Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1.05)x−1. Explain how Victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. Justify your reasoning.
WILL GIVE BRANLIEST
Solution :
Amount of money Victoria has = $200
The amount modelled by function = h(x) = 200
According to the function,
s(x) = (1.05)x - 1
It means that the total amount of the interest that Victoria will receive s(x) is equal to original amount of $200 which multiplied by the rate of interest (1.05) and then multiplied by the time that Victoria keeps the money in the bank (x) minus 1.
The total amount of money she will have in her bank account as interest accrues after she deposits her $200 is 200 [tex](1.05)^{x-1}[/tex]
Exponential functions
THe standrd exponential function is exprressed as:
y = a(1±r)^t
Given the following parameters
h(x) = a = 200
s(x) = [tex](1.05)^{x-1}[/tex]
Combining both expressions will given 200 [tex](1.05)^{x-1}[/tex]
Hence the total amount of money she will have in her bank account as interest accrues after she deposits her $200 is 200 [tex](1.05)^{x-1}[/tex]
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Which property of equality was used to solve this equation? x − 5 = -14 x − 5 + 5 = -14 + 5 x = -9
Answer:
Additive property
Step-by-step explanation:
Given
[tex]x - 5 = -14[/tex]
Required
The property used
In the 2nd step, 5 was added to both sides, i.e.
[tex]x - 5+5 = -14 + 5[/tex]
The above is an illustration of additive property of equality, i.e. Adding or subtracting the same variable or constant to both sides of an equation
Do not round your answer. Type in the number with the decimal. 15% of 25 is
Answer:
to add on to what the other dude said its 4
Step-by-step explanation:
The following two-way table describes student's
after school activities. Find the probability that a
randomly selected student is in music/drama:
Grado
Sports
Music/Drama
Work
Sophomore
20
7
3
Junior
20
13
2
Senior
25
5
5
P(Music/Drama) = [?]
Round to the nearest hundredth.
Please HELP MEEE!!!!!!
Answer:
1/4
Step-by-step explanation:
Firstly, we need to get the total number of students on the table
We have this as;
20 + 20 + 25 + 7 + 13 + 5 + 3 + 2 + 5 = 100
Now, we sum up the values we have in the music/Drama column
We have this as;
7 + 13 + 5 = 25
so the probability of selecting a student in the music/drama group is the number of music/drama students divided by the total number
That would be
25/100 = 1/4
Logan was going to go to
Disneyland in America so he got
$450 from the bank. Then he
changed my travel plans, to go to
Eurodisney in Paris. How many
Euros will he have to spend?
Exchange Rate
GBP to Dollars £1: $1.50
GBP to Euros £1: €1.38
Given that PQ/ST = QR/TU= RS/US, select the postulate or theorem that you can use to conclude that the triangles are similar.
Answer: SSS Similarity Theorem (Choice A)
This is because we have three pairs of corresponding sides that form the same ratio, as shown by the given equation PQ/ST = QR/TU = RS/US.
That equation is basically the shorthand version of PQ/ST = QR/TU and QR/TU = RS/US combined together as one.
write a formula that describes the value of an initial investment of $100 that loses value at a rate of 8% per year compounded continuously
Answer:
[tex]A = 100(.92)^{t}[/tex]
Step-by-step explanation:
What are the slope of the y intercept of the line represented by the points shown on the table
8u^2- 42u^2
Help plzz
Answer:
- 34u^2
Step-by-step explanation:
8u^2 - 42u^2
= ( 8 - 42 )u^2
= - 34u^2
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{The only thing we can do to solve for this equation is to COMBINE}\\\large\textsf{the LIKE TERMS. }[/tex]
[tex]\mathsf{8u^2 - 42u^2}\\\mathsf{= (8u^2- 42u^2)}\\\mathsf{= 8 - 42 \rightarrow \bf -34}\\\textsf{Thus this means }\mathsf{8u^2 - 42u^2}\textsf{ has to equal to }\mathsf{ \bf -34u^2}\\\\\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \bf-34u} \mathsf{\bf ^2}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\frak{Amphitrite1040:)}[/tex]
Can someone help me I don't understand
Step-by-step explanation:
Hey there!
From the above right angled triangle ABC;
Taking Angle ABC as reference angle;
Angle ABC = ???
Perpendicular (p) = AC = 15
Base (b) = AB = 47
Now;
Taking ratio of sin;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep value;
[tex] \tan( \alpha ) = \frac{15}{47} [/tex]
Simplify it;
[tex] \tan( \alpha ) = 0.3191489[/tex]
Take tan to next side;
Angle ABC (alpha) = tan'(0.3191489)
Therefore, the measure of angle ABC is 17.70°.
Hope it helps!
Help me to do this question plz plz plz
Answer:
Unknown
Step-by-step explanation:
You need to reduce the fractions the best you can and solve from there :) not to sure tho I am only 13
97 percent of 245m what is the answer
Answer:
multiply them
Step-by-step explanation:
trust me on this one i love using that hack
Download guathmath and put it my code please it's an app with tutors it's faster! WFHUZJ
Answer: Advertisement?
Do I need an explanation? : Y e s I d o
plz help me with this
Answer:
x=100
Step-by-step explanation:
100 and x are vertical angles and vertical angles are equal
x = 100
Answer:
100 degrees
Step-by-step explanation:
Angle x is formed from two intersecting segments. Opposite angles of intersecting lines or segments are congruent therefore since the opposite angle is given at 100 degrees, x must also be 100.
Write the equation of the line perpendicular to y=1/2x+3 that contains (5,-4)
Answer:
y = -2x + 6
Step-by-step explanation:
y = -2x + b
-4 = -2(5) + b
-4 = -10 + b
6 = b
There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three gardens in square feet
Answer:
62 sq ft
Step-by-step explanation:
3 · 3 = 9
The first garden's area is 9 square feet.
7 · 7 = 49
The second garden's area is 49 square feet.
2 · 2 = 4
The third garden's area is 4 square feet.
We add 9 + 49 + 4.
9 + 49 + 4 = 62
The total area of the three gardens is 62 square feet.
Write the next thee numbers in each number pattern. Describe the pattern.
a) 2, 4, 3, 6, 5, 10, 9, 16, …
b) 7, 5, 8, 6, 9, 7, 10, …
Answer:
a) 2, 4, 3, 6, 5, 10, 9, 16, ...
Step-by-step explanation:
A school in Delhi has its own flag, which is rectangular and divided into 4 rows and 6 columns. The word ‘SCHOOL' is inscribed in the first row, ‘FLAG' in the fourth row, and a purple coloured rhombus is in the middle
The question is incomplete. The complete question is :
A school in Delhi has its own flag, which is rectangular and divided into 4 rows and 6 columns. The word ‘SCHOOL’ is inscribed in the first row, ‘FLAG’ in the fourth row, and a purple colored rhombus is in the middle, as shown in the given figure.
Based on this picture of the school flag, answer the following questions:
(a) What fraction of the flag has the purple rhombus?
Solution :
From the figure, the total number of squares in the flag of 4 rows and 6 columns are : 4 x 6 = 24 blocks
The purple colored rhombus is made on the half of the 4 blocks.
i.e. [tex]$\frac{1}{2} \times 4 = 2\ \text{blocks}$[/tex]
Therefore, the fraction of the flag that has the purple rhombus is :
[tex]$=\frac{2}{24}$[/tex]
[tex]$=\frac{1}{12}$[/tex]
Which expression is equivalent to (a^-8b)
(a^-5b^3)
Assume a≠0,b≠0.
Answer:
Step-by-step explanation:
I think it is C
Sophie Ruth is eating a
50
5050-gram chocolate bar which contains
30
%
30%30, percent cocoa.
How many grams of cocoa are in the chocolate bar?
grams
Answer:
15 grams
Step-by-step explanation:
There is a 50 gram chocolate bar that contains 30% cocoa. So we are basically finding 30% of 50. We break 30 into 3*10 and 50 into 5*10. 5*3 = 15.
Therefore, there are 15 grams of cocoa in the chocolate bar.
I hope this helps.
please help I beg you you will get marked branliest asap
Answer:
its D I think........ not 100% sure
a box has a length of 6x inches. the width equals one third the length, and the height equals half the length. if the volume equals 972 cubic inches, what does x equal?
a box has a length of 6x inches
l=6xthe width equals one third the length
w=[tex]\sf{\dfrac{1}{3}×6x }[/tex] w=2xthe height equals half the length.
h=[tex]\sf{\dfrac{1}{2}×6x }[/tex] h=3xwe know that,Volume of a rectangle box=l×w×h
According to the question,if the volume equals 972 cubic inches,
l×w×h=volume6x × 3x × 2x=972 36x^3=972 cubic unitx=972/36x=27Therefore:-The value of x is 27
a box has a length of 6x inches
so,
l=6xBut,the width equals one third the length
[tex]w=\dfrac{1}{3}×6x \\\\w=2x [/tex]
again,the height equals half the length.
[tex]h=\dfrac{1}{2}×6x \\\\h=3x[/tex]
we knows:-
Volume of a rectangle box=l×b×h
From the question,if the volume equals 972 cubic inches,
l×w×h=volume6x × 3x × 2x=97236x^3=972 cubic unitx=972/36x=27.Final solution:
.°.The value of x is 27.
