Select the correct expression.
Select the expression that is equivalent to the expression below.
Answer:
[tex]8\sqrt[3]{-8x^3y^6z^{13}}[/tex]
Step-by-step explanation:
[tex]8\sqrt[3]{-8x^3y^6z^{13}}\\\\=8\sqrt[3]{(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z}\\\\=8\left[(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z \right]^{\tfrac 13}\\\\=-8\cdot 2 \cdot x \cdot y^2 \cdot z^4 \cdot z^{\tfrac 13}\\\\=-16xy^2 z^4 \sqrt[3]z[/tex]
A pair of shoes is $50, plus 10% tax. What is the total amount you will pay?
Answer:
$55
Step-by-step explanation:
Given:
A pair of shoes is $50, plus 10% tax.
To Find:
What is the total amount you will pay?
Solve:
Tax = Increase - Add on
Thus,
$50 × 10% = 5
$50 + 5 = $55
Hence, the total amount you will pay is $55.
Kavinsky
what is the equation of the line that passes through the point (3,6) and has a slope of -1/3
ASAP PLS
[tex]\Large\texttt{Answer\::}[/tex]
Please consult the "Calculations" section of this ans .
[tex]\Large\texttt{Calculations\::}[/tex]
The information we're given is below :
slope : -1/3Point crossed by the line : (3, 6)As per given information , we can do the following :
Write the line's equation in point slope formPoint - slope form looks like so :
y-y₁=m(x-x₁)
y-6=-1/3(x-3)
y-6=-1/3x+1
y=-1/3x+1+7
y=-1/3x+6
↑ [tex]\small\textsc{EQUATION OF THE LINE}[/tex]
[tex]\small\textit{hope\:helpful~}[/tex]
which expression is equivalent (7x3)2(x8)1/2
Answer:
B. 49x^10
Step-by-step explanation:
(7x^3)^2 * (x^8)^1/2
multiply the exponents
49x^6 * x^4
add the exponents
49x^10
Alyssa has a points card for a movie theater. She receives 70 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs 245 points for a free movie ticket. How many visits must Alyssa make to earn a free movie ticket?
let x be the amount of times she visited the movie theater
[tex]70+12.5x=245\\\\12.5x=175\\\\x=14[/tex]
Alyssa needs to make 14 visits to earn a free movie ticket.
This is our y intercept
Rate of pay=12.5This is our slope.
So our equation is
p=12.5v+70Here v is visits
245=12.5v+7012.5v=175v=14visitsA bag contains 5 green and 3 white balls (the balls are identical in all respect except colour). A ball is drawn at random from the bag without looking into the bag. What is the probability of getting a green ball? Is it more or less than getting a white ball?
Answer:
Probability of getting a green ball is more than that of getting a white ball.
Step-by-step explanation:
There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.
Therefore, P(a green ball) = 5/8
In the same way,P(a white ball) = 3/8
5/8 > 3/8Thus, clearly the probability of getting a green ball is more than that of getting a white ball.
tony wants to buy a new radio for his car. It cost $350. He wants to purchase it in four months. How much will he have to save each month?
Help help help help help help
A bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1 What is the Compound Probability of reaching in at random and extracting a Yellow marble followed by a Blue marble with NO REPLACEMENT?
The probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Total number of marbles = 3+4+2+1 = 10
P(Yellow) = 1/10
P(Blue) = 4/9
Probability of extracting a Yellow marble followed by a Blue marble:
= (1/10)(4/9)
= 4/90
= 2/45
Thus, the probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1
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I need help with 3 and 4
Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
( 3 )
the given figure resembles a rectangle !
now ,
[tex]Area \: of \: rectangle = length \times breadth \\ \\ given \: - \: length = 12 \: ft \\ \therefore \:breadth = x \: ft \\ \\ Area = 108 \: ft {}^{2} \\ \\ \implies \: length \times breadth = 108 \: ft {}^{2} \\ \\ \implies \: x \times 12 = 108 \\ \\ \implies \: x = \cancel\frac{108}{12} \\ \\ \bold\red{\implies \: x = 9 \: ft}[/tex]
_____________________________
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( 4 )
the given figure resembles a parallelogram!
[tex]Area \: of \: parallelogram = height \times base \\ \\ \implies \: height = x \: cm\\ \\ \implies \: base = 16 \: cm \\ \\ \: Area \: = 96 \: cm {}^{2} \\ \\ \implies \: x \times 16 = 96 \\ \\ \implies \: x = \cancel\frac{96}{16} \\ \\ \bold\red{\implies \: x = 6 \: cm}[/tex]
hope helpful :D
[tex]\huge \underbrace \mathfrak \red{Answer}[/tex]
To find :-
To get the value of 'di in figure 3 and 4.
Figure 3
According to the figure, we know that it is a quadrilateral. It's all sides are at 90°.So we can assume that it can be rectangle. In the figure, length of one side is given and area of figure is given and we have the length of another side.Solution :-
Area of rectangle = length × width
area = 108 ft², length = 12 ft, width = x
[tex]108 = 12 \times x \\ \frac{108}{12} = x \\ 9 = x[/tex]
Therefore, the value of x in this figure is 9 ft.[tex] \\ [/tex]
Figure 4
According to figure, we finds out that it is quadrilateral as it has 4 sides. It has all parallel sides. We can assume that it is parallelogram as the sides which are facing each other are parallels. And here value of one side is given which is base and area is given, we have to find here is height.Solution :-
Area of parallelogram = base × height
Area = 96 cm², base = 16 cm, height = x
[tex]96 = 16 \times x \\ \frac{96}{16} = x \\ 6 = x[/tex]
Therefore, the value of x is 6 cm.For the function defined by y = StartFraction 1 Over x squared EndFraction, if x is doubled, what is the effect on y?
a.
y is quartered
c.
y stays the same
b.
y is doubled
d.
y is tripled
Please select the best answer from the choices provided
Answer:
a. y is quartered.
Step-by-step explanation:
y=1/x^2
when x is doubled, the equation becomes:
y=1/(2x)^2=1/(4x^2)
Answer:
If we double x, then the new value of x becomes 2x. So we can find the effect on y by substituting 2x for x in the given function.
y = 1/x^2
When x is replaced by 2x, we get:
y' = 1/(2x)^2
= 1/4x^2
Therefore, y' = (1/4)y
So, if x is doubled, then y is quartered (option a is the correct answer)
Find the exact value of Tan(-420)
A ----------------- transforms some electrical energy into other forms of energy.
Answer:
A solar panel is the best way to transform electrical energy into other forms of energy
Twelve subtracted from twelve times a number is -84. What is the number? A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use x as your variable. The equation is B) Solve your equation in part [A] for x. Answer: 0 =
Answer:
x=-6
Step-by-step explanation:
Let x be the number
A) 12x-12=-84
B) 12x=-72
x=-6
NO LINKS!!!! Exponential Growth and Decay Part 3
Answer:
6. 14.9 years
7. 4.8 years
8. 28.91 years
Step-by-step explanation:
Exponential growth or decay is described by the function ...
y = a·b^t
where 'a' is the initial value, and 'b' is the growth (or decay) factor. The growth (or decay) factor is one added to the growth rate.
__
This equation can be solved for t to get ...
y/a = b^t . . . . . . . divide by a
log(y/a) = t·log(b) . . . . take logarithms
t = log(y/a)/log(b) . . . . divide by the coefficient of t
Note that the time period is in the same units as the growth rate. (If the growth rate is per quarter, then the value of t will be in quarters.)
__
6.The initial value is a=8000; the final value is y=35000; and the growth rate is 10%/4 = 0.025 per quarter. The above equation will give the time period in quarters.
t = log(35000/8000)/log(1+0.025) ≈ 59.77 . . . quarters
Anisha will have $35,000 after 59.77/4 = 14.9 years.
__
7.No loan payment period is given, so we assume that the $43000 represents the repayment of the entire loan. The growth rate is 6% per year. The time required for the loaned amount to accumulate to a value of $43,000 is ...
t = log(43,000/32,500)/log(1 +0.06) ≈ 4.80 . . . years
If the loan period is 4.80 years, Kevin will have paid 43,000 to pay it off.
__
8.The growth rate is 0.024/12 = 0.002 per month. The number of months to achieve the desired balance is ...
t = log(3200/1600)/log(1 +0.024/12) ≈ 346.92 . . . . months
The balance in the account will be $3200 after 346.92/12 = 28.91 years.
_____
Additional comment
As a crude check on the answers, the "rule of 72" can be used. It says the doubling time is approximately 72 divided by the growth rate in percent. That is, a 10% growth rate will cause the value to double in approximately 72/10 = 7.2 years.
In the first problem, the value grows from 8000 to 35000, which represents a little more than 2 doublings (8000 to 16000 and 16000 to 32000). So, it is reasonable to expect the time period to be near 2 times 7.2 years, or 14.4 years. The value of 14.9 years is not unreasonable.
Answer:
Compound interest formula
[tex]\Large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedQuestion 6Given:
A = $35,000P = $8,000r = 10% = 0.1n = 4t = time (in years)[tex]\begin{aligned}8000\left(1+\frac{0.1}{4}\right)^{4t} & = 35000\\(1.025)^{4t} & = \frac{35000}{8000}\\(1.025)^{4t} & = 4.375}\\\ln (1.025)^{4t} & = \ln 4.375\\4t \ln 1.025 & = \ln 4.375\\4t & = \frac{\ln 4.375}{\ln 1.025}\\t & = 0.25\left(\frac{\ln 4.375}{\ln 1.025}\right)\\t & = 14.9427947\end{aligned}[/tex]
Therefore, she will have $35,000 in 15 years.
Question 7Given:
A = $43,000P = $32,500r = 6% = 0.06n = 1t = time (in years)[tex]\begin{aligned}32500\left(1+\frac{0.06}{1}\right)^{1t} & = 43000\\32500(1.06)^{t} & = 43000\\(1.06)^{t} & = \frac{43000}{32500}\\(1.06)^{t} & = \frac{86}{65}\\\ln (1.06)^{t} & = \ln \left(\frac{86}{65}\right)\\t \ln 1.06 & = \ln \left(\frac{86}{65}\right)\\t & = \dfrac{\ln \left(\frac{86}{65}\right)}{\ln 1.06}\\t & = 4.804621116\end{aligned}[/tex]
Therefore, Kevin will have paid $43,000 on the loan in 4 years and 10 months.
Question 8Given:
A = $3,200P = $1,600r = 2.4% = 0.024n = 12t = time (in years)[tex]\begin{aligned}1600\left(1+\frac{0.024}{12}\right)^{12t} & = 3200\\1600(1.002)^{12t} & = 3200\\(1.002)^{12t} & = \frac{3200}{1600}\\(1.002)^{12t} & = 2\\\ln (1.002)^{12t} & = \ln 2\\12t \ln (1.002) & = \ln 2\\12t & = \dfrac{\ln 2}{\ln 1.002}\\t & = \frac{1}{12}\left(\dfrac{\ln 2}{\ln 1.002}\right)\\t & = 28.91000404\end{aligned}[/tex]
The balance of the account will be $3,200 in 28 years and 11 months.
Hey guys may yall help please and thank you !!
Answer: 12? im pretty sure
Step-by-step explanation: 1/4 of a unit so 4 for 1 unit, 4 x 3 is 12 units for 3
write 1.86×10⁵ as an ordinary numbe
[tex]\boxed{\sf 186,000}\boxed[/tex]
Answer:
186,000
Step-by-step explanation:
1. Multiply 10 to the 5th power:
[tex]10^{5}[/tex] = 100,000
2. Multiply:
1.86 × 100,000 = 186,000
hope this helps :)
If v₁ = (3,7) and V₂ = (-2,4), then v₁v₂ is equal to which of the following?
A. (-6,28)
B. 34
C. 22
D. (-21,-8)
find the area of following quadeilaterals
???????
Find the perimeter of a triangle that has the side lengths given below.
6 cm, 7√3 cm, √27cm
Give the answer as a radical expression in simplest form.
The perimeter of a triangle that has the side lengths is 6 + 10√3 cm
How to determine the perimeter?The side lengths are given as:
6 cm, 7√3 cm and √27 cm
The perimeter is the sum of the side lengths.
So, we have:
P = 6 + 7√3 + √27
Express 27 as 9 * 3
P = 6 + 7√3 + √(9 * 3)
Take the square root of 9
P = 6 + 7√3 + 3√3
Evaluate the sum
P = 6 + 10√3
Hence, the perimeter of a triangle that has the side lengths is 6 + 10√3 cm
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please. Will give brainliest
Answer:
The answer is c
scince I am not student so I don't use book n pen sorry
a box in a shape of a rectangle prism has a length of 3 5/8 inches a width of 2 1/2 inches and a height of 4 inches. what is the volume of the box
Answer:
volume is 36.25inches
145/4
Step-by-step explanation:
L= 3 5/8inches
W= 2 1/2inches
H= 4inches
VOLUME = L×W×H
3 5/8 × 2 1/2 × 4 =
29/8 × 5/2 × 4 = 36.25inches
36.25→145/4
If you dont know the answer or get it wrong i will report
Step-by-step explanation:
law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
extended Pythagoras :
c² = a² + b² - 2×a×b×cos(C)
and : the sum of all angles in a triangle is always 180°.
1.
b² = 42.1² + 37² - 2×42.1×37×cos(13) =
= 105.8575002...
b = 10.28870741...
b/sin(13) = 37/sin(C)
sin(C) = 37 × sin(13)/b = 0.808963525...
C = 53.99478824...° ≈ 54°
A = 180 - 13 - 54 ≈ 113°
2.
c² = 18² + 13² - 2×18×13×cos(115) = 690.7853465...
c = 26.28279564...
c/sin(115) = 18/sin(A)
sin(A) = 18 × sin(115)/c = 0.62069273...
A = 38.36673893...°
B = 180 - 115 - A = 26.63326107...°
3.
the length of b is missing.
this cannot be solved without the missing information
how many solutions does the following equation have? 3x+6 =3(x+2)
Answer:
Infinite solutions
Step-by-step explanation:
3x+6 = 3(x+2)
3x+6 = 3x+6
6 = 6
Phu takes out a $2,400 discounted loan using a simple interest rate of 8% for a period of 18 months. What is the effective interest rate, re
Answer:
9.1
Step-by-step explanation:
To calculate the total interest payable, we use the formula
I=P0rt,
and substituting our values yields
I=$2,400×0.08×1812=$288.
Therefore the total amount he receives at loan drawdown is $2,400−$288=$2,112. To calculate the effective interest rate, we use to formula
A=P0(1+ret).
In this instance we have A=$2,400,P0=$2,112 (redefined from the value above) and t=1.5. We substitute into the formula to get
$2,400=$2,112(1+1.5re).
Solve for re.
24002112=1+1.5re
24002112−1=1.5re
24002112−11.5=re
This gives re=0.0909⋯=9.0909…%, which is 9.1%
Zahra gave out a survey to some students in her school about their favorite color. Students could choose between purple and red. 187 of those surveyed said their favorite color was purple. 45% of the students surveyed said their favorite color was red. How many students were surveyed in total?
Answer:
340 people did the survey in total.
What is Algebra?
Algebra is a branch of mathematics that deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they do not have predefined values.
These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to determine their values.
Given:
People who like the color purple = 187
Moreover, 45% of people prefer the color red.
Purple color enthusiasts = 100 - 45 = 55%
Let the total number of people polled be x.
So, 55% of x = 187
55/100x = 187
x= 18700/ 55
x= 340
Therefore, the answer is 340.
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PLEASE HELP I NEED THIS FAST. Find the volume of each rectangular prism
Find the positive solution for c:
8 2 + 15 2 = c 2
Answer:
15
Step-by-step explanation:
8² + 15² = c²
To find : Value of c
8² = 8 x 8 = 64
15² = 15 x 15 = 225
c² = 225
225 = 15 x 15 = 15²
So,
c² = 15²
c = 15
HELP ME ON THIS PLSS Kathy swims at least 6 laps everyday. Write an inequality to show how long Kathy swims each day.
Answer:
x ≥ 6.
Step-by-step explanation:
Given : Kathy swims at least 6 laps every day.
To find: Write an inequality to show how long Kathy swims each day.
Solution : We have given that Kathy swims at least 6 laps every day.
We can see from given statement Kathy can swim 6 laps or greater then 6 laps in a day.
Then we use greater than or equal to sign ( for at least)
Since x ≥ 6.
Therefore, x ≥ 6.
Find the value of y for the given value of x. Round to the nearest hundredth.
y = 0.05 − 10 ln x; x = 0.09
Answer:
[tex]y\approx24.129[/tex]
Step-by-step explanation:
[tex]y=0.05-10\ln x;\: x=0.09\\y=0.05-10\ln(0.09)\\y\approx24.129[/tex]
Answer:
24.129
the answer is that and I need 20 characters