Due in 5 minutes 1/2x +8 ≤10

The closest answer is 3xLn3 which is (B).

If k(x) = 3x, then f(x) can be expressed as the integral of k(x) with respect to x:

f(x) = ∫ k(x) dx = ∫ 3x dx = (3/2)x² + C

where C is the constant of integration.

To find f'(x), the derivative of f(x) with respect to x, we simply differentiate the expression for f(x):

f'(x) = d/dx [(3/2)x² + C] = 3x

A differential equation is a mathematical equation that relates a function and its derivatives. Specifically, a differential equation describes how a quantity changes as a function of its own rate of change.

Differential equations are commonly used in physics, engineering, and other sciences to model and analyze natural phenomena.

For example, the motion of a simple pendulum can be described using a differential equation that relates the position and velocity of the pendulum to its acceleration and the forces acting upon it.

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Answer:

To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.

8a^3b^2 can be written as:

8a^3b^2 = 2^3 * 2 * a * a * a * b * b

12ab^4 can be written as:

12ab^4 = 2^2 * 3 * a * b * b * b * b

The common factors are 2, a, and b^2.

Therefore, the GCF of 8a^3b^2 and 12ab^4 is:

2 * a * b^2 = 2ab^2

Answer:

3246

Step-by-step explanation:

To calculate this equation, we need to follow the order of operations, also known as PEMDAS. First, we evaluate anything inside parentheses, which in this case is (82-33), giving us 49. Next, we perform division, so we have 6 ÷ 49. Then, we multiply 49 and 66, resulting in 3234. Finally, we add 12 to 3234, leading to the final answer of 3246. Therefore, the value of the expression 12+6÷(82-33)x66 is 3246.

Answer:

3246

Step-by-step explanation:

Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.

To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:

      2x^2 - 3x + 2

P(x) = --------------

       (x - 1 - i)(x - 1 + i)

Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:

x = [3 ± sqrt(9 - 4*2*2)] / (2*2)

 = [3 ± sqrt(1)] / 4

 = 1/2 or 2

Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

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according to the question 77% population use a cell phone that is less than 1 year old.

Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.

given,

The probability distribution for the age of a randomly selected young adult's cell phone can be represented using a probability mass function (PMF) as follows:

P(X = 3) = 0.01 (1% use a cell phone that is 3 years or older)

P(2 ≤ X ≤ 3) = 0.02 (2% use a cell phone that is 2-3 years old)

P(1 ≤ X ≤ 2) = 0.20 (20% use a cell phone that is 1-2 years old)

P(X < 1) = 0.77 (77% use a cell phone that is less than 1 year old)

Note that the values of the PMF correspond to the probabilities of the different age categories for the cell phones of young adults. The PMF satisfies the two main properties of a probability distribution: 1) the probabilities are non-negative, and 2) the sum of the probabilities is equal to 1.

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Answer:

Step-by-step explanation:

C

Answer:

Here

Step-by-step explanation:

The volume of a rectangular prism is found by multiplying the length, width, and height.

Volume = Length x Width x Height

Volume = 11 ft x 8 ft x 4 ft

Volume = 352 cubic feet

The surface area of a rectangular prism is found by adding up the areas of all six faces.

Surface area = 2lw + 2lh + 2wh

Surface area = (2 x 11 ft x 8 ft) + (2 x 11 ft x 4 ft) + (2 x 8 ft x 4 ft)

Surface area = 176 + 88 + 64

Surface area = 328 square feet

Therefore, the volume of the rectangular prism is 352 cubic feet and the surface area is 328 square feet.

It should be noted that to determine the amplitude of a sinusoidal function from a graph:

Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.

Find the vertical distance between the peak and the midline of the graph (the line halfway between the highest and lowest points).

The amplitude of the sinusoidal function is half of this vertical distance.

Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.

Find the vertical coordinate of the midline of the graph (the line halfway between the highest and lowest points).

Write the equation of the midline as y = the vertical coordinate of the midline.

To determine the maximum value of a sinusoidal function from a graph:

Identify the highest point (peak) of the graph of the sinusoidal function.

The maximum value of the sinusoidal function is the vertical coordinate of this peak.

To determine the minimum value of a sinusoidal function from a graph:

Identify the lowest point (valley) of the graph of the sinusoidal function.

The minimum value of the sinusoidal function is the vertical coordinate of this valley.

To determine the period of a sinusoidal function from a graph:

Identify two consecutive peaks or valleys of the graph of the sinusoidal function.

Find the horizontal distance between these two points.

The period of the sinusoidal function is twice this horizontal distance.

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The width of the rectangle is 5.

The area of a rectangle is given by the formula:

Area = Length x Width

where Length and Width are the measurements of the two adjacent sides of the rectangle.

For example, if a rectangle has a length of 6 units and a width of 4 units, then its area would be:

Area = Length x Width

Let's start by using the formula for the area of a rectangle:

Area = Length x Width

We are given that the area of the rectangle is 30xF²y and that one of its sides (length) is 6xy. Substituting these values into the formula, we get:

30x²y = (6xy) x Width

Simplifying the right-hand side by multiplying 6xy by Width, we get:

30x²y = 6x²y x Width

Dividing both sides by 6x²y, we get:

Width = 30x²y / 6x²y

Simplifying the right-hand side by canceling out the common factors of 6, x², and y, we get:

Width = 5

Therefore, the width of the rectangle is 5.

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Using equations, we can find the required equation for each of the cases as follows:

1. t = cd

2. t = qh

3. t = wm

Equations are mathematical expressions that have two algebraic expressions on either side of the equals (=) symbol. It proves that the expressions printed on the left and right sides are equally valid. In each mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation. We'll consider that to be a term.

As per the question,

The total number of caps per day = c

Total number of caps made = t

Total number of days = d.

Now, the required equation will be:

t = c × d

⇒ t = cd

Coming to the next question,

Quizzes graded per hour = q.

Total number of quizzes = t.

Total number of hours = h.

So, the required equation will be:

t = q × h

⇒ t = qh.

Coming to the final question,

Words typed per minute = w.

Total number of words = t.

Total number of minutes = m

So, the required equation will be:

t = w × m

⇒ t = wm.

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For pythagorean theorem  the triangle is a 3, 4 ,5 triangle 15 would be the length 5, and 9 would be the lenght 3. So we would multiply each side to getthe answer your lookin for. Which the third side would be, I think im right, i just did this in my head but im only 11 so dont bully me plsssss

ANSWER 12

The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

Null hypothesis: The proportion of homes in Oregon heated by natural gas is the same as the reported national average of 45%.

Alternative hypothesis: The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

We can use a two-tailed z-test to test this hypothesis.

The test statistic is calculated as:

z = (p - P) / √[P(1-P)/n]

where p is the sample proportion, P is the hypothesized population proportion (0.45), and n is the sample size.

Using the values given in the problem, we have:

p = 175/314 = 0.557

P = 0.45

n = 314

Plugging these values into the formula, we get:

z = (0.557 - 0.45) / √[0.45(1-0.45)/314] = 3.039

Using a standard normal distribution table, we find that the probability of getting a z-value of 3.039 or higher (in absolute value) is less than 0.005.

Since the significance level is 0.05, which is greater than the p-value, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Therefore, the proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

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If the radius of smaller-saw is 1.25 in, and radius of larger-saw is 2 inches, then larger-saw is 4.71 inches greater the smaller-saw.

The "Circumference" of a circle is defined as the distance around the boundary of a circle, it is also called perimeter of circle;

The diameter of the smaller saw can be calculated as:

⇒ diameter = 2 × radius = 2 × 1.25 inches = 2.5 inches;

The diameter of the larger saw is 1.5 inches greater than the diameter of the smaller saw, which means,

⇒ diameter of larger saw = diameter of smaller saw + 1.5 inches,

⇒ diameter of larger saw = 2.5 inches + 1.5 inches = 4 inches;

So, Circumference of circle is = 2 × π × radius;

The Circumference of "smaller-saw" = 2 × 3.14 × 1.25 inches,

⇒ circumference of smaller saw = 7.85 inches;

circumference of "larger-saw" = 2 × 3.14 × 2 inches

⇒ circumference of larger saw = 12.56 inches;

The difference in circumference between the two saws is:

⇒ circumference of larger saw - circumference of smaller saw

⇒ 12.56 inches - 7.85 inches = 4.71 inches;

Therefore, the circumference of the larger saw is 4.71 inches greater than the circumference of the smaller saw.

