A scientist studied the migration patterns of two types of whales. The humpback whale traveled 2,000 miles in 25 days. The gray whale traveled 2,250 miles in 30 days. Assuming the humpback whale travels the same distance each day, what is the unit rate for the humpback whale in miles per day?

Sin 75° - sin 15° can be expressed as the product √2/2.

To express the product sin 7x cos 4x as a sum or difference, we can use the following trigonometric identity:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Let a = 11x and b = -3x. Then we have:

sin(11x - 4x) = sin(7x)cos(4x) - cos(7x)sin(4x)

Rearranging terms, we get:

sin(7x)cos(4x) = sin(11x)cos(3x) - cos(7x)sin(4x)

Therefore, sin 7x cos 4x can be expressed as the difference of sin 11x cos 3x and cos 7x sin 4x.

Answer: D) sin 11x cos 3x - cos 7x sin 4x

To express sin 75° - sin 15° as a product, we can use the following trigonometric identity:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Let a = 75° and b = 15°. Then we have:

sin(75° - 15°) = sin(75°)cos(15°) - cos(75°)sin(15°)

Since sin(75°) = cos(15°), we can simplify this expression to:

sin(60°)cos(15°) - cos(75°)sin(15°)

Using the fact that sin(60°) = √3/2 and cos(75°) = sin(15° + 60°) = sin(75°), we can further simplify:

(√3/2)cos(15°) - sin(75°)sin(15°)

Using the fact that cos(15°) = √[(1 + cos(30°))/2] = (√3 + 1)/2√2 and sin(75°) = cos(15° + 60°) = -sin(15°), we can simplify further:

(√3/2)((√3 + 1)/2√2) - (-sin(15°))(sin(15°))

= (√3(√3 + 1) - 2sin^2(15°))/4

Using the fact that sin(15°) = (√6 - √2)/(4√2), we can substitute to get:

= (√3(√3 + 1) - (6 - 2√3 - 2))/(16)

= (√3 + 1 - √3 + 2)/4

= √2/2

Therefore, sin 75° - sin 15° can be expressed as the product √2/2.

Answer: A) √2/2

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The probability that a card is a spade or a king, given that it is black is 3/26 or 0.1154 or 11.54%

In a standard deck of cards, we have the following readings

Black cards = 26

Black spade or king = 3

So, we have the probability formula to be

Probability = Black spade or king/Black cards

This gives

Probability = 3/26

Evaluate

Probability = 0.1154

Express as percentage

Probability = 11.54%

Hence, the probability that a card is a spade or a king, given that it is black is 3/26

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a. The probability P(X < 10) is U(0, 50) is 0.20.

b. The probability P(X > 595) is U(0, 1,000) is 0.405.

c. The probability P(21 < X < 49) is U(19, 68) is 0.4762.

a. For a uniform continuous distribution U(0, 50), the probability of an event X < 10 can be calculated by dividing the length of the interval [0, 10] by the length of the entire interval [0, 50]. Since the lengths of both intervals are equal, the probability is 10/50 = 0.20.

b. Similarly, for a uniform continuous distribution U(0, 1,000), the probability of an event X > 595 can be calculated by dividing the length of the interval [595, 1,000] by the length of the entire interval [0, 1,000]. The length of the interval [595, 1,000] is 1,000 - 595 = 405, and the length of the entire interval is 1,000 - 0 = 1,000. Thus, the probability is 405/1,000 = 0.405.

c. For a uniform continuous distribution U(19, 68), the probability of an event 21 < X < 49 can be calculated by dividing the length of the interval [21, 49] by the length of the entire interval [19, 68]. The length of the interval [21, 49] is 49 - 21 = 28, and the length of the entire interval is 68 - 19 = 49. Therefore, the probability is 28/49 = 0.5714.

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Answer:

2 (x + 7)

Step-by-step explanation:

2x + 14

2 (x+7)

I hope this helps

Answer:

\(2(x+7)\)

Step-by-step explanation:

Factoring is when takes out the GCF (greatest common factor) between two numbers. Between the numbers \(( 2x + 14 )\) The GCF is (\(2\)). Hence one divides both numbers by (\(2\)), groups the numbers and then writes (\(2\)) on the outside.

