Answer:
-3x + 8
Step-by-step explanation:
Simplify. combine like terms (terms with the same amount of variables).
Subtract -2x and x: -2x - x = -3x
-3x + 8 is your answer.
~
If a categorical independent variable contains 4 categories, then ________ dummy variables will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4
If a categorical independent variable contains 4 categories, then four dummy variables will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4
How many dummy variables are needed to represent the categorical variable?
We need 1 less dummy variable than outcomes for the categorical variable.
categorical variable has 2 outcomes
So, we need 2-1 = 1 dummy variable.
Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.
b. Write the multiple regression equation relating the dependent variable to the independent variables.
Note: Depending your your professor, this can be written one of the following ways...
yhat = a + b1 x1 + bx2
yhat = b0 + b1 x1 + b2 x2
yhat = beta0hat + beta1hat x1 + betahat2 x2
where x1 is the ratio variable
and x2 is the dummy variable
c. Interpret the meaning of the coefficients in the regression equation.
b0 = the predicted value of y when x1 and x2 both equal 0.
b1 = the change in y when x1 increases by 1 unit holding x2 constant.
b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant
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the probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. the probability that a man watches the show, given that his wife does, is 0.7. find the probability that
The probability is that the married couple watches the show is 0.35.
According to the statement
We have to find the probability is that the probability that married couple watches the show is 0.35.
For this purpose, we know that the
Probability is the ratio of the number of outcomes to the total number of possible outcomes.
With the given information
a married man watches a certain television show is 0.4
the probability that a married woman watches the show is 0.5.
the probability that a man watches the show, given that his wife does, is 0.7
Then
Let M be the event that a married man watches a certain T.V.
And N be the event that a married woman watches the show.
The probability become
\(P(M)=0.4\) \(P(F)=0.5\)
and the
\(P(\frac{M}{F} )=0.7\)
Then
The probability become is the
P(M∩F)=0.7*0.5
And
\(P=0.7*0.5\)
\(P=3.5\)
So, The probability is that the married couple watches the show is 0.35.
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Question:
The probability that a married man watches a certain TV show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Then
the probability that married couple watches the show.
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delivered.
a. What is the constant rate of change? What does it represent?
b. What is the initial value? What might that represent?
The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.
The given problem can be solved as follows,
(a) The graph given is a straight line that passes through (0, 40) and (10, 240).
The constant rate of change is equivalent to the the slope of the line given as,
⇒ (240 - 40)/(10 - 0) = 20
(b) The initial value of the graph is given as the y-intercept of the line.
Which is given as 40.
It might represent the fixed cost.
Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.
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The missing graph is attached here.
when testing the difference between two independent samples, which test occurs when the null hypothesis states the difference between the parameters is less than or equal to zero, and the alternative hypothesis states that the difference is greater than zero?
The alternative hypothesis states that the difference is greater than zero.
What Are Tails in a Hypothesis Test?
First, we need to cover some background material to understand the tails in a test. Typically, hypothesis tests take all of the sample data and convert it to a single value, which is known as a test statistic. You’re probably already familiar with some test statistics.
For example, t-tests calculate t-values. F-tests, such as ANOVA, generate F-values. The chi-square test of independence and some distribution tests produce chi-square values. All of these values are test statistics.
Keep in mind that this t-distribution assumes that the null hypothesis is correct for the population. Consequently, the peak (most likely value) of the distribution occurs at t=0, which represents the null hypothesis in a t-test. Typically, the null hypothesis states that there is no effect. As t-values move further away from zero, it represents larger effect sizes. When the null hypothesis is true for the population, obtaining samples that exhibit a large apparent effect becomes less likely, which is why the probabilities taper off for t-values further from zero.
Hence the answer is the alternative hypothesis states that the difference is greater than zero.
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h(x) = x²- 5x + 7
a). h(2)
b).h(-5)
c). h(-8)
a manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.6 years, and standard deviation of 1.3 years. if you randomly purchase one item, what is the probability it will last longer than 14 years? round answer to three decimal places
If a manufacturer have a normally distributed lifespan, with a mean of 11.6 years, and standard deviation of 1.3 years, the probability that a randomly purchased item will last longer than 14 years is 0.966 or 96.6%.
We can use the standard normal distribution to calculate the probability that an item will last longer than 14 years. First, we need to calculate the z-score:
z = (14 - 11.6) / 1.3 = 1.846
Next, we can use a standard normal distribution table or a calculator to find the probability associated with a z-score of 1.846. Using a standard normal distribution table, we find that the probability is 0.9664.
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Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models (this is the product mix). The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes Zen, Inc.’s sales product mix for a week is?
Each model should be produced on a weekly basis to maximize net profit is $75,900.
What is Net profit?
In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.
As given,
Number of products sold:
T ≥ 1.5G
Maximize Profit Z = 150T + 130G
Labor Constraint:
Labor hours Available:
Production Department:
Number of labor hours available per day = 58 × 7 = 406
Number of days in a week = 5
Number of lobor ours available per week = 406 × 5 = 2030
Assembly Department:
Number of labor hours available per day = 25 × 7 = 175
Number of days in a week = 5
Number of labor hours available per week = 175 × 5 = 875.
Labor hours Required:
Labor hours required for G1 model:
Labor hours required at Production department = 3.5G
Labor hours required at assembly department = 2G
Labor hours required for T1 model:
Labor hours required at Production department = 4T
Labor hours required at Assembly department = 1.5T
Total labor hours required at Production department = 3.5G + 4T
Total labor hours required at Assembly department = 2G + 1.5T.
Constraint:
Labor hours required ≤ Labor hours Available.
Production department Labor constraint
3.5G + 4T ≤ 2030
Assembly department Labor constraint:
2G + 1.5T ≤ 875
The function:
Maximum Profit Z = 150T +130G
Constraint:
3.5G +4T ≤ 2030
2G + 1.5T ≤ 875
T ≥ 1.5G
Suppose that for example:
10.5G +12T = 6090
16G + 12T = 7000
Solve both equations simultaneously,
5.5G = 7000 - 6090
5.5G = 910
G = 910/5.5
G = 363
Since, T > G
Hence,
T = 363,
G = 165
Calculate Profit:
150T + 130G = 150 × 363 + 130 × 165
= 54450 + 21450
= 75900
Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.
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Which of the following represents the total area of the figure?
44 ft²
400 ft²
440 ft²
484 ft²
Answer:
484 ft²
Step-by-step explanation:
The area of the given figure= area of right angled triangle ABC + area of rectangle BCDE + area of triangle DEF
=1/2 * base*height+ length*height+ 1/2*base*height
here base of triangle is equal to height of triangle ABC
=1/2*8*22+22*16+1/2*22*4
=484 ft²
Cleveland, OH, where the maximum and minimum temperatures were 70
∘
F and 58
∘
F respectively, experienced a mean temperature of
∘
F (round up if necessary). a. 58 b. 60 c. 64 d. 66 11. The mean temperature derived from the maximum and minimum temperatures at Cleveland indicates degree days were accumulated. a. heating (HDD) b. cooling (CDD) 12. Therefore, Cleveland accumulated degree day(s) on 6-7 September 2022. a. 0 b. 1 c. 3 d. 7 13. Based on the plotted temperatures across the rest of Ohio, remaining stations HDD on 6-7 September 2022. a. accumulated b. did not accumulate You can observe and calculate HDD or CDD as we progress into the fall and through the winter. Wind Chill HDD and CDD values and their effect on homeowners' utility bills may stress tight budgets through the seasons. Since energy bills are dependent on the human who uses the energy, another factor for homeowners to consider when budgeting energy consumption is wind chill. The wind chill is an air temperature index that takes into account heat loss from exposed skin caused by the combined effect of wind and low air temperature. Outdoors, the cooling effect of wind along with the ambient temperature is reflected by using the wind chill equivalent temperature. Go to NWS Daily Weather Map for the most recent map. The pane to the left allows you to select any date back to 1 January 2003. Each day's map series includes the surface map, colorcoded maps of maximum and minimum temperatures, mid-tropospheric flow at the 500−mb level, and total precipitation. The surface and 500−mb maps are for 12Z(8a.m. EDT or 7a.m. EST, etc.) while the temperatures and precipitation maps are for the entire day. Clicking on the maps opens a more detailed map. Bring up the daily weather map set for 23 January 2022 . Scroll down and click on either the Maximum or Minimum Temperature map. 14. For 23 January 2022, on the North Dakota-Minnesota border, Fargo had a minimum temperature of −25
∘
F. With the minimum temperature there, assume Fargo was experiencing a wind speed of 10mph. With the NWS Wind Chill Chart in Figure 4A-5 from Investigation 4A, the wind chill for this combination of temperature and wind speed would have been
∘
F. a. −16 b. −20 c. −35 d. −41 e. −47
The mean temperature in Cleveland, OH, was 64°F. The accumulated degree days for Cleveland on 6-7 September 2022 were 1. The rest of Ohio accumulated degree days during the same period.
Based on the given information, the maximum temperature in Cleveland was 70°F and the minimum temperature was 58°F. To find the mean temperature, we add the maximum and minimum temperatures and divide by 2: (70°F + 58°F) / 2 = 128°F / 2 = 64°F.
Degree days are a measure of heating or cooling requirements. In this case, since the mean temperature in Cleveland was lower than a certain base temperature, degree days were accumulated. The base temperature is typically set at 65°F for cooling and 55°F for heating. Since the mean temperature in Cleveland was below the base temperature, the accumulated degree days are heating degree days (HDD).
For the specific date of 6-7 September 2022, Cleveland accumulated 1 heating degree day (HDD). This means that the average temperature for that period was 1 degree below the base temperature of 55°F.
The remaining stations in Ohio also accumulated heating degree days (HDD) on 6-7 September 2022. This indicates that the temperatures across the rest of Ohio were below the base temperature during that period.
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A slice is cut from a circular pizza with a diameter of 18 inches. The arc length, or curved edge of the pizza, that was cut measures 6.5 inches. What is the measure of the central angle that was used when cutting the pizza to the nearest tenth?
A- 0.4 radians
B-0.7 radians
C- 1.4 radians D- 2.8 radians
The measure of the central angle that was used when cutting the pizza to the nearest tenth is 0.7 radians.
We are given that
Diameter of pizza =d=18 inches,
The distance across a circle through the center is called the diameter. The distance from the center of a circle to any point on the boundary is called the radius. The radius is half of the diameter: 2r=dhence radius of circular pizza =r\(=\frac{\mathrm{d}}{2}=\frac{18}{2}=9$\) inches,
Also, the arc length of a slice of pizza =L=6.5 inches.
Since we know that
As per central angle definition in geometry, it is the angle subtended by the arc of the circle at the center of the circle. The two radii make the arms of the angle. Central angle helps to know the proportion of the curve with respect to the circle.Central angle \($(\theta)=\frac{\text { Arc length }}{\text { Radius of circle }}=\frac{\mathrm{L}}{\mathrm{r}}$\)Equation 1 where \($\theta$\) is measured in radians.
Put the values of L and r in equation1, Central angle \($(\theta)=\frac{\mathrm{L}}{\mathrm{r}}$\)\(& =\frac{6.5}{9} \\\)
\(& =\frac{65}{90} \\\)
\(& =\frac{13 \times 5}{18 \times 5} \\\)
\(& =\frac{13}{18} \\\)
\(& =0.7 \text { radians }\end{aligned}\)
Therefore, the measure of the central angle to the nearest tenth is 0.7 radians.
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Billy is running away from a Wells Fargo bank at a speed of 13 kilometers per hour (units are km/h ). If the distance between the bank and the border to Mexico is 1.9 km, will he be able to get there before the cops arrive in 9 minutes? How long will it take for him to reach the border? (Hint: speed = distance / time, 1 hour =60 minutes )
No, Billy will not be able to reach the border before the cops arrive in 9 minutes.
To determine whether Billy can reach the border before the cops arrive, we need to calculate the time it would take him to cover the distance of 1.9 km.
Using the formula speed = distance / time, we can rearrange the formula to solve for time. Rearranging, we have time = distance / speed.
Given that Billy's speed is 13 km/h, we can calculate the time it would take him to cover 1.9 km.
time = 1.9 km / 13 km/h = 0.146 hours
To convert hours to minutes, we multiply by 60:
0.146 hours * 60 minutes/hour = 8.76 minutes
Therefore, it would take Billy approximately 8.76 minutes to reach the border. Since the cops are expected to arrive in 9 minutes, he would not be able to make it before they arrive.
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Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
A recently televised broadcast of a popular television show had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned to the show. A 0.01 significance level is used to test an advertiser’s claim that among the households with TV sets in use, less than 20% were tuned in to the show. Find the P-value.
1.9998
0.9999
0.0001
0.0002
The p-value of the given hypothesis is; 0.9999
How to find the p-value of the statistics?The formula for the z-score of proportions is;
z = (p^ - p)/√(p(1 - p)/n)
where;
p^ is sample proportion
p is population proportion
n is sample size
We are given;
p^ = 15% = 0.15
p = 20% = 0.2
n = 5000
Thus;
z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)
z = -8.8388
From p-value from z-score calculator, we have;
P(Z < -8.8388) = 1 - 0.0001 = 0.9999
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Name the smallest even number divisible by 6 and 9.
Answer:
18
Step-by-step explanation:
Which polynomial function has zeros at -3, 0, and 4?
f(x) = (x + 3)(x2 + 4)
f(x) = (x2 - 3)(x - 4)
f(x) = x(x + 3)(x - 4)
f(x) = x(x - 3)(x + 4)
Answer:
If 5 is zero then (x - 5) is a factor.
Only 4. has this factor.
Step-by-step explanation:
Which equation can be used to find d, the number of dollar coins Giuliana has?
The equation of the number of dollar cins giuliana has, is found to be
0.25(22 – d) + d = 10.75.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Giuliana has 22, quarters and dollar coins worth a total of $10.75.
Let the number of dollar coins be represented by d, while the number of quarter coins be represented by (22-d). Therefore, the sum of the total amount that is with Giuliana can be written as,
(1 x d) + (0.25 x (22-d)) = 10.75
d + 0.25(22-d) = 10.75
Hence, the equation can be used to find d, the number of dollar coins Giuliana has is 0.25d + 22 – d = 10.75.
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What is the value of x in the equation
3x-4y=65, when y=4?
x=1372
x=21
X =23
x=27
Answer:
x = 27
Step-by-step explanation:
3x - 4(4) = 65
3x - 16 = 65
3x = 81
x = 27
13=2f+5
What does f =
Answer:
4
Step-by-step explanation:
Step 1:
13 = 2f + 5 Equation
Step 2:
8 = 2f Subtract 5 on both sides
Step 3:
f = 8 ÷ 2 Divide
Answer:
f = 4
Hope This Helps :)
Answer:
I did this before! heres what i did: 13=2f+5
We simplify the equation to the form, which is simple to understand
13=2f+5
We move all terms containing f to the left and all other terms to the right.
-2f=+5-13
We simplify left and right side of the equation.
-2f=-8
We divide both sides of the equation by -02 to get f.
f=4
855 online photos: a poll surveyed internet users and found that of them had posted a photo or video online. can you conclude that more than half of internet users have posted photos or videos online? use the level of significance and the critical value method.
Since the calculated test statistic (2.836) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that more than half of internet users have posted photos or videos online.
To test the hypothesis that more than half of internet users have posted photos or videos online, we can use a one-sample proportion test. Let p be the true proportion of internet users who have posted photos or videos online. The null and alternative hypotheses are:
H0: p <= 0.5
Ha: p > 0.5
We will use a significance level of 0.05.
Using the given information, we have:
n = 855
x = (56/100) * 855
= 479.6 (rounded to nearest whole number, 480)
The sample proportion is:
p-hat = x/n
= 480/855
= 0.561
The test statistic is:
z = (p-hat - p0) / √(p0 * (1 - p0) / n)
where p0 is the null proportion under the null hypothesis. We will use p0 = 0.5.
z = (0.561 - 0.5) / √(0.5 * (1 - 0.5) / 855)
= 2.836
Using a standard normal distribution table or calculator, the critical value for a one-tailed test at a 0.05 level of significance is approximately 1.645.
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Pounds would be a good unit to measure everything but
A oranges.
B milk
c sugar.
D potatoes
Answer:
B.Milk
Step-by-step explanation:
3x - 5(x -5) = - 3 + 5x + 7
Answer:
x=3
Step-by-step explanation:
3x-5x+25= 5x+4
-2x+25=5x+4
+2x. +2x
25=7x+4
-4. -4
21=7x
/7. /7
3=x
Hopes this helps please mark brainliest
Answer:
x = 3Step-by-step explanation:
3x - 5(x -5) = - 3 + 5x + 7
3x - 5x + 25 = 4 + 5x
3x - 5x -5x = 4 - 25
-7x = -21
x = -21 : (-7)
x = 3
Imagine you are dealing with 15 class classification problem. What is the maximum number of discriminant vectors that can be produced by lda?.
For a 15-class classification problem, the maximum number of discriminant vectors would be 14.
In Linear Discriminant Analysis (LDA), the maximum number of discriminant vectors that can be produced is equal to the number of classes minus one.
For a 15-class classification problem, the maximum number of discriminant vectors would be 15 - 1 = 14.
LDA aims to determine a linear combination of features that maximizes the separation between different classes while minimizing the variance within each class.
The resulting discriminant vectors are used to project the data onto a lower-dimensional space, where the classification task becomes simpler.
It's important to note that the number of discriminant vectors is determined by the number of classes and not the number of samples in the dataset.
However, it's also worth mentioning that in practice, the number of available samples and the characteristics of the data can impact the effectiveness of LDA and the interpretability of the results.
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A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to
buy each player a bottle of water and an energy bar. The price of one energy bar is $2.
Let w equal the price of a bottle of water. Write an equation that
represents the situation.
Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50
Step-by-step explanation: i dont know what to write??
What expense category could be eliminated through good financial planning?
I need help please with this equation
Answer:
The chosen topic is not meant for use with this type of problem.
−
3
,
(
1
,
3
)
5
,
(
1
,
1
)
4
,
(
2
,
−
4
)
Step-by-step explanation:
even if an independent variable has an effect on the dependent variable, it is still possible to obtain a sample mean that is very similar to the original population mean. what outcome is likely if this happens?
even if an independent variable has an effect on the dependent variable, it fail to reject the null hypothesis and make a type II error
Even if a treatment is effective in the real world (it has an effect), it is still possible to obtain a sample mean that is so similar to the population mean that the sample mean doesn't fall in the critical, or rejection, region. If this happens, you are likely to fail to reject the null hypothesis and make a type II error.
Since that sample mean is so similar to the population mean, the treatment effect may not be detected on analysis even though it is in fact significant, this will cause the research to erroneously concluded that the treatment effect is zero and accept the null hypothesis when it is actually not zero. This is a type II error. Type II error in statistics means the non-rejection of a false null hypothesis and type I error is the rejection of a correct null hypothesis.
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if y varies directly as x and y=7 when x equals 3 find y when x=7
Answer: y=3
Step-by-step explanation:
if they directly vary than they just flip flop
2. Solve for b.
(a - 3)
Answer:
Step-by-step explanation:
Sum of angles inside triangle is 180
b + (a -3) + 90 =180
b + a - 3 + 90 = 180
b + a + 87 = 180
b + a + 87 -87 = 180-87
b + a = 180-87
b + a = 93
b = 93 -a
With all this talk of money in class recently, you've been daydreaming about receiving an unexpected $10,000 inheritance from a long-lost aunt you didn't even know you had. If you did receive such a generous gift, you plan on depositing all the money in a bank account. Several interest options are currently available.
a) [3 pts] One bank pays 1.8% annual interest compounded daily. Write an equation for the value of the money in this account after t years. b) [3 pts] Calculate the effective annual interest rate (EAY) for the above account. Round the interest rate to the nearest thousandth of a percent. c) [3 pts] What annual interest rate, compounded quarterly, would give you the same effective annual interest rate as 1.8% compounded daily (which you found in part b)?
a) The equation for the value of the money in the account after t years, with 1.8% annual interest compounded daily, can be given by:
V(t) = 10000 * (1 + 0.018/365)^(365*t)
The formula for compound interest is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is $10,000, the annual interest rate is 1.8%, the interest is compounded daily (n = 365), and t represents the number of years. Plugging these values into the formula, we get V(t) = 10000 * (1 + 0.018/365)^(365*t).
b) To calculate the effective annual interest rate (EAY) for the account, we use the formula:
EAY = (1 + r/n)^n - 1
Using the values r = 1.8% and n = 365, we can calculate the EAY as follows:
EAY = (1 + 0.018/365)^365 - 1 ≈ 0.0183 or 1.83%
Rounding the interest rate to the nearest thousandth of a percent, the effective annual interest rate (EAY) for the account is approximately 1.83%.c) To find the annual interest rate, compounded quarterly, that would give the same EAY as 1.8% compounded daily, we need to solve for r in the formula:EAY = (1 + r/n)^n - 1
Let's denote the quarterly interest rate as r_q and the number of times interest is compounded per year as n_q = 4 (quarterly compounding). We want to find r_q such that the equation holds true:(1 + r_q/4)^4 - 1 = 0.0183
By solving this equation, we can find the annual interest rate, compounded quarterly, that gives the same EAY as 1.8% compounded daily.
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The high school soccer team can have no more
than 22 players on the roster. Write and solve an
inequality finding the number of players the
coach may choose if the coach already has 13
players.
Answer:
13 + x ≤ 22
x ≤ 9
Step-by-step explanation:
Total players = 22
Players available = 13
Players remaining = x
The inequality can be written as:
Players available + Players remaining ≤ Total players
13 + x ≤ 22
x ≤ 22 - 13
x ≤ 9