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Which sets of values can be the measures of the exterior angles of a triangle?
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Answer:

The probability that one marble drawn at random is not blue is 70%

Answer:

To translate the argument into symbolic form, we can assign variables:

P: He drives fast

Q: He will not crash

The argument can then be expressed as:

If P, then ~Q

To determine if the argument is valid or invalid, we need additional information or premises. An argument is considered valid if the conclusion follows logically from the premises.

If there are additional premises provided, please provide them so that we can evaluate the validity of the argument.

Step-by-step explanation:

To determine the minimum number of visits Wyatt needs to earn his first free movie ticket, we can set up an inequality using the information provided. So,  the inequality that represents this is: 25 + 11.5x ≥ 230

Let x be the number of visits Wyatt needs.
We know that Wyatt receives 25 reward points just for signing up and earns 11.5 points for each visit. So, the total number of points he earns can be represented by the equation: 25 + 11.5x

To earn his first free movie ticket, Wyatt needs at least 230 points.

Therefore, the inequality that represents this is: 25 + 11.5x ≥ 230

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The value of x for this problem, considering the two secant theorem, is given as follows:

x = 15.

The value of c is obtained applying the two secant segment theorem, which means that the following equation will hold true:

8(8 + 19) = 9(9 + x).

(we add the two parts), with the outer part being the multiplier.

Solving the equation, we have that the value of x is given as follows:

27 x 8 = 9/(9 + x)

9 + x = 3 x 8

9 + x = 24

x = 15.

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Answer:

Domain: All real numbers except -2

Step-by-step explanation:

The domain of a function is "the set of all possible inputs for the function". In other words, it's all the possible x's you can put into the function without any problems. What do I mean?

Well, take f(x) = x from |R to |R for example. (|R is the set of all real numbers.) The domain of this function is all real numbers. Why? Well, you can put any real number as x, and there wouldn't be any problems!

Another example is f(x) = 1/x from |R to |R. Now, we have a problem. If x = 0, then we would have f(x) = 1/0, and that's undefined. So 0 is not in the domain. But everything else is! So the domain is all real numbers except 0.

Same thing with f(x) = (5x-2)/(x+2) from |R to |R. If x = -2, then we would have f(x) = -12/0, which is also undefined. So the domain of f(x) = (5x-2)/(x+2) from |R to |R is all real numbers except -2.

Answer:

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Let the distance we are looking for be d.

If cat runs d meters, then mouse runs 160 m less because of the head, and the ratio of the distance they cover is 9/7.

Set up an equation to reflect it:

Solve it for d:

So, the cat must run 720 m to catch the mouse.

There are approximately 1.0875 milligrams of iron in 87 grams of food that contains 0.00125% iron.

To find the amount of iron in 87 grams of food, we first need to convert the percentage into a decimal. The food contains 0.00125% iron, which is equivalent to 0.0000125 as a decimal.

Next, we multiply the decimal by the weight of the food to determine the amount of iron in grams. So, 0.0000125 x 87 = 0.0010875 grams of iron.

Since we want the answer in milligrams, we need to convert grams to milligrams. There are 1,000 milligrams in one gram. Therefore, 0.0010875 grams is equal to 1.0875 milligrams.

It's worth noting that this calculation assumes a homogeneous distribution of iron throughout the food sample. In reality, the iron content may vary within different parts of the food or across different food items.

Additionally, the accuracy of the iron content measurement and the precision of the percentage value provided can also impact the final result.

Therefore, it's always advisable to consult reliable sources or conduct laboratory tests for precise and accurate nutrient information.

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The 6 numbers for the given probabilities can be:

(2, 4, 5, 6, 7, 8)

There are 6 numbers, we know that:

probability of any event = (outcomes that meet the event)/6

Then, if:

probability of an even number = 2/3 = 4/6

This means that there are 4 even numbers.

if:

P Number chosen is less than 5  = 1/3 = 2/6

There are 2 numbers less than 6.

And there is a 50% of gettting a prime, so there are two primes.

Then the 6 numbers could be:

(2, 4, 5, 6, 7, 8)

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For the given sample data, the variance is 48.4 and the standard deviation is approximately 6.96. These measures provide information about the spread or variability of the data points around the mean.

To find the variance and standard deviation for the given sample data: 2, 9, 12, 15, 19, 21, we first need to calculate the mean (X) of the data set.

Calculating the Mean:

Mean (X) = (2 + 9 + 12 + 15 + 19 + 21) / 6

= 78 / 6

= 13

The mean (X) of the data set is 13.

Calculating the Variance:

Variance (S^2) is a measure of the dispersion or spread of the data. It can be calculated using the formula:

S^2 = Σ(Xi - X)^2 / (n - 1)

where Xi represents each individual data point, X is the mean, and n is the sample size.

Using the given data set and the calculated mean, we can calculate the variance:

[tex]S^2 = [(2 - 13)^2 + (9 - 13)^2 + (12 - 13)^2 + (15 - 13)^2 + (19 - 13)^2 + (21 - 13)^2] / (6 - 1)[/tex]

=[tex][(-11)^2 + (-4)^2 + (-1)^2 + (2)^2 + (6)^2 + (8)^2] / 5[/tex]

= [121 + 16 + 1 + 4 + 36 + 64] / 5

= 242 / 5

= 48.4

The variance (S^2) of the data set is 48.4.

Calculating the Standard Deviation:

The standard deviation (S) is the square root of the variance. It measures the average amount of variation or dispersion from the mean.

S = √(S^2)

= √48.4

≈ 6.96

The standard deviation (S) of the data set is approximately 6.96.

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Answer:

4 × 5 × 0 = 0, so 450 = 0.

Step-by-step explanation:

6 × 5 × 2 = 60

5 × 3 × 5 = 75

4 × 8 × 2 = 64

A woman invests $6,998.66 at 8% and about $24,001.34 at 9.5% .Let's assume that the amount invested at 8% is x dollars. Then the amount invested at 9.5% is (31,000 − x) dollars.The annual income from the investment at 8% would be 0.08x dollars.

Similarly, the annual income from the investment at 9.5% would be 0.095(31,000 − x) dollars.

As per the question, the investment at 9.5% provides $407.50 more income than the investment at 8%, so we can write this in equation form:0.095(31,000 − x) − 0.08x = 407.50.

Solve for x:

0.095(31,000 − x) − 0.08x = 407.50.2945(31,000 − x) − .08x = 407.503,027.50 − .2945x − .08x = 407.50.

Combine like terms :3,027.50 − .3745x = 407.50

Subtract 3,027.50 from both sides:− .3745x = − 2,620

Divide both sides by − .3745:x ≈ 6,998.66

We invested about $6,998.66 at 8% and (31,000 − 6,998.66) ≈ $24,001.34 at 9.5%.

Therefore, a woman invests $6,998.66 at 8% and about $24,001.34 at 9.5%.

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Answer:

Step-by-step explanation:

A. 10

just look at the highest exponent.

Answer:

view the photo

Step-by-step explanation:

Each step of Cho's solution should be matched to its appropriate justification as follows;

[tex]B=(x_1+\frac{a}{b} (x_2-x_1),(y_1+\frac{a}{b} (y_2-y_1))[/tex]    ⇒  Fractional distance formula

[tex]=(x_1+\frac{3}{4} (x_2-x_1),(y_1+\frac{3}{4} (y_2-y_1))[/tex]        ⇒  Substitute a = 3 and b = 4.

[tex]=(2+\frac{3}{4} (6-2),(4+\frac{3}{4} (8-4))[/tex]               ⇒  (x₁, y₁) → (2, 4) and (x₂, y₂) → (6, 8)

= (2 + 3), (4 + 3)                                     ⇒  Simplify (1st use)

= (5, 7)                                                   ⇒  Simplify (2nd use).

In this scenario, line ratio or fractional distance formula would be used to determine the coordinates of the point C on the directed line segment AB that partitions the segment into a ratio of 3 to 4.

In Mathematics and Geometry, line ratio or fractional distance formula can be used to determine the coordinates of point C and this is modeled by the following mathematical expression:

C(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

[tex]C=(x_1+\frac{a}{b} (x_2-x_1),(y_1+\frac{a}{b} (y_2-y_1))\\\\C=(2+\frac{3}{4} (6-2),(4+\frac{3}{4} (8-4))[/tex]  

C = (2 + 3), (4 + 3)

C = (5, 7)

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Answer: 76kg

Step-by-step explanation:

If the mass of sugar in one jar is 19kg, then the mass of 4 such jars of sugar can be found by multiplying the mass of one jar by 4:

Therefore, the total mass of 4 jars of sugar is 76kg.

__________________________________________________________

The mass of sugar is 19 kg. What is the total mass of 4 such jar of a sugar?

The total mass of four jars of sugar is 76 kg.

The total mass of four jars of sugar can be found by multiplying the mass of one jar by 4:

[tex]\large\rm{Total\: mass = 19\: kg \times 4 = \boxed{\rm{\:76\: kg\:}}}[/tex]

[tex]\therefore[/tex] The total mass of four jars of sugar is 76 kg.

- Mass is a measure of the amount of matter an object contains. It is a fundamental property of an object and is typically measured in units such as kilograms or grams. Mass is different from weight, which is the force of gravity acting on an object's mass. Mass is an intrinsic property of an object and remains constant regardless of its location, while weight can vary depending on the gravitational field it is in. Essentially, mass determines an object's resistance to acceleration or change in motion.

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Let x be the number of pounds of Kenyan coffee and y be the number of pounds of Sumatran coffee. We know that x + y = 26 and 9x + 11y = 260.

Solving the system of equations, we get

x = 14 and y = 12

Therefore, the Coffee Counter should use 14 pounds of Kenyan coffee and 12 pounds of Sumatran coffee to make a 26 pound blend that sells for $10.00 per pound.

To confirm, the average price of the blend is: (9*14 + 11*12) / 26 = 10.00

So the answer is 14,12

Answer:

To graph the position function f(t), velocity function v(t), and acceleration function a(t) for the given scenario, we'll start by calculating these functions using the given equation:

s(t) = 152t - 16t^2

To find the velocity function, we'll take the derivative of the position function with respect to time:

v(t) = ds(t)/dt = f'(t) = d/dt (152t - 16t^2)

Using the power rule of differentiation, we get:

v(t) = 152 - 32t

Next, to find the acceleration function, we'll take the derivative of the velocity function with respect to time:

a(t) = dv(t)/dt = f''(t) = d/dt (152 - 32t)

Since the derivative of a constant is zero, the acceleration function simplifies to:

a(t) = -32

Now that we have the position function f(t), velocity function v(t), and acceleration function a(t), we can plot their graphs.

(a) Graph of f(t) = 152t - 16t^2:

The graph of f(t) will be a downward-opening parabola with a maximum point. Since the range is restricted to 0 ≤ t ≤ 9.5, the graph will be limited within that range.

(b) Graph of v(t) = 152 - 32t:

The graph of v(t) will be a linear function with a negative slope of -32. It will start with a positive velocity and decrease linearly until it reaches zero at t = 4.75 (half of the time interval), and then it will continue to decrease with negative velocity.

(c) Graph of a(t) = -32:

The graph of a(t) will be a horizontal line at -32, indicating a constant acceleration of -32 ft/s^2.

(d) To complete the statement (e), please provide the specific parts that need to be completed.

(e) Statement incomplete. Please provide the specific parts that need to be completed.

(f) Statement incomplete. Please provide the specific parts that need to be completed.

The value of the resistor needed in this scenario is approximately 1.2 ohms.

To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.

Using Ohm's Law, we have the formula:

V = I * R

Where:

V is the voltage across the resistor (12 volts in this case),

I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),

R is the resistance of the resistor (which we need to find).

Rearranging the formula, we have:

R = V / I

Plugging in the values:

R = 12 volts / 10 amps

R = 1.2 ohms

Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.

It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.

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Answer:

increase by 87.5%

Step-by-step explanation:

150 ÷ 80 - 100 = 87.5

new value ÷ original value - 100= percentage change

The volume of the cylinder is 132ft³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cylinder is expressed as;

V = πr²h

where r is the radius and h is the height.

π = 3

radius = 2ft

height = 11ft

Volume = 3 × 2² × 11

V = 132 ft³

Therefore the volume of the cylinder is 132ft³

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(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By applying a reflection over the x-axis to the parent absolute value function g(x) = |x + 2| - 4, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

x and y represent the data points.

m represent the slope.

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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The class had cleaned x × A square miles before lunch.

Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).

If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:

Area cleaned before lunch = x × A

Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.

Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).

If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:

Before lunch, the area was cleaned = x A

We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.

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Answer:

B.  10

Step-by-step explanation:

A:

cost = 20 + 3x

B:

cost: 30 + 2x

20 + 3x = 30 + 2x

x = 10

Answer:

positive correlation

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Solution: --

The ratio of red to blue is 1:2. The grid is 12 pieces. So. There are 4 shades of red and 8 blue shadows. math.

The graph that represents a function among the options given is the last option. See image below.

To determine if a graph represents a function, check if any vertical line intersects the graph in more than one point. If every vertical line intersects the graph at most once, then the graph represents a function.

Considering the options given, the last option shown in the image given will have only one point intersected on the graph if we run a vertical line on it. The rest will have at more than one point.

Therefore, the graph that is a function is the last option.

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Answer:

Step-by-step explanation:

[tex]y=(\frac{1}{g} )x[/tex]

Constant up a proportionally is  [tex]\frac{1}{g}[/tex].

f(x) = -215 and [tex]g(x) = -98x^2[/tex] satisfy the given conditions, and h(x) = (f o g)(x) is equal to [tex]-215 - 98x^2.[/tex]

To find the functions f(x) and g(x) such that h(x) = (f o g)(x) and g(x) = 1-7x, we need to substitute the expression for g(x) into the equation for h(x).

Given: g(x) = 1 - 7x

Substituting g(x) into h(x), we have:

[tex]h(x) = (1 - 7)^3 - 2(1 - 7x)^2 + 4(1 - 7x) - 1[/tex]

Simplifying the expression further:

[tex]h(x) = (-6)^3 - 2(1 - 7x)^2 + 4(1 - 7x) - 1[/tex]

[tex]= -216 - 2(1 - 14x + 49x^2) + 4(1 - 7x) - 1[/tex]

[tex]= -216 - 2 + 28x - 98x^2 + 4 - 28x - 1[/tex]

[tex]= -215 - 98x^2[/tex]

Therefore, f(x) = -215 and [tex]g(x) = -98x^2.[/tex]

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