Answer:
slope: 6
y-intercept: -4
easy: y = 6x -4
PLEASE HELP GEOMETRY 20 POINTS
Answer:
fourth option
Step-by-step explanation:
The largest angle in the triangle is opposite the longest side
The smallest angle in the triangle is opposite the shortest side
largest side is WX = 14
shortest side is VW = 9
then smallest to largest angles are
∠ X , ∠ W , ∠ V
In this figure, AB∥CD and m∠3 = 114°.
What is m∠6?
Answer:
66
Step-by-step explanation:
180 - 114) These angles are supplemental. They add to 180
66
Answer:
m<6=66°
Step-by-step explanation:
Because m<2 and m<3 are both on a straight line, we know they must add to 180°:
m<2 + m<3 =180
We know m<3=114°, so:
m<2 +114 = 180
m<2 = 66
Since AB|CD, m<2 and m<6 are corresponding angels, making them equal, and so m<6=66°.
A box contains 4 pears and 7 oranges. Three fruits are taken out at random and eaten. Find the
probability that
(1) 2 pears and 1 orange are eaten, in any order,
(ii) the third fruit eaten is an orange,
(iii) the first fruit eaten was a pear, given that the third fruit eaten is an orange.
(i) The probability that 2 pears and 1 orange are eaten in any order is equal to [tex]\frac{14}{55}[/tex]
(ii) The probability that the third fruit eaten is an orange is equal to [tex]\frac{7}{15}[/tex]
(iii) The probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to [tex]\frac{6}{11}[/tex]
What is Probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. It is more likely that an event will occur if its probability is higher.For example, the probability of tossing a coin and getting a head is equal to [tex]\frac{1}{2}[/tex]What are Combinations?
Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.The formula for calculating the number of alternative configurations by picking only a few items from a set of objects with no repetition is written as follows in mathematics, [tex]{n \choose k }=\frac{n!}{k!(n-k)!}[/tex]Here, it is given that the box contains 4 pears and 7 oranges in the box.
So, the total number of fruits in the box = 4 + 7 = 11
Combination when 2 pears is chosen out of 4 pears from the box [tex]= {4 \choose 2} = \frac{4!}{2!(4-2)!} =6[/tex]
Combination when 1 orange is chosen out of 7 oranges from the box [tex]= {7 \choose 1} = \frac{7!}{1!(7-1)!} =7[/tex]
Combination when 2 pears and 1 oranges are taken from the box containing a total of 11 fruits [tex]= {11 \choose 3} = \frac{11!}{3!(11-3)!} =165[/tex]
So, the probability that 2 pears and 1 orange are eaten, in any order,
[tex]P(A) =\frac{ {4 \choose 2} \times {7 \choose 1} }{ {11 \choose 3} } \\\implies P(A) = \frac{6 \times 7}{165} \\\implies P(A) = \frac{14}{55}[/tex]
Now, the probability that the third fruit eaten is an orange is given as,
[tex]P(B)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}+{1 \choose 7}{1 \choose 6}{1 \choose 5}}{A(11,3)} \\P(B)=\frac{460}{990} \\P(B)=\frac{7}{15}[/tex]
Next, we can find the probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is a conditional probability problem where one event depends on another event.
The probability that the third fruit is orange P(A) is equal to 7/15
The probability that the first fruit eaten was a pear is calculated as,[tex]P(C)= \frac{{1 \choose 4}{1 \choose 3}{1 \choose 7}+{11 \choose 4}{1 \choose 7}{1 \choose 6}}{A(11,3)} \\P(C)=\frac{252}{990} \\P(C)=\frac{14}{55}[/tex]
So, according to conditional probability,
Probability of C given A,
[tex]P(C/A)=\frac{P(C \cap A)}{P(A)} \\\implies P(C/A)=\frac{\frac{14}{55} }{\frac{7}{15} } \\\implies P(C/A)=\frac{6}{11}[/tex]
There, the (i) probability that 2 pears and 1 orange are eaten in any order is equal to [tex]\frac{14}{55}[/tex]
(ii) probability that the third fruit eaten is an orange is equal to [tex]\frac{7}{15}[/tex]
(iii) probability that the first fruit eaten was a pear, given that the third fruit eaten is an orange is equal to [tex]\frac{6}{11}[/tex]
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some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 150 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?
