Need help in Question no: 8.
With workings please.
Thank you.

The box and whisker plot that has the greatest interquartile range from the options given is option 3.

In order to calculate the interquartile range of a dataset, we can determine or find the difference between the values at the edges of the rectangular box in a box and whisker plot that displays the data set.

This also implies that we subtract the first quartile from the third quartile.

From the options given, we see that in option 3, the box and whisker plot has the largest interquartile range. This is because: Q3 - Q1 is approximately 9.

9 is higher than the interquartile ranges of the other datasets, therefore, option 3 is the right option.

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Answer:

1265 kg of protein

Step-by-step explanation:

If 55kg is eaten in one day then in 23 days there will be x kgs.

To find 'x':

55 x 23 = 1265

The indefinite integral of ∫ (4x⁴ - 5)⁵ . 32x³ dx is (4x⁴ - 5)⁶/3 + C.

The solution of the indefinite integral is calculated by using substitution method.

Let u = 4x⁴ - 5

du/dx = 16x³

dx = du/(16x³)

Substituting into the integral;

∫ (4x⁴ - 5)⁵ . 32x³ dx =  ∫ u⁵ . 32x³ du/(16x³)

∫ u⁵ . 32x³ du/(16x³) =  ∫ 2u⁵ du

∫ 2u⁵ du =  2∫u⁵ du

2∫u⁵ du = 2 (u⁶/6 + C)

2 (u⁶/6 + C)  = u⁶/3 + C

Substituting back for u;

∫ (4x⁴ - 5)⁵ . 32x³ dx = (4x⁴ - 5)⁶/3 + C

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The possible perimeter for the rectangle would be 28(Letter D)

Answer:8.52%

Step-by-step explanation:

There are 14 utensils in the drawer, and then there will be one less in the bowl after each successive utensil is removed. There are then 3 possibilities for the same kind being removed on all pulls:

P(3 spoons) = (6/14)*(5/13)*(4/12)

P(3 forks) = (5/14)*(4/13)*(3/12)

P(3 knives) = (3/14)*(2/13)*(1/12)

Add all of these outcomes together and you'd get about 8.52%

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

We have,

3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.

Now, first convert all quantity in same unit.

3 ½ cups of flour

= 3 cups + 0.5 cups

= 3 cups and 8 ounces.

and, 2 ⅔ cups of sugar

= 2 cups + 0.67 cups,

= 2 cups and 10.72 ounces.

and, 1 ¾ cups of cocoa

=1 cup + 0.75 cups

= 1 cup and 12 ounces.

So, the total amount

= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

= 7 cups

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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The area of the front cover a face perpendicular to the thickness is 72 in².

Given:

A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.

The volume of the dictionary will be 216in².

Volume = W×L×H

Surface = volume/ height

= 216/3

= 72 in²

Hence, the area of the front cover of a face perpendicular to the thickness is 72 in².

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Answer:

[tex]x=4.865[/tex]

Step-by-step explanation:

We know the area of a rectangle to be [tex]base*height[/tex]. In this instance, [tex]base=(2x+10)in[/tex], [tex]height=(3x) in[/tex], and [tex]area=288in^2[/tex]

The next step is to plug these known values into the [tex]area=base*height[/tex] equation. It'll look like this:

[tex]288=(2x+10)*(3x)=6x^2+30x[/tex]

This simplifies to:

[tex]48=x^2+5x[/tex]

Next, we want to rewrite the equation so we can apply the quadratic formula to it. We are going to do this by subtracting 48 from each side. The new equation looks like this:

[tex]x^2+5x-48=0[/tex]

Next, we plug this into the quadratic formula:

[tex]x=\frac{-(5)+\sqrt{5^2-4(1)(-48)} }{2(1)}=4.865[/tex]

[tex]x=\frac{-(5)-\sqrt{5^2-4(1)(-48)} }{2(1)}=-9.865[/tex]

The second value of x is negative, and since a side length cannot be negative this leaves us with just the first answer of [tex]x=4.865[/tex].

