Matteo bought a car that cost $12500. He put $4000 down and financed the rest at 3.8%/a compounded monthly. He wants to pay off his car in 19 months. a. How money does he need to pay each month? how much will he end up paying for his car
Answers
Answer:
a. $461.67
b. $12771.73
Step-by-step explanation:
You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.
AmortizationThe formula for the monthly payment is ...
A = P(r/12)/(1 -(1 +r/12)^-n)
where P is the amount borrowed at interest rate r compounded monthly for n months.
Here, the down payment of $4000 reduces the loan amount to ...
$12500 -4000 = 8500
a. Monthly paymentSo, the monthly payment is ...
A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67
Matteo needs to pay $461.67 each month.
b. Total paidThe total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:
total = $4000 +19×461.67 = $12771.73
Matteo will end up paying $12771.73 for his car.
Related Questions
transformation(s) can map APQR onto ASTU?
Which
O translation only
O rotation only
O rotation, then reflection
O reflection, then translation
Answers
D.) reflection, then translation
Explanation:
The triangles shown are congruent by the SSS congruent theorem.
Hopes this helps <3
What are the vertex and range of y = |2x + 6| + 2? (0, 2); 2 < y < ∞ (0, 2); −∞ ≤ y < ∞ (−3, 2); 2 < y < ∞ (−3, 2); −∞ ≤ y < ∞
Answers
The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞
How to determine the vertex and the range?From the question, we have the following parameters that can be used in our computation:
y = |2x + 6| + 2
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
y = |2x + 6| + 2
This gives
y = 2|x + 3| + 2
This means that the vertex is
Vertex = (-3, 2)
Remove the x value
y = 2
Because the leading coefficient is positive, then the vertex is a minimum
i.e. y ≥ 2
So, the range is 2 ≤ y < ∞
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A man distributes his savings of 4000 among his three sons in the ratio 4:3:3. Find the amount received by his first son.
Answers
Answer:
First son: 4
Second son: 3
Third son: 3
Sum ratio =10
First son= 4/10*4000=1600
Determine the slope of the line that contains the points with coordinates (1, 5) and (-2, 7).
Answers
Answer:
2/3x
Step-by-step explanation:
What is 19x( _________X26)=(19X39)X26
Answers
Answer:
(39 * 26)
Step-by-step explanation:
If (19 * 39) * 26
19 * (39 * 26)
Your answer is 39.
Messages arrive to a computer server according to a Poisson distributionwith a mean rate of 17 per hour. Determine the length of an interval oftime such that the probability that no messages arrive during this intervalis 0.94.
Answers
The length of an interval of time such that the probability that no messages arrive during this interval is 0.94 is 56.88 seconds.
We have to find the length of the time interval that the probability of no messages arrive during this interval is 0.94
Let X be the no.of messages arrive to the server
X follows the poisson distribution with mean λ = 17
Let t be the time interval
The probability of no messages arrive during this interval is 0.94
Then P(0) = 0.94
e⁻⁽λt⁾ = 0.94
λt = ln0.94
17 t = ln(0.94)
t = ln(0.94)/17
t = 0.026872 / 17 hrs
t = 0.0158
Convert 0.0158 hours to seconds
That is t=0.0158(60)(60)
=56.88seconds
Hence in 56.88 seconds the time interval that the probability of no messages arrive during this interval is 0.94 .
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The Maryland Department of Transportation reported the following data on driving Speed (miles per hour, mph) and fuel efficiency or Mileage (miles per gallon, mpg), for ten mid-size automobiles: 1 23 4 5 6 7 89 10 Automobile Speed (mph 30 50 40 55 30 25 60 25 50 55 Mileage (mpg)2 25 25 2330 32 2 32625 a. Compute the sample bivariate correlation coefficient. b. Interpret the strength (magnitude) and sign (direction) of the sample bivariate correlation coefficient. Test whether the population bivariate correlation coefficient difers significantly from zero at α-0.01. c.State the null and alternative hypotheses associated with the test. d. What is the calculated value of the associated test statistic? e. What is the critical value of the associated test statistic? f.State your decision regarding the null hypothesis. g. State your conclusion (meaning, describe what the decision means in this problem)
Answers
On solving the provided question we can say that - correlation coefficient of the question is r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] = -0.91
What is correlation coefficient ?The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.
