6. What is the value of n? 3/8n - 1/3 = 5/6

Answer:

4

Step-by-step explanation:

Answer:2+2 = 4.............

Answer:

7 miles.

Step-by-step explanation:

6+8+7+6+7+8/6

42/6

= 7 miles

The answer is 7 miles.

At the end of the 4-year period, you will have approximately $8,044.66 in your account.

To calculate the future value of the one-time deposit with monthly compounding, we can use the formula:

Future Value = Principal * (1 + (Annual Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)

In this case, the principal amount is $6,020, the annual interest rate is 7% (APR), and the investment period is 4 years. Since the interest is compounded monthly, there are 12 compounding periods in a year.

Using the formula, we can calculate the future value:

Future Value = $6,020 * (1 + (0.07 / 12))^(12 * 4)

Calculating this, the future value is approximately $8,044.66.

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if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter.

If the sample size is 28 and the population standard deviation is increased, there will be a direct impact on the confidence interval. This is because the confidence interval is calculated based on the sample mean and the standard deviation. If the population standard deviation is increased, it means that there is more variability in the population. This increase in variability will lead to wider confidence intervals.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the confidence interval is determined by the sample size, the standard deviation, and the level of confidence.
In this case, if the population standard deviation is increased, it means that the sample standard deviation will also increase. The sample mean will be relatively more variable than it would be if the population standard deviation was lower. This increase in variability will cause the confidence interval to become wider, as there is more uncertainty in the estimate of the population parameter.
In summary, if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter. It is important to note that increasing the sample size can help to reduce the impact of increased population standard deviation on the confidence interval, as a larger sample size provides more accurate estimates of the population parameter.

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

We have to find the probability of not getting odd, whole rolling a 6 sided die ~

Actually dices have 3 odd numbers (1 , 3 , 5) and 3 non - odd numbers (2 , 4 ,6)

When we roll a dice, we may get any of the six numbers, so total possible outcomes are 6

and, The number of Favorable outcomes is 3, i.e non - odd numbers.

\( \qquad \sf  \dashrightarrow \: p(not \: odd) = \dfrac{favourable \: outcomes}{total \: \: outcomes} \)

\( \qquad \sf  \dashrightarrow \: p(not \: odd) = \dfrac{3}{6} \)

\( \qquad \sf  \dashrightarrow \: p(not \: odd) = \dfrac{1}{2} \: \: \: or \: \: \: 0.5\)

Answer:

½

Step-by-step explanation:

Not odd (even) numbers from 1 - 6 = 2, 4, 6

Any of these 3 numbers can come when rolling a cubical 6 - sided dice.

Then,

P (not odd)

= Favourable outcomes / total number of outcomes

= 3/6

= ½

_____

Hope it helps ⚜

(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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Answer:

-22.1

Step-by-step explanation:

f(x) = 3x – 8,

Let x = -4.7

f(-4.7) =3(-4.7) -8

        =-14.1-8

        -22.1

The amount Levi spends on this skateboard is $148.39.

Tax is an amount levied on goods and services by the government. Taxes increases the price of goods and services.

The amount Levi spends on this skateboard = value of the tax + cost of the skateboard

value of the tax = 6% x $139.99

0,06 x $139.99 = $8.40

The amount Levi spends on this skateboard = $8.40 + $139.99 = $148.39

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The distance of point from the axis of rotation of the second hand is 8.2 cm.

Here,

A point located on the second hand of a large clock has a radial acceleration of 0.09 cm/s2.

We have to find the distance of point from the axis of rotation of the second hand.

What is Rotation?

The circular motion of an object around the circle is called Rotation.

Now,

Let us consider the equation for the centripetal acceleration given by;

\(a_{c} = \frac{v^{2} }{r}\)

where, v is the velocity and r is the radius.

Now, the velocity can be expressed as;

\(v = wr = \frac{2\pi r}{T}\)

where, ω is the angular velocity and T is the period.

Solving for the radius using these equations given as;

\(a_{c} = \frac{v^{2} }{r}\\\\v^{2} = a_{c} r\\\\(\frac{2\pi r}{T} )^2 = a_{c} r\\\\\frac{4\pi ^{2}r^{2} }{T^{2} } = a_{c} r\\\\r = \frac{T^{2} a_{c} }{4\pi ^{2} } \\\\r = \frac{(60s)^2(0.09 cm/s^2)}{4\pi ^{2} } \\\\r = 8.2 cm\)

Hence, The distance of point from the axis of rotation of the second hand is 8.2 cm.

