Answer:
a = 11
b = 6
Step-by-step explanation:
\( \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - b \sqrt{3} \\ \\ \frac{(5 + 2 \sqrt{3} )}{(7 + 4 \sqrt{3}) } \times \frac{(7 - 4 \sqrt{3})}{(7 - 4 \sqrt{3})} = a - b \sqrt{3} \\ \\ \frac{(5 + 2 \sqrt{3)} (7 - 4 \sqrt{3} )}{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } a - b \sqrt{3} \\ \\ \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{49 - 48} = a - b \sqrt{3} \\ \\ \frac{11 - 6 \sqrt{3}}{1} = a - b \sqrt{3} \\ \\ 11 - 6 \sqrt{3} = a - b \sqrt{3} \\ \\ equating \: like \: terms \: on \: both \: \\ sides, \: we \: find : \\ \\ a = 11 \\ \\ b = 6\)
-64,-47,-30,-13 arithmetic or geometric or neither.
Answer:
Arithmetic
Step-by-step explanation:
Given sequence
-64,-47,-30,-13We can observe it is increasing sequence
The rate of increase is linear and equal to 17
Therefore it is an arithmetic progression
-64,-47,-30,-13 is arithmetic .
\( \huge \red {explanation}\)
this is arithmetic progression because ;
it is a increasing sequence the rate of increase is linear and equal to 17 . so, the required answer is arithmetic .Scientific notation (dividing): (6.8 * 10^-8) / (2.5 * 10^-4) = ________ * 10^____
Answer:
Step-by-step explanation:
2.72*10^-4
The area of a certain square is 900 square inches. What is the perimeter of this square in inches?
Answer:
The perimeter of a square with an area of 900 square feet is 120 ft.
Step-by-step explanation:
Calculation of the perimeter of the square:
Since the area is 900 square feet
We know that
The area of square =
So, length of one side should be 30
Now the perimeter should be
= 4(30)
= 120 ft.
Hence, The perimeter of a square with an area of 900 square feet is 120 ft.
The perimeter of a square with an area of 900 square feet is 120 ft.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
Given that the area of a certain square is 900 square inches.
The perimeter of the square is the sum of all the sides of the square and the formula is written as,
P = 4a
The value of side 'a' will be calculated as,
Area = a²
a = √900
a = 30 inch
The perimeter will be calculated as,
P = 4a
P = 4 x 30
P = 120 inch
Therefore, the perimeter of a square with an area of 900 square feet is 120 ft.
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CAN SOMEBODY EXPLAIN HOW TO DO THIS IT'S MY 5TH TIME ASKING AND NOBODY EVEN HELPS ME!
i used caps to get ur attention 7u7
Answer:
10x20+10x6=260
Step-by-step explanation:
Answer:
260 cm²
Step-by-step explanation:
Area of the rectangle
= l × w
= 20 × 10
= 200 cm²
Area of the triangle
= ½bh
= ½ × 20 × 6
= ½ × 120
= 60 cm²
Area of the total figure
= Area of the rectangle + Area of the triangle
= 200 cm² + 60 cm²
= 260 cm²
________
Hope it helps ⚜
In this scenario, what is the test statistic? A business journal tests the claim that the percent of small businesses that patent products is greater than 49%. Sample size =30 small businesses Sample proportion =0.60 Calculate the test statistic using the formula: z0=p′−p0/sqrt{p0⋅(1−p0)\n} p′ = sample proportion, n = sample size, and p0 = population proportion under the null hypothesis Round your answer to 2 decimal places.
The test statistic is approximately 1.22, rounded to two decimal places.
The test statistic measures the deviation of the sample proportion from the population proportion under the null hypothesis and helps determine the statistical significance of the claim.
To calculate the test statistic, we use the formula:
z0 = (p′ - p0) / sqrt(p0 * (1 - p0) / n)
Where:
p′ = sample proportion = 0.60
p0 = population proportion under the null hypothesis = 0.49
n = sample size = 30
Plugging in the values, we have:
z0 = (0.60 - 0.49) / sqrt(0.49 * (1 - 0.49) / 30)
Calculating the expression within the square root:
sqrt(0.49 * (1 - 0.49) / 30) ≈ 0.090
Substituting back into the formula:
z0 = (0.60 - 0.49) / 0.090 ≈ 1.22
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5x + 2y = 8 x + y = 4 if you want to solve the system of equations by addition which of the following could you do
Answer: x= 0, y = 4
Step-by-step explanation:
5x+2y=8
X+y=4 -> y=4-x
5x + 2(4-x)=8 -> 5x + 8-2x=8 -> 3x=0 -> x=0
y=4-x=4-0=4
What is the equation of the line that passes through the point (6, -6) and has a slope of -5/3
Answer:
y= -5/3x + 4
Step-by-step explanation:
hope this helps :)
The following lines: y=2/3(x) and y=-3/2(x) are...
O Intersectings=
O Neither
O Parallel
O Perpendicular
Need ASAP
Answer:
the answer to this question is parallel
I need help really bad plsss
Answer:
0
Step-by-step explanation:
(f-g)(x) = 12-sqrt(x)
plugging in 144, we get 12 - 12 = 0
one could also do f(x)-g(x) which would yield 24-24=0
Find the inverse of the following function: f(x) = 8√x for x ≥ 0
Answer:
B
Step-by-step explanation:
y = 8√x (square both of side)
y² = 64x
x = y²/64
f-¹(x) = x²/64
The inverse is B.) f-¹(x) = x²/64 for, x≥0
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, given that, f(x) = 8√x for x ≥ 0
Let, f(x)=y
Then, we get,
y = 8√x (square both of side)
y² = 64x
x = y²/64
i.e. f-¹(x) = x²/64
Hence, The inverse is B.) f-¹(x) = x²/64 for, x≥0
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after being nominated for an mtv music award, the probability of winning is 25%. if ariana grande has been nominated for five awards, what is the chance that she will win at least one award? how many awards should she expect to win? what is the standard deviation associated with this probability?
The probability of winning at least one award is 1 - 0.2373 = 0.7627 or 76.27%.
If the probability of winning an MTV music award after being nominated is 25%, the probability of not winning is 75%. Thus, the probability of not winning any of the five awards is (0.75)^5 = 0.2373.
As for how many awards Ariana Grande should expect to win, we can use the expected value formula: E(x) = n * p, where n is the number of trials (in this case, 5) and p is the probability of success (0.25). Therefore, E(x) = 5 * 0.25 = 1.25. So, Ariana Grande can expect to win about 1 award.
Finally, to calculate the standard deviation associated with this probability, we can use the formula: σ = sqrt(n * p * (1-p)). Plugging in the values, we get σ = sqrt(5 * 0.25 * 0.75) = 0.866. Therefore, the standard deviation associated with this probability is approximately 0.866.
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How do I find the angles
Answer: See attached
Step-by-step explanation:
We can use the knowledge of straight angles being equal to 180° and our knowledge of vertical angles as well as corresponding angles.
See attached for a visual and all the angle measurements laid out.
A store is offering a 25% discount on all items.Also, employees get a 10% employee discount. If you are an employee which discount would you want to be applied first to save the most money?
Given two points which represent the endpoints of the diameter of a circle, which of the following statements is true?
A.
The x-coordinate of the center of the circle must be the same as at least one of the x-coordinates of the given endpoints of the diameter.
B.
The center of the circle is the midpoint of the given endpoints of the diameter.
C.
The center of the circle cannot be found without additional information.
D.
The y-coordinate of the center of the circle must be the same as at least one of the y-coordinates of the given endpoints of the diameter.
The correct statement is B. The center of the circle is the midpoint of the given endpoints of the diameter.
In a circle, the center is located at the midpoint of any diameter. A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle. Therefore, if we are given the endpoints of a diameter, we can determine the center of the circle by finding the midpoint of these endpoints. This means that the x-coordinate of the center will be the average of the x-coordinates of the endpoints, and the y-coordinate of the center will be the average of the y-coordinates of the endpoints.
Option A is not necessarily true because the x-coordinate of the center may or may not be the same as the x-coordinates of the given endpoints.
Option C is incorrect because the center of the circle can be found by determining the midpoint of the diameter.
Option D is not necessarily true because the y-coordinate of the center may or may not be the same as the y-coordinates of the given endpoints.
Therefore, the correct statement is B. The center of the circle is the midpoint of the given endpoints of the diameter.
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if we use 3/4 of an 8 ounce container how much of the container is used
Answer: 6 ounces
Step-by-step explanation:
From the question, we are informed that 3/4 of an 8 ounce container is used and told to calculate how much of the container is used.
To solve this, we have to multiply 3/4 by 8 ounces. This can be mathematically written as:
= 3/4 × 8
= 6 ounces
It means that 6 ounces of the container are used
Translate into an inequality
A number w increased by 8 is at most -23
1) less than 2) greater than 3) less/equal to 4)greater/equal to
Answer:
w + 8 ≥ -23
Step-by-step explanation:
Barton wants to know how much his packed suitcase weighs before he leaves to catch a flight. The airline will charge an extra fee if his suitcase weighs more than 50 pounds. Which method should Barton use to get the most accurate and appropriate measurement?
Barton should use a luggage scale to get the most accurate and appropriate measurement of his packed suitcase before he leaves to catch a flight. A luggage scale is a compact and portable device that is designed specifically to weigh luggage. Using a luggage scale is easy and convenient as it allows travelers to weigh their bags accurately, ensuring that they are within the airline's weight limit. To use a luggage scale, Barton should follow these simple steps:
Step 1: Attach the luggage strap Barton should attach the luggage strap to the handle of his suitcase.The strap should be attached in such a way that it can support the weight of the suitcase without slipping or coming off.
Step 2: Turn on the luggage scale Barton should turn on the luggage scale and wait for it to calibrate. This usually takes a few seconds. Once the scale is calibrated, it will display a zero reading.
Step 3: Lift the suitcase Barton should lift the suitcase by the luggage strap until it is off the ground. The luggage scale will display the weight of the suitcase on its digital display. This reading is the weight of the suitcase including all the contents inside.
Step 4: Check the weight If the weight of the suitcase is less than 50 pounds, Barton can go ahead and catch his flight without worrying about any extra charges. If the weight of the suitcase is more than 50 pounds, Barton will have to remove some items from the suitcase or pay the extra fee charged by the airline.
Therefore, using a luggage scale is the most accurate and appropriate method for travelers like Barton to measure their suitcase weight before boarding their flight.
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Answer:
use a standard digital bathroom scale.
Step-by-step explanation:
Suri makes $15 per hour and gets a weekly bonus of $25. Juan makes $14 per hour and gets a weekly bonus of $50. Is it possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week?
Yes, because the slopes of the equations are different so the system of equations will have one solution.
No, because the slopes of the equations are different so the system of equations will have no solutions.
Yes, because the slopes of the equations are the same so the system of equations will have infinitely many solutions.
No, because the slopes of the equations are the same so the system of equations will have no solutions.
Answer:
Yes, because the slopes of the equations are different so the system of equations will have one solution.
Step-by-step explanation:
What is 5/42 as a decimal rounded to 3 decimal places?
Answer:
0.119
Step-by-step explanation:
hope this helps
Answer:
0.119
Step-by-step explanation:
Well 5/42 is quite easy! Just do some long division it'll work easily! That'll give you 0.119047619 it's a long decimal! Then just round it to get 0.119. I hope the explanation helped if you don't get long division you should watch some videos it'll be helpful.
Find f(x)= x^4-2x^2+3
a) find the local max and minimum values
b) Find the intervals of concavity and the inflection point
c) find the intervals on which the function is increasing or decreasing
a) The given function is f(x) = x⁴ − 2x² + 3. We can find the local maxima and minima of the function using its first derivative
:f(x) = x⁴ − 2x² + 3f'(x) = 4x³ − 4xIf f'(x) = 0, then x = 0 or x = ±1.
The critical values of f(x) are −1, 0, and 1.Therefore, the function has local maxima at x = ±1 and a local minimum at x = 0.b) We need to find the intervals of concavity and the inflection point of the given function.
To find the concavity, we will use the second derivative
:f(x) = x⁴ − 2x² + 3f'(x) = 4x³ − 4xf''(x) = 12x² − 4If f''(x) = 0, then x = ±sqrt(3/2).The critical values of f''(x) are −sqrt(3/2) and sqrt(3/2).
