Answer50.5
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Simplify the expression. 4+5/3^2−2^
2
The simplified expression is 25/9, of the given expression. 4 + (5/3)² − 2².
What is the exponentiation?
An exponential function is a mathematical function of the following form: f (x) = ax. where x is variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately
To simplify the expression, we need to follow the order of operations, which is:
Evaluate any expressions inside parentheses or brackets.
Exponents (ie, powers and square roots, etc.)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Using this order, we can simplify the expression as follows:
4 + (5/3)² - 2²
= 4 + (25/9) - 4 ..........5/3 squared is 25/9 and 2 squared is 4
= (36/9) + (25/9) - (36/9) ..........rewrite 4 as 36/9 to have a common denominator of 9
= 25/9
Therefore, the simplified expression is 25/9.
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What is the hexadecimal expansion of (ABC)16 + (2F5)16
Loren already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 30 years in an account paying 10% interest, how much could the annuity provide each month?
Loren could receive a monthly payout of approximately $4,646.81 from the annuity to last for 30 years at a 10% annual interest rate.
What is annuity?
A contract between you and an insurance company known as an annuity entails you making a lump sum payment or a series of payments in exchange for regular payments starting either right away or in the future.
To calculate the monthly payout that Loren can receive from an annuity for 30 years, use the formula for the present value of an annuity -
PV = PMT x [(1 - (1 + r)^(-n)) / r]
Where PV is the present value of the annuity (the amount of money Loren has at retirement), PMT is the monthly payout, r is the monthly interest rate (10%/12 = 0.00833), and n is the number of monthly payments (30 years x 12 months/year = 360 months).
Substituting the given values into the formula -
$500,000 = PMT x [(1 - (1 + 0.00833)^(-360)) / 0.00833]
Solving for PMT -
PMT = $500,000 / [(1 - (1 + 0.00833)^(-360)) / 0.00833]
PMT = $4,646.81
Therefore, The value is obtained as $4,646.81.
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Find the value of y.
y
3 cm
9 cm
2 cm
y = [?] cm
Enter a decimal rounded to the nearest tenth.
Answer:
The value of y is 10 cm
What is the future value of $2,500 deposited for one year earning a 14 percent interest rate annually
Answer: $2,850
Step-by-step explanation:
Hope this helped you. Brainliest if possible! :D
I also answered first! (Please don't copy my answer for anyone that answer this question!) :D
Find the volume of the rectangular prism with square bases as pictured below
with a = 2 cm and b = 4 cm. Do not include units in your answer.
The volume of the rectangular prism is 32 square centimeters.
What is a prism?A prism is a polyhedron in three dimensions with two identical ends.
The volume of the rectangular prism
= base area of the prism x the height of the prism.
Given:
The base of the prism is squared shape.
And the side of the square is 4 centimeters.
b = 4 and the height is 2 centimeters.
The volume of the rectangular prism,
= base area x height
= (4 x 4) x 2
= 32 square centimeters.
Therefore, the volume of the prism is 32 square centimeters.
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The complete question is given in the attached image.
the length of each side of a square was decreased by 2 inches, so the perimeter is now 48 inches. What was the orginal length of each side of the square?
The original length of each side of the square was 14 inches.
Define a square.A square is a geometric form with two dimensions that has four equal sides and four angles that are each 90 degrees (also known as right angles). With all sides being the same length and all angles being right angles, it is a particular case of a rectangle and a parallelogram. A square's sides are all perpendicular to one another, and its diagonals are at right angles to one another. Squares exhibit rotational symmetry of order 4 because they are symmetrical in both their vertical and horizontal axes.
Let's assume that the original length of each side of the square was "x" inches.
When each side of the square is decreased by 2 inches, the new length of each side will be (x-2) inches.
The perimeter of the new square is given as 48 inches. Since a square has four equal sides, the perimeter of a square is given by the formula:
Perimeter = 4 * Side
So, for the new square, we have:
48 = 4 * (x-2)
Simplifying the above equation, we get:
12 = x-2
Adding 2 to both sides, we get:
x = 14
Therefore, the original length of each side of the square was 14 inches.
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Determine if this equation is true or false:
Answer:
The equation is false
Step-by-step explanation:
(x+5)^2 = x^2+25
FOIL the left hand side.
(x+5)(x+5)
x^2 +5x+5x+25
x^2 +10x+25
This does not equal x^2+25.
this is the first part of a three-part problem. express 18√8 in the form a√b, where a and b are integers and b is as small as possible. Hint(s): Factor √8 as the product of two square roots, one of which is the square root of a perfect square.
Answer:
18√8 = 3√2 * 3√2
Step-by-step explanation:
I factored the square root of 8 into the square root of 2 times the square root of 2, because I believe that the square root of 8 was supposed to be factored based upon the hint provided.
This resulted in the expression 3√2 * 3√2, which is equivalent to 3*3*sqrt(2) * sqrt(2).
The magnitude of earthquake can be detected using the Richter Scale (R)
(
R
)
as function of the earthquake amplitude (A)
(
A
)
and standard wave amplitude (A0)
(
A
0
)
, where R=log(AA0)
R
=
l
o
g
(
A
A
0
)
. Given that the earthquake amplitude is 288 times as great as wave amplitude, what is the magnitude of this earthquake using the Richter scale to one decimal place
The magnitude of the earthquake, as measured on the Richter Scale, is 2.5.
What is Richter Scale ?
The Richter Scale is a logarithmic scale used to measure the magnitude of earthquakes. It was developed by seismologist Charles Richter in the 1930s and is named after him.
The Richter Scale measures the amplitude of the seismic waves produced by an earthquake, which are detected by seismographs. The amplitude is a measure of the size of the earthquake, and is related to the amount of energy released by the earthquake.
Given by the question:
The Richter Scale equation for the magnitude (R) of an earthquake is:
R = log(A/A0)
where A is the amplitude of the earthquake and A0 is a standard wave amplitude.
We are given that the earthquake amplitude (A) is 288 times as great as the standard wave amplitude (A0):
A = 288 A0
Substituting this into the Richter Scale equation, we get:
R = log(288 A0 / A0)
R = log(288)
Using a calculator or a logarithm table, we can evaluate the logarithm of 288 to get:
R = 2.46
Rounding this to one decimal place, we get:
R ≈ 2.5
Therefore, the magnitude of the earthquake, as measured on the Richter Scale, is 2.5.
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A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation for the simple harmonic motion, in the form: _____ d = sinwt.
Answer:
How many centimeters are there in 58 inches?
1 in. = 2.54 cm
Step-by-step explanation:
Solution of 1- 2y/3 - y + 2y = 1/y + 2, Please.
Therefore , the solution of the given problem of equation comes out to be y = (3 - √21) / 2
A linear equation is precisely what?A straightforward regression curve is created using the equation y= mx+b. The y-intercept is m, and the slope is B. The phrase "math equation combining numerous variables" is sometimes used to describe the prior line even though it represents distinct components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations. Y=mx+b.
Here,
Starting with the given equation:
1 - 2y/3 - y + 2y = 1/y + 2
Simplifying the left side:
1 - y/3 = 1/y + 2
Multiplying both sides by 3y:
3y - y² = 3 + 6y
Bringing all terms to one side:
y² + 3y - 3 - 6y = 0
Simplifying:
y² - 3y - 3 = 0
Using the quadratic formula:
y = (3 ± √21) / 2
Therefore, the solutions for y are:
y = (3 + √21) / 2
or
y = (3 - √21) / 2
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During the summer, Curran and AJ
started their own business mowing
lawns. Before starting any work, Curran
spent $20 to ! ll up the gas tank for the
lawnmower. The boys agreed that each
person would earn the same amount
after Curran was reimbursed the money
he spent for gas. After a week of work,
the boys were paid a total of $177.
Curran ! lled up the gas tank just once.
How much did each boy earn?
The boys agreed that each person would earn the same amount after Curran was reimbursed the money he spent on gas. After a week of work, the boys were paid a total of $177. thus each boy earned $88.50.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
Let's denote the amount each boy earns by x.
According to the given information, Curran spent $20 for gas, which he should be reimbursed for. This means that the total revenue of the business was $177 + $20 = $197.
