Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.

x = 3 is the true solution to 2 ln e superscript ln 5 x baseline = 2 ln 15, using the concept of simplification.

Make something simpler by simplifying it. In mathematics, reducing an expression, fraction, or issue to a simpler form is referred to as simplification. With calculations and solutions, the problem is made simple.

In order to achieve consistency in efforts, costs, and time, procedures must be simplified. It gets rid of variation and variety that is superfluous, harmful, and unproductive. It is termed simplification to use and interpret the function in order to make it simpler or easier to grasp.

The equation can be simplified by using the fact,

ln(eˣ) = x

This gives,

2 ln(5x) = 2·ln(15)

Comparing arguments, we see that,

5x = 15

x = 3

Check if it is true or not:

2 ln(e^(ln(5·3))) = 2·ln(15)

2 ln(e^2.70805) = 2·2.70805

2 ln(15) = 5.41610

and,

2·2.70805 = 5.41610

So, it is true.

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The function, f(x) = -50 and g(x) = -17

A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

Instance: f(x) = x/2 ("f of x equals x divided by 2")

we are given that f(x) = -3[tex]x^{2}[/tex] -2 and g(x) = 4x - 1

we need to find f(4) and g(-4)

f(4) = -3([tex]4^{2}[/tex]) - 2

f(4) = -3*16 - 2

f(4) = -48-2

f(4) = -50

g(x) = 4x - 1

g(-4) = 4 *-4 -1

g(-4) = -16-1

g(-4) = -17

The function f(x) = -50  and g(x) = -17

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Answer:

The answer is 71

What is chemist?

A chemist is a person who specializes in the science of chemistry, which is the study of matter and its properties, structure, composition, behavior, and the changes it undergoes. Chemists are trained in the scientific discipline of chemistry and use their knowledge to study and manipulate matter. This can include anything from the analysis of materials for their chemical makeup, to the development of new products and processes. Chemists can work in a variety of fields, including pharmaceuticals, materials science, biochemistry, research and development, and more. They must be well-versed in the principles and theories of chemistry, as well as in the practical aspects of their work. Through their work, chemists contribute to the advancement and application of science.

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Answer: the answer is 15

Step-by-step explanation:

Answer: Not a Question

Step-by-step explanation:

No question mark and not a math quiestion

Answer:

y= 3x + 5

Step-by-step explanation:

Some examples

(1,8)

8= 3 (1) + 5

8 = 3 + 5

8= 8

(2,11)

11= 3 (2) + 5

11= 6 + 5

11= 11

So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

The valid bounding condition for the sum of the subset problem is:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

This means that each item can either be included in the subset (x[i] = 1) or not included in the subset (x[i] = 0).

The sum of the weights of the items in the subset should not exceed the maximum capacity constraint, m. So the bounding condition for the weight of the subset is:

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

This means that the sum of the weights of the items in the subset should be less than or equal to the maximum capacity constraint.

So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

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Using the formula for binomial probability distribution and the provided values, The answer is 0.775 .

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (p) and fail—is known as the binomial distribution with parameters n and p in probability theory and statistics (1-p).

It's formula is:

[tex]P(x) = C(n,x)*p^{x}*q^{n-x}[/tex]

p = 0.89

q= 1-p = 0.11

n=15

P(x>=13) = P(13)+P(14)+P(15)

=0.279+0.322+0.174

=0.775

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What is covariance

Covariance measures the directional relationship between the returns of two assets. A positive covariance means that the asset returns move together, a negative covariance means they move in opposite directions.

What does covariance between two variables mean?

Covariance measures the direction of the relationship between two variables. A positive covariance means that both variables tend to be high or low at the same time. Negative covariance means that as one variable increases, the other tends to decrease.

correlation coefficient

Correlation coefficient measures the strength of association between two variables. The most common correlation coefficient, called the Pearson product-moment correlation coefficient, measures the strength of linear association between variables measured on an interval or ratio scale.

according to the question given data,

the greater the absolute size of the correlation coefficient, the greater is the covariation between the two variables ,or the stronger is their relationship,(true)

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Answer:

0

Step-by-step explanation:

If it lies on the y line then it is horizontal. This means the slope is 0 and so is the x value.

Answer:

d ≈ 8.5 units

Step-by-step explanation:

calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (2, - 1 ) and (x₂, y₂ ) = B (- 4, 5 )

d = [tex]\sqrt{(-4-2)^2+(5-(-1))^2}[/tex]

   = [tex]\sqrt{(-6)^2+(5+1)^2}[/tex]

   = [tex]\sqrt{36+6^2}[/tex]

   = [tex]\sqrt{36+36}[/tex]

   = [tex]\sqrt{72}[/tex]

   ≈ 8.5 units ( to 1 decimal place )

Answer:

5

Step-by-step explanation:

The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."

Using this definition, we can simplify the expression "10^log5" as follows:

10^log5 = 10^y

Where "y" is the exponent to which the base "10" must be raised to produce the result "5."

To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:

log(10^y) = y

Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:

log(5) = y

Solving for "y," we find that "y = log(5)."

Therefore, the expression "10^log5" can be simplified to:

10^log(5) = 10^(log(5)) = 5

So the simplified result is 5.

The unidentified term is 3m.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, an equation (x-0.2n)² = x-1.2mn+0.04n²

We know that, (a-b)² = a²-2ab+b²

Comparing the given equation with the above identity, we get,

a = x, b = 0.2n and 2ab = 1.2mn

Therefore, 2x×0.2n = 1.2mn

x = 3m

Hence, the unidentified term is 3m

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Answer:

5/13

Step-by-step explanation:

[tex]CE=\sqrt{10^2 + 24^2}=26 \\ \\ \cos E=\frac{10}{26}=\frac{5}{13}[/tex]

If the radius of the hole is 3 inches than the volume of the resulting solid is 410.29 in³    .

In the question ,

it is given that ,

the manufacturer drills a hole in the metal sphere that has radius of 5 inches ,

the radius of hole in sphere is 3 inches .

the volume of the metal sphere is = (4/3)×π×r³

= (4/3)×π×5³

= 523.33 in³

the volume of the hole of radius 3 inches is = (4/3)×π×3³

= 113.04 in³

So , the volume of the remaining solid is = 523.33 - 113.04

= 410.29 in³  .

Therefore , the Volume of the resulting solid is 410.29 in³    .

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Answer:

2400

Step-by-step explanation:4152 is just 173% of d.

We create an equation d = 4152/1.73

after solving you get 2400.

8 ÷ 640 x 100,000 = 12,500 defective computer chips

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Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

An inequality is a mathematical statement that shows the relative size of two values.

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

What is inequality?

An inequality is a mathematical statement that shows the relative size of two values.

What is linear inequality?

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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Total number of ways four people line up in the straight line with the given condition is equal to 18 ways.

As given in the question,

Total number of people = 4

Given condition :

First position can not occupied by youngest person:

First position occupied in 3 ways

Second position occupied in 3 ways

Third position occupied in 2 ways

fourth position occupied in 1 ways

Total number of ways = 3 × 3 × 2 × 1

                                  = 18 ways

Therefore, the number of ways four people stand in straight line is equal to 18 ways.

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The value of the side AC is 40 if the points  B, D, and F are midpoints of

the sides of ΔACE.

The midpoint theorem states that in order to determine the midpoints of a triangle's sides, "a line segment linking any two of its midpoints is said to be parallel to the triangle's third side and also half the length of the third side."

Divide the distance between the two endpoints by 2, then do it again. The two terminal x coordinates can alternatively be combined, then the result divided by two. Draw a line from a midway to the opposite corner. The centroid of a triangle is the point at where the three medians intersect.

Given,

The points B, D, F are midpoints of the sides of a triangle ACE.

And also given that,

EC =32 and DF=20, AC=?

So, FD=1/2(AC)

AC=2(FD)

AC=2(20)

AC=40

Therefore, the value of the side AC is 40 if the points  B, D, and F are

midpoints of the sides of ΔACE.

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The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

In an alternative method, a linear polynomial over a field from which the coefficients are extracted is equalized to zero to produce a linear equation. The values that, when used as placeholders for the unknowns, result in the equality being true are the solutions to this kind of equation.

In this specific situation, where the variable is appropriately referred to as the unknown, the term "linear equation" frequently applies indirectly.

The Cartesian coordinates of a point on the Euclidean plane can be read as each solution in the case of two variables.

