While only 5% of babies have learned to walk but the adage of 10 months, 75% have learned to walk by 13 months of age. If the age at which Bavaria develop the ability to walk can be described by normal distribution model, find the mean and standard deviation of the normal model

Answer:

m^2-2 and -6x^3+7x^2-x+1

The population density of city-B is greater, so, the public bus must be used for city-B.

Population density (in agriculture: standing stock and standing crop) is a measurement of population per unit area.

The total population of city A= 51,242

The total area of city A =89.22 mi^2

The population density of city A is given by;

\(\rm Population \ density=\dfrac{Total \ population }{Total \ Area}\\\\ Population \ density=\dfrac{51,242}{89.22}\\\\ Population\ density=574.3331\)

The total population of city B = 50178

The total area of city B =8.12 mi^2

The population density of city B is given by;

\(\rm Population \ density=\dfrac{Total \ population }{Total \ Area}\\\\Population \ density=\dfrac{50178}{8.12}\\\\Population \ density=6179.55665\)

Hence, the population density of city-B is greater, so, the public bus must be used for city-B.

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Answer:

b is the answer

Step-by-step explanation:

Answer:

D. (2, -3/4)

Step-by-step explanation:

y=1/8x-1

-5x+4y=-13

5x+4(1/8x-1)=-13

x=2

y=1/8x2-1

y=-3/4

Answer: √20 c. √50 d. ³√16 e. ³√8 f. 4√125 g. 2³√64 h. √⅓ i. √⅜ j. ³√9/8

Step-by-step explanation:

Answer:

y=c-ax/b

Step-by-step explanation:

Subtract ax from both sides.

by=c−ax

Divide both sides by b

by/b=c-ax/b

Dividing by b undoes the multiplication by b.

y=c-ax/b

Answer:  y=c-ax/b

Step-by-step explanation:

Subtract ax from both sides.

by=c−ax

Divide both sides by b

by/b=c-ax/b

Dividing by b undoes the multiplication by b.

y=c-ax/b

I think this is right?? XP

Answer:

Step-by-step explanation:

Given that:

Johnathan looked at two different portions of cereals at the supermarket.

They are:

Sunshine Cornflakes: 24-ounce box for $4.32

Bright Start Cornflakes: 36-ounce box for $5.76

To calculate the cost of one ounce of Sunshine cornflakes, we have:

24-ounce box for $4.32

1 - ounce box  will be x

x = ($4.32 × 1 ounce box) / 24 ounce box

x = $0.18

1 - ounce box  will be = $0.18

To calculate the cost of one ounce of Bright star cornflakes, we have:

36-ounce box for $5.76

1 - ounce box will be = ( $5.76 × 1 ounce box) / 36 ounce box

1 - ounce box will be = $0.16

Since 1 - ounce box of Bright star cornflakes is lesser than 1 - ounce box of Sunshine Cornflakes.

Then,  Bright star cornflakes costs ($0.18 - $0.16) = $0.02 per ounce box lesser than Sunshine Cornflakes.

Thus, Bright star cornflakes will be a better buy.

The value of x of the quadrilateral using the concept of similar quadrilaterals is; x = 1.5

Two quadrilaterals are referred to as similar quadrilaterals when the three corresponding angles are the same and as a result the fourth angles automatically become the same due to the fact that the interior angles of a quadrilateral sum up to 360 degrees and two adjacent sides have equal ratios.

Thus, we can say by the concept of similar quadrilaterals that;

AB/LM = BC/MN

Thus;

14/(x + 9) = 10/(x + 6)

14(x + 6) = 10(x + 9)

14x + 84 = 10x + 90

14x - 10x = 90 - 84

4x = 6

x = 1.5

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The only point that lies on both lines is (-4,5).

To determine which of the points (−4,5), (4,3), and (1,2) lie on both the lines −x1−4x2=−16 and −3x1−5x2=−13, we need to check if the coordinates of each point satisfy both of the equations.

For the first line, we can rewrite it as x2 = (-x1 + 16)/4 and for the second line, we can rewrite it as x2 = (-3x1 + 13)/5.

Substituting the coordinates of each point into these equations, we get:

For the point (-4,5):

-4(2) + 16/4 = -4 + 4 = 0, and

-3(-4) + 13/5 = 12/5 + 13/5 = 25/5 = 5.

Therefore, (-4,5) satisfies both equations.

For the point (4,3):

4(2) + 16/4 = 8 + 4 = 12, and

-3(4) + 13/5 = -12 + 13/5 = -47/5.

Therefore, (4,3) does not satisfy both equations.

For the point (1,2):

-1(2) + 16/4 = -2 + 4 = 2, and

-3(1) + 13/5 = -3 + 13/5 = 2/5.

Therefore, (1,2) does not satisfy both equations.

Therefore, the only point that lies on both lines is (-4,5).

When given two equations, the solution can be found by solving the system of equations. To solve a system of equations, one should find the values of x and y that satisfy both equations. The solution to the system is the point (x,y) that satisfies both equations.

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The values of a, b, c, and the critical and inflection points, we can plot the graph by considering the shape and behavior of the polynomial function.

To sketch a graph with specific characteristics, such as 4 roots, 6 critical points, and 6 inflection points, we need to consider a higher degree polynomial function. Let's construct a polynomial function that satisfies these requirements.

To have a single root, we can use a linear factor, (x - a). To have double roots, we can use a quadratic factor, (x - b)^2. And for a triple root, we can use a cubic factor, (x - c)^3.

Considering these factors, let's construct a polynomial function:

f(x) = (x - a)(x - b)^2(x - c)^3

To have 4 roots, we need to choose appropriate values for a, b, and c.

To have 6 critical points, we can set the derivative of f(x) equal to zero and solve for x. The number of critical points corresponds to the number of distinct solutions.

f'(x) = 0

Expanding and solving for x, we'll obtain 6 values for x that correspond to the critical points.

To have 6 inflection points, we can set the second derivative of f(x) equal to zero and solve for x. The number of inflection points corresponds to the number of distinct solutions.

f''(x) = 0

Expanding and solving for x, we'll obtain 6 values for x that correspond to the inflection points.

After determining the values of a, b, c, and the critical and inflection points, we can plot the graph by considering the shape and behavior of the polynomial function.

Please note that without specific values for a, b, and c, it's not possible to provide an exact graph. The process described above is a general approach to construct a graph with the given characteristics.

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Answer:

44

Step-by-step explanation:

A circle is 360 degrees.

145 +136 + 35= 316

360-316= 44

44 Degrees

the discriminant is negative, there are no real solutions for y. Therefore, the differential equation has no equilibrium solutions.To find the equilibrium solutions of the differential equation dy/dt = y + 5/(1-y), we set dy/dt equal to zero:

0 = y + 5/(1-y)

Next, we can multiply both sides of the equation by (1-y) to eliminate the denominator:

0 = y(1-y) + 5

Expanding and rearranging the equation, we get:

y² - y + 5 = 0

This is a quadratic equation in terms of y. We can solve it by using the quadratic formula:

y = (-(-1) ± √((-1)² - 4(1)(5))) / (2(1))

Simplifying further:

y = (1 ± √(1 - 20)) / 2

y = (1 ± √(-19)) / 2

Since the discriminant is negative, there are no real solutions for y. Therefore, the differential equation has no equilibrium solutions.

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Thus the hydrogen ion concentration is 1.67 * 10^-10 M.

The molar concentration refers to the concentration in mole per liter. Now we know that the pOH has to do with the concentration of the hydroxide ion concentration.

We know that;

pH = 14 - 4.223 = 9.777

Now

[H^+] = (Antilog -9.777)

[H^+] = 1.67 * 10^-10 M

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The value for h(-1) is 4

The value for  h'(-1) is 1

Given the tangent line to the graph of y=h(x) at the point (-1,4) passes through (3,6), to get h(-1) and h'(-1), we should calculate the following:

Gradient of the tangent line:

Gradient=change in y axis/change in x axis=Δy/Δx

Using the x and y coordinates (-1,4) and (3,6)

Gradient=(6-4)/(3--1)

             =2/4

            =1/2

Gradient=1/2 or 0.5

Equation of the tangent line:

This should be in the form of y=mx+c, where m is the gradient of the line

We use the gradient and one of the x and y coordinates get the equation of the tangent line

Gradient=change in y axis/change in x axis=Δy/Δx, and gradient was found as 1/2

Δy/Δx=1/2

(y-4)/(x--1)=1/2

(y-4)/(x+1)=1/2

2y-8=x+1

y=(1/2)x+4.5

Equation of the tangent line is y=(1/2)x+4.5 or y=0.5x+4.5

And y=h(x)

So, h(x)=0.5x+4.5

Calculate h(-1), here x=-1:

h(x)=0.5x+4.5

h(-1)=(0.5*-1)+4.5

      =4

h(-1)=4

Calculate h'(-1), x=-1:

Here we get the derivative of the equation of the tangent line h(x)=0.5x+4.5,

h'(x)=0.5x^0+0

h'(-1)=1+0

h'(-1)=1

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Each model should be produced on a weekly basis to maximize net profit is $75,900.

What is Net profit?

In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.

As given,

Number of products sold:

T ≥ 1.5G

Maximize Profit Z = 150T + 130G

Labor Constraint:

Labor hours Available:

Production Department:

Number of labor hours available per day = 58 × 7 = 406

Number of days in a week = 5

Number of lobor ours available per week = 406 × 5 = 2030

Assembly Department:

Number of labor hours available per day = 25 × 7 = 175

Number of days in a week = 5

Number of labor hours available per week = 175 × 5 = 875.

Labor hours Required:

Labor hours required for G1 model:

Labor hours required at Production department = 3.5G

Labor hours required at assembly department = 2G

Labor hours required for T1 model:

Labor hours required at Production department = 4T

Labor hours required at Assembly department = 1.5T

Total labor hours required at Production department = 3.5G + 4T

Total labor hours required at Assembly department = 2G + 1.5T.

Constraint:

Labor hours required ≤ Labor hours Available.

Production department Labor constraint

3.5G + 4T ≤ 2030

Assembly department Labor constraint:

2G + 1.5T ≤ 875

The function:

Maximum Profit Z = 150T +130G

Constraint:

3.5G +4T ≤ 2030

2G + 1.5T ≤ 875

T ≥ 1.5G

Suppose that for example:

10.5G +12T = 6090

 16G + 12T = 7000

Solve both equations simultaneously,

5.5G = 7000 - 6090

5.5G = 910

    G = 910/5.5

    G = 363

Since, T > G

Hence,

T = 363,

G = 165

Calculate Profit:

150T + 130G = 150 × 363 + 130 × 165

                     = 54450 + 21450

                     = 75900

Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.

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Answer:

7x6+5=47

6x5+7=37

7x5+6=41

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

P = 49

Step-by-step explanation:

The square root of 49 = 7

Answer:

49

Step-by-step explanation:

√p = 7

it means that p = 7×7 = 49

because √ p it means = √ a x a = a

hope you understand!

if not, I'll explain it

Answer:

C. 24,000

Step-by-step explanation:

According to the table, 8000 homes of 100,000 are predicted to have 4 or more telephones

From the table, we have the following parameters:

So, the probabilty that a home has 4 or more telephones  is:

P = 12/150

In a community of 100,000 homes, the expected number of homes that has 4 or more telephones is:

E(x) = 12/150 * 100,000

Evaluate

E(x) = 8000

Hence, 8000 homes are predicted to have 4 or more telephones

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Answer:

Time when Jessie starts doing her he: 4:30

Time talked to complete the hw : 40minutes

Time Jessie finishes the hw: 5:10

The equation of the tangent plane to the surface at the point (2, 5, 9) is \(-6x + 6y + z - 27 = 0\).

To find the equation of the tangent plane to the surface defined by the function \(f(x, y) = x^2 - 2xy + y^2\) at the point (2, 5, 9), we need to calculate the gradient of the function and use it to determine the equation.

The gradient of \(f(x, y)\) is given by:

\(\nabla f(x, y) = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right)\)

Taking the partial derivatives:

\(\frac{\partial f}{\partial x} = 2x - 2y\)

\(\frac{\partial f}{\partial y} = -2x + 2y\)

Evaluating these partial derivatives at the point (2, 5), we get:

\(\frac{\partial f}{\partial x}(2, 5) = 2(2) - 2(5) = -6\)

\(\frac{\partial f}{\partial y}(2, 5) = -2(2) + 2(5) = 6\)

Therefore, the gradient at the point (2, 5) is \(\nabla f(2, 5) = (-6, 6)\).

The equation of the tangent plane can be written as:

\((-6)(x - 2) + 6(y - 5) + (z - 9) = 0\)

Simplifying this equation, we get:

\(-6x + 12 + 6y - 30 + z - 9 = 0\)

\(-6x + 6y + z - 27 = 0\)

Hence, the equation of the tangent plane to the surface at the point (2, 5, 9) is \(-6x + 6y + z - 27 = 0\).

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Answer:

x = 15

Step-by-step explanation:

Hope This Helps!

The conditions for conducting one-sample t-procedures are as follows:

1. Random Sample: The data should be obtained from a random sample or a randomized experiment to ensure that it is representative of the population of interest. This condition helps to minimize bias and ensure the validity of statistical inference.

2. Independence: The observations within the sample should be independent of each other. In other words, the values should not be influenced by each other and should be selected or measured independently. Violation of independence can lead to inaccurate results.

3. Normality or Large Sample Size (Central Limit Theorem): The population from which the sample is drawn should follow a normal distribution, or the sample size should be sufficiently large. If the population is known to be normally distributed, there are no specific requirements on the sample size. However, if the population distribution is unknown, the sample size should generally be at least 30 to apply the Central Limit Theorem, which states that the sample mean tends to follow a normal distribution, regardless of the population distribution shape.

4. Outliers: The presence of outliers can have a significant impact on the results of t-procedures. It is important to check for and address any outliers in the data. Outliers can distort the distribution and violate the assumptions of the t-test.

5. Equal Variances (for two-sample t-test): In the case of a two-sample t-test, if comparing two groups, the variances of the two populations should be equal. This assumption is necessary for calculating the correct degrees of freedom and obtaining accurate results. If the variances are not equal, a modified version of the t-test, called the Welch's t-test, can be used instead.

It is important to carefully assess these conditions before conducting one-sample t-procedures to ensure that the results are valid and reliable. Violations of these conditions may require alternative statistical tests or adjustments to the analysis.

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Answer:

D

Step-by-step explanation:

Answer:

23.14

Step-by-step explanation:

= 20.59 x (12.4/100)

= 2.55316

= 2.55316 + 20.59

= 23.14316

= 23.14

I hope this helps.

Answer:

23.14

Step-by-step explanation:

Convert the percentage into decimal form then multiply Marty's current pay rate by that decimal. Add that number to the current pay rate, then round to the nearest penny.

Answer:

X=5

Step-by-step explanation:

Answer:

x = -13/4

Step-by-step explanation:

2x + 1 : 4x + 13 = "number of purple tiles" : "number of white tiles"

We know that "of the tiles" are purple, so we can also write:

(number of purple tiles) / (number of total tiles) =

Combining these two equations, we get:

(2x + 1) / (2x + 1 + 4x + 13) =

Simplifying the denominator, we get:

(2x + 1) / (6x + 14) =

Cross-multiplying, we get:

(2x + 1) = (6x + 14)

Expanding the brackets, we get:

2x + 1 = 6x + 14

Subtracting 2x from both sides, we get:

1 = 4x + 14

Subtracting 14 from both sides, we get:

-13 = 4x

Dividing both sides by 4, we get:

x = -13/4

However, since x represents the number of tiles, it doesn't make sense for it to be negative. Therefore, there must have been a mistake in the question or my working so I'm not entirely sure. Hopefully the work can help out a little though.

The points that lies on the same line are (-3, 12), and, (-1, 4).

Here, we have,

The given coordinate points are (-2, 8) and (5,-20).

Here, slope (m)= 8+20/-2-5

= 28/-7

=-4

Substitute m= -4 and (x, y)=(-2,8) in y=mx+c, we get

8 = 8+c

or, c = 0

So, the equation of a line is y= -4 x

Now,

(-6, -2) in the given equation is -2=-4 (-6)

-2≠ 24

(-3, 12)  in the given equation is y= -4 x

12 = 12

(4, 16) in the given equation is y= -4 x

16 ≠ -16

(0, 6) in the given equation is y= -4 x

6 ≠ 0

(-1, 4) in the given equation is y= -4 x

4 = 4

(7,5) in the given equation is y= -4 x

5 ≠ -28

Therefore, the points that lies on the same line are (-3, 12), and, (-1, 4).

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Log(1), log(-1), log(i) and ii are all numbers written in the form a + bi. Log(1) = 0; log(-1) = undefined; log(i) = 0.5i; ii = -1; a = -1 and b = 0 because the number is in the form a + bi.

Given numbers are;• log(1)• log(-1)• log(i)• iiFor all numbers written in the form a + bi, we must find a and b. Here's how to do it: log(1)In this case, the log is taken in base 10. The result of this is 0. So, we have: log(1) = 0Therefore, a=0 and b=0 because the number is not in the form a + bi. log(-1)In this case, the log is taken in base 10. The result of this is undefined. This is because there is no power to which we can raise 10 to get -1. So, we have: log(-1) = undefinedTherefore, a=undefined and b=undefined because the number is not in the form a + bi. log(i)In this case, the log is taken in base 10. The result of this is 0.5iπ. So, we have: log(i) = 0.5iπTherefore, a=0 and b=0.5π because the number is in the form a + bi. iiIn this case, we are finding the square of i. i is a complex number given as i = 0 + 1i. Therefore, we have: i2 = (0 + 1i)2= (0)2 + 2(0)(1i) + (1i)2= -1This is because i2 = -1. Now, we can write ii as: ii = i × i= (0 + 1i) × (0 + 1i)= 0 + 0i + 0i + 1i2= -1So, we have: ii = -1Therefore, a=-1 and b=0 because the number is in the form a + bi.

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The area of the triangle in the diagram is one square foot.

We know that the area of a triangle of base B and height H is given by the formula:

Area = B*H/2

On the diagram we can se that the measure of the base is 3 ft, and the height is 2/3 ft, then the area of that triangle will be:

Area = (3 ft)*(2/3 ft)/2 = 1 ft²

The area of the triangle is one square foot.

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Answer:

6.44

Step-by-step explanation:

Since, there is a 4 in the hundredths and in the thousandths place there is a 3, then the answer should round off to 6.44 because you only round the 4 up to a 5 if the number in the thousandths place is 5 or greater.

Hope this helps!

a) The x-component of vector a is -7.5 m/s². b) The y-component of vector a is 0 m/s². c) The x-component of vector v is 294.8 m/s. d) The y-component of vector v is -170 m/s. e) The x-component of vector r is 9.422 m. f) The y-component of vector r is 5.596 m.

a) The x-component of a vector is the magnitude of its displacement in the x-direction. In this case, the x-component of vector a is given as -7.5 m/s², indicating that the vector points in the negative x-direction.

b) The y-component of a vector is the magnitude of its displacement in the y-direction. Since vector a is stated to be in the negative x-direction, it does not have any displacement in the y-direction. Therefore, the y-component of vector a is 0 m/s².

c) For vector v, the x-component is given as 340 m/s. Since the vector is directed 30 degrees below the positive x-axis, the x-component can be found by multiplying the magnitude by the cosine of the angle. Thus, the x-component of vector v is approximately 294.8 m/s.

d) Similar to the x-component, the y-component of vector v is found by multiplying the magnitude by the sine of the angle. Given that vector v is 30 degrees below the positive x-axis, the y-component is calculated as -170 m/s.

e) Vector r has a magnitude of 11 m and is directed 31 degrees above the positive x-axis. To find the x-component, we multiply the magnitude by the cosine of the angle. Thus, the x-component of vector r is approximately 9.422 m.

f) Similarly, the y-component of vector r is determined by multiplying the magnitude by the sine of the angle. With an angle of 31 degrees above the positive x-axis, the y-component of vector r is approximately 5.596 m.

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