In a laboratory experiment, the population of bacteria in a petri dish started off at 7500 and is growing exponentially at 14% per day. Write a function to represent the population of bacteria after t days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent.

The value of x is 24.

If chosen at random, the probability that he plays two games is 7/29

John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The diagrams are used in probability, logic, statistics, linguistics, and computer science to teach basic set theory and to show basic set relationships.

To find the value of x:

x + (42 - x) + (42 -x ) + (30-x) + 186 -42 + x - x -30 + x

=>150x + x = 174

x= 24.

From the Venn diagram, the number of students that play both games is 42

Hence, the probability is 42/174

Simplified further, it becomes:

7/29

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If and only if f(a) = 0, a polynomial f(x) has a factor (x-a). It's one of the techniques for factoring a polynomial.

A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

The factor theorem can help us determine if a factor is a "root" or "zero" of a polynomial. In other words, if we have a polynomial function, the factor theorem allows us to check if a particular value (usually represented by the variable x) is a solution to the polynomial equation, which means that when we plug in that value for x, the resulting output of the polynomial function will be zero. If it is, then we know that (x - a) is a factor of the polynomial, where "a" is the solution we found.

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Answer: this is true

Step-by-step explanation:

The volume of the rectangular prism is 480 cubic inches.

Volume is a three-dimensional space measurement. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Let's label the dimensions of the rectangular prism as length (l), width (w), and height (h).

From the given information, we know that the cross section formed by the horizontal plane and the prism is a rectangle with dimensions 8 in. and 12 in. This means that the length and width of the rectangular prism are at least 12 in. and 8 in., respectively.

Similarly, the cross section formed by the vertical plane and the prism is a rectangle with dimensions 5 in. and 8 in. This means that the height and width of the rectangular prism are at least 5 in. and 8 in., respectively.

Therefore, the faces of the rectangular prism are:

A face with dimensions l x w = 12 in. x 8 in.

A face with dimensions l x h = 12 in. x 5 in.

A face with dimensions w x h = 8 in. x 5 in.

To find the volume of the rectangular prism, we can use the formula:

Volume = length x width x height

Since we don't know the exact dimensions of the rectangular prism, we can use the minimum dimensions we found earlier. Therefore, the volume of the rectangular prism is:

Volume = 12 in. x 8 in. x 5 in. = 480 cubic inches

So the volume of the rectangular prism is 480 cubic inches.

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See below for the steps to find the coordinates

To find the x and y coordinates of a point on a coordinate plane, follow these steps:

Lastly, write down the coordinates as an ordered pair (x, y)

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The margin of error for a sample taken from 150 households, with a 95% level of confidence and assuming a standard deviation of 0.5, is approximately 0.080 or 8.0%

To determine the margin of error for a sample taken from 150 households, we need to know the sample size and the level of confidence we want to have in our estimate.

Assuming a 95% level of confidence and a standard deviation of 0.5 (which is a conservative estimate when the population size is much larger than the sample size), the margin of error can be calculated using the following formula:

Margin of error = Z * (σ / √n)

where Z is the Z-score for the desired level of confidence, σ is the standard deviation of the population (or an estimate of it), and n is the sample size.

For a 95% level of confidence, the Z-score is 1.96. Assuming a standard deviation of 0.5, we can calculate the margin of error as:

Margin of error = 1.96 * (0.5 / √150) = 0.080

Therefore, the margin of error for a sample taken from 150 households, with a 95% level of confidence and assuming a standard deviation of 0.5, is approximately 0.080 or 8.0%. This means that the estimate obtained from the sample is likely to be within 8.0% of the true population parameter with 95% confidence.

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On the number line, mark the endpoint at 10 with a closed circle.  

Next, draw a ray to the right of 10.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would collect like-terms and rearrange the expression as follows;

1,558 + 60x ≥ 2,158

60x ≥ 2,158 - 1,558

60x ≥ 600

x ≥ 10

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Complete Question:

Solve the inequality from part A for x. 1,558 + 60x ≥ 2,158.

Then use the drawing tools to graph the solution set on the number line.