[tex]S_{xx} =[/tex]∑[tex]x^2[/tex] - (∑x[tex])^2[/tex] /n = 19300- ((420)^2 /10)= 1660
[tex]S_{yy} =[/tex] ∑[tex]y^2[/tex] (∑y[tex])^2[/tex]/n = 7454- ((270)^2 /10) = 164
[tex]S_{xy} =[/tex]∑[tex](xy)^2[/tex]/n -475
The correlation coefficient is:
r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] = -0.91
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In order to understand the relation between smoking and hypertension (HT), a tea of researchers designed a study that looks at the numbers of smokers and nonsmokers with no HT, pre-HT, stage 1 HT, and stage 2 HT. Which one of the following statements is correct? a. A chi-square test of independence should be run for the study, because the outcome smoker vs. nonsmoker-is a continuous variable, and the grouping variable-no HT, pre-HT stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups. b. A chi-square test of independence should be run for the study, because the outcome smoker vs. nonsmoker-is a dichotomous variable, and the grouping variable-no HT, pre-H stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups. c. An independent samples t test should be run for the study, because the outcome-smoker vs. nonsmoker-is a categorical variable, and the grouping variable no HT, pre-HT, stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups. d. An independent samples t test should be run for the study, because the outcome-smoker vs. nonsmoker-is a continuous variable, and the grouping variable no HT, pre-HT, stage 1 HT, and stage 2 HT-categorizes the sample into matched (or dependent) groups.
Answers
Correct option is C
In order to understand the relation between smoking and hypertension (HT) a tea of researchers designed a study that looks at the numbers of smokers and nonsmokers with no HT, pre-HT, stage 1 HT, and stage 2 HT.
An independent samples t test should be run for the study because the outcome smoker vs nonsmoker is a categorical variable and the grouping variable no HT, pre-HT, stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups.
Variables
In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
Probability
Probability is simply likely something is to happen. Whenever unsure about the outcome of an event, we can talk about the probabilities of certain outcome. The analysis of events governed by probability is called statistics.
Correct option is C
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let x be a continuous random variable. we know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. we are interested in estimating the mean of x, which we denote by h. we will use 1.5 as a conservative value (upper bound) for the standard deviation of x. to estimate h, we take n i.i.d. samples x1,x2,...,xn, which all have the same distribution as x, and compute the sample mean
Answers
The randomized variable's sample distribution would be as follows: H+/- 1.96 * √3)/√n
A random variable in mathematics would be a variable for whom the value is the numerical result of an unpredictable event and a random number generator X on a sample space. S denotes the rule that gives each of the outcomes S in a collection a numerical value.
In this case, we have assumed that x is a constant random variable with values ranging from 0 to 3, but we are unsure of its distribution, mean, or variance.
The mean of x, which we designate by the letter h, is what we're now interested in estimating. To provide a conservative estimate (upper bound), we'll choose 1.5 for the standard deviation of x.
In this case, we must estimate h. To do this, we select the sample size n, the samples x1, x2,.., xn, all of which share the same dissemination as x, and accurately measure the sample mean.
Therefore, we have used a normal distribution to determine the variation of x as (0,6),
And it equals to 3, then apply CLT resulting in
=> H+/- 1.96 * √3)/√n
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Find the area of this triangle. Round to the nearest tenth. PLEASE HELP
Answers
Answer:
74.8 m²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}[/tex]
From inspection of the given triangle:
C = 115°a = 11 mb = 15 mSubstitute the values into the formula and solve for area:
[tex]\implies A=\dfrac{1}{2} \cdot 11 \cdot 15 \cdot \sin 115^{\circ}[/tex]
[tex]\implies A=\dfrac{165}{2} \sin 115^{\circ}[/tex]
[tex]\implies A=74.77039243[/tex]
[tex]\implies A=74.8\; \sf m^2\;(nearest\;tenth)[/tex]
Therefore, the area of the triangle is 74.8 m² rounded to the nearest tenth.
which of the following are defined? you can assume that all vector fields have 3 components and f(x,y,z)f(x,y,z) is a scalar field.
Answers
div( curl( grad f )) - scalar field; the divergence of a vector field is a scalar field
What is vector ?A quantity with both direction and magnitude, particularly when used to depict the distance between two points in space.
What is Scaler Field ?In a scalar field, each point in a space—possibly actual space—is assigned a single integer.
According to the given information
(a) You can only determine the curl of a vector field; curl f is meaningless.
(b) grad f - vector field; when you take a gradient of something , it results in a vector field
(c) div F - scalar field; take the divergence of a vector field, it results in a scalar field
(d) A vector field is produced by the operation curl(grad f) on a vector field.
(e) grad F - meaningless; gradients are only used for scalar fields
(f) grad( div F ) - vector field; the gradient of a scalar field is a vector field
(g) div( grad f ) - scalar field; if you take divergence of a vector field, the result is a scalar field
(h) Grad (div f) is useless; one cannot take a scalar field's divergence into account.
(i) vector field; a vector field is a vector field's curl (curl F).
(j) div(div F) is useless; it is impossible to calculate a scalar field's divergence.
(k) ( grad f ) x ( div F ) - meaningless; you cant cross a scalar field by a vector field !
(l) The divergence of a vector field is a scalar field, and its formula is div(curl(grad f))
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let sn be the number of successes in n independent bernoulli trials, where the probability of success for each trial is 1/2. evaluate the following limits.
(a) n→[infinity]lim P( 2n− 3n ≤S n ≤ 2n + 3n)
(b)n→[infinity] lim P( 2n− 4n ≤S n ≤ 2n+ 4n)
(c) n→[infinity]lim P(2n−20≤Sn ≤ 2n+20)
Answers
The following limits -
Option a) = 1
Option b) = 0
Option c) = 0
According to the question given,
The probability of success of each trial is = [tex]\frac{1}{2}[/tex]
Let us consider options a),
n→[infinity]lim P( [tex]2n - 3n \leq S n \leq 2n + 3n[/tex] ),
We could conclude that if n tends to infinity, the probability of having [tex]2n - 3n[/tex] successes in n number of trials = the probability of having [tex]2n - 3n[/tex] successes in n number of trials.Since in the question, the probability of success for each trial is 1/2, so we could say that, [tex]2n - 3n[/tex] successes = [tex]2n - 3n[/tex] successesTherefore, the limit is = 1
Taking option b),
We could conclude that if n tends to infinity, the probability of having [tex]2n - 4n[/tex] successes in n number of trials = 0Since in the question, the probability of success for each trial is 1/2, so we could say that, [tex]2n - 4n[/tex] successes = 0Therefore, the limit is = 0
Taking option c),
We could conclude that if n tends to infinity, the probability of having [tex]2n - 20[/tex] successes in n number of trials = 0Since in the question, the probability of success for each trial is 1/2, so we could say that, [tex]2n - 20[/tex] successes = 0Therefore, the limit = 0
Therefore, the following limits are - a) 1, b) 0, c) 0
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the scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. complete a linear equations that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches. click on the variables and number you want to select and drag them into the boxes.
Answers
The linear equation obtained is y = 0.3X + 18.3
What is linear equation?A linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x represents an unknown variable. The solutions of linear equations are often graphed on a coordinate plane, forming a straight line. Linear equations can be used to model many real-world situations, such as population growth, the rate of change of a physical quantity, or the total cost of an item. Linear equations can also be used to solve systems of equations, where several equations must be solved simultaneously.
Given that data :
x = year ;
y = trunk diameter, in inches
Year ________trunk diameter
1 __ 18.6
3 __ 19.2
5 __ 19.8
7 __ 20.4
9 ___21.0
11 __ 21.6
13 __ 22.2
Using the linear regression calculator :
The linear equation obtained is :
y = 0.3X + 18.3
Where ;
Slope = 0.3 ; intercept, c = 18.3
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based on his past record, luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. assume that in one practice luke will attempt 5 shots of the arrow and that each shot is independent from the others. let the random variable x represent the number of times he hits the inner ring of the target in 5 attempts. the probability distribution of x is given in the table. P(X) 0 000001 0,00045 0.00810 0.07290 03280S 0.59049
What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X?
(A) 0.40951
(B) 0.50000
(C) 0.59049
(D) 0.91854
(E) 0.99144
Answers
The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
P(target) equals 0.90
Let the random variable X stand in for the number of times the arrow is fired at the target's ring.
The probability distribution of X is
x: 0 1 2 3 4 5
P(x): 0.00001 0.00045 0.00810 0.07290 0.32805 0.59049
Hence, The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.
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indicate if dijkstra's algorithm will be able to find the shortest path for this particular graph. (assume the source vertex is m) yes no it will loop forever the algorithm will never start
Answers
By using Dijkstra's algorithm, it can be concluded that-
It will loop forever.
Third option is correct
What is Dijkstra's algorithm?
Dijkstra's algorithm is used to find the shortest path between the nodes of a graph.
Here, a node is fixed which is called the source node and the distance from the source node to all other nodes are calculated.
The minimum distance gives the shortest path.
For the first option,
The first option is incorrect because the shortest path will not be obtained. There does not exist path between every pair of vertices
For the second option
The second option is incorrect because all the conditions of Dijkstra's algorithm are fulfilled but here, infinite looping takes place.
For the fourth option
The fourth option is incorrect because there exist a path between the point M and every other vertex in the graph.
So the third option is correct
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Complete Question
The complete question has been attached
form differential equations for all circles in the xy plane
Answers
The differential equation that can represent all circles in the xy plane is given as follows:
[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
How to obtain the differential equations for a circle?The equation of a circle of center (h,k) and radius r is given as follows:
(x - h)² + (y - k)² = r².
The equation can be arranged to isolate the variable y as follows:
(y - k)² = r² - (x - h)²
y - k = square root (r² - (x - h)²)
y = square root (r² - (x - h)²) + k
To obtain the differential equation, then this equation must be differentiated towards variable x as follows:
[tex]\frac{dy}{dx} = \frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k)[/tex]
Applying the chain rule, along with the derivative for the square root, we have that:
[tex]\frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k) = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
Meaning that the differential equation is given as follows:
[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
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A forest covers 41000acres. A survey finds that 0.2% of the forest is old-growth trees. How many acres of old-growth
trees are there?
Answers
Solve the equation. *Will give Branliest!*
-1/6x-5=2/3x
Answers
Answer:
[tex]x=-6[/tex]
Step-by-step explanation:
Solve for x.
Combine [tex]x[/tex] and [tex]\frac{1}{6}[/tex].
Combine [tex]x[/tex] and [tex]\frac{2}{3}[/tex].
[tex]-\frac{x}{6} -5=\frac{2x}{3}[/tex]
Move all terms containing x to the left side of the equation.
Subtract [tex]\frac{2x}{3}[/tex] from both sides of the equation.
[tex]-\frac{x}{6} -5-\frac{2x}{3}=0[/tex]
To write [tex]-\frac{2x}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].
[tex]-\frac{x}{6}-\frac{2x}{3}*\frac{2}{2}-5 =0[/tex]
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
[tex]-\frac{x}{6}-\frac{2x*2}{6}-5 =0[/tex]
Combine the numerators over the common denominator.
[tex]\frac{-x-2x*2}{6}-5 =0[/tex]
Simplify the numerator.
Factor [tex]x[/tex] out of [tex]-x-2x*2[/tex].
[tex]\frac{x(-1-2*2)}{6}-5 =0[/tex]
[tex]\frac{x(-1-4)}{6}-5 =0[/tex]
[tex]\frac{x*-5}{6}-5 =0[/tex]
Move the negative in front of the fraction.
[tex]-\frac{5x}{6} -5=0[/tex]
Add 5 to both sides of the equation.
[tex]-\frac{5x}{6}=5[/tex]
Multiply both sides of the equation by [tex]-\frac{6}{5}[/tex].
[tex]-\frac{6}{5}(-\frac{5x}{6})=-\frac{6}{5}*5[/tex]
Simplify the left side by cancelling the common factors of 5 and 6.
[tex]x=-\frac{6}{5} *5[/tex]
Move the leading negative in [tex]-\frac{6}{5}[/tex] into the numerator.
[tex]x=\frac{-6}{5} *5[/tex]
Cancel the common factor of 5.
[tex]x=-6[/tex]
A rating/review would be much appreciated. Wish you a happy holiday season!
Answer:
x = - 6---------------------------------
Given equation:
-1/6x - 5 = 2/3xFist, multiply both sides by 6 to clear the fraction:
6(-1/6)x - 6(5) = 6(2/3)x- x - 30 = 4xCollect the terms with the variable and solve for x:
4x + x = - 305x = - 30x = - 30/5x = - 68.) Graph f(x)=-x-3
a.) Evaluate f(-4).
b.) Evaluate f(5).
c.) Evaluate f(0).
d.) Circle any ordered pairs that are included in the function:
(-3,0) (-10,7) (13,10)
Answers
From the the graph f(x) = -x-3
Part a
The value of f(-4) = 1
Part b
The value of f(5) = -8
Part c
The value of f(0) = -3
The function is given that
f(x) = -x-3
The function is the mathematical statement that shows the relationship between the independent variable and dependent variable. The function consist of the different variables, numbers and mathematical operator.
The function is
f(x) = -x - 3
Part a
The value of f(-4)
Substitute the value of x in the function
f(-4) = - (-4) - 3
= 4 - 3
= 1
Part b
The value of f(5)
f(5) = -5 - 3
= -8
Part c
The value of f(0)
f(0) = -0 - 3
= -3
Therefore, the value of f(-4), f(5) and f(0) are 1, -8 and -3 respectively
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Suppose that you were trying to use the Putzer method to exponentiate the matrix A which has eigenvalues dı = 4 and A2 = 6, in that order. ao(t) is always the function et. Choose the correct equation for a1(t) da1 О (а) 6a1 + e4t a1(0) = 1 dt da1 : 4a1 + e4t P (g) da1 a1(0) = 1 (c) dt -4a1 + ett a1(0) = 0 da1 (d) dt 4a1 + et a1(0) = 0 da1 (e) : 6a1 + e4t a1(0) = 0 dt da1 (f) dt — 4а, + e# a,(0) — 1
Answers
The correct equation for a1(t) is dt -4a1 + e4t a1(0) = 0.
What is equation?An equation is a mathematical expression that shows the relationship between two values or variables. It typically consists of an equal sign (=), two expressions separated by an operator, and sometimes additional symbols like parentheses, fractions, or exponents. Equations are used to describe physical laws and conditions, solve problems, and make predictions. For example, the equation for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.
This is because the eigenvalue of A which corresponds to the coefficient of a1(t) is 4, so the equation should contain e4t. The initial condition is a1(0) = 0, since the initial value of a1(t) is 0.
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Los Angeles workers have an average commute of 27 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 15 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that a randomly selected LA worker has a commute that is longer than 35 minutes.
c. Find the 70th percentile for the commute time of LA workers. minutes
Answers
(a) Distribution of X is a bell curve with mean of 27 min
(b) The probability of a randomly selected LA worker has a commute that is longer than 35 minutes is 79.81%
(c) 70th percentile for the commute time of LA workers is 34.866
Given,
Mean = 27 minutes
Standard Deviation = 15 minutes
a. The distribution is a bell curve, with the peak of the curve corresponding to the mean = 27 minutes.
b. We have to find the probability that a randomly selected LA worker will have a commute of over 35 minutes. This value will fall on the right hand side of the bell curve, i.e, on the right side of the mean. For that, we need to find the z-score for 35.
z score, z = [tex]\frac{35-27}{15} = 0.53[/tex]
Using the z-tables, we get the z-value to the left of 0.53 as 0.2019, and therefore, the z-value to the right will be 1 - 0.2019 = 0.7981, which gives us a probability percentage of around 79.81%.
c. Here, we have to find the 70th percentile for the commute time for the LA workers. Let us take the marker as 0.70 on the bell-curve, so a z-score that gives us a value of 0.70 should be the right answer.
The answer to that is 0.5244.
Now, a little calculation:
0.5244 x 15 = 7.866 = x - 27
x = 34.866
Final answers:
a. A bell curve
b. 0.7981
c. 34.866
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a. The distribution is a bell curve, with the peak of the curve corresponding to the mean = 27 minutes.
b. Using the z-tables, we get the z-value to the left of 0.53 as 0.2019, and therefore, the z-value to the right will be 1 - 0.2019 = 0.7981, which gives us a probability percentage of around 79.81%.
c. Here, we have to find the 70th percentile for the commute time for the LA workers. Let us take the marker as 0.70 on the bell-curve, so a z-score that gives us a value of 0.70 should be the right answer.
The answer to that is 0.5244.
0.5244 x 15 = 7.866 = x - 27
x = 34.866
Could I have some help with the question below:
In each part, find the two unit vectors in R^2 that satisfy the given conditions:
The two unit vectors parallel to the line y=5x+5 are: _ and _
The two unit vectors parallel to the line 2x+4y=1 are: _ and _
The two unit vectors perpendicular to the line y=2-5x are: _ and _
Answers
The two unit vectors parallel to the line y=5x+5 are [tex]u_{+}[/tex] =⟨1, 5⟩/√26 and [tex]u_{-}[/tex] =⟨1, 5⟩/√26.
What are vectors?Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.
Part A:
The given equation of line is y=5x+5.
It's all about slope. The vectors parallel to the line must have the same slope as the line. The line here is y=5x+5., and has slope 5. We can say the rise is 5 and the run is 1 and write the vector.
[tex]u_{\pm}[/tex] =⟨1, 5⟩
Magnitude =|u| =√(1²+5²)
= |±√26|
= √26
So, the two unit vectors are
[tex]u_{+}[/tex] =⟨1, 5⟩/√26 and [tex]u_{-}[/tex] =⟨1, 5⟩/√26
Part B: 2x+4y=1
x+2y=1/2
y=-x/2+1/4
Here slope is -1/2, where rise is -1 and run is 2
[tex]u_{+}[/tex]= ⟨2, -1⟩ and [tex]u_{-}[/tex]= ⟨-2, 1⟩
Magnitude =|u| =√(2²+(-1)²)
= √5
So, the two unit vectors are
[tex]u_{+}[/tex] =⟨2, -1⟩/√5 and [tex]u_{-}[/tex] =⟨-2, 1⟩/√5
Part C: The given equation is y=2-5x
Here slope is -5, slope perpendicular to line is -1/5
So, rise is -1 and run is 5
[tex]u_{\pm}[/tex] =⟨5, -1⟩
Magnitude =|u| =√(5²+(-1)²)
= √26
So, the two unit vectors are
[tex]u_{+}[/tex] =⟨5, -1⟩/√26 and [tex]u_{-}[/tex] =⟨-5, 1⟩/√26
Therefore, the two unit vectors parallel to the line y=5x+5 are [tex]u_{+}[/tex] =⟨1, 5⟩/√26 and [tex]u_{-}[/tex] =⟨1, 5⟩/√26.
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the base of s is a circular disk with radius 5r. parallel cross-sections perpendicular to the base are squares.
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The volume of the solid is 250r³ when the base of s is a circular disk with radius 5r.
Given that,
We have to discover the described solid's volume, v. The parallel cross-sections perpendicular to the base of s are squares, and the base of s is a circular disk with radius 5r.
We know that,
A cylinder is a solid with square cross sections parallel to the bases and circular bases. Its height is equal to the base circle's diameter.
The radius = 5r,
So the height = diameter = 10r
Volume of the cone is base × height= πr²×h
=π(5r)²×(10r)
=250πr³
Therefore, The volume of the solid is 250r³ when the base of s is a circular disk with radius 5r.
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help me solve this please
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Thus, the required trig values corresponding to the cosФ = -3/5 have been shown,
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
cosФ = -3/5
cosФ = -3/5 = base / hypotenuse,
perpendicular = √5² - 3² = 4
sinФ = perpendicular / hypotenus
= 4/5
Simultaneously,
cosecФ = 5/4
secФ = -5/4
tanФ = -4/3
cotФ = -3/4
Here,
sin and cosec are positive because this function as a positive positive value between π/2 and π, while else trigonometric function as a negative value for π/2 to π.
Thus, the required trig values are shown above.
