if a variable x is normally distributed with a mean of 60 and a standard deviation of 15, what is

The average speed of the family during their walk  over a time period of 1.35 hours is 1.407 km/hr

Let us say that the distance covered by the family is x

so , according to the formula of average speed

Average speed = total distance covered/total time taken

Hence,

average speed = [tex]\frac{0.75+1.15}{1.35} km/hr[/tex]

                          = [tex]\frac{1.9}{1.35} km/hr[/tex]

                          = 1.407 km/hr

therefore, the average speed of the family is 1.407 km/hr

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Answer:

120

Step-by-step explanation:

3 mons = 12 weeks

$20 every 2 weeks, so average $10 / week

so 12*10 = 120

The parametric equation of the line through a parallel to b is X = [-3, 5] + t[1/4, 1]

An equation is a mathematical statement that shows the equality or balance of two expressions. It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.

The equation of a line can be represented in both point-slope form and in parametric form. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

In this case, we have two points, a and b, on the line. We can use these points to find the slope of the line, which is given by:

m = (y2 - y1) / (x2 - x1) = (b[1] - a[1]) / (b[0] - a[0]) = (3 - 5) / (-5 - (-3)) = (3 - 5) / -8 = -2 / -8 = 1/4

y - a[1] = (1/4)(x - a[0])

To convert this equation to parametric form, we can use t as the parameter and express x and y in terms of t:

x = a[0] + t

y = a[1] + (1/4)t

So the parametric equation of the line through a parallel to b is given by:

X = [-3, 5] + t[1/4, 1]

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The line representing the equation 7x1 + 4x2 [tex]\leq[/tex] 28 goes through the following two points: (0,7) and (4,0).

Hence, option (c) is the correct choice.

The constraint equation is g(x,y)=c, and we state that x and y are constrained by g(x,y)=c.

Constrained maximum and constrained minimum points are locations (x,y) that are maxima or minima of f(x,y) with the condition that they meet the constraint equation g(x,y)=c.

As per the data given,

We have,

The equation of the constraint: 7 x_1+4 x_2[tex]\leq[/tex] 28

7 x_1+4 x_2 [tex]\leq[/tex] 28

So, putting the value of x_2=0

We will get the above expression as:

7 x_1=28

=>x_1=4

So, the points will be (4,0)

Now, putting the value of x_1=0

Thus, we will get:

4 x_2=28

=>x_2=7

So, the points will be (0,7)

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Point (4,0) and (0,7) (C) were passed through by the line equation of 7x1 + 4x2 = 28.

From the case, we know that:

Line equation: 7x1 + 4x2 = 28

Passed through points?

To answer this question, we can try to find some conditions:

First, we will try to find the valuf f x2 if x1 = 0:

(x1 = 0)

7(0) + 4.x2 = 28

0 + 4.x2 = 28

4.x2 = 28

x2 = 7 --> (0,7)

Next, we try if x2=0, then x1 = ...

(x2 = 0)

7x1 + 4(0) = 28

7x1 = 28

x1 = 4 --> (4,0)

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The number of adults for 24 students is 6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Mr.Cates, the principal at a local middle school, made a rule that there must be 1 adult for every 4 students attending a field trip.

Let the number of students be y and the number of adults be x.

Now, the equation is y=4x

If y=12

Then, x=3

If y=24

Then, x=6

If y=40

Then, x=10

Therefore, the number of adults for 24 students is 6.

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"Your question is incomplete, probably the complete question/missing part is:"

Mr.Cates, the principal at a local middle school, made a rule that there must be 1 adult for every 4 students attending a field trip

Complete the table to show the number of adults for 12, 24 and 40 students.

Number of Students          Number of Adults

              12                                 _____

              24                                 _____

              40                                 _____

The formula for calculating a square pyramid's surface area is SA = P l / 2, where P l is the product of the base perimeter and the slant height.

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The smaller number of the given sum is 15.

Completed question :

The sum of two numbers is 80. If the larger number exceeds four times the smaller by 5, what is the smaller number?

Given data :

Given, sum of two numbers is 61.

Let the smaller number be x

Thus the larger will be 61 - x

Also given, larger number exceeds four times the smaller number by 4.

Therefore, 61 - x = 4x + 5

5x = 56

x = 15

Thus the smaller number is 15.

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The number of subsets that [n] have which contain exactly one element 1 and 2 is 2⁽ⁿ⁻¹⁾ .

Let us assume that [n] means the set {1, 2, 3, ..., n}.

Now For a subset having n elements ,we have  = 2ⁿ total subsets, including the empty set and the set itself.

If we are looking for subsets that contain exactly one of the elements 1 and 2, there are two possibilities:

⇒ The subset contains element 1 but not element 2,

⇒ The subset contains element 2 but not element 1.

If we remove 1 and 2 from this , then the set [n] contains (n-2) elements,

So , the number of subsets become =  2⁽ⁿ⁻²⁾  subsets.

So , there is two ways to have exactly one of elements 1 or 2: add {1} to the subsets described, or add the subset {2} to subsets just described.

Therefore ,  [n] will contain 2⁽ⁿ⁻²⁾ subsets exactly one of 1 or 2

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The value is -6

We are given a sequence {an} such that sn = 3n - 9. We can find an by using the formula sn = an + d(n - 1).

Substituting the values for sn and d (which is 1 in this case), we get

an = 3n - 9 - (n - 1)

an = 2n - 10

Therefore, when k = 1, an = 2(1) - 10 = -6.

The answer value is -6.

Expand it to 2 liens

The answer is -6, which can be obtained by using the formula an = 3n - 9 - (n - 1).

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Answer:0.592

Step-by-step explanation:

16/27 = 0.59259259

round it to 3 decimal points so 0.593

Answer:

0.593

Step-by-step explanation:

16/27 = 0.59259259

round it to 3 decimal points so 0.593

While equations 24 and 25 are equivalent, equation 23 is not since the two equations are not the same.

When the solution set for two equations is the same, the equations are said to be equivalent. For instance, the equations x + 2 = 6 and 2x = 8 have the same solution set when we solve them both as follows: x + 2 = 6. Take 2 away from both sides.

For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2. When two items or amounts are exactly the same, such as when 12 is equal to 12, but 12 is equivalent to 2/4 since they symbolise.

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While equations 24 and 25 are equivalent, equation 23 is not since the two equations are not the same.

The "4" in the integral is actually the height (or thickness) of each slice that we are using to find the volume of the solid.

In this case, we are taking infinitesimal slices perpendicular to the x-axis and the height of each slice is 4.

Let's consider the cross-sectional area of each slice. The cross-section is a square with side length equal to the diameter of the semicircular base, which is 2 * 9 = 18. The area of the square is 18^2 = 324.

However, we also need to take into account the shape of the semicircle. As we move up the solid, the area of the cross-section decreases as the height of the slice decreases. This is because the cross-sectional square is inscribed inside the semicircle, and as the height decreases, so does the width of the square. To account for this, we need to find the width of the square as a function of the height of the slice.

Let y be the height of the slice, then the width of the square is equal to the diameter of the semicircle minus twice the height of the slice. The diameter of the semicircle is 18, so the width of the square is 18 - 2y.

The area of the cross-section at height y is then given by:

A(y) = (18 - 2y)^2

A(y) = 324 - 72y + 4y^2

To find the volume of the solid, we integrate the area of the cross-section with respect to the height of the slice, from 0 to 9:

V = ∫_0^9 A(y) * 4 dy

V = ∫_0^9 (324 - 72y + 4y^2) * 4 dy

V = ∫_0^9 1296 - 288y + 16y^2 dy

V = 1296 * y - 144y^2 + 8y^3 |_0^9

V = 1296 * 9 - 144 * 9^2 + 8 * 9^3

V = 11304 - 1296 + 729 = 8737 cubic units

So, the volume of the solid is 8737 cubic units.

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Let's consider the cross-sectional area of each slice. The cross-section is a square with side length equal to the diameter of the semicircular base, which is 2 * 9 = 18. The area of the square is 18^2 = 324.

A(y) = (18 - 2y)^2

A(y) = 324 - 72y + 4y^2

V = ∫_0^9 A(y) * 4 dy

V = ∫_0^9 (324 - 72y + 4y^2) * 4 dy

V = ∫_0^9 1296 - 288y + 16y^2 dy

V = 1296 * y - 144y^2 + 8y^3 |_0^9

V = 1296 * 9 - 144 * 9^2 + 8 * 9^3

V = 11304 - 1296 + 729 = 8737 cubic units

Answer:

1.25 as decimal

5/4 as fraction

1 1/4 as mixed number

Step-by-step explanation:

Hope it helps! =D

Answer: 14

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

The number that meets all the conditions is 36. It is divisible by 3 and 6, but not by 4 and 5. The sum of the digits is 9, which is an odd number, and the difference between the digits is 3, which is also odd. an incomparable number.

The direction of the force on side 1 is 45° downwards from the positive x-axis. The direction of the force is the opposite of the angle obtained in step 3, which is 45° downwards from the positive x-axis.

