The length and width of the piece of metal are 20 and 30 inches respectively.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Dimension of the rectangle;
Width(w)
Length,L= 10 + w
volume of the box = length * width * height
Dimension of the box;
length of box, (x + 10) - 4 = x + 6
width of box,(x - 4)
height of box = 2
The volume of the box is 1102 in³;
⇒V=lwh
⇒V=2 (x -4)( x + 6) =
⇒1102 in³ = 2x² + 4x - 48
⇒2x² + 4x - 880 = 0
⇒x + 2x - 440 = 0
⇒(x + 22)(x - 20) = 0
⇒x = 20
⇒x=-22 (value of the dimesion will not be negative.
The width of an original piece of metal is;
Width,w=20 inches
length,l= 30 inches
Hence. the length and width of the piece of metal are 20 and 30 inches respectively.
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find the slope of the lined graph
Answer:
1
Step-by-step explanation:
The points go rise:1 up:1 so the slope is 1.
Answer:
hey!! we can taIk here
Step-by-step explanation:
Factor out the GCF from the given polynomial.
14x-2
Answer:
2(7x-1)
Step-by-step explanation:
14 & 2 gcf 2 factor and wal lah!
A bowl contains 28 black, 21 red, 23 blue, and 10 green balls
A ball is drawn at random. P (blue).
Answer:
P (blue) = 23 / 82
Step-by-step explanation:
There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls
or,
23 / 82
So, the probability of a blue ball being chosen is 23/82
(or a 28% chance [rounded])
If (1, 0) is an ordered pair of the function F(x), which of the following is an
ordered pair of the inverse of F(x)?
If the ordered pair (1, 0) represents the function F(x), then the ordered pair (0, 1) represents the inverse of F(x). Option A is correct.
What is a function?A connection between independent variables and the dependent variable.is defined by the function.
The complete question is
"If (1,0) is an ordered pair of the function f(x), which of the following is an ordered pair of the inverse of f(x)?
A. (0,1)
B. (0,0)
C. (1,0)
D. (1,1)"
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
The relation between them is shown as y if dependent and x is the independent variable.
If the ordered pair (1, 0) represents the function F(x), then the ordered pair (0, 1) represents the inverse of F(x).
F(x)∈ (1, 0)
F⁻¹(x)∈(0, 1)
Hence, option A is correct.
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Calculate the discriminant to determine the number of real roots of the equation.
y = x2 + 3x + 9
one real root
no real roots
three real roots
two real roots
find D which is the discriminant and with D < 0.
therefore the equation has an imaginary root and not a real root.
Solve the following radical equation.
√2x-3 =2
Answer:
First, we have to add 3 to both sides.
[tex]\sqrt{2x} - 3 + 3 = 2 + 3[/tex]
Then we simplify the equation,
[tex]\sqrt{2x} = 5[/tex]
Divide both sides of the equation by [tex]\sqrt{2}[/tex]
[tex]\frac{\sqrt{2x} }{\sqrt{2}} = \frac{5}{\sqrt{2}}[/tex]
Finally, simplify.
[tex]x = \frac{5\sqrt{2}}{2}[/tex]
Therefore, our answer is [tex]x = \frac{5\sqrt{2}}{2}[/tex]
3.5
Step-by-step explanation:
square means 1/2.so,1/2(2x-3)=(2)^2
then square cancel by square. 2x-3=4
2x=4+3, 2x=7then divided by 2.
x=3,5
The height of Canadian women was distributed normally with a mean of 161 cm
and a standard deviation of 6 cm. Determine the likelihood that a Canadian woman chosen
randomly will have a height that is between 158 cm and 163 cm.
Includes a sketch of the region under the curve below.
2014
b) The probability that a Canadian woman's height will be larger than x cm is 1%.
Determine x, to the nearest centimeter.
The probability of having a height that is between 158 cm and 163 cm is 0.69011 and the value of x is 169 centimeters
The probability of having a height that is between 158 cm and 163 cmThe given parameters are:
Mean = 161Standard deviation = 6Calculate the z-scores at x = 158 and x = 163 using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z = \frac{158 - 161}{6} = -0.5[/tex]
[tex]z = \frac{163 - 161}{6} = 0.33[/tex]
The probability is then represented as:
P(158 ≤ x ≤ 161) = P(-0.5 ≤ z ≤ 0.33)
Using the z table, we have:
P(158 ≤ x ≤ 161) = 0.69011
Hence, the probability of having a height that is between 158 cm and 163 cm is 0.69011
The value of x in the probabilityThe probability is represented as:
P(X ≥ x) = 1%
Express as decimal
P(X ≥ x) = 0.10
The z-score at p = 0.10 is:
z = 1.282
Substitute z = 1.282 in [tex]z = \frac{x - \mu}{\sigma}[/tex]
[tex]1.282 = \frac{x - \mu}{\sigma}[/tex]
Make x the subject
[tex]x = 1.282\sigma + \mu[/tex]
Substitute values for standard deviation and mean
x = 1.282 * 6 + 161
Evaluate
x = 168.692
Approximate
x = 169
Hence, the value of x is 169 centimeters
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19 Which figure(s) below can have a triangle as a two-dimensional cross
section?
