this box plot shows the heights (in feet) from a sample of two different type of elephants compare the outliers and interquartile ranges

Answer:

[tex]4x^{3}+8x^{2} +4x+3[/tex]

Step-by-step explanation:

Hello

To simplify the polynomial we must eliminate the parentheses

by definition

[tex]ax^{n}*bx^{m} =abx^{n+m}[/tex]

[tex](2x-1)(2x^{2} +5x+3)+(3x+6)\\(4x^{3} +10x^{2} +6x-2x^{2} -5x-3)+(3x+6)\\\\We\ add\ the\ similar\ terms\\\\(4x^{3}+8x^{2} +x-3)+(3x+6)\\\\4x^{3}+8x^{2} +4x+3[/tex]

I hope it helps

Have a great day

Answer:

Its A

Step-by-step explanation:

Just took it.

The dollars worth of zinc which is contained in hair cut in the United States every year is:

                         $ 2,220,000

The total kilograms of hair that are  cut in the United States are: 25,000,000 kg

Also, the amount of zinc present in 1kg of hair is: 0.0002 kg

Hence, the amount of zinc present in 25,000,000 kg of hair is:

25,000,000×0.0002=5,000 kg

Also, cost of 1 kg of zinc= $ 444

Hence, cost of 5,000 kg of zinc will be: 5,000×444

Hence, cost of 5,000 kg of zinc=$  2,220,000

Answer:

20,000

Step-by-step explanation:

25,000,000 * 0.0002 =5,000

5,000 * 4 = 20,000

Answer:

  L = 720 cm² ; S = 1239.6 cm²

Step-by-step explanation:

The area of a hexagon is given by the formula ...

  A = (3/2)√3·s²

where s is the side length. Then the area of the two hexagonal bases will be ...

  base area = 3√3·(10 cm)² ≈ 519.6 cm²

__

The lateral area is the product of the perimeter of the base and the height of the prism:

  L = 6×(10 cm)×(12 cm)

  L = 720 cm²

The totals surface area is the sum of lateral area and base area:

  S = L + base area = (720 +519.6) cm²

  S = 1239.6 cm²

Answer:

L = 720 cm2 ; S = 1239.6 cm2

Step-by-step explanation:

Got lucky ('<')

The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is:

                              16.65 ft.

Let L denote the total length of the ladder.

In right angled triangle i.e. ΔAGB we have:

[tex]L^2=h^2+(x+4)^2[/tex]

( Since by using Pythagorean Theorem)

Also, triangle ΔAGB and ΔCDB are similar.

Hence, the ratio of the corresponding sides are equal.

Hence, we have:

[tex]\dfrac{h}{8}=\dfrac{x+4}{x}[/tex]

i.e.

[tex]h=\dfrac{8(x+4)}{x}[/tex]

Hence, on putting the value of h in equation (1) we get:

[tex]L^2=(\dfrac{8(x+4)}{x})^2+(x+4)^2\\\\i.e.\\\\L^2=\dfrac{64(x+4)^2}{x^2}+(x+4)^2\\\\i.e.\\\\L^2=(x+4)^2[\dfrac{64}{x^2}+1]----------(2)[/tex]

Now, we need to minimize L.

Hence, we use the method of differentiation.

We differentiate with respect to x as follows:

[tex]2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1]+(x+4)^2\times \dfrac{-128}{x^3}\\\\i.e.\\\\2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1+(x+4)\times \dfrac{-64}{x^3}]\\\\\\i.e.\\\\\\2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1-\dfrac{64}{x^2}-\dfrac{256}{x^3}]\\\\\\i.e.\\\\\\2L\dfrac{dL}{dx}=2(x+4)[1-\dfrac{256}{x^3}][/tex]

when the derivative is zero we have:

[tex]2(x+4)[1-\dfrac{256}{x^3}]=0\\\\i.e.\\\\x=-4\ and\ x=\sqrt[3]{256}[/tex]

But x can't be negative.

Hence, we have:

[tex]x=\sqrt[3]{256}[/tex]

Now, on putting this value of x in equation (2) and solving the equation we have:

[tex]L^2=277.14767[/tex]

Hence,

[tex]L=16.6477\ ft.[/tex]

which on rounding to two decimal places is:

[tex]L=16.65\ ft.[/tex]

Using the Pythagorean theorem, the length of the shortest ladder that will reach from the ground over the 8 ft fence to the wall of the building 4 ft away is approximately 8.94 ft.

This problem is an example of a right triangle problem in trigonometry. The fence and the ground form the two legs of a right triangle and the ladder forms the hypotenuse. The 8ft fence is perpendicular to the 4ft distance from the building, forming a 90-degree angle.

To find the length of the shortest ladder from the ground over the fence to the wall of the building, we need to use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the formula is h² = a² + b², where h is the length of the ladder (hypotenuse), 'a' is the height of the fence (8 ft), and 'b' is the distance from the fence to the building (4 ft).

Therefore, the length of the shortest ladder can be solved as follows:
h² = 8² + 4² = 64 + 16 = 80
By taking the square root of both sides, we find that h (the length of the ladder) is approximately 8.94 ft, rounded to two decimal places.

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Answer:

  D.)  f(x) = 197(1.03)^(7x); grows at a rate of approximately 3% daily

Step-by-step explanation:

The growth equation can be written in terms of a rate compounded 7 times per week:

  f(x) = 197×1.25^x = 197×(1.25^(1/7))^(7x)

  f(x) ≈ 197×1.0324^(7x) . . . . x represents weeks, a daily growth factor is shown

The daily growth rate as a percentage is the difference between the daily growth factor and 1, expressed as a percentage:

  (1.0324 -1) × 100% = 3.24%

The best match is choice D:

  f(x) ≈ 197(1.03^(7x)); grows approximately 3% daily

The correct answer to this question is D

Answer:

1 in 18

Step-by-step explanation:

The highest possible number Hillary can get is 12, meaning that the only odd number above 10 which she can get is 11.

There are two possible ways in which Hillary can get 11:

(a) Hillary rolls a 5 on her first cube and a 6 on her second cube

(b) Hillary rolls a 6 on her first cube and a 5 on her second cube

There are 34 other possible outcomes which Hillary can have when rolling her number cubes, for a total of 36 possible outcomes.

Since 2 of these outcomes result in a roll of 11, Hillary has a 2 in 36 chance of rolling an 11, which can be simplified as 1 in 18.

Answer:

1/18

Step-by-step explanation:

Let [tex]x[/tex] be the number of liters of the 10% solution she needs to use. She'd end up with a 6% solution with a volume of [tex]9+x[/tex] liters. The starting solution contains 0.04*9 = 0.36 liter of salt. Each liter of the 10% solution contributes 0.1 liter of salt, so that

[tex]0.36+0.1x=0.06(9+x)[/tex]

Solve for [tex]x[/tex]:

[tex]0.36+0.1x=0.54+0.06x[/tex]

[tex]0.04x=0.18[/tex]

[tex]x=4.5[/tex]

so Mayra needs to add 4.5 liters of the 10% solution.

Answer:

126 trees should she plant per acre to maximize her harvest.

Step-by-step explanation:

Let x be the additional tress that must be plant after planting 100 tress.

So, total number of trees = 100 + x trees

Also, Each additional tree planted decreases the yield of each tree by 3 bushels.

So , net bushels by each tree = 35 - 3x

The revenue function becomes

f(x) = (100 + x)(35 - 3x)

Thus,

Differentiating it by using chain rule as:

f'(x) = (100 + x)35 + 100(35 - 3x)

f'(x) = 3500 + 35x + 3500 - 300x

f'(x) = 7000  - 265x

For maxima of f(x), f'(x) = 0

7000  - 265x = 0

Thus,

x = 26.4151

Since, x represents tress, so, x is 26.

So, total tress she would plant to earn maximum revenue = 100 + 26 = 126 trees

Answer:

(x - 2)²/2² + (y + 1)²/3² = 1 ⇒ The bold values and signs are the answers

Step-by-step explanation:

* Lets revise the equation of the ellipse  

- The standard form of the equation of an ellipse with center (h , k)  

 and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1  

- The coordinates of the vertices are (h ± a , k)

- To change the form of the equation of the ellipse to standard form we

 will using the completing square

∵ The equation of the ellipse is 9x² + 4y² - 36x + 8y + 4 = 0

- Lets collect x in bracket and y in bracket

∴ (9x² - 36x) + (4y² + 8y) + 4 = 0

- We will take a common factor 9 from the bracket of x and 4 from the

 bracket of y

∴ 9(x² - 4x) + 4(y² + 2y) + 4 = 0

- Lets make 9(x² - 4x) a completing square

∵ √x² = x ⇒ the 1st term in the bracket

∵ 4x ÷ 2 = 2x ⇒ the product of the 1st and 2nd terms

∵ 2x ÷ x = 2 ⇒ the 2nd term in the bracket

∴ The bracket is (x - 2)²

∵ (x - 2)² = x² - 4x + 4 ⇒ we will add 4 in the bracket and subtract 4

  out the bracket

∴ 9[(x² - 4x + 4) - 4] = 9[(x - 2)² - 4]

- Lets make 4(y² + 2y) a completing square

∵ √y² = y ⇒ the 1st term in the bracket

∵ 2y ÷ 2 = y ⇒ the product of the 1st and 2nd terms

∵ y ÷ y = 1 ⇒ the 2nd term in the bracket

∴ The bracket is (y + 1)²

∵ (y + 1)² = y² - 2y + 1 ⇒ we will add 1 in the bracket and subtract 1

  out the bracket

∴ 4[(y² + 2y + 1) - 1] = 4[(y + 1)² - 1]

- Lets write the equation with the completing square

∴ 9[(x - 2)² - 4] + 4[(y + 1)² - 1] + 4 = 0 ⇒ simplify

∴ 9(x -2)² - 36 + 4(y + 1)² - 4 + 4 = 0 ⇒ add the numerical terms

∴ 9(x - 2)² + 4(y + 1)² - 36 = 0 ⇒ add 36 to both sides

∴ 9(x - 2)² + 4(y + 1)² = 36 ⇒ divide both sides by 36

∴ (x - 2)²/4 + (y + 1)²/9 = 1

∵ 4 = 2² and 9 = 3²

∴ (x - 2)²/2² + (y + 1)²/3² = 1

* The standard form of the equation of the ellipse is

  (x - 2)²/2² + (y + 1)²/3² = 1

Answer: (x - 2)²/2² + (y + 1)²/3² = 1

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:

We need the Pythagorean Theorem here.

If you have a right triangle, you can use the equation a^2+b^2=c^2 where a and b are legs and c is the hypotenuse.

Plug in your information.

(3/7)^2+(4/7)^2=c^2

Simplify what you can.

9/49+16/49=c^2

25/49=c^2

Square root both sides.

5/7=c

Answer:

5/7.

Step-by-step explanation:

Let the hypotenuse = h , then:

h^2 = (3/7)^2 +(4/7)^2    ( By the Pythagoras Theorem).

h^2 = 9/49 + 16/49

h^2 = 25/49

h =  5/7.

Answer:

  8.3 cm

Step-by-step explanation:

The product of lengths to the near and far point of intersection with the circle is the same in all cases:

  (7 cm)(7 cm) = (y)(11 cm +y) = (4 cm)(4 cm +x)

Since we're only interested in x, we can divide by 4 and subtract 4:

  49 cm² = (4 cm)(4 cm +x)

  (49/4) cm = 4 cm +x . . . . . . divide by 4 cm

  8.25 cm = x . . . . . . . . . . . . . subtract 4 cm

To the nearest tenth, x = 8.3 cm.

_____

For a tangent segment, the two points of intersection with the circle are the same point, so the product of lengths is the square of the length.

___

The angles depend on the size of the circle, which is not given.

Answer:

Option B

Step-by-step explanation:

The two acute angles of a right triangle are equal.

[tex] \angle \: A + 18 = 180[/tex]

[tex]\angle \: A= 90 - 18 = 72 \degree[/tex]

Recall the mnemonics SOH-CAH-TOA

The tangent ratio is opposite over adjacent.

[tex] \tan(18) = \frac{AC}{21} [/tex]

[tex]AC = 21 \tan(18) [/tex]

[tex]AC = 6.8[/tex]

The sine ratio is opposite over hypotenuse

Using the sine ratio,

[tex] \sin(72) = \frac{21}{AB} [/tex]

[tex]AB = \frac{21}{ \sin(72) } = 22.1[/tex]

Answer:

it 55

Step-by-step explanation:

Answer:

Either:  1 neg, 3 pos, 0 imaginary; 1 neg, 1 pos, 2 imaginary

Step-by-step explanation:

Look for the positive possibilities first.  Count the numbe of sign changes then subtract 2, if possible, as many times as you can.

There are 3 sign changes.  So the possible positive roots are either 3 or 1.

Now look for the negative possibilities.  Replace each x with a -x and then count the sign changes.  Replacing with -x's gives you this polynomial:

[tex]f(-x)=-3x^4-5x^3-x^2-8x+4[/tex]

There is only one sign change here, so the possible negative roots is 1.  Start with the negative roots to find the possible combinations of positive, negative, and imaginary, since there is only 1.