Since each person earns the same amount, we can set up an equation:
2x + $20 = $197
Simplifying and solving for x, we get:
2x = $177
x = $88.50
Therefore, each boy earned $88.50.
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a large company is being sued for false advertisement because 18% of the flashlights in its shipping boxes are defective, but the company claims that only 8% are defective. you plan to use hypothesis testing to determine whether there is significant evidence that the company is falsely advertising. part a: state the null and alternative hypotheses for the significance test. (2 points) part b: in the context of the problem, what would a type i error be? a type ii error? (2 points) part c: if the hypothesis is tested at a 10% level of significance instead of 5%, how will this affect the power of the test? (3 points) part d: if the hypothesis is tested based on the sampling of 100 boxes of flashlights rather than 1,000 boxes of flashlights, how will this affect the power of the test? (3 points) source stylesformatfontsize
The required solution for the hypothesis testing is shown.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here, we have,
Part A:
The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.
The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.
H0: p ≤ 0.05
Ha: p > 0.05
where p represents the proportion of defective batteries.
Part B:
A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.
A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.
Part C:
If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.
Part D:
If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.
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Find the y-intercept and slope of line. y=-7x-5
Answer:
Step-by-step explanation:
La ecuación y = -7x - 5 es una ecuación lineal en la forma y = mx + b, donde "m" es la pendiente y "b" es el punto de intersección en el eje y. Por lo tanto, podemos identificar la pendiente y el punto de intersección de la línea directamente de la ecuación.
Pendiente:
La pendiente "m" de la línea se encuentra en el coeficiente que acompaña a "x" en la ecuación de la línea. En este caso, la pendiente es "-7", por lo que la pendiente de la línea es -7.
Punto de intersección:
El punto de intersección "b" se encuentra en el término independiente de la ecuación de la línea, que es el número que no tiene una "x" al lado. En este caso, el punto de intersección es "-5", por lo que la línea cruza el eje y en el punto (0,-5).
Por lo tanto, la pendiente de la línea es -7 y el punto de intersección es (0,-5).
Answer: Y-intercept: -5, Slope of the line: -7 or -7/1
Step-by-step explanation:
The equation for the slope is y=mx+b.
m= slope of the line
b= y-intercept
So when you take the equation y=-7x-5, you take out those plugged in values.
So the slope of the line is -7 (or -7/1) and the y-intercept is -5.
A tank of water has a base a circle of radius 2 meters and vertical sides. If water leaves the tank at a rate of 2 liters per minute, how fast is the water level falling in centimeters per hour? [1 liter is 1000 cubic centimeters].
The water level is falling at a rate of approximately 0.152 centimeters per hour.
The radius r of the circular base is given as 2 meters, or 200 centimeters. Substituting this and rearranging the above equation, we get:
dh/dt = (dV/dt)/(πr²) = (-2000 cm³/min)/(π(200 cm)²) ≈ -0.00253 cm/min
To find the rate of change of water level in centimeters per hour, we can convert the above result to centimeters per hour by multiplying it by 60:
dh/dt ≈ -0.00253 cm/min × 60 min/hour ≈ -0.152 cm/hour
Therefore, the water level is falling at a rate of approximately 0.152 centimeters per hour.
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What is the area of the figure?
6 ft
5 ft/
4 ft
3 ft
The area of the sector is 16.1 ft².
What is the area of a sector?The formula for the area of a sector of a circle is given as;
A = θ/360⁰ x ( r² )
where;
r is the radius of the circle andθ is the angle of the sectorThe angle of the sector is calculated as follows;
sin (θ/2) = 3 / 5
sin (θ/2) = 0.6
θ/2 = sin⁻¹ ( 0.6 )
θ/2 = 36.87⁰
θ = 2 x 36.87⁰
θ = 73.74⁰
The area of the sector is calculated as;
A = (73.74 / 360 ) x π (5²)
A = 16.1 ft²
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Least Common Denominator
The required least common denominator for the given expression is 4x³(x + 3). Option C is correct.
What is a rational fraction?A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.
Here,
The given rational expression,
= 1/x² - 1/4x² + 12x
In the question, we have been asked to determine the least common denominator for the given rational expression.
Since least common denominator is given expression,
= x² (4x² + 12x)
= 4x³(x + 3)
Thus, the required least common denominator for the given expression is 4x³(x + 3). Option C is correct.
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Tyreek is planning on driving to Outer Banks from Philadelphia. On the map, Tyreek is using, each inch represents 50 miles. If the distance on the map from Philadelphia to OBX is 7/34 inches, how far is it in actual miles? Show your work.
The distance from Philadelphia to Outer Banks is given by A = 10.294 miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the distance on the map be represented as
1 inch = 50 miles
So , the distance between Philadelphia to Outer Banks is = ( 7 / 34 ) inches
And , the distance between Philadelphia to Outer Banks = ( 7/34 ) x 50 miles
On simplifying the equation , we get
The distance between Philadelphia to Outer Banks A = 0.20588 x 50
The distance between Philadelphia to Outer Banks A = 10.294 miles
Hence , the distance is 10.294 miles
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Find the area of the shaded sector of the circle.
The area of the shaded sector of the circle is 7.27 m^2
What is the area of a circle?The area of a circle is the amount of two-dimensional space taken up by the circle. It can be calculated by using the formula A = πr2, where A is the area, π is 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to any point on the circle. The diameter of a circle, which is the distance from one side to the other, is twice the radius. Therefore, the area of a circle can also be calculated by using the formula A = πd2/4, where d is the diameter of the circle.
The area of the shaded sector of the circle is 7.27 m^2.
This can be calculated using the formula A = (π/180) x r^2 x θ, where r is the radius (18 m in this case), and θ is the angle in degrees (110° in this case).
Therefore, A = (π/180) x (18^2 x 110) = 7.27 m^2.
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make an infinite set of sets of natural numbers such that all of their pairwise symmetric differences are infinite
Answer:
Step-by-step explanation:
To construct an infinite set of sets of natural numbers such that all of their pairwise symmetric differences are infinite, we can define the following sequence of sets:
S_1 = {1, 2, 3, ...}
S_2 = {2, 3, 4, ...}
S_3 = {1, 3, 5, ...}
S_4 = {2, 4, 6, ...}
S_5 = {1, 4, 7, ...}
S_6 = {2, 5, 8, ...}
...
In general, S_n is the set of natural numbers that are congruent to n mod 2. For example, S_1 is the set of all odd natural numbers, S_2 is the set of all even natural numbers, and so on.
To show that all of their pairwise symmetric differences are infinite, we can consider any two distinct sets S_n and S_m. Without loss of generality, assume that n < m. Then, the symmetric difference between S_n and S_m is the set of natural numbers that are congruent to n or m mod 2, but not both:
S_n Δ S_m = {k ∈ N : (k ≡ n mod 2) XOR (k ≡ m mod 2)}
Since n < m, we can see that every other natural number is in this set, and therefore it is infinite. Hence, the sequence {S_n} is a set of sets of natural numbers such that all of their pairwise symmetric differences are infinite
Let A = {a, s, i, m, o, v}
How many partitions are possible for this set?
Answer:
Step-by-step explanation:
The number of partitions possible for a set A with n elements is given by the Bell number, denoted as Bn.
For a set A = {a, s, i, m, o, v} with 6 elements, the number of partitions possible is given by the 6th Bell number, which can be computed as follows:
B6 = ∑k=1 to 6 {6 choose k} * Sk
where Sk is the Stirling number of the second kind, which counts the number of ways to partition a set of n elements into k non-empty subsets.
Using this formula, we can compute the Bell number for n = 6 as follows:
B6 = {6 choose 1} * S1 + {6 choose 2} * S2 + {6 choose 3} * S3 + {6 choose 4} * S4 + {6 choose 5} * S5 + {6 choose 6} * S6
S1 = 1, S2 = 15, S3 = 25, S4 = 10, S5 = 1, S6 = 0 (using a table of Stirling numbers)
B6 = (6 choose 1) * 1 + (6 choose 2) * 15 + (6 choose 3) * 25 + (6 choose 4) * 10 + (6 choose 5) * 1 + (6 choose 6) * 0
= 1 + 90 + 200 + 150 + 6 + 1
= 448
Therefore, there are 448 possible partitions of the set A = {a, s, i, m, o, v}.
100 people are given a standard antibiotic to treat an infection and another 100 are given a new antibiotic. In the first group, 90 people recover; in the second group, 85 people recover. Let p1 be the probability of recovery under the standard treatment and let p be the probability of recovery under the new treatment. We are interested in estim p1 - p2. Provide an estimate, standard error, an 80 percent confidence interval, and a 95 percent confidence interval for θ.
An 80 percent confidence interval, and a 95 percent confidence interval for θ are (0.0471,0.0529) and (0.0455 , 0.0545) respectively.
What is confidence interval?
A confidence interval is a range of estimates for an unknown quantity in frequentist statistics.The most frequent confidence level is 95%, but other levels, such 90% or 99%, are infrequently used for generating confidence intervals.
The true value of an unknown parameter is calculated using a confidence interval, a sort of interval computation used in statistics, based on the observed data. The interval provides a level of confidence in its estimation of the deterministic parameter, which is measured by the confidence level.
P1= 90/100= 0.9
P2= 85/100= 0.85
The estimate θ =P1-P2 =0.05
p = (X_1+X_2)/(n_1+n_2) = (90+85)/(100+100) = 0.88
Standard deviation =√{P*(1-P)*(1/n1+1/n2)}
= √(0.88*0.12*0.02)
=0.0023
80% confidence interval for θ:
(0.0471 , 0.0529)
95% confidence interval for θ: (0.0455 , 0.0545)
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Fatima's curtain company is making curtains for a local hotel. She wants each curtain to be 48 inches long. At the fabric store, fabric is sold by the foot. If Fatima's curtain company wants to make 62 curtains, how many feet of fabric will she need? 1 inch= foot 4 - 12
Answer:
So, Fatima's curtain company needs to purchase 248 feet of fabric to make the curtains for the local hotel.
Step-by-step explanation:
To find out how many feet of fabric Fatima's curtain company needs, we first need to calculate the total length of fabric required for all 62 curtains.
Each curtain is 48 inches long, so the total length of fabric required for one curtain is:
48 inches = (48/12) feet = 4 feet
Therefore, the total length of fabric required for 62 curtains is:
62 curtains x 4 feet/curtain = 248 feet of fabric
So, Fatima's curtain company needs to purchase 248 feet of fabric to make the curtains for the local hotel.
Select the correct equation in the list PLSS HELP
3x - 8y = -19 would be -6x + 16y = 38. Option A is correct when we multiply the equation by factor -2
How to solve the equationThe systems of equation that would be equivalent to
3x - 8y = -19 can be gotten by using a common factor that can get us the solution
3x - 8y = -19 we would multiply this by 2
6x - 16y = -38 this is not in the solution
Then we have to multiply the first equation by -2
-2(3x - 8y = -19)
-6x + 16y = 38
Therefore the first option is equivalent to the first equation in the system
proof using 7 and 5
- 6 * 7 + 16 * 5 = 38
-42 + 80 = 38
Also 3x - 8y = -19
= 3 * 7 - 8 * 5 = -19
21 - 40 = -19
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say we throw a sequence of balls into n bins uniformly and independently until all bins contain at least one ball. let z be a r.v. for the number of times we threw a ball into a bin that already had at least one ball in it. write an expression for e[z]
An expression for e[z] by the given data is E[z] = (n-1)/n * H_n-1.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_nT_{n+1} - T_n
for all positive integer values of n.
We are given that;
Balls are thrown uniformly and independently in all bins
Now,
We can express z as the sum of these binary random variables:
[tex]z = z_1 + z_2 + ... + z_{n-1}[/tex]
The random variables z_i are not independent, since the probability of throwing a ball into a bin that already has at least one ball in it depends on the number of balls already in the bin.
However, we can still use the linearity of expectation to calculate the expected value of z:
[tex]E[z] = E[z_1 + z_2 + ... + z_{n-1}][/tex]
By the linearity of expectation, we can distribute the expectation over the sum:
[tex]E[z] = E[z_1] + E[z_2] + ... + E[z_{n-1}][/tex]
Using these probabilities, we can calculate the expected value of each z_i:
[tex]E[z_i] = 1 * P(z_i=1) + 0 * P(z_i=0)= P(z_i=1)[/tex]
= (i-1)/n-i+1
Substituting this into the expression for E[z], we get:
[tex]E[z] = (1-1/n) + (2-1/n-1) + ... + (n-1-1/2)= (n-1)/n + (n-1)/n-1 + ... + 1/2[/tex]
This is a finite arithmetic series with n-1 terms, with first term (n-1)/n and common difference -1/n. Using the formula for the sum of an arithmetic series, we get:
[tex]E[z] = (n-1)/n + (n-2)/n + ... + 1/n= (n-1)/n * (1 + 1/2 + ... + 1/(n-1))[/tex]
This sum is known as the n-th harmonic number, denoted H_n.
Therefore, by arithmetic sequence the answer will be E[z] = (n-1)/n * H_n-1
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Somebody help me please!!!!
Point F is on the line segment EG. Given EG=5x+7, EF=5x, and FG=2x-7, determine the numerical length of FG.
Answer:
[tex]\text{Numerical length of $\overline{FG}$ = 7}[/tex]
Step-by-step explanation:
We are given the following data:
[tex]EG = 5x + 7\\EF = 5x\\FG=2x-7\\[/tex]
Point F is the line segment [tex]\overline{EG}[/tex]
So F is between E and G
We get the relationship
EG = EF + FG
→ 5x + 7 = 5x + (2x - 7)
→ 5x + 7 = 5x + 2x - 7
→ 5x + 7 = 7x - 7
Moving x terms to the left and the constant 7 from left to the right gives
→ 5x - 7x = -7 +(-7)
→ -2x = -14
→ x = -14/-2 = 7
Therefore length of FG = 2x - 7
= 2(7) - 7
= 14 - 7
= 7
The area of the scale model of a garden is 15 square feet. The scale model is enlarged by a scale factor of 3 to create the actual garden. Which expression finds the area of the actual garden?
Answer:
15 x [tex]3^{2}[/tex]
Step-by-step explanation:
since each side is increased by 3, total enlargement of area will be [tex]3^{2}[/tex] times
pls give simpe working out
Answer:
b = 82
Step-by-step explanation:
Given
a =46 degrees
c = 52 degrees
Since XY is a straight line, it has an angle of 180 degrees
So, Angle a + angle b + angle c = 180 degrees
46 + angle b + 52 = 180
angle b + 98 = 180
angle b = 180 - 98
angle b = 82 degrees
Therefore angle b is equal to 82 degrees
Answer:
180 in a straight line
Step-by-step explanation:
there is 180⁰ in straight line.
46 + 52 is 98
180 - 98 is 82
Everybody's blood pressure varies over the course of the day. In a certain individual the resting diastolic blood pressure at time t is given by
B(t) = 90 + 9 sin(t/12),
where t is measured in hours since midnight and B(t) in mmHg (millimeters of mercury). Find this person's diastolic blood pressure at the following times. (Round your answers to one decimal place.)
Person's diastolic blood pressure at 6:00am is 94.5 mmHg.
What is diastolic blood pressure?Diastolic blood pressure is the lower number in a blood pressure reading. It indicates the pressure in the arteries when the heart muscle is resting between beats and refilling with blood. A normal diastolic blood pressure is between 80 and 90 mmHg (millimeters of mercury).
For example, if a person's blood pressure reading is 120/80 mmHg, the diastolic blood pressure is 80 mmHg. This means that the pressure in the arteries when the heart is at rest is 80 mmHg. High diastolic blood pressure (greater than 90 mmHg) is a risk factor for heart attack, stroke, and other cardiovascular problems.
The formula for diastolic blood pressure at time t is given by B(t) = 90 + 9 sin(t/12). To find the diastolic blood pressure at 6:00am, need to plug in t = 6 into the formula.
B(6) = 90 + 9 sin(6/12) = 90 + 9 sin(0.5) = 90 + 9(0.4794) = 94.5 mmHg.
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