I. cone
II. cylinder
III. cube
IV. square pyramid
(1) I, only
(2) IV, only
(3) I, II, and IV, only
(4) I, III, and IV, only
The figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only
How to determine the figures?The cross-section of three-dimensional figures are as a result of slicing the figure along its axis.
When the cube is sliced with its plane, it gives a triangle faceWhen a cone is sliced vertically, it gives a triangle faceOne of the faces of a square pyramid is a triangle; so it has a triangle faceHence, the figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only
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Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
The solution to the given system of equation is (4, 4)
Factorizing quadratic functionsFrom the solved steps, the final quadratic functions is given as;
x^2 - 8x + 16 = 0
Factorize to have;
x^2 - 4x - 4x + 16 = 0
x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0
x = 4 and 4
Hence the solution to the given system of equation is (4, 4)
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A petri dish contains cells of a certain strain of bacteria. Each bacterial cell in the dish divides in half approximately every 6 minutes. The curve of best fit that models the number of bacterial cells in the dish is given by the equation f(x) = 4.2 • 1.1x, where x represents the number of minutes and y represents the number of cells. Approximately how many bacterial cells will be in the petri dish after 30 minutes?
The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the number of cells after x minutes, hence:
y = 4.2(1.1)ˣ
After 30 minutes:
y = 4.2(1.1)³⁰ = 73.3
The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3
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A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.
Answer:
33,75 clients(huh?)
Step-by-step explanation:
75 / 100 = 0,75(1% of all clients)
0,75 * 45 = 33,75(number of business clients)
Please help! I don’t think my answers are correct. Photo is attached.
Answer:
Step-by-step explanation:
(a). In set notation:
B. { x | x < 2 }
(b).
( - ∞ , 2 )
(c). See attachment.
I need help ASAP PLEASE > How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3? (Please explain with your on words)
Answer:
The graph has been moved 7 units to the left and 8 units down.
Step-by-step explanation:
When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.
When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.
Hi there !
What is a Pythagoras theorem ?
Nonsense = Reported
Thank you
Answer:
Hi! I think you are referring to the Pythagorean Theorem.
Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.
The formula is a squared + b squared = c squared
If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:
3 squared + 4 squared = x squared
(Let x = the longer side)
3 squared = 9
4 squared = 16
9+16 = x squared
25 = x squared
x = 5
So there you go, that's the Pythagorean theorem.
Let me know if this helped!
Answer:
a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Step-by-step explanation:
What are the solutions to the equation x^2+9x+12=6
Answer:
[tex]x= -\dfrac {9}2 +\dfrac{\sqrt{57}}{2},~~x = -\dfrac {9}2 - \dfrac{\sqrt{57}}{2}[/tex]
Step-by-step explanation:
[tex]~~~~~~~x^2 +9x +12 = 6\\\\\implies x^2 +9x = 6-12\\\\\implies x^2 +9x = -6\\\\\implies x^2 +2 \cdot \dfrac 92 \cdot x +\left(\dfrac 92\right)^2 -\left( \dfrac 92 \right)^2 = -6\\\\\implies \left(x+ \dfrac 92 \right)^2 -\dfrac{81}{4}= -6\\\\\implies \left(x +\dfrac 92 \right)^2 = -6 + \dfrac{81}4\\\\\implies \left(x + \dfrac92 \right)^2 = \dfrac{57}{4}\\\\\implies x+ \dfrac 92 = \pm\sqrt{\dfrac{57}4}\\\\\implies x = -\dfrac {9}2 \pm\dfrac{\sqrt{57}}{2}[/tex]
Using the GCF factor the given expression: 21xy + 14y
7(3xy + 2y)
7y(3x + 2)
3(7xy + 14y)
7xy(3 +2)
ASAP
Since 7y is common to both factors, therefore the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
Greatest common factor of an expressionThe greatest common factor is the value that will divide an expression without leaving a remainder.
Given the expression 21xy + 14y
Find the factors
21xy = 7 * 3 * x * y
14y = 7 * 2* y
From the factors above, it is clear that 7 and y are the greatest common factors.
Since 7y is common to both factors, therefore the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
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Factor out
21xy=3×7×y×x14y=2×7×ySo
7y is common hence 7y is GCFNow factor up
7y(3x+2)Option B
Carlos invests $4540 at a rate of r% per year compound interest.
At the end of 10 years he has earned $1328.54 in interest.
Calculate the value of r.
Answer:
Initial balance$1000
interest rate 8%
Term 20yrs
Step-by-step explanation:
The final balance is $4,926.8.The total compound interest is $3,926.8.
The value of r is 2 %.
What is simple & compound interest?Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. Formula. S.I. = (P × T × R) ⁄ 100.