-     1       1

+    3       1

i     0       2

Since this is a 4th degree, the number of roots we have has to add up to equal 4.

Answer:

3

Step-by-step explanation:

The points they have in bold is probably a hint to the problem.

The points they have in bold are (1,2) on curve g which means g(1)=2

and (3,2) on curve f which means f(3)=2.

g(x)=f(kx)

We know g(1)=2 so if we replace the x's with 1, we get:

g(1)=f(k*1)

g(1)=f(k)

2=f(k).

Now we just need to solve f(k)=2 for k.

We know the point (3,2) is on f so f(3)=2.

If you compare:

f(k)=2

and

f(3)=2

then you should see that k=3.

C.) Are the same length

How you know-

No matter how long the rectangle is the diagonals always will measure the same length. Think about two sides of a square, they have to equal the same length because if they were not the same then the shape wouldn't be a square.

The best answer is the diagonals of the rectangle are the same length.

The diagonal of rectangle is a line segment drawn between the opposite vertices of the rectangle. The properties of diagonals of a rectangle are as follows:

1. The two diagonals of a rectangle are congruent. In other words, the length of the diagonals is equal.

2. The two diagonals bisect each other and divide the rectangle into two equal parts.

3. The length of the diagonal of rectangle can be obtained using the Pythagoras theorem.

4. When the diagonals bisect each other, the angles of a rectangle at the center become one obtuse angle and the other an acute angle.

5. When two diagonals bisect each other at 90° it is called a square.

6. Since the diagonal of rectangle divide the rectangle into two right-angled triangles, it is considered the hypotenuse of these triangles.

We know the diagonal property of rectangle that

1. The diagonals of the rectangle bisect each other.

2. The diagonals of the rectangle are equal.

The best answer is the diagonals of the rectangle are the same length.

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Answer:

c for the question that says what point is on [tex]y=\log_a(x)[/tex] given the options.

9  for the question that reads: "If [tex]\log_a(9)=4[/tex], what is the value of [tex]a^4[/tex].

Step-by-step explanation:

We are given [tex]y=\log_a(x)[/tex].

There are some domain restrictions:

[tex]a \text {is number between } 0 \text{ and } 1 \text{ or greater than } 1[/tex]

[tex]x \ge 0[/tex]

a) couldn't be it because x=0 in the ordered pair.

b) isn't is either for the same reason.

c) \log_a(1)=0 \text{ because } a^0=1[/tex]

So c is so far it! Since (x,y)=(1,0) gives us [tex]0=\log_a(1)[/tex] where the equivalent exponential form is as I mentioned it two lines ago.

d) Let's plug in the point and see: (x,y)=(a,0) implies [tex]0=\log_a(a)[/tex].

The equivalent exponetial form is [tex]a^0=a[/tex] which is not true because [tex]a^0=1 (\neq a)[/tex].

If [tex]\log_a(9)=4[/tex]. then it's equivalent exponential form is: [tex]a^4=9[/tex].

Guess what it asked for the value of [tex]a^4[/tex] and we already found that by writing your equation [tex]\log_a(9)=4[/tex] in exponential form.

Note:

The equivalent exponential form of [tex]\log_a(x)=y[/tex] implies [tex]a^y=x[/tex].

Answer:

15 degrees

Step-by-step explanation:

Draw a horizontal segment approximately 4 inches long. Label the right endpoint A and the left endpoint C. Label the length of AC 4.2 meters. That is the horizontal distance between the eye and the blackboard.

At the right endpoint, A, draw a vertical segment going up, approximately 1 inch tall. Label the upper point E, for eye. Label segment EA 1 meter since the eye is 1 meter above ground.

At the left endpoint of the horizontal segment, point C, draw a vertical segment going up approximately 2 inches. Label the upper point B for blackboard. Connect points E and B. Draw one more segment. From point E, draw a horizontal segment to the left until it intersects the vertical segment BC. Label the point of intersection D.

The angle of elevation you want is angle BED.

The length of segment BC is 2.1 meters. The length of segment CD is 1 meter. That means that the length of segment BD is 1.1 meters.

To find the measure of angle BED, we can use the opposite leg and the adjacent leg and the inverse tangent function.

BD = 1.1 m

DE = 4.2 m

tan <BED = opp/adj

tan <BED = 1.1/4.2

m<BED = tan^-1 (1.1/4.2)

m<BED = 15

Answer: 15 degrees

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The angle of elevation is 15°.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Given that Tony's seat in the classroom, his eyes are 1.0 m above ground. On the wall 4.2 m away, he can see the top of a blackboard that is 2.1 m above ground. Therefore, The angle of elevation,

tan(x) = (2.1 - 1.0)/4.2

x = tan⁻¹ (1.1/4.2)

x = 14.68° ≈ 15°

Hence, the angle of elevation is 15°.

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Answer:

B.  2cos3θsinθ.

Step-by-step explanation:

Use the identity

sin x - sin y   = 2 [cos(x + y)/2]sin [x - y)/2].

So we have:

sin4θ - sin2θ = 2 cos (4θ+2θ)/2 sin (4θ-2θ)/2

= 2cos3θsinθ.

Answer:

I don't know if you want to find this answer using the quadratic formula or not, the question is no the greatest but i will solve it the best that i can. Or

Step-by-step explanation:

I used the discriminant which is √[tex]b^{2}[/tex]-4ac

Then I filled the numbers in, and found that 9 gets plug in for b and this becomes 9 squared, and that becomes 81. 4 is multiplied to 4 and 1 and becomes 16. Then 81 and 16 are subtracted and we get 65. We then find the square root, and will find that the answer is C.

Hoped this helped thanks, if you need more help let me know.

The required value of the given expression is (-9). which is the correct answer would be an option (B).

A quotient is defined as when dividing one number by another, the result is called the quotient.

To determine the value of the expression.

The given expression is given in the question.

⇒ 3b ÷ c⁽¹⁻ᵃ⁾

Here a = 4, b = 9, and c = 1

Substitute the value of a,b, and c in the expression

⇒ 3(9) ÷ (1)⁽¹⁻⁴⁾

⇒ 27 ÷ (1)⁽¹⁻⁴⁾

⇒ 27 ÷(1)⁽⁻³⁾

Reciprocal the term in the denominator,

⇒ 27 × (1 /(-3)

⇒ 27/(-3)

Apply the division operation,

⇒ (-9)

Therefore, the required value of the given expression is (-9).

Hence, the correct answer would be an option (B).

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The question seems to be incomplete the correct question would be

Evaluate the expression if a = 4, b = 9, and c = 1.

3b ÷ c⁽¹⁻ᵃ⁾

A. –27 B. –9 C. 9 D. 27

Answer:

B

Step-by-step explanation:

We are given:

[tex]y=4x[/tex]

[tex]2x^2-y=0[/tex]

We are going to put 4x in place of the second y since the first y equaled it:

[tex]2x^2-4x=0[/tex]

So we can factored this equation:

[tex]2x(x-2)=0[/tex]

This implies 2x=0 or x-2=0.

2x=0

Divide both sides by 2:

x=0

x-2=0

Add 2 on both sides:

x=2

If x=0 and y=4x, then y=4(0)=0 so we have (0,0) is an intersection.

If x=2 and y=4x, then y=4(2)=8 so we have (2,8) is an intersection.

Answer:

the answer to the problem given is b

Answer:  ordinal

Step-by-step explanation:

There are 4 levels of measurements scales :-

1. Nominal scale : It is used when we categorize the data on the basis of the characteristic such as Religion, Gender , etc.

2. Ordinal scale : It is used when we can order attributes according to their ranks. For example : First > Second > Third and so on.

3. Interval scale : It provides the characteristic of the difference between any two categories. For example : Fahrenheit scale to measure temperature.

4. Ratio scale : It has all the qualities of nominal, ordinal, and interval measures and in addition a "true zero" point. For example : Age.

From the above definitions , A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes are ordinal measures.

Answer:

  240

Step-by-step explanation:

The x^k term will be ...

  (6Ck)(x^k)(4^(6-k))

For k=4, this is ...

  (6C4)(x^4)(4^2) = 15·16·x^4 = 240x^4

The coefficient of x^4 is 240.

_____

nCk = n!/(k!(n-k)!)

Answer:

B, the x coordinate is zero

Step-by-step explanation:

The y axis is the line where the x coordinate is zero

The x axis is the line where the y coordinate is zero

We are looking for the y axis, so x=o

Answer:

For me the answer was B (the x-coordinate is 0)

Step-by-step explanation:

Answer:

  f(x) appears to be match the trig function sin(x)

Step-by-step explanation:

The function is an odd function that is periodic with a period of 2π. It is symmetrical about either of ±π/2. It matches sin(x) in every detail shown.

Answer:

A.

Step-by-step explanation:

(x − 7)^2=

=x^2 − 14x + 49

Answer:

x^2 -14x+49

Step-by-step explanation:

(x − 7)^2

(x-7) (x-7)

FOIL

first x*x = x^2

outer -7*x = -7x

inner -7*x = -7x

Last = -7*-7 = 49

Add them together

x^2 -7x-7x +49

x^2 -14x+49

Answer:

The center of the hyperbola is (-5 , 7)

The left vertex is (-5 , -6)

The other vertex is (-5 , 20)

Step-by-step explanation:

* Lets explain the equations of the hyperbola

- The standard form of the equation of a hyperbola with  center (h , k)

  and transverse axis parallel to the x-axis is (x - h)²/a² - (y - k)²/b² = 1

- The hyperbola is open horizontally

- The coordinates of the vertices are (h ± a , k)

- The standard form of the equation of a hyperbola with center (h , k)

  and transverse axis parallel to the y-axis is  (y - k)²/a² - (x - h)²/b² = 1

- The hyperbola is open vertically

- The coordinates of the vertices are (h , k ± a)

* Lets solve the problem

∵ The equation of the hyperbola is - (x + 5)²/9² + (y - 7)²/13² = 1

- Lets rearrange the terms of the equation

∴ The equation is (y - 7)²/13² - (x + 5)²/9² = 1

∴ The hyperbola opens vertically

∵ (y - k)²/a² - (x - h)²/b² = 1

∴ a = 13 , b = 9 , h = -5 , k = 7

∵ The coordinates of its center are (h , k)

∴ The center of the hyperbola is (-5 , 7)

∵ The hyperbola opens vertically

∴ Its vertices are (h , k - a) the bottom one and (h , k + a) the up one

∴ The bottom vertex is (-5 , 7 - 13) = (-5 , -6)

∴ The bottom vertex is (-5 , -6)

∴ The other vertex is (-5 , 7 + 13) = (-5 , 20)

∴ The other vertex is (-5 , 20)

Answer:

Center: (-5,7)

Opens Vertically: (-5,-6)

The other vertext : (-5, 20)

Step-by-step explanation:

D) 13.5 cm squared (13.5 cm²)

In this question, it's asking you to find the area of the rectangle.

In order to solve this question, we need to use the helpful information that the question gives us.

Important Information:

With the information above, we can solve the problem.

To find the area of the rectangle, we would need to multiply the length times the width.

length × width (or l × w)

We know that the length is 3 and the width is 4.5, so we would multiply 3 and 4.5 in order to get the area of the rectangle.

[tex]3 * 4.5=13.5[/tex]

When you're done multiplying, you should get 13.5. With the unit, it would be 13.5 cm² (area of a rectangle is always squared).

This means that the area of the rectangle is 13.5 cm²

Answer:

(0, -3)

Step-by-step explanation:

The vertex is halfway between the directrix and the focus.  The vertex is at (0, 0) and the directrix is a (0, 3).  There are 3 units between them, so that means that the focus is 3 units the other way at (0, -3).

Based on the scenario given above, the the coordinates of its focus is known to be (0, -3).

A parabola is known to be a kind of plane curve that is said to be often mirror-symmetrical  and it is one that can be called closed to U-shaped.

Note that the vertex is said to be in the middle between the directrix and the focus.  So the vertex is at (0, 0) and also the directrix is a (0, 3).  

Since there are found to be 3 units between them, we can say that  the focus is 3 units the other part at (0, -3).

Therefore, Based on the scenario given above, the the coordinates of its focus is known to be (0, -3).

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Answer:

5

Step-by-step explanation:

2/5 = 40%

40% of 8 Carrots = 3.2

3 Carrots on Platter

5 Carrots in Plastic Bag

Answer:

12 carrots

Step-by-step explanation:

To get the answer, you need to multiply and divide.

x ÷ 3 · 2 = 8

Now, we need to do the equation backwards to find x.

8 ÷ 2 · 3 = 4 · 3 = 12 carrots

Answer:

Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.

Let μd be the mean of the differences in the  number of days with symptoms of a diaper rash.

The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.

Here the appropriate null and alternative hypotheses will be :

H0: μd=0  (null)

Ha: μd>0 (alternative)

This given study is a matched pair design study, so we are using  μd : the mean of the differences.

Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.

Answer:

Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.

Let μd be the mean of the differences in the number of days with symptoms of a diaper rash.

The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.

Here the appropriate null and alternative hypotheses will be :

H0: μd=0 (null)

Ha: μd>0 (alternative)

This given study is a matched pair design study, so we are using μd : the mean of the differences.

Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.