Answer:
Sum is 20,935.
Step-by-step explanation:
This is an arithmetic progression.
Sum:
[tex]S = \frac{n}{2} (2a + (n - 1)d) [/tex]
n is the number of terms, n = 79
S is the sum
a is the first term, a = -8
d is common difference, d = -1-(-8) = 7
substitute:
[tex]S = \frac{79}{2} (2 \times - 8 + (79 - 1) \times 7)) \\ \\ S = \frac{79}{2} ( - 16 + 546) \\ \\ S = \frac{79}{2} (530) \\ S = 20935[/tex]
Morgan puts $3,200 into an investment account that earns compound
interest at a rate of 0.6% per month. Calculate the accumulated amount in
Morgan's account at the end of the 15th month.
Answer:
3500.416
Step-by-step explanation:
Compound interest formula
A = A0(1 + r/n)^nt
3200(1 + 0.6%)^15
3200(1 + 0.006)^15
3200(1.006)^15
How many gallons each of 25% alcohol and 5% alcohol should be mixed to obtain 20 gal of 16% alcohol?
Answer:
✓ x gal of 25% 20-x gal of 5% pure alcohol is x(.25)+(20-x)(.05)=20*.16=3.2 so .25x+1-.05x=3.2 gallons of 25% .20x=2.2 gallons of 5% x=11 gallons of 25%.
Step-by-step explanation:
Hope this helps~ ;D
find the value of n, if (n+1)! = 6*(n-1)!
Answer:
2
Step-by-step explanation:
(n+1)!=1×2×...×(n-1)×n×(n+1)
6*(n-1)!=1×2×...×(n-1)
--> n×(n+1)=6
-->n=2
Selena's gross annual salary as the Content editor of a fashion Magazine is Rs 40000 she contribute 10% of her salary. before she pays taxes to a retirement account 25% of her remaining salary is then consumed in state and federal taxes. what is the selenas annual in take home salary if she also has to pay Rs 30 for health Insurance each month.
Answer:
Selena's annual intake home salary is $ 26,640.
Step-by-step explanation:
Since Selena's gross annual salary as the content editor of a fashion Magazine is $ 40,000, and she contributes 10% of her salary before she pays taxes to a retirement account, and 25% of her remaining salary is then consumed in state and federal taxes, To determine what is Selena's annual intake home salary if she also has to pay $ 30 for health Insurance each month, the following calculation must be performed:
40,000 - (40,000 x 0.1) - (40,000 x 0.9 x 0.25) - (30 x 12) = X
40,000 - 4,000 - 9,000 - 360 = X
26.640 = X
Therefore, Selena's annual intake home salary is $ 26,640.
At 2pm, the temperature was 9°F. At 11pm, the temperature was -11°F. What was the change in
temperature?
Answer:
21 degrees
Step-by-step explanation:
I did it on the calculator
Which equation has a constant of proportionality equal to 2?
Answer:
[tex]{ \tt{y = 2x}}[/tex]
Answer:
2y=x
Step-by-step explanation:
Under which transformation can the image be a different size than the original
figure?
A. translation
B. rotation
C. dilation
D. reflection
C. Dilation.
Dilation can resize the image.
Translation will shift the imagine's position but won't change its actual size.
Rotation will mangle with image's orientation but also won't change its size.
Reflection is just a type of rotation which as established, also won't change its size.
Hope this helps.
Someone help please
66 because you have to solve the problem next time
A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 2 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 15 feet from the wall?
Answer:
The area of the triangle formed is increasing at a rate of 29.75 square feet per second.
Step-by-step explanation:
A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.
Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.
According to the Pythagorean Theorem:
[tex]\displaystyle x^2+y^2=1521[/tex]
Let's take the derivative of both sides with respect to time t. Hence:
[tex]\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right][/tex]
Implicitly differentiate:
[tex]\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]
Simplify:
[tex]\displaystyle x\frac{dx}{dt} + y \frac{dy}{dt} = 0[/tex]
The area of the triangle formed will be given by:
[tex]\displaystyle A = \frac{1}{2} xy[/tex]
Again, let's take the derivative of both sides with respect to time t:
[tex]\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right][/tex]
From the Product Rule:
[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)[/tex]
At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.
[tex]\displaystyle y = \sqrt{1521-(15)^2}=36[/tex]
The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:
[tex]\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}[/tex]
Evaluate for dy/dt:
[tex]\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}[/tex]
Finally, using dA/dt, substitute in appropriate values:
[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)[/tex]
Evaluate. Hence:
[tex]\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}[/tex]
The area of the triangle formed is increasing at a rate of 29.75 square feet per second.
(c³d)a(cd⁷)a
Simplify
Answer:
= c^4 d^8 a^2
Step-by-step explanation:
Apply exponent rule: aa= a^2
= c^3 da^2 cd^7
= c^4 da^2 d^7
= c^4 d^8 a^2
If anyone can give me the answer that will be greatly appreciated :)
42-x=58
or, -x=58-42
with change in side sign also chamges we change sides to make like terms in one side and unlike in amother side.
or, -x= 16
or,x=-16.
therefore x=-16...
Hope this helps you.
HHHEELPP HELP HELP!!
I need the answer ASAP!!!!
Answer:
Step-by-step explanation:
B because the vertex is at point (3, 4) which is greatest.
Answer:
[tex]\text{b. } y=-(x-3)^2+4[/tex]
Step-by-step explanation:
Algebraically, we want to compare the y-coordinates of the vertex, since all the functions shown are parabolas that are concave down.
Let's break the format down:
The negative sign in front of each of the functions indicate that the parabolas will be concave down (open downwards), which means the vertex represents the function's maximum. The term inside the parentheses when applicable to just indicates the horizontal/phase shift.
Since the first term being squared is negative, we want to minimize its value to produce the greatest possible y-value.
Therefore, substitute whatever value of [tex]x[/tex] that makes each [tex]x^2[/tex] term equal to 0. (Maximum value of [tex]-x^2[/tex] is 0).
Therefore, we can simplify compare the last terms in each equation.
Equation A's last term is 3.
Equation B's last term is 4.
Equation C's last term is -5.
Equation D's last term is 0.
Since equation B has the greatest last term, it will have the greatest possible y-value.
James, Aimee and Zack have
weighed their suitcases. Each
weighs a prime number of
kilograms and the total weight
is 40kg.
an
What's the difference between
the lightest and heaviest
suitcase?
Answer:
29Kg
Step-by-step explanation:
P1=2Kg
P2=7Kg
P3=31Kg
P3-P1=29Kg
To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.
I was lucky and I got the result after few steps :-)
2-[6÷2+{6×1/2+(7/2-3/2)}]
Answer:
-6
Step-by-step explanation:
2 - [6 ÷ 2 + {6 × 1/2 + (7/2 - 3/2)}] =
Follow the correct order of operations.
Do one step at a time and copy everything else each time, so you don't lose track of any operation.
= 2 - [6 ÷ 2 + {6 × 1/2 + 4/2}]
= 2 - [6 ÷ 2 + {6 × 1/2 + 2}]
= 2 - [6 ÷ 2 + {3 + 2}]
= 2 - [6 ÷ 2 + 5]
= 2 - [3 + 5]
= 2 - 8
= -6
Answer:
-6
hope this helps
Step-by-step explanation:
2_(6÷2+(6*1/2+(7/2-3/2))) solve the ones in bracket first
(7/2-3/2)=2
2-(6÷2+(6×1/2+2))
6×1/2+2
6×1/2=3
3+2=5
2-(6÷2+5)
6÷2=3
3+5=8
2-8
=-6
Help please
Please help
9514 1404 393
Answer:
4. True
5. False
Step-by-step explanation:
4. The number of x-intercepts produced by the quadratic formula may be 0, 1, or 2. It will be 0 if the two roots are complex. It will be 1 if the two roots lie in the same place (one root with multiplicity 2). It is true that there may be only one x-intercept.
__
5. The value of 'b' in the quadratic formula is the coefficient of the linear term. In the given quadratic, it is -5, not 5.
What is the equation of the following line? Be sure to scroll down first to see
all answer options
Answer:
y=1/4x
Step-by-step explanation:
Just did the math ;D
I’m honestly not the best at math, can someone help?
Answer:
1/8
Step-by-step explanation:
Using the factor tree, we see that there is 8 possible outcomes ( right hand side)
There is only 1 way to go from left to right and have 3 wins
P(3 wins) = good outcomes / total
=1/8
Which is the correct calculation of the y-coordinate of point A? 0 (0 - 0)2 + (1 - y2 = 2 O (0 - 1)² + (0- y2 = 22 (0-0)² + (1 - y2 = 2 (0 - 1)2 + (0-y2 = 2
Answer:
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
Step-by-step explanation:
The equation of the circle is represented by the following expression:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.
[tex]r[/tex] - Radius of the circle.
If we know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]r = 2[/tex], then the equation of the circle is:
[tex]x^{2} + y^{2} = 4[/tex] (1b)
Then, we clear [tex]y[/tex] within (1b):
[tex]y^{2} = 4 - x^{2}[/tex]
[tex]y = \pm \sqrt{4-x^{2}}[/tex] (2)
If we know that [tex]x = 1[/tex], then the y-coordinate of point A is:
[tex]y = \sqrt{4-1^{2}}[/tex]
[tex]y = \sqrt{3}[/tex]
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
During a certain 9-year period, the Consumer Price Index (CPI) decreased by
45%, but during the next 9-year period, it decreased by only 5%. Which of
these conditions must have existed during the second 9-year period?
A. Deflation
B. Stagnation
C. Conflation
D. Inflation
Answer:
deflation ,,,,
Step-by-step explanation:
I hope it's helpful for you ☺️Deflation must have existed during the second 9-year period.
What is deflation?Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.
The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.
Given data ,
Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.
In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.
Hence , the process is deflation in the second year
To learn more about deflation click :
https://brainly.com/question/30060490
#SPJ7
Can someone possibly help me?
Answer:
72
Step-by-step explanation:
To be divisible by 4, the number must be even, so we can eliminate 63 and 73 (There are other restrictions for 4, we just want to eliminate answers that cannot be true)
We have only 2 answers left
64 and 72
To be divisible by 3, the sum of the digits must be divisible by 3
6+4 = 10 which is not divisible by 3
7+2 = 9 9/3 =3
I need help with this
Answer: D
Step-by-step explanation:
When a coordinate is reflected over the y-axis, it changes from (x, y) to (-x, y)
The three coordinates of ΔCDE are
C = (-8, -1)D = (-6, -5)E = (-2, -4)After the y-axis reflection, they'll become:
C' = (-(-8), -1) = (8, -1)D' = (-(-6), -5) = (6, -5)E' = (-(-2), -4) = (2, -4)I hope this is correct :\
0.
DETAILS
Model the data using an exponential function f(x) = Ab".
X
0
1
2
f(x)
400
240
144
f(x) =
Need Help?
Read It
Solve for xxx.
x=x=x, equals
Answer:
Step-by-step explanation:
BC/AB = DE/AD
1/2 = x/(2+1)
x = 1.5
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
See this attachment
find the area of this unusual shape.
Answer:
104 m^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w = 10*8 = 80
Then find the area of the triangle
A = 1/2 bh = 1/2 (8) * 6 = 24
Add the areas together
80+24 = 104 m^2
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!! THIS IS NOT A TEST OR AN ASSESSMENT!!! Please help me answer these questions. Chapter 12 part 1
1. What is a recursive formula?
2. What is a factorial?
3. What is the relationship between sequences, series and sigma notation?
Answer:
1. What is a recursive formula?
A recursive formula is a formula that defines each term of a sequence using preceding terms of the sequence.
2. What is a factorial?
factorial the product of all positive integers less than or equal to n:
3. What is the relationship between sequences, series and sigma notation?
A series can be represented in a sigma notation.
A series can be represented in a sigma notation.A series is a sum of a sequence of terms.
Kids with cell phones: A marketing manager for a cell phone company claims that the percentage of children aged 8-12 who have cell phones differs from 52%. In a survey of 832 children aged 8-12 by a national consumers group, 449 of them had cell phones. Can you conclude that the manager's claim is true? Use the a 0.10 level of significance and the P-value method. 1. State the appropriate null and alternate hypotheses.2. Compute the test statistic.
Answer:
Low-value method
Step-by-step explanation:
consumers group
Find the percentile rank for each test score in the data set. 12, 28, 35, 42, 47, 49, 50 What value corresponds to the 60th percentile
Answer:
Percentile rank:
12 = 7th
28 = 21st
35 = 36th
42 = 50th
47 = 64th
49 = 79th
50 = 93rd
- Vth number i.e. 47 is the value that corresponds to the 60th percentile.
Step-by-step explanation:
As we know,
Percentile rank = [(Number of values below x) + 0.5]/total number of values * 100
For 12,
Percentile rank = [0 + 0.5]/7 * 100
= 7th
For 28,
Percentile rank = [1 + 0.5]/7 * 100
= 21st
For 35,
Percentile rank = [2 + 0.5]/7 * 100
= 36th
For 42,
Percentile rank = [3 + 0.5]/7 * 100
= 50th
For 47,
Percentile rank = [4 + 0.5]/7 * 100
= 64th
For 49,
Percentile rank = [5 + 0.5]/7 * 100
= 79th
For 50,
Percentile rank = [6 + 0.5]/7 * 100
= 93rd
Now,
n = 7
60th percentile = 60% of n
So,
60% of n = 60/100 * 7
= 0.6 * 7
= 4.2
After rounding it off,
5th value is the 60th percentile i.e. 47.
The hypotenuse of a right triangle is 16 units and the length of one of the legs is 12 units. What is the length of the other leg in simplest radical form?
A. 2√13
B. 4√11
C. 2√17
D. 4√7
Answer:
D, 4√7
Step-by-step explanation:
Answer:
Step-by-step explanation:
c = 16
a = 12
b = ?
a^2 + b^2 = c^2
12^2 + b^2 = 16^2
144 + b^2 = 256
b^2 = 256 - 144
b^2 = 112
b^2 = 16 * 7
sqrt(b^2) = sqrt(16)*sqrt(7)
b = 4 * sqrt(7)
Solve for x Solve for x Solve for x
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
The two right triangles share angle A, so the similarity statement can be written ...
ΔABC ~ ΔADE
Corresponding sides are proportional, so we have ...
BC/DE = AB/AD
x/12 = 3/(3+9)
x = 3 . . . . . . . . . . multiply by 12
Answer:
x=3
this is correct!!!
f(x) = x ^ 2 - x - 6; g(x) = 2x ^ 2 + 5x + 2 Find: (f/g)(X)
Answer:
[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]
Step-by-step explanation:
Given
[tex]f(x) =x^2 -x - 6[/tex]
[tex]g(x) = 2x^2 + 5x + 2[/tex]
Required
[tex](\frac{f}{g})(x)[/tex]
This is calculated as:
[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]
So, we have:
[tex](\frac{f}{g})(x) = \frac{x^2 - x - 6}{2x^2 + 5x + 2}[/tex]
Expand
[tex](\frac{f}{g})(x) = \frac{x^2 +2x - 3x - 6}{2x^2 + 4x+x + 2}[/tex]
Factorize
[tex](\frac{f}{g})(x) = \frac{x(x +2) - 3(x + 2)}{2x(x + 2)+1(x + 2)}[/tex]
Factor out x + 2
[tex](\frac{f}{g})(x) = \frac{(x- 3)(x + 2)}{(2x + 1)(x + 2)}[/tex]
Cancel out x + 2
[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]
