Joel built a model town. He constructed three buildings that each had a volume of 18 cm cubed. Each building looked different. What might Joe's buildings have looked like?

The equation of the function in slope-intercept form is: y = -4x + 5.

The slope-intercept form of an equation that represents a function is expressed as y = mx + b.

Given the table:

x  |  y  

-2   13

2    -3

6    -19

10   -35

Step 1: Using two pairs of values from the table, (-2, 13) and (2, -3), find the slope:

Slope (m) = change in y / change in x = (-3 - 13) / (2 - (-2))

m = -16/4

m = -4

Step 2: Find the y-intercept (b) by substituting m = -4 and (x, y) = (2, -3) into y = mx + b.

-3 = -4(2) + b

-3 = -8 + b

-3 + 8 = b

5 = b

b = 5

Step 3: Write the equation in slope-intercept form by substituting b = 5 and m = -4 into y = mx + b.

y = -4x + 5

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The quotient of the division 10x² + 3x - 77 ÷ 2x + 7 is 5x - 16

The quotient expression is given as

10x² + 3x - 77 ÷ 2x + 7

The long division expression is represented as

2x + 7 | 10x² + 3x - 77

So, we have the following division process

            5x - 16

2x + 7 | 10x² + 3x - 77

            10x²  + 35x

          --------------------------------

             -32x - 77

             -32x - 112

          -------------------------------------

                      35

Hence, the quotient of the long division is 5x - 16

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It takes approximately 1.2 minutes to move the cans to the storage area when both conveyor belts are used.

We can begin the problem by using the formula:

work = rate x time

Let's denote the rate of the first belt as R1 and the rate of the second belt as R2. Then, we can write:

R1 = 200 pounds / 2 minutes = 100 pounds per minute

R2 = 200 pounds / 3 minutes ≈ 66.67 pounds per minute

When both belts are used, they work together to move the same 200 pounds of cans. Therefore, we can add their rates to get the total rate:

R = R1 + R2 = 100 + 66.67 = 166.67 pounds per minute

To find the time it takes to move the cans to the storage area, we can rearrange the formula:

time = work / rate

The total work is 200 pounds, so we have:

time = 200 pounds / 166.67 pounds per minute ≈ 1.2 minutes

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Answer:

The answer C  earn it

Answer:

-1

Step-by-step explanation:

Given,

f(x) = -x² + 4x - 1 and x = 0

Putting the value of x we get,

f(0)= \(-0^{2}\) + (4 X 0) - 1

    = -0+0-1

    =-1

∴f(x)= -1

So, the required value is -1

Answer:

288 !

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

Answer:

-2.1

Step-by-step explanation:

its a 0.1 step.

hope you understand

Answer:

Thats incorrect. 684+270=954. 654+ would be saying a number thats 654 or higher. But not stating the real total.

Step-by-step explanation:

Hope this helped!! :)

Hydraulic engineers in the US use the acre-foot as a unit of water 9. A thunderstorm dumped 2.9 inches of rain in 30 minutes, resulting in a total volume of 4046.86 cubic feet of water. The volume of rainwater is calculated as 36 km² × 2.9 in × (1 ft/12 in) = 2.35 km³, which equals 325,851 US gallons. The total volume of water that fell on the town is 218,241 acre-feet.

Hydraulic engineers in the United States often use, as a units of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre (where 1 acre =43560ft ) of land to a depth of 1ft. A severe thunderstorm dumped 2.9in. of rain in 30 min on a town of area 36 km2.

Given:

Area of town = 36 km²

Depth of rain = 2.9 inches

Time taken for rain = 30 minutes

We know, 1 acre = 43,560 ft².

∴ 36 km² = 36 × 10³ × 10³ m² = 36 × 10⁶ m²

1 acre = 43,560 ft² = 43,560/10.764 = 4046.86 m²

1 ft = 12 in

Therefore, 1 acre-ft of water = 4046.86 ft² × 1 ft = 4046.86 cubic feet of water= 4046.86/43560 = 0.092903 acre-ft of water

The volume of rainwater, V = area × depth

= 36 km² × 2.9 in × (1 ft/12 in)

= 2.35 km³Since 1 km³ = 264,172,052.3581 US gallons

1 acre-ft of water = 325,851 gallons2.35 km³ = 2.35 × 10⁹ acre-ft

Therefore, the volume of water that fell on the town is 2.35 × 10⁹ × 0.092903 = 218,241 acre-feet.

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Answer:

FA: Chord

BO: Radius

CO: Radius

DO: Radius

EO: Radius

CE: Diameter

Step-by-step explanation:

Hello!

Some lines in a circle:

Segment FA

This has endpoints inside the circle, but doesn't go through the center. This is a chord.

Segment BO

BO has an endpoint on the center and and an endpoint on the perimeter. This is a radius.

Segment CO

This is also a radius, it has an endpoint on the center and another endpoint on its perimeter.

Segment DO

This is a radius, it has n endpoint on the center and another endpoint on the perimeter

Segment EO

Another radius, with a an endpoint on the center and another endpoint on the perimeter.

Segment CE

A diameter. It has two endpoints on the perimeter of the circle and goes through the center of the circle.

Answer:

a)polynomial highest degree of polynomial = 5

b) polynomial highest degree of polynomial = 6

c)polynomial highest degree of polynomial = 4

d)polynomial highest degree of polynomial = 1

e) polynomial highest degree of polynomial = 0

f)polynomial highest degree of polynomial = 5

g)polynomial highest degree of polynomial =4

h)polynomial highest degree of polynomial = 8

i)polynomial highest degree of polynomial =6

j)polynomial highest degree of polynomial =4

k)polynomial highest degree of polynomial =8

i)polynomial highest degree of polynomial =4

Hope it helps

Answer:

\sqrt{7}i or -\sqrt{7}i

Step-by-step explanation:

square root both sides of the equation

since you can't sqrt a negative number, you substitute sqrt of -1 to i

Which gets the answer.

well, the volume of that triangular prism will just be the area of the triangle times the length.

now, what's the area of that triangular face?  well, let's say it has a base of "b" and a height of 3, whilst the prism has a length of 6, Check the picture below.

\(\stackrel{\textit{triangle's area}}{\cfrac{1}{2}(b)(3)}\stackrel{\textit{prism's length}}{(6)}~~ = ~~4\frac{1}{2}\implies 9b=\cfrac{9}{2}\implies b=\cfrac{9}{18}\implies b=\cfrac{1}{2}\)

To find the interval of convergence of the series sigma^infinity_n=1 (5x)^n/n, we will follow these steps: Apply the Ratio Test to find the radius of convergence, Test the series' behavior at the endpoints of the interval specified by the radius of convergence.

Step 1: Ratio Test
Consider the series |a_n+1/a_n| = |((5x)^(n+1)/(n+1))/((5x)^n/n)| = |5x| * |n/(n+1)|. We want to find the limit as n approaches infinity: lim (n->infinity) (|5x| * |n/(n+1)|).

lim (n->infinity) (|n/(n+1)|) = 1, so lim (n->infinity) (|5x| * |n/(n+1)|) = |5x|. For convergence, we need this limit to be less than 1.

|5x| < 1

Divide both sides by 5:

|x| < 1/5

This means -1/5 < x < 1/5, so our interval is (-1/5, 1/5).

Step 2: Test endpoints
At x = -1/5, the series becomes sigma^infinity_n=1 (-1)^n/n. This is an alternating series that converges by the Alternating Series Test since the terms decrease in magnitude and tend to zero as n approaches infinity.

At x = 1/5, the series becomes sigma^infinity_n=1 (1)^n/n, which is the Harmonic series (sigma^infinity_n=1 1/n). The Harmonic series is known to diverge.

Therefore, the interval of convergence is [-1/5, 1/5), which includes the left endpoint but not the right endpoint.The test for the convergence or divergence of the power series is called Integral test

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The Law of Sines says that for a given triangle, the ratio between the sine of an angle and the length of the opposite side is the same for all three angles in a triangle. the sine values of all three internal angles will be the samethe sine values of all three internal angles will be proportional to each otherthe ratio between the sine of the angle and the opposite side will match for all three internal anglesthe sine values of all three angles will be different

In a triangle, we have three angles and three sides. The Law of Sines says that for any triangle, the ratio between the sine of an angle and the length of the opposite side will be the same for all three angles. In other words, the sine values of each angle are proportional to the length of the opposite side.

To put this in mathematical terms, let's consider a triangle with angles A, B, and C, and sides a, b, and c respectively. The Law of Sines can be written as:

sin(A)/a = sin(B)/b = sin(C)/c

This means that if we know the length of any two sides and the measure of the angle opposite one of those sides, we can use the Law of Sines to find the measure of the other angles and sides.

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Gram-negative bacteria generally include lipopolysaccharide (LPS) in their cell walls. Therefore, the type of cell we would find lipopolysaccharide in its cell wall is gram-negative bacteria.  

Compared to gram-positive bacteria, gram-negative bacteria have a more intricate cell wall construction. Gram-negative bacteria's outer membrane contains a significant amount of LPS, which is essential for maintaining structural integrity and providing defence against foreign invaders. It is made up of a lipid portion that is embedded in the outer membrane and a polysaccharide section that extends outside of it.

The distinctive traits and abilities of gram-negative bacteria, such as their resistance to some antibiotics and their capacity to incite inflammatory reactions in host species, are made possible by the presence of LPS in the cell wall.

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The size sample would be needed to estimate the proportion of black with an error of no more than 0.05 and a confidence level of 95% is 289.

The size sample can be calculated with the equation as follows:

\(n=(\frac{Z_{1-\frac{a}{2} }^ }{a})^{2} P (1-P)\)

where,

n = size sample

\(Z_{1-\frac{a}{2} }^{2}\) = 1.96 for \(a\)=0.05

\(P\) = population

\(a\) = margin of error

Therefore,

\(n=(\frac{1.96^{}}{0.05})^{2} 0.25(1-0.25)\)

\(n=(\frac{1.96^{}}{0.05})^{2} 0.25(0.75)\)

\(n=288.12\) ≈ 289

The number of size sample is 289

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The quadratic spline interpolants f(x) passes through all given data points, x and y.

Given x and y values,

x: 1, 2.25, 3.7, 5.1

y: 4.25, 6, 13.7, 15.1

The quadratic spline interpolant for the given data is given by

f(x) = {4.25(x − 2.25)(x − 3.7)}/(1−2.25)(1−3.7) + {6(x − 1)(x − 3.7)}/(2.25−1)(2.25−3.7) + {13.7(x − 1)(x − 2.25)}/(3.7−1)(3.7−2.25) + {15.1(x − 1)(x − 2.25)}/(5.1−1)(5.1−2.25)

It can be written in the following format:

f(x) = {4.25(x − 2.25)(x − 3.7)}/2.0625 + {6(x − 1)(x − 3.7)}/2.1875 + {13.7(x − 1)(x − 2.25)}/8.97 + {15.1(x − 1)(x − 2.25)}/13.815

The graph of the quadratic spline interpolant is shown below:

quadratic spline interpolant graph

The quadratic spline interpolant f(x) passes through all given data points, x and y.

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Answer:

73=y

X=35

This is because the triangle is a total of 180 and the line has a value of 180

assume you want 15 participants in each condition of your experiment, which uses a 2x3 factorial design has total number of participants 15 x 3 = 45 participants

A 2x3 factorial design is composed of two independent variables and three levels for each variable. The number of participants required for each condition is equal to the number of levels in each variable (2 x 3 = 6). To determine the total number of participants required for the experiment, multiply the number of participants per condition by the number of conditions (15 x 6 = 90). If the experiment uses a repeated measures design, then the total number of participants required is half of this amount (90 / 2 = 45).

15 x 3 = 45 participants

assume you want 15 participants in each condition of your experiment, which uses a 2x3 factorial design has 15 x 3 = 45 participants

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Answer: 6

Step-by-step explanation: 8 x 6 = 48, so therefore 8)48 would be 6.

Answer:

8 / 48

Step-by-step explanation:

quotient = 0

remainder = 8

Brainiest please

A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...

Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.

The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Example'

The cumulative distribution function for the above probability distribution is calculated as follows:

The probability that \(X\) is less than or equal to is 0.1,

the probability that \(X\) is less than or equal to 2 is 0.1+0.3 = 0.4,

the probability that \(X\) is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and

the probability that \(X\) is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.

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The measure of angle C is B) 30 degrees.

To find the measure of angle C, we can use the fact that the sine of angle C is equal to the ratio of the length of the opposite side to the hypotenuse. That is, sin(C) = 5/10 = 1/2. From the unit circle, we know that sin(30 degrees) = 1/2. Therefore, angle C must be 30 degrees.

Alternatively, we can use the fact that the triangle is a 30-60-90 triangle. In such a triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is sqrt(3) times the length of the shorter leg.

In our triangle, the shorter leg is 5, so the hypotenuse is 10, and the longer leg is 5*sqrt(3). Therefore, angle C must be B) 30 degrees, which is the measure of the smaller angle in a 30-60-90 triangle.

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Answer:

9 days

Step-by-step explanation:

Day 1 20 min

Day 2 20 min

Day 3 30 min

Day 4 30min

Day 5 40 min

Day 6 40 min

Day 7 50 min

Day 8 50 min

Day 9 60 min

Answer:

find the LCM of the dimensions of the slabs

=420

The threshold for what constitutes a small p-value depends on the significance level chosen for the test.

a) If the null hypothesis is true, the test statistic will have the t distribution with n-1 degrees of freedom.

This statement is true. When conducting a hypothesis test on a population mean with unknown variance, the test statistic follows a t-distribution with n-1 degrees of freedom under the null hypothesis.

b) In this scenario, the methods used in STAT2040 will only work if n > 30.

This statement is false. The methods used in STAT2040, such as the t-test for a population mean, can be used for sample sizes smaller than 30, but the distribution of the test statistic may not be exactly t-distributed in such cases.

c) If the null hypothesis is true, the p-value will have a continuous uniform distribution between 0 and 1.

This statement is false. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true. The p-value depends on the test statistic, the null hypothesis, and the alternative hypothesis, and does not have a fixed distribution.

d) A very small p-value implies strong evidence against the null hypothesis.

This statement is true. A small p-value indicates that the observed test statistic is unlikely to have occurred by chance alone, assuming the null hypothesis is true. This provides evidence against the null hypothesis and supports the alternative hypothesis. The threshold for what constitutes a small p-value depends on the significance level chosen for the test.

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To determine which numbers are solutions we need to solve the inequality:

Therefore the numbers less than zero are solutions.

From the options given we conclude that -3 is solutions to the inequality, therefore the answer is 4.

Answer:

Step-by-step

3

In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.

Given that,

In the picture there are 2 problems.

We have to find the difference and similarities of question in the picture.

The similarities are they 2 are word problems.

Another similarity is they two have to find 2 question.

1. How much money for 10 days and How many days to collect the money $1.05?

2.How much gallon of water need for 50 minutes and How much time take to fill the pool?

Another similarity is they two have to justified the answer in a mathematical model.

Now,

The difference is,

First question has given sisters and money problem where as the second has given pool and gallon water problem.

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