Terryl invests $1500 in two mutual funds. In the first year, one fund grows 3.8% and the other grows 6%. Write a polynomial to represent the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate.
The polynomial that represents the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate is;
p(x) = x(1 + 6/100)
g(x) = (1500 - x)(1 + 3.8/100)
How to find the compound interest?The compound interest is defined as a form of interest whereby the rate of interest is applied on the amount obtained after every given interval of time.
We are given that;
The total amount invested in the two mutual funds = $1500.
The growth rate of the first mutual fund = 6%.
The growth rate of the second mutual fund = 3.8%.
If the amount invested in the first mutual fund is x, then the amount invested in second mutual fund is 1500 - x.
The growth for both mutual funds can then be represented by;
First mutual fund; p(x) = x(1 + 6/100)
The second mutual fund; g(x) = (1500 - x)(1 + 3.8/100)
Thus, the polynomial expression for both the mutual funds are;
p(x) = x(1 + 6/100) and g(x) = (1500 - x)(1 + 3.8/100) respectively.
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Vehicles entering an intersection from the east are equally likely to turn left, turn right, or proceed straight ahead. If 50 vehicles enter this intersection from the east, use technology and the normal approximation to the binomial distribution to find the exact and approximate probabilities of the following. (Round your answers to four decimal places.)
a. 15 or fewer turn right.
b. at least two-thirds of those in the sample turn.
Answer:
a)
0.3632 = 36.32% approximate probability that 15 or fewer turn right.
0.369 = 36.9% exact probability that 15 or fewer turn right.
b)
0.4801 = 48.01% approximate probability that at least two-thirds of those in the sample turn.
0.4868 = 48.68% exact probability that at least two-thirds of those in the sample turn.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Vehicles entering an intersection from the east are equally likely to turn left, turn right, or proceed straight ahead.
This means that [tex]p = \frac{1}{3}[/tex]
50 vehicles
This means that [tex]n = 50[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 50\frac{1}{3} = 16.67[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50\frac{1}{3}\frac{2}{3}} = 3.33[/tex]
a. 15 or fewer turn right.
Using continuity correction, this is [tex]P(X \leq 15 + 0.5) = P(X \leq 15.5)[/tex], which is the pvalue of Z when X = 15.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.5 - 16.67}{3.33}[/tex]
[tex]Z = -0.35[/tex]
[tex]Z = -0.35[/tex] has a pvalue of 0.3632
0.3632= 36.32% approximate probability that 15 or fewer turn right.
Using a binomial probability calculator, to find the exact probability, we get a 0.369 = 36.9% exact probability that 15 or fewer turn right.
b. at least two-thirds of those in the sample turn.
Turn either left or right, so:
[tex]p = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}[/tex]
The standard deviation remains the same, while the mean will be:
[tex]\mu = E(X) = np = 50\frac{2}{3} = 33.33[/tex]
Two thirds of the sample is 33.33, so at least 34 turning, which, using continuity correction, is [tex]P(X \geq 34 - 0.5) = P(X \geq 33.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 33.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33.5 - 33.33}{3.33}[/tex]
[tex]Z = 0.05[/tex]
[tex]Z = 0.05[/tex] has a pvalue of 0.5199
1 - 0.5199 = 0.4801
0.4801 = 48.01% approximate probability that at least two-thirds of those in the sample turn.
Using a binomial probability calculator, we find a 0.4868 = 48.68% exact probability that at least two-thirds of those in the sample turn.
Find all solutions of sin x - sqrt(1 - 3sin^2 x) = 0
sinx-✓(1-3sin2x)=0
-✓(1-3sin2x)=-sinx
apply squared both sides
(-✓(1-3sin2x)^2=(-sinx)^2
1-3sin2x=sin2x
collect like terms
-3sin2x-sin2x+1=0
-4sin2x+1=0
-4sin2x=-1
devide both sides by -4
sin2x=-1/-4
sin2x=0.25
sinx*sinx =0.25
[sinx]^2 = 0.25
apply square root both sides
✓(sinx)2 = ✓0.25sinx=0.5 x=sin^-(0.5)x=30°check quadrant where sin is positive, sin is +ve in second quandrant180-x= Theta(X)
180-30=X
X=150°
therefore, all angles for sinx -✓(1-3sin2x)=0 are (X= 30° and 150°)
harry has a poster that is 3 feet wide he wants to draw 1/6 of a foot wide how many columns can gerry draw
why do the hands on the clock form an angle?
