Jessica is filling her swimming pool with water. The pool will hold 500 gallons of water,
and Jessica can pump water in at a rate of 30 gallons per hour. Write an equation that
will show how many gallons of water are in the pool as Jessica is filling it.

Answer:

35

Step-by-step explanation:

All you need to do is substitute!

(3x2)^2-1

6^2-1

36-1

= 35

Hope this helps!!

The total cost of buying 3 pairs is $830 and in six months we will make $1,500.

So, the money we pay when we buy 3 pairs of Nike Kobe 3:

The total cost of buying 3 pairs: 320+240+270 =  $830

The money we will make in six months:

Therefore, the total cost of buying 3 pairs is $830 and in six months we will make $1,500.

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Answer:

125,44

Step-by-step explanation:

Loss = 112÷100*12

=13,44

Therefore : 112 + 13%

=112 + 13,44

=125,44

Answer:

d

Step-by-step explanation:

the ratio of height : shadow of statue is 15 : 20 = 3 : 4

the ratio of height : shadow of person will also be 3 : 4

jet height of person be h , then

\(\frac{h}{4}\) = \(\frac{3}{4}\) ( cross- multiply )

4h = 12 ( divide both sides by 4 )

h = 3

then the person is 3 feet tall

Answer:

d) 3 feet

Step-by-step explanation:

Answer:

Infinite solutions

Step-by-step explanation:

Both lines have the same slope and y-intercept, therefore they are the same line and intersect at all points, resulting in infinite solutions.

The polynomial P(x) is obtained by multiplying the previous polynomial with r₁ and subtracting r₂.

Repeat the previous steps with a new value of x if the degree of the polynomial is equal to or greater than d.

We have the black box oracle for a polynomial p that takes in an input x and returns p(x). The polynomial is of an unknown degree and has positive integer coefficients. The procedure to compute what the polynomial is using only two evaluations of the black box is given below:

Let t₁ = P(a)

Let t₂ = P(b)

Let r₁ = t₁

Let r₂ = (t₂ - t₁(b - a)) / (b - a)

This gives a polynomial (x - a)(x - b) / d.

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Answer:

Its positive 18/30 and by simplifying its 3/5.

Step-by-step explanation:

Answer:

Random assignment is necessary for internal validity, whereas random assignment is necessary for external validity

Step-by-step explanation:

The 95% confidence interval for the mean test score in the population is

(639.51, 639.89).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation shown below as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are shown as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 407 - 1 = 406 df, is t = 1.96.

The parameters for this problem are given as follows:

\(\overline{x} = 639.7, s = 19.3, n = 407\)

The lower bound of the interval is given as follows:

\(639.7 - 1.96 \times \frac{19.3}{\sqrt{407}} = 639.51\)

The upper bound of the interval is given as follows:

\(639.7 + 1.96 \times \frac{19.3}{\sqrt{407}} = 639.89\)

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The statement that is not true is d. The slope of the regression line is the estimated value of y when x equals zero.

The slope of the regression line represents the change in the dependent variable (y) for a unit change in the independent variable (x).

It is not necessarily the estimated value of y when x equals zero. The value of y when x equals zero is given by the y-intercept, not the slope of the regression line.

From that we conclude that the correct option is d, the false statetement is "the slope of the regression line is the estimated value of y when x equals zero."

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Answer:

d= 8.6 ft

Step-by-step explanation:

In similar triangles, the corresponding sides are in proportion.

\(\boxed{\dfrac{AW}{MZ}=\dfrac{AJ}{MJ}=\dfrac{WJ}{ZJ}}\)

To find the value of x,

\(\dfrac{AJ}{MJ}=\dfrac{WJ}{ZJ}\\\\\\\dfrac{6}{7}=\dfrac{d}{10}\\\\\\\dfrac{6}{7}*10=d\)

d = 8.6 ft

Answer: B

Step-by-step explanation:

4(12x-6)=6(-4+5x)+18x

distribute

48x-24=-24+30x+18x

simplify

48x-24=48x-24

add 24 to both sides

48x=48x

divide by 48 on both sides

x=x

infinitely many solutions

Minimum sample size needed  such that mean of the sample is smaller than 35 and sum is 1280 is 37.

To find the minimum sample size, we need to determine the smallest number of elements in a sample that would produce an average less than 35.

To do this, we use the formula for the mean, which is the sum of the elements divided by the number of elements.

If we let x be the minimum sample size, then the sum of the elements in the sample must be smaller than 35x. Since the sum of the elements in the sample is known to be 1280, we can set up an inequality:

1280/x < 35

Solving for x, we get:

x > 1280 / 35 = 36.36

Since x must be a whole number, we round up to the next whole number, which is 37.

However, it's important to note that this is a theoretical minimum and there could be many sets of 37 elements whose sum is 1280 but whose average is less than 35.

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Complete question:

Given a sample having variable size given that sum of the sample is 1280 what is the minimum sample size needed such that mean of the sample is smaller than 35.

a. This is easily determined from examining the plot. \(p(x)\) is clearly increasing for \(4\le x\le12\) and \(x\ge19\) (more or less).

b. The population was 10000 wherever the plot of \(p(x)\) intersects the horizontal line \(p=100\). This happens twice at around \(x\approx1.5\) and \(x\approx7\).

c. The years 1994 and 2002 correspond to \(x=4\) and \(x=12\), respectively. Judging by the plot, we have \(p(4)\approx50\) and \(p(12)\approx150\), so the average rate of change in the population is

\(\dfrac{p(12) - p(4)}{12 - 4} \approx \dfrac{150 - 50}8 = \dfrac{25}2 = 12.5\)

i.e. the population increased at an average rate of 12,500 fruit bats per year between 1994 and 2002.

d. We have \(p(0)\approx180\) and \(p(20)\approx110\), so the average rate of change over the duration of the study is

\(\dfrac{p(20) - p(0)}{20 - 0} \approx \dfrac{110 - 180}{20} = -\dfrac72 = -3.5\)

i.e. the population decreased at an average rate of 3,500 fruit bats per year between 1990 and 2010.

a. \(4\leq x\leq 12\) and \(x\geq 19\)

b. x ≅ 15 and x ≅ 7 because  the plot of \(p(x)\)  intersects or meets the horizontal line \(p= 100\) at both intervals

c. 12. 5

The population increased at an average rate of 12,500 fruit bats per year between 1994 and 2002

d. -3. 5

The population decreased at an average rate of 3,500 fruit bats per year between 1990 and 2010

a. This is easily determined from examining the plot.  is clearly increasing for  and  (more or less).

\(4\leq x\leq 12\) and \(x\geq 19\)

b. The population was 10000 wherever the plot of \(p(x)\)  intersects or meets the horizontal line \(p= 100\) . This happens twice at x ≅ 15 and x ≅ 7 .

c. The years 1994 and 2002 correspond to x = 4  and x = 12 , respectively.

From the plot, we have p(4) ≅ 50  and p(12)≅ 150

The average rate of change in the population is:

\(\frac{p(12) - p(4)}{12 -4}\)

= \(\frac{150 - 50}{12 - 4}\)

= 12. 5

Thus explains that the population increased at an average rate of 12,500 fruit bats per year between 1994 and 2002.

d. We have p(0) ≅ 180 and p(20)≅ 110, so the average rate of change over the duration of the study is;

= \(\frac{p(20)- p(0)}{20 - 0}\)

= \(\frac{110 - 180}{20}\)

= -3. 5

Hence, the population decreased at an average rate of 3,500 fruit bats per year between 1990 and 2010

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Answer:19,500

Step-by-step explanation: Yw.

The value of Sin(P) = Sin(30°) = 1/2

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Triangle PQR is given.

Angle QRP is a right angle.

∠QRP = 90°

And the other two angle measures are,

∠RPQ = 30°, and ∠PQR = 60°.

The value of Sin(P) = Sin(30°) = 1/2

Therefore, SinP = 1/2.

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Answer:

7 hours

Step-by-step explanation:

each day she practices 1 hour and there are 7 days in a week so 7 hours by the end of the week

Answer:

500 kilowatt-hours.

Step-by-step explanation:

Let k = number of kilowatt-hours.

\(0.15k+30=105\\0.15k=75\\k=500\)

Therefore, Dalton used 500 kilowatt-hours of electricity.

The formula for the circumference of a circle is "c = 2 pi r", where "c" represents the circumference, "pi" represents the mathematical constant pi (approximately equal to 3.14159), and "r" represents the radius of the circle.

This formula relates the distance around a circle to its size, and is useful for calculating various measurements related to circles, such as arc length and sector area. It is important to note that the formula for the circumference of a circle assumes the circle is a perfect, unbroken curve, and thus may not be accurate for circles that are not perfectly round.

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The expected time for completion of Activity "X" on a PERT chart is 9 hours.

PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.

Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:

Optimistic time (O) = 6 hours

Most likely time (M) = 9 hours

Pessimistic time (P) = 12 hours

Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9

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Answer:

A. This conclusion was drawn using the law of detachment

Step-by-step explanation:

Definition:

Law of Detachment

If p equals q and p is also true. Then q is true.

if a number is a whole number, then it is an integer.

3 is a whole number (true statement) , so it 3 is an integer. (must be true)

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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a. Probability is denoted as P(z ≥ 1.25). b. Probability is P(z ≤ -0.5). c. Probability is denoted as P(z1 ≤ z ≤ z2). d. The probability is P(z1 ≤ z ≤ z2).

To calculate the probabilities for a normally distributed random variable with μ = 10 and σ = 2, we can use the standard normal distribution and z-scores. We will convert the given values into z-scores and then use the standard normal distribution table or a statistical calculator to find the probabilities.

a. P(x ≥ 12.5):

First, we calculate the z-score for x = 12.5:

z = (x - μ) / σ = (12.5 - 10) / 2 = 1.25

Using the standard normal distribution table or a calculator, we find the probability P(z ≥ 1.25). Let's assume this probability is denoted as P(z ≥ 1.25).

b. P(x ≤ 9):

Similarly, we calculate the z-score for x = 9:

z = (x - μ) / σ = (9 - 10) / 2 = -0.5

Using the standard normal distribution table or a calculator, we find the probability P(z ≤ -0.5). Let's assume this probability is denoted as P(z ≤ -0.5).

c. P(10.88 ≤ x ≤ 15.3):

We calculate the z-scores for both values:

For x = 10.88:

z1 = (10.88 - 10) / 2

For x = 15.3:

z2 = (15.3 - 10) / 2

Using the standard normal distribution table or a calculator, we find the probability P(z1 ≤ z ≤ z2). Let's assume this probability is denoted as P(z1 ≤ z ≤ z2).

d. P(4.72 ≤ x ≤ 12.46):

We calculate the z-scores for both values:

For x = 4.72:

z1 = (4.72 - 10) / 2

For x = 12.46:

z2 = (12.46 - 10) / 2

Using the standard normal distribution table or a calculator, we find the probability P(z1 ≤ z ≤ z2). Let's assume this probability is denoted as P(z1 ≤ z ≤ z2).

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Suppose x is a normally distributed random variable with μ=10 and σ=2. Find each of the following probabilities.

a. P(x ≥ 12.5) b. P(x ≤ 9) c. P(10.88 ≤ x ≤ 15.3) d. P(4.72 ≤ x ≤ 12.46)

The measure of side e is, 16.3 inches.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In ΔDEF, m ∠E = 54°, d = 14 in., and f = 20 in.

Now, We know that;

⇒ cos E = (d² + f² - e²) / 2df

Substitute all the values, we get;

⇒ cos 54° = (14² + 20² - e²) / 2×14×20

⇒ 0.59 = (196 + 400 - e²) / 560

⇒ 0.59 × 560 = 596 - e²

⇒ 330.4 = 596 - e²

⇒ e² = 596 - 330.4

⇒ e² = 265.6

⇒ e = √265.6

⇒ e = 16.3 inches

Thus, The measure of side e is, 16.3 inches.

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The probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is 0.68.

Given data ,

According to store records, approximately  1/ 4 of all customers who go to the service department ask for help finding an item.

All the  customers who go to the service department will not ask for help.

Now, the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is

P(X>=1)   = 1 - P(X<1)

               = 1 - (1/4)⁰ (3/4)⁴

               = 1 - (3/4)⁴

               = 0.68

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment.

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Answer:

\( →\sqrt{ - 16} + \sqrt{49} \)

\(→( \sqrt{ - 1} \times \sqrt{16} ) + ( \sqrt{49} )\\=i \sqrt{16}+\sqrt{49} \\ = 4i + 7 \\ = \boxed{7 + 4i}✓\)