Please help and give a good explanation because I don't understand this!!! Rewrite the expression in terms of ln(25) and ln(7). ln(7/5)

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The expression -15 + (-23) simplifies to -38.

To simplify -15 + (-23), we can combine the negative numbers together. The negative sign in front of the 23 indicates that the number is being subtracted. Therefore, -15 + (-23) can be rewritten as -15 - 23.

To perform the subtraction, we start with -15 and subtract 23. Since we are subtracting a larger number from a smaller number, the result will be negative. Subtracting 23 from 15 gives us 8, and since we are subtracting, the answer is -8.

Therefore, -15 + (-23) simplifies to -38. The negative sign indicates that the result is a negative number.

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When c = 8, b is approximately equal to 6.17, correct to three significant figures.

To solve for the value of b when c = 8, we'll use the given information and the proportional relationships between a, b, and c.

We know that a is proportional to b², which can be expressed as a = kb², where k is the proportionality constant. Additionally, a is also proportional to √c, which can be expressed as a = mc^0.5, where m is another proportionality constant.

Using these two proportional relationships, we can set up the following equations:

a = kb²  (Equation 1)

a = mc^0.5  (Equation 2)

Since a is proportional to both b² and √c, we can equate the right-hand sides of Equations 1 and 2:

kb² = mc^0.5

Now, let's substitute the given values to find the proportionality constant k:

When b = 4.5 and c = 2.25:

k(4.5)² = m(2.25)^0.5

20.25k = 1.5m

Now, let's solve for m in terms of k:

m = (20.25k) / 1.5

m = 13.5k

Substituting this value of m back into Equation 1, we get:

a = (13.5k)c^0.5

Now, we need to find the value of k. To do this, we can use the given values:

When b = 4.5 and c = 2.25:

a = kb²

a = k(4.5)²

a = 20.25k

Since we don't have the value of a, we can assume a value of a for the given case. Let's assume a = 1 for simplicity:

1 = 20.25k

k = 1 / 20.25

k = 0.0494 (rounded to four decimal places)

Now, we have the value of k. We can substitute it into our equation for m:

m = 13.5k

m = 13.5 * 0.0494

m = 0.6663 (rounded to four decimal places)

Finally, we can use the value of m and the given value of c = 8 to find the value of b:

a = mc^0.5

1 = 0.6663 * 8^0.5

1 = 0.6663 * 2.8284

1 = 1.8807 (rounded to four decimal places)

Now, we can solve for b:

a = kb²

1.8807 = 0.0494 * b²

b² = 1.8807 / 0.0494

b² = 38.1147

b = √38.1147

b ≈ 6.17 (rounded to three significant figures)

Therefore, when c = 8, b is approximately equal to 6.17, correct to three significant figures.

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There are probably more, but here are some key similarities and differences

Similarities:

- both have a variable to the exponent 0 (anything to the power of 0 = 1)

         y = b(x^0)     and     x = b(y^0)     where b is any real number

- they are both in the form of a variable being equal to a number

Differences:

- they are perpendicular

- vertical lines are x = b (no y in the equation) whereas horizontal lines

 are y = b (no x in the equation)

Answer: answer is 1

The sum of 10 terms after excluding from the first and last term of the given AP. is: 1055

The formula for the sum of n terms of an arithmetic sequence is:

Sₙ = ⁿ/₂[2a + (n - 1)d]

Where:

n is number of terms

a is first term

d is common difference

There are 16 terms in the sequence and as such:

S₇ = ⁷/₂[2a + (7 - 1)d] = 126

⁷/₂[2a + 6d] = 126

7a + 21d = 126     ------(1)

Total sum of the last 7 terms is 441. Thus:

a + 9d + a + 10d + a + 11d + a + 12d + a + 13d + a + 14d + a + 15d = 441

7a + 84d = 441   ----(2)

Subtract eq 1 from eq 2 to get:

63d = 315

d = 315/63

d = 5

7a + 21(5) = 126

7a + 105 = 126

7a = 21

a = 3

The 16th term is:

3 + 15(5) = 78

Thus, the next ten terms are:

83, 88, 93, 98, 103, 108, 113, 118, 123, 128

Total = 83 + 88 + 93 + 98 + 103 + 108 + 113 + 118 + 123 + 128

Total = 1055

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Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

Answer: (a)Increasing: (-1,-6) to (0,6) (b)decreasing: (-6,-1) to (-4,-3) (c)constant: (-4,-3) to (-1,-6)

Hope this helps!

Answer:

(a)  (-∞, -6) ∪ (-1, 0)

(b)  (-6, -4)

(c)  (-4, -1) ∪ (0, ∞)

Step-by-step explanation:

A function is increasing when the gradient is positive.

A function is decreasing when the gradient is negative.

A function is constant when the gradient is zero.

An arrow shows that the function continues indefinitely in that direction.

Use the x-values when describing the intervals.

Note:  Use parentheses for the defined endpoints of the intervals as we cannot say if the function is increasing, decreasing or contestant at the defined points on the graph.

Part (a)

Intervals for which the function is increasing:

Part (b)

Interval for which the function is decreasing:

Part (c)

Intervals for which the function is constant:

Answer:

1. 10

2. 4

3. 8

Step-by-step explanation:

You have to fill in the given values for y and undo in reverse order to find x.

1. y = 6

6 = x - 4

6 (+ 4) = x - 4 (+ 4)

10 = x

2. y = 0

0 = x - 4

0 (+ 4 ) = x - 4 (+ 4)

4 = x

3. y = 4

4 = x - 4

4 (+ 4) = x - 4 (+ 4)

8 = x

I hope this helps! Have a lovely day!! :)

Answer:

So the odds of rolling an even number are 3:(6−3)=1:1

Step-by-step explanation:

Answer:

Step-by-step explanation:

he height of the storage unit is equal to twice its radius (since the diameter is twice the radius), so the height is 2 x 8 = 16 feet.

The storage unit is in the shape of a cylinder, so we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height:

V = π(8^2)(16)

V = π(64)(16)

V = 3,218.69 cubic feet (rounded to two decimal places)

Therefore, the volume of the storage unit is approximately 3,218.69 cubic feet.

Answer:

-18/7

Step-by-step explanation:

The equation represents the total cost of turkey and amount is y= 3.25x.

We have,

The turkey costs $3. 25 per pound.

let x be the amount in pounds and y be the total cost in dollar.

Then, the relation between x and y

Total cost = 3.25 (amount in  poind)

y = 3.25 x

Thus, the required equation is y= 3.25x.

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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The rate of change of the side of the square is 1.5 centimeters per second when the area is 3 square centimeters.

Let's denote the side length of the square as s, and the area of the square as A. Then we know that \(A = s^2\). We are given that \(dA/dt = 30 cm^2/s\), which means that the area of the square is increasing at a rate of \(30 cm^2/s\). We want to find ds/dt, the rate of change of the side of the square.

Using the chain rule, we have:

\(dA/dt = d/dt (s^2) = 2s ds/dt\)

Solving for ds/dt, we get:

\(ds/dt = (1/2s) dA/dt\)

When the area is \(3 cm^2\), the side length is \(s = \sqrt{3} cm\). Plugging in dA/dt = 30 cm^2/s and s = sqrt(3) cm, we get:

\(ds/dt = (1/2(\sqrt{3})) (30) = 1.5 cm/s\)

Therefore, the rate of change of the side of the square is 1.5 cm/s when the area is 3 cm^2.

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The coordinates of point Q that partitions line segment AB into the ratio 1:3 is (-0.75, 4.5).

In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 3.

In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:

Q(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given points into the formula for line ratio, we have;

Q(x, y) = [(1(6) + 3(-3))/(1 + 3)],  [(1(0) + 3(6))/(1 + 3)]

Q(x, y) = [(6 - 9)/(4)],  [(0 + 18)/4]

Q(x, y) = [-3/4],  [18/(4)]

Q(x, y) = [-0.75, 4.5]

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The values for the highlighted variables is a=-1,b=-9,c=9,d=3,e=3,f=2 and g=3/2.

Given:

3x/2x-6 + 9/6-2x

Rewrite 6-2x as 2x-6 by taking (-1) as common factor:

= 3x/2x-6 + 9/(-1)(2x-6)

so a = -1

= 3x/2x+6 + -9/2x-6

so b = -9

The LCM of 2x - 6 and 2x - 6 is 2x -6.

= 1*3x + 1*-9 / 2x-6

= 3x - 9 / 2x -6

so c = 9

(3x - 9) = 3(x-3)

(2x - 6) = 2(x - 3)

= 3(x-3)/2(x-3)

so d =3,e=3 and f=2 , g = 3/2.

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Full question:

Enter the values for the highlighted variables to complete the steps to find the sum:

3x/2x-6 + 9/6-2x = 3x/2x-6 + 9/a(2x-6) = 3x(2x-6)+6(2x-6)=3x-c 2x-6 =d(x-x) f(x-3) = g

A- -1

B= -9

C= 9

D= 3

E= 3

F= 2

G= 1.5

Answer:

you can put the number on one side of the equation then the "x" part on the other side.

with c) 4x = 6-10

           4x = -4

            x = -4/4

            x = -1

with d) 7x - 1 = 4x + 8

           7x - 4x = 8 + 1

           3x  = 9

           x = 9/3

           x = 3

Answer:

c) x = -1.  d) x = 3

Step-by-step explanation:

c) move like terms together. then get x by itself

10 + 4x = 6

-10

4x = -4

4x/4 = -4/4

x = -1

d) move like terms together.  then get x by itself

7x-1 = 4x+8

+1          -4x

3x = 9

3x/3 =9/3

x = 3

Answer: The box is large enough to ship the coat.

15000cm to the power of 3>10000cm to the power of 3

Step-by-step explanation:

V box=25x30x20

         =750+20

         =15000cm to the power of 3

So the box is large enough to ship the coat

We know that the function (f+ g)(x) = 13x^2 + 8x + 2 and (f+ g)(-2) = 38.

