What’s the answer to this

The value of [tex]\( \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right] \)[/tex] is:
[tex]\ln \sqrt{x^{3}} - \ln \left(2 \cdot \sqrt[3]{(4 x+1)^{7}}\right)\][/tex]

To find the value of \[tex]( \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right] \)[/tex], we can use the following steps:

1. Factor out [tex]\( \left(x^{3}-2\right)^5 \)[/tex]:
[tex]\[ \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right][/tex] = [tex]ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}}{1}\right]\][/tex]

2. Use the product rule for logs:
[tex]\[ \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}}{1}\right] = \ln \left(x^{3}-2\right)^5 + \ln \left(\frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right)\][/tex]

3. Evaluate each logarithm separately:
[tex]\[ \ln \left(x^{3}-2\right)^5 = 5\ln \left(x^{3}-2\right) \]\[ \ln \left(\frac{\sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right)[/tex] = [tex]\ln \sqrt{x^{3}} - \ln \left(2 \cdot \sqrt[3]{(4 x+1)^{7}}\right)\][/tex]

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We can calculate the percentages according to the amounts provided in the prompt, and then make a number line to illustrate each percentage as follows:

a) The price of the book decreased by 20%.

$15.00             $12.00

  |-----------------|------->

      100%            80%

b) The percentage decrease in the number of students who take the bus to school is 25%.

200               150

  |-----------------|------->

     100%            75%

Calculating percentages involves finding a portion of a whole expressed as a fraction of 100. To calculate a percentage, divide the part by the whole and then multiply the result by 100.

For example, if 20 out of 100 students are absent, the percentage of absent students is:

(20/100) x 100 = 20%.

With that in mind, we can conclude that we have correctly answered this question.

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Based on the information in the table, the graph shows a diagonal going down from left to right.

To graph in a Cartesian plane we must be clear that it is a tool to graph the coordinates. The first number of the coordinate corresponds to the x-axis (horizontal) and the second number corresponds to the y-coordinate (vertical). According to the above, we can infer the graph would look like this (image attached). This graph corresponds to a function because it is a constant, in this case it is a diagonal line that descends from left to right.

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The equation that represents the variation is given by F = 42m/p

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

F varies directly as m and inversely with p, hence:

F ∝ m/p

Let k represent the constant of proportion. Therefore:

F= k*m/p

F = 36 when m = 6 and p = 7. Hence:

36 = k*6 / 7

k = 36 * 7 / 6

k = 42

The equation is F = 42m/p

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a is correct

Question 1 (1 point )If y varies directly as x and y = 15 when x = 12, find y when x = 32. The value of y when x = 32 is 40.How to solve direct variation problems?A direct variation is a function that can be expressed in the form y = kx, where k is a nonzero constant. Two quantities x and y are said to be in direct variation if they satisfy this relationship. To solve direct variation problems, you can use the following formula: y = kx, where k is the constant of variation.The solution to the problem is given below:Given:y varies directly as xx = 12, y = 15To find:y when x = 32Formula:Since y varies directly as x, we have:y = kxLet's substitute x and y values in the above equation:15 = k × 1215/12 = kk = 5/4Thus, the equation of the direct variation is: y = (5/4) xTo find the value of y when x = 32, substitute 32 for x:y = (5/4) × 32y = 40Therefore, y = 40 when x = 32. Hence, the option (a) is correct.

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A circular park of radius 14 m has a road of 7 m width all around on its outside then the  area of the road is approximately 153.943 square meters.

The circular park has a radius of 14 m. This means that the diameter of the park is 2 x 14 = 28 m. The road around the park has a width of 7 m. This means that the total width of the park and the road is 28 + 7 + 7 = 42 m. The area of the circular park can be found using the formula for the area of a circle: Area of park =[tex]π x r^2 = π x 14^2 = 615.752 m^2[/tex] (rounded to 3 decimal places)

The area of the park and the road can be found by calculating the area of the larger circle and subtracting the area of the park: Area of park and road =[tex]π x (r+7)^2 - π x r^2 = π x (14+7)^2 - π x 14^2 = π x 21^2 - π x 14^2 = π x (441 - 196) = π x 245 = 769.695 m^2[/tex] (rounded to 3 decimal places)

To find the area of just the road, we need to subtract the area of the park from the area of the park and road: Area of road = Area of park and road - Area of park = 769.695 - 615.752 =[tex]153.943 m^2[/tex] (rounded to 3 decimal places)

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For the given figure, the area of the shaded region is obtained as 100 m².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of shaded region can be obtained as -

Area of shaded region =  Area of rectangular concrete path - Area of rectangular lawn

The formula for area of rectangle is -

Area of rectangle  =  Length × width

The area of rectangular concrete path is -

Length  =  (30+2) m  =  32 m

width  =  (18+2) m  =  20 m

Area of rectangular concrete path  =  32 × 20

Area of rectangular concrete path  =  640 m²------(1)

The area of rectangular lawn is -

Length  =  30 m and width  =  18 m

Area of rectangular lawn  =  30 × 10

Area of rectangular lawn  =  540 m²------(2)

To find the are of shaded region subtract equation (2) from (1) =

Area of shaded region = (1) - (2)

Area of shaded region =  (640 – 540) m²

Area of shaded region =  100 m²

Therefore, the total area of concrete is 100 m².

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A rectangular lawn 18 m by 30 m is surrounded by a concrete path 1 m wide. Draw a diagram of the situation and find the total area of concrete.

The probability that the battery lasts less than 25 hours is 0.3446.

The probability of P(Z > -1.5) is 0.9332. The value of -1.5 has to be positive for this computation because the normal distribution curve is symmetrical about the z = 0 line. The probability of being at z = -1.5 is the same as being at z = +1.5. Thus, the probability is found by referencing the z-table for the area under the curve to the right of the mean: 0.9332.

The probability of P(Z < 1.15) is 0.8749. The area below z = 1.15 is needed for this calculation. The probability that the standard normal random variable is less than 1.15 is 0.8749.iii) The probability of P(Z > 0.35) is 0.3632. The area under the curve to the right of the mean is needed. The probability that the standard normal random variable is greater than 0.35 is 0.3632.

Given that, the amount of time the battery lasts in a toy racing car is normally distributed with a mean of 26 hours and a standard deviation of 2.5 hours. Let X denote the time a battery lasts, which is a normally distributed random variable. Find the following probabilities:a) P(25 < X < 29)To calculate the probability,

we first standardize the values of 25 and 29 using the formula below:

z1 = (25 - 26) / 2.5 = -0.4 and z2 = (29 - 26) / 2.5 = 1.2 Now, we find the probability as shown:P(-0.4 < Z < 1.2) = P(Z < 1.2) - P(Z < -0.4) = 0.8849 - 0.3446 = 0.5403 Thus, the probability that the battery lasts between 25 and 29 hours is 0.5403.b) P(X > 29)

To find the probability, we first standardize the value of 29 using the formula below:z = (29 - 26) / 2.5 = 1.2 Now, we find the probability as shown:P(Z > 1.2) = 1 - P(Z < 1.2) = 1 - 0.8849 = 0.1151 Thus, the probability that the battery lasts longer than 29 hours is 0.1151.c) P(X < 25)To find the probability, we first standardize the value of 25 using the formula below:z = (25 - 26) / 2.5 = -0.4 Now, we find the probability as shown:P(Z < -0.4) = 0.3446

Thus, the probability that the battery lasts less than 25 hours is 0.3446.

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Answer:

V = (4/3)π(4^3) = 256π/3 cubic units

By using the "acosd" function in MATLAB, you can easily calculate the angles of obtuse triangles in real-life objects.

The shapes of obtuse triangles occur in real-life objects such as kites and architectural designs. An obtuse triangle is a type of triangle that has one obtuse angle, which means that one of its angles is greater than 90 degrees.

These types of triangles can be seen in many real-life objects, such as kites, which often have an obtuse angle at the top where the two sides of the kite meet. Similarly, architectural designs often include obtuse angles in order to create unique and interesting shapes.

In terms of using MATLAB to calculate the angles of an obtuse triangle, you can use the "acosd" function to calculate the angle in degrees. For example, if you have a triangle with sides of length 3, 4, and 5, you can use the following code to calculate the angle between the sides of length 3 and 4:

angle = acosd((3^2 + 4^2 - 5^2)/(2*3*4));

This will give you an angle of 90 degrees, which is a right angle. However, if you change the lengths of the sides to create an obtuse triangle, such as a triangle with sides of length 3, 4, and 6, you can use the same code to calculate the obtuse angle:

angle = acosd((3^2 + 4^2 - 6^2)/(2*3*4));

This will give you an angle of approximately 98.13 degrees, which is an obtuse angle. By using the "acosd" function in MATLAB, you can easily calculate the angles of obtuse triangles in real-life objects.

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Gabe or Gabriel is a new child in the novel, "The Giver" and was described as a symbol of hope and new beginnings.

As a new child, Gabe is not yet fully indoctrinated into the rules and customs of the community, making him more open to the memories transmitted by Jonas.

This presentation of Gabe's character aligns with the novel's recurring motif of babies symbolizing hope and regeneration in literature.

The novel "The Giver" was authored by Lois Lowry. It is set in a futuristic society that has eliminated all pain, fear, war, and hatred and appears to be utopian at first glance.

The story is written from the point of view of Jonas, an eleven-year-old boy, selected to be the new Receiver of Memory.

Through training, Jonas learns about the joys and pains of life and becomes increasingly disillusioned with the society he lives in.

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Step-by-step explanation:

The correct order of the functions in decreasing order of their periods is:

y = -10sin(pi/5 - 2pi)

y = 2/3cot(pi/4)+6

y = 5csc(3x)+6

y = 1/2tan(5pi/6 + pi)

y = -3cos(x+2pi)

Note: The periods of trigonometric functions are determined by the coefficient of the independent variable (x in this case). The period of y = asin(bx + c) or y = acos(bx + c) is 2pi/b, and the period of y = atan(bx + c) or y = acot(bx + c) is pi/b. The period of y = acsc(bx + c) or y = asec(bx + c) is 2pi/|b|.

ΔTUV is not congruent to ΔT'U'V', as the transformation involved a rotation and translation, but they have similarities.

ΔABC and ΔDEF have the same angles but different side lengths, so they are similar but not congruent triangles.

What are the similarities?

The situations that describe similar but not congruent triangles are given below:

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The area οf οnly the frame is apprοximately 50.27 square inches.

The area οf a circle is the amοunt οf surface inside the bοundary οf a circle. It is a measure οf hοw much space the circle takes up in twο-dimensiοnal space. The fοrmula tο calculate the area οf a circle is:

[tex]A = \pi r^2[/tex]

where A is the area οf the circle and r is the radius οf the circle.

The diameter οf the mirrοr with the frame is 17 inches, and the diameter οf οnly the mirrοr (withοut the frame) is 15 inches.

Therefοre, the width οf the frame is:

17 inches (diameter οf mirrοr with frame) - 15 inches (diameter οf οnly mirrοr) = 2 inches

Sο the radius οf the mirrοr withοut the frame is:

r₁= (15 inches / 2) = 7.5 inches

The area οf the mirrοr withοut the frame is:

A₁= π(7.5)² square inches ≈ 176.71 square inches

The radius οf the mirrοr with the frame is:

r₂= (17 inches / 2) = 8.5 inches

The area οf the mirrοr with the frame is:

A₂= π(8.5)² square inches ≈ 226.98 square inches

The area οf οnly the frame is the difference between these twο areas:

=A₂-A₁

=π(8.5)²- π(7.5)² square inches

≈ 50.27 square inches

Therefοre, the area οf οnly the frame is apprοximately 50.27 square inches.

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Step-by-step explanation:

the acorn falls from the height of 25 feet above the ground, it means the initial time when it falls is t = 0. The time when it lands on the ground is t = 1.25

So the acorn was in the air for 1.25 seconds

Answer:

Decimal: 0.25

Fraction: 1/4

Step-by-step explanation:

2 / 3 * 3/8

2/3 X* 3/8

=  

2 × 3

3 × 8

=  

6/ 24

=  

6 ÷ 6

24 ÷ 6

=  

1/4

Please mark this answer brainliest if it helps!

Answer:200

Step-by-step explanation:

A+B=25

A^2+B^2= 225

we use short multiplication formulas:

(A+B)^2=A^2+B^2+2AB

and solve the equation

25^2=225+2AB

625=225+2AB

625-225=2AB

400=2AB

AB=200

Part 1: Triangles are similar by Side-Side-Side similarity.

Part 2: Triangles are similar angle-Angle (AA) similarity.

Part 1: Ratios must be equal for triangle similarity.

Taking the ratios of the sides:

17/37.4  = 20/44 = 25/55

On solving

0.4545 = 0.4545 = 0.4545

As the ratios are equal, triangles are similar.by Side-Side-Side similarity.

Part 2:

∠F = ∠H (given)

∠EGF = ∠JGH (vertically opposite)

By Angle-Angle (AA) similarity.

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The correct question is 1 and 2.

The first mechanic wοrked fοr 10 hοurs, and the secοnd mechanic wοrked fοr 15 - 10 = 5 hοurs.

Let x be the number οf hοurs the first mechanic wοrked, then the number οf hοurs the secοnd mechanic wοrked wοuld be (15 - x).

The tοtal cοst οf the first mechanic wοuld be 65x, and the tοtal cοst οf the secοnd mechanic wοuld be 45(15 - x) = 675 - 45x.

Tοgether, their tοtal cοst wοuld be 65x + (675 - 45x) = 20x + 675.

We knοw that their tοtal cοst was $875, sο we can set up the equatiοn:

20x + 675 = 875

Subtracting 675 frοm bοth sides, we get: 20x = 200

Dividing bοth sides by 20, we get: x = 10

Therefοre, the first mechanic wοrked fοr 10 hοurs, and the secοnd mechanic wοrked fοr 15 - 10 = 5 hοurs .

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The equation with y as the subject is y = x^m / (4x^n - 2)

To solve for y as the subject of the equation, we need to isolate y on one side of the equation. Here's how we can do it,

First, we can rearrange the equation to get all the y terms on one side:

4x^n y - 2y = x^m

Next, we can factor out y from the left-hand side,

y(4x^n - 2) = x^m

Finally, we can divide both sides by (4x^n - 2) to isolate y,

y = x^m / (4x^n - 2)

Therefore, the equation with y as the subject is:

y = x^m / (4x^n - 2)

where m and n are the constants given in the original equation.

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The given question is incomplete, the complete question is:

Hence , write down the equation with y as the subject ( in terms of x ). The value of m and q must be indicated. equation 4x^ny -2y - x^m = 0, m and n are constant

The expression −25(y-x) can be expanded by multiplying -25 to each term inside the parentheses:

-25(y - x) = -25y + 25x

Therefore, the expanded form of the expression is -25y + 25x.

The new monthly salary after two increases of 6.9% and 15% is 2867.

The new monthly salary after two increases is calculated as follows:

First Increase:

The initial salary of 2332 increases by 6.9%. This is calculated by multiplying the salary by the percentage increase, i.e. 2332 x 0.069 = 160.68. The new salary after the first increase is 2332 + 160.68 = 2492.68.

Second Increase:

The salary after the first increase of 2492.68 is further increased by 15%. This is calculated by multiplying the salary by the percentage increase, i.e. 2492.68 x 0.15 = 373.90. The new salary after both increases is 2492.68 + 373.90 = 2866.58.

Rounded to the nearest dollar, the new monthly salary after both increases is 2867.

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Answer:

x=120 and y=60

Step-by-step explanation:

As we know, a straight line is 180 degrees.

To find x, you would do 180= 60 + x to get 120.

I forget how but I know y= 60 because its the same angle as 60 degrees.

Answer:

n=15.1

Step-by-step explanation:

14.8=n-0.3

14.8+0.3=n

15.1=n

m= y2-y1/x2-x1

m= 5-5/2+6= 0

Answer: The slope is equal to zero

Step-by-step explanation:

Find the slope of (-6,5) and (2,5)

First subtract the x coordinates 2 and -6

which equals 8

Next subtract the y coordinates 5 and 5

which equals o

Then you get 8/0 and when you simplify you get 0, so the slope is zero.

We want to find the number of yards Adrian ran during the last game, which is represented by the variable a. Adrian ran 90 yards during the last football game.

Let's define the variables we will use in this problem:

r: the number of yards Reggie ran during his previous personal best.

m: the number of yards Monte ran during the last game.

a: the number of yards Adrian ran during the last game.

From the problem statement, we know that:

Reggie ran for 180 yards during the last game, which is 40 more yards than his previous personal best: r + 40 = 180.

Monte ran 50 more yards than Adrian during the same game: m = a + 50.

Monte ran the same amount of yards Reggie ran in one game for his previous personal best: m = r.

We want to find the number of yards Adrian ran during the last game, which is represented by the variable a. To solve for a, we need to use the information we have to create an equation that relates a to the other variables.

From the equation r + 40 = 180, we can solve for r by subtracting 40 from both sides: r = 180 - 40 = 140.

Substituting m = r into the equation m = a + 50, we get: r = a + 50.

Now we can substitute the value of r we found earlier into this equation: 140 = a + 50.

Solving for a, we subtract 50 from both sides: a = 90.

Therefore, Adrian ran 90 yards during the last football game.

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The probability that at least nine flashlights will work is 0.3874 or 0.387 to three decimal places.

Given: A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages.

Suppose that 90% of all batteries from a certain supplier have acceptable voltages. Among ten randomly selected flashlights,

Let p be the probability that any single battery has an acceptable voltage.

Let X be the number of flashlights out of 10 that work.

Then X has a binomial distribution with n=10 and p=0.9.

The probability that at least nine of the ten flashlights work is P(X≥9).

We have

[tex]P(X=9)= 10C_9 \times 0.9⁹ \times 0.1 = 0.3874

P(X=10)= 10C_10 \times 0.9¹⁰ \times 0 = 0[/tex]

P(X≥9)  = P(X=9) + P(X=10)

            = 0.3874 + 0

            = 0.3874

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The answer is d. While it is possible for a parallelogram to be a square, it is not a valid conclusion given only the information that ABCD is a parallelogram and has diagonals AB and BD.

A parallelogram is a four-sided plane figure with two pairs of parallel and equal sides. Opposite sides of a parallelogram are of equal length and the opposite angles are of equal measure. The area of a parallelogram is determined by multiplying the length of one side with the height of the parallelogram. Parallelograms are quadrilaterals, which means they have four sides, and are classified by their angles and sides.

To determine if the parallelogram is also a square, additional information such as the length of the sides or angles of the parallelogram would need to be known.

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Complete questions as follows-

Which of the following is not a valid conclusion given parallelogram ABCD with diagonals AB and BD?
a
AB=CD
b
AC=BD
c
d
m