A bag contains 3 red, 4 black and 2 white balls. what is the probability of drawing a red ball and then a white ball, if each ball is returned to the bag immediately after it is drawn? 2/27 1/9 1/3 4/27 2/9
If a borrower obtains an interest-only loan of $112,500 at an annual interest rate of 6%, what is the monthly interest payment (rounded to the nearest $1)?
Which equation could be used to calculate the sum of the geometric series? 1/4+2/9+4/27+8/81+16/243?
Answer: Sum of the geometric series will be [tex]\frac{763}{972}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\frac{1}{4}+\frac{2}{9}+\frac{4}{27}+\frac{8}{81}+\frac{16}{243}[/tex]
Here,
[tex]a=\frac{2}{9}\\\\r=\frac{a_2}{a_1}\\\\r=\frac{\frac{4}{27}}{\frac{2}{9}}=\frac{4}{27}\times \frac{9}{2}=\frac{2}{3}\\\\n=4[/tex]
As we know the formula for "Sum of n terms in geometric series ":
[tex]S_n=\frac{a(1-r^n)}{1-r}\\S_n=\frac{\frac{2}{9}(1-\frac{2}{3}^4)}{1-\frac{2}{3}}\\S_n=\frac{130}{243}[/tex]
So, Complete sum will be
[tex]\frac{130}{243}+\frac{1}{4}=\frac{520+243}{972}=\frac{763}{972}[/tex]
Hence, Sum of the geometric series will be [tex]\frac{763}{972}[/tex]
Evaluate 8- m/n+p ^2 when m=8 n=2 p=7
Answer: 53.
Step-by-step explanation:
The given expression : [tex]8-\dfrac{m}{n}+p^2[/tex]
To find : The value of the above expression for the values m=8, n=2 and p=7.
For that , we just substitute the gives values m=8, n=2 and p=7 in the above expression by using Substitution property , we get
[tex]8-\dfrac{8}{2}+(7)^2[/tex]
Simplify,
[tex]=8-4+49[/tex]
[tex]=4+49=53[/tex]
Hence, the correct value of the given expression when m=8 n=2 p=7 is 53.
Simplify the square root of 48 ( this can be expressed as √48)
A group consists of 6 men and 5 women. three people are selected to attend a conference. in how many ways can 3 people be selected from this group of 11? in how many ways can 3 men be selected from the 6 men? find the probability that the selected group will consist of all men.
1.
[tex] \displaystyle
\binom{11}{3}=\dfrac{11!}{3!8!}=\dfrac{9\cdot10\cdot11}{2\cdot3}=165 [/tex]
2.
[tex] \displaystyle\binom{6}{3}=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20 [/tex]
3.
[tex] |\Omega|=165\\
|A|=20\\\\
P(A)=\dfrac{20}{165}=\dfrac{4}{33}\approx12\% [/tex]
The domain of {(x, y): y = 2x² + 1 is
Answer:
Domain: (- ∞, ∞)
Explanation:
The equation y = 2x² + 1 is a somewhat narrow parabola translate up 1 unit on the y-axis from the origin (0, 0). The domain of a graph indicates which x-values the diagram can potentially reach, or how far it can travels on the x-axis.
Because it is a parabola, it goes infinitely in both directions of the x-axis. Therefore, its domain is (-∞ ,∞)
Final answer:
The domain of the function y = 2x² + 1 is all real numbers, which is expressed as [tex]\( (-\infty, +\infty) \)[/tex]
Explanation:
The domain of a function refers to the set of all possible input values for which the function is defined. In the case of the function [tex]\( y = 2x^2 + 1 \)[/tex], it is a quadratic function, meaning it is defined for all real numbers [tex]\( x \).[/tex]
The function[tex]\( y = 2x^2 + 1 \)[/tex] involves squaring [tex]\( x \)[/tex], which can result in any real number. Since there are no restrictions on the values that[tex]\( x \)[/tex] can take, the domain of this function is all real numbers. Mathematically, we denote this domain as[tex]\( (-\infty, +\infty) \)[/tex].
This implies that for any real number you substitute in for [tex]\( x \)[/tex], the function [tex]\( y = 2x^2 + 1 \)[/tex] will produce a corresponding real number for [tex]\( y \).[/tex] There are no values of [tex]\( x \)[/tex] for which the function becomes undefined or non-existent.
Graphically, this function represents a parabola that opens upwards, covering all real values of [tex]\( x \)[/tex] along the x-axis. Therefore, the domain encompasses the entire real number line without any gaps or exclusions.
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 115 grams of a radioactive isotope, how much will be left after 3 half-lives? Use the calculator provided and round your answer to the nearest gram.
After 3 half-lives, approximately 14 grams of the radioactive isotope will be left.
We have,
To calculate the remaining mass of a radioactive isotope after a certain number of half-lives, we can use the formula:
Remaining Mass = Initial Mass * (1/2)^(Number of Half-Lives)
Given:
Initial Mass = 115 grams
Number of Half-Lives = 3
Substituting the values into the formula, we get:
Remaining Mass = 115 * (1/2)^3
Calculating this expression:
Remaining Mass = 115 * (1/2)³
Remaining Mass = 115 * (1/8)
Remaining Mass = 14.375
Rounding to the nearest gram, the remaining mass is approximately 14 grams.
Therefore,
After 3 half-lives, approximately 14 grams of the radioactive isotope will be left.
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The equation of the line through ab *write your answer in slope-intercept form
A certain website averages 4.9 hours of downtime per month with a standard deviation of 0.5 hours. In April, it had 3.5 hours of downtime. What z-score does the 4.5 correspond to?
Alexis and tasha challenge each other to a typing test. Alex typed 54 words in one minute which was 123% of what tasha typed. how many words did tasha type in one mintue
If you were to add the length of all the 3/8 pieces which are 4 (number of pieces) what would be the total length
To find the total length of four 3/8-inch pieces, you multiply the length of one piece (3/8 inch) by the number of pieces (4), which equals 1.5 inches.
To calculate the total length of all the 3/8-inch pieces, we multiply the length of one piece by the number of pieces, which is 4. The mathematical expression for this is:
Total length = length of one piece x number of pieces
Total length = 3/8 x 4
To perform the multiplication, multiply the numerators and then the denominators:
Total length = (3 x 4)/(8 x1)
Total length = 12/8 inches
Now, simplify the fraction by dividing the numerator and the denominator by the greatest common divisor, which is 4:
Total length = (12/4)/(8/4)
Total length = 3/2 inches
And since 3/2 inches is equal to 1.5 inches, the total length of all four pieces is 1.5 inches.
If f is a function such that f(b)-f(a)/b-a=2, then which of the following statements must be true?
20 POINTS!
Yes or No?
Answer:
yes it is
Step-by-step explanation:
A regular pentagonal prism has 9-cm base edges. A larger, similar prism of the same material has 36-cm case edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller prism? A)volume B) weight
Solve the problem. 13) from the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. how far apart are the cars? round your answers to the nearest 0.1 ft.
The problem is about finding the distance between the cars using the angles of depression and the height of the cliff. Calculate individual horizontal distances first and then find their difference which gives us the distance between the cars.
Explanation:This problem can be solved using trigonometry. We've a 1000-foot cliff and a valley below where the two cars are located. From the edge of the cliff, if we draw two lines of sight to the cars, we can get two right triangles. The angles of depression to the cars are 21° and 28°, which are the angles between these lines of sight and a horizontal line.
We can use the tangent of these angles, which is the ratio of the opposite side (the vertical distance from the cliff to the cars) and the adjacent side (the horizontal distance from the cliff baseline to the cars). We know the vertical distance - it's 1000 ft (height of the cliff). So, we can calculate the horizontal distances (D1 and D2) to the cars as D1 = 1000/tan(21°) and D2 = 1000/tan(28°) respectively.
The difference between D1 and D2 will give the distance between the cars.
The calculations might give the distance in decimals, and the problem asks to round the answer to the nearest 0.1 ft.
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If x varies directly with y and x=3.5 when y=14 find x when y=18
Which graph represents the function g(x)=x−1−−−−−√+1 ?
Answer:
First graph
Step-by-step explanation:
Given function,
[tex]g(x)=\sqrt{x-1}+1[/tex]
∵ The point from which the graph of the function passes through will be satisfy the function,
In the first graph,
Graph is passing through (1, 1), (5, 3) and (10, 4),
[tex]1=\sqrt{1-1}+1[/tex]
[tex]3=\sqrt{5-1}+1[/tex]
[tex]4=\sqrt{10-1}+1[/tex]
So, all points (1, 1), (5, 3) and (10, 4) satisfy the function,
In the second graph,
Graph is passing through (-1, -1), (3,1) and (8,2),
Since,
[tex]-1\neq \sqrt{-1-1}+1[/tex]
So, all points of graph 2 do not satisfy the function,
In the third graph,
Graph is passing through (1, -1), (5, 1) and (10, 2),
[tex]-1\neq \sqrt{1-1}+1[/tex]
So, all points of graph 3 do not satisfy the function,
In the fourth graph,
Graph is passing through (-1, 1), (3, 3) and (8, 4),
[tex]1\neq \sqrt{-1-1}+1[/tex]
So, all points of graph 4 do not satisfy the function
Please help! Vectors and angles
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree
We have been given that a ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157°.
Further we have been given that current has a velocity of 5 knots along a bearing of 213°.
Therefore, angle between the direction of ship and direction of current will be
[tex]\theta = 213 - 157 = 56^{0}[/tex]
We can find the magnitude of resultant by using parallelogram law of vectors.
[tex]R=\sqrt{P^{2}+Q^{2}+2PQcos(\theta)}[/tex]
Upon substituting [tex]P=22, Q = 5 \text{ and }\theta = 56[/tex] in this formula, we get
[tex]R=\sqrt{22^{2}+5^{2}+2\cdot 22\cdot 5cos(56)}\\ R=\sqrt{484+25+220\cdot0.55919}\\ R=\sqrt{632.0224}\\ R=25.14 \text{ knots}[/tex]
Therefore, resultant velocity of the ship is 25.14 knots.
We find the angle of resultant from P, that direction of ship using the formula
[tex]\alpha = arctan(\frac{Qsin(\theta)}{P+Qcos(\theta)})[/tex]
Upon substituting the values, we get
[tex]\alpha = arctan(\frac{5sin(56)}{22+5cos(56)})\\ \alpha = arctan(\frac{4.14518}{24.79596})\\ \alpha = arctan(0.16717)\\ \alpha = 9.49^{0}[/tex]
Therefore, bearing of the resultant is [tex]157+9.49 = 166.49^{0}[/tex]
Hence, option (A) is the correct choice!
WHERE MY MATH FOLK AT?!?!
A cylindrical container, which will be used to collect oil, has a circumference of 15.5 in. and a height of 8 in.
Which estimate best approximates the amount of oil the container can hold?
-6(14-7) healppppp plzzzz
WILL GIVE BRAINLIEST... HELP ASAP!!!!!!
1. Circle A with center at (3, 4) and radius 2 is similar to circle B with center at (−4, −5) and radius 3. Below is an incorrect informal argument for proving two circles are similar:
Step 1 Translate circle B to the right 9 units and up 7 units to form concentric circles.
Step 2 Dilate circle B to be congruent to circle A using scale factor of k = r sub two over r sub one equals two over three
Step 3 When an object is dilated, the dilated object is similar to the pre-image, thus the two circles are similar.
What is the first incorrect step, and how can it be fixed?
A. All steps are correct
B. Step 1, translate circle B to the right 7 units and up 9 units
C. Step 2, use scale factor of K= r^2/r^1=3/2
D. Step 3, replace dilated with translated.
An image of two concentric circles is shown with r2 = 8 and r1 = 3:
2. Image shows a pair of concentric circles. The radius of the smaller circle is r sub 1 and the radius of the second is r sub 2.
In order to prove the two circles are similar, the radius r1 was increased to make the circles congruent. What is the scale factor used in the above image?
A. k=8/3
B. K=3/8
C. K=1/5
D. K=5
First one is B. Because if you're moving from -4 to 3 you don't move 9 units right instead you move 7.
At a particular music store, CDs are on sale at $14.00 for the first one purchased and $12.00 for each additional disc purchased. Maria spends $86.00 on CDs. How many CDs has Maria purchased?
Answer: 7
Step-by-step explanation:
Use a coordinate grid to create a map of a town with at least five different locations, such as a house, a post office, a school, a library, and a mall. Each location must be plotted where two grid lines cross. In addition, no two locations can lie on the same vertical grid line or the same horizontal grid line.
A. Post your diagram.
B. Use the Pythagorean theorem to find the distance between two of your locations.
Find the width of a rectangular patio with a length of 16 ft and an area of 200 square feet
50 POINTS FOR ALGEBRA ANSWERS
1. What are the zeros of the function?
f(x)=x3−x2−6x
A. −3 , 0, and 2
B. −3 , 0, and 1
C. −2 , 0, and 3
D. −1 , 0, and 3
2. The equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff.
What is the initial velocity when the rock is thrown?
3. Factor.
x2−6x+8
x2−6x+8= ( )( )
4. What are the zeros of the function f(x)=x2+2x−35 ?
There are two.
5. Let f(x)=x2−6x+13 .
What is the vertex form of f(x)?
What is the minimum value of f(x)?
6. Let f(x)=4x and g(x)=4x+1−2 .
Which transformations are needed to transform the graph of f(x) to the graph of g(x) ?
7. What is the average rate of change of the function over the interval x = 0 to x = 4?
f(x)=2x−1/3x+5
Enter your answer, as a fraction.
8. Which function grows at the fastest rate for increasing values of x?
A. g(x)=19x
B. h(x)=2x
C. f(x)=8x2−3x
D. p(x)=5x3+3
9. The equation of the linear regression line represents the relationship between the score a student earned on an aptitude test, x, and their final score in a statistics class, y.
yˆ=1625x+24.9
What does the slope of the line represent?
A. For every 25 points earned on the aptitude test, the student earned 16 fewer points in the statistics class.
B. For every 16 points earned on the aptitude test, the student earned 25 fewer points in the statistics class.
C. For every 25 points earned on the aptitude test, the student earned 16 additional points in the statistics class.
D. For every 16 points earned on the aptitude test, the student earned 25 additional points in the statistics class.
In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
Answer:
2024
Step-by-step explanation:
took the test
Simplify 2y (3-x) + 7 (x-2y)
Which of the following is not needed when making a box plot?
A - Mean
B - Minimum
C - Median
D - Third Quartile
A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the equation -2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?