Answer:
The first option is the right answer $ 845.16
Step-by-step explanation:
1.089.26-120=969.26
969.26+325=1.294.26
1.294.26-425=869.26
869.26-24.10= 845.16
Given that (-6,5) is on graph of f(x) find the corresponding point for the function f(x)-4
The new graph will go down 4 point so y coordinate will go down 4. (-6,5) becomes ( -6, 1)
The corresponding point for the function f(x)-4 is (-6, 1) if the point (-6,5) is on the graph of f(x).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a point (-6, 5) is on graph of f(x) find the corresponding point for the function f(x)-4
As we know, if f(x) is subtracted by 4 the function f(x) will go down by 4 units.
The corresponding point on the function f(x)-4 will be:
= (-6, 5-4)
= (-6, 1)
Thus, the corresponding point for the function f(x)-4 is (-6, 1) if the point (-6,5) is on the graph of f(x).
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A recent hailstorm caused $900 worth of body damage to Kristen’s car. Based on Kristens insurance policy given below, how much will Karen receive after she files her claim.
Answer:
525
Step-by-step explanation:
Elizabeth is going to flip a fair coin 100100100 times. what is the best prediction for the number of times that the coin will land tails up
Answer:
50050050
Step-by-step explanation:
There is a 50% chance for the coin to either land on heads or tales so you divide 100100100 by 2 to get 50050050 this would work with anything else say you need to figure out the chance of a coin landing on heads and the coin flips 550 times to figure out the chance you do 550 divided by 2 and you get 225. But anyways the answer is 50050050. the reason you divide by two is because the coin has 2 sides, if it were a dice, for instance, you would divide by 6 because it has 6 sides
This table shows how many sophomores and juniors attended two school events. A student is selected randomly from this group.
Answer: B. 0.45
Step-by-step explanation:
From the given table, the total number of students = 137
The number of students are sophomores =35+42=77
Let A be the event that students are sophomores.
Then probability that students are sophomores is given by :
[tex]\text{P(A)}=\dfrac{77}{137}[/tex]
The number of sophomores who attended the jazz concert = 35
Let B be the event that students attended the jazz concert .
The probability that students attended the jazz concert and are sophomores is given by :
[tex]\text{P(A and B)}=\dfrac{35}{137}[/tex]
Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-
[tex]P(B|A)=\dfrac{\text{P(A and B)}}{\text{P(A)}}\\\\=\dfrac{\dfrac{35}{137}}{\dfrac{77}{137}}\\\\\\=\dfrac{35}{77}=0.454545454545\approx0.45[/tex]
a chemical company makes two brands of antifreeze. the first brand is 40% pure antifreeze, and the second brand is 65% pure antifreeze. in order to obtain 150 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used ?
first brand: ? gallons
second brand: ? gallons
Answer:
first brand 55 gallons
second brand 95 gallons
Step-by-step explanation:
What is the x-coordinate of the solution of the following system of equations?
3x + y = 6
x - y = 6
Answer:
x = 3
Step-by-step explanation:
By rearranging the equations,
y = 6 - 3x
y = x - 6
x - 6 = 6 - 3x
4x - 6 = 6
4x = 12
x = 3
Answer:
x = 3
Step-by-step explanation:
Follow the elimination method like so:
3x + y = 6 The Ys cross each other out.
x - y = 6 Add to get:
4x = 12
4x = 12 Divide to get:
4 4
x = 3
Hope this helps! :)
This rectangular prism is intersected by a plane that contains points D, E, K, and L.
What is the perimeter of the cross section?
Enter your answer in the box. Round only your final answer to the nearest tenth.
m
A rectangular prism with height 5 meters, length 12 meters, and width 4 meters. The vertices are labeled as G, D, H, L, E, F, J, and K.
The length of diagonal EK is sqrt(5^2 + 4^2) ≈ 6.403m
Hence perimeter = 2*(12 + 6.403) → 36.8 m (to the nearest tenth of a metre)
The perimeter of the cross-section is 36.8 m.
Calculations and Parameters:Given that the length of diagonal EK is
[tex]\sqrt{(5^2 + 4^2) }[/tex]
≈ 6.403m
Thus, the perimeter would be
2*(12 + 6.403)
→ 36.8 m.
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Given: f(x) = 2x + 5 and g(x) = x2 and h(x) = -2x
h(g(f(x))) = ?
Answer:
-2(2x +5)² = -8x² -40x -50
Step-by-step explanation:
Evaluate from the inside out, according to the order of operations.
h(g(f(x))) = h(g(2x +5)) = h((2x +5)²) = -2(2x +5)² = -2(4x² +20x +25)
= -8x² -40x -50
I personally prefer the factored form, but that is not considered "simplified."
A vegetable garden and a surrounding path are shaped like a square that together are 12 ft wide. The path is 2 feet wide. The the total area of the path.
Answer:
80 ft²
Step-by-step explanation:
The area of the path is equal to the area of the overall square minus the area of the garden.
Area of a square is the side length squared:
A = s²
The overall square has a side length of 12 feet. The side length of the garden is 12 - 2 - 2 = 8 feet. So the area of the path is:
A = 12² - 8²
A = 144 - 64
A = 80
The area of the path is 80 ft².
Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?
[p and q are integers] (5 points)
Step 1x2 + 8x + 15 - 1 = 0 - 1
Step 2x2 + 8x + 14 = -1
Step 3(x + 4)2 = -1
Step 1x2 + 8x + 15 - 2 - 0 - 2
Step 2x² + 8x + 13 = -2
Step 3(x + 4)2 = -2
Step 1x2 + 8x + 15 + 1 = 0 + 1
Step 2x2 + 8x + 16 = 1
Step 3(x + 4)2 = 1
Step 1x2 + 8x + 15 + 2 = 0 + 2
Step 2x2 + 8x + 17 = 20
Step 3(x + 4)2 = 2
Answer:
Step 1: x^2 + 8x + 15 + 1 = 0 + 1
Step 2: x^2 + 8x + 16 = 1
Step 3: (x + 4)^2 = 1
Step-by-step explanation:
You want the constant on the left to be the square of half the x-coefficient.
(8/2)^2 = 4^2 = 16
You already have a constant that is 15, so you need to add 1 to both sides of the equation. That is the Step 1 shown here. Step 2 is simplifying the result of Step 1. Step 3 is rewriting the trinomial as the square of a binomial.
Answer:
Step 1 x2 + 8x + 15 + 1 = 0 + 1
Step 2 x2 + 8x + 16 = 1
Step 3 (x + 4)2 = 1
Step-by-step explanation:
took the test
Based on a poll of 100 citizens, a community action group claims that 38% of the population is in favor of the construction of a senior center using tax dollars. A business group claims that the poll is not valid and that 65% of the citizens favor the construction of the senior center using tax dollars.
To determine whether this sample supports the population proportion of 0.38, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.65. The minimum sample proportion from the simulation is 0.42, and the maximum sample proportion from the simulation is 0.72.
The margin of error of the population proportion is found using an estimate of the standard deviation.
What is the interval estimate of the true population proportion?
Answer:
(0.55, 0.75)
Step-by-step explanation:
The range can be estimated to be 6 standard deviations wide. Therefore, the standard deviation is:
σ = (0.72 - 0.42) / 6
σ = 0.05
The margin of error is ±2σ, so:
ME = ±0.10
Therefore, the interval estimate is:
(0.65 - 0.10, 0.65 + 0.10)
(0.55, 0.75)
The standard deviation is a measure of a collection of values' variance or dispersion. The interval estimate of the true population proportion is (0.55, 0.75).
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
A.) The range is around 6 standard deviations broad. As a result, the standard deviation is:
σ = (0.72 - 0.42) / 6
σ = 0.05
B.) Because the margin of error is ±2σ, therefore, we can write,
Margin Of Error = (±0.05)×2 = ±0.10
C.) The interval can be estimated as,
Interval = 0.65±0.10
= 0.65-0.10, 0.65+0.10
= 0.55, 0.75
Hence, the interval estimate of the true population proportion is (0.55, 0.75).
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the equation of a parabola is given. y=-1/12x^2-2x-1
What are coordinates of the focus?
[tex]-(x^2+24x+144)=12y+12...[/tex]Answer:
(-12, 8)
Step-by-step explanation:
The standard form of this parabola, the one we can use to determine the vertex coordinates and the value of p is:
[tex](x-h)^2=4p(y-k)[/tex]
where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus. We need that p value to determine how far above the vertex the focus is. In this case, the focus will lie on the same x-coordinate as the focus, we just need to find how far that distance away is. That requires us to do some algebraic gymnastics on that original equation. Putting it into vertex form.
Begin by multiplying everything by 12 to get rid of the pesky fraction:
[tex]12y=-x^2-24x-12[/tex]
Now we need to complete the square. The easiest way to do this is to have just the x terms on one side of the equals sign and everything else on the other side, so we will add 12 to both sides:
[tex]-x^2-24x=12y+12[/tex]
The leading coefficient when you complete the square has to be a positive 1; ours is a negative 1, so factor out the negative:
[tex]-(x^2+24x)=12y+12[/tex]
The rules for completing the square are as follows: Take half the linear term (ours is a 24), square that half, then add it into the parenthesis.
Half of 24 is 12 so
[tex]-(x^2+24x+144)=12y+12[/tex]
BUT...since this is an equation, if we add something to one side we have to add it to the other side too. BUT we didn't just add in a 144, we have to take into account the -1 sitting outside the parenthesis that will not be ignored. So we didn't add in 144, we added in -1(144) which is -144.
[tex]-(x^2+24x+144)=12y+12-144[/tex]
What we have done on the left by completing the square is to create a perfect square binomial. Rewriting it as such and combining like terms on the right:
[tex]-(x+12)^2=12y-132[/tex]
Don't forget the purpose of this is to find the value of p. We're almost there. On the right, factor out a 12:
[tex]-(x+12)^2=12(y-11)[/tex]
From this we can determine the coordinates of the vertex and the value of p. The vertex sits at (-12, 11).
The equation for p is 4p = 12 so p = 3
That means that the focus is 3 units below the vertex on the same x coordinate. The focus then is at (-12, 8)
A park has a large circle painted in the middle of the playground area. The circle is divided into 4 equal sections, and each section is painted a different color. The radius of the circle is 10 \text{ meters}10 meters10, space, m, e, t, e, r, s.
Answer:
What is the area AA of each section of the circle?
Give your answer in terms of pi.
A = 25πm²
Step-by-step explanation:
Given the radius of the circle to be 10
The question is to find area of each sections of the circle .
The formula for calculating the area of a circle is area equals to πr²
A = πr²
Given r = 10m
The next step is to substitute the values into the equations
A = π (10m)²
A = 100πm²
Since the circle is divided into 4 equal sections, we need to find the area of each sections by dividing the complete area of the circle by 4
Therefore,
A = 100πm²/4
A = 25πm²
Answer:
25π[tex]m^{2}[/tex]
Step-by-step explanation:
ANSWER INCLUDED: What is the solution of log3x + 4 4096 = 4?
x=-1
x=0
x=4/3
x=3
We solve for x by simplifying both sides of the equation, then isolate the variable.
ANSWER:
C (x=4/3)
Answer:
C [tex]x=\frac{4}{3}[/tex]
Step-by-step explanation:
The given logarithmic equation is:
[tex]\log_{3x+4}(4096)=4[/tex]
We rewrite in exponential form; to get;
[tex]4096=(3x+4)^4[/tex]
We rewrite the LHS as a certain natural number exponent 4.
[tex]8^4=(3x+4)^4[/tex]
The exponents are the same, hence the bases must also be the same.
[tex]\implies 3x+4=8[/tex]
[tex]\implies 3x=8-4[/tex]
[tex]\implies 3x=4[/tex]
Divide both sides by 3;
[tex]\implie x=\frac{4}{3}[/tex]
The correct answer is C
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
x =
Answer:
67.1
Step-by-step explanation:
we need to use trig to work this out
(Soh Cah Toa)
The answer will be 67.11461952384143
to nearest tenth its
67.1
Answer:
x = 67.1°
Step-by-step explanation:
Cos(x) = Adj./Hypo.
Cos(x) = 28/72
Cos(x) = 0.3889
x = 67.1°
42. What is the surface area of a sphere with a circumference of 50 feet round the answer to the nearest 10th.
43. The volume of a sphere is 2254 pi m^3. What is the surface of the sphere to the nearest 10th?
44. What is the scale factor of a cube with a volume of 729 m^3 to a cube with a volume of 6859?
Answer:
Part 42) The surface area of the sphere is [tex]SA=795.8\ ft^{2}[/tex]
Part 43) The surface area of the sphere is [tex]SA=1,781.6\ m^{2}[/tex]
Part 44) The scale factor is [tex]\frac{19}{9}[/tex]
Step-by-step explanation:
Part 42) What is the surface area of a sphere with a circumference of 50 feet round the answer to the nearest 10th
step 1
Find the radius of the sphere
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=50\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]50=2(3.14)r[/tex]
[tex]r=7.96\ ft[/tex]
step 2
Find the surface area of the sphere
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
substitute the value of r
[tex]SA=4(3.14)(7.96)^{2}[/tex]
[tex]SA=795.82\ ft^{2}[/tex]
round to the nearest 10th
[tex]795.82=795.8\ ft^{2}[/tex]
Part 43) The volume of a sphere is 2254 pi m^3. What is the surface of the sphere to the nearest 10th?
step 1
Find the radius of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=2,254\pi\ m^{3}[/tex]
substitute and solve for r
[tex]2,254\pi=\frac{4}{3}\pi r^{3}[/tex]
Simplify
[tex]1,690.5=r^{3}[/tex]
[tex]r=11.91\ m[/tex]
step 2
Find the surface area of the sphere
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
substitute the value of r
[tex]SA=4(3.14)(11.91)^{2}[/tex]
[tex]SA=1,781.6\ m^{2}[/tex]
Part 44) What is the scale factor of a cube with a volume of 729 m^3 to a cube with a volume of 6859?
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z -----> the scale factor
x ----> the volume of the larger cube
y ----> the volume of the smaller cube
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]x=6,859\ m^{3}[/tex]
[tex]y=729\ m^{3}[/tex]
substitute
[tex]z^{3}=\frac{6,859}{729}[/tex]
[tex]z=\frac{19}{9}[/tex]
[tex](\frac{6,859}{729})[/tex]
Please help me with this please
Answer:
338 in
Step-by-step explanation:
Tangents to a circle from an external point are congruent, thus counting from the bottom left in a clockwise direction gives
perimeter = 98 + 22 + 22 + 27 + 27 + 22 + 22 + 98 = 338 in
Colin and Jezebel are employees at Game Zone. They recorded the number of computer games they sold each week for the past 9 weeks. Colin 15 20 21 9 3 16 9 14 17 Jezebel 10 14 20 11 4 26 5 8 20 (a) All of the games sold of which person had the greatest spread? Explain how you know. (b) The middle 50% of the games sold of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Colin's and Jezebel's sold games?
Answer:
Step-by-step explanation:
1. a) spread is the range which is given as Max(S)- Min(S)
Colin =
[tex]3,9,9,14,15,16,17,20,21\\\\range=21-3=18\\\\[/tex]
Jezebel=
[tex]=4,5,8,10,11,14,20,20,26\\\\range=26-4=22[/tex]
Jezebel had a greatest spread.It was 22 while for Colin was 18
2. a) The middle 50% of the game sold is the difference between the third quartile and first quartile of the data
Colin=
[tex]=3,9,9,14,15,16,17,20,21\\\\median=15\\\\lower half=3,9,9,14\\\\\\Q1=(9+9) /2 =9\\\\\\Upper half= 16,17,20,12\\\\\\Q3=(17+20)/2 = 18.5\\[/tex]
⇒The middle 50% = Q3-Q1 = 18.5- 9 = 9.5
Jezebel
[tex]=4,5,8,10,11,14,20,20,26\\\\\\=lower half= 4,5,8,10\\\\\\upper half=14,20,20,26\\\\\\Q1=(5+8)/2 = 6.5\\\\Q3= (20+20)/2 = 20[/tex]
⇒The middle 50% = Q3-Q1 = 20-6.5 = 13.5
Colin had the least spread of 9.5 as compared to Jezebel who had 13.5
c)The answers in part 2a and 2 b tels us that the middle section that contained 50% of the scores was more in Jezebel record than in Colin records.
Are all cubes similar? If so, explain why. If not, give an exapmle of two cubes that are not similar.
Yes, all cubes are similar.
Similarity in geometry refers to the property where two shapes have the same shape but not necessarily the same size. In the case of cubes, all cubes share the same shape characteristics: they have six square faces, with each face having four equal sides and all angles being right angles. The only difference between one cube and another is their size, or the length of their sides. Similarity does not depend on size; it is solely based on shape. Therefore, regardless of how large or small a cube is, it maintains its geometric properties and thus, all cubes are similar to each other. This means any two cubes you pick, regardless of their size, will be similar as they share these fundamental properties.
A lake near the Arctic Circle is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 333 weeks, the sheet is only 1.251.251, point, 25 meters thick.
Answer:
S(t) = 2 - 0.25*t
Step-by-step explanation:
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.
When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.
S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).
Therefore the equation formed will be linear.
The equation will be of the form y = mx + b
Here S(t) = mt + b
Here m is the slope which is the rate at which ice is melting.
Putting t = 0
S(t) = 2
Putting t = 3,
S(t) = 1.25
Therefore, m*0 + b = 2 or, b = 2
and 3m + b = 1.25
or, 3m = 1.25 - 2 = -0.75
or, t = -0.25
Hence, function's formula = S(t) = -0.25*t + 2
i.e. S(t) = 2 - 0.25*t
Answer:
y = 2 - 0.25x
Step-by-step explanation:
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.
When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.
S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).
Therefore the equation formed will be linear.
The equation will be of the form y = mx + b
Here S(t) = mt + b
Here m is the slope which is the rate at which ice is melting.
Putting t = 0
S(t) = 2
Putting t = 3,
S(t) = 1.25
Therefore, m*0 + b = 2 or, b = 2
and 3m + b = 1.25
or, 3m = 1.25 - 2 = -0.75
or, t = -0.25
Hence, function's formula = S(t) = -0.25*t + 2
i.e. S(t) = 2 - 0.25*t
Please help! Thanks
Answer:
not geometric
Step-by-step explanation:
A geometric series is one where the nth term is multiplied by a common ratio to get the n+1 term.
1 1/2 1/4 1/8 1/16 .....
is a geometric series. the fourth term (1/8) is multiplied by 1/2 to get 1/16.
The series you have been given is not geometric. It reduces to
1/3 1/4 1/5 1/6 which does not give you a common number to multiply the nth term to get to the n+1 term.
Use the formula to evaluate the infinite series. Round to the nearest hundreth if necessary.
25 + 5 + 1 + . . .
Answer:
31.25
Step-by-step explanation:
The initial term is 25 and the common ratio is 5/25 = 1/5. The formula tells you the sum is ...
25/(1 -1/5) = 25/(4/5) = 31.25
If we factor 25 from the sum, we have
[tex]\displaystyle 25\left(1+\dfrac{1}{5}+\dfrac{1}{25}+\ldots\right)=25\sum_{i=0}^\infty \left(\dfrac{1}{5}\right)^i = 25 \dfrac{1}{1-\frac{1}{5}} = 25\dfrac{1}{\frac{4}{5}}=25\cdot \dfrac{5}{4} = \dfrac{125}{4}[/tex]
The Jeffer's company has a debt ratio (total debt to total assets) of 0.365. If their total assets are $739,000, what is their total debt?
A) $269,735
B) $469,265
C) $1,008,735
D) $2,024,657
The answer is D 2,024,657
Answer:
A
Step-by-step explanation:
0.365 x 739,000= 269,735
Please help me ..... (:
Answer:
162.43
Step-by-step explanation: I hope its helps it's been a couple of years since I have done geometry
Answer:
the total area of the octagon is 8(20.3 in²), or 162.4 in²
Step-by-step explanation:
A regular octagon has 8 pie-shaped sections. Each is triangle of height 7 in and base 5.8 in.
Thus, the area of each such section is, by A = (1/2)(b)(h(),
A = (1/2)(5.8 in)(7 in) = 20.3 in².
There are 8 such sections.
Thus, the total area of the octagon is 8(20.3 in²), or 162.4 in²
What is the rate of change between the interval x= pi and x= 3pi/2
Answer:
[tex]\frac{6}{\pi }[/tex] or 1.9099
Step-by-step explanation:
Look for y values at each of those given values of "x" and apply the slope formula. When x = pi. y = -1 so the coordinate is [tex](\pi,-1)[/tex]. When x = 3pi/2, y = 2 so the coordinate is [tex](\frac{3\pi }{2},2)[/tex]
Plug those values into the slope formula:
[tex]\frac{2-(-1)}{\frac{3\pi }{2}-\pi}[/tex]
You need a common denominator of pi:
[tex]\frac{3}{\frac{3\pi-2\pi}{2} }=\frac{3}{\frac{\pi }{2} }[/tex]
Do the math on that to get a slope of [tex]\frac{6}{\pi } =1.9099[/tex]
how do you find the vertex of 2x+y^2=0
[tex]\bf \textit{vertex of a horizonal parabola, using f(y) for "x"} \\\\ x=\stackrel{\stackrel{a}{\downarrow }}{a}y^2\stackrel{\stackrel{b}{\downarrow }}{+b}y\stackrel{\stackrel{c}{\downarrow }}{+c} \qquad \left(f\left(-\cfrac{ b}{2 a}\right)~~~~ ,~~~~ -\cfrac{ b}{2 a} \right) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 2x+y^2=0\implies 2x=-y^2\implies x=\cfrac{-y^2}{2}\implies x=\stackrel{\stackrel{a}{\downarrow }}{-\cfrac{1}{2}}y^2\stackrel{\stackrel{b}{\downarrow }}{+0}y\stackrel{\stackrel{c}{\downarrow }}{+0} \\\\\\ -\cfrac{b}{2a}\implies -\cfrac{0}{2\left(-\frac{1}{2} \right)}\implies 0\qquad therefore\qquad (f(0)~~,~~0)\implies \stackrel{vertex}{(0,0)}[/tex]
you can see it this way, x = -(1/2)y² is just a horizontal parabola opening to the left-hand-side, the -1/2 is just a stretch transformation of the parent function x = y², but as much as it stretches, their vertex is the same, at the origin.
Kevin is responsible for delivering sacks of grains to a grocery shop on the tenth floor of a departmental store. Each sack weighs 364 pounds and Kevin weighs 150 pounds. The capacity of the elevator is 2,000 pounds. If six sacks are to be taken at a time, what should be the weight of each sack? Question 6 options: at the most 308 pounds at least 308 pounds exactly 308 pounds at the most 803 pounds
Answer:
at the most 308 pounds
Step-by-step explanation:
Given
Weight of each sack = 364 pounds
Weight of Kevin = w = 150 pounds
Weight that lift can take = 2000 pounds
In order to find the weight of sacks that can be put into the elevator we have to subtract the weight of Kevin from the capacity of the lift.
So, actual weight of sacks that can be taken =[tex]2000-150[/tex]
= 1850 pounds
As 6 sacks have to be taken, to find the weight of one sack
Required weight of one sack = [tex]\frac{1850}{6}[/tex]
= 308.33 pounds
So, each sack has to weigh at the most 308 pounds ..
The correct option is a. at the most 308 pounds. Each sack should weigh at most 308 pounds to ensure that the elevator's weight limit is not exceeded when Kevin is in the elevator with six sacks.
To determine the weight each sack can be so that the elevator capacity is not exceeded, we must consider the total weight limit of the elevator and the weight of Kevin.
The elevator has a capacity of 2,000 pounds. Kevin weighs 150 pounds, and he will be riding the elevator with the sacks. Therefore, the total weight available for the sacks is:
2,000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1,850 pounds.
If six sacks are to be taken at a time, we divide the total available weight by the number of sacks to find the maximum weight each sack can have:
1,850 pounds / 6 sacks = 308.333... pounds.
Since the weight of each sack must be a whole number, we round down to the nearest whole number, which is 308 pounds. This ensures that the elevator's capacity is not exceeded.
Therefore, This allows for a small margin of error in the weight of the sacks, which is safer and more practical than having the sacks weigh exactly 308 pounds each.
Please help me withe this proof as well.
- D is the midpoint of AB, E is the midpoint of BC
Answer: A. Given
I left off DB||FC because that's not given. But we can construct it.
Construct line through C parallel to AB. Extend DE to intersect and call the meet F.
- DB || FC
By Construction
----
- Angle B congruent to angle FCE
Answer: D. Alternate Interior Angles
We have transversal BC across parallel lines AB and CF, so we get congruent angles ABC and FCB aka FCE
- angle BED congruent to angle CEF
Answer: H. Vertical angles are congruent
When we get lines meeting like this we get the usual congruent and supplementary angles.
- Triangle BED congruent to Triangle CEF
Answer: F. Angle Side Angle
We have BE=CE, DBE=FCE, BED=CEF
- DE congruent to FE and DB congruent to FC
Answer: C. CPTCTF
Corresponding parts ...
- AD congruent to DB and DB congruent to FC therefore AD congruent to FC
Answer: E. Transitive Property of Congruent
Things congruent to the same thing are congruent
- ADFC is a parallelogram
Answer: G. AD and FC are congruent and parallel
Presumably this is a theorem we have already established.
- DE || AD
Answer: B. Definition of a parallelogram
convert y-(51)=15.2(x-(2)) to standard form
I don’t know what the answer is I wish I could help
The answer is y=56.2x-112.4
Janis is helping organize the school dance. She asked 30 randomly selected students to select their favorite theme for the dance. The top choice for 6 students was Glow-in-the-Dark. The total number of students in the middle school is 200. Based on the results of the survey, how many students should Janis expect to choose Glow-in-the-Dark as their favorite theme?
Answer:
Step-by-step explanation:
6 of 30 chose Glow in the Dark
That is 1/5 of the students
Out of 200, 40 would choose glow in the dark
40 is 1/5 of 200
The answer is 40
Out of 200, 40 students should Janis expect to choose Glow-in-the-Dark as their favorite theme.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
6 of 30 chose Glow in the Dark.
So, if there are 200 middle school students then the number of students choose Glow-in-the-Dark as their favorite theme
= 6/30 x 200
= 1/5 x 200
= 40
Learn more about Unitary Method here:
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