Which of the following equations best describes exponential decay?
A. y=a b', with 0 B. y a b', with 0 C. y a b', with 0 D. y=a b', with a > 0
Please select the best answer from the choices provided
A
B
D

Answer:

1

Step-by-step explanation:

Using the Pythagorean theorem, the length of the third side is [tex]\sqrt{(\sqrt{5})^2-2^2}=1[/tex].

The equation with 'n' as the independent variable is m = -2n - 13.

To rearrange the equation so that n is the independent variable, you can start by moving all of the terms with n on one side of the equation and all of the other terms on the other side.

You can start by subtracting 1 from both sides of the equation to get

m = -2(n + 6) - 1.

Then, you can distribute the -2 on the right side of the equation to get

m = -2n - 12 - 1.

Finally, you can combine the constants on the right side of the equation to get m = -2n - 13.

Therefore, the equation with 'n' as the independent variable is m = -2n - 13.

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The differences that exists between r and p are:

When points in a scatter plot are plotted against a linear regression line based on those points, as in the example when solving for cumulative savings over time, the sample correlation coefficient (r) is a measurement of how closely the points are associated.

The correlation coefficient (ρ) is a metric for estimating how closely two variables' movements are related. The Pearson product-moment correlation is used to calculate the most popular correlation coefficient, which is used to assess the linear relationship between two variables.

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The graph of the inequality y > 1 - 3x is shown in figure.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The equation of inequality is,

⇒ y > 1 - 3x

Now,

Since, The inequality is,

⇒ y > 1 - 3x

Hence, The graph of inequality y > 1 - 3x is shown in image by shaded ''red region.''

Thus, The red region of the graph is shows the graph of inequality

y > 1 - 3x.

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There are  2.97 * 10^9 ways that the colors can be chosen.

We talk about the term permutation when we have to make a selection and the order of the selection has been taken to be important. In that case the order bcd would be different from the order cbd.

Hence, we could be able to use the formula for the permutation of the colors that are in the box and we would have the result as the use of the formula;

P = n!/ (n - r)!

n in this case would be the number of the boxes that we have and we would thus have;

P = 65!/(65 - 5)!

P = 65 * 64 * 63 * 62 * 61 * 60!/60!

P = 2.97 * 10^9 ways

Thus, in the selection of the colors from the boxes, we can see that it is possible to do the selection using permutation in about  2.97 * 10^9 ways.

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Missing parts;

A company that makes crayons is trying to decide which 5 colors to include in a promotional mini-box of 5 crayons. The company can choose the 5 mini-box colors from its collection of 65 colors. How many mini-boxes are possible?

The number of hours it take if she bikes at an average rate of 8 miles per hour is 1.25 hour.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

Given that, Kiran's aunt plans to bike 10 miles.

1. She bikes at an average rate of 8 miles per hour

We know that, Time=Distance/Speed

= 10/8

= 1.25 hour

2. She bikes at an average rate of r miles per hour

Now, time =10/r hours

3. Kiran wants to join his aunt but only has 45 minutes to exercise.

Now, distance =Speed×Time

= 8×45/40

= 6 miles

4. Average rate need to be if they have t hours

Average rate =(10+6)/(t

= 16/t miles per hour.

Therefore, the number of hours it take if she bikes at an average rate of 8 miles per hour is 1.25 hour.

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"Your question is incomplete, probably the complete question/missing part is:"

Kiran's aunt plans to bike 10 miles.

1. How long will it take if she bikes at an average rate of 8 miles per hour?

2. How long will it take if she bikes at an average rate of r miles per hour?

3. Kiran wants to join his aunt but only has 45 minutes to exercise. What will him to finish on time?

4. What will their average rate need to be if they have t hours to exercise?

The measure of angle ∠4 will be 76°. Then the correct option is C. The measure of angle ∠4 will be 104°. Then the correct option is D.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.

Angles ∠1 and ∠2 are the supplementary angle. Then the equation is given as,

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 165

x = 33

The measure of angle 1 is calculated as,

∠1 = 3(33) + 5

∠1 = 99 + 5

∠1 = 104

Then the measure of the angle 2 is given as,

104 + ∠2 = 180

∠2 = 76

Angle 4 and angle 2 are opposite angles. Then we have

∠4 = ∠2

∠4 = 76

Angle 1 and angle 3 are opposite angles. And angle 3 and angle 5 are alternate angles.

∠1 = ∠3

∠5 = ∠3

∠5 = 104

The measure of angle ∠4 will be 76°. Then the correct option is C. The measure of angle ∠4 will be 104°. Then the correct option is D.

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Answer:

14125

Step-by-step explanation:

2,825x5=14125

Answer:

The amount paid in total was  £14125

Step-by-step explanation:

Population that went to the rugby match = 2825

Cost of 1 ticket = £5

Cost of 2825 tickets = 2825x5

=  £ 14125

Hence the amount paid in total was  £14125

d. The extra variability is caused by variations in the df value.

T-statistics are used to test hypotheses about the mean of a population when the standard deviation of the population is unknown and the sample size is small.

The t-distribution is similar to the standard normal distribution (z-distribution) but it has flatter tails and is more spread out. This extra spread is caused by the fact that the t-distribution is based on the sample size, which is reflected in the degrees of freedom (df) value.

The larger the sample size, the closer the t-distribution is to the standard normal distribution, and the more similar the t- and z- statistics will be.

In contrast to this, as the sample size decrease, the t-distribution becomes more spread out and t- statistics are therefore more variable than z-scores.

This increased spread means that t-statistics have a higher chance of falling into the tails of the distribution, which leads to a greater likelihood of a type I error (rejecting a true null hypothesis) or a lower power (failing to reject a false null hypothesis).

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The Ortega family will have a fraction of 11/16 amount of confetti left to use next year.

We shall convert the fractions to have similar denominators and simply apply subtraction for the numerators as follows:

fraction of confetti used = 1/4

pound of confetti made = 15/16

LCM of 4 and 16 is 16 so;

fraction of confetti used = 1/4 × 16/16

fraction of confetti used = 4/16

amount of confetti left = (15 - 4)/16

amount of confetti left = 11/16

Therefore, the Ortega family will have the fraction of 11/16 of confetti left.

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Answer:

1)12+c

2)12-c

3)12/c

4)12c

Answer:

4.65 British pound sterling

Step-by-step explanation:

[tex]7.50*0.62 = 4.65[/tex]

7.5 U.S. dollars = 4.65 British pound sterling

Yes, the base angles of an isosceles triangle are equal to each other.

The base angles of an isosceles triangle are equal because of the symmetry of the triangle. In an isosceles triangle, the two sides that are opposite the congruent angles are also congruent in length. This means that the triangle has a line of symmetry, or a line that divides it into two congruent halves. Since the triangle is symmetrical, the base angles are equal in measure.

Another way to understand why the base angles of an isosceles triangle are equal is to consider the definition of an isosceles triangle. An isosceles triangle is defined as a triangle with at least two congruent sides. Since the base angles are opposite the congruent sides, they must also be congruent. Therefore, the base angles of an isosceles triangle are equal.

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yes , base angles of isosceles triangle are equal 1 because An isosceles triangle is a triangle with two sides of equal length and the base angles of the isosceles triangle are equal in length.

The sides of equal length are called the legs of the triangle, and the third side is called the base. The base angles of an isosceles triangle are the angles formed by the base and the legs of the triangle. Since the base angles are formed by the base and the legs of the triangle, which are both congruent (i.e., have the same length), the base angles must also be congruent. In other words, the base angles of an isosceles triangle are equal.

The vertex angle of an isosceles triangle is the angle formed by the two legs at the apex of the triangle. This angle is always larger than the base angles, and its measure is equal to the sum of the measures of the base angles. For example, if the base angles of an isosceles triangle have a measure of 45 degrees each, the vertex angle will have a measure of 90 degrees (45 + 45). In summary, the base angles of an isosceles triangle are congruent and equal, and the vertex angle is larger than the base angles and is equal to the sum of the measures of the base angles.

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The sum of the number in the binary form is 1001010 and the values of m is 0 and n is 1.

Binary Number System: A binary number is a number that is stated in the binary system or base 2 numeral system, according to mathematics. It uses the symbols 1 (one) and 0 to represent different numeric values (zero). The notation with 2 as a radix is known as the base-2 system.

The binary number can be expressed in decimals as follows:

[tex]11111_2 = 1*2^4 + 1*2^3+1*2^2+ 1*2^1+1*2^0\\\\11111_2= 31\\\\10000_2= 1*2^4\\\\10000_2 = 16[/tex]

The sum of all the numbers is:

27 + 31 + 16 = 74

To convert the decimal in the binary form, divide the number continuously and note the remainder until it cannot be divided any further.

