Answer:
She needs to have approximately $6950 on that account.
Step-by-step explanation:
Since the account has an interest rate of 9% annually, then it's compounded and the earnings can be found by the following expression:
[tex]M = C*(1 + r)^t[/tex]
Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed in years.
She needs the money in 3 years, therefore t = 3. Applying this to the problem we have:
[tex]9000 = C*(1 + 0.09)^3\\9000 = C*(1.09)^3\\C*1.295 = 9000\\C = \frac{9000}{1.295}\\C = 6949.81[/tex]
She needs to have approximately $6950 on that account.
c. Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 4 feet. What is the area of the shade?
Answer:
A=12 feet²
Step-by-step explanation:
1/2*base*height=area
(1/2)*4*6=12
Solve the system of equations by using substitution
Y=2x+3
Y=x+2
Since our first equation reads y = 2x + 3, we can substitute a 2x + 3
in for y in our second equation and then solve from there.
So we have 2x + 3 = x + 2.
Now subtract x from both sides to get x + 3 = 2.
Now subtract 3 from both sides to get x = -1.
To find y, plug -1 back into either equation.
I have chosen to plug it into the second.
So we have y = (-1) + 2 which simplifies to 1.
So our solution to this system is (-1, 1).
85 points!! | All of the following expressions have the same value, when x= -2 and y= 4, except
-2xy
0-4x2
0x²y
0 (-2) ²y
Answer:
They have two sets of equal answers...
Step-by-step explanation:
-2 * 2 * 4 = -16
0 - 4 * -2 * -2 = -16
0 * -2 * -2 * 4 = 0
0 * 4 * 4 = 0
A random sample of 18 graduates of a certain secretarial school typed an average of 80.6 words per minute with a standard deviation of 7.2 words per minute. Assuming a normal distribution for the number of words typed per minute, compute the 95% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.
Answer: ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 80.6 words per minute
Standard deviation r = 7.2
Number of samples n = 18
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
80.6+/-1.96(7.2/√18)
80.6+/-1.96(1.697056274847)
80.6 +/- 3.33
= ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.48 ppm and a standard deviation of 3.25 ppm. Suppose that you draw a random sample of 10 printers.
Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 18.06 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion)
Answer:
0.288
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740[/tex]
Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.
This is 1 subtracted by the pvalue of Z when X = 18.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18.06 - 17.48}{1.027740}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a pvalue of 0.712
1 - 0.712 = 0.288
The answer is 0.288
Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.
Answer:
1130
Step-by-step explanation:
since radius of the circle was given and the formula of the area is pie r square
Which of the following numbers are in setA? Check all that apply.
A = {x | x is a positive, odd integer less than 7}
0
1
2
5
3
Answer:
1, 3, 5.
Step-by-step explanation:
The members of the set are {1, 3, 5}.
Note 0 is an even integer so is not included in the set.
Also 0 is neither negative or positive.
Age (years) Population Under 15 2600 15 - 64 16000 Over 64 4000 Calculate the child dependency ratio from the chart above. Round to 3 decimals places.
Answer:
16.25%
=0.163 (correct to 3 decimal places)
Step-by-step explanation:
The child dependency ratio of a population is defined as the number of children (Under 15 years) divided by the working-age population (15–64 years old).
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{{\mathrm{ Population}\,\left( \text{Under 15} \right)}}{{\mathrm{ Population}\,\left( {15-64} \right)}}\times 100[/tex]
From the given table:
Population Under 15 years = 2600
Population of the working class (between 15-64) = 16000
Therefore:
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{2600}{16000}\times 100\\\\=16.25\%[/tex]
=0.163 (correct to 3 decimal places)
Which graph represents the function f(x) = |x| – 4? On a coordinate plane, an absolute value graph has a vertex at (0, 4). On a coordinate plane, an absolute value graph has a vertex at (negative 4, 0). On a coordinate plane, an absolute value graph has a vertex at (0, negative 4). On a coordinate plane, an absolute value graph has a vertex at (4, 0).
Answer:
(0, -4)
Step-by-step explanation:
The graph that represents the function is (c) on a coordinate plane, an absolute value graph has a vertex at (0, -4)
The equation of the function is given as:
[tex]f(x) = |x| - 4[/tex]
The above function is an absolute value function shifted down by 4 units
Hence, the graph that represents the function is a graph that has its vertex at (0,-4)
Read more about absolute value graphs at:
https://brainly.com/question/2166748
someone answer this
Answer:
16
Step-by-step explanation:
The right triangle shown is a 30:60:90 triangle.
30:60:90 right triangles have a 1:sqrt(3):2 ratio between their sides.