Answer:

[tex]\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]

Step-by-step explanation:

The area of a rectangle is equal to the base × height:

[tex]\large \textsf{$\rm A $ $= (2x+10)\times(3x)$}\\ \\\large \textsf{$\rm \phantom{A}=$ $6x^2+30x$, and since A = 288,}\\ \\\large \textsf{$\therefore 288 = 6x^2+30x$}[/tex]

Rearranging this equation, we get:

[tex]\large \textsf{$6x^2+30x-288=0$}\\\\\large \textsf{$6(x^2+5x-48)=0$}\\\\\large \textsf{$\therefore x^2+5x-48=0$}[/tex]

Here we are left with a quadratic equation, which we can solve using the quadratic formula:

[tex]\Large \boxed{\textsf{$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$}} \textsf{ where $ax+bx+c=0$}[/tex]

Plugging values into the formula, we get:

[tex]\Large \textsf{$x = \frac{-(5)\pm \sqrt{(5)^2-4(1)(-48)}}{2(1)}$} \\\\\Large \textsf{$x=4.87, -9.87$,} \large \textsf{ but length cannot be negative.}\\\\\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]

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Step-by-step explanation:

a probability is airways the ratio

desired cases / totally possible cases

2 questions, each with a true or false answer option.

that gives us

2 × 2 = 4 answer options in total (the totally possible cases).

but only one of the four combinations is completely right.

so, the probability is

1/4

the 4 possibilities are

true true

false false

true false

false true

formally we can get to the result that way :

the first question has 2 options.

the probabilty to get it right is therefore

1/2

the same for the second question

1/2

but both have to be right for the desired result (question 1 AND question 2 have to be right), so, we need to combine both individual probabilities :

1/2 × 1/2 = 1/4

Note that the probability of both questions being right by guessing is 0.25 or 1/4.

P (both correct) = P(correct on Q1 ) x p(correct on Q2)
=   0.5 x 0.5
= 0.25 or 1/4

Note that probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are.

Statistics is the study of occurrences guided by probability.

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The range of the monthly sales goals is; 37,000.

We are given the stem plot :

Stem  Leaf

1          2, 5, 5, 8

2          4, 4, 6

3          4, 6

4          7, 8, 9

The largest number is 49 and the smallest is 12. Since is in thousands, the numbers become 49,000 and 12,000.

Range = highest value - the lowest value

Range = 49,000 - 12,000 = 37,000

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The length of arc on equator is 69.08 miles.

We have

Radius of Earth = 3960 miles

Angle = 1 degree

So, the length of arc on equator is

= θ/360 x 2πr

= 1/360 x 2 (3.14) (3960)

= 69.08 miles

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The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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Answer:

A. To convert pounds to kilograms, we need to multiply by 0.453592. Therefore, the fish from region A weighs about 130 kg (286 x 0.453592), rounded to the nearest whole number.

B. Similarly, the fish from region B weighs about 279 kg (614 x 0.453592), rounded to the nearest whole number.

The number of blue cars and the number of red cars are 3 and 5 respectively

Let b and r represent the number of blue cars and  the number of red cars respectively.

There are a total of 8 cars, we have:

b + r = 8

There are 135 clowns in total. Blue cars hold 20 clowns and red cars only hold 15, we have:

20b + 15r = 135.

Thus, we have a system of equations with two variables:

b + r = 8   ---- (1)

20b + 15r = 135  ---- (2)

We can use elimination to solve for b and r.

Let's use elimination. Multiplying the first equation by 20 and second equation by 1:

20 * (b + r = 8)                  = 20b + 20r = 160  (subtract)

1 * (20b + 15r = 135)         = 20b + 15r = 135

                                      ...............................................

                                                      5r = 25

                                      ...............................................

r = 25/5

r = 5

Using (1):

b + r = 8

b + 5 = 8

b = 8 - 5

b = 3

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Answer:

satiscal

Step-by-step explanation:

The value of angle k is 129⁰.

The value of angle b is 64.5⁰.

The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.

k + 113 + 118 = 360 (sum of angles in a circle)

k + 231 = 360

k = 360 - 231

k = 129⁰

The value of angle b is calculated by applying the principle of intersecting chord theorem.

b = ¹/₂ arc k

b = ¹/₂ x 129

b = 64.5⁰

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The construction of an equilateral triangle is shown in the solution.

Steps -

When the length of three sides of the triangle is given, then follow the below steps to construct the required triangle.