Any piece of luggage must have a length, width, and height combined that is less than or equal to 150 cm. A traveler requests to take a package with the maximum permitted volume. if the length and width are to be equal, then the dimensions would be 48*96*72
Any piece of luggage must have a length, breadth, and height combined that is 216 cm or less.
L+W+H=216 (because we want the max volume, we may ignore the "less than part" and set them equal) (since we want the max volume, we can ignore the "less than part" and set them equal)
L = W if the length and width are equal.
Let's construct this new equation by swapping L for W.
Arrange H to the left so that H=216-2W when 2W+H = 216
Consequently, what is volume V=L*W*H=W=W2*(216-2W) =216W2-2W3 div./dW=432W-6W?
2\s432W-6W^2=0
72w-w2=0 divided by 6 on both sides.
W = 72 L H = 72 cm
L=2W is the only item that has altered.
Given that L+W+H=216 and that V=L*W*H=2W*W*(216-3W) =432W2-6W, 3W+H=216
864W-18W2 x 3 V prime
Set V prime to 0, solve it by dividing both sides by 18, and you'll get W = 48. dimensions will be
48, 96, and 72 cm in width ,lenght and height
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Find the x-intercept of the line 8x+8y=–
1
Answer:
x-intercept is [tex]\frac{-1}{8}[/tex]
Step-by-step explanation:
The x-intercept is the Value of x when y = 0
So for our Equation , 8x + 8y = -1
At y = 0 , 8x + 0 = -1
Then 8x = -1
Then x = -1/8
Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
2x + 7y = -35
4x + 14y = -42
Answer:
Step-by-step explanation:
354
Which number line represents the solution set for the inequality –4(x + 3) ≤ –2 – 2x?
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the left.
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
Mark this and return
The correct answer to inequality is option A .
What is inequality equation?
The mathematical expressions with inequalities area unit those with unequal sides on each side.
Main body:
For this case we have the following inequality:
-4(x+3)≤ -2 -2x
Applying distributive property on the left side we have:
-4x - 12≤ -2 -2x
Adding 2x to both sides of the inequality we have:
-4x +2x -12 ≤-2
-2x-12≤-2
Adding 12 to both sides of the inequality we have:
-2x-12 +12≤ -2 +12
Dividing by 2 to both sides of the inequality:
-2x ≤ 10
Multiplying by -1 on both sides, taking into account that the sense of inequality changes:
x≥ -10/2
x ≥ -5
hence, the solutions are given by all values greater than or equal to -5.
so , option A is correct.
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gold is sold by the troy ounce (31.103 g). what is the volume (in cm3) of 2 troy ounces of pure gold?
1.62 is the volume (in cm3) of 2 troy ounces of pure gold .
What is full answer for density?
A material substance's density is defined as its mass per unit volume. Density is defined as d = M/V, where M stands for mass, and V for volume. The unit of density that is most frequently used is grams per cubic centimeter.We determine the volume, V, corresponding to the given amount of gold. We do this by dividing the given mass, m, by the density, d, such that
V = m/d
m = 31.03 g
d = 19.3 g/ml
We proceed with the solution
V = m/d
= 31.03/19.3
≈ 1.62 ml
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What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?
A. y+3=4(x+1)
B. y−1=4(x−3)
C. y+1=4(x+3)
D. y−3=4(x−1)
Answer:
A. y+3=4(x+1)
Step-by-step explanation:
Lets find an equation having the form y=mx+b, where m is the slope and b the y-intercept. We are given the slope, so let's add that first:
y = 4x + b
That was easy. No how can we find the value for b? We are given a point that the line passes through: (-1,-3). If the line gors through this point, then it must be a valid solution to the equation. Let's use that point in the equation and solve for b:
y = 4x + b
-3 = 4*(-1) + b for point (-1,-3)
-3 = -4 + b
b = 1
The equation becomes y = 4x + 1
Put this into point slope form:
y = 4x + 1
y+3 = 4x + 1 + 3
y+3 = 4x + 4
y+3 = 4(x + 1)
See the attached graph.
when data are collected using a qualitative, nominal variable, what is true about a frequency table that summarizes the data?
