Answer:
$4,723.21
Step-by-step explanation:
Formula for COMPOUND INTEREST:
A = P ( 1 + r/n) ^ nt
Where A = principal money + interest earned,
P = Principal Money
r = interest rate in decmial
n = no. of times i.rate is compounded
nt = time
Since the qns asked to be compounded /monthly', you have the following formula:
A = 3250 ( 1 + 7.5%/12) ^ 60
7.5% is a yearly rate so divide it by 12 (as in 12 months)
60 = 5 years x 12 months
so use a calculator and you'll get $4723.206, round off and it's $4723.21
To find out how much Connie's investment in a savings account with a 7.5% annual interest rate compounded monthly will be worth in five years, use the compound interest formula. After calculations, her investment will be worth $4,723.21 in five years.
The student asks about the future value of an investment made in a savings account with compound interest. To calculate the amount Connie's investment will be worth in five years, we can use the compound interest formula, which is A = P(1 + r/n)^(nt). Here, P is the principal amount ($3,250), r is the annual interest rate (7.5% or 0.075 as a decimal), n is the number of times the interest is compounded per year (12, since it's monthly), and t is the number of years (5).
Using these values, we calculate the future value (A) as follows:
Convert the percent interest to a decimal: 7.5% = 0.075.
Divide the annual rate by the number of compounding periods: 0.075/12.
Add 1 to the interest rate per period: 1 + (0.075/12).
Calculate (1 + (0.075/12)) raised to the power of the total number of compounding periods: (1 + (0.075/12))^(12*5).
Multiply the principal by this amount: $3,250 × (1 + (0.075/12))^(12*5).
Connie's investment will grow to $$4,723.21 after five years, using compound interest.
Evaluate the expression when x=3 and z=−6. z÷x=
z÷x
-6÷3
=-2
Answer is -2
Answer:
(-6)/3 = -2
Step-by-step explanation:
you have to change the variables with the numbers
what is a perfect square trinomial
Answer:
well a perfect square of trinomial if it can be factored into a binomial multiplied to itself. so theres step by step to
Step-by-step explanation:
For example, in the trinomial x2 - 12x + 36, both x2 and 36 are perfect squares.welcome
Answer is provided in the image attached.
Solve 5 divided by 2 5/7
5 ÷ 2 * 7 + 5/7
Simplify 2 * 7 to 14
5 ÷ 14 + 5/7
Simplify 14 + 5 to 19
5 ÷ 19/7
Use this rule: a ÷ b/c = a * c/b
5 * 7/19
Simplify
35/19
Convert to a mixed fraction
= 1 16/19
Answer:
[tex]\large\boxed{1\dfrac{16}{19}}[/tex]
Step-by-step explanation:
[tex]5\div2\dfrac{5}{7}\qquad\text{convert the mixed number to improper fraction}\\\\2\dfrac{5}{7}=\dfrac{2\cdot7+5}{7}=\dfrac{19}{7}\\\\=5\div\dfrac{19}{7}=5\cdot\dfrac{7}{19}=\dfrac{(5)(7)}{19}=\dfrac{35}{19}=1\dfrac{16}{19}[/tex]
If a bicyclist rides for 120 minutes at an average speed of 18 miles per hour, how far was the ride?
At what speed must a bicyclist ride to cover 12 miles in 4 hours?
It was 2 hours
A bicyclist ride 3 mph (miles per hour) to cover 12 miles in 4 hours
The distance of the first ride, ridden for 120 minutes at 18 mph, was 36 miles. To cover 12 miles in 4 hours, the bicyclist must ride at a speed of 3 mph.
To find the distance of the first ride, we can use the formula:
Distance = Speed × Time
Given that the bicyclist rides for 120 minutes (2 hours) at an average speed of 18 miles per hour:
Distance = 18 miles/hour × 2 hours = 36 miles
So, the distance of the first ride was 36 miles.
To find the speed the bicyclist must ride to cover 12 miles in 4 hours, we use the same formula:
Speed = Distance / Time
Given that the distance is 12 miles and the time is 4 hours:
Speed = 12 miles / 4 hours = 3 miles per hour
The bicyclist must ride at a speed of 3 miles per hour to cover 12 miles in 4 hours.
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Solve for X. Assume that the lines that appear tangent are tangent.
Answer:
The value of x is 1
Step-by-step explanation:
Remember that
The radius of the circle is perpendicular to the lines that are tangent to the circle
Applying the Pythagoras Theorem
[tex]6.1^{2}+(10x)^{2}=6.1^{2}+(9x+1)^{2}[/tex]
Simplify
[tex](10x)^{2}=(9x+1)^{2}[/tex]
[tex]10x=(9x+1)\\ \\ 10x-9x=1\\ \\x=1[/tex]
wha is the area of a rectangle with vertices at (4, 3), (11, 3), (11,9), and (4, 9)?
Answer:
42 units^2.
Step-by-step explanation:
We are given that it is a rectangle so its area is the product of the length of adjacent sides.
Length of the horizontal line = 11 - 4 = 7 units ( from the first 2 points) and the length of an adjacent side is 9 - 3 = 6 units (from the second and third points).
Area = 7 * 6 = 42.
Answer:
area of rectangle = 42
Step-by-step explanation:
area of rectangle = length × width
= 7 × 6
= 42
nPr if n = 8 and r = 5
For this case we have that by definition, the formula to count the total number of different permutations is:
[tex]nP_ {r} = \frac {n!} {(n-r)!}[/tex]
SUstituyendo:
[tex]n = 8\\r = 5[/tex]
We have:
[tex]8P_ {5} = \frac {8!} {(8-5)!} = \frac {8!} {3!} = \frac {8 * 7 * 6 * 5 * 4 * 3!} {3! } = 6720[/tex]
ANswer:
[tex]8P_ {5} = 6720[/tex]
A sales clerk makes $200 in commission on $1,700 worth of furniture. What’s her commission rate?
Answer:
200 divided by 1700=.1176
move decimal two to the right =11.76% or 12% commission
Each of these numbers represents the weight of a student in kilograms. What is the median of this data set?
39, 48, 45, 48, 51, 46, 52, 51, 43, 41
Answer:
47
Step-by-step explanation:
www.alcula.com/calculators/statistics/median/
Each of these numbers represents the weight of a student in kilograms. Hence, the median of the given data set is 47.
How to find the median of data?Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong the same number of observations.
Each of these numbers represents the weight of a student in kilograms.
39, 48, 45, 48, 51, 46, 52, 51, 43, 41
We need to find the median of this data set.
In order to find the median, arrange the data in ascending order.
39, 41, 43, 45, 46, 48, 48, 51, 51, 52,
[tex]M= \dfrac{46 + 48 }{2} \\\\M = \dfrac{94}{2} \\\\M= 47[/tex]
Hence, the median of the given data set is 47.
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For which value of 0 is sin0=-1:
A. Pi/2
B. Pi
C. 3Pi/2
D. 2Pi
Answer:
C. 3Pi/2 or 270 degrees
Step-by-step explanation:
The first step is to ignore the negative sign and then evaluate the arcsin of 1 to obtain the reference angle of θ in the first quadrant;
θ = arcsin(1)
θ = 90 degrees or equivalently pi/2
Since the sine of θ was given as -1, this will imply that θ lies either in the third or forth quadrant where the sine of an angle is negative.
To obtain the value of θ in the third quadrant we simply add 180 degrees of pi radians to our reference angle;
90 + 180 = 270 degrees
pi/2 + pi = 3/2 pi
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows:
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3
What is the best measure of spread for the first period and why?
median because there is and outlier
Final answer:
The best measure of spread for the first period is the range, which is found by subtracting the smallest value from the largest value in the dataset.
Explanation:
The best measure of spread for the first period is the range.
The range is found by subtracting the smallest value from the largest value in a dataset. For the first period, the smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
The range is a good measure of spread because it gives the distance between the minimum and maximum values, providing an idea of how much the data values vary.
At Random Stationary, the sales records of 24 employees were examined. Twelve of the employees worked the morning shifts and 12 of them worked the afternoon shifts. The following statistical information was calculated from the number of sales of each employee chosen.
Based on these samples, what generalization can be made?.
To make generalizations from sales data of the Random stationery employees or car salespersons, statistical analysis using histograms, frequency polygons, time series graphs, and box plots is necessary to visually interpret the distribution and variance within the data.
Explanation:Understanding Sales Data and Statistical Representation
When reviewing the sales data of Random Stationary's employees or the weekly sales of car salespersons, we are engaging in the statistical analysis of a chosen sample. Here, histograms, frequency polygons, time series graphs, and box plots are used to graphically represent data obtained from these samples. These visual tools allow us to interpret data distributions and make generalizations about the overall population from which the sample was taken.
Examples of Data Representation
In the provided example regarding the number of cars sold by 65 randomly selected salespersons, data is summarized in a frequency table. This leads to the construction of a histogram or a box plot where the central tendency and the dispersion of data can be observed. Similarly, in a workplace setting like that of Yoonie’s personnel reviews, the central limit theorem suggests that sampling distributions approach a normal distribution as sample size increases. This is especially true when concluding population averages from sample means.
Making Generalizations from Samples
When looking at the data from Random Stationary’s employees or any other such gathered data, mean, median, mode, range, and standard deviation can provide insights into sales performance. By examining the data visually through box plots, one can comment on the spread and concentration of data, which indicates whether sales performance is consistent or variable across shifts or individuals. Random sampling methods, systematic sampling, and stratified sampling all contribute to acquiring data that can help make valid generalizations when applied correctly.
Morning shift workers generally have lower sales (mean: 32, median: 36, mode: 20) compared to afternoon shift workers (mean: 46, median: 33, mode: 31), with afternoon workers showing a wider range (18).
To make generalizations based on the provided statistical information, let's break down each measure of central tendency and spread for both morning shift workers and afternoon shift workers.
1. **Mean**: The mean is the average value of a set of numbers. It is calculated by adding up all the numbers and then dividing by the total count.
- For morning shift workers: Mean = (Sum of sales for morning shift workers) / 12 = 32
- For afternoon shift workers: Mean = (Sum of sales for afternoon shift workers) / 12 = 46
2. **Median**: The median is the middle value in a set of numbers when they are arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.
- For morning shift workers: Median = 36
- For afternoon shift workers: Median = 33
3. **Mode**: The mode is the value that appears most frequently in a set of numbers.
- For morning shift workers: Mode = 20
- For afternoon shift workers: Mode = 31
4. **Range**: The range is the difference between the largest and smallest values in a dataset.
- For morning shift workers: Range = Largest value - Smallest value = B - I (not provided)
- For afternoon shift workers: Range = 62 - 44 = 18
what is the slope of a line that is perpendicular to line t on the graph
Answer:
Slope = 6
Step-by-step explanation:
Taking two points on line l to find its slope: (0, 3) and (6, 2).
Slope of line l = [tex]\frac{3-2}{0-6} =-\frac{1}{6}[/tex]
We know that the slope of a line which is perpendicular to another line has a slope which is a negative reciprocal of the other line.
Therefore, the slope of the line which is perpendicular to line l will have a slope of 6.
Answer: 6
Step-by-step explanation: I just got it right lol
what is mean
what is a interquartile range
what is range
Step-by-step explanation:
Mean is the average and that means you add up all the numbers and divide it by its amount.
Interquartile Range is the range of Quartile 3 minus Quartile 1
Range is the highest number minus the lowest number
mean the sum of a set of data divided by the number of items in the set
range the difference between the largest and smallest data points
interquartile range the difference between the upper quartile and the lower quartile
How many solutions does the equation -6y+13+9y=8y-3
Answer:
Single Solution of 3.2 (16/5)
Step-by-step explanation:
3x = 8x -16 <--- I combine like terms.
-5x = -16
-16/-5 = x
x = 3.2
BTW Negative times a Negative equals a positive.
To find the solutions to the equation -6y + 13 + 9y = 8y - 3, combine like terms, isolate the variable, and solve for y. The equation has one solution, which is y = 3.2.
Explanation:To find the solutions to the equation -6y + 13 + 9y = 8y - 3, we need to simplify the equation and solve for y. First, combine like terms by adding the y terms on the left side and the constant terms on the right side. This gives us 3y + 13 = 8y - 3. Next, subtract 3y from both sides to isolate the variable term on the right side. This gives us 13 = 5y - 3. Then, add 3 to both sides to isolate the variable term. This gives us 16 = 5y. Finally, divide both sides by 5 to solve for y. This gives us y = 16/5 or y = 3.2.
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Which of the equations below represents a line perpendicular to the x-axis?
А. = — бу
В. X= 6
C. X= у
D. X= бу
Reset
Submit
Answer:
Option B
Step-by-step explanation:
we know that
A line perpendicular to the x-axis is a line parallel to the y-axis
so
the equation of the line is of the form x=(+/-)a
The slope of the line is undefined
where
a is a real number
therefore
x=6 is a line perpendicular to the x-axis
Answer:
B. [tex]x = 6[/tex]
Step-by-step explanation:
The x-axis is the line of [tex]0 = y[/tex] [horizontal line], therefore the ONLY live perpendicular to that would be [tex]x = 6[/tex], which is a vertical line, giving you a right angle in the centre.
I am joyous to assist you anytime.
Need Help FAST!!!!!!!!!!
Answer:
This is a graph of y = -x,
slope of graph = -1,
Y-intercept = 0
This line passes through the origin, so its equation follows the form
[tex]y=mx[/tex]
The slope [tex]m[/tex] can be computed using the "rise over run" technique: each time you increase x by 1, y decreases by 2. So, the slope is -2.
The equation is thus
[tex]y=-2x[/tex]
solve -2p^2=16p+24 please help
Answer:
p = - 6, p = - 2
Step-by-step explanation:
Given
- 2p² = 16p + 24
Subtract 16p + 24 from both sides
- 2p² - 16p - 24 = 0 ← in standard form ( divide all terms by - 2)
p² + 8p + 12 = 0
To factor the quadratic
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the p- term (+ 8)
The factors are + 6 and + 2, since
6 × 2 = 12 and 6 + 2 = 8, thus
(p + 6)(p + 2) = 0
Equate each factor to zero and solve for p
p + 6 = 0 ⇒ p = - 6
p + 2 = 0 ⇒ p = - 2
Liz earns a salary of $2,100 per month, plus a commission of 4% of her sales. She wants to earn at least $2,900 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.
Let S = the amount of sales.
She earns 4% of her sales, this would be written as 0.4S ( you multiply the percent as a decimal by the amount of sales).
You then need to add that amount to her salary so you now have 0.4s + 2100
She wants to earn at least 2900 so the inequality becomes:
2900 ≥ 0.4s + 2100
Her sales would need to be:
800 ≥0.4s
s≥ 800/0.4
s ≥ 2000
^^^^^^^^^^^^^^^^^^^^
Answer:
Option B.
Step-by-step explanation:
The constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.
Given that the graph is a straight line, we can find the constant of proporctionality just by selecting a point, and then dividing the y-value by the x-value.
We can see from the graph that when y=5, x=4. Then, the constant of proportionality comes to be:
k = 5/4 = 1.25.
Then, the correct option is Option B.
What is the answer? Please help!
Answer:
Choice B: BD/DA = CE/EA
Step-by-step explanation:
Slope is rise over run. For the two slopes to be equal, the rise over run of the two triangles must be equal.
The rise over run for triangle ABD is BD/DA.
The rise over run of triangle ACE is CE/EA.
For the slopes to be equal, BD/DA = CE/EA
Answer: Choice B.
Write a rule to describe the function shown.
x y
−6 −4
−3 −2
0 0
3 2
Answer:
y= 2/3 x
Step-by-step explanation:
First plot the points on a Cartesian plan
You will notice a straight line passing through the origin (0,0)
Find the gradient of the line;
m=change in y/change in x
m=2-0/3-0 =2/3
Find the equation of the line
y-2/x-3 =2/3
3(y-2) = 2(x-3)
3y-6= 2x-6
3y=2x-6+6
3y=2x
y=2/3 x + 0
Which graph shows the solution -2a-5>3
Answer:
Check attached graph
Step-by-step explanation:
Given inequality is [tex]-2a-5>3[/tex].
Now we need to graph the given inequality to find the correct choice.
[tex]-2a-5>3[/tex]
[tex]-2a-5+5>3+5[/tex]
[tex]-2a>8[/tex]
[tex]-\frac{2a}{-2}<\frac{8}{-2}[/tex]
[tex]a<-4[/tex]
that means line will go on the left side of -4.
since we have <, so there will be an open circle at -4.
Hence final graph of the given problem looks like:
find each angle measure in the regular polygon
Answer:
120°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6, hence
sum = 180° × 4 = 720°, thus
angle measure = 720° ÷ 6 = 120°
What’s the axis of symmetry for the quadratic equation y=3x^2+5x-2? Would really appreciate it if someone knew! :)
The y axis? As the graph is symmetrical on either side of it
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left( -\cfrac{5}{2(3)}~~-2-\cfrac{5^2}{4(3)} \right)\implies \left(-\cfrac{5}{6}~~,~~-2-\cfrac{25}{12} \right)\implies \stackrel{\stackrel{axis~\hfill }{coordinate\qquad }}{\left(-\cfrac{5}{6}~~,~~-\cfrac{49}{12} \right)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=-\cfrac{5}{6}}~\hfill[/tex]
let's notice, that the squared variable is the "x", and therefore this is a vertical parabola whose axis of symmetry is the vertical line equation of the x-coordinate of its vertex.
A car is traveling at a speed of 100
miles per hour. What is the car's speed in kilometers per hour? How many kilometers will the car travel in 5
hours? In your computations, assume that 1
mile is equal to 1.6
kilometers. Do not round your answers.
The car will travel 800 kilometers in 5 hours.
What is the unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given
1 mile = 1.6 km
100 mile = 1.6 * 100 = 160 km
in 1 hr car travels 160 km
in 5 hrs car travels = 160 * 5 = 800 km
The car will travel 800 kilometers in 5 hours.
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In 5 hours, the car will travel 800 kilometers.
To convert the car's speed from miles per hour to kilometers per hour, you multiply by the conversion factor of 1.6 kilometers per 1 mile. Therefore, a speed of 100 miles per hour is equivalent to 100 × 1.6 = 160 kilometers per hour.
Next, to calculate how many kilometers the car will travel in 5 hours at the speed of 160 kilometers per hour, you simply multiply the speed by the time. The car will travel 160 km/h × 5 h = 800 kilometers in 5 hours.
*Estimate* 0.17 x 193
Answer:
38
Step-by-step explanation:
0.17 is about 0.2, and 193 is about 190.
0.2 * 190 = 38.
So 0.17 * 193 is about 38
32.81 is your answer
10 + brainiest please help!
Answer:
the correct answer is between a and b. So I think the answer is b
Answer:
The answer is B.
Step-by-step explanation:
(5)[tex]\frac{3}{4}[/tex]+[tex]\frac{1}{5}[/tex](4)
[tex]\frac{15}{20}[/tex]+[tex]\frac{4}{20}[/tex]=[tex]\frac{19}{20}[/tex]
The first step is to multiply the left side by 5 and the right side by 4 because you want the denominator to be the same. Then you add [tex]\frac{15}{20}[/tex]+[tex]\frac{4}{20}[/tex] to get [tex]\frac{19}{20}[/tex]:)
Please answer right away
Answer:
The third alternative is correct
Step-by-step explanation:
In hypothesis testing, the null hypothesis H0 is the hypothesis of no difference and as such it always contains an equality sign. The equality sign could be either of the following alternatives;
=, equal to
≤, less than or equal to
≥, greater than or equal to
In the question presented the claim is that students who practice taking all of their regular tests on the computer will do better on the state's final exam than the students taking their regular tests by paper and pencil.
This implies that the average on the state exam of students using paper and pencil tests is less than the average of the students using computer tests. Since the null hypothesis must contain an equality sign, the third alternative becomes our null hypothesis, H0.
An office tower is shown in the attached diagram. It consists of a rectangular prism with a square base and a square based right pyramid.
a. Calculate the height of the tower from the ground to the top of the roof's apex.
b. Determine the volume of air inside the building, including the inside of the pyramid-shaped top.
Answer:
[tex]\boxed{\text{a. 111.1 m; b. 56 575 m}^{3}}[/tex]
Step-by-step explanation:
a. Height
(i) Height of prism
The height of the prism is 70 m.
(ii) Height of pyramid
Consider the red triangle in the diagram.
The diagonal of the square base is given by
d² = a² + a² = 2a²
d² = 2(26)² = 2 ×676 = 1352 m²
d = √1352 = 36.77 m
The base of the triangle R is
R = ½d = ½ × 36.77 = 18.38 m
Now,
h² + R² = e²
h² + 18.38² = 45²
h² + 338 = 2025
h² = 1687
h = 41.07 m
(iii) Total height
Total height = height of prism + height of pyramid = 70 + 41.07 = 111.1 m
b. Volume
(i) Volume of prism
V = lwh
V = 70 × 26 × 26 = 47 320 m³
(ii) Volume of pyramid
The formula for the volume of a square pyramid is
V = ⅓a²h
V = ⅓ × 26² × 41.07 = 9255 m³
(iii) Total volume
Total volume = volume of prism + volume of pyramid
V = 47320 + 9255 = 56 575 m³
The total height of the building is [tex]\boxed{\textbf{111.1 m}}[/tex]
The total volume of the building is [tex]\boxed{\textbf{56 575 m}^{3}}[/tex]