The answer is: " - 1,458 ".
Step-by-step explanation:
We are asked to simplify: " -2(3²)³ " ; into standard form.
Take note of the 'order of operations'—by using the mnemonic:
"Please Excuse My Dear Aunt Sally."
in which:
_______
Parentheses, if they occur, take top priority.
then :
Exponents, if they occur, take second priority.
then :
Multiplication—and/or:
Division—if they occur; take third priority; yet, multiplication does not necessarily take priority over division. Rather, multiplication and/or division, if Either occurs, take the next priority—in the order in which they occur from the far left of the expression to the end.
then :
Addition—and/or:
Subtraction—if they occur; take the last priority; yet, addition does not necessarily take priority over subtraction. Rather, addition and/or subtraction, if Either occurs, take the last priority—in the order in which they occur from the far left of the expression to the end.
____
Our given expression: " -2(3²)³ " ; is the same as:
" - 2* (3²)³ " ; We have parentheses, exponents, and multiplication;
So; we need to find the value of: " (3²)³ " ;
and multiply that value by -2 ;
So, let's start with calculating: " (3²)³ " ;
Method 1)
" (3²)³ = (3* 3)³ = 9³ = 9 * 9 * 9 = (9 * 9) * 9 = 81 * 9 = 729 " .
Method 2)
Note the multiplication property of exponents:
(aᵇ)ᶜ = a⁽ ᵇ *ᶜ ⁾ ;
As such: " (3²)³ = 3⁽²*³⁾ = 3⁶ " ;
= 3 * 3 * 3 * 3 * 3 * 3 ;
= (3 * 3) * 3 * 3 * 3 * 3 ;
= 9 * 3 * 3 * 3 * 3 ;
= (9 * 3) * 3 * 3 * 3 ;
= (27) * 3 * 3 * 3 ;
= (27) * (9)* 3 ;\
= 27 * 27 ;
₁
₄
2 7
* 2 7
¹ 1 8 9
⁺_5 4
7 2 9
= 729
____
Now, multiply 729 by -2 ;
{Note that a negative value, when multiplied by a positive value, results in a negative value.}\
₁
7 2 9
* - 2
- 1 4 5 8 ; which is our answer to: " -2(3²)³ " ; written in standard form.
The answer is: " - 1,458 ".
____
Hope this is helpful to you.
Best of luck to you!
____
Annie has 5 pets, Eve has 3 and Molly has 10. What is the
mean amount of pets?
Answer: 6
Step-by-step explanation: the mean is the average. 5+3+10 = 18 and then you divide by the people (3) to get 6.
The length of a rectangle is 7 cm more than the width. If the perimeter is 58 cm, find the length and width.
Answer:
length = 32.5, Width = 25.5
Step-by-step explanation:
Let x rep the width. Let x plus 7 rep the length.
x + x + 7 = 58
2x=58-7
2x=51
2x/2 = 51/2
x= 25.5
x plus 7 =
= 25.5 + 7
=32.5
✨️Hope that helps✨️
Two numbers have a sum of 139 and a difference of 31. What are the two numbers?
Answer:
Thus, one of the numbers is 85
Step-by-step explanation:
Answer:
Step-by-step explanation:
If a population of 1000 people were to increae by 5% every year, what would the population be in 20 year?
The population in the next 20 years would be 2653 people. The result is obtained by the equation of estimating the future population.
How to estimate future population?
The future population can be estimated by the following equation:
P = P₀ × (1 + i)ⁿ
Where
P = population in the expected yearP₀ = current populationi = growth raten = number of periodsIf the recent population is 1000 people and the growth rate is 5% per year, what would the population be in the next 20 years?
The population in the next 20 years would be
P = P₀ × (1 + i)ⁿ
P = 1000 × (1 + 0.05)²⁰
P = 1000 × (1.05)²⁰
P = 1000 × 2.6533
P = 2653 people
Hence, the population in the next 20 years would be 2653 people.
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the spread of the sampling distribution of is the spread of the corresponding population distribution sampling distribution
The spread of the sampling distribution of x is smaller than the spread of the corresponding population distribution sampling distribution.
In the given question,
We have to find the spread of the sampling distribution of x is............... the spread of the corresponding population distribution sampling distribution.
As we know that,
The size of the sample as well as its dispersion affect the sampling distribution's spread. We calculate the sampling distribution's spread as the population's standard deviation divided by the sample size's square root.
So, the spread of the sampling distribution of x is smaller than the spread of the corresponding population distribution sampling distribution.
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The right question is
The spread of the sampling distribution of x is .......... the spread of the corresponding population distribution sampling distribution.
larger than
smaller than
the same as
exactly 1/2
Let f(x) = 4x-8 and g(x)=x+3. Find f(g(x)) and g(f(x)).
f(g(x)) = (Simplify your answer.)
g(f(x)) =
(Simplify your answer.)
Answer:
[tex] \huge{ \bold{f(g(x)) = 4x + 4}} \\ \\ \huge{ \bold{g(f(x)) = 4x - 5}}[/tex]
Step-by-step explanation:
f(x) = 4x-8
g(x)=x+3
In order to find f(g(x)) you substitute g(x) into f(x) that's where ever you find x in f(x) you replace it with g(x) and solve
We have
[tex]f(g(x)) = 4(x + 3) - 8 \\ = 4x + 12 - 8 \\ = 4x + 4[/tex]
In order to find g(f(x)) you substitute f(x) into g(x) that's where ever you find x in g(x) you replace it with f(x) and solve
We have
[tex]g(f(x)) = (4x -8) + 3 \\ = 4x - 8 + 3 \\ = 4x - 5[/tex]
Hope this helps you
A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is.
A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is
Given n(sample size) = 84
Population mean(μ) = 180
Standard Deviation(σ) = 36
Standard error of the mean = σx-bar = σ/√n = 36/√84 = 36/9.165 = 3.927
Standardizing the sample mean we have
Z = (x-bar - μ)/σx-bar = (x-bar - μ)/σ/√n
x-bar = 180
Z(x-bar=185 at point C) = (185 - 180)/3.927 = 5/3.927 = 1.273
Z(x-bar=181 at point D) = (181 - 180)/3.927 = 1/3.927 = 0.254
The area ABCD is the probability that the sample mean will lie between 181 and 185.
The shaded Area ABCD = (Area corresponding to Z = 2 or x-bar = 185) - (Area corresponding to Z = 1 or x-bar = 181)
Area corresponding to Z = 1.273 = 0.898
Area corresponding to Z = 0.254 = 0.598
The shaded Area ABCD = 0.898-0.598 = 0.300
Therefore the probability that the sample mean will lie between 181 and 185 is 0.300.
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At Berry Fun Farm, Liz picked 12 pints of berries. If 25% of the pints were blueberries, how many pints of blueberries did Liz pick?
Answer: 25% of 12 is 3
Step-by-step explanation:
Since there 25% is 1/4 of 100%, you'd need to divide.
There are 12 pints of berries.
If 1/2 of 25% is 6 since [tex]2 \sqrt{12}=6[/tex], you can say that the percentage would be 2/4.
Now, divide 12 by 4: [tex]4\sqrt{12}=3[/tex]
3 in this case would be the 1/4 and the 1/4 is substituting 25%
So there are 3 pints of blueberries.
Help me pls.
100 points for those who work it out
Both areas are equal, 4 cm²
Answer:
Area of triangle = 4 cm²
Area of square = 4 cm²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
From inspection of the given diagram:
b = 2 cmh = 4 cmSubstitute the values into the formula to find the area of the triangle:
[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \times 2 \times 4\\A&=1 \times 4\\A&=4\;\sf cm^2\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
From inspection of the given diagram:
s = 2 cmSubstitute the value into the formula to find the area of the square:
[tex]\begin{aligned}\implies A&=2^2\\A&=2 \times 2\\A&=4\;\sf cm^2\end{aligned}[/tex]
The area of the triangle is 4 cm², and the area of the square is 4 cm², thus proving that the triangle and the square have the same area.
3) Hugh has a goal of exercising 12/4 hours a day. He plans to go on several runs
today. His runs take him 4/6 of an hour. How many runs will Hugh need to go on?
Solve the following system of equations algebraically:
y = x2 - 7x - 5
y = 2x - 5
Answer:
x = 0; y = -5
x = 9; y = 13
Step-by-step explanation:
y = x² - 7x - 5
y = 2x - 5
Use substitution to set the two right sides equal.
x² - 7x - 5 = 2x - 5
x² - 9x = 0
x(x - 9) = 0
x = 0 or x - 9 = 0
x = 0 or x = 9
Now for each x value, we find a corresponding y vlaue.
x = 0
y = 2x - 5 = 2(0) - 5 = -5
x = 9
y = 2x - 5 = 2(9) - 5 = 13
Answer:
x = 0; y = -5
x = 9; y = 13
Answer:
(0,-5) and (9,13)
Step-by-step explanation:
Step 1: Set up
You can solve system of equations algebraically either by elimination or substitution.You know there is going to be two solutions because of x²Step 2: Solve
Substitution:
[tex]y=x^{2} -7x-5[/tex][tex]y=2x-5[/tex]Since both equations have been solved for y, you can just set them equal to each other.[tex]2x-5=x^{2} -7x-5[/tex][tex]9x-x^{2} =0[/tex][tex]-x(x-9)=0[/tex][tex]x=0\\x=9[/tex]Then plug both x values into one of the equations to get their corresponding y values.[tex]y=2(0)-5=-5[/tex][tex]y=2(9)-5=18-5=13[/tex]Elimination:
[tex]y=x^{2} -7x-5[/tex][tex]y=2x-5[/tex]Since both equations have been solved for y, multiply one equation by -1 in order to cancel the y variable and solve for x.[tex]y=x^{2} -7x-5[/tex][tex]-y=-2x+5[/tex][tex]0=x^{2} -9x+0[/tex][tex]0=x^{2} -9x[/tex][tex]0=x(x-9)[/tex][tex]x=0\\x=9[/tex]Then plug both x values into one of the equations to get their corresponding y values.[tex]y=2(0)-5=-5[/tex][tex]y=2(9)-5=18-5=13[/tex]what equations could i use with 1 2 3 4 5 to get 35
Answer:
(5x5) + (5x2)
Step-by-step explanation:
is that helpful i dont really get what youre asking
Answer:
1+2*3*5+4
Step-by-step explanation:
Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of. 5. How many subscribers must they sample to obtain this interval?.
They must sample 385 subscribers to obtained this interval.
What do you mean by sample?
An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values.
According to the given question,
We have:
95% confidence interval for z-score is 1.96
Using this formula to find the number of subscribers they must sample to obtain this interval
n≥ (zσ/2 ÷ 2ME)²
Where:
n= Sample
zσ = Z-score
ME = margin of error
Let put in the formula,
n≥ [1.96 / 2(0.05)]²
n≥ [1.96 / 0.1]²
= (19.6)²
= 384.16
=385 (Rounded)
Therefore, they must sample 385 subscribers to obtained this interval.
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a rock is thrown off a 200-foot cliff. the trajectory of the rock is modeled by the function h(t)=(-10t^2)+200, where h is the height in feet and t is the time in seconds. when will the rock hit the ground.
Answer:
4.47 seconds.
Step-by-step explanation:
Given function:
[tex]h(t)=-10t^2+200[/tex]
where:
h is the height (in feet).t is the time (in seconds).The rock will hit the ground when h(t) = 0.
Therefore, set the function to zero and solve for t:
[tex]\begin{aligned}h(t)&=0\\\implies -10t^2+200&=0\\10t^2&=200\\t^2&=20\\t&=\pm\sqrt{20}\\t&=-4.47, 4.47\;\; \sf (2\;d.p.)\end{aligned}[/tex]
As time is positive, t = 4.47 s only.
the distribution of sample means approaches a normal curve as \ \ \ \ \ \ \ \ increases to infinity?
The correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'
In this question, we have been given a statement 'the distribution of sample means approaches a normal curve as _________ increases to infinity'
We need to complete the statement.
The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.
This means, the distribution of sample means approaches a normal curve as the sample size i.e., n increases to infinity.
Therefore, the correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'
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help me the pic is the queston
The Tabel corresponds to which of the following scatterplots?
Answer :
Step-by-step
In △abc, ​gf=17 in.​ what is the length of cf¯¯¯¯¯? enter your answer in the box. in.
The length of CF is 51 inches.
Complete question:
( In triangle ABC in which AD,BE and CF are the medians ),
In △ABC, GF=17 in. What is the length of CF¯¯¯¯¯? Enter your answer in the box.
What is the median in a triangle?
A line segment that joins a vertex to the mid-point of the side that is opposite to that vertex
The centroid G divides each median into the ratio 2:1, so GF is 1/3 of CF. That is, ...
CF = 3(GF) = 3(17 in)
CF = 51 in
So, the length of CF is 51 inches.
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please help me asap
According to the solving the co-ordinate mid-point D is (-4,0).
What is Mid-Point?A point on a line which bisects the same line is a mid point. It divides the line in two equal halves.
The mid-point is equidistant from both the ends of the given line.
Middle point formula in coordinate geometry
M={(x1+x2)/2,(y1+y2)/2}
According to the Given information:We need to find the coordinates of mid-point D of line AB, where
A is (-6x,4y)
B is (-2x,-4y)
By using Mid-point formula for coordinate D, we get
x=-6+(-2)/2
⇒ x=-6-2/2
⇒x=-8/2
⇒x=-4
And y coordinate
y=4+(-4)/2
⇒y=4-4/2
⇒y=0/2
⇒y=0
The coordinates of mid-point D of line AB is (-4,0)
Hence, D is (-4,0)
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Which equation represents the line that is
perpendicular to the graph of 4x + 3y = 9 and
passes through (-2, 3)?
A. 3x-4y=-18
B. 3x+4y=18
C. 3x-4y=-6
D. 3x+4y=6
The equation that represents the line that is perpendicular to the graph of 4x + 3y = 9 and passes through (-2,3) is
[tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
Let us revise some rules
1. The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]
2. The slope of a line whose equation is ax + by = c is [tex]m = \frac{-a}{b}[/tex], where a is the coefficient of x and b is the coefficient of y
The equation of the given line is 4x + 3y = 9
[tex]m = \frac{-a}{b}[/tex]
whereas a is the coefficient of x and b is the coefficient of y
Therefore the coefficient of x = 4 and the coefficient of y = 3
a = 4 and b = 3
[tex]m = \frac{-a}{b}[/tex]
The slope of the perpendicular line to the given line is [tex]\frac{-1}{m}[/tex]
That means reciprocal the fraction and change its sign
The slope of the perpendicular line = [tex]\frac{3}{4}[/tex]
The form of the equation is y = mx + b
- Substitute m by [tex]\frac{3}{4}[/tex]
y = [tex]\frac{3}{4}[/tex] x + b
To find b substitute x and y in the equation by the coordinates
of a point on the line
The perpendicular line passes through point (-2 , 3)
x = -2 and y = 3
3 = [tex]\frac{3}{4}[/tex](-2) + b
3 = [tex]\frac{-3}{2}[/tex]+ b
Add to both sides
[tex]\frac{9}{2}[/tex] = b
y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation that represents the line that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Hence the answer is perpendicular to graph of 4x+3y=9 and passes through (-2,3) is [tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
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If shown, AB and CD are straight lines. Find x in each case.
NEED HELP ASAP
If AB and CD are straight lines. Then x is 45 degrees.
What is Angle?Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Given,
AB and CD are straight lines
The angle at O is 360 degrees which makes complete circle.
Few of the angles are given.
x+x+4x+90=360
6x+90=360
Subtract 90 from both sides
6x=270
x=45 degrees.
Hence the value of x is 45 degrees.
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About 75% of the wate produced in the U. S i recyclable. Micah’ family ha 40 pound of trah. He want to etimate how much of thi trah i recyclable
Answer:
30 lb
Step-by-step explanation:
75% of trash is recyclable.
40 lb trash.
75% of 40 lb = = 40/100 × 75 lb = 0.40 × 75 lb = 30 lb
Answer: 30 lb
Ximena is going to invest in an account paying an interest rate of 2.2% compounded continuously. How much would Ximena need to invest, to the nearest ten dollars, for the value of the account to reach $5,100 in 6 years?
Ximena need to invest $2384 so that account value reach $5,100 in
6 years.
As given in the question,
We have to find Principal ' P'
Given interest rate R = 2.2%
Amount = $5100
time t = 6 years
Formula used
Amount = P + P( 1 + R%)^t
Putting values in the formula
5100 = P + P (1 + 2.2%)^6
5100 = P ( 1 + (1 + 2.2%)^6)
5100 = P (1 + (1.022)^6)
5100 = P (1 + 1.139)
5100 = P (2.139)
P = 5100/2.139
P = 2384.291 ≈ 2384
Therefore, Ximena need to invest $ 2384 to reach $5,100 in 6 years with interest rate 2.2%.
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Answer:
P=4470
Step-by-step explanation:
i did it
A clerk is marking up merchandise 32%. The original price of an item is $450. What will be the retail price?
Answer:
$594
Step-by-step explanation:
450x1.32=$594
450+32%=$594
Solve the compound inequality.
3x -4 > 5 or 1 - 2x≥7
Answer:
3x -4 >5 = x > 3.
1 -2x>7 = x ≥ -3
Step-by-step explanation:
A tram moved downward 35 meter in 7 econd at a contant rate. What wa the change in the tram' elevation each econd?
If a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter
The total distance that tram moved downwards = 35 meters
Total time taken = 7 seconds
Here we have to use the unitary method
The change in the tram's elevation for each second = The total distance that tram moved downwards / Total time taken
Substitute the values in the equation
The change in the tram's elevation for each second = 35 /7
Divide the terms
= 5 meters
Hence, if a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter
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115% = 38x + 161y
What is 100%?
Answer:
100% is 32.3x + 136.85y------------------------
Given115% = 38x + 161yFind 100%100% = 115% - 15% (38x + 161y) - 15% = (38x + 161y)*(1 - 0.15) = (38x + 161y)*0.85 =38x*0.85 + 161y*0.85 = 32.3x + 136.85yAnswer:
32.3x + 136.85y
Step-by-step explanation:
Let's take it as,
→ z = 100%
Forming the equation,
→ z + 15% = 38x + 161y
Now the value of z will be,
→ z + 15% = 38x + 161y
→ z = 38x + 161y - (1 - (15/100))
→ z = (38x + 161y) × (1 - 0.15)
→ z = (38x + 161y) × (0.85)
→ [ z = 32.3x + 136.85y ]
Hence, the answer is above.
Last year, Jacky's age was six times the age of his son. If Jacky's son was 5 years old last year, find the age of Jacky this year.
Use the given information to prove that SVR = SUT
The ΔSVR ≅ ΔSUT by side angle side property of triangle.
What is congruency in triangles?The size of the sides and angles determines whether two or more triangles are congruent. The three sides and three angles of a triangle define its size and shape, accordingly. Two triangles are said to be congruent if their respective side and angle pairs are the same.
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
In triangle SVR and triangle SUT
SR = ST (given)
∠RSV = ∠TSU ( Common)
SV = SU (given)
So, the ΔSVR ≅ ΔSUT by SAS property.
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Out of 30 problems on a
test, Jose got 3 wrong.
What percentage did Jose
get correct?
Answer:
Step-by-step explanation:
3 is 10% of 30. Therefore, the other 27 is the resulting 90% of the whole number of 30.
