Joan completed the race 1.66 standard deviations faster than the typical female of her age group. The standard deviation will be denoted by the symbol “” and the women's average finish time by the symbol “”. Then, Joan's remaining time was plus 1.66.
What is the assuming of normal distribution?The proportion of women who finished the race sooner than Joan. In this case, it is possible to apply the normal distribution.
The percentage of values to the left of z = 1.66 can then be calculated or found using a standard normal distribution table. The number of women who finished the race ahead of Joan is represented by the percentage in the table below.
According to a normal distribution table or calculator, there are approximately 0.9525 numbers to the left of the value z = 1.66.
Therefore, This means that out of the 410 female runners in Joan's age group, about 0.9525 × 410 = 391.23 of them beat her. The final count is 391 women, rounded to the next whole number.
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Suppose a biologist tagged 53 penguins in antarctica during mating season. The next year, they caught 82 and found that 11 of them had tags. Estimate the total number penguins in the area.
It can be estimated that there are 395 penguins in the area.
What is Proportion ?Proportion is a mathematical comparison between two numbers. According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".
We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.
The proportion should therefore be [tex]x:53=82:11[/tex] where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:
[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]
Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.
395 penguins are in the area according to our estimation.
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You deposit $9000 in an account earning 5% interest compounded continuously. The amount of money in the account after t years is given by A(t)=9000e^0.05t
How much will you have in the account in 14 years? $ Round your answer to 2 decimal places.
How long will you have in the account in 14 years? ______years. Round your answer to 2 decimals
How long does it take for the money in the account to double? ____ years. Round your answer to 2 decimal places
The amount of money which would be in the account after 14 years is; $18,123.77.
The number of years it'd take for the money to double is; 13.86 years.
What is the doubling time of the compound interest arrangement?Since the given model of the account is;
A (t) = 9000e^0.05t
After 14 years, it follows that; t = 14.
Therefore;
A (14) = 9000e^0.05(14)
A (14) = 9000 × 2.013752707
A (14) = $18,123.77.
Also, the doubling time implies that; A (t) = 18,000
Therefore, 18000 = 9000e^0.05t
2 = e^0.05t
0.05t = ln (2)
t = ln (2) / 0.05
t = 13.86 years.
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find the sum of the series. make sure you use the formula and show your work for credit.
please help me I didn't get this at all!
Answer:
The sum of the series is 260.
------------------------
Each term of given series is expressed as:
tₙ = 3n - 1This is an arithmetic progression with 13 terms and the first and last terms are:
t₁ = 3*1 - 1 = 2t₁₃ = 3*13 - 1 = 38Use the sum of the first terms of AP formula:
Sₙ = (t₁ + tₙ)*n/2S₁₃ = (2 + 38)*13/2 = 40*13/2 = 20*13 = 260Answer:
The sum of the series is 260.
Step-by-step explanation:
[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]
The given sigma notation means:
Sum of the series with nth term (3n - 1), starting with n = 1 and ending with n = 13.As (3n - 1) is linear, the series is arithmetic.
The first term (n = 1) is:
a₁ = 3(1) - 1 = 2The second term (n = 2) is:
a₂ = 3(2) - 1 = 5The third term (n = 3) is:
a₃ = 3(3) - 1 = 8… and the last term (n = 13) is:
a₁₃ = 3(13) - 1 = 38Therefore, we need to find 2 + 5 + 8 + ... + 38.
Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.
[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]
Therefore, the sum of the series is 260.
BIL
K-7 ft-X-8 ft-
K
-20 ft-
✈
The simplified expression of K-7 ft-X-8 ft-K-20 ft is -35ft-X
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is K-7 ft-X-8 ft-K-20 ft
We need to simplify the given expression.
Add the like terms
-7 ft-X-8 ft-20 ft
-27ft-X-8 ft
-35ft-X
Hence, -35ft-X is the simplified expression of K-7 ft-X-8 ft-K-20 ft
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
After 1 day, each woman would have made 8 scarves.
How many scarves would each woman have made?The expression that represents the number of scarves that Greta can make each day is:
Number of scarves she can make = number of scarves already made + (number of scarves she can make per day x number of days)
= 7 + d
The expression that represents the number of scarves that Evelyn can make each day is:
Number of days x number of scarves she can make per day
d x 8 = 8d
When both of them make the same number of scarves, the two expressions above would be equal.
7 + d = 8d
7 = 8d - d
7 = 7d
d = 7/7
d = 1 day
Number of scarves that would be made in 1 day = 8 x 1 = 8 scarves
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Help with question 12 (a & b):
A beginning employee will produce 3 items per day
An experienced employee will produce 17 items per day
The number of items per dayBeginning employee
From the question, we have the following parameters that can be used in our computation:
[tex]P\left(d\right)=3\ +\ 15\left(1-e^{-0.2d}\right)[/tex]
Next, we plot the graph (see attachment)
A beginner employee is represented as d = 0
From the graph, we have
P(0) = 3
An experienced employee
Using the graph as a guide, we have
The maximum number of production approximates to 17
This represents the number of items per day for an experienced employee
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The ratio of first- class, second- class and third-class passengers who survived the ship wreak is
101:59:89. How many passengers were saved if the total number of first-class passengers were 202?
Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.
If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.
Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.
Step-by-step explanation:
Devaughn is 8 years older than Sydney. The sum of their ages is 94. What is Sydney's age?
Answer:
Step-by-step explanation:
S+8=D
S+D equals 94.
94/2= 45+2=47
47-8=39
Sydney is 39
Answer:
43
Step-by-step explanation:
94-8= 86
86/2= 43
43+8= 51
a:43
prove it :
51+43= 94
6-90. Evaluate the expression 10-2x for the x-values given below.
(show work)
a. x=2
b. x = 1/2
c. x = -2
Answer:
Step-by-step explanation:
Evaluate the expression 10 - 2x for the x-values given below.
a. x = 2 \quad b. x = \frac {1}{2}\quad c. x = -2
a.x=2b.x=
2
1
a.x=-2
RECAP NEED HELP PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
The required measure of angle x in the triangle is 35°.
What are trigonometric equations?
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
From triangle,
Sin x = perpendicular/hypotenuse
Sin x = 4/7
Sin x = 0.57
X =sin⁻¹(0.57)
X = 34.9
x = 35°
Thus, the required measure of angle x in the triangle is 35°.
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12x + 7 < −11
OR
5x-8>40
Answer:
x <-1.5
or
x <9.6
Step-by-step explanation:
12x + 7 < - 11
12x < -11 - 7
12x < - 18
12x/12 < -18/12
x = -1.5
OR.
5x - 8 > 40
5x > 40 + 8
5x > 48
5x/5 > 48/5
x > 9.6.
The lunch special at Rachel's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 3 drinks, and 2 desserts to choose from. How many lunch specials are possible?
Answer:
3 lunch specials are possible.
I need the modulus of: I 9+40i I
I = absolute value
The required modulus is 41 .
Complex Numbers:A real and imaginary number combo with the formula a + bi , where
a and b are real numbers, and
i is the "unit imaginary number" √(−1)
a and b may also have zero values.
We are aware that complex numbers are made up of both actual and fictitious numbers.
The imaginary part, y, is multiplied by I the square root of -1, and the real part, x.
Modulus of x+iy = [tex]\sqrt{x^2 +y^2}[/tex]
Here, 9 and 40 are substituted for x and y.
i.e. 9+40i
We square the coefficients, add them, and then find the square root to obtain the modulus.
|9+40i| =[tex]\sqrt{9^2 +40^2} =\sqrt{81+1600} =\sqrt{1681}[/tex][tex]=41[/tex]
By long division method we find that
|9+40i| =41
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Find the magnitude of the sum
of these two vectors:
The magnitude of the sum of these two vectors is 2.9486m
What is cosine rule?In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.
The parameters that will help us to find the magnitude are
/OB/ = 3.14m
/OA/ = 2.71 m
Let /AB/= x
Sum of the angles is (-60+30)⁰ = 30⁰
Using cosine rule
x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰
x² = 9.8596+7.3441 -8.5094
x²= 17.2037 -8.5094
x²= 8.6943
x = √8.6943
x = 2.9486
Therefore, the magnitude of the sum
of these two vectors is 2.9486m or 2.9m approximately
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The lengths of the three sides of a triangle are x + 15 , 2x + 15 and x + 12 (where x cannot equal zero). What is the perimeter of the triangle?.
The perimeter of the triangle is 3x + 42.This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42.
The perimeter of a triangle is the sum of the lengths of its three sides. In this problem, the lengths of the three sides of the triangle are given as x + 15, 2x + 15, and x + 12, where x cannot equal zero. To calculate the perimeter of the triangle, we need to add these three lengths together. This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42. Therefore, the perimeter of the triangle is 3x + 42.
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(-5,4)A(−5,4), B(4,4)B(4,4), C(4,1)C(4,1), D(1,1)D(1,1), E(4,-3)E(4,−3), F(4,-6)F(4,−6), G(-5, -6)G(−5,−6)
The total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Divide the figure is into two rectangles and a triangle.
The points B, C, E, and F form a rectangle with base BC and height 7 units.
The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.
The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.
The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.
Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 45 + 6 = 51 square units.
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The number of a country's unemployed workers increased from 3.4 million to 5.5 million last year. If the country's population remained constant at 76 million, how did its unemployment rate change last year? A. It increased by about 27%. B. It decreased by about 27%. C. It increased by about 3%. D. It decreased by about 3%.
The rate at which its unemployment changes is, 54.6 %
What is the rate?Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.
So formula for the rate is,
m = change in one quantity/change in another quantity = Δy/Δx
Given that,
The initial number of unemployed workers was 3.4 million and the final number was 5.5 million.
The change in the number of unemployed workers is:
5.5 million - 3.4 million = 2.1 million
To find the initial number of employed workers, we need to subtract the initial number of unemployed workers from the total population:
76 million - 3.4 million = 72.6 million
Now, we can calculate the initial unemployment rate as:
3.4 million / 72.6 million = 0.0469 or 4.69%
Similarly, the final unemployment rate is:
5.5 million / 76 million = 0.0724 or 7.24%
The change in the unemployment rate is:
(0.0724 - 0.0469) / 0.0469 ≈ 0.546 or 54.6%
Therefore, the unemployment rate increased by about 54.6%, which is closest to answer choice A. It increased by about 27%.
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Find the value of x.
(4x+12) 64°
OA. 19
OB. 3.5
O c. 26
OD. 13
Answer: OD. 13
Step-by-step explanation:
NEED HELPP!!!!!!!!!!!!
Answer:
the last one
Step-by-step explanation:
first you have to distribute the 5 to all the variables.
when you do that you get
x---9x5=45
y---1x5=5
z---4x5=20
hope it helped
please mark brainliest
A young channel catfish weighs about 0. 1 pound. During the next 8 weeks, its weight increases by about 23% each week.
Weight is 0.229 pounds after 4 weeks.
As a young channel catfish only weights 0.1 pounds,
It gains weight over the following 8 weeks at a rate of roughly 23% every week.
In this case, the exponential growth function is as follows:
Exponential formulas are provided by.
[tex]y=a(1+r)^{x}[/tex]
where an is the starting amount, r is the growth rate, x is the duration, and y is the weight at the end of "x" weeks.
Our values are a = 0.1, r = 0.23 (or 23%), and t = 4.
As a result,
[tex]y=0.1(1+0.23)^{4} \\[/tex]
y = 0.1(2.289)
y = 0.229
Consequently, the weight at 4 weeks is 0.229 pound.
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Complete question:
A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.
Which of the following expressions is equivalent to the logarithmic expression below? log4 7/x^3
Answer:
D
Step-by-step explanation:
using the rules of logarithms
• log a - log b = log ([tex]\frac{a}{b}[/tex] )
• log [tex]x^{n}[/tex] = nlog x
then
[tex]log_{4}[/tex] [tex]\frac{7}{x^3}[/tex]
= [tex]log_{4}[/tex] 7 - [tex]log_{4}[/tex] x³
= [tex]log_{4}[/tex] 7 - 3[tex]log_{4}[/tex] x
This net will be folded to form a prism.
A net of a rectangular prism. From top to bottom, the rectangles are labeled B, D, E, F. The left side is labeled A and the right side is labeled C.
Which pairs of faces will be opposite one another when the prism is created? Check all that apply.
D and F
A and C
A and B
B and F
B and E
B and C
E and F
A and F
Answer:
i think the answer is A and C, B and E
Answer:
D and F
A and C
B and E
Step-by-step explanation:
Suppose f(x)= 10x-4
Compute the following:
A.) f(x-2)+f(2x)
A.) f(x-2)+f(2x)
To find this expression, we can substitute the definition of f(x) into the expression and simplify:
f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]
= 10x - 20 - 4 + 20x - 4
= 30x - 28
Therefore, f(x-2)+f(2x) = 30x - 28.
Compute f(2a) - f(a) for any value of a ?Given f(x) = 10x - 4, we need to find f(2a) - f(a).
f(2a) = 10(2a) - 4 = 20a - 4
f(a) = 10a - 4
Therefore,
f(2a) - f(a) = (20a - 4) - (10a - 4)
= 10a
Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.
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Kylie has 6 boxes. Each box contains 4 cakes. Kylie writes a calculation to find out how many cakes she has in tota 6×4 (a) Write a different way to calculate the total number of cakes. You must not use multiplication.
Answer:
Step-by-step explanation:
6x4=24
another way of writing it is using addition
add 4, six times
so
4+4+4+4+4+4
6 boxes each has four cakes
Find the value of X , Y, and z in the parallelogram below.
Answer:
[tex]x = -64\\\\y = -63\\\\z = -57[/tex]
Step-by-step explanation:
Diagonally opposite angles of a parallelogram are equal
Therefore
-y - 3 = 60
Add 3 to both sides; -3 terms on left side cancel out
- y = 60 + 3
- y = 63
Multiply both sides by -1
-1(-y) = -1(63)
y = - 63
Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.
Rephrased,
The consecutive or adjacent angles are supplementary which means they add up to 180°
We see that -2z + 6 and 60° are adjacent angles
So
- 2z + 6 + 60 = 180
-2z + 66 = 180
-2z = 180 - 66
-2z = 114
z = 114/-2
z = -57
Similarly
-2x - 8 + 60 = 180
-2x + 52 = 180
-2x = 180 - 52
-2x = 128
x = 128/-2
x = -64
The confidence interval for a population proportion is (0.61, 0.81). What the the sample proportion and the margin of error.
The margin of error for the confidence interval for a population is 0.71 ± 0.1.
What is margin of error?The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.
The margin of error is given as:
MOE = U - L / 2
MOE = 0.81 - 0.61 / 2
MOE = 0.2 / 2
MOE = 0.1
The interval is:
Interval = P ± 0.1
Interval = (0.61 + 0.1) ± 0.1
Interval = 0.71 ± 0.1
Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.
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In complete sentences, explain how to determine the angle measurement for this angle.
WRITER
28
90
50
40 50 60 70
140 130 120 110
£10
umumla
150
30 20 10
160 170 180
UPLOAT
(2
The procedure for angle measurement by the protractor is mentioned below:
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
To measure an angle using a protractor, follow these steps:
1. Place the protractor on the angle you want to measure, with the base of the protractor aligned with one side of the angle.
2. Make sure the protractor is centered and level, with the zero-degree mark on the protractor aligned with the vertex (corner) of the angle.
3. Read the measurement of the angle from the protractor, where the second side of the angle intersects with the protractor scale. The measurement is usually given in degrees.
If the angle is larger than 180 degrees, you may need to use a full-circle protractor or measure the angle in two parts and add the measurements together.
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Consider function f. f(x)=square x-1 which graph represents f?
The graph that represents the function f(x) = sqrt(x - 1) is given by the following option:
C. Graph Y.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.For this problem, the function is defined as f(x) = sqrt(x - 1), meaning that the parent square root function was moved one unit right, and thus the correct graph is given by graph Y.
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Multiply
-1/5. (-2/7)
Write answer in simplest form.
Answer:
2/35
Step-by-step explanation:
[tex](-\frac{1}{5})(-\frac{2}{7}) = \frac{2}{35}[/tex]
A roll of gasket material is 9 in wide. What length is needed to obtain 19 sq ft of the material? (Careful: The numbers are not expressed in compatible units.)
f
A length of ft is needed to obtain 19 sq ft of gasket material.
(Type an integer, proper fraction, or mixed number.)
The length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.
What is length?
The length of something measured from end to end or along its longest side, or the length of a specific section of something.
Convert the width from inches to feet:
Since there are 12 inches in a foot, the width in feet is:
9 / 12 = 0.75 ft
Calculate the length needed:
We know that the area of the gasket material is 19 sq ft, and the width is 0.75 ft. Let L be the length needed in feet. Then we have:
Area = Width x Length
19 sq ft = 0.75 ft x L
Solving for L, we get:
L = 19 sq ft / 0.75 ft
L = 25.33 ft (rounded to two decimal places)
Therefore, the length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.
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