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a survey of 800 randomly selected adults in a certain country found that 82% believed that protecting the right of those with unpopular views is a very important component of a strong democracy. verify the central limit theorem conditions
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On solving the question - At α = 0.05, two tailed critical value, Lower Bound =[tex]0.757[/tex], Upper Bound = 0.803, (0.757, 0.803)
What is 95% Confidence interval?An estimation range for an unknowable parameter is referred to as a confidence interval in frequentist statistics. The most popular confidence level is 95%, however other levels, such 90% or 99%, are occasionally used for computing confidence intervals. A constant that indicates the intended degree of significance based on the normal distribution is multiplied by the standard error once it has been calculated to get the confidence interval. Intervals with 95% certainty have a constant value of 1.96.
The number of people in the sample that felt protecting the rights of those with unpopular views is a very important component of a strong democracy is 1200*.78 = 936
Yes, the sample size is large enough, since the expected number of successes is 936, and the expected number of failures is 1200-936= 264, both of which are greater than or equal to 10.
95% Confidence interval :
At α = 0.05, two tailed critical value
Lower Bound =[tex]0.757[/tex]
Upper Bound = 0.803
(0.757, 0.803)
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Please help me!!!!!!!!!!!!
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Answer:
A
Step-by-step explanation:
change 'its' to it's which is a contraction for 'it is'
The Daily Total Number Of Students Who Used The State University Swimming Pool On 40 Days During The Summer Is As follows:
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The frequency table with the classes is:
Category Frequency
85 99 7
100-114 8
115-129 13
130-144 7
145-159 5
In the given question,
The daily total number of students who used the state university swimming pool on 40 days during the summer is given.
A frequency table with the classes is 85 99, 100-114, 115-129, 130-144, and 145-159.
First we make table of given frequency and write the given number who lies in between that numbers.
Category Numbers in interval
85-99 90, 93, 98, 89, 86, 97, 98
100-114 110, 107, 108, 110, 102, 105, 109, 104
115-129 121, 119, 128, 129, 128, 115, 120, 129, 118, 122, 126, 118, 116
130-144 142, 132, 139, 137, 131, 132, 131
145-159 145, 149, 149, 152, 159
As we know that the frequency is the total numbers that cones between given interval.
Now the frequency is:
Category Frequency
85 99 7
100-114 8
115-129 13
130-144 7
145-159 5
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The right question is:
The daily total number of students who used the state university swimming pool on 40 days during the summer is as follows:
90 98 137 108 128 115 152 122 110 132 149 131 102 109 118 126 121 145 89 149 86 120 97 118 142 139 128 110 105 104 131 159 93 119 107 129 132 129 98 116
For a frequency table with the classes 85 99, 100-114, 115-129, 130-144, and 145-159.
Triangle Congruence: Question 3
In the proof, what is the reason for (5) ?
Given: V W║Z Y
W X=Y X
Prove: ΔVWX ΔXYZ
Select one:
SSA
H
SAS
ASA
SSS
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In the proof the reason for (5)ΔVWX ≅ ΔXYZ is ASA , the correct option is (d) .
In the question ,
it is given that ,
Given: VW parallel to ZY and WX = YX
to Prove: ΔVWX ≅ ΔXYZ .
the statement to prove ΔVWX ≅ ΔXYZ are given as
(1) VW parallel to ZY ....given
(2) m∠W = m∠Y ...alternate interior angle .
(3) WX = YX ...given
(4) m∠VXW = m∠ZXY .....vertically opposite angle
(5) ΔVWX ≅ ΔXYZ
In statement (5) , Since two angles and 1 side is included in proving the given two triangles congruent ,
the reason will be ASA congruence , that is option (d) .
Therefore , the reason for (5) is ASA .
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Calculate the difference and enter below. 3-9
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Answer:
-6 is your answer
Step-by-step explanation:
I hope that's right
Add a department store a coat that normally sells for $50 it's on sale for $35 what is the percent of the decrease? HELP
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Answer: 30%
Step-by-step explanation: To find the percent of decrease, you have to subtract the greater number from the smaller one, then divide it by the first number that comes in the sentence x 100. So, using that formula, we subtract 35 from 50 to get 15, then we do 15/50 x 100 to get 30 or 30%. I hope this helped you understand a little more about the percentage decrease.