What is the difference of the polynomials?

The number of lego planes that can be build in 40 minutes is A = 2.33

Given data ,

Johnny can build in 3 1/2 lego planes in 60 minutes

On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:

From the proportion , we get

To find out how many planes he can build in 40 minutes, we can multiply the amount he can build in one minute by 40:

3.5 / 60 = A / 40

Multiply by 40 on both sides , we get

A = 2.33

Hence , Johnny can build approximately 2.33 lego planes in 40 minutes

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The area of the triangle is 6 sq units.

The area of the triangle is calculated by applying the following formula;

A = ¹/₂ x b x h

where;

The base of the triangle = 3 - 0 = 3

The vertical height of the triangle = 5 - 1 = 4

Area = ¹/₂ x 4 x 3

Area = 6 sq units.

Thus, the area of the triangle is a function of base and height.

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Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Given values:

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies B=180^{\circ}-A-C[/tex]

[tex]\implies B=180^{\circ}-29^{\circ}-63^{\circ}[/tex]

[tex]\implies B=88^{\circ}[/tex]

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

Solve for a:

[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

[tex]\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}[/tex]

[tex]\implies a=13.0876493...[/tex]

[tex]\implies a=13.1[/tex]

Solve for b:

[tex]\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

[tex]\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}[/tex]

[tex]\implies b=26.9194211...[/tex]

[tex]\implies b=26.9[/tex]

[tex]\hrulefill[/tex]

Given values:

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies C=180^{\circ}-A-B[/tex]

[tex]\implies C=180^{\circ}-72^{\circ}-35^{\circ}[/tex]

[tex]\implies C=73^{\circ}[/tex]

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

Solve for a:

[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

[tex]\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}[/tex]

[tex]\implies a=20.8847511...[/tex]

[tex]\implies a=20.9[/tex]

Solve for b:

[tex]\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

[tex]\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}[/tex]

[tex]\implies b=12.5954671...[/tex]

[tex]\implies b=12.6[/tex]

The correct statement regarding the measure of variability used to represent the data is given as follows:

The IQR of 10 is the most accurate to use, as the data is skewed.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.

The charity received 18 donations, hence the quartiles are given as follows:

Hence the IQR is given as follows:

IQR = 22.5 - 12.5

IQR = 10.

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The area of the semicircle is 47.5 square centimeters

We have to find the area of the semi circle

The diameter of the semicircle is 11 cm

Radius is half of the diameter

Radius = 5.5 cm

Let us find the area of semicircle  by formula 1/2(πr²)

Radius = 1/2×3.14×(5.5)²

= 1/2×3.14×30.25

=47.4925 square centimeters

Hence,  the area of the semicircle is 47.5 square centimeters

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Answer: We can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events.

In this case, we want to find the probability that a randomly selected senior is a varsity athlete or on the honor roll. We can define the events as follows:

A = the event that a senior is a varsity athlete

B = the event that a senior is on the honor roll

From the problem statement, we know:

P(A and B) = 10/200 = 1/20

P(A) = 70/200 = 7/20

P(B) = 68/200 = 17/50

Plugging these values into the formula:

P(A or B) = P(A) + P(B) - P(A and B)

= 7/20 + 17/50 - 1/20

= 21/50

Therefore, the probability that a randomly selected senior is a varsity athlete or on the honor roll is 21/50.

The area of the composite shape is 125units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A composite shape can be defines as a shape created with two or more basic shapes.

The composite shape can be divided into 2 equal squares and a rectangles.

Area of the square = l²

= 5× 5 = 25

For two squares it will be;

25 × 2

= 50 units²

area of the rectangle = l× w

where w is the width

A = 15 × 5

= 75 units²

Therefore the area of the composite shape = 50 + 75 = 125 units²

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The function that is the inverse of the exponential function y = 4ˣ is lnx/ln4

The inverse of a function f is denoted by [tex]f^{-1[/tex] and it exists only when f is both one-one and onto function. Note that  [tex]f^{-1[/tex]  is NOT the reciprocal of f. The composition of the function f and the reciprocal function  [tex]f^{-1[/tex]  gives the domain value of x.

(f o  [tex]f^{-1[/tex] ) (x) = ( [tex]f^{-1[/tex]  o f) (x) = x

For a function 'f' to be considered an inverse function, each element in the range y ∈ Y has been mapped from some element x ∈ X in the domain set, and such a relation is called a one-one relation or an injunction relation.

The standard exponential function is given as y = abˣ

Given the function,

y = 4ˣ

Replace y with x

[tex]x = 4^y[/tex]

Make y the subject of the formula,

[tex]lnx = ln4^y\\\\lnx = yln4[/tex]

Divide both sides by ln4

lnx/ln4 = y

Hence the function that is the inverse of the exponential function y = 4ˣ is lnx/ln4

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Okay, let's solve this step-by-step:

X/5-y = m-1

Add y to both sides:

X/5 = m

Multiply both sides by 5:

X = 5m

So in this equation, X = 5m.

To find y, we subtract m-1 from both sides of the original equation:

X/5 = 5m

X/5 - (m-1) = 5m - (m-1)

X/5 - m + 1 = 4m

(X - 5m) / 5 = m - 1

X - 5m = 5(m - 1)

X = 20m - 5

So if we let m = any value, we can calculate y. For example:

If m = 3, then:

X = 20*3 - 5

= 55 - 5 = 50

50/X = 5(m - 1) = 5*2 = 10

y = 10

Does this make sense? Let me know if you have any other questions!

The price per inch of the wrap is $0.01 or 100cent

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

For example, If the age of Roy is x what will be his age in five years time.

His age five years time will be x+5

9 foot roll cost $1.08

1 foot = 12 inches

9 feet = 9 × 12

= 108 inches

Therefore 108 inches = 1.08

1 inch = 1.08/108

= $0.01

= 100cents

therefore the price of the wrap per inch is $0.01 or 100 cent.

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Answer:

Step-by-step explanation:

$6.80 x 19 pounds = $129.2

$4.70 x 18 pounds = $84.6

            +___________________

             37 pounds = $213.8

$213.8 divided by 37 pounds = 5.77837......

                                                  = $5.78 per pound

The total amount to each person end up paying $20.54.

To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.

To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.

The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.

Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.

To split this evenly among the five people, we divide by 5:

$102.72 ÷ 5 = $20.54

So each person will end up paying $20.54.

20% of $85.60 is ($85.60 * 0.20) = $17.12

Add the tip to the total bill:

$85.60 + $17.12 = $102.72

Divide the total amount by the number of people (5): $102.72 / 5 = $20.54

Therefore, the answer is B. $20.54.

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The probability of the values of X that are less than 21 is 0.97725.

We have,

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given:

u = 20

and SD = 2.25

To find P(X < 21)

So, P(X < 21 )

= 1 - P(X > 21)

Now, P(X > 21)

= P(Z >  [(21–20)/2.25]

= P( Z > 1/2.25)

= P(Z > 0.444)

= 0.02275

So, the required probability = P(Z < 21) = 1 - 0.02275= 0.97725

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complete question:

Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.

Another representation of (1, 1/4 π)  in which r> 0, 2π < θ < 4π is (1, 3/4 π)

In Bi-polar Coordinates, the point (1, 1/4 π) can be represented in polar coordinates as (r, θ).

Where r is the distance from the origin to the point and θ is the angle between the positive x-axis and the line segment connecting the origin to the point.

a. For r> 0, 2π < θ < 4π

Add 2π to the original angle of 1/4 π:

(r, θ+2π) = (1, 1/4 π + 2π)

              = (1, 9/4 π)

b. For r < 0, 0 < θ < 2π,

Add  π and reflect the original point across the origin:

(r, θ+π) = (-1, 1/4 π + π)

           = (-1, 5/4 π)

c. For r> 0, -2π < θ < 0,

Subtract 2π from the original angle of 1/4 π:

(r, θ-2π) = (1, 1/4 π - 2π)

             = (1, -7/4 π)

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The value of Sin A is 5/13.

Option A is the correct answer.

We have,

Sin A = Perpendicular / Hypotenuse

Sin A = BC / AB

And,

BC = 5

AB = 13

Substituting.

