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The explicit formula for the geometric sequence is,

⇒ tn = 7 (2ⁿ - 1)

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The geometric sequence is,

⇒ 7,14,28,56,112,…

Here, First term = 7

And, Common ratio = 14 / 7 = 2

We know that;

The explicit formula for the geometric sequence is,

⇒ tn = t₁ (rⁿ - 1) / (r - 1)

Substitute all the values we get;

The explicit formula for the geometric sequence is,

⇒ tn = 7 (2ⁿ - 1) / (2 - 1)

⇒ tn = 7 (2ⁿ - 1)

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Answer: 172.0 degrees

Step-by-step explanation:

In 180 degrees, there are [tex]\pi[/tex] radians. That means each radian is equal to:

[tex]\frac{180}{\pi }[/tex]

= 57.3248408

Then we simply multiply that by 3 to get:

3 * 57.3248408

= 171.974522

Rounded to the nearest tenth is 172.0

Answer:

172

Step-by-step explanation

180 degrees is equal to one pi.

That means each radian is equal to:= 57.3248408

Then multiply that number by 3

Written out is: 3 x 57.3248408 = 171.97452

When rounded to the nearest tenth is 172.0

Assuming a thickness of 1 millimeter for the cardboard, the amount of cardboard utilized to build the candy box is roughly 240 cubic centimeters.

Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.

Here,

Part A: To find the height of the base, we need to use the formula for the volume of a triangular prism:

V = Bh/2,

where B is the area of the base and h is the height.

We can assume the base of the triangular prism is an equilateral triangle with side length s. The area of an equilateral triangle can be found using the formula:

B = (s² * √(3))/4

We can use this formula to find the side length of the triangle:

s = √((4B)/(√(3)))

Substituting the known values, we have:

1200 = (s² * √(3))/2 * h

solving for h:

h = 1200 * 2 / (s² * √(3))

Substituting the value for s:

h = 1200 * 2 / ((√((4B)/(√(3)))² * √(3))

h = 1200 * 2 / (((4B)/(√(3))) * √(3))

h = 1200 * 2 / (4B)

h = 300 / B

We can find the value of B using the formula:

B = (s² * √(3))/4

Substituting the value for s:

B = (√((4B)/(√(3)))² * √(3))/4

B = (4B)/(3 * √(3))

B = 4B / (√(9))

B = 4B / 3

Solving for B:

B = 300 / h

So, the height of the base is approximately 30 cm.

Part B: To find the amount of cardboard used to make the candy box, we need to find the surface area of the triangular prism and multiply it by the thickness of the cardboard.

The surface area of a triangular prism can be found using the formula:

A = B + Bs + Bh

Where B is the area of the base, Bs is the area of the side of the triangular prism and Bh is the area of the top and bottom of the triangular prism.

We know that B = (s² * √(3))/4 and Bh = B, so

A = B + Bs + Bh = B + 2Bh = 2B + 2Bs

The surface area of the triangular prism is approximately 240 square centimeters.

Assuming the cardboard has a thickness of 1 millimeter, the amount of cardboard used to make the candy box is approximately 240 cubic centimeters.

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Answer:1950 US tons

Step-by-step explanation:

Using Amber's method of plotting, a graph representing the two seperate equations is attached.

3x^2: Is a curve and color green

- 4x : is a straight line graph, with red color

A graph is a pictorial representation of a an expression. It is used in several disciplines to represent and interpret data easily. Since graphs are pictures it show the relationship between functions or data presented with less difficulty.

here, we have,

The first graph is a curve because the expression involved is a polynomial this is to say the variable is raised to a power that is not 1 or zero.

The second graph is not a curve because the variable x has a power of 1

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based on the sample data, we have evidence to mean support Nicole's belief that the true mean systolic blood pressure among elderly females is higher than 115 mmHg.

The mean of a dataset, sometimes referred to as the arithmetic mean, is the sum of all results multiplied by the number of values . This is the most popular way to measure central tendency and is sometimes refereed to as the "mean."

The sample mean systolic blood pressure of 124 mmHg is higher than the reported mean of 115 mmHg on the doctor's website. Additionally, the sample standard deviation of 22 mmHg indicates that there is some variability in the systolic blood pressure values among the sample of 18 elderly females.

Using a t-distribution table with 17 degrees of freedom (since we have a sample size of 18), we can calculate that the critical value for a one-tailed test at a significance level of 0.05 is 1.740.

t-statistic using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (124 - 115) / (22 / sqrt(18)) = 2.35

Since the calculated t-value of 2.35 is greater than the critical value of 1.740, we can reject the null hypothesis and conclude that the sample mean systolic blood pressure of 124 mmHg is significantly different from the reported mean of 115 mmHg.

Therefore, based on the sample data, we have evidence to support Nicole's belief that the true mean systolic blood pressure among elderly females is higher than 115 mmHg.

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The coefficient of x^2 in the expansion of (x + 2)^3 is 6

From the question, we have the following parameters that can be used in our computation:

(x + 2)^3

Next, we expand the expression

So, we have the following representation

(x + 2)^3 = x^3 + 3x^2 * 2 + 3x * 2^2 + 2^3

Evaluate the expression

(x + 2)^3 = x^3 + 6x^2 + 12x + 8

The coefficient of x^2 in the expression  x^3 + 6x^2 + 12x + 8 is 6

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The linear function for the total amount added to the account each month is given as follows:

T(n) = 650 + 740n.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Then the parameters for this problem are given as follows:

Hence the function is given as follows:

T(n) = 650 + 740n.

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Michael has made 3.21 batches of granola.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Michael has a granola recipe that requires 14 pounds of oats to make one batch of granola.

If Michael uses 45 pounds of oats while making granola,

then number of batches he made,

= 45 /14

= 3.21

Hence, he made 3.21 batches.

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The procedure to determine the function's behavior is explained in this problem.

The problem is incomplete, hence the general procedure to obtain the function's behavior was presented.

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The quotient of a number and -5, decreased by 9, is 2.”So, the number is -55.

The dividend is the quantity being divided (15 in this case), and the divisor is the quantity being divided (3 in this case). Quotient is what remains after division. A quotient is the result of dividing one number by another. It is the number of times one number is contained within the other, or the answer to a division problem.

It is known as the quotient to divide two numbers. Six times two is the ratio, which equals three. The Latin word for ratio, "how many times," is quotient. This is very logical: by dividing two numbers, you are calculating "how many times" the second number enters the first.

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The area under the curve between the mean and a z-score

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

1. z = (x[tex]- \mu) /\sigma[/tex]

z= (52350 - 46292)/ 4320

z = 1.40

P(X> 52350 )= P( z> 1.40) = P(z< -1.40)

P(Z>1.40) = 0.0808, which is 8.08%

2. Now, z = (x[tex]- \mu) /\sigma[/tex]

z= (45000- 46292)/ 4320

z = -0.30

and, z = (x[tex]- \mu) /\sigma[/tex]

z= (52350 - 46292)/ 4320

z = 1.40

Then, you must find the area between Z = -0.30 and Z = 1.40

So, P(Z<1.40) - P(Z < - 0.30)

= P(Z > - 1.40) - P(Z < - 0.30)

= 1 - P(Z< -1.40) - P( Z < -0.30)

The area under the curve to the left= 1 - 0.0808 - 0.3821 = 0.5371

3.  z = (x[tex]- \mu) /\sigma[/tex]

z= (38500- 46292)/ 4320

z = -1.8

Thus, the area under the curve to the right of Z = - 1.80 and to the left of Z = - 0.3

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Answer:

Step-by-step explanation:

70000 + t600

Answer:

202.5 square yards.

Step-by-step explanation:

We know the whole square is 15 * 15 = 225

Now, we need to find the area of the triangles and subtract that.

We can predict that the sides are 3 and 7.5. Doing that we get the area of 11.25 for each.

225- (11.25*2)=202.5

A professor asserts that more than 77% of all scientists believe in evolution, and the p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).

A type of statistic hypothesis known as a hypothesis claims that a certain group of data has no statistical power. The viability of hypotheses is investigated using sample data. Sometimes refer to as "zero," and represented as H0. The premise that researchers make is that there is a link between the variables. The null hypothesis, on the contrary hand, asserts that such a link does not exist. Despite its inability to seem relevant, the null hypothesis is a critical component of research.

given

You must understand the distribution of your test statistic on the supposition that the null hypothesis is correct in order to calculate the p-value.

Left-tailed test: cdf as the p-value (x).

Test with a right-tail: p-value = 1 - cdf (x).

p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).

A professor asserts that more than 77% of all scientists believe in evolution, and the p-value for the two-tailed test is 2 mincdf(x), 1 - cdf(x).

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Answer:

Step-by-step explanation:

The value of the investment can be calculated using the compound interest formula:

A = P * (1 + (r/n))^(nt)

Where:

A = final amount

P = principal amount (5070)

r = annual interest rate (0.05)

n = number of times the interest is compounded in a year (4)

t = number of years (15)

So,

A = 5070 * (1 + (0.05/4))^(4*15)

A = 5070 * (1.0125)^60

A = 5070 * 2.693260689

A = 13,652.14

The value of the investment after 15 years compounded quarterly at 5% per year is $13,652.14, rounded to the nearest cent.

The correct options are A and B. This indicates that the two sides of the triangle are equal and one angle is also equal.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

For the triangle ABC to be congruent to A'B'C' the best condition would be that the two sides of the triangle must be congruent and one angle should be congruent.

The correct options are A and B in which the two sides AB≅A'B', BC≅B'C' and the angle ∠A ≅ ∠A'. The second statement is also true that two sides AB≅A'B', BC≅B'C' and the angle ∠B ≅ ∠B' by side angle side property.

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Answer: 90

Step-by-step explanation: Regular Polygons have all their angles equal. Since there are 4 sides the total sum of the angles are 360. Divide it by four and you get your answer of 90.

Answer:

90 degrees

Step-by-step explanation:

A regular polygon has sides with the same length.

Because this is a 4-sided regular polygon, this shape would be a square.

Since all angles inside of a polygon must equal 360, we can divide this number by the amount of angles in this polygon.

360 degrees/4 angles = 90 degrees/angle

Based on the picture above:

From the answer above, the way to determine the type of angle is to measure the angle.

if the angle is 90° then it is a right angle.

If the angle is 0-90° then it's an acute angle

If the angle is above 90° and below 180° then it is an obtuse angle

If the angle is 180° then it is called a straight angle.

The following is a more complete explanation:

1. Right Angles

Right angles have a measure of 90º and are perpendicular in shape. This angle is usually denoted by ∟. Examples of surrounding objects that have right angles include books, tables, cupboards, clock hands that show 3 o'clock, and so on.

2. Straight Angle

A straight angle has an angle of 180º. As the name implies, this angle is straight and flat. Examples of objects that have straight angles include a ruler and clock hands that show 6 o'clock.

3. Acute Angles

Acute angles have angles greater than 0º and less than 90º. As the name implies, this angle is pointed. Objects that have acute angles such as pencil tips, pizza slices, iron tips, and clock hands that show 1 and 2 o'clock.

4. Obtuse Angle

Contrary to an acute angle, an obtuse angle has an angle greater than 90º but less than 180º. As the name suggests, objects that have this angle are obtuse, such as laptops wide open, beach chairs, camping tents, and clock hands that show 4 and 5 o'clock.

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The probability that a randomly chosen bike in the parade was a recumbent bicycle will be 5/46.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the chance is given as,

P = (Favorable event) / (Total event)

A city held a bike parade. 10 bikers rode recumbent bicycles, and 82 bikers rode other types of bicycles.

The total number of bikers is given as,

Total bikers = 82 + 10

Total bikers = 92

Then the probability is given as,

P = 10 / 92

P = 5 / 46

The probability that a randomly chosen bike in the parade was a recumbent bicycle will be 5/46.

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The 270° counterclockwise rotation about the origin is a transformation that turns each point (x, y) in the original triangle to (-y, x) in the new triangle.

A triangle is a three-sided polygon and is one of the basic shapes in geometry. It is a closed figure composed of three straight line segments, connected at their endpoints. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. Triangles are classified by their angles and their sides. Triangles can be right, acute, obtuse, isosceles, equilateral, and scalene. Right triangles have one angle that is equal to 90 degrees. Acute triangles have all angles that are less than 90 degrees. Obtuse triangles have one angle that is greater than 90 degrees. Isosceles triangles have two sides that are equal in length.

Triangle LMN' with vertices L'(1, 6), M'(3, 8), and N'(3, 3), Triangle LMN' with vertices L'(6, -6), M'(-8, -8), and N'(-8, -3), Triangle LMN' with vertices L'(-6, 6), M'(-8, 8), and N'(-8, 3)

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Answer: To find out how many meters of ribbon Mrs. Marin needs, we first need to convert the required length of 38 centimeters per costume to meters.

1 meter = 100 centimeters, so we divide 38 by 100:

38 cm / 100 cm/m = 0.38 m

So each costume requires 0.38 meters of ribbon.

To find the total amount of ribbon needed for 50 costumes, we multiply the amount of ribbon per costume by the number of costumes:

0.38 m/costume * 50 costumes = 19 meters

So Mrs. Marin needs 19 meters of blue ribbon for the 50 costumes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1ST AVENUE

grocery

store

bank movie

theater

KING STREET

library

drugstore

laundromat

gym

hotel

PALM STREET

2ND AVENUE

ATM

The unit rate for 56 meters in 32 hours (1.75 m/h) is greater than the unit rate for 40 meters in 25 hours (1.6 m/h).

In mathematics, rate is a concept used to describe the change in one quantity with respect to another. It is usually represented as a fraction or a ratio and can be thought of as a measure of how fast one quantity is changing with respect to another.

For example, the rate of change of position with respect to time is called velocity. The rate of change of velocity with respect to time is called acceleration. Similarly, the rate of change of any function with respect to its independent variable is called the derivative of the function, and it represents the instantaneous rate of change at a given point.

Rate can also be used to describe the relationship between two quantities that are changing at the same time. For example, in economics, the interest rate is the ratio of the amount of interest earned or paid to the amount of money invested or borrowed. In science, the rate of a chemical reaction is the change in the concentration of a reactant or a product over time.

Overall, the concept of rate is a useful and important idea in mathematics and has many applications in science, engineering, economics, and other fields. It provides a means for analyzing and comparing changes in quantities and for understanding the relationships between different quantities.

The unit rate for 56 meters in 32 hours is [tex]\frac{56}{32}[/tex] = 1.75 meters per hour. The unit rate for 40 meters in 25 hours is [tex]\frac{40}{25}[/tex] = 1.6 meters per hour.

So, the unit rate for 56 meters in 32 hours (1.75 m/h) is greater than the unit rate for 40 meters in 25 hours (1.6 m/h).

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0.156 is the  unit rate games per loss.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Plug in the values from the table to the above formula.

Slope is nothing but rate of change.

m=17-12/68-36

m=5/32

m=0.156

Hence, 0.156 is the unit rate games per loss.

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Therefore , the solution of the given problem of unitary method comes out to be  Gross pay of Danial Ducan is $1162.5.

To finish a work using the unitary strategy, multiply the quantity with two after determining the size of a small slice. The unit variable technique, to put it simply, works to isolate a coded object from a specific group or sets of sets. For instance, 40 pens would cost 400 pounds (expression $1.01) = Rs. There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait.

Here,

Given :

Danny Duncan worked 55 hours in 1 week.

earns $15 per hour.

To find the Danny's gross pay:

overtime is at time and half.

So,

=> Gross pay = 55*15 + 55/2 *15

=> Gross pay = 825 + 337.5

=>  Gross pay = 1162.5

Therefore , the solution of the given problem of unitary method comes out to be  Gross pay of Danial Ducan is $1162.5.

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Answer:

1.2

Step-by-step explanation:

To find the diameter, you must multiply the radius by two