Answers
Answer:
50 square units
Step-by-step explanation:
Using the formula provided, [tex]a = \frac{1}{2}h(b_1+b_2)[/tex], substituting the height (5), b1 (8) and b2 (12), we can solve for the formula.
[tex]a = \frac{1}{2}\cdot5(8+12)\\\\a = \frac{1}{2}\cdot5(20)\\\\a = \frac{1}{2}100\\\\a = 50[/tex]
Hope this helped!
Answer:
50 units²
Step-by-step explanation:
The area of a trapezoid can be found using the following formula.
[tex]A=\frac{1}{2}h(b_{1} +b_{2} )[/tex]
The height of the trapezoid is 5 units. The bases are 8 units and 12 units.
[tex]h= 5 \\b_{1} = 8\\b_{2} = 12[/tex]
Substitute the values into the formula.
[tex]A=\frac{1}{2}*5(8+12)[/tex]
Solve inside the parentheses. Add 8 and 12.
8+12=20
[tex]A=\frac{1}{2}*5(20)[/tex]
Multiply 5 and 20.
5*20= 100
[tex]A=\frac{1}{2}*100[/tex]
Multiply 1/2 and 100 or divide 100 by 2.
100 * 1/2= 50 or 100/2= 50
[tex]A= 50[/tex]
Add appropriate units. For this problem, the units are units².
[tex]A= 50 units^2[/tex]
The area of the trapezoid is 50 square units.
Related Questions
Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation.
Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance.
Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
A) Average income per household
B) The number of cars on the road
C) The number of citizens in the United States
D) Average mileage per vehicle
Answers
Answer:
The correct answer is:
A) Average income per household
Step-by-step explanation:
Correlation of variables is the statistical relationship between two variables. A correlation is positive if both variables move in the same direction (e.g both are increasing, or both are decreasing), and negative if the variables move in different directions - as one variable increases, the other decreases.
Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables, especially when there is a third variable (lurking) that has an effect on the outcomes that is not included as an explanatory or response variable.
In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable, which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.
x(z + 3) + 1 + 3 − y; use x = 6, y = −5, and z = 2
Answers
Answer: 39
Step-by-step explanation:
x(z+3)+1+3-y
plug in the values given for each variable
6(2+3)+1+3-(-5)
use pemdas to solve
6(5)+1+3+5
30+1+3+5
31+8
39
Answer: 39
Step-by-step explanation:
Given: x=6, y=-5, z=2
To solve this problem, plug all the variables in.
--------------------------------------------------------------------
x(z+3)+1+3-y
Plug in
=(6)[(2)+3]+1+3-(-5)
Take off parentheses
=6(2+3)+1+3+5
Add 2 and 3, and also add 1 and 3
=6(5)+4+5
Multiply 6 and 5, and add 4 and 5
=30+9
Add 30 and 9
=39
Hope this helps!! :)
Please let me know if you have any question
mike has $1.55 in dimes and nickels. if he has 7 more nickels than dimes, how many of each does he have?
Answers
Answer:
15 nickels and 8 dimes
Step-by-step explanation:
Create a system of equations where d is the number of dimes and n is the number of nickels:
0.1d + 0.05n = 1.55
n = d + 7
Solve with substitution by plugging in d + 7 as n:
0.1d + 0.05(d + 7) = 1.55
0.1d + 0.05d + 0.35= 1.55
0.15d + 0.35 = 1.55
0.15d= 1.2
d = 8
Plug in 8 as d to find n:
n = d + 7
n = 8 + 7
n = 15
So, there are 15 nickels and 8 dimes
Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x+ 4, and 20? Assume that the longest side of the triangle is of length 20 units.
Answers
just finished this question the answers: D / 14
The value of x could be 8<x<12.
What is Triangle Inequality?According to the Triangle Inequality Theorem, any two triangle sides must add up to more than the third side's length.
Using Triangle Inequality
x+ x+4 > 20
2x+ 4 >20
2x > 16
x> 8
The angle across from the side with length 20 is the largest angle because it is the longest side length.
Therefore, x must be less than the value(s) that make that angle exactly 90 degrees. Simply determine the values of x for angles that are 90 degrees from the side with a length of 20.
Using Pythagorean theorem
x²+ (x+4)² = 20²
x² + x² +16 +8x = 400
2x² + 8x - 384= 0
x²+ 4x -192= 0
x= -16, 12
So, x has to be less than 12 i.e., x < 12
Hence, the value of x could be 8<x<12.
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The midpoint of (-4,15) and (22,3)
Answers
Answer:
(9, 9)
Step-by-step explanation:
midpoint of (-4,15) and (22,3)
[tex] = \bigg( \frac{ - 4 + 22}{2}, \: \: \frac{15 + 3}{2} \bigg) \\ \\ = \bigg( \frac{18}{2}, \: \: \frac{18}{2} \bigg) \\ \\ = ( 9, \: \: 9) \\ \\ [/tex]
18u^4w^6y^7+12u^9w^8
Answers
Answer:
[tex]6u^4w^6(3y^7+2u^5w^2)[/tex]
Step-by-step explanation:
[tex]18u^4w^6y^7+12u^9w^8[/tex]
we can only take common factor
18 and 12 have 6 as a common factor
in variables we have
[tex]u^4w^6y^7[/tex] and [tex]u^9w^8[/tex] so we see clearly that it is [tex]u^4w^6[/tex]
so we have
[tex]6u^4w^6(3y^7+2u^5w^2)[/tex]
as far as you can go
A bottle contains 2 liters of water. The bottle leaks 80 milliliters of water every 3 minutes. Will the bottle be empty in 1 hour? Explain why or why not. (1 liter = 1,000)
Answers
Answer:
No
Step-by-step explanation:
2 liters = 2,000
80/3 = 26.6
the bottle leaks 26.6 milliliters in a min
26.6 * 60 = 1596
1596 / 1000 = 1.596 ( to convert to liters)
the bottle will leak 1.596 an hour
No, the bottle will not empty in one hour because the bottle will leak 1.596 an hour.
What is Unitary Method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary MethodFirst, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
Volume of bottle = 2 liters = 2,000 ml
For three minutes bottle leaks = 80 ml
In one minute bottle leak= 80/3
= 26.6 ml
In one minutes the bottle leak
=26.6 * 60
= 1596 ml
=1.596 liters
1596 / 1000 = 1.596 ( to convert to liters)
No, the bottle will not empty in one hour because the bottle will leak 1.596 an hour.
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Alisa, Mykia, and Martin decide to share the responsibility of walking their dog every
day. There are 365 days in a year, How many days each year does Alisa need to was
the dog?
Answers
Step-by-step explanation:
No of friends = 3
No of days = 365 days
Days Alisa needs to walk the dog = 365 ÷ 3 = 121. 66
Find the slope of the line containing the pair of points (7, 0) and (10, 6). The slope is nothing. (Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.)
Answers
Answer:
Slope= 2
Step-by-step explanation:
To calculate the slope of a line containing the two points on a coordinate plain, the below formula is used.
Slope = (y2-y1)/(x2-x1)
Y2= 6
Y1= 0
X2=10
X1= 7
Slope = (y2-y1)/(x2-x1)
Slope=(6-0)/(10-7)
Slope= 6/3
Slope= 2
Manny created a scatter plot and drew a line of best fit, as shown.
720
-18
-16
-14
+12
+10
-6
-2
2.
6
8
10
12
14
16
+++
18 20
What is the equation of the line of best fit that Manny drew?
Answers
Answer:
y = 2x + 7
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
We are only focusing on the line of best fit.
Step 1: Find 2 coordinates
(0, 7) y-intercept
(2, 11) random
Step 2: Find slope m
m = (11 - 7)/(2 - 0)
m = 4/2
m = 2
y = 2x + b
Step 3: Rewrite linear equation
y = 2x + 7
Answer:
y = 2x + 7
Step-by-step explanation:
The midpoint of AB is M(6, -1). If the coordinates of A are (4,-4), what are the
coordinates of B?
Answers
Answer:
(8, 2)
Step-by-step explanation:
(x, y)=(6, -1)
(x1+x2)/2=6
(y1+y2)/2=-1
------------------
(4+x2)/2=6
4+x2=6*2
4+x2=12
x2=12-4
x2=8
---------------
(-4+y2)/2=-1
-4+y2=-1*2
-4+y2=-2
y2=-2-(-4)
y2=-2+4
y2=2
(x2, y2)=(8, 2)
A color printer prints 11 pages in 4 minutes.
How many pages does it print per minute?
Answers
Solution: 11/4=2.75
Answer:
2.75
Step-by-step explanation:
11/4 = 2.75
Hoped I helped
A pre-paid cell phone company charges $10.4 as a monthly access fee and $0.18 per minute of calling time. Express the monthly cost C in terms of minutes of call time. What will the monthly cost be if you make 315 minutes of calls this month?
Answers
Answer:$67.10
Step-by-step explanation:
Using the first statement we can generate the equation c= 0.18m + 10.4 where c is the cost and m is the number of minutes. So if you make 315 minutes of call then input that for m and solve for c.
c= 0.18(315) + 10.4
c= 67.10
How much is the total cost to mail this package?
Answers
Answer:
19.44
Step-by-step explanation:
Without doing the calculations, determine whether -47-(-33) or -47+(-33) is greater
Answers
Answer:
-47-(-33) is greater
Step-by-step explanation:
the negative number and the subtraction end up to be addition
6x - 3y + 2z - y - 4z + 2x
Answers
Step-by-step explanation:
8x-4y-2z
I think the question is incomplete
if f(x)=ln x then limx→2 f(x)= 1 2 Infinite Does Not Exist None of the above
Answers
Answer:
[tex]\lim_{x \to 2^{+}} f(x) = 2[/tex]
None of the above.
Step-by-step explanation:
f(x) = [x], in the graphing calculator, is f(x) = int(x).
This means we take the floor of x, or round down all the time.
The question is asking us to find the limit as x approaches 2 from the right. Since the graph from [2, 3) is going to be y = 2, we know that if we are approaching from the right of x → 2, we will approach y = 2 (shown in graph).
If we were to approach x → 2 from the left, then we would approach y = 1 (shown in graph).
If we were to approach from both the left and the right, then we would get DNE.
Nico earns $32.50 for each hour he works. last week Nico warned $1,300, and this week he earned $1,040. how many more hours did nick work last week than this week?
Answers
Answer:
8 hours
Step-by-step explanation:
$1,300/$32.50 = 40
$1,040/$32.50 = 32
40-32=8
Answer:
8 hours
Step-by-step explanation:
First, find the difference in the money
1300-1040=260
Then divide by 32.5
260/32.5=2600/325
8
So he worked for 8 more hours
It costs $109 per night to rent a motel room in Georgia. There is a one-time $30 non-refundable deposit required. How much will it cost your family to rent a room for a week in Hampton?
Answers
Answer:
$793.00
Step-by-step explanation:
109x7=763
763+30=793
A 6 inch personal pizza has 630 calories, with 240 of those from fat. A 12 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 12 inch pizza.
Answers
Answer:
157.5.
Step-by-step explanation:
If the 6-inch pizza has 630 calories, the 12-inch pizza has double.
6 x 2 = 12.
Therefore, the 12-inch pizza has 1,260.
630 x 2 = 1,260.
There are 8 slices in a pizza, making the answer 1,260 / 8.
1,260 / 8 = 157.5
An estimation could be 150 if you round 630 to 600.
Hope this helps!
The number of calories in one slice of a 12-inch pizza would be 157.5.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
We have been given that the 6-inch pizza has 630 calories,
Therefore, the 12-inch pizza has double i.e. 1,260 calories.
To determine the number of calories in one slice of a 12-inch pizza.
We have to apply the division operation in 1,260 between 8,
⇒ 1,260 / 8.
⇒ 157.5
If we round 630 to 600, an estimate would be 150.
Hence, the number of calories in one slice of a 12-inch pizza would be 157.5.
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Could anyone help me with this?
Answers
To find x, subtract 37 from 90
90 - 37 = x
x = 53
Here is the scale model of a fountain at a museum the scale is 1:30 how many boulders are in the real fountain
Answers
Answer:
When we do a scale model of something (like a building, a house, or whatever) al the properties of the original thing must also be in the model.
So for example, you want to do a model of a house, and in the backyard of the house there are 4 trees, then in the model of the house you also need to put 4 trees in the backyard (indifferent of the scale of the model).
Then the number of boulders in the really fountain should be the same as the number of boulders in the scale model of the fountain.
Answer:
c. 10
Step-by-step explanation:
i just took the test
Compare and Contrast the following diagrams by creating a list of at least 5
complete sentences.
Answers
Answer:
Both diagrams describe the representation of an object in space.
Step-by-step explanation:
1. The first diagram is a 2-dimensional plane in space.
2. it has two axes, the x-axis and y-axis, which is the length and width of the plane.
3. Both axes are perpendicular to each other.
4. The second diagram is a 3-dimensional plane with axis x, y and z representing the width, length and height of the plane respectively.
5. All three axes are perpendicular to each other like in the 2-dimensional plane.
How would you write the equation with a slope of 2/3 and a y-intercept of (0,-3)?
Answers
Answer:
y = (2/3)x - 3
Step-by-step explanation:
Slope-intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept.
The point is given to you. Note that:
(x , y) = (0 , -3) ∴
x = 0
y = -3
The slope = m = 2/3
Plug in the corresponding numbers to the corresponding variable:
y = mx + b
-3 = (2/3)(0) + b
-3 = 0 + b
b = -3
Plug in -3 for b in the equation:
y = mx + b
y = (2/3)x -3
y = (2/3)x - 3 is your equation.
