Answer:
$81.03
Step-by-step explanation:
Given
[tex]n = 1[/tex] --- annually
[tex]t =3[/tex] --- time
[tex]r = 5\%[/tex] --- rate
[tex]PV = \$70[/tex] ---- Present value
Required
The future value
This is calculated as:
[tex]FV = PV * (1 + \frac{r}{n})^{nt}[/tex]
This gives:
[tex]FV = 70 * (1 + \frac{5\%}{1})^{1*3}[/tex]
[tex]FV = 70 * (1 + 5\%)^3[/tex]
[tex]FV = 70 * (1.05)^3[/tex]
[tex]FV = 70 * 1.157625[/tex]
[tex]FV = 81.03375[/tex]
The future value to the nearest cent is: $81.03
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1. If the distribution is approximately normal, find the probability that there will be fewer than 69 broken pretzels in a run.
Answer:
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1.
This means that [tex]\mu = 73.5, \sigma = 5.1[/tex]
Find the probability that there will be fewer than 69 broken pretzels in a run.
This is the p-value of Z when X = 69.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 73.5}{5.1}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.
If we attempt to create a square using the tiles that represent the algebraic expression x^2 +bx,
1. How many x-tiles would you add to the length of the x-square tile?
2. How many unit tiles would you need to complete the square?
I dont understand the question
can anyone help with this problem?
Answer:
The numerator factors to
[tex](x + 2)(x - 1)[/tex]
The denomenator factors to
[tex](x + 4)(x - 1)[/tex]
PLEASE I NEED HELP ASAP!!
Answer:
Option C
Step-by-step explanation:
System of equations have been given as,
y - 4x = 16
y = 4x + 16 ------(1)
By comparing with slope-intercept form of the linear equation,
y = mx + b
Here, m = slope of the line
b = y-intercept
Therefore, m₁ = 4
2y = 8x + 16
y = 4x + 8 -------(2)
Slope of the line m₂ = 4
m₁ = m₂
Therefore, both the lines are parallel and both will not intersect each other.
Hence, there will be no solution of the system of equations.
Option C will be the correct option.
Help and explain please.
Answer:
a2 + b2 = c24 + b2 = 49b = [tex] \sqrt{45} [/tex]A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.
Which equation can be used to solve for x, the side length of the original square?
x2 − 2x − 120 = 0
x2 + 2x − 120 = 0
x2 − 2x + 120 = 0
x2 + 2x + 120 = 0
Answer:
x² - 2x - 180 = 0
Step-by-step explanation:
A square piece of paper has an area of x² square units
w = x
l = x
A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper.
this leaves
l = x
w = x - 2
x(x - 2) = 180
x² - 2x = 180
x² - 2x - 180 = 0
Answer:
x2 − 2x − 120 = 0
Step-by-step explanation:
Area of Square-A square's area is calculated by multiplying each side's length by itself. That is, Area A = s x s, with s denoting the length of each square side. A square with each side measuring 8 feet in length has an area of 8 times 8, or 64 square feet.
Given data is-Let x the length side of the original square paper
we know that the area of the original square paper is equal to
[tex]A1=x*x=x^{2} units{2}[/tex]
the area of the remaining piece of paper is equal to
[tex]$A 2=x^{2}-2 x$\\$A 2=120$ units $^{2}$[/tex]
so
[tex]$x^{2}-2 x=120$$x^{2}-2 x-120=0$[/tex]
therefore, the side length of the original square is x2 − 2x − 120 = 0
To know more about area of square click here-
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What is the solution to A=7x+40
9514 1404 393
Answer:
x = (A -40)/7
Step-by-step explanation:
Maybe you want to solve for x.
A = 7x +40 . . . . . given
A -40 = 7x . . . . . subtract 40
(A -40)/7 = x . . . divide by 7
The value of x will be ...
x = (A -40)/7
Choose which method to use: Law of Sines or Use Law of Cosines.
Answer:
we have
b=3mm
c=5mm
a=?
angle =62°
By using cosine rule.
a²=b²+c²-2bc cos angle
a²=3²+5²-2×3×5 cos 62°
a²=19.92
a=√19.92
a=4.5
I had choose cosine rule.
If g(x)=4vx then g(45)
is
Answer:
(2) 12√5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
g(x) = 4√x
g(45) is x = 45 for function g(x)
Step 2: Evaluate
Substitute in x [Function g(x)]: g(45) = 4√45Simplify: g(45) = 4(3√5)Multiply: g(45) = 12√5In how many ways can a
president, vice president, and
treasurer be selected for a
club if the club has 40
members?
[?] ways
Note: „Pr =
(n-r)!
n!
PLEASE HELP
Answer:
59,280
Step-by-step explanation:
the answer is base in my previous learning.. hope it helps..
A circle has a radius of 3. An arc in this circle has a central angle of 60°.
What is the length of the arc?
Either enter an exact answer in terms of 7 or use 3.14 for 7 and enter your answer as a decimal.
Answer:
π
Step-by-step explanation:
s = (∅/360) * (2πr)
s = (60/360) * (2π*3)
s = (1/6) * (6π)
s = π
How many students will be in each group...?
Mr. Hooper and Mr. Dale are playing a one-on-one basketball game in Madison Square Garden, 60 5th grade scholars from Beloved will attend the game.
They will travel to the game in groups with x teachers. Complete the table. How many scholars will be in each group if x = 3
X
30 x
1
30
3
6
4 students
6 students
10 students
90 students
9
10 11 12 13 14 15 16 17 18
Answer:
10 students
Step-by-step explanation:
Hope this helps!
Please see the attachment below. Also if you can, please show work. :)
Answer:
x = 5.2
Step-by-step explanation:
Its because 8 / 2 = 4 so that means 5.2 / 2 = 2.6 :)
(You might wanna check because im not sure)
HELP ME WITH THIS PLEASE. THANK YOU
Answer:
I think it's 2
Step-by-step explanation:
Answer:
1/11 is correct.
Step-by-step explanation:
You can see that the 3 is spun 2 times, but we need to know how many times he spun in total.
2 + 3 + 2 + 4 + 5 + 2 + 1 + 3 = 22
2/22 = 1/11
Have a nice day!
Giving 40 points and brainiest to answer these trigonometry questions
BC = 8i + 6
This is the answer for the first question, i'm so so sorry but i'm not sure what the answer is to the second one.
Gary has 4 pencils 12 markers and 24 crayons, what is the ratio of pencils?
Answer:
1:10 [simplified from 4:40)
Step-by-step explanation:
4 pencils+ 12 marker+ 24 crayons=40
4 pencils: 40 items
1 pencil : 10 items
i dunno if this was right but there you gooo lol</3
A quiz consists of six multiple choice questions. Each question has four choices. A student who forgot to study guesses randomly on every question. What is the probability that the student answers at most four questions correctly?
Answer:
0.9945 = 99.45% probability that the student answers at most four questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student answers correctly, or he/she does not. The probability of the student answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A quiz consists of six multiple choice questions.
This means that [tex]n = 6[/tex]
Each question has four choices. Student guesses randomly.
This means that [tex]p = \frac{1}{4}[/tex]
What is the probability that the student answers at most four questions correctly?
This is:
[tex]P(X \leq 4) = 1 - P(X > 4)[/tex]
In which
[tex]P(X > 4) = P(X = 5) + P(X = 6)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{6,5}.(0.25)^{5}.(0.75)^{1} = 0.0053[/tex]
[tex]P(X = 6) = C_{6,6}.(0.25)^{6}.(0.75)^{0} = 0.0002[/tex]
[tex]P(X > 4) = P(X = 5) + P(X = 6) = 0.0053 + 0.0002 = 0.0055[/tex]
[tex]P(X \leq 4) = 1 - P(X > 4) = 1 - 0.0055 = 0.9945[/tex]
0.9945 = 99.45% probability that the student answers at most four questions correctly
1. What is the slope of the line through the points (-4, 2) and (—16,-6) PLEASE HELP
Answer:
2/3
(-4, 2) and (-16, -6)
slope = m = (y2 - y1) / (x2 - x1) = (-6 - 2) / (-16 - -4) = -8 / -12 = 2 / 3 = 0.667
I hope you got it right :)
Give the coordinates of point D.
A. (-2,-4)
B. (-4,2)
C. (-4,-2)
D. (4, -2)
I need help! :) +no links please and thank you!
Answer:
Step-by-step explanation:
(14×2)+(14×4)
7×(3+5)
c, e and g
A farmer brought 15 watermelons to a picnic. Each watermelon was cut into 6 slices. If each person ate only one slice, how many people had watermelon?
Answer:
how much people are there
... . . ..........
The function f(x)=12sin(x−π4) is used to describe a water wave. The value x is the time in seconds, and f(x) is the position of the wave in feet above or below the normal water level.
On which of these intervals does f−1(x) exist?
A
[0,π]
B
[3π4,7π4]
C
[π4,5π4]
D
[0,2π]
Option C, [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex] is the correct answer such that the function, [tex]f(x)=12sin(x-4\pi)[/tex] where, [tex]x[/tex] is the time in [tex]seconds[/tex] and [tex]f(x)[/tex] is the position of the water wave in [tex]ft[/tex] above and below the normal water level.
inverse of the functionThe inverse of the function is the mirror image of the function with respect to the dependent variable.
How to determine the inverse of the function?From the figure, the interval of water wave above the normal water level is [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex].
So, the interval of the mirror image of the function with respect to the dependent variable [tex]x[/tex] is [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex].
As a result, Option C is the correct answer.
Learn more about the inverse of the function here- https://brainly.com/question/2541698
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The sales manager gathered information on the numbers of sales calls made and the number of copiers sold for a random sample of sales representative. Is there a positive correlation between calls made and copiers? Test at the 0.05 level of significance. Determine the 90% prediction interval for 60 number of calls made. *
Calls,X Sold. Y
20 40
20 50
40 60
50 90
40 80
20 40
40 60
30 60
Answer:
b
Step-by-step explanation:
The relationship between two quantities that increase or decrease together is called A. indirect variation B. variation C. indirect option D. direct variation E. direct option
Answer:
D. direct variation
Step-by-step explanation:
Answer:
yes it is direct variation
Step-by-step explanation:
well I'm sorry I Don't know if it's going to be step by step but my own understanding is that what ever happens on one side will affect the other side so if there is an increase in A there will be an increase in B so there's a form of equilibrium. so let's say we throw two stones A and B into a fast flowing river we expect that the water will flow so the more the velocity of the river the faster the stone will flow so as the river is flowing the stone is floating as well but an indirect variation as the river increases it's velocity the stone decreases it's movement so in direct variation as the river increases it's velocity the stone does as well. I hope this is well detailed and I answered your question , thank you
A sewing class has 185 yards of fabric to make quilts. Each quilt requires 8 yards of fabric. How much fabric will remain after all the quilts are made?
About 0.34 of the length of a cat is its tail. Write this decimal as a percent.
If 25% of a number is 50 and 35% of the same number is 70, find 10% of that number.
Answer:
10%×200=20
Step-by-step explanation:
25%×200=50
35%×200=70
hamburger eaten monthly
Answer:
Full question?
Step-by-step explanation:
greatest common factor of 27q^2 - 9
Answer:
9(3q^2−1)
Step-by-step explanation:
HELP HELP HELP HELP
What is the equation of the trend line in the scatter plot ?
Answer:
(0,9),(9,2)
Step-by-step explanation: