Answer:
Equilibrium price for widgets = 13.22
Step-by-step explanation:
At equilibrium, quantity demand, Qd = quantity supplied, Qs
Demand
P = 14 – 0.39Q
P - 14 = - 0.39Q
Q = (P - 14) / - 0.39
Supply
P = 0.61Q + 12
P - 12 = 0.61Q
Q = (P - 12) / 0.61
Qd = Qs
(P - 14) / - 0.39 = (P - 12) / 0.61
Cross product
(P - 14) * 0.61 = - 0.39 * (P - 12)
0.61P - 8.54 = - 0.39P + 4.68
0.61P + 0.39P = 4.68 + 8.54
P = 13.22
Check
Q = (P - 14) / - 0.39
= (13.22 - 14) / - 0.39
= -0.78 / -0.39
= 2
Q = (P - 12) / 0.61
= (13.22 - 12) / 0.61
= 1.22 / 0.61
= 2
Therefore,
Equilibrium price for widgets = 13.22
Equilibrium quantity = 2
An automobile manufacturing plant produced vehicles today: were sedans, were trucks, and were motorcycles. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles. What is the probability that two motorcycles will be selected
Answer:
120 / 561
Step-by-step explanation:
An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected
16/34 X 15 X 33
HELP ME ASAP PLEASEEEEEEEE
Answer:
5 : -1.5
10: -4
y = 1 -.5x
noticed the pattern of subtracting .5 .... then plugged in x = 4
and saw that -2 had to be combined with "1" to end up with a "-1"
Step-by-step explanation:
Kasey has three pieces of wood that measure 9 inches, 12 inches, and 21 inches. Can she make a right triangle
with the three pieces of wood (without cutting or overlapping)?
Answer: No
Step-by-step explanation:
Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:
9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.
A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. If you spin this spinner 1000 times, how many times do you expect it to land on Red?
Answer:
83 spins
Step-by-step explanation:
Number of red spins = n
Number of orange spins = 8n
Number of yellow spins = 3n
Total number of trials = 240
Total number of spins :
(n + 8n + 3n) = 240
12n = 240
n = 240 / 12
n = 20
Number of red spins = 20
(1000/240) * n
4.1666666 * 20
= 83.333
= 83 spins
Find the distance between the two points rounding to the nearest tenth (if necessary). ( − 8 , 6 ) and ( − 6 , 0 )
Answer:
[tex]\sqrt{40\\}[/tex], [tex]2\sqrt{10}[/tex], or 6.3 (rounded).
Step-by-step explanation:
Use the distance formula, [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \\x_1 is -8, y_1 is 6, x_2 is -6, y_2 is 0.[/tex]
On a unit circle, the terminal point of 0 is (1/2, square root of 3/2) what is 0
Answer: pi/6
explanation: took test
The value of θ on a unit circle where the terminal point of θ is (1/2,square root 3/2), is 60°.
Terminal PointThe measure of the angle in degrees or radians over the circle, at the endpoint on the coordinate plane is known as terminal point
How to solve this problem?Given On a unit circle, the terminal point of θ is [tex](\frac{1}{2},\frac{\sqrt{3} }{2} )[/tex]According to image below the value of θ at terminal point (1/2,square root 3/2) is 60 degrees.Thus the value of θ at terminal point on a unit circle (1/2,square root 3/2) is 60 degrees.
Learn more about Terminal Point here:
https://brainly.com/question/25870256
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The cars of a circular Ferris wheel at an amusement park are equally spaced about the wheel's circumference. They are numbered consecutively beginning with 1. The cars numbered 14 and 30 lie on opposite ends of a diameter. How many cars are on the Ferris wheel?
Answer:
32 cars
Step-by-step explanation:
we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32
Math step-by-step:
30-14=16
16×2=32
plzzz helppp i need to pass this classs
Answer:
C
Step-by-step explanation:
x + 40 + 100 + x=360. (sum of angles at a point)
2x+140=360
2x=360-140
2x=220
x=220/2
x=110⁰
The speed of a toy car is 20 m/s. The time taken for a trip is 200seconds. Find the
distance covered in meter
Distance = time/ speed
Distance = 200 seconds / 20 m/s
Distance = 10 meters
Answer:
Distance:
[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 20 \times 200}} \\ { \tt{ = 4000 \: metres}}[/tex]
Needing a little help
53. A right triangle has a hypotenuse measuring 15 inches and one leg measuring 9 inches What is the length, in inches, of the other leg of the triangle?
A. 3
B.6
C. 10
D. 12
Answer:
D
Step-by-step explanation:
Pythagorean
[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)
=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]
PLS HELP!!! The problem is in the photo attached
Answer:
The answer is C!
Step-by-step explanation:
Answer:
D
NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"
Step-by-step explanation:
PERE
Given: ZABC is a right angle and ZDEF is a right angle.
Prove: All right angles are congruent by showing that ZABC = ZDEF.
What are the missing reasons in the steps of the proof?
