The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10.
. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.

Answer:

$5,250

Step-by-step explanation:

2/7x - [4/5(2/7x)] = 300

2/7x - 8/35x = 300

10/35x = 8/35x = 300

2/35x = 300

2x = 10500

x = 5250

The null and alternative hypotheses can be stated as follows:

c. H0: µ = 12, Ha: µ ≠ 12

The null hypothesis (H0) assumes that the population mean content of the bottles is 12 ounces, indicating perfect adjustment of the filling machine. The alternative hypothesis (Ha) states that the population mean content is not equal to 12 ounces, suggesting that the machine is not in perfect adjustment.

The rejection region for α = 0.01 can be specified as:

c. |t| > 2.68

This means that we would reject the null hypothesis if the absolute value of the calculated t-statistic is greater than 2.68.

To calculate the p-value, we need the t-statistic corresponding to the sample mean and standard deviation. With a sample mean of 11.88 ounces, a standard deviation of 0.35 ounces, and a sample size of 49, we can calculate the t-statistic. The p-value represents the probability of observing a sample mean as extreme as the one obtained, assuming the null hypothesis is true.

The p-value cannot be determined without the t-statistic value or the corresponding degrees of freedom.

Without the p-value, we cannot draw a definitive conclusion. To make a conclusion, we would compare the calculated t-statistic to the critical t-value based on the chosen significance level (α = 0.01). If the calculated t-statistic falls within the rejection region (|t| > 2.68), we would reject the null hypothesis. If the calculated t-statistic falls outside the rejection region, we would fail to reject the null hypothesis.

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The ordered pair (3, - 2) is not a solution to the equation 2x - y = 4

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x,y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, an equation 2x - y = 4 now if  (3, - 2) is an ordered pair then putting the numerical value of x must satisfy the y value.

when x = 3,

2(3) - y = 4.

6 - y = 4.

- y = 4 - 6.

- y = - 2.

y = 2.

So,  (3, - 2) is not a solution to an equation 2x - y = 4.

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Answer:

18 square units

Step-by-step explanation:

the area of a parallelogram is represented by length times width

or l * w

l is 3 and w is 6

when you multiply them you get 18

you have to add the square in front of your type of unit too

The equation represents the number of gel pens, 'p' produced in 'm' minutes will be P = 8m.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a machine produces 480 gel pens per hour. The equation for the number of pens in hours can be written as,

P = 480 / 60 m

Here, P is the number of pens and 'm' is

P = 8m

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The system of equations is.

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

And the solutions are y = 50 and x = 10.

Let's define the two variables:

With the given information we can write two equations, then the system will be:

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

Now let's solve it.

We can isolate x on the first  to get:

\(\text{x} = 60 - \text{y}\)

Replace that in the other equation to get:

\(15\times(60 - \text{y}) + 10\text{y} = 800\)

\(-2\bold{y} = 900 - 800\)

\(-2\bold{y} = 100\)

\(\text{y} = \dfrac{100}{-2} = \bold{50}\)

Then \(\bold{x=10}\).

Therefore, the solutions are y = 50 and x = 10.

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what that makes no sense

The value of the puzzle is 17

The value of the triangle :

Value of Circle :

Value of whole yellow square :

Value of half-yellow square :

Using the above information:

Triangle + Circle + half-square

10 + 5 + 2 = 17

Therefore, the solution to the puzzle is 17

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First of all, we need to define Experimental probability and Theoretical probability.

• Theoretical probability, is what we expect to happen, but sometiimes it isn't what actually happens.

• On the other hand, ,experimental probability, is what it actually happens when we conduct several tries.

In our sample, let's see how many "9" we have in each random number:

• Number 1: We have 1 nine (7918)

• Number 2: We have 1 nine (7910)

• Number 3: We don't have any 9 (2546)

• Number 4: We have 1 nine (1390)

• Number 5: We don't have any nine (6075)

• Number 6: We don't have any nine (1230)

• Number 7: We don't have any nine (2386)

• Number 8: We have 1 nine (0793)

• Number 9: We have 1 nine (7359)

• Number 10: We don't have any nine (3048)

• Number 11: We don't have any nine (2816)

• Number 12: We don't have any nine (6147)

• Number 13: We have 1 nine (5978)

• Number 14: We don't have any nine (5621)

• Number 15: We have 1 nine (9732)

• Number 16: We have 1 nine (9436)

• Number 17: We don't have any nine (3806)

• Number 18: We have 1 nine (5971)

• Number 19; We don't have any nine (6173)

• Number 20: We don't have any nine (1430)

Now, we can count how many numbers have a nine:

Total is nine (numbers 1, 2, 4, 8, 9 13, 15, 16, 18)

Therefore, the experimental probability is:

Total number of 9 in the sample/Total of random numbers in the sample

9/20 = 0.45

Interpretation: The experimental probability of the sample is 45%

Answer:

(cosB-1)(cosB+6)

Step-by-step explanation:

use u substitution . u = cosB

u^2+5u-6

factor

(u-1)(u+6)

put cosB back in for u

(cosB-1)(cosB+6)

(a) Consider the sequence {1/n}, where n is a positive integer greater than 1. This sequence does not contain 0 or 1 as a term, but it contains the subsequence {1}, which converges to 1, and the subsequence {1/n}, which converges to 0.

(b) Consider the sequence {(-1)^n × n}, which alternates between positive and negative values but is unbounded. However, the subsequence {n} is increasing and unbounded, but it converges to infinity.

(c) Consider the sequence {a_n}, where a_n = 1/n for n = 1, 2, 3, ..., and let x be any positive real number. Since 1/n converges to 0 as n approaches infinity, we can choose a term in the sequence such that 1/n < x. Let N be the smallest integer such that 1/N < x. Then the subsequence {a_N} converges to x. Since x was arbitrary, this sequence contains subsequences converging to every point in the infinite set {1, 1/2, 1/3, 1/4, 1/5, ...}.

(d) Consider the sequence {(-1)ⁿ}, which alternates between 1 and -1 but is unbounded. However, the subsequence {1, -1, 1, -1, ...} is bounded and converges to 1.

(e) Consider the sequence {n/(n+1)}, which is bounded between 0 and 1 but does not converge. However, any subsequence of this sequence is either eventually increasing or eventually decreasing and must converge to either 0 or 1. Therefore, there are no subsequences that converge.

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Answer:

Step-by-step explanation:

First Choice

Answer:

\(m_{perpendicular}\) = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + 6y = - 24 ( subtract x from both sides )

6y = - x - 24 ( divide through by 6 )

y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form

with slope m = - \(\frac{1}{6}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6

5.2 inches 13.12 cm

50m

42.195 kilometers

Answer: 20% of 160 is 32.

Step-by-step explanation:

The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.

To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.

Let us now find the 20% of 160.

20% = 0.2

percentage = 160 × 0.2

= 32

Answer: C. Circle

Step-by-step explanation: i got it right good luck

When the circle is rotated then it forms the sphere. Then the correct option is C.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Whenever the 2D shape is rotated we get 3D solid.

A.  Triangle - when the triangle is rotated then it forms the cone.

B.  Square - when the square is rotated then it forms the cylinder.

C.  Circle - when the circle is rotated then it forms the sphere.

D.  Ellipse - when the ellipse is rotated then it forms the flat sphere.

Thus, the correct option is C.

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Answer:

Hey there!

The correct answer would be f(x)=(x-3)^2

Let me know if this helps :)

Answer:

48 boys

Step-by-step explanation:

Answer:

(-5, 4) The x value is -5, and the y value is 4.

The percentage of people aged 20 to 34 that  have IQs between 125 and 150 of people aged 20 to 34 have IQs between 125 and 150 is 21.94%

Percentage simply means a proportion of the number as a fraction of 100

What percent of people aged 20 to 34 have IQs between 125 and 150?

Let X = Scores on the standard IQ test for the 20 to 34 age group

This implies that  X ~ Normal(x=110, б² = 25)

The z-score probability distribution for the normal distribution is given by;   Z  =   (x-ц)/б ~ N(0,1)

Recall that  population mean = 110 and standard deviation = 25

Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X  125)

 P(X < 150) = P(  <  ) = P(Z < 1.60) = 0.9452

 P(X  125) = P(    ) = P(Z  0.60) = 0.7258

The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.

Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%

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The way that the definitions of the absolute value of a number, connect is that the absolute value of a number is the positive representation of the number's distance from zero.

The absolute value of a number is the numerical value of a real number without regard to its sign. In other words, the absolute value of a number is the number's distance from zero on the number line. The absolute value of a number is always positive or zero, and is written as the number inside of absolute value notation, which is two vertical lines on either side of the number, like so: |number|. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

The distance from zero is the same as the magnitude of a number, and the absolute value of a number is a non-negative representation of its magnitude. So, in other words, the absolute value of a number is its distance from zero on the number line. The two definitions are connected because the absolute value of a number is a positive representation of its distance from zero.

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Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.

We know that, to find volume:

Volume = π * \(r^2\) * h

For the smaller stockpot:

Radius (r) = 2.5 inches

Height (h) = 10 inches

Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches

For the larger stockpot:

Radius (r) = 2.5 inches

Height (h) = 16 inches

Volume = π * (2.5)² * 16

             ≈ 628.32 cubic inches

Thus, the volume of larger one is 628.32 cubic inches.

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Answer:

x=3

Step-by-step explanation:

3(5x + 7) = 9x + 39

15x + 21 = 9x + 39

15x - 9x = 39 - 21

6x = 18

x = 3

Answer:

C = 14 pi inches

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

49 pi  = pi r^2

Divide each side by pi

49 pi/pi = pi /pi r^2

49 = r^2

Take the square root of each side

7 = r

The circumference is given by

C = 2 * pi *r

C = 2 * pi *7

C = 14 pi inches

Answer:

The median female birth weight is  

less than

the median male birth weight.

The range of female birth weight is  

less than

the range of male birth weight.

Which birth weight measure is the same for both genders?

minimum

9514 1404 393

Answer:

  y = 4/3x -(4 2/3)

Step-by-step explanation:

The vertical difference between the two marked points is ...

  2 -(-6) = 8

The horizontal difference between them is ...

  5 -(-1) = 6

The slope is the ratio of these values:

  m = ∆y/∆x = 8/6 = 4/3

The point-slope form of the equation of the line can be written using this slope and the upper point:

  y -y1 = m(x -x1)

  y - 2 = 4/3(x -5) . . . . substitute known values.

This is an equation for the line.

__

This can be rearranged to slope-intercept form:

  y = 4/3x -20/3 +2

  y = 4/3x -14/3

  y = 4/3x -(4 2/3)

Answer: 3.34897977     -7

Step-by-step explanation:

The fraction 13/7 lies between the fractions 6/6 and 6/7.

We have,

Between the fractions 6/6 and 6/7, there are infinitely many fractions.

To find a fraction that lies between these two fractions, we can take their average.

The fraction 6/6 simplifies to 1, and the fraction 6/7 cannot be simplified further.

To find the average, we add the two fractions and divide the sum by 2:

(6/6 + 6/7) / 2

To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 6 and 7, which is 42.

Converting the fractions to have a common denominator:

(6/6) x (7/7) + (6/7) x (6/6) / 2

Simplifying the expression:

(42/42 + 36/42) / 2

Combining the numerators:

(78/42) / 2

Dividing:

78/42 = 13/7

Thus,

The fraction 13/7 lies between the fractions 6/6 and 6/7.

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Answer:

(a) $83 for 6 snacks

(b) \(y = 65 + 3x\) --- for x snacks

Step-by-step explanation:

Given

Let:

\(n \to people\)

\(ticket =\$13\) --- per individual

\(snacks = \$3\) --- per individual

Solving (a): Amount for 6 snacks

The amount paid (y) is:

\(y = ticket * n + snacks * 6\) ---- because she bought 6 snacks

\(y = 13 * n + 3 * 6\)

\(y = 13n + 18\)

\(n = 5\) ---- Annabelle and the 4 kids.

So:

\(y =13*5+18\)

\(y =65+18\)

\(y =83\)

Solving (b): For x snacks

The amount paid (y) is:

\(y = ticket * n + snacks * x\) ---- because she bought x snacks

\(y = 13* 5 + 3* x\)

\(y = 65 + 3x\)