Answer:
13F
Step-by-step explanation:
-15+28
Find an equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.
The equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16x - 8y + 8z = 32
We know that the equation of plane passing through point (x₁, y₁, z₁) is given by,
A(x - x₁) + B(y - y₁) + C(z - z₁) = 0
where, A, B, and C are direction ratios
In the question, the plane passes through point (0, -3,1)
Let (x₁, y₁, z₁) = (0, -3,1)
Using above formula the equation of the plane will be in the form,
A(x -0) + B(y - (-3))+C(z - 1) = 0
Ax + B(y + 3)+C(z - 1) = 0 ..........(1)
The required plane is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.
So, their normal to the required plane would be perpendicular to the normal of both the planes.
The normal to the required plane is a cross-product of the normals of planes.
A cross-product of the normals of planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16i - 8j + 8k
So, the direction ratios,
A = 16, B = -8, C = 8
So equation (1) becomes,
16x - 8(y + 3) + 8(z - 1) = 0
16x - 8y - 24 + 8z - 8 = 0
16x - 8y + 8z - 32 = 0 is the required equation of the plane
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The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.
a. If the car has gone 140 miles, how much gas was used? Show your thinking.
b. Write an equation that represents the inverse function: the gallons of gas as a function of distance in miles
a)
g = m / 40
g = 140 /40
g = 3.5
b)
m = 40g
m / 40 = g
12.2 Apples and Oranges
At the corner produce market, apples cost $1 each and oranges cost $2 each.
1. Find the cost of:
a. 6 apples and 3 oranges
b. 4 apples and 4 oranges
c. 5 apples and 4 oranges
d. 8 apples and 2 oranges
Unit 3: Linear Relationships
Lesson 12: Solutions to Linear Equations
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The total cost of 6 apples and 3 oranges is $6 + $6 = $12.
The total cost of 4 apples and 4 oranges is $4 + $8 = $12.
The total cost of 5 apples and 4 oranges is $5 + $8 = $13.
The total cost of 8 apples and 2 oranges is $8 + $4 = $12.
What is linear equation and the total cost of given terms?a). 6 apples at $1 each = $63 oranges at $2 each = $6The total cost of 6 apples and 3 oranges is $6 + $6 = $12.b). 4 apples at $1 each = $44 oranges at $2 each = $8The total cost of 4 apples and 4 oranges is $4 + $8 = $12.c). 5 apples at $1 each = $54 oranges at $2 each = $8The total cost of 5 apples and 4 oranges is $5 + $8 = $13.d). 8 apples at $1 each = $82 oranges at $2 each = $4The total cost of 8 apples and 2 oranges is $8 + $4 = $12.In all the above examples, we simply multiplied the number of apples by the cost per apple and the number of oranges by the cost per orange. Then we added the two amounts to find the total cost.To learn more about linear equation refer:
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Evaluate 0.0007 multiplied by 100
Answer:
0.07
Step-by-step explanation:
[tex]0.0007*100=0.07[/tex]
Basically, you move the 7 two places to the left since 100 has 2 zeroes.
A 4-pack of coffee mugs costs $2.20. What is the unit price?
Answer:
The unit price for a coffee mug is $0.55.
Step-by-step explanation:
The unit price is simply just the price per unit.
We have a 4-pack of coffee mugs that costs $2.20.
He have 4 units and the price per 4 units.
Lets evaluate the price per 1 unit.
[tex]\frac{2.20}{4} =\frac{x}{1}[/tex]
Lets solve for [tex]x[/tex].
Divide [tex]x[/tex] by 1.
[tex]x=\frac{2.20}{4}[/tex]
Divide 2.20 by 4.
[tex]x=0.55[/tex]
Is figure B a scale factor of figure A What is x
Answer:
Step-by-step explanation:
Step 1:
Make a proportion:
10/5 = 22/x
Step 2:
Cross multiply:
10x=22*5
10x=110
Step 3:
Divide by 10 to isolate x:
x=11
We want to know how a tudent’ level of education and their gender impact both their annual income and amount of tudent loan debt. However, we want to account for the annual income of the tudent’ parent a well. So which Statitical Tet are you going to ue?
The best statistical test to be used is multiple linear regression analysis.
Multiple linear regression is a statistical method that allows you to examine the relationship between two or more independent variables (in this case, level of education, gender, and annual income of the student's parents) and one dependent variable (annual income and student loan debt).
It will help you determine how much of the variation in the dependent variable is explained by the independent variables, and the strength and direction of the relationships between the variables.
In this case, this test will allow us to determine the impact of a student's level of education, gender, and the annual income of their parents on their annual income and student loan debt while accounting for the possible confounding effect of the annual income of their parents on these variables.
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a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300 in the last week. If he earned Rs 2,000 on Saturday, find his average of daily income of the week.
Answer: To find the average of daily income of the week, we need to find the total income of the week and divide it by the number of days in the week.
We know that the average daily income of the week is Rs 1,300 and we know that he earned Rs 2,000 on Saturday. To find the total income for the week, we can add the Saturday income to the average daily income for the 6 days.
Therefore, the total income for the week = Rs 1,300 (average daily income) x 6 (days) + Rs 2,000 (Saturday income) = Rs 7,800 + Rs 2,000 = Rs 9,800
To find the average daily income for the week, we divide the total income by the number of days in the week (7)
Average daily income = Rs 9,800 / 7 = Rs 1,400
Therefore, the average daily income of the plumber for the week is Rs 1,400.
Step-by-step explanation:
a bag contains 16 black balls and 14 white balls. two balls are drawn at random from the bag, one after the other without replacement. what is the joint probability the first ball drawn was black and the second ball drawn was also black?
Answer:
Step-by-step explanation:
A peron i remodeling the front entrance to hi home and need to cut an arch for the top of an entranceway. The arch need to be 18 ft wide and 3 ft high. To draw the arch, he will ue tring with chalk attached at an end a a compa.
The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.
The radius of the arch is 9 feet.
The formula for calculating the radius of an arch is [tex]R = (width / 2) / sin(90°)[/tex].
Therefore, the radius of the arch is:
R = (18 ft / 2) / sin(90°) = 9 ft
To calculate the radius of the arch he needs to draw, the person can use the formula R = (width / 2) / sin(90°). In this case, the width of the arch is 18 feet, so the radius of the arch is 9 feet, calculated as R = (18 ft / 2) / sin(90°). The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.
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hEEEELLLLLPPPPPP
Select all of the terms that apply to the shape.
hexagon
convex
irregular polygon
octagon
decagon
concave
heptagon
pentagon
regular polygon
nonagon
the shape is a arow pointing up and downn
Pentagon, irregular polygon and convex polygon are the names that apply to the given form.
What is a polygon?A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
A pentagon is a polygon with five sides, and if these sides are uneven, it is an irregular pentagon, also known as an irregular polygon.
A convex polygon is one with all of its internal angles smaller than 180°.
As a result, the terms for the given form are pentagon, irregular polygon, and convex polygon.
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The question seems incomplete, the missing figure has been attached below
7. The cost of half a dozen candles is R30. What is the cost of one candle?
Answer: 5R
Step-by-step explanation:
Half a dozen =6 pieces
R30/6=5R
How much is one dozen?
One dozen is equal to 12, so one half of a dozen is 6.
If 6 candles are priced at R30, we can divide R30 by 6 to get the cost of 1 candle.
30 ÷ 6 = 5.
Therefore, each candle costs R5.
HELPP GEOMETRY HOMEWORK
All of the angles in an acute triangle are less than 90 degrees. Triangles are referred to as right triangles when one of their angles is 90 degrees.
What is called triangle?The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles. With three sides and three vertices, triangles are a particular kind of polygon in geometry.
It has three straight sides and is a two-dimensional figure. As a 3-sided polygon, a triangle is included. Three triangle angles added together equal 180 degrees. In one plane, the triangle is contained. When three straight lines cross, a triangle is the result. There are always three sides and three corners to a triangle (angles). A triangle's vertex is the location at which two of its sides meet.
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Create a proportion for each set of similar triangles, that can be used to find the missing side lengths indicated. Then solve the proportion.
The values of x from the given figures are 3 √29 and 24 respectively.
What is triangle ?
Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.
Given
In the figure,
The two given triangles are similar ,
So, in the first figure it is given that they are similar ,
√29 / 5 = x / 15
x = √29 * 15 / 5
x =√29 * 3
x = 3 √29
And in the second figure , here also they gave they are similar
so we get,
12 / 13 = x / 26
x = 12 * 26 / 13
x = 12 * 2
x = 24
Hence, The values of x from the given similar triangles are 3 √29 and 24 respectively.
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Please answer this edpuzzle! PLEASE! Whoever answers it first, I will mark you brainliest.
The simplified algebraic expression for this problem is given as follows:
5x + 2y + 11.
How to simplify the algebraic expression?The algebraic expression for this problem is defined as follows:
9x + 2y + 3 - 4x + 8.
To simplify the expression, we combine the like terms, which are the terms that have the same unknown variable, hence:
9x - 4x = 5x.2y.3 + 8 = 11.Hence the simplified algebraic expression for this problem is given as follows:
5x + 2y + 11.
Meaning that the third option is the correct option.
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PLEASEEEEEEEEEE HELPPPP
The expression for the cost of gasoline and oil will be C. 3.35c + 2.65g
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, it should be noted that Joe bought g gallons of gasoline and c cans ofg oil. The prices were givn as well.
The expression for the cost of gasoline and oil will be:
= 3.35 × c + (2.65 × g)
= 3.35c + 2.65g
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Assuming all the workers employed at the beanbag factory are of equal ability,
what might the beanbag factory do to address the diminishing marginal returns it
experiences after the hire of its third worker?
A. Fire the manager.
B. Invest in more equipment.
C. Hire more workers.
D. Wait for its workers to improve.
Assuming all the workers employed at the beanbag factory are of equal ability, the beanbag factory invest in more equipment to address the diminishing marginal returns it experiences after the hire of its third worker. So the option B is correct.
It is assumed that all of the factory's employed employees have the same level of skill. Additionally, it must follow that if they are working to their maximum ability, they will be able to accomplish the same amount of work as before.
Since the third man was hired, the quantity of work the three of them have completed has decreased, making it clear that he is to blame for the diminishing returns.
Therefore, it seems sense to fire the individual since he is either not performing to his full capacity or encouraging other employees to do the same.
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $3300 and his stock in Company B was worth $4140. The stock in Company A has increased 4% since last year and the stock in Company B has increased 5%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth Answers fast!
The total percentage increase in the investor's stock account was of 4.55%.
The values of the stocks of Company A and Company B, after the increase are given, respectively, by:
Company A: 3300 x 1.04 = $3432.
Company B: 4140 x 1.05 = $4347.
The total values are given as follows:
Before the increase: 3300 + 4140 = 7440.
After the increase: 3432 + 4347 = 7779.
The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:
P = (7779 - 7440)/7440 x 100% = 4.55%.
The total percentage increase in the investor's stock account was of 4.55%.
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Determine whether the pairs of triangles are congruent.
Answer:
1. yes
2. No
Step-by-step explanation:
1. The triangles are congruent
2. It's not matching
Find the image of (-1,3) obtained by translating 2 units down, followed by a rotation of 270 counterclockwise about the origin.
The image of the point (-1, 3) is (1, 1).
What is Translation?A translation is a transformation that moves every point in a figure the same distance in the same direction.
For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .
Given:
Pint( -1, 3).
Translating unit = 2 units down
According to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, move it to your new x-coordinate, and then take the opposite of the x-coordinate and set it as your new y-coordinate:
Extended Rotation Rules
270°-clockwise rotation [90°-counterclockwise rotation] = (x, y) → (-y, x)
270°-counterclockwise rotation [90°-clockwise rotation] =(x, y) → (y, -x)
and, 180°-rotation = (x, y) → (-x, -y)
Thus, the 270°-counterclockwise rotation [90°-clockwise rotation] will be
[-1, 1] moves to [1, 1].
Hence, the translation is (1, 1).
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7. Segment MN has endpoints at M(-12,-5) and N(8, 10). A third point Q is located on MN such that MQ:ON=2:3. Answer the following questions. (a) Find the coordinates of Q. Show how you arrived at your answer.
Answer:
To find the coordinates of Q, we can use the concept of proportional division of line segments.
Given that MQ:ON = 2:3, it means that the ratio of the length of MQ to ON is 2:3.
Let's first find the vector that represents the direction of MN, which is the vector pointing from M to N. We can find this by subtracting the coordinates of M from the coordinates of N:
(8,10) - (-12,-5) = (20, 15)
This is the vector <20,15>
Now, we can find the point Q, which is located two thirds of the way from M to N, by multiplying the vector <20,15> by 2/5 and adding the result to the coordinates of M:
Q = M + (2/5) * <20,15>
= (-12,-5) + (2/5) * <20,15>
= (-12,-5) + <8,6>
= (8,1)
So, the coordinates of Q are (8,1)
Label each item as factor by grouping or factor using substitution.
To factor a trinomial of the form
a x 2 + bx + c, multiply the trinomial
by a. Rewrite the first two terms
using ax. Substitute a single variable
for ax. Factor the trinomial. Substitute ax
back in for the variable. Divide by a.
Step-by-step explanation:
I Don't even know what the answer is
Ms. Lambert took her family to Pimento Garden on Sunday for dinner. The total bill was $73.25, and she wanted to leave an 18% tip. How much
money should she leave for the tip? *Make sure your answer rounded to correct money form.
Answer: The answer is $13.19.
Step-by-step explanation:
1- Turn the percentage into a decimal by moving the percent sign twice to the left.
2- Multiply the bill by the decimal.
3-youll get 13.185 so you'll round up to 13.19.
hope this helps!!
Which line is parallel to the line y=12x+5
Refer to the initial crosstabulations. For those players with low handicaps (better players), which group (male or female) shows the highest percentage saying the greens are too fast? For the low handicappers, the men have a higher percentage who think the greens are too fast. Refer to the initial crosstabulations. For those players with higher handicaps, which group (male or female) shows the highest percentage saying the greens are too fast? For the high handicappers, the women have a higher percentage who think the greens are too fast. At each handicap level, how does the percentage of women who think the greens are too fast compare to the percentage of men who feel the same? Select When the crosstabulations are aggregated across handicap level, do you still conclude the same thing when comparing the percentage of women who complain that the greens are too fast with the percentage of the men who feel the same? Select Note: This exercise is an example of Simpson's Paradox
As per the given parentage, the highest percentage saying the greens are too fast is females.
In math the term percentage is defined as the number or ratio that can be expressed as a fraction of 100.
Here we have know that the number male players are
Male Golfers Greens Condition
Handicap Too fast Fine
Under 15 10 40
15 or more 25 25
And the female players are,
Male Golfers Greens Condition
Handicap Too fast Fine
Under 15 1 9
15 or more 39 51
Then the total value of them is calculated as,
Too fast Fine Total
Male 35 65 100
Female 40 60 100
So, the group with the highest percentage of too fast is the females.
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the 140 employees in a factory are either right handed or left handed
The frequency table is given below.
The probability that a person chosen is a left-handed female is 31/140.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total number of employees = 140
Male:
Number of male = 65
Right-handed.
= Total number of right-handed - Female right handed
90 - 44 = 46
Left-handed.
= 65 - 46
= 19
Female:
Number of females.
= Total employees - Number of males
= 140 - 65
= 75
Right-handed.
= 75 - 31
= 44
Left-handed.
= 31
Now,
The frequency table.
RH = 46
LH = 19
Male = 65
140
Female = 75
RH = 44
LH = 31
Now,
The probability that a person is a left-handed female.
= Number of left-handed females / Total number of employees
31/140
Thus,
The frequency table is given above.
The probability that a person is a left-handed female is 31/140.
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Write a value for n that would make the inequality true. ⁿ⁄₉ > ½ n = _____________________
The value for n that would make the inequality true is 4.5
What is an inequality?You should understand that a statement of an order relationship with greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is inequality.
The given inequality is ⁿ⁄₉ > ½
This implies that 2(n) > 1(9)
Opening the brackets to have
2n > 9
Making n the subject of the relation by dividing both sides by 2
2n/2 > 9/2
Therefore n = 4.5
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what is the answer to this question
Answer:82 cm squared
Step-by-step explanation:
Just draw imaginary lines on the shape to turn it into a bunch of squares and rectangles, then find the area of those and add them together.
Kinda hard to explain since there are multiple ways to do it, but I hope that this still helps!
What is square root 25x²y^2/square root xy in simplest form? Assume X>o and y>0.
a. three times the total number of adults was 17 less than the number of children who visited the petting zoo. write an equation to model this relationship.
If the 3 times of total number of adults was 17 less than number of children who visited the petting zoo , then the equation to model this relationship is written as c = 3a + 17 ;
let the number of children in the petting zoo be = c ;
and the number of adults in the petting zoo is = a ;
given that the the number of children are 3 times the number of adults ;
that means ⇒ c = 3a ;
and also given that the difference between the number of children and number of adults is 17 .
This situation can be represented as :
⇒ c - 3a = 17 ;
⇒ c = 3a + 17 .
Therefore , the equation to model this relationship is "c = 3a + 17" .
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