48,62,81,94,27 to their nearest tens​

Answer:

24 boys

Step-by-step explanation:

You can solve this using simultaneous equations.

You know the number of boys plus the number of girls is 52, so b + g = 52.

You also know the number of boys is 6/7 the number of girls, so b = 6/7g

Then you can substitute this into the first equation - 6/7g + g = 52, so 13/7g = 52.

Solving that equation, 52 / 13/7 = 28, so there are 28 girls.

You then work out the number of boys by doing 52- the number of girls, so 52- 28 = 24 boys

Hope this helps, let me know if you have any questions :)

Answer:

in 7 minutes he solve 10 problems

he solve one problem in = 7/10= 0.7 minute

he solve 35 problem in = 0.7x35= 24.5 minute

Step-by-step explanation:

hope it helps ❤️

Fractions

We have the fractions:

2/5 and 3/10

The denominators of the fractions are 5 and 10.

We need to find a common number for 5 and 10. There are several numbers that are common multiples of both 5 and 10. We only need to find the first multiples of each:

5 , 10 , 15 , 20 , 25 , 30 , ...

10 , 20 , 30 , 40 , ....

We can see the numbers {10,20,30,...} are common multiples of 5 and 10. We can select any of those as our solution, but we prefer to pick the first one: 10.

To find 10 out of 5, we need to multiply it by 2, thus the whole fraction must be multiplied by 2:

2/5 = 4/10

Now 4/10 and 3/10 have a common denominator.

As mentioned, we have found the least possible denominator, but there are many others.

we have the quadratic equation

we have that

a=1

b=-1

c=-12

Applying the formula to solve a quadratic equation

The values of u are

u=4 and u=-3

therefore

The answer is

Answer:

a 22950

b 4590

Step-by-step explanation:

7.5% of 306,000 is 22950

20% of 22950 is 4590

Answer:  \(-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9\)

=======================================================

Explanation

Let:

\(x = \sqrt{2}\\\\y = \sqrt{6}-\sqrt{3}\\\\\)

We can then say:

\((\sqrt{2}-\sqrt{3}+\sqrt{6})(\sqrt{6}-\sqrt{3})\\\\(\sqrt{2}+\sqrt{6}-\sqrt{3})(\sqrt{6}-\sqrt{3})\\\\(x+y)(y)\\\\xy+y^2\\\\2\sqrt{3}-\sqrt{6}+9-6\sqrt{2}\\\\-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9\\\\\)

Check out the screenshot below for the scratch work on how I computed the \(xy\) and \(y^2\) terms.

Vector equation of the line tangent to the graph of r(t) at the point p0 on the curve r(t) = (3t - 1) i + 13t j + 4 k.

To find a vector equation of the line tangent to the graph of r(t) at the point P0 on the curve r(t) = (3t - 1) i + 13t j + 16 k, where P0 is given as (-1,4), we can use the following steps:

Step 1: Find the derivative of r(t) with respect to t:

r'(t) = 3 i + 13 j

Step 2: Evaluate the derivative at the point P0:

r'(-1) = 3 i + 13 j

Step 3: Use the point P0 and the vector r'(-1) to form the vector equation of the tangent line:

r(t) = P0 + r'(-1) t

where t is a scalar parameter.

Plugging in the values, we get:

r(t) = (-1)i + 4j + (3i + 13j)t

Simplifying, we get:

r(t) = (3t - 1) i + 13t j + 4 k

Therefore, the vector equation of the line tangent to the graph of r(t) at the point P0 on the curve

r(t) = (3t - 1) i + 13t j + 16 k  is

r(t) = (3t - 1) i + 13t j + 4 k.

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Option - B : Decision support system is a flexible tool for data analysis, since its reports do not have a fixed format.

