Answer:
60 sq in
Step-by-step explanation:
Perimeter = 2l + 2w
If l = w+4
Perimeter = 2(w+4) + 2w
Perimeter = 4w+8
32 = 4w + 8
24 = 4w
6 = w
If w = 6, l = 6+4 = 10
Area = l * w
Area = 10 * 6
Area = 60
A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year
Answer:
[tex]P(x \le 3) = 0.9920[/tex]
Step-by-step explanation:
Given
[tex]p = 6\%[/tex] --- proportion of drivers that had accident
[tex]n = 14[/tex] -- selected drivers
Required
[tex]P(x \le 3)[/tex]
The question is an illustration of binomial probability, and it is calculated using:
[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(x \le 3) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3)[/tex]
[tex]P(x=0 ) = ^{14}C_0 * (6\%)^0 * (1 - 6\%)^{14-0} = 0.42052319017[/tex]
[tex]P(x=1 ) = ^{14}C_1 * (6\%)^1 * (1 - 6\%)^{14-1} = 0.37578668057[/tex]
[tex]P(x=2 ) = ^{14}C_2 * (6\%)^2 * (1 - 6\%)^{14-2} = 0.15591149513[/tex]
[tex]P(x=3 ) = ^{14}C_3 * (6\%)^3 * (1 - 6\%)^{14-3} = 0.03980719024[/tex]
So, we have:
[tex]P(x \le 3) = 0.42052319017+0.37578668057+0.15591149513+0.03980719024[/tex]
[tex]P(x \le 3) = 0.99202855611[/tex]
[tex]P(x \le 3) = 0.9920[/tex] -- approximated
Jack’s backpack weighs 15 pounds. Fernando’s backpack weighs less than Jack’s. Which graph shows how much Fernando’s backpack can weigh?
Answer:
A
Step-by-step explanation:
c and d out of the question
b has its circle filled in meaning it could be 15lbs, which it's not
A correct answer by default
Answer:b
Step-by-step explanation: it has a filled in diamond which mean it's that...
Simplify the following expression
Answer:
[tex]\frac{98p^{6}}{q}[/tex]
Step-by-step explanation:
Distribute the exponents
[tex](\frac{(7^{-2}p^{-6}q^{-8})}{2q^{-9}} )^{-1}[/tex]
[tex](\frac{q}{98p^{6}} )^{-1}[/tex]
Distribute the -1
[tex]\frac{98p^{6}}{q}[/tex]
Can someone do #4 and #5
Answer:
First, find two points on the graph:
(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 8)Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]
16 + (-3) = 16 - 3 = 13
According to this diagram, what is tan 62°?
62°
17
18
280
90°
15
O A.
8
17
OB.끝
O c. 1
8
15
D.
15
8
O
E.
17
15
F.
15
17
Answer:
15/8
Step-by-step explanation:
tan(62)=P/B
tan(62)=15/8
5 A machine puts tar on a road at the rate of 4 metres in 5 minutes.
a) How long does it take to cover 1 km of road
b) How many metres of road does it cover in 8 hours?
Answer:
5 a) Total = 20.83 hrs = 20 hrs and 50 mins (1250mins total)
5 b) Total = 96 meters. = 0.096km in 8 hrs.
Step-by-step explanation:
1km = 1000 meters
5 mins = 4 meters
1000/4 = 250 multiplier
250 x 5mins = 1250 minutes
1250/60 = 20hrs + 50 minutes
50 / 60 = 0.83 = 20.83hrs
b) 8 hrs = 8 x 60 = 480 minutes
480/5 = 24 multiplier of 4 meters
24 x 4 = 96 meters
Which two shapes make up the digital camera below?
Rectangular prism and cylinder make up a camera.
What is rectangular prism and cylinder?A cube is a rectangular prism with all of its sides being the same length, a triangular prism has a triangle as its base, and a rectangular prism has a rectangle as its foundation. Another form of right prism that has a circle as its basis is a cylinder.
A rectangular prism includes a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it contains three dimensions- the base width, the height, and the length. The top and base of the rectangular prism exist rectangular. The pairs of opposite faces of a rectangular prism exist as identical or congruent.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it includes been regarded as a prism with a circle as its base.
Hence, Rectangular prism and cylinder make up a camera.
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This graph represents which of these expressions?
