Find the discount for a $455 designer purse that is on sale for 30% off.

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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To find the number that corresponds to 22% of a given value, you can divide the given value by 22% (or 0.22).

Let's use this approach to find the number:

3300 ÷ 0.22 = 15,000

So, 22% of 15,000 is equal to 3300.

Answer:

x = 15000

Step-by-step explanation:

If you are using a calculator, simply enter 3300×100÷22, which will give you the answer.

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

The required angle is .

Given the triangle and name it as triangle ABC. In triangle ABC, ∠C = 29 and AB =6.78, BC=4, AC = 10.

To find angle A in triangle ABC, use the Law of Cosines, which states:

[tex]c^2 = a^2 + b^2[/tex]- 2ab x cos(C)

That implies,

AB = 6.78 (side a)

BC = 4 (side b)

AC = 10 (side c)

∠C = 29°

Substituting the given values into the Law of Cosines formula, gives:

[tex]10^2 = 6.78^2 + 4^2[/tex] - 2 x 6.78 x 4 x cos(29°)

Simplifying the equation:

100 = 46.2084 + 16 - 54.24 x cos(29°)

Rearranging the equation to isolate the cosine term:

54.24 x cos(29°) = 46.2084 + 16 - 100

54.24 x cos(29°) = -37.7916

Solve for the cosine term:

cos(29°) = -37.7916 / 54.24

cos(29°) = -0.696

To find angle A,  use the inverse cosine (cos⁻¹) function:

∠A = cos⁻¹(-0.696)

Calculating the value of angle A using a calculator or trigonometric table, we find:

∠A = 133.64°

Therefore, angle A in triangle ABC is approximately 133.64°.

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Answer:

y = -x + 8

Step-by-step explanation:

Let's break down the equation step by step to understand it better.

The equation in point-slope form is given as:

y - y1 = m(x - x1)

In this case, we have:

y - 0 = -1(x - 8)

The point-slope form uses a specific point (x1, y1) on the line and the slope (m) of the line.

Here, the point (x1, y1) is (8, 0), which represents a point on the line. This means that when x = 8, y = 0. The graph has a point at (8, 0), which confirms this information.

The slope (m) is -1 in this equation. The slope represents the rate at which y changes with respect to x. In this case, since the slope is -1, it means that for every unit increase in x, y decreases by 1. The negative sign indicates that the line has a downward slope.

By substituting the values into the equation, we get:

y - 0 = -1(x - 8)

Simplifying further:

y = -x + 8

This is the final equation of the line in slope-intercept form. It tells us that y is equal to -x plus 8. In other words, the line decreases by 1 unit in the y-direction for every 1 unit increase in the x-direction, and it intersects the y-axis at the point (0, 8).

If the graph has points at (0, 8) and (8, 0), the equation y = -x + 8 accurately represents that line.

The algorithm justifies the answer of 3/5 as the fraction each person gets.

Representation of the fractions on the second row:

From what you described, two of the loaves were divided into thirds.

This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.

Therefore, each person receives one fifth from this remaining third.

So, the representation of the fractions on the second row would be:

Each person receives 1/3 (one third) from the two loaves.

Each person receives 1/5 (one fifth) from the remaining third.

Algorithm/Abstract strategy to justify the 3/5 found as the answer:

To find the final answer of 3/5, we can follow the steps you provided:

Divide two loaves into thirds, giving each person 1/3.

Divide the remaining third from the second loaf into fifths, giving each person 1/5.

Combining the fractions, each person has 1/3 + 1/5.

To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:

1/3 = 5/15 (multiplying numerator and denominator by 5)

1/5 = 3/15 (multiplying numerator and denominator by 3)

Now, we can add the fractions:

5/15 + 3/15 = 8/15

Therefore, each person receives 8/15 of a loaf.

Simplifying this fraction, we get 3/5.

Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.

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Answer:

.35x = 140(.15)

.35x = 21

x = 60 oz of 35% salt.

The scientist will need 60 oz of the 35% salt solution and 80 oz of water.

The center of mass of the system is approximately (3.7, 2.6).

The center of mass of a system of objects is the point where all the weight of the system appears to be concentrated. It can be defined as the average location of the weighted parts of the system.

The center of mass of a system is dependent on the mass of the objects in the system and their positions.

Let's determine the center of mass of the system with masses of 2, 3, and 5 at the points (-1, 2), (1, 1), and (3, 3), respectively. Let's name the masses m1, m2, and m3, respectively, and the coordinates (x1, y1), (x2, y2), and (x3, y3).

The x-component of the center of mass is given by the formula:

x= (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)

The y-component of the center of mass is given by the formula:

y= (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)

By using the given values, let's calculate the x and y components of the center of mass:

x = (2 x -1 + 3 x 1 + 5 x 3) / (2 + 3 + 5) = 37/10 ≈ 3.7y

= (2 x 2 + 3 x 1 + 5 x 3) / (2 + 3 + 5)

= 26/10 = 2.6

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Answer:

1.452

Step-by-step explanation:

1.45169 rounded to the thousandths place would be 1.452

The nearest tenth, approximately 93.5% of Container A is full after the water is pumped into Container B.

To determine the percentage of Container A that is full after the water is pumped into Container B, we need to compare the volumes of the two containers.

The volume of a cylinder can be calculated using the formula: V = πr^2h, where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height.

For Container A:

Radius (r) = Diameter / 2 = 12 ft / 2 = 6 ft

Height (h) = 14 ft

For Container B:

Radius (r) = Diameter / 2 = 10 ft / 2 = 5 ft

Height (h) = 20 ft

Now, let's calculate the volumes of the two containers:

Volume of Container A = π * (6 ft)^2 * 14 ft ≈ 1,679.65 ft^3

Volume of Container B = π * (5 ft)^2 * 20 ft ≈ 1,570.8 ft^3

To find the percentage of Container A that is full, we need to calculate the ratio of the volume of water in Container B to the volume of Container A:

Ratio = Volume of Container B / Volume of Container A

Ratio = 1,570.8 ft^3 / 1,679.65 ft^3 ≈ 0.9347

Finally, to convert this ratio to a percentage, we multiply it by 100:

Percentage = Ratio * 100

Percentage ≈ 0.9347 * 100 ≈ 93.5%

Therefore, to the nearest tenth, approximately 93.5% of Container A is full after the water is pumped into Container B.

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Answer:

1 < m < 4

Step-by-step explanation:

If the roots of function f(x) are not real, then the discriminant (the part under the square root sign) will be negative.

Set the discriminant less than zero and rewrite in standard form:

[tex]\begin{aligned}16-4m(-m+5)& < 0\\16+4m^2-20m& < 0\\4m^2-20m+16& < 0\\4(m^2-5m+4)& < 0\\m^2-5m+4& < 0\end{aligned}[/tex]

Factor the quadratic:

[tex]\begin{aligned}m^2-5m+4& < 0\\m^2-4m-m+4& < 0\\m(m-4)-1(m-4)& < 0\\(m-1)(m-4)& < 0\end{aligned}[/tex]

The leading coefficient of the quadratic m² - 5m + 4 is positive.

Therefore, the graph will be a parabola that opens upwards.

This means that the interval where the parabola is below the x-axis (negative) is between the zeros of the quadratic. Since the zeros are m = 1 and m = 4, the solution to the inequality is 1 < m < 4.

Therefore, the values of m for which the roots of function f(x) will be non-real are 1 < m < 4.

Answer: 8C3

Step-by-step explanation: You need to use Combinations for this. Out of 8, you need to select 3, so answer is 8C3.

Multiply three consecutive digits backwards starting from 8, and divide by 3 factorial

(8*7*6)/(3*2*1)

=56

The values of b and c is 5 and 6.

To factorize the trinomial x² + 5x + 6, we need to find two integers whose product is 6 and whose sum is 5.

From the given table, we can see that the integers 2 and 3 satisfy these conditions.

Therefore, we can rewrite the trinomial as:

x² + 5x + 6 = x² + 2x + 3x + 6

x² + 2x + 3x + 6 = (x² + 2x) + (3x + 6)

Now, we can factor out the common terms from each group:

x² + 2x + 3x + 6 = x(x + 2) + 3(x + 2)

                          = (x + 2)(x + 3)

Therefore, the factored form of the trinomial x² + 5x + 6 is (x + 2)(x + 3).

Regarding the values of b and c, we can see that b = 5 and c = 6 in the trinomial x² + 5x + 6.

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Answer:

total annual cost: 49313

cost per mile: 14 cents

Step-by-step explanation:

find total annual cost by adding everything up

find cost per mile by doing 4897/34500

cost/ miles

we use variable cost since the only thing that might change each year is the amount of miles they drive

fixed costs are fixed and don't change

Answer:

880 feet

Step-by-step explanation:

To find out how many feet a car traveling at 60 miles per hour travels in 10 seconds, we need to convert the speed from miles per hour to feet per second.

1 mile = 5,280 feet (5280 feet = 1 mile)

1 hour = 60 minutes

1 minute = 60 seconds

To convert 60 miles per hour to feet per second, we can use the following steps:

First, convert miles per hour to feet per minute:

60 miles/hour * 5280 feet/mile = 316,800 feet/hour

Then, convert feet per hour to feet per minute:

316,800 feet/hour / 60 minutes/hour = 5,280 feet/minute

Finally, convert feet per minute to feet per second:

5,280 feet/minute / 60 seconds/minute = 88 feet/second

Therefore, a car traveling at 60 miles per hour would travel 88 feet in 1 second. In 10 seconds, it would travel:

88 feet/second * 10 seconds = 880 feet.

If the dimensions of your driveway are 10.2 ft. by 15.7 ft and the tarp covers your entire driveway,  the square feet are covered is [tex]160.14ft^{2}[/tex]

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

With the given conditions,  we can formulate the expression as

;10.2 ft. * 15.7 ft

=160.14

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Blue Jelly beans are 0.1764 part of total .

Given,

Total beans = 17

Blue = 3

Red =2

White =4

Green =8

Now,

Out of total , green jelly beans = 8/17

Out of total , red jelly beans = 2/17

Out of total , white jelly beans = 4/17

Out of total , blue jelly beans = 3/17

Hence the blue jelly beans are 0.1764 part of total jelly beans .

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Answer:

To write the result in lowest terms, we need to simplify the fractions by dividing both the numerator and the denominator by their greatest common factor (GCF). Here are the solutions for each problem:

1.) -15-(5)= -20. This is already in lowest terms because it is an integer.

2.) 5/9 divided by 10/18= (5/9) * (18/10) = 90/90 = 1. This is in lowest terms because the GCF of 90 and 90 is 90.

3.) 2/5+4/7= (14/35)+(20/35) = 34/35. This is in lowest terms because the GCF of 34 and 35 is 1.

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Answer:

Step-by-step explanation:

To find the volume of the storage bin, we need to calculate the volumes of both the cylindrical portion and the conical top, and then add them together.

The volume of the cylindrical portion can be calculated using the formula:

V_cylinder = π * r^2 * h

where r is the radius and h is the height of the cylindrical portion.

Substituting the given values, we have:

V_cylinder = π * (4.9 ft)^2 * 9.7 ftV_cylinder ≈ 748.07 ft³ (rounded to two decimal places)

The volume of the conical top can be calculated using the formula:

V_cone = (1/3) * π * r^2 * H_cone

where r is the radius and H_cone is the height of the conical top.

The height of the conical top can be obtained by subtracting the height of the cylindrical portion from the overall height:

H_cone = H - h = 16.3 ft - 9.7 ft = 6.6 ft

Substituting the given values, we have:

V_cone = (1/3) * π * (4.9 ft)^2 * 6.6 ftV_cone ≈ 243.24 ft³ (rounded to two decimal places)

To find the total volume, we add the volume of the cylindrical portion and the volume of the conical top:

Total volume = V_cylinder + V_cone

Total volume ≈ 748.07 ft³ + 243.24 ft³

Total volume ≈ 991.31 ft³ (rounded to one decimal place)

Therefore, the volume of the storage bin is approximately 991.3 ft³ (rounded to the nearest tenth).

Thus the required volume is, 975.05  ft³

Given that,

radius = r = 4.9

Height of cylindrical potion = h = 9.7

Overall height = 16.3

Since,

total height = Height of the cylinder + height of the cone

Height of the cone = 16.3 - 9.7

                                = 6.6 m

Since we know that,

Volume of a cylinder = πr² h

⇒ π (4.9)²(9.7)

⇒ 731.29 ft³

Since we also know that

Volume of a cone = (1/3)πr² h

= 731.29/3

= 243.76  ft³

Volume of the bin = volume of cone + volume of cylinder

= 731.29 ft³  + 243.76  ft³

Hence the volume be,

= 975.05  ft³

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Step-by-step explanation:

triangle EFG is an isosceles triangle

angle G

= 180°-58°

= 122° (adj. angles on a str. line)

angle F

= (180°-122°)÷2

= 29° (angles in a triangle)

1

Because the number 97 is a prime number

Answer:

The greatest common factor (GCF) of two numbers is the largest number that divides evenly into both numbers. Since 97 is a prime number and 24 is not divisible by 97, the GCF of 97 and 24 is 1.

Answer:

D

Step-by-step explanation:

the right triangle contains h , the horizontal leg and the sloping side which is the hypotenuse of the right triangle.

the horizontal leg is half the measure of the side of the square base.

horizontal leg = 8 ÷ 2 = 4

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

h² + 4² = 10² ( subtract 4² from both sides )

h² = 10² - 4² ( take square root of both sides )

h = [tex]\sqrt{10^2-4^2}[/tex]

To determine the number of light bulbs expected to last between 2030 hours and 2060 hours, we need to calculate the z-scores corresponding to these values and then use the z-score formula to find the proportion of light bulbs within this range.

The z-score formula is given by:

z = (x - μ) / σ

where:

x = value

μ = mean

σ = standard deviation

For 2030 hours:

z1 = (2030 - 2000) / 25

For 2060 hours:

z2 = (2060 - 2000) / 25

Now, we can use the z-scores to find the proportions associated with each value using a standard normal distribution table or calculator. The table or calculator will provide the area/proportion under the normal curve between the mean and each z-score.

Let's calculate the z-scores and find the proportions:

z1 = (2030 - 2000) / 25 = 1.2

z2 = (2060 - 2000) / 25 = 2.4

Using a standard normal distribution table or calculator, we can find the proportions corresponding to these z-scores:

P(z < 1.2) ≈ 0.8849

P(z < 2.4) ≈ 0.9918

To find the proportion of light bulbs expected to last between 2030 hours and 2060 hours, we subtract the cumulative probabilities:

P(2030 < x < 2060) = P(z1 < z < z2) = P(z < z2) - P(z < z1)

P(2030 < x < 2060) ≈ 0.9918 - 0.8849

Finally, we multiply this proportion by the total number of light bulbs (665) to get the estimated number of light bulbs expected to last between 2030 hours and 2060 hours:

Number of light bulbs ≈ (0.9918 - 0.8849) * 665

Rounding to the nearest whole number, the expected number of light bulbs that would last between 2030 hours and 2060 hours is approximately 71.[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

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Edwin needs to sell 44,625 jars of jam to break even.

To determine how many jars of jam Edwin needs to sell to break even, we'll calculate the breakeven point using the following formula:

Breakeven Point = Fixed Expenses / (Selling Price per Unit - Variable Cost per Unit)

Given information:

Selling Price per Unit (SP) = $1.90

Variable Cost per Unit (VC) = $1.10

Fixed Expenses = $35,700.00 per year

Plugging in the values into the formula:

Breakeven Point = $35,700 / ($1.90 - $1.10)

Breakeven Point = $35,700 / $0.80

Breakeven Point = 44,625 jars

Therefore, Edwin needs to sell 44,625 jars of jam to break even.

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The Equation of line is y= -3/2x + 60

From the graph we take two coordinates as (2, 0) and (0, 3)

We know the formula for slope

Slope= (Change in y)/ (Change in x)

Slope = (3-0)/ (0-2)

Slope= 3 / (-2)

Slope= -3/2

Now, Equation of line

y - 0 = -3/2 (x-  2)

y= -3/2x + 6

Thus, the Equation of line is y= -3/2x + 60.

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a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

We have,

To find the mean and standard deviation for the first year of the contract, we can use the given information and the properties of the normal distribution.

Given:

The mean salary for professors in the previous year = $62,000

Standard deviation in the previous year = $2,000

Raise in the first year = $1,500

Mean for the first year of the contract:

The mean salary for the first year can be obtained by adding the raise to the previous mean:

Mean = Previous Mean + Raise

Mean = $62,000 + $1,500

Mean = $63,500

The standard deviation for the first year of the contract:

Since each professor receives the same raise, the standard deviation remains the same:

Standard Deviation = $2,000

Therefore, for the first year of the contract, the mean salary is $63,500, and the standard deviation remains $2,000.

Now,

In the second year of the contract, each professor receives a 3% raise based on their salary during the first year of the contract.

To find the mean and standard deviation for the second year, we can use the given information and the properties of the normal distribution.

Mean for the second year of the contract:

To calculate the mean for the second year, we need to add a 3% raise to the mean salary of the first year:

Mean = Mean of the first year + (3% * Mean of the first year)

Mean = $63,500 + (0.03 * $63,500)

Mean = $63,500 + $1,905

Mean = $65,405

The standard deviation for the second year of the contract:

Since each professor receives a raise based on their salary from the first year, the standard deviation also increases. To calculate the standard deviation, we multiply the standard deviation from the first year by the percentage increase:

Standard Deviation = Standard Deviation of the first year * (Percentage Increase / 100)

Standard Deviation = $2,000 * (3 / 100)

Standard Deviation = $2,000 * 0.03

Standard Deviation = $60

Therefore, for the second year of the contract, the mean salary is $65,405, and the standard deviation is $60.

Thus,

a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

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Based on the functions given, it should be noted that the values will be 2, -2x and -8x.

Using the definition of the derivative, we have:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

= lim(h->0) [2(x + h) - 2x] / h

= lim(h->0) 2h / h

= lim(h->0) 2

= 2

Therefore, f'(x) = 2.

For f(x) = 9 - x²:

Using the definition of the derivative, we have:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

= lim(h->0) [9 - (x + h)² - (9 - x²)] / h

= lim(h->0) [9 - (x² + 2xh + h²) - 9 + x²] / h

= lim(h->0) [-2xh - h²] / h

= lim(h->0) (-2x - h)

= -2x

Therefore, f'(x) = -2x.

For f(x) = -4x²:

Using the definition of the derivative, we have:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

= lim(h->0) [-4(x + h)² - (-4x²)] / h

= lim(h->0) [-4(x² + 2xh + h²) + 4x²] / h

= lim(h->0) [-4x² - 8xh - 4h² + 4x²] / h

= lim(h->0) [-8xh - 4h²] / h

= lim(h->0) (-8x - 4h)

= -8x

Therefore, f'(x) = -8x.

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