Answer:
-7*6^n
Step-by-step explanation:
The sequence is -7*6^n.
A few examples of this are the following,
ex.)
-7*6^0 = -7
-7*6^1 = -42
-7*6^2 = -252
A certain t-shirt costs $10 less than half the cost of a pair of pants. If the t-shirt costs $15, how much is the cost of the pair of pants?
15 divided by two is 7.5 and ten plus 7.5 is 17.5…. It says less than half the cost so I would round down to get $17 for the pain of pants
The cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A certain t-shirt costs $10 less than half the cost of a pair of pants. If the t-shirt costs $15.
Let x be the cost of the pair of pants.
The value of x can be found as follows:
x = 15/2 + 10
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.
x = $17.5
Thus, the cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.
Learn more about the linear equation here:
brainly.com/question/11897796
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3000 dollars is invested in a bank account at an interest rate of 7 percent per year, compounded continuously. Meanwhile, 20000 dollars is invested in a bank account at an interest rate of 5 percent compounded annually.
To the nearest year, when will the two accounts have the same balance?
9514 1404 393
Answer:
after 89 years
Step-by-step explanation:
For principal p, interest rate r, and number of years t, the two account balances are ...
a = p·e^(rt) . . . . continuous compounding
a = p(1+r)^t . . . . annual compounding
Using the given values, we have
3000·e^(0.07t) . . . . . compounded continuously
20000·1.05^t . . . . . . compounded annually
We want to find t so these are equal.
3000·e^(0.07t) = 20000·1.05^t
0.15e^(0.07t) = 1.05^t . . . . divide by 20,000
ln(0.15) +0.07t = t·ln(1.05) . . . . take natural logarithms
ln(0.15) = t·(ln(1.05) -0.07) . . . . subtract 0.07t
t = ln(0.15)/(ln(1.05) -0.07) ≈ -1.8971/-0.02121 . . . . . divide by the coefficient of t
t ≈ 89.4 ≈ 89
The two accounts will have the same balance after 89 years.
Which value is the closet approximation of the square root of 27
A 4.5
B 5
C 5.5
D 5.9
10,4,7
The above set 4 numbers have a mean of 8
what could the mystery number
11 is the mystery number
Answer:
The mystery number is 11
Step-by-step explanation:
→ Set up an equation
( 10 + 4 + 7 + x ) ÷ 4 = 8
→ Multiply both sides by 4
21 + x = 32
→ Minus 21 from both sides
x = 11
for what value of x does 4^x=(1/8)^x+5?
Use main properties of powers
(a^m)^n=a^{m\cdot n};(am)n=am⋅n;
\dfrac{1}{a^n}=a^{-n}an1=a−n
to simplify given equation.
1.
4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.
2.
\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.
3. Then the equation is
2^{2x}=2^{-3x-15}.22x=2−3x−15.
The bases are the same, so equate the powers:
2x=-3x-15,
2x+3x=-15,
5x=-15,
x=-3.
Answer: for x=-3.
2. Sum of two numbers = 16
Difference of the numbers = 6
Find the numbers.
What is their product?
Answer:
Step-by-step explanation:
let the numbers be x and y.
x+y=16
x-y=6
add
2x=22
x=22/2=11
11+x=16
x=16-11=5
product xy=11×5=55
Travel Agency offers vacation packages. Each vacation package includes a city, a month, and an airline. The agency has 3 cities, 3 months, and 1 airline to choose from. How many different vacation packages do they offer?
=___
Two high school basketball players each played 5 games. Their stats are summarized below:
Player A: Stats on 5 games → mean points scored = 25, standard deviation = 4
Player B: Scored 23, 27, 28, 22, 25 points on 5 consecutive games
Suppose a university basketball scout (a person who finds new players for a university's team) is deciding which player to recruit. Who should they choose? Justify your response. [3 marks]
HINT: Compare mean and variance of each player.
Answer:
Player B.
Step-by-step explanation:
Player A has a mean score of 25.
Let's calculate Player B's mean score and compare it to Player A's.
23 + 27 + 28 + 22 + 25 / 5 = 125 / 5 = 25.
So, Player A and Player B have the same mean score.
This doesn't tell the scout which player is "better", so let's look at the variance.
The other statistic given for Player A is the standard deviation for their points. The given number is 4. Let’s calculate the standard deviation for Player B, and compare it to player A.
