Erin has a set of 10 index cards. Each index card is 3 ½ inches long. If she were
to lay the index cards in one long row, how long would the row be?
*

In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.

The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:

a > |c - b| and b > |c - a|,

where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides

Answer:

Step-by-step explanation:

The square root of a number can be both positive and negative, so to find all possible values of d, we need to take both the positive and negative square root of 3520.

Starting with the positive square root:

d = √3520 = √(55^2 * 8) = 55 * √8 = 8 * √55

And for the negative square root:

d = - √3520 = - √(55^2 * 8) = - 55 * √8 = - 8 * √55

So the two possible values of d are 8√55 and -8√55.

At the school play, 225 adult tickets were sold.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The number of adult tickets sold be 'x',

Therefore, The number of student tickets would be 'x - 68'.

Therefore, The expression can be formed as,

x + (x - 68) = 382.

2x - 68 = 382.

2x = 450.

x = 225.

So, The number of adult tickets sold is 225.

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Answer:A decrease of 20%.

First we must subtract out new total from our old total.

9390 - 7512 is 1878. This means that there is a difference of 1878. Next we must divided both 7512 and 1878 into 9390.

7512/9390 is 0.8 & 1878/9390 is 0.2

As a percentage that is 80% and 20%.

This means that the new amount of sugar only makes up 80% of the old amount. That means that there was a decrease of 20% of kilograms of sugar.

I hope this helped & Good Luck <3 !!!

Answer:

D

Step-by-step explanation:

ASA = 2 non included angles + 1 included side

by knowing angle c is congruent to angle z we can prove the triangles are congruent by ASA postulate.

The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

AC = XZ

∠ A = ∠ X

Now, To prove the triangles are congruent by ASA , we get;

AC = XZ

∠ A = ∠ X

⇒ ∠ Z = ∠ C

or, ∠ B = ∠ Y

Thus, The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

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Answer:

Step-by-step explanation: The expression for f(x) is not a valid mathematical equation. It should specify the relationship between x and the output value of f(x). If the correct equation for f(x) is given, we can then find the expression for (f + g)(x) and g(x).

Assuming that the equation for f(x) is as follows:

f(x) = 12 + x

Then, the expression for (f + g)(x) can be found by adding f(x) and g(x):

(f + g)(x) = f(x) + g(x) = 12 + x + (5 - x) = 17

So, (f + g)(x) is a constant function with a value of 17 for all values of x.

And the expression for g(x) was already given:

g(x) = 5 - x

On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

by fraction

4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.

20/3.5=5.7 or 6

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Answer:

26 kangaroos on the farm
32 goats on the farm

Step-by-step explanation:

To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.

Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.

Adding these two quantities, we have:

4g + 2k = 180

Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.

Adding these two quantities, we have:

g + k = 58

Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.

Let's use substitution method:

From the second equation, we can find g:

g = 58 - k

Substituting this in the first equation, we get:

4(58 - k) + 2k = 180

Expanding and solving, we get:

232 - 4k + 2k = 180

232 - 2k = 180

-2k = -52

k = 26

So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:

g = 58 - k = 58 - 26 = 32

Therefore, there are 32 goats on the farm.

The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We can use the formula for the margin of error for a 95% confidence interval:

margin of error = z× (standard deviation / √n)

where z is the z-score for a 95% confidence interval, which is 1.96.

a. The desired margin of error is $0.10:

0.10 = 1.96(0.25 /√n)

√n = 1.96×0.25 / 0.10

√n= 4.9

n = 4.9^2

n = 24.01

So the appropriate sample size for a margin of error of $0.10 is at least 25.

b. The desired margin of error is $0.07:

0.07 = 1.96 (0.25 / √n)

√n = 1.96 × 0.25 / 0.07

√n= 6.97

n = 6.97²

n = 48.53

So the appropriate sample size for a margin of error of $0.07 is at least 49.

c. The desired margin of error is $0.05:

0.05 = 1.96 (0.25 / √n)

√n= 1.96 × 0.25 / 0.05

√n= 9.8

n = 9.8²

n = 96.04

So the appropriate sample size for a margin of error of $0.05 is at least 97.

Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

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Answer:yo no se como ablar ingles

Step-by-step explanation: perdoname

The amount of force between two objects 10 mm away from each other is G[tex]m_1m_2[/tex] / 100.

