A figure is drawn on the coordinate plane. Its points are located at D (-4, 4), E (4, 4), F (4, -2) and G (-4, -2). What is the difference between the perimeter and area of the figure.

Equation [tex]3x^{2}[/tex] - 10 = 0 has two real and irrational roots, which are [tex]±\sqrt{10}[/tex]. Therefore, the best description of the roots is "real and irrational."

To use the discriminant to describe the roots of the equation [tex]3x^{2}[/tex] - 10 = 0, we can first recall that the discriminant is the expression under the square root sign in the quadratic formula, which is [tex]b^{2}[/tex] - 4ac for the general quadratic equation [tex]ax^{2}[/tex] + bx + c = 0. In this case, we have a = 3, b = 0, and c = -10, so the discriminant is:

[tex]b^{2}[/tex] - 4ac = [tex]0^{2}[/tex] - 4(3)(-10) = 120

Since the discriminant is positive, the roots of the equation are real. Furthermore, since the discriminant is not a perfect square, the roots are irrational. Specifically, the roots can be found using the quadratic formula:

[tex]x = (-b +- \sqrt{(b² - 4ac)} ) / (2a)[/tex]

= [tex](0 +- \sqrt{120} ) / (2(3))[/tex]

= [tex]+-\sqrt{10}[/tex]

Thus, the equation [tex]3x^{2}[/tex] - 10 = 0 has two real and irrational roots, which are [tex]+- \sqrt{10}[/tex]. Therefore, the best description of the roots is "real and irrational."

Learn more about roots here:

https://brainly.com/question/12029673

#SPJ1

The answer is 4228.3

The volume of a hemisphere with a radius of 9.7 cm can be found using the formula:

V = (2/3)πr^3

where r is the radius of the hemisphere and π is approximately 3.14159.

Substituting r = 9.7 cm, we get:

V = (2/3)π(9.7 cm)^3

V ≈ 4228.278 cm^3

Rounding this to the nearest tenth of a cubic centimeter, we get:

V ≈ 4228.3 cm^3

Therefore, the volume of the hemisphere is approximately 4228.3 cubic centimeters.

To know more about volume of hemisphere visit : https://brainly.com/question/23118911

#SPJ1

Answer: $14,983.50

Step-by-step explanation:

The measurement for side DH which is perpendicular to BC is 6 + √(3) cm.

To find the measurement of DH, use the given information and apply some geometry concepts.

First, use the fact that FC is parallel to AB and AD is parallel to BC to conclude that triangle ABD is similar to triangle FCB (by the AA similarity criterion).

Next, use the fact that A line F is parallel to BE and triangle A line F and B is similar to triangle EFB to conclude that A  F/EB = AB/BE (by the similarity ratio of corresponding sides).

Using these two similarities, set up a proportion:

AB/BD = FC/CB

Substituting the given values:

AB/BD = 12/BD = 6/BC = 6/6 = 1

Therefore,  AB = BD.

Now, using the fact that EG is perpendicular A line F to conclude that triangle AEG is a right triangle.

Using the Pythagorean theorem, find the length of AG:

AG² = AE² + EG² = (A line F - FE)² + EG² = (12 - BD)² + 5²

But we know that AB = BD, so substitute AB for BD:

AG² = (12 - AB)² + 5²

Next, use the fact that DH is perpendicular to BC to conclude that triangle BHD is a right triangle.

Using the Pythagorean theorem, find the length of BD:

BD² = BH² + DH²

But AB = BD, so substitute AB for BD:

AB² = BH² + DH²

Now set up a system of equations:

AG² = (12 - AB)² + 5²

AB² = BH² + DH²

Substituting AB² for BH² + DH² in the first equation:

AG² = (12 - AB)² + 5² = (12 - AB)² + AB²

Expanding and simplifying:

AB² - 24AB + 119 = 0

Solving for AB using the quadratic formula:

AB = (24 ± √(24² - 41119))/2 = 12 ± 5√(3)

Since AB = BD:

BD = AB = 12 ± 5√(3)

We can discard the negative solution because BD must be positive.

Now we can use the Pythagorean theorem to solve for DH:

DH² = AB² - BH² = AB² - (BC - DH)² = (12 ± 5√(3))² - (6 - DH)²

Expanding and simplifying:

DH² = 33 ± 60√(3) - (36 - 12DH + DH²)

Simplifying further:

DH² - 12DH - 3 ± 60√(3) = 0

Solving for DH using the quadratic formula:

DH = 6 ± √(3)

Discard the negative solution because DH must be positive. Therefore, the measurement of DH is DH = 6 + √(3) cm.

Find out more on parallel sides here: https://brainly.com/question/22647242

#SPJ1

Image transcribed:

In the given figure,

FC//AB, AD// BC, A line F// BE,

EG I A line F and DH L.B.C. IF G

EG = 5cm, A line F =12cm and

BC = 6cm, find the measurement

of DH.

The new beta-blocker medicine is effective in lowering high blood pressure.

A hypothesis test can be used to test the claim that a new beta-blocker is effective at the significance level α (significance level).

Let us define the null and alternative hypotheses as follows:

Null Hypothesis (H0):

This drug does not affect high blood pressure.

Alternative hypothesis (Ha):

The drug is effective in lowering high blood pressure.

To test this hypothesis, we can use a two-sample proportional z-test comparing rates of success (lowering blood pressure) in two independent populations (treatment and control groups).

First, we need to calculate the sample proportions and the standard errors of their differences. Let p1 = treatment group success rate,

p2 = control group success rate,

and p = pooled rate.

p1 = 157/290 = 0.541

p2 = 90/170 = 0.529

p = (157 + 90) / (290 + 170) = 0.536

The standard error of the difference in proportions can be calculated as:

SE = sqrt[p*(1-p)(1/n1 + 1/n2)]

= square[0.536(1-0.536)*(1/290 + 1/170)]

= 0.056

Then you can compute the test statistic z.

z = (p1 - p2) / SE

= (0.541 - 0.529) / 0.056

= 2.143

Finally, we can compute the p-value associated with the test statistic z, assuming a standard normal distribution.

p-value = P(Z > 2.143) = 0.0169

The p-value (0.0169) is less than the significance level α, so we neglect the null hypothesis and can say that this drug is effective in lowering high blood pressure.

The chosen importance is not specified in the question, so it is not sure if it's important at that level. If α is given, you can compare the p-value to α and make a decision based on that.  

learn more about hypothesis test

brainly.com/question/30588452

#SPJ4

The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates  [tex](1,4)[/tex] and [tex](5,6)[/tex] .

The best way to determine which graph shows a line that fits the data is to plot the line on the scatter plot and see how well it fits with the points.

Let's start with option A, which shows a line passing through the coordinates 5 comma 7 and 10 comma 9. When we plot this line on the scatter plot, we can see that it doesn't fit the data very well.

The line doesn't pass through many of the points and seems to be a poor representation of the relationship between the x and y values.

Option B shows a line passing through the coordinates 2 comma 7 and 6 comma 7. Again, when we plot this line on the scatter plot, we can see that it doesn't fit the data very well.

The line passes through some points, but not all of them, and it doesn't seem to represent the relationship between the x and y values very well.

Option C shows a line passing through the coordinates 1 comma 4 and 5 comma 6. When we plot this line on the scatter plot, we can see that it fits the data fairly well. The line passes through several of the points and seems to capture the overall trend of the data.

Option D shows a line passing through the coordinates 1 comma 4 and 3 comma 8. When we plot this line on the scatter plot, we can see that it fits the data fairly well. The line passes through several of the points and seems to capture the overall trend of the data.

Therefore, The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates  [tex](1,4)[/tex] and [tex](5,6)[/tex] .

Learn more about graph here:

brainly.com/question/19040584

#SPJ1

The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates  (1,4) and (5,6).

Option A Some points are too far from the line when we draw a line through the points (5, 7, and 10). It is not the minimum distance between the line and the scattered data. So, it's not a line on the scatter plot that fits the data.

Option B When we draw a line through (2,7) and (6,7) then the distance between the line and the scattered is still much. So, it's not a line on the scatter plot that fits the data.

Option C When we draw a line through (1,4) and (5,6) then most of the points are nearer to the line and it defines a relation between the points and the line more efficiently.  So, this line is the best-fit line for this scattered graph.

Option D When we draw a line through (1,4) and (3,8) then some points are too far from this line. It is not the minimum distance between the line and the scattered data. So, it's not a line on the scatter plot that fits the data.

Therefore, the graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates (1,4) and (5,6).

Learn more about graph here:

brainly.com/question/19040584

#SPJ1

Answer:

The formula for area of a parallelogram is A=bh

x=10.3

Step-by-step explanation:

We don't have the base but we have the height.

the base is x and the height is 5

if the area is 51.5

we should divide the height to find the base.

51.5÷5=10.3

so the base is 10.3

Check if answer is correct:

b=10.3

h=5

a= 51.5

10.3(5)=51.5

a= 51.5cm²

I hope this helps as long as you know the formula it's easy :D

Answer:

To solve for y in the inequality 5(2y - 1) < -15, we can simplify the expression on the left-hand side as follows:

5(2y - 1) < -15

10y - 5 < -15 // Distribute the 5 on the left side

10y < -10 // Add 5 to both sides

y < -1 // Divide both sides by 10 and flip the inequality

Therefore, the solution is y < -1.

Answer:

∠2 = 125°

Step-by-step explanation:

∠1 and ∠2 form a straight angle of 180° (∠3 and ∠4 aswell)

∠1 = ∠3, because they are cross angles (∠3 and ∠4 aswell)

We can write an equation according to this and find y:

(8y - 9)° = (6y + 7)°

8y - 6y = 7 + 9

2y = 16 / : 2

y = 8

∠1 = 8 × 8 - 9 = 55°

∠2 = 180° - 55° = 125°

∠3 =∠1 = 6 × 8 + 7 = 55°

∠4 = 180° - 55° = 125°

Answer:

[tex]a_{n}[/tex] = 5n

Step-by-step explanation:

there is a common difference between consecutive terms, that is

10 - 5 = 15 - 10 = 20 - 15 = 5

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 5 and d = 5 , then

[tex]a_{n}[/tex] = 5 + 5(n - 1) = 5 + 5n - 5 = 5n

The probability that their mean is above 215 is 0.0359.

Therefore the answer is (a) 0.0359.

To find the probability that the mean rating of 36 applicants is above 215, we can use the central limit theorem, which states that the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. So, the mean of the distribution of sample means is 200, and the standard deviation is 50/sqrt(36)=8.33.

We can then standardize the sample mean using the z-score formula:

z = (x* - μ) / (σ / sqrt(n))

where x* is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values, we get:

z = (215 - 200) / (8.33) = 1.8.

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score greater than 1.8 is 0.0359. Therefore, the answer is (a) 0.0359.

To know more on central limit theorem

https://brainly.com/question/18403552

#SPJ4

Answer:

Step-by-step explanation:

10-16=to 4

Answer:

30.5

Step-by-step explanation:

35/2 is 17.5 add 13 is 30.5

Answer:

[tex]35 \div 2 + 13 \\ = 17.5 + 13 \\ = 30.5[/tex]

Answer:

68%

Step-by-step explanation:

If someone works 48.5 hours in a week and their regular work week is 40 hours, then they would have worked 8.5 hours of overtime.

What is meant by a week?

A week is a unit of time equal to seven days, usually beginning on Monday and ending on Sunday. It is commonly used to measure and organize time.

What is meant by hours?

Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.

According to the given information

In most cases, overtime pay is calculated as 1.5 times the employee’s regular hourly rate.

If someone works 48.5 hours in a week and their regular workweek is 40 hours, then they would have worked 8.5 hours of overtime.

To know more about week visit

brainly.com/question/14515714

#SPJ1

The expected counts are large enough to use a chi-square distribution to calculate the p-value because the predicted-counts are at least 5, the degree-of-freedom that should be used is 2.

The "degree-of-freedom" is defined as the number of independent parameters or variables that must be specified to completely describe a system or equation.

We see that the projected counts(expected-counts) are large enough to use a chi-square distribution if all predicted counts are at least 5,

So, This condition is satisfied and it satisfies that the expected counts are large enough to use a chi-square distribution to calculate the p-value.

In the table we see that the number of categories are three : {Red, Black, Green},

So, degree of freedom is = (number of categories) - 1 = 3 - 1 = 2.

Therefore, the degree of freedom is 2.

Learn more about Degree Of Freedom here

https://brainly.com/question/30398137

#SPJ4

The given question is incomplete, the complete question is

Confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. The information table is given below.

What degrees of freedom should you use?

Christopher paid more interest than he would have if he had made all 24 monthly payments, the unearned interest is negative. The total amount needed to repay the loan using the Rule of 78 is  $7,500.75

Part A:

To determine the amount of unearned interest, we need to first calculate the total interest that Christopher would have paid if he had made all 24 monthly payments.

Total interest = Monthly payment x Number of payments - Principal

Total interest = $475 x 24 - $7,500

Total interest = $11,400 - $7,500

Total interest = $3,900

However, Christopher only made 18 monthly payments. To determine the amount of unearned interest, we need to subtract the interest he actually paid from the total interest calculated above.

Interest paid = Monthly payment x Number of payments made

Interest paid = $475 x 18

Interest paid = $8,550

Unearned interest = Total interest - Interest paid

Unearned interest = $3,900 - $8,550

Unearned interest = -$4,650

Since Christopher paid more interest than he would have if he had made all 24 monthly payments, the unearned interest is negative.

Part B:

To determine the amount needed to repay the loan using the Rule of 78, we first need to calculate the total amount of interest that would have been paid if Christopher had made all 24 monthly payments.

Total interest = Principal x Rate x Rule of 78 factor

where Rate = Annual interest rate / 12

and Rule of 78 factor = Number of remaining payments / Sum of digits of all payments

The annual interest rate is not provided, so let's assume it is 6%.

Rate = 6% / 12

Rate = 0.005

The sum of digits of all payments is 1 + 2 + ... + 24 = 300.

Rule of 78 factor = (24 - 18) / 300

Rule of 78 factor = 0.02

Total interest = $7,500 x 0.005 x 0.02

Total interest = $0.75

The total amount needed to repay the loan using the Rule of 78 is the principal plus the total interest calculated above.

Total amount = Principal + Total interest

Total amount = $7,500 + $0.75

Total amount = $7,500.75

Part C:

To support our answers to Part A and Part B, we can compare the total interest paid using the actual method of repayment (18 monthly payments) and the Rule of 78 method of repayment.

Using the actual method, Christopher paid $8,550 in interest.

Using the Rule of 78 method, the total interest would have been $0.75.

As we can see, the Rule of 78 method results in a much lower amount of interest. This is because the Rule of 78 assigns more of the interest to the earlier payments, so paying off the loan early results in less total interest paid.

Regarding the unearned interest, we calculated a negative amount of $4,650 using the actual method of repayment. This is because Christopher paid more interest than he would have if he had made all 24 monthly payments.

Learn more about annual interest rate at https://brainly.com/question/14837917

#SPJ1

The first step in selecting a sample for a survey is to define the population of interest.

This involves specifying the group of individuals or objects that the researcher wants to make inferences about based on the survey results. Once the population is defined, the researcher can then select a sampling method to choose a representative subset of individuals from the population to participate in the survey.

The choice of sampling method depends on various factors, such as the research question, the nature of the population, and the available resources. Common sampling methods include random sampling, stratified sampling, cluster sampling, and convenience sampling.

To know more about conduct a survey:

https://brainly.com/question/14983379

#SPJ4

Answer:

834

Step-by-step explanation:

5 + 3(4 - 3 + 2) x [tex]9^{2}[/tex] + 100

5 + 3(3) x 81 + 100

5 + 9 x 81 + 100

5 + 729 + 100

834

Helping in the name of Jesus.

Answer:

Gabriel left $1.53 in tips.

Step-by-step explanation:

Sales tax: 9.50*0.075=0.7125

9.50+0.71=10.21

Total with Sales Tax: $10.21

Tip: 10.21*0.15=1.5315

Answer:

14

Step-by-step explanation:

14 is the answer of the question

As a result, 390 cm equals the length x to the nearest whole number as a right triangle is equal to the sum of the squares of the other two sides .

The relation between the opposite sides of a right triangle is a central idea in mathematics known as Pythagoras' theorem. According to this rule, the square of the hypotenuse's length—the side that faces the right angle—in a right triangle is the same as the total of the squares of both the lengths of the other two sides. The following is a mathematical formulation of the theorem   where a and b are really the lengths of the right triangle's two shorter sides (called its legs), and c is the height of the hypotenuse.

given

The Pythagorean theorem, which asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the other two sides, can be used to determine the length x.

cos 34°= b/h

that is 0.829 = 450 cm/ h

h = 450/0.829

h = 542cm

sin 34° = p/h

that is, sin34° = x/542

0.559=x/542

so, x= 542×0.559

x= 390 cm

As a result, 390 cm equals the length x to the nearest whole number as a right triangle is equal to the sum of the squares of the other two sides .

To know more about Pythagorean theorem visit:

brainly.com/question/14930619

#SPJ1

Prisoners are considered a special population because they are segregated from the main population sample. This means that they are separated from the general public due to their incarceration, which results in a unique set of characteristics and circumstances that differentiate them from the broader population.

One reason why prisoners are considered a special population is because they are readily accessible for experimentation and interviews. Researchers and interviewers can easily obtain access to prisoners within the confines of the prison environment, making it convenient for conducting studies and gathering data. However, this accessibility also raises ethical concerns, as prisoners may be more vulnerable to coercion and exploitation in research settings

Another reason is that prisoners are exposed to risks that are not common in the general population. They often face higher levels of violence, mental health issues, and substance abuse problems, which may influence the findings of any study conducted on this group. Moreover, the prison environment itself can affect the behavior and attitudes of prisoners, making it difficult to generalize the results to the wider population.

Additionally, prisoners are not a true representative population sample. Due to the specific demographics of those incarcerated, findings from research conducted on prisoners may not accurately represent the larger society. It is important for researchers to consider this factor when interpreting and applying the results of their studies.

In conclusion, prisoners are considered a special population because they are segregated from the main population sample, readily accessible for experimentation and interviews, exposed to risks, and not a true representative population sample. When conducting research with prisoners, it is crucial for researchers to consider these unique factors and to adhere to ethical guidelines to ensure that the rights and well-being of this vulnerable population are protected.

To know more about prison environment refer here:

https://brainly.com/question/20041629

#SPJ11

Answer:

11)   -14d¹¹

12)   4n⁴

Step-by-step explanation:

11)   (-2d²)(7d⁹) = (-14d²⁺⁹) = -14d¹¹

12)  n¹⁰ / n⁶ = n¹⁰⁻⁶ = n⁴

When multiplying the same variable, add the exponents.

When dividing the same variable, subtract the exponents.

The equation of the line that passes through the point (5, 0) and has a slope of 6/5 is:

y = (6/5)x - 6To find the equation of the line that passes through the point (5, 0) and has a slope of 6/5,

we will use the point-slope form of the equation of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Step 1: Plug in the given point (5, 0) as (x1, y1) and the slope (6/5) as m.
y - 0 = (6/5)(x - 5)
Step 2: Simplify the equation.
y = (6/5)(x - 5)
Step 3: Distribute the slope (6/5) on the right side.
y = (6/5)x - 6
For similar question on slope.

https://brainly.com/question/3493733

#SPJ11

The circumference of a tire with a diameter of 16 inches is 50.3 inches (rounded to one decimal place), calculated using the formula C = π * d.

Multiplication is a mathematical operation that involves adding a number to itself a certain number of times, or combining equal groups of objects to find the total quantity. It is represented by the "x" symbol and is used to find the product of two or more numbers. For example, 2 multiplied by 3 is equal to 6 (2 x 3 = 6). Multiplication is one of the fundamental arithmetic operations and is used in various mathematical concepts and applications in everyday life.

The circumference of a tire is the distance around its outer edge. It can be calculated using the formula C = π * d, where d is the diameter of the tire. The diameter is the distance from one edge of the tire to the opposite edge, passing through the center. In this case, given that the diameter of the tire is 16 inches, substituting this value into the formula gives C = π * 16 = 50.3 inches (rounded to one decimal place). Therefore, the correct answer is 50.3 inches, as it represents the circumference of a tire with a diameter of 16 inches. The other options provided are not correct, as they do not accurately calculate the circumference based on the given diameter.

Therefore, The circumference of a tire with a diameter of 16 inches is 50.3 inches (rounded to one decimal place), calculated using the formula C = π * d.

To know more about multiplication visit :

https://brainly.com/question/1135170

#SPJ1

Answer:

Step-by-step explanation:

1.  48 96 192      (multiplying by 2)

2. 30 37 44        ( adding 7)

3. 25 18 11          ( subtracting 7)

4. 110 232 456  ( adding 7, 14, 28, 56  and so on)

5. 230 470 950  (adding 15, 30, 60 120 and so on)

Answer: 1. Since the inequality can never be true, there is no solution.

Step-by-step explanation:

The 99% confidence interval for the mean difference between the before and after scores is (-0.5 ,4.5).

A writing-test is taken for sample of students which are randomly selected,   before and after they completed formal writing-course.

The results of the test scores before and after the test are :

Before ⇒ 80, 70,  92,  99,  97,  93,  76,  63,  68,  71,   74

After    ⇒ 79,  69,  90,  96, 95,  91,   75,  64,  62,  64,  76

So,

Diff(d) ⇒   1,      1,     2,     3,   2,   2,     1,    -1,     4,     7,    -2,

⇒ d²   ⇒   1,      1,     4,     9,   4,   4,     1,     1,     16,   49,   4,

Sum of difference = Σd = 22, and

Sum of d² = 114;

Mean difference is = 2,

The degree of freedom (df) = 11 - 1 = 10,

So, the standard deviation (S.D.) =√(Σd²-(Σd)²/n)/(n-1) = 2.645751 , and

the standard error (Se) = (S.D.)/√n = 2.6457/√11 = 0.7977,

For 99% confidence interval , 10 degree of freedom , t-value is = 3.169,

We know that, confidence interval = {(sample mean) ± t × standard error};

So, Margin of error = t × standard error = 2.527987 ≈ 2.5,

The lower confidence limit is = 2 - 2.5 = -0.5,

The upper confidence limit is = 2 + 2.5 = 4.5,

Therefore, the required 90% confidence interval is (-0.5 ,4.5).

Learn more about Confidence Interval here

https://brainly.com/question/28013993

#SPJ4

The given question is incomplete, the complete question is

A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores. Round the limits to the nearest tenth.

Before 70   80   92   99   93   97    76   63   68   71   74

After    69   79   90   96   91    95   75   64   62   64   76

In the equation , value of n is 13/3.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given statement is  n more than 18 then,

=> n+18

It is equal to seven times the difference of n and three then,

=> n+18 = 7(n-3)

Now simplifying the given equation then

=> n+18= 7n-21

=> 18+21=7n-n

=> 6n=39

=> n = 39/6 = 13/3

Hence the value of n is 13/3.

To learn more about equation refer the below link

https://brainly.com/question/29336774

#SPJ1