A psychologist selects a random sample of 25 handicapped students and measures their manual dexterity scores, then if she wants to improve her precision she should use a larger sample size.
Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population. By increasing sample size, you can improve the accuracy of your estimates, which means that the result will be more "statistically significant" for any given estimate or size of effect. The accuracy of the average results will increase with sample quantity. Smaller error margins and the identification of outliers in the data are two further benefits of larger sample sizes.
If they observe an effect that is almost significant, some researchers decide to increase their sample size. This is done rather than concluding that there is no effect because the researcher believes he is short on samples. Because the standard error is reduced as sample size increases, confidence intervals are narrower. c) The statement "there is a 95% likelihood that the population mean is between 350 and 400" is similar to the statement "there is a 95% confidence interval for the population mean is (350, 400)".
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Correct Question:
A psychologist selects a random sample of 25 handicapped students and measures their manual dexterity scores. she uses this data to test the hypothesis that the mean dexterity score is different than 45. What would you advise her?
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One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the mean for this sample?
X f
5 or more 2
4 3
3 2
2 1
1 1
0 1
M = 4
M = 3.5
M = 31/10 = 3.1
The mean cannot be determined for these data.
The arithmetic mean for this value is M=3.1.we can calculate this data from frequency distribution.
what is arithmetic mean?It is sum of collection of number divided by the count of numbers.Its value can be positive or negative both.The collection is often a set of results from an experiments and observational study.
what is the use of arithmetic mean?It is often used as a parameter in statistical distribution or as a result to summarize the observations of an experiment survey.It is simplest way to used to measure the average.Its also measure frequency distribution by considering all of the observations.
Now we are using formula for arithmetic mean
A.M= Sum of (fx)/sum of (f)
by putting values in this formula we have
A.M= 31/10
A.M= 3.1
Hence 3.1 is the arithmetic mean for given frequency data.
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A group of friends is playing a board game. As part of the game, each player is given the same number of cards. There are 6 players and 58 cards. How many cards will each player get if each player gets the same number of cards?
Answer:Each player would get 9 cards each with a reaminder of 4 cards left
Step-by-step explanation:6 times 9 is 54 + 4 is 58
Answer: 9
Step-by-step explanation:
To figure out the given problem below:
P = 6
C = 58
You have to divide the problem.
So [tex]58[/tex] ÷ [tex]6 = 9[/tex].
Four different paints are advertised as having the same drying time. To check the manufacturers' claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded for each sample. The data obtained follow.Excel File: data 16-21.xls Paint 1 Paint 2 Paint 3 Paint 4 128 137 135 133 144 133 142 146 130 143 137 124 136 141 131a. Use a = .05 to test for any significant differences in mean drying time among the paints. If an amount is zero, enter "0.
The sum of squares of error, treatment, within and between four painters are: 330, 692, 110 and 43.25.
The data provided is for the dying time of four different types of paint.
One-way ANOVA can be used to determine whether all the four paints have the same drying time.
Use Excel to perform the one-way ANOVA.
Go to Data → Data Analysis → Anova: Single Factor
A dialog box will open. Select the data. Select "Grouping" as Columns.
Press OK.
The output is attached below.
The required values are as follows:
(1) Sum of Squares of Treatment (Between Subjects):
SST = 330
(2) Sum of Squares of Error (Within Subjects):
SSE = 692
(3) Mean Squares Treatment (Between Subjects):
MST = 110
(4) Mean Squares Error (Within Subjects):
MSE = 43.25
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What is the population standard deviation?
{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2
The population standard deviation of {5, 8, 8, 5} is 3
The given population is
{5, 8, 8, 5}
The mean of the population = Sum of the terms / Number of Terms
Find the values and substitute the values in the equation
Sum of terms = 5 + 8 + 8 +5
= 26
Number of terms = 4
The mean of the population= 26 / 4
= 6.5
The variance of the population = (5 - 6.5)^2 + (8 - 6.5)^2 + (8 - 6.5)^2 + (5 - 6.5)^2
= (-1.5)^2 + (1.5)^2 + 1.5^2 + (-1.5)^2
= 2.25 + 2.25 + 2.25 + 2.25
= 9
The standard deviation of the population = [tex]\sqrt{9}[/tex]
= 3
Therefore, the standard deviation is 3
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Factor completely 5x(x+3) + 6 (x+3)
Answer:
(x + 3)(5x + 6)------------------------------
Given
Expression 5x(x+3) + 6 (x+3)To factor it completely, factor out the common factor x + 3:
5x(x+3) + 6 (x+3) = (x + 3)(5x + 6)fit a multiple regression model to describe the relationship between weight and the predictors length and age. (use x1 for length and x2 for age. round your numerical values to two decimal places.)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is multiple regression?
A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
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Alex tracked the number of cups of coffee he drank each day for the following month and
created a new probability distribution.
Number of Cups of Coffee, X 0
1 2 3 4
Relative Frequency, P(X) 0.035 0.579 0.286 0.080 0.020
According this new data, Alex is expected to drink 1.471 cups per day.
4. Calculate s(X) of Alex's new probability distribution. (1 point)
0.599
0.775
1.471
4.223
The standard deviation of Alex's new probability distribution is given as follows:
0.775.
How to obtain the standard deviation of a discrete distribution?The standard deviation of a discrete distribution is calculated as the square root of the sum of the differences squared between each observation and the mean, multiplied by their respective probabilities.
Hence the standard deviation of Alex's new probability distribution is calculated as follows:
S(X) = square root(0.035 x (0 - 1.471)² + 0.579 x (1 - 1.471)² + 0.286 x (2 - 1.471)² + 0.08 x (3 - 1.471)² + 0.02 x (4 - 1.471)²)
S(X) = 0.775.
Meaning that the second option is correct.
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Name: Sally Jonas, single, 1 exemption.
Pay Rate: $5.95 per hour
Hours Worked: M-8, T-7, W-8, T-9, F-8
Total Hours Worked :
Wage for Week :
FICA Tax (7.65 %) :
Federal Tax :
State Income Tax (at 3%) :
City Income Tax (1.5%) :
Total Tax :
Paycheck after Taxes :
The total hours worked is 40 hours, the total wage for the week is $238, the Total tax is 12.15%, and the paycheck after taxes is $209.44
What is tax?Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses.
Given:
Pay Rate: $5.95 per hour,
Hours Worked: M-8, T-7, W-8, T-9, F-8,
FICA Tax (7.65 %),
State Income Tax (at 3%),
City Income Tax (1.5%),
Calculate the total working hours as shown below,
Total working hours = 8 + 7 + 8 + 9 + 8 = 40 hours
Calculate the total tax,
Total tax = 7.65 + 3 + 1.5 = 12.15%
Calculate total wage,
Total wage = no of hours × 5.95
Total wage = 40 × 5.95 = $238
Paycheck after-tax deduction = Total wage - 12.15 % of $238
Paycheck after-tax deduction = 238 - 28.56
Paycheck after-tax deduction = $209.44
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Write an algebraic representation for the reflection
Answer:
A reflection of a point over the line y=−x is shown. The rule for a reflection in the origin is (x,y)→(−y,−x) .
I need help with this its hard.
you are measuring a process, and you are given the following information: overall average: 131 population stdev: 5 sample size: 11 determine the upper control limit if your desired confidence interval is 99.73%. enter your answer to one decimal place. it's ok if you get a negative number; in that case, just enter the minus sign in front of it.
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
Given 131 population
standard deviation = 5
sample size = 11.
mean = 131/11 = 11.9.
determine the upper control limit if desired
confidence interval is 99.73%
What is Confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.
Confidence interval = sample mean ± margin of error
Upper limit = sample mean + margin of error.
margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex].
margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].
value of z* for 99.73% confidence interval is 3.00.
so margin of error = 4.5.