Given:
Principal(P)= $4540
Rate = ?
Time=10 years
CI=$1328.54
We have to find the value of r.
According to given question we have
By the use of compound interest we have
[tex]CI=p((1+\frac{r}{100} )^{10} -1)\\\\1328.54 =4540 ((1+\frac{r}{100} )^{10} -1)\\\\\0.292= ((1+\frac{r}{100} )^{10} -1)\\[/tex]
After simplifying we get,
r=2 %
Therefore, the value of r is 2 %.
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Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
This function shows a horizontal translation of the parent function to the left and 2 units up.
Square root functionThe parent function of a square root function is expressed as:
f(x) = √x
According to the question, we are to plot the expression f(x) = √x+ 3 - 2
This function shows a horizontal translation of the parent function to the left and 2 units up. The required graph will be in the 2nd quadrant of the graph as shown;
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Answer:
It should be the first one.
AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC
Answer:
60°
Step-by-step explanation:
Arc BC and Angle BWC are the same number of degrees.
When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.
Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.
180° - 120° is 60°
Angle BWC is 60° so Arc BC is 60°
What is the slope of a line perpendicular to the line whose equation is 2x+3y=21. Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
therefore then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}[/tex]
Answer:
2x+3y=21.
the answer is [tex]\frac{3}{2}[/tex]
simplify the answer I think. x = 2 + y = 3 = 21
x = 2
x + 1 = 3
y = 3
y - 1
2 + 1 = 3
3 - 1 = 2
The answer will only be [tex]\frac{3}{2}[/tex] no y = [tex]\frac{3}{2}[/tex] just [tex]\frac{3}{2}[/tex]
Don't forget to look at the picture
vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months and vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 months
how do I solve this and do I have enough information to answer the question and what step would take to solve the problem and how do I calculate the results
The calculation of the interest based on the price given shows that vehicle B has a lower interest.
How to calculate the price?From the information given, vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months. The interest will be:
= (25000 × 5 × 5)/100
= $6250
Vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 months. The interest will be:
= (29000 × 4 × 5)/100
= $5800
Therefore, the calculation of the interest based on the price given shows that vehicle B has a lower interest.
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A box has candies in it: are taffy, are peppermint, and are caramel. (Each candy falls into only one of these categories.) Brian wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the first candy selected is taffy and the second candy is caramel?
Do not round your intermediate computations. Round your final answer to three decimal places.
Probability that the first candy selected is taffy and the second candy is caramel is 0.144.
The data missing in the question is
A box has 18 candies in it: 3 are peppermint, 4 are caramel, and 11 are taffy.
What is Probability ?Probability can be defined as the study of likelihood of an event to happen.
It has a range of 0 to 1.
Probability is the ratio of the expected outcomes / total coutcome.
Total outcomes = 18
The probability that the first candy is taffy is 11/18
Now as there is no replacement , the total outcomes can be 17
The probability that the second candy is caramel is 4/17
Probability that the first candy selected is taffy and the second candy is caramel = (11/18)(4/17)
= 0.144
Therefore the Probability is 0.144
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Explain a time in your life you underwent metamorphosis
Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time
Step-by-step explanation:
I Hope This Helps!
Can someone explain me this please
Consider a space shuttle which has a mass of about 1.0 x 105 kg and circles the Earth at an altitude of about 200.0 km. Calculate the force of gravity that the space shuttle experiences
uhm i don't understand wut to put below the formula please make it clear thank you alot
Answer:
The force of gravity experienced by the shuttle would be 1.6675×10^N
A group of kids just finished trick-or-treating. The number of pieces of candy collected by each of the 5 kids is listed below.
31,33,36,41,34
Find the standard deviation of the data set. Round your answer to the nearest hundredth.
Evaluate the expression.
x² + 10x + 3 = -21?!?!!?!?!!!?
Answer:
-6,-4
Step-by-step explanation:
if you have to evaluate its 4
and there is 2 solutions
Find the measure of the remote exterior angle. m/x (198-5n)
m2y = (5n+37)
m²z = (n+7)
The measure of the remote exterior angle is 128°.
How to calculate the angle?From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)
198 - 5n = 6n + 44
Collect like terms
154 = 6n + 5n
154 = 11n
n = 154/11
n = 14
The value of angle x will be:
= 198 - 5n
= 198 - 5(14)
= 198 - 70
= 128
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Suppose a nuclear power plant disaster occurs. How could GDP be a "false beacon" in this case?
If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.
Why would GDP be a false beacon?Two of the components of GDP are government spending and private investment.
If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.
GDP would therefore increase.
This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.
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Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,128 was collected on the sale of 1,336 tickets. How many of each type of ticket were sold?
Answer:
Adults = 448
Students = 888
Step-by-step explanation:
Write equations with info given
A = Adult tickets
S = Student tickets
5A+1S=3,128
A+S=1336
Subtract equations from each other
4A=1792
Solve for A
A=448
Plug A into second equitation
448+S=1336
Solve for S
S=888