ZABC, ZDEF are
right angles
M2ABC = 90°
m2DEF = 90°
m2ABC = m_DEF
ZABC = ZDEF
Given
A
B
A:
B:
C:
Intro
Answers:
A) Definition of right anglesB) SubstitutionC) Definition of congruence=========================================
Explanation:
A) The term "right angle" is another way of saying "90 degree angle". This is a definition. Think of a definition in a dictionary. B) The substitution property allows us to replace one thing for another, as long as the two things are equal. The transitive property works as a similar idea.C) If two angles have the same measure, then they are congruent. This is the definition of congruence (or one form of it).In this exercise we have to use the knowledge of angles, in this way we can say that:
A) Right angles
B) Substitution
C) Congruence
So punctuating some necessary definitions we have that:
A) This alternative is a right angle, that is, an angle that has 90 degrees.
B) The substitution property allows us to replace one thing for another, as long as the two things are equal.
C) IIn this alternative, we are dealing with congruent angles, that is, angles that have the same measure, normally less than 90 degrees.
See more about angles at brainly.com/question/15767203
Enter the equation of the line in slope-intercept form.
Slope is 4, and (5,2) is on the line.
The equation of the line is y =
Answer:
y = 4x -18
Step-by-step explanation:
y-2 = 4(x-5)
y = 4x -20+2
y = 4x -18
Answer:
y = 4x-18
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 4x+b
Substitute the point in the equation and solve for b
2 = 4(5)+b
2 = 20+b
2-20 = b
-18 =b
y = 4x-18
Which expression is equivalent to 2(a+2b)-a-2b
o 3a+2b
o 3a-2b
o a-2b
Answer:
a -2b
Step-by-step explanation:
2(a+2b)-a-2b
Distribute
2a+4b -a-2b
Combine like terms
a -2b
for 10 points Valerie set out to bicycle from TBLS to the beach, a distance of 10 miles. After going a short
while at 15 miles per hour, the bike developed a flat tire, and the trip had to be given up. The
walk back to TBLS was made at a dejected 3 miles per hour. The whole episode took 48
minutes. How many miles from TBLS did the flat occur?
Answer:
2 miles
Step-by-step explanation:
Given that :
Total distance = 10 miles
Distance = speed * time
Let distance from TBLS to flat Tyre spot = d
Time = distance / speed
Since the distance to and distance fro took a total of 48 minutes;
Hence ;
d/15 + d/3 = 48 minutes
48 minutes = 48/60 = 0.8 hours
d/15 + d/3 = 0.8
(d + 5d) / 15 = 0.8
d + 5d = 15 * 0.8
6d = 12
d = 12 / 6
d = 2 miles
Distance from TBLS to point bicycle had flat tyre is 2 miles
Can someone help me with this math homework please!
Answer:
X1 = 2 Y1 = -5
Step-by-step explanation:
math simple slope
Now measure the lengths of the sides of polygon ABCD and tbe lengths of the sides of the translated images. Record the measurements in the table.
Answer:
3.16, 3.16, 3.16
3.16, 3.16, 3.16
1.41, 1.41, 1.41
3.16, 3.16, 3.16
Step-by-step explanation:
Answer:
Length Length Length
3.16 3.16 3.16
3.16 3.16 3.16
1.41 1.41 1.41
3.16 3.16 3.16
Step-by-step explanation:
You have 80$ panted cost 29$ And shirts cost 12$. Mom told you to buy one pair of pants and use the rest of the money to buy shirts. Use this information to write and solve and inequality how many shirts can you buy
Answer: 4 Shirts
Step-by-step explanation:
Given
Person has [tex]\$80[/tex]
Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]
Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts
Spent money must be equal or less than the total money. The inequality becomes
[tex]\Rightarrow 80\geq29x+12y[/tex]
For 1 pair of pants that is, 1 pants
[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]
That is maximum number of shirts that can be bought are 4.
If ABCD is dilated by a factor of 2, the
coordinate of A' would be:
Answer: -5, -1
Step-by-step explanation:
Mr. James asked his students that which of the following equations can be formed using the expression x = 5:
a)2 x + 3 = 13
b)3x + 2 = 13
c)x –5 =
1d)4x –9 = 21
Answer:
[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]
Match each cone's measures to its corresponding volume.
Answer:
base area=16π in² height=6 in ⇒ base area= πr²
16π²=π(r)²
r=4 in
v=1/3 ×π (4)²×(6)
v=32π in²
-------------
v=1/3 π(12/2)²×5
v=1/3π(31)×5=
v=60π in³
-------------
v=1/3 π×(25×4)=
v=100π/3 in³
OAmalOHopeO
Is the relationship shown by the data linear? If so, model the data with an equation. x y –7 5 –5 9 –3 13 –1 17
Given:
The table of values is:
x : -7 -5 -3 -1
y : 5 9 13 17
To find:
Whether the given data is linear and then find the equation.
Solution:
The given data is linear if the slope and rate of change is constant.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using the slope formula. we get
[tex]\dfrac{9-5}{-5-(-7)}=2[/tex]
[tex]\dfrac{13-9}{-3-(-5)}=2[/tex]
[tex]\dfrac{17-13}{-1-(-3)}=2[/tex]
Since the rate of change is constant, i.e., 2, therefore the given data is linear.
The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-5=2(x-(-7))[/tex]
[tex]y-5=2(x+7)[/tex]
[tex]y-5=2x+14[/tex]
Adding 5 on both sides, we get
[tex]y-5+5=2x+14+5[/tex]
[tex]y=2x+19[/tex]
Therefore, the equation for the given data is [tex]y=2x+19[/tex].
Given: `bar(DE)` and `bar(DF)` are midsegments of `Delta` ABC as shown. Prove: A midsegment of `Delta`ABC is half the length of the side of `Delta`ABC to which it is parallel. Match each statement to its corresponding reason. Scroll down to see all the choices. Drag the items on the left to the correct location on the right.
Answer:
here
Step-by-step explanation:
In Owen's class, there are 15 girls and 12 boys. Write the ratio of boys to girls.
Answer:
4 : 5
Step-by-step explanation:
boys : girls
12 15
Divide each by 3
12/3 : 15/3
4 : 5
Answer: 4:5
Step-by-step explanation:
To simplify the ratio 12:15, divide both numbers by the GCF of the 2 numbers (3). This gives you the simplified ratio, 4:5.
Please help me find this box guys I’m struggling
Answer:
(0,-9)
Step-by-step explanation:
To find the y-intercept, substitute x=0
y=(0)^2+4(0)-9
=-9
Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation
Answer:
see explanation
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
The equation of the axis of symmetry which is also the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 4x - 9 ← is in standard form
with a = 1, b = 4 , then
x = - [tex]\frac{4}{2}[/tex] = - 2
x = - 2 is the equation of the axis of symmetry
Substitute x = - 2 into the equation for corresponding y- coordinate of vertex
y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13
vertex = (- 2, - 13 )
To find the y- intercept let x = 0 and solve for y
y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9
y- intercept = (0, - 9)
From the standard form of the parabola
• If a > 0 then vertex is a minimum
• If a < 0 then vertex is a maximum
Here a = 1 , that is > 0
vertex (- 2, - 13 ) is a minimum
CANNNN SOMEONEEEEE HELPPPP MEEE OUTTTTT !!!!!
Answer:
sin X = 21/ 29
Step-by-step explanation:
Since this is a right triangle
sin X = opp side/ hypotenuse
sin X = 21/ 29
Answer:
[tex]\boxed{\sf sinX =\frac{21}{29}}[/tex]
Step-by-step explanation:
We need to find out the value of sinX using the given triangle . Here we can see that the sides of the triangle are 21 , 29 and 20.
We know that the ratio of sine is perpendicular to hypontenuse .
[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]
Here we can see that the side opposite to angle X is 21 , therefore the perpendicular of the triangle is 21. And the side opposite to 90° angle is 29 . So it's the hypontenuse . On using the ratio of sine ,
[tex]\sf\longrightarrow sinX =\dfrac{ p}{h}=\dfrac{ZY}{ZX}[/tex]
Substitute the respective values ,
[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ X =\dfrac{21}{29}}}[/tex]
Hence the required answer is 21/29 .
if triangle 3 shows a 100 degree rotation of triangle 1 about point p what is the degree of intersection of lines m and n?
The given transformations are rigid transformations, such that
the image and the preimage have the same dimensions.
Correct responses:
The degree of the intersection of lines m and n is; 50°This image also shows two A. reflection about lines m and then line n. How can the angle between the lines be determined, and what is a reflection?Given;
The images of triangle 1 are; Triangle 2, and triangle 3
Taking the image of line m as line m, we have;
Required:
The degree of the intersection of lines m and n
Solution:
Triangle 2 is the reflection of triangle 1 across line m, and
triangle 3 is the reflection of triangle 2 across line n
The distance of triangles 1 and 2 from line m are equal
The distance of triangle 2 and 3 from line n are equal.
Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is
equal to the degree of rotation of triangle 2 to triangle 3, θ₂,
we have;
θ₁ = θ₂
100° = θ₁ + θ₂ = 2·θ₁
θ₁ = θ₂ = 100° ÷ 2 = 50°
The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°
The degree of the intersection of lines m and n = 50°The transformation to give triangle 2 from triangle 1 is a reflection about line m.
Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.
Therefore;
The image also shows two A. Reflections about line m and then line n.Learn more about rigid transformations here:
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Ryan rented a truck for one day. There was a base fee of $16.99, and there was an additional charge of 74 cents for each mile driven. Ryan had to pay $133.17 when he returned the truck. For how many miles did he drive the truck?
Answer:
157 miles
Step-by-step explanation:
total cost = flat fee + cost per mile * miles
133.17 = 16.99 + .74 * m
Subtract 16.99 from each side
116.18 = .74m
Divide each side by .74
116.18 / .74 = .74m/.74
157 = m
Find the surface area and the volume of the prism.
10
26
18