(\(2x + 14\))

\(2(x+7)\)

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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Answer:

\(f(2)=5\)

Step-by-step explanation:

We are given a function f(x) = 3x - 1.

We are asked to find f(2).

First, note that f(x) is also y. In addition, any variables can be used, such as g(x) or y(f).

Either way, as long as the variable in the parentheses is present in the equation, the number that is in its place can be substituted as the variable in the function.

Therefore, in an instance of f(3) = 3x + 1:

\(f(3)=3x+1\\\\f(3)=3(3)+1\\\\f(3)=9+1\\\\f(3)=10\)

First, substitute 2 as x in f(x):

\(f(x)=3x-1\\\\f(2)=3x-1\)

Then, substitute 2 as x in the equation:

\(f(2)=3x-1\\\\f(2)=3(2)-1\\\\f(2)=6-1\\\\f(2)=5\)

Therefore, f(2) = 5.

Hello :D

All of the sports are equal in numbers. Therefore, they are all popular.

Hope this helps

Answer:

Soccer

Step-by-step explanation:

Soccer has over 4.0 billion viewers so it outranks many base sports Hope This Helps :)

The equation of the straight line is 8x - y = 85.

It is given that the slope of the line is 8 and passes through the point (3,11).

We have to find the equation of the line.

We know that,

Equation of a line is :-

\(y -y_1 = m (x - x_1)\)

Where,

x and y are variables

m is the slope of the line

\((x_1,y_1)\) are the coordinates of the point that passes through the line.

Here,

\((x_1,y_1)\) = (3,11)

m = 8

Hence,

Equation of the line = y - 3 = 8(x - 11)

y - 3 = 8x - 88

8x - y = -3 + 88

8x - y = 85

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The given statistical study - "For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn" is a correlational study.

What is a correlational study?                                                                                                                                                                         Correlational study is a research design that helps to measure and describe the relationship between variables without the researcher influencing or manipulating any variables. Correlation allows researchers to test how variables are related to one another, providing a way to find new relationships, understand phenomena, and make predictions.

Classify each statistical study as experimental or correlational. According to the given problem, data are collected on the dollar amount withdrawn for a sample of college students using the ATM in the campus center. As there is no manipulation of variables involved and no control group is assigned, this is a correlational study.

Therefore, the given statistical study - "For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn" is a correlational study.

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Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The rationale that supports this statement is:

​Situational experiences are interpreted differently.

Now, According to the question:

Let's Know:

What is the Rationale of the Study?

The rationale of the study explains the reason why the study was conducted (in an article or thesis) or why the study should be conducted (in a proposal). This means the study rationale should explain to the reader or examiner why the study is/was necessary.

We know that :

There are different levels and combinations of concerns among individual students.

Hence, The rationale that supports this statement is:

​Situational experiences are interpreted differently.

In the question;

There are different levels and combinations of concerns among individual students.

what is the rationale that supports this statement?

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Answer:

b

Step-by-step explanation:

15/6=2.5

100/2.5=40

Answer:

2/3-4x+7-2=-9.x+5/6

2/3+7/1-2/1-5/6=-9.x+4x

12+126-36-15/18=-5x

87/18=-5x

29/6=-5x

29/6÷5=-5x÷5

29/6*1/5=-5x÷5

29/30=-x

-29/30=x

-0.9667=x

named width in java with a value of 1.55.

double length = 3.5; double width = 1.55;

Double is a data type in Java that supports storing decimal numbers. It is used to represent values that include a fractional component and is a 64-bit floating-point data type. When exact decimal numbers are required, as in financial or scientific computations, the double data type is frequently utilized. A double's range is roughly  ±\(5.0 \times 10^{-324}\) to ±\(1.7 \times 10^{308\) having a 15–17 decimal digit degree of accuracy.

For example:

double myDouble = 3.14; Alternatively, you may define a double variable without first giving it a value and then give it one later on in your code.

3.5 double length, 1.55 double width;

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A using the limit definition derivative of f(x) = 7x²2 + 4x using the limit definition is f'(x) = 14x + 4.

To find the derivative of the function f(x) = 7x²2 + 4x using the limit definition of the derivative, we need to evaluate the following limit:

f'(x) = lim(h→0) [f(x + h) - f(x)] / h

Let's start by substituting f(x) into the limit expression:

f'(x) = lim(h→0) [(7(x + h)²2 + 4(x + h)) - (7x²2 + 4x)] / h

Now, we expand and simplify the expression inside the limit:

f'(x) = lim(h→0) [(7(x²2 + 2xh + h²2) + 4(x + h)) - (7x²2 + 4x)] / h

f'(x) = lim(h→0) [7x²2 + 14xh + 7h²2 + 4x + 4h - 7x²2 - 4x] / h

Next, we can cancel out like terms:

f'(x) = lim(h→0) (14xh + 7h²2 + 4h) / h

Now, we can factor out an h from the numerator:

f'(x) = lim(h→0) h(14x + 7h + 4) / h

The h term cancels out:

f'(x) = lim(h→0) 14x + 7h + 4

Finally, we can evaluate the limit as h approaches 0:

f'(x) = 14x + 7(0) + 4

f'(x) = 14x + 4

Therefore, the derivative of f(x) = 7x²2 + 4x using the limit definition is f'(x) = 14x + 4.

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Answer:

17

Step-by-step explanation:

The value of the line segment MO will be 17 units.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the length of the line segment Mo = 3x - 10, and N is the point on the line MO and Mn = 8, and NO = x.

The value of the line segment MO will be calculated as below:-

MO = MN + NO

3x - 10 = 8 + x

3x - x = 8 + 10

2x = 18

x = 18 / 2

x = 9

The value of the segment MO will be:-

MO = 3x - 10

MO = ( 3 x 9 ) - 10

MO = ( 27 ) - 10

MO = 17

Therefore, the value of the line segment MO will be 17 units.

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Answer:

Basic Of Algebra. Basics of Algebra cover the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0. This introduces an important algebraic concept known as equations .

Answer:

45

Step-by-step explanation:

arcAE = 180

arcABC : arcCDE = 3:1

ABC:CDE = 135:45

∠T = 1/2(135 - 45) = 45

Use the Far Arc -- Near Arc Formula:  m∠T = 1/2(far-arc - near-arc) = 1/2(arcABC -arcCDE)

so let's recall that a full circle has a total of 360°, and we also know that these two arcs are on 3 : 1 ratio.

Now, let's notice the points A and E, the line AE passes through the center of the circle, that means the arc made by ABCE is half the circle or 180°.

So if we just divide 180 by (3 + 1) and then distribute accordingly to each arc, we'll see how many degrees each arc really has

\(\stackrel{\widehat{ABC}}{3}~~ : ~~\stackrel{\widehat{CDE}}{1}\qquad \implies \qquad \stackrel{\widehat{ABC}}{3\cdot \frac{180}{3+1}}~~ : ~~\stackrel{\widehat{CDE}}{1\cdot \frac{180}{3+1}} \\\\\\ \stackrel{\widehat{ABC}}{3\cdot 45}~~ : ~~\stackrel{\widehat{CDE}}{1\cdot 45}\qquad \implies \qquad\stackrel{\widehat{ABC}}{135}~~ : ~~\stackrel{\widehat{CDE}}{45}\)

Check the picture below.

Answer

8.7

All the first digits are even numbers..and the numbers behind the decimal points are odd numbers

Answer:

8.7

Step-by-step explanation:

I'm assuming you want the term between 6.5 and 10.9

The sequence is aritmetic with a

common difference of 6.5 - 1.3 = 4.3 - 2.1 = 2.2

6.5 + 2.2 = 8.7

The given statement "A and B are n x n matrices. The determinant of A is the product of the diagonal entries in A" is False because the product of the diagonal entries in A for n x n matrix will not be equal to determinant of A.

The determinant of a matrix is a scalar value that can be calculated using a specific formula. The formula for finding the determinant of an n x n matrix involves finding the sum of products of the elements in certain combinations of rows and columns.

The product of the diagonal entries is only one element in the calculation of the determinant of a matrix, and it is not equal to the determinant unless the matrix has all zeros except on the diagonal.

For example, consider the following 2x2 matrices:

A = [2 3; 4 5]

B = [1 0; 0 1]

The determinant of A is (25) - (34) = -2

The product of the diagonal entries in A is 2*5 = 10, which is not equal to the determinant.

The determinant of B is (11) - (00) = 1

The product of the diagonal entries in B is 1*1 = 1, which is equal to the determinant.

Therefore, the statement "The determinant of A is the product of the diagonal entries in A" is false in general, and the determinant of a matrix is typically calculated using a more involved formula that takes into account all the elements in the matrix.

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Answer:

I don't know if you have its answer please tell

10*3

Answer: (30 x r) - 7

Step-by-step explanation:

The statement tells us several important things:

1. Of all the money collected from sales, 8.5% is for sales tax.

2. Of all the money collected from the sales, $125 goes to pay the rent for the space that I am using.

3. After deducting the taxes and the rented space, they divide the remaining money into 7 equal parts, which corresponds to $175.

To find the value of the money collected we first calculate the money that is known, i.e. the $175 for 7 of the growers and the $125 for the rent of the space.

This amount of money corresponds to the percentage remaining after taxes are taken out.

The percentage of this amount of money is 91.5%, the percentage of this amount of money is 91.5%.

In conclusion, the answer is $1476

Answer:

3x - 35 = 130

Step-by-step explanation:

Vertically opposite angles are congruent.

3x - 35 = 130

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Assuming that all four beads must be used in each necklace, there would be only one necklace that can be formed using 2 blue beads, one red bead, and one yellow bead.
You can form 2 unique necklaces using 2 blue beads, one red bead, and one yellow bead. The arrangements are:
1. Red - Blue - Blue - Yellow
2. Yellow - Blue - Blue - Red

To solve this problem, we need to determine the number of unique ways we can arrange the beads on a necklace.

Since this is a circular arrangement, we need to account for rotations and reflections. This means that if we have a necklace with beads arranged in a certain order, we can rotate the necklace and get a different arrangement, but it will still be considered the same necklace. Similarly, if we can reflect the necklace (flip it over), we will get a different arrangement, but it will still be considered the same necklace.

To find the total number of unique arrangements, we can use the formula:

N = (n!)/(r!(n-r)!)

where:

N is the number of unique arrangements

n is the total number of items to choose from (in this case, 4 beads)

r is the number of items to choose (in this case, we want to choose all 4 beads)

Using this formula, we get:

N = (4!)/(4!(4-4)!)

N = (4!)/(4!0!)

N = 1

Therefore, there is only one unique necklace that can be formed using 2 blue beads, one red bead, and one yellow bead.

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Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

The null hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is less than or equal to 57%. The alternative hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is greater than 57%.

To test this, you would use a one-sample proportion test. The test statistic is calculated using the sample proportion (60%) and the hypothesized proportion (57%) and the sample size (800).

You would then compare the calculated test statistic to the critical value from a z-table (using a two-tailed test and a 0.02 level of significance) to determine whether or not to reject the null hypothesis.

Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

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Answer: 38

Step-by-step explanation:

24 divided by 5 = 4.8 per hour

4.8 times 8 = 38.4 or 38 in 8 hours

It can burn 38 in 8 hours

Answer:

0.8 is the probability that a single detection system will detect a missile attack.

Step-by-step explanation:

The value of the expression -13x-7y is -8.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations are

-9x + y = 2   .....(i)

-4x - 8y = -10 ....(ii)

Solve the equation by using system of equations.

Multiply equation (i) by 8 and add with equation (ii)

-72x + 8y = 16

-4x - 8y = -10

___________

-76x = 6

x = 6/-76

x = - (3/38)

Putting x = - (3/38) in equation (i):

-9[- (3/38)] + y = 2

27/38 + y = 2

y = 2 - 27/38

y = 49/38

Putting x = - (3/38) and y = 49/38 in -13x-7y:

-13(-3/38)-7(49/38)

= 39/38 - 343/38

= -304/38

= -8

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