Alex tested three brands of batteries to learn which would last the longest in a flashlight. He placed two brand “A” batteries in a flashing, turned the flashlight on, and measured the time and the light shined. He repeated the experiment with battery brands “B” and “C” using the same flashlight. He recorded the data on the bar graph below.

Which of these is an accurate conclusion that Alex can make about the batteries he tested?

A. Brand “C batteries lasted twice as long as brand “A” batteries.

B. Brand “C” batteries listed three times longer than brand “B” batteries

C. The light was twice as bright with brand “A” batteries than with brand “B” batteries.

D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.

Complete question :

The American Automobile Association (AAA) reports that of car accidents, 56% are caused by aggressive driving. If 3 accidents are chosen at random, find the probability for the following. Please round the final answers to 2 or 3 decimal places.

None are caused by aggressive driving.

At least 1 is caused by aggressve driving

Answer:

P(none caused by aggressive driving ) = 0.085184

P(atleast one caused by aggressive drive) = 0.914816

Step-by-step explanation:

Given:

Percentage accidents caused by aggressive driving = 56%

Hence,

Probability that an accident is caused by aggressive driving : p(aggressive) = 0.56

p(not aggressive) = 1 - p(aggressive)

p(not aggressive) = 1 - 0.56 = 0.44

A.) If 3 accidents are chosen at random ; probability that none is caused by aggressive driving :

Independent probability :

1st accident * 2nd accident * 3rd accident

P(not aggressive) * p(not aggressive) * p(not aggressive)

0.44 * 0.44 * 0.44 = 0.085184

B.) probability that atleast one is caused by aggressive driving :

Probability that atleast 1 is caused by aggressive driving = (1 - probability that none is caused by aggressive driving)

= 1 - 0.085184 = 0.914816

Answer:

the answer is 50!!! it sure is

D. y=2sec[2(x+pi )]-2

Step-by-step explanation:

The correct option is that C. Carmen disagreed and said, "No, the answer is 72x^12"

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

It should be noted that when dividing exponents with same base, we will subtract the powers and when multiplying them, we will add the powers.

Here, the study team was discussing how to multiply 6x^10 by 12x^2. Therefore, this will be:

= 72 × x^(10 + 2)

= 72x^12.

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Answer: 31.57

Step-by-step explanation:

41% of 77 is what?

41% of 77 is Y

Equation: P% * X = Y

Solving our equation for Y

Y = P% * X

Y = 41% * 77

Converting percent to decimal:

p = 41%/100 = 0.41

Y = 0.41 * 77

Y = 31.57

The number would you add to both sides of x² + 7x = 4 to complete the square option C 7²/2.

Suppose the considered quadratic equation is of the form

ax^2 + bx + c = 0

Then, completing the squares method tries to make a squared term in terms of x in the left side, so that x comes in linear form, instead of quadratic.

The given quadratic equation is

x² + 7x = 4

add  7²/2 to both sides of x² + 7x = 4 to complete the square

7²/2 = 49/4

x² + 7x + 49/4 = 4+ 49/4

(x + 7/2)² = 4+ 49/4

Thus, option C 7²/2 is correct.

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x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

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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.

From what I see in the problem, the expression is

\((\frac{3^a^2}{3a^-1} )^k\)

To solve, plug in a and k.

\((\frac{3^(5)^2}{3*5^-1} )^-2\)

3*5^2=75

(3*5)^-1 = 1/15

\(75 / \frac{1}{15} = 5\)

5^-2 = 1/25

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

Let y represent the population after x years.

Given that the growth rate is 4.5% per year and the current population is 1500.

Hence a = 1500, b = 100% + 4.5% = 104.5% = 1.045

y = 1500(1.045)ˣ

After 6 years:

y = 1500(1.045)⁶ = 1953

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

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The evaluation of the trigonometric identities to find the sine of the sum of angles A and B, using the values for cos(A) and sin(B) indicates;

15. sin(A + B) = -52/85

16. A + B is in Quadrant III

Trigonometric identities are equations involving trigonometric ratios that are true for the values of the input variables.

15. cos(A) = -15/17, sin(B) = 4/5

The trigonometric identity for the sine of the  addition of two angles, the addition formula indicates that we get;

sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)

cos(B) = √(1 - (4/5)²) = √(1 - 16/25) = 3/5

sin(A) = √(1 - (-15/17)²) = 8/17

Therefore; sin(A + B) = (8/17) × (3/5) + (-15/17) × (4/5) = -52/85

16. π/2 < A < π, and 0 < B < π/2

Therefore; π/2 + 0 < A + B < π + π/2

The solution from the previous question indicates that we get;

sin(A + B) = -52/85

The sine of an angle is negative in the third and fourth quadrant

The fourth quadrant is; π + π/2 < θ < 2·π

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Answer: Graph 2

Step-by-step explanation:

The intervals in which the function is decreasing. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\). Option 3

We're given a function f(x) = 2 sin x - x, which describes a curve on a graph. We want to find the intervals where this curve is decreasing (going down) within the range of -π to π.

To find when the function is decreasing, we look at its slope. The slope tells us if the curve is going up or down. We find the slope by taking the first derivative of the function: f'(x) = 2 cos x - 1.

We now have an equation for the slope, f'(x) = 2 cos x - 1. A negative slope means the function is decreasing. So, we want to find where f'(x) is less than 0 (negative).

We set up the inequality: 2 cos x - 1 < 0. We solve it to find the x-values where the slope is negative. The solution is cos x < 1/2.

From the inequality cos x < 1/2, we find the intervals within the range of -π to π where the function is decreasing. These intervals are [-π, -π/3] and [π/3, π].

The above answer is in response to the question below as seen in the picture.

Determine the interval(s) in \([-\pi, \pi ]\) on

which f(x) =  2 sin x - x

is decreasing.

1. \([-\frac{\pi }{3}, \frac{\pi }{3} ]\)

2. \([-\frac{\pi }{6}, \frac{\pi }{6} ]\)

3. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\)

4. \([-\pi , -\frac{-2\pi }{3} ], [\frac{2\pi }{3}, \pi ]\)

5. \([-\pi , - \frac{5x}{6} ], [\frac{\pi }{6}, \pi ]\)

6. \([-\frac{\pi }{6}, \frac{5\pi }{6} ]\)

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The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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In a case where a = 11 ft, b = 5 ft, and c = 7 ft, the surface area of the geometric shape formed by this net is B. 145 sq. ft.

The concept that will be used here is area of triangle, we will we need need to know the area of the first 2 triangles

The area of the triangle can be expressed as :

A =( 1/2 bh)

A = (1/2 ba)

Then substitute the values we have,

a = [1/2 (11 ft.) (5 ft)]

a =  27.5 sq ft.

Then we can find the value of the area as :

A = [1/2 c*b]

If we substitue the values we,

a = [1/2 (5 ft) (7 ft)]

= 17.5 sq. ft

Then we can proceed to calculate the area of the rectangle which can be done using the formula:

A = (lw) where a = (11 ft.)(5 ft.) = 55 sq. ft

We can now find the summation of all the a's as :

[2(27.5) + 2(17.5 ) + 55 ]

= 145 sq. ft.

Therefore, option B is correct.

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missing options:

A. 167 sq. ft.

B. 145 sq. ft.

C. 117.5 sq. ft.

D. 147 sq. ft.

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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$2.4 is the discount used to purchase a pair of sunglasses

percentage, a relative value indicating hundredth parts of any quantity.

Given that Alexandra bought a pair of sunglasses online for $24.

She used a coupon code to get a 20% discount.

The website also applied a 10% processing fee to the price after the discount.

20%-10%=10%

Now 10% of price is 24

10/100×24=x

2.4=x

24+2.4=26.4 is the actual price.

Hence, $2.4 is the discount used to purchase a pair of sunglasses

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Step-by-step explanation:

to\(3w - 7 = \sqrt{8w - 7} \\ {(3w - 7)}^{2} = ({ \sqrt{8w - 7} })^{2} \\ 9 {w}^{2} - 42w + 49 = 8w - 7 \\ 9 { w}^{2} - 42w - 8w + 49 + 7 = 0 \\ 9 {w}^{2} - 50w + 56 = 0 \\ (9w - 14)(w - 4) = 0 \\ w = \frac{14}{9} \: or \: w = 4\)

to make sure the answer

substitute w = 14/9 and w = 4 to the equation.

if w = 14/9

\(3w - 7 = \sqrt{8 w - 7} \\ 3 \times \frac{14}{9} - 7 = \sqrt{8 \times \frac{14}{9} - 7} \\ - \frac{ 7}{3} = \frac{7}{3} \)

we know that if we substitute w = 14/9, the answer is not the same.

if w = 4

\(3w - 7 = \sqrt{ 8 w - 7 } \\ 3 \times 4 - 7 = \sqrt{8 \times 4 - 7} \\ 5 = 5\)

if we substitute w = 4 the answer is the same.. we can conclude the the answer of 3w - 7 = √8w - 4 is 4

Answer:is the first answer 15.875 and the second answer 17 x 28 ÷5

Step-by-step explanation:

Answer:

8 mm

Step-by-step explanation:

Answer attached....

Hope it helps :)

Answer:

a = 8mm is the answer

Step-by-step explanation:

a = ?

b = 6mm

c = 10mm

By using the Pythagoras theorem,

a² + b² = c²

a² + 6² = 10²

a² + 36 = 100

a² = 100 - 36

a² = 64

a = 8

∴ a = 8mm is the length of the missing leg

For a variety of reasons, files on your computer shouldn't be destroyed. One, you might have to keep them since your work is crucial. Two, I should have them just in case.

A computers is a piece of electrical equipment used to manipulate data or information. It has the ability to store, retrieve, and process data.You may already be aware of the fact you are able to use a computers to surf the Internet, send emails, type documents, and play games.

Modern computers are given their names after the jobs that they replaced. The term "computer" was first used in the English language in the 17th century to refer to a person who performed mathematical computations. It made its first mention of a calculator in 1897. The "human" computer is now outdated in the age of the "machine."

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Answer:

See below

Step-by-step explanation:

The perimeter of a rectangle is \(P=2L+2W\) where L is the length and W is the width.

The scientific notation of the given number is 1.24×10⁻⁶.

The given number is 0.00000124.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 0.00000124=1.24×10⁻⁶.

Therefore, the Scientific notation of the given number is 1.24×10⁻⁶.

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Answer:

12 packages of water

5 packages of cheese sticks

Step-by-step explanation:

The LCM (least common multiple) of 5 and 12 is 60.

w = # of pkgs of water

c = # of pkgs of cheese sticks

5w = 12c = 60

w = 60/5 = 12

c = 60/12 = 5

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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