  Decision support systems, a subset of business intelligence, are created to help organisations make sensible business decisions based on vast volumes of analysed data. Huge volumes of data are analysed using an interactive information system called a decision support system (DSS) to aid in the direction of business choices. A DSS aids management, operations, and planning levels of an organisation in making better decisions by assessing the importance of uncertainties and the tradeoffs involved in selecting one option over another. A DSS uses a variety of raw data, papers, personal knowledge, and/or business models to aid users in making decisions. A DSS may make use of relational data sources, cubes, data warehouses, electronic health records (EHRs), income projections, sales projections, and other sources.

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The given series in the sigma notation can be written as \(\sum_{n = 1} ^ 5 10n - 8\).

An arithmetic series is a set of integers where each term is made up of the common difference, a fixed amount, and the sum of the terms before it. In other words, the terms of the series may be represented as follows if the first term of an arithmetic series is a and the common difference is d:

a, a + d, a + 2d, a + 3d, ...

The given series is 2 + 12 + 22 + 32 + 42.

The total number of terms are 5.

The first term is 2, and the common difference is:

d = 12 - 2 = 10

Now, using the nth term of sequence we have:

an = 2 + (n - 1) 10

= 10n - 8

= \(\sum_{n = 1} ^ 5 10n - 8\)

Hence, the given series in the sigma notation can be written as \(\sum_{n = 1} ^ 5 10n - 8\).

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The probability that this project will be completed within 130 days is 0.8413.

Expected duration (ED) = (Optimistic + 4 x Most Likely + Pessimistic) ÷ 6.

Optimistic = 41

Most Likely = 50

Pessimistic = 59ED = (41 + 4 × 50 + 59) ÷ 6 = 50

Duration = 50

Optimistic = 54

Most Likely = 60

Pessimistic = 66ED = (54 + 4 × 60 + 66) ÷ 6 = 60

Duration = 60

Optimistic = 58

Most Likely = 70

Pessimistic = 82ED = (58 + 4 × 70 + 82) ÷ 6 = 70

Duration = 70

Optimistic = 32

Most Likely = 41

Pessimistic = 44ED = (32 + 4 × 41 + 44) ÷ 6 = 41

Duration = 41

Total Project Duration = 50 + 60 + 70 + 41 = 221

Expected time for completing project = 221 days

The standard deviation of the critical path is obtained by using the following formula:

σ = P - O/6

Where σ represents the standard deviation of the critical path, P represents the pessimistic time, and O represents the optimistic time.

σ = 66 - 54/6 = 2.

Then, the probability that this project will be completed within 130 days:

z = (130 - 221) / 2 = -45.5P(z < -45.5) = 0 (due to negative value)

P(z < -4.5) = 0 (from normal distribution table)

Thus, the probability that this project will be completed within 130 days is 0.8413.

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The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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Answer:

True

Step-by-step explanation:

Answer:

1,908÷36=53 estimation equals 50

Step-by-step explanation:

It is 50 because 53 is close to 50 not 60 if it equaled 55 or 56 then yeah it would be 60 but in this case it is 50!

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Minimum SOP expression of the given Boolean function F(X, Y, Z) is given as XY' + Z' + YX + YX + Y + Z.

Minimum SOP expression for the function f(x, y, z)

The given Boolean expression of f(x, y, z) is

f(x, y, z) = xyz + xyz + xyz’

Using the Boolean property of the distributive law and combining the common term xyz, we get

f(x, y, z) = xyz + xyz + xyz’= xyz + xyz’= xz(y + y’)

= xz·1

= xz

Minimum SOP expression of the given Boolean function f(x, y, z) is xz.

Minimum SOP expression for the function F(X, Y, Z)

The given Boolean expression of F(X, Y, Z) is

F(X, Y, Z) = (X + Y') Z + (XZ) + Y

Using the Boolean property of the distributive law and combining the common term XZ, we get

F(X, Y, Z) = (X + Y') Z + (XZ) + Y= XZ + YZ' + XYZ' + XY + Y

= XY'Z' + XYZ' + XY + Y+ XZ (since Y + Y’ = 1)

Again using the Boolean property of the distributive law, we get

F(X, Y, Z) = XY'Z' + XYZ' + XY + Y + XZ= XY'Z' + XYZ' + XZ + XY + Y

The Boolean expression obtained is a Sum of Products (SOP).

Minimum SOP expression of the given Boolean function F(X, Y, Z) is given as XY' + Z' + YX + YX + Y + Z.

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Answer:

The correct option is;

E) The average wait time to make payment and the number of cashiers working in a store

Step-by-step explanation:

An inversely proportional relationship is a relationship between two variables one where the increase in the magnitude one variable leads to the reduction in the magnitude of a second variable written mathematically as follows;

y ∝ 1/x

Therefore, given that as the number of cashiers at a store increases, the number of customers attended to per unit time by all the cashiers together increases, and the number of wait time observed by a customer to pay for the goods bought decreases.

Answer:

B.) The total number of stores visited and the average time spent in each store

E.) The average wait time to make a purchase and the number of cashiers working in a store

Step-by-step explanation:

It is correct I just took the test :)

Answer:

7%

Step-by-step explanation:

Perimeter of a rectangle

P = 2(w + l)

where:

Given:

Therefore, the perimeter of the original rectangle is:

⇒ P = 2(30 + 20)

⇒ P = 2(50)

⇒ P = 100 cm

If the width is increased by 5%:

⇒ new width = 30 × 1.05 = 31.5 cm

If the length is increased by 10%:

⇒ new length = 20 × 1.1 = 22 cm

Therefore, the new perimeter will be:

⇒ P = 2(31.5 + 22)

⇒ P = 2(53.5)

⇒ P = 107 cm

Percentage Increase

\(\sf PI=\dfrac{final\:value-initial\:value}{initial\:value} \times 100\)

Substitute the values:

\(\begin{aligned} \implies \sf Percentage\:increase & = \sf \dfrac{new\:perimeter-original\:perimeter}{original\:perimeter} \times 100\\\\& = \sf \dfrac{107-100}{100} \times 100\\\\& = \sf 7\%\end{aligned}\)

By applying Cramer's rule to the given system of simultaneous equations, The solution is x = 2, y = 3, and z = 4.

Cramer's rule is a method used to solve systems of linear equations by evaluating determinants. In this case, we have three equations with three variables:

1x + 5y + 2z = 5

x + 2y + 10z = 4

2x + 4y + 20z = 10

To apply Cramer's rule, we first need to find the determinant of the coefficient matrix, D. The coefficient matrix is obtained by taking the coefficients of the variables:

D = |1 5 2|

   |1 2 10|

   |2 4 20|

The determinant of D, denoted as Δ, is calculated by expanding along any row or column. In this case, let's expand along the first row:

Δ = (1)((2)(20) - (10)(4)) - (5)((1)(20) - (10)(2)) + (2)((1)(4) - (2)(2))

  = (2)(20 - 40) - (5)(20 - 20) + (2)(4 - 4)

  = 0 - 0 + 0

  = 0

Since Δ = 0, Cramer's rule cannot be directly applied to solve for x, y, and z. This indicates that either the system has no solution or infinitely many solutions. To further analyze, we calculate the determinants of matrices obtained by replacing the first, second, and third columns of D with the constant terms:

Dx = |5 5 2|

    |4 2 10|

    |10 4 20|

Δx = (5)((2)(20) - (10)(4)) - (5)((10)(20) - (4)(2)) + (2)((10)(4) - (2)(2))

    = (5)(20 - 40) - (5)(200 - 8) + (2)(40 - 4)

    = -100 - 960 + 72

    = -988

Dy = |1 5 2|

    |1 4 10|

    |2 10 20|

Δy = (1)((2)(20) - (10)(4)) - (5)((1)(20) - (10)(2)) + (2)((1)(10) - (2)(4))

    = (1)(20 - 40) - (5)(20 - 20) + (2)(10 - 8)

    = -20 + 0 + 4

    = -16

Dz = |1 5 5|

    |1 2 4|

    |2 4 10|

Δz = (1)((2)(10) - (4)(5)) - (5)((1)(10) - (4)(2)) + (2)((1)(4) - (2)(5))

    = (1)(20 - 20) - (5)(10 - 8) + (2)(4 - 10)

    = 0 - 10 + (-12)

    = -22

Using Cramer's rule, we can find the values of x, y, and z:

x = Δx / Δ = (-988) / 0 = undefined

y = Δy / Δ = (-16) / 0 = undefined

z = Δz / Δ

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The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model. The optimal number of notebooks to make in each order is 590 units. The annual ordering cost (AOC) is approximately $892.20. The Annual Holding Cost (AHC) is $3540. The annual product cost (APC) is $233,460. The annual total cost of managing inventory (ATC) is approximately $237,892.20. The total number of orders in the year (N) is 33. The estimated time between each order (T) is approximately 7.58 days. The daily demand is approximately 77.82 units. The reorder point (ROP) is approximately 311 units.

The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model.

To find the optimal number of notebooks to make in each order, we can use the EOQ formula:

EOQ = √[(2 * Demand * Ordering Cost) / Holding Cost]

EOQ = √[(2 * 19455 * 27) / 6]

EOQ ≈ 589.96

Since the number of notebooks must be a whole number, the optimal number to order would be 590 notebooks.

The annual ordering cost (AOC) can be calculated by dividing the annual demand by the EOQ and multiplying it by the ordering cost:

AOC = (Demand / EOQ) * Ordering Cost

AOC = (19455 / 590) * 27

AOC ≈ $892.20

The Annual Holding Cost (AHC) is calculated by multiplying the EOQ by the holding cost per unit:

AHC = EOQ * Holding Cost

AHC = 590 * 6

AHC = $3540

The annual product cost (APC) is calculated by multiplying the annual demand by the cost per unit:

APC = Demand * Cost per unit

APC = 19455 * 12

APC = $233,460

The annual total cost of managing inventory (ATC) is the sum of the annual ordering cost, annual holding cost, and annual product cost:

ATC = AOC + AHC + APC

ATC = 892.20 + 3540 + 233460

ATC ≈ $237,892.20

The total number of orders in the year (N) can be calculated by dividing the annual demand by the EOQ:

N = Demand / EOQ

N = 19455 / 590

N ≈ 33

The estimated time between each order (T) can be calculated by dividing the number of working days in a year by the total number of orders:

T = Number of working days / N

T = 250 / 33

T ≈ 7.58 days

The daily demand is calculated by dividing the annual demand by the number of working days in a year:

Daily Demand = Demand / Number of working days

Daily Demand = 19455 / 250

Daily Demand ≈ 77.82 units/day

The reorder point (ROP) is the number of units at which a new order should be placed. It can be calculated by multiplying the daily demand by the lead time (time taken for the supplier to deliver the order):

ROP = Daily Demand * Lead Time

ROP = 77.82 * 4

ROP ≈ 311.28 units

Therefore, the reorder point would be approximately 311 units.

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The chance that the weight of the product is between 115 and 118 pounds is approximately 0.064.

In this case, we have:

z = (115 - 120) / 30 = -0.1667

z = (118 - 120) / 30 = -0.0667

Now we need to find the area under the standard normal curve between these two values. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we can look up the values of -0.1667 and -0.0667 and find the corresponding probabilities. We subtract the smaller probability from the larger one to get the area between the two values.

Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution to find the probability directly.

Either way, we get a probability of approximately 0.0641 or 0.0640, depending on the method used.

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The value of cosec A is approximately 2.702

From the question, we are to determine the value of cosec A.

cosec A - cot A = 1/3

We can rewrite cosec A as 1/sin A and cot A as cos A/sin A:

1/sin A - cos A/sin A = 1/3

Combining the fractions on the left side, we get:

(1 - cos A)/sin A = 1/3

Cross-multiplying, we get:

3(1 - cos A) = sin A

Expanding the left side, we get:

3 - 3cos A = sin A

Squaring both sides, we get:

9 - 18cos A + 9cos^2 A = sin^2 A

Using the identity sin²A + cos²A = 1, we can substitute cos²A = 1 - sin²A:

9 - 18cos A + 9(1 - sin²A) = sin²A

Simplifying, we get:

10sin²A - 18cos A + 9 = 0

Using the identity sin²A = 1 - cos²2 A, we can substitute sin²A = 1 - cos²A:

10(1 - cos²A) - 18cos A + 9 = 0

Expanding and simplifying, we get:

-10cos²A - 18cos A + 19 = 0

We can solve this quadratic equation for cos A using the quadratic formula:

cos A = (-b ± √(b²- 4ac))/2a

where a = -10, b = -18, and c = 19:

cos A = (-(-18) ± √((-18)²- 4(-10)(19)))/(2(-10))

= (9 ± √(421))/10

Since cosec A is the reciprocal of sin A, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin A:

sin²A = 1 - cos²A = 1 - ((9 ± √(421))/10)²

Taking the positive square root, we get:

sin A = sqrt(1 - ((9 + √(421))/10)²)

Now we can find cosec A using the formula cosec A = 1/sin A:

cosec A = 1/√(1 - ((9 + √(421))/10)²)

Hence, the value of cosec A is 2.702 (rounded to three decimal places)

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Null hypothesis: There is no significant difference in the performance of the five sorghum cultivars under rainfed conditions.

Blocking: The blocking in this study was useful as indicated by the non-significant F-value for the blocks. It helps reduce the impact of potential confounding factors by creating homogeneous groups within the experiment.

Efficiency of experimental design: It cannot be determined from the given information whether another experimental design would have been more efficient.

Target population: The target population in this study is the set of all sorghum cultivars under rainfed conditions.

Null hypothesis: The null hypothesis for this study would state that there is no significant difference in the performance of the five sorghum cultivars under rainfed conditions. This means that the means of the treatments (sorghum cultivars) are equal.

Blocking: The blocks in the study were used to control for any potential variability among different locations or environmental conditions. By assigning each treatment randomly within each block, the effect of the blocking factor can be separated from the treatment effect. In this study, the non-significant F-value for the blocks suggests that the blocking was effective in reducing the impact of potential confounding factors.

Efficiency of experimental design: The given information does not provide enough details to determine whether another experimental design would have been more efficient. The choice of design depends on various factors such as the nature of the experiment, available resources, and specific objectives.

Target population: The target population in this study refers to the set of all sorghum cultivars under rainfed conditions. The study aims to draw conclusions about the performance of these cultivars in similar conditions.

Reason for blocking: Blocking may have been used in this study to account for spatial or environmental variation that could potentially affect the performance of the sorghum cultivars. By blocking, the experimenters aimed to create groups of experimental units that are similar within each block, reducing the variability caused by these factors and allowing for a more accurate assessment of the treatment effects.

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A line plot for the weight of each piece of fruit, in pounds is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the weight of each piece of fruit, in pounds on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the data set is skewed.

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Answer:

38

Step-by-step explanation:

:) hope this helps

Answer:

82

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

The first thing you do here is subtract 120 from 325

325-120=205

The next step is to divide 205 by 2.50 to find how many students attended

205/2.50=82

Therefore 82 students paid the $2.50 price to attend the dance

The correct line of code that completes this operator which transforms a Point by dx and dy is shown below: Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Note that the function operator+ takes two arguments: an integer dx and an integer dy.

The function returns a point, which is created by adding dx to x and dy to y.The completed code is shown below:class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Therefore, the correct answer is: `Point(x_+dx,y_+dy)`

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The missing numbers in the expressions are:

a. x²

b. 4x²

c. 24x

d. 36x

e. 9x²

f. 1

Every combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).

Let's use the equation 5x + 7 as an example.

Now here,

We can see that by simplifying the expressions we can see that all of them are in the form of (a+b)².

So, using the same to simplify the equations we get the missing numbers.

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