Answers
For the rectangle given the correct option is B) HL.
What is a rectangle?
A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.
A rectangle is given with parallel sides equal.
Two opposite angles are 90°.
A diagonal is drawn.
The given information describes a rectangle, which is a special case of a parallelogram with all angles equal to 90°.
In a rectangle, the diagonals are congruent and bisect each other.
Therefore, the correct option is (HL) hypotenuse-leg, which is a special case of the congruence rule for right triangles.
If we consider the right triangle formed by one of the diagonals and one of the sides of the rectangle, we can see that we have a right triangle with hypotenuse equal to the diagonal and leg equal to one of the sides of the rectangle.
Since the diagonals are congruent and the sides of the rectangle are equal, we have a case of HL congruence.
Option (a) AAS (angle-angle-side) and option (c) SSS (side-side-side) do not apply to this situation since we only have information about one side and one diagonal of the rectangle.
Option (d) "Not equal and congruent" is not a valid answer choice as congruent objects, by definition, must be equal.
Therefore, option B is the correct answer.
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Related Questions
to plot the point for a library at (2, - 3) 2 units to
Answers
Determine whether a triangle can be formed with the given side lengths.
Question 3and4 pls
Answers
Answer:
In question 3 a triangle can be formed however in question 4 it can't be formed
Step-by-step explanation:
there is a theorem that states that two sides of a triangle when added up should be greater than the third one which isn't true in question 4 as
12+9=21 so its equal to the third side but not greater hence a triangle can't be formed
4. Find each interior angle
Sort from smallest to largest
Answers
Answer:
50, 75, 90, 105, 110
Step-by-step explanation:
All angles of a pentagon add up to 540 degrees
So;
Finding all the inner angles first;
x = 180 - 50 = 130
y = 180 - 75 = 105
So, 130 + 105 + 90 + (2x + 10) + (2x + 5) = 540
or, 4x = 200
Therefore, x = 50
2x + 5 = 105
2x + 10 = 110
Hence, the angles in ascending order are:
50, 75, 90, 105, 110
Suppose - 2x²-20x-51 ≤ f(x) ≤ 2x²+20x +49 for all x values near -5, except possibly at -5.
Evaluate lim f(x).
X→-5
Answers
By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.
What is the squeeze theοrem ?The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.
We have the inequality:
-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49
We can rewrite this inequality as:
-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1
Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.
As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:
-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1
0 ≤ lim f(x) ≤ 1
Therefοre, by the squeeze theοrem, we have:
lim f(x) = 0 as x apprοaches -5.
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A nurse’s aide has earned $21,670. She earned $1,970 this month. How much is deducted this
month for Social Security? For Medicare?
Answers
Answer:
The Social Security tax rate is 6.2% and the Medicare tax rate is 1.45%. To calculate the amount deducted from the nurse's aide's earnings this month for Social Security and Medicare:
Social Security:
Multiply the earnings for the month by the Social Security tax rate:
$1,970 x 0.062 = $121.94
Therefore, $121.94 is deducted from the nurse's aide's earnings this month for Social Security.
Medicare:
Multiply the earnings for the month by the Medicare tax rate:
$1,970 x 0.0145 = $28.54
Therefore, $28.54 is deducted from the nurse's aide's earnings this month for Medicare.
WILL GIVE THE BRAINLIEST AND 5 STARS!!!!
The vertices of △ABC are (−6, 2), (−4, 6), and (−2, 2), and the vertices of △DEF are (5,-2), (3, −6), and (1, −2). Which of these sequences of transformations of △ABC exhibit the congruence between the two triangles? Select TWO that apply.
Responses
a rotation of 180° about the origin and a translation of 1 unit left
a rotation of 180° about the origin and a translation of 1 unit left
a reflection across the x-axis and a translation 1 unit right
a reflection across the x-axis and a translation 1 unit right
a rotation of 180° about the origin and a translation of 1 unit right
a rotation of 180° about the origin and a translation of 1 unit right
a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit right
a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit right
a reflection across the y-axis and a translation 1 unit left
a reflection across the y-axis and a translation 1 unit left
a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left
Answers
The answer of the given question based on the triangle which is sequences of transformations of △ABC exhibit the congruence between the two triangles the answer is given below,
What is Congruent triangle?Congruent triangles are two or more triangles that have same shape and size. In other words, they have same angles and same side lengths.
The congruence between the two triangles can be exhibited by the following two sequences of transformations:
a) a rotation of 180° about the origin and a translation of 1 unit left
c) a rotation of 180° about the origin and a translation of 1 unit right
Option b) and option e) involve a translation and a reflection that do not preserve orientation, so they do not result in a congruent triangle.
Option d) involves two reflections, which do not commute, so the order matters. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit right, followed by a reflection across the line x = -1, which does not result in a congruent triangle.
Option f) is similar to option d) in that it involves two reflections that do not commute. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit left, followed by a reflection across the line x = 1, which also does not result in a congruent triangle.
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REASONING How many times greater is the area of the floor covered by the larger speaker than by the smaller
speaker?
2h-
-2b₂-
speaker.
SAM
-2b₁-
Tb₁4
The area of the floor covered by the larger speaker is times greater than the area of the floor covered by the smaller
Answers
The area of the floor covered by the larger speaker is 2(two) times greater than the area of the floor covered by the smaller speaker.
How to calculate the area covered by the speakers?The shape of the big speaker is similar to the shape of the smaller speaker but with different dimensions.
The shape of the larger speaker has the following dimensions:
base = 2b
height = 2h
The shape of the smaller speaker has the following dimensions :
base = b
height = h
Scale factor = 2b/b = 2
Therefore, the larger speaker is 2(two) times greater than the area of the floor covered by the smaller speaker.
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A newspaper editor starts a retirement savings plan in which $275 per month is deposited at the beginning of each month into an account that earns an annual interest rate of 6.4% compounded monthly. Find the value of this investment (in dollars) after 20 years. (Round your answer to the nearest cent.)
Answers
Answer:
Step-by-step explanation:
x= 20 (12) =240, Interest%= 6.4, Pv + 0, PMT= 275,temporarily skip FV,P/Y and C/Y= 12,
After 20 years, the value is $133,970.26
The simple interest value of the investment after 20 years is approximately $30,637.45
What do you mean by future value?Future value (FV) is the value of an investment at a future date, based on a series of regular payments (or a lump sum) and assuming a certain interest rate over a period of time. In other words, it's the amount of money an investment will be worth after earning a certain rate of interest over a certain period of time.
What is simple interest?Simple interest is a method of calculating interest on a loan or investment, where interest is only charged on the original principal amount. In other words, the interest is not compounded over time.
In the given question:
We can use the formula for the future value of an annuity:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where: FV = future value
PMT = monthly payment
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values, we have:
FV = 275 x [(1 + 0.064/12)^(12*20) - 1] / (0.064/12)
FV = 275 x (1.00533²⁴⁰ - 1) / 0.00533
FV = 275 x 111.034
FV = 30,637.45
Therefore, the value of the investment after 20 years is approximately $30,637.45.
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Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
(1,6)
, (2,10)
, (3,4)
, (4,4)
, (5,8)
, (6,2)
, (7,2)
Answers
The Pearson correlation coefficient r for the given points is: 0.191.
How to find the r Pearson correlation coefficient r?We can use the formula for Pearson correlation coefficient r:
r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)²][nΣ(y²) - (Σy)²])
where n is the number of data points, Σ represents the sum, x and y are the variables, and xy, x², and y² represent the products and squares of the variables.
We can first calculate the sums and products:
n = 7
Σx = 28
Σy = 36
Σ(x²) = 140
Σ(y²) = 248
Σ(xy) = 152
Using these values, we can plug them into the formula for r:
r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)² ][nΣ(y²) - (Σy)²])
= [7(152) - (28)(36)] / sqrt([7(140) - (28)^2][7(248) - (36)²])
= 56 / 293
= 0.191
Therefore, the Pearson correlation coefficient r is 0.191.
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A couple are planning to have four children. (Assume that it is equally likely for a boy or a girl to be born.)
What is the probability that all four of their children will be girls?
What is the probability that at least one will be a girl?
What is the probability that all four will be of the same sex?
What is the probability that not all four will be of the same sex?
Answers
Answer:
1/4
Explanation:
The denominator is four because it represents the four possibilities about what gender the babies will be. The numerator is 1 because there is one chance out of four that (insert gender ratio) will be picked.
Examples:
There is one chance out of four chances that all four of the children will be girls.
There is one chance out of four chances that at least one child will be a girl.
There is one chance out of four chances that all four will be of the same sex.
There is one chance out of four chances that not all four will be of the same sex.
James has to fill 40 water bottles for the soccer team. Each bottle holds 1 pint of water.
How many gallons of water does James need in all?
Answers
Answer:
James needs 5 gallons of water.
Step-by-step explanation:
1 gallon = 8 pints
40 ÷ 8 = 5
5 gallons
5) y=-2
4x – 3y = 18
Answers
Answer:3
Step-by-step explanation:
you'll write -2 instead of every y (in this case there is only one y) so,
4x-3(-2)=18
4x=18-6
4x=12
x=3
I need help on this question
Answers
Answer: i think the answer is A
Step-by-step explanation:i think bc i is a quadratic function
Answer: D
Step-by-step explanation:
A and B don't make sense, since the maximum value > 0, and the function is more negative than positive. C and D are our remaining answers. C would be incorrect, since if X reaches \infinity , the function isn't infinite. The only way to make C correct, is a sudden spike in the function to infinity. So, the only correct answer is D.
Hope this helps (please respond if I'm wrong)
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.
sin88°=
Answers
We get sin88° ≈ 0.99. Rounding to the nearest hundredth, sin88° ≈ 0.99.
Describe Sine?In trigonometry, the sine function is one of the primary trigonometric functions that relates the ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse. The sine function is defined as:
sine (θ) = opposite / hypotenuse
where θ is the measure of the acute angle in radians or degrees.
The sine function is a periodic function, meaning it repeats itself after every 2π radians or 360 degrees. The graph of the sine function is a wave that oscillates between -1 and 1, with the midline at y = 0. The amplitude of the wave is 1, which represents the maximum height of the wave above and below the midline.
The sine function is used in many real-world applications, such as in engineering, physics, and astronomy to model waves, oscillations, and periodic phenomena. It is also used in geometry to calculate the sides and angles of triangles, as well as in calculus to solve differential equations and to describe the motion and behavior of complex systems.
Using a calculator, we get sin88° ≈ 0.99. Rounding to the nearest hundredth, sin88° ≈ 0.99.
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Which system describes the following situation? Craig has 80 cents in nickels and dimes. He has
four more nickels than dimes.
Od+n=4 and 10d + 5n = 80
On-d=4 and 10d + 5n = 80
Od+n=4 and 10d - 5n = 80
O d-n=4 and 10d + 5n = 80
Answers
Od+n=4 and 10d + 5n = 80
This is because the problem states that Craig has four more nickels than dimes, which can be represented as Od+n=4. The problem also states that he has 80 cents in total, which can be represented as 10d + 5n = 80.
The earth rotates through one complete revolution every 24 hours. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 24 hours. Find the angular and linear velocity of a person standing on the equator. The radius of earth is approximately 4000 miles.
Answers
Answer:
w = 7.27 x 10-5 rad/s
v = 467.99 m/s
Explanation:
First, we will find the angular velocity of the person:
Angular Velocity =w= Angular Distance
Time
Angular distance covered 1 rotation = 2π
radians
Time = (24 h)(3600 s/1h) = 86400 s
Therefore,
2π rad 86400 s 3
w = 7.27 x 10-5 rad/s
Now, for the linear velocity:
v = rw
where,
v = linear velocity = ?
r = radius of earth = (4000 miles)(1609.34 m/1 mile) = 6437360 m
Therefore,
v = (6437360 m) (7.27 x 10-5 rad/s)
v = 467.99 m/s
In Vincent garden 1/6 of the flowers are daisies, and 1/8 of the flowers are snapdragons.
Answers
In Vincent's garden, about 34/48 of the flowers are neither daisies nor snapdragons.
We need to find the fraction of flowers in Vincent's garden that are neither daisies nor snapdragons. To do this, we need to subtract the fractions of daisies and snapdragons from 1.
The fraction of flowers that are daisies is 1/6, and the fraction that are snapdragons is 1/8. To find the common denominator, we can multiply 6 and 8 to get 48.
So, the fraction of flowers that are neither daisies nor snapdragons is:
1 - 1/6 - 1/8
= 48/48 - 8/48 - 6/48
= (48 - 8 - 6)/48
= 34/48
Therefore, 34/48 of the flowers in Vincent's garden are neither daisies nor snapdragons.
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According to The Food and Drug Administration (FDA), 400 milligrams (mg) a day is considered a safe amount of daily caffeine consumption which is about 4 to 5 cups of coffee. We suspected that people who visit coffee shops in the morning drink more coffee on average than people who visit coffee shops in the afternoon. During one day, we randomly sampled 8 people who entered a given coffee shop in the morning and 8 people who entered the coffee shop in the afternoon. We recorded each person's average daily caffeine consumption (in mg).
( Could I pleas get help on the missing questions )
a. standard error of (xmorning - xafternoon) =
b.Construct an approximate 95% confidence interval for morning - afternoon
Lower bound =
Upper bound =
Answers
The apprοximate 95% cοnfidence interval fοr mοrning - afternοοn caffeine cοnsumptiοn is (70.37, 229.63) mg.
What is standard errοr?Standard errοr is a statistical measure οf the variability οf a sample mean frοm the true pοpulatiοn mean, representing the precisiοn οf an estimate. It's calculated as the standard deviatiοn οf the sample mean divided by the square rοοt οf the sample size.
a. The standard errοr οf (xmοrning - xafternοοn) can be calculated as fοllοws:
Standard errοr = sqrt[(s₁²/n₁) + (s₂²/n₂)]
b. Tο cοnstruct an apprοximate 95% cοnfidence interval fοr mοrning - afternοοn caffeine cοnsumptiοn, we can use the fοllοwing fοrmula:
(xmοrning - xafternοοn) +/- t(alpha/2, df) * standard errοr
Assuming a twο-tailed test and a significance level οf 0.05, the degrees οf freedοm are 14 (8+8-2).
Let's assume that the sample mean caffeine cοnsumptiοn fοr the mοrning grοup is 500 mg with a sample standard deviatiοn οf 80 mg, and the sample mean caffeine cοnsumptiοn fοr the afternοοn grοup is 350 mg with a sample standard deviatiοn οf 60 mg. Plugging in the values intο the fοrmula, we get:
(xmοrning - xafternοοn) +/- t(alpha/2, df) * standard errοr
= (500 - 350) +/- 2.145 * sqrt[(80²/8) + (60²/8)]
= 150 +/- 79.63
= (70.37, 229.63)
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What is a log can kate use to fill remaining 1/3 meters
Answers
Answer:
It is not clear what is meant by "a log can Kate use to fill remaining 1/3 meters." However, if we assume that Kate has a gap of 1/3 meters that she needs to fill, she could use a log that is 1/3 meters long to fill the gap. Alternatively, she could use any other object that is 1/3 meters long to fill the gap.
Making Connections: Selecting a Career
Apply Your Knowledge I will double the points if you get this completely done (that means both documents completed with the correct answers)
Answers
Top Career Choice: Registered Nurse
Job Description: Registered Nurses (RNs) are responsible for providing and coordinating patient care.
Personal Attributes: Compassionate, Detail-oriented, Patient, Good communication skills, Ability to work under pressure, Physical and emotional stamina
Education: A Bachelor of Science in Nursing (BSN) is the preferred degree for RNs.
Experience: RNs typically gain experience through clinical rotations during their nursing program, as well as through internships or residency programs.
Certification: RNs can earn additional certifications in specialties such as critical care, emergency nursing, or pediatric nursing.
Employment: RNs can work in a variety of settings, including hospitals, clinics, long-term care facilities, and schools.
Why is making a career choice important in one way?Making a career choice opens the door to financial security. The earning potential of an occupation is a major consideration for most people when choosing a suitable career. Choosing the right profession means you will be able to have economic security, which is an important factor in our overall well-being.
Full question "Making Connections: Selecting a Career. Apply Your Knowledge" Top Career Choice, Job Description, Personal Attributes, Education, Experience, Certification, Employment, Job Outlook, Earnings, Work Environment, Related Occupations
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In a certain study, the odds against a car crash on the road are stated as "22:3". What is the probability of a car crash on the road? Enter the probability as a reduced fraction.
Answers
Therefore, the likelihood of a vehicle accident just on road is 3/25. The ultimate solution is 3/25 because there is no other way to simplify this fraction.
What is the probability calculation?The probability is typically defined as the proportion of favourable findings to all results inside the poll area. The formula for probability of an event is P(E) = (Number of positive occurrences) (Sample space).
If the odds against a car crash on the road are stated as "22:3", it means that for every 22 unfavorable outcomes (no car crash), there are 3 favorable outcomes (car crash).
The total number of outcomes is 22 + 3 = 25.
Therefore, the probability of a car crash on the road is:
3 favorable outcomes / 25 total outcomes = 3/25
So, the probability of a car crash on the road is 3/25. This fraction cannot be reduced further, so the final answer is 3/25.
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A road is5/9 of a mile long. A crew needs to repave 2/3 of the road. How long is the section that needs to be repaved?
Answers
The sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.
The length οf the rοad is 5/9 οf a mile.
Tο find the length οf the sectiοn that needs tο be repaved, we can multiply
the length οf the rοad by the fractiοn that represents the fractiοn οf the rοad that needs tο be repaved:
length οf sectiοn tο be repaved = (2/3) * (5/9) mile
Multiplying the numeratοrs and denοminatοrs separately, we get:
length οf sectiοn tο be repaved = (2 * 5) / (3 * 9) mile
Simplifying the fractiοn, we get:
length οf sectiοn tο be repaved = 10/27 mile
Therefοre, the sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.
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what 2 distributive property expressions equal to 108
Answers
The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The distributive property is given as:
a(b + c) = ab + ac
3(20 + 16) = 3(20) + 3(16) = 60 + 48 = 108
Also:
4(13 + 14) = 4(13) + 4(14) = 52 + 56 = 108
The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108
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Please answer this for me quick i have another one after this
Answers
The value of x/y is 3/25, Hence the correct option is b.
What is the equatiοn?An equatiοn is a mathematical statement that shοws that twο expressiοns are equal. It cοntains an equal sign (=) that separates the twο expressiοns. An equatiοn can have variables, cοnstants, cοefficients, and arithmetic οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, and expοnentiatiοn.
Starting with the given equation:
(5x+y)/y = 8/5
5x+y = 8
y = 5
When y = 5
Then,
5x + (5) = 8
5x + (5) = 8
5x = 3
x = 3/5
Therefore x/y = (3/5)/5 = 3/25
Thus, The value of x/y is 3/25, Hence the correct option is b.
So the correct option is not listed in the answer choices.
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What is the perimeter of △ DEF to the nearest tenth? A. 19.4 B. 20.1 C. 25.3 D. 43.3
Answers
Based on the above, the Perimeter of the triangle DEF is 43.3 units
What is an equation?A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, reduction, multiplication, division, exponents, and so forth.
Given the triangle DEF. Using trigonometric ratio:
sin(38) = EF / 18EF = 11.1
Also: cos(38) = DF / 18DF = 14.2
The perimeter of triangle
DEF = DE + EF + DF
= 18 + 11.1 + 14.2 = 43.3 units
Hence, the Perimeter is 43.3 units
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a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with garlic rocessed tablet form. Cholesterol levels were measured before and after the treatment. The chan before-after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.1 and a standard devi 16.5. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol afte reatment. What does the confidence interval suggest about the effectiveness of garlic in reducing Cholesterol? Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. E What is the confidence interval estimate of the population mean μ? mg/dL
Answers
]Therefore , the solution of the given problem of deviation comes out to be the confidence interval contains both positive and negative values.
Standard deviation : What is it?Statistics uses variance as a gauge of difference. The image of that figure is used to compute the average variance between the collection and the mean. It includes those data points itself into the calculations, unlike many other real measures of variability, by comparing also every figure to the mean.
Here,
Since the population standard deviation is unknown and the sample number is less than 30, we can use a t-distribution to build the confidence interval. The confidence interval's calculation is:
=>CI = x t /2 × (s/n).
Since we need a 99% confidence range, = 0.01 and /2 = 0.005, and (n-1) = (49-1) = 48 is the number of degrees of freedom.
We discover that t/2 = 2.678 using the t-distribution table with 48 degrees of freedom and 0.005 significance level.
When we enter the numbers, we obtain:
=> CI = 3.1 ± 2.678 * (16.5/√49) = 3.1 ± 7.34
The estimated mean net change in LDL cholesterol following treatment, according to the 99% confidence range, is (4.24, 10.44) mg/dL.
We cannot say with 99% certainty that garlic is effective at lowering cholesterol because the confidence interval contains both positive and negative values.
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please answer asap for homework
Answers
The width of the patio, given the area of the pool and the patio, can be found to be 19. 59 ft
How to find the width ?The area of the pool is said to be equal to the area of the patio which means that to find the width of the patio, you need to find the area of the pool which is :
= 16 ft x 24 ft
= 384 ft ²
The patio is such that the width is the same on every side which makes it a square shaped patio. The width of the patio is therefore:
Width = √ Area of square patio
= √ 384
= 19. 59 ft
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Find the size of the angels labeled with letters. On is the center of the circle
Answers
Answer:
Step-by-step explanation:
[tex]i=80[/tex]° (opposite angles in a cyclic quadrilateral are supplementary)
[tex]e=84[/tex]° (An exterior angle of a cyclic quadrilateral is equal to the interior
angle at the opposite vertex.)
An exercise machine with an original price of $840 is on sale at 19% off.
a. What is the discount amount?
b. What is the exercise machine's sale price?
a. discount amount = $
Answers
Answer:
New price of exercise machine = $680.40
Step-by-step explanation:
19% of 840 = 159.6
840 x 19 = 15960
15960 / 100 = 159.60
840 - 159.60 = 680.40
A towns population has been decreasing at a constant rate. In 2010 the population was 7,900. By 2012 the population had dropped to 7,700. assume this trend continues. Identify the year in which the population will reach 0. Show work.
Answers
Answer:
Step-by-step explanation:
To identify the year in which the population will reach 0, we need to determine the rate at which the population is decreasing, and use that rate to predict when the population will be 0.
We can use the two data points given to find the rate of population decrease. Let P be the population and t be the time in years since 2010. Then we have:
P(0) = 7900 (population in 2010)
P(2) = 7700 (population in 2012)
We can find the rate of population decrease by using the formula for the slope of a line:
slope = (P(2) - P(0)) / (t(2) - t(0)) = (7700 - 7900) / (2 - 0) = -100/year
The negative sign indicates that the population is decreasing, and the magnitude of the slope (-100/year) tells us the rate at which it is decreasing.
To find the year in which the population will reach 0, we can use the point-slope form of a line:
P - P(0) = slope * (t - t(0))
where P is the population, t is the time in years since 2010, P(0) is the population in 2010, and t(0) is 0 (the year 2010).
Substituting the known values, we get:
P - 7900 = -100 * (t - 0)
Simplifying, we get:
P = -100t + 7900
To find the year in which the population will reach 0, we set P = 0 and solve for t:
0 = -100t + 7900
100t = 7900
t = 79
Therefore, the population will reach 0 in the year 2010 + 79 = 2089.
The solution is, the population will reach 0 in the year 2089.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
To identify the year in which the population will reach 0, we need to determine the rate at which the population is decreasing, and use that rate to predict when the population will be 0.
We can use the two data points given to find the rate of population decrease. Let P be the population and t be the time in years since 2010. Then we have:
P(0) = 7900 (population in 2010)
P(2) = 7700 (population in 2012)
We can find the rate of population decrease by using the formula for the slope of a line:
slope = (P(2) - P(0)) / (t(2) - t(0))
= (7700 - 7900) / (2 - 0)
= -100/year
The negative sign indicates that the population is decreasing, and the magnitude of the slope (-100/year) tells us the rate at which it is decreasing.
To find the year in which the population will reach 0, we can use the point-slope form of a line:
P - P(0) = slope * (t - t(0))
where P is the population, t is the time in years since 2010, P(0) is the population in 2010, and t(0) is 0 (the year 2010).
Substituting the known values, we get:
P - 7900 = -100 * (t - 0)
Simplifying, we get:
P = -100t + 7900
To find the year in which the population will reach 0, we set P = 0 and solve for t:
0 = -100t + 7900
100t = 7900
t = 79
Therefore, the population will reach 0 in the year 2010 + 79 = 2089.
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