A baby gains 11 pounds in its first year of life. The baby gained 4 1/4 pounds during the first four months and 3 1/2 pounds in it's second four months. how much did the baby gain in the last four months?​

Answer:

The interest is $12

Step-by-step explanation:

You just put the percent in a decimal form(6%-0.06)Then you multiply 200 with 0.06. And the answer you get is the interest

Hope that helps :)

The function f(x) = -5x^4 + 20x^3 + 10 is concave down on the interval (0, 2) and concave up on the intervals (-∞, 0) and (2, +∞). The inflection points are (0, 10) and (2, 90).

To determine the intervals on which the function f(x) = -5x^4 + 20x^3 + 10 is concave up or concave down and identify any inflection points, we need to find the second derivative of the function and examine its sign changes.

First, let's find the first derivative of f(x) with respect to x:

f'(x) = -20x^3 + 60x^2

Next, we find the second derivative by taking the derivative of f'(x):

f''(x) = -60x^2 + 120x

Now, to determine the intervals of concavity, we need to find where the second derivative is positive (concave up) and where it is negative (concave down). We can do this by solving the inequality:

f''(x) > 0

-60x^2 + 120x > 0

Simplifying the inequality:

-60x(x - 2) > 0

Now, we can identify the critical points by setting each factor equal to zero:

-60x = 0

x = 0

x - 2 = 0

x = 2

We have two critical points: x = 0 and x = 2.

Now, we can construct a sign chart for f''(x) to determine the intervals of concavity:

scss

Copy code

  |     -60x     |    +120x     |

-------------------------------------

x  | (-∞, 0)  | (0, 2) | (2, +∞) |

f''(x) |     -       |     +      |     -       |

From the sign chart, we can see that f''(x) is negative (concave down) on the interval (0, 2) and positive (concave up) on the intervals (-∞, 0) and (2, +∞).

To find the inflection point(s), we need to determine where the concavity changes. In this case, the concavity changes at x = 0 and x = 2, which are the critical points we found earlier. Therefore, we have two inflection points: (0, f(0)) and (2, f(2)).

Finally, to find the y-values of the inflection points, we substitute the x-values into the original function:

f(0) = -5(0)^4 + 20(0)^3 + 10 = 10

f(2) = -5(2)^4 + 20(2)^3 + 10 = -80 + 160 + 10 = 90

Hence, the inflection points are (0, 10) and (2, 90).

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There are 364 different committees of 3 people. There are 436 different committees of 4 people.

There are different scenarios for which we can calculate the number of possible committees. Here are a few examples:

To calculate the number of different committees of 3 people, we can use the combination formula, which is:

\(${n \choose k} = \frac{n!}{k!(n-k)!}$\)

where n is the total number of people and k is the number of people needed for the committee. Using this formula, we get:

\(${14 \choose 3} = \frac{14!}{3!(14-3)!} = \frac{14!}{3!11!} = 364$\)

Therefore, there are 364 different committees of 3 people that can be formed from this group.

To solve this problem, we can use the principle of inclusion-exclusion. First, we calculate the total number of committees of 4 people, which is:

\(${14 \choose 4} = \frac{14!}{4!(14-4)!} = \frac{14!}{4!10!} = 1001$\)

Next, we calculate the number of committees that do not include a freshman, which is:

\(${12 \choose 4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!} = 495$\)

Similarly, we calculate the number of committees that do not include a sophomore, a junior, and a senior, which are:

\(${11 \choose 4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!} = 330$\)

\(${10 \choose 4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$\)

\(${9 \choose 4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126$\)

Now we can apply the principle of inclusion-exclusion, which is:

Total number of committees - (number of committees without a freshman + number of committees without a sophomore + number of committees without a junior + number of committees without a senior) + (number of committees without a freshman and without a sophomore + number of committees without a freshman and without a junior + number of committees without a freshman and without a senior + number of committees without a sophomore and without a junior + number of committees without a sophomore and without a senior + number of committees without a junior and without a senior) - number of committees without any freshmen, sophomores, juniors, or seniors.

Plugging in the values, we get:

$1001 - (495 + 330 + 210 + 126) + (66 + 120 + 165 + 84 + 55 + 35) - 1 = 436$

Therefore, there are 436 different committees of 4 people that can be formed, with at least one person from each grade level.

Note that for the last step, we subtracted 1 because there is only one committee that has no freshmen, sophomores, juniors, or seniors.

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Answer:

x = 15

Step-by-step explanation:

Break the bracket, we get :

3(2x+5) = 6x + 15
6x + 15 = 3x + 4x = 7x

6x + 15 = 7x

15 = 7x - 6x = x

So, x = 15

The correct answer is (B) Approximately normal with mean 65 years and standard deviation (10.6)/√5 years.

To determine the distribution of the 200 sample mean ages, we need to consider the properties of the sampling distribution of the mean.

According to the Central Limit Theorem, when the sample size is sufficiently large, the sampling distribution of the mean tends to follow a normal distribution regardless of the shape of the population distribution.

In this case, we have 200 trials with each trial consisting of a random sample of 5 senators' ages. The sample size of 5 is relatively small, so the Central Limit Theorem may not be applicable.

However, the sample size of 5 is larger than 30% of the total population size (100 senators), which is a general rule of thumb for the Central Limit Theorem to still hold reasonably well.

Therefore, we can approximate the distribution of the 200 sample mean ages as approximately normal with a mean equal to the population mean of 65 years.

To determine the standard deviation of the sampling distribution of the mean, we divide the population standard deviation (10.6 years) by the square root of the sample size.

Thus, the correct answer is (B) Approximately normal with mean 65 years and standard deviation (10.6)/√5 years.

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The length of the base of the parallelogram is 16 inches.

What is parallelogram?

A parallelogram is a four-sided plane figure with opposite sides parallel and congruent (having the same length). This means that the opposite sides of a parallelogram are parallel to each other and have the same length. Additionally, the opposite angles of a parallelogram are equal in measure, which means they have the same degree of rotation.

Let's use the information given in the problem to set up an equation and solve for the length of the base.

From the problem, we know that the height of the parallelogram is 5 inches.

h = 5

We also know that the base of the parallelogram is six more than twice the height. Let's use b to represent the length of the base:

b = 2h + 6

Now we can substitute the value we know for the height and solve for the base:

b = 2(5) + 6

b = 10 + 6

b = 16

Therefore, the length of the base of the parallelogram is 16 inches.

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The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30

The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.

The remainder following the division of 17 and 30 by the number N are the same.

Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;

17/N = Q + R/17

30/N = b·Q + R/17

30/N - 17/N = 13/N

The substitution property indicates that we get the following equation;

30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q

30/N - 17/N = b·Q - Q

13/N = b·Q - Q = (b - 1)·Q

13/N = (b - 1)·Q

The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13

13 is a prime number, therefore, the factors of 13 are 13 and N

Therefore, the possible values of N are 13 and 1

The largest value N can have is therefore, 13

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When performing a hypothesis test on the population mean (μ) when the population standard deviation (σ) is known, the null hypothesis (H0) can never be rejected if the sample mean falls within the acceptance range determined by the chosen significance level and the critical values.

In hypothesis testing for the population mean when the population standard deviation is known, the null hypothesis (H0) represents the claim or assumption that the population mean is equal to a specific value. The alternative hypothesis (Ha) states that the population mean is not equal to the specific value.

To determine whether to reject or fail to reject the null hypothesis, we compare the sample mean to the expected value under the null hypothesis. If the sample mean falls within the acceptance range determined by the chosen significance level and the critical values, we do not have sufficient evidence to reject the null hypothesis. The acceptance range is defined by the margin of error around the expected value, and it indicates the range of values that can be considered reasonably close to the expected value.

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Answer:

A and D are the only ones correct

Step-by-step explanation:

I did it

Answer: A D

Step-by-step explanation:

There u go

The function g(x, y, z) that satisfies g = (y - 3z, x + 2z, 2y - 3x) can be defined as g(x, y, z) = (y - 3z, x, 2y - 3x).

To determine a function g(x, y, z) that satisfies g = (y - 3z, x + 2z, 2y - 3x), we need to find expressions for each component of g in terms of x, y, and z.

For the first component, g₁(x, y, z), we can simply assign y - 3z since it matches the first component of the given vector (y - 3z, x + 2z, 2y - 3x).

For the second component, g₂(x, y, z), we assign x + 2z, again matching the second component of the given vector.

Finally, for the third component, g₃(x, y, z), we assign 2y - 3x, which matches the third component of the given vector.

Therefore, the function g(x, y, z) that satisfies g = (y - 3z, x + 2z, 2y - 3x) is g(x, y, z) = (y - 3z, x, 2y - 3x).

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The Percent increase in the number of mobile users in India from last year to this year is 25%.

The percent increase in the number of mobile users in India from last year to this year, we can use the following formula:

Percent Increase = (New Value - Old Value) / Old Value * 100

Given that there were 432 million mobile users last year and it increased to 540 million mobile users this year, we can substitute these values into the formula:

Percent Increase = (540 million - 432 million) / 432 million * 100

Simplifying the calculation:

Percent Increase = 108 million / 432 million * 100

Percent Increase = 0.25 * 100

Percent Increase = 25

Therefore, the percent increase in the number of mobile users in India from last year to this year is 25%.

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To start, let's sketch the graph of the curve y = x from x = 0 to x = 20. This is simply a diagonal line that passes through the points (0,0) and (20,20), as shown below:

```
   |
20  |    *
   |   *  
   |  *  
   | *    
   |*    
0  --------------
  0   10   20
```

Now, we want to revolve this curve around the x-axis to create a solid shape. Specifically, we want to create a paraboloid, which is a three-dimensional shape that looks like an upside-down bowl.

To find the volume of this paraboloid, we need to use calculus. The basic idea is to slice the solid into very thin disks, and then add up the volumes of all the disks to get the total volume.

To do this, we'll use the formula for the volume of a cylinder, which is:

V = πr^2h

where r is the radius of the cylinder and h is its height. In our case, each disk is a cylinder with radius r and height h, where:

- r is equal to the y-value of the curve (i.e. r = y = x), since the disk extends from the x-axis to the curve.
- h is the thickness of the disk, which is a very small change in x. We can call this dx.

So, the volume of each disk is:

dV = πr^2dx
  = πx^2dx

To find the total volume of the paraboloid, we need to add up the volumes of all the disks. This is done using an integral:

V = ∫(from x=0 to x=20) dV
 = ∫(from x=0 to x=20) πx^2dx

Evaluating this integral gives us:

V = π/3 * 20^3
 = 8000π/3

So the exact volume of the paraboloid is 8000π/3.

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Answer:

7.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let's evaluate :

Answer:

Angle k is 34.5 degrees

Step-by-step explanation:

a circle makes 360 degrees total.  okay so u have to consider the angles given. m arc go= 127

m<0 = 54.5

54.5 times 2 = 109

109 is arc gk

109 + 127+ 55= 291

360-291=69= arc OU

69 divided by 2 is 34.5

Angle k is 34.5 degrees

To find the largest four-digit value of t such that the expression is an integer, we need to set up an equation and solve for t.

Let's denote the given expression as x:

x = √(t - √(t - √(t - √(t - ...)))

To simplify the expression, we notice that the inner square root can be represented by x itself. So we can rewrite the equation as:

x = √(t - x)

Squaring both sides to eliminate the square root:

x^2 = t - x

Rearranging the equation:

x^2 + x - t = 0

To find the largest four-digit value of t, we can iterate through the values of t starting from 9999 and solve the quadratic equation for x. We are looking for a positive integer solution for x. Once we find the largest value of t that satisfies this condition, we have our answer.

By solving the quadratic equation for different values of t, the largest four-digit value of t that satisfies the condition is 9985.

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Answer:

Ok so a tree diaphragm is used in math. The answer is b a written list because it’s a little small diaphragm used for math also I’m in sixth grade

Step-by-step explanation:

The Radical Form (√x)  ,the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

The equation √x - 2 + 4 = x for x, we can follow these steps:

1. Begin by isolating the radical term (√x) on one side of the equation. Move the constant term (-2) and the linear term (+4) to the other side of the equation:

  √x = x - 4 + 2

2. Simplify the expression on the right side of the equation:

  √x = x - 2

3. Square both sides of the equation to eliminate the square root:

  (√x)^2 = (x - 2)^2

4. Simplify the equation further:

  x = (x - 2)^2

5. Expand the right side of the equation using the square of a binomial:

  x = (x - 2)(x - 2)

  x = x^2 - 2x - 2x + 4

  x = x^2 - 4x + 4

6. Move all terms to one side of the equation to set it equal to zero:

  x^2 - 4x + 4 - x = 0

  x^2 - 5x + 4 = 0

7. Factor the quadratic equation:

  (x - 1)(x - 4) = 0

8. Apply the zero product property and set each factor equal to zero:

  x - 1 = 0   or   x - 4 = 0

9. Solve for x in each equation:

  x = 1   or   x = 4

Therefore, the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

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Since a phone with one payment plan and one accessory is given away at random, we need to consider only the rows where the payment plan is 1 and the column where the accessory is a headset. Looking at the table, we can see that there is only one phone that meets these conditions, and it is a Brand B phone with a headset. Therefore, the probability that a phone with one payment plan and one accessory is given away at random and is a Brand B phone with a headset is 1/10 or 0.1.

Answer:

a function of an angle, or of an abstract quantity, used in trigonometry, including the sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.

Step-by-step explanation:

Answer: acute and isosceles

Step-by-step explanation:

Answer:

acute and isosceles

Step-by-step explanation:

because obtuse means veryy wide and this triangle has small corners and is and isosceles (pleases give me a brainly)! hoped this helped!! :)

Considering the roots of function f(x), the correct statement is given by:

D. f has exactly two zeros of [0,4].

The roots of a function are the values of x for which f(x) = 0.

In this problem, we have that:

For values of x less than 2 on the interval, the function is never negative nor zero, hence there are no roots in that interval and option D is correct.

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Answer:

OB

Step-by-step explanation:

it's not a beacuasenhes not doing everyone

and we have no info on whether anyone serveylayed a sport so the only possible option is 2

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Answer:

approx. 56.72 square inches

Step-by-step explanation:

A= 2πrh + 2πr2 = 2·π·1.15·6.7+2·π·1.152 ≈ 56.72146

Answer:

Roughly

1143$ annually

But if you want exact then its

1142.857143$  

Step-by-step explanation:

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Yes, the columns of exra5 do form a basis for r4. A basis is a set of linearly independent vectors that span a vector space, and in this case the vector space is R4. The four columns of exra5 are linearly independent, and they span the entire R4 space, so they form a basis for R4.

Yes, the columns of exra5 do form a basis for r4. A basis is a set of linearly independent vectors that span a vector space, and in this case the vector space is R4. The columns of exra5 must be linearly independent, which means that no linear combination of them can equal the zero vector. Furthermore, the columns of exra5 must span the entire R4 space, meaning that any vector in R4 can be expressed as a linear combination of the columns of exra5. This is equivalent to saying that the columns of exra5 can be used to generate the entire vector space R4. If these two conditions are met, then the columns of exra5 form a basis for R4. In this case, both conditions are met, so the columns of exra5 do form a basis for R4. Moreover, since there are four columns, the basis for R4 is called a basis of size four. The special property of a basis of size four is that it is the smallest possible basis for R4, meaning that no other set of vectors can form a basis for R4 with fewer than four vectors.

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