This exercise uses the normal probability density function and requires the use of either technology or a table of values of the standard normal distribution. The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.96 per access line per month, with a standard deviation of $2.25. Company A's operating expenses were $28.00 per access line per month. Assuming a normal distribution of operating expenses, estimate the percentage of regional phone companies whose operating expenses were closer to the mean than the operating expenses of Company A were to the mean. (Round your answer to two decimal places.)

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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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 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 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 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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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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Given statement solution is :- Outputs and values g(2/3) = 2/3.

To summarize:

g(0) = 0

g(-1) = undefined

g(2) = undefined

g(2/3) = 2/3

To find the values of g(x) for the given inputs, we substitute each input into the function g(x) = x / √([tex]1 - x^2[/tex]). Let's calculate the values:

g(0):

Substitute x = 0 into the function:

g(0) = 0 / √([tex]1 - 0^2[/tex])

= 0 / √(1 - 0)

= 0 / √1

= 0

Therefore, g(0) = 0.

g(-1):

Substitute x = -1 into the function:

g(-1) = (-1) / √(1 - [tex](-1)^2[/tex])

= (-1) / √(1 - 1)

= (-1) / √0

Since the square root of 0 is undefined, g(-1) is undefined.

g(2):

Substitute x = 2 into the function:

g(2) = 2 / √([tex]1 - 2^2[/tex])

= 2 / √(1 - 4)

= 2 / √(-3)

Since the square root of a negative number is undefined in the real number system, g(2) is undefined.

g(2/3):

Substitute x = 2/3 into the function:

g(2/3) = (2/3) / √(1 - [tex](2/3)^2[/tex])

= (2/3) / √(1 - 4/9)

= (2/3) / √(5/9)

= (2/3) / (√5/√9)

= (2/3) / (√5/3)

= (2/3) * (3/√5)

= 2√5 / 3√5

= 2/3

Therefore, outputs and values g(2/3) = 2/3.

To summarize:

g(0) = 0

g(-1) = undefined

g(2) = undefined

g(2/3) = 2/3

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Answer:

 3.98

Step-by-step explanation:

Answer:

the second method may be through graph

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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Answer:

The slope is 5.

Hope this helps!

Step-by-step explanation:

( x, y )

( 6, 50 ) and ( 12, 80 )

[tex]\frac{80-50}{12 - 6} < = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

[tex]\frac{30}{6} = \frac{5}{1} = 5[/tex]

The slope is 5.

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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Answer:

$280

Step-by-step explanation:

7•40=$280

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]

Answer:

10 millimeters

Step-by-step explanation:

The diameter of the button is twice the radius. Therefore, the diameter of Jasmine's pants button is 10 millimeters.

Answer:

A. 4ab² + 2x

Step-by-step explanation:

If you want to get rid of those pesky parentheses, you have to use the superpower of distributive property. It lets you multiply everything inside the parentheses by the number outside. For example:

4(ab²+1/₂c + x) = 4ab² + 2c + 4x

Boom! No more parentheses!

To combine like terms, you have to add or subtract the numbers in front of the terms that have the same variable and exponent. For example:

2x - 4x = -2x

Bam! Only one x left!

Here are the steps to simplify the expression:

4(ab²+1/₂c + x) - 2(c+x)

= 4ab² + 2c + 4x - 2c - 2x (use superpower)

= 4ab² + 4x - 2x (combine like terms)

= 4ab² + 2x (simplify)

So, the answer is A. 4ab² + 2x.

Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).

To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.

The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.

For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.

To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.

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Answer:9/41

SOH = opposite over hypotenuse

Step-by-step explanation:

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!

Table C shows the sample space for choosing 2 marbles from the bag with replacement. The probabity and there are 25 possible pairs.

The sample space for choosing 2 marbles from the bag with replacement consists of all possible pairs of marbles that can be chosen, where the order in which they are chosen does not matter.

Since there are 5 marbles in the bag and we are choosing 2 of them, there are 5 choices for the first marble and 5 choices for the second marble, for a total of [tex]5*5 = 25[/tex] possible pairs.

Table C shows the sample space for choosing 2 marbles from the bag with replacement. Each row and column in the table represents a different marble that can be chosen, and each cell represents a pair of marbles that can be chosen.

For example, the cell in row 2 and column 3 represents the pair of marbles consisting of the red marble and the clear marble. Tables A and B show the sample space for choosing 2 marbles from the bag without replacement. In this case, the order in which the marbles are chosen does matter, and each marble can only be chosen once.

Therefore, there are only 5 choices for the first marble, but only 4 choices for the second marble (since one marble has already been chosen), for a total of[tex]5 * 4 = 20[/tex] possible pairs.

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The complete question is:

A bag contains five green marbles, three blue marbles, two red marbles, and two yellow marbles. One marble is drawn out randomly.

a) Are the four different colour outcomes equally likely? Explain.

b) Find the probability of drawing each colour marble i.e., P(green), P(blue), P(red) and P(yellow)

c) Find the sum of their probabilities.

Mrs. Garcia invested $2240 in the 8.5% account and $4091 in the 8% account.

Let x be the amount invested in the 8.5% account, and y be the amount invested in the 8% account. Since the total investment is $6331, we have x + y = 6331.

The total interest received is $517.68, which can be expressed as 0.085x + 0.08y = 517.68, where 0.085 and 0.08 are the decimal equivalents of the interest rates.

We can now solve this system of equations to find x and y. One possible method is to use substitution, where we solve for one variable in terms of the other from one of the equations, and substitute it into the other equation. From x + y = 6331, we have y = 6331 - x. Substituting this into the second equation, we get:

0.085x + 0.08(6331 - x) = 517.68

Simplifying and solving for x, we get:

0.005x + 506.48 = 517.68

0.005x = 11.2

x = 2240

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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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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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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 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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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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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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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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Answer:no idea

Step-by-step explanation: