given the vertex at (-4, 5) and a-value of 5, write the vertex form of the quadratic equation.

Answer:

-8

Step-by-step explanation:

Following Order of Operations rules, we evaluate anything within parentheses first:

8-[12-(-4)] = 8 - 16 = -8

The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

A two-sided confidence interval is appropriate because the research question is about whether the average mileage is significantly different from 300 miles.

(a) To determine if a one-sided or two-sided confidence interval is appropriate for this situation, we need to consider the research question and the nature of the hypothesis being tested. If the research question is specifically focused on whether the average mileage is less than or greater than 300 miles, then a one-sided confidence interval would be appropriate. On the other hand, if the research question is broader and seeks to determine whether the average mileage is significantly different from 300 miles (i.e., it could be less or greater), then a two-sided confidence interval would be appropriate.

(b) To compute a 95% confidence interval, we can use the formula:

CI =X ± (Z * (σ/√n))

Where X is the sample mean, Z is the z-value corresponding to the desired confidence level (in this case, 95% corresponds to Z = 1.96 for a large enough sample), σ is the population standard deviation (unknown, so we use the sample standard deviation), and n is the sample size.

Plugging in the given values:

CI = 285 ± (1.96 * (50/√226))

Simplifying the expression:

CI = 285 ± (1.96 * 3.322)

CI = [278.15, 291.85]

Interpretation: The 95% confidence interval for the average mileage from Pullman to home is [278.15, 291.85]. This means that we are 95% confident that the true average mileage of all Washington State University students falls within this interval. It suggests that based on the sample data, the average mileage is likely to be between 278.15 and 291.85 miles.

(c) If the confidence level is decreased to 90%, the new confidence interval will be narrower since a smaller confidence level requires less certainty, resulting in a narrower interval. Conversely, if the confidence level is increased to 99%, the new confidence interval will be wider as a higher confidence level demands greater certainty, leading to a wider interval to capture a larger range of potential values. Therefore, the answer is D. narrower for a confidence level of 90% and A. wider for a confidence level of 99%.

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The matches between the functions and the growth or decay factors are as follows:

y = 0.3(0.5)^x matches with Decay factor 50%

y = 3(0.85)^x matches with Decay factor 15%

y = 800(1.15)^x matches with Growth factor 15%

y = 1200(1.05)^x matches with Growth factor 5%

y = 2000(45)^x matches with Decay factor 20%

Matching the functions to the correct growth or decay factors, we have:

y = 0.3(0.5)^x -> Decay factor 50%

This function exhibits exponential decay with a base of 0.5, indicating a decay factor of 50%.

y = 3(0.85)^x -> Decay factor 15%

This function demonstrates exponential decay with a base of 0.85, representing a decay factor of 15%.

y = 800(1.15)^x -> Growth factor 15%

This function displays exponential growth with a base of 1.15, indicating a growth factor of 15%.

y = 1200(1.05)^x -> Growth factor 5%

This function represents exponential growth with a base of 1.05, indicating a growth factor of 5%.

y = 2000(45)^x -> Decay factor 20%

This function exhibits exponential decay with a base of 45, indicating a decay factor of 20%.

In summary, the matches between the functions and the growth or decay factors are as follows:

y = 0.3(0.5)^x matches with Decay factor 50%

y = 3(0.85)^x matches with Decay factor 15%

y = 800(1.15)^x matches with Growth factor 15%

y = 1200(1.05)^x matches with Growth factor 5%

y = 2000(45)^x matches with Decay factor 20%

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The probability that the life span of the monitor will be more than 17,340 hours is approximately 0.0359, rounded to four decimal places.

We can use the standard normal distribution to solve this problem by standardizing the value of 17,340 hours to a z-score:

z = (17340 - 15000) / 1300 = 1.8

Using a standard normal distribution table or calculator, we find that the probability of getting a value greater than 1.8 is 0.0359.

Therefore, the probability that the life span of the monitor will be more than 17,340 hours is approximately 0.0359, rounded to four decimal places.

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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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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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To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Answer:

Y=3 over 2 -4

Step-by-step explanation:

Step-by-step explanation:

Multiply 5 by itself until you get 125.

Therefore, the area of the trapezoid is 40 square centimeter.

The formula for the area of a trapezoid is Area = (1/2) * (b1 + b2) * h, where b1 and b2 are the lengths of the bases, and h is the height.

Given the measurements of the trapezoid as one base being 6 cm, the second base being 4 cm, and the height being 8 cm, we substitute these values into the formula:

Area = (1/2) * (6 + 4) * 8

Simplifying the expression within the parentheses:

Area = (1/2) * 10 * 8

Performing the multiplication:

Area = 5 * 8

Further simplifying the expression:

Area = 40

Area = (1/2) * (6 + 4) * 8

= (1/2) * 10 * 8

= 5 * 8

= 40 square cm

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Answer:

Im not sure that really makes sense but I think your grade would be 90% if you did 8/9 or somewhere around that

Step-by-step explanation:

The statement that is true about Scientific process and method is the scientific process is a continuous process of collecting data and refining hypothesis.  

Studies and researches are done by a scientific method which follows certain standards and protocols. The method starts with an observation, a question is asked why it happens and formulating a hypothesis. Either we can do a controlled experiment to test whether the hypothesis is correct or not, or we can do a non-experimental hypothesis, where experimenting will not be ethical.

The scientific process is a continuous process, which need to be collecting data and refining hypothesis. Even our data support hypothesis, the data might not be true in some cases. So work on a scientific concept is never complete. Even if we have data on causes and effects of a natural phenomena, we could not necessarily predict it every time, example: earthquake. Also, while collecting data, we should be fair in its treatment. We can't take data that only support our hypothesis.

So, the correct statement is option c. Scientific process is a continuous process of collecting data and refining hypotheses.

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Answer:it is 4

4*4=16,4*11=44,  4*7=28

Step-by-step explanation:

The greatest common factor of 16, 44, and 28 is 4.

The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.

We also know that distributive property states a(b + c) = ab + ac.

Given, are three numbers 16, 44, and 28.

All numbers are divisible by 2 but it is not GCD.

The GCD of three numbers 16, 44, and 28 is 4 as 4 is the highest number

that cam divides each of these numbers.

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the sum of squares of number of 6,7 and 8 is 149.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

the product of three consecutive positive integers is 8 times thier sum.

So if 1st number is x

So the sum will be x+x+1+x+2 = 3x+3

and multiply will be x(x+1)(x+2)

according to question x(x+1)(x+2) = 24(x+1)

x³+3x²+2x = 24x+24

x = 6

So all the numbers will be 6,7 and 8

Hence the sum of their square is 36+49+64= 149

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Redundant bits are additional bits added to the data bits to achieve this purpose.

The number of redundant bits necessary for a code is related to the number of data bits to ensure error detection and correction in transmitted data. In general, redundant bits are additional bits added to the data bits to achieve this purpose.

To determine the number of redundant bits (r) needed for a specific number of data bits (k), you can use the following inequality:

\(2^r ≥ k + r + 1\)

Here, r is the number of redundant bits, and k is the number of data bits.

Step-by-step explanation:

1. Identify the number of data bits (k) in the code.
2. Use the inequality\(2^r ≥ k + r + 1\)to find the minimum value of r (redundant bits) that satisfies the inequality.
3. The value of r obtained will be the number of redundant bits necessary for the code.

By adding redundant bits to the data, it helps in detecting and correcting errors during data transmission, thereby ensuring the accuracy and reliability of the information being communicated.

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Answer:a18 b7

Step-by-step explanation:

i’m right

The row and column totals will be the same as for the observed frequency is 86.4.To find the expected number of people who get fewer than 6 hours of sleep per night and are age 39 or younger, you can use the formula for expected frequency:

Expected Frequency = (Row Total * Column Total) / Grand Total

Let's call the expected frequency "EF."

For the "fewer than 6 hours" row, the total is 72. For the "39 or younger" column, the total is 240. The grand total is 500.

Plugging in the values into the formula:

EF = (72 * 240) / 500

Calculating the result:

EF = 86.4

So, the expected frequency is 86.4, which means that you would expect 86.4 people in the sample to get fewer than 6 hours of sleep per night and be age 39 or younger.

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Answer:

x=40

Step-by-step explanation:

If the large angle is bisected, the two smaller angles are equal

x+30 = 3x-50

Subtract x from each side

x+30 -x = 3x-50-x

30 = 2x-50

Add 50 to each side

30+50 = 2x-50+50

80 =2x

Divide by 2

80/2 = 2x/2

40 =x

Answer:

x = 40

Step-by-step explanation:

since line KN bisects that angle, the two parts are equal to each other:

(x+30) = (3x-50)

x + 30 = 3x - 50

-2x = -80

x = 40

you can even check it to see if both angles are equal to each other by substituting 40 for x:

(40 + 30) = (3*40 - 50)

70 = 70

this checks out, so the answer is correct

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

A = (-6, 3) B = (-3,0) C = (-7,1)

Step-by-step explanation:

Subtract 4 from every X coordinate and subtract 1 from every Y coordinate. So you can write out each point like this A(-2-4,4-1) B(1-4,1-1) and C(-3-4,2-1)

(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x

The probability mass function p(x) can be derived from the cdf by taking differences:

p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06  x = 10.1  x = 20.17 x = 30.36  x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)

The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.

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Answer:

x/3=y/2

Step-by-step explanation:

x+3/3 = y+2/2

2(x+3)=3(y+2)

2x+6=3y+6

2x=3y

x/3=y/2

The eigenvalues of the matrix [0 -3; 1 -2] with multiplicity two twice are 2, 2, and -3.

The matrix given is:

[ 0 -3 ]

[ 1 -2 ]

To find the eigenvalues of this matrix, we need to solve the characteristic equation:

det(A - λI) = 0

where A is the matrix, λ is the eigenvalue, and I is the identity matrix. Substituting the given matrix, we get:

det([0 -3; 1 -2] - λ[1 0; 0 1]) = 0

Simplifying the above expression, we get:

det([-λ -3; 1 -2 - λ]) = 0

Expanding the determinant, we get:

(-λ) * (-2 - λ) - (-3) * 1 = 0

Simplifying the above expression, we get:

λ^2 - 2λ + 3 = 0

Solving the above quadratic equation, we get:

λ = (2 ± √(-8)) / 2 = 1 ± i√2

Since the given matrix has multiplicity two for one of the eigenvalues, the correct answer is (c):

λ = 2 (multiplicity two) and λ = -3.

Therefore, the eigenvalues of the matrix [0 -3; 1 -2] with multiplicity two twice are 2, 2, and -3.

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Answer:

c

Step-by-step explanation:

week 4 = 11

start = 3

11 - 3 = 8

answer is c

The correct Answer is: C. 8 inches

Step-by-step explanation:

If the plant started out at 3 inches and finished after 4 weeks at 11 inches, we can do 11-3 to find how much growth the pepper plant had.

11 - 3 = 8, therefore our answer is

C. 8 inches

Answer:

Standard Form

ax^2 +bx + c = 0

Notice you can already solve for the y-intercept which is (0,4) or y=4

It is not required to calculate the standard error of a sample mean or the standard error of an estimate in general.

False. The standard error is a measure of the variability of the sample mean and is calculated using the sample standard deviation and sample size, without necessarily requiring the calculation of the pooled variance.

The pooled variance, on the other hand, is a statistic used in hypothesis testing when comparing means from two independent samples, assuming that the two populations have equal variances. It is calculated by pooling the variances of the two samples, weighted by their degrees of freedom, and is used to calculate the standard error of the difference between the means.

While the pooled variance can be used to calculate the standard error of the difference between two means, it is not required to calculate the standard error of a sample mean or the standard error of an estimate in general.

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Answer:

part a: 840 if she withdrew the first month down to 730 and the rate it decreases is 110 then it is 840

part b: 110every month she withdraws 55 dollars because 55 plus 55 is 110

so every 2 months she would have withdrawn 110 dollars

Step-by-step explanation:

2 pounds is equivalent to approximately 9 cups. both are unit of measurement of weight.

There are several ways to convert weight measurements, such as pounds, to volume measurements, such as cups. However, it is important to note that the conversion will vary depending on the substance being measured.

In general, one pound of a dry ingredient such as flour or sugar is equivalent to approximately 2 cups. Therefore, 2 pounds is equivalent to approximately 4 cups. However, this conversion may vary depending on the substance and the measurement method.If you are measuring a liquid, 1 pound is equivalent to 16 ounces.

1 cup is equivalent to 8 ounces. Therefore 2 pounds is equivalent to 32 ounces or 4 cups.It's also important to note that weight measurements are more precise than volume measurements, as volume measurement can be affected by factors such as how tightly packed the ingredient is, so it is best to use weight measurements for accurate measurements.

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Answer:

1 5/7

Step-by-step explanation:

\(\frac{12}{7} \\= 12\div 7 = 1\: remainder\: 5\\\\= 1 \frac{5}{7}\)

Answer: 1 and 5/7

Step-by-step explanation: To write an improper fraction as a mixed number,

divide the denominator into the numerator.

So here, we have 7 divided into 12.

7 divides into 12 one time, 1 × 7 is 7, and 12 - 7 is 5.

So 7 divides into 12 one time with a remainder of 5.

So we have 1 whole and 5 out of 7 parts or 1 and 5/7.

So the improper fraction 12/7 can be written

as the mixed number 1 and 5/7.