Upper limit = 11.9 + 4.5
Upper limit = 16.4
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
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Nina is driving to her friend’s house. For the first part of the drive, she drove at a constant speed of 55 miles per hour for 36 minutes. For the second part of the drive, she drove at a constant speed of 17.5 miles per hour for 14 miles. What is the total distance, in miles, and total amount of time, in minutes, that Nina drove to her friend’s house?
Answer:
miles: 55(36/60) = 55(0.6) = 33 miles
mins: 60(14/17.5) = 60(0.8) = 48 minutes
Total amount of time, in minutes
36 minutes + 48 minutes84 minutesThe total distance, in miles
33 miles + 14 miles47 milesStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The required distance and time are 47 miles and 84 minutes, respectively.
What is speed?Speed is measured as the ratio between the distance and time, and the SI unit of speed is m/s.
We know that speed = distance / time
Finding for distance =
55(36/60) = 55(0.6) = 33 miles
Therefore, The total distance, in miles =
= 33 miles + 14 miles
= 47 miles
For Time =
60(14/17.5) = 60(0.8) = 48 minutes
Therefore, Total amount of time, in minutes =
36 minutes + 48 minutes
= 84 minutes
Hence, The required distance and time are 47 miles and 84 minutes, respectively.
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making the assumption of no compounding interest, suppose you purchase a perpetuity bond from sense/net corporation for $3,000 with an annual coupon rate of 3% . specify all answers to the nearest dollar, and assume a discount rate equal to that of the current interest rate.
Therefore for computing the annual return we simply fund with coupon rate in percentage is 90 dollar
What is a percent simple definition?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
The additional sum of money over the principal sum of deposit or loan is called compound interest.
The yearly return on $ 3 ,000 investment will be $90.
This can be estimated as:
Investment = $3,000
Coupon rate in percentage = 3%
The computation of yearly return can be estimated as:
= $3,000 × 3%
= $90
Therefore for computing the annual return we simply fund with coupon rate in percentage.
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Calculate the area, in square units, bounded by f(x) = 3x³ -3x²-x+8 and
g(x) = 2x³ - 10x² + 29x + 8 over the interval [1, 5].
Answer:
164
Step-by-step explanation:
Assuming that you are allowed to use graphing tools:
f(x) is below g(x) for interval [1,3]
g(x) is below f(x) for interval [3,5]
Rules of finding area between two graphs:
[tex]\int\limits^a_b {|upper - lower|} \, dx[/tex]
For interval [1,3]:
[tex]\int\limits^3_1 {g(x) - f(x)} \, dx[/tex]
[tex]\int\limits^3_1 {|(2x^{3} - 10x^{2} +29x+8)-(3x^{3}-3x^{2} -x+8) } \, dx[/tex]
[tex]\int\limits^3_1 {-x^{3} -7x^{2} +30x} \, dx[/tex]
[tex]= [-\frac{1}{4}x^{4} - \frac{7}{3}x^{3} + 15x^{2}]^3_1[/tex]
[tex]= [-\frac{1}{4}3^{4} - \frac{7}{3}3^{3} + 15*3^{2}] - [-\frac{1}{4}1^{4} - \frac{7}{3}1^{3} + 15*1^{2}][/tex]
[tex]= -\frac{81}{4} - \frac{189}{3} + 135+\frac{1}{4} + \frac{7}{3}- 15\\[/tex]
[tex]= \frac{118}{3}[/tex]
For interval [3,5]
[tex]\int\limits^5_3 {f(x)-g(x)} \, dx[/tex]
[tex]\int\limits^5_3 {|(3x^{3}-3x^{2} -x+8)-(2x^{3} - 10x^{2} +29x+8)|} \, dx[/tex]
[tex]\int\limits^5_3 {|x^{3}+7x^{2} -30x|} \, dx[/tex]
[tex]= [\frac{1}{4}x^{4} +\frac{7}{3}x^{3} - 15x^{2}]^5_3[/tex]
[tex]= [\frac{1}{4}5^{4} +\frac{7}{3}5^{3} - 15*5^{2}] -[\frac{1}{4}3^{4} +\frac{7}{3}3^{3} - 15*3^{2}][/tex]
[tex]= \frac{625}{4} +\frac{875}{3} - 375 -\frac{81}{4}} -\frac{189}{3} + 135[/tex]
[tex]=\frac{374}{3}[/tex]
Total area
[tex]= \frac{118}{3} + \frac{374}{3}\\[/tex]
[tex]= 164[/tex]
whenever suzan sees a bag of marbles, she grabs a handful at random. she has seen a bag containing four red marbles, five green ones, three white ones, and two purple ones. she grabs eight of them. find the probability of the following event, expressing it as a fraction in lowest terms. she has at least one green one.
For this problem, it is best to consider E to be the case in which she has all of the green ones, and then apply the formula for calculating the probability of a complement.
. To determine the likelihood that she will receive all of the green ones, we must first determine two values: the total number of possible outcomes, n(S), and the total number of favorable outcomes for the given event. Because she selects 8 marbles from a total of 11, n(S) = C(11, 8) = 165. To get all the green ones, she must first select three red marbles from a set of three, and then select the remaining five marbles.
from the 8 non-red ones. There are (3,3)(8, 5) = 56 ways to do this. Thus,
() =56/165
. The probability of not occurring is then (′) = 1 −56/165=109/165
, so this is the probability that she does get all the green one.
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If V is the subspace spanned by (1,1,1) and (2,1,0): (a) Find a matrix A that has V as its row space (b) Find a matrix B that has V as its nullspace. (c) Multiply A and B.
A matrix B that has V as its nullspace. (c) Multiply A and B is [tex]I (4 by 4 ).[/tex]
[tex]\mathbb{R}^4[/tex]
What is a Nullspace vector?
The null space of A is all the vectors x for which Ax = 0, and it is denoted by null(A). This means that to check to see if a vector x is in the null space we need only to compute Ax and see if it is the zero vector.
- All vectors whose components are equal.
- All vectors whose components add to zero.
- All vectors that are perpendicular to [tex](1,1,0,0)$ and $(1,0,1,1)$.[/tex]
- The column space and the nullspace of (4 by 4 ).
Solution. These bases are not unique.
[tex]- $(1,1,1,1)$.- $(1,-1,0,0),(1,0,-1,0)$, and $(1,0,0,-1)$.- $(1,-1,-1,0)$ and $(1,-1,0,-1)$.[/tex]
- The columns of are a basis of its column space: [tex]$(1,0,0,0),(0,1,0,0)$, $(0,0,1,0)$, and $(0,0,0,1)$.[/tex]The nullspace contains the zero vector only. By convention, the empty set is the basis of such a space.
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There are 8 ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon.
1 L≈ 0.26 gallons
7 KL= cups
Suraj took a slice of pizza from the freezer and put it in the oven.
The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is graphed.
What was the pizza's temperature after 2 minutes?
The temperature of the pizza that Suraj took from the freezer, after 2 minutes, given the graph, is 10 degrees Celsius.
How to find the temperature ?The temperature of the pizza that Suraj took from the freezer and put in the oven, is shown on the graph. To find the temperature of this pizza after 2 minutes, given the line in the graph, look at the point where the 2 minutes on the x - axis, intercepts with the line.
This point on the y - axis is 10 degrees Celsius.
This simply means that at 2 minutes, Suraj's pizza slice had a temperature of 10 degrees Celsius.
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Consider a propeller driven aircraft in forward flight at a speed of 150 mph. The propeller is set up with an advance ratio such that the propeller disc average flow speed is 170 mph. The propeller diameter is 6 ft. The aircraft flies at sea level. a. Calculate the thrust of the propeller. b. Calculate the induced velocity c. Calculate the velocity in the downstream far field away from the propeller disc. d. Calculate the power absorbed by the fluid (energy added per unit mass x mass flow rate) e. Calculate the propeller power (thrust * flight speed) f. If propeller efficiency is defined by the ratio of e to d, calculate the propeller efficiency.
a) The thrust of the propeller is 23,834 lbf and b) The induced velocity is 8.44 mph c) The velocity in the downstream far field away from the propeller disc is 161.56 mph
a)The thrust of the propeller can be calculated using the equation,
Thrust = 2πρR^2V^2, where ρ is the air density, R is the propeller radius, and V is the average velocity of the propeller disc. For sea level at a speed of 150 mph, the air density is about 0.002377 slugs/ft^3.
the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf
b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph
c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph
d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp
e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp
f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%
Hence, d) The power absorbed by the fluid is 42.7 hp e) the propeller power (thrust flight speed) is 4,844.08 hp f) The propeller efficiency is 113.6%
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Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the marbles into groups so each group has the same contents. How many groups can Malik make, so there would be the same contents (red and blue marbles) in each group? There should be no marbles left over.
Answer:
This is a math equation about GCD { GREATEST COMMON DIVISOR }
7 groups
Each group [ 4 red marbles / 5 blue marbles ]
Step-by-step explanation: { I will use the . as mutiply }
So first let's take a little of analysis
We take a as the groups that should be made, a ∈ N*
In the question, we can see: 28 can be divisible to a / 35 can be divisible to a
Because of that, we know that a is the smallest so a is: GCD ( 28, 30 )
Now, let's factorize numbers into prime factors:
28 = [tex]2^{2} . 7[/tex]
35 = 5.7
Choose common prime factors: 2,3,5,7
[ Because we are doing GCD, we will need to choose the common prime factors as index number the smallest. ]
GCD ( 28, 30 ) = 7
So a = 420 groups
The red marbles in each group: 28 ÷ 7 = 4 marbles
The blue marbles in each group: 35 ÷ 7 = 5 marbles
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pls help due in 1 hour!!!!!!
Step-by-step explanation:
{(3, 7), (3, 6), (5, 4), (4, 7)} Is not a function
{(1, 5), (3, 5), (4, 6), (6, 4)} is a function
{(2, 3), (4, 2), (4, 6), (5, 8)} is not a function
{(0, 4), (3, 2), (4, 2), (6, 5)} is a function
16. A department store marks up winter boots at $150. This represents a 50% markup on cost. What's the cost of the boots?
A. $300
B. $100
C. $150
D. $200
The cost of the boots is (b) $100
How to determine the cost of the boots?From the question, we have the following parameters that can be used in our computation:
Markup rate = 50%
Markup price of the boot = $150
The cost of the boots can be calculated using the following equation
Markup price of the boot = cost of the boots * (1 + Markup rate)
Substitute the known values in the above equation, so, we have the following representation
150 = cost of the boots * (1 + 50%)
This gives
150 = cost of the boots * (1.5)
Divide by 1.5
cost of the boots = $100
Hence, the cost of the boots is $100
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Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit (in dollars) of the product according to the following formula. y = 32(3p + 1)−2/5, p > 0
(a) What is the rate of change in sales volume when the price is $22? (Round your answer to three decimal places.) dy dp = -0.107 CORRECT ANSWER
(b) Interpret your answer to part (a). (Round your answer to the nearest whole number.) If the price increases $1, the sales volume will decrease by : ?
The rate of change in sales volume when the price is $22 is -0.107 and When the price increases $1, the sales volume will decrease by -48
The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity
According to the question,
y denotes the weekly sales volume and p denotes the price per unit
Equation is [tex]y = \frac{32}{3p + 1^{\frac{-2}{5}}}[/tex]
(a) We have to find the rate of change in sales volume when price is $22
Differentiating the equation w.r.t p,
[tex]\frac{dy}{dp} = \frac{-32(3)}{(3p + 1^\frac{-2}{5})^2}[/tex]
Putting value of p = 22
=> [tex]\frac{dy}{dp} = \frac{-32(3)}{(3(22) + 1^\frac{-2}{5})^2}[/tex]
=> -96 / (66 + 1 - 2(22)(1))²
=> -96 / 897
=> -0.107
(b) To find If the price increases $1, the sales volume will decrease by
Replacing p = 1
=> dy/dp = -96/2
=> -48
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Help please!! So confused, determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number if necessary.
The perimeter of the right triangle is 26 units.
From the given graph, the measure of side AB= 8 units and the measure of side BC= 7 units.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
By Pythagoras theorem,
AC²=AB²+BC²
⇒ AC²=8²+7²
⇒ AC²=113
⇒ AC=10.63
≈ 11 units
Perimeter =AB+BC+AC
= 8+7+11
= 26 units
Therefore, the perimeter of the right triangle is 26 units.
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For what value of x is the equation 2(x + 1) - x = 10
Answer:
x=8
Step-by-step explanation:
Simplify 2(x+1)−x.
Simplify each term.2x+2−x=10
Subtract x from 2x.x+2=10
Move all terms not containing x to the right side of the equation.
Subtract 2
from both sides of the equation.x1−2
Subtract 2 from x = 10-2
subtract 2 from 10
hope that helps!
Answer: 8
Step-by-step explanation:
First, let's write out the equation:
2(x+1) - x = 10
So, we need to find the value of x.
Let's take an estimate of what x could be.
So, we know it has to be 5-10, because that is over when we add x to one, then multiply by 2.
So, numbers 5-7 couldn't be it, because the value of x is lower than 10. So, we have to guess if it's 8 or 9
Let's use both numbers to solve if it's correct:
2(8+1) - 8 =10
18 - 8 = 10
or
2(9+1) - 8 =10
20 - 8 = 12
So, we have 8 as our answer.
So, x = 8
igure 30-44a shows a wire that forms a rectangle (w 20 cm, h 30 cm) and has a resistance of 5.0 m . its
The magnitude of the current induced in the wire is 1.2×10^{-8} and direction of the current induced in the wire is counter clockwise.
In the given question,
A rectangle (W = 20 cm, H = 30 cm) and has a resistance of(R) = 5.0 mΩ.
B(s) = 4.0 μT and B(b) = -2.5
t(s) = 2.0 s
From the question
dB(1)/dt = B(s)/t(s)
dB(1)/dt = 4 μT/2
As μ = 10^{-6}
dB(1)/dt = 2×10^{-6} T/s
dB(2)/dt = 1/2dB(1)/dt
dB(2)/dt = 2×10^{-6} /2
dB(2)/dt = 1×10^{-6} T/s
dB(3)/dt = B(b)dB(1)/dt
dB(3)/dt = -2.5×2×10^{-6} T/s
dB(3)/dt = -5×10^{-6} T/s
Now the change in magnetic field is,
dB/dt = dB(1)/dt + dB(2)/dt + dB(3)/dt
dB/dt = 2×10^{-6} + 1×10^{-6}/2 - 5×10^{-6}
dB/dt = - 2×10^{-6}
Now finding the area
Area = 1/2 wh
Firstly converting the w and h in m
So w = 0.20 m, h = 0.30 m
Area = 1/2 *0.20*0.30
Area = 0.03 square m
The induced EMF is
EMF = -AdB/dt
EMF = -(0.03)*(- 2×10^{-6})
EMF = 0.06×10^{-6}
The magnitude of the current induced in the wire is
I = EMF/R
I = 0.06×10^{-6}/5
I = 0.012×10^{-6}
I = 1.2×10^{-8}
Now, the direction of the current induced in the wire is counter clockwise.
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The right question is:
Figure (a) shows a wire that forms a rectangle (W = 20 cm, H = 30 cm) and has a resistance of 5.0 mΩ. Its interior is split into three equal areas, with magnetic fields B(1), B(2), and B(3). The fields are uniform within each region and directly out of or into the page as indicated. Figure (b) gives the change in the z components B(z) of the three fields with time t; the vertical axis scale is set by B(s) = 4.0 μT and B(b) = -2.5 B(s) and the horizontal axis scale is set by t(s) = 2.0 s. What are the magnitude and direction of the current induced in the wire?
Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y = square root 6x
To use upper and lower sums to approximate the area of the region under the curve y = √6x, we need to divide the interval of integration into a certain number of subintervals of equal width.
Let's say that we want to divide the interval [a, b] into n subintervals of equal width. We can then define the points x0, x1, ..., xn as follows:
x0 = a
x1 = a + (b - a)/n
x2 = a + 2(b - a)/n
...
xn = b
The width of each subinterval is (b - a)/n.
We can then use these points to define the upper sum and lower sum as follows:
Upper sum = ∑ (b - a)/n * max(f(x))
Lower sum = ∑ (b - a)/n * min(f(x))
where the sum is taken over all subintervals, and max(f(x)) and min(f(x)) represent the maximum and minimum values of the function f(x) on each subinterval, respectively.
To calculate the upper and lower sums, we need to evaluate the function f(x) at each of the points x0, x1, ..., xn. For example, if we want to calculate the upper sum using 4 subintervals, we would evaluate the function at the points x0, x1, x2, and x3, and then use these values to calculate the upper sum using the formula above.
Once we have calculated the upper and lower sums, we can use them to approximate the area of the region under the curve. The area of the region is approximately equal to the average of the upper and lower sums.
For example, if the upper sum is 1.5 and the lower sum is 0.5, then the area of the region is approximately (1.5 + 0.5)/2 = 1.
In general, as we increase the number of subintervals, the upper and lower sums will get closer and closer to the actual area of the region, and the approximation will become more accurate.
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If the point (K,-5) lies on the line whose equation is 3x + y = 7, then the value of K is
Answer:
K = 4
Step-by-step explanation:
The x-y point ( K, -5 ) means that ...
x = K and y = -5
Let's plug in K and -5 for y in the equation to find the value of K (which is the same as x).
3(K) + (-5) = 7
3K - 5 = 7
3K = 7 + 5
3K = 12
K = 4
You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest.
a. How much do you need in your account at the beginning
Answer: you need to have at least $312,500 in your account at the beginning.
Step-by-step explanation:
The total amount of money you will need to withdraw over the 25-year period is $30,000 * 25 years = $750,000. To find the total amount of interest you will earn, we need to use a compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^nt
where A is the total amount of money you will have in your account after 25 years, P is the initial amount of money in your account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In our case, we have A = $750,000, P = ?, r = 8%, n = 1 (since the interest is compounded annually), and t = 25. Plugging these values into the formula, we get:
$750,000 = P * (1 + 0.08/1)^1 * 25
We can simplify this equation to:
$750,000 = P * 1.08^25
To find the value of P, we can divide both sides of the equation by 1.08^25:
$750,000 / 1.08^25 = P
We can use a calculator to compute the value of 1.08^25, which is approximately 2.4. This means that the initial amount of money you need in your account is $750,000 / 2.4 = $312,500.
Therefore, to be able to withdraw $30,000 each year for 25 years and earn 8% interest on your account, you need to have at least $312,500 in your account at the beginning.
find each angle measure to nearest degree Cos C= 0.9613
The angle C can be obtained rom the computation below as 16 degrees.
What is the angle?We know that the cosine is one of the angular measures that we have. The trigonometric ratios that we have are the sine the cosine and the tangent. We can be able to obtain the angle of the when we take the inverse of the cosine of the angle.
Now we know that the cosine of the angle can be defined as the ratio of the adjacent and the hypotenuse. The value of the cosine of the angle can be gotten from the table of the standard measure of the angles or by the use of a calculator.
We then have that;
Cos C= 0.9613
C = Cos-1( 0.9613)
By the time we make use of a good calculator we obtain the angle as;
C = 16 degrees
This is the value of the angle.
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