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The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos²θ sinθ

y = 4 sin²θ cosθ

We have,

We can use the following conversions from polar to Cartesian coordinates:

x = r cosθ

y = r sinθ

To convert the polar equation r = 4 sin(θ)cos(θ) into Cartesian coordinates, we substitute r with its equivalent value 4 sin(θ)cos(θ) and use the above conversions:

x = (4 sinθ cosθ) cosθ

y = (4 sinθ cosθ) sinθ

Simplifying these expressions, we get:

x = 4 cos^2θ sinθ

y = 4 sin^2θ cosθ

The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos^2θ sinθ

y = 4 sin^2θ cosθ

or, in standard form:

x = 4xy

This is the Cartesian equation in terms of x and y, obtained by replacing sinθ and cosθ with x and y, respectively.

Thus,

The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos²θ sinθ

y = 4 sin²θ cosθ

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The total value of the annuity in 26 years is 179163.85 dollars.

Given that, Deandre deposits $97 each month in an annuity that pays 7.7 % interest, compounded quarterly.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Here, 26 years = 26×4

= 104

Now, A=97(1+7.5/100)¹⁰⁴

A=97(1+0.075)¹⁰⁴

A=97(1.075)¹⁰⁴

A=97×1847.05

A=$179163.85

Therefore, the total value of the annuity in 26 years is 179163.85 dollars.

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The number of ways to choose the starting 11 players with all seniors playing is 4845.

We have,

Since the coach wants all seniors to play, we must choose the remaining

(11 - 7 = 4) players from the remaining (6 + 6 + 8 = 20) players who are not seniors.

The number of ways to choose 4 players from 20 players is given by the combination formula:

[tex]^{20}C_4[/tex]

= 20! / (4! * 16!)

= 4845

Therefore,

The number of ways to choose the starting 11 players with all seniors playing is 4845.

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The values of x and y are given as follows:

The dimensions are obtained applying the proportions in the context in the problem.

The conversion rate between feet and inches is given as follows:

1 feet = 12 inches.

Hence the dimensions of the picture are given as follows:

The height of the entire frame is of 8 ft, while y is half the height outside the picture, thus the value of y is obtained as follows:

y = 0.5(8 - 2) = 3 ft.

The value of x is given as follows:

x = 0.5(12 - 4.5)

x = 3.75 ft.

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Answer:

(p + 2)(3b - 7)

Step-by-step explanation:

3b(p + 2) - 7(p + 2) ← factor out common factor (p + 2) from each term

= (p + 2)(3b - 7)

The value of arc LN in the intersecting chords is 100⁰.

The value of arc LN is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

arc LN = 2 x m∠LMN

From the diagram, we have, m∠LMN = 50⁰

The value of arc LN is calculated as follows;

arc LN = 2 x 50⁰

arc LN = 100⁰

Thus, the value of arc LN is based on intersecting chord theorem.

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The amount of paint needed to paint all the surfaces of the 11 poles is; 1260 ft².

It follows from the task content that the amount of paint required to paint all the surfaces of the 11 poles is required to be determined.

First, since the surface area of a cylindrical pole is; A = 2πr (r + h).

where height,h = 22 and radius, r = diameter / 2 = 1.6 / 2 = 0.8 feet.

Therefore, A = 2 × 3.14 × 0.8 (22 + 0.8)

A = 114.5472 ft²

Therefore, for all 11 poles; the total area is; 11 × 114.5472 = 1260 ft² to the nearest whole number.

Ultimately, the quantity of paint needed is such that it is sufficient for an area of; 1260 ft².

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The volume of C.a .cylinder is twice the volume of a cone.

The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.

The cylinder's volume  can be expressed as π r² h,  along with the surface area  which can be expressed as 2π r h + 2π r² and this can be used to get the values.

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The measure of arc CFE is 246⁰.

The measure of arc FED is 190⁰.

The value of the angle CFE is 57⁰.

The value of the angle DEF is 85⁰.

The value of the angles is calculated by applying intersecting chord theorem.

This theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

angle CFE = 180 - 123 (opposite angles of a cyclic quadrilateral)

angle CFE = 57

arc CDF = 2 x 57

arc CDF = 114

arc CFE = 360 - 114 = 246⁰

angle DEF = 180 - 95

angle DEF = 85

arc DCF = 2 x 85 = 170

arc FED = 360 - 170 = 190

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Answer:

13 years

Step-by-step explanation:

The required graph has been attached below that represents the function f(x) = 5 cos (2x).

The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.

Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.

The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).

Thus, the graph has been attached below that represents the given function.

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