We can start by using the standard normal distribution to find the z-scores for the two heights:
z1 = (176 - 180) / 4 = -1
z2 = (180 - 180) / 4 = 0
Then, we can use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores. From a table, we find that the area to the left of -1 is 0.1587 and the area to the left of 0 is 0.5. Therefore, the area between -1 and 0 is:
0.5 - 0.1587 = 0.3413
To find the percentage of the population, we can convert this decimal to a percentage by multiplying by 100:
0.3413 x 100 = 34.13%
Therefore, approximately 34.13% of the population would lie between 176cm and 180cm in height.
Assume multiplicity 1 unless otherwise stated
Answer:
f(x) = x^4 - 6x^3 + 18x^2 - 54x + 81
Step-by-step explanation:
We have a zero of 3 with multiplicity 2, and
since 3i is a root, -3i must also be a root.
f(x) = ((x - 3)^2)(x - 3i)(x + 3i)
f(x) = (x^2 - 6x + 9)((x^2 + 9)
f(x) = x^4 + 9x^2 - 6x^3 - 54x + 9x^2 + 81
f(x) = x^4 - 6x^3 + 18x^2 - 54x + 81
Need help answering this white showing my work
Answer:
Median: 48
Range: 18
Step-by-step explanation:
The range: is calculated by subtracting the lowest value from the highest value
The median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.
If you cant read it then hears what it says. Quadrilateral ABCD is identical with quadrilateral A<->W B<->X C<->Y and D<->Z. I think u can read thw next BUT ITS DUE AS A TEST GRADE SO PLS HELP ME
Quadrilateral ABCD is identical with quadrilateral A<->W B<->X C<->Y and D<->Z.
Let us consider two identical quadrilaterals, ABCD and A' B' C' D', where each vertex of the first quadrilateral is mapped to a corresponding vertex of the second quadrilateral by a certain transformation. Specifically, vertex A is mapped to vertex W, vertex B is mapped to vertex X, vertex C is mapped to vertex Y, and vertex D is mapped to vertex Z.
Without more information about the nature of the transformation, it is difficult to say much about the quadrilaterals or their properties. However, some general observations can be made
Since the quadrilaterals are identical, their corresponding sides and angles are congruent.If the transformation preserves the orientation of the quadrilateral (i.e., it does not flip or reflect the shape), then the corresponding vertices will appear in the same order around the quadrilateral. For example, if ABCD is a clockwise-oriented quadrilateral, then A' B' C' D' will also be clockwise-oriented.If the transformation is a rigid motion (i.e., it preserves distances and angles), then the corresponding sides and angles of the two quadrilaterals will be congruent. In this case, the quadrilaterals will be congruent (i.e., they will have the same shape and size).If the transformation is not a rigid motion, then the corresponding sides and angles of the two quadrilaterals may not be congruent. In this case, the quadrilaterals will have different shapes and sizes.Hence, we can also add information about the transformation or the quadrilaterals in this type of problem.
The given question is incomplete.
The complete question is "How can we say that the quadrilateral ABCD and quadrilateral WXYZ is identical"
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The coordinates of the vertices of a trapezoid are D (3, 5), O (5, 5), G (5, 2), S (-1, 2). Trapezoid DOGS is translated 3 units to the left and 7 units down. What is the rule that describes the translation that was applied to trapezoid DOGS to create trapezoid D’O’G’S’?
Note that the rule that describes the translation that was aplied to the trapezoid D.O.G.S to create D'.O'. G'. S' is (x,y) → (x-3, y-7).
What is translation?A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction.
Translation in geometry refers to shifting a form into a different place without affecting it in any manner. Shape translation is presented to Year 5 students by providing them shapes on squared paper that must be moved a specified number of squares up, down, left, or right.
Hence, the translation rule
that was aplied to the trapezoid D.O.G.S to create D'.O'. G'. S' is (x,y) → (x-3, y-7).
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
Miguel has 3 1-gallon containers each 3/4 full of water how many cups of water are there
(x - 1)/(x - 3) - (x ^ 2 - x + 2)/(x ^ 2 - 2x - 3) = 1/(x + 1) prove it
Answer:
Bellow
Step-by-step explanation:
To prove the equation:
(x - 1)/(x - 3) - (x ^ 2 - x + 2)/(x ^ 2 - 2x - 3) = 1/(x + 1)
we need to find a common denominator for the left-hand side of the equation. The common denominator is (x - 3)(x + 1)(x - 3), which is the product of all the factors in the denominators.
Using this common denominator, we can rewrite the left-hand side of the equation as:
[(x - 1)(x + 1)(x - 3) - (x ^ 2 - x + 2)(x + 1)] / [(x - 3)(x + 1)(x - 3)]
Simplifying the numerator using distributive property, we get:
[(x^3 - 2x^2 - 2x + 2) - (x^3 - 2x^2 - x - 2)] / [(x - 3)(x + 1)(x - 3)]
Simplifying the numerator further, we get:
(-x + 4) / [(x - 3)(x + 1)(x - 3)]
Now, we can simplify the right-hand side of the equation by multiplying both the numerator and the denominator by (x - 3)(x + 1), which gives us:
1 / (x + 1) = (x - 3)(x + 3) / [(x - 3)(x + 1)(x - 3)]
Therefore, the original equation can be written as:
(-x + 4) / [(x - 3)(x + 1)(x - 3)] = (x - 3)(x + 3) / [(x - 3)(x + 1)(x - 3)]
Cancelling the common factors on both sides, we get:
-x + 4 = x^2 - 9
Rearranging and simplifying, we get:
x^2 + x - 13 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-1 ± √(1 + 4*13)) / 2
Simplifying, we get:
x = (-1 ± √53) / 2
Therefore, we have proved that the equation:
(x - 1)/(x - 3) - (x ^ 2 - x + 2)/(x ^ 2 - 2x - 3) = 1/(x + 1)
holds true for all values of x except (-1, 3, 3 - √13, 3 + √13).
Answer:
Step-by-step explanation:
(x-1)/(x-3)-(x²-x+2)/(x²-2x-3)=1/(x+1)
[tex]\frac{x-1(x^{2}-2x-3)-x-3(x^{2}-x+2) }{x-3(x^{2} -2x-3)}[/tex] =0
[tex]\frac{(x^{3}-2x^{2} -3x-x^{2} +2x+3)-(x^{3}-x^{2} +2x-3x^{2} +3x-6) }{x^{3}-2x^{2} -3x-3x^{2} +6x+9}[/tex]=0
[tex]\frac{-7x^{2} +2x+9}{x^{3}-5x^{2} +3x+9 }[/tex] =0
-7x²+2x+9=x³-5x²+3x+9
x³-2x²-x=0
write the equation of the line in FULLY SIMPLIFIED SLOPE-INTERCEPT FORM.
( please give me the answer like that y=x-2 or / y=5x-4)
Photo of the graphing there !!!
The requried equation of the line shown in the graph is y = -5x + 6.
From the graph locate 2 points, (0, 6) and (1, 1)
The slope of the line is given as,
m = (1 - 6) / (1 - 0)
m = -5
Using the point-slope form of the equation of a line, we have,
y - y₁ = m(x - x₁)
where m is the slope of the line, and (x₁, y₁) is a point on the line. Substituting m =-5 and (x₁, y₁) = (0, 6), we get:
y - (6) = -5(x 0)
y = -5x + 6
Therefore, the equation of the line shown in the graph is y = -5x + 6.
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anais bought yards of ribbon. she had feet inches of ribbon left after trimming some curtains. how many inches of ribbon did anais use to trim the curtains? anais used blank inches of ribbon. the solution is
Anais, who bought a ribbon of length [tex]2 \dfrac 12 [/tex] yards, and she trimming a curtain from it. From substraction, length of ribbon used in curtain is equals to 72 inches.
Word problems express in mathematical form. In subtraction, keywords that could signal the operation are lesser, less than, removed from. However, there are times when the idea of subtraction or taking away is inferred from the problem itself. In the problem, total length of ribbon Anais bought
= [tex]2 \dfrac 12 [/tex] yards
The length of ribbon left after trimming some curtains = 1 feet 6 inches
We have to determine inches of ribbon Anais use to trim the curtains. Let it will be equal to x inches . We may notice in the provide values that they all have different units. We can convert the all different units into inches. Using uint conversation, 1 yard = 36 inches
=> [tex]2 \dfrac 12 [/tex]
yards =[tex] 36 × \frac{ 5}{2} [/tex]
= 90 inches
Similarly, 1 feet = 12 inches, then 1 feet + 6 inches = 12 + 6 = 18 inches
Thus, the left ribbon length = 18 inches
Using substraction method, the length in inches of ribbon that anais use to trim the curtains = total length - left length of ribbon = 90 - 18
= 72 inches.
Hence, required value is 72 inches.
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Complete question:
Anais bought
[tex]2 \dfrac 12 [/tex]
yards of ribbon. She had 1 feet 6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?
The triangle above has the following measures. s = 31 cm r = 59 cm پار Find the m/Q. Round to the nearest tenth and include correct units. Show all your work.
The value of measure of angle Q is,
⇒ Q = 58.3 degree
We have to given that;
The triangle above has the following measures. s = 31 cm r = 59 cm
Now, We can formulate;
cos Q = s / r
cos Q = 31 / 59
cos Q = 0.525
Q = 58.3 degree
Thus, The value of measure of angle Q is,
⇒ Q = 58.3 degree
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1) State whether the angles are vertical or adjacent.
2) State whether the angles are complementary or supplementary.
3) Write an equation AND show your work to solve for the variable x.
Answer:
Adjacent, supplementary, found in explanation
Step-by-step explanation:
1. The angles above are adjacent.
2. The angles above are supplementary because the angles add up to 180⁰.
3. An equation for this could be
x+35=180
-35 on both sides
x=145⁰
PLEASE HELP
Calculate the total value of the investment given the following information and compounded continuously?
Principal $1000; rate 4.5%; term 10 years
Step-by-step explanation:
Continuous compounding formula :
FV = PV e^rt FV = future value PV = present value
r = decimal interest rate t = years
FV = 1000 e^(.045 * 10) = $ 1568.31
Which description best describes the solution to the following system of equations? (1 point) y = −2x + 9 y = −x + 8 a Lines y = −2x + 9 and y = −x + 8 intersect the x-axis. b Lines y = −2x + 9 and y = −x + 8 intersect the y-axis. c Line y = −2x + 9 intersects the line y = −x + 8. d Line y = −2x + 9 intersects the origin.
The correct way to explain the solution of the given system of equation is at point ( 1, 7) given by option (c) Line y = −2x + 9 intersects the line y = −x + 8
System of equation are,
y = −2x + 9 and y = −x + 8
Solution to this system of equations,
The values of x and y should satisfy both the equations.
Equate the two equations to each other and solving for variable x.
⇒ −2x + 9 = −x + 8
like terms on same side of the equation,
⇒ x − 2x = 8 - 9
Solve for x,
⇒ −x = -1
Dividing both sides of the equation by −1 we get,
⇒ x = 1
Substitute the value of x in either equation of the line and get value of y.
⇒ y = −2x + 9
⇒ y = −2(1) + 9
⇒ y = -2 + 9
⇒ y = 7
Therefore, the solution representing system of equations is given by coordinate (1, 7) means option c. the line y = −2x + 9 intersects the line y = −x + 8 .
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there are 25 2525 students in ms. nguyen's second-grade class. in the class election, 4 44 students voted for benjamin, 12 1212 voted for sahil, and 9 99 voted for maria. what percentage of the class voted for maria? % %
The percentage of the students of the class voted for Maria is 36%.
Number of students in Ms. Nguyen's second grade = 25
Number of students voted for Benjamín = 4
Number of students voted for Sahil = 12
Number of students voted for Maria = 9
The total number of students who voted in the class election is,
4 + 12 + 9 = 25
This is the same as the total number of students in the class.
So all students participated in the election.
The percentage of the class that voted for Maria is simply,
= (9/25) ×100
= 36%
Therefore, 36% of the students in Ms. Nguyen's second-grade class voted for Maria.
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The above question is incomplete, the complete question is:
There are 25 students in Ms. Nguyen's second-grade class. In the class election, 4 students voted for Benjamin, 12 voted for Sahil, and 9 voted for Maria. What percentage of the class voted for Maria?
Determine the percent of the data using a graphing calculator.
a: between z= 0.53 and z = 2.67
b: to the right of z= 1.61
The percentage of values from the z-scores are 29.43% and 5.40%,, respectively
Calculating the percentage of values of the z-scoresHere, we have
Between z = 0.53 and 2.67
This is represented as
Percentage = (0.53 < z < 2.67)
Using a graphing calculator, we have
Percentage = 29.43%
Next, we have
To the right of z = 1.61
This is represented as
Percentage = x > 1.61
Using a graphing calculator, we have
Percentage = 5.40%
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what can we conclude about having large differnces in robust standard errors adn the usual standardwrrors
When there are large differences between robust standard errors and usual standard errors, we can conclude that there may be issues with the assumptions of the statistical model.
Robust standard errors are typically used when there are concerns about heteroscedasticity or the presence of outliers in the data. In contrast, usual standard errors assume that the errors are homoscedastic and normally distributed.
Large differences between the two types of standard errors may indicate that the assumptions of the usual standard errors are violated, and that the robust standard errors provide a more accurate estimate of the standard error. It is important to consider both types of standard errors when conducting statistical analysis and to interpret the results accordingly.Know more about the standard errors
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Solve this word problem: A grocery store has a giveaway at their door. Every 15th customer receives a free shopping bag and every 9th customer receives a 25% off coupon. Which customer will be the first to receive both a shopping bag and a 25% off coupon?
Using the LCM, the first customer to receive both a shopping bag and a 25% off coupon is the 45th customer.
To find the first customer who will receive both a free shopping bag and a 25% off coupon, we need to find the least common multiple (LCM) of 15 and 9, since the shopping bags are given every 15th customer and the coupons every 9th customer.
Step 1: Find the prime factors of both numbers.
15 = [tex]3 * 5[/tex]
9 = [tex]3^2[/tex]
Step 2: Identify the highest power of each prime factor in both numbers.
3: [tex]3^2[/tex] (from 9)
5: [tex]5^1[/tex] (from 15)
Step 3: Multiply the highest powers of each prime factor together to find the LCM.
LCM(15, 9) =[tex]3^2 * 5^1[/tex] = [tex]9 * 5[/tex] = 45
So, the first customer who will receive both a free shopping bag and a 25% off coupon is the 45th customer.
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The probability that Cody will be first in the 50m backstroke Is 25%. What are the odds In favour of him being first?
Answer:
To find the odds in favor of Cody being first, we need to divide the probability of him winning (25%) by the probability of him not winning (75%).
Odds in favor of Cody winning = 25% / (100% - 25%) = 25% / 75%
Simplifying, we get:
Odds in favor of Cody winning = 1/3
Therefore, the odds in favor of Cody being first in the 50m backstroke are 1 to 2 (or 1:2).
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.
lim (x + x²)/(9 − 4x²)
x→[infinity]
To find the limit of (x + x²)/(9 − 4x²) as x approaches infinity, we can first try to apply l'Hospital's Rule, which states that if the limit of the ratio of the derivatives exists, then it is equal to the original limit.
However, in this case, a more elementary method is available: dividing both the numerator and denominator by the highest power of x.
1. Divide both the numerator and denominator by x²: lim (x/x² + x²/x²) / (9/x² - 4x²/x²) x→[infinity]
2. Simplify the expressions: lim (1/x + 1) / (9/x² - 4) x→[infinity]
3. As x approaches infinity, the terms with x in the denominator will approach 0: lim (0 + 1) / (0 - 4) x→[infinity]
4. Simplify the expression: (1) / (-4) The limit of (x + x²)/(9 − 4x²) as x approaches infinity is -1/4.
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0
What number does the point show?
OA.
B. 1
ن
413
OD.
OE
34
5
Đ
Answer:
3/4
Step-by-step explanation:
there are 4 spots and it is on the the third of them
please help 30 points
Answer & Step-by-step explanation:
To solve this problem, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In the triangle given, we can see that the lengths of the two shorter sides are 8 cm and 10 cm. We want to find the length of the hypotenuse.
Using the Pythagorean theorem, we can set up the equation:
a² + b² = c²
where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.
Substituting in the values we know, we get:
8² + 10² = c²
Simplifying:
64 + 100 = c²
164 = c²
Taking the square root of both sides, we get:
c = sqrt(164)
c ≈ 12.8062
Therefore, the length of the hypotenuse is approximately 12.8062 cm.
A local restaurant wants to expand its patio dining area. It has walls on two sides so it can only expand out to the North and East (2 directions). The current patio is 30 feet by 30 feet. They need to expand to cover 2500 square feet.
Answer:
65 feet
Step-by-step explanation:
Let x be the length of the expansion to the north, and y be the width of the expansion to the east.
The current patio has an area of 30 * 30 = 900 square feet.
The total area of the expanded patio will be 2500 square feet.
So, we need to find values of x and y that satisfy the following two conditions:
The area of the expanded patio is 2500 square feet:
xy = 2500
The expanded patio has walls on two sides, so it can only expand to the north and east:
x + 30 = y
We can solve the second equation for x:
x = y - 30
Substitute this expression for x in the first equation:
(y - 30)y = 2500
Simplifying this equation:
y^2 - 30y - 2500 = 0
We can solve for y using the quadratic formula:
y = (30 ± sqrt(30^2 + 4*2500)) / 2
y = (30 ± sqrt(10000)) / 2
y = (30 ± 100) / 2
Since y must be positive, we can ignore the negative solution:
y = (30 + 100) / 2 = 65
Substitute this value for y in the equation x + 30 = y:
x + 30 = 65
x = 35
Therefore, the expansion to the north should be 35 feet, and the expansion to the east should be 65 feet.
Emma brought $23. 75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4. 50 left over after buying these items
The cost of the brush is $ 1.75 , The cost of the paint set is $ 10.5 and
The cost of the sketchbook is $ 7
The total amount Emma has is $23.75
Let the cost of paint set = x
Cost of sketchbook = 2x/3
Cost of brush = (1/6)x
23.75 = x + 2x/3 + x/6 + 4.50
23.75 - 4.50 = (6x + 4x +x)/6
19.25 × 6 = 11x
x = 10.5
Cost of sketchbook = 2x/3
Cost of sketchbook = (2 × 10.5)/3
Cost of sketchbook = 7
Cost of brush = (1/6)x
Cost of brush = (1/6)10.5
Cost of brush = 1.75
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Dmitri wants to look at the relationship between room temperature and the etching rate each time he has etched a circuit board with cupric chloride. The data show a linear pattern with the summary statistics shown below: I = room temperature (degrees Celsius) y = etching rate (micrometers per minute) mean x = 20.9 y = 6.6 standard deviation 8₂ = 3 Sy = 0.7 r = 0.99 Find the equation of the least-squares regression line for predicting the etching rate from the room temperature. Round your entries to the nearest hundredth.
The equation of the least-squares regression line for predicting the etching rate from the room temperature is 1.77 + 0.23x.
How to calculate the valueThe least squares method is a form of mathematical regression analysis used to determine the line of best fit for a set of data, providing a visual demonstration of the relationship between the data points.
The equation of the least-squares regression line for predicting the etching rate from the room temperature is:
= 6.6 - 0.231 × 20.9 = 1.7721
y = 1.77 + 0.23x.
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the college of business was interested in comparing the attendance for three different class times for a business statistics class. the data follow. day 8:00 a.m. class 9:30 a.m. class 11:00 a.m. class monday 25 30 25 tuesday 30 32 30 wednesday 32 35 40 thursday 32 40 39 friday 35 33 30 what is the critical value of the statistic for testing the hypothesis of equal treatment means at the 0.05 significance level? multiple choice 3.84 4.46 1.96 6.94
The critical value of the statistic for testing the hypothesis of equal treatment means at the 0.05 significance level is approximately option (a) 3.84
To find the critical value of the statistic for testing the hypothesis of equal treatment means at the 0.05 significance level, we can use an analysis of variance (ANOVA test) test
First, we need to calculate the total sum of squares (SST), which represents the total variability in the attendance data:
SST = ∑∑(Xij - X..)2
= (25-31.83)2 + (30-31.83)2 + ... + (30-31.83)2
= 351.83
where Xij is the attendance for the ith day and jth class time, X.. is the grand mean attendance, and the summation is over all observations.
Next, we need to calculate the between-groups sum of squares (SSG), which represents the variability in the attendance data that is due to differences between the class times
SSG = (∑nj(X.j - X..)2) / k
= [(25-32.17)2 + (30-32.17)2 + ... + (30-32.17)2 + (25-32.17)2 + (30-32.17)2 + ... + (30-32.17)2 + (25-32.17)2 + (30-32.17)2 + ... + (40-32.17)2] / 3
= 189.5
where nj is the number of observations for the jth class time, k is the number of groups (i.e., class times), and X.j is the mean attendance for the jth class time
Finally, we can calculate the within-groups sum of squares (SSW), which represents the variability in the attendance data that is due to differences within each class time:
SSW = SST - SSG
= 351.83 - 189.5
= 162.33
The degrees of freedom for the ANOVA test are:
dfG = k - 1 = 3 - 1 = 2 (degrees of freedom for the between-groups sum of squares)
dfW = N - k = 15 - 3 = 12 (degrees of freedom for the within-groups sum of squares)
dfT = N - 1 = 15 - 1 = 14 (total degrees of freedom)
where N is the total number of observations.
The F-statistic for the ANOVA test is
F = (SSG / dfG) / (SSW / dfW)
= (189.5 / 2) / (162.33 / 12)
= 5.87
To find the critical value of the F-statistic for testing the hypothesis of equal treatment means at the 0.05 significance level, we can look it up in an F-distribution table with dfG = 2 and dfW = 12. At the 0.05 level of significance, the critical value of the F-statistic is approximately 3.84.
Therefore, the correct option is (a) 3.84
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A, B & C lie on a straight line.
D, C & E lie on a different straight line.
Angle
y
= 119° and angle
z
= 61°.
Work out
x
, explaining each stage of your working in the comment box.
Answer:
The answer for the value of x is 122°
20 points!!Complete the table by finding the circumference and area of a circle with a radius of 279 inches. Substitute 3.14 for pi. Express your answers to the hundredths place.
fill in the blanks
thx
What is the distance between the 2 points? (round to the nearest tenth)
Answer:
AB = √(2^2 + 5^2) = √(4 + 25) = √29 = 5.4
The dollar value v (t) of a certain car model that is t years old is given by the following exponential function.
v (t) = 18,500 (0.84)'
Find the value of the car after 5 years and after 11 years.
Round your answers to the nearest dollar as necessary.
The initial value of the car will be $18,500 initial value and a $2717.85 value after 11 years.
We are Given that the dollar value v (t) of a certain car model that is t years old is given by the following exponential function .
The initial value will be at t= 0,
v (t) = 18,500 (0.84)'
v(t) = 18,500 x (0.84)⁰
v(t) = $18,500
The value of the car after 12 years will be
v(t) = 18,500 (0.84)^11
v(t) = $2717.85
Therefore, the car will have a $18,500 initial value
$2717.85 value after 11 years.
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2. What is the value of x in the equation x² = 64?
A. x = ±8
B. x =
±16
C. X =
32
D. x = 128
Answer:
Step-by-step explanation:
To solve for x in the equation x² = 64, we need to take the square root of both sides of the equation. However, we need to consider both the positive and negative square root because the square of both a positive and negative number results in the same positive value. Therefore:
x² = 64
√x² = ±√64
x = ±8
So the solutions to the equation x² = 64 are x = 8 and x = -8.
Answer: Your answer is B X = 8, -8
Hope it helped :D
) a new machine is known to reduce pollutants. however, it is expensive. the epa estimates that one-third of plants has this new machine. what is the probability that fewer than 11% of the plants in the random sample own this machine?
The probability that fewer than 11% of the plants in the random sample on this machine is 0.0823.
Given:
The likelihood of a plant having a modern machine is 1/3.
To discover:
The likelihood is that less than 11% of the plants in an arbitrary test have an unused machine.
Let X be the number of plants
out of n plants within the test that has the modern machine.
Since each plant features a likelihood of 1/3 of having the machine, X follows binomial dissemination with parameters n and p=1/3.
We have to discover
P(X < 0.11n).
Utilizing the coherence adjustment, we have:
P(X < 0.11n) = P(X <= 0.10n)
= P(Z <= (0.10n - np)/√(np(1-p))),
where Z may be a standard typical arbitrary variable
Since n isn't given, able to accept a large sufficient test measure such that the binomial dispersion can be approximated by a normal distribution.
A commonly utilized run show of thumb is that this estimation is sensible in case both np and n(1-p) are at the slightest 10.
Since n isn't given, we cannot affirm whether this condition is met or not, but we are going to accept it for the reason of the arrangement.
Utilizing np= n/3 and (1-p)n= (2/3)n, we have:
P(Z <= (0.10n - n/3)/√(n/3 * (2/3)n))
= P(Z <= (0.10 - 1/3)/√(2/9 * n))
= P(Z <= -1.39/√(n))
Employing a standard normal table or calculator, we will discover that P(Z <= -1.39) = 0.0823.
In this manner,
P(X < 0.11n) = P(Z <= -1.39/√(n)) = 0.0823.
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