4 There were 822 students signed up to run in timed races. If exactly 6 students ran in each race, how many races were there?​

Answer: -7/1

Step-by-step explanation: When graphing both points and drawing a line through it, count how many times it goes up or down and then count how many times it goes left or right.

3/4+6/7 = (21 + 24)/28 = 45/28

The answer is C. 45/28

Answer:

1/3 pound per person

Step-by-step explanation:

(All)    (People)   (Amount per person)

1.32  /  4          = .33                        

.33 = 1/3

The correct statement is- Once the Compromise of 1850 was passed, Northerners and Southerners readily accepted its terms, putting their suspicions to rest.

The statement describes how both Northerners and Southerners were suitable to fluently accept the terms of the concession of 1850 and put their reservations to rest after its end. The Concession of 1850 was a series of legislative measures aimed at resolving the growing pressures between the Northern and Southern countries of the United States over issues similar to slavery and the balance of power.

The statement suggests that the terms of the concession were satisfactory to both sides, allowing for a sense of agreement and resolution. It implies that the concession addressed the enterprises and interests of both Northerners and Southerners, leading to their amenability to accept it. By accepting the concession and its terms, both regions were suitable to palliate their reservations or dubieties, potentially reducing pressures between them.

This statement highlights the significance of the concession of 1850 in furnishing a temporary resolution to the contentious issues of the time, indeed though these issues would latterly contribute to the raising conflicts that ultimately led to the American Civil War.

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Every polynomial function of odd degree with real coefficients will have at least one real root or zero.

This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.

The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.

For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.

It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.

The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.

In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.

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Answer:

According to the given data, if it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6.

Step-by-step explanation:

Past studies indicate that about 60 percent of the trees in a forested region are classified as softwood.

A botanist studying the region suspects that the proportion might be greater than 0.60.

The botanist obtained a random sample of trees from the region and conducted a test of H0:p=0.6 versus Ha:p>0.6.

Therefore, he p-value of the test was 0.015, indicating the past studies.

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Answer:

The first offer: 100.80 for 4kg

Step-by-step explanation:

To find the best offer, we just need to find the price per kilogram, and we do this by dividing the price by the number of kg:

100.80 for 4kg: 100.8/4 = 25.2 per kg

170.50 for 5kg: 170.5/5 = 34.1 per kg

260.60 for 6kg: 260.6/6 = 43.43 per kg

320.40 for 7kg: 320.4/7 = 45.77 per kg

The first offer has the smaller price per kg, so it is the best offer.

The problem includes finding out the volume of water displaced per unit time by the sphere and the mean velocity, relative to the cylinder wall of the water in the gap surrounding the midsection of the sphere. Also, we have to calculate the volume flow rate of the air.

1) Volume of water displaced per unit time by the sphere. It is given that a sphere of diameter 300 mm is falling axially down a 304 mm diameter vertical cylinder which is closed at its lower end and contains water. So, let's determine the volume of water displaced per unit time by the sphere.

Volume of the sphere, V = (4/3)πr³Volume of the cylinder, V = πr²hWhere, r = radius of the sphere = 150 mm (diameter 300 mm)Diameter of the vertical cylinder = 304 mm.

Radius of the cylinder, R = 152 mm Diameter of the vertical cylinder = 304 mmRadius of the cylinder, R = 152 mmHence, the height of the cylinder is given by h = 300 mm - 150 mm = 150 mm = 0.15 mVolume of the sphere, V = (4/3)π(0.15)³ = 0.014137 m³Volume of the cylinder, V = π(0.152)²(0.15) = 0.008562 m³.

Therefore, the volume of water displaced per unit time by the sphere is given by:

Volume of water displaced = Volume of the sphere = 0.014137 m³.

2) Mean velocity of water relative to the cylinder wallLet v1 be the velocity of the sphere and v2 be the velocity of water relative to the cylinder wall.

The volume flow rate through the gap = Volume of the sphere/Time taken to pass through the cylinderHere, the sphere passes through the cylinder in one second.

Therefore, the volume flow rate is equal to the volume of the sphere.

Volume flow rate through the gap = Volume of the sphere = 0.014137 m³/sec.

Volume flow rate through the cylinder = Volume of the water displaced = 0.014137 m³/secArea of the gap = πR² - πr²Where R is the radius of the cylinder, which is equal to 152 mmTherefore, R = 0.152 m and r = 0.15 m.

Area of the gap = π(0.152)² - π(0.15)²Area of the gap = 0.0008095 m²The mean velocity of water relative to the cylinder wall, v2 is given by:

v2 = Volume flow rate through the cylinder/Area of the gapv2 = 0.014137/0.0008095 = 17.44 m/secTherefore, the mean velocity of water relative to the cylinder wall is 17.44 m/sec.

3) Volume flow rate of the airLet the diameter of the duct carrying air be d = 0.4 m.

Radius of the duct = d/2 = 0.2 mVelocity profile obeys the law u = -4 R² + k where u (m/s) is the velocity at radius r (m), k = 0.16 m/sThe velocity at the wall, u = 0 (since the velocity of air in contact with the wall is zero).

Hence, the velocity at radius R, u = -4 R² + kVolume flow rate of air is given by:

Volume flow rate, Q = ∫0R 2πru drWhere R is the radius of the duct.Radius varies from 0 to 0.2 mThe above expression can be written as:Q = ∫0R 2π(r(-4R² + k)) drQ = ∫0R -8πR² dr + ∫0R k2πr drQ = -2πR³ + kπR².

Therefore, the volume flow rate of the air is given by:Q = kπR² - 2πR³Q = 0.16π(0.2)² - 2π(0.2)³Q = 0.0064π - 0.02513Q = -0.01873 m³/s

Thus, the volume of water displaced per unit time by the sphere is 0.014137 m³/sec, the mean velocity of water relative to the cylinder wall is 17.44 m/sec, and the volume flow rate of air is -0.01873 m³/s.

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The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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True. In compound time signatures, the top number represents the number of beats per measure. Compound time signatures are typically used for music that has a more complex rhythmic structure, and they are characterized by the subdivision of each beat into three equal parts (known as triplets).

The most common compound time signatures are 6/8, 9/8, and 12/8, with each representing six, nine, and twelve beats per measure respectively.
In 6/8 time, for example, there are two beats per measure, each of which is subdivided into three equal parts. This results in a feeling of two larger beats, each consisting of three smaller beats. In 9/8 time, there are three beats per measure, each of which is subdivided into three equal parts. This results in a feeling of three larger beats, each consisting of three smaller beats. Similarly, in 12/8 time, there are four beats per measure, each of which is subdivided into three equal parts, resulting in a feeling of four larger beats, each consisting of three smaller beats.
Overall, the top number in a compound time signature represents the number of larger beats per measure, while the bottom number represents the duration of each beat (usually an eighth note).

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Step-by-step explanation:

Susan message=34.66

Frank message=27.6

Dan message=28

Answer:

yes

no

yes

yes

Answer:

nope

sorry lad

Step-by-step explanation:

Answer:the greatest number of shirts she can buy = 8

Step-by-step explanation:

Amount of money Olivia  has =$90

cost of pair of jeans =$22

such that if she buys the pair of jean, Money left to buy shirts = $90-$22= $68

If 1 Shirt= $8

Number of shirts she can buy with $68 = $68/$8=  8.5= 8 1/2

Therefore the greatest number she can buy = 8 shirts.

The point at which the line intersects the plane is (x, y, z) = (979/49, 127/49, 78/49).

To find the point at which the line intersects the plane, we need to find the values of x, y, and z that satisfy both the equation of the line and the equation of the plane.

The equation of the line can be written in vector form as:

r = < -3, 2, 0 > + t< 40, 3, 6 >

where r = < x, y, z > is a point on the line, and t is a scalar parameter.

To find the point at which the line intersects the plane, we need to substitute the values of x, y, and z from the vector equation of the line into the equation of the plane and solve for t.

Substituting x = -3 + 40t, y = 2 + 3t, and z = 6t into the equation of the plane, we get:

(-3 + 40t) + (2 + 3t) + (6t) = 12

Simplifying this equation, we get:

49t = 13

Therefore, t = 13/49.

Substituting this value of t back into the vector equation of the line, we get:

r = < -3, 2, 0 > + (13/49)< 40, 3, 6 >

= < -3 + (520/49), 2 + (39/49), (78/49) >

= < 979/49, 127/49, 78/49 >

Therefore, the point at which the line intersects the plane is (x, y, z) = (979/49, 127/49, 78/49).

Hence, the answer is (x,y,z) = (979/49,127/49,78/49).

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Answer:the answer is d. 14x-4

Step-by-step explanation:

Answer:

G. 226 mm

Step-by-step explanation:

C=2(3.14)(36)

Answer:

The vertical line test is a way for you to see if a graph represents a function. It allows you to identify if any x values have more than one y value.

A graph would be a function if every input (x) has exactly one output (y). A graph would not be a function if an input (x) has more than one output (y).

Step-by-step explanation:

In a function, every input within the domain of the function must have exactly one output. If the graph has an input that has more than one output, then it is not a function. The vertical line test is what allows you to see if a graph is a function or not.

Answer:

When given a graph, the vertical line test can be used to determine functionality. The vertical line test would represent a function if no more than one point of the graph of a relation, this shows that only one output value for each input value. If this doesn't apply or more than one point is on the line then it would not represent a function.

Step-by-step explanation:

Draw vertical lines to intersect on a graph.

The relation is a function if there’s only one point of intersection on a graph.

The relation is not a function if there’s more than one point of intersection on a graph.

The vertical line test is used to determine if each input has exactly one output.

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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The approximate volume of the larger candle is 244 cubic centimeters.

To find the volume of the larger candle, we need to compare the side lengths of the smaller and larger candles. Let's denote the side length of the smaller candle as "s."

According to the information given, the side length of the larger candle is five-fourths (5/4) as long as the side length of the smaller candle. Therefore, the side length of the larger candle can be calculated as (5/4) * s.

The volume of a square pyramid is given by the formula V = (1/3) * s^2 * h, where s is the side length of the base and h is the height.

Since both the smaller and larger candles have the same shape, their volume ratios will be equal to the ratios of their side lengths cubed.

Let's substitute the values into the volume ratio equation:

(125 / V_larger) = (s_larger / s_smaller)^3

Given that V_smaller = 125 cubic centimeters, we can rewrite the equation as:

(125 / V_larger) = ((5/4) * s_smaller / s_smaller)^3

Simplifying the equation:

(125 / V_larger) = (5/4)^3

Calculating (5/4)^3:

(125 / V_larger) = (125 / 64)

Cross-multiplying the equation:

125 * 64 = V_larger * 125

Solving for V_larger:

V_larger = (125 * 64) / 125

Approximating the value:

V_larger ≈ 64 cubic centimeters

The approximate volume of the larger candle is 244 cubic centimeters, rounded to the nearest cubic centimeter

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You cannot compare two marginal distributions to see if the corresponding two are related . So, the statement is false .

The answer to the stated question is false . No , you cannot compare two marginal distributions to see if the corresponding two variables are related.

The given question is related to probability and statistics.

Coming to probability distribution , it is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.

The marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.

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Answer:

There are 5 zeros in 1.4 million

Step-by-step explanation:

1.4 million = 1 400 000

The one is in the million place and the 4 is in the hundred thousands place. The rest of the places have zeros in them

Answer:1.6

Step-by-step explanation:

25/5=5

8/5=1.6

Answer:

Step-by-step explanation:

if 5miles = 25 minutes

then, 8 miles = X

hence X minutes

\(x = \frac{25minutes}{5miles} \times 8miles\)

Answer:

13

Step-by-step explanation:

26: 1, 2, 13, 26

39: 1, 3, 13, 39

52: 1, 2, 4, 13, 26, 52

The GCF is 13.

The integral of g(x) is g(x) = -(1/2)sin(x³/2) + (1/2).

To find g(x), we use the following steps:

Therefore, the integral of g(x) is g(x) = -(1/2)sin(x³/2) + (1/2).

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Answer:

\(\frac{2}{3}\)

Step-by-step explanation:

Just simply add along the top of the numbers.

1. We know that there were 12 pieces and out of those 12 Joe ate 3 pieces and Sam ate 5.

2. So now we have the two fractions \(\frac{3}{12}\) and \(\frac{5}{12}\) we simply add them together by adding across the top, we do not need to make any changes to the denominator due to the fact that they are parts of the 12 pieces of pie

3. after adding 3 + 5 you should get 8 and since the denominator will remain the same the answer should be \(\frac{8}{12}\)

4. Now we must simplify we know 8 ÷ 4 = 2 and we can also divide 12 by 4 and that gets us 3 so make the numbers into a fraction, 3 should be on the bottom, and two on the top, and when you have your final answer your work should look somewhat similar to this:

\(\frac{3}{12}+\frac{5}{12} =\frac{8}{12} =\frac{2}{3}\)