On the number line, ________________.  

Next, draw a ray to the ____ of 10.

Answer:

Figure B

Step-by-step explanation:

A translation is when you move every point of a figure in the same direction and same distance. It must retain the original shape of the figure and be superimposable. Figure C is a reflection, not a translation.

The five-number summary calculator is a statistical method. It is used to find the third quartile, first quartile, median, minimum, and maximum value of the given data set.

A five-number summary calculator is a statistical test that includes five items. The items are Q₁ or first quartile, Q₃ or third quartile, the median, the maximum, and the minimum. This helps to give an idea about the data set. This also helps to calculate ascending order, descending order, and interquartile of the given data set.

In this method, we first input the list of numbers or data. Then, we arrange those numbers. From this, the minimum value and the maximum value will be found. Then, the median is calculated using the formula for odd and even numbers of terms. Then, the median of the lower half numbers gives the first quartile and the upper half number gives the third quartile.

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Answer:

The relationship is additive because the value of y is 6 more than the value of x

Step-by-step explanation:

did the test and there's a plus sign in the equation so y would be 6 more than the value of x

The relationship between x and y in the equation y = x + 6, is Linear relationship, because the value of y can be represented in a straight line.

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Given the equation:

y = x + 6

This is a linear equation.

The slope is 1 and the initial value (y intercept) is 6

Hence, the relationship between x and y in the equation y = x + 6, is Linear relationship.

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The derivative of cosx is -sinx

Derivative defines the change in the dependent variable with respect to a small change in the independent variable

This means that if we have

y = cosx

where x is the independent variable and y is the independent variable, then the derivative of cosx i.e y will be the amount of change in y due to a small change in x.

i.e, dy/dx = -sinx

we also write this as

d/dx (cosx) = -sinx

This can be proved by the first principle where

[tex]f'(x) = \lim_{h \to 0} \frac{ [f(x + h) - f(x)] }{h}[/tex]

Hence we get

d/dx (cosx)

[tex]f'(x) = \lim_{h \to 0} \frac{ [cos(x + h) - cosx] }{h}[/tex]

[tex]= \lim_{h \to 0}\frac{[-2sin\frac{x+h+x}{2} sin\frac{x+h-x}{2}]}{h}[/tex]

[tex]= \lim_{h \to 0}\frac{ [-2sin\frac{2x+h}{2} sin\frac{h}{2} ]}{h}[/tex]

[tex]= \lim_{h \to 0}\frac{ [-sin\frac{2x+h}{2} sin\frac{h}{2} ]}{h/2}[/tex]

Now we know that [tex]\lim_{x \to0} \frac{sinx}{x} = 1[/tex]

Hence we get

-sinx

Therefore derivative of cosx = -sinx

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The volume of the cylnder is  9,728.5 ft³

For a cylinder of radius R and height H, the volume is given by:

V = pi*R^2*H

Where pi = 3.14

Here we know that the height is.

H = (20 + 1/2) ft = 20.5 ft

And the diameter is (1 + 1/5) times the height, then:

D = (1 + 1/5)*(20 + 1/2) ft = (1.2)*(20.5)ft = 24.6ft

And the radius is half of that, so:

R = 12.3ft

Then the volume is:

V = 3.14*(12.3ft)^2*20.5ft = 9,728.5 ft³

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Answer:

The equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.

Step-by-step explanation:

Answer:

12 quarters, 15 dimes

Step-by-step explanation:

Let q be the number of quarters and d be the number of dimes. We set up and solve this system of equations:

.10d + .25q = 4.50

d = 3 + q

.10(3 + q) + .25q = 4.50

.30 + .10q + .25q = 4.50

.30 + .35q = 4.50

.35q = 4.20

q = 12, d = 15

Answer:

Step-by-step explanation:

∠1+∠2= 25+52=77° ⇒ 1

∠4=180-103=77

∴∠4=∠1+∠2

The closure of set a) includes the boundary, unit circle, and origin; the closure of set b) includes the boundary, line segments, origin, and closed disk; the closure of set c) includes the boundary and origin; the closure of set d) includes the boundary, imaginary axis, origin, and closed half-plane to the right of the imaginary axis.

