Subject:Mathematics ​

Answer:

0.13 cm per second

Step-by-step explanation:

Lets convert the minutes to seconds:

3/4 minutes = 3/4(60) = 45 seconds

The snail traveled 5.85 cm in 45 seconds

To find out the speed per second, we set up a proportion:

\(\frac{5.85}{45} = \frac{x}{1}\)      where 45 and 1 represent the number of seconds, and 5.85 and x represent the distance in that set of time

Let's solve for x, or the distance in 1 second:

\(\frac{5.85}{45}=\frac{x}{1}\\\\\\\frac{5.85*1}{45x}\\\\\\x = \frac{5.85}{45}\\\\\\\\\\x = 0.13\)

The snail travels 0.13 cm per second.

-Chetan K

2411.52units³ is the required volume of the cylinder.

The formula for finding the area of the oblique cylinder is expressed as:

V = πr²h

where

r is the radius

h is the height

Substitute the given parameters

V = π(8)²×12
V = 3.14 × 64 × 12
V = 2411.52units³

Hence the required volume of the cylinder is 2411.52units³

Learn more on volume of cylinder here: https://brainly.com/question/9554871

#SPJ1

Answer:

  $104.49

Step-by-step explanation:

The future value of the account is given by the formula ...

  FV = P(1 +r)^t

The interest earned is the difference between that future value and the original amount deposited.

  I = FV -P

__

For the given investment, rate, and time, we find the interest to be ...

  I = $650((1 +0.0125)^12 -1) = $650(0.160755) = $104.49

Mr. Vance's account will have earned $104.49 in interest at the end of 12 years.

The exact value of the given expression is:(sqrt(15) + 2)/8.We are given that sin(theta) = 1/4 and tan(theta) > 0, where 0 ≤ theta ≤ 2pi. We need to find the exact value of cos(theta/2).

From the given information, we can find the value of cos(theta) using the Pythagorean identity:

cos(theta) = sqrt(1 - sin^2(theta)) = sqrt(15)/4.

Now, we can use the half-angle formula for cosine:

cos(theta/2) = sqrt((1 + cos(theta))/2) = sqrt((1 + sqrt(15)/4)/2) = sqrt((2 + sqrt(15))/8).

Therefore, the exact value of cos(theta/2) is:

cos(theta/2) = sqrt((2 + sqrt(15))/8).

Alternatively, if we rationalize the denominator, we get:

cos(theta/2) = (1/2)*sqrt(2 + sqrt(15)).

Thus, the exact value of cos(theta/2) can be expressed in either form.In the second part of the problem, we are given an expression:

sqrt(10)/4 * sqrt(6)/4 + sqrt(8 + 2sqrt(15))/4 * sqrt(8 - 2sqrt(15))/4.

We can simplify this expression by recognizing that the second term is of the form (a + b)(a - b) = a^2 - b^2, where a = sqrt(8 + 2sqrt(15))/4 and b = sqrt(8 - 2sqrt(15))/4.

Using this identity, we get:

sqrt(10)/4 * sqrt(6)/4 + sqrt(8^2 - (2sqrt(15))^2)/16

= sqrt(10*6)/16 + sqrt(64 - 60)/16

= sqrt(15)/8 + sqrt(4)/8

= (sqrt(15) + 2)/8.

For such more questions on Expression:

https://brainly.com/question/1859113

#SPJ11

The time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d). So the answer is d. 40 minutes

Let's set up the equation based on the given information:

1/24 is the rate at which Sean and Colleen work together (clearing the yard in 24 minutes).

Let's denote the time it takes Colleen to clear the yard alone as c minutes. According to the given information, it would take Sean 20 minutes longer than Colleen to clear the yard alone, so Sean's time is (c + 20) minutes.

To set up the equation, we can combine their individual rates of work:

1/c is Colleen's rate of work (clearing the yard in c minutes).

1/(c + 20) is Sean's rate of work (clearing the yard in c + 20 minutes).

Given that their combined rate is 1/24, we can set up the equation:

1/c + 1/(c + 20) = 1/24

To solve this equation and find the value of c, we can multiply both sides by the common denominator of 24c(c + 20):

24(c + 20) + 24c = c(c + 20)

Simplifying and rearranging the equation:

24c + 480 + 24c = c^2 + 20c

48c + 480 = c^2 + 20c

Rearranging the terms and setting the equation equal to zero:

c^2 - 28c - 480 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. By factoring, we find:

(c - 40)(c + 12) = 0

This gives two possible values for c: c = 40 or c = -12.

Since time cannot be negative, we discard the solution c = -12.

Therefore, the time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d).So the answer is d. 40 minutes.

To learn more about  equation click here:

brainly.com/question/22849621

#SPJ11

Answer:

First step, correct answer is (3,1)

Step-by-step explanation:

1.it should be x+2(3x-8)=5

2. x+6x-16=5

3.7x=21

4. 7x/7=21/7

5. x=3

then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in

)  3x-8=y

6. 3(3)-8= 1

7. x=3, y=1

ANSWER:

x° = 24°

y° = 72°

Analysis on picture hope it helps

The amount of money that Anna made from the sale of the given book is; $112500

We are told that;

Percentage commission on each sale of a book to a publisher = 15%

Amount paid for the client's book by ABC publisher = $750000

Since Anna is paid 15% of the sales, then it means that;

Amount of money gotten by anna for this sale is;

Amount earned = 15% * 750000

Amount earned = $112500

We conclude that is the amount anna made for the sale of the book of her client to the publisher.

Read more about percentage problems at; https://brainly.com/question/843074

#SPJ1

Punnett squares can provide a good estimate of the expected ratios of offspring based on the genetic makeup of their parents, their accuracy depends on several factors and should not be relied upon as the sole determinant of actual ratios in every case.

A Punnett square is a simple diagram used to predict the probability of inheriting a particular trait in offspring based on the genetic makeup of their parents. While Punnett squares can provide a good estimate of the expected ratios of offspring, they are not always perfectly accurate.

The accuracy of Punnett squares depends on a number of factors, such as the completeness of the genetic information used to construct the square, the genetic variability of the population being studied, and the influence of environmental factors on gene expression.

Punnett squares are a useful tool for understanding basic principles of genetics and making predictions about the outcomes of crosses, but they should not be relied upon as the sole determinant of actual ratios in every case. Additional data and experimental evidence may be necessary to confirm or refine the predictions made using Punnett squares

Learn more about Punnett square here

brainly.com/question/25608427

#SPJ4

The change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

We have,

Length of coasts along the hill = 62.2 meters,

And,

The angle car make with the ground = 28.3°,

And,

The mass of the car = 1234 kg,

Now,

We know,

From the Work Energy Theorem that,

The change in Potential energy = The work done on the mass.

And,

Work done i.e. W = F × s × CosΘ

Here,

F = Force,

s = Distance car cover,

And,

Θ = Angle car make with the ground,

And,

We know that,

Force i.e. F = mass × acceleration due to gravity = m × g

And,

g= Acceleration of gravity = 9.8 m/s²

So,

Now,

Putting values,

i.e.

F = 1234 × 9.8 = 12093.2 Newton

Now,

Using the Formula of Work done,

i.e.

W = F × s × CosΘ,

Putting values,

i.e.

W = 12093.2 × 62.2 × Cos(28.3°)

On solving we get,

W = 662,292.459 Joule

So,

Chane in potential energy = 662,292.459 Joule

Hence we can say that the change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

Learn more about potential energy here

https://brainly.com/question/2961707

#SPJ4

For any positive integer n, the theorem states that the integer 8^n + 13 is divisible by 7. This means that when we raise 8 to any positive power and add 13, the resulting number will always be divisible by 7.

To understand why 8^n + 13 is divisible by 7 for any positive integer n, we can use the concept of modular arithmetic. Modular arithmetic deals with remainders when dividing numbers. In this case, we are interested in divisibility by 7.

Let's examine the pattern when we raise 8 to different powers and add 13:

- For n = 1: 8^1 + 13 = 8 + 13 = 21, which is divisible by 7.

- For n = 2: 8^2 + 13 = 64 + 13 = 77, which is divisible by 7.

- For n = 3: 8^3 + 13 = 512 + 13 = 525, which is divisible by 7.

We can observe that for each value of n, 8^n + 13 results in a number that is divisible by 7. This pattern continues for any positive integer n.

To provide a more formal explanation, we can use modular arithmetic notation. The statement can be expressed as: 8^n + 13 ≡ 0 (mod 7). This notation means that 8^n + 13 leaves a remainder of 0 when divided by 7, or in other words, it is divisible by 7.

This theorem can be proven using mathematical induction, where we show that the statement holds for n = 1, and assuming it holds for a particular value of n, we prove that it also holds for n + 1. The proof involves manipulating the expression 8^n + 13 using the properties of modular arithmetic.

Learn more about mathematical induction here:

https://brainly.com/question/31244444

#SPJ11

Complete question:

Main theorem. Assume that n is any positive integer. Then the integer \(8^{n}\)+13 is divisible by 7.

The algebraic expression in u for CSC(COS⁻¹(u)) is 1/√(1 - u²).

Here, we have,

To write the trigonometric expression CSC(COS⁻¹(u)) as an algebraic expression in u,

we can use the reciprocal identities of trigonometric functions.

CSC(theta) is the reciprocal of SIN(theta), so CSC(COS⁻¹(u)) can be rewritten as 1/SIN(COS⁻¹(u)).

Now, let's use the definition of inverse trigonometric functions to rewrite the expression:

COS⁻¹(u) = theta

COS(theta) = u

From the right triangle definition of cosine, we have:

Adjacent side / Hypotenuse = u

Adjacent side = u * Hypotenuse

Now, consider the right triangle formed by the angle theta and the sides adjacent, opposite, and hypotenuse.

Since COS(theta) = u, we have:

Adjacent side = u

Hypotenuse = 1

Using the Pythagorean theorem, we can find the opposite side:

Opposite side = √(Hypotenuse² - Adjacent side²)

Opposite side = √(1² - u²)

Opposite side =√(1 - u²)

Now, we can rewrite the expression CSC(COS^(-1)(u)) as:

CSC(COS⁻¹(u)) = 1/SIN(COS⁻¹(u))

CSC(COS⁻¹)(u)) = 1/(Opposite side)

CSC(COS⁻¹)(u)) = 1/√(1 - u²)

Therefore, the algebraic expression in u for CSC(COS⁻¹(u)) is 1/√(1 - u²).

To learn more about trigonometric relations click :

brainly.com/question/14450671

#SPJ4

Answer:

D

Step-by-step explanation:

If two polygons are similar, the corresponding sides must be C. congruent.

A polygon is a two-dimensional geometric figure with at least three straight sides and angles. Triangles, squares, rectangles, and pentagons are all examples of polygons. Polygons are classified according to the number of sides and angles they have. When two polygons are similar, their corresponding angles are congruent, and their corresponding sides are proportional. That is, if two polygons are similar, their corresponding angles are equal in measure, and their corresponding sides are in proportion to each other. Therefore, if two polygons are similar, the corresponding sides must be congruent.

An explanation of the remaining answer options: A. Complementary refers to angles. Angles are complementary if their sum is 90 degrees. Therefore, this answer option is irrelevant to the question.B. Supplementary refers to angles. Angles are supplementary if their sum is 180 degrees. Therefore, this answer option is irrelevant to the question.D. Linear pairLinear pair refers to two adjacent angles that form a straight line. Therefore, this answer option is irrelevant to the question.

Learn more about  similarity in polygons:https://brainly.com/question/1493409

#SPJ11

The intersection of A and B (A ∩ B) is {5}. So, the correct choice is:

A. A∩B = {5}

To obtain the intersection of sets A and B (A ∩ B), we need to identify the elements that are common to both sets.

Set A: {2, 4, 5}

Set B: {5, 7, 8, 9}

The intersection of sets A and B (A ∩ B) is the set of elements that are present in both A and B.

By comparing the elements, we can see that the only common element between sets A and B is 5. Therefore, the intersection of A and B (A ∩ B) is {5}.

Hence the solution is not an empty set and the correct choice is: A. A∩B = {5}

To know more about sets refer here:

https://brainly.com/question/14468525#

#SPJ11

Answer:

1110

Step-by-step explanation: If it was multiplication it would 1110 but you cat divide 185 by 6 so if it was 186, not 185 and you divided by 6 you would get 31 hope this helps

A check or quadrangle is defined by the intersection of pairs of diagonals of a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides are parallel and have the same length. The opposite angles of a parallelogram are equal. A parallelogram is a unique type of quadrilateral with specific characteristics.

A quadrangle or check is defined as the intersection of pairs of diagonals of a parallelogram. In other words, it is the area inside the parallelogram that is divided into four triangles, each of which shares a common vertex in the center of the parallelogram.

The diagonals of a parallelogram are the line segments that connect the opposite vertices of a parallelogram. When these diagonals intersect, they form four triangles, which are also known as the parallelogram's "sub-triangles." The point where the diagonals intersect is called the center of the parallelogram, and it divides each diagonal into two equal parts.

To know more about parallelogram refer here:

https://brainly.com/question/1563728#

#SPJ11

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

Find out more information about geometric sequence here:

brainly.com/question/11266123

Answer:

b

Step-by-step explanation:

To run a one-proportion hypothesis test for Jerry using the One Proportion applet, we would need to enter sample size, hypothesized proportion and number of successes.

To run a one-proportion hypothesis test for Jerry using the One Proportion applet, we would need to enter the following values:

-The sample size (n) - the number of participants in Jerry's study.

-The number of successes (x) - the number of participants who showed a preference for the new product in Jerry's study.

-The hypothesized proportion (p0) - the proportion of participants who are expected to show a preference for the new product based on the null hypothesis. This value is typically set to the proportion stated in the null hypothesis.

The significance level (alpha) - the level of significance used to determine the critical value and p-value for the test. This value is typically set to 0.05.

Once these values are entered into the One Proportion applet, we can run the analysis and obtain the test statistic (z-score), the critical value, and the p-value. We can then compare the p-value to the significance level to determine whether to reject or fail to reject the null hypothesis.

To know more about "Null hypothesis" refer here:

https://brainly.com/question/30535681#

#SPJ11

Answer:

Your answer is: x = 15/7

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Hope this helped : )

Answer:

B. \(\sqrt{5}\)

Step-by-step explanation:

Answer:

224

Step-by-step explanation:

56 * 4 =224

Answer:

224

Step-by-step explanation:

the pattern is 4 times the space the number is in

ex: 4,8,12,16 because 16 is the 4th number and 4x4= 16

hope this helps!

Have a wonderful day :D

Multiplication operation is not closed for polynomials, The polynomial is (x³+4x²+2x-5)(x²+3x+1). Option B is correct,

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)

Because the outcome of multiplying or adding two polynomials is always another polynomial, division, addition, and subtraction are closed operations for polynomials. Polynomials, on the other hand, do not have a closed division formula; when two polynomials are divided, a polynomial result is not necessarily obtained.

Thus, the multiplication operation is not closed for polynomials, The polynomial is (x³+4x²+2x-5)(x²+3x+1). Option B is correct,

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ1

Answer:

Step-by-step explanation:

Point D lies on the line, so it is invariant.

Point E is a distance of 4 units away from the line y=-1, so E is now (1, -1-4)=(1, -5).

By the same logic, F' is now (3, 0).

The image points of triangle reflected across the line y = -1 is D'(-1,-1) ,E'(1,-5) , F'(3, 0) .

The given point P is "reflected" in the mirror and appears on the other side of the line an equal distance it. Drag the point P to see this. The reflection of the point P over the line is by convention named P' (pronounced "P prime") and is called the "image" of point P.

According to the question

Triangle points given

D(-1,-1), E(1,3), F(3, -2)

and reflected across the line y = -1

As, we have to reflect from  y = -1 , there will be no change in x axis in image points only y axis will be change .

D(-1,-1)

x axis = -1

y axis = -1

x' axis = -1

y' axis = distance from -1 to -1 = 0

therefore,

y' axis = -1

D'(-1,-1)

E(1,3)

x axis = 1

y axis = 3

x' axis = 1

y' axis = distance from 3 to -1 = |3 -(-1 ) |= 4 unit

therefore, 4 unit form -1 in negative

y' axis = - 5

E'(1,-5)

F(3, -2)

x axis = 3

y axis = -2

x' axis = 3

y' axis = distance from -2 to -1 = |-2 -(-1 )| = 1 unit

therefore, 1 unit form -1 in positive

y' axis = 0

F'(3, 0)

Hence, the image points of triangle reflected across the line y = -1 is D'(-1,-1) ,E'(1,-5) , F'(3, 0) .

To know more about  image points here:

https://brainly.com/question/13102915

#SPJ2

Answer:

djal3924+3820&282039392#283830818385

Answer:

(3X+4)^2

Step-by-step explanation:

Answer:

unknown number : x

(x * 3 + 4)^2

= (3x + 4)^2

since you're squaring the result it's the same as squaring the whole equation

Hope it helps

Yes, the new method for detecting avobenzone in sunscreen is valid/accurate at a 95% confidence level.

The standard reference material provided by the FDA contains 0.250 mg of avobenzone per gram of sunscreen. The working group analyzed the standard and obtained measurements of avobenzone content in six samples, which were found to be 0.256, 0.279, 0.328, 0.305, 0.312, and 0.230 µg/g.

To determine the validity and accuracy of the new detection method, we need to assess if the measurements obtained from the samples are within an acceptable range of the known avobenzone content provided by the standard.

At a 95% confidence level, we can calculate a confidence interval to evaluate the accuracy of the new method. The confidence interval is a range within which we can reasonably expect the true avobenzone content of the sunscreen samples to fall. If the known avobenzone content provided by the standard falls within this confidence interval, it indicates that the new method is valid and accurate.

By performing the necessary calculations, we can determine the confidence interval. Comparing the range of the measurements obtained from the samples (0.230 to 0.328 µg/g) with the known avobenzone content provided by the standard (0.250 mg/g), we find that the measurements overlap with the known value. Therefore, we can conclude that the new method is valid/accurate for the detection of avobenzone in sunscreen at a 95% confidence level.

Learn more about Confidence intervals

brainly.com/question/32546207

#SPJ11