Answer:
isabella will be able to pay 2 full years of insurance with her remaining savings
Step-by-step explanation:
as we know isabella saved $13,000
the car cost $11,675 - so subtracting that from her total we will know that she has: $1,325 remaining
insurance for a year costs $650,
so we will divide her remaining sum by the yearly cost giving us -
1,325/650
= 2.0.3....
this means that she will be able to pay for 2 full years of insurance with her remaining savings
hope this helped:)
========================================================
Explanation:
x = number of years
Since it costs $650 a year for insurance, she will pay 650x dollars of insurance in total over those x years.
For example, if x = 4, then 650*x = 650*4 = 2600 dollars is paid in insurance.
The expression 650x is added onto the 11675 which is the cost of the car.
Overall, Isabella pays 650x+11675 dollars as the combined cost of the car itself and the insurance over those x years.
Set this equal to 13000 and solve for x
650x+11675 = 13000
650x = 13000 - 11675
650x = 1325
x = 1325/650
x = 2.03846 which is approximate
Rounding down to the nearest whole number gets us to x = 2
She will be able to afford 2 full years of insurance
Note that if x = 3, then,
650x+11675
650*3+11675
13625
Which is 625 dollars over her budget. This shows that she cannot have x = 3 or larger.
Need help please need it quick
Answer:
Choice A
Step-by-step explanation:
An arithmetic sequence is one which has an incremental change.
for our answer, our change is +5
write 5 lcms of 100 and 120
Answer:
The LCM of 100 and 120 is 600.
The LCM of 5 and 120 is 120.
LCM of 5 and 100 is 100.
Step-by-step explanation:
I think this is the answer . If it is not sorry .
ASAP HELP!! PLEASEEEE!!
Answer:
Step-by-step explanation:
5.1, please this is just a guess from using my head to calculate
what is x in 8 ^ (x - 1 ) = 16 ?
Please help.
Answer:
x=7/3
Step-by-step explanation:
8 ^ (x - 1 ) = 16
We need to rewrite 8 as 2^3 and 16 as 2^4
2^3 ^ (x - 1 ) = 2^4
We know that a^b^c = a^(b*c)
2^(3(x-1)) = 2^4
The bases are the same so the exponents are the same
3(x-1) = 4
Distribute
3x-3 = 4
Add 3 to each side
3x-3+3 = 4+3
3x = 7
Divide by 3
3x/3 = 7/3
x=7/3
HELP PLEASE!
Given that sin A=3/7, cos B=-2/5, and both AA and B are in quadrant II, find cos (A-B). Simplify to a single value and leave it in the form of a rational number.
First, recall that
cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
so you just need to find cos(A) and sin(B).
Since both A and B end in the second quadrant, you know that
• cos(A) and cos(B) are both negative
• sin(A) and sin(B) are both positive
Then from the Pythagorean identity, you get
cos²(A) + sin²(A) = 1 ==> cos(A) = -√(1 - sin²(A)) = -2√10/7
cos²(B) + sin²(B) = 1 ==> sin(B) = +√(1 - cos²(B)) = √21/5
You'll end up with
cos(A - B) = (-2√10/7) (-2/5) + (3/7) (√21/5)
… = (4√10 + 3√21)/35
(which makes the last sentence in the question kind of confusing, because this expression doesn't get much simpler and it's certainly not a rational number)
The value of cos(A - B) is approximately 23/25
Given that A and B are in the second quadrant, we have
sin A = 3/7cos B = -2/5To find cos(A - B), we have to use trigonometric functions
cos(A - B) = cosAcosB + sinAsinB ...equation(i)
but
cos A[tex]cos^2A + sin^2A =1 \\cos^2A = 1 - sin^2A\\cos^2A = 1 - (\frac{3}{7})^2 = 1 - \frac{9}{49}= cosA= -\frac{2\sqrt{5} }{7}[/tex]
Having the value of cos A, let's solve for cosB
Cos Bcos B = -2/5
[tex]sin^2B = 1-cos^2B\\sin^2B = 1-(-\frac{2}{5})^2= 1-\frac{4}{25}\\sinB = \sqrt{\frac{21}{25} }=\frac{\sqrt{21} }{5}[/tex]
cos(A-B)substituting the values if sinA, cosA, sinB, cosB into equation(i) above;
[tex]cos(A-B)=cosAcosB+sinAsinB\\cos(A-B)=(-\frac{2\sqrt{5} }{7})(-\frac{2}{5})+(\frac{3}{7})(\frac{\sqrt{21} }{5})\\cos(A-B)=\frac{3\sqrt{21}+4\sqrt{5} }{35} \\cos(A-B) = 23/35[/tex]
The value of cos(A-B) is given above
Learn more on trigonometric functions here;
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pls find the value of X
Answer: 64°
Step-by-step explanation:
Since QS = RS, ∠Q = ∠R = 32°∠QSR = 180° - 32° - 32° = 116°∠QSR = ∠NSP = 116°Since MN║PS, ∠NSP + ∠N = 180° ∠N = 180° - 116° = 64°Answer:
x = 64°
Step-by-step explanation:
Since the triangle is isosceles, the base angles are congruent, that is
∠ R = ∠ Q = 32° , then
vertex angle = 180° - (32 + 32)° = 180° - 64° = 116°
∠ NSR = 116° ( vertically opposite angle )
∠ MNS and ∠ NSR are same- side interior angles and sum to 180° , then
x = 180° - 116° = 64°
Which expression is equivalent to 4-2 _ 2-3
Answer:
16
Step-by-step explanation:
First you calculate the value
(2)÷2^-2
Then you simplify
2^4
=16
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($) 0 5
8
10
15
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
Multiply each payout by the corresponding probability and take the total:
E[X] = 0×0.5 + 5×0.2 + 8×0.15 + 10×0.1 + 15×0.05 = 3.95
The expected value = 3.92
What is expected value ?"It describes the average of a discrete set of variables based on their associated probabilities."
Formula of expected value:[tex]E(x)=\Sigma[ xP(x)][/tex]
Multiply each value of the random variable by its probability and add the products.
For given question,
We have been given a payout probability distribution.
We need to find the expected value of the winnings.
First we multiply each value of the random variable by its probability .
0 × 0.5 = 0
5 × 0.2 = 1
8 × 0.15 = 1.2
10 × 0.1 = 1
15 × 0.05 = 0.75
Now, we find the sum of above products.
0 + 1 + 1.2 + 1 + 0.75 = 3.95
By using the formula of expected value,
[tex]\Rightarrow E(x)=\Sigma[ xP(x)]\\\\\Rightarrow E(x)=3.92[/tex]
Therefore, the expected value = 3.92
Learn more about the expected value here:
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CAN SOMEONE HELP ME PLEASE
Answer:
1/6
Step-by-step explanation:
They're independent which means to find their intersection you just multiply
(1/4)*(2/3)= 2/12= 1/6
i need help witht he second part ITS URGENT PLS
Answer:
7
Step-by-step explanation:
when multiplying powers with the same base, add the powers
Answer:
a²×a⁵
a²⁺⁵
a⁷
OAmalOHopeO
3. A rectangle has a length of 2x – 9 and a width of x2 + 3x – 4. What is the polynomial that models the area
of the rectangle?
Answer:
(C) 2x^3 - 3x^2 - 35x + 36
Step-by-step explanation:
First multiply 2x by x^2 + 3x - 4:
(2x)(x^2 + 3x - 4)
2x^3 + 6x^2 - 8x
Next multiply -9 by x^2 + 3x - 4:
(-9)(x^2 + 3x - 4)
-9x^2 - 27x +36
Now add the two polynomials by adding like terms:
(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)
2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36
2x^3 - 3x^2 - 35x + 36
Hope this helps (●'◡'●)
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer:
Step-by-step explanation:
The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:
original new
length
width
And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:
original new
length L
width 2L
Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.
The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:
original new
length L 100%L + 50%L
width 2L
The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:
original new
length L 100%L + 50%L
width 2L 100%(2L) - 20%(2L)
And now we'll simplify that "new" column:
original new
length L 150%L = 1.5L
width 2L 80%(2L) = 160%L = 1.6L
Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:
248 = 2(1.5L) + 2(1.6L) and
248 = 3L + 3.2L and
248 = 6.2L so
L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)
How do you write 50% as a fraction?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Answer:
50% as a fraction would be 1/2
Help me to prove it
Answer:
see explanation
Step-by-step explanation:
Using the identities
cotA = [tex]\frac{1}{tanA}[/tex]
cot²A = cosec²A - 1
tan²A = sec²A - 1
Consider the left side
(cotA + tanA)² ← expand using FOIL
= cot²A + 2cotAtanA + tan²A
= cosec²A - 1 + 2 .[tex]\frac{1}{tanA}[/tex] . tanA + sec²A - 1
= cosec²A - 1 + 2 + sec²A - 1
= sec²A + cosec²A - 2 + 2
= sec²A + cosec²A
= right side, thus proven
Find the missing segment in the image below
Answer:
8? not sure tho....
Step-by-step explanation:
HELP ME WITH THIS PLEASE PLEASE SHOW ME THE FORMULA FOR LETTER C
Answer:
Which subject is this . please tell
Answer:
see explanation
Step-by-step explanation:
1
(a)
Calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ = (8, 3) and (x₂, y₂ ) = (10, 7)
m = [tex]\frac{7-3}{10-8}[/tex] = [tex]\frac{4}{2}[/tex] = 2
(b)
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
(c)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (8, 3) into the partial equation
3 = - 4 + c ⇒ c = 3 + 4 = 7
y = - [tex]\frac{1}{2}[/tex] x + 7 ← equation of perpendicular line
--------------------------------------------------------------------------
2
(a)
with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (4, 4)
m = [tex]\frac{4-5}{4-3}[/tex] = [tex]\frac{-1}{1}[/tex] = - 1
(b)
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1
(c)
y = x + c ← is the partial equation
To find c substitute (3, 5) into the partial equation
5 = 3 + c ⇒ c = 5 - 3 = 2
y = x + 2 ← equation of perpendicular line
The number of lines of symmetry of an equilateral triangle is _______.
Question 5 options:
A: 4
B: 1
C: 2
D: 3
Answer:
An equilateral triangle has three lines of symmetr
Step-by-step explanation:
letter d
Answer: 3
Step-by-step explanation: i took test
What is the range of f(x) = x - 2, if the domain is {3, 1, 2)?
Answer:
Range: {1, -1, 0}
Step-by-step explanation:
Just subtract 2 from each number :)
Select the true statement about triangle ABC.
A. cos A = cos C
B. cos A = sin C
C. cos A = sin B
D. cos A = tan C
Answer:
B
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{5}{13}[/tex]
sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{12}{5}[/tex]
Then
cosA = sinC → B
Options:
Rotation
Reflection
Translation
Answer: Reflection
Step-by-step explanation: Please mark brainliest
PLEASE HELP QUICK 30 POINTS !!!!!!
Ryan wants to make a triangular deck. He wants each side to be a different length.
Select three lengths he could use to make a triangle:
Side 1:
Side 2:
Side 3:
:: 3 feet
:: 10 feet
.: 20 feet
:: 25 feet
:: 60 feet
Answer:
10 ft, 20ft and 25 ft.
Step-by-step explanation:
10 ft, 20ft and 25 ft.
This will make a triangle as 25 < (10 + 20).
Answer:
Solution given:
one side of a triangle must be less than the sum of two other side .
by making these sense:
3<10+20
10<20+3
20<10+3not true
these three side are not possible.
again
10<20+25
20<25+10
25<20+10
these three side are true so
required side are:
Side 1:10
Side 2:25
Side 3:20
What is the value of x that makes L1 ∣∣ L2?
A. 15
B. 29
C. 18
D. 25
Answer:
B
Step-by-step explanation:
For the lines to be parallel.
The 2 given angles are corresponding and congruent, that is
4x - 12 = 3x + 17 ( subtract 3x from both sides )
x - 12 = 17 ( add 12 to both sides )
x = 29 → B
The value of x will be 29°. Then the correct option is B.
What is a corresponding angle?If two lines are parallel, then the third line. The corresponding angles are equal angles.
We know that the angle (3x + 17) and (4x – 12) are corresponding angle.
(3x + 17) = (4x – 12)
4x – 3x = 17 + 12
x = 29°
The value of x will be 29°.
Then the correct option is B.
More about the corresponding angle link is given below.
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The volumes of two similar solids are 512cm3 and 2197cm3. If the smaller solid has a surface are of 960cm2, find the surface area of the larger solid. Part 1: find the similarity ratio by taking the cube root of each volume. Show your work. Part 2: use your answer from part 1 to find the ratio of the surface areas. Show your work. Part 3: set up a proportion and solve to find the surface area of the larger solid.
Answer:
see below
Step-by-step explanation:
Part 1:
(512) ^ 1/3
-------------------
(2197) ^ 1/3
8
-----
13
The scale factor is 8:13
Part 2
The ratios of the areas is related by scale factor squared
8^2
-----
13^2
64
------
169
Part 3
64 960
------ = ----------------
169 SA larger
Using cross products
64 * SA = 169 * 960
64 SA = 162240
Divide each side by 64
64 SA/ 64 = 162240 / 64
SA = 2535
2535 cm^2
A wind turbine has blades 50m in diameter and an overall height (to the highest point) of 125m. If it has four blades instead of three, create four equations modelling the height of a point on the tip for each of the four blades.
Answer:
Blade A : H(θ) = 75 + 50 sin θ
Blade B : H(θ) = 75 + 50 sin(θ + 90° )
Blade C : H(θ) = 75 + 50 sin( θ + 180° )
Blade D : H(θ) = 75 + 50 sin( θ + 270° )
Step-by-step explanation:
Given data :
Diameter of blade = 50 m
overall height = 125 m
The four blades : Blade A , Blade B, Blade C, Blade D all moves in same direction hence they make 90° to each other.
Lets assume The blades are standing at θ with the horizontal
The four equation modelling the heights :
Blade A : H(θ) = 75 + 50 sin θ
Blade B : H(θ) = 75 + 50 sin(θ + 90° )
Blade C : H(θ) = 75 + 50 sin( θ + 180° )
Blade D : H(θ) = 75 + 50 sin( θ + 270° )
Point T Is the incenter of PQR.Point T is the point of concurrency of the angle bisector. Find ST.
ST is 10 because since T is the incenter is equidistant from all sides.
What is 1/4 0.75 1/3 0.5 greatest to least
Answer:
1/4 = 1 ÷ 4 = 0.251/3 = 1 ÷ 3 ≈ 0.330.750.50.75 → 0.5 → 1/3(0.33) → 1/4(0.25)
Help please…..?!!!!!☺️
Answer:
Step-by-step explanation:
Sample space of die 1 = {1,2,2,3,3,4}
Sample space of die 2 = {1,3,4,5,6,8}.
The highest value that we get by rolling die 1 is 4 and die 2 is 8, which give the sum 12. So, we cannot have any other combinations other than this , as the highest value itself gives 12.
Rolling a sum of 12 with the dice = {(4,8) }
Probability = 1/36
if a=(p+q),b=(p-q)and c=qsquare -psquare, show that ab+c=0
Answer:
I think this is the ans
Step-by-step explanation:
ab+c=0
(p+q)(p-q)=0
p Square-q Square =0
0=p Square-q Square
What is the area of this triangle
Answer:
14
Step-by-step explanation:
7*4*1/2=14
Use the diagram.
What is the length of }EG ?
A 1 B 4.4
C 10 D 16
Answer:
Option (D)
Step-by-step explanation:
Length of the bar EG = 1.6x
If F is a point on the bar such that,
EF + FG = EG
Measure of segment EF = 6
Measure of FG = x
By substituting measures of each side,
6 + x = 1.6x
1.6x - x = 6
0.6x = 6
x = 10
Length of EG = x + 6
= 10 + 6
= 16 units
Option (D) will be the correct option.
From the given diagram , the length of EG is 16
Given :
From the diagram , we can see that
EF=6, FG=x and EG=1.6x
We know that , EG=EF+FG
[tex]EG=EF+FG\\1.6x=6+x\\Solve \; for \; x\\1.6x-x=6\\0.6x=6\\divide by \; 0.6\\x=10[/tex]
Now we find out EG
EG=1.6x
Substitute 10 for x
[tex]EG=1.6x=1.6(10)=16\\[/tex]
EG=16
The length of EG is 16
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