~
Example 2
Find the equation of the tangent to the circle
x + y2 + 4x - 10y = 12 at the point (3, 1).
Answers
Answer:
-5x + 4y = -11.
Step-by-step explanation:
If it's a circle then it must be x^2 not x.
x^2 + y^2 + 4x - 10y = 12
Using implicit differentiation:
2x + 2y y' + 4 - 10 y' = 0
y'( 2y - 10) = -2x - 4
y' = (-2x - 4)/(2y - 10)
y' = (-x - 2) / (y - 5) = the slope of the tangent.
At (3, 1), y' = (-3-2) / (1 - 5)
= 5/4.
So the required equation is
y - y1 = 5/4(x - x1) where x1 = 3 and y1 = 1.
y - 1 = 5/4(x - 3)
y = 5/4(x - 3) + 1
Multiply through by 4:
4y = 5(x - 3) + 4
4y = 5x - 15 + 4
In standard form the equation is:
-5x + 4y = -11.
Suppose that we have a pair of random variables X and Y with joint distribution
X
2 4 6
2 0.04 0.02 0.04
Y 4 0.12 0.06 0.12
6 0.24 0.12 0.24
(a) If we have M = max(X Y) the larger of the two observations, then calculate P{M = 6}.
(b) Show that X ami Y are independent.
Answers
Answer:
P (m=6)= 0.60
Marginal probability of y= 0.4 , 0.2 and 0.4
Marginal probability of x= 0.1 0.3 and 0.6
Step-by-step explanation:
The data given is
X 2 4 6
2 0.04 0.02 0.04
y 4 0.12 0.06 0.12
6 0.24 0.12 0.24
So the maximum value M= max (X Y) is (2,6) (6,4)(6,6)
We pick the larger value for each of the two observations
P (m=6) = 0.24+ 0.12+ 0.24= 0.60
X 2 4 6 Marginal
2 0.04 0.02 0.04 0.1
y 4 0.12 0.06 0.12 0.3
6 0.24 0.12 0.24 0.6
M. 0.4 0.2 0.4 1
The total is always equal to 1 .
X and Y are independent as the product of the marginal probability gives the joint probability.
We find the marginal probability by adding the rows and columns and then check if their product equal the given joint distribution which is true.
A section of the theater has been reserved for 378 people . If each row in the theater seats 18 people, how many rows have been reserved
Answers
Answer:
21 reserved rows
Step-by-step explanation:
If A section of the theater has been reserved for 378 people and each row seats 18 then
378 divided by 18 = 21 reserved rows
Answer:
21 rows have been reserved
Step-by-step explanation:
You divide 378 by 18
Customers of a phone company can choose between two plans for long distance calls. The first plan has a $17 monthly fee and charges an additional $0.08 for each minute of calls. The second plan has an $8 monthly fee and charges an additional $0.13 for each minute of calls. How many minutes of calls Will the costs of the two plans be equal?
Answers
Answer:
180 minutes of calls
Step-by-step explanation:
Let x represent the minutes of calls
The first plan's cost can be represented by 0.08x + 17
The second plan can be represented by 0.13x + 8
Set them equal to each other and solve for x:
0.08x + 17 = 0.13x + 8
17 = 0.05x + 8
9 = 0.05x
180 = x
So, it will take 180 minutes of calls for the plans to be equal.
Simplify by factoring. √1350x^4
Answers
Answer:
15[tex]x^{2}[/tex][tex]\sqrt{6}[/tex]
Step-by-step explanation:
√1350x^4= √2*5*5*3*3*3x^4 = 5*3x^2√2*3 =5[tex]x^{2}[/tex][tex]\sqrt{6}[/tex]
Any help would be appreciated!
Answers
Answer:
this might help you....
Answer:
See below.
Step-by-step explanation:
In the figure above, ∠WXY and ∠YXZ are a linear pair.
What is a Linear Pair?
A Linear Pair is 2 angles that are adjacent, and form a straight line when combined. A Linear Pair contains 2 Supplementary Angles, angles that add up to 180°.
Their measures add up to 180°.
In order to find y, because they're a linear pair, we can set up an equation with the 2 angles equal to 180°.
[tex]4y+6y+30=180[/tex]
Combine Like Terms:
[tex]10y+30=180[/tex]
Subtract 30 from Both Sides:
[tex]10y=150[/tex]
Divide by 10:
[tex]\frac{10y}{10} = \frac{150}{10} \\y = 15.[/tex]
The value of y is 15.
Now since we know the value of y, we can substitute 15 into each angle to find their measure.
Substitute:
[tex]4(15)=60\\6(15)+30=120[/tex]
The measure of ∠WXY is 60° and the measure of ∠YXZ is 120°.