7.24 × 10^4 - 7.21 × 10^3 in scientific notation

Answer: Let's start by calculating the probability that an 18-year-old driver is involved in an accident:

P(accident) = 124/2000 = 0.062

Let's assume that the insurance company pays the full cost of the accident, which is $15,000. Then the expected cost of covering one 18-year-old driver is:

Expected cost = P(accident) x Cost of accident = 0.062 x $15,000 = $930

If the insurance company wants to make a 20% profit on policies, they need to charge a premium that covers their expected cost plus their desired profit. The premium, denoted by P, can be calculated as follows:

P = (Expected cost + Desired profit) / (1 - Profit margin)

where Profit margin is the percentage of the premium that represents the profit. In this case, Profit margin is 20%, or 0.20.

Substituting the values we have calculated, we get:

P = ($930 + 0.20 x $930) / (1 - 0.20)

= $1,236.00

Therefore, the insurance company should charge 18-year-old drivers a premium of $1,236.00 to make a 20% profit on policies.

Step-by-step explanation:

Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\tan(53^o )=\cfrac{\stackrel{opposite}{17}}{\underset{adjacent}{x}}\implies x=\cfrac{17}{\tan(53^o )}\implies x\approx 12.81~meters[/tex]

Answer:

To calculate the fixed expenses each month, we need to add up all the monthly expenses:

Mortgage: $985.64

Cell phone: $58.30

Groceries: $154.00 x 2 = $308.00

Clothing (with 25% job-related): $180.00

Water & electric: $128.40

Weekly dinner & movie: $55.00 x 4 = $220.00

Total monthly fixed expenses: $1,880.34

To calculate how much could be saved per month, we need to first calculate the discretionary income:

Realized income: $2,943.20

Fixed expenses: $1,880.34

Discretionary income: $2,943.20 - $1,880.34 = $1,062.86

25% of discretionary income: 0.25 x $1,062.86 = $265.72

Therefore, the amount that could be saved per month by putting 25% of the discretionary income in a savings account is $265.72.

The slope of the equation is 1/2 and the y-intercept is -5.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

Step 1:

The relationship between x and y can be expressed as:

y = (1/2)x - 5

This equation says that y is equal to half of x, with 5 subtracted from that value.

Step 2:

To graph this equation using the slope-intercept form (y = mx + b), we can identify the slope and y-intercept.

The slope of the equation is 1/2, which means that for every increase of 1 unit in x, y increases by 1/2 unit.

The y-intercept is -5, which is the point where the line crosses the y-axis.

To graph the equation, we can start by plotting the y-intercept, which is the point (0, -5).

Next, we can use the slope to find another point on the line. Since the slope is 1/2, we can move up 1 unit and right 2 units (since the slope is rise over run, or change in y over change in x). This gives us the point (2, -4).

We can now draw a line that connects these two points, which represents the relationship between x and y.

The two points are:

(0, -5)

(2, -4)

The graph of the equation is in the attached image.

Hence, The slope of the equation is 1/2 and the y-intercept is -5.

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The proof that AE is tangent to circle C is given below:

The angle addition postulate is a fundamental concept in geometry that states that the measure of an angle formed by two adjacent angles can be obtained by adding the measures of the two angles.

More specifically, given two adjacent angles with measures A and B, the measure of the angle formed by the two adjacent angles (denoted as AOB) can be found by adding the measures of the two angles:

A + B = AOB

This postulate is often used in geometric proofs and can be applied to any adjacent angles, including those formed by intersecting lines, parallel lines, or polygons.

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Answer: Dan

Step-by-step explanation: In Mrs. Barkley's class, only Dan followed the directions of using the ratio of 4 gems for every 3 flowers.

Dan:

4    20

3  = 15  You can use cross-products to check to see if they are equivalent.

3 x 20 = 4 x 15

60 = 60

Mary:

4       22

3    = 18

4 x 18 = 3 x 22

72 is not equal to 66

Nancy:

4       18

3    = 24

4 x 24 = 3 x 18

96 is not equal to 54

Jason:

4        26

3   =   20

4 x 20 = 3 x 26

80 is not equal to 78

In still air, the jet's speed is 1030 mph, while the wind's speed 240 miles per hour.

