Answer: $107,836.69 or about $107,837 (to the nearest dollar)
Step-by-step explanation:
Formula to the accumulated amount received after investing principal amount (P) at rate of interest (r) compounded monthly for t months :
[tex]A=P(1+\dfrac{r}{12})^{t}[/tex]
As per given , A = $130,000
r= 7.5% = 0.075
t= 30 months
Now,
[tex]130000=P(1+\dfrac{0.075}{12})^{30}\\\\\Rightarrow 130000=P(1+0.00625)^{30}\\\\\Rightarrow 130000=P(1.00625)^{30}\\\\\Rightarrow 130000=P \times1.20552661036\\\\\Rightarrow\ P=\dfrac{130000}{1.2055266}=107,836.69[/tex]
Hence he need to invest $107,836.69 .
Number of times the individual changed jobs in the last 5 years is what kind of variable? A. This variable is a continuous numerical variable that is interval-scaled. B. This variable is a discrete numerical variable that is interval-scaled. C. This variable is a categorical variable that is ordinal-scaled. D. This variable is a discrete numerical variable that is ratio-scaled. E. This variable is a continuous numerical variable that is ratio-scaled. F. This variable is a categorical variable that is nominal-scaled.
Answer: D. This variable is a discrete numerical variable that is ratio-scaled.
Step-by-step explanation:
A Discrete variables are variables which are countable in a finite amount of time. For example, you can count the amount of money in your bank wallet, but same can’t be said for the money you have deposited in eveyones bank account as this is infinite.
So the number of times an individual changes job in a five years period is a perfect example of a discrete numerical variable that is ratio scaled because it can be counted.
algebra 2
50 POINTS
HELP
Answer:
{-3, 2}U{2, 5}
Step-by-step explanation:
For an equation to be negative, it would need to be in a negative range (below the x-axis or the coordinates are negative y-values). Therefore, we can examine this question and see that the graph is negative when the function crosses the x-axis at -3 and it remains negative until you reach 2 on the x-axis.
Therefore, the first set of negative values is (-3, 2).
Secondly, applying the same logic as before, the function decreases at 2 and then touches the x-axis again at 5. Therefore, the second negative value would be (2, 5).
The negative values are {-3, 2}U{2, 5}.
Answer:
{-3, 2}U{2, 5}
Step-by-step explanation:
the perimeter of a rectangle is 12cm. If the length is 2 less than 3 times the width, find the length
Answer:
The length of the rectangle would be 4.
Step-by-step explanation:
We can start by naming the width x.
Therefore, the length would 3x-2.
The perimeter of the rectangle would then be:
2(3x-2+x)
We can set up the given equation
2(3x-2+x)=12
Solve for x.
Divide both sides by 2.
3x-2+x=6
Combine like terms.
4x-2=6
Add 2 to both sides.
4x=8
Divide both sides by 4.
x=2
The width would then be 2.
We can plug that into the expression for length.
3x-2
3(2)-2
6-2
4
The length of the rectangle would be 4.
Ana must take 11.25 mL of Medicine A daily. She must take 5.5 mL of Medicine B daily. How many more ml of Medicine A than Medicine B must she take
daily?
Answer:
5.75
Step-by-step explanation:
11.25 - 5.5 = 5.75.
So, Ana must take 5.5 more mL of Medicine A than Medicine B.
Hope this helps!
How do you write 1/46 in simplest form.
Answer:
1/46 is already in the simplest form.
Answer:
1/46 is already in its simplest form.
What is mAngleRST in degrees?
Answer:
The measure of angle RST = 120°
Step-by-step explanation:
Answer:
The measure of angle RST = 120°
hope this helps
Suppose Q is the midpoint of PR. Use the information to find the missing value.
11) PQ = 3x + 14 and QR = 7x - 10 x =
Answer:
x = 6
Step-by-step explanation:
Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.
Therefore, PQ = QR. Which is:
[tex] 3x + 14 = 7x - 10 [/tex]
Solve for x. Collect like terms
[tex] 3x -7x = - 14 - 10 [/tex]
[tex] -4x = -24 [/tex]
Divide both sides by -4x
[tex] x = 6 [/tex]
The value of β is:
60º
45º
90º
30º
75º
Answer:
60°
Step-by-step explanation:
The definition of cosine tells you ...
cos(β) = 3/6 = 1/2
β = arccos(1/2) . . . . use the inverse cosine function to find the angle
β = 60°
_____
The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...
1 : √3 : 2
The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.
Solve M= 2HA + 2HT for H.
Answer:
H = M/(2A +2T)
Step-by-step explanation:
Factor out H and divide by its coefficient.
M = 2HA +2HT
M = H(2A +2T)
M/(2A +2T) = H
H = M/(2A +2T)
Which x values is the graph below discontinuous
Answer:
-3,-1,1,3,5
Step-by-step explanation:
Find the area of the region that lies inside the first curve and outside the second curve.
r= 10cos( θ)
r= 5
Answer:
Step-by-step explanation:
From the given information:
r = 10 cos( θ)
r = 5
We are to find the the area of the region that lies inside the first curve and outside the second curve.
The first thing we need to do is to determine the intersection of the points in these two curves.
To do that :
let equate the two parameters together
So;
10 cos( θ) = 5
cos( θ) = [tex]\dfrac{1}{2}[/tex]
[tex]\theta = -\dfrac{\pi}{3}, \ \ \dfrac{\pi}{3}[/tex]
Now, the area of the region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e
[tex]A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \ \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ 5^2 d \theta[/tex]
[tex]A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \ \theta d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ d \theta[/tex]
[tex]A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} \dfrac{cos \ 2 \theta +1}{2} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}[/tex]
[tex]A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} {cos \ 2 \theta +1} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}[/tex]
[tex]A =25 \begin {bmatrix} \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}} \ \ - \dfrac{25}{2} \begin {bmatrix} \dfrac{2 \pi}{3} \end {bmatrix}[/tex]
[tex]A =25 \begin {bmatrix} \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3}) \end {bmatrix} - \dfrac{25 \pi}{3}[/tex]
[tex]A = 25 \begin{bmatrix} \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} + \dfrac{\pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}[/tex]
[tex]A = 25 \begin{bmatrix} \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}[/tex]
[tex]A = \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}[/tex]
The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.
Simplify and Show all of your work please!
Answer:
[tex]\Huge \boxed{\mathrm{9}}[/tex]
Step-by-step explanation:
[tex]\Rightarrow \displaystyle \frac{18 \div 2 * 3}{5-2}[/tex]
Dividing first.
[tex]\Rightarrow \displaystyle \frac{9 * 3}{5-2}[/tex]
Multiplying and subtracting.
[tex]\Rightarrow \displaystyle \frac{27}{3}[/tex]
Division.
[tex]\Rightarrow 9[/tex]
the product of a number and 3 of that number and six is the same as the sum
Which operation would you do third in the following problem?
8 (10-4)
6
addition
subtraction
multiplication
division
Answer:
multiplication
Step-by-step explanation:
it seems the best
Round to the nearest cent.
6. $10.407
Answer:
the answer is 10.41. If you have a number 5 or more you round the nearest number on the left up 1 if it's 4 or less it stays the same it doesn't go up or down.
411,500 science notation
Answer:
the answer is 4.115 x 10^5
Step-by-step explanation:
hope that helps
Explain How you got that answer
Answer:
[tex]\huge\boxed{Center= (-3,4) , Radius = 5\sqrt{2} }[/tex]
Step-by-step explanation:
Given equation is
[tex]x^2 + y^2 + 6x-8y - 25 = 0[/tex]
Adding 25 to both sides
[tex]x^2 + y^2 +6x-8y = 25[/tex]
Completing squares
[tex]x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25[/tex]
Both of their "b" is -3 and 4 respectively
So, adding (-3)² => 9 and (4)² => 16 to both sides
[tex](x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5\sqrt{2)^2}[/tex]
Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex], where center = (h,k) and radius = r.
We get:
Center = (-3,4)
Radius = [tex]5\sqrt{2}[/tex]
To save for her newborn son's college education, Kelli Peterson will invest $1,500.00 at the end of each year for the next 18 years. The interest rate she expects to earn on her investment is 9%. How much money will she have saved by the time her son turns 18?
Answer:
9% of $1500 is $15 so she gains an extra $15 for each of the 18 years
$1500 in the bank each year for 18 years is $27000 after 18 years
$15 each year as well so that’s an extra $270 in the bank
The total in the bank is the sum of what she has invested and the interest so the total in the bank is $27270
Step-by-step explanation:
please help ive been stuck on this for a very long time
By Thales' theorem:
[tex]\[\begin{array}{l}\frac{{18}}{{2x + 2}} = \frac{{24}}{{3x + 1}}\\18(3x + 1) = 24(2x + 2)\\54x + 18 = 48x + 48\\6x = 30\\x = 5\\A.\end{array}\][/tex]
16p - 32q + 5 when p= 2 and q = 1
Answer:
0
Step-by-step explanation:
16x2= 32 and 32x1=32 so 32-32=0
S. Determine which is the best buy. Show calculations and explain your answer Ed's Bagels 4 for $.89 Best Bagels Only $1.39 for 6
Answer:
eds bageles are $.22 per bagel and best bagels are $.23 per bagel.
Step-by-step explanation:
Solve for w 98 = 7w Simplify your answer as much as possible.
Answer:
W = 14
Step-by-step explanation:
7w=98
Divide
w=98/7
Done
w=14
Hope this helps! :)
(pls mark brainliest)
Answer:
w = 14
Step-by-step explanation:
98 = 7w
98/7 = 7w/7
14 = w
Hope this helps.
what is 67% of 89.5?
Answer:
59.96
Step-by-step explanation:
when 67% if 89.5 is expressed in numbers,
[tex]\frac{67}{100}*89.5\\ \frac{5996.5}{100}\\ =59.96[/tex]
Find an equation of the line passing through the point (−3,−7) that is perpendicular to the line y= −5x+4
Answer:
y = 1/5x - 6.4
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes, so the slope will be 1/5
Then, plug the slope and the point into the equation y = mx + b to find b
y = mx + b
-7 = 1/5(-3) + b
-7 = -0.6 + b
-6.4 = b
Then, plug this and the slope into the equation
y = 1/5x - 6.4 will be the equation
Total employment for metal workers in 2019 is projected to be 210,000. If this is a 5% increase from 2009, approximately what was the total employment in 2009?
Answer:
200,000
Step-by-step explanation:
To solve this, you can divide the 2019 total projected employment (210,000) by 1 + the growth rate (.05) to find the 2009 total employment.
210,000 / (1 + .05) = 200,000
I hope this helps!
-TheBusinessMan
Find the equation of the line perpendicular to y=2x-6 that passes through the point (1,5). If possible, write the equation in slope-intercept form.
Answer:
[tex]y=-0.5x+4.5[/tex]
Step-by-step explanation:
The slope of [tex]y=2x-6[/tex] is:
[tex]2[/tex]The negative reciprocal of that slope is:
[tex]m=-\frac{1}{2}[/tex]So the perpendicular line will have a slope of [tex]-1/2[/tex]:
[tex]y - y_1 = (-\frac{1}{2} )(x - x_1)[/tex]And now put in the point [tex](1,5)[/tex]:
[tex]y-5=(-\frac{1}{2})(x-1)[/tex]And that answer is OK, but let's also put it in [tex]y=mx+b[/tex] form:
[tex]y-5=-\frac{x}{2}+\frac{1}{2}[/tex][tex]y=-\frac{x}{2}+\frac{11}{2}[/tex][tex]y=-0.5x+4.5[/tex]Now change matrix B to a 3 x 3 matrix and enter
these values for B:
B=
1.2 1.4 3.1
2.2 1.1 5.6
3.7 4.2 6.7
The 3×3 Matrix is [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]
What is Matrix?
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object
What is 3×3 Matrix?A 3 x 3 matrix is calculated for a matrix having 3 rows and 3 columns
Given,
B=
1.2 1.4 3.1
2.2 1.1 5.6
3.7 4.2 6.7
Then the 3×3 matrix is
[tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]
Hence, The 3×3 Matrix is [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]
Learn more about Matrix and 3×3 Matrix here
https://brainly.com/question/12759849
#SPJ2
Answer:
Step-by-step explanation:
c11 =
⇒ 56.1
c12 =
⇒ 12.1
c13 =
⇒ 236
What will be the remainder when 6x ^5+ 4x^4 -27x^
3
- 7x² + 27x + 3/2 is divided by (2x^2 - 3)
^2
Answer:
Remainder = (3145/8)x - 408
Step-by-step explanation:
We want to find the remainder when 6x^(5) + 4x⁴ - 27x³ - 7x² + 27x + 3/2 is divided by (2x² - 3)²
Let's expand (2x² - 3)² to give ;
(2x - 3)(2x - 3) = 4x² - 6x - 6x + 9 = 4x² - 12x + 9
So,we can divide now;
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
First of all, we'll divide the term with the highest power inside the long division symbol by the term with the highest power outside the division symbol. This will give;
3/2x³
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
6x^(5)-18x⁴-(27/2)x³
We now subtract the new multiplied term beneath the original one from the original one to get;
3/2x³
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
6x^(5)-18x⁴-(27/2)x³
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
22x⁴+(27/2)x³+27x +3/2
We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;
(3/2)x³ + (11/2)x²
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
6x^(5)-18x⁴-(27/2)x³
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
22x⁴+(27/2)x³+27x +3/2
22x⁴-66x³ + (99/2)x²
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
We now subtract the new multiplied term beneath the immediate one from the immediate one to get;
(3/2)x³ + (11/2)x²
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
6x^(5)-18x⁴-(27/2)x³
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
22x⁴+(27/2)x³-7x²+27x +3/2
22x⁴-66x³ + (99/2)x²
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
(159/2)x³-(113/2)x²+27x+(3/2)
We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;
(3/2)x³ + (11/2)x² + (159/8)x
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
6x^(5)-18x⁴-(27/2)x³
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
22x⁴+(27/2)x³-7x²+27x +3/2
22x⁴-66x³ + (99/2)x²
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
(159/2)x³-(113/2)x²+27x+(3/2)
(159/2)x³-(477/2)x²+(1431/8)x
We now subtract the new multiplied term beneath the immediate one from the immediate one to get;
(3/2)x³ + (11/2)x² + (159/8)x
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
6x^(5)-18x⁴-(27/2)x³
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
22x⁴+(27/2)x³-7x²+27x +3/2
22x⁴-66x³ + (99/2)x²
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
(159/2)x³-(113/2)x²+27x+(3/2)
(159/2)x³-(477/2)x²+(1431/8)x
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
182x²-(1215/8)x + (3/2)
We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;
(3/2)x³+(11/2)x²+(159/8)x+(91/2)
______________________
4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2
6x^(5)-18x⁴-(27/2)x³
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
22x⁴+(27/2)x³-7x²+27x +3/2
22x⁴-66x³ + (99/2)x²
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
(159/2)x³-(113/2)x²+27x+(3/2)
(159/2)x³-(477/2)x²+(1431/8)x
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
182x²-(1215/8)x + (3/2)
182x²-545x + 819/2
We now subtract the new multiplied term beneath the immediate one from the immediate one to get;
182x² - (1215/8)x + (3/2) - 182x² + 545x - 819/2 = (3145/8)x - 408
Remainder = (3145/8)x - 408
3 πd=12 π
what does d equal?
__________
D = 4
__________
i blelieve this is it.
Answer:
d =4Step-by-step explanation:
[tex]3\pi d = 12 \pi\\\\divide\:both\:sides\:of\:the\:equation\:by\: 3\:\pi\\\frac{3 \pi d}{3\pi} = \frac{12 \pi}{3\pi} \\\\d=4[/tex]
Solve the problem. A variable x has the possible observations shown below. Possible observations of x: -3 -1 0 1 1 2 4 4 5 Find the z-score corresponding to an observed value of x of 2.
Answer:
The z-score corresponding to an observed value of x of 2 is 0.215.
Step-by-step explanation:
We are given that a variable x has the possible observations shown below;
Possible observations of X: -3, -1, 0, 1, 1, 2, 4, 4, 5.
Firstly, we will find the mean and the standard deviation of X, i.e;
Mean of X, ([tex]\mu[/tex]) = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{(-3)+ (-1)+ 0+ 1+ 1+ 2+ 4+ 4+ 5}{9}[/tex]
= [tex]\frac{13}{9}[/tex] = 1.44
Standard deviation of X, ([tex]\sigma[/tex]) = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{(-3-1.44)^{2}+(-1-1.44)^{2}+......+(4-1.44)^{2}+(5-1.44)^{2} }{9-1} }[/tex]
= 2.603
Now, the z-score corresponding to an observed value of x of 2 is given by;
z-score = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{2-1.44}{2.603}[/tex] = 0.215.