Since the side opposite from the 30 degree is 8, and x is opposite from the 90 degree angle, 8 and x have a 1:2 ratio, or 8:16.
what is the solution set for the equation (x-2)(x-8)=0
Answer:
x=2 x =8
Step-by-step explanation:
(x-2)(x-8)=0
Using the zero product property
x-2 = 0 x-8 = 0
x=2 x =8
Answer:x = 2 and x = 8
Step-by-step explanation:
( 2 - 2)( 8 - 8)
(0)(0)
=0
What is the solution set up 7x^2+3X=0
Answer:
X=0,X=-3/7
Step-by-step explanation:
7x^2+3x=0
x(7x+3)=0
x=0
7x+3=0
7x=-3
x=-3/7.
Answer:-3/7
Step-by-step explanation:
Firstly add -3x to both sides of equation. 7x^2+3x-3x=0+-3x
7x^2=-3x
Divid both sides by X
7x^2/X=-3/X
7x=-3
Divid both sides by 7
7x/7=-3/7
X=-3/7
please help me on this work please !
g(-4)
Please help!!
Answer:
1
Step-by-step explanation:
g(-4) means what is the y value when x is -4.
Find x=-4, and when x=-4. y=1
Answer:
1
Step-by-step explanation:
Solve for the value of x
Answer:
x = 8
Step-by-step explanation:
The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...
4 +7x = 60
7x = 56 . . . . . . subtact 4
x = 8 . . . . . . . . .divide by 7
A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 10 kilograms of the 40% silver alloy?
Answer:
the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
Step-by-step explanation:
Suppose, the weight of the alloy with 50% silver content is x kilograms.
As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be: kilograms
The percentage of silver content in the mixed alloy is 40%. So the equation will be calculated as
[tex]0.5x+0.25(10-x)=0.4\times10\\0.5x+2.5-0.25x=4\\0.25x=1.5\\\Rightarrow x=\frac{1.5}{0.25} = 6[/tex]
So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
Identify the domain of a radical function with an odd index.
Answer:When n is an odd number, [tex]\sqrt[n]{a}[/tex] is a real number for all values of a. Then, the domain is the real domain.
For all the people that have to do algebra and dont want to do it yourself there is a website or you can download it on your phone its called*** MATH PAPA*** ****IT SHOWS YOU STEP BY STEP AND GIVES YOU THE ANSWER*** Just input the equation
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the total number of rooms in the house. Consequently the appraiser decided to fit the simple linear regression model, ^y=β0+β1x , where y= the appraised value of the house (in thousands of dollars) and x= the number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained:
Answer:
Step-by-step explanation:
Hello!
The statistical model predicts the appraised value of houses in a section of the county East Meadow (Y) in relationship with the number of rooms of the house (X)
For a sample of n=64 houses the simple linear regression was estimated:
^Y= 74.80 + 24.93X
Range of X: 5 - 11
Range of Y: 160 - 300 ($ thousands of dollars)
Interpretation of the estimates of the y-intercept and the slope
y-intercept:
74.80 thousand dollars is the estimated average value of a house in a section of the county East Meadow when the house has zero rooms.
Slope:
24.93 [tex]\frac{thousand dollars}{rooms}[/tex] is the modification of the estimated average value of a house in a section of the county East Meadow when the number of rooms increases on one.
I hope this helps!
Hypothesis Test for Two Populations including:t-Test for μ1-μ1t-Test for μdF-Test forWe are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the followingStore A Store BnA=21 nB=16SA=28.284 SB=20Which of the following is critical values of F at 95% confidence?A. a and dB. 2.57C. 0.3891D. 0.3623E. 2.76
Answer:
The critical values of F at 95% confidence are 0.359 and 2.788.
Step-by-step explanation:
We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:
Store A Store B
nA = 21 nB = 16
SA = 28.284 SB = 20
And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.
AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.
The test statistics for F-test is = [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex] ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]
where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.
Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;
2.788 for right-part and 0.359 for the left-part.
what is X:
|4x−1|=3
|x|=−4
Answer:
1
Step-by-step explanation:
Two competing gyms each offer childcare while parents work out Gym A charges $9.00 per hour of childcare. Gym B
charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?
Answer:
They charge an equal amount of money each hour.
Answer:
Gym B and Gym A charge the same hourly rate for childcare.
Step-by-step explanation:
answer on edge
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 4 students' scores on the exam after completing the course: 12,7,13,11 Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The 80% confidence interval for the average net change is (8.596, 12.904).
Critical value t=1.638.
Step-by-step explanation:
First, we calculate the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{4}(12+7+13+11)\\\\\\M=\dfrac{43}{4}\\\\\\M=10.75\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{3}((12-10.75)^2+(7-10.75)^2+(13-10.75)^2+(11-10.75)^2)\\\\\\s=\dfrac{20.75}{3}\\\\\\s=6.92\\\\\\[/tex]
We have to calculate a 80% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=10.75.
The sample size is N=4.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.63}{\sqrt{4}}=\dfrac{2.63}{2}=1.315[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=4-1=3[/tex]
The t-value for a 80% confidence interval and 3 degrees of freedom is t=1.638.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.638 \cdot 1.315=2.154[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 10.75-2.154=8.596\\\\UL=M+t \cdot s_M = 10.75+2.154=12.904[/tex]
The 80% confidence interval for the average net change is (8.596, 12.904).
16 of 22
Save & Exit
Sample Space: Tutorial
Activity
In this exercise, you'll use the formula for the probability of the complement of an event.
Another game you've set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points
depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails).
Question 1
Find the total number of possible outcomes in each trial of this game.
Answer:
The number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
Given
Rolling of a 6 sided die followed by tossing of a fair coin
Required
Number of possible outcomes
The first step is to list out the possible outcomes of rolling a die and tossing a coin
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {Head, Tail}
Let Head be represented by H and Tail be represented by T;
So,
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {H, T}
The question states that a roll of a 6 sided die is followed by a toss of a fair coin
This means that each trial is {A roll of die and A toss of coin}
So, the sample space is as follows
Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}
Number of outcomes in the sample space is 12.
Hence, the number of possible outcomes in each trial of this game is 12
Answer:
the total number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
uhhhhhh none :) kk bye <3
Express each percent as a fraction in simplest form.
a. 85%
b. 5 72%
c. 12.55%
Answer:
(a) 17/20 b.5/18/25 c. 1.255
Find the values of x in the figure below. Express your answer in simplest radical form.
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...
Data on U.S, Work-Related fatalities by cause follow (The World Almanac,2012)Cause of Fatality Number of Fatalities Transportation Incidents 1795 Assaults and violent acts 837 Contacts with objects and equipment 741 Falls 645 Exposure to harmful substances 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. a. What is the probability the fatality resulted froma fall? b. What is the probability the fatality resulted from a transporation incident? c. What cause of fatality is least likely to occur? What is th probability the fatality resulted from this cause?
Answer:
a) Probability the fatality resulted from a fall = 0.1422
b) Probability the fatality resulted from a transportation incident = 0.3958
c(i) The cause of fatality that is least likely to occur is fatality due to fires and explosions with the lowest number of fatalities, 113.
c(ii) Probability that the fatality resulted from fires and explosions = 0.0249
Step-by-step explanation:
Data on U.S, Work-Related fatalities by cause follow (The World Almanac, 2012)
Cause of Fatality | Number of Fatalities Transportation Incidents | 1795
Assaults and violent acts | 837
Contacts with objects and equipment | 741
Falls | 645
Exposure to harmful substances | 404
Fires and explosions | 113
Total number of fatalities = 1795+837+741+645+404+113 = 4,535
Assume that a fatality will be randomly chosen from this population.
a. What is the probability the fatality resulted from a fall?
The probabilty of an event is given mathematically as the number of elements in that event divided by the Total number of elements in the sample space.
P(E) = n(E) ÷ n(S)
Probability the fatality resulted from a fall = (645/4535) = 0.14223 = 0.1422
b. What is the probability the fatality resulted from a transportation incident?
Probability the fatality resulted from a transportation incident = (1795/4535) = 0.39581 = 0.3958
c(i) What cause of fatality is least likely to occur?
The cause of fatality that is least likely to occur is the cause of fatality with the lowest frequency or number of fatalities. And this is fatality due to fires and explosions with the lowest fatalities of 113
c(ii). What is the probability the fatality resulted from this cause?
This is the probability that the fatality resulted from fires and explosions.
Probability that the fatality resulted from fires and explosions = (113/4535) = 0.02492 = 0.0249
Hope this Helps!!!
I really need help :( anybody ??
_______________________________
Hey!!
Answer:{2,4,5}
Explanation:
RangeLet R be relation from A to B.The set of second components or the set of elements of B are called range.
Hope it helps..
_______________________________
Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?
Answer:
He is incorrect. Ray RO and ray RL are not opposite rays.
Step-by-step explanation:
Two angles are linear pair if they are supplementary and share a leg.
∠ORP and ∠LRP are not supplementary, because ray RO and ray RL are not opposite rays.
Therefore, ∠ORP and ∠LRP are not linear pair.
correct me if this is wrong
you will get alot of points if you answer this explain your answer
Answer:
The surface area of stand is 46 feet.
First
taking the upper rectangular prism only.
so we get
l=3
w=1
h=3
surface area of rectangular prism = 2lw+2lh+2hw
= 2×3×1+2×3×3+2×3×1
= 30
taking the lower rectangular prism only.
surface area of rectangular prism = 2lw+2lh+2hw
=2×7×2+2×1×7+2×2×1
=46
add both the rectangular prism.
we get,
30+46
76
Yes, $15 is enough
Taking out the square of all the rectangle the total would be 52m²
52/25×6.79 ( as 6.79 dollars for 25 m²)
$14.1232
Answer:
freecoins
Step-by-step explanation:
