A public opinion survey is administered to determine how different age groups feel about an increase in the minimum wage. Some of the results are shown in the table below.
For Against No Opinion
21-40 years 20 5
41-60 years 20 20
Over 60 years 55 15 5
The survey showed that 40% of the 21 - 40 year-olds surveyed are against an increase, and 15% of the entire sample surveyed has no opinion. How many 21 - 40 year-olds surveyed are for an increase? How many 41 - 60 year-olds are against an increase?
Answer:
25 ; 35
Step-by-step explanation:
Given :
____________For __ Against __ No Opinion
21-40 years _________20 _______5
41-60 years ___20 ______________20
Over 60 years _55____ 15________ 5
Given that :
40% of 21-40 are against
Then :
40% = 20
To a obtain 100% of 21 - 40
40% = 20
100% = x
Cross multiply
0.4x = 20
x = 20/0.4
x = 50
100% of 21 - 40 = 50 people
For = 50 - (20 + 5)
= 50 - 25
= 25
2.)
Total who have no opinion :
(5 + 20 + 5) = 30
30 = 15%
Total number surveyed will be , x :
30 = 15%
x = 100%
Cross multiply :
0.15x = 30
x = 30/0.15
x = 200
Number of 41 - 60 against an increase, y:
(25 + 20 + 5 + 20 + y + 20 + 55 + 15 + 5) = 200
165 + y = 200
y = 200 - 165
y = 35
help with algebra pls help
9514 1404 393
Answer:
a. 1.48 seconds
Step-by-step explanation:
You want to find the larger value of t such that h(t) = 10.
-16t^2 +25t +8 = 10
16t^2 -25t +2 = 0 . . . . subtract the left side to get standard form
Using the quadratic formula, we find the values of t to be ...
t = (-(-25) ± √((-25)^2 -4(16)(2)))/(2(16)) = (25±√497)/32
t ≈ 0.08 or 1.48
The ball goes in the hoop about 1.48 seconds after it is thrown.
__
Additional comment
The quadratic formula tells us the solution to ...
ax² +bx +c = 0
is given by ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, we have a=16, b=-25, c=2. Of course, our variable is t, not x, but the relation is the same.
Can the following two triangles be proven congruent through AAS?
A. Yes, since three pairs of angles are congruent, ∠C≅∠V
∠
C
≅
∠
V
, ∠B≅∠W
∠
B
≅
∠
W
, and ∠A≅∠U
∠
A
≅
∠
U
, the triangles are congruent through AAS.
B.No, since ∠C≅∠V
∠
C
≅
∠
V
, ∠B≅∠W
∠
B
≅
∠
W
, and a pair of included sides are congruent, AC⎯⎯⎯⎯⎯⎯⎯⎯≅UV⎯⎯⎯⎯⎯⎯⎯⎯⎯
A
C
¯
≅
U
V
¯
, the triangles aren’t congruent through AAS.
C.Yes, since two pairs of angles are congruent,∠C≅∠V
∠
C
≅
∠
V
and ∠B≅∠W
∠
B
≅
∠
W
, and a pair of non-included sides are congruent, AC⎯⎯⎯⎯⎯⎯⎯⎯≅UV⎯⎯⎯⎯⎯⎯⎯⎯⎯
AC¯≅UV¯, the triangles are congruent through AAS.
D.No, since only two pairs of angles are congruent, the triangles aren’t congruent through AAS.
Answer:
C. YES
Step-by-step explanation:
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
What is the product of x(x + 1)?
1. 2x + x
2. x2+ 2x
3. 212 + x
4. x2 + x
Answer:
4. x²+x
Step-by-step explanation:
the product of x(x + 1) = (x)(x) + (x)(1)
= x²+x
Joaquin drew the triangle below.
On a coordinate plane, triangle K L J has points (3, 6), (4, 0) and (negative 5, 0).
Which statement must be true about a figure that is congruent to Joaquin’s triangle?
It has two angles on the x-axis.
It has a side that is 9 units long.
It has a side that lies on the x-axis.
It has an obtuse angle.
Answer:
It has a side that is 9 units long.
Step-by-step explanation:
Answer:
B) It has a side that is 9 units long.
Step-by-step explanation:
Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.
if 8km=5miles.how many miles are in 56m?
Answer:
89.6 miles
Step-by-step explanation:
[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{56}[/tex]
5x = 448
x=89.6
Step-by-step explanation:
if 8km=5
x =56km
5x=8×56
5x=448
x=89.6 miles
PLEASE HELP SOON Find the value of x. Round to the nearest tenth. 27° х 34° 11 X = ? [?] 9 Law of Sines: sin A sin C sin B b a Enter
The picture of the problem has been attached below :
Answer:
13.5
Step-by-step explanation:
Applying the sine rule to solve for x
SinA /a = SinB / b = SinC/ c
Sin 34 / x = Sin 27/11
Cross multiply :
11 * sin34 = x * sin 27
6.1511219 = 0.4539904x
Divide both sides by 0.4539904
6.1511219/0.4539904 = x
13.549 = x
x = 13.5
Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
(a) f (x, y) = x^2 - y^2; x^2 + y^2 = 1
Max of 1 at (plusminus 1, 0), min of - 1 at (0, plusminus l)
(b) f (x, y) = 3x + y; x^2 + y^2 = 10
Max of 10 at (3, 1), min of - 10 at (- 3, - 1)
(c) f (x, y) = xy; 4x^2 + y^2 = 8
Max of 2 at plusminus (1, 2), min of - 2 at plusminus (l, - 2)
Answer:
a) f(x,y) = - 1 minimum at P ( 0 ; -1 )
b) f (x,y) = 10 maximum at P ( 3 , 1 ) and f (x,y) = - 10 minimum at Q ( - 3 , - 1 )
c) Max f ( x , y ) = 2 for points P ( 1, 2 ) and T ( -1 , -2 )
Min f ( x , y ) = -2 for points Q ( 1 , - 2 ) and R ( -1 , 2 )
Step-by-step explanation:
A) f(x,y) = x² - y² subject to x² + y² = 1 g(x,y) = x² + y²- 1
δf(x,y)/ δx = 2*x δg(x,y)/ δx = 2*x
δf(x,y)/ δy = - 2*y δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ* δg(x,y)/ δx
2*x = λ*2*x
δf(x,y)/ δy = λ* δg(x,y)/ δy
- 2*y = λ*2*y
Then, solving
2*x = λ*2*x x = λ*x λ = 1
- 2*y = λ*2*y y = - 1
x² + y²- 1 = 0 x² + ( -1)² - 1 = 0 x = 0
Point P ( 0 ; -1 ) ; then at that point
f(x,y) = x² - y² f(x,y) = 0 - ( -1)² f(x,y) = - 1 minimum
b) f( x, y ) = 3*x + y g ( x , y ) = x² + y² = 10
δf(x,y)/ δx = 3 δg(x,y)/ δx = 2*x
δf(x,y)/ δy = 1 δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ 3 = 2* λ *x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ 1 = 2*λ * y (2)
x² + y² - 10 = 0 (3)
Solving that system
From ec (1) λ = 3/2*x From ec (2) λ = 1/2*y
Then (3/2*x ) = 1/2*y 3*y = x
x² + y² = 10 ⇒ 9y² + y² = 10 10*y² = 10
y² = 1 y ± 1 and
y = 1 x = 3 P ( 3 , 1 ) y = - 1 x = -3 Q ( - 3 , - 1 )
Value of f( x , y ) at P f (x,y) = 3*x + y f (x,y) = 3*(3) +1
f (x,y) = 10 maximum at P ( 3 , 1 )
Value of f( x , y ) at Q f (x,y) = 3*x + y f (x,y) = 3*(- 3) + ( - 1 )
f (x,y) = - 10 minimum at Q ( - 3 , - 1 )
c) f( x, y ) = xy g ( x , y ) = 4*x² + y² - 8
δf(x,y)/ δx = y δg(x,y)/ δx = 8*x
δf(x,y)/ δy = x δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ y = λ *8*x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ x = λ *2*y (2)
4*x² + y² - 8 = 0 (3)
Solving the system
From ec (1) λ = y/8*x and From ec (2) λ = x/2*y Then y/8*x = x/2*y
2*y² = 8*x² y² = 4*x²
Plugging that value in ec (3)
4*x² + 4*x² - 8 = 0
8*x² = 8 x² = 1 x ± 1 And y² = 4*x²
Then:
for x = 1 y² = 4 y = ± 2
for x = -1 y² = 4 y = ± 2
Then we get P ( 1 ; 2 ) Q ( 1 ; - 2)
R ( - 1 ; 2 ) T ( -1 ; -2)
Plugging that values in f( x , y ) = xy
P ( 1 ; 2 ) f( x , y ) = 2 R ( - 1 ; 2 ) f( x , y ) = - 2
Q ( 1 ; - 2) f( x , y ) = -2 T ( -1 ; -2 ) f( x , y ) = 2
Max f ( x , y ) = 2 for points P and T
Min f ( x , y ) = -2 for points Q and R
Solve 7 pleaseeeeeeeeeeeeeeeee
Answer:
5040
Step-by-step explanation:
I assume you really mean 7!
you understand what "!" means ?
n! = n×(n-1)×(n-2)×(n-3)×...×3×2×1
so,
7! = 7×6×5×4×3×2×1
now all you need is a calculator.
7! = 5040
Solve the inequality. |X+19|<7
Answer:
x<-12
Step-by-step explanation: hope this helps!
Find the indicated side of the
right triangle.
45
у
9
45
х
x = [?]
Enter
Answer:
9
Step-by-step explanation:
A right rectangular prism has a length of 5 centimeters, a width of 8 centimeters, and a height of 4 centimeters. What is the volume of the prism?
Answer:
volume of prism is 160 cm
A computer monitor is listed as being 22 inches. This distance is the diagonal distance across the screen. If the screen measures 12 inches in height, what is the actual width of the screen to the nearest inch?
22 inches
18.43 inches
25.05 inches
32.5 inches
Answer
The width of the screen is 18.43.
Explanation
Use the Pythagorean Theorem (a^2+b^2=c^2) to find the height.
In a right triangle, a and b are legs. In this instance, a and b would be the height and width of the computer monitor. Let's say the height is a and the width is b (you're trying to find b). The hypotenuse of a right triangle is c. For the computer monitor, c is the diagonal.
So put in everything you know to find b; 12^2+b^2=22^2.
12^2 is 144 and 22^2 is 484. Now you have 144+b^2=484. When you simplify, you get b^2=340. When you simplify again, you find that b is about 18.43.
Express 20% as a decimal number
Answer: 0.2
Step-by-step explanation: 20/100=1/5
and 1/5 equals 1 divided by five so it is 0.2
the cost of 10 oranges is $6. what is the cost of an orange ?
Answer Choices:
$0.40
$0.60
$4
$6
Answer:
$0.60
Step-by-step explanation:
To find the cost of 1 orange, divide the $6 by 10:
6/10 = 0.6
Hope it helps (●'◡'●)
A roll of carpet that contains 250 yd of carpet will cover how many rooms if each room requires 7 3/4 yards of carpet?
Answer: 32 room
Step-by-step explanation:
[tex]7\frac{3}{4} =\frac{4(7)+3}{4} =\frac{28+3}{4} =\frac{31}{4}=7.75[/tex]
If 1 room = 7.75 yd of carpet ⇒ x rooms = 250 yd of carpet
Use proportions & cross-multiply to solve:
[tex]\frac{1}{7.75} =\frac{x}{250}\\7.75x=250\\x=\frac{250}{7.75} =32.258[/tex]
So 250 yd of carpet can cover about 32 rooms.
The figure below is a rhombus.
w = [? ]°
Answer:
Step-by-step explanation:
2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the formula for trapezium = 0.5x b+axh
Given:
Base=
Top (a) =
Height =
3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.
Applying the formula for parallelogram=bxh
Given:
Base=
Height=
pahelp po thanks
Answer:
2. 2200 m²
3. 703 m²
Step-by-step explanation:
2. Given,
Base (b) = 45m
Top (a) = 35m
Height (h) = 55m
Area = (a+b)*h/2
= (45+35)*55/2
= 85*55/2 = 2200 m²
3. Given,
Base (b) = 19m
Height (h) = 37m
Area = b*h
= 19*37
= 703 m²
(The * sign represents the multiplication sign)
Answered by GAUTHMATH
Answer:
2. area = 2200 m²
3. area = 703 m²
Step-by-step explanation:
2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the
formula for trapezium = 0.5 * (b+a) * h
Given:
Base= 45 m
Top (a) = 35 m
Height = 55 m
area = 0.5 * (b+a) * h
area = 0.5 * (45 m + 35 m) * 55 m
area = 2200 m²
3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.
Applying the formula for parallelogram = b * h
Given:
Base= 19 m
Height= 37 m
area = b * h
area = 19 m * 37 m
area = 703 m²
Please help
A stamp collection consists of 10 albums each containing 42 pages. How many stamps are in the total collection if 40 stamps fit on a page?
(1) 92
(2) 820
(3) 1,680
(4) 2,080
(5) 16,800
Step-by-step explanation:
Total number of albums = 10 albums[tex] \; [/tex]Number of pages in each album = 42 pages Stamps fit on 1 page = 40 stampsAs total number of pages in each album is 42 pages, so
➝ Total number of pages in 10 albums = (42 × 10) pages
➝ Total number of pages in 10 albums = 420 pages
Now, as the number of stamps fit on 1 page is 40 stamps, so
➝ Stamps fit on 420 pages = (420 × 40) stamps
➝ Stamps fit on 420 pages = 16,800 stamps
Therefore, 16,800 stamps are in the total collection.
Would you kindly help me.Im having a hard time understanding and I've been crying a lot trying to understand it
Find the L. C. M in division method of the following
a) 18,27
b) 21,38
Answer:
hope it will be helpful to you.....
Which triangle must be a right triangle and why?
O AA'B'C' is right because it is the image of AABC.
O AADC is right because AA' intersects AC at A.
O ABCC' is right because B lies of the line of
reflection.
O ABGC is right because G. CC')
Answer:
it would be the last one.
Step-by-step explanation:
its looking for a right triangle, a right triangle has one 90 degree angle. all of the other triagles have acute angles making them smaller than 90 degrees
Triangle BGC is the right triangle, because BG is perpendicular to CC'.
The line passing through points E, F, and G in the image is now perpendicular to the lines is DF and CG.
So we know that our triangle will be made with some of these lines.
For example, the right triangles in the figure are:
BFD, BGC, B'FD', and B'GC'.
Then, the concluded statement is ΔBGC, because BG ⊥CC.
There says that "Triangle BGC is the Right because BG is perpendicular to CC.
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The volume of a cube is 2,744 m3. What is the side length of the cube?
Answer:
The length is 14 and the area is 196 cm².
The side length of the cube is 14 meters.
We have,
Volume of Cube = 2744 m³
To find the side length of a cube when given its volume, you can use the formula:
Side length = ∛(Volume)
So, substitute this value into the formula to calculate the side length:
Side length = ∛(2,744)
= ∛ 14 x 14 x 14
= 14 m
Therefore, the side length of the cube is 14 meters.
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There are 4 routes from Danbury to Hartford and 6 routes from Hartford to Springfield. You need to drive from Danbury to Springfield for an important meeting. You don’t know it, but there are traffic jams on 2 of the 4 routes and on 3 of the 6 routes. Answer the following:
a. You will miss your meeting if you hit a traffic jam on both sections of the journey. What is the probability of this happening?
b. You will be late for your meeting if you hit a traffic jam on at least one, but not both sections of the trip. What is the probability of this?
c. What is the probability that you will hit no traffic jam?
Answer:
a. P) = 0.25
b. P) = 0.25
c. P) = 0.5
Step-by-step explanation:
a) 1/4 as 1/2 x 1/2 = 1/4 = 0.25 This becomes reduced as we are multiplying one complete probability journey by another complete probability journey.
b) see above as 1/2 x 1/4 and 1/4 x 1/2 = 2.5 = 1/4 = 0.25
or we can Set to 1 and 1 - 3/4 = 1/4. = 0.25.
c) 1/2 as half of the journeys have traffic jams so its 1 - 1/2 = 1/2 = 0.5
HELP HELP HELP MATH⚠️⚠️⚠️⚠️⚠️
Find four consecutive integers with the sum of 2021
Answer:
This problem has not solution
Step-by-step explanation:
lets the integers be:
x
x+1
x+2
x+3
so:
x+(x+1)+(x+2)+(x+3)=2021
x+x+x+x+1+2+3=2021
4x+6=2021
4x=2021-6=2015
x=2015/4=503.75
x is not a integer
solve for the solution of each linear equation.
1. 3x+1=4
2. 7x-6=0
3. 4x-5=19
4. 9x+6=8
5. 8x-7=15
Answer:
no.1 answer 0
Step-by-step explanation:
3x + 1= 4
or; 3x = 4 - 1
or; x = 3 ÷ 3
x = 0
Please help solve
-5<14-4x≤3
Answer:
Interval notation (-5,3]
For which equation is (4, 3) a solution?
y=x+3
y=3 x-4
y= 2 x-5
y= 2 x-1
please say how you got your answer
Answer:
y = 2x - 5
Step-by-step explanation:
We can use trial and error to solve this.
4 = x and 3 = y
y = x + 3: 4 + 3 = 7 ≠ 3 (not what we want)
y = 3x + 4: (3 x 4) - 4 = 8 ≠ 3 (not what we want)
y = 2x - 5: (2 x 4) - 5 = 3 (what we want)
y = 2x - 1: (2 x 4) - 1 = 7 ≠ 3 (not what we want)
The answer is y = 2x - 5
What is equivalent to 3(5x-4)
Answer:
15x - 12
Step-by-step explanation:
3(5x-4)
We can find an equivalent expression by distributing the 3 to what's inside of the parenthesis (5x and -4)
3(5x-4)
* Distribute *
3 * 5x = 15x
3 * -4 = -12
An equivalent expression would be 15x -12
Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2 - 4x = -2 has.
Answer:
We can use three solution and they are
(1)completing the square
(2)quadratic formula
(3) factorisation method
The quadratic equation 2x^2 - 4x = -2 has two values .
What is quadratic equation ?According to our definition, a quadratic equation is one with degree 2, implying that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: y = x^2 + 3x + 1.Kind of solutions -(1)completing the square
(2)quadratic formula
(3) factorization method
Given,
quadratic equation 2x^2 - 4x = -2
2x² - 4x + 2 =0
Now solve this equation by factor,
2x² - 4x + 2 = 0
2x² - ( 2+2)x +2 = 0
2x² - 2x -2x + 2 = 0
2x(x- 1 ) -2 ( x -1) = 0
(2x - 2) ( x- 1) =0
2x - 2 = 0 or x - 1 = 0
x = 1 or x = 1
So, this equation has 2 value of x.
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