To decrease your household water usage by 10% a month means that a household using 4000 gallons of water a month would cut down to using

Step-by-step explanation:

To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.

In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.

Answer: 82

Step-by-step explanation:

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

\(\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}\)

Part b.

Consider V(3X + 2Y)

\(\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}\)

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

\(3 X+2 Y \sim N(18,77)\)

Thus,

\(P(3 X+2 Y < 18)=0.5\)

Part d.

Consider P(3X + 2Y < 28)

\(Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}\)

\(\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}\)

Therefore, the values for the given normal random variables are found.

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The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

Answer:

10.34 cm.

Step-by-step explanation:

First we need to calculate the angle between the hour and minute hand

We see that there are 5 *  5-minute intervals between the 2 hands and the clock has 12 * 5-minute intervals, so:

This is 5/12 * 360 = 150 degrees,

So we apply the Cosine Rule to the triangle:

x^2 = 4.5^2 + 6.2^2 - 2*4.5*6.2cos150

= 107.014

x = √107.14 = 10.34.

Missing length is 10.3cm to 1.d.p

The clock is a circle divided into 12

360/12=30 degrees for each part

1) 7 to 8

2) 8 to 9

3) 9 to 10

4) 10 to 11

5) 11 to 12

5 parts

30 x 5 = 150 degrees

We've got an angle between 2 lengths - cosine rule comes to mind for me.

a = root 6.2^2 + 4.5^2 - 2x6.2 4.5 x cos 150

= 10.34476764

length is 10.3cm to 1.d.p

(the others are to 1.d.p too)

Hope this helps!

Answer:

-6 47/20

Step-by-step explanation:

Given a rectangular peice of paper

Length = 34 cm

Width = 16 cm

So, the area of the rectangle = 34 x 16 = 544 cm²

Two semicircles cut out of it

The diameter of the circle = d = 16 cm

So, the radius of the circle = r = d/2 = 8 cm

The area of the two semicircles = area of the complete circle

so, the area of the circle = πr² = 3.14 x 8² = 200.96 cm²

So, the area of the remaining paper = area of the rectangle - area of the circle

= 544 - 200.96 = 343.04 cm²

So, the answer will be Area = 343.04 cm²

Step-by-step explanation:

Sin60=x÷25

x=25Sin60

x=21.05

The probability of a child under 18 being allergic to multiple foods is approximately 32%. This means that out of every 100 children with an allergy, we would expect 32 of them to be allergic to more than one food.

To solve this problem, we need to use the information provided in the question. We know that 32% of those with an allergy are allergic to multiple foods. This means that out of every 100 people with an allergy, 32 of them are allergic to more than one food.

If we assume that allergies are equally common in all age groups, then we can use this percentage to estimate the probability of a child under 18 being allergic to multiple foods. However, it is important to note that this assumption may not be entirely accurate, as some allergies are more common in children than in adults.

Assuming that allergies are equally common in all age groups, the probability of a child under 18 being allergic to multiple foods is approximately 32%. This means that out of every 100 children with an allergy, we would expect 32 of them to be allergic to more than one food.

It is important to note that this is just an estimate based on the information provided in the question. In reality, the probability of a child being allergic to multiple foods may be higher or lower depending on a variety of factors such as genetics, environment, and diet.

In order to get a more accurate estimate of the probability of a child being allergic to multiple foods, we would need to collect more data and analyze it using statistical methods. However, based on the information provided in the question, we can conclude that there is a significant likelihood that a child under 18 with an allergy is also allergic to multiple foods.

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A spherical balloon is being filled with air at the constant rate of 8 cm³/sec How fast is the radius increasing when the radius is 6 cm?

Rate of change of radius of sphere 0.0176 cm/sec.

A spherical balloon is filled with air at the constant rate of 8 cm³/sec.

Formula used: Volume of sphere = (4/3)πr³

Differentiating both sides with respect to time 't', we get: dV/dt = 4πr²dr/dt, where dV/dt is the rate of change of volume of a sphere, and dr/dt is the rate of change of radius of the sphere.

We know that the radius of the balloon is increasing at the constant rate of 8 cm³/sec. When the radius is 6 cm, then we can find the rate of change of the volume of the sphere at this instant. Using the formula of volume of a sphere, we get: V = (4/3)πr³

Substitute r = 6 cm, we get: V = (4/3)π(6)³ => V = 288π cm³ Differentiating both sides with respect to time 't', we get: dV/dt = 4πr²dr/dt, where dV/dt is the rate of change of volume of sphere, and dr/dt is the rate of change of radius of the sphere. Substitute dV/dt = 8 cm³/sec, and r = 6 cm,

we get:8 = 4π(6)²(dr/dt)

=>dr/dt = 8/144π

=>dr/dt = 1/(18π) cm/sec

Therefore, the radius is increasing at the rate of 1/(18π) cm/sec when the radius is 6 cm.

Rate of change of radius of sphere = 1/(18π) cm/sec= 0.0176 cm/sec.

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Answer:

Y=-2x-3

Step-by-step explanation:

Y=mx+b

it goes down by 2

Answer:

here you go. :)

Step-by-step explanation:

Look at the image attached

Answer:

x = 2, 4

Step-by-step explanation:

Hi there!

x=√(2x-4)+2

Move 2 to the left:

x-2 = √(2x-4)

Square both sides:

x²-4x+4 = 2x-4

Combine like terms:

x²-6x+8 = 0

Factor:

(x-2)(x-4) = 0

Therefore, x = 2, 4.

I hope this helps!

Answer:

3,409.6 steps

Step-by-step explanation:

Given parameters:

Duration of the walk  = 9.00am to 3.00pm

Number of steps walked  = 20458 steps

Unknown:

Number of steps per hour =?

To solve this;

            Number of steps per hour  = \(\frac{Number of steps}{Duration}\)

  Duration  = 9 am to 3pm  = 6hrs

  Now input the parameters:

         Number of steps per hour = \(\frac{20458}{6}\)   = 3,409.6 steps

Total number of steps per hour is 3,409.6 steps/hour.

Answer: 5x + 6y

Step-by-step explanation:

Let's say that the Nguyen family's sprinkler was used for x hours and the Hernandez family's sprinkler was used for y hours.

So, the amount of water output by Nguyen family's sprinkler in x hours is 40x L.The amount of water output by Hernandez family's sprinkler in y hours is 25y L.Both families used their sprinklers for a combined total of 60 hours, so:x + y = 60...........(1)The combined water output of both sprinklers was 2025 L. Thus,

40x + 25y = 2025

From equation (1), we have y = 60 −

x Substitute y in equation (2) with 60 −

x:40x + 25(60 − x) = 202540x + 1500 − 25x = 202515x = 525

x = 35 hours. Substituting x in equation (1), we have y = 60 − x = 60 − 35 = 25 hours.

Answer:Hours Nguyen family's sprinkler was used: 35 hours .Hernandez family's sprinkler was used: 25 hours.

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Answer:

Step-by-step explanation:

quit

To calculate the variable cost per unit using the high-low method, the change in total cost is divided by the change in activity level.

The high-low method is a cost analysis technique used to estimate the variable and fixed components of a mixed cost. It involves using the highest and lowest levels of activity to calculate the variable cost rate and then using this rate to estimate the fixed cost component.

To calculate the variable cost per unit using the high-low method, first, the total cost and activity level are recorded for the highest and lowest levels of activity. Then, the change in total cost is calculated by subtracting the total cost at the lower level of activity from the total cost at the higher level of activity. Similarly, the change in activity level is calculated by subtracting the lower level of activity from the higher level of activity. Finally, the change in total cost is divided by the change in activity level to obtain the variable cost per unit.

It is important to note that the high-low method assumes a linear relationship between cost and activity, which may not always hold true. Therefore, this method should be used with caution and other cost analysis techniques should also be considered.

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Answer:

7. To perform a t-test when the sample size is small, the sample must show no evidence of strong skewness and must contain no outliers.

Step-by-step explanation:

These are the two conditions required for performing a t test

- Sample Size: A small sample size can reduce the statistical power of a t-test, making it more challenging to detect significant differences between groups. Generally, a larger sample size is desirable to obtain more reliable and representative results.

- Skewness: Skewness refers to the asymmetry of the distribution of data. In a t-test, assuming normality of the data is important for accurate results. If the data exhibits strong skewness, the assumption of normality may be violated. In such cases, alternative non-parametric tests or transformations of the data may be more appropriate.

- Outliers: Outliers are extreme values that significantly differ from the rest of the data. They can have a disproportionate impact on the results of a t-test, particularly when the sample size is small. Outliers can distort the mean and affect the assumptions of normality and homogeneity of variance.

While the presence of skewness or outliers does not prohibit the use of a t-test with a small sample size, it is important to interpret the results with caution and consider alternative approaches if necessary. Robust statistical methods, such as non-parametric tests or bootstrapping, can be useful when dealing with non-normal or outlier-prone data, especially with small sample sizes. Additionally, visual inspection of the data distribution, such as through histograms or box plots, can help identify potential skewness or outliers.

The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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The measures of angles of the kite are ∠JHL = 91°

Given data ,

Let the kite be represented as KLHJ

where the measure of angle ∠HLK = 128°

And , the measure of ∠JKL = 50°

Now , kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles

So , the angles are

128° + 50° + 2x = 360°

On simplifying , we get

2x = 360° - 178°

2x = 182°

Divide by 2 on both sides , we get

x = 91°

Hence , the angle of kite is 91°

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Answer:

2(3x+4)

Step-by-step explanation:

Multiply the 2 by the 3x to get 6x

Multiply the 2 by the 4 to get 8

Add 6x and 8

6x+8

Answer:

B. 2(3x+4) is correct

Step-by-step explanation:

2*3x= 6x and 2*4= 8 so you have all ur terms

(a) The value of the function f.g(x) = f(x²+9) = (x²+9)²
(b) The value of the function g.f(x) = g(x²) = x⁴+9
(c) The value of the function f.f(x) = f(x²) = (x²)²
(d) The value of the function g.g(x) = g(x²+9) = (x²+9)²+9

Domains of each:
(a) All real numbers
(b) All real numbers
(c) All real numbers
(d) All real numbers

For composite functions, you insert the second function into the first function.

(a) f.g(x) = f(g(x)) = f(x²+9) = (x²+9)²
(b) g.f(x) = g(f(x)) = g(x²) = x⁴+9
(c) f.f(x) = f(f(x)) = f(x²) = (x²)²
(d) g.g(x) = g(g(x)) = g(x²+9) = (x²+9)²+9

The domain of a function is the set of input values for which the function is defined. Since all these composite functions are polynomial functions, they are defined for all real numbers.

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The area of the Trapezium given in the question is 28ft²

The area of a trapezium is calculated using the relation :

Using the parameters given for our compuation:

height, h = 4

b1 = 9

b2 = 5

Inputting the parameters into our formula :

Area = 4/2(5 + 9)

Area = 2(14)

Area = 28ft²

Therefore, the area of the Trapezium is 28ft²

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The general form of such a model that predicts the volume of sales (Y) as a function of advertising (X) in which sales increase as advertising increases, but at a decreasing rate is given by  Y^ = b0 + b1X + b2X². Option C.

The general form of the model that fits the description of the sales model that is given in the problem is C. Y^ = b0 + b1X + b2X². Where Y^ represents the predicted or estimated value of Y. b0, b1, and b2 are the coefficients of the model, and they represent the intercept, the slope, and the curvature of the relationship between X and Y, respectively.

In this model, the variable X has a quadratic relationship with the variable Y because of the presence of the squared term X². This indicates that the effect of X on Y is not linear but curvilinear, which means that the effect of X on Y changes as X increases. Specifically, the effect of X on Y increases initially but then levels off or diminishes as X becomes larger. Answer option C.

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The case refers to the scenario where people in a city are asked if they support increasing the driving age to 18 years old. The variable in this case is the age at which individuals are allowed to start driving.

One possible significance of this case is that it sheds light on the public's perception and attitude towards driving and road safety. The fact that there is a debate about the optimal age at which to start driving highlights the importance of ensuring that drivers are competent and responsible enough to handle the risks and challenges associated with driving. Therefore, the results of this survey can help policymakers and stakeholders to make informed decisions about road safety regulations and policies.

In this case, the scenario talks about whether people in a city support increasing the driving age to 18 years old. The variable in this case is the age at which individuals are allowed to start driving. This survey is essential to bring out the public's perception and attitude towards driving and road safety. The results of the survey will help policymakers to take appropriate decisions to ensure road safety regulations and policies.

Thus, the survey will help the government and policymakers to gather data about what the public thinks about the issue. They can analyze the data, find out the areas that need to be addressed, and take appropriate action to increase road safety.

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The balance in the account after three years, rounded to the nearest dollar, is $2711.

To find the balance after three years for an account that pays 2.5% annual interest compounded monthly when $2500 is deposited in the account, you need to use the formula for compound interest.

A = P(1 + r/n)^(nt), whereA is the balance after three years, P is the principal amount ($2500), r is the annual interest rate (2.5%),

n is the number of times the interest is compounded per year (12 months), and t is the time in years (3 years).

Substituting the values in the formula,

we get:A = 2500(1 + 0.025/12)^(12*3)A

= 2500(1.00208333)^36A

= 2500(1.084297)A = $2710.74

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If we define our population as all the households in the city of Chicago and use the Chicago telephone directory to draw our sample units, we would likely have a survey with sample frame error. Correct option is A.

Sample frame error occurs when the sampling frame, in this case, the Chicago telephone directory, does not accurately represent the population of interest.

In this case, the telephone directory would exclude households without a landline phone or those who choose not to have their phone number listed. This means that the sample would not include all households in the population, leading to biased results.

A representative survey (option B) would be one in which the sample accurately represents the population in terms of relevant characteristics such as age, gender, income, education, and other important demographic factors.

In contrast, a survey containing error (option C) is a general term that includes both sampling error and non-sampling error, such as measurement error or response bias.

Finally, a census (option D) is a study in which data is collected from all individuals or units in a population, not just a sample. Therefore, using a telephone directory to draw a sample from the population does not constitute a census.

In conclusion, using the Chicago telephone directory to draw a sample of households would likely result in a survey with sample frame error, which can lead to biased results and limit the generalizability of the findings to the entire population.

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Answer:

x= 15/2 im pretty sure

Step-by-step explanation:

We want to solve the given linear equation, we will find that the solution is x = -3.7

Here we have the equation:

3.8 = 2*x - 11.2

We want to solve this for x, so we can start by subtracting 11.2 in both sides to get:

3.8 - 11.2 = 2*x

-7.4 = 2*x

Now we can divide both sides by 2:

-7.4/2 = x = -3.7

So the solution is x = -3.7

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