Answer:
The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)
I hope this helps you!
What is the circumference of this circle? Use π = 3.14
The circumference of this circle is equal to 50.24 centimeters.
What is a circle?In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle simply refers to the set of all data points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr or C = πD
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Based on the image of this circle (See attachment), we can logically deduce that its radius is equal to 8 centimeters.
Substituting the given parameters into the circumference of a circle formula, we have;
Circumference of circle, C = 2 × 3.14 × 8
Circumference of circle, C = 50.24 centimeters.
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13.A rectangle and a square have the same perimeter 120 cm. Find the side of the square. If the rectangle has a breadth 5cm less than that of the square. Find the breadth, length and area of the rectangle.
Answer:
Step-by-step explanation:
Please help, I will mark you brainiest, thank you!!
Answer:
x = 20
Step-by-step explanation:
The small square at the vertex indicates a 90º angle
Therefor
x + (3x + 10) = 90
Combine like terms
4x + 10 = 90
Subtract 10 from both sides
4x = 80
Divide both sides by 4
x = 20
which expression is 6 groups of 4?
Answer:
6x4=24
Step-by-step explanation:
Pls hurry by Friday! Whoever answers first will get points
Answer:
14 inches for every side
Step-by-step explanation:
44/4 = 22
circumfrence of half circle is 3.14r = 22
22/3.14 is about 7
the radius is half the side length so multiply 7 by 2 to get 14
mark brainliest please
Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater
First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.
The assumption is equivalent to the following two statements:
(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]
(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]
Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].
On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].
Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.
How do I solve this system of equations using the elimination method.(I don't just want the answer, I want an explanation on how to get the answer.)
y=3x+13
2x=y-9
Answer:
y=3x+13
2x=y-9
Step-by-step explanation:
i need to know :(
Answer:
Step-by-step explanation:
Substitute 1 in 2 and solve for x.
2x=y-9
2x=3x+13-9
2x = 3x+4
-x = 4
x = -4
Then use equation 1 to solve for x.
y = 3x+13
y = -12+13
y= 1
nts
Insurance companies are interested in the average health costs each year for their dients, so that they can
determine the costs of health insurance. Match the vocabulary word with its corresponding example.
All of the insurance company's dients
The cost each year for health care
The average health care cost each year for all of the insurance company's dients
The average health care cost each year for the 400 dients that the insurance company
included in this study
The 400 dients that the insurance company included in this study
The list of the 400 annual health care costs for the dients that the insurance company
indude in the study
a. Parameter
b. Population
c. Sample
d. Statistic
e. Data
of Variable
All of the clients of the insurance company are the population, and the parameter is the annual average cost of health care for all of the clients of the insurance company.
what is variable ?A variable in mathematics is a word or an alphabet that stands in for an unknowable quantity, value, or number. In the context of algebra or algebraic expression, the variables are employed specifically. Consider the linear equation x+9=4, which has 9 and 4 as constants and uses x as a variable. There are many variables, including height, age, wealth, province of birth, academic standing, and kind of dwelling. The independent variable is often plotted on the x-axis whereas the dependent variable is typically plotted on the y-axis. The independent variable's value also determines
given
Information: The 400 clients' annual health care costs that the insurance provider included in the analysis.
-Variable: The expense of health care per year
400 clients were used as a sample in this study by the insurance business.
The insurance provider included 400 consumers in this survey, providing statistics on the average annual cost of health care for each of them.
-Parameter: The annual average cost of health care for all customers of the insurance provider.
All of the clients of the insurance company are the population, and the parameter is the annual average cost of health care for all of the clients of the insurance company.
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In JKL, KL = 14, LJ = 3, and JK =12. Which statement about the angles of JKL must be true?
Answer:
D. [tex]L > J > K[/tex]
Step-by-step explanation:
Givenwe are given the vertecies (angles) of the trianglewe are given the side lengths of the triangleWhat to UtilizeThus, we have to utilize the angle relationships in a triangle.
Angle Relationships in a Triangle⭐The largest side is always opposite of the largest angle
⭐The smallest side is always opposite of the smallest angle
Application1. Identify the side lengths of triangle JKL
KL = 14LJ = 3JK = 122. Determine which vertecies are opposite of each side length (draw the figure)
Angle L is opposite of JK (14)Angle K is opposite of LJ (3)Angle J is opposite of KL (12)3. Determine which angles are the greatest, smallest, and in-between
Angle L is the LARGEST angle because it is opposite of the LARGEST side lengthAngle K is the SMALLEST angle because it is opposite of the SMALLEST side lengthWe know that angle J isn't the LARGEST or SMALLEST, but is in the middle4. Write what you found in #3 in terms of inequalities
∠L > ∠J > ∠K
angle L is greater than angle J, and angle J is greater than angle Kif this response helped you, please mark it the "brainliest"!
Who is right and why are they right?
answer for brainliest no wrong answers please :)
9514 1404 393
Answer:
4%
Step-by-step explanation:
The amount of simple interest is given by ...
I = Prt . . . . . amount P invested at annual rate r for t years
This can be solved for r:
r = I/(Pt)
Using the given values, we find the rate to be ...
r = 16/(200·2) = 16/400 = 4/100 = 4%
The annual interest rate is 4%.
Suppose that you take a random sample of 259 people leaving a grocery store over the course of a day and find that 12% of these people were overcharged. Find a 95% confidence interval for the actual percentage of shoppers who were overcharged.
a. 5.7% to 18.3%
b. 8.85 to 15.15%
c. 7% to 17%
d. 9.5% to 14.5%
Answer:
8.04% to 15.96%
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose that you take a random sample of 259 people leaving a grocery store over the course of a day and find that 12% of these people were overcharged.
This means that [tex]n = 259, \pi = 0.12[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.96\sqrt{\frac{0.12*0.88}{259}} = 0.0804[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 + 1.96\sqrt{\frac{0.12*0.88}{259}} = 0.1596[/tex]
So 8.04% to 15.96%
Can y’all help me on question 16?!
Answer and Step-by-step explanation:
The answer is D. z = x + 6
This is because the values for x, when plugged in for x, correlates to the values of y shown in the table.
#TeamTrees #PAW (Plant And Water)
Which of the following is a
representation of 11!
Answer: B.
Step-by-step explanation:
I need the answer fast pls⇒
Answer:
530
Step-by-step explanation:
870-340 = 530
___________
I’ll give points + brainalist for the correct answer (:
List 3 examples of chemical digestion
________
________
________
List 3 examples of mechanical digestion
________
________
________
Answer:
3 examples of mechanical digestion:
Mastication
Swallowing
Peristalsis
Can someone help me? It would mean the world if u helped me have a nice day! <3
Answer:
4500 ml kkkkkkkkkkkkkkkkkk
Find the surface of the triangular prism
Answer:
Step-by-step explanation:
6²+8²=36+64=100=10²
so it is a right angled triangular prism.
surface area=2×(1/2 ×8×6)+(6+8+10)×7
=48+980
=1028 sq. m.
Answer:
225.32
Step-by-step explanation:
Hope this helped :)
-6x<21 on number line
Answer:
[tex]x > -3.5[/tex]
Step-by-step explanation:
Given
[tex]-6x < 21[/tex]
Required
Plot a number line
First, solve for x
[tex]-6x < 21[/tex]
Divide by -6
[tex]\frac{-6x}{-6} > \frac{21}{-6}[/tex]
[tex]x > -3.5[/tex]
See attachment for number line
Can y’all help me on question 29?!
Answer:
D
Step-by-step explanation:
If the necklace must cost less than $12.75, then it would be shown either $12.75 > p (being greater than p) or p < $12.75 ( meaning that P is worth less than $12.75. And with that, the cost must have a maximum of $12.75 making D the answer.
We want to estimate the percentage of political figures who will make a social media
presence by posting an average of 1,000 posts per year next year. How many accounts
must we include in the sample next year, if we want our proportion estimate to be within
20 percentage points at a 90% level of confidence?
Answer:
0.0208
Step-by-step explanation:
Using the formula for calculating margin of error is expressed as;
M = z * √p(1-p)/n
z is the z score at 90 % interval
p is the proportion
n is the sample size
p = 0.2
n = 1000
z = 1.645
M = 1.645 * √0.2(1-0.2)/1000
M = 1.645 * √0.2(0.8)/1000
M = 1.645 * 0.01264
M = 0.0208
Hence the margin of error is 0.0208
for a sample size n = 24 and a population parameter of p = 0.4, a normal curve can be used to approximate the sampling distribution.
A. True
B. False
Answer:False
Step-by-step explanation:
Find the product 1 1/4 x 5 3/5
I need help with this question that in this picture
Answer:
What subject
Step-by-step explanation:
¿Cuál es el ángulo suplementario de 9º?
Answer:
171 degrees
Step-by-step explanation:
x + 9 = 180
x = 171