Given equation is:

-4x+y=16

For x-intercept, y=0

-4x+0=16

-4x=16

x= -4

The x-intercept has an ordered pair (-4, 0)

For y-intercept, x=0

-4(0)+y=16

y=16

The y-intercept has an ordered pair(0,16)

Therefore, The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

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The number of pounds of clay used to make 21 small vases is 10 and one half pounds.

Sandy uses three and one half pounds of clay to make 7 small vases. Using proportion, the number of pounds of clay that she can use to make 21 small vases can be calculated as follows;

Therefore,

7 small vases = 3 1 / 2 pounds of clay(7 / 2)

21 small vases = ?

cross multiply

pounds of clay used to make 21 small vases = 7 / 2 × 21 ÷ 7

pounds of clay used to make 21 small vases = 147 / 2 ÷ 7

pounds of clay used to make 21 small vases =  147 / 2 × 1 / 7

pounds of clay used to make 21 small vases = 21 / 2

Therefore,

pounds of clay used to make 21 small vases = 10 1 / 2

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Answer:

[tex]A \approx 38 \, \textrm{cm}^2[/tex]

Step-by-step explanation:

The area of a triangle is defined as:

[tex]A_\triangle = \dfrac{1}{2}bh[/tex]

where [tex]b[/tex] is the length of its base and [tex]h[/tex] is its height.

So, we can plug the given values into this formula along with the inch to centimeter conversion to get the answer to this problem.

[tex]A=\dfrac{1}{2}\left(4.75\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)\left(2.5\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)[/tex]

And simplify.

[tex]A \approx 38 \, \textrm{cm}^2[/tex]

It will be 13min until there are 20 grams of the element remaining.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, and is the initial amount, b is the decay factor, and y is the final amount.

Here, we have

This is a compound decay problem, which goes by the formula:

F = P(1-r)ˣ

Where

F is the future amount (we want it to be 20)

P is the present amount (240 now)

r is the rate of decay per minute (17.4% = 17.4/100 = 0.174)

x is the time it takes (what we want to find)

Substitute all values in the formula and we get

20 = 240(1-0.174)ˣ

20 = 240(0.826)ˣ

0.0833 = 0.826ˣ

㏑0.0833 = ㏑0.826ˣ

㏑0.0833 = x ㏑0.826

x = ㏑0.0833/㏑0.826

x = 13

Hence, it will be 13min until there are 20 grams of the element remaining.

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Answer:

$1944

Step-by-step explanation:

18x12=216

216x$9=$1944

Answer:

£1944

Step-by-step explanation:

The area of the floor is 216 feet²

18 x 12 = 216

216 x 9 = 1944

By looking at the definition of mutually exclusive and independent event, the statement for both events are true.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.

(a) True. The given event is both mutually exclusive as well as independent

(b)True. The given event is both mutually exclusive as well as independent

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The value of y in the given figure is 108°.

The angles formed by a transversal line on the same side and position of the line, if lines are parallel then the corresponding angle are congruent.

Given is a figure, where two line AB and CD are being intersected by a transversal FE,

Let FE intersects AB and CD at P and O, respectively, (refer to the figure attached)

Since, AB ║ CD

Therefore, ∠ FPB  ≅ ∠ POD by the definition of corresponding angles,

2x+16 = 3x-12

x = 28

∠ POD = 28×3-12 = 72°

∠ POD and ∠ EOD are forming linear pair and therefore are supplementary,

∠ POD + y = 180°

72° + y =180°

y = 180°-72°

y = 108°

Hence, y = 108°

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The perimeter of the image is 70 meters and its area is 210 square meters.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter.

Area=(1/2)×base× height

=(1/2)×21×20

=210 square meters

Perimeter=a+ b+ c

=21+20+29

=70meters

Therefore, The perimeter of the image is 70 meters and its area is 210 square meters.

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The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .

total length of four-bit strings = 16

Let S represent the collection of all four-bit bit strings.

Let A represent the occurrence of a randomly generated string beginning with 1.

Let B represent the scenario where a string created at random contains two consecutive 0s.

S has 8 strings that begin with the letter "1."

P( A ) = 8 / 16 = 1 / 2

Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100

P(A ∩ B)  = 3 / 16

Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,

3/16 / 1/2

= 3 / 8

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Answer:

congruence is compatibility or agreement while equal is the same or equivalent to one another.