Sin A = 5/13

Thus,

The value of Sin A is 5/13.

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The solution set of given inequalities are represented by Part A.

The given inequalities are

⇒ y ≥ x + 1 and y + x > -1

Hence, The related equations of both inequalities are

y = x + 1

Put x=0, to find the y-intercept and put y=0, to find x intercept.

y = 0 + 1

y = 1

And, 0 = x + 1

x = - 1

Therefore, x-intercept of the equation is (-1,0) and y-intercept is (0,1).

Similarly, for the second related equation

y + x = - 1

y + 0 = - 1

y = - 1

0 + x = - 1

x = - 1

Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).

Now, join the x and y-intercepts of both lines to draw the line.

Now check the given inequalities by (0,0).

0 ≥ 0 + 1

0 ≥ 1

It is a false statement, therefore the shaded region is in the opposite side of origin.

0 + 0 ≥ - 1

0 ≥ - 1

It is a true statement, therefore the shaded region is about the origin.

Hence, From the below figure we can say that the solution set of given inequalities are represented by Part A.

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Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.

Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.

In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.

The number of pages Li Wei can read in a week = 90

The number of pages Collen can read in a week = 126

Li Wei's reading rate per hour = 30 pages

Collen's reading rate per hour = 24 pages

Let the hours that Li Wei and Colleen can be on the same page= x

The total number of pages Li Wei can read = 90 + 30x

The total number of pages Colleen can read = 126 + 24x

For Li Wei and Colleen to be on the same, the two expressions are equated.

90 + 30x = 126 + 24x

6x =  36

x = 6

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The volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.

Given the height (h) of a cone as 22 m and the diameter (d) of its circular base as 22 m, we can find the radius (r) of the circular base using the formula:

r = d/2 = 22/2 = 11 m

Here, Jan made a mistake in the work of the surface area of the cone because she used the wrong value of slant height (l=22) in the calculation.

The volume (V) of a cone is given by the formula:

V = (1/3)πr²h

Substituting the values of r and h, we get:

V = (1/3)π(11)²(22)

V = 2786.2 cubic meters

The surface area (A) of a cone is given by the formula:

A = πr(r + l)

here l is the slant height of the cone, which can be found using the Pythagorean theorem:

l = √(r² + h²)

l = √(11² + 22²)

l = √(605)

l = 24.6

Substituting the values of r and l, we get:

A = π(11)(11 + 24.6)

A ≈ 1229.51 square meters

Therefore, the volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.

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The percentage of the data values that are greater than 130 is 25%

From the question, we have the following parameters that can be used in our computation:

The box plot

From the box plot, the five-number summary are

40, 70, 110, 130, and 150

In the above five-number summary, we have

Third quartile = 130

This means that the percentage of the data values that are greater than 130 is 25%

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1. Event A includes the outcomes of H and T,

2. while event AC includes all the possible outcomes of rolling a number cube, which are 1, 2, 3, 4, 5, and 6.

1. Event A is defined as tossing a heads on a coin, regardless of the outcome of rolling a number cube. Therefore, the outcomes in event A are H (heads) and T (tails), since either of these outcomes could occur when rolling a number cube and tossing a coin.

2. Event AC is the complement of event A, i.e., it is the set of outcomes that are not in event A. Since event A contains H and T, the outcomes in event AC are the remaining outcomes that are not in event A, which are all the possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, and 6.

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a) The fourth and sixth data points have significantly different ratios.

a) Let's calculate the ratios:

For the first data point:

= 11.5 gallons / $25.23 = 0.4555 gallons per dollar

For the second data point:

= 7.2 gallons / $15.80 = 0.4557 gallons per dollar

For the third data point:

= 10 gallons / $21.94 = 0.4556 gallons per dollar

For the fourth data point:

= 14.3 gallons / $40.63 = 0.3519 gallons per dollar

For the fifth data point:

= 6.8 gallons / $14.92 = 0.4555 gallons per dollar

For the sixth data point:

= 9.7 gallons / $27.56 = 0.3517 gallons per dollar

However, the fourth and sixth data points have significantly different ratios.

b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.

The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.

To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.

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The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.

The formula to convert the temperature from Celcius to Fahrenheit is:

[tex]\textdegree F = (\textdegree C * 1.8) + 32[/tex]

We need to calculate the temperature change of [tex]6 \textdegree C[/tex] in Fahrenheit:

[tex]\Delta \textdegree C = 6\\\Delta \textdegree F = \Delta \textdegree C * 1.8 = 10.8[/tex]

The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.

We can calculate the  Fahrenheit temperature of the water and the desired temperature in Fahrenheit:

[tex]^{\circ}C = 19\\^{\circ}F = (19 * 1.8) + 32 = 66.2[/tex]

[tex]^{\circ}C = 25\\^{\circ}F = (25 * 1.8) + 32 = 77[/tex]

The current temperature of the pool is [tex]66.2 ^{\circ} F[/tex] and the desired temperature is [tex]77 ^{\circ} F[/tex].

Therefore the temperature needs to be increased by:

[tex]\Delta ^{\circ}F = 77 - 66.2 = 10.8 ^{\circ}F[/tex]

which is the same temperature change we calculated earlier in Fahrenheit.

Therefore, the temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.

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Answer:

d = [tex]\sqrt{58}[/tex]

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (- 5, 8 )

d = [tex]\sqrt{(-5-2)^2+(8-5)^2}[/tex]

   = [tex]\sqrt{(-7)^2+3^2}[/tex]

   = [tex]\sqrt{49+9}[/tex]

   = [tex]\sqrt{58}[/tex]

Answer:

a₁₀₀ = 1074

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₃ = 7 and a₁₂ = 106 , then

a₁ + 2d = 7 → (1)

a₁ + 11d = 106 → (2)

solve the equations simultaneously to find a₁ and d

subtract (1) from (2) term by term to eliminate a₁

(a₁ - a₁) + (11d - 2d) = 106 - 7

0 + 9d = 99

9d = 99 ( divide both sides by 9 )

d = 11

substitute d = 11 into (1) and solve for a₁

a₁ + 2(11) = 7

a₁ + 22 = 7 ( subtract 22 from both sides )

a₁ = - 15

Then

a₁₀₀ = - 15 + (99 × 11) = - 15 + 1089 = 1074

The basic ratio of minutes of painting to minutes of instruction is 7 : 6

From the question, we have the following parameters that can be used in our computation:

Painting = 63 minutes

Instruction = 54 minutes

The ratio can be represented as

Ratio = Painting : Instruction

When the given values are substituted in the above equation, we have the following equation

Painting : Instruction = 63 : 54

Simplify

Painting : Instruction = 21 : 18

Simplify

Painting : Instruction = 7 : 6

This  ratio cannot be simplified

Hence, the solution is 7 : 6

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The value of number of students who failed in both mathematics and English is 40.

Since, Given that;

60% of the 1000 students passed the examination,

Hence, we can calculate the number of students who passed the exam as follows:

60/100 x 1000 = 600

So, 600 students passed the examination.

Now, let's find the number of students who failed the examination.

Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:

40/100 x 1000 = 400

Of the 400 failing students, we know that 60% failed in mathematics.

So, the number of students who failed in mathematics is:

60/100 x 400 = 240

Similarly, we know that 50% of the failing students failed in English.

So, the number of students who failed in English is:

50/100 x 400 = 200

Now, we need to find the number of students who failed in both subjects.

We can use the formula:

Total = A + B - Both

Where A is the number of students who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.

Substituting the values we have, we get:

400 = 240 + 200 - Both

Solving for Both, we get:

Both = 240 + 200 - 400

Both = 40

Therefore, the number of students who failed in both mathematics and English is 40.

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Using z - score, the percentage of students above 83 is 15.9%

To find the number of students that scored above 83 can be calculated using z - score formula.

This is given as

z = x - μ / σ

Substituting the values into the formula;

z = 83 - 75 / 8

z = 1

The z-score is 1

Let's find the percentage of z -score under the score

p(x > 83) = 1 - P(x < 83) = 0.15866

p = 15.9%

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