, the As a result, angles the regular polygon has ten sides.

An angle is a shape in Euclidean geometry that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration of two rays or lines that share a termination. The English term "angle" derives from the Latin word "angulus," which means "horn." The vertex is the point at where the two rays, also known as the angle's sides, converge.

The interior angle of a regular polygon with n sides is calculated as follows:

(n-2) * 180° / n = interior angle

The internal angle of the polygon is presented to us as 144°. When we plug this into the formula, we get:

144° = (n - 2) * 180° / n

144° * n = (n - 2) * 180°

144° * n = 180° * n - 360°

144° * n + 360° = 180° * n

360° = 36° * n

n = 10

As a result, the regular polygon has ten sides.

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If her hοuse actually 56 feet wide, then scale οf her drawing is scale = 56 feet / (drawing width)

The slοpe is a mathematical cοncept that refers tο the steepness οf a line. It is cοmmοnly denοted by the letter "m" and can be calculated using the fοrmula:      

slοpe (m) = (change in y) / (change in x)

Withοut having the actual measurements οf the drawing, we cannοt determine the scale.

Tο find the scale οf a drawing, yοu need tο knοw the actual measurements οf the οbject being drawn as well as the cοrrespοnding measurements in the drawing. Fοr example, if yοu knοw that the actual width οf Rοse's hοuse is 56 feet and the width οf the hοuse in the drawing is 8 inches, yοu can determine the scale by using the fοllοwing fοrmula:

scale = actual width/drawing width

Using this fοrmula with the given infοrmatiοn, we get:

scale = 56 feet / (drawing width)

Therefοre, we dο nοt have the drawing width, we cannοt calculate the scale.

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Answer:-2,-5

Step-by-step explanation:

7-4=3

You move 3 units up

You land on -2, -2

the higher units you move up, the higher the number gets to.

5 miles each day so 5×7=35 miles a week

Answer:

The correct equation is:

b - 3/4 = 3 1/4

Explanation:

Lily used 3/4 of a chocolate bar, so the remaining chocolate bars can be found by subtracting 3/4 from the total number of chocolate bars b:

b - 3/4 = remaining chocolate bars

The problem tells us that there are 3 1/4 remaining chocolate bars, so we can substitute this value in the equation and solve for b:

b - 3/4 = 3 1/4

b = 3 1/4 + 3/4

b = 4

Therefore, the counselor put 4 chocolate bars on the table.

The correct answer is A) test statistic T equals -1.952; P value, 0.0414.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true. In the scientific process, the hypothesis is developed before any pertinent research—aside from a basic background review—has been conducted.

The null hypothesis that there is no difference between the triglyceride test levels is sufficiently refuted by the available data.

With 9 degrees of freedom and a significance threshold of 0.05, this can be ascertained by comparing the derived test statistic (T) with the critical value of t from the t-distribution table. We reject the null hypothesis if the estimated T value is in the rejection zone (i.e., T value is smaller than the critical value of t).

The computed T value in this instance is -1.952, which is in the rejection region (i.e., less than the critical value of t of -1.833). Hence, we get to the conclusion that there is enough data to imply that the new diet has an effect on lowering triglyceride levels and reject the null hypothesis that there is no difference between the triglyceride test levels.

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1. Answer (a) Positive. The leading coefficient of the polynomial on the right is positive.

Answer (b) 3, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.

2. Answer (a) 2, Answer (b) 1

3. Answer (a) 3, Answer (b) 1 and 5

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can have constants and variables, and they usually have multiple terms that are separated by addition or subtraction.

1. The leading coefficient of a polynomial is the coefficient of the highest degree term. In the graph, the highest degree term is x3, and it is positive. Therefore, the leading coefficient of the polynomial on the right is positive.

The degree of a polynomial is the highest power of the variable in the equation. In the graph, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.

2. The number of real zeros of a polynomial is the number of times the polynomial crosses the x-axis. In the graph, the polynomial crosses the x-axis twice, so it has 2 real zeros.

The number of imaginary zeros of a polynomial is the number of times the polynomial bounces off the x-axis. In the graph, the polynomial bounces off the x-axis once, so it has 1 imaginary zero.

3. The polynomial p(x) bounces off the x-axis at x=3 because the polynomial changes direction at this point.

The polynomial p(x) crosses the x-axis at x=1 and x=5 because the polynomial intersects the x-axis at these points.

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