1. Draw a right triangle, with the two points of the side as the vertices.

2. Using the Pythagorean theorem, calculate the length of the side.

3. Use the inverse tangent function to calculate the angle between the two points.

4. The direction of the force is the opposite of the angle obtained in step 3, which is 45° downwards from the positive x-axis.

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The rule of translation of LMN to L'M'N is: Shift right by 3 units and shift up by 1 unit.

What is a translation of triangles?

A translation of a triangle is a transformation in which a triangle is moved from one position to another, without changing its shape or size.

From the graph, we can see that LMN is translated to L'M'N'

The coordinates of L is:

L = (-6,-4)

The coordinates of L' is:

L' = (-3, 3)

Subtract L from L'

(x, y) = L'-L

(x, y) = (-3,-3)-(-6, -4)

(x, y) = (-3+6,-3+ 4)

x, y)= (3, 1)

Hence, The rule of translation of LMN to L'M'N is: Shift right by 3 units and shift up by 1 unit.

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The final balance of all transaction is $45,880 both in Total Assets and Total Liabilities and Equities.

Please refer to the attached table below for the completed and balanced table.

We will discuss how each transaction is recorded:

a. When Pamela deposit $42,000 to the business bank, it will be recorded as cash inflow and her capital.

b. The purchase of office supplies will be recorded on account. Then, the supplies will record $2,080 and the same account will be recorded under accounts payable.

c. Record cash inflow of $5,760 and the same amount under fees earned.

d. Paid rent by cash will decrease the amount of cash by $2,550 and the same amount is recorded under Rent Expense account.

e. Cash outflow by $940 and decrease on the accounts payable account by the same amount.

f. Records accounts receivable of $4,720 and fees earned with the same amount.

g. Records cash outflow by $850. Records $570 under automobile expense and $280 for Miscellaneous expense.

h. Cash outflows by $1,790 and salaries expense by the same amount.

i. The amount of supplies decreases by $850 and records under the account of supplies expense by the same amount.

j. Cash outflow by $1,700 and records under Drawings account for the same amount.

Please note that all expenses should be recorded as a negative value.

Finally, we can check and confirm that our records are balance by comparing the total Assets and Total liabililties and Equity we have. The total assets is $45,880 and so the Total Liabilities and Equity.

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The argument is deductive if the arguer thinks that the truth of the premises unquestionably establishes the validity of the conclusion.

The argument is inductive if the arguer thinks that the truth of the premises offers only solid grounds for thinking the conclusion is probably true.

An argument from a particular example to a general rule is known as induction. Deduction leads to a valid conclusion, whereas inductive reasoning merely leads to a likely result based on experience. This is how induction differs from the deduction.

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The linear scan strategy for counting the number of negative values in an array involves sequentially going through each element of the array and checking if it is negative.

If the element is negative, the count is incremented. Once the end of the array is reached, the count is returned.

For example, consider an array A = [-2, 3, -1, 4, -7, 9]. The linear scan strategy would be as follows:

1. Initialize count to 0

2. Check if A[0] = -2 is negative, if yes, increment count. Count = 1

3. Check if A[1] = 3 is negative, if no, continue. Count = 1

4. Check if A[2] = -1 is negative, if yes, increment count. Count = 2

5. Check if A[3] = 4 is negative, if no, continue. Count = 2

6. Check if A[4] = -7 is negative, if yes, increment count. Count = 3

7. Check if A[5] = 9 is negative, if no, continue. Count = 3

8. Return count = 3.

Therefore, the linear scan strategy for counting the number of negative values in array A is 3.

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The rate of petrol consumption in km per llitre given the distance covered and the capacity of Petrol used is 12.5 km per liter

Total distance covered by the car = 500 km

Total capacity of Petrol used = 40 litres

The rate of petrol consumption in km per llitre = Total distance covered by the car / Total capacity of Petrol used

= 500 km / 40 liters

= 12.5 km per liter

Therefore, the unit rate of Petrol consumption of the car is 12.5 km per liter

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Answer:

Step-by-step explanation:

According to the weeklybdays of a Calendar, the weekdays are scheduled as:-

Sunday-Monday -Tuesday-Wednesday-Thursday-Friday-Saturday

So, this shows that Monday comes only after Sunday. du to which the present day scheduled is Monday and the day before today(yesterday) is scheduled to be Sunday.

The overall order of the reaction is the sum of the orders of the individual reactants, a + b. Therefore, the overall order of the reaction is 2 (1 + 1 = 2).

A. The order of the reaction in X is 1.

B. The order of the reaction in Y is 1.

C. The overall order of the reaction is 2.

The orders of a reaction can be determined from the initial rates obtained from the different experiments. The reaction rate is proportional to the concentrations of the reactants raised to the powers of the order of each reactant.

In experiment 1, the initial rate (2.83 M/s) is proportional to the concentration of X raised to the power of a (2.83 = k[X]^a). Therefore, a = 1.

In experiment 2, the initial rate (2.83 M/s) is proportional to the concentration of Y raised to the power of b (2.83 = k[Y]^b). Therefore, b = 1.

In experiment 3, the initial rate (25.47 M/s) is proportional to the concentration of X raised to the power of a (25.47 = k[X]^a) and the concentration of Y raised to the power of b (25.47 = k[Y]^b). Therefore, a = 1 and b = 1.

The overall order of the reaction is the sum of the orders of the individual reactants, a + b. Therefore, the overall order of the reaction is 2 (1 + 1 = 2).

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There is a 0.43% chance or probability of correctly guessing the ages of all six children.

The probability of correctly guessing the ages of all six children in a family where each child is at least one year old and the sum of their ages is an integer that is at most 31 can be calculated using combinations.

The total number of possible combinations of ages that meet the criteria can be found by multiplying the number of different outcomes for each child's age, giving us 6 x 6 x 6 x 6 x 6 x 6, or 46,656.

To calculate the probability, we need to divide the number of possible combinations that meet the criteria (46,656) by the total number of possible combinations (1,073,741,824).

This gives us the probability of 0.00433, or 0.43%.

This means that there is a 0.43% chance of correctly guessing the ages of all six children.

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Answer:

38.88 is what she paid

Step-by-step explanation:

0.28x54=15.12

15.12 = 28% of 54

the remaining percentage is 72%

15.12/28=0.54

0.54=1%

1x72 to get 72 percent so,

0.54*72=38.88

The area of the rectangle with the coordinates A(-2, 2), B(6, 2), C(6, 3), and D(-2, 3) is therefore 15 units.

A rectangle is a polygon with four right angles within Euclidean plane geometry. Users may also refer to it as an equilateral triangular quadrilateral, meaning that all of its edges are equal. A straight angles could also be present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90º vertices as well as equal parallel sides make up a quadrilateral with the look of a rectangle. As a result, it's also known as a vector graphics rectangle. A square is also refereed to as a parallelogram since its opposite angles are parallel and equal.

given

Rectangle's given coordinates are A(-8, 3), B(-3, 3), C(-3, 6), and D. (-8,6)

d = (((x2 - x1)2+(y2 - y1)2) is the distance between the places.

AB = √[{-3 - (-8)}² + (3 - 3)²] = 5 units

BC = √[{-3 - (-3)}² + (6 - 3)²] = 3 units

CD = √[{-8 - (-3)}² + (6 - 6)²] = 5 units

AD = √[{-8 - (-8)}² + (6 - 3)²] = 3 units

5 units for length and 3 units for width.

region of the rectangle,

A = length times width

5 * 3 Equals 15 units, or a.

The area of the rectangle with the coordinates A(-2, 2), B(6, 2), C(6, 3), and D(-2, 3) is therefore 15 units.

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When using the Tare function on a balance, start by placing the glassware on the balance. Then Press the tare/zero button to cancel out the mass. Finally, add your sample to the glassware and record the mass of your sample.

The Tare function on a balance is an important tool for accurately recording the mass of a sample. To use this function, start by placing the glassware on the balance. This will provide a baseline reading of the glassware’s mass.

Then, press the tare/zero button to cancel out the mass of the glassware. This will reset the balance to zero. Finally, add your sample to the glassware. This will give you the mass of your sample alone, without the mass of the glassware included.

It is important to use the Tare function to get the most accurate reading of your sample’s mass. With the Tare function, you can make sure the mass you record is the mass of your sample alone.

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Formula f(x):

f(x) = a* (X-Xv)² + Yv

a = principal coefficient

(x,y)=peak point

To get knots quickly, squares must be written in canonical form. That means f(x) must have the form above.

The quadratic function is a polynomial function that has variables/variables with the highest power being 2 (two).

In general, quadratic functions have the following general form:

f(x) = ax²+ bx + c, a ≠ 0

with f(x) = y which is the dependent variable, x is the independent variable, while a, and b are the coefficients and c is a constant.

This is of course different from what is called a quadratic equation, in which a quadratic equation has a variable with the highest power being two and is in the form of an equation.

The general form of the quadratic equation is as follows:

ax² + bx + c = 0, a ≠ 0

where x is the independent variable, a and b are the coefficients, and c is a constant.

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