It is the rate of change of an object's position with regard to time and a frame of reference. Although it may appear difficult, velocity is essentially speeding in a particular direction. Due to the fact that it is a vector quantity, velocity must be defined in terms of both magnitude (speed) and direction. It has a metre per second SI unit (ms-1).

The distance travelled in relation to the time it took to travel that distance is how speed is defined. As speed simply has a direction and no magnitude, it is a scalar quantity.

Jet's velocity against wind is 2370/3=790 mile per hour and flying with wind it is 10160/8= 1270 miles per hour.

According to question,

Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x−y and with wind is x+y and therefore

x−y=790 and x+y=1270

Adding the two 2x= 2060 and x=1030

and y=240

Hence velocity of jet in still air is 1030 miles per hour and velocity of wind is 240 miles per hour.

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The volume of the composite figure that comprises two cuboids is calculated as: 150 ft³.

The volume of a cuboid is given by the formula:

V = l × w × h

where V is the volume, l is the length, w is the width, and h is the height of the cuboid.

The shape in number 16 comprises two cuboids. Find each and add together.

Volume of smaller cuboid = l × w × h = 5 × 3 × 2

= 30 ft³

Volume of larger cuboid = l × w × h = 10 × 6 × 2

= 120 ft³

The total volume = 150 ft³

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For the given expression -  xº is greater than 0x as,  xº = 1 and 0x = 0.

The power or exponent of a number tells us how many times that number must be multiplied by itself in order to utilise it in a multiplication. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.

According to the law, we must add the exponents to obtain the product of exponential statements that have the same base.

According to the law, we must subtract the exponents in order to divide two exponential expressions with the same base.

Given expression:

xº  = 1 (any number raised to power 0 is always 1)

0x = 0 (any value multiplied with 0 becomes 0).

Thus, xº is greater than 0x as,  xº = 1 and 0x = 0.

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The number of packs of peanut m&m's did they sell that day is 378 packs.

The distance traveled by the plane is 1,008 miles.

The time taken by the plane is 7.78 hours.

Let

Number of peanut sold = x

Ratio of peanut to plain

7 : 10 = x : 540

7/10 = x/540

7 × 540 = x × 10

3,780 = 10x

divide both sides by 10

x = 3,780 / 10

x = 378

When t = 2.8 hours

d = 360t

d = 360(2.8)

d = 1,008 miles

Therefore, the time taken for the plane to fly 2800 miles is;

d = 360t

2800 = 360t

divide both sides by 360

t = 2,800/360

t = 7.78 hours

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To find the constant k for this type of bacteria, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is Euler's number (approximately 2.71828), and k is the constant we're looking for.

We know that the bacteria doubles in number every 25 minutes, which means that after 25 minutes, the number of bacteria will be 2 times the initial number (N0). Therefore, we can write:

N(25) = 2 * N0

Substituting this into the formula, we get:

2 * N0 = N0 * e^(k*25)

Dividing both sides by N0 and simplifying, we get:

2 = e^(25k)

Taking the natural logarithm of both sides, we get:

ln(2) = 25k

Solving for k, we get:

k = ln(2)/25 ≈ 0.0278

Therefore, the equation for modeling the exponential growth of this type of bacteria is:

N(t) = N0 * e^(0.0278t)

*IG:whis.sama_ent

An equation of this line in slope-intercept form is equal to y = 2x + 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (7 + 1)/(0 + 4)

Slope (m) = 8/4

Slope (m) = 2

At data point (0, 7) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 7 = 2(x - 0)  

y - 7 = 2x

y = 2x + 7

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Step-by-step explanation:

Simply divide   lessons   by days      

    69 lessons / 45 days = 1  8/15  =  1.53 lessons per day

The value of c in cubic and quadratic function is -6

When x = -1, the equation of the line becomes:

y = 3(-1) + 4 = 1

We can substitute this value of y into the equation of the curve:

1 = -2(-1)³ - 3(-1)² + 8(-1) + c

Simplifying and solving for c, we get:

1 = 2 - 3 + 8 + c

c = -6

Therefore, the value of c is -6.

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The ratio of US to British coins is 25 to 4.

The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.

First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.

Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.

Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.

25 : 10 :: 10 : 2

Multiplying both sides by 2, we get:

50 : 20 :: 10 : 2

Simplifying, we get:

The ratio of US to British coins is 25 to 4.

2. To calculate Amanda's monthly pay, we can use the formula:

m = 10h + 50

where m is the total money Amanda receives in a month, and h is the number of hours she works.

The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.

3. To calculate the cost of the holiday package for d days, we can use the formula:

C = 190 + 50d

where C is the cost of the holiday package, and d is the number of days.

The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.

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The law of demand applies during online sales of shoes; that is when consumers rush to buy products at 50% discount.​

In Mathematics and Economics, the law of demand can be defined as an economic theory which states that there exist a negative relationship between the price of a product (good) and the quantity of the product (good) that is being demanded by consumers.

This ultimately implies that, holding all the other factors constant, there would be a significant decrease (fall or decline) in the demand for a product (good) and service when the price of a product (good) and service in the market increases (rises), and vice-versa in accordance with the law of demand.

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Complete Question:

The law of ___________applies during online sales of shoes; that is when consumers rush to buy products at 50% discount​

1.  The new volume will be 60 cubic feet. 2. Molly will earn $31.25 if she sells all of the dog beds after subtracting the cost of the fabric.

In general, volume refers to the amount of space occupied by an object or substance, measured in three dimensions: length, width, and height. It is a physical quantity that is typically expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

1. The volume of the cuboid is calculated as follows:

Volume = length x width x height

Volume = 5 ft x 3 ft x 2 ft

Volume = 30 cubic feet

If we double the height, the new height will be 2 x 2 ft = 4 ft. The new volume can be calculated as:

New Volume = length x width x new height

New Volume = 5 ft x 3 ft x 4 ft

New Volume = 60 cubic feet

Therefore, the new volume will be 60 cubic feet.

2. Step 1: Determine how many dog beds Molly can make with the fabric she bought.

Molly bought 12.5 yards of fabric, and she uses 2.5 yards of fabric for each dog bed. We can use division to find how many dog beds she can make:

12.5 yards / 2.5 yards per dog bed = 5 dog beds

Therefore, Molly can make 5 dog beds with the fabric she bought.

Step 2: Calculate the cost of the fabric for each dog bed.

Molly bought the fabric for $4.50 per yard, and she uses 2.5 yards of fabric for each dog bed. Therefore, the cost of the fabric for each dog bed is:

$4.50 per yard x 2.5 yards per dog bed = $11.25 per dog bed

Step 3: Calculate the revenue from selling one dog bed.

Molly sells each dog bed for $17.50.

Step 4: Calculate the profit from selling one dog bed.

Profit = revenue - cost

Profit = $17.50 - $11.25

Profit = $6.25

Step 5: Calculate the total revenue from selling all of the dog beds.

Molly can make 5 dog beds, and each dog bed sells for $17.50. Therefore, the total revenue is:

5 dog beds x $17.50 per dog bed = $87.50

Step 6: Calculate the total cost of the fabric for all of the dog beds.

Molly uses 2.5 yards of fabric for each dog bed, and she can make 5 dog beds. Therefore, the total cost of the fabric is:

2.5 yards per dog bed x 5 dog beds = 12.5 yards

$4.50 per yard x 12.5 yards = $56.25

Step 7: Calculate the total profit from selling all of the dog beds.

Profit = revenue - cost

Profit = $87.50 - $56.25

Profit = $31.25

Therefore, Molly will earn $31.25 if she sells all of the dog beds after subtracting the cost of the fabric.

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Answer:

After 5 half-lives, the remaining mass of the radioactive isotope will be 155 * (1/2)^5 = 4.84375 grams. Rounded to the nearest gram, the answer is 5 grams.