Hi! I'd be happy to help you with your question.

Given the functions f(x) = 9x^2 + 8x + 2 and g(x) = 4x^2, we need to find (f+ g)(x) and (f+ g)(-2).

To find (f+ g)(x), simply add the functions f(x) and g(x) together:

(f+ g)(x) = f(x) + g(x) = (9x^2 + 8x + 2) + (4x^2) = 13x^2 + 8x + 2

Now, we need to find (f+ g)(-2) by substituting -2 for x in the combined function:

(f+ g)(-2) = 13(-2)^2 + 8(-2) + 2 = 13(4) - 16 + 2 = 52 - 14 = 38

So, (f+ g)(x) = 13x^2 + 8x + 2 and (f+ g)(-2) = 38.

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Answer:

angle 3 = angle 6

angle 1 = angle 5

angle 2 + angle 5 + angle 6 = 180°

Answer:

Step-by-step explanation:

1+1=2

2+8=10

10-7=3

3

Using the concepts of mean and median, it is found that the correct option is:

C. The mean will decrease, and the median will stay the same.

The mean of a data-set is the sum of all observations divided by the number of observations. It is affected by all values in the data-set.

The median of a data-set is the value that separates the bottom 50% from the upper 50% of values. It is not affected by outliers.

In this problem, there are 5 elephants, hence the median is the weight of the (5 + 1)/2 = 3rd elephants, hence it stays the same.

For the mean, as the weight of the smallest elephant decreases, the mean also decreases, hence option C is correct.

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complete question:

Liam works at a zoo. He was looking at some data showing the masses of their 5 African elephants. The mean mass of the elephants was 3800 Kg and the median mass was 3600 Kg. The smallest elephant, named Lola, weighed 2700 Kg. Lola then got very sick and lost weight until her mass reached 1800 Kg. How will Lola's mass decreasing affect the mean and median?

A. Both the mean and median will decrease

B.The median will decrease, and the mean will stay the same.

C.The mean will decrease, and the median will stay the same.

D.The mean will decrease, and the median will increase.

Answer:

See below

Step-by-step explanation:

# liters  x  1000   = ml  sold

The area bounded by y = cos(x) and y = 2x sin(x) is approximately 0.366 square units.

To find the area bounded above by y = cos(x) and below by y = 2x sin(x), we need to find the points of intersection of these two curves.

Setting y = cos(x) and y = 2x sin(x) equal to each other, we get:

cos(x) = 2x sin(x)

Dividing both sides by sin(x), we get:

cot(x) = 2x

This equation does not have an exact solution, but we can use numerical methods to approximate the value of x where the two curves intersect. Using a graphing calculator or computer algebra system, we find that the intersection occurs at approximately x = 0.8603.

Next, we need to determine which curve is on top in the interval [0, 0.8603] and which is on top in the interval [0.8603, π/2].

For x in [0, 0.8603], we have:

cos(x) > 2x sin(x)

Therefore, the curve y = cos(x) is above y = 2x sin(x) in this interval.

For x in [0.8603, π/2], we have:

cos(x) < 2x sin(x)

Therefore, the curve y = 2x sin(x) is above y = cos(x) in this interval.

So the area bounded by the curves is given by:

∫[0,0.8603] (cos(x) - 2x sin(x)) dx + ∫[0.8603,π/2] (2x sin(x) - cos(x)) dx

Evaluating these integrals using calculus or numerical methods, we get:

Area ≈ 0.366 square units (rounded to 3 decimal places)

Therefore, the area bounded by y = cos(x) and y = 2x sin(x) is approximately 0.366 square units.

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The mass of 6.56 pints of blood is 3.92 grams.

Given

The density of blood = 1.060 g/mL and mass of 6.56 pints

We have 1L = 2.113 pints

The density of a substance can be defined as the ratio of the mass of the substance to the volume of the substance. In chemistry, density is used to measure the concentration of the substance in the solution.

The expression for density = mass/volume

ρ = m/V

m = ρV

Mass = 1.060(1000ml/1L) × 6.56(1L/ 2.113)

= 3290.8 /1000

= 3.29g

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The statement describes the percentage of people in the nation who eat out without making any inferences or assumptions.

The statement made by the person is a descriptive statement. This means that the statement simply describes the percentage of people in the nation who always eat out. It does not make any assumptions or inferences based on the data or evidence given. A descriptive statement is one that simply states facts or information without making any assumptions or interpretations about it. It is important to note that a descriptive statement does not imply any cause and effect relationship between the facts or data given. For example, in this statement, there is no inference being made that the people who eat out are healthier or more likely to be successful than people who don't eat out. It is simply stating the percentage of people in the nation who always eat out.

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Answer:

Subtract 3z from each side

Step-by-step explanation:

9z+3=3z+15

Subtract 3z from each side

9z-3z+3=3z-3z+15

6z +3 = 15

Subtract 3 from each side

6z+3-3 = 15-3

6z = 12

Divide by 6

6z/6 = 12/6

z=2

Answer:

9z-3z+3=15

Step-by-step explanation:

move variable to the left hand side