[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3600\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]
[tex]A = 3600\left(1+\frac{0.02}{12}\right)^{12\cdot 18}\implies A=3600(\frac{601}{600})^{216} \implies A \approx 5158.44[/tex]
PLS HELPPPP ILL GIVE BRAINIEST IF CORRECT
The 6 participants in a 200-meter dash had the following finishing times (in seconds).
28, 28, 29, 31, 28, 24
Assuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
Answer:
Step-by-step explanation:
To find the standard deviation of the population, we first need to find the mean of the population.
Mean = (28 + 28 + 29 + 31 + 28 + 24) / 6 = 28
Next, we need to find the variance of the population.
Variance = [(28 - 28)^2 + (28 - 28)^2 + (29 - 28)^2 + (31 - 28)^2 + (28 - 28)^2 + (24 - 28)^2] / 6
Variance = (0 + 0 + 1 + 9 + 0 + 16) / 6 = 2.67
Finally, we can find the standard deviation of the population by taking the square root of the variance.
Standard deviation = sqrt(2.67) ≈ 1.63
Therefore, the standard deviation of the population is approximately 1.63 seconds.
The school fundraising committee is hosting a BBQ dinner. They sell meal tickets for
$8.50 per dinner and receive a $200 donation. How many meal tickets will they need to
sell in order to raise at least $2,000?
Answer:212
Step-by-step explanation:
$2000 - $200 = $1800
$1800/$8.50 = 211.76 round up to 212
The diagram shows the floor plan of Jill's dining room.
Jill is going to cover the floor with wooden floorboards.
1.5m
Diagram NOT
accurately drown
The floorboards are sold in packs. One pack of floorboards will cover 2.25 m²
Work out how many packs Jill needs.
You must show all your working.
Answer: look at the image and better give me brainliest
Step-by-step explanation:
Sophia is training for a triathlon. She swims 40 meters in 50 seconds, moving at a constant speed. What is the rate in meters per second?
Answer:
0.80 m/s
Step-by-step explanation:
rate = 40 m / 50 s = 0.8 m/s
Una bomba llena un tinaco en 16 minutos si el Tina cómo conservar 3/8 de su capacidad en cuántos minutos llenar completamente
Es para hoy
It will take the pump 80 minutes to fill the tank completely.
We can find the time to fill the tank by subtracting the current amount of the tank (3/8 of its capacity) from its total capacity. Then, dividing that amount by the flow rate of the pump (which is 1/16 of its capacity per minute).
The calculation is given as:
Remaining amount to fill = Total capacity - Current amount = 1 - 3/8 = 5/8
Time to fill completely = Remaining amount ÷ Flow rate = 5/8 ÷ (1/16) = 80 minutes
So, it will take the pump 80 minutes to fill the tank completely.
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____ The given question is incorrect, the correct question is given below:
If a pump fills a tank in 16 minutes and the tank currently has 3/8 of its capacity, then we can calculate how many minutes it will take to fill the tank completely.
AC and BE intersect at point P. If m∠APE = 70°, then what is the measure of m∠EPD?
The angles m∠APE and m∠EPD are complementary angles and so the measure of angle m∠EPD is equal to 20° which makes option D correct.
What are complementary anglesIn geometry, if two angles are said to be complementary, then the total of their sum is equal to 90°.
The angles m∠APE and m∠EPD are complementary angles so we evaluate for the angle m∠EPD as follows:
m∠APE + m∠EPD = 90°
70° + m∠EPD = 90°
m∠EPD = 90° - 70° {subtract 70° from both sides}
m∠EPD = 20°.
Therefore, the measure of angle m∠EPD is equal to 20°.
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Draw a horizontal line of length 7cm. Construct the perpendicular bisector using a pair of compasses.
The perpendicular bisector of line 7 cm is given below.
What is perpendicular bisector?
A perpendicular bisector is a line that divides the given into two halves which also makes an angle of 90° at the where it intersects the given line.
Steps to construct perpendicular bisector for the given line 7 cm.
Step 1 : Draw a line 7 cm using pencil and scale and named as AB.
Step 2: Take a measurement more than half of a line AB and draw a arc from A on both sides of the line AB.
Step 3: Repeat the step 2 from the point B.
Step 4: Join the arc by the straight line and named as MN, which is the required perpendicular bisector of line AB.
Hence the perpendicular bisector is shown in the figure.
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In order to ride a rollercoaster a rider must be greater than 48 inches tall
The inequality equation is x ≥ 48 inches
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the minimum height to ride the roller coaster be represented as x
Now , the required height to ride the roller coaster is = 48 inches
So , the individual must be equal to 48 inches tall
x = 48 inches
And , the individual could be greater than 48 inches tall
x > 48 inches
Substituting the values in the equation , we get
x ≥ 48 inches
Hence , the inequality is x ≥ 48 inches
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Tania is riding a train for $43. 6$ miles to get to her destination. The train has $14. 3$ more miles to travel before arriving at Tania's destination.
Which equation and solution correctly represent how many miles, $m$ , the train has already traveled?
A
$m\ +\ 14. 3\ =\ 43. 6$
$m\ =\ 29. 3$
B
$m\ +\ 43. 6\ =\ 14. 3$
$m\ =\ 29. 3$
C
$m\ +\ 14. 3\ =\ 43. 6$
$m\ =\ 57. 9$
D
$43. 6\ +\ 14. 3\ =\ m$
$m\ =\ 57. 9$
The correct equation and solution are: D
$43. 6\ +\ 14. 3\ =\ m$
$m\ =\ 57. 9$
This equation represents the total distance traveled by the train (43.6 miles + 14.3 miles) and gives the correct answer of 57.9 miles traveled by the train.
In equation D, we add the 43.6 miles traveled with the 14.3 miles left to travel to find the total distance traveled by the train, which is 57.9 miles. This equation and solution correctly represent the number of miles traveled by the train.
The other equations and solutions do not accurately represent the information given in the problem and do not lead to the correct answer.
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Two rectangles are joined together to form a single large area. The rectangles do not overlap.
The first rectangle has side lengths of 10 meters and 2 meters. The second rectangle has side
lengths of 2 meters and 6 meters.
The combined area of the two rectangles is 32 square meters.
What is rectangle?
Rectangle is a two-dimensional shape with four straight sides, where all angles are right angles (90 degrees). The opposite sides of a rectangle are equal in length and parallel to each other, so rectangles have two pairs of equal sides.
The first rectangle has an area of 10 meters * 2 meters = 20 square meters.
The second rectangle has an area of 2 meters * 6 meters = 12 square meters.
When the two rectangles are joined together, the combined area of the two rectangles is 20 square meters + 12 square meters = 32 square meters.
So the combined area of the two rectangles is 32 square meters.
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If <1 and <2 are complementary angles, and m<2 is 24 degrees, find m<3
Answer:
see below
Step-by-step explanation:
if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
so <1 and <2 = 90
m<3 = 90
the mean radius of the earth is 6.37 x 10^6 meters, while the mean radius of the moon is 1.74 x 10^6 meters. approximately how many times larger is the diameter of the earth than the diameter of the moon?
The diameter of the earth is 3.66 times larger than the diameter of the moon.
The mean radius of the earth is 6.37 x 10^6 meters,
Re = 6.37 x 10^6 meters
The mean radius of the moon is 1.74 x 10^6 meters.
Rm = 1.74 x 10^6 meters
To compare the size of the diameter,
D = De/Dm = 6.37 x 10^6 / 1.74 x 10^6
Diameter of the earth is 3.66 times larger than the diameter of the moon.
In geometry, a circle's diameter is any straight line segment whose centre is on the circle and whose ends are on the circle. The longest chord of the circle is another name for it. Either of the two approaches can be used to determine the diameter of a sphere.
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Ray BF is an angle bisector of angle BCD. Find the measure of angle CBF if the measure of angle CBF = 3z+7, the measure of angle FBD = 5z-29 and the measure of CBD is 34
As a result, the angle CBF has a 61 degree value.
What is meant by an angle?When two consecutive lines or beams intersect at a single terminus, an angle is created. The apex of an arc is the location where two points come together.
Since Ray BF splits angle BCD into two equal portions because it is an angle bisector, the measures of angle CBF and angle DBF are the same. Consequently, we can write:
3z + 7 = 5z - 29
Simplifying and solving for z:
2z = 36
z = 18
Now we can substitute z = 18 into the expression for the measure of angle CBF:
3z + 7 = 3(18) + 7 = 61
Therefore, the measure of angle CBF is 61 degrees.
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Calculate the missing values. For the next six month period Sammy wants to calculate the monthly deviation from the average. Month Sales Average Deviation July $1,750 1,460. 83 Aug. $1,800 1,460. 83 Sept. $1,625 1,460. 83 Oct. $1,395 1,460. 83 -65. 83 Nov. $1, 215 1,460. 83 Dec. $ 980 1,460. 83
The missing values of Deviation of July is 289.17, August is 339.17, September is 14800.17, whereas, October, November and December are -65.83, 10690.17 and -480.83 respectively.
When determining the standard deviation: By combining the data points and dividing the result by the number of data points, you may determine the mean, or average, of the data points. Each data point's mean should be subtracted, and the results should then be squared.
Month sales Average Deviation:
July $1,750 1,460.83 289.17
August $1,800 1,460.83 339.17
September $1,6251, 1,460.83 14800.17
October $1,395 1,460.83 -65.83
November $1, 2151 1,460.83 10690.17
December $980 1,460.83 -480.83
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Question 3(Multiple Choice Worth 2 points)
(04.03 MC)
Which equation represents the vertical asymptote of the graph?
o x = -8
o y = -8
o x = 0
o y = 0
The equation representing the vertical asymptote of the graph is given as follows:
x = -8.
What is the vertical asymptote of a function?The vertical asymptotes of a function f(x) are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
From the graph, we can see that the function is not defined at x = 8, only to the left and to the right of x = 8, going to either negative infinity or positive infinity at both sides.
Hence the equation representing the vertical asymptote of the graph is given as follows:
x = -8.
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3 3/7 divided 4 4/5+1 1/7 * 4 3/8
Answer:
40/7
Step-by-step explanation:
3 3/7 divided 4 4/5+1 1/7 * 4 3/8
3 3/7 = 24/7
4 4/5 = 24/5
1 1/7 = 8/7
4 3/8 = 35/8
So, our equation is
24/7 divided 24/5 + 8/7 · 35/8
120/168 + 8/7 · 35/8
120/168 + 280/56
120/168 + 840/168
960/168
240/42
120/21
40/7
thankssss so much <3
The value of y for that, the three horizontal lines would be parallel, is 7√2/ 16.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
A right-angled triangle.
Sin60° = Perpendicular/hypotenuse
Hypotenuse = 8
To find the value of y for that, the three horizontal lines be parallel:
The parallel lines are equally spaced.
So,
8 / 16 = y / 7√2/8
y = 7√2/ 16
Therefore, the value of y is 7√2/ 16.
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help me answer this its about graphs
The points that can be included to keep the graph a function are given as follows:
P and U.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
On a graph, a function is represented if the graph contains no vertically aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.
Hence the points we can include on the graph to keep it a function are given as follows:
P, as there is no other output defined at x = -9.U, as there is no other input defined at x = 5.More can be learned about relations and functions at brainly.com/question/10283950
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Which statement about the following equation is true?
3x2 – 8x + 5 = 5x2
The solutions of the quadratic equation 3x² – 8x + 5 = 5x² will be 0.4595 and negative 4.5495.
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 equation be ax² + bx + c = 0. Then the roots of the equation will be given as,
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
The equation is given below.
3x² – 8x + 5 = 5x²
Simplify the equation, then we have
3x² – 8x + 5 = 5x²
2x² + 8x – 5 = 0
Then the roots of the equation are given as,
x = [ -8 ± √(8² - 4 · 2 · (-5))] / (2 · 2)
x = (- 8 ± 10.198) / 4
x = (- 8 + 10.198) / 4 , (- 8 - 10.198) / 4
x = 0.5495, -4.5495
The solutions of the quadratic equation 3x² – 8x + 5 = 5x² will be 0.4595 and negative 4.5495.
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What is the value of a in the equation 3 a plus b equals 54, when b equals 9? c
the value of a will be 15 in equation 3 a plus b equals 54 when b equals 9.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, equation 3 a plus b equals 54 when b equals 9
In numerical form,
3a + b = 54
and b = 9
Comparing these equations
3a + 9 = 54
3a = 45
a = 15
Therefore, the value of a will be 15 in equation 3 a plus b equals 54 when b equals 9.
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V to the 3rd power=1
My answer is coming 84.. But actual answer will be 42 how.. Pls help
Answer:
that answer should be wrong?
Answer:
-84
Step-by-step explanation:
To simplify the expression 20^2 - 22^2, we'll first square both 20 and 22:
20^2 = 20 * 20 = 400
22^2 = 22 * 22 = 484
Now, we can substitute these values back into the original expression:
400 - 484 = -84
So 20^2 - 22^2 = -84.
Pls help me with this w/ work (explanation)
Tysm!
Answer:
1. 62.8
2. 3.14
Step-by-step explanation:
It is important to note that the circumference formula is pi times 2 times radius. Radius for bigger circle is 10 so its circumference would be 62.8 (3.14 times 2 times 10) where was the radius for small circle is 31.4 (3.14 times 2 times 5) so subtract 31.4 from 62.8 and you get your answer.
4. for the calories of each burger: a. find q1, q2, q3, the range and the iqr. b. calculate the outlier boundaries for the data set. are there any outliers? c. determine the value at the 70 th percentile
a. The values of Q1 = 355, Q2 = 510, Q3 = 910, range = 980 and IQR = 555.
b. The lower bound is not applicable and the upper bound is 1195. There are no outliers.
c. The value at the 70th percentile is approximately 725.6 calories.
a. For the calories of each burger, we will find the Q1, Q2, and Q3, range, and IQR as follows -
Q1 (25th percentile): The median of the lower half of the data set.Arranging the calorie values in order from smallest to largest we get,
250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.
The median of the lower half (from 250 to 540) is the average of the two middle values: (300 + 410) / 2 = 355.
Therefore, Q1 = 355.
Q2 (50th percentile or median): The middle value of the data set.Arranging the calorie values in order from smallest to largest we get,
250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.
The middle value is the median: Q2 = 510.
Q3 (75th percentile): The median of the upper half of the data set.Arranging the calorie values in order from smallest to largest we get,
250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.
The median of the upper half (from 670 to 1230) is the average of the two middle values: (840 + 980) / 2 = 910.
Therefore, Q3 = 910.
Range: The difference between the largest and smallest values.Range = 1230 - 250 = 980.
IQR (Interquartile Range): The difference between Q3 and Q1.IQR = Q3 - Q1 = 910 - 355 = 555.
b. To calculate the outlier boundaries, we need to first calculate the lower and upper limits as follows -
Lower bound: Q1 - 1.5 x IQR
Upper bound: Q3 + 1.5 x IQR
Lower bound: 430 - 1.5 x 310 = -25
Upper bound: 740 + 1.5 x 310 = 1195
Since there are no negative values for the calories of the burgers, the lower bound is not applicable. The upper bound is 1195, which is higher than the highest value in the dataset (1090). Therefore, there are no outliers.
c. To determine the value at the 70th percentile, we need to first order the calorie values from lowest to highest as follows -
250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 740, 840, 980, 1090, 1230
Next, we will calculate the percentile rank of the 70th percentile -
Percentile rank = (70/100) x (n + 1) = 10.6
Since the percentile rank is not a whole number, we need to interpolate between the 10th and 11th values in the ordered list:
10th value: 710
11th value: 740
Using linear interpolation, we get:
Value at the 70th percentile = 710 + 0.6 x (740 - 710) = 725.6
Therefore, the value at the 70th percentile is approximately 725.6 calories.
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The complete question is -
For the calories of each burger:
a. find q1, q2, q3, the range, and the IQR.
b. calculate the outlier boundaries for the data set. are there any outliers? c. determine the value at the 70th percentile.
in 2012 the number of graduating seniors taking the act exam was 1666809 in 1995 the total of 945477 graduating seniors took the exam. by what percent did the number increase over this period of time
The number increase by a percentage of 76.29 over the given period of time.
To calculate the percent increase, we need to find the difference between the two values and divide that by the original value, then multiply by 100 to express the answer as a percentage:
If in 1995, a total of 945477 graduating seniors took the exam, and in 2012, the number of graduating seniors taking the ACT exam was 1666809, then the percent increase from 1995 to 2012 is:
(1666809 - 945477) / 945477 = 0.7629 x 100 = 76.29%
Therefore, the number of graduating seniors taking the ACT exam increased by 76.29% between 1995 and 2012.
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Based on the ordered pairs in the data below, state, whether there is no correlation, a weak correlation, or a strong correlation. If there is a data correlation determine whether the correlation is negative or positive.
The data given has: a) A strong correlation, b) A positive correlation
What is correlation?
Correlation is a statistical measure that expresses the extent to which two variables are linearly related, meaning they change together at a constant rate.
We have ordered pairs in the data as:
x y
1 2
2 3
3 8
4 10
5 26
6 38
7 46
8 50
9 68
Plotting the graph (attached)
Clearly, on plotting the scatter plot on the basis of table of values, we see that the relation is a strong correlation since we can find a relationship between variable x and y.
i.e. the points will lie above or below the curve which is formed by connecting some points of the scatter plot and are not scattered away.
Hence, the data above has: A strong correlation.
Also, the graph is a positive correlation since with the increasing value of x the y-value also increases.
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What rule would you allow to test weather (x,y) is on line l
Just evaluate the line in the values of the point and check if the equation is true or not.
What rule would you allow to test weather (x,y) is on line l?So let's say line l has an equaiton known:
y = a*x +b
To check if a point is on the line, just replace the values of the point on the line equation, if the equation is true, then that point belongs to the line, if don't, then the point does not belong to the line.
That is the only way to check that.
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what piece of information would have to be marked on the triangle to show congruence by the hl theorem
The piece of information which would have to be marked on the triangle to show congruence by the HL theorem is ac = dc which is denoted as option C.
What is HL theorem?It states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.'
In triangle ABC and triangle EDC, hypotenuses of triangles are AB and DE respectively.To use HL hypotenuse and one leg of triangles must be equal which means that :
AB = DE (hypotenuse)
AC = DC (leg)
This means that the additional information which will allow you to prove the triangles congruent by the HL Theorem is AC = DC.
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The full question is:
What additional information will allow you to prove the triangles congruent by the HL Theorem?
choices
A = E
bce= 90
ac = dc
ac=bd
"20 decreased by the sum of 6 and b."
Answer:
20 - (6 + b)
Step-by-step explanation:
ur mom
Jake is traveling 12 mph in his boat. After 3 hours. How far will he have traveled?.
Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.
What is Distance?
Distance is defined as the space between two points in space.
To find out how far Jake will have traveled after 3 hours, we can use the formula:
distance = speed x time
where speed is the rate at which Jake is traveling and time is the duration of the travel. In this case, the speed is 12 mph and the time is 3 hours.
So, the distance traveled after 3 hours is:
distance = 12 mph x 3 hours = 36 miles
Therefore, Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.
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