The equation that represents the total cost of the TV is Option B: 1/4x + 1/3 × 3/4x + 1/4x + 20 + 120 = x.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let's represent the total cost of the TV with the variable x.
According to the problem, Adam's first payment was 1/4 of the total price, so he still owed 3/4 of the price.
His second payment was 1/3 of the remaining amount, which is 1/3 × 3/4x = 1/4x, leaving him with 3/4x - 1/4x = 1/2x to pay.
His third payment was $20 more than the first payment, so it was 1/4x + 20, leaving him with 1/2x - (1/4x + 20) = 1/4x - 20 to pay.
Finally, his last payment was $120, so the remaining amount he owed was 1/4x - 20 - 120 = 1/4x - 140.
Adding up all of these payments, we get -
1/4x + 1/4x + 20 + 1/4x - 140 + 120 = x
Simplifying this equation, we get -
3/4x = 100
Multiplying both sides by 4/3, we get -
x = 400/3
Therefore, the equation is obtained as 1/4x + 1/3 × 3/4x + 1/4x + 20 + 120 = x.
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Adam bought a TV and paid it in four payments. His first payment was 1/4 of the total price. His second payment was 1/3 of the remaining amount. His third payment was $20 more than the first payment. His last payment was $120. Which equation represents the total cost of the TV?
a. 1/4x + 1/3x + 20 + 120 = x
b. 1/4x + 1/3 × 3/4x + 1/4x + 20 + 120 = x
c. 1/4x + 1/3 × 1/4x + 20 + 120 = x
d. 1/4x + 1/3x + 20 = 120
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?
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.
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
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
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 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?
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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In Vincent garden 1/6 of the flowers are daisies, and 1/8 of the flowers are snapdragons.
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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4. Find each interior angle
Sort from smallest to largest
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
What is a log can kate use to fill remaining 1/3 meters
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.
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.
sin88°=
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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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.)
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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what 2 distributive property expressions equal to 108
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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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
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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If this circle has a radius of 13.2 and m∠f=140°, calculate the area of the intercepted sector (shaded blue). Round answers to two decimal places. Use the π button on your calculator.
The area οf a sectοr is 67.76π.
What is an area οf the sectοr?The quantity οf space included within the sectοr's perimeter is referred tο as the sectοr's area in a circle. A sectοr always starts at the circle's center. The area οf a circle encοmpassed between its twο radii and the arc next tο them is knοwn as the sectοr οf a circle.
Here, we have
Given: If this circle has a radius οf 13.2 and m∠f=140.
We have tο find the area οf the intercepted sectοr.
The area οf the sectοr is given as θ/360*πr²
Where,
θ = central angel οf the sectοr, m∠f=140°
r = radius = 13.2
Area οf sectοr = 140/360*π(13.2)²
= 67.76π
Hence, the area οf a sectοr is 67.76π.
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The area οf a sectοr is 67.76π.
What is an area οf the sectοr?The quantity οf space included within the sectοr's perimeter is referred tο as the sectοr's area in a circle. A sectοr always starts at the circle's center. The area οf a circle encοmpassed between its twο radii and the arc next tο them is knοwn as the sectοr οf a circle.
Here, we have
Given: If this circle has a radius οf 13.2 and m∠f =1 40.
We have tο find the area οf the intercepted sectοr.
The area οf the sectοr is given as θ/360 × πr²
Where,
θ = central angel οf the sectοr, m∠f=140°
r = radius = 13.2
Area οf sectοr = 140/360*π(13.2)²
= 67.76π
Hence, the area οf a sectοr is 67.76π.
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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.
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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please answer asap for homework
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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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.
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
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)
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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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 =
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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I need help on this question
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)
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.
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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5) y=-2
4x – 3y = 18
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
Find the theoretical probability.
Simplify completely.
7
6
8 1
5
4
2
3
P(4) =
1
?
The theoretical probability of 4 is 1/8
What is theoretical probability?Theoretical probability is the measure of the likelihood of an event occurring based on the mathematical analysis of its underlying assumptions and properties.
How to determine the theoretical probabilityFrom the question, we have the following parameters that can be used in our computation:
The spinner
From the spinner, we have
Sections = 8 different sections
Occurence of 4 = 1
Using the above as a guide, we have the following:
P(4) = Occurrence of 4/Sections
Substitute the known values in the above equation, so, we have the following representation
P(4) = 1/8
Hence, the solution is 1/8
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Please answer this for me quick i have another one after this
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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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)
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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Find the size of the angels labeled with letters. On is the center of the circle
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.)
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?
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.
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 = $
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
to plot the point for a library at (2, - 3) 2 units to
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
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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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?
Answer:
James needs 5 gallons of water.
Step-by-step explanation:
1 gallon = 8 pints
40 ÷ 8 = 5
5 gallons
Determine whether a triangle can be formed with the given side lengths.
Question 3and4 pls
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