All physical things with mass are drawn to the gravitational force, which can be thought of as an attracting force. It is the known natural force that is by far the weakest.

Given:

Distance = 10 mm

As, the Gravitation force between two objects

F = G[tex]m_1m_2[/tex] / r²

or, F = G[tex]m_1m_2[/tex] / 10²

F = G[tex]m_1m_2[/tex] / 100

Also, the force between two objects decreases as the far they are apart from each other.

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The Question attached is Incomplete/ inappropriate, the Complete Question is

What would be the amount of force between two objects 10 mm away from each other having the [tex]m_1[/tex] and [tex]m_2[/tex]?

The required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching to infinity.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
Given expression,

= 3ˣ

put x = 4
= 3⁴ = 81

Now put x = -4
= 3⁻⁴
= 1/3⁴

= 1/81

Since x gets larger as x = 0, 1, 2, 3, and so on 3ˣ get 1, 9, 27, 81 and so on approaching to infinity.

Thus, the required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching infinity.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The identity to be used here is [ (a - b)² = a² - 2ab + b² ]

First, try to get the given expression in form of terms on the RHS of the above identity

[tex]\qquad \sf  \dashrightarrow \: 4y {}^{2} - 6yz + 9 {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 {}^{2})( {y}^{2}) - 2(3)(y)(z) + (3 {}^{2} ) {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (3z) {}^{2} [/tex]

[ it's in form of a² - ab + b² now, add and deduct ab here ]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (9z) {}^{2} - (2y)(3z) + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - 2(2y)(3z) + (3z) {}^{2} + (2y)(3z)[/tex]

[ Apply the identity ]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + 6yz[/tex]

[ That's probably the answer, it can't be simplified more ]

To factorize the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex], we can use the quadratic formula.

We have the quadratic expression [tex]\sf\:ax^2 + bx + c \\[/tex], where $$\sf\:a = 4$$, $$\sf\:b = -6y $$, and $$\sf\:c = 9z^2 $$.

The quadratic formula states that for any quadratic equation of the form [tex]\sf\:ax^2 + bx + c = 0 \\[/tex], the solutions for $$\sf\:x $$ can be found using the formula:

[tex]\sf\:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]

Applying this formula to our quadratic expression, we get:

[tex]\begin{align}\sf\:x &= \frac{-(-6y) \pm \sqrt{(-6y)^2 - 4(4)(9z^2)}}{2(4)} \\ &= \frac{6y \pm \sqrt{36y^2 - 144z^2}}{8} \\ &= \frac{6y \pm \sqrt{36(y^2 - 4z^2)}}{8} \\ &= \frac{6y \pm 6\sqrt{y^2 - 4z^2}}{8} \\ &= \frac{3}{4}y \pm \frac{3}{4}\sqrt{y^2 - 4z^2}\end{align} \\[/tex]

Thus, the factored form of the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex] is [tex]\sf\:(\frac{3}{4}y + \frac{3}{4}\sqrt{y^2 - 4z^2})(\frac{3}{4}y - \frac{3}{4}\sqrt{y^2 - 4z^2}) \\[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

✨[tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Step-by-step explanation:

answer, verified answer

The equation of line passing through the points (-2, 4) & (4, 2) is :

y = -1/3 x + 6

The value of b = 6

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

To find the equation of the line passing through the two points (-2, 4) and (4, 2), we can use the point-slope form of a line. The point-slope form of a line is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is any point on the line.

To find the slope of the line, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two given points.

Plugging in the values for the given points, we get:

m = (2 - 4) / (4 - (-2))

m = -2 / 6

m = -1/3

Next, we can use one of the given points to write the equation in point-slope form:

y - 4 = -1/3 (x - (-2))

y - 4 = -1/3 x + 2

y = -1/3 x + 6

This is the equation of the line passing through the two given points (-2, 4) and (4, 2).

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The candidates received ;

Person A = 734 votes

Person B = 793 votes

Person C = 798 votes

From the information given, we have that;

Now, substitute the values

Person A + Person B + Person C = 2325

Person B - 59 + Person B + Person + B = 2325

Let Person B = x

x -59 + x + x + 5 = 2325

collect like terms

3x = 2325 +54

Add the like terms

3x = 2379

Make 'x' the subject of formula

x = 2379/3

x = 793 votes

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Answer:

x = 5, y = 1

Step-by-step explanation:

For x :

Substitute y into the equation : 5x + 3 ( -1/5x + 2 ) = 28

Simplify : 22/5x + 6 = 28

Isolate x : x = 5

For y :

Substitute x for 5 : y = -1/5 * 5 + 2

Solve: y = 1

Answer:

2nd answer : it is equivalent but not completely factored

Step-by-step explanation:

the "pulling out" of 3 as factor was completely correct.

but

3(x² - 4) can be further factored.

remember :

(a + b)(a - b) = (a² - b²)

therefore,

(x² - 4) = (x + 2)(x - 2)

and then

3(x + 2)(x - 2)

would be a complete factorization.

Answer: B) The expression is equivalent, but is not completely factored

Step-by-step explanation:

Answer: 50 Cups

Step-by-step explanation:

16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48

Two cups in a pint so add 2 to 48 which is 50

Answer:

You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Step-by-step explanation:

To convert between gallons, quarts, and pints, we need to use the following conversions:

1 gallon = 4 quarts

1 quart = 2 pints

Here's the step-by-step process to convert the given volume to cups:

Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts

Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts

Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts

Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts

Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups

Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

The values of x and y for the parallelogram PQRS are respectively, 2 & 7

Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.

Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.

Given that,

The parallelogram PQRS has diagonals PR and SQ that intersects at T,

T is the midpoint of PR and T is the midpoint of SQ

If T is the midpoint of PR, then PT = TR

Given  PT = y and TR = 3x+1

y = 3x+ 1 _____(i)

Also, If T is the midpoint of SQ, then ST = TQ

Given QT=3y and TS=4x+13

3y = 4x+ 13 ____(ii)

Substitute equation 1 into 2;

3y = 4x+ 13

3(3x+1) = 4x+ 13

open the parenthesis

9x+3 = 4x+13

club like terms

9x-4x = 13-3

5x = 10

x = 10/5

x = 2

Substitute x = 2 into equation 1

From 1; y = 3x+1

y = 3(2)+1

y = 6+1

y = 7

Hence, the values are x = 2 and y = 7

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The complete questions :

Parallelogram PQRS has diagonals PR and SQ that intersect at T find the values of x and y PT=y TR=3x+1 QT=3y TS=4x+13

The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

50:7

Step-by-step explanation:

You just put ":" in between the numbers requested.

The solution to the question on the equilibrium of the cheese and bagels have been given below

a) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.

This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.

These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.

The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.

b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.

This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.

These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.

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The value of x in the triangle is 5 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The perimeter of a triangle is the sum of the whole three sides of the triangle.

Hence,

x + 2x + 3 + x + 9 = 32

4x + 12 = 32

subtract 12 from both sides of the equation

4x + 12 = 32

4x + 12 - 12 = 32 - 12

4x = 20

divide both sides of the equation by 4

x = 20 / 4

x = 5

Therefore,

x = 5

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Answer:

It would be a little over 2 hours or so since 16:41 is just 4:41.

2 hours and 16 minutes

Step-by-step explanation:

You're welcome.

Answer:

Step-by-step explanation:

1.1. Advantages of Selling Prepaid Electricity

Two advantages of selling prepaid electricity are:

a) Reduced costs for the municipality: Prepaid meters eliminate the need for the municipality to send meter readers to each property and manually read the meter. This can save the municipality time and money.

b) Improved cash flow: By receiving payment before the electricity is used, the municipality can improve its cash flow as it will have funds available to purchase more electricity.

1.2. Number of Units Mr Nkomo Received When He Bought Prepaid Electricity for R68,02

The rate per kWh including VAT is R1,33. To determine the number of units Mr Nkomo received, we can use the formula:

Units = Amount / Rate

Units = R68,02 / R1,33

Units = 51.04 kWh

So, Mr Nkomo received 51.04 kWh of electricity when he bought prepaid electricity for R68,02.

1.3. Cost of 310 kWh of Electricity

The rate per kWh including VAT is R1,33. To determine the cost of 310 kWh of electricity, we can use the formula:

Cost = Units * Rate

Cost = 310 kWh * R1,33

Cost = R411,30

So, Mr Nkomo will have to pay R411,30 for 310 kWh of electricity.

1.4. Percentage Profit the Municipality Makes When a Customer Buys 290 kWh of Electricity

To determine the percentage profit the municipality makes when a customer buys 290 kWh of electricity, we need to calculate the cost price and the selling price of the electricity. The cost price of electricity is R1,33 per kWh. The selling price is given in the table as R144,72 for 2-50 kWh, R186,06 for 51-350 kWh, R261,87 for 351-600 kWh, and R308,37 for over 600 kWh.

Since the cost price is R1,33 per kWh and the selling price is different for different ranges of units, we need to calculate the cost and selling price for each range of units and find the average.

For 2-50 kWh:

Cost = 2-50 kWh * R1,33

Cost = 50 kWh * R1,33

Cost = R66,50

Selling price = R144,72

Profit = Selling price - Cost

Profit = R144,72 - R66,50

Profit = R78,22

Percentage profit = (Profit / Cost) * 100

Percentage profit = (R78,22 / R66,50) * 100

Percentage profit = 17.7%

For 51-350 kWh:

Cost = 51-350 kWh * R1,33

Cost = 350 kWh * R1,33

Cost = R466,50

Selling price = R186,06

Profit = Selling price - Cost

Profit = R186,06 - R466,50

Profit = R29,56

Percentage profit = (Profit / Cost) * 100

Percentage profit = (R29,56 / R466,50) * 100

Percentage profit = 6.3%

For 351-600 kWh:

Cost = 351-600 kWh * R1,33

Cost = 600 kWh * R1,33

Cost = R798,00

Selling price = R261,87

Profit = Selling price - Cost

Profit = R261,87 - R798,00

Profit = -536,13

Percentage profit = (Profit / Cost) * 100

Percentage profit = (-536,13 / R798,00) * 100

Percentage profit = -67.3%

For over 600 kWh:

Cost = over 600 kWh * R1,33

Cost = R1,33 * 1000

Cost = R1330,00

Selling price = R308,37

Profit = Selling price - Cost

Profit = R308,37 - R1330,00

Profit = -1021,63

Percentage profit = (Profit / Cost) * 100

Percentage profit = (-1021,63 / R1330,00) * 100

Percentage profit = -76.7%

The average percentage profit for the municipality is calculated by finding the total profit and total cost for each range of units and then dividing the total profit by the total cost.

For the range 2-50 kWh, the total profit is R78,22 and the total cost is R66,50, so the average percentage profit is (R78,22 / R66,50) * 100 = 17.7%.

For the range 51-350 kWh, the total profit is R29,56 and the total cost is R466,50, so the average percentage profit is (R29,56 / R466,50) * 100 = 6.3%.

For the range 351-600 kWh, the total profit is -536,13 and the total cost is R798,00, so the average percentage profit is (-536,13 / R798,00) * 100 = -67.3%.

For the range over 600 kWh, the total profit is -1021,63 and the total cost is R1330,00, so the average percentage profit is (-1021,63 / R1330,00) * 100 = -76.7%.

The average percentage profit for the municipality for the four ranges of units is calculated as follows:

Average percentage profit = (17.7% + 6.3% - 67.3% - 76.7%) / 4

Average percentage profit = -34.05%

Therefore, Mr Nkomo's claim that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34% is NOT VALID.

Answer:

Right, Isosceles

Step-by-step explanation:

The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.

The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.

Translation the graph of the function  [tex]y=f(x)[/tex]a units to the right gives you the function [tex]y=f(x-a)[/tex]

If the graph of the function [tex]f(x)=3^{x}[/tex] is translated 6 units to the right, then the function becomes

[tex]g(x)=f(x-6)=3^{x-6}[/tex]

Answer: correct choice is A

The probability that their average length is less than 10 inches is; 5.71%

The formula for z-score is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

x' = 10 inches

μ = 9.7 inches

σ = 1.2 inches

n = 40

Thus;

z = (10 - 9.7)/(1.2/√40)

z = 0.3/0.1897367

z = 1.58

From online p-value from z-score calculator, we have;

P(z < 1.58) = 0.0571 or 5.71%

Read more about probability from the z-score at; https://brainly.com/question/25638875

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