The number of classes is equal to the number of variables plus 2. A pie chart can be used to summarize the data. The upper and lower class limits must be calculated. correct option is (A).
A Pie Chart is a way of summarizing a set of nominal data or displaying the different values of a given variable. This of chart is a circular divided into a series of of segments. each segment represents a particular category. A pie chart uses percentage to compare information.
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The question was incomplete. Check below the complete question.
When data is collected using a qualitative, nominal variable (in other words, male or female), what is true about a frequency distribution that summarizes the data?
A) The upper and lower class limits must be calculated.
B) Class midpoints can be computed.
C) The "2 to the k rule" can be applied.
D) The number of classes corresponds to the number of a variable's values
The owner of a small store buys coats for $45. 00 each. Answer parts a and b. A. He sells the coats for $63. 00 each. What percent of the purchase price is the sale price? The sale price is nothing% of the purchase price
The percentage of the purchase price of the sales price is 55.6%
Given:
The owner of a small store buys coats for $45. 00 each.
He sells the coats for $63. 00 each. What percent of the purchase price is the sale price = ?
Profit = selling price - cost price
Profit = 90-50 = $40
percent of the purchase price is the selling price will be
Purchase or cost price/selling price × 100
= 50/90 ×100 = 55.56%
hence we get the percentage as 55.56%
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5.
People Remaining
2000
1800
1600
1400
1000
600
400
200
Hurricane Evacuation
1
2
(3. 1200)
3
4
Time (h)
S
(6.800)
Answer:
Step-by-step explanation: do your work
it 5x=_2
if 2=394.76366368379232
then how much would
938738393x2+8732893673-8238339x2=
Answer:
Following is a very common example of calculating Sales Commission based on levels of Reven…
•=IF(C9>15000,20%,IF(C9>12500,17.5%,IF(C9>10000,15%,IF(C9>7500,12.5%,IF(C9>5000,10%,0))…
This formula says IF(C9 is Greater Than 15,000 then return 20%, IF(C9 is Greater Than 12,500 th…
While it’s remarkably similar to the earlier Grades example, this formula is a great example of how difficult it can be to maintain large IF statements – what would you need to do if your organization decided to add new compensation levels and possibly even change the existing dollar or percent
Step-by-step explanation:
Which equations might miguel write? check all that apply. y < 2x – 1 y ≤ 2x – 4 y > 2x – 4 y < 2x 4 y < 3.5x – 4 y < 4x – 4
Answer: 3, 4, 6
Step-by-step explanation: just did it on edge
Jacob is a long-distance runner. His race is 10,000m. How far is the distance in miles?
Answer:
10000 meters = 6.214 miles
About 6 miles
Step-by-step explanation:
Soultion: How many meters are in a mile?
1600 meters: roughly 1 mile or 4 laps around the track.
Answer: 6.214
Which expression equals 24? Responses A (4 x 2) + 3(4 x 2) + 3 B (4 + 3) - 2(4 + 3) - 2 C (4 x 2)(3)(4 x 2)(3) D (2 + 4)(3)(2 + 4)(3) E (4 - 2) + 3
The expression that equals 24 is (4 x 2)(3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
(The options are given twice, consider once)
Consider option C.
(4 x 2)(3)
=8 (3)
=8 x 3
=24
So, the expression that equals 24 is (4 x 2)(3).
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A mill uses 4 times as much power as a lathe. If the total power used by a mill and 3 lathes is 1540 kilowatts, find the power used by a single lathe.
Answer:
Step-by-step explanation
Answer:
220 kW
Step-by-step explanation:
You want the power used by a single lathe when a mill uses 4 times as much, and a mill plus 3 lathes uses 1540 kW.
SetupLet p represent the power used by a single lathe. Then a mill uses 4p, and the given total is ...
(4p) +3p = 1540
Solution7p = 1540 . . . . . . collect terms
p = 220 . . . . . . . divide by 7
A single lathe uses 220 kW.
Find the missing length indicated.
Answer:
14 unitsStep-by-step explanation:
Let the missing part be x.
According to triangle proportionality theorem we have:
x/28 = 6 /(18 - 6)x = 28*6/12x = 14The missing length will be 14 units.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown is figure.
Now,
Let the missing length = x
So, By the definition of triangle proportionality theorem, we get;
⇒ x/28 = 6 /(18 - 6)
Solve for x as;
⇒ x/28 = 6 /(18 - 6)
⇒ x/28 = 6 / 12
⇒ x/28 = 1 / 2
⇒ x = 28/2
⇒ x = 14
Thus, The missing length will be 14 units.
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if a+b+1.5 is an even integer what is the next consecutive integer
The next consecutive even integer represented by the statement is a + b + 3.5
How to determine the next consecutive integers?The statement in the question is represented as
a+b+1.5 is an even integer
As a general rule of numbering;
Consecutive integers are integers that have a difference of 1These numbers can be negative or positiveIn this case, the integers have a difference of 2
This is so because, they are even integers and even integers have a difference of 2
Solving further, we can represent the integer with x
So, we have
Current integer = a+b+1.5
Rewrite properly
This gives
Current integer = a + b + 1.5
Recall that:
even integers have a difference of 2
This means that
Next consecutive integer = Current integer + 2
Substitute the known values in the above equation, so, we have the following representation
Next consecutive integer = a + b + 1.5 + 2
Evaluate the sum in the above equation
Next consecutive integer = a + b + 3.5
Hence, the next integer is a + b + 3.5
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Lance is a part-time employee at Subway. One M-W & Friday he works from 4pm-9pm with a non paid 30 minute lunch. On Saturday he works from 12pm til 6pmwith a non paid thirty minute lunch. If he earns $11.75 per hour, how many hours and minutes has he worked and what is his gross pay.
Lance had a gross pay of $117.5 working on Friday and Saturday
How is his gross payTo determine his gross pay, we have to find the number of hours he worked and multiply it by his hourly wage.
This can be done by;
4pm - 9pm = 5 hours.
But he had a non-paid 30 minutes break which will give us his work hours on Friday as 4 hours 30 minutes or 4.5 hours.
On Saturday, he worked from 12pm - 6pm which will give us a work time of 6 hours. He also took a non-paid 30 minutes lunch and his total work time on Saturday is 5 hours 30 minutes or 5.5 hours.
If we add the total numbers of hours worked, we will get
4.5 + 5.5 = 10 hours.
Now we can multiply this by the hourly wage.
10 * 11.75 = 117.5
His gross pay is $117.5
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f(x) = 3x+2
What is f(5)?
Albert has y stickers.
Latika has more stickers than Albert.
John has times as many stickers as Latika.
Write down an expression, in terms of y , for the number of stickers John has.
The algebraic expression, in terms of y , for the number of stickers John has is given by 4(y + 2)
How to write algebraic expression?Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Number of stickers Albert has = yNumber of stickers Latika has = y + 2Number of stickers John has = 4(y + 2)The expression for the number of stickers John has = 4(y + 2)
For instance, if y = 3
Number of stickers Latika has = y + 2
= 2 + 2
= 4 stickers
Number of stickers John has = 4(y + 4?2)
= 4(3 + 2)
= 4(5)
= 20 stickers
Therefore, the expression which can be used to represent the number of stickers John has is 4(y + 2)
Complete question:
Albert has y stickers.
Latika has 2 more stickers than Albert.
John has 4 times as many stickers as Latika.
Write down an expression, in terms of y , for the number of stickers John has.
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Calvin states that it is not possible to find the equation of a line
parallel to y=2 and passing through the point (5,-1) using the
point-slope form because the equation of the line does not have
an x-term. Explain the error in Calvin's reasoning.
The equation of a line y = 2 in point-slope form can be written as
(y + 1) = 0(x - 5).
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, An equation of a line y = 2 which is a line parallel to the x-axis at
y = 2.
As it is parallel to the x-axis the slope of the line is zero passing through points (5, - 1).
The equation of a line in point-slope form is (y - y₁) = m(x - x₁).
∴ (y + 1) = 0(x - 5).
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If f(x) = -2x + 12, find f(6).
The function f(x) = - 2 · x + 12 evaluated at x = 6 has an output equal to 0.
How to evaluate a linear function
Functions are have three features: Input, relation, output. The input is the independent variable, generally known as x, the relation is how the input and output are related, the output is the dependent variable, generally know as y.
In this problem, we should substitute on the input, make all algebraic operations associated to the relation and determine the variable within the output.
The procedure is now shown:
First, substitute on the input:
x = 6
y = - 2 · 6 + 12
Second, make the algebraic operations involved in the relation:
y = - 2 · 6 + 12
y = - 12 + 12
Third, determine the value within the output.
y = 0
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Graph a scatter plot using the given data.
In the question various points of x and y re given to plot the graph.
here is the plot attached below:
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The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 1,536 cm2, find the dimensions (in cm) of the poster with the smallest area.
The dimensions of the poster with the smallest area are = 64cm X 56cm where Width of the poster is 64 and Height of the poster is 56.
In order to establish a condition equation that represents the printed area's width (w) in terms of its height (h), we must first use what we know about the printed area.
Ap(w,h)=wh [Printed area]
Ap(w,h)=wh [ Substitute Ap(w,h)=1536]
1536=wh
w=1536h [width ''w'' in terms of height ''h'' ]
The smallest surface area must be determined. We need to find out the area as a function of the variable h using the condition equation.
W=w+16 [ Width of the rectangular poster ]
H=h+24 [ Height of the rectangular poster ]
Ar(w,h)=(w+16)(h+24) [Area of the rectangular poster ]
Ar(w,h)=(w+16)(h+24)
Put the value of W in terms of ‘h’ that we got above.
Ar(w)=(1536h+16)(h+24)
Ar(w)=36864h+16h+1920
Ar(w)=36864/w+16w+1920 (objective function)
Determine the domain of objective function
D={w∈R:w>0} [Domain of the Objective area function]
Ar(w)=36864/w+16w+1920
A′r(w)=−36864w2+16 [First derivative of the Objective area function]
A′r(w)=0 [critical point condition]
−36864/w2+16=0
16=36864/w2
w2=36864/16
w2=2304
w=±48
w=−48 [w=−48∉D]
w=48 [w=48∈D]
w=48 [Critical point of the Objective area function ]
Applying sufficient condition for extremes (Second derivative test)
A′r(w)=−36864/w2+16
A′′r(w)=73728/w3[Second derivative of the Objective area function]
A′′r(48)=0.6 [A′′r(48)>0]
w=48 [Minimum point of the Objective area function ]
Calculate the dimensions of the rectangular poster with minimum area
w=48 Width of the print area
h=1536/48=32 (Height of the print area)
W=48+16=64 (Width of the rectangular poster)
H=32+24=56 (Height of the rectangular poster)
The dimensions of the poster with the smallest area are: ⟹64cm×56cm
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Help me with this two problems pls!
Use each unit rate to find the total.
Andy drove 840 miles in 12 hours. how far could he drive in 3 hours?
Unit rate (speed):
Distance:
Pira drives 825 miles to California.The trip takes him 17 hours. He uses 38 gallons of gas on the trip, which costs him $125
Find his speed
Find his gas mileage
Find the unit price he paid for gas.
Answer: andy drove 280 miles in 3 hours
Step-by-step explanation: are you seriousseious right now?
the downtown business association (dba) in a certain city plans to increase its membership by a total of nnn businesses per year. there were bbb businesses in the dba at the beginning of this year. which function best models the total number of businesses, yyy, the dba plans to have as members xxx years from now?
The function most accurately predicts the total number of companies, y, that the DBA expects to include among its members in x years is y = b + n(x).
Given info,
The Downtown Business Association (DBA) intends to add n new businesses to its membership every year. At the start of this year, the DBA contained b companies. Which function most accurately predicts the total number of companies, y, that the DBA expects to include among its members in x years?
Now,
According to the given information;
y = b + n + n + n + n + n + . . . . . . x times
y = b + n(x)
Hence, the function best models the given case is y = b + n(x)
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What represents a linear function?.
The graph of a straight line represents a linear function.
What is a linear function?Any function with one or two variables and no exponents is said to be linear.
The graph of a linear function is a straight line.
Therefore, the graph of a straight line represents a linear function.
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Graph the equation y = −4/3x+4
Answer: Here's a graph:
