Suppose you are depositing an amount today in an account that earns 5% interest, compounded annually. If your goal is to have $5000 in the account at the end of six years, how much must you deposit in the account today?
Answer:
If you walk into a bank and open up a savings account you will earn interest ... include the amount of money deposited called the principal, the annual interest rate ...
Answer:
3731.08
Step-by-step explanation:
let x= the present value (or principle)
[tex]5000=x(1.05)^6\\\frac{5000}{1.05^6}=x\\x=3731.076983[/tex]
Two angles of a triangle measure 22° and 530. What is the measure of the
third angle?
9514 1404 393
Answer:
105°
Step-by-step explanation:
The sum of measures of angles in a triangle is 180°. The third angle is ...
180° -22° -53° = 105°
can anybody help with this question or at least help me solve one thanks !!!!!
Answer:
Step-by-step explanation:
1) the triangle on the right is half of an equilateral one, so the minor leg is 9
the left one has the two legs congruent
so we have
2x^2 = 81
x^2 = 81/2
x = 9/√2 = 9/2 √2 (at the numerator)
2) the top triangle has the congruents leg
hypotenuse^2 = 2(6√6)^2
hypotenuse^2 = 2(216)
hypotneuse^2 = 432
hypotenuse = √2^4 * 3^2 * 3
hypotenuse = 12√3
the triangle in the bottom is half of the an equilateral one, so
x = 12√3 * 2 = 24√3
3) the left triangle has congruent legs
7^2 = leg^2 + leg^2
49 = 2leg^2
leg^2 = 49/2
leg = 7/√2 = (7√2)/2
the right triangle is half of an equilateral one
x = 7√2/2 * √3 = 7/2 √6 (at the numerator)
4) the rifht triangle has two congruent legs
hy^2= 2(7√6)^2
hy^2 = 2(294)
hy^2 = 588
hy = √2^2 * 7^2* 3
hy = 14√3
the triangle on the left is half of an equilteral one: so
x = 14
How many triangles of any size are there in a star?
There are many shapes of a star. It depends on the shape of the star. If you’re referring to this star, then the number of triangles is 5.
Hope this answers your question!
Find the 13th term of the geometric sequence 3 -15 75
Answer:
732,421,875
Step-by-step explanation:
You have to find the pattern which in this case is just multiplying by 5 every absolute number. the negatives are only every other one. from knowing this you just have to find all the numbers until 13 and the 13th term in this sequence is 732,421,875
Help me find the mode
Answer:
28
Step-by-step explanation:
The value with maximum frequency is mode.
so here 28 is mode because it is repeates maximum number of times.
Below are monthly rents paid by 30 students who live off campus.
590 590 590 790 560 450 550 890 600
480 580 520 420 600 510 520 710 775
460 480 620 550 570 365 590 660 680
700 580 630
Required:
a. Find the mean, median, mode, and standard deviation.
b. Which measure or measures of central tendency are most appropriate for this data set?
c. Do the measures of central tendency agree?
Answer:
Mean = 587
Median = 585
Mode = 590
Standard deviation = 112.538
The mean and the median
Yes, both mean and median have close values
Step-by-step explanation:
Given the data:
365, 420, 450, 460, 480, 480, 510, 520, 520, 550, 550, 560, 570, 580, 580, 590, 590, 590, 590, 600, 600, 620, 630, 660, 680, 700, 710, 775, 790, 890
The mean, m = Σx / n = 17610 / 30
Mean = 587
The median = 1/2(n+1)th term
Median = 1/2(31)th term
Median = 15.5th = (580+590) / 2 = 585
The mode = 590 (observation with highest frequency, 4)
Standard deviation, s = √Σ(x-m)²/(n-1)
s = 112.538
What are the domain and range of the function hx) = 5x+3+1?
-10
8
2.
-10
6
4
-8
10
- 2
6
s
-10
O domain: all real numbers greater than 1
range: all real numbers
O domain: all real numbers
Step-by-step explanation:
domain : i think is x > 4/3
range : y >4
What is the sum of
7x/x2 - 4 And 2/ x+2
9514 1404 393
Answer:
(9x -4)/(x^2 -4)
Step-by-step explanation:
Perhaps you intend the sum ...
7x/(x^2 -4) +2/(x +2)
[tex]=\dfrac{7x}{(x+2)(x-2)}+\dfrac{2}{x+2}=\dfrac{7x+2(x-2)}{(x+2)(x-2)}\\\\=\boxed{\dfrac{9x-4}{x^2-4}}[/tex]
plz i need the answer today
sorry
i dont know
i wish i could help
Answer:
Step-by-step explanation:
The following function is probability mass function. -2 -1 0 1 2 1/8 2/8 2/8 2/8 1/8 Determine the mean, , and variance, , of the random variable. Enter the exact answers (as fractions if necessary).
Answer:
The mean of the random variable is 0.
The variance of the random variable is [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
We are given the following probability distribution:
[tex]P(X = -2) = \frac{1}{8}[/tex]
[tex]P(X = -1) = \frac{2}{8}[/tex]
[tex]P(X = 0) = \frac{2}{8}[/tex]
[tex]P(X = 1) = \frac{2}{8}[/tex]
[tex]P(X = 2) = \frac{1}{8}[/tex]
Mean:
Sum of each value multiplied by its probabilities. So
[tex]E(X) = -2\frac{1}{8} -1\frac{2}{8} + 0\frac{2}{8} + 1\frac{2}{8} + 2\frac{1}{8} = \frac{-2 -1 0 + 1 + 2}{8} = \frac{0}{8} = 0[/tex]
The mean of the random variable is 0.
Variance:
Sum of the difference squared between each value and the mean, multiplied by its probabilities. So
[tex]V(X) = \frac{1}{8}(-2-0)^2 +\frac{2}{8}(-1-0)^2 + \frac{2}{8}(0-0)^2 + \frac{2}{8}(1-0)^2 + \frac{1}{8}(2-0)^2 = \frac{4 + 2 + 0 + 2 + 4} = \frac{12}{8} = \frac{3}{2}[/tex]
The variance of the random variable is [tex]\frac{3}{2}[/tex]
The mapping diagrams below show 4 different relationship between input and output values.
Answer:
A. B and C are functions
Step-by-step explanation:
Given
See attachment for mapping diagrams
Required
Which represent function
For a mapping to be considered a function, each element of the input set must only point to 1 element of the output set.
Base on the above analysis, we have:
Map A
1 points to 6; 2 to 7; 3 to 8; and 4 to 9
This is a function
Map B
2 points to 0; 4 to 0; 6 to 0; and 8 to 0
This is a function
Map C
1 points to 8; 3 to 8; 5 to 9; and 7 to 9
This is a function
Map D
0 points to 2 and 5; 3 points 7 and 9
This is not a function
Jeff works in a factory that makes car parts. Jeff can make 7 car parts every twenty minutes. Jeff will start work at ten o’clock in the morning and not stop working until he has made a total of 56 car parts. At what time will Jeff have made a total of 56 car parts?
Answer:
5:00
Step-by-step explanation:
If the number of parts made increases by 7 every hour and Jeff starts at 10:00, then
10:00 - 7 pts
11:00 - 14 pts
12:00 - 21 pts
1:00 - 28 pts
2:00 - 35 pts
3:00 - 42 pts
4:00 - 49 pts
5:00 - 56 pts
please help thx with steps
Answer:
440cm³
.45
1.49538 ft
43.6
Step-by-step explanation:
1.
Start by finding the area of the base
.5*(a+b)*h
.5*(8+14)*4= 44
Then just multiply this by distance between the ends
44*10=440
2.)
To get from 2.7 to 9 we muiltply by 9/2.7= 3.33333333
which means that
3.333333333x=1.5
x=.45
3.)
Height:shadow
6.5:1.8
5.4:x
To get from 6.5 to 5.4 we multiply it by (5.4/6.5) or .8307
which means to get from 1.8 to x we muiltply 1.8*.8307= 1.49538
4.)
Same kind of deal as the last one
to get from 13 to 27 we mulitply by (27/13) or 2.076923 which means to get from 21 to x we multuply 21*2.076923=43.6
Here is the answer for the volume of the trapezoidal prism.
We make two rectangular prisms out of the shape, or a rectangular prism and two triangles.
For this case, I'll just do the two prisms.
Here is the formula for volume we'll be using.
V = lwh (shape's volume = length × width × height), or
V = bh (shape's volume = base area × height)
A reference of the rectangular prism can be identified because the length of the horizontal crest is marked at 8 centimeters.
Following V = lwh, we already have the length we need.
The width of the reference prism that doesn't include the diagonal triangular prisms is 10 centimeters.
l = 8 cm
w = 10 cm
And as indicated by the line inside,
h = 4 cm
We'll label this first volume calculation V[tex]_{1}[/tex].
V[tex]_{1}[/tex] = 8 cm × 10 cm × 4 cm
Now for the second volume.
Since two congruent right triangular prisms can come together to equal a second rectangular prism whose volume is two times their original shapes, we can use the same formula
V = lwh
And in order to determine what values are needed, we
subtract the length of the trapezoid's base from the rectangular prism's.And that's it. No adjustments are made in the width or height. Those measurements are equal to the reference rectangular prism (center prism).
14 cm - 8 cm = 6 cm
l = 6 cm
w = 10 cm
h = 4 cm
This part of the enumeration will be V[tex]_{2}[/tex].
V[tex]_{2}[/tex] = 6 cm × 10 cm × 4 cm
V[tex]_{1}[/tex] + V[tex]_{2}[/tex] = V[tex]_{t}[/tex], or the actual volume of the trapezoidal prism.
(8 cm × 10 cm × 4 cm) + (6 cm × 10 cm × 4 cm) = 320 cm + 240 cm = 560 cm.
You round to 2 decimal places, so V[tex]_{t}[/tex] = 560.00 cm.
2. x = 0.45[tex]\frac{2.7}{x} = \frac{9.0}{1.5}[/tex]
Let's look at the right side.
9.0, or 9, divided by 1.5 equals 6.
Now your equation looks like
[tex]\frac{2.7}{x} = 6[/tex]
You want to get the variable x by itself so that there aren't any real number values that stop the proportion from being simplified.
So, we multiply x on both sides.
[tex]\frac{2.7}{x}[/tex] * [tex]x[/tex] = [tex]6[/tex] * [tex]x[/tex]
On the left side of the = sign, the x on the denominator is being cancelled out.
Now it looks like
[tex]2.7 = 6[/tex] * [tex]x[/tex]
Divide 6 from both sides to cancel the 6 from the right side and get the new value of x by itself.
2.7 ÷ 6 = 0.45
0.45 is already in the hundredths, so there's no need to round up or down.
3. Height of tree = 19.5 ftAll you have to do here is find the ratios of the two figures to their shadows.
It's going to look like the [tex]2^{nd}[/tex] problem because all we're doing is finding the missing variable.
[tex]\frac{h}{s}[/tex] will represent the height-shadow ratio.
For a 6.5-foot human to cast a 1.8-foot shadow,
[tex]\frac{h}{s}_1 = \frac{6.5}{1.8}[/tex]
6.5 ft ÷ 1.8 ft ≅ 3.611
All we have to do now is find a tree height that divides by its shadow, 5.4, to get roughly 3.611.
We can solve that by multiplying 3.611 with the shadow's height.
3.611 * 5.4 = 19.5
The tree is 19.5 feet tall.
4. x = 43.6
These two triangles aren't congruent, but similar.
Like the last two problems, finding the ratio between the sides is key to solving the problems.
This time, the ratios of the two given sides for each triangle will let us solve the side-side-side (SSS) rule, if we take it a step further and use the Pythagorean Theorem. For now, just solve the target of the problem.
[tex]\frac{27}{13} = \frac{x}{21}[/tex]
27 ÷ 13 = 2.077
[tex]2.077 = \frac{x}{21}[/tex]
[tex]2.077[/tex] * 21 = [tex]\frac{x}{21}[/tex] * 21
Cancel the 21s from the denominator and factor on the right side.