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The given question is incomplete, the complete question is

A carpenter has two different-sized circular saws. The smaller saw has the radius as 1.25 inch. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.

How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π

Step 1:  Order from least to greatest

51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98

Step 2:  Determine the median of the lower half of the data

There are 12 numbers which means that there is going to be 6 numbers on both sides of the data. So using the first 6 numbers we will be able to determine the median of the lower half of the data.

51, 56, 62, 72, 79, 81

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

[tex](62 + 72) \div 2 = \bold{67}[/tex]

Step 3:  Determine the median of the upper half of the data

So using the first 6 numbers we will be able to determine the median of the upper half of the data.

82, 85, 89, 95, 97, 98

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

[tex](89 + 95) \div 2 = \bold{92}[/tex]

Answer: The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.

The function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5.

The y-intercept is the point where the graph intersects the y-axis. In other words, the y-intercept of a function is the value of y when x = 0.

Therefore, let's find the function with y-intercept as 1.

Hence,

h(x) = 0.5(2)ˣ + 0.5

Let's make x = 0 to check if the value of y = 1

Therefore,

h(x) = 0.5(2)ˣ + 0.5

h(0) = 0.5(2)⁰ + 0.5

h(0) = 0.5(1) + 0.5

h(x) = 0.5 + 0.5

h(x) = 1

Therefore, the function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5

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Answer:

B

[tex]6^{-7}[/tex] is equivalent to 1/279936 which is basically [tex]\frac{1}{6^{7}}[/tex]

The probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.

A discrete probability distribution has countable alternative values for the random variable and a stated probability for each one. Since the potential values are 0, 1, or 2, and the probability of each conceivable value can be determined, the probability distribution of the number of heads acquired after two coin flips is an example of a discrete probability distribution.

In contrast, a continuous probability distribution has a continuous range of possible values for the random variable and a probability of zero for any given value.

Given that, the probability of tripping is given as: 0.35.

Now, the probability of tripping on the 4th period is given by:

[tex]P(X=k) = (1-p)^{(k-1)} * p[/tex]

Now, for k = 4 and p = 0.35 we have:

[tex]P(X=4) = (1-0.35)^{(4-1)} * 0.35[/tex]

P(X=4) = 0.0279

Hence, the probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.

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Answer:

-2a⁴ b⁶ c³

Step-by-step explanation:

2a² b c³ (-a² b⁵)

determine the signs for multiplication or division

-2a²bc³a²b⁵

multiply the monomials

-2a⁴b⁶c³

(then done)

2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

What is scatterplot?

A scatter plot is a particular type of plot or mathematical diagram by using Cartesian coordinates to display values for typically two variables for a set of values. It represents the correlation between two sets of data which may be linear or non linear sometimes strongly positive linear sometimes it may be curvilinear sometimes it may be null.

In the first plot it visibly showing a graph for straight line that is strong positive linear scatter plot. Same for the last but there is a little difference that it is negative linear scatter plot.

For the second one there is a null scatter plot. So there is no correlation.

For the 3rd graph there is a curvilinear relation in the scatterplot.

Hence, 2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

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The solution to the given composite function is; C: 4x² - 4x - 2

From the question, we are given the individual functions as;

f(x) = x² - 3

g(x) = 2x - 1

Now when it comes to composite functions, we know that;

(f ° g)(x) = f[g(x)]

Substitute the known values in the above equation, so, we have the following representation

(f ° g)(x) = f(2x - 1) = (2x - 1)² - 3 = 4x² - 2x - 2x + 1 - 3 = 4x² - 4x - 2

This is the final solution of the composite function expression.

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The solution to the given composite function is; Option D: 2x² - 7

Composite functions are defined as functions where the output of one function is used as the input of another. Wheb we have a function f and another function g, then the function fg(x), said as “ f of g of x”, is the composition of the two functions.

The given functions are:

f(x) = x² - 3

g(x) = 2x - 1

We want to find (g ° f)(x) . We know that:

(g ° f)(x) = g[f(x)]

Thus:

(g ° f)(x) = g(x² - 3)

= 2(x² - 3) - 1

= 2x² - 6 - 1

= 2x² - 7

This is the final result of the composite function expression.

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The length of LG in the plane is

To find the distance between two points in a 2D plane, we can use the distance formula:

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

Using this formula, we can find the distance between L(4,4) and G(9,9):

distance = √((9 - 4)^2 + (9 - 4)^2)

= √(5^2 + 5^2)

= √50

= 5√2

Therefore, the distance between L(4,4) and G(9,9) is 5√2, which is approximately 7.07 units.

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Hence ,the basketball team  scored 83 points in  the first game.

Basketball is a team sport in which two teams,  most commonly of five players each,  opposing one another on a rectangular court,  compete with the primary objective of shooting a basketball through the defender's hoop,  while preventing the opposing team from shooting through their own hoop.

A team is a group of individuals (human or non-human) working together to achieve their goal.As defined by Professor Leigh Thompson of the Kellogg School of Management, team is a group of people who are interdependent with respect to information, resources, knowledge and skills and who seek to combine their efforts to achieve a common goal

Let x be  the number of points  scored in the first game.

According  to the  question,

747 = 9 x

now  9 divided by both sides,

x = [tex]\frac{747}{9}[/tex]

than we get:

x = 83

Therefore,  the basketball team  scored 83 points in  the first game.

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Complete question is:

A basketball scored 747 points for the season.This was 9 times the number of points they scored in the first game.How many points were scored in the first game.

The equation for f(x) can be written as f(x)= 15(3/5)ˣ

An exponential function is a mathematical function of the form f(x) = aˣ, where 'a' is a positive constant and 'x' is any real number. The graph of an exponential function is characterized by a rapid increase or decrease as 'x' increases or decreases, respectively. Exponential functions have many applications in fields such as finance, biology, and physics.

From this table we know this thing that when x=0, y=15

when x=1, y=9

a×b⁰=15⇒ a=15 as b⁰=1

a×b¹=9⇒ ab=9

so b=9/a

b= 9/15⇒3/5

After putting the values we get the result f(x)=15×(3/5)ˣ

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The correct answer is C. The circumference of a circle varies directly as the radius.

It is calculated by multiplying the diameter of a circle by pi, or by measuring the length of a curved line that encloses the shape.

The relationship between the circumference of a circle and its radius is a linear equation, where the circumference is equal to two times pi times the radius, or C = 2πr.

The circumference of a circle varies directly as the radius, meaning that if the radius of a circle is doubled, the circumference will also double.

This linear relationship can be used to approximate the value of pi, which is a constant ratio between the circumference and the diameter of any circle.

Therefore, the statement that justifies why the measurements of the circumference and radii of circles with different areas can be used to approximate the value of pi is that the circumference of a circle varies directly as the radius.

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Answer:two lines are parallel if their slopes are equal and they have different y-intercepts

Step-by-step explanation:

Answer:

The distance from home to second base is approximately 84.85 feet in a slow pitch softball diamond that is 60 feet on each side.

Step-by-step explanation:

In a softball diamond that is 60 feet on each side, the distance from home to second base is approximately 84.85 feet. This is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the distance from home to second base forms the hypotenuse of a right triangle with legs that are each 60 / sqrt(2) feet long. Using the Pythagorean theorem, we can calculate that the distance from home to second base is approximately 84.85 feet.

By using the properties of logarithms, The logarithm "log₅(98)" can be written as log₅(2) + log₅(7) + log₅(7).

We use the "product' and "quotient" logarithmic identities to write log₅(98) in terms of log₅(2) and log₅(7):

⇒ logₐ(b × c) = logₐ(b) + logₐ(c)      ....(product rule)

⇒ logₐ(b/c) = logₐ(b) - logₐ(c)           ...(quotient rule)

First, we write the number "98" as the product of 2 and 7, which is :

⇒ log₅(98) = log₅(2 × 7 × 7),

Using the product rule, we can split this into three logarithms;

⇒ log₅(2 × 7 × 7) = log₅(2) + log₅(7) + log₅(7),

So, we have,

⇒ log₅(98) = log₅(2) + log₅(7) + log₅(7),

Therefore, log₅(98) is equal to log₅(2) + log₅(7) + log₅(7).

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The given question is incomplete, the complete question is

Use the properties of logarithms to write the logarithm in terms of log₅(2) and log₅(7).

The logarithm is log₅(98).

Answer:you need to include the expression

Step-by-step explanation:

once you have the expression, substitute the numbers given for each variable and use order of operations to