Answer:
5/y^3
Step-by-step explanation:
which expression is equivalent to 5y^-3
for example a^-1 = 1/a
5y^-3 = 5/y^3
the area of a triangular garden is 200 square feet. If the base is 30 feet more than its height, what is the base of the garden?
The base of the triangular garden is calculated as 40 ft
The given parameters include:
the area of the triangular garden, A₁ = 200 ft²let the height of the triangular garden = hthe base of the triangular garden, b = 30 ft + hThe area of a triangle is given as;
[tex]Area \ = \frac{1}{2} \times \ base \times \ height\\\\A = \frac{1}{2} bh\\\\2A = bh\\\\b = \frac{2A}{h} \\\\Recall, \ b= 30 + h\ \ \ and \ A = 200\\\\30+ h = \frac{2(200)}{h} \\\\30 \ + h = \frac{400}{h} \\\\30h + h^2 = 400\\\\h^2 + 30h - 400= 0\\\\Factorize \ the \ above \ expression\\\\h^2 + 40h- 10h- 400 = 0\\\\h(h + 40) - 10(h + 40) = 0\\\\(h- 10)(h+40)= 0\\\\h = 10 \ \ or \ \ -40\\\\since\ the \ height \ can't \ b e\ negative\\\\h = 10 \ ft\\\\[/tex]
Now solve for 'b' = 30 ft + 10 ft = 40 ft
Therefore, the base of the garden is 40 ft
To learn more about area of a triangle visit: https://brainly.com/question/2391510
Elijah invested $ 830 in an account paying an interest rate of 4.9% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years?
Answer:
$9986
Step-by-step explanation:
You got 13*4=52 quarters in 13 years.
Amount = 830*(1+0.049)^52
Amount = 9986.27
Find the area of the figure. (Sides meet at right angles.)
Answer:
[tex]9 \times 2 = 18 \: \: \\ 4 \times 5 = 20 \\ 20 + 18 = 38 \\ 38 {in}^{2} [/tex]
hi please give brainly
HURRY! HELP PLS
Janelle is conducting an experiment to determine whether a new medication is effective in reducing sneezing she finds 1000 volunteers with sneezing issues and divides them into two groups the control group does not receive any medication the treatment group received the medication the patients in the treatment group show reduced signs of sneezing what can genetic include from this experiment?
Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing.
What is a control experiment?A control experiment can be defined as a type of experiment in which a condition assumed to be a probable cause of an effect is compared with the same situation without involving or using the suspected condition.
What is a treatment group?A treatment group refers to a group of participants in an experiment that are exposed to some manipulation in the independent variable such as an administration of medication to a particular group.
Thus, Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing because the treatment group show reduced signs of sneezing.
Read more on an experiment here: https://brainly.com/question/17542127
If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be? If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be
Answer:
24feet
Step-by-step explanation:
the first rope well give it letter X and the longer rope we'll give it 2x since it's twice then we add the two unknown numbers which must lead to a total of 36feet when we add the unknown digits we'll get 3x then simply the unknown digit with the total and u'll get 12 replace the X from the first letters with 12by multiplying
Write an equation that represents the line.
Use exact numbers.
Answer: y=2/3X- 4/3
Step-by-step explanation:
Slope = (4-2)/(4-1)=2/3
Y-2=2/3(x-1)
Y-2=2/3x-2/3
Y=2/3X-2/3+2
Y=2/3X-4/3
Please help im new and i need help!
Please help me if you onlw the answers please!!
9514 1404 393
Answer:
a) 2.038 seconds
b) 5.918 meters
c) 1.076 seconds
Step-by-step explanation:
For the purpose of answering these questions, it is convenient to put the given equation into vertex form.
h = -4.9t² +9.2t +1.6
= -4.9(t² -(9.2/4.9)t) +1.6
= -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²
= -4.9(t -46/49)² +290/49
__
a) To find h = 0, we solve ...
0 = -4.9(t -46/49)² +290/49
290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9
√(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds
The ball takes about 2.038 seconds to fall to the ground.
__
b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:
290/49 m ≈ 5.918 m
The maximum height of the ball is about 5.918 m.
__
c) We want to find t for h ≥ 4.5.
h ≥ 4.5
-4.9(t -46/49)² +290/49 ≥ 4.5
Subtracting 290/49 and dividing by -4.9, we have ...
(t -46/49)² ≥ 695/2401
Taking the square root, and adding 46/49, we find the time interval to be ...
-√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49
The difference between the interval end points is the time above 4.5 meters. That difference is ...
2√(695/2401) ≈ 1.076 . . . . seconds
The ball is at or above 4.5 meters for about 1.076 seconds.
__
I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.
_____
Additional comment
I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.
"Vertex form" for a quadratic is ...
y = a(x -h)² +k . . . . where the vertex is (h, k) and 'a' is a vertical scale factor.
In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)
Solve the following system of equations using the elimination method
8x + 2y= 30
7x+2y= 24
A) (3.-12)
B) (-53)
C) 1-6,-5)
D) 16,9)
Answer:
(6, -9)
Step-by-step explanation:
let: 8x + 2y = 30 be equation (a).
7x + 2y = 24 be equation (b).
[tex]{ \bf{equation \: (a) - equation \: (b) : }}[/tex]
[tex] (8 - 7)x + (2 - 2)y = (30 - 24) \\ x + 0y = 6 \\ x = 6[/tex]
substitute for x in equation (a):
[tex] (8 \times 6) + 2y = 30 \\ 48 + 2y = 30 \\ y = - 9[/tex]
In one year, a government collected $6770 per person in taxes. If the population was 220,000,000, how much did the government collect in taxes that year?
Answer:
$1,489,400,000,000
Step-by-step explanation:
Multiply to get the solution.
220,000,000 × 6770 = 1,489,400,000
juan compra 12 dulces por 30 pesos, si al dia siguien el precio del dulce se incremento a 3.5 pesos cuanto se ahorro juan por cada dulce al comprarlos con el precio anterior
Write the greatest and smallest number of 8 suing following digits. 1,2,3,4,5,6,7,8
Answer:
Not very sure what you mean,
But in the provided set, 8 is the greatest number, and 1 is the smallest.
Hope this helps!!
Given the triangle below, what is the length of the third side, rounded to the nearest whole number?
Answer:
Step-by-step explanation:
You need the Law of Cosines for this, namely:
[tex]x^2=21^2+14^2-2(21)(14)cos58[/tex] where x is the missing side.
[tex]x^2=441+196-311.5925[/tex] and
[tex]x^2=325.4075[/tex] so
x = 18.0 or just 18
Which equation shows a slope of 3 and a y-intercept of (0,7)?
y = 7x + 3
y = −7x + 3
y = 3x
y = 3x + 7
Answer:
[tex]{ \tt{y = 3x + 7}}[/tex]
Step-by-step explanation:
General equation of a line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
m is the slope, and c is the y-intercept:
m = 3, and c = 7
You are studying 112 returning combat veterans with deployment related injuries. You are testing a cognitive impairment screen to detect traumatic brain injuries (TBI). There are six veterans with confirmed TBI and five of them screen positive. There are 93 veterans who do not have TBI and screen negative. There are a total 18 veterans who screen positive. One of the veterans has a negative screen and wants to know the probability that he does not have a TBI. You tell him:_________
Answer:
0.9894 = 98.94% probability that he does not have a TBI.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Negative screen
Event B: Does not have a TBI.
Probability of a negative screen:
93 are negative and do not have a TBI.
1 is negative and has a TBI.
Out of 112.
So
[tex]P(A) = \frac{93+1}{112} = \frac{94}{112}[/tex]
Probability of a negative screen and not having a TBI:
93 are negative and do not have a TBI, out of 112, so:
[tex]P(A \cap B) = \frac{93}{112}[/tex]
One of the veterans has a negative screen and wants to know the probability that he does not have a TBI.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{93}{112}}{\frac{94}{112}} = \frac{93}{94} = 0.9894[/tex]
0.9894 = 98.94% probability that he does not have a TBI.
If an angle of a right angle triangle is 81 find the remaining angle in grades
Answer:
9
Step-by-step explanation:
90+81+mising angle=180, missing angle is 9
Use the order of operations to evaluate this expression (-2+1)
Answer:
12
Step-by-step explanation:
2²×3
I hope its correct
Answer:
4
[tex] {( - 2 + 1)}^{2} + 5(12 \div 3) - 9 \\ 2 + 1 + 5 \times 4 - 9 \\ 3 + 20 - 9 \\ 23 - 9 \\ 14[/tex]
rose says the quantity of four dollars is a terminating decimal. Sharon says it is an integer.Do you agree witheither of them
Answer:
Agree with Sharon
Step-by-step explanation:
A terminating decimal includes numbers beyond the decimal point.
An integer is a whole number.
4 is a whole number so it's an integer which is what Sharon said.
11
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
Reset
Next
Answer:
B. 1 + ln 2 - ln x
General Formulas and Concepts:
Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex] Logarithmic Property [Dividing]: [tex]\displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(\frac{2e}{x})[/tex]
Step 2: Simplify
Expand [Logarithmic Property - Dividing]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2e) - ln(x)[/tex]Expand [Logarithmic Property - Multiplying]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + ln(e) - ln(x)[/tex]Simplify: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + 1 - ln(x)[/tex]Rewrite: [tex]\displaystyle ln(\frac{2e}{x}) = 1 + ln(2) - ln(x)[/tex]Translate sentence into inequality
A number c increased by 8 is greater than 30.
Step-by-step explanation:
the inequality is
[tex]c + 8 > 30[/tex]
Kayla made two paper chains. The paper links on one represented the number of days until her birthday, and the other showed the days until summer vacation. Altogether, she made 135 links for her chains. The birthday chain had twice as many links as the vacation chain. How many links are on Kayla's birthday chain?
Answer:
90 days
Step-by-step explanation:
b= number of days til her birthday
s = number of days til summer
b+s =135
b = 2s
2s+s = 135
3s = 135
Divide by 3
3s/3 =135/3
s =45
b = 2s = 2(45) = 90
Calculate the volume pyramid whose height de Priangular by of a 20cm, and has base of 8cm by 12cm by 150mm
Answer:
see it
Step-by-step explanation:
Factorise: 25x^2 - 1/49
Answer:
[tex] (5x + \frac{1}{7} )(5x - \frac{1}{7} )[/tex]Step-by-step explanation:
Given,
[tex] {25x}^{2} - \frac{1}{49} [/tex]
[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]
Since,
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
Then,
[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]
Building A is 170 feet shorter than building B. The total height of the two buildings is 1520 feet. what is the height of each building?
Answer:
Step-by-step explanation:
If A is 170 less than B, than the equation for that is:
A = B - 170 (1) where the word "is" means equals and less than is subtraction.
If the total of A + B is 1520, then
A + B = 1520 (2). Sub equation (1) into equation (2):
(B - 170) + B = 1520 and
2B - 170 = 1520 and
2B = 1690 so
B = 845. Building B is 845 feet tall and Building A is
A = 845 - 170 (this is equation (1) with the height of B subbed in) so
A = 675 feet
675 + 845 should equal 1520 according to our equation. And of course it does.
Answer: 675 + 845 should equal 1520 according to our equation. And of course it does.
The graph shows the distribution of lengths of songs (in seconds). The distribution is approximately Normal, with a mean of 227 seconds and a standard deviation of 31 seconds.
A graph titled Song length has length (seconds) on the x-axis, going from 103 to 351 in increments of 31. The highest point of the curve is at 227.
What percentage of songs have lengths that are within 31 seconds of the mean?
34%
68%
95%
99.7%
its everything between 196 and 258 seconds (at max 31secs away from the mean). imagine straight upward lines separating this area from the rest.
34% would be way too low, 95 and above way too much.
only 68% is remotely plausible.
PLEASE HELP ME !!!!
How many solutions does the system of equations below have?
y = x - 3
3y-3x = -9
A. Exactly 1 solution
B. At least 1 solution
C. More than 1 solution
D. No solution
9514 1404 393
Answer:
C. More than 1 solution
Step-by-step explanation:
Divide the second equation by 3.
y -x = -3
Add x.
y = x -3
This matches the first equation exactly, meaning that any solution to the first equation is also a solution to the second equation. There are an infinite number of possibilities. There is "More than 1 solution."
The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)
Answer:
a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c) the required probability is 0.2000
Step-by-step explanation:
Given the data in the question;
During a specific ten-hour period, one defective circuit board was found.
Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.
Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.
f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex]; ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]
= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
Now,
a) the probability that it was produced during the first hour of operation during that period;
P( Y < 1 ) = [tex]\int\limits^1_0 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^1_0[/tex]
= [tex]\frac{1}{10} [ 1 - 0 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) The probability that it was produced during the last hour of operation during that period.
P( Y > 9 ) = [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^{10}_9[/tex]
= [tex]\frac{1}{10} [ 10 - 9 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c)
no defective circuit boards were produced during the first five hours of operation.
probability that the defective board was manufactured during the sixth hour will be;
P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )
= P( 5 < Y < 6 ) / P( Y > 5 )
we substitute
[tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]
[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]
= ( 6-5 ) / ( 10 - 5 )
= 0.2000
Therefore, the required probability is 0.2000
How can you create and graph a piecewise function that has restrictions on the domain?
Answer:
Use inequalities.
At certain x values.
Step-by-step explanation:
[tex]3 \leqslant x \leqslant 6[/tex]
[tex] - \infty < x < \infty [/tex]
[tex]x = 6[/tex]
Parallel Lines:
If the two lines are parallel and cut by a transversal line, what is the value of x?
Step-by-step explanation:
The corresponding angles theorem tells us that angles that correspond with each other are equal. In this case, B and C are corresponding angles.
(2x+8) = 60
2x = 60 - 8
2x = 52
x = 26
i need help!!! due by 12
Answer:
1. $11747.083
2. $29,253
3. $24222.04
4. $1542.23
Step-by-step explanation:
Message for explanation if you want.
I need to know the answer ASAP
Answer:
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The numerical coefficient is sqrt(8/3), so all you have eliminated is D.
Now you have to consider the literal all by itself.
sqrt(x^2)/sqrt(x) can be written as (sqrt(x^2/x)) = sqrt(x)
x^2 when divided by x leaves x
another way of looking at it is sqrt(x)*sqrt(x) / sqrt(x) = sqrt(x)
So the answer is sqrt(8/3 * x)