43.617 = x
x = 43.6 because you round to one decimal.
Solve AABC. Round your answers to the nearest hundredth, if necessary
Answer:
[tex]C=25^{\circ},\\a\approx 10.72,\\b\approx 11.83[/tex]
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be [tex]180-90-65=25^{\circ}[/tex].
In any triangle, the Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex].
Therefore, we have:
[tex]\frac{\sin 90^{\circ}}{b}=\frac{\sin 25^{\circ}}{5},\\\\b=\frac{5\sin90^{\circ}}{\sin 25^{\circ}}=11.8310079158\approx \boxed{11.83}[/tex]
[tex]\frac{a}{\sin 65^{\circ}}=\frac{5}{\sin25^{\circ}},\\a=\frac{5\sin 65^{\circ}}{\sin25^{\circ}}=10.7225346025\approx \boxed{10.72}[/tex]
in which quadrants does (-1,4)
Answer:
second quadrant is the answer of your question
hope it is helpful to you
In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculate the 95% confidence interval for the proportion of students who get coaching on the SAT .
Answer:
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
427 had paid for coaching courses and the remaining 2733 had not.
This means that [tex]n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147[/tex]
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
The list shows the number of students in various college classes: 32, 19, 89, 102, 157, 25, 189, 36, 48
What is the median?(Q2)?
Answer:89
Step-by-step explanation:
Step-by-step explanation:
The median is the middle value of the data set arranged in ascending order, that is smallest to largest.
Please Evaluate
27 ÷ 3(3)
Answer:
3
Step-by-step explanation:
27 ÷ 3(3)
3(3) is equal to 3 * 3, which is 9.
27 ÷ 9 = 3.
PLEASE HELP!!! ASAP PLEASE !! IM BEGGING !!!!!!!
Answer:143!!
Step-by-step explanation:answer : 143
What is the result of subtracting the second equation from the first?
-4x-2y=-2
x-2y=9
Please tell me if I should answer with the point (10, 5) or some way else.
Please help asap
I might give brainliest
Answer:
5x = 11.
Step-by-step explanation:
-4x - 2y = -2
x - 2y = 9
Subtracting:
-4x - x - 2y - (-2y) = -2 - 9
-5x - 2y + 2y = -11
-5x = -11
5x = 11.
What is the value ? 10-8,10-2,10-12,10-14,10-25
easy math question help solve for x
Answer:
x=100
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
53+ (x-22) = 131
x+31 = 131
Subtract 31 from each side
x +31-31 = 131-31
x = 100
Over a season in a women's basketball league Jackson scored 41 more points than the second-highest scorer, Leslie. Together, Jackson and Leslie scored 1205 points during the season. How many points did each player score over the course of the season?
Answer:
Here are the aswers
Step-by-step explanation:
jackson=618
leslie=587
I hope this helps?!?
Help PLSSS!!!!! I will give brainlyest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 17 1/2 or decimal form = 17.5
Step-by-step explanation: Hope this helped!
Answer:
17.5 Statues im pretty sure.
Step-by-step explanation:
7/8 divided by 1/20
A publishing house is selling subscriptions to magazines for 10% off the original price.
If a subscription to Time Magazine usually costs $50, how much will it cost on sale?
A) $5
B) $45
C) $42
D) $55.56
Answer:
B. 45
Step-by-step explanation:
50x.10=5 discount
50-5=45
z= 8i – 172
Re(z) =
Im(z)
Andre wrote the inequality to plan his time. Describe what 3x + 10 ≤ 30 represent in this inequality.
Step-by-step explanation:
3x + 10 ≤ 30 3x ≤ 30 - 10 3x ≤ 20x ≤ 20/3area of a circle with a diameter of 8 inches
Answer:
8 divided by two equals the radius 4
3.14*4^2=50.24
Hope This Helps!!!
Can someone help me I am stuck on this question =-(
Answer:
0.2376, 2.376, 23.76, 237.6
Step-by-step explanation:
