Zack's biology lab group is studying how quickly bacteria grow when exposed to sunlight. At the beginning of the experiment, Zack looked at the sample under a microscope and counted 5 bacteria. After the sample was exposed to sunlight for one hour, Zack looked again and counted 35 bacteria. Write an exponential equation in the form y=a(b)x that can model the number of bacteria, y, after x hours in sunlight. Use whole numbers, decimals, or simplified fractions for the values of a and b.

When each value of the data in one of the sample linked to the data value in another given sample , then samples are known as paired samples.

Therefore, paired samples is representing the linking of data values of one sample to the data values of other sample.

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Answer:

Step-by-step explanation:

Answer: No Solution

1. Substitute the given value of x into the equation:

-2(y+2)+2y=4

2. Solve the equation for y

No Solution :-)

GIVE BRANLIEST

Infinitely many solutions

∞

x - y = 2

2x - 2y = 4

x = y + 2

2•(y +2) - 2y = 4

0 = 0 =>  Infinitely many solutions

Step-by-step explanation:

a. To create a quadratic equation that models the arrow's height, we need to find the coefficients of the equation that best fit the data. One common method is to use a least squares regression to fit the data to a quadratic equation in the form y = ax^2 + bx + c. There are several ways to perform this regression, but one common method is to use a spreadsheet program or a graphing calculator with regression capabilities.

b. Based on the quadratic equation that models the arrow's height, we can predict the height of the arrow at any distance from the archer. If Coach Deline is 500 feet away from the archer, we can plug 500 into the equation as x and find the corresponding y value. If the y value is greater than 0, then the arrow is still in the air and has not hit the ground. If the y value is equal to 0, then the arrow has hit the ground. If the y value is less than 0, then the arrow has hit the ground and passed it. Based on this information, we can determine if the arrow will hit Coach Deline or not.

Answer:

Step-by-step explanation:

assuming its a right triangle 30 deg with sides being 9 3 10 and angles being 30 60 90

The sum of an infinite geometric series is given by a+ar+ar^2  where a is the first term and r is the common ratio.

The sum of the series  can be represented by :

a / ( 1 - r)  = 12

a = 12 ( 1- r )    (1)

So....note that the sum of the  terms  with odd powers of r  can be represented by :

ar  + ar^3  + ar^5 + ar^7 +  ..... + ar^(2n - 1)  =  5   (2)

And note that the sum of the  terms  with even powers of r  can be represented by :

a  +  ar^2  + ar^4 + ar^6 + ar^8 +  ..... + ar^(2n)  =  7   (3)

Multiply (2)  by r on both sides

ar^2  + ar^4  + ar^6 + ar^8 +  ..... + ar^(2n )  =  5r     (4)

Subtract   (4)  from (3)

a  = 7 - 5r    (5)

Sub (5)  into (1)

7 - 5r  = 12(1 - r)

7 - 5r  =  12 - 12r

7r = 5     →   r  =  5/7

Check

a = 7 - 5(5/7)  =  24/7

a / ( 1 - r)  =

(24/7) / ( 1- 5/7)  =

(24/7) / ( 2/7)  =

24 / 2   =

12

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The dilation of the triangle JKL is with a scale factor of d = 1/2

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be represented as ΔJKL

Now , the coordinates of J = J ( 8 , 12 )

The coordinates of K = K ( 4 , 8 )

The coordinates of L = L ( 12 , 6 )

Now , let the dilated triangle be represented as ΔJ'K'L'

Now , the coordinates of J' = J' ( 4 , 6 )

The coordinates of K' = K' ( 2 , 4 )

The coordinates of L' = L' ( 6 , 3 )

So , the scale factor is given by d = y₂/y₁

Scale factor d = 1/2

Hence , the scale factor of the dilation is 1/2

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Answer:

The expression 4 - 2y - 8y + 7.5 can be simplified as follows:

4 - 2y - 8y + 7.5

= 4 - (2y + 8y) + 7.5

= 4 - 10y + 7.5

= 4 + 7.5 - 10y

= 11.5 - 10y

So, the simplified answer is 11.5 - 10y.

Answer:  -10y+11.5

Step-by-step explanation:

The length of the other side of the garden is, 5 m.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The length of one side of the garden is 3m.

And, The area of the garden Is 15 m².

Now, We know that;

Area of rectangle = Length × Width

Substitute all the values, we get;

⇒ 15 = 3 × x

⇒ x = 15 / 3

⇒ x = 5 m

Thus, The length of the other side of the garden is, 5 m.

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Answer:

A. The perimeter can also be represented by the expression 8x−2 because 4(4x−6) can be simplified to 8x−2.

a. The number of passengers for each cruise line in thousands:

4,133,000 passengers ÷ 1,000 = 4,133 passengers

2,369,000 passengers ÷ 1,000 = 2,369 passengers

1,295,000 passengers ÷ 1,000 = 1,295 passengers

928,000 passengers ÷ 1,000 = 928 passengers

679,000 passengers ÷ 1,000 = 679 passengers

So, the answer is 4,133; 2,369; 1,295; 928; 679.

b. The mean number of passengers can be found by adding the number of passengers for each cruise line and then dividing the total by the number of cruise lines, which is 5.

(4,133 + 2,369 + 1,295 + 928 + 679) ÷ 5 = 10,514 ÷ 5 = 2,102.8 passengers

So, the mean number of passengers is 2,102.8 passengers.

c. The range is the difference between the highest and lowest number of passengers, which is:

4,133 - 679 = 3,454 passengers

So, the range is 3,454 passengers.

d. The standard deviation can be calculated using the formula for the standard deviation of a sample. However, this calculation is quite complex and requires a significant amount of mathematical knowledge and computational resources. Without access to those resources, the standard deviation cannot be calculated

The standard deviation is a measure of the amount of variation or dispersion from the mean. It shows how spread out the values in a set of data are. To calculate the standard deviation, the difference of each value from the mean is squared and then divided by the number of items in the set. The standard deviation provides a way to quantify the degree of variation of the values around the mean. It is a useful tool for understanding how much each value in a set deviates from the average.

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The area of this house in square meters is 152.24.

To convert square feet to square meters, you can use the conversion factor of 1 square foot = 0.092903 square meters.

A house is advertised as having 1640 square feet under the roof.

So, the area of the house in square meters is:

1640 square feet * 0.092903 square meters/square foot = 152.24 square meters.

Unit Conversion: It is defined as the changing from one quantity unit to another quantity unit followed by the method of division, and multiplication by a conversion factor.

Thus, the area of this house in square meters is 152.24 if the house is advertised as having 1640 square feet under the roof.

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There are 4.6×10⁵ nanometer present in "4.6×10⁻⁴ meter " .

The Unit nanometer (nm) is a very small unit of length measurement, used to measure the size of particles, proteins, and other small objects.

One meter is equivalent to 10⁹ nanometers, so converting from meters to nanometers is done by multiplying by 10⁹ .

To convert 4.6 × 10⁻⁴ meters to nanometers, we simply need to multiply the value by 10⁹ :

⇒ (4.6 × 10⁻⁴ meters)×(10⁹ nanometers/meter)

⇒ 46,000 nanometers = 4.6×10⁵ nanometers  .

Therefore, 4.6×10⁻⁴ meter is equivalent to 4.6×10⁵ nanometers .

The given question is incomplete , the complete question is

How many "nm" are there in 4.6×10⁻⁴ m ?

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the probability that there is at least one person who wins no games.

P( A1 ∪ A2 U A3 ) = 16/81 + 16/81 + 16/81 - 1/81 - 1/81 - 1/81 - 0 = 5/9

Number of players = 3

number of times game is repeated = 4

P( any person wins a game ) = 1/3

P ( any person does not win a game ) = 1 - 1/3 = 2/3

P ( any person wins no game in 4 attempts ) = ( 2/3 )^4 = 16/81

Note : each player has equal chance of winning

Find the probability that there is at least one person who wins no games

lets represent the probability of each player not wining a game with alphabet A

A1 = player 1 wins no game

A2 = player 2 wins no game

A3 = players 3 wins no game

Applying the inclusion-exclusion formula

P( A1 ∪ A2 U A3 ) = P(A1 ) + P(A2) + P(A3) - P( A1 ∩ A2 ) - P( A2 ∩ A3 ) - P( A1            ∩ A3 )  + P( A1 ∩ A2 ∩ A3 )

where

P( A1 ∩ A2 ) = P( A1 wins all games )

P ( A1 wins all games in 4 attempts ) = ( 1/3 )^4 = 1/81

P( A1 ∩ A2 ∩ A3 ) = P ( no players wins any game in 4 attempts ) = 0

Hence

P( A1 ∪ A2 U A3 ) = 16/81 + 16/81 + 16/81 - 1/81 - 1/81 - 1/81 - 0 = 5/9

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The surface area of the triangular prism is 270 ft².

The surface area of a triangular prism is the sum of the areas of all 5 faces. To find the area of the triangle, you can use the formula:

A = (B × h) ÷ 2, where B is the base and h is the height.

To find surface area of triangular prism we can calculate each area of all faces :

A1 = 13 × 7 = 91 ft²

A2 = 12 × 7 = 84 ft²

A3 = 5 × 7 = 35 ft²

A4 = (12 × 5) ÷ 2 = 30 ft²

A4 = (12 × 5) ÷ 2 = 30 ft²

Surface Area = A1 + A2 + A3 + A4 + A5

Surface Area = 91 + 84 + 35 + 30 + 30

Surface Area = 270 ft²

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The volume of the pyramid is given by the equation V = 400 cm³

The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.

Volume of Pyramid = ( 1/3 )a²H

Given data ,

Let the volume of the pyramid be represented as V

Now , the equation will be

The height of the pyramid H = 12 cm

The base side length of the pyramid a = 10 cm

So , Volume of Pyramid = ( 1/3 )a²H

Substituting the values in the equation , we get

Volume of Pyramid V = ( 1/3 ) x 10² x 12

Volume of Pyramid V = 4 x 100

Volume of Pyramid V = 400 cm³

Hence , the volume of the pyramid is 400 cm³

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Since the cell population doubles at constant intervals, we can use the formula for exponential growth: N = N0 * 2^(t/k), where N0 is the initial population, t is the time elapsed, and k is the doubling time.

Since we are told that the population will double four hours from now, and since we are not given the initial population or the doubling time, we cannot determine the final population when the bacteria will be destroyed.

As the division two hours ago and the division just now, the population quadrupled that is two doubling periods, so each doubling period is about an hour.

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The monthly payment to the nearest cent is $1381.51,

The total of all monthly payments over the 30 years is $497,343.6,

and her total interest for the 30 years is $284,343.6.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given amount borrowed = $213,000

time period = 30 years

interest rate = 6.75% = 0.0675

to find the monthly payment,

so M = [tex]\frac{p(\frac{r}{n} )(1 + \frac{r}{n} )^{nt}}{(1 + \frac{r}{n} )^{nt} - 1}[/tex]

here n = 12 for the monthly payment

M = monthly payment

p = principal

t = time =  30 years

r = trate = 0.0675

p = $213000

so 1 + r/n = 1 + 0.0675/12

1 + r/n =  1.005625

M = [213000(0.005625)(1.00625)³⁶⁰] ÷ [(1.00625)³⁶⁰ - 1]

M = $1381.51

B:  What's the total of all monthly payments over the 30 years,

there will be 360 payments in 30 years,

a total amount of 360 payments = $1381.51*360

a total amount of 360 payments = $497,343.6

C: What's her total interest for the 30 years

total interest in 30 years = $497,343.6 - $213000

total interest in 30 years = $284,343.6.

Hence monthly payment is  $1381.51,

total of all monthly payments is $497,343.6,

and total interest for the 30 years is $284,343.6.

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The required final answer is option a) Incentre

The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".

It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.

The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.

The incentre is always within the triangle and is equidistant from all three sides of the triangle, making

it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.

Thus, required answer is "Incentre".

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Time taken to have both planes at same altitude = 1.2 seconds.

Relative speed can be defined as the speed of a moving body with respect to another. When two bodies move in the same direction, their relative speed is computed by their difference. But when two bodies are moving in the opposite direction, the relative speed is calculated by adding the speed of both the bodies.

Given,

Plane A is at altitude of 3329 feet.

Plane B is at altitude of 4000 feet

Plane A is gaining altitude at Distance between them

= 4000 - 3329 feet

= 671 feet

Speed of plane A = 605 feet per second.

Speed of plane B = 45.25 feet per second

Since both plane are moving upwards

Relative speed = 605 - 45.25 = 559.75 feet per second

Time of both planes to be on same altitude

= 671/559.75

= 1.198 seconds.

≈ 1.2 seconds.

Hence, it will take 1.2 seconds to have both planes at same altitude.

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Answer:The product of a number t and eight is twelve: t * 8 = 12

Twice the sum of a number m and five is the difference of nine and n: 2(m + 5) = 9 - n

Twenty-one is the quotient of a number y and 4: y / 4 = 21

Thrice the difference of number b and one is the product of a number c and ten: 3(b - 1) = c * 10

Step-by-step explanation:

Answer:

1. b-7= 10

2. T-(8)=12 or T X 8 =12

3. 2 (X+5)

4. 21= 4/y

5. 3 (b-1)= C (10)

He is over budget by $1,333.33 - $800 = $533.33 per month.

Budget can be defined as a financial plan that outlines expected income and expenditures for a specific period of time, usually a month or a year. It is a tool used to manage personal to ensure that there is enough money coming in to cover all of the necessary expenses and to prioritize spending in a way that aligns with one's financial goals.

Budget helps to track and control spending, identify areas where expenses can be reduced and make adjustments as needed to stay on track.

If he gives away 60% of his budget, then his monthly budget is $800 / 0.6 = $1,333.33.

So, he is over budget by $1,333.33 - $800 = $533.33 per month.

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Answer

Because 1 = 100%, it is certain that the sun will rise tomorrow

Step-by-step explanation:

The value of P(1.41 < Z < 2.85)  is 0.0771.

Hence, the correct answer is d.

A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.

The whole area under the curve is one, or one hundred percent.

The mean and variance of a normal distribution are governed by two factors.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.

The answer is approximate:

P(1.41 < Z < 2.85)

= P(Z < 2.85) - P(Z < 1.41)

= 0.9927 - 0.9185

= 0.0742

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The complex number in trigonometric form is given as follows:

8.49 with an angle of 45º.

A complex number has a real part and an imaginary part, and is defined as follows:

z = a + bi.

In which:

Considering that the x-axis gives the real part, and the y-axis gives the imaginary part, the number in this problem is given as follows:

z = -6 - 6i.

For the trigonometric form, we have that:

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When the opposite sides of a parallelogram ABCD are equal, the values of x and y are 17 and 10, respectively.

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a sort of quadrilateral with opposing pairs of sides that are parallel and equal. Parallelograms are classified into four categories, three of which are exceptional. Parallelograms, squares, rectangles, and rhombuses are the four kinds. A parallelogram is a quadrilateral with opposing sides that are parallel and equal. It has equal interior opposite angles.

Here,

in parallelogram ABCD, opposite sides is equal.

4y-3=37

4y=40

y=10

3x-9=42

3x=51

x=17

The values of x and y is 17 and 10 in parallelogram ABCD when opposite sides is equal.

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Answer:
Question 1:
Of the 37 children that can't swim, 11 are in Year 4.

Therefore, 26 children in Year 4 can swim.

Question 2:

There are 21 children in Year 5 who can swim.

In Year 6, there are 30 children, 18 of which can swim.

Therefore, a total of 21 + 18 = 39 children who can swim.

The return on a mutual fund, time to completion of a task and the volume of beer sold as 16 ounces are the examples of continuous variables.

Discrete and continuous variables are the two categories into which they fall in mathematics.

A continuous variable is a variable that can take either an infinite or an uncountable number of values. For example, if a variable is continuous throughout a non-empty range of real numbers, it can take on any value within that range. As a result, it is argued that the set of real numbers between x and y, where x, y R, and x y, is uncountable and infinite.

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The values of x in the circles and secant lines are 2.3, 4 and 1

To calculate x, we make use of the tangent-secant line theorem which stated that

c² = b * d

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

Shape (10)

(14 + x + 2) * 14 = 16^2

This gives

16 + x = 18.3

Collect and evaluate the like terms

x = 2.3

Shape (11)

(4x + 9) * 9 = 15^2

This gives

4x + 9 = 25

Collect and evaluate the like terms

x = 4

Shape (12)

x * (x + 8) = 3^2

This gives

x^2 + 8x - 9 = 0

Factorize

(x + 9)(x - 1) = 0

So, we have

x = -9 and x = 1

x = -9 is invalid

Hence, the value is 1

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The one of many solutions of the system is x = 0 and y = 0.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

x + 6y = 0

30y = -5x

Simplifying,

x + 6y = 0

Both are the same equation,

so there are infinitely many solution possibles.

Therefore, solution is x = 0 and y = 0.

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Answer:

b = 3

Step-by-step explanation:

2b + 5b - 7 = 14

7b - 7 = 14 ( add 7 to both sides )

7b = 21 ( divide both sides by 7 )

b = 3

the value from the replacement set is 3