Recall that we add up the squares of the difference between each score and the mean, divide it by the total number of data, and square root that. So, the standard deviation for player B is sqrt(2^2 + 2^2 + 3^2 + 3^2 + 0^2 / 5) = sqrt (26/5) = sqrt (5.2) = 2.3.
Excellent. We have player A’s standard deviation, as well as player B’s standard of deviation. Since player B’s standard deviation is less than player A’s, it can be inferred that player B has more consistent results than player A, and the scout should get Player B.
Hope this helps!
The Volume of a sphare is 28/3 times the surface area calculate The surface area and the Volume of the sphere, correct to the nearest whole number.
Given:
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
To find:
The surface area and the volume of the sphere.
Solution:
Volume of a sphere:
[tex]V=\dfrac{4}{3}\pi r^3[/tex] ...(i)
Surface area of a sphere:
[tex]A=4\pi r^2[/tex] ...(ii)
Where, r is the radius of the sphere.
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
[tex]V=\dfrac{28}{3}\times A[/tex]
[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]
Multiply both sides by 3.
[tex]4\pi r^3=112\pi r^2[/tex]
[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]
[tex]r=28[/tex]
Using (i), the volume of the sphere is:
[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]
[tex]V\approx 91989[/tex]
Using (ii), the surface area of the sphere is:
[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]
[tex]A=9856[/tex]
Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.
A group of three undergraduate and five graduate students are available to fill certain student government posts. If four students are to be randomly selected from this group, find the probability that exactly two undergraduates will be among the four chosen.
Answer:
[tex]Pr = 0.4286[/tex]
Step-by-step explanation:
Given
Let
[tex]U \to\\[/tex] Undergraduates
[tex]G \to[/tex] Graduates
So, we have:
[tex]U = 3; G =5[/tex] -- Total students
[tex]r = 4[/tex] --- students to select
Required
[tex]P(U =2)[/tex]
From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.
First, we calculate the total possible selection (using combination)
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
So, we have:
[tex]Total = ^{U + G}C_r[/tex]
[tex]Total = ^{3 + 5}C_4[/tex]
[tex]Total = ^8C_4[/tex]
[tex]Total = \frac{8!}{(8-4)!4!}[/tex]
[tex]Total = \frac{8!}{4!4!}[/tex]
Using a calculator, we have:
[tex]Total = 70[/tex]
The number of ways of selecting 2 from 3 undergraduates is:
[tex]U = ^3C_2[/tex]
[tex]U = \frac{3!}{(3-2)!2!}[/tex]
[tex]U = \frac{3!}{1!2!}[/tex]
[tex]U = 3[/tex]
The number of ways of selecting 2 from 5 graduates is:
[tex]G = ^5C_2[/tex]
[tex]G = \frac{5!}{(5-2)!2!}[/tex]
[tex]G = \frac{5!}{3!2!}[/tex]
[tex]G =10[/tex]
So, the probability is:
[tex]Pr = \frac{G * U}{Total}[/tex]
[tex]Pr = \frac{10*3}{70}[/tex]
[tex]Pr = \frac{30}{70}[/tex]
[tex]Pr = 0.4286[/tex]
y = –2x2 - 4x – 6 has how many real roots?
Answer:
Step-by-step explanation:
None
They are both imaginary or complex. You can check that out by calculating the discriminate. If you get a minus answer, then there are no real roots. Let's try it.
a = - 2
b = - 4
c = - 6
D = sqrt(b^2 - 4*a * c)
D = sqrt( (-4)^2 - 4*(-2)(-6) )
D = sqrt( 16 - 48)
D = sqrt(-32) which is negative and there are no real roots.
4. a) x2 + xy2 + y 4
Answer:
x2 + xy2 + y 4=（x+y^2)^2-xy^2
Step-by-step explanation:
Find the principle that yields and interest of Rs.2240 at the rate of 10% p.a. in a years 6 months.
Step-by-step explanation:
I=PRT/100
p=I/RT×100
p=2240/10×2×100
p=11200
Please help i do not understand
Answer:
OPTION A
I CHOSE OPTION A AS THE ANSWER BECAUSE OPTI0N D CANNOT BE TRUE ACCORDING TO THE QUESTION AND OPTION B AND C ARENT TRUE BECAUSE IT WAS MENTIONED THAT AT 3 HOURS THE COST WOULD BE 140 $ BUT IN OPTION B IT SHOWS THAT THEY ALREADY ACHIEVED 200$ BEFORE IT EVEN BECAME 3 HOURS AND IT ISNT OPTION C BECAUSE IT CROSSED 150$ WHILE IT WAS 3 HOURS SO MOST LIKELY THE ANSWER IS TO BE OPTION A.
HOPE THIS HELPS YOU....
EVALUATE: 10x – 2y3 (if x = 5 and y = 2)
Answer:
10*(5) - 2*(2)^3
= 50 - 2*8
= 50 - 16
=34
Answer:
Step-by-step explanation:
với x=5 và y=2
phương trinh trở th a
10* 5 - 2 * 2^ 3
=50 - 2*8
=50 - 16
=34
757divide 100=to in hours and minutes
Answer:
Step-by-step explanation:
757 minutes = 12 hours 37 minutes
marked price of an item is 4000, what will be it's selling price having 20% discount and 10% vat.
Answer:
I HOPE IT WILL HELP
EXPLANATION IS IN THE PHOTO .
1. You are a contestant on the Wheel of Fun. The spinner contains 4 red panels,
5 yellow panels, a bankrupt panel, 7 blue panels and two free spin panels.
Utilize this given information to calculate the following probabilities:
a. Probability of a spin landing on a red panel.
b. Probability of a spin landing on anything but a blue panel.y that
C. Probability of a spin landing on a yellow or red.
d. Probability of a spin landing on a any non-color panel.
Okay
Answer:
We have:
4 red panels
5 yellow panels
1 bankrupt panel
7 blue panels
2 free spin panels
for a total of:
4 + 5 +1 + 7 + 2 = 19 panels.
And we can assume that all the panels are equal, so the probability of landing on every single one is the same.
a) Probability of a spin landing on a red panel.
This will be equal to the quotient between the number of red panels (4) and the total number of panels (19)
P = 4/19 = 0.211
b) Probability of a spin landing on anything but a blue panel
There are 7 blue panels and a total of 19 panels.
then 19 - 7 = 12 panels are not blue.
The probability of not landing on a blue panel will be equal to the quotient between the number of panels that are not blue (12) and the total number of panels (19)
P = 12/19 = 0.632
c) Probability of a spin landing on a yellow or red.
There are 4 red and 5 yellow ones, so there are 4 + 5 = 9 panels that are either red or yellow.
The probability is computed in the same way as in the above cases, here we have:
P = 9/19 = 0.473
d) Probability of a spin landing on any non-color panel.
The non-color panels are:
1 bankrupt panel and 2 free spin panels, for a total of 3 non-color panels.
The probability is computed in the same way as above, so we get:
P = 3/19 = 0.158
Amy has four more 20c coins than 5c coins. The total value of all her 20c and 5c is $3.80. How many 5c coins does Amy have?
Answer:
Amy has 12 5¢ coins
Step-by-step explanation:
Let x represent 20¢ coins and y represent 5¢ coins.
Amy has four more 20¢ coins than 5¢ coins. Hence:
[tex]x=y+4[/tex]
And the total value of all her coins is $3.80. Thus:
[tex]0.2x+0.05y=3.8[/tex]
This yields a system of equations:
[tex]\displaystyle \begin{cases} x=y+4 \\ 0.2x+0.05y=3.8\end{cases}[/tex]
We can solve by substitution. Substitute the first equation into the first:
[tex]\displaystyle 0.2(y+4)+0.05y=3.8[/tex]
Distribute:
[tex]\displaystyle 0.2y+0.8+0.05y=3.8[/tex]
Combine like terms:
[tex]\displaystyle 0.25y = 3[/tex]
And divide both sides by 0.25. Hence:
[tex]y=12[/tex]
Thus, Amy has 12 5¢ coins.
Using the first equation:
[tex]x=y+4[/tex]
Substitute:
[tex]x=(12)+4=16[/tex]
Thus, Amy has 16 20¢ coins.
In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.
draw the graphs of the lines represented by the equations 3x-4y=1 and 4x-3y=6 in the same graph. also find the coordinates of the point where the two lines intersect
Answer:
I've attached the graph with it, the intersection point is,
x = 3, y = 2
Please help me this on the picture
Answer:
Step-by-step explanation:
please hurry!!
What is the equation, in point-slope form, of the line that
is parallel to the
given line and passes through the point
- 1, - 1)?
Answer:
y + 1 = 2(x+1)
Step-by-step explanation:
hope this helps
the Marked price of an article is rupees 1600 if it is sold for rupees 1472 what is the discount rate
Step-by-step explanation:
1600-1472=128
128/1600×100
Use the circle to represent the following situation and show how you came up with the answer.
For lunch, you stop at a Pizza Express, where they sell pizza whole or by the slice. The area of one slice of a 16" pizza is 33.49in².
What angle does one slice make?
Answer:
look below bestie
Step-by-step explanation:
ok so i dont know most of it (sryy) but the area of the entire pizza is 535.84in², the radius of the pizza is about 13.05 and yea. thats all i got
What is the product of the polynomials below?
(3x2 - 2x - 3)(5x2 + 4x + 5)
Answer
15x^4+2x^3+8x^2-15
Answer:
15^4+2^3−8^2−22−15
Step-by-step explanation:
(3^2−2−3)(5^2+4+5)
Distribute:
3(5^2+4+5) ⋅ ^2−2(5^2+4+5) − 3(5^2+4+5)
15^4+12^3+15^2 − 2(52+4+5) − 3(52+4+5)
15^4+12^3+15^2 − 10^3−8^2−10 − 3(52+4+5)
15^4+12^3+15^2 − 10^3−8^2−10 − 15^2−12−15
Combine like terms:
15^4+12^3−10^3+15^2−8^2−15^2−10−12−15
15^4+2^3+15^2−8^2−15^2−10−12−15
15^4+2^3−8^2−10−12−15
15^4+2^3−8^2−22−15
15^4+2^3−8^2−22−15
hope it helps :)
please mark brainliest!
Help with this question
Step-by-step explanation:
Hey there!
Given;
-6(2x-9) + (7-6x) = 0
Simplify it.
-12x + 54 + 7 - 6x = 0
-18x +61 = 0
Therefore, answer is option B.
Hope it helps!
Which expression is equivalent to −24x+72?
−24(x−72)negative 24 times open paren x minus 72 close paren
−24(x−3)negative 24 times open paren x minus 3 close paren
24(x+3)24 times open paren x plus 3 close paren
24(x+72)
Answer:-24(x-3) = -24x (-24)(-3)
Step-by-step explanation:
Answer:
eat my hand where the pic
Step-by-step explanation:
yeah
PLEASE HELP. In the triangles below, DF MN, DG MP, D P. Can you prove that DFG MNP? Explain your answer. (15 points)
Complete question is;
In the triangles attached , DF is congruent to MN,DG is congruent to MP, angle D is congruent to angle P. Can you prove that triangle DFG is congruent to MNP.
Answer:
Proved below
Step-by-step explanation:
From the attached triangles, we can see that;
∠D corresponds to ∠M
∠F corresponds to ∠N
∠G corresponds to ∠P
But we are told that ∠D is congruent to ∠P. Thus, since we have 2 other congruent sides in the triangles, we can conclude that Side-Angle-Side Postulate (SAS) congruency theorem that triangle DFG is congruent to MNP.
7.
For which discriminant is the graph possible?
A. b2 – 4ac = 0
B. b2 – 4ac = –1
C. b2 – 4ac = 4
Answer:
C. b2 – 4ac = 4
Step-by-step explanation:
Answer:
The graph is possible for
Step-by-step explanation:
we know that
The discriminant of a quadratic equation of the form
is equal to
If D=0 the quadratic equation has only one real solution
If D>0 the quadratic equation has two real solutions
If D<0 the quadratic equation has no real solution (complex solutions)
In this problem , looking at the graph, the quadratic equation has two real solutions (the solutions are the x-intercepts)
so
therefore
The graph is possible for
...............................................................................................................................................
Answer:
b^2 – 4ac = 4
...............................................................................................................................................
10700 by 100 + 5192by 1000 - 412
Answer:
the answer is -299.808 well that's what I think it's
Answer:
-299.808
Step-by-step explanation:
= 10700/100 + 5192/100 - 412
= 107 + 5.192 - 412
= -299.808
