The value of the account in the year 2009 will be $682.
The acount's balance, in t years after 1999, can be modeled by the following equation.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
$330 in an account in the year 1999This means that $590 in the year 20072007 is 8 years after 1999, so P(8) = 590.We use this to find r.Determine the value of the account, to the nearest dollar, in the year 2009.2009 is 10 years after 1999, so this is A(10).The value of the account in the year 2009 will be $682.learn more about solutions here:
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at intel, the sizes of processor chips have a mean of 1 cm with a standard deviation of 0.2 cm. multiple random samples, each consisting of 35 processor chips, are taken. the sample mean and standard deviation for each sample are recorded to form a sampling distribution. what is the mean and standard deviation of this sampling distribution?
The mean and standard deviation of this sampling distribution is 1 cm and 0.033 cm, respectively.
The sample mean is the arithmetic mean of all the samples of processor chips. The mean of the sample group is known as the sample mean.
Let X denote the multiple random samples of 35 processor chips and each of which represents the size of the processor chips.
Let 'x' be the sample mean of all the random samples X which represents the size of the processor chips.
The mean of the size of processor chips= μ =1 cm
The mean of the sampling distribution x of sample means is equal to the mean of the sizes of the processor chips μ
Mean of sampling distribution x = mean of the size of the processor chips μ
⇒ x = μ
x = 1 cm
The mean of this sampling distribution is 1 cm.
The standard deviation is the amount of variation among the set of values. It is the measure of the dispersion of values in the data set.
The size of the processor chips has a standard deviation of 0.2 cm so σ = 0.2 cm
Let 'x' be the standard deviation of random samples X of the size of processor chips.
Number of random multiple samples of processor chips, n =35
The standard deviation of this sampling distribution can be calculated by using the below formula;
x = σ/[tex]\sqrt{n}[/tex]
Substituting the value of \sigma as "0.2" cm and the value of "n" as 35 in the above formula, we get;
x = 0.2/√35
x = 0.033 cm
The standard deviation of this sampling distribution is 0.033 cm.
The mean of this sampling distribution is 1cm and the standard deviation of this sampling distribution is 0.033 cm.
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what is the probability that a couple will have at least four sons if they plan to have 5 children and if the probability of having a son equals the probability of having a daughter? (enter your probability as a fraction.)
0.1875 is the probability of having a daughter .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.Let X = No. of sons
n = 5 and p = 0.5, because probability of having son and daughter is same.
X follows Binomial distribution with parameter n and p. Then its pmf is,
P(X= x) = \binom{n}{x}p^xq^{(n-x)} \ \ \ \ \ x = 0,1,----5
Now,
P(X= 5) = \binom{5}{5}(0.5)^5 (0.5)^{(5-5)} \\ \\ \\ P(X= 5) = 0.03125
Probability of haveing at least four sons
P(X\ge4) = P(X=4) +P(X=5) \\\\ P(X\ge4) = 0.15625 + 0.03125 \\\\ P(X\ge4) = 0.1875
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PLS HELP !! ITS DUE tommorow!!
In the given square, the values of f and g are equal that is 4√3cm.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.So, the values of f and g are:
From the given diagram we know that ABCD is a square.So, all sides are the same.The area of ABCD is 48cm².
Now, calculate for sides as follows:The formula for the area of the square: A = s²Then,
A = s²48 = s²s = √48s = √2×2×2×2×3s = 2×2√3s = 4√3Since f and g are 2 sides of the square, their values are 4√3cm.
Therefore, in the given square, the values of f and g are equal that is 4√3cm.
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Graph this system of equations on the coordinate plane:
y=4/3x+4
3y=-2x-6
The graph the system of linear equations on a coordinate plane is added as an attachment
How to graph the system of linear equations on a coordinate plane?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y=4/3x+4
3y=-2x-6
Rewrite the equations in the system of equations as follows:
So, we have the following representation
y = 4/3x + 4
3y = -2x - 6
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, 0)
This means that the solution to the system of equations is (-3, 0)
See attachment for the graph of the system of equations
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Are these parallel or perpendicular or neither? 3x+2y=10 and 2x+3y=-3
Answer:
These lines are neither parallel nor perpendicular.
Step-by-step explanation:
Parallel lines are lines that never intersect and perpendicular intersect at a ninety degree angle.
Using desmos, you can find your solution.
I hope this helps
-No one
How do you solve #4 - #9?
4. There is no enough information.
5. ΔPEF ≅ ΔREF are congruent by SAS.
6. ΔKMO ≅ ΔOLK are congruent by SSS.
7. No enough information.
8. ΔPAN ≅ ΔKLC are congruent by SSS.
9. ΔABC ≅ ΔDEF are congruent by SSS.
What is the SSS and SAS Theorems?The SSS and SAS are theorems of triangle congruence that can be used to prove that two triangles are congruent. To prove that two triangles are congruent by SSS, both triangles must have three pairs of corresponding lengths that are congruent, while SAS is used when the two triangles have two pairs of congruent sides that are corresponding, and a pair of congruent included angles.
4. There is no enough information to prove triangles HNJ and RDF are congruent by neither SAS nor SSS.
5. Triangles PEF and REF are congruent by SAS.
6. Triangles KMO and OLK are congruent by SSS.
7. No enough information.
8. Triangles PAN and KLC are congruent by SSS.
9. Triangles ABC and DEF are congruent by SSS.
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What is the slope of the secant line that intersects the graph of f(x) = √4x+1 at x = = 0 and x = 6?
=
a) 4 x -3 x 2 =
b) -2 x 5 x -4 =
c) -3 x -1 x -6 =
Answer:
a) 4 x -3 x 2 = -24
b) -2 x 5 x -4 = 40
c) -3 x -1 x -6 = -18
Answer:
a.4 x -3 x 2 =
use the rules for multiplication
-(4×3×2)
-(12×2)
=2
----------------------------------
b. -2 x 5 x -4 =
note:
-2×5(-4)
multiplying an even number of negative terms makes the product positive.
-2×5= 10
10×-4
=40
----------------------------------
C. -3 x -1 x -6 =
note:
multiplying an odd number of negative terms makes the product negative.
-(3×1×6)
=-18
find the area of a rhombus whose diagonals are the lengths 36cm and 22.5 cm
Answer:
area of rhombus=1/2*36*22.5
=405cm^2
Step-by-step explanation:
Three consecutive even integers have the property that when the product of the first two is taken, the result is four less than the square of the third one. What are the integers?
The three consecutive even integers are -2, 0 and 2.
How to calculate the value?Let the three consecutive even integers be x, x+2 and x+4.
Since the product of the first two is taken, the result is four less than the square of the third one. This will be:
x(x + 2) = (x + 4)² - 4
x² + 2x = x² + 8x + 16 - 4
x² + 2x = x² + 8x + 12
Collect like terms
x² - x² + 2x - 8x - 12
-6x - 12 = 0
-6x = 12.
Divide
x = -12/6
x = -2
x + 2 = -2 + 2 = 0
x + 4 = -2 + 4 = 2
They're -2, 0, and 2.
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N is an integer. Work out:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
According to the integer N,
a) The smallest possible value of N is 6.5 if N >= 6.5
b) The largest possible value of N is -2 if N < - 3
c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.
Integer
Integer refers a collection of whole numbers and negative numbers.
Given,
Here we have the integer N.
And we need to find the following:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
Part a). smallest possible value of N if N >= 6.5
Here the smallest number is 6.5 because other value are greater than this one.
Part b). the largest possible of N if N < -3
The largest possible number is -2, because the other values on N are less than -2.
Part c). the possible values of N if N >= -2 and N <2.
Here the possible values between these are {-2, -1, 0, 1}.
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The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
professor elderman has given the same multiple choice final exam in his principles of microeconomics class for many years. after examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. what is the probability professor elderman's class of 36 has a class average below 78
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
Given that;
In his principles of microeconomics subject, Professor Elderman has utilized the same multiple-choice final exam for many years. He looks over the last ten years' worth of statistics and discovers that the scores have a mean of 76 and a standard deviation of 12.
µ = 76 , σ = 12 , n = 36
Using Normal Distribution;
For x = 70
z = (x - µ) / (σ/√n) = (70-76)/(12/√36) = -3.00
P( average greater than 70 ) = P(X>70)
= 1 - P(X<70)
= 1 - P(Z<-3.00)
= 1 - 0.0013
= 0.9987
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
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question 6 what if we use a p-value cutoff of 10%? do we reject, fail to reject, or are we unable to tell using our confidence interval? assign cutoff ten percent to the number corresponding to the correct answer. reject the null / data is consistent with the alternative hypothesis fail to reject the null / data is consistent with the null hypothesis unable to tell using our staff confidence interval
0.10 > 0.05 is value of p - value of the data .
What does P stand for?
The likelihood, for a particular statistical model, that the statistical summary would be equal to or more extreme than the actual observed findings when the null hypothesis is true is known as the P value.The p-value is the likelihood that, assuming the null hypothesis is true, a result will be at least as dramatic as the one that was actually seen in the biological, clinical, or epidemiological investigation.If we use 10% p - value cutoff = 0.10
then as 0.10 > 0.05
reject the null / data is consistent with the alternative hypothesis .
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Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answer:
Domain: {2, 3, 4, 5} Range: {12, 13, 14}
Step-by-step explanation:
The relationship is a function even though two different inputs have the same output.
a passenger train traveled 240 miles in the same amount of time it took a freight train to travel miles. the rate of the freight train was miles per hour slower than the rate of the passenger train. find the rate of the passenger train.
The rate of the passenger train is 60mph.
We know that,
Speed = Distance / Time
Time = Distance / Speed
s = speed of passenger train
speed of freight train = (s - 20)
T = 240 / s
T = 160 / (s-20)
240 / s = 160 / (s-20)
240(s - 20)/s(s - 20) = 160s/s(s - 20)
240(s - 20)/s(s - 20) - 160s/s(s - 20) = 0
240(s - 20) - 160s = 0s(s - 20)
240s - 4800 - 160s = 0
80s - 4800 = 0
80s = 4800
Hence the speed of the freight train is 40mph, while the speed of the passenger train is 60mph.
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Susan has two coupons for a bicycle. Coupon A: 20% off of a $81 bicycle Coupon B: $19 rebate on a $81 bicycle Choose the coupon that gives the lower price. Then fill in the blank with the correct value.
The coupon that gives the lower price, based on the percentage discounts is Coupon B.
How to find the better coupon?To find the coupon that gives the lower price, apply the coupons to the price of the bicycle to see which value would be less after the coupon is applied.
Coupon A value after discount is:
= 81 x ( 1 - discount)
= 81 x ( 1 - 20%)
= $64.80
Coupon B value after discount is:
= 81 - 19
= $62
The coupon that gives the lower price is Coupon B.
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Please Help!
Solve the inequality and graph it’s solution.
the letters that spell mississippi are each written on separate tiles lying facedown on a table. a tile is selected at random, the letter is recorded, and then the tile is placed facedown on the table. then the process repeats. what is the theoretical probability of choosing a tile with the letter p? responses 14 1 fourth 411 4 over 11 111 1 over 11 211
The theoretical probability of choosing a tile with the letter p is 1/8
The letter of the word MISSISSIPPI are written on separate tiles lying down on the table and tile is chosen at random and the the letter is noted and then the tile is lied again on the table.
Probability of the event is,
P(E) = Total favorable outcomes/Total possible outcomes.
Total possible outcomes in this case are 11 because there are a total of 11 letters.
The total favorable outcomes that the chosen letter is P is,
Total favorable outcomes = ¹¹C₁/(2!)(2!)(2!)
Total favorable outcomes = 11/8
Probability P that chosen number is P is,
P = (11/8)/11
P = 1/8
So, the probability that the chosen tile is with letter P is 1/8.
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five whole numbers are written in order
4 6 x y 10
median and mean of the five numbers are the same.
Workout the values of x and y
The values of x and y if the mean and median are equal are:
x = 7
y = 8.
What is the Mean and Median of a Data Set?The mean is the total sum of the values in a data set divided by the number of values of the data set.
The median of a data set is the center value when the data distribution is ordered.
Given the ordered data set as, 4, 6, x, y, and 10.
The center value is x. Therefore, the median of the data set is x.
The mean of the data = (4 + 6 + x + y + 10)/5
The mean of the data = (20 + x + y)/5
The mean and the median are equal, therefore:
(20 + x + y)/5 = x
20 + x + y = 5x
20 + y = 5x - x
20 + y = 4x
The value of x cannot be less than 6, if x = 7, we woud have:
20 + y = 4(7)
20 + y = 28
y = 28 - 20
y = 8
The values of x = 7, y = 8.
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If $3000 is invested at tan interest rate if 4.8%, compounded hourly for two years what is the ending balance?
The final balance is $97,920.
Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.
Given this, The principal is $3000.
Interest rate = 4.8%
Time = 2 years We must find the final balance.
The end balance formula is
C = P[ 〖(1+r)〗^n – 1]
C = 3000[ 〖(1+4.8)〗^2 – 1]
C = 3000 [ 〖(5.8)〗^2 – 1]
C = 3000 [ 33.64 – 1]
C = 3000 ( 32.64)
C = 97,920
Therefore the ending balance is $97,920
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simplify (4i+1)^2
show all work
The simplified answer is 8i-15.
What do you mean by iota?
Iota is a mathematical concept that is represented by the symbol i and has the value of [tex]i^{2}=-1[/tex] , or i =[tex]\sqrt{-1}[/tex] . It is an imaginary unit number that is denoted by i. You could have run into instances when the discriminant is negative while attempting to solve quadratic equations.
According to the given question,
We have: [tex](4i+1)^{2}[/tex]
Now, we will solving this by formula,
[tex](a+b)^{2}=a^{2} +b^{2}+2ab[/tex]
Putting the values in it,
[tex](4i+1)^{2}=(4i)^{2}+1^{2}+2(4i)(1)\\=16i^{2} +1+8i\\ =16(-1)+8i+1\\=8i-16+1\\=8i-15[/tex]
Therefore, the required answer is 8i-15.
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The points (4, -3) and (x, 3) lie on the same straight line.
If the slope of the line is 2, what is the value of x ?
answer:
(1,3)
step-by-step explanation:
desmos.
The value of x will be equal to 7 for the given slope of 2 for the line.
What is the slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.
The slope of the line is calculated by the formula,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
2 = ( 3 + 3 ) / ( x - 4)
2(x-4) = 6
2x - 8 = 6
2x = 8 + 6
2x = 14
x = 14 / 2
x = 7
Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.
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please help me with this math problem
Answer:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
Step-by-step explanation:
When adding or subtracting fractions that have different denominators, first rewrite the fractions as equivalent fractions with the same denominator. To do this, find the lowest common multiple (LCM) of the denominators.
The given subtraction is:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}[/tex]
The LCM of the denominators 2 and 8 is 8. Therefore, we need to rewrite the first fraction as an equivalent fraction with 8 as its denominator. To do this, multiply its numerator and denominator by 4:
[tex]\implies \sf \dfrac{1}{2} \times\dfrac{4}{4}=\dfrac{4}{8}[/tex]
Therefore:
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}[/tex]
To subtract fractions with the same denominator, simply subtract the numerators. (The denominator stays the same).
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}=\dfrac{4-1}{8}=\dfrac{3}{8}[/tex]
Final solution
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
Solve for w.
63 =
3
Simplify your answer as much as possible.
W =
Answer:
That doesn't even make any sense you can't simplify or solve for anything if there isn't the right equation???????
Step-by-step explanation:
An ice skater is penalized 1.2 points for a fall. Write an expression for the ice skater’s final score.
The expression for the given case can be written as F = P - 1.2n.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The addition and subtraction can only take place between like terms.
Given that,
The penalty for an ice skater for a fall is 1.2 points.
Suppose the total points of ice skater be P, the number of falls be n and the final score be F.
Then following expression can be written for final score,
F = P - 1.2n
Hence, the expression for ice skater's final score is F = P - 1.2n.
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Let the function f be defined as p (x) = -5 (-3x + 4) and function g be
defined as m (x)= 5x - 2 (5x - 6). What value of x satisfies the
equations m (x)= p (x)?
If the functions are equal. Then the value of the variable 'x' will be 1.6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let the capability f be characterized as p(x) = - 5(- 3x + 4) and work g be characterized as m(x) = 5x - 2(5x - 6).
If the functions are equal. Then the value of the variable 'x' will be given as,
m(x) = p(x)
- 5(- 3x + 4) = 5x - 2(5x - 6)
15x - 20 = 5x - 10x + 12
15x - 20 = - 5x + 12
20x = 32
x = 1.6
If the functions are equal. Then the value of the variable 'x' will be 1.6.
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If ΔLMN is similar to ΔPQR, what is the length of PR?
If ΔLMN is similar to ΔPQR then length of PR = 15 by corresponding sides of similar triangles property.
What is the relation between corresponding sides of two similar triangles?
Two figures are said to be similar if they have same shape but size may vary.If two triangles are similar then their :-Corresponding angles are congruent. Corresponding sides are in the same ratio.ΔLMN is similar to ΔPQR
Corresponding angles are equal - ∠L = ∠P, ∠M = ∠Q, ∠N = ∠R.Corresponding sides are in same ratio - [tex]\frac{LM}{PQ} = \frac{LN}{PR} = \frac{MN}{QR}[/tex]According to the given data:
ΔLMN is similar to ΔPQR, therefore their corresponding sides are in same ratio,
LM/PQ = 8/6
LN/PR = 20/(2x - 1)
Substituting the values and solving for 2x -1 which is given length of PR
[tex]\frac{8}{6} = \frac{20}{2x -1} \\\\8(2x -1) = (20)(6)\\\\PR = 2x - 1 = \frac{120}{8} \\\\[/tex]Therefore, length of PR = 15.
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The endpoints of AB¯¯¯¯¯¯¯¯ are given. Find the coordinates of the midpoint M. Then find AB. Round your answers to the nearest tenth, if necessary.
A(−5, 1), B(4,−5)
The coordinates of the midpoint M for the line segment AB are (-1/2, -2).
Describe the meaning of mid point of line segment?The halfway of such a line segment is its center. It is equally from both endpoints and serves as the segment and endpoint centroid. It cuts the portion in half.As per the stated values;
Th end points of the line segment AB are given as;
A(−5, 1) = (x1, y1)
B(4,−5) = (x2, y2)
The formula for the evaluation of the coordinates of the mid point is-
Mid point - M(x, y)
x = (x1 + x2)/ 2
x = (-5 + 4) /2
x = -1/2
y = (y1 + y2)/2
y = (1 - 5)/2
y = -2
Thus, the coordinates of the midpoint M for the line segment AB are (-1/2, -2).
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Sean drew a vertical line segment and labeled the top endpoint W and the other endpoint X.
He then found the midpoint of WX and labeled it Y. Starting at Y and moving to the right, he
drew a line segment of length WY perpendicular to WX, and he labeled the new endpoint Z.
Finally, he drew a line segment parallel to YZ, also of length WY, starting at W and moving to
the right.
What letter did Sean draw?
E
F
L
T
PLEASE HELP
Sean drew a letter (b)F.
What is Geometry construction?
Drawing precise shapes, angles, or lines is referred to in geometry as "construction." These structures only require a compass, a straightedge (a ruler), and a pencil.
according to the question, WX is a straight line having a midpoint at Y.
YZ is drawn perpendicular to WX. And parallel to YZ a line segment is drawn After this Geometrical construction, a letter is drawn which is F.
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