74 ÷ 2= 37= 0

37 ÷ 2 = 18 = 1

18 ÷ 2 = 9 = 0

9 ÷ 2 = 4 = 1

4 ÷ 2 = 2 = 0

2 ÷ 2 = 1 = 0

1 ÷ 2 = 0 = 1

So, the number in the binary form is 1001010 and the value of m is 0 and n is 1.

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The number that goes beneath the radical symbol is 40.

To find the distance between the two points (-4,3) and (2,5), you can use the distance formula:

distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in the values, you get:

distance = √[(2 - (-4))^2 + (5 - 3)^2]

Simplifying the expression, you get:

distance = √[6^2 + 2^2]

Which simplifies to:

distance = √[36 + 4]

Simplifying further, you get:

distance = √40

So the distance between the two points is √40. The number that goes beneath the radical symbol is 40.

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Answer:

40

Step-by-step explanation:

calculate the distance d using the distance formula

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

with (x₁, y₁ ) = (- 4, 3 ) and (x₂, y₂ ) = (2, 5 )

d = [tex]\sqrt{(2-(-4))^2+(5-3)^2}[/tex]

  = [tex]\sqrt{(2+4)^2+2^2}[/tex]

  = [tex]\sqrt{6^2+4}[/tex]

  = [tex]\sqrt{36+4}[/tex]

  = [tex]\sqrt{40}[/tex]

The percentage by mass of Na in the sample will be 60%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A 250 g sample is composed of 150 g of sodium (Na) and 100 g of chlorine (CI).

Then the percent by mass of Na in the sample will be given as,

P = (150 / 250) x 100

P = 0.60 x 100

P = 60%

The percentage by mass of Na in the sample will be 60%.

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These system of equations has been solved graphically and their solution is equal to the ordered pair (-1, 7).

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = 2x + 9     ........equation 1.

y = 6 - x       ........equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (-1, 7).

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Answer: DC

Step-by-step explanation: shortest angle is on the opposite side of the shortest side

The radical form of the number √ ( - 27 ) is given by the equation A = 3i√3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

The value of n = √( -27 )

Now , the value -1 can be represented as the complex number i

where i² = 1

So , the number n can be written as

A = √ ( 3i )² 3

A = √9i² (3)

A = √27i²

A = √-27

On simplifying the equation , we get

A = 3i√3

Therefore , the value of A is A = 3i√3

Hence , the equation is A = 3i√3

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The following ratio can be completed as;

3 17

6 34

9 51

12 68

15 85

Let

The unknown number = x

3 : 17 = 6 : x

3/17 = 6/x

cross product

3 × x = 6 × 17

3x = 102

divide both sides by 3

x = 102/3

x = 34

So,

3 : 17 = 6 : 34

6 : 34 = 9 : x

6/34 = 9/x

cross product

6 × x = 9 × 34

6x = 306

divide both sides by 6

x = 306/6

x = 51

Therefore, ratio is the comparison between two or more numbers.

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The area of the shaded region of the circle with radius of 5 cm and sector with an angle of 60° is 76.3 cm²

The area of a part of a circle can be found by finding the difference between the area of the circle and the area of the unshaded part of the circle.

The triangle formed by the two radii of length 5 cm with an included angle of 60°, and the chord at the boundary of the shaded region is an isosceles triangle which with the vertex angle of 60°, indicates that the triangle is an equilateral triangle.

The formula for the area, A, of an equilateral triangle of side length s is; A = ((√3)/4) × s²

The side length of the equilateral triangle formed by the radii is; s = 5 cm

Therefore;

Area of the equilateral triangle in the question is; [tex]A_{\Delta}[/tex] = ((√3)/4) × 5²

Area of the minor sector formed by the two radii, [tex]A_{sector}[/tex] = (60°/360°) × π·r²

[tex]A_{sector}[/tex] = π×5²/6

The area of the shaded region = Area of the circle - [tex]A_{sector}[/tex] -  [tex]A_{\Delta}[/tex]

Therefore;

Area of the shaded region = π×5² - π×5²/6 - ((√3)/4) × 5² ≈ 76.3

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Answer:

$4.40

Step-by-step explanation:

To find the cost of each coffee in dollars, you can use the inequality:

2.39 + 4c < 20

This inequality states that the total cost of the cookie and the four coffees is less than $20.

To solve for c, the cost of each coffee in dollars, you can start by combining like terms on the left-hand side of the inequality:

2.39 + 4c = 20 - 2.39

4c = 17.61

Then, divide both sides of the inequality by 4 to solve for c:

c = 17.61 / 4

c = $4.40

So, the cost of each coffee in dollars is $4.40.

Answer:

The percent error of the measurement is 6.7%

Step-by-step explanation:

The percent error of a measurement is a measure of how accurate the measurement is compared to the actual value. It is calculated using the following formula:

percent error = (measured value - actual value) / actual value * 100%

In this case, the measured value is 1.4 inches and the actual value is 1.5 inches. Plugging these values into the formula, we get:

percent error = (1.4 - 1.5) / 1.5 * 100% = -0.1 / 1.5 * 100% = -6.67%

This means that the measurement was off by 6.7% compared to the actual value.

It's important to note that a negative percent error indicates that the measured value is less than the actual value, while a positive percent error indicates that the measured value is greater than the actual value. In this case, the measured value of 1.4 inches is less than the actual value of 1.5 inches, so the percent error comes out to be negative.

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The overall average for the entire class was 85.08. The solution is obtained using the concept of arithmetic mean.

What is arithmetic mean?

A number is derived by dividing the total number of values in a set by the total number of elements in the set, and this is what is meant by the term "arithmetic mean."

We are given that the average score of the 10 girls was 88.

This means that the total score of girls was 10*88 = 880

Also, the average score of the 14 boys was 83.

This means that the total score of boys was 14*83 = 1162

The total number of students in the class = 10+14 = 24

The combined score of boys and girls = 880 + 1162 = 2042

Thus, the overall average for the entire class was

2042/24 = 85.08

Hence, the overall average for the entire class was 85.08.

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A amount 1 ounce shot of whiskey contains 0.4 ounces of alcohol, a 5 ounce glass of wine has 0.75 ounces, and a 12 ounce beer has 1.5 ounces.

1 ounce shot of 80 proof whiskey:

0.4 ounces of alcohol = 40% alcohol * 1 ounce

= 0.4 ounces

5 ounce glass of wine:

0.75 ounces of alcohol = 12% alcohol * 5 ounces

= 0.6 ounces

12 ounce beer:

1.5 ounces of alcohol = 5% alcohol * 12 ounces

= 0.6 ounces

A 1 ounce shot of 80 proof whiskey contains 0.4 ounces of alcohol, which is 40% of the total volume. A 5 ounce glass of wine has 0.75 ounces of alcohol, which is 12% of the total volume. A 12 ounce beer has 1.5 ounces of alcohol, which is 5% of the total volume. Each of these drinks contains different amounts of alcohol, so it is important to know the strength of each drink in order to know how much alcohol is being consumed.

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The 1 ounce shot of 80 proof whiskey, a 5 ounce glass of wine, and a 12 ounce beer are same amount of alcohol  .

There are several types of liquor such as beer, wine, whiskey.

They have things in common such as  having natural products such as fruits, grains, or others. There is a determining factor that differentiates them is the percentage of alcohol present in it .

Drinks such as Whiskey have 40% alcohol. While others like beer have between 4% to 5% alcohol.

the percent of alcohol in wine is between 9 to 12% .

Therefore, In different amounts of different alcoholic beverages, we can have the same amount of alcohol.

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The possible solutions for the stones Emily may buy as required in the task content are; ( 4, 0) , ( 0, 5 ) and ( 7.5, 0).

It follows from the task content that the possible solutions to Emily's turquoise stone purchased situation be determined.

Let the number of $4 stones Emily can buy be; x

Let the number of $6 stones Emily can buy be; y.

Therefore, the inequalities which correctly represents the situation are;

x + y ≥ 4

4x + 6y ≤ 30.

By solving the given inequalities graphically; it follows that the solutions sets area enclosed by the point coordinates; ( 0, 4 ), ( 0, 5 ), ( 4, 0 ) and ( 7.5, 0 ).

On this note, the possible solutions for the number of $4 and $6 stones she can buy are; ( 4, 0) , ( 0, 5 ) and ( 7.5, 0).

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The probability that Sumit actually saw a shark is 1/36.

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

According to the question, we can say

Let us assume that Sumit has actually seen 1 creature.

The probability that it is a Shark and Sumit reports it correctly = (1/8)(1/6) = (1/48)

The probability that it is not a Shark and Sumit claims that it is = (7/8)(5/6) = (35/48)

Therefore,

The probability that Sumit actually sees a Shark, given that he claimed to have seen one = [(1/8)(1/6)] / [(1/8)(1/6) + (7/8)(5/6)] = 1/36

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Answer:

Step-by-step explanation:

No, the parenthesis is not important. With or without them, they will equal the same thing, which is 3.