Using an exponential function, it is found that the approximate number of crimes in the year of 2016 was of 2502.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, there were 550 crimes in the initial year observed, and the growth rate is of 6%, hence the parameters are A(0) = 550, r = 0.06, and the equation is given by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 550(1 + 0.06)^t[/tex]
[tex]A(t) = 550(1.06)^t[/tex]
2016 is 26 years after 1990, hence:
[tex]A(26) = 550(1.06)^{26} \approx 2502[/tex]
The approximate number of crimes in the year of 2016 was of 2502.
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The equation y=37.8xy=37.8x represents the number of miles, yy, that Julian can drive his car for every xx gallons of gas. Find the rate of change.
The rate of change of Julian given the equation y = 37.8x is 37.8
How to find the rate of changeThe equation:
y = 37.8x
where,
y = number of miles that Julian can drivex = gallons of gas used37.8 = constant = rate of changeIf x = 3 gallons
y = 37.8x
= 37.8 × 3
y = 113.4 miles
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18. Find the surface area of the prism.
Step-by-step explanation:
the total surface area is the sum of the individual areas on the surface.
we have
2 triangles (top and bottom)
1 front rectangle
2 rectangles in the back
the area of a triangle is
baseline × height / 2
1.7 × 0.5 / 2 = 0.425 in²
both triangles together : 2×0.425 = 0.85 in²
the area of a rectangle is
length × width
so, the front is
1.7 × 1.5 = 2.55 in²
one back rectangle is
1 × 1.5 = 1.5 in²
both back areas are 2×1.5 = 3 in²
so, the total surface area is
0.85 + 2.55 + 3 = 6.4 in²
line c has a slope of -9/2. line d is parallel to like c. what is the slope of line d?
Answer:
-9/2
Step-by-step explanation:
parallel lines have the same slope/gradient
help me please!! will choose brainlyest if you get it right
Rebecca has $128 to spend. She
spends $78 on a running shoes.
Tank tops cost $12.50 each. Write and
solve an inequality to find how many
tank tops she can buy.
Answer:
12.5x =10x+10
12.50x=x10+10
subtract 10x from both sides
2.5x=10
divide by 2.5
x=4
To train for a marathon, Lily plans on running 4 miles per day for the first week and then increasing that daily distance by 1 mile each of the following weeks.
Which of these equations represent the problem.
The equation which represent the problem is given by an = 4 + 1.00(n - 1)
How to write equation?Number if miles Lily run per day first week = 4 miles
Additional miles per day each week = 1 mile
let
n = total miles
The equation:
an = 4 + 1.00(n - 1)
When n = week 2an = 4 + 1(n - 1)
= 4 + 1(2 - 1)
= 4 + 1(1)
= 4 + 1
= 5 miles
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how much money is 1 quarter,1 dime and 1 nickle?
answer:40
Step-by-step explanation:
a quarter is 25
a dime is 10
a nickle is 5
25+10+5=40
Write the polar equation 0= pi/3
Answer:
1
(
π
3
)
)
Step-by-step explanation:
Explanation:
Substitute
tan
(
y
x
)
for
θ
tan
(
y
x
)
=
π
3
Obtain
y
x
on the left by using the inverse tangent on both sides:
tan
−
1
(
tan
(
y
x
)
)
=
tan
−
1
(
π
3
)
y
x
=
tan
−
1
(
π
3
)
Multiply both sides by x:
y
=
(
tan
−
1
(
π
3
)
)
x
Geometry shapes I need help asap
answer quickly please
The line TU is tangent to the circle whose center is at point S
The measure of angle U is 84 degrees
How to determine angle U?From the question, we understand that:
Angle STV = 84 degreesTU is tangent to circle SThis second highlight means that:
Angle STU = 90 degrees
And:
Angle STU = Angle STV + Angle VTU
This gives
90 = 84 + Angle VTU
Subtract 84 from both sides
Angle VTU = 6
The measure of angle U is then calculated as:
U + Angle VTU + Angle UVT = 180 ------ sum of angles in a triangle
This gives
U + 6 + 90= 180
Evaluate the sum
U + 96 = 180
Subtract 96 from both sides
U = 84
Hence, the measure of angle U is 84 degrees
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When solving, at what point do you know that your solutions are imaginary? Does x^2 +9 =0 have real or imaginary solutions? How do you know?
Answer:
Real solutions
Step-by-step explanation:
I know that because I am smart
The regular admission price to an amusement park is $28. You have a
coupon for 25% off the regular admission. Find the total cost of admission
to the park when the sales tax is 6% of the reduced price.
Answer:
$22.26
Step-by-step explanation:
To solve, all we need to do is 28(1-.25) to get 21, then we set up the equation 21(1+.03) and we get our total for the price.
we subtract in the first place, because it is a discount, and we add in the second one because it is a sales tax.
please rate and mark as brainlest.
Write the expression. Then, complete the statements.
twice the difference of a number and seven
The word "twice" means
.
The words "the difference of" indicate
.
The expression is written as
Answer:
The equation is 2(x-7)
Hope it is correct
Answer: Write the expression. Then, Complete the statements.
.
.
twice the difference of a number and seven
Step-by-step explanation:
1. multiplication by 2
2. subtraction in parentheses
3. 2(n-7)
Solve for h.
2 < -19 - 7h
Answer:
h < -3
Step-by-step explanation:
2 < -19 - 7h
2 + 19 < -7h
21 < - 7h
21/7 < -h
bringing -h to the left
-h > 3
changing the sign to positive h
h < -3
solution set : {h < -3}
Hope that helps...
(100 POINTS !!) Identify the vertex of the parabola.
Answer:
(-4,0)
Step-by-step explanation:
A teacher of a dance class collected data and created a histogram as shown.
Which statement accurately describes the information in the graph?
A.
The data describes the ages of the teachers of an art class.
B.
The data describes the ages of the students in an art class.
C.
The data describes the ages of the students in a dance class.
D.
The data describes the ages of the teachers of a dance class.
Answer:
C
Step-by-step explanation:
this was quite the toungue twister
What is the slope of the line that is parallel to the line whose equation is 4x+y-2=0?
Answer:
4x+y-4=0
Step-by-step explanation: For an equation to be parallel to another all it needs is the same slope but a different y-intercept. So you can really other equations like 4x+y-3=0, 4x+y-5=0, 4x+y-6=0, etc. can be the answer to your problem.
Solve and show the answer in simplest terms 1 over 8 + 1 over 2 + 1 over 4
Answer:
7 over 8
Step-by-step explanation:
Change all the numerators over the least common denominator. 1+4+2 over 8.
A rectangular red sticker has a perimeter of 40 millimeters and an area of 64 square
millimeters. What are the dimensions of the sticker?
millimeters by millimeters
Submit
Answer:
16 x 4.
Step-by-step explanation:
What multiplies into 64?
could be 16 and 4?
16 x 2 = 32
4 x 2 = 8
32 + 8 = 40, therefore, this is correct.
Multiplication and __are inverse operations. addition subtraction O division
Answer:
Division is the opposite of multiplication
Step-by-step explanation:
Opposites:
Addition and subtraction
multiplication and division
differentiation and integration.
Miranda's heart beats 3 times every 2 secounds. At that rate, how many times does her heart beat in 1 minute?
What is the measure of the
missing angle?
64°
97°
?
116°
O
o
78°
72°
80°
83°
Answer:
? = 83°
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the angles and equate to 360°
? + 116° + 97° + 64° = 360° , that is
? + 277° = 360° ( subtract 277° from both sides )
? = 83°
Answer:
it is an obtuse angle so that should get rid of some of the answer choices
Step-by-step explanation:
(PLS HELPP EASYY POINTS )
A company makes piñatas for special events such as birthday parties. One of their piñatas is in the form of a cone shaped hat. How much space do they have inside the piñata for candy if the piñata is 2 feet tall and 1.5 feet wide? Round to the nearest hundredth
I don't recognize this problem, please make sure the input is complete.
Is the following relation a function yes or no
It's function of sinus
...........
A new car is purchased for $31,000 and over time its value depreciates by one half
every 6.5 years. How long, to the nearest tenth of a year, would it take for the value
of the car to be $3,800?
Using an exponential function, it is found that it would take 19.68 years for the value of the car to be $3,800.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^\frac{t}{n}[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal, after each n years.In this problem:
The initial value is of $31,000, hence A(0) = 31000.It depreciates by one-half every 6.5 years, hence r = 0.5, n = 6.5.Then, the equation is:
[tex]A(t) = A(0)(1 - r)^\frac{t}{n}[/tex]
[tex]A(t) = 31000(1 - 0.5)^\frac{t}{6.5}[/tex]
[tex]A(t) = 31000(0.5)^\frac{t}{6.5}[/tex]
The value would be of $3,800 at t for which A(t) = 3800, hence:
[tex]A(t) = 31000(0.5)^\frac{t}{6.5}[/tex]
[tex]3800 = 31000(0.5)^\frac{t}{6.5}[/tex]
[tex](0.5)^\frac{t}{6.5} = \frac{3800}{31000}[/tex]
[tex](0.5)^\frac{t}{6.5} = 0.12258064516[/tex]
[tex]\log{(0.5)^\frac{t}{6.5}} = \log{0.12258064516}[/tex]
[tex]\frac{t}{6.5}\log{0.5} = \log{0.12258064516}[/tex]
[tex]t = 6.5\frac{\log{0.12258064516}}{\log{0.5}}[/tex]
t = 19.68.
It would take 19.68 years for the value of the car to be $3,800.
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Answer:
t≈19.7
Step-by-step explanation:
I do not have one, I apologize.
Find the area of the parallelogram
Answer:
30.42 in^2.
Step-by-step explanation:
Find the height:
sin 45 = 1/√2 = h/7.8
h = 7.8 /√2
the base = height = 7.8 /√2
Area = h * b
= (7.8 /√2)2
= 30.42.
I need helppppppppppppppppppp
Answer:
See explanation
Step-by-step explanation:
look at the photo
I hope it will help you <3
Answer:
Step-by-step explanation:
*The other person that answered may be correct, but this was my way of solving the functions.
x = y - 4
-2x + 3y= 6
Solve each system by equation
Answer:
Point form=(-6,-2)
Equation Form= x=-6, y=-2
Step-by-step explanation:
100 POINTS !!! Find the axis of symmetry and the vertex of the graph of y = 6x2 − 24x + 11. x = 2; (2, −13) x = 4; (4, 11) x = −2; (−2, 83) x = −4; (−4, −11)
Let's see
[tex]\\ \rm\rightarrowtail y=6x^2-25x+11[/tex]
Graph attached
vertex(-2,-13)Axis of symmetry
x=-2Answer:
axis of symmetry: x = 2
vertex: (-2, 13)
Step-by-step explanation:
Given function
[tex]\sf y=6x^2-24x+11[/tex]
Vertex form
[tex]\sf y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
Expand vertex form:
[tex]\sf \implies y=ax^2-2ahx+ah^2+k[/tex]
Compare coefficients of expanded vertex form with given function:
coefficient of [tex]\sf x^2[/tex]:
⇒ a = 6
coefficient of [tex]\sf x[/tex]:
⇒ -2ah = -24
⇒ ah = 12
⇒ 6h = 12
⇒ h = 2
constant:
⇒ [tex]\sf ah^2+k=11[/tex]
⇒ [tex]\sf 6 \cdot 2^2+k=11[/tex]
⇒ [tex]\sf 24+k=11[/tex]
⇒ [tex]\sf k=-13[/tex]
Vertex
Vertex = (2, -13)
Axis of symmetry
Axis of symmetry is when x = h
Therefore, axis of symmetry is x = 2
Mrs. o'brien used a compass to draw two circles on a coordinate plane. circle a is centered at (3,-1)
and has a radius of 4 units. circle b is centered at (4, 5) and has a
radius of 3 units. select all of the
transformations that can be performed on circle a to prove that it is similar to circle b.
To prove that circle A is similar to circle B, it needs to be moved 1 unit right and 6 units up and then dilated by a scale factor of 3/4
What is transformation?
Transformation is the movement of a point from its initial location to a new location.
Types of transformation are rotation, translation, dilation and reflection.
To prove that circle A is similar to circle B, it needs to be moved 1 unit right and 6 units up and then dilated by a scale factor of 3/4
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