Therefore, the function is concave upward on the intervals (−∞, −sqrt(3/2)) and (sqrt(3/2), ∞) and concave downward on the interval (−sqrt(3/2), sqrt(3/2)).
The inflection point of the function is at x = ±sqrt(3/2).c) To find the intervals on which the function is increasing or decreasing, we need to analyze the sign of the first derivative:
f(x) = x⁴ − 2x² + 3f'(x) = 4x³ − 4xThe function is decreasing on the interval (−∞, 0) and increasing on the intervals (0, 1) and (−1, ∞).
Thus, the function is increasing on (0, ∞) and decreasing on (−∞, 0).So, the intervals of increase are (0, ∞) and intervals of decrease are (−∞, 0).
Therefore, the simple answer is:
a) The function has a local maximum at x = ±1 and a local minimum at x = 0.
b) The function is concave upward on the intervals (−∞, −sqrt(3/2)) and (sqrt(3/2), ∞) and concave downward on the interval (−sqrt(3/2), sqrt(3/2)).
The inflection point of the function is at x = ±sqrt(3/2).c) The function is increasing on (0, ∞) and decreasing on (−∞, 0).
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A business analyst deposited $50,000 into an account earning an annual interest rate of 5.5% compounded monthly. If the analyst leaves the money in the account for 2 years, how much interest (in dollars) is earned on the account?
The interest earned on the account is $5,750.53 when $50,000 is deposited for 2 years at an annual interest rate of 5.5% compounded monthly.
To calculate the interest earned on the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $50,000, the annual interest rate (r) is 5.5% (or 0.055 as a decimal), the interest is compounded monthly (n = 12), and the money is left in the account for 2 years (t = 2).
Plugging these values into the formula, we have:
A = 50000(1 + 0.055/12)^(12*2)
Simplifying the equation, we get:
A = 50000(1 + 0.004583333333333333)^(24)
A = 50000(1.004583333333333333)^(24)
A = 50000(1.115010680047)
A = 55750.53400235
To find the interest earned, we subtract the principal amount from the final amount:
Interest = A - P
Interest = 55750.53400235 - 50000
Interest = 5750.53400235
Therefore, the interest earned on the account is $5,750.53 (rounded to two decimal places).
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What is x?
3/6=5.5/x
Answer:
x = 11
Step-by-step explanation:
3/6=5.5/x
Cross multiply.
3 * x = 6 * 5.5
x = 2 * 5.5
x = 11
the midpoints of the sides of a regular hexagon abcdef are joined in order to form a smaller regular hexagon. what fraction of the area of abcdef is enclosed by the smaller hexagon?
A regular hexagon can be divided into six equilateral triangles by drawing lines from the center of the hexagon to each of its vertices.
Each of these equilateral triangles has an area that is one-sixth of the total area of the regular hexagon.
When the midpoints of the sides of the regular hexagon are joined to form a smaller regular hexagon, it can be seen that the smaller hexagon is made up of six equilateral triangles, each of which has half the area of the equilateral triangles in the larger hexagon. This is because the sides of the smaller hexagon are half the length of the sides of the larger hexagon.
Therefore, the fraction of the area of the larger hexagon that is enclosed by the smaller hexagon is:
\(6 * (1/2)^2 = 6 * 1/4 = 3/2\)
This means that the smaller hexagon encloses 3/2 of the area of the larger hexagon.
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Someone plz help me I will give brainliest
Answer:
$33.81
Step-by-step explanation:
Strawberries = $2.49 Per Pound (Bought 3)
Blueberries = $3.19 Per Pound (Bought 2)
Pineapples = $4.99 Per Pound (Bought 4)
So we have to multiply each price with the number of fruits bought.
So, For Example, Strawberries: $2.49 × 3 = $7.47
After you did all three individually, add them all up.
Strawberries : $7.47
Blueberries : $6.38
Pineapple : $19.96
Total = $33.81
Hope This Helps!The country of Sylvania has decided to reduce the number
3
of its illiterate citizens by
5 each year. This year there are
9000 illiterate people in the country.
Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today.
