Using proportions, it is found that the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each lb has 0,0005 tons. Hence the total weight in tons that we want to put in the elevator is:
T = (175 + 240 + 80 x 50) x 0.0005 = 2.2075 tons.
Hence, the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.
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Consider [tex]$\triangle ABC$ such that $BC = 3AC$ and $\angle A = \pi/6$[/tex]
What are [tex]\[12 \sin(\angle B), 12 \sin(\angle C)\][/tex] in that order?
The answer to the question is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
Sin rule is,
sin(A)/BC = sin(B)/AC = sin(C)/AB
sin(B) = (sin(A)×AC)/BC
sin(C) =(sin(B)×AB)/AC
To solve this question we apply sin rule,
Now we take
12 sin(∠B) =12 (sin(∠A)×AC)/BC
12 sin(∠B) =12 (sin(π/6)×(x/3x)) where ∠A =π/6 and AC=x, BC =3x
12 sin(∠B) =12 ((1/2)×(1/3))
12 sin(∠B) =12/6 = 2
12 sin(∠B) = 2
now we find the value of 12 sin(∠C)
12 sin(∠C) = 12(sin B)×(AB/BC)
now put the value of 12 sin(∠B) = 2
12 sin(∠C) = 2×(AB/BC)
12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]
12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]
cos (π/6) = √3/2 and BC/AC =3
then
12 sin(∠C) = 2×[(√3/2)+3×(cos B)]
cos B= √1-sin²B
12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]
12 sin(∠B) = 2
sin B = 1/6
12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]
12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]
12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]
12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]
12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]
12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]
12 sin(∠C) = 2×[(1/2)(√3+√35)]
12 sin(∠C) = √3+√35
Hence the answer is,
12 sin(∠B) = 2, 12 sin(∠C) = √3+√35
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Part A Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence. In this case, you know the measure of two adjacent sides and the angle opposite to one of them. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. (Hint: Try constructing a triangle where the known angle is opposite to the shortest known side.) If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.
In the case above, the side-side-angle (SSA) is no valid means for establishing triangle congruence.
What is the triangle congruence about?Using the image attached:
m angle A = M angle A
AB = A¹B¹
BC = B¹C¹
Looking at the image of both angles you will see that both are not congruence because Two triangles can be regarded as congruent if and when all its three corresponding angles or sides are said to be equal and all the three corresponding angles are also said to have equal measure.
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On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
Answer:
(a) F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Step-by-step explanation:
Wherever the function crosses the x-axis, its sign changes. This lets us make a map of the signs of the function, and identify intervals where it is positive and negative.
Sign changesThe x-intercepts are said to be at x ∈ {-0.7, 0.76, 2.5}. These three crossing points divide the graph into four (4) intervals. The sign of the function is given as positive at x=0 and negative at x = 1.9. So, our sign map is ...
< -0.7 . . . . . negative
-0.7 to 0.76 . . . . . positive (2 at x=0, for example)
0.76 to 2.5 . . . . . negative (-5.7 at 1.9, for example)
> 2.5 . . . . . positive
Choosing from the descriptions, the one that matches is ...
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Guys I need help! You and your friend are rolling number cubes. Each cube has 6 sides with the numbers 1 to 6. If a sum of 7 is rolled, your friend gets 1 point.
If a 2, 3, or 4 is rolled, you get 1 point.
After 108 rolls each, what scores should you expect?
1. Friend: 54; You: 54
2. Friend: 54; You: 18
3. Friend: 18; You: 18
4. Friend: 18; You: 54
Elvira College has an enrollment of 1,000 students and is located in a small Midwestern town named Johnsonville. Johnsonville has a total population of 2,500 people. The nearest town is 20 miles away. Most of the residents shop locally, but they travel about once a month to the larger city and pick up the large-ticket items. Johnsonville has one fairly good-size supply store named Jameson's Grocery. The only other place in town where you might buy supplies is at the gas station/convenience store located on the edge of town. What competitive situation is Jameson's Grocery experiencing?
Since there are only two (2) sellers in the town with many buyers, the competitive situation which Jameson's Grocery is experiencing is an oligopoly.
What is an oligopoly?An oligopoly can be defined as a market structure which comprises a small number of business firms (sellers) that are offering identical (similar) products to many buyers, wherein none of the sellers can limit the significant influence of others.
In this scenario, we can infer and logically deduce that the competitive situation which Jameson's Grocery is experiencing is an oligopoly because there are only two (2) sellers in the town with many buyers (1,000 students).
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What is EBC? ASAP please
We know that if [tex]m\angle ABD=2(m\angle DBC)[/tex], then [tex]m\angle ABD=\frac{2n}{3}[/tex] and [tex]m\angle DBC=\frac{n}{3}[/tex].
Since BE bisects [tex]\angle DBC[/tex], we know that [tex]\angle DBE \cong \angle EBC[/tex], and thus [tex]\angle EBC=\boxed{\frac{n}{6}}[/tex]
in the number pattern below, in which row is 2007
1
2. 3.
4. 5. 6.
....
The number 2007 is in the 63rd row
How to determine the number of row?The pattern is given as
1
2 3
4 5 6
The sum of n natural numbers is:
Sum = 0.5n(n + 1)
Assume n = 62
Sum = 0.5 * 62 * (62 + 1)
Sum = 1953
Assume = 63
Sum = 0.5 * 63 * (63 + 1)
Sum = 2016
2007 is between 1953 and 2016
Since 2016 is greater than 1953, we can conclude that 2007 is in row 63
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The population of fruit flies increases by a factor of 100 each week. How many fruit flies will there be after two weeks if there are 25 fruit flies in the beginning? Write an expression to represent this situation.
25 * (1002)
100 + (100 * 2)
100 + (25 * 2)
2 + (25 * 100)
Answer:
y=250000
Step-by-step explanation:
y=ab^x
y=25*100^2
A ball of radius 14 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.
The volume of the spherical solid resulting of the drill is of 11,226 units³.
What is the volume of a sphere?The volume of a sphere of radius r is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, we have two spherical balls, one of radius 14 and other of radius 4, hence their volumes are given as follows:
[tex]V_1 = \frac{4\pi 14^3}{3} = 11494[/tex]
[tex]V_2 = \frac{4\pi 4^3}{3} = 268[/tex]
The volume of the resulting solid is the difference of the volumes, hence:
V = 11494 - 268 = 11,226 units³.
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please help me on this
Venn Diagram:
41 - 14 = 27 for only cats63 - 14 - 27 = 22 for only dogs100 - 27 - 22 - 14 = 37 outsideNeither a cat or dog: 37/100
A dog: (22+14)/100 = 36/100 = 18/50 = 9/25
A dog but not a cat: 22/100 = 11/50
State engineers have determined that a bridge cannot carry more than 700,000 pounds evenly dispersed.
The legal limit for 6-axle trucks is 100,000 pounds and the legal limit for Z-axle trucks is 34,000 pounds.
How many 6-axle trucks can travel on the bridge at one time? How many 2-axle trucks? (Assume that
there are no other vehicles on the bridge.) Write an inequality to solve the problem, then graph the solution.
The inequality of the bridge's legal limit 100000x + 34000y ≤ 700000
How to determine the inequalityThe given parameters are:
Maximum = 700,000 pounds6-axle trucks = 100,000 pounds2-axle trucks = 34,000 poundsRepresent the 6-axle trucks with x and the y-axle trucks with y.
So, we have the following inequality
100000x + 34000y ≤ 700000
The number of 6-axle trucks at one time
Here, we assume that y = 0.
So, we have:
100000x ≤ 700000
Divide by 100000
x ≤ 7
Hence, the number of 6-axle trucks at one time is 7
The number of 2-axle trucks at one time
Here, we assume that x = 0.
So, we have:
34000x ≤ 700000
Divide by 34000
x ≤ 20.58
Round down
x ≤ 20
Hence, the number of 2-axle trucks at one time is 20
See attachment for the inequality of 100000x + 34000y ≤ 700000
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TRUE or FALSE: The square root of R2 (the coefficient of determination) is r, the correlation coefficient. (remember that square roots are always positive)
The The square root of R² (the coefficient of determination) is not r, the correlation coefficient. Therefore, it's false.
What is a correlation coefficient?It should be noted that the correlation coefficient is used to measure how string the relationship between two variables are.
The correlation formula tells us the linear relationship between the variables. R² is the square of the correlation coefficient.
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1. Calculate the area of the kite shown in the figure below:
9 cm
9 cm
35
What are the zeros of g(x)= x³ + 6x² - 9x-54?
Answer:
3,-3
Step-by-step explanation:
g(3)= (3)³+6(3)²-9(3)-54
= 27+54-27-54
=81-81
= 0
g(-3) = (-3)³+6(-3)²-9(-3)-54
= -27+54+27-54
= 27-27
= 0
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Directions: Indicate product of FOIL for the problem
The product of the given binomial is x⁴ -y².
How to find product using FOIL method ?FOIL stands for Firsts , Outsides , Insides , Lasts and while determining product of binomials this sequence is followed.
The binomials given are
( x² +y ) (x² -y)
x² (x² -y) + y * x² + y* (-y)
------------ ------ --------
Firsts Outsides insides Lasts
After simplification
x⁴ - x²y + x²y -y²
x⁴ -y²
The product of the given binomial is x⁴ -y².
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Make a scatter plot of the data. Then find an equation of the quadratic function that models the data.
The equation of the quadratic function that models the data is y = x^2 + 3x + 4
How to determine the scatter plot?A quadratic function is represented as:
y = ax^2 +bx + c
Next, we enter the data values on the table to a graphing calculator.
From the graphing calculator, we have:
a = 1, b = 3 and c = 4
Substitute these values in y = ax^2 +bx + c
So, we have
y = x^2 + 3x + 4
Hence, the equation of the quadratic function that models the data is y = x^2 + 3x + 4 and the scatter plot is (a)
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6. Error Analysis A classmate says the endpoints of
the midsegment of the trapezoid in Problem 3 are
d+a
(2/2) and (dª). What is your classmate's
error? Explain.
M
R(2b, 2c) A(2d, 2c)
N
P(2a, 0)
Answer:
They used coordinates P(a,0), A(d,c), and R(b,c) instead of the given coordinates.
Given f(x) = 4x + 1 and g(x) = x^, choose
the expression for (fᵒg)(x).
Answer: 4x^2 + 1
Step-by-step explanation:
I am assuming g(x) = x^2
4(x^2) + 1
4x^2 + 1
Answer:
[tex](fog)(x)=4x^2+1[/tex]
Step-by-step explanation:
Assume [tex]g(x)=x^2[/tex]
[tex](fog)(x)[/tex] is a composition of two functions such that [tex](fog)(x)=f(g(x))[/tex].
Consider the function:
[tex]f(x)=4x+1[/tex]
Replace [tex]x[/tex] with [tex]g(x)[/tex] into the equation:
[tex]f(g(x))=4\cdot g(x)+1[/tex]
Substitute [tex]g(x)=x^2[/tex] on the right side of the equation:
[tex]f(g(x))=4\cdot x^2+1[/tex]
Therefore, the expression for [tex](fog)(x)[/tex] is [tex]4x^2+1[/tex].
HELP!
An invertible function is represented by the values in the table.
x −3 −2 −1 0 1 2 3
f(x) 4.4 0.6 −0.8 −1 −1.2 −2.6 −6.4
Which graph shows the inverse of this function?
Using it's concept, it is found that the graph on top right represents the inverse function.
How to find the inverse of a function of pairs (x,y)?The inverse of the function is given by the set that contains point (y,x), that is, the coordinates are exchanged.
Considering the table given, the graph of the inverse function will contain these following points:
(4.4, -3), (0.6, -2), (-0.8, -1), (-1,0), (-1.2, 1), (-2.6, 2), (-6.4, 3).
Hence it is the top right graph.
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find the surface area a planet if its circumference is about 18,000 miles long. Round to the nearest thousand square miles
The surface area of the planet is 103,184,713.4 miles².
What is the surface area?A planet has the shape of a sphere.
The first step is to determine the radius of the planet from the circumference.
Radius = circumference / (π x 2)
18,000 / (3.14 x 2) = 2,866.24 miles
Surface area of a sphere = 4πr²
4 x 3.14 x ( 2,866.24²) = 103,184,713.4 miles²
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A blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is Blue Jay going to store for the winter, and how many trees?
Answer:
4 trees and 76 acorns.
Step-by-step explanation:
Let the amount of trees be x.
[tex]18x+4=20x-4\\\\\implies2x=8\\\\\implies x=4[/tex]
There are 4 trees, and there are [tex]18x+4[/tex] acorns or 76 acorns.
Hope you have a nice day, and also you should mark brainliest :)
Answer:
76 acorns and 4 trees
Step-by-step explanation:
Let X be the number of acorns (a) Ms. Blue Jay plans to store.
We are told that she could hide 18 acorns (a) per tree (t) which we'll write as 18a/t. This would result in 4 leftover acorns.
We then learn that if she hides 20 acorns per tree, 20a/t, she will have space for an extra four acorns.
There are t trees in both cases. We can write these two scenarios as:
1) 18t + 4 = X [18 acorns are in each tree, t, plus there are 4 left over.]
2) 20t -4 = X [20 acorns per tree, t, with room to store 4 more]
These two are equal to each other:
18t + 4 = 20t - 4
2t = 8
t = 4
There are 4 trees.
Since 18t+4 = X, the total number of acorns is18*4+4 = 76 acorns and 4 trees.
Check to see if 76 acorns works for the second scenario:
Will hiding 20 acorns per tree leave room for 4 acorns if there are 76 acorns?
(4 trees)*(20 acorns/tree) = 80 acorns can be stored. If Ms. Jay only has 76 acorns, there will be room for 4 more acorns.
State whether each of the following is an
open or closed question.
a) Why do you enjoy cooking?
b) What is your favourite fruit?
c) How tall are you?
d) Do you enjoy cooking?
e) What did you do on your holiday?
Find a linear inequality with the following solution set. Each grid line represents one unit.
Answer:
y≤-x+1
Step-by-step explanation:
Since the line is slanted down and crossing through a point every one unit the slope is negative one. The line is also crossing 1 on the y-axis. This is the y-intercept. The last thing we need to know is which sign to use, less than, greater than, less than or equal to, greater than or equal to. We can immediately cross out less than and greater than because it is a solid line. The sign used on the graph is less than or equal to because it is a solid line shaded to the left. Now, we can use the formula with the information we have found to create the linear inequality.
Formula: y≤x+b
I put the less than or equal to sign there instead of the equal sign because the line graphed is less than or equal to. Plug in the information we have.
y≤-x+1
Using function notation.
f(x)≤-x+1
I have also attached a picture for you to see it is correct.
Hope this helps!
If not, I am sorry.
Tasha wants to graph a line that is parallel to the line with equation y=3x. Give two examples of linear equations that represent lines she should draw: one that us above the original line and one that is below the original line
Answer:
y = 3x + a (a > 0) - above the original line
y = 3x + b (b < 0) - below the original line
Step-by-step explanation:
Pick any number you want for a or b, as long as the number meets the condition I wrote down.
Answer:
y=3x+1 and y=3x-1
Step-by-step explanation:
y=3x+1 is above because it has a positive slope (3) while y=3x-1 is below because it has a negative slope (-3).
PLS HELP ME I PUT THIS OUT ONCE BUT DIDNT GET HELP !
Hope this helped!
This is just what I drew. I believe the answer for B could be somewhat different than what I drew.
Have a nice day!
Which inequality is true? 1.5 greater-than 2 and one-half
One-half greater-than 0.5
Negative 2.5 greater-than negative 1.5
Negative 3 and one-half greater-than negative 4.5
The inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have inequalities given:
[tex]1.5 > 2\dfrac{1}{2}[/tex]
or
1.5 > 2.5 (false)
1/2 > 0.5
0.5 > 0.5 (false)
-2.5 > -1.5 (false)
[tex]-3 \dfrac{1}{2} > -4.5[/tex]
-3.5 > -4.5 (true)
Thus, the inequality negative 3 and one-half greater-than negative 4.5 or -3.5 > -4.5 is true.
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Explain why you need to state the domain before simplifying a rational function. you should use at least one example in your explanation.
Knowing which x-values would result in division by zero can help you avoid using certain x-values. Finding the domains of rational functions is therefore likely to be your initial step.
What is a rational function?A function that measures two polynomials in comparison. Because one is divided by the other, just like a ratio, it is a "rational function."
All real numbers x, except those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.
For instance, the set of all real numbers other than x=0 is the domain of the parent function f(x)=1/x.
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Can someone help with this geometry question? It’s urgent
Answer:
Step-by-step explanation:
So if you look at the first photo I sent you'll see I marked three points. So the first point is going to be the two lines meet and the other two are going to be at 0 degrees and 48 degrees. After that you're going to draw a line to connect 2 of the dots to the middle one or the one connecting the two. After this you're going to put the protractor back on the triangle and line it up and then draw a point at 24 degrees (half of 48 degrees) and then draw a line to it. And this will be the bisector. And then after that label all the points. Also for the congruency thing just do the same thing except without an angle bisector through it.
To calculate a margin of error, you multiply the standard error by the number of standard deviations from the mean, which is also called a _____.
half the confidence interval is the answer.
The margin of error is a statistical measure that explains the difference between the actual and expected results of a random survey sample. Simply put, tolerances allow you to measure the level of unpredictability of your data and findings.
The margin of error is the amount added and subtracted in the confidence interval. The standard error is the standard deviation of the sample statistics when many samples of the same size can be obtained.
E = zs√n. The quantity E is called the margin of error. The margin of error is half the width of the confidence interval. The confidence interval may be given as ˉx ± E. For example, 9.95 ± 0.43.
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which is longest?
A. the diagonal of a square with 6 cm sides
B. the diagonal of a rectangle with length 7 cm and width 5 cm
C. the hypotenuse of a right triangle with legs 4 cm and 9 cm long
D. the leg of a right triangle with the other leg 10 cm and the hypotenuse 15 cm long
Answer:
12cm
Step-by-step explanation:
where:
c
is the hypotenuse, and
a
and
b
are the other two sides (legs).
Let
a
=
9 cm
Rearrange the equation to isolate
b
2
. Plug in the values for
a
and
c
, and solve.
b
2
=
c
2
−
a
2
b
2
=
(
15 cm
)
2
−
(
9 cm
)
2
Simplify.
b
2
=
225 cm
2
−
81
cm
2
b
2
=
144 cm
2
Take the square root of both sides.
b
=
√
144 cm
2
Simplify.
b
=
12 cm