Answer:
x > 43
Step-by-step explanation:
Open circle at 43, which means it is not equal to 43
Line goes to the right, which means x is greater than
x > 43
Answer:
B
Step-by-step explanation:
2(4×+2)=10
[tex]6 \times + 4 = 10 \\ \\ 6 \times = 10 - 4 \\ \\ 6 \times = 6 \\ \\ [/tex]
that is the answer
Answer:
x = 3/4
Step-by-step explanation:
2(4x + 2) = 10 Remove the brackets
8x + 4 = 10 Subtract 4 from both sides
8x = 6 Divide by 8
x = 6/8
x = 3/4
Check
2(4*3/4 + 2) =?10
2( 3 + 2) = 10
2*5 = 10
10 = 10
Your parents deposit 2 50-dollar bills at the bank.
How much money did they deposit?
Answer: $100
Step-by-step explanation:
Considering 50 + 50 = 100
This means that the amount of money is $100
Complete the table for the given rule.
Rule: y is 0.75 greater than x
x y
0
3
9
The complete table is
x y
0 0.75
3 3.75
9 9.75
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression or equation.
According to the given question.
We have values of x.
Also, one rule that y is 0.75 greater than x.
So, we have a equation for finding the value of y i.e.
[tex]y = x + 0.75..(i)[/tex]
For finding the value of y
At x = 0, substitute x = 0 in equation (i)
[tex]y = 0 + 0.75\\\implies y = 0.75[/tex]
At x = 3, substitute x = 3 in equation (i)
[tex]y = 3+0.75\\\implies y = 3.75[/tex]
At x = 9, substitute x = 9 in equation (i)
[tex]y = 9+0.75\\\implies y = 9.75[/tex]
Hence, the complete table is
x y
0 0.75
3 3.75
9 9.75
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Write the additive inverse of each of the following rational numbers:
Answer:
(1)-3/4, (2) 5/21, (3)4/43
HELPPPPP ASP PLZZZZZ
Answer:
[tex](f-g)(x)[/tex]
[tex]f(x)-g(x)[/tex]
[tex]x^{2} -6x-27-x+9[/tex]
[tex]x^{2} -7x-18[/tex]
----------------------
[tex](f*g)(x)[/tex]
[tex]=f(x)g(x)[/tex]
[tex](x^{2} -6x-27)(x-9)[/tex]
[tex]=x^{3} -15x^{2}+27x+243[/tex]
----------------------
[tex]\frac{f}{g} (x)[/tex]
[tex]\frac{x^{2} -6x-27}{x-9}[/tex]
[tex]\frac{(x-9)(x+3)}{x-9}[/tex]
[tex]x+3[/tex]
-----------------------
[tex](f+g)(x)[/tex]
[tex]f(x)+g(x)[/tex]
[tex]=x^{2} -6x-27+x-9[/tex]
[tex]=x^{2} -5x-36[/tex]
------------------------
OAmalOHopeO
------------------------
Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y=-4x-5
Step-by-step explanation:
The slope of the line is - 4, the equation of line is y=-4x-5
John runs a computer software store. Yesterday he counted 140 people who walked by the store, 63 of whom came into the store. Of the 63, only 25 bought something in the store.
(a) Estimate the probability that a person who walks by the store will enter the store. (Round your answer to two decimal places.)
(b) Estimate the probability that a person who walks into the store will buy something. (Round your answer to two decimal places.)
(c) Estimate the probability that a person who walks by the store will come in and buy something. (Round your answer to two decimal places.)
(d) Estimate the probability that a person who comes into the store will buy nothing. (Round your answer to two decimal places.)
Answer:
.................
Step-by-step explanation:
............
look at the image for the question
1. A helicopter is at a position from two VORS (VHF Omnidirectional
Radio Range, an aircraft navigation system operating in the VHF band -
not covered in chapter) as in the diagram shown below. Given the angles
shown, find the third angle.
Helicopter
74.0°
66.0°
VOR
VOR
The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees
The diagram is not shown; however, the question can still be answered.
The given angles are:
[tex]\theta_1 = 74.0^o[/tex]
[tex]\theta_2 = 66.0^o[/tex]
Represent the third angle as [tex]\theta_3[/tex]
The helicopter and the 2 VORs form a triangle.
So, we make use of the following theorem to calculate the third angle
[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle
Substitute known values
[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]
[tex]140.0^o + \theta_3= 180^o[/tex]
Collect like terms
[tex]\theta_3= 180 -140.0^o[/tex]
[tex]\theta_3= 40^o[/tex]
Hence, the third angle is 40 degrees.
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Find the area of the figure. (Sides meet at right angles.)
Answer:
56
Step-by-step explanation:
A=(3*4)+(4*(4+3+4))=56
Find an upper bound for E(h) the error of the machine approximation of the two-point forward difference formula for the first derivative and then find the h corresponding to the minimum of E(h).
The two-point forward difference formula for f'(x) is:_________
Answer:
I doubt it is not going to be a great
Please Help!! Whoever helps and gets it correct gets Brainliest and 5 star rating!!
Answer:
the reasoning states that "all the numbers begin with a 7 or an 8"
however this is not accurate as they can be in different placements
which can make a big difference in the total estimate.
for example:
the number could've been an 8, or an 80
they both begin with an 8
however have totally different values and could have messed up the total estimated number.
hope this helps :D
Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.
Answer:
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b
From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:
2 inches = 1/6 ft
1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]
k =7.5*72
k =540
To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs
Step-by-step explanation:
Round 573.073 to the greatest place
Answer:
574
Step-by-step explanation:
To round a two-digit number to the nearest ten, simply increase it or decrease it to the nearest number that ends in 0: When a number ends in 1, 2, 3, or 4, bring it down; in other words, keep the tens digit the same and turn the ones digit into a 0
Hope this helps <3
if U>T, R>Q, S>T and T>R, which of the following is TRUE?
1. S>Q
2. U > S
3.U > R
A. 1 only
B. 2 only
C. 1 and 2
D. 2 and 3
Answer:
C. 1 and 2
Step-by-step explantation:
First, i would order them as U>T, T>R, R>Q, S>T
we can rewrite them as
U>T>R>Q,
now adding S, we get U>S>T>R>Q,
so U>S
We can also rewrite all of them as inequalities:
U-T>0
T-R>0
R-Q>0
S-T>0
Add R-Q and T-R
(R-Q)+(T-R)>0
-Q+T>0
T>Q, but because S>T we can say S>Q
Paul can install a 300-square-foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take Paul and Matt to install the floor working together?
4 hours
9.9 hours
13.2 hours
30 hours
Answer:
9.9 hours
Step-by-step explanation:
The formula to determine the time together is
1/a+1/b = 1/c where a and b are the times alone and c is the time together
1/18 + 1/22 = 1/c
The least common multiply of the denominators is 198c
198c(1/18 + 1/22 = 1/c)
11c+ 9c = 198
20c = 198
Divide by 20
20c/20 =198/20
c =9.9
Answer:
B - 9.9 hrs
Step-by-step explanation:
took the test.
8.9 x 10^3 in standard notation
Answer:
that is n standard notation mah frand
8.9 × 10^3 being scientific notation of " 8900 "
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{8.9}\times\large\textsf{10}^\mathsf{3}\\\\\mathsf{10^3}\\\mathsf{= 10\times10\times10}\\\mathsf{= 100\times10}\\\mathsf{= \bf 1,000}\\\\\large\textsf{8.9}\times\large\textsf{1,000}\\\\\large\textsf{= \bf 8,900}\\\\\\\boxed{\boxed{\huge\text{Answer: \boxed{\underline{\underline{\bf 8,900}}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\boxed{\huge\text{}\boxed{\frak{Amphitrite1040:)}}}[/tex]
find the missing side of the triangle
Answer:
x = 34
Step-by-step explanation:
Pytago:
x[tex]30^{2} + 16^{2} = x^2\\x = \sqrt{30^2 + 16^2} \\x = 34[/tex]
Find an equation of the plane orthogonal to the line
(x,y,z)=(0,9,6)+t(7,−7,−6)
which passes through the point (9, 6, 0).
Give your answer in the form ax+by+cz=d (with a=7).
The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.
The tangent vector for the line is
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
so that
a = 7, b = -7, c = -6, and d = 21
An equation of the plane orthogonal to the line 7x - 7y - 6z = 21.
The given line is orthogonal to the plane you want to find,
So the tangent vector of this line can be used as
The normal vector for the plane.
The tangent vector for the line is,
What is the tangent vector?A tangent vector is a vector that is tangent to a curve or surface at a given point.
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has the equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just
translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it in standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
So that, a = 7, b = -7, c = -6, and d = 21.
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State if the scenario involves a permutation or a combination. Then find the number of possibilities.
A team of 15 basketball players needs to choose two players to refill the water cooler.
Permutation/Combination:
Answer:
Answer:
Permutation ; 210 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 players from 15 ; since order does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
15P2 = 15! ÷ (15 - 2)!
15P2 = 15! ÷ 13!
15P2 = (15 * 14) = 210 ways
Reason Can you subtract a positive integer from a positive integer
and get a negive result? Explain your answer.
Answer:
No
Step-by-step explanation:
No matter the situation, when you multiply a negative by a negativeyou get a positive and a positive by a positive you get a positive. but if its two different like a negative and a positive then its NEGITIVE.
let's say you have 23 and you're multiplying by 2.
It's always increasing so it doesnt ever reach the negitive numbers.
