What is the minimum value of the function over the interval -5 < x < 5?

h(x) = log[(x – 3)^2 + 2]

Answer:

d≥24

Step-by-step explanation:

19≤−5+d

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

−5+d≥19

Add 5 to both sides.

d≥19+5

Add 19 and 5 to get 24.

d≥24

Answer:

c

Step-by-step explanation:

Answer:

61 miles

Step-by-step explanation:

Since the distance Mia travels is constant, we can find the distance travelled over four days by multiplying 15 1/4 by 4:

(15 1/4) * 4 = 61

Thus, Mia travels 61 miles in 4 days

Probability of receiving a hand with exactly three suits \(= (4 * (13^3)) / 2,598,960\)

What is Combinatorics?

Combinatorics is a branch of mathematics that deals with counting, arranging, and organizing objects or elements. It involves the study of combinations, permutations, and other related concepts. Combinatorics is used to solve problems related to counting the number of possible outcomes or arrangements in various scenarios, such as selecting items from a set, arranging objects in a specific order, or forming groups with specific properties. It has applications in various fields, including probability, statistics, computer science, and optimization.

To calculate the probability of receiving a hand with exactly three suits when dealt 5 cards from a well-shuffled deck of cards, we can use combinatorial principles.

There are a total of 4 suits in a standard deck of cards: hearts, diamonds, clubs, and spades. We need to calculate the probability of having exactly three of these suits in a 5-card hand.

First, let's calculate the number of favorable outcomes, which is the number of ways to choose 3 out of 4 suits and then select one card from each of these suits.

Number of ways to choose 3 suits out of 4: C(4, 3) = 4

Number of ways to choose 1 card from each of the 3 suits\(: C(13, 1) * C(13, 1) * C(13, 1) = 13^3\)

Therefore, the number of favorable outcomes is \(4 * (13^3).\)

Next, let's calculate the number of possible outcomes, which is the total number of 5-card hands that can be dealt from the deck of 52 cards:

Number of possible outcomes: C(52, 5) = 52! / (5! * (52-5)!) = 2,598,960

Finally, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:

Probability of receiving a hand with exactly three suits =\((4 * (13^3)) / 2,598,960\)

This value can be simplified and expressed as a decimal or a percentage depending on the desired format.

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(a) Find y′ by implicit differentiation.

y′= 14x/3y²

(b) Solve the equation explicitly for y and differentiate to get y ' in terms of x.

y′= 14x/3y²

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part

(a). y′= 14x/3y²

(a) Find y′ by implicit differentiation.

7x^2 - y^3 = 8

Differentiate both sides with respect to x.

Differentiate 7x^2 with respect to x using power rule which states that if

y = xⁿ, then y' = nxⁿ⁻¹.

Differentiate y^3 with respect to x using chain rule which states that if

y = f(u) and u = g(x),

then y' = f'(u)g'(x).

Therefore,

y' = d/dx[7x²] - d/dx[y³]

= 14x - 3y² dy/dx

For dy/dx,

y' - 14x

= -3y² dy/dx

dy/dx = y' - 14x/-3y²

=14x/3y²

(b) Solve the equation explicitly for y and differentiate to get y ' in terms of x.

7x² - y³ = 8y³

= 7x² - 8y

= [7x² - 8]^(1/3)

Differentiate y with respect to x by using chain rule which states that if

y = f(u) and u = g(x), then

y' = f'(u)g'(x).

Therefore,

y' = d/dx[(7x² - 8)^(1/3)]

= 14x/3(7x² - 8)^(2/3)

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part

(a).y' = 14x/3(7x² - 8)^(2/3)

y' = 14x/3y²

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The given lengths of 3 feet, 3 feet, and 7 feet cannot form a triangle because they do not satisfy the Triangle Inequality Theorem, which is the sum of the lengths of any two sides is greater than the length of the third side.

To form a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Let's apply this theorem to the given lengths of 3 feet, 3 feet, and 7 feet:

The sum of the first two sides is 3 + 3 = 6 feet, which is less than the length of the third side of 7 feet. So, the first two sides cannot form a triangle.

The sum of the first and third sides is 3 + 7 = 10 feet, which is greater than the length of the second side of 3 feet. However, the sum of the second and third sides is 3 + 7 = 10 feet, which is also greater than the length of the first side of 3 feet.

Therefore, neither of the two combinations of sides satisfy the Triangle Inequality Theorem, and so it is impossible to form a triangle with sides of 3 feet, 3 feet, and 7 feet.

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Answer:

(-2,-1)

Step-by-step explanation:

f(x)=3 - 2x

y = 3 - 2x

if x = - 2

y =3 - 2(-2)

= -1

Required ordered pair is (-2,-1)

Answer:Answer:

(-2,-1) (2,-1) (-1,5)

Step-by-step explanation:

f(x)=3 - 2x

y = 3 - 2x

if x = - 2

y =3 - 2(-2)

= -1

Required ordered pair is (-2,-1)

Step-by-step explanation:

Answer:

x = 33

Step-by-step explanation:

(x + 13) + (4x + 2) = 180

x + 13 + 4x + 2 = 180

5x + 15 = 180

5x = 180 - 15

5x = 165

x = 165/5

x = 33

Check:

(x + 13) + (4x + 2) = 180

(33 + 13) + 4(33) + 2 = 180

46 + 132 + 2 = 180

46 + 134 = 180

Total possible outcomes  = (2)⁴ = 16  

Probability of getting all tail   = 1/16  

Probability of getting all heads   = 1/16

Probability = 1/16 + 1/16 = 2/16 = 0.125 = 12.5%

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The probability of randomly selecting the chair and the ranking member is 1/105 or approximately 0.0095.

There are 15 members of the Senate Committee on Homeland Security and Governmental Affairs, two of whom are selected to serve as the committee chair and ranking member. Each member is equally likely to be chosen for either of these positions.

To begin, we must first determine the total number of ways two members can be selected from a committee of 15. This is calculated using the combination formula:

nCr = (n!)/((r!)(n-r)!)where n = 15 and r = 2.

Thus,

nC2 = (15!)/((2!)(15-2)!)

nC2 = (15x14)/(2x1)nC2

= 105

Now we must determine the probability of selecting one member to be the committee chair and the other to be the ranking member.

This is calculated as follows: P = 1/105 or approximately 0.0095. Hence, the probability of randomly selecting the chair and ranking member is 1/105 or approximately 0.0095.

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Answer:

Make the denominators equal by L.C.M

--> 8/20 + 5/20

--> 13/20

Answer:

-0,73

Step-by-step explanation:

\( - 11 \div 15\)

\( = - 0.73\)

Answer:100-K

Step-by-step explanation:

"100 decreased by a number K" can be written algebraically as:

100 - K

This expression represents the result of subtracting the value of K from 100.

Answer:

6.3 dollar

Step-by-step explanation:

its just magic

Answer:

$6.30 of shipping and handling.

Step-by-step explanation:

The gold necklace is priced at $63 dollars. We would have to take 10% of the price to find the shipping fee.

10% of 63 = 63 * 0.1 = 6.30

The shipping and handling fee would be $6.30.

Hope this helps.

Given: A table of velocity values. Let us find an upper estimate for the total distance traveled using n = 4 subdivisions and n = 2 subdivisions.The table of velocity values is shown below.