a) The closure of the set {-pi < arg(z) < pi, z ≠ 0} includes all points on the boundary of this region. This boundary consists of the real axis (where arg(z) = 0), the imaginary axis (where arg(z) = ±pi/2), and the unit circle centered at the origin (where |z| = 1). The closure of the set also includes the point at the origin, since this is a limit point of the set.

b) The closure of the set {|Re(z)| < |z| ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the unit circle centered at the origin (where |z| = 1/2) and the line segments connecting this circle to the x-axis (where |z| = |Re(z)|). The closure of the set also includes the origin and the points on the closed disk centered at the origin with radius 1/2.

c) The closure of the set {Re(1/z) ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the line Re(z) = 1/2 (where the imaginary part of z can take on any value) and the point at the origin, since this is a limit point of the set.

d) The closure of the set {Re(z^2) > 0} includes all points on the boundary of this region. This boundary consists of the imaginary axis (where Re(z^2) = 0) and the rays emanating from the origin at angles ±π/4 (where Re(z^2) is positive). The closure of the set also includes the origin and the points on the closed half-plane to the right of the imaginary axis.

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Answer:

Step-by-step explanation:

For y=7x, if y = 2, you have to do the same for x.

Example; 7x = y, 7(2) = (2), 14 = 2, 14,2

(please comment if I did anything wrong)

Answer:

Domain = {2, -5, 5, -7 }

Range = { 0, 1 , 3 , 8 }

Answer:

Let's define the variables:

h: the number of hours the driver worked.

d: the number of miles the truck drove.

We know that the driver is paid $16 per hour, so the cost of the driver's labor is:

16h

We also know that the truck incurs an expense of $1.25 per mile driven, so the cost of gas and maintenance is:

1.25d

The total expenses for the driver, gas, and maintenance were $205, so we can set up the following equation:

16h + 1.25d = 205

We also know that the average speed of the truck was 20 miles per hour, so we can set up the following equation:

d = 20h

So the system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove is:

16h + 1.25d = 205

d = 20h

These two equations can be solved simultaneously to find the values of h and d that satisfy both equations.

The number 20 can be represented as a decimal by simply writing it as 20.0 or 20.00

The number 20 can be represented as a decimal by simply writing it as 20.00 or 20.000 This is because decimal notation is a way of writing numbers that uses a decimal point to separate the whole number part from the fractional part.

In this case, since 20 is a whole number and has no fractional part, we can represent it in decimal form by adding a decimal point and a zero or two zeros after it to indicate that there are no decimal places.

Alternatively, we can also represent 20 as a decimal by dividing it by 1, which does not change its value, and then expressing the quotient as a decimal. Since 20 divided by 1 equals 20, we can write 25 as a decimal by dividing 25 by 1 and writing the quotient as follows:

20 ÷ 1 = 20.000000... (with the decimal places repeating indefinitely)

However, in most cases, it is sufficient to represent 20 as 20.0 or 20.00, since these notations convey that the number has no fractional part.

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The value of 350 milliliters to ounce after conversion the unit is equal to  11.8349 ounce.

Formula used to convert milliliters to ounce is written as:

One milliliter is equal to 0.033814 fluid ounce .

Now substitute the value 350 milliliters to convert into ounce we get,

⇒ 350 milliliters = ( 350 ) × (  0.033814 ) fluid ounce

⇒ 350 milliliters = ( 11.8349 ) fluid ounce

Therefore, the converted value of the milliliters to ounce for 350 milliliters is equal to  ( 11.8349 ) fluid ounce.

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Answer:

20 millilitres of oil

Step-by-step explanation:

You need to first find how much goes into 1 litre of oil and to do that we divide the two numbers

80/2 = 40

Now we know that for every 1 litre we need 40 millitres

Since .5 is half of 1 we just need to take half of 40

half of 40 = 20

20 millilitres of oil

The length of the hypotenuse is 8√2 units.

According to the Pythagoras theorem, we can write -

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

        (h)² = (b)² + (p)²

Given is a 45 - 45 - 90 triangle with a leg length of 8.