Step-by-step explanation:

The answer is X + 5 = 10

X = 5

Answer:

thats 4th grade math... 0_0               but the answer is 414 ft².

Step-by-step explanation:

So you need to do 23x18 which equals 414. Listen to your teacher in class please kid. But you do you boo

Answer: The margin of error (ME) for a 90% confidence interval using a normal distribution with a known population standard deviation is given by:

ME = z* (σ/√n)

where z* is the z-score corresponding to the desired confidence level (in this case, 90% confidence), σ is the population standard deviation, and n is the sample size.

Using a z-score table or calculator, we find that the z-score corresponding to a 90% confidence level is 1.645.

Substituting the given values, we have:

ME = 1.645 * (40 / √100) = 6.58

Therefore, the margin of error for a 90% confidence interval for the mean score of all students on this test is 6.58. We can report the 90% confidence interval as:

180.23 ± 6.58 or (173.65, 186.81)

Step-by-step explanation:

Answer:The diagram shows the market demand and supply curves for the bread market. You know that there are 250 identical bakeries operating in the market

Step-by-step explanation:

Answer:

Step-by-step explanation:

If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q =  3x² - x + 2 + x² + 5x - 6 =

4x^2 +4x - 4

D = 16 + 64 = 80

x12 = [tex]\frac{-4+-\sqrt{80} }{8}[/tex]

Answer:

To find the slope of the line tangent to the graph of the function at x = -3, we need to find the derivative of the function and evaluate it at x = -3.

First, let's find the derivative of the function y = x^4 + 2x^3 + 2x + 2:

y' = 4x^3 + 6x^2 + 2

Now, let's evaluate y' at x = -3:

y'(-3) = 4(-3)^3 + 6(-3)^2 + 2

= -108 + 54 + 2

= -52

Therefore, the slope of the line tangent to the graph of the function y = x^4 + 2x^3 + 2x + 2 at x = -3 is -52.

Answer:

39/2 or 19.5

Step-by-step explanation:

To evaluate the expression 1/2x + 2y when x = 7 and y = 8, we can substitute the values of x and y into the expression and perform the necessary calculations.

Given:

x = 7

y = 8

Plugging these values into the expression, we get:

1/2(7) + 2(8)

Now, we can follow the order of operations (PEMDAS/BODMAS) to simplify the expression:

1/2(7) + 2(8)

= 1/2 * 7 + 2 * 8 (Multiplication has higher precedence than addition)

= 7/2 + 16 (Performing the multiplications)

= 7/2 + 32/2 (Finding the common denominator for addition)

= (7 + 32)/2 (Adding the numerators)

= 39/2 (Simplifying the fraction)

So, the value of the expression 1/2x + 2y when x = 7 and y = 8 is 39/2 or 19.5.

The radioactive isotope has a final mass of 523 grams.

Herein we find the case of a radioactive isotope, whose mass is decreasing exponentially in time. Whose expression is described below:

m(x) = a · (1 - r / 100)ˣ

Where:

If we know that a = 1500, r = 10 and x = 10, then the mass of the radioactive isotope is:

m(10) = 1500 · 0.90¹⁰

m(10) = 523.018

The final mass of the radioactive isotope is equal to 523 grams.

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Thus, the solution of the given cosine function is obtained for the angles-  θ = 30º and θ = 330º between the intervals of [0,2pi).

The ratio of the triangle's side next to the angle to the hypotenuse is known as the cosine function. Thus, the cosine function does have a period of 2π, we can say.

Normally, radians rather than degrees are used when examining the cosine function in this manner. The common unit of measurement for angles in mathematics is the radian. 360° is equivalent to two radians, or one full circle.

Given data:

1-cosθ = (2-√3)/2

cosθ = 1-(2-√3)/2

isolating the cosθ function:

cosθ = 1-(1-[√3/2])

cosθ = 1-1+√3/2

cosθ = √3/2

Now,

cos is  √3/2 for ∏/6 = 30º and for 11∏/6 = 330º (Interval - [0,2pi))

Thus, the solution of the given cosine function is obtained for the angles-

θ = 30º and θ = 330º between the intervals of [0,2pi).

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