The required future value of the annuity is $127,336.80.
Jones Company borrowed money that must be paid back in 12 years. To ensure that the debt is repaid by the end of the 12th year, the corporation invests $8,000 at the end of each year at a rate of 5% compounded yearly.
Compute the future value of the annuity as follows:
Future value = Annuity - FVIFA
FVIFA is taken from the table, and substitutes the value of the annuity in the above formula
Future value = $8,000 × 15.9171
Apply the multiplication operation, and we get
Future value = $127,336.80
Therefore, the required future value of the annuity is $127,336.80.
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each term in the following sequence is six more than the previous term what is the value of x+z? x,y,z,7,13
The following list has six more terms than the preceding one. What does x+z equal if it is -10?
What, for instance, does sequence mean?A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit with in sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.
t1=X\st2=y\st3=Z
t4=7\st5=13
common distinction Since d=6, t4=t3+d 7=t3+6 t3=7-6 t3=1=Z
Z=1\st3=t2+d
X + Z= (-11) + 1 X+Z = -10 because 1 = t2+6 t2= 1-6 t2= -5 = y y= -5 t2= t1+d -5= t1+6 t1= -5 -6 t1= -11 =X X = -11
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(True or False) the correlation coefficient is based on each observation's values' deviations from the mean for both variables.
The correlation coefficient mostly based on all the observation's values' with the deviations from about the mean for both variables. So, it's true.
A correlation coefficient is a statistical degree of the diploma to which modifications to the cost of 1 variable are expecting extrade to the cost of another. In definitely correlated variables, the cost will increase or decreases in tandem. A correlation coefficient is a variety of among -1 and 1 that tells you the electricity and path of a courting among variables.
In different words, it displays how comparable the measurements of or greater variables are throughout a dataset. Both quantify the path and electricity of the connection among numeric variables. When the correlation (r) is negative, the regression slope (b) might be negative. When the correlation is positive, the regression slope might be positive.
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line rs intersects triangle bcd at two points and is parallel to segment dc. triangle b c d is cut by line r s. line r s goes through sides d b and c b. lines d c and r s are parallel. width
This question is related to the properties of similar figures. So, the true statements are
ΔBCD is similar to ΔBSR
BR/RD = BS/SC
BR * SC = RD * BS
Given that, RS is parallel to DC, so
∠BDC = ∠BRS (they are angles on the same side of transversal)
Similarly, we have
∠BCD = ∠BSR (they are angles on the same side of transversal)
∠CBD = ∠CBD (reflexive property)
ΔBCD ~ ΔBSR by Angle Angle Angle rule of congruency
ΔBCD ~ ΔBSR we therefore have,
BC/BS = BD/BR
(BS + SC)/ BS = (BR + RD) /BR
1 + SC/BS = 1 + RD/BR
SC/BS = RD/BR
Taking reciprocal on both sides, we have
BR/RD = BS/SC
From the above proven property, BR/RD = BS/SC
On cross multiplication, we get
BR * SC = RD * BS
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Angles Q and R form a right angle. Angle Q is twice as large as Angle R. What is the measure of Angle Q, in degrees?
The measure of the angle Q in degrees is 90° if angles Q and R form a right angle.
What is meant by right angle?A right angle is defined as an angle that is exactly 90 degrees in geometry and trigonometry. If a ray is positioned so that its terminal is on a line and the angles are also equal, the angles are said to be at right angles. The phrase derives from the Latin angulus rectus, where rectus denotes the upright vertical line that is perpendicular to a horizontal base line.
Perpendicular lines—defined as lines that meet at right angles—and orthogonality—defined as the ability to intersect at right angles—are closely connected and crucial geometrical notions.
Q and R create a right angle given.
Therefore, the angle formed by either Q or R is 90 degrees.
Angle R is doubled by the given angle Q.
From there, Q must have an angle of 90 degrees.
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Flying against the wind an airplane travels 7360 kilometers in 8 hours. Flying with the wind the same plane travels 6100 kilometers in 5 hours what is the rate of the plane in still air and what is the rate of the wind
you have 40 stickers. Eight of the stickers glow in the dark. what fraction of stickers, in fifths, do not glow in the dark
Answer:
4/5
Step-by-step explanation:
8/40 is 1/5
Therefore 1/5 DO glow in the dark.
5/5 minus 1/5 is 4/5
4/5 of the stickers don’t glow in the dark.
suppose the cost of a car produced in the united states is $20,000. the current exchange rate is us$1= €0.85. What is the cost of the car in euros?
The cost of the car in euros is 17,000 euros
Given that,
Let's say an automobile made in the United States costs $20,000. At this time, one US dollar is worth 0.85 euros. A automobile made in the United States costs $20,000 to construct.
To find : that the car's price in euros ?
The information provided lets us know that,
The car's price in euros= 20,000 * 0.85
= 17,000 euros
Therefore, the car's price in euros is 17,000 euros.
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An online poll asked: "Do you believe the Loch Ness monster exists?" Among 20,111 responses, 67 % were "yes." Use a 0.05 significance level to test the claim that most people believe that the Loch Ness monster exists. How is the conclusion affected by the fact that Internet users who saw the question could decide whether to respond?
a.Identify the null and alternative hypotheses for this test. Choose the correct answer below.
b. Identify the test statistic for this hypothesis test.
c.Identify the P-value for this hypothesis test.
d.Identify the conclusion for this hypothesis test.
a) Null Hypothesis; p = 0.5
Alternative Hypothesis; p < 0.5
b) The test statistic is; z = 48.216
c) The p-value is < 0.00001.
d) The conclusion of the hypotheses is that we reject the null hypothesis and conclude that the claim that most people believe that the Loch Ness monster exists is true.
How to carry out hypothesis testing?Hypothesis testing is defined as the method used to find the probability of the hypothesis that is to be proved in the future on the basis of the small population sample.
Now, we are told that Among 20,111 responses, 67 % were "yes." Thus;
Sample proportion; p^ = 67%
The population proportion is not given and as such we will use; p = 50% = 0.5
Thus;
Null Hypothesis; p = 0.5
Alternative Hypothesis; p < 0.5
The formula for the test statistic is;
z = (p^ - p)/√(p(1 - p)/n)
z = (0.67 - 0.5)/√(0.5(1 - 0.5)/20111)
z = 48.216
The p-value from online p-value from z-score calculator is;
p-value < 0.00001.
The p-value is less than the significance value and so we reject the null hypothesis and conclude that the claim that most people believe that the Loch Ness monster exists is true.
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HELP!!!!!! 40 POINTS!!!!
Knowing that correlation coefficients have values between -1 and 1 and that the closer the value is to -1 or 1, the stronger the correlation -- which of the following correlation coefficients would represent the strongest correlation?
A. -0.5
B. 0.02
C. -0.97
D. 0.87
The strongest correlation is represented by -0.97. It can be find out using knowledge of correlation coefficients.
What is the correlation coefficient between 1 and -1?
The formula returns a value between 1 and -1 :
where 1 indicates a strong positive relationship and -1 indicates a strong negative relationship.
According to the rule of correlation coefficients , the strongest correlation is considered when the value is closet to either (+1) or (-1).
So, in given options -0.97 is closet to (-1).
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Flour is sold in 3-pounds bags.how many pounds are in 7 bags.
Answer: 21
Step-by-step explanation: multiply 7 by 3, which = 21
The inclusion of seasonal dummy variables to a multiple regression model may help eliminate autocorrelation if the data are characterized by seasonal fluctuations. A. perfect multicollinearity. B. bias in OLS slope estimates caused by autocorrelation. C. near multicollinearity. D. All of the options are correct.
The correct option among the given is option B , bias in OLS slope estimates caused by autocorrelation.
In the presence of autocorrelation, as in the case of heteroscedasticity, the OLS estimators are still linearly unbiased, consistent, and asymptotically normally distributed, but they are no longer efficient (i.e., minimum variance).
A dummy variable is a binary variable with a value of either 0 or 1. Such variables are added to a regression model to represent binary factors, which are either observed or not observed.
A dummy variable can be used to indicate whether a data point possesses a specific property. A dummy variable, for example, can be used to indicate whether a car engine is 'Standard' or 'Turbo.' Or whether a participant in a drug trial is in the placebo or treatment groups.
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Find the derivative using the Fundamental Theorem of Calculus, part 1, which states that if f(x) is continuous over an interval [a, b], and the function F(X) is defined by F(X) - F'(x) = f(x) over [a, b]. [*re) or, then del tot Additional Materials eBook 4.
then Find the derivative using the Fundamental Theorem of Calculus, part 1, which states that if f(x) is continuous over an interval (a, b), and the function F(x) is defined by F(X) - F'(x) = f(x) over [a, b]. de la intu In(u) du 6.
Evaluate the definite integral using the Fundamental Theorem of Calculus, part 2, which states that iffis continuous over the interval [a, b] and F(x) is any antiderivative of f(x), then Giºrno dx = F(b) – Fla). [x?- ») 3x) dx Х
On solving the question, by the help of, Fundamental Theorem of Calculus, we got answer [tex]3xe^x[/tex]
What is fundamental Theorem of Calculus?A theorem that connects the ideas of differentiating a function from integrating a function is known as the fundamental theorem of calculus. The two processes are inverses of one another, with the exception of a constant number that is dependent on the starting point for computing area.
When asked to compute the derivative of an integral, utilize the calculus fundamental theorem rather than evaluating the integral.
FTOC informs us that:
[tex]\frac{d}{dx} [\int\limits^{3x}_t {3lnt} \, dxt] = 3xe^x[/tex]
(That is, the integral's derivative returns the original function to us.)
We are required to locate:
h'(x) where h(x)= [tex]\int\limits^{3x}_t {3lnt} \, dxt= 3xe^x[/tex]
what we want
[tex]h'(x) = \frac{d}{dx} [\int\limits^{ex}_t {3lnt} \, dxt] = 3xe^x.............................A[/tex]
(Note that the first integral's upper limits are not in the proper format for the FTOC to be applied immediately.) The chain rule and a replacement can be used to alter the definite integral. Let:
[tex]u = e^x = \frac{du}{dx} = e^x[/tex]
Using the chain rule and substituting into the integral [A], we obtain:
[tex]\frac{d}{dx} [\int\limits^{ex}_t {3lnt} \, dxt] =[/tex][tex]\frac{d}{dx} [\int\limits^{u}_t {3lnt} \, dxt] = 3xe^x[/tex]
= [tex]e^x \frac{d}{du} [\int\limits^{ex}_t {3lnt} \, dxt] = 3xe^x[/tex]
now we got answer - [tex]3xe^x[/tex]
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Solomon has taken two tests each out of ten. his average score is 18. if the product of his scores is 56. what did he score in each test ?
The scores of both test Solomon took are 14 for the first test and 4 for the second test.
How to calculate the score of bother test?let a represent the first score and b represent the second score.
since the average score is 18, you get (a + b) / 2 = 18
multiply both sides of this equation by 2 to get a + b = 36
the product of her scores is 56 means that a × b = 56.
you have 2 equations that need to be solved simultaneously.
they are a + b = 36 and a × b = 56
solve for a in the second equation to get a = 56 / b.
replace a with 56/ b in the first equation to get 56/ b + b = 18
multiply both sides of this equation by b to get 56 + b^2 = 18b
subtract 14b from both sides of this equation and arrange the terms in descending order of degree to get b^2 - 18b + 56 = 0
Factorise the quadratic equation to get the following:
(b-4 ) ( b - 14) = 0
Solve for b to get b = 4 and b = 14
Therefore, the product of the of the two scores:
= 14×4 = 56. This means that he scored 14 in first test and 4 in the second test.
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assume a small rectangular-shaped gully is two meters deep, four meters wide, and 50 meters long. calculate the metric tons of soil lost during its formation. assume the bulk density of this soil is 1.48 mg/m3. one metric ton is equal to 1000 kilograms or 2204.6 pounds. show your work
Metric tons of soil lost during its formation [tex]2.96*10^-7[/tex]
Gully is 2 meter deep 4 meter wide and 50 meters long.
So we know if Gully length = l width =w height =h
then volume of gully is l*b*h.
by same way volume of gully is 50*4*2 = 200 [tex]m^3[/tex]
Bulk density of this soil is 1.48 mg/m^3.
How many metric tons of soil lost during its formation?
1000kg = 1 metric ton.
density = 1.48mg/m^3 = [tex]1.48*10^-6[/tex] kg/m^3
means for 1 m^3 volume we lost [tex]1.48*10^-6[/tex] kg of soil.
for 200m^3 volume we lost [tex]200*1.48*10^-6[/tex] kg of soil.
[tex]296*10^-6[/tex] kg of soil.
to convert kg into metric ton we have to divide 1000.
[tex]296*10^-6[/tex]/1000 = [tex]296*10^-9[/tex] = [tex]2.96*10^-7[/tex]
So Metric tons of soil lost during its formation [tex]2.96*10^-7[/tex]
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Sara is decorating her new game room. She wants to paint the room purple, but she has only red and blue paint. She knows that by combining red and blue she will get purple. In order to make the shade of purple she wanted, she combines three liters of red paint with four liters of blue paint. She realized that she would need a total of 56 liters of purple paint to cover the whole room. She began to make a table to help him think about the problem, but is unsure of what to do next.
Answer:
she needs 24l red and 32l blue paint
Step-by-step explanation:
3:4 ratio with 56 liters of
Simplify :
- [ 4 - 3 (-2 + 5) ^2]
The simplified value of the expression is 23
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
To find the value:
- [ 4 - 3 (-2 + 5)²]
= - [ 4 - 3 (3)²]
= - [ 4 - 3*9]
= - [ 4 - 27]
= - [ -23]
= 23
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Which number sentence is true?
A.
B.
C.
D.
Answer:
you forgot the sentences dude
Assume that all variables are implicit functions of time t. Find the indicated rate. x^2 + 5y^2 + 2y = 75; dx/dt = 14 when x = 6 and y = -3: find dy/dt
The answer to the given question, assuming that all variables are implicit functions of time t, the indicated rate x^2 + 5y^2 + 2y = 75; dx/dt = 14 when x = 6 and y = -3 is dy/dt = 6.
What is implicit function?An implicit function is a function which is defined by an implicit equation, written in terms of both dependent and independent variables. While an explicit function is a function which is represented in terms of an independent variable.
In this case, we have equation:
x^2 + 5y^2 + 2y = 75
We use the chain rule to bridge it:
2x(dx/dt) + 10y(dy/dt) + 2(dy/dt) = 0
Since x = 6; y = -3; and dx/dt = 14, then:
2x(dx/dt) + 10y(dy/dt) + 2(dy/dt) = 0
2*6*14 + 10*(-3)*(dy/dt) + 2*(dy/dt) = 0
168 + (-30)(dy/dt) + 2(dy/dt) = 0
168 - 28(dy/dt) = 0
28(dy/dt) = 168
dy/dt = 6
Hence, the indicated rate x^2 + 5y^2 + 2y = 75; dx/dt = 14 when x = 6 and y = -3 is dy/dt = 6.
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When finding f(g(x)) what do you need to know about the domains and ranges
of f(x) and g(x)? Explain
All x-values that are within the scope of both f and g make up the domain of the (f g)(x).
How can the domain of f/g)(x be determined?All x-values that are within the scope of both f and g make up the domain of the (f g)(x). In this case, f has a domain of "x | x 0" and g has a domain of "all real numbers," thus (f g)(x) also has a domain of "x | x 0" since these values of x fall within both f and g's domains.Utilizing graphs is another method for determining the domain and range of functions. The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.To learn more about Domain refer to:
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1/3 divided by 4=?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Answer:1/12
Step-by-step explanation:
Suppose that 14 inches of wire costs 84 cents. At the same rate, how many inches of wire can be bought for 42 cents
How do you regroup 4 digit numbers?
We take carry 1 if there is more then 9 when we are adding or subtracting in the regrouping 4 digit number.
Given that,
We have to find how do we regroup 4 digit numbers.
We know that,
When performing operations like subtraction and addition, regrouping is accomplished by creating groups of tens. Regrouping refers to rearranging integers into place value-based groupings to facilitate operations. Because you must rearrange the numbers into place value to complete the procedure, it is known as regrouping.
Addition with regrouping or addition with carryover refers to additions where the addends' digit sums exceed 9 in any of the columns. Finding the digit sum of two integers requires regrouping. Only the units place digit of the total is then written in the appropriate column.
(1) (1)
3 1 9 5
+ 6 2 3 7
--------------------
9 4 3 2
Therefore, We take carry 1 if there is more then 9 when we are adding or subtracting in the regrouping 4 digit number.
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select every definite integral below that can be evaluated using the fundamental theorem of calculus (there may be more than one).
The basic theorem of calculus states that the function must be differentiable throughout the specified limit interval. So all options are correct.
In the given question, we have to select every definite integral below that can be evaluated using the fundamental theorem of calculus (there may be more than one).
The given integrals are:
[tex]\int_{-\pi}^{\pi}sin^7(4x)cos^8(3x)dx[/tex][tex]\int_{-5}^{12}(x\text{In}x+2x-1)dx[/tex][tex]\int_{0}^{4}(12x^{16}-5x^{11}+81x^{8}-208432x^{2}+x-2)dx[/tex][tex]\int_{-1}^{1}\frac{1}{x}dx[/tex][tex]\int_{1}^{9}|x|dx[/tex]As we know that,
A definite integral is a formal estimate of the area beneath a function. Integrals can reflect a region's (signed) area, the total value of a function that changes over time, or the amount of a given thing given its density.
The basic theorem of calculus states that the function must be differentiable throughout the specified limit interval.
Within the specified limit interval, the integral in the supplied option is differentiable.
Therefore, each choice is valid.
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An employee in the 12% tax bracket
invests $1000.00 in a Roth IRA. When the
employee retires, her salary is in the 22%
tax bracket. What tax will be assessed on
the initial investment at retirement?
A. Since the employee used a Roth IRA, she will pay no taxes on her
investment at retirement.
B. Not enough information to answer
C. $120.00
D. $220.00
A. Since the employee used a Roth IRA, she will pay no taxes on her investment at retirement.
The Roth IRA is a type of individual retirement account (IRA) that allows the investor to contribute after-tax money to the account. This means that the investor pays taxes on the contributions upfront, but the investment grows tax-free and can be withdrawn tax-free at retirement. Therefore, the employee in this scenario will not have to pay any taxes on her initial investment of $1000.00 at retirement, regardless of her tax bracket at that time.
Help me please Ahaheinendjdn
In the figure shown, the measures of all angles are equal, and AB = EF.
I need help with this please help me
the answer is B because it is congruent and since AB=EF it's also B
Find the distance between the two points rounding to the nearest tenth (if necessary). (1,−6) and (−8,−4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.2[/tex]
ind the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4x3, y = 4x, x20; about the x-axis
The Volume of the solid formed by the curves y = 4x³ , y = 4x, x ≥ 0 ; about the x axis is 64π/21 .
In the question ,
it is given that ,
the given curves are y = 4x³ , y = 4x, x ≥ 0 ,
we have to find the volume about x axis ,
the region formed by the given curves about x axis is shown below in the figure .
So , the Volume of the required region is
V = [tex]\int\limits^1_0 {\pi [(4x)^{2} - (4x^{3} )^{2} }] \, dx[/tex]
On simplification ,
we get ,
V = [tex]\pi \int\limits^1_0 { [16x^{2} - 16x^{6} }] \, dx[/tex]
V = π[ x³/3 - x⁷/7 ]¹₀
= 16π( 1/3 - 1/7 - 0 - 0)
= 16π((7 - 3)/21)
= 64π/21
Therefore , the required Volume is 64π/21 .
The given question is incomplete , the complete question is
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4x³ , y = 4x, x ≥ 0 ; about the x-axis .
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1. suppose we wish to predict average customer spending. we take a small sample of size 50 and find the sample mean to be $200/mo. with a sample standard deviation of $10/mo. place a 99% confidence interval around the population average spending.
The average customers are spending in the range of ( 196.36 , 203.64) for the given mean and standard deviation.
As given in the question,
Sample size 'n' = 50
Sample mean 'μ ' is equal to 200
Standard deviation 'σ' = 10
z-score for 99% Confidence interval = 2.576
Confidence interval = mean ± z ( σ / √n )
Substitute the values we get,
Confidence Interval = 200 ± 2.576( 10 / √50)
= 200± 2.576 ( 1.414)
= 200 ± 3.642464
Lower bound of the required confidence interval = 200 - 3.642464
= 196.36
Upper bound of the required confidence interval = 200 + 3.642464
= 203.64
Therefore, the average customer is spending between ( 196.36 , 203.64) range from the given mean and standard deviation.
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if a researcher offers beer drinkers an extra incentive to recruit their friends who also drink beer to participate in the study, s/he is using a(n) sample.
If a researcher offers beer drinkers an extra incentive to recruit their friends who also drink beer to participate in the study, s/he is using a(n) snowball sample.
What is snowball sampling?
Snowball sampling is a nonprobability sampling technique used in sociology and statistics research where current study participants recruit future study participants from among their acquaintances.
Thus, it can be said that the sample group is expanding like a snowball.
A non-probability sampling technique called "snowball sampling" enlists current research participants to assist in the recruitment of future study participants.
For instance, a researcher looking to understand leadership styles might ask people to list other influential people in their neighborhood.
Hence, if a researcher offers beer drinkers an extra incentive to recruit their friends who also drink beer to participate in the study, s/he is using a(n) snowball sample.
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