Equal Opp. Angles Theorem -

We can write using the Pythagoras theorem as -

x² = 8² + 8²

x² = 64 + 64

x² = 128

x = √(2 x 2 x 2 x 2 x 2 x 2 x 2)

x = √(2² x 2² x 2² x 2 )

x = 8√2

Therefore, the length of the hypotenuse is 8√2 units.

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The number of seconds that the ball isat its maximum height is 5 seconds.

It should be noted that to find the time at which the softball is at its maximum height, we need to find the vertex of the parabolic equation h = -4t^2 + 40t + 5.5.

The vertex of a parabola of the form h = at^2 + bt + c is given by the formula t = -b / (2a).

In this case, a = -4 and b = 40, so the time at which the ball reaches its maximum height is:

t = -b / (2a) = -40 / (2*(-4)) = 5 seconds.

Therefore, the ball is at its maximum height after 5 seconds.

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Two softball players are practicing catching fly balls. One player throws a ball to the other and the path of the softball is modeled by the equation h = -4t2 +40t +5.5, where h is the height (in feet) of the softball and is the time in seconds that have elapsed. b

After how many seconds is the ball at its maximum height?

The correlation coefficient is a number that measures the strength of the linear association between two numerical variables.

The correlation coefficient is a statistical measure used to determine the strength and direction of the linear relationship between two numerical variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger correlation, and values closer to 0 indicate a weaker correlation. A negative correlation means that as one variable increases, the other decreases, while a positive correlation means that both variables increase or decrease together. The correlation coefficient is an important tool in many fields, such as finance, economics, and healthcare, where it can help identify patterns and predict future outcomes based on past data.

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Answer:

The surface area of the triangular prism is 180 square centimeters.

Step-by-step explanation:

To find the surface area of a triangular prism, we need to find the area of each face and add them up. Let's call the base of the triangle b, the height of the triangle h, and the height of the prism (the distance between the two triangular faces) H.

The triangular faces each have an area of (1/2)bh, so the total area of the two triangular faces is bh. The rectangular faces each have an area of Hb, so the total area of the two rectangular faces is 2Hb. Finally, the top and bottom faces each have an area of b^2, so the total area of these two faces is 2b^2.

Adding all of these areas together, we get:

Surface area = bh + 2Hb + 2b^2

Substituting the given values, we get:

Surface area = (6 cm)(8 cm) + 2(5 cm)(6 cm) + 2(6 cm)^2

Surface area = 48 cm^2 + 60 cm^2 + 72 cm^2

Surface area = 180 cm^2

Therefore, the surface area of the triangular prism is 180 square centimeters.

Answer:

30^

Step-by-step explanation:

To write 0.3 as a percent, multiply 0.3 by 100. Append % symbol in the product obtained. So, 0.3 as a percent is 30 %. We can write in just two steps to calculate any decimal into a percent.

The required height of domino number 7 is 11.76 cm (rounded to two decimal places).

Arithmetic progression is the series of numbers that have common differences between adjacent values.

Here,
Since each subsequent domino is 13% taller than the one before, we can find the height of each domino by multiplying the height of the previous domino by 1.13.

Starting with the height of the smallest domino, we can calculate the height of each subsequent domino using this rule:

Height of domino n = Height of domino (n-1) × 1.13

Using this formula, we can find the height of each domino:

Height of domino 1 = 5.00 cm × 1.13 = 5.65 cm

Height of domino 2 = 5.65 cm × 1.13 = 6.38 cm

Height of domino 3 = 6.38 cm × 1.13 = 7.21 cm

Height of domino 4 = 7.21 cm × 1.13 = 8.16 cm

Height of domino 5 = 8.16 cm × 1.13 = 9.22 cm

Height of domino 6 = 9.22 cm × 1.13 = 10.41 cm

Height of domino 7 = 10.41 cm × 1.13 = 11.76 cm

Therefore, the height of domino number 7 is 11.76 cm (rounded to two decimal places).

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Answer:l^3x+28l=-6

or 0

Step-by-step explanation: