John Napier developed logarithms and Henry Briggs helped him to improve on the concept.

True

False

The sequence is an arithmetic sequence.

A rule for each term is t(n) = 7 - 4(n - 1).

Arithmetic sequence is a sequence of numbers where the numbers are arranged in a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence is 7, 3, –1, –5, –9, ....

First term = 7

Second term = 7 + -4 = 3

Third term = 7 + (-4 × 2) = -1

....................

Here each term is getting by adding -4 to the preceding term.

So -4 is the common difference.

nth term of the sequence is t(n) = 7 - 4(n - 1).

Hence the sequence is arithmetic sequence and any term of the sequence is t(n) = 7 - 4(n - 1).

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If so far the George's string is 44 inches long , then his string is not long enough , so he need to make it longer .

To find whether George's string is long enough, we first convert both measurements to same unit of measurement.

that means we convert length of the string in inches to feet by dividing it by 12 ; because  there are 12 inches in a feet  ;

⇒ (44 inches)/(12 inches/feet)  

⇒ 3.67 feet  ;

The George's string is currently 3.67 feet long and he needs a string that is 4 feet long  .

So , his current string is not long enough and he needs to make it longer. He needs to add another 0.33 feet to his string  .

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The given question is incomplete , the complete question i

George needs a string that is 4 feet long. So far his string is 44 inches. Is it long enough or does he need to make it longer ?

The values of x for the given equations are:

1. The value of x = 0

2. The values of x are ±1

3. The values of x are 0 and -7/16

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

To find the values of x in each of the equations, we need to simplify them using algebraic operations:

1. 8x² = 6x² + 5x²

Combining like terms on the right-hand side:

8x² = 11x²

Subtracting 6x² from both sides:

2x² = 0

Dividing both sides by 2:

x² = 0

Taking the square root of both sides:

x = 0

Therefore, the only solution to this equation is x = 0.

2.Similarly, we can calculate values of x for this equation:

-7x² + 6 = x² - 7x²

x² = 1

Taking the square root of both sides:

x = ±1

Therefore, the solutions to this equation are x = 1 and x = -1.

3. 7x² + 9x² = -6x² - 7x

x(16x + 7) = 0

Using the zero product property:

x = 0 or 16x + 7 = 0

Solving for x in the second equation:

16x = -7

Dividing both sides by 16:

x = -7/16

Therefore, the solutions to this equation are x = 0 and x = -7/16.

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By using shipping volume, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift.

To solve this problem, we need to work backwards from the shipping volume and use the given processing rates to determine the required processing volumes for each stage of the process.

First, we can calculate the total number of hours of packing and shipping required to process 168,000 units:

168,000 units ÷ 175 units per person per hour = 960 hours

Next, we can determine the volume of items that need to be packed by Group B in order to ship this total volume. Since Group B processes 65% of the volume, we can set up the following equation:

0.65x = 168,000 units

where x is the total volume of items processed by all packing groups. Solving for x, we get:

x = 168,000 units ÷ 0.65 = 258,461.54 units

So the total volume of items processed by all packing groups is approximately 258,461.54 units. We can now use the given processing rates to determine the required processing volumes for each stage:

Picking: 100% of 258,461.54 units = 258,461.54 units

Packing Group A: 35% of 258,461.54 units = 90,461.54 units

Packing Group B: 65% of 258,461.54 units = 168,000 units

Therefore, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift. The answer is 168,000.

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____The given question is incorrect, the correct question is given below:

Team % of Volume Items processed per person per hour Picking 100% 150 Packing Group A 35% 105 Packing Group B 65% 70 Shipping 100% 175 How many items will be processed by Packing Group B in order to ship a total of 168,000 units for the shift?

46,  

70,  

84,000,  

109,200,  

168,000

We will prove that if we remove the root of a k-th order binomial tree, it results in k binomial trees of smaller orders.

Base case: If k = 1, the binomial tree consists of a single node. Removing the root node leaves an empty tree, which can be considered as a collection of 0 binomial trees of smaller orders.

Induction hypothesis: Assume that the statement is true for a k-th order binomial tree.

Induction step: We need to prove that the statement is true for a (k+1)-th order binomial tree, which is formed by joining two k-th order binomial trees.

Remove the root node of the (k+1)-th order binomial tree. This results in two trees, each of which is a k-th order binomial tree.

By the induction hypothesis, removing the root node of each of the two k-th order binomial trees results in k binomial trees of smaller orders.

Thus, removing the root node of the (k+1)-th order binomial tree results in a total of 2k binomial trees of smaller orders, which completes the proof.

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Answer: AE

Step-by-step explanation:

if you look at the picture you can tell that Ae is a ray because rates tend to have 2 points and 2 sides one going on forever. that's why there's an arrow near "a"

The measurement closest to the number of miles between the two towns is 227.5 miles.

A method for finding the answer to linear equations in two variables is cross-multiplication. It turns out to be the quickest way to resolve two linear equations. To cross multiply two fractions, multiply the first fraction's numerator by the second's denominator and the second fraction's numerator by the first fraction's denominator.

Given that, distance between Dallas and Houston is about 364 kilometers.

The measurement of:

8 km = 5 miles

364 km = x miles

Using the method of cross multiplication, we have:

x = 364 (5) / 8

x = 227.5 miles

Hence, the measurement closest to the number of miles between the two towns is 227.5 miles.

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Answer: To find the father's and son's ages, we can set up two simultaneous equations:

Let's say the son's age is "x"

Then, the father's age would be x + 25

And the sum of their ages is x + (x + 25) = 53

So, 2x + 25 = 53

Solving for x, we get:

2x = 28

x = 14

Therefore, the son is 14 years old, and the father is 14 + 25 = 39 years old.

To use the elimination method, we can add the two equations:

x + (x + 25) = 53

2x + 25 = 53

Simplifying, we get:

2x = 28

x = 14

And the father's age would be x + 25 = 14 + 25 = 39 years old.

Step-by-step explanation:

Answer:

Step-by-step explanation: Sure! Here's a step-by-step solution to find the amount of red icing Ashley needs for one cake:

Divide the total amount of red icing by the number of cakes: 10 1/2 ÷ 3 1/2 = 3.

Simplify the result from step 1: 3 = 3 ounces of red icing per cake.

So Ashley needs 3 ounces of red icing to write a message on one cake.

The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%

The weight of two granite specimen = 22 pounds

The weight of the crate = 20 pounds

The weight of shipping crate = 8 pounds

The total weight of the whole shipment = 22+20+8 = 50 pounds.

Therefore the percentage of shipping crate as compared to the total weight;

= 8/50 × 100/1

= 800/50

= 16%

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Answer:

$10 / hour

Step-by-step explanation:

$40 ÷ 4 hours = 10/hour

Answer:  Part A: Zach is paid $10 per hour

Part B: The equation would be p = 10h

Step-by-step explanation: Part A :Zach worked 4 hours and was paid $40. The question asks How much is Zach's paid per hour? Per hour means to find the unit rate and in order to find the unit rate in this case, you have to divide the $40 by the 4 to get how much Zach got per hour.

1.$40/4=10

Therefore, Zach is paid $10 per hour.

Part B: In the question it says Which equation shows the relationship between , h, the number of hours worked. The number of hours Zach worked was 4 hours. So, h = 4. Then for the next part of the problem, and p the amount paid.  We know that Zach got paid $40. So p = 40. Now that we know our numbers, we could put the equation together.

1. P = 10h is the same as $40 = 10 x 4.

There's the answer, Hope it helps! Have a nice day!

The probability of committing type 1 error best describes notion of significance level of hypothesis test.

What is probability?

Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.

Complete Question:

Which one of the following best describes the notion of the significance level of a hypothesis test?

i) the probability of committing a type 1 error

ii) the probability of committing a type 2 error

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The width of the floor if the length is (x - 13) units is (x+13) units.

The area of Rectangle is length times of width.

Given that area of the floor is (x²-169) sq units.

We have to find the width of the floor when  length is (x - 13) units.

Area=Length×Width

x²-169=(x-13)width

We know that (a²-b²)=(a+b)(a-b)

(x-13)(x+13)=x-13width

Divide both sides by (x-13)

x+13=width

Hence, the width of the floor if the length is (x - 13) units is (x+13) units.

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There are 10/4 ways ( [tex]\frac{10}{4}[/tex] ) to accomplish the given task by wearing the ties for a week according to the permutations and combinations.

Given if you wear tie for a week, where one need t wear 4 of his ties from the 10 of total. The number of ways to wear the ties will be equal to the value. So there are many ways to wear a tie of different types and also to remove the tie there are different ways. Now we will see the ways to wear a tie accordingly.

According to the permutations and combination rules the formula will be:

Number of ways: (Number of ties want to wear) / (Number of Total ties)

Therefore total number of ways to wear ties = 10/4

Number of ways this can be accomplished is 10/4

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The probability of the flight being overbooked is 0.38742 or 38.7%.

To calculate the probability of the flight being overbooked, we need to use a probability formula. In this case, we can use the binomial probability formula. The formula is as follows:

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

Where:

P(x) is the probability of x number of events occurring.

n is the total number of trials.

p is the probability of success.

q is the probability of failure.

nCx is the number of ways to choose x items from a set of n items.

Let's say a plane has 8 seats. The airline sells 10 tickets for this flight. The probability of all ten passengers showing up for the flight is quite low. Based on past experience, the airline knows that only 90% of ticketed passengers usually show up for a flight. This percentage is also known as the "show-up rate."

In our case:

n = 10 (total number of passengers)

p = 0.9 (probability of a passenger showing up)

q = 0.1 (probability of a passenger not showing up)

We want to find the probability of having more than 8 passengers show up, which would mean the flight is overbooked. To do that, we need to calculate the probability of having 9 or 10 passengers show up. We can use the formula to calculate this:

P(9 or 10) = P(9) + P(10)

P(9 or 10) = ¹⁰C₉ x 0.9⁹ x 0.1¹ + ¹⁰C₁₀ x 0.9¹⁰ x 0.1⁰

P(9 or 10) = 0.38742 or 38.7%

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Complete Question:

Airlines usually overbook for a flight (sell more tickets than the numbers of available seats). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.

A plane has 8 seats. If the airline sells 10 tickets for this flight, what is the probability that the flight will be overbooked?

By expression, x - y = x' - y' , Distance of 3rd and 4th obstacle is equal to distance of 7th and 9th obstacle.

Distance is a numerical measurement of how far apart objects or points are, it is the length along a line or line segment between two points on the line or line segment.

Given,

The distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine.

Distance of 7th obstacle = x

Let,

Distance of 9th obstacle = y

Distance of 3rd obstacle = x'

Distance of 4th obstacle = y'

Distance between obstacle 3 and 7 = x - x'

Distance between obstacle 4 and 9 = y - y'

Distance between obstacle three and obstacle four = x' - y'

Distance between obstacle seven and obstacle nine.= x - y

According to the question

x-x' = y-y'

⇒ x - y = x' - y'

Hence, Distance between third and fourth obstacle is same as distance between 7th and 9th obstacle.

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The value of the functions at 9m is

Generally, In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range). The values in the range are determined by applying the function to the values in the domain.

Functions can take many forms and be expressed in different ways, including:

Linear functions: a function that produces a straight line when graphed. It has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Quadratic functions: a function that produces a parabola when graphed. It has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Therefore, this function

- f(x) = 4x

g(x) = 9x¹/2

for

F(x)=4x

F(9)=4*9

f(9)=36

for

g(x) = 9x¹/2

g(9)=9√9

=27

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The toy rocket will hit the ground after approximately 3.86 seconds.

The rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:

0 = -4.97t^2 + 38.5t + 5.6

-5.6 = -4.97t^2 + 38.5t

4.97t^2 - 38.5t - 5.6 = 0

This is a quadratic equation and can be solved using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 4.97, b = -38.5, and c = -5.6.

Plugging in these values, we get:

t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)

t = (38.5 ± √(1466.25 + 113.92)) / 9.94

t = (38.5 ± √1580.17) / 9.94

The square root of 1580.17 is 39.67, so:

t = (38.5 ± 39.67) / 9.94

t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94

The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.

The toy rocket will hit the ground after approximately 3.86 seconds.

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The values of x for which f(x) = g(x) are -1 and 4

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

f(x) = -2x + 4

g(x) = x^2 - 5x

Using the above as a guide, we have the following:

Using the above as a guide, we have the following:

x = -1 and x = 4

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The transformation represents a horizontal of 2 units to the right and a vertical of 5 units up

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the initial coordinates of the point be represented as P

Now , the coordinates of P = P ( x , y )

And , the transformed point be represented as Q

Now , the coordinates of Q = Q ( x - 2 , y + 5 )

when x → ( x - 2 )

The graph is moved 2 units to the right

And , when y → ( y + 5 )

The graph is moved 5 units up

Substituting the values in the equation , we get

The transformation is 2 units to the right and 5 units up

Hence , the transformation is 2 units to the right and 5 units up

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Answer:

170 feet per second

Step-by-step explanation:

To answer the question you need to find the unit rate. To find the unit rate divide the denominator with the numerator in a way that the denominator becomes 1.

5,100/30 = 170

The skydiver falls at a rate of 170 feet per second before opening the parachute.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

It takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute.

Hence, Height for this is,

⇒ 5100 / 30

⇒ 170 feet per second

Thus, the skydiver falls at a rate of 170 feet per second before opening the parachute.

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Answer:

75

Step-by-step explanation:

trust me bro

Answer:

Step-by-step explanation:

The answer is 4x^2y+8x^3+y^2-2xy

Answer:

A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure,divide it into simple, nonoverlapping figures. Find the area of each simplerfigure, and then add the areas together to find the total area of the compositefigure

Step-by-step explanation:bc of the way u gave it im showing it to u

Answer:

B.

The equation you can use to find the area of a sphere when given radius is:

V = 4/3πr 3

Fitting 5 into the equation:

V = 4/3π5 3

V = 523.598776

Therefore, B is the correct answer.

The expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

We can write the Pythagoras theorem as - The sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.

Mathematically -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right triangle ABC

We an write the expression to measure {x} as -

{x - 10} + {2x +40} + 90 = 180

Therefore, the expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

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The equation is 16 + 2x = 3(x - 4) and the solution is x = 28

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

Sixteen increased by twice a number is 3 times the number decreased by 4​

Let the variable be x

So, we have

16 + 2x = 3(x - 4)

Open the brackets

16 + 2x = 3x - 12

Evaluat the like terms

x = 28

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Answer:

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)

Step-by-step explanation:

To simplify the expression, we need to simplify the numerator and denominator separately, and then simplify the entire expression.

Starting with the numerator:

4x^2 + 12x - 16

For the denominator:

The first fraction: 2x + 10 can be simplified as follows: 2x + 10 = (2)(x) + (2)(5) = 2x + 10

The second fraction: 6x + 24 over x^2 + 9x + 20

We can simplify the denominator by using partial fraction decomposition. To do that, we need to write the denominator as a sum of simpler fractions, each with a numerator that is a constant. In other words, we write:

6x + 24 / (x^2 + 9x + 20) = (A x + B) / (x^2 + 9x + 20) + (C x + D) / (x^2 + 9x + 20)

Multiplying both sides by the denominator, we get:

6x + 24 = (A x + B)(x^2 + 9x + 20) + (C x + D)(x^2 + 9x + 20)

Expanding the right-hand side, we obtain:

6x + 24 = Ax^3 + (A 9 + B) x^2 + (A 20 + B 9 + C) x + (B 20 + D)

Comparing the coefficients of the polynomials on both sides, we get the following system of linear equations:

A = 0

B = 6

C = 0

D = -24

Therefore, the partial fraction decomposition of the denominator is:

6x + 24 / (x^2 + 9x + 20) = (6x + 24) / (x^2 + 9x + 20)

Putting it all together, we have:

4x^2 + 12x - 16 / (2x + 10) / (6x + 24) / (x^2 + 9x + 20) = (4x^2 + 12x - 16) / (2x)(6x + 24) / (x^2 + 9x + 20) = 2x - 4 / (x^2 + 9x + 20)

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)