Answer:
Step-by-step explanation:
1.) angle 1 and angle to form a linear pair (given)
2.) angle 1 and 2 are supplementary (supplement theorem)
3.) measure of angle 1 + measure of angle 2 = 180 degrees (def. of supplementary angles)
4.) angle 1 and 3 are supplementary (given)
5.)measure of angle 1 + measure of angle 3 = 180 degrees (def. of supplementary angles)
6.) measure of angle 1+ measure of angle 2 = measure of angle one + measure of angle 3 (congruent supplements theorem)
7.) measure of angle 2 = measure of angle 3 (subtraction property of equality)
8.) angle 2 is congruent to angle 3 (definition of congruence)
A fair die is rolled 72 times and the percentage of 6s is recorded. What is the probability that at most 10% of the rolls are 6s
Answer:
P ([tex]\hat p[/tex] ≤ 0.10)
Step-by-step explanation:
The probability in terms of statistics for this given problem can be written as follows.
Let consider X to the random variable that represents the number of 6's in 7 throws of a dice, then:
X [tex]\sim[/tex]Bin ( n = 72, p = 0.167)
E(X) = np
E(X) = 72× 0.167
E(X) = 12.024
E(X) [tex]\simeq[/tex] 12
p+q =1
q = 1 - p
q = 1 - 0.167
q = 0.833
V(X) = npq
V(X) = 72 × 0.167 × 0.833
V(X) = 10.02
V(X) [tex]\simeq[/tex] 10
∴ X [tex]\sim[/tex] N ([tex]\mu = 12, \sigma^2 =10[/tex])
⇒ [tex]\hat p = \dfrac{X}{n} \sim N ( p, \dfrac{pq}{n})[/tex]
where p = 0.167 and [tex]\dfrac{pq}{n}[/tex] = [tex]\dfrac{0.167 \times 0.833}{72}[/tex] = 0.00193
∴ P(at most 10% of rolls are 6's)
i.e
P ([tex]\hat p[/tex] ≤ 0.10)
If log.. (125) = 3, then x =
which equation represents a line that is parallel to y= -4x+3 and passes through the point (-3,2)
Answer:
The answer is
[tex]y = - 4x - 14[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
From the question
y = - 4x + 3
Comparing with the general equation above
Slope / m = - 4
Since the lines are parallel their slope are also the same
Slope of parallel line = (-3 , 2) and slope
- 4 is
[tex]y - 2 = - 4(x + 3) \\ y + 2 = - 4x - 12 \\ y = - 4x - 12 - 2[/tex]We have the final answer as
[tex]y = - 4x - 14[/tex]Hope this helps you
Answer:
y=-4x-14
Step-by-step explanation:
At the grocery store, Mr. Abroms saw eggplants that cost $1.79 each, apples that cost $0.59 each, bags of spinach that cost $2.55 each, and cartons of orange juice that cost $3.89 each. Which of these statements below are true? Choose the three correct answers.
Answer:
Option 1, 3 and 5 are correct
Step-by-step explanation:
Given
Eggplants = $1.79 each
Apples = $0.59 each,
Bags of spinach = $2.55 each
Cartons of orange juice = $3.89 each
Required
Select three true statements
To do this, we'll check the options one after the other
1. 4 eggplants cost about $0.50 less than 3 bags of spinach
First, we need to calculate the cost of 4 eggplants
4 Eggplants = 4 * 1 Eggplants
4 Eggplants = 4 * $1.79
4 Eggplants = $7.16
Next, we calculate the cost of 3 bags of Spinach
3 bags of Spinach = 3 * 1 bag of Spinach
3 bags of Spinach = 3 * $2.55
3 bags of Spinach = $7.65
Determine the difference
Difference = |Eggplants - Bags of Spinach|
Difference = |$7.16 - $7.65|
Difference = |-$0.49|
Difference = $0.49
This statement is true because $0.49 approximates to $0.50
2. Total cost of 4 apples and 2 eggplants $0.50 is more than $6.00
First, we need to calculate the cost of 4 apples
4 Apples = 4 * 1 Apples
4 Apples = 4 * $0.59
4 Apples = $2.36
Next, we calculate the cost of 2 Eggplants
2 Eggplants = 2 * 1 Eggplant
2 Eggplants = 2 * $1.79
2 Eggplants = $3.58
Add this two results together
Total = 4 Apples + 2 Eggplants
Total = $2.36 + $3.58
Total = $5.94
This statement is false because the sum is less than $6.00
3. Total cost of 4 eggplants, 4 apples and 1 carton of orange juice is $13.41
In (1) & (2) above
4 Eggplants = $7.16
4 Apples = $2.36
1 carton of orange juice = $3.89
Add the above together
Total = $7.16 + $2.36 + $3.89
Total = $13.41
This statement is true because the sum is $13.41
4. Total cost of 5 eggplants is greater than cost of 4 bags of spinach
First, we need to calculate the cost of 5 eggplants
5 Eggplants = 5 * 1 Eggplants
5 Eggplants = 5 * $1.79
5 Eggplants = $8.95
Next, we calculate the cost of 4 bags of Spinach
4 bags of Spinach = 4 * 1 bag of Spinach
4 bags of Spinach = 4 * $2.55
4 bags of Spinach = $10.20
This statement is false because 4 Eggplants costs less than $ bags of spinach
5. Total cost of 2 eggplants, 2 apples and 2 cartons of orange juice is $9.99 more than cost of 1 bag of spinach
From (2) above
2 Eggplants = $3.58
Next, we need to calculate the cost of 2 apples
2 Apples = 2 * 1 Apples
2 Apples = 2 * $0.59
2 Apples = $1.18
Next, we need to calculate the cost of 2 cartons of orange juice
2 Cartons = 2 * 1 Carton
2 Apples = 2 * $3.89
2 Apples = $7.78
Sum these up
Total = $3.58 + $1.18 + $7.78
Total = $12.54
1 Bag of spinach = $2.55 each
Subtract 1 Bag of spinach from the $12.54
Difference = $12.54 - $2.55
Difference = $9.99
This statement is true because the difference is $9.99
PLEASE ANSWER I REALLY NEED AND PEOPLE DONT ANSWER :(
1: identify the terms, coefficients, and constants in the expression 14x + 19.
Answer:
term=14x+19
cofficient=14+19
constant=19
Answer:
Terms :
14x , 19
Coefficients:
14
Constants:
19
Hope it helps.
There are 11 reams of paper in a case. How many total reams of paper are in 12 cases?
4
*
The moon is 250,000 miles away. How many inches is it away from earth?
Answer:
about 15 billion
Step-by-step explanation:
(3/5) divided by 4
please help !!!
Answer:
3/20
Step-by-step explanation:
3/5 ÷ 4
Copy dot flip
3/5 * 1/4
3/20
n ΔABC, AB = 10 and BC = 5. Which expression is always true? A. 5 < AC < 10 B. AC = 5 C. 5 < AC < 15 D. AC = 10
Answer:
A. 5 < AC < 10
Step-by-step explanation:
If ∆ABC is a right angled triangle, we use the Pythagoras formula:
c² = a² + b²
Where c = longest side
When given sides AB, AC and BC, the formula becomes:
AB² = AC² + BC²
Where AB = Longest side
In the question,
AB = 10 and BC = 5.
10² = AC² + 5²
AC² = 10² - 5²
AC² = 100 - 25
AC² = 75
AC = √75
AC = 8.6602540378
Therefore, the expression that is always true = A. 5 < AC < 10
Express (1+i)²-3(2-i)³ in the from of a+ib
[tex](1+i)^2-3(2-i)^3=1+2i-1-3(8-12i-6+i)=2i-6+33i=\boxed{-6+35i}[/tex].
Hope this helps.
What is 5x times (3x2 - 5)?
3x2 + 5x -5
A
B 15x2-5
с
15x3 - 5
15x3 - 25x
Answer:
15x3-25x
Step-by-step explanation:
5x(3x2 -5)
step1: distribute 5x to both sides
Step 2: 3x2 would change into 15x3 (because you're multiplying by 5x)
Step3: -5 would turn into -25x (because you are multiplying by 5x also)
Step4: put both answers together and your end product would be (15x3 - 25x)
Answer:
15x3-25x
Step-by-step explanation:
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
What is the cost of a chicken shawarma wrap?
$10.99
What is the cost of one order of spiced potatoes?
$4.99
If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95..........Eq 1
5x + 4y = $74.91..........Eq 2
Step-by-step explanation:
Cost of a chicken sharwarma wrap = a
Cost of an order of spiced potatoes = b
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
So we have:
3x + 2y = $42.95..........Eq 1
5x + 4y = $74.91..........Eq 2
We use Elimination method
Multiply Equation 1 by coefficient of y in Equation 2
Equation 2 by coefficient of y in Equation 1
3x + 2t= $42.95 .............Equation 1 × 4
5x + 4y = $74.91 ................Equation 2 × 2
12x + 8y = 171.80..............Equation 3
10x + 8y = 149.82..............Equation 4
Subtract Equation 3 from Equation 4
2x = 21.98
x = 21.98/2
x = 10.99
Therefore, x = Cost of Chicken sharwarma wrap = $10.99
Subtitute 10.99 for 9in Equation 1
3x + 2y = $42.95 .............Equation 1
3(10.99) + 2y = 42.95
32.97 + 2y = 42.95
2y = 42.95 - 32.97
2y = 9.98
y = 9.98/2
y = 4.99
y = Cost of an order of spiced potatoes = $4.99
Hence,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
Find the equation of the line using the point-slope formula. Passes through the point (−5, 8) and is parallel to the graph y = 4/5x+1
Answer: y=4/5x+12
Step-by-step explanation:
Slope-intercept form: y=ax+b, where a is the slope and b is the y-intercept
When a line is parallel to another line, they will have the same slope. So the slope of the new line is also 4/5.
y=4/5x+b
To find the y-intercept, we simply plug in the point it passes through.
y=4/5x+b
8=4/5(-5)+b
8=-4+b
b=12
y=4/5x+12
Hope this helps!! :)
Please let me know if you have any question
“Simplify the following expression by combining like terms. 5x-y-3x+10+x+2y
Answer:
3x+10+y
Step-by-step explanation:
5x-y-3x+10+x+2y
5x-3x+x+10-y+2y
3x+10+y
Answer:
3x+y+10
Step-by-step explanation:
Since we are trying to combine like terms, we must rearrange the terms, and group the terms with an x, together, a y together, and the constants. Doing that, we get
(5x+x-3x)+(2y-y)+10
Now we start with the x terms, and we add 5x+x=6x and then 6x-3x= 3x, so you have 3x, and now for the y terms
we have 2y-y=y and lastly we have a ten, so adding them together, we get
3x+y+10
Please help e it’s from my math class
Answer:
a - 1/2
Step-by-step explanation:
there are 3 even and 3 odd numbers so the probability is half of them
Please help dood pls
Answer:
[tex]\Large \boxed{\mathrm{\bold{B.} } \ x=7, \ y = 4\sqrt{2} }[/tex]
Step-by-step explanation:
We can split the shape into a right triangle and a rectangle.
tan θ = opp/adj
Let c be the missing base for the right triangle.
tan45 = 4/c
c = 4/tan45
c = 4
x = 3 + 4
x = 7
sin θ = opp/hyp
sin45 = 4/y
y = 4/sin45
y = [tex]4\sqrt{2}[/tex]
You have two recipes that together use a pound of butter. One recipe takes a 1/4 pound more than the other one. How much butter does each recipe use?
Answer:
First recipe needs = 3/8
Second recipe needs = 5/8
Step-by-step explanation:
Given:
Two recipes needs butter = 1 pound
One recipe needs 1/4 pound more
Find:
Each recipe needs butter
Computation:
Assume;
First recipe needs = x
Second recipe needs = x + (1/4)
Two recipes needs butter = First recipe needs + Second recipe needs
x + x + (1/4) = 1
2 x = 1 - (1/4)
2 x = 3/4
x = 3/8 pound
First recipe needs = 3/8
Second recipe needs = x + (1/4) = (3/8) + (1/4) = 5/8
Second recipe needs = 5/8
4(3 • 2) + (8 – 3)2 – 62 + 3 • 9 - 23 + 1
Answer:
-23
Step-by-step explanation:
value of tan(90 - cot^-1(1/3))
Answer:
0.36
Step-by-step explanation:
We need to solve the first bracket first and then the others,
Value of Cos^ - 1(1/3) =70.53°
Then, 90 - the value of cosine
=19.47°
Then, put the new in the calculator:
Tan (19.47°)
and the answer comes 0.3535294237
then I use the nearest formula and got the answer = 0.36
Elias completely covered a square canvas using 77.8 in.² of fabric without any overlap. Which measurement is closest to the side length of this canvas in inches? 8 in. 9 in. 19 in. 39 in. say the number and tell me why you got it.
Answer:
9 inStep-by-step explanation:
Since the square canvas was completely covered using 77.8 in.² of fabric without any overlap, to get the side length of the canvas, we will use the formula for calculating the area of a square.
Area of a square = Length * Length
A = L*L
A = L²
Given the Area of the area of the square canvas as 77.8 in², on substituting this values into the formula to get L we have;
77.8 = L²
Take the square root of both sides
√77.8 = √L²
L = √77.8
L = 8.82 in
L ≈ 9inches
The length 8.82in gotten was approximated to 9in because the first value after the decimal point is greater that 4 and once we have such case 1 will be added to the value before the decimal point i.e 8 to make it 9.
Hence measurement that is closest to the side length of this canvas in inches is 9inches.
Erin is considering joining one of 2 clubs. Club A has no registration fee, but charges $105 per month. Club B charges members $80 per month plus a one-time registration fee of $375. For how many months is club A the cheaper option? Use system of equations
Answer:
4 months
Step-by-step explanation:
Club A
registration fee: $0
monthly fee: $105
After every month, the total cost increases by $105.
month 0: $0
month 1: $105
month 2: $210
month 3: $315
month 4: $420
month 5: $525
month 6: $630
Club B
registration fee: $375
monthly fee: $80
Notice how Club B's total reaches Club A's total after 2 months.
month 0: $375
month 1: $455
month 2: $535
month 3: $615
month 4: $695
Find the slope and y-intercept (if possible) of the equation of the line. 14x − 6y = 66
Answer:
The slope would be 7/3
The y-intercept would be -11
Step-by-step explanation:
To find the answer rearrange your equation.
First subtract 14x from both sides, getting -6y= -14x + 66.
Then divide both sides by -6, getting y= 7/3x -11
This is now written in y=mx+b form. Your m is your slope and b is the y intercept!
Item 1 Evaluate. 1 1 3 +2 2 5 3 3 8 2 11 15 3 11 15 3 11 30
Answer:
add the expressions 832
Simplify. (-2xy4)^4
Step-by-step explanation:
[tex] {( - 2x {y}^{4} })^{4} [/tex]
[tex] = {( - 2)}^{4} \times {x}^{4} \times { {y}^{4} }^{4} [/tex]
[tex] = 16 {x}^{4} {y}^{16} [/tex]
Identify the correlation you would expect to see between the average amount of snowfall (inches) and the number of school closings.
Answer:
Simple Linear Regression Correlation
Step-by-step explanation:
When it snows normally the schools continue .But constant snowing affects the schools continuity. As more and more snow falls more schools are closed.
There may be a situation where all the schools are closed at a certain temperature.
So it is a simple linear regression correlation because in it there are two variables and one variable is dependent on the other. In this example the schools are dependent on the average snowfall.
If there's a snow blizzard or extreme weather all the schools are definitely closed .
It can be represented by a graph.
add. 4x² – 5xy + 3y?, 8x + 7xy - 6y?, -2x? - 9xy + 13y
Answer:
0x²-7xy+10y²
Step-by-step explanation:
4x²-5xy+3y² + 8x²+7xy-6y²
4x²+8x²-5xy+7xy+3y²-6y²
=12x²+2xy-3y²
12x²-5xy+3y² + -2x²-9xy+13y²
12x²-5xy+3y² - 2x²-9xy+13y²
12x²-2x²-5xy-9xy+3y²+13y²
= 10x²-7xy+10y²
Hoped I helped
Why is 1 a factor of every number
Answer:
because 1 is the smallest factor of a multiple and greatest factor of a multiple is the multiple itself
Step-by-step explanation:
hope that help and u can understand it :\
The electrical resistance of a wire, R, varies directly as its length, L, and inversely as its cross sectional area, A. If the resistance of a wire is 0.08 ohm when the length is 100 ft and its cross-sectional area is 0.05 in^2 , what is the resistance of a wire whose length is 4000 ft with a cross-sectional area of 0.02in^2 ? a) Write the variation equation. (R=k(l/a) b) Determine the value of the quantity indicated.
Answer:
see below
Step-by-step explanation:
a R=k(L/A)
Substitute what we know into the equation
.08 = k (100/.05)
.08 = k 2000
Divide each side by 2000
.08/2000 = k
.00004 = k
R=.00004 (L/A)
b R=.00004 (L/A)
We know L = 4000 and A = .02
R=.00004 (4000/.02)
R = 8
what is the percentage of the total variation in candy bar sales explained by the regression model? a. 78.39% b. 88.54% c. 100% d. 48.19%
Complete question :
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
City - - - - - - - Price ($) -- - Sales
River City - - 1.30 - - - - - - 100
Hudson - - - 1.60 - - - - - 90
Ellsworth - - - 1.80 - - - - - 90
Prescott - - - - 2.00 - - - - 40
Rock Elm - - 2.40 - - 38
Stillwater - - 2.90 - - 32
Answer:
78.39%
Step-by-step explanation:
Given the data :
Price (X) :
1.30
1.60
1.80
2.00
2.40
2.90
Sales (y) :
100
90
90
40
38
32
The percentage of the total variation in candy bar sales explained by the regression model can be obtained from the value of the Coefficient of determination(R^2) of the regression model. The Coefficient of determination is a value which ranges between 0 - 1 and gives the proportion of variation in the dependent variable which can be explained by the dependent variable.
R^2 value is obtained by getting the squared value of R(correlation Coefficient).
The R value obtained using the online R value calculator on the data is : - 0.8854
Hence, R^2 = (-0.8854)^2 = 0.7839
Expressing 0.7839 as a percentage ;
0.7839 × 100 = 78.39%
3. Michael goes on a Camel Safari in Africa.
He travels 5 km north, then 4 km east, and
then 5 km south.
Distance:
Displacement:
Answers:
Distance = 14 km
Displacement = 4 km east
==============================================
Explanation:
The total distance is simply the sum of the values given. So he traveled a total of 5+4+5 = 9+5 = 14 km overall.
----------------------
The displacement is where a drawing may come in handy. Draw an xy axis. Place point A at the origin (0,0). This is where Michael starts his trip. Then move up to (0,5) to indicate he goes 5 km north. Call this point B.
Afterward, mark point C at (4,5) to show he has gone 4 km east. Finally, point D is at (4,0) because he went 5 km south
The displacement is only concerned with two points: The start and end point. Nothing else matters. We started at A(0,0) and ended at D(4,0). So we've gone 4 km east overall. The direction is important when it comes to displacement. Simply saying "4 km" isn't enough. So in a sense, we could take a shortcut from A directly to D, bypassing the other points B and C.
See the diagram below for a visual.