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Answer:

I don't know what inductive reasoning is but, the next two numbers in the pattern are -243 and +729

Step-by-step explanation:

each number is being multiplied by a factor of (-3).

In a heap, the height is defined as the number of edges on the longest path from the root to a leaf node. The height of a heap with n elements is at most log₂(n+1).

To find the minimum and maximum numbers of elements in a heap of height h, we can use the formula:

The minimum number of elements in a heap of height h is 2^h (a complete binary tree of height h with the minimum number of nodes).

The maximum number of elements in a heap of height h is 2^(h+1) - 1 (a complete binary tree of height h with the maximum number of nodes).

Therefore, the minimum and maximum numbers of elements in a heap of height h are:

Minimum: 2^h

Maximum: 2^(h+1) - 1

Note that not all values of h are valid heap heights. A heap must be a complete binary tree, so its height can only take on values that satisfy the formula: \(h < = log₂(n+1),\)where n is the number of elements in the heap.

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Answer:

(2,4)

Step-by-step explanation:

Answer: 2520 groups

Step-by-step explanation:

To calculate the number of groups that can be chosen with four SE students and three CPRE students, we need to consider the number of ways to select the students from each group separately.

The number of ways to choose four SE students from the nine available is given by the combination formula, denoted as "9 choose 4" or C(9, 4), and can be calculated as:

C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126

Similarly, the number of ways to choose three CPRE students from the six available is:

C(6, 3) = 6! / (3! * (6 - 3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20

To determine the total number of groups, we multiply the number of choices for SE students and CPRE students:

Total number of groups = C(9, 4) * C(6, 3) = 126 * 20 = 2520

Therefore, there are 2520 different groups of seven students that can be chosen, consisting of four SE students and three CPRE students.

The standard equation of the sphere with the given characteristics, center (-1, -6, 3), and radius 5 is

\((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).

The standard equation of a sphere is \((x-h)^{2} +(y-k)^{2}+ (z-l)^{2} =r^{2}\), where (h, k, l) is the center of the sphere and r is the radius.
Using this formula and the given information, we can write the standard equation of the sphere:
\((x-(-1))^{2}+ (y-(-6))^{2} +(z-3)^{2}= 5^{2}\)
Simplifying, we get:
\((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).
Therefore, the standard equation of the sphere with center (-1, -6, 3) and radius 5 is \((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).

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Answer:

\(|3r-15| = -3r+15\) if \(r<5\)

Step-by-step explanation:

Given that:

r < 5

To simplify:

|3r−15|

Solution:

First of all, let us learn about Modulus function:

\(f(x) =|x| =\left \{ {x, \ if\ {x>0} \atop -x\ if\ {x<0}} \right.\)

In other words, we can say:

Modulus function has a role to make its contents positive.

If the contents are positive, the result will be equal to its contents only.

If the contents are negative, it will add a negative sign to the contents to make it positive.

Now, let us consider the given condition:

\(r < 5\)

Multiply both sides with 3. (As 3 is a positive number, the equality sign will not change.)

\(3r < 15\)

Subtracting 15 from both sides:

\(3r-15<15-15\\\Rightarrow 3r-15<0\)

Now, we know that \(3r-15<0\), let us use the definition of Modulus function.

Add a negative sign to the contents because the contents are already negative.

\(\\\Rightarrow |3r-15| = -(3r-15)\\\Rightarrow -3r+15\)

So, the answer is:

\(|3r-15| = -3r+15\) if \(r<5\)

(W = Col a) is Column space of the given

matrix = span{[1 -1 3]T, [-3 0 -1]T, [4 -5 6]T}

We can find a matrix a such that W = Col a. Here, we have to determine if the vector u is in the column space of matrix a and whether it is in the null space of a.

The given vector u = [5 -3 5]

The given matrix = [1 -3 4-1 0 -53 -3 6]. Finding the matrix a such that W = Col a

First, we need to understand what is column space, and null space and then we will calculate the matrix a. Col a, also known as Column Space, is defined as the span of the columns of a matrix. It is the vector space formed by all the linear combinations of the columns of the matrix.

A Null Space is the kernel of the transformation of the matrix.

The column space of a matrix = range of the matrix.

By using the Gauss Elimination Method.

Let's convert the given matrix to the Reduced Row Echelon Form. [1 -3 4 | 5 -1 0 | -53 -3 6 | -4 ]

The last row has no pivots. So, we have to remove the zero rows.

So, the new reduced row echelon form of the given matrix is, [1 -3 4 | 5-1 0  | -53 -3 6 | -4 ]

Now, we have 3 pivots in 3 rows. We can see that the first 3 columns of the given matrix are linearly independent.

Hence, the span of the first 3 columns will be the Column space of the given matrix.

So, W = Col a

= span{[1 -1 3]T, [-3 0 -1]T, [4 -5 6]T}

Now, we need to check whether the vector u is in the column space of matrix a or not.

The given vector u = [5 -3 5]Let's check whether u is in the column space of matrix a or not. We can use the Rank-Nullity Theorem to check whether the given vector u is in the column space of matrix a or not.

Let's calculate the rank and nullity of the matrix a.

The rank of the matrix a = 3

The nullity of the matrix a = 0 As the rank of the matrix a = 3, which is equal to the number of elements in the given vector u.

Hence, u is in the column space of matrix a. We can express u as a linear combination of the columns of matrix a.

We have to check whether the vector u is in the null space of matrix a or not. A vector is in the null space of a matrix if its image is the zero vector.

The vector u is not in the null space of matrix a as the image of the vector u is not equal to the zero vector. Hence, the vector u is not in the null space of matrix a.

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Answer:

90+1,2 = 200

Step-by-step explanation:

maaf kalo salah

Answer:

5x - 10

Step-by-step explanation:

7x - 2(x + 5)

= 7x - 2x -10

Please mark me brainliest if my answer is correct! Thanks!

= 5x - 10

Answer:

10e + 11

Step-by-step explanation:

12e + 6 - 2e + 5 ← collect like terms

= (12e - 2e) + (6 + 5)

= 10e + 11

Answer:

x=3

Step-by-step explanation:

First, you want to isolate x by itself so you subtract 2.8 on each side.

2.4x+2.8-2.8=10-2.8

2.4x=7.2

Then, you would want to divide 2.4 to both sides.

2.4x/2.4=7.2/2.4

Finally, you have your answer.

x=3

Answer:

25

Step-by-step explanation:

Substituting x = 8 into the expression

5(8 + 1) - 20

= 5(9) - 20

= 45 - 20

= 25

Answer:

25

Step-by-step explanation:

see Image below:)

Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

Answer: 46, 57, 68

Step-by-step explanation:

If you look at the sequence, you see that every time, it goes up by 11, so just add 11 three more times after the last number

The simplified expression is \(21x^2 - 25x - 28\) in the given case.

An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, x, ÷) that represents a mathematical phrase or idea. Expressions can be simple or complex, and they can contain variables, constants, and functions.

"Expression" generally refers to a combination of numbers, symbols, and/or operations that represents a mathematical, logical, or linguistic relationship or concept. The meaning of an expression depends on the context in which it is used, as well as the specific definitions and rules that apply to the symbols and operations involved. For example, in the expression "2 + 3", the plus sign represents addition and the meaning of the expression is "the sum of 2 and 3", which is equal to 5.

To simplify the expression, first distribute the -3x and (3x + 4) terms:

\(-3x(4 - 5x) + (3x + 4)(2x - 7) = -12x + 15x^2 + (6x^2 - 21x + 8x - 28)\)

Next, combine like terms:

\(-12x + 15x^2 + (6x^2 - 21x + 8x - 28) = 21x^2 - 25x - 28\)

Therefore, the simplified expression is \(21x^2 - 25x - 28.\)

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

The z-score is approximately 1.16. Therefore, the value of c, rounded to two decimal places, is 1.16.

To determine the value of c such that P(Z > c) = 0.8729, where Z follows the standard normal distribution, we need to find the corresponding z-score for the given probability.

Using a standard normal distribution table or a calculator, we can find the z-score associated with the given probability. In this case, the probability is 0.8729, which represents the area under the standard normal curve to the left of the z-score.

Looking up the z-score for a cumulative probability of 0.8729, we find that the z-score is approximately 1.16.

Therefore, the value of c, rounded to two decimal places, is 1.16.

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Answer:

~201

Step-by-step explanation:

Use the area formula:  \(A=\pi r^2\)

22/7 x 64 = 201.14

which rounds to 201

So on solving the provided question, we can say that - in the circle angle DGF = 59 .

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in the circle

angle AGC = angle DGF

so angle DGF = 59

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Answer:1.23777

Step-by-step explanation: Calculators answer