a cylinder with a height of 32 mm and a diagonal 40 mm what is the surface area

Answer:

a < 42

Step-by-step explanation:

Question : 4a + 9a - 6a < 42

Answer :

4a + 9a - 6a < 42

Combine like terms.

13a - 6a < 42

7a < 42

Divide both sides by 7.

a < 42

Hope this helps you :-)

Let me know if you have any other questions :-)

Answer:

\(\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: Solution :- \: a \: < \: 6 }}}}}}}}\)

Step-by-step explanation:

We need to solve the below given inequality \(\downarrow\)

For this, we need to combine all the like terms at first. So

We know that, 42 is divisible by 7. So, let's divide both the sides of the inequality by 7.

_________

Hope it helps!

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\(\mathfrak{Lucazz}\)

Given the following numbers:

57, 50, 37, 48, 58, 45, 61

n = 7

Mean

The mean of a data set is the sum of all the data divided by the count n

Answer: 50.9

Median

The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number:

37, 45, 48, 50, 57, 58, 61

Answer: 50

Mode

The mode is the number in a data set that occurs most frequently. But, If all numbers occur the same number of times there is no mode.

Answer: there is no mode

Midrange

There is a very simple formula to follow when calculating the midrange. The midrange formula is

Answer: 49

The function f(t) = log(t – 1) + 2 is increasing and has a domain of (1, ∞) option (A) is correct.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

\(\rm a^b = c\\log_ac =b\)

The question is incomplete.

The complete question is:

Which function is increasing and has a domain of (1, ∞);

As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Graph the function f(t) = log(t – 1) + 2 on a coordinate plane.

As we can see in the graph, the graph of a function has a domain:

(0 , ∞)

And the function is increasing.

Thus, the function f(t) = log(t – 1) + 2 is increasing and has a domain of (1, ∞) option (A) is correct.

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Answer:

A. f(t) = log(t – 1) + 2

Step-by-step explanation:

I took the test

Answer:

Dilation

Step-by-step explanation:

Given: The first triangle has side lengths of 6, 10, 8 and the second triangle has side lengths of 3, 5, 4 such that these two right triangles have identical angle measures but different side lengths.

To choose: the correct option

Dilation refers to a transformation when a figure is reduced or enlarged.

Each side of the large triangle is halved to get the small triangle.

So, Dilation transformation maps the large triangle onto the small triangle

The transformation is because the Dilation.

The geometric transformation is a bijection of a set that has a geometric structure by itself or another set.

Given that the first triangle has side lengths of 6, 10, 8 and the second triangle has side lengths of 3, 5, 4 such that these two right triangles have identical angle measures but different side lengths.

So, we need to identify the type of transformation.

We see that the measures of the sides are decreased by a scale factor of 2.

So we can say there is a dilation,

Dilation refers to a transformation when a figure is reduced or enlarged.

Each side of the large triangle is halved to get the small triangle.

So, Dilation transformation maps the large triangle onto the small triangle.

Hence the correct option is Dilation.

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Answer:

3. Sanford Township, Minnesota

4. Inner Mongolia, China

5. Arunachal Pradesh, India

6.Almaty Region, Kazakhstan

7.Madhya Pradesh, India

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

-f(x) reflects the graph over the x-axis. Instead of increasing everywhere, it decreases everywhere.

__

2f(x) stretches the graph vertically by a factor of 2. The y-intercept of (0, 1) gets moved to (0, 2)

__

f(x) +2 shifts the graph up 2 units. The horizontal asymptote moves from y=0 to y=2.

__

f(x+2) shifts the graph left 2 units. The point (2, 4) on the original graph gets translated to the y-axis to become the new y-intercept (0, 4).

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

the answer is one hundred and eight 108

Step-by-step explanation:

108 bro trust me

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The first equation will be multiplied by 3 and that of the second by 4.

An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.

Given that are two equations to be solved by using elimination method,

-4x+4y = 32.....(i)

3x-y = 12......(ii)

To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4

-12x+12y = 96.....(iii)

12x-4y = 48....(iv)

Solving the equations, we get,

8y = 144

y = 18

Put y = 18 in eq (ii)

3x-18 = 12

3x = 30

x = 10

Hence, the first equation will be multiplied by 3 and that of the second by 4.

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Given:

f(x) = 5x - 2

g(x) = 1 - 2x

Let's find (fg)(x).

To solve the function operation, we have:

(fg)(x) = f(x) * g(x)

Thus, we have:

Solving further:

Expand using FOIL method, then apply distributive property

ANSWER:

Answer:

The population was 3040 people in 8 years.

Step-by-step explanation:

find unit rate;

3800/10 = 380

380 x 8 = 3040

The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.

To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.

The velocity vector is the derivative of the position function r(t):

\(v(t) = (d/dt)(t^3/3, t^2, 2t)\)

\(= (t^2, 2t, 2)\)

The speed of the particle at any given time t is:

|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)

= √(t^4 + 4t^2 + 4)

= √((t^2 + 2)^2)

To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.

distance = ∫[from -1/3 to 9] |v(t)| dt

= ∫[from -1/3 to 9] |t^2 + 2| dt

= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt

= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)

Evaluating the definite integrals:

distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]

= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]

= [1/27 + 2/3] + [729/3 + 18]

= 1/27 + 2/3 + 729/3 + 18

= 1/27 + 18/27 + 729/3 + 18

= (1 + 18 + 729)/27 + 18

= 748/27 + 18

= 27.63 + 18

= 45.63 units (approximately)

Therefore, the particle travels approximately 45.63 units along the path.

To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.

average speed = distance / time

= 45.63 / (28/3)

= 45.63 * (3/28)

= 4.9179 units per unit time (approximately)

The displacement is the straight-line distance between the initial and final positions of the particle.

displacement = |r(9) - r(-1/3)|

= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|

= |(27, 81, 18) - (-1/27, 1/9, -2/3)|

= |(27 + 1/27, 81

= 2781.

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The confidence level for the true average strain is (24.69,27.31) and the prediction level is (20.01,31.99) and also it is estimated that prediction level is much wider than the confidence level

Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.

a)

We must calculate the true average strain in a way that conveys precision and reliability.

We have to use t-test in our problem because sample size is less than 30.

We Know that,

True average value is determined by formula,

\(\mu\pm t*\frac{S}{\sqrt{n}}\)

where μ is sample mean,

s is sample standard deviation.

Degree of freedom=n-1

=20-1

=19

t-value at 95% confidence interval=1.7281

\(26\pm 1.728*\frac{3.4}{\sqrt{20}}\\\\=26\pm1.728*0.7606\\\\=26\pm1.31\\\\=24.69,\ 27.31\)

b)

predicted value can be calculated by formula,

\(\mu \pm t*S\sqrt{1+\frac{1}{n}}\\\\=26\pm 1.728*3.4\sqrt{1+\frac{1}{20}}\\\\=26\pm 1.728*3.4*1.02\\\\=26\pm5.99\\\\=20.01,\ 31.99\)

As a result, we conclude that the prediction interval is greater than the confidence interval.

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Answer:

4a + 13b

Step-by-step explanation:

-2a + 5b + 6a + 8b

combine like terms:

4a + 13b

Answer:

4a+13b

Step-by-step explanation:

-2a+6a+5b+8b. group like terms

4a+13b

n = - 1

Hi !

6 = - 2(10n + 7)

6 = - 20n - 14

20n = - 6 - 14

20n = - 20

n = - 20 : 20

n = - 1

6 = - 2(10×-1 + 7)

6 = - 2(-10 + 7)

6 = - 2(-3)

6 = 6 (true)

Good luck !

Answer:

n = -1 OR -1 = n

Step-by-step explanation:

6 = -2(10n +7)

First we remove the brackets by multiplying the inner numbers by -2

6 = -20n - 14

Then we add 14 on both sides

20 = -20n

We make n the subject and divide both sides by -20

n = -1 OR -1 = n

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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Angle EFG is an angle with a measure of 42 degrees is drawn below.

Given that, angle EFG= 42 degrees.

Angle EFG is an angle with a measure of 42 degrees. To draw angle EFG, first draw a line segment and mark two points on the line segment. Label the two points E and F. Then, using a protractor, measure out an angle with a measure of 42 degrees from the line segment EF, starting from point E. Finally, mark the end of the angle as point G.

Therefore, angle EFG is an angle with a measure of 42 degrees is drawn below.

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Answer:

2.5

Step-by-step explanation:

Answer:

\(2\frac{1}{2}\) or 2.5

Step-by-step explanation:

\(\frac{5}{8}*4\\ \\ =\frac{5}{8}*\frac{4}{1} \\ \\ =\frac{5*4}{8*1} \\ \\ =\frac{20}{8} \\ \\ =\frac{5}{2} \\ \\ =2\frac{1}{2} or 2.5\)

The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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The domain of the function is whole numbers less than or equal to 200

The given parameters;

The function for the amount of money the baseball stadium makes from ticket sales is given as;

M(x) = 8x

where;

Since the maximum capacity of the stadium is 200, the number of spectators should be less or equal to 200.

x ≤ 200

Thus, the domain of the function is whole numbers less than or equal to 200

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Answer:

Step-by-step explanation:

Solve the equation x^2-16x + 54 = 0 by completing the square. Fill in the values of a and b to complete the solutions.

✓ Answer:Step-by-step explanation:I take it that a and b are defined below.y = a(x - b)^2 + cy = (x^2 - 16x ) + 54y = (x^2 - 16x + (16/…

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

Answer:

k=9

Step-by-step explanation:

8k-6=(k+3)+6k first remove the unnecsarry parentheses which would make it 8k-6=k+3+6k

then collect the like terms and get 8k-6=7k+3 then move the variable to the left and change its sign to get 8k-7k-6=3.

then collect the like terms a final time which would get you k=3+6 to then get k=9  

hope this helps!

The value of total weight of the fish Nicholas and his father caught, in pounds is,

⇒ 87/4 pounds

We have to given that;

Nicholas caught a fish that weighed 14 1/2 pounds.

And, His father caught a fish that weighed half as much as the fish Nicholas caught.

Hence, The weight of fish caught  by his father is,

⇒ 14 1/2 ÷ 2

⇒ 29/2 × 1/2

⇒ 29/4

Thus, The value of total weight of the fish Nicholas and his father caught, in pounds is,

⇒ 14 1/2 + 29/4

⇒ 29/2 + 29/4

⇒ 58/4 + 29/4

⇒ 87/4 pounds

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The difference in length between the longest ski trail and the shortest ski trail is 7/4.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Length of the longest ski trail = 3 1/8 = 25/8

Length of the shortest ski trail = 1 3/8 = 11/8

Difference in length between the longest ski trail and the shortest ski trail:

= 25/8 - 11/8

= 14/8

= 7/4

Thus, the difference in length between the longest ski trail and the shortest ski trail is 7/4.

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Answer:

m=70°

Step-by-step explanation:

*∠WXY and ∠ZXY are supplementary angles (180°)*

110°+m=180°

110°+m-110°=180°-110°

m=70°

Hope it helps!

The margin or error associated with the confidence interval is 5.62 points

The sample size of the third grade children = 20

The confidence interval for the population mean score  = 90%

The mean score = 64 points

The standard deviation = 12 points

The degree of freedom = The sample size - 1

= 20 - 1

= 19

The critical value of t at degree of freedom 19 = ±2.093

The margin error = Critical value of t × \(\frac{s}{\sqrt{n} }\)

Substitute the values in the equations

The margin error = 2.093 × \(\frac{12}{\sqrt{20} }\)

= 2.093 × 2.68

= 5.62 points

Therefore, the margin error is 5.62 points

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The answers to 4 decimal places are=

(a) 0.0884

(b) 0.0190

(c) 0.9596

(d) 0.2921

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

According to our question-

a= 2.25-1.25

0.0884

b= 3.04-2.04

0.0190

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Answer:

A. Shifted 3 unit right and 2 unit down

Step-by-step explanation:

Let's determine the reason for the answer.

We will use a reference point, only one point to determine the reason.

Because the both shape are identical.

Let's use point A

The position of A is 2 on the y axis and 1 on the x axis

While the position of A' is 0 on the y axis and 4 on the X asis

Let's know how many units where moved from the position.

A' -A

For X axis

4-1= 3

For y axis

0-2= 2(we need only the magnitude)

So its 2 units Down and 3 unit right