The functiοn that gives the number οf illiterate peοple in Sylvania is
\(\mathrm{P(t) = 9000(2/5)^t}\)
What are functiοns in mathematics?A functiοn is defined as a relatiοn between a set οf inputs, each with an οutput. Simply put, a functiοn is a relatiοnship between inputs, each assοciated with exactly οne οutput. Each functiοn has a dοmain and cοdοmain οr scοpe.
Hοw tο identify relatiοn and functiοn?Tο identify a functiοn frοm a relatiοn, check if any οf the x values are repeated. If it's nοt repeated, it's a functiοn. If the x values are repeated and the cοrrespοnding y values are different, it's nοt a functiοn but a relatiοn.
Sοlutiοn accοrding tο the questiοn:
Given, Tοtal number οf illiterate peοple = 9000
Amοunt = 3/5
Fοr the first year = 9000 × (1 - 3/5) = 9000(2/5)
Nοw, fοr "t years":
P(t) = 9000(2/5)
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Find the value of x. *
Please help me.
Answer:
x=50
Step-by-step explanation
The two angles add up to 180, so 2x+4+76 = 180
2x+80=180
2x=100
x=50
10. at a pizza shop there is a deal going on that you can get a pizza for $3.00. you can choose thick or thin crust, red or white sauce, and one topping of either pepperoni, sausage, or vegetarian. create a tree diagram to display the sample space on your worksheet. how many total outcomes are there?
The number of total outcomes is 12.
Here is a tree diagram for the pizza options:
Copy code
/ | \
Thick Thin
/ | \
Red White Red White
/ | \ / | \ / | \
Pep Saus Veg Pep Saus Veg Pep Saus Veg
There are two (2) options for the crust, two (2) options for the sauce, and three (3) options for the topping. Therefore, the total number of outcomes is:
Total Outcomes = 2 (options for crust) x 2 (options for sauce) x 3 (options for topping)
Total Outcomes = 12
Therefore, there are 12 total outcomes.
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A family visits a car show to research information on vehicles they might consider purchasing. Brochures for each vehicle provide helpful information for the vehicle. Which of the following is an example of a discrete quantitative variable that might be included in the brochure? number of seats type of transmission presence of a sunroof fuel efficiency (in mpg)
Answer:
The correct option is;
Number of seats
Step-by-step explanation:
A quantitative variable is a variable that has a numeric value used to describe the measured characteristic of an item
A discrete variables are countable variables within given finite amount of time
Therefore, a discrete quantitative is a countable variable that indicates the measured value of an item or feature'
In the question, the discrete quantitative variable that might be included in the brochure is Number of seats.
Answer: The number of seats
Step-by-step explanation: Because a discrete quantitative variable is a variable whose value is obtained by counting. you’re welcome:)
If a military person donates 15% blood for 10 dollars and the civilian person donates 23% for 20 dollars blood both people of color donate blood in Encinitas California 92007 by the 7-11 place. How much blood would they donate altogether please do not forget to do the math and please let me know how much is it
Altogether, they would donate a total of 380 milliliters of blood.
To calculate the total amount of blood donated by the military person and the civilian person, we need to determine the amount of blood donated by each individual and then sum them up. Let's go through the steps:
Calculate the amount of blood donated by the military person:
The military person donates 15% of their blood for 10 dollars. Since we don't have the specific measurement of their blood volume, we can assume a standard unit. Let's assume their total blood volume is 1 liter (1000 milliliters).
15% of 1000 milliliters = 0.15 * 1000 = 150 milliliters.
Calculate the amount of blood donated by the civilian person:
The civilian person donates 23% of their blood for 20 dollars. Using the same assumption of a blood volume of 1 liter (1000 milliliters):
23% of 1000 milliliters = 0.23 * 1000 = 230 milliliters.
Calculate the total amount of blood donated:
To find the total amount of blood donated, we sum up the amounts donated by the military person and the civilian person:
Total blood donated = 150 milliliters + 230 milliliters = 380 milliliters.
Therefore, altogether, they would donate a total of 380 milliliters of blood.
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What is the equation of this line?
A.) y=1/2x-2
B.) y=2x-2
C.) y=-1/2-2
D.) y=-2x-2
Answer:
Plug the x and y values to get it
Step-by-step explanation: