Assume the annual day care cost per child is normally distributed with a mean of ​$9000 and a standard deviation of ​$1000. What percent of day care costs are more than ​$8600 ​annually?

Answer: 4000

Step-by-step explanation:

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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Step-by-step explanation:

Given:

\(\textbf{F} = (2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}\)

This field will have a scalar potential \(\varphi\) if it satisfies the condition \(\nabla \times \textbf{F}=0\). While the first x- and y- components of \(\nabla \times \textbf{F}\) are satisfied, the z-component doesn't.

\((\nabla \times \textbf{F})_z = \left(\dfrac{\partial F_y}{\partial x} - \dfrac{\partial F_x}{\partial y} \right)\)

\(\:\:\:\:\:\:\:\:\: = 3x^2 - 2x \ne 0\)

Therefore the field is nonconservative so it has no scalar potential. We can still calculate the work done by defining the position vector \(\vec{\textbf{r}}\) as

\(\vec{\textbf{r}} = x \hat{\textbf{i}} + y \hat{\textbf{j}} + z \hat{\textbf{k}}\)

and its differential is

\(\textbf{d} \vec{\textbf{r}} = dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}}\)

The work done then is given by

\(\displaystyle \oint_c \vec{\textbf{F}} • \textbf{d} \vec{\textbf{r}} = \int ((2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}) • (dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}})\)

\(\displaystyle = (x^2y + xz^3) + x^3y + xz^3|_{(1, -2, 1)}^{(3, 1, 4)}\)

\(= 422\)

Based on the interval, the average rate of change of the function is 4.0

The graph that completes the question is added as an attachment

From the graph, we can see  that the equation of the graph is a quadratic equation

Also, from the question:

We have the interval to be:

The interval is given as

x = -4 to x = 2

This can be represented as

(a, b) = (-4, 2)

From the attached graph, we have

f(-4) = 22

f(2) = -2

The estimate of the average rate of change f is calculated as(to one decimal place)

Rate = [f(b) - f(a)]/[b - a]

Substitute the known values in the above equation

This gives

Rate = [f(2) - f(-4)]/[2 + 4]

Substitute the known values in the above equation

So, we have

Rate = [-2 - 22]/[2 + 4]

Evaluate

Rate = -4.0

Hence, the estimate (to one decimal place) of the average rate of change of the graph is 4.0

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The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

the graph of the equation y = 2 x - 2 is being obtained.

We are given the equation:

y = 2 x - 2

We need to make the graph of the equation.

We will first find some points on this equation:

x              y

0             -2

1               0

2              2

3              4

4              6

5              8

Now, we will plot these points on the graph and join them with a dark line to obtain the graph of the equation y = 2 x - 2.

Therefore, the graph of the equation y = 2 x - 2 is being obtained.

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Answer:

49.97% probability of getting one child of each sex

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The probability that a couple’s first child is a boy is 0.512.

This means that \(p = 0.512\)

The will have two children:

This means that \(n = 2\)

(a) What is the probability of getting one child of each sex?

This is P(X = 1).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 1) = C_{2,1}.(0.512)^{1}.(0.488)^{1} = 0.4997\)

49.97% probability of getting one child of each sex

There is a probability of 94/315 that the problem will be solved.

We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.

The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.

The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.

The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.

The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.

To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:

2/7 + 4/7 + 4/9 = 94/315

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(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

From the question:

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

Open the brackets and have the following:

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [equation has already been normalized since the coefficient of x² is 1]

Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [subtract 25 from both sides]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

Answer: $60  

Step-by-step explanation:beauce $50 of a 20% of a tip is $10. 20% tip equals $10.

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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Answer:

A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

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Answer:

(14, 2).

Step-by-step explanation:

x - y = 12

y = 2

Solving this system:

Plug y = 2 into the first equation:

x - 2 = 12

x = 14.

Therefore the  point of intersection is at (14, 2).

When we talk of rigid transformation, we refer to transformation that occurs, and the size of the shape is not affected. Of the three options, dilation is the only sort of transformation that affects the size of the object.

DILATION

Answer:

5.5

Step-by-step explanation:

3 + 2x + 2 = 15

4 + 2x = 15

2x = 11

x = 5.5

The rate of current will be "4.5 mph" and the rate Pratap can row in still water will be "8.5 mph".

Given:

Let,

As we know,

→ \(Speed = \frac{Distance}{Time}\)

then,

→ \(x+y = \frac{26}{2}\)

→ \(x+y = 13\)

→       \(x = 13-y\)

In return trip took him time "6.5 hours",

→ \(x -y =\frac{26}{6.5}\)

→ \(x -y = 4\)

By substituting the value of "x", we get

→ \(13-y-y=4\)

      \(13-2y=4\)

              \(2y= 13-4\)

                \(y = \frac{9}{2}\)

                   \(= 4.5 \ mph\) (Rate of the current)

By substituting the value of "y", we get

→ \(x = 13-a\)

   \(x = 13-4.5\)

      \(= 8.5 \ mph\) (Pratap can row in still water)

Thus the above answer is correct.

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Answer:

3 triangles can be make with 60,60,60 degrees.

Answer:

6555

Step-by-step explanation:

Again you can you Distributive property to answer this question here is how-To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Answer:

6555

Step-by-step explanation:

The steps which you would take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/2.

5. Reflect the intermediate image.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

?

Step-by-step explanation:

Answer:

degrees of freedom = 15

tc= 1.746

Step-by-step explanation:

The degrees of freedom is given by n-1 where n is the sample size .

so the degrees of freedom for a t distribution is 16-1= 15

Now we have to find tc for 95%  confidence interval. For this we look at the t- table under the 1-0.95= 0.05  for alpha for 15 degrees of freedom and the value is 1.746

This area is to  the right side under the t distribution with the given degrees of freedom for the given alpha.

It can also be found out by other calculators such as graphing calculator.

Using the degree of freedom formula and the Tcritical distribution, the degree of freedom and Tcritical value are 15 and 2.131 respectively

Given that :

Hence, the degree of freedom, df = 16 - 1 = 15

The t critical value :

Tcritical = \(t_{\frac{0.05}{2}}, 15 = 2.131 \)

Hence, the Tcritical value is 2.131.

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The graph of the equation 3x + 4y = 0 is a straight line with a negative slope passing through the origin.

The given equation, 3x + 4y = 0, represents a linear graph in the Cartesian coordinate system. Let's analyze its characteristics.

First, note that the equation is in the standard form for a linear equation, which is Ax + By = C, where A, B, and C are constants. In this case, A = 3, B = 4, and C = 0.

To graph this equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating y, we have y = (-3/4)x + 0. Since the y-intercept (b) is 0, the line intersects the y-axis at the origin (0,0).

Next, we can examine the slope. The coefficient of x, -3/4, represents the ratio of the change in y (vertical) to the change in x (horizontal) as we move along the line. In this case, the slope is negative, indicating that the line descends from left to right. The magnitude of the slope, 3/4, implies that for every 4 units moved horizontally to the right, the line goes 3 units down vertically.

Therefore, we can conclude that the graph of the equation 3x + 4y = 0 is a straight line passing through the origin (0,0) with a negative slope. It extends indefinitely in both directions, with the line getting steeper as we move to the right.

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\(x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z\)

Therefore, it's \(2z^5-7z\).

10-10=69.420!!!!!!!!!!

Answer:

(a) 167

(b) 7

(c) 97

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean μ is:

\(CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

The margin of error is:

\(MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

Then the formula to estimate the sample size is:

\(n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}\)

(a)

For 99% confidence interval the critical value of z is:

z = 2.58.

The standard deviation is, 250.

Compute the sample size as follows:

\(n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}\)

   \(=[\frac{2.58\times 250}{50}]^{2}\\\\=(12.9)^{2}\\\\=166.41\\\\\approx 167\)

The sample size that should be used is 167.

(b)

Now the standard deviation is, 50.

Compute the sample size as follows:

\(n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}\)

   \(=[\frac{2.58\times 50}{50}]^{2}\\\\=(2.58)^{2}\\\\=6.6564\\\\\approx 7\)

The sample size that should be used is 7.

(c)

Now a 95% confidence level is used.

For 95% confidence interval the critical value of z is:

z = 1.96.

Compute the sample size as follows:

\(n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}\)

   \(=[\frac{1.96\times 250}{50}]^{2}\\\\=(9.8)^{2}\\\\=96.04\\\\\approx 97\)

The sample size that should be used is 97.