Given h of x equals 3 times the square root of x plus 2 end root, which of the following statements describes h(x)?

The probability is approximately 0.9167 or 91.67%.

To find the probability that the sum of two dice numbers does not exceed 10, we need to determine the favorable outcomes (sums less than or equal to 10) and the total possible outcomes when rolling two dice.

There are 36 possible outcomes when rolling two dice because each die has six faces (1, 2, 3, 4, 5, and 6), and the total number of outcomes is obtained by multiplying the number of outcomes for each die (6 * 6 = 36).

Now let's determine the favorable outcomes (sums less than or equal to 10):

When the sum is 2: There is only one combination (1 + 1).

When the sum is 3: There are two combinations (1 + 2 and 2 + 1).

When the sum is 4: There are three combinations (1 + 3, 2 + 2, and 3 + 1).

When the sum is 5: There are four combinations (1 + 4, 2 + 3, 3 + 2, and 4 + 1).

When the sum is 6: There are five combinations (1 + 5, 2 + 4, 3 + 3, 4 + 2, and 5 + 1).

When the sum is 7: There are six combinations (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1).

When the sum is 8: There are five combinations (2 + 6, 3 + 5, 4 + 4, 5 + 3, and 6 + 2).

When the sum is 9: There are four combinations (3 + 6, 4 + 5, 5 + 4, and 6 + 3).

When the sum is 10: There are three combinations (4 + 6, 5 + 5, and 6 + 4).

Adding up the favorable outcomes, we get: 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.

Therefore, the probability that the sum of the two dice numbers does not exceed 10 is given by:

Probability = Favorable outcomes / Total outcomes = 33 / 36 = 11/12 ≈ 0.9167.

So, the probability is approximately 0.9167 or 91.67%.

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Answer:

m = 1/2

Step-by-step explanation:

Look at the points on the graph and determine what the slope would be using the slope formula. y2-y1 / x2-x1.

2 - 0 / 0 - (-4)

2/4

1/2

Answer:

the slope of the line is 2

Step-by-step explanation:

use the formula for the slope of a line: y2-y1/x2-x1

this will give you 2-0/0-(-4) = 2/4

simplified to 2 for the slope.

if the answer you need is just the slope ten it would be 2

if you're looking for the equation of the line it would be y=2x+2

A) To maximize production of chemical Z subject to the budgetary constraint, the optimal values are: Units of chemical P, p = 625 and Units of chemical R, r = 150. B) The maximum number of units of chemical Z under the given budgetary conditions is approximately 60,000 units.

A) To maximize production of chemical Z subject to the budgetary constraint, we need to determine the optimal values for p and r.

Let's set up the budget equation based on the given information:

500p + 2500r = 625,000

Now, let's rewrite the expression for z in terms of p and r:

\(z = 100p * 0.8r^{0.2\)

To simplify the problem, we can rewrite z as:

\(z = 80p * r^{0.2\)

Now, we can substitute the value of z into the budget equation:

\(80p * r^{0.2} = 625,000 - 500p\)

Simplifying further:

\(80p * r^{0.2} + 500p = 625,000\)

B) To find the maximum number of units of chemical Z, we need to solve the equation above and substitute the optimal values of p and r back into the expression for z. Since solving the equation analytically can be complex, numerical methods or optimization techniques are typically used to find the optimal values of p and r that satisfy the equation while maximizing z.

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The sum of forecast errors is also known as total forecast error. Therefore, the correct answer is option A, which is "2."

The absolute error of the given data is calculated by subtracting the actual value from the forecasted value, followed by the absolute value.

The errors are then summed up to get the mean absolute deviation. The value used for ||18−20|| in the calculation of MAD and summing up the forecast errors is 2.

Therefore, the correct answer is option A, which is "2."Formula for calculating MAD:MAD = Σ ( | A_i - F_i | ) / n

Where: MAD is the mean absolute deviation|A_i - F_i| represents the absolute error between the actual value (A) and the forecasted value (F)n is the total number of observations, Sum of forecast errors:Σ ( A_i - F_i )Where: A_i is the actual valueF_i is the forecasted value

The sum of forecast errors is also known as total forecast error.

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer: 12:30 p.m

Step-by-step explanation:

h=hours

97.5=60+12.5h

12.5h=37.5

h=3

9:30 a.m.+h=

9:30 a.m.+ 3=12:30 p.m

Answer:

DB

It's the only line that is not a segment.

Step-by-step explanation:

Answer:

274.89

Step-by-step explanation:

The 2 doesn't affect the next 2 which doesn't affect the 7, that affects the 0 and makes it 1, which doesn't affect the 5, which affects the 8, that affects the 6 and makes it a 7, which affects the next 8, which becomes a 9. Phew!

Hope this helps!

I think the answer is A.CMIIW

Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949

Let W be the event that the robot's camera observes a window

It is given that the Probability of observing a window there is no window at its location is given 0.2

P(W/ L1) = 0.2 ( L1 which does not have a window)

Also, probability of observing a window is 0.9

P(W/ L2) = 0.9 ( L2 has window)

Now we have to find updated probabilities for the robot being in L1 i.e:- P(L1/W) & P(L1/w)

w means the camera does not observe a window.

By Bayes Rule,

P(L1/W) = P(L1)P(W/L1)/P(L1)P(W/L1)+P(L2)P(W/L2)

            = (0.7x 0.2)/ (0.7x0.2) + (0.3x0.9)

            = (0.14)/ 0.14+0.27

            ≈0.341 (rounded to 3. decimal places)

Thus  the probability of being in L1 if the camera observes a window is nearly 0.341.

P(L1/w) = P(L1)P(w/L1)/P(L1)P(w/L1)+P(L2)P(w/L2)

As P(W/L1) = 0.2;

P(w/L1) = 1 - P(w/L1) = 1-0.2 = 0.8

Also P(W/L2) = 0.1;

P(w/L2) = 1 - P(w/L2) = 1-0.9 = 0.1

P(L1/w) = (0.7 X 0.8)/ (0.7X0.8) + (0.3X0.1)

           =(0.56)/ (0.56+0.03) = (0.56/ 0.59)

           ≈ 0.949 (rounded to 3 decimal places).

Thus the probability of being in L1 if observe not the window is nearly 0.949.

Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949

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Answer: 14

Step-by-step explanation: I solved the equation

Answer:

14 dollars

Step-by-step explanation:

Answer:

\(12-t+6t^2\)

Step-by-step explanation:

Find the one with the highest exponent 2.

\(12-t+6t^2\) is the only one

Answer:

h(t) = 12 -t+6t^2

Step-by-step explanation:

A quadratic function has the highest power of the variable as 2 and must have a power of 2

h(t) has a power of 3

g(t) has a power of 3

k(t) has a power of 4

The percent increase in players from last year to this year = 20%

We know that the formula for the percentage change a quantity is :

(P) = [Final value - Initial value] / Initial value x 100

Here, a baseball team had 80 players show up for tryouts last year and this year 96 show up for tryouts.

initial number of players = 80

current number of players = 96

So, using above formula the percent increase in players is:

P = [(96 - 80) / (80)] x 100

P = (16 / 80) x 100

P = 0.20 x 100

P = 20%

Therefore, the percentage of increase in players =  20%.

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Answer:

z = 3

Step-by-step explanation:

z - (-12) = 15

z + 12 = 15

z = 15 - 12

z = 3

Thus, The value of z is 3

-TheUnknownScientist

Answer:

3

Step-by-step explanation:

z+12=15

z+12-12=15-12

z=3

Step-by-step explanation:

The formula for area is l x b. This stands for length and breadth. I can multiply 1000(100) to get 100,000m. The area of the lawn is 100,000 m.

HOPE IT HELPS YOU

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The range of the test scores in Mr. Miller's math class is 42.

Mathematically, the range refers to the difference between the highest value and the lowest value in a data set.

The range is computed by subtraction of the lowest value from the highest value.

Mr. Miller can use the range to measure the spread or dispersion of the test scores.

Test Scores:

52, 61, 69, 76, 82, 84, 85, 90, 94

Highest score = 94

Lowest score = 52

Range = 42 (94 - 52)

Thus, we can conclude that for the math students in Mr. Miller's class, the range of their test scores is 42.

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The points which lie on the circle represented by the equation as required are

It follows from the task content that the points which lie on the circle whose equation is as given are to be determined.

Since the given equation is; (x-2)² + (y+6)² ='5²

By testing each pair of coordinates we have;

For (-2, -3);

For (5, -10);

For (5, -2);

For (2, -6);

For (-2, 1);

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The dimensions need to be picnic table is 3 ft x 6 ft.

What is quadratic equation?

An algebraic equation of the second degree in x is a quadratic equation.

The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The coefficient of x2 must be a non-zero term  in order for an equation to meet the definition of a quadratic equation. Quadratic equations include the second and no higher power of an unknown number or variable.

18 square feet limits the area and amount of working material, and we have a rectangular table with

Width = w

Length = w + 3

Length x Width = Area

(w +3)w = 18

w2 + 3w = 18

w2 + 3w  - 18 = 0

factoring

(w + 6) (w - 3)

w cannot be -6

w = 3 ft

L = w + 3 = 3 +3 = 6 ft

So we have a Width of 3 ft and a Length of 6 ft

3 ft x 6 ft = 18 ft²

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The simplified expression of |(1/4-1/5)+(-3/4+1/8)| is |-0.57|.

In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD). As an illustration, LCM (4, 5) = 20. In this case, the LCM 20 may be divided by both 4 and 5, hence these two numbers are referred to as the divisors of 20.

When the fractions' denominators differ, LCM can also be used to add or subtract any two fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction.

The given expression is:

|(1/4-1/5)+(-3/4+1/8)|

Take the LCM:

|(5 - 4)/ 20 + (-24 + 4)  32|

|1/20 - 20/32|

Take the LCM:

|(32 - 400) / 640|

|-368 / 640|

|-0.57|

Hence, the simplified expression of |(1/4-1/5)+(-3/4+1/8)| is |-0.57|.

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Although part of your question is missing, you might be referring to this full question: If the 1st person saves 1/4 of total, 2nd person saves 2/3 of total, and 3rd person saves 1/10, which fraction left to pay for the birthday party?

The fraction left to pay for the birthday party is 17/30.

The calculation is as follows:

1 * 1/4 = 1/4 … (1)

1/4 * 2/3 = 2/12 … (2)

2/12 * 1/10 = 2/120 … (3)

Fraction left to pay:

= 1 - (1/4 + 2/12 + 2/120)

= 1 - (30/120 + 20/120 + 2/120)

= 1 - (52/120)

= 1 - 13/30

= 30/30 - 13/30

= 17/30

Thus, the fraction left to pay for the birthday party is 17/30.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, where the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

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Answer:

The measurement of angle H is 58°

Answer:

77

Step-by-step explanation:

G =2H+6=180

2H+6=180

2H=180-6

2H=154

H=154/2

=77

The circumference of the circle is given as follows: C = 109.9 in.

The relationship between the diameter of a circle and it's circumference is presented in this problem.

We have,

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:

r = 0.5 x 35

r = 17.5 in.

Then the circumference of the circle is given as follows:

C = 2 x pi x 17.5

C = 109.9 in.

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Missing Information

The problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.

Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.

Step-by-step explanation:trust me

Answer: B

Step-by-step explanation:

The result of 3.0×\(10^{15}\) over 5.0×\(10^6\) in scientific notation is 6×\(10^8\)

The first number = 3.0×\(10^{15}\)

The second number = 5.0×\(10^6\)

3.0×\(10^{15}\) over 5.0×\(10^6\) means we have to divide the first number by the second number

The scientific notation is the a method of representing the a very large number or a very small number in a simple way. The general from of the scientific notation is when a number from 1 to 10 is multiplied by the power of 10.

Here we have to divide 3.0×\(10^{15}\) by 5.0×\(10^6\)

3.0×\(10^{15}\)  ÷ 5.0×\(10^6\) = (3/5) × \(10^{15-6}\)

= 0.6×\(10^9\)

= 6×\(10^8\)

Hence, the result of 3.0×\(10^{15}\) over 5.0×\(10^6\) in scientific notation is 6×\(10^8\)

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Answer: They are both parallel because they are horizontal lines, and their slope is both 0. You can do (y2-y1)/(x2-x1), but you would see that the y will be the same for both coordinates so the slope would be 0/x.

Step-by-step explanation:

The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Answer:

Yes, Samuel dart does land on the dart board

Step-by-step explanation:

The given parameters are;

The height from the floor to the bulls eye = 5 feet 8 inches

The size of the standard board = 18 inches diameter

The distance of the bulls eye from the wall to the left = 11 feet

The distance the dart Samuel throws land from the left wall = 11.5 feet

The distance above the ground, the dart Samuel throws land = 5.5 feet

Whereby Samuel throws the dart directly at the dartboard, we have;

The location of the bulls eye = (11, 5.67)

The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625

The unit of the radius is in feet

The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)

Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;

(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²

Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;

Yes, Samuel dart does land on the dart board.

From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;

Samuel's dart does not land on the dartboard.

We are given;

Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft

Diameter of the standard dartboard = 18 in = 1.5 ft

Thus, radius; r = 1.5/2 = 0.75 ft

Distance of the bulls eye from the wall to the left = 11 ft

Distance of dart thrown by Samuel from the left wall = 11.5 ft

Height of dart thrown by Samuel above the ground = 5.5 ft

We know that general equation of a circle is;

(x - a)² + (y - b)² = r²

Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft

And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft

Thus;

(x - 11)² + (y - 5.67)² = 0.75²

(x - 11)² + (y - 5.67)² = 0.5625

Now, since he throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor. Thus;

r² = (11.5 - 11)² + (5.5 - 5.67)²

r² = 0.2789

r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.

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To solve the given equation 2tan²x + sec²x - 2 = 0, we can use trigonometric identities to simplify it and find the solutions.

Let's manipulate the equation step by step:

2tan²x + sec²x - 2 = 0

Using the identity sec²x = 1 + tan²x:

2tan²x + (1 + tan²x) - 2 = 0

Simplifying further:

3tan²x - 1 = 0

Now, let's solve this equation for tan²x:

3tan²x = 1

tan²x = \(\frac{1}{3}\)

Taking the square root of both sides:

tanx = \(\pm\sqrt{\frac{1}{3}}\)

The solutions for tanx are:

tanx = \(\sqrt{\frac{1}{3}}\) and \(-\sqrt{\frac{1}{3}}\)

To find the solutions for x, we'll determine the corresponding angles using the inverse tangent function:

\(x = \arctan\left(\sqrt{\frac{1}{3}}\right)\)

\(x = \arctan\left(-\sqrt{\frac{1}{3}}\right)\)

Using a calculator, we can find the values of x in the range [0, 2π):

x ≈ 0.61548 rad and x ≈ 2.52674 rad

Now, let's check the options provided:

a. \(x = \frac{\pi}{3} + \pi k\), where k is any integer

Substituting k = 0, we have x = π/3, which is not one of the solutions we found.

b. \(x = \frac{\pi}{6} + \pi k\), where k is any integer

Substituting k = 0, we have x = π/6, which is one of the solutions we found.

c. \(x = \frac{2\pi}{3} + \pi k\), where k is any integer

Substituting k = 0, we have x = 2π/3, which is not one of the solutions we found.

d. \(x = \frac{5\pi}{3} + \pi k\), where k is any integer

Substituting k = 0, we have x = 5π/6, which is one of the solutions we found.

Based on our analysis, the correct solutions are:

b. \(x = \frac{\pi}{6} + \pi k\), where k is any integer

d. \(x = \frac{5\pi}{3} + \pi k\), where k is any integer

Therefore, the answer is (b) and (d).

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