The formula for distance traveled is given by:$\Delta x=\sum_{i=1}^n v(t_i)\Delta t$The upper estimate for the total distance traveled using n = 4 subdivisions is:Distance traveled $= \Delta x = \sum_{i=1}^4 v(t_i) \Delta t$Here, $\Delta t = \dfrac{12-0}{4}=3$.Let us now substitute the values of velocity in the above formula.$\Delta x = v(0)3 + v(3)3 + v(6)3 + v(9)3 + v(12)3$$\Delta x = 0(3) + 3(3) + 9(3) + 15(3) + 21(3)$$\Delta x = 0 + 27 + 81 + 135 + 189$$\Delta x = 432$The upper estimate for the total distance traveled using n = 4 subdivisions is 432.The distance traveled using n = 2 subdivisions is:$\Delta x = \sum_{i=1}^2 v(t_i) \Delta t$Here, $\Delta t = \dfrac{12-0}{2}=6$.Let us now substitute the values of velocity in the above formula.$\Delta x = v(0)6 + v(6)6 + v(12)6$$\Delta x = 0(6) + 9(6) + 21(6)$$\Delta x = 0 + 54 + 126$$\Delta x = 180$Which of the two answers in part (A) is more accurate?Answer: n = 4 is more accurate than n = 2. Because, if we use more subdivisions, it gives us a better estimate. In other words, as n increases, the accuracy of our estimate increases.The lower estimate for the total distance traveled using n = 4 is:$\Delta x = \sum_{i=1}^4 v(t_i) \Delta t$Here, $\Delta t = \dfrac{12-0}{4}=3$.Let us now use the lower estimate and substitute the minimum value of velocity in the formula.$\Delta x = v(0)3 + v(3)3 + v(6)3 + v(9)3 + v(12)3$$\Delta x = 0(3) + 3(3) + 6(3) + 9(3) + 12(3)$$\Delta x = 0 + 9 + 18 + 27 + 36$$\Delta x = 90$Hence, the lower estimate for the total distance traveled using n = 4 is 90.

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The velocity v(t) in the table below is increasing for 0 t 12. The lower estimate for the total distance traveled using n = 4 is 90.

Given: A table of velocity values. Let us find an upper estimate for the total distance traveled using n = 4 subdivisions and n = 2 subdivisions.

The formula for distance traveled is given by:\($\Delta x=\sum_{i=1}^n v(t_i)\Delta t$\).

The upper estimate for the total distance traveled using n = 4 subdivisions is: Distance traveled \($= \Delta x = \sum_{i=1}^4 v(t_i) \Delta t$\).

Here, \($\Delta t = \dfrac{12-0}{4}=3$\).

Let us now substitute the values of velocity in the above formula.

\($\Delta x = v(0)3 + v(3)3 + v(6)3 + v(9)3 + v(12)3$$\Delta x = 0(3) + 3(3) + 9(3) + 15(3) + 21(3)$$\Delta x = 0 + 27 + 81 + 135 + 189$$\Delta x = 432$\)The upper estimate for the total distance traveled using n = 4 subdivisions is 432.

The distance traveled using n = 2 subdivisions is: \($\Delta x = \sum_{i=1}^2 v(t_i) \Delta t$\)

Here, \($\Delta t = \dfrac{12-0}{2}=6$.\)

Let us now substitute the values of velocity in the above formula.\($\Delta x = v(0)6 + v(6)6 + v(12)6$$\Delta x = 0(6) + 9(6) + 21(6)$$\Delta x = 0 + 54 + 126$$\Delta x = 180$\)

Answer: n = 4 is more accurate than n = 2, because, if we use more subdivisions, it gives us a better estimate. In other words, as n increases, the accuracy of our estimate increases.

The lower estimate for the total distance traveled using n = 4 is: \($\Delta x = \sum_{i=1}^4 v(t_i) \Delta t$\)Here,

\($\Delta t = \dfrac{12-0}{4}=3$\).

Let us now use the lower estimate and substitute the minimum value of velocity in the formula.

\($\Delta x = v(0)3 + v(3)3 + v(6)3 + v(9)3 + v(12)3$$\Delta x = 0(3) + 3(3) + 6(3) + 9(3) + 12(3)$$\Delta x = 0 + 9 + 18 + 27 + 36$$\Delta x = 90$\).

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

Step-by-step explanation:

the product of 3 and n in mathematics is 3n or 3 times n The product of a number and three" should be  3n

where n is the number.

IN the answer of the question you would have to explain something like this:

Let n be the number. The product then is  3n

The reason for this is that you could also let n stand for the number, in which case the answer would be 3n

.                                                                        

Answer:

A = 135 cm²

Step-by-step explanation:

The figure is composed of 2 triangles.

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

The total area is the sum of the area of both triangles

A = \(\frac{1}{2}\) × 18 × 7 + \(\frac{1}{2}\) × 18 × 8

   = 9 × 7 + 9 × 8

   = 63 + 72

   = 135 cm²

"A 1993 study showed that teachers tend to favor males over females, thereby creating an inequality in mixed-gender schools."

The sentence that provides the best supporting evidence for the claim that dividing schools by gender improves education is:

"A 1993 study showed that teachers tend to favor males over females, thereby creating an inequality in mixed-gender schools."

This sentence presents a specific study conducted in 1993 that found evidence of teacher bias favoring males over females in mixed-gender schools. This evidence supports the idea that by separating males and females into different schools, the inequality caused by this bias can be mitigated or eliminated, potentially leading to improved education.

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Answer:

x = 46

Step-by-step explanation:

These 2 angles would add up to 180 degrees.

So 41 + (3x+1) = 180

Let's solve for x.

41 + 3x + 1 = 180

Combine like terms.

42 + 3x = 180

subtract 42 from both sides

3x = 180-42

3x = 138

divide both sides by 3

x = 46

Answer:

The answer is below

Step-by-step explanation:

From the image attached we can see that the width of the garden is 6 ft. The length of the garden is the slanting side of the triangle (hypotenuse).

Let x be the length of the garden. The height of the triangle = 40 ft - 15 ft = 25 ft.

The base of the triangle = 80 ft - 75 ft = 5 ft.

The length of the garden is gotten using Pythagoras:

x² = 25² + 5²

x² = 650

x = 25.5 ft.

The area of the garden = length * width = 25.5 * 6 = 153 ft²

Hence the approximate area = 160 ft²

Answer:

-8x² - 106x + 175 = 0

Step-by-step explanation:

Given:

(2x - 7)²- 6(2x - 7)(x-3) = 0

Find:

Solution of the following explanation

Computation:

(2x - 7)²- 6(2x - 7)(x-3) = 0

[(2x)² + (7)² - (2)(2x)(7)] - (12x - 42)(x-3) = 0

[4x² + 49 - 28x] - [12x² - 36x - 42x + 126] = 0

[4x² + 49 - 28x] - [12x² - 78x + 126] = 0

-8x² - 106x + 175 = 0

Types of cardioid are Standard cardioid, Nephroid, Limacon, Deltoid, astroid, hypocycloid, and epitrochoid, each with its own unique properties and applications in mathematics and science.

A cardioid is a geometric shape that is formed by tracing a point on a circle as it rotates around another circle of the same size. There are several types of cardioids, each with its own unique properties and characteristics.

Standard cardioid: This is the most common type of cardioid and is formed by tracing a point on a circle as it rotates around another circle of the same size, with the point always being twice as far from the center of the second circle as it is from the center of the first circle.

Nephroid: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is twice its size. The name "nephroid" comes from the Greek word "nephros," which means kidney, as the shape of the curve resembles a kidney.

Limacon: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is slightly larger than itself. The shape of the curve resembles a figure eight.

Deltoid: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is three times its size. The shape of the curve resembles a triangle.

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Answer:

Add x to both sides so the problem will become -2y =8+x, then you divide both sides by -2 to get y by itself. You will now have y=-4+-x. you'll need to double check this but it should be right. remember that slope intercept form is y=mx + b

Answer:

no, he would write 30 text messages in 10 minutes

Step-by-step explanation:

Answer:Its A

Step-by-step explanation:

Its A because its right believe me

equivalent to One-fourth x is One-half x + one-half x; equation 7 is correct

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same. The given equation is equivalent to the expression one half and one half x.

Given information;

The expression given in the problem is,

(1/4) x \(x\)

Equivalent expression;

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.

For given expression,

1/4 x \(x\)

As the above function is the function of x. Thus it can be written as,

f(x)= 1/4 x \(x\)

The number four is the product of number 2 and number 2. Thus,

f(x)=(1/2x2) x \(x\)

f(x)=(1/2 x 1/2) x \(x\)

Hence the given equation is equivalent to the expression one half and one half x.

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When salt is added to water, the boiling point of water is increased. The boiling point elevation depends on the concentration of salt added. The addition of salt increases the boiling point of water.

The extent of the increase in boiling point is directly proportional to the amount of salt added. Boiling point is defined as the temperature at which the vapor pressure of a liquid is equal to the pressure exerted on it by the surrounding atmosphere.

In layman's terms, this means that a liquid boils when its vapor pressure equals atmospheric pressure. Boiling point of a liquid can be increased or decreased by the addition of solutes such as salt.When a solute such as salt is added to water, the boiling point of water increases due to the phenomenon of boiling point elevation.

This is because the solute particles in the water interfere with the formation of water vapor molecules at the surface of the liquid. As a result, more energy is required to boil the water, which means that the boiling point is elevated.

The amount of elevation is directly proportional to the concentration of salt added. In short, the addition of salt to water increases the boiling point of water.

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1) The standard deviation is 0.275

2) The approximate probability is 0.165

Sampling distribution: The sampling distribution is a probability distribution of a statistic determined from a larger number of samples. A statistic, such as a mean or a standard deviation, is a numerical quantity calculated from data and used to make inferences about the population's parameters.

For the first question, we can use the hypergeometric distribution to find the sampling distribution of the mean when we choose any 2 pumpkins out of 4.

Let X be the number of pumpkins preferred by the 2 children we sample. Then X follows a hypergeometric distribution with N = 4 (total number of pumpkins), n = 2 (number of pumpkins we choose), and K = {0, 1, 2} (possible number of pumpkins preferred).

The probability mass function of X is given by:

P(X = k) = (K choose k) * (N - K choose n - k) / (N choose n)

where (a choose b) is the binomial coefficient "a choose b".

Using this formula and the given weights, we can calculate the probabilities for k = 0, 1, and 2:

P(X = 0) = (2 choose 0) * (2 choose 2) / (4 choose 2) = 1/6

P(X = 1) = (2 choose 1) * (2 choose 1) / (4 choose 2) = 2/3

P(X = 2) = (2 choose 2) * (2 choose 0) / (4 choose 2) = 1/6

Now we can find the mean and standard deviation of the sampling distribution of the mean, which is approximately normal by the central limit theorem since the sample size is relatively small:

Mean = E(X) = n * (K/N) = 2 * [(00.2)+(10.3)+(2*0.35)] / 4 = 0.95

Standard deviation = sqrt(n * K/N * (1 - K/N) * (N - n)/(N - 1))

= sqrt(2 * 0.95 * (1 - 0.95) * 2/3)

= 0.275

For the second question, we can use the central limit theorem to approximate the sampling distribution of the sample mean. Since we have a large sample size (n = 50), the sample mean X follows an approximately normal distribution with mean μ = 4.0 g and standard deviation

σ/sqrt(n) = 1.5/sqrt(50) ≈ 0.212 g.

Then, we can calculate the z-scores for the lower and upper bounds of the interval:

z_1 = (3.5 - 4.0) / 0.212 ≈ -2.36

z_2 = (3.8 - 4.0) / 0.212 ≈ -0.94

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(Z < -2.36) ≈ 0.009

P(Z < -0.94) ≈ 0.174

Then, we can find the probability that X falls within the interval [3.5, 3.8] by taking the difference between these probabilities:

P(3.5 ≤ X ≤ 3.8) ≈ P(-2.36 ≤ Z ≤ -0.94) ≈ 0.174 - 0.009 ≈ 0.165

Therefore, the approximate probability that the sample average amount of impurity X is between 3.5 and 3.8 g is 0.165.

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