Answer:
Step-by-step explanation:
To solve this problem, we need to use the formula for compound interest:
A = P*e^(rt)
where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).
For Sophie's account, we have:
P = $92,000
r = 6 1/8% = 0.06125 (as a decimal)
t = 14 years
A = 92000*e^(0.06125*14)
A = $219,499.70 (rounded to the nearest cent)
For Damian's account, we have:
P = $92,000
r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)
t = 14*12 = 168 months
A = 92000*(1+0.005521)^168
A = $288,947.46 (rounded to the nearest cent)
Now we can subtract Sophie's final amount from Damian's final amount to find the difference:
Difference = $288,947.46 - $219,499.70
Difference = $69,447.76
Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.
Construct a 97 percent confidence interval around a sample mean of 31. 3 taken from a population that is not normally distributed with a standard deviation of 7. 6 using a sample of size 40?
Also for an error calculation of 5, what sample size should we consider?
The sample size is 12 with an error calculation of 5 if 97% of the confidence interval is around a sample mean of 31. 3.
Percent confidence = 97
Sample mean = 31. 3
Standard deviation = 7. 6
Sample size = 40
Error calculation = 5
The formula for a confidence interval using the t-distribution is:
CI = x ± tα/2 * (s/√n)
CI = 31.3 ± 2.423 * (7.6/√40)
CI = 31.3 ± 3.940
CI = (27.36, 35.24)
The population mean with an error of 5,
n = (Zα/2 * σ / E)^2
Assuming a 95% confidence level, the sample size is,
n = (1.96 * 7.6 / 5)^2
n = 11.69
Therefore we can conclude that the sample size is 12 with an error calculation of 5.
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Find the trigonometric ratios and the measures of the angles or the unknown lengths of these right tiangles, Round off angles to the nearest whole degree, trigonometric values to four decimal places, and lengths of sides to two decimal places.)
The value of x= 10.2.
What is trignometric ratios?This is the boundary or contour length of a 2D geometric shape.
Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
Hence, The value of x= 10.2.
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In a Healthy Jogging event, a few hundred participants were expected to jog 7 800 000 metres altogether. They had jogged 25 000 metres in the first few minutes. How many thousands must be added to 25 000 to make 7 800 000?
we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.
Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.
Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.
We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-
7800000-25000= 7775000m
hence, to make 7800000 from 25000 we have to add 7775000.
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The question may have one or more than one option correct
[tex]\displaystyle\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx[/tex]
The correct option is/are
A) 22/7 - π
B) 2/105
C) 0
D) 71/15 - 3π/2
Answer:
To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:
[tex]\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}[/tex]
Using partial fractions, we can write:
[tex]\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}[/tex]
Multiplying both sides by (x+i)(x-i), we get:
[tex]x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)[/tex]
Substituting x=i, we get:
[tex]i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ci + 2B[/tex]
Substituting x=-i, we get:
tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ai + 2D[/tex]
Substituting x=0, we get:
[tex]0 = Bi + Di[/tex]
Substituting x=1, we get:
[tex]0 = A+B+C+D[/tex]
Solving these equations simultaneously, we get:
A = -22/7 + π
B = 0
C = 22/7 - π
D = -2/5
Therefore, the integral can be written as:
[tex]\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx[/tex]
Integrating each term separately, we get:
[tex]\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)[/tex]
[tex]\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)[/tex]
[tex]\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)[/tex]
Therefore, the correct options are:
A) [tex]\pi-\frac{22}{7}[/tex]
B) [tex]\frac{2}{105}[/tex]
C) 0
D) [tex]\frac{71}{15}-\frac{3\pi}{2}[/tex]
Using the standard domain for the sine function, which of the following expressions corresponds to the (1 point) composite function
sin(arccosx)
? Review Guidelines: If you guessed the answer to this question, or did not answer it correctly, go back and review the composition of trigonon Composition of Trigonometric Functions lesson.
(0pts) x 2
+1
(0pts) x 2
−1
(0pts) 1−x
(1pt)
1−x 2
The composite function -11-x^2 can be written in terms of the standard domain for the sine function as sin[−11−x2]. This function can be evaluated by substituting the value of x into the expression.
To do this, simply substitute the value of x into the equation:[tex]sin[-11-x^2][/tex]and evaluate the result. For example, if x=5, the equation would be sin[-11-5^2], which would evaluate to sin(-26).
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find the percent of the discount: a $30 board game on sale for 21
well, we know the discount is just 30 - 21 = 9, so hmm if we take 30(origin amount) to be the 100%, what's 9 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 30 & 100\\ 9& x \end{array} \implies \cfrac{30}{9}~~=~~\cfrac{100}{x} \\\\\\ 30x=900\implies x=\cfrac{900}{30}\implies x=30[/tex]
What is the first step in
solving this equation?
4|2-v|-3= 25
The Answer: The first step is Rearranging the Equation
v=9
v=-5
Step-by-step explanation:
STEP
1
:
Rearrange this Absolute Value Equation
Absolute value equalitiy entered
4|-v+2|-3 = 25
Another term is moved / added to the right hand side.
4|-v+2| = 28
STEP
2
:
Clear the Absolute Value Bars
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is 4|-v+2|
For the Negative case we'll use -4(-v+2)
For the Positive case we'll use 4(-v+2)
STEP
3
:
Solve the Negative Case
-4(-v+2) = 28
Multiply
4v-8 = 28
Rearrange and Add up
4v = 36
Divide both sides by 4
v = 9
STEP
4
:
Solve the Positive Case
4(-v+2) = 28
Multiply
-4v+8 = 28
Rearrange and Add up
-4v = 20
Divide both sides by 4
-v = 5
Multiply both sides by (-1)
v = -5
Which is the solution for the Positive Case
STEP
5
:
Wrap up the solution
v=9
v=-5
If you walk for 1. 5 hours and at 3mph then for the next 0. 5 hours how fast do you run for an average of 4 mph
In order to have an average speed of 4 mph for the entire trip, you would need to run at a speed of 7 mph for the next 0.5 hours after walking for 1.5 hours at 3 mph.
Let's begin by calculating the total distance covered during the entire trip, which is:
distance = (time walked) x (walking speed) + (time ran) x (running speed)
We know that the time walked is 1.5 hours and the walking speed is 3 mph, so the distance covered during walking is:
distance walked = (time walked) x (walking speed) = 1.5 x 3 = 4.5 miles
We also know that the average speed for the entire trip is 4 mph, and that the total time for the trip is 2 hours. Therefore, the distance covered during the entire trip is:
distance = (average speed) x (total time) = 4 x 2 = 8 miles
So the distance covered during running is:
distance ran = distance - distance walked = 8 - 4.5 = 3.5 miles
Now we can use the formula for average speed:
average speed = total distance / total time
To find the running speed, we need to solve for the running time, which is:
time ran = distance ran / running speed
Substituting this expression into the average speed formula, we get:
4 = (distance walked + distance ran) / (1.5 + time ran)
4 = (4.5 + 3.5) / (1.5 + distance ran / running speed)
Simplifying this expression, we get:
1.5 + distance ran / running speed = 2
distance ran / running speed = 0.5
Substituting the values we calculated, we get:
3.5 / running speed = 0.5
Solving for the running speed, we get:
running speed = 3.5 / 0.5 = 7 mph
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b) The nearest-known exoplanet from earth is 4.25 light-years away.
About how many miles is this?
Give your answer in standard form.
The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
Hence, The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
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how can you make different trapezoids given two sides and one angle? draw trapezoids with side lengths of 8 yd and 5 yd and an angle of 45
A. you can make the parallel sides of each trapezoid different
B. you can make all four sides of each trapezoid different.
C. you can make all four angles of each trapezoid different.
D. all trapezoids will be the same given two sides and an angle
You can make all four sides of each trapezoid different. Since a trapezoid has four sides, we can change the length of each of the remaining two sides to create different trapezoids. option B is correct.
What is a trapezoid?A trapezoid is a four-sided polygon with two parallel sides and two non-parallel sides. It is sometimes called a trapezium outside of North America. The parallel sides of a trapezoid are called bases, while the non-parallel sides are called legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid is calculated by taking the average of the bases and multiplying it by the height. Trapezoids are commonly encountered in geometry and are used in many real-world applications, such as in construction and engineering.
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Due today help pls!!!!
Answer:
32.1m
Step-by-step explanation:
[tex]2\pi r*(\frac{x}{360})=[/tex] arc length of sector of a circle
2 radii + arc length of a sector of a circle= perimeter of the sector
x=90 degrees
r=9
substitute values to find the arc length
[tex]2(9)*\pi *(\frac{90}{360} )= arc length\\arclength=14.1\\[/tex][tex]14.1+2(9)=32.1[/tex]
a
49⁰
Find the measure of a.
127⁰
72⁰
Answer:
112°
Step-by-step explanation:
Finding the unknown angle in a quadrilateral:
Sum of all angles of a quadrilateral = 360
a + 49 + 72 + 127 = 360
a + 248 = 360
a = 360 - 248
a = 112°
A bag contains 8 green cubes, 12 black cubes and 16 white cubes. What is the ratio of green to black to white cubes in its simplest form?
Answer:
Total number bags is 36
green cubes is 8white cubes is 16Black cubes is 121:2:3 the answer
PLS HELP MEEEEEEE ASAP
Answer:
[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]
Step-by-step explanation:
[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]
Each side has length of a?
[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]
Remove brackets of 3(2a+5b)
Write the equation of the line that passes through the points (- 9, - 9) and (- 8, 1) Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line
The point-slope form of the line equation that passes through the points (- 9, - 9) and (- 8, 1) is equals to the y= 10x + 81.
The standard equation of a line is, y = mx + b where m is the slope and b is the y-intercept. This is a very useful form of the linear equation when comparing lines. We have to determine the equation of the line that passes through the points (- 9, - 9) and (- 8, 1). First we determine the value of slope of line. The formula for slope of line that passing through the points (x₁,y₁),(x₂,y₂) is [tex]m = \frac{y_2 - y_1}{x_2- x_1} [/tex]
here, x₁ = -9, y₁ = -9 , x₂ = -8, y₂ = 1, so
[tex]m = \frac{1-(-9)}{-8-(-9)} = \frac{10}{1} = 10[/tex]
The point-slope form for line passing through points (x₁,y₁),(x₂,y₂) is y − y₁ = m(x − x₁)
=> y - (-9) = 10( x -(-9))
=> y + 9 = 10( x + 9)
=> y + 9 = 10x + 90
=> y = 10x + 81
Hence required equation is y = 10x + 81.
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Suppose you roll a special 37-sided die. What is the probability that one of the following numbers is rolled? 35 | 25 | 33 | 9 | 19 Probability = (Round to 4 decimal places) License Points possible: 1 This is attempt 1 of 2.
The probability of rolling one of these five numbers is 5/37.
Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:
35 | 25 | 33 | 9 | 19.
The total number of sides of a die is 37. As a result, there are 37 numbers in the die.
Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.
Therefore, the probability of rolling any of these numbers is:
1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37
So, the probability of rolling one of these five numbers is 5/37.
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helpppppppppppppppppp
1. how long is the hall which has a perimeter if 3480 cm and 300cm wide?
2. joe walks across the rotonda and travels 400meters, how many more meters will a car travel around it than the distance the pedestrian walk?
3.father will fence the rectangular yard with a length of 120m and a width of 100m,
how many meters of wire will her use for the fence?
Answer:
(3480 - 600)/2 = 1440cm
Step-by-step explanation:
Look at this series: 7, 10, 8, 11, 9, 12,. What number should come next?
At the book store, you purchased some $3 clearance mystery books and $8 regular-priced science fiction books. How many of each did you buy if you spent a total of $77?
Answer:
we bought 12 $3 clearance mystery books and 5 $8 regular-priced science fiction books.
Step-by-step explanation:
What is the width of a rectangle with the length of 7/8 feet and an area of 5 ft
The width of the rectangle whose length of one side is 7.8 feet and the area enclosed is 5 feet is given as 40/7 feet.
Area refers to the field on the ground which is enclosed by the closed polygon. It is defined within the boundary of the closed polygon. Open polygons cannot have a deterministic area. In the given problem, the length of one side is 7/8 feet and the area of the rectangle is 5 feet.
It is known that area of rectangle is equal to the product of its length and its width.
∴Area of rectangle = Length × width
⇒ 5 = 7/8 × width
⇒ width = (5 × 8)÷7 = 40/7 feet
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[Scaling PDFs] Suppose that X and Y are the sampled values of two different audio signals. The mean and variance of an audio signal are uninteresting: the mean tells you the bias voltage of the microphone, and the variance tells you the signal loudness. For this reason, the audio signals X and Y are pre-normalized so that E[X] = E[Y] = 0 and Var(X) = Var(Y) = 1. An audio signal Z is said to be "spiky" if P{|Z| > 302} > 0.01, i.e., one-in-hundred samples has a large amplitude. (a) Suppose that X is a uniformly distributed random variable, scaled so that it has zero mean and unit variance. (1) What is P{|X|> ox}? (2) What is P{[X] > 30x}? (3) Is X spiky? Be sure to consider both positive and negative values of X. (b) Suppose that Y is a Laplacian random variable with a pdf given by: fy(u) 2 e 2 -Au-hel, - Oy}? (2) What is P{İY| > 30y}? (3) Is Y spiky? Be sure to consider both positive and negative values of Y.
0, which is less than 0.01.
Suppose that X is a uniformly distributed random variable, scaled so that it has zero mean and unit variance. (1) What is P{|X|> ox}? (2) What is P{[X] > 30x}? (3) Is X spiky? Be sure to consider both positive and negative values of X.
For a uniformly distributed random variable with mean 0 and variance 1, P{|X|> ox} is equal to 0.5. (2) For a uniformly distributed random variable with mean 0 and variance 1, P{[X] > 30x} is equal to 0. (3) X is not spiky since P{|X| > 30x}
0.000045, which is greater than 0.01.
Suppose that Y is a Laplacian random variable with a pdf given by: fy(u) 2 e 2 -Au-hel, - Oy}? (2) What is P{İY| > 30y}? (3) Is Y spiky? Be sure to consider both positive and negative values of Y.
Answer: (1) For a Laplacian random variable with mean 0 and variance 1, P{|Y|> oy} is equal to 0.5. (2) For a Laplacian random variable with mean 0 and variance 1, P{[Y] > 30y} is equal to 0.000045. (3) Y is spiky since P{|Y| > 30y}
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If you are given the opposite side and hypotenuse, which trig function should you us?
A. Contangent
B. Cosine
C. Tangent
D. Sine
Answer:D
Step-by-step explanation:
The formula for sine is opposite/hypotenuse. This is the only formula that you can use with the given information.
Interpret the IQR and median in the context of the data set.
Interpret the IQR in the context of the data set. Select the correct choice below, and fill in the answer box to complete your choice.
(Type a whole number.)
A. It means the length where half of the garter snakes are shorter and the other half are longer. The IQR is inches.
OB. The length of garter snake that occurs the most frequently is inches.
OC. The difference between the longest garter snake and the shortest garter snake is
OD. The range of the middle 50% of the lengths of gartersnakes is
inches.
inches.
Length of a Garter Snake (in.)
10 15 20 25
An interpretation of the IQR and median in the context of the data set include the following: D. The range of the middle 50% of the lengths of garter snakes is 4 inches.
How to interpret the box-and-whisker plot?Based on the information provided about the given box-and-whisker plot (see attachment), the five-number summary for the given data set include the following:
Minimum = 10.First quartile = 24.Median = 27.Third quartile = 29.Maximum = 30.What is a range?In Mathematics, the range of a data set can be calculated by using this mathematical expression;
Range = Highest number - Lowest number
Range = 30 - 10
Range = 20
Interquartile range (IQR) = Q₃ - Q₁
Interquartile range (IQR) = 29 - 24
Interquartile range (IQR) = 5
Middle 50% of the lengths = 20/5 = 4 inches.
In conclusion, the median is the middle of the data set and it means 50 percent of the lengths of the garter snakes are greater and 50 percent are less than 27 inches.
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if the area of the quadrilateral ABCS is 924cm^2 and the length of the diagonal AC is 33cm,find the sum of lengths of the perpendicular from points B and D to AC.
please answer with full steps asap
3BE² + 3DF²- (2AC²- AB) is the answer of the following question
The calculation is as follows
Let E and F be the feet of the perpendiculars from B and D, respectively, to AC. We can use the fact that the area of a quadrilateral is equal to half the product of the diagonals multiplied by the sine of the angle between them to find the length of the diagonal BD.
Since ABCS is a quadrilateral, we have:
Area of ABCS = (1/2) * AC * BD * sin(angle between AC and BD)
Substituting the given values, we get:
924 = (1/2) * 33 * BD * sin(angle between AC and BD)
sin(angle between AC and BD) = 924 / (16.5 * BD)
Now, consider triangles ABC and ACD. Using the Pythagorean theorem, we can write:
AB² + BC² = AC² (1)
CD²+ BC² = AC² (2)
Adding equations (1) and (2), we get:
AB² + 2BC²+ CD²= 2AC²
Substituting AC = 33 and rearranging, we get:
BC² = (2AC²- AB² - CD²) / 2
We can also write:
BE²= AB²- AE² (3)
DF² = CD²- CF²(4)
Adding equations (3) and (4), we get:
BE² + DF²= AB²+ CD² - AE²- CF²
Substituting BC²from earlier, we get:
BE²+ DF² = 2AC² - BC²- AE²- CF²
We want to find BE + DF. Squaring both sides of equation (3), we get:
BE²= AB² - AE²
AE²= AB²- BE²
Similarly, squaring both sides of equation (4), we get:
DF²= CD²- CF²
CF²= CD² - DF²
Substituting these expressions into the equation for BE²+ DF², we get:
BE²+ DF² = 2AC² - BC² - (AB² - BE²) - (CD²- DF²)
Simplifying, we get:
BE² + DF²= 2AC² - BC²- AB²- CD² + 2BE² + 2DF²
Collecting like terms, we get:
BE²+ DF²- 2BE² - 2DF²= 2AC²- BC² - AB² - CD²
Simplifying, we get:
BE²- DF² = 2AC²- BC²- AB²- CD²- 2BE² - 2DF²
Substituting the values we know, we get:
BE²- DF²= 2(33)²- BC²- AB² - CD²- 2BE²- 2DF²
Rearranging, we get:
3BE²+ 3DF² - BC²- AB²- CD²= 2(33)² - 924
Substituting BC^2 from earlier, we get:
3BE²+ 3DF² - (2AC²- AB)
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approximate the definite integral using the trapezoidal rule and simpson's rule. compare these results with the approximation of the integral using a graphing utility. (round your answers to four decimal places.) 3 1 ln(x) dx, n=4
Trapezoidal Simpson's Graphing Utility
From the graphing utility, we get the value of the integral as, Integral = 0.7206 Comparing the values of the integrals obtained from Trapezoidal rule, Simpson's rule and graphing utility, we find that the integral value obtained from the graphing utility is closest to the Simpson's rule.
We are given the definite integral ∫31ln(x)dx and we are required to approximate the integral using the trapezoidal rule and Simpson's rule. Also, we are supposed to compare these results with the approximation of the integral using a graphing utility using n=4.Trapezoidal Rule. The trapezoidal rule for numerical integration is a method to approximate the definite integral using linear interpolation.
This rule approximates the definite integral by dividing the total area into trapezoids. The formula for trapezoidal rule is given by:(Image attached)Here, a = 3 and b = 1The value of h can be calculated as follows;h=(b−a)/nh=(3−1)/4=0.5We need to calculate the values of f(1), f(1.5), f(2), f(2.5), f(3) using n = 4(Image attached)The value of integral using the trapezoidal rule is,Integral = 0.7201.
Simpson's rule is used to approximate the value of definite integral. Simpson's rule involves approximating the integral under the curve using the parabolic shape. This is done by dividing the area under the curve into small sections and then approximating each section with a parabolic shape. The formula for Simpson's rule is given as:(Image attached)Here, a = 3 and b = 1
The value of h can be calculated as follows;h=(b−a)/nh=(3−1)/4=0.5We need to calculate the values of f(1), f(1.5), f(2), f(2.5), f(3) using n = 4(Image attached)The value of integral using the Simpson's rule is,Integral = 0.7200Comparing with Graphing UtilityIntegral = 0.7201 (from Trapezoidal rule)Integral = 0.7200 (from Simpson's rule).
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find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7.
The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.
Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:
Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.
Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.
Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.
Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.
The numbers of the form 35n in the interval [1000, 9999] are
1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.
To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.
Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is
9000 - 399 - 204 + 285 = 4680.
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. Mr. Govind coaches cricket at a primary school. In order to not disturb the classes, he takes the children from the class, 6 at a time. During the 45 minutes' session, 2 children bat at a time. All children in the session get an opportunity to bat and every child bats for the same amount of time. How many minutes does each pair get to bat?
Each pair of children gets to bat for 7.5 minutes.
How to find out how much time each pair gets to bat ?To find out how much time each pair gets to bat, we need to divide the total session time by the number of pairs of children who bat.
Number of pairs of children who bat = 6 groups x 1 pair/group = 6 pairs
Total time for the session = 45 minutes
Time per pair of children who bat = Total time / Number of pairs of children who bat
= 45 minutes / 6 pairs
= 7.5 minutes per pair
Therefore, each pair of children gets to bat for 7.5 minutes.
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the nutty professor sells cashews for $7.70 per pound and brazil nuts for $4.80 per pound. how much of each type should be used to make a 27 pound mixture that sells for $6.41 per pound?
The amount that each type would be 11.87 lbs of cashews and 15.13 lbs of brazil nuts
1. First, find the total cost of 27 lbs of the mixture: 27 lbs x $6.41/lb = $171.07.
2. Next, find the cost of cashews and brazil nuts in the mixture. Cashews cost $7.70/lb and brazil nuts cost $4.80/lb.
3. Subtract the cost of the brazil nuts from the total cost of the mixture: $171.07 - (27 lbs x $4.80/lb) = $105.27.
4. Divide the cost of the cashews ($105.27) by the cost of one pound of cashews ($7.70): $105.27/$7.70 = 13.66 lbs.
5. Subtract the number of pounds of cashews (13.66) from the total pounds of the mixture (27) to find the number of pounds of brazil nuts: 27 - 13.66 = 15.13 lbs.
6. Therefore, the mixture should contain 11.87 lbs of cashews and 15.13 lbs of brazil nuts.
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