3c+2=20
c
ok anwer this
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2x + 17 grows no faster than 3x as x approaches infinity.

To show that 2x + 17 is O(3x), we need to find two positive constants, C and k, such that:

|2x + 17| <= C|3x| for all x > k

We can start by simplifying the left-hand side:

|2x + 17| = 2x + 17 (since x is always non-negative)

Next, we can simplify the right-hand side:

|3x| = 3x

Now, we need to find C and k that satisfy the inequality:

2x + 17 <= C*3x for all x > k

Dividing both sides by 3x, we get:

(2/3) + (17/3x) <= C for all x > k

Since (2/3) is a constant, we only need to find a value of k such that (17/3x) is less than some other constant. Let's choose k = 1, then:

(17/3x) < 6 for all x > 1

So, we can choose C = 6 and k = 1. Therefore, we have shown that:

|2x + 17| <= 6|3x| for all x > 1

This satisfies the definition of 2x + 17 being O(3x), which means that 2x + 17 grows no faster than 3x as x approaches infinity.

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Answer:

looks like your understanding is pretty good! I'm not sure how you missed the first 2... you should check those two against your understanding.

Step-by-step explanation:

a) 2

b) 1

Answer:

{2, -3, -3/2}

Step-by-step explanation:

hi! we can set each of the binomials equal to 0 to find the zeros of this polynomial.

x-2=0

x=2

x+3=0

x=-3

2x+3=0

2x=-3

x=-3/2

The set includes all of the zeros for the polynomial would be; {2, -3, -3/2}.

They are mathematical expressions involving variables raised with nonnegative integers and coefficients(constants that are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.

We have been given the function f(x)=(x-2)(x+3)(2x+3)

Each of the binomials is equal to 0 to determine the zeros of this polynomial.

1. x-2=0

x=2

2. x+3=0

x=-3

3. 2x+3=0

2x=-3

x=-3/2

Hence, the set includes all of the zeros for the polynomial would be; {2, -3, -3/2}.

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Answer:

C. 15.8

Step-by-step explanation:

√a²+b² =c²

√15²+5²=15.8²

BTW are you trying to sneek out. lol

*plz mark brainliest*

The lowest point on the graph occurs at point (3π/2,  -1)

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation

The attached graph shows sine function graph plotted with the interval [0, 2pi]

The lowest point is observed to occur at  (3π/2,  -1)

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Answer: 11

Step-by-step explanation: -16 / -4 = 4

4 - (-7) = 11

Answer:

11

Step-by-step explanation:

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

A. The required vectors to component form as:  -7(u • v) = -21√(6).

B. u and w are neither parallel nor orthogonal.

Part A:

The vectors are given as:

u = −2(cos 30°i + sin30°j),

v = 6(cos 225°i + sin225°j),

w = 8(cos 120°i + sin120°j)

So we have:

u = -2(√(3)/2 i + 1/2 j) = -√(3) i - j

v = 6(-√(2)/2 i - sqrt(2)/2 j) = -√(2) i - √(2) j

w = 8(-1/2 i + √(3)/2 j) = -4i + √(3) j

To find -7(u • v), we first need to find the dot product of u and v:

u • v = (-√(3))( -√(2) ) + (-1)(-√(2)) = √(6)

Then, we can multiply by -7:

-7(u • v) = -7(√(6)) = -√(6)

Therefore, -7(u • v) = -21√(6).

Part B:

To determine if u and w are parallel, orthogonal, or neither, we can use the dot product:

u • w = (-√(3))(-4) + (-1)(4√(3)) = -8√(3)

Since the dot product is not equal to 0, we know that u and w are not orthogonal. To determine if they are parallel, we can compare their direction vectors:

The direction vector of u is < -√(3), -1 >, and the direction vector of w is < -4, 4√(3) >.

If u and w are parallel, then their direction vectors will be scalar multiples of each other.

So we need to check if there exists a scalar k such that:

< -√(3), -1 > = k < -4, 4√(3) >

This is equivalent to the system of equations:

-k × 4 = -√(3)

k × 4√(3) = -1

Solving for k, we get:

k = √(3)/12

Since k is not a real number, we know that u and w are not parallel.

Therefore, u and w are neither parallel nor orthogonal.

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The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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The null hypothesis (H0) states that the bag filling machine works correctly at the 447 gram setting, while the alternative hypothesis (Ha) suggests that the bags are underfilled or overfilled.

In hypothesis testing, the null hypothesis (H0) represents the assumption that there is no significant difference or effect, while the alternative hypothesis (Ha) suggests that there is a significant difference or effect. In this case, the null hypothesis states that the bag filling machine works correctly at the 447 gram setting, meaning that the bags are filled accurately.

The alternative hypothesis suggests that the bags are either underfilled or overfilled, indicating a deviation from the intended weight.

To determine if there is sufficient evidence to support the alternative hypothesis, statistical analysis needs to be conducted. Since the population standard deviation is known (25), we can use a one-sample t-test. By comparing the sample mean (438 grams) with the hypothesized mean (447 grams), we can calculate the test statistic and compare it with the critical value at the 0.02 level of significance.

If the test statistic falls within the critical region (rejecting the null hypothesis), it would indicate that there is sufficient evidence to conclude that the bags are underfilled or overfilled. Conversely, if the test statistic falls outside the critical region (failing to reject the null hypothesis), it would suggest that there is insufficient evidence to support the claim of underfilled or overfilled bags.

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Answer:

The answer is 6 feet.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Area of circle: 1662.57 cm

Circumference of circle: 144.57 cm

Step-by-step explanation:

Formula of area of circle:

pi x r2 or radius x radius

So, it's 22/7 x 23 x 23 = 1662.571429

Formula of circumference of circle:

2 x pi x radius OR

pi x diameter

Let's use the second method, to find diameter it is radius x 2 = 46

So,

46 x 22/7 = 144.5714286

Answer:

the square route of 16=√4²=4

Answer:

4

Step-by-step explanation:

16/4 is 4 and they're both the same number

Step-by-step explanation:

Answer:

it's b on edge

Step-by-step explanation:

Answer:

3 gallons a minute

Step-by-step explanation:

when you begin filling the tub it only needs 15 additional gallons until it's full

if it takes 5 minutes then the rate at which the tub if filling is 3 gallons per minute

The standard equation for the given situation of the bathtub is w = 5t + 12.

The standard equation to model this linear situation:

w = 5t + 12

where:

w is the number of gallons of water in the bathtub after t minutes

5 is the rate at which the bathtub is being filled (in gallons per minute)

12 is the initial number of gallons of water in the bathtub

To come up with this equation, we know that the bathtub holds 32 gallons of water and initially contains 12 gallons of water. We also know that after 5 minutes, the bathtub is full. This means that in 5 minutes, 32 - 12 = 20 gallons of water were added to the bathtub. Since the bathtub is being filled at a constant rate, we can assume that this rate of 20 gallons per 5 minutes is also the rate at which the bathtub is being filled at any other time.

We can now plug these values into the standard equation for linear relationships:

w = rt + b

where:

w is the dependent variable (the number of gallons of water in the bathtub)

r is the slope of the line (the rate at which the bathtub is being filled)

b is the y-intercept (the initial number of gallons of water in the bathtub)

In this case, we have:

w = 20t + 12

This equation models the linear relationship between the number of gallons of water in the bathtub and the number of minutes it has been filling.

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Correct Question:

A bathtub that holds 32 gallons of water contains 12 gallons of water. You begin filling it, and after 5 minutes the tub is filled. Write a standard equation.

Answer:

Stream is 2.15 kilometers of the race.

Step-by-step explanation:

If the two obstacles are 1.3 kilometers each, and the sprint is 0.25 kilometers of the race, we simply have to add these together and subtract from the total distance of 5 kilometers. 1.3+1.3+0.25 is 2.85 kilometers. 5-2.85=2.15.

Answer:

2.15 km

Step-by-step explanation:

The obstacle parts of the race are 2*1.3 = 2.6 kilometers long.

The total length of the race is 5 kilometers.

The stream part of the race is 5-0.25 - 2.6 = 2.15 kilometers long.

So the answer is 2.15 km

Answer:

\(\frac{75}{4\pi }\) inches or approximately 5.97 inches  

Step-by-step explanation:

Use the cone volume formula: V = \(\pi\)r²\(\frac{h}{3}\)

The diameter is 8 inches, so the radius will be 4 inches.

Plug in the radius and volume, and solve for h

V = \(\pi\)r²\(\frac{h}{3}\)

100 = \(\pi\)(4²)(\(\frac{h}{3}\))

100 = 16\(\pi\)\(\frac{h}{3}\)

Divide each side by 16\(\pi\)

\(\frac{25}{4\pi }\) = \(\frac{h}{3}\)

Cross multiply and solve for h:

4\(\pi\)h = 75

h = \(\frac{75}{4\pi }\)

So, the cone's height is \(\frac{75}{4\pi }\) or approximately 5.97 inches  

Answer:

X=20°

Step-by-step explanation:

Angle in a straight line is 180°

=> 7x+40°=180°

=> 7x=180°-40°

=> 7x=140°

=> x=20°

Hope this helps you.

His/her lowered score was most likely due to statistical regression.

The missing options in the question are:

A. compensation rivalry  B. Demoralization C.  Differential selection

D.  Testing E.  Statistical regression

From the question, we have:

A change (whether higher or lower) in the score is caused by statistical regression.

This is so because several variables could attribute to the change in the score.

The relationship between these variables is referred to as statistical regression

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After calculating the value of x in the all angle sum equation of ΔRST, we have come to find that m∠S = 38°.

An angle is a figure generated by two rays or lines that have a common terminal in Plane Geometry. The term "angle" is derived from the Latin word "angulus," which meaning "corner." The two rays are known as the sides of an angle, while the common terminus is known as the vertex.

The plane angle does not have to be in Euclidean space. Dihedral angles are created by the intersection of two planes in Euclidean or other space. An angle is identified by the symbol "∠". The angle measurement between the two beams can be represented by the Greek letter θ,α, β etc.

We have given that

m∠R = (x+17)°

m∠S = (2x−2)°

m∠T = (5x+5)°

We know all the angles of a triangle add upto 180°

m∠R + m∠S + m∠T = 180°

(x+17)° + (2x−2)° + (5x+5)° =180°

8x + 20 = 180°

8x = 160°

x = 160°/8

x = 20°

And therefore, m∠S = (2(20)−2)°

                                  = (40 - 2)°

                                  = 38°

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So the polynomial 2x² + x³ - 7x + 1 in standard form is x³ + 2x² - 7x + 1.

To rewrite the polynomial 2x² + x³ - 7x + 1 in standard form, we need to write the terms in descending order of degree.

So we start with the highest degree term:

x³

Then we add the next highest degree term: 2x²

Followed by the next highest degree term: -7x

Finally, we add the constant term: +1

Putting all the terms together, we get:

x³ + 2x² - 7x + 1

So the polynomial 2x² + x³ - 7x + 1 in standard form is x³ + 2x² - 7x + 1.

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Answer:

Yes ,because (x+1) is the factor of all degree 4 polynomial

The probability that at least one out of three bulbs lasts 1000 hours or more is 0.973 or approximately 97.3%.

To solve this problem, we need to use the concept of complementary probability. Complementary probability states that the probability of an event occurring plus the probability of its complement (the event not occurring) equals 1. Therefore, we can find the probability of at least one bulb lasting 1000 hours or more by finding the complement of the probability that all three bulbs fail before 1000 hours.

The probability that a single bulb fails before 1000 hours is 0.3. Therefore, the probability that it lasts 1000 hours or more is 0.7. Using this probability, we can find the probability that all three bulbs fail before 1000 hours as follows:

Probability of all three bulbs failing = 0.3 x 0.3 x 0.3 = 0.027

This means that the probability of at least one bulb lasting 1000 hours or more is the complement of 0.027, which is:

Probability of at least one bulb lasting 1000 hours or more = 1 - 0.027 = 0.973 or 97.3%

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The rate of filling water in the tank is 23450t gallons per hour.

Let's assume that the time taken to fill the tank is t hours.

The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.

The tank is originally empty, which means its volume = 0 gallons.

After 5 hours,

t= 5 hours

The volume of water filled in is given by \(V(5) = 23450 * 5= 1,17,250\) gallons of water.

Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.

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Meters and seconds are the two units of measurement required to describe speed.

A ball freely falling at 20 m/s will in the next second have a speed of 30 m/s.This is because the speed of a freely falling item rises by 9.8 m/s per second owing to gravity's acceleration. The ball begins at a speed of 20 m/s and adds 9.8 m/s to its initial speed after one second, ending in a final speed of 20 + 9.8 = 29.8 m/s (approx. 30 m/s).

Meters and seconds are the two units of measurement required to describe speed. These units are used to calculate the distance travelled by an item as well as the time it takes to traverse that distance. In this scenario, the ball's speed is measured in metres per second (m/s), which is the distance the ball travels in one second.

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Answer:

C. 27.5

Step-by-step explanation:

since 24 and 31 are one standard deviation below or above the mean, we could subtract the two values and divide them by two to help find the mean.

we would first subtract the two values

we would then divide that number by 2 since we are finding the average between the two numbers

using the 3.5, you add it to the lower value (24) and subtract it from the higher value (31)

since both calculated numbers were equal, we know that we calculated the mean correctly.

Answer:

2/935

Step-by-step explanation:

I have attached an image of the equation to use. Assuming that this is without replacement, we'll be taking out one piece out of the bag every time that one is chosen.

Therefore, for probability, the fraction is part/whole. We first have 9 red to 36 pieces in total, but if we take one out, we'll get 8 red left in the bag, and 35 pieces in total. This continues until we fulfill the prophecy (I don't know. qualifications?) that 4 of the pieces are red.

You can try this for yourself, but once simplified, it should be 3024/1413720, which simplifies to 2/935.

Please let me know if you need more clarification or have issues! probability can be confusing :)

Answer:

2/935

Step-by-step explanation:

dito^

Answer:

\(A_{total} = 295\ cm^2\)

Step-by-step explanation:

Step 1:  Determine the area of the bottom rectangle

\(A = l * w\)

\(A = 20\ cm * 10\ cm\)

\(A = 200\ cm^2\)

Step 2:  Determine the area of the top rectangle

\(A = l * w\)

\(A = (20\ cm - 5\ cm - 5\ cm) * (7\ cm)\)

\(A = 10\ cm * 7\ cm\)

\(A = 70\ cm^2\)

Step 3:  Determine the area of the triangles

\(A = \frac{h * b}{2}\)

\(A=\frac{(22\ cm - 10\ cm - 7\ cm)*(\frac{20\ cm - 5\ cm - 5\ cm}{2})}{2}\)

\(A=\frac{5\ cm * 5\ cm}{2}\)

\(A = 12.5\ cm^2\)

Since we have found the area of one right triangle we need to multiply by 2 to get the area for both of the triangles.

\(A = 12.5\ cm^2*2\)

\(A = 25\ cm^2\)

Step 4:  Determine the total area

\(A_{total} = 200\ cm^2 + 70\ cm^2 + 25\ cm^2\)

\(A_{total} = 295\ cm^2\)

Answer: \(A_{total} = 295\ cm^2\)