help me with this question please

The expression equivalent to [tex]V(8y^4√√x / 5x * By^2√x / 5 * 5√√x * 8y^2 / 5x√√x * 8y^4) is V(Bx^7) * x^(1/4) / 5.[/tex]

The given expression is:

[tex]V(8y^4 * √√x / 5x) * (By²√x / 5) * √√x * 8y^2 / (5x√√x * 8y^4)[/tex]

To simplify this expression, let's break it down step by step:

Step 1: Simplify the terms inside the square root (√) and the fourth root (√√):

[tex]√√x = x^(1/4)√√x * 8y^2 = 8y^2 * x^(1/4)[/tex]

Step 2: Simplify the terms with exponents:

[tex]8y^4 * x^(1/4) = 8y^4x^(1/4)8y^2 * x^(1/4) = 8y^2x^(1/4)5x * x^(1/4) = 5x^(5/4)5x√√x = 5x^(5/4)[/tex]

Step 3: Simplify the remaining terms:

[tex]V(8y^4x^(1/4) / 5x) * (By^2x^(1/4) / 5) * 5x^(5/4) / (8y^4)[/tex]

Step 4: Cancel out common factors:

[tex]V(x^(1/4) / 5) * (Bx^(1/4) / 5) * x^(5/4)[/tex]

Step 5: Combine the expressions under the square root:

[tex]V(Bx^(1/4) * x^(1/4) * x^(5/4)) / 5 * 5 * x^(1/4)[/tex]

Step 6: Simplify the exponents:

V[tex](Bx * x * x^5) / 5 * 5 * x^(1/4)[/tex]

Step 7: Combine the terms inside the square root:

V([tex]Bx^7) / 5 * 5 * x^(1/4)[/tex]

Step 8: Simplify the remaining expression:

V(B[tex]x^7) * x^(1/4) / 5[/tex]

Therefore, the expression equivalent to [tex]V(8y^4√√x / 5x * By^2√x / 5 * 5√√x * 8y^2 / 5x√√x * 8y^4) is V(Bx^7) * x^(1/4) / 5[/tex]

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The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

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Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

[tex]\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}[/tex],

where [tex]\displaystyle \nabla \times \mathbf{H}[/tex] is the curl of the magnetic field intensity [tex]\displaystyle \mathbf{H}[/tex], [tex]\displaystyle \mathbf{J}[/tex] is the current density, and [tex]\displaystyle \frac{\partial \mathbf{D}}{\partial t}[/tex] is the time derivative of the electric displacement [tex]\displaystyle \mathbf{D}[/tex].

In this problem, there is no current density ([tex]\displaystyle \mathbf{J} =0[/tex]) and no time-varying electric displacement ([tex]\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0[/tex]). Therefore, the equation simplifies to:

[tex]\displaystyle \nabla \times \mathbf{H} =0[/tex].

Taking the curl of the given magnetic field intensity [tex]\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}[/tex]:

[tex]\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}[/tex].

Using the curl identity and applying the chain rule, we can expand the expression:

[tex]\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].

Since the magnetic field intensity [tex]\displaystyle \mathbf{R}[/tex] is not dependent on [tex]\displaystyle y[/tex] or [tex]\displaystyle z[/tex], the partial derivatives with respect to [tex]\displaystyle y[/tex] and [tex]\displaystyle z[/tex] are zero. Therefore, the expression further simplifies to:

[tex]\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].

Differentiating the cosine function with respect to [tex]\displaystyle x[/tex]:

[tex]\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].

Setting this expression equal to zero according to [tex]\displaystyle \nabla \times \mathbf{H} =0[/tex]:

[tex]\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0[/tex].

Since the equation should hold for any arbitrary values of [tex]\displaystyle \mathrm{d} x[/tex], [tex]\displaystyle \mathrm{d} y[/tex], and [tex]\displaystyle \mathrm{d} z[/tex], we can equate the coefficient of each term to zero:

[tex]\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0[/tex].

Simplifying the equation:

[tex]\displaystyle \sin( 10^{10} t-600x) =0[/tex].

The sine function is equal to zero at certain values of [tex]\displaystyle ( 10^{10} t-600x) [/tex]:

[tex]\displaystyle 10^{10} t-600x =n\pi[/tex],

where [tex]\displaystyle n[/tex] is an integer. Rearranging the equation:

[tex]\displaystyle x =\frac{ 10^{10} t-n\pi }{600}[/tex].

The equation provides a relationship between [tex]\displaystyle x[/tex] and [tex]\displaystyle t[/tex], indicating that the magnetic field intensity is constant along lines of constant [tex]\displaystyle x[/tex] and [tex]\displaystyle t[/tex]. Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density [tex]\displaystyle B[/tex] is related to the magnetic field intensity [tex]\displaystyle H[/tex] through the equation [tex]\displaystyle B =\mu H[/tex], where [tex]\displaystyle \mu[/tex] is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

[tex]\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}[/tex].

To determine which numbers are divisible by 3 among the given options, we need to check if each number is divisible by 3 without leaving a remainder.

Let's examine each option:

a. 551: To check if 551 is divisible by 3, we can add up its digits: 5 + 5 + 1 = 11. Since 11 is not divisible by 3, 551 is not divisible by 3.

b. 461: Adding up the digits of 461: 4 + 6 + 1 = 11. Similarly, since 11 is not divisible by 3, 461 is not divisible by 3.

c. 816: Summing up the digits of 816: 8 + 1 + 6 = 15. Since 15 is divisible by 3 (15 ÷ 3 = 5), 816 is divisible by 3.

d. None of these: Since options a and b are not divisible by 3, and option c (816) is divisible by 3, the correct answer is "d. none of these."

Therefore, among the given options, only the number 816 is divisible by 3.

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

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

The options that are not possible measure of angle DCB would be 30°,27° and 34°. That is option A,B and C.

To determine the possible measure of the missing angle, the rules of the triangle needs to be obeyed.

The triangle represented above is an example of an Isosceles triangle which is a type of triangle that has both two equal sides and two equal angles.

Therefore, the <DCB should also be equal to 35° and not 30°,27° and 34°.

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Answer:

Ryan had a head start of 10 meters

Step-by-step explanation:

The algebraic expression for the given phrase is: 17x - 8x. To simplify this expression, we can combine like terms by subtracting the coefficients of x. The simplified expression is: 9x.

In the given phrase, "The product of 8 and a number" can be represented as 8x, where x represents the number. Similarly, "The product of 17 and the number" can be represented as 17x. Since we are subtracting the product of 8x from the product of 17x, the algebraic expression becomes 17x - 8x.

To simplify the expression, we combine like terms. The coefficients of x are 17 and -8. Since we are subtracting 8x from 17x, we subtract the coefficient of 8x from the coefficient of 17x, resulting in 17x - 8x. Combining like terms gives us 9x.

In conclusion, the simplified expression for the phrase "The product of 8 and a number, which is then subtracted from the product of 17 and the number" is 9x.

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[tex]\sqrt{200y^2} ~~ \begin{cases} 200=&2\cdot 10\cdot 10\\ & 2\cdot 10^2 \end{cases}\implies \sqrt{2\cdot 10^2 y ^2}\implies 10y\sqrt{2}[/tex]

To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

[tex]\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a[/tex]

Now,

[tex]\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a[/tex]

[tex]\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5[/tex]

[tex]\text{Area of pentagon} =52.5[/tex]

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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Answer:

Quadratic equation. Linear would be a straight line and exponential would continue to grow; only quadratic equations are shaped like parabolas.

linear

if you add 2 cats to a tree and took one down you would have 0 in the tree so if you add 2+2=4 you can find every answer in the book.

your wellcomed

So this is the set of all x-values where the function y = 16x - 71 + 3sin(5x) is continuous.

The function y = 16x - 71 + 3sin(5x) is continuous everywhere since it is a sum of continuous functions. The function 16x is a polynomial, which is continuous for all values of x. The function 3sin(5x) is also continuous for all values of x since it is a composition of continuous functions (sin(x) and 5x), and the constant term -71 is also continuous.

Therefore, we do not need to find any specific points of continuity or discontinuity – the function is continuous for all x.

To describe the set of x-values where the function is continuous in interval notation, we can simply write:

(-∞, ∞)

This interval includes all real numbers.

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Answer:

D; 7 1/2

Step-by-step explanation:

:)

Answer:

correct choice is the last one

Step-by-step explanation:

let h = cost of 1 hamburger meal

let c = cost of 1 chicken nugget meal

5h + 6c = 39

9h + 2c = 35

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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[tex]\cfrac{5}{6}x=4-\cfrac{11}{12}x\implies \stackrel{\textit{multplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{5}{6}x \right)=12\left( 4-\cfrac{11}{12}x \right)}\implies 10x=48-11x \\\\\\ 21x=48\implies x=\cfrac{48}{21}\implies x=\cfrac{16}{7}\implies x=2\frac{2}{7}[/tex]

The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%.

To find the coefficient of variation for each set of data, we need to calculate the mean and standard deviation for each set. The coefficient of variation is then calculated by dividing the standard deviation by the mean and multiplying by 100.

Let's calculate the coefficient of variation for each set of data:

Bank A (single line):

Mean: Calculate the mean of the data set.

Mean = (6.5 + 6.6 + 6.7 + 6.7 + 7.1 + 7.4 + 7.5 + 7.7 + 7.7 + 7.7) / 10 = 7.03 minutes

Standard deviation: Calculate the standard deviation of the data set.

Standard deviation = √[(6.5 - 7.03)² + (6.6 - 7.03)² + ... + (7.7 - 7.03)²] / 10 ≈ 0.565 minutes

Coefficient of variation:

Coefficient of variation = (0.565 / 7.03) * 100 ≈ 8.04%

Bank B (individual lines):

Mean: Calculate the mean of the data set.

Mean = (4.0 + 5.4 + 5.9 + 6.2 + 6.8 + 7.7 + 7.7 + 8.5 + 9.4 + 9.8) / 10 = 7.5 minutes

Standard deviation: Calculate the standard deviation of the data set.

Standard deviation = √[(4.0 - 7.5)² + (5.4 - 7.5)² + ... + (9.8 - 7.5)²] / 10 ≈ 1.916 minutes

Coefficient of variation:

Coefficient of variation = (1.916 / 7.5) * 100 ≈ 25.55%

Comparing the variation:

The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%. Since the coefficient of variation measures the relative variability of the data, we can conclude that the waiting times at Bank B (individual lines) have a higher variation compared to Bank A (single line).

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Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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Answer:

a. z = +2.00

Answer: The position is 24 points above the mean

b. z = +.50

Answer: The position is 6 points above the mean

c. z= -1.00

Answer: The position is 12 points below the mean

d. Z= -0.25

Answer: The position is 3 points below the mean

Step-by-step explanation:

We can use the relation,

[tex]z = (x-u)/S[/tex]

Where u is the mean and S is the standard deviation,

S = 12,

Rearranging, we get,

[tex]Sz = x - u\\12z=x-u\\12z + u = x[/tex]

Where x gives the position relaive to the mean.

So, for z = +1,

we get,

x = u + 12

Hence x is 12 points above the mean (u)

Now answering the questions,

a. z = +2

x = u + (12)(2)

x = u + 24

Hence the position is 24 points above the mean

b. z = +0.50

x = u + 12(o.5)

x = u + 6

hence the position is 6 points above the mean

c. z = -1.00

x = u + 12(-1)

x = u - 12

Hence the position is 12 points below the mean

d. z = -0.25

x = u + (12)(-0.25)

x = u - 3

Hence the position is 3 points below the mean

ANSWER

61.8 m^[2].

We first examine what we have which is:

A parallelogram with base 14m and height 8m

A circle with DIAMETER 8m

Given our area formulas, we know we have our b and h in our parallelogram formula given. If our circle diameter is 8m, our circle radius must be 4m. Therefore, we have every element of our formulas we need.

parallelogram area = b*h = 14*8 = 112m^[2]

circle area = pi*r^[2] = pi*4m^[2]=16*3.14=50.24m^[2].

now we just subtract our circle area from our parallelogram area, and round our answer to the nearest tenth (the first place to the right of the decimal):

112m^[2]-50.24m^[2]=61.76 m^[2].

Rounded to the nearest tenth, this number becomes 61.8 m^[2].

Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

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Answer:

4/10 simplified  2/5

if it does not help I am so sorry

Step-by-step explanation:

84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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Let's analyze Jenny's bowling expenses, considering the cost of renting bowling shoes and the price per game. By determining the total amount she paid and using the given information, we can calculate the number of games Jenny bowled.

Step-by-step explanation:

Let's set the number of games Jenny bowled as 'x'.

Jenny paid $2.75 for renting the bowling shoes and $4.25 for each game. The total amount she paid is $24.

The total amount Jenny paid for the games can be represented as: $4.25 * x.

So, the equation can be set up as:

$2.75 + $4.25 * x = $24.

To find the value of 'x', we need to solve the equation.

Subtracting $2.75 from both sides:

$4.25 * x = $24 - $2.75.

$4.25 * x = $21.25.

Dividing both sides by $4.25:

x = $21.25 / $4.25.

x = 5.

Answer: Therefore, Jenny bowled a total of 5 games.

An inequality to find the possible values of x is: D. x > 7.

In Euclidean geometry, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < n < b + c

Where:

n, b, and c represent the side lengths of this triangle.

By using the law of sine law, the value of x can be determined as follows;

28/sin(100°) = 20/sin(α)

sin(α) = sin(100°) × 20/28

α = arcsin(0.7034) = 44.70°

β = 180° - 110° - 44.70°

β = 25.3°

x/sin(β) = 28/sin(100°)

x = 28/sin(100°) × sin(25.3°)

x = 12.15

Based on the Triangle Inequality Theorem, we have:

20 + 12.15 > (5x - 7)

32.15 > (5x - 7)

5x > 39.15

x > 7.83

Read more on inequality here: https://brainly.com/question/16875793

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