Identify the slope and y-intercept in the line y=3/4 x - 3
m=
b=
Answer:
The slope is 3/4 and the y intercept is -3
Step-by-step explanation:
y=3/4 x - 3
This equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 3/4 and the y intercept is -3
Answer:
[tex]{ \bf{slope = \frac{3}{4} }} \\ \\ { \bf{y - intercept : - 3}}[/tex]
Step-by-step explanation:
General equation of line:
[tex]{ \bf{y = mx + b}}[/tex]
Slope is m and y-intercept is b:
[tex]{ \tt{y = \frac{3}{4}x - 3 }}[/tex]
Slope= ¾
y-intercept = -3
1. A triangular piece of wood has side lengths 14 cm, 19 cm and 30 cm. The angle between the 14 cm and 19 cm sides need to be known to see if it will fit properly into a cabinet. What is the angle, accurate to one decimal place, between the 14 cm and 19 cm sides?
Answer:
130.1°
Step-by-step explanation:
Using the cosine rule:
[tex] = { \cos }^{ - 1} ( \frac{ {14}^{2} + {19}^{2} - {30}^{2} }{2 \times 14 \times 19} )[/tex]
= 130.146°
The measure of angle is 72.8° (accurate to one decimal place ) between the 14 cm and 19 cm sides.
What is the Cosine Rule?The Law of Cosines (also called the Cosine Rule) is defined as it relates all three sides of a triangle with an angle of a triangle.
c² = a² + b² − 2ab cos(C)
The cosine rule, also known as the law of cosines, relates all 3 sides of a triangle with an angle of a triangle. it relates the lengths of the sides of a triangle to the cosine of one of its angles.
Given data as :
Length of side a = 14 cm
Length of side b = 19 cm
Length of side c = 20 cm
The angle of C is the between the side a and side b
According to the cosine rule,
c² = a² + b² − 2ab cos(C)
Substitute the values of a, b and c in the Cosine Rule,
20² = 14² + 19² - 2(14)(19)cos(C)
400 = 196 + 361 - 532cos(C)
400 = 557 - 532cos(C)
532cos(C) = 557 - 400
532cos(C) = 157
cos(C) = 157/532
cos(C) = 0.2951
(C) = cos⁻¹(0.2951)
(C) = 72.83
(C) = 72.8° (accurate to one decimal place)
Hence, the measure of angle is 72.8° (accurate to one decimal place ) between the 14 cm and 19 cm sides.
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The 4 answer it gives
X=-3
X=-1
X=1
X=3
Answer:
x=3
Step-by-step explanation:
If we look at the point of intersection on the graph they intersect at point (3,-1) but x=3 and y=-1 therefore x=3.
What is the order of rotational symmetry for the figure?
Answer:
it should be 3
Step-by-step explanation:
I hope this help
Is the data set "color of the coal taken from a rail car" quantitive or qualitative? If it is quantitative is it descents or continuous?
A quantitative , discrete
B quantitative continuous
C qualitative
D neither
Answer:
It's A.)
Step-by-step explanation:
Solve for t.
( 124 + 6 x 8 ) ÷ 2 = t
( 124 + 6 x 8 ) ÷ 2 = t
=> ( 124 + 48 ) ÷ 2 = t
=> 172 ÷ 2 = t
=> 86 = t
Hi there!
[tex]\large\boxed{t = 86}[/tex]
To solve, we must use PEMDAS:
P: Parenthesis
E: Exponents
M: Multiply
D: Divide
A: Add
S: Subtract
Evaluate the inside of the parenthesis:
(124 + 6 × 8)
Multiply first:
(124 + 48)
Evaluate:
124 + 48 = 172
Divide by 2:
172 ÷ 2 = 86 = t
A baseball stadium has 15,002 seats. The lower level has 50 fewer than three times as many seats as the upper level. The middle level has 40 more than twice as many seats as the upper level. You solved for x and found that the upper level has 2,502 seats.
Answer:
upper level chairs = 2,502 chairs
Lower level chairs = 7,456 chairs
Middle level chairs = 5044 chairs
Step-by-step explanation:
A baseball stadium holds 15,002 seats. The lower level has 50 fewer than three times as many seats as the upper level. The middle level has 40 more than twice as many seats as the upper level. The upper level has( ) seats.
Total chairs in the stadium = 15,002
Let
upper level chairs = x
Lower level chairs = 3x - 50
Middle level chairs = 2x + 40
Total = lower level + middle level + upper level
15,002 = (3x - 50) + (2x + 40) + x
15,002 = 3x - 50 + 2x + 40 + x
15,002 = 6x - 10
15,002 + 10 = 6x
15,012 = 6x
x = 15,012 / 6
x = 2,502
upper level chairs = x = 2,502 chairs
Lower level chairs = 3x - 50
3(2,502) - 50
= 7506 - 50
= 7,456 chairs
Middle level chairs = 2x + 40
= 2(2502) + 40
= 5004 + 40
= 5044 chairs
At a coffee shop, the first 100 customers'
orders were as follows.
Small
Large
Medium
Hot
un
48
22
Cold
8
12
5
5
What is the probability that a customer ordered
a large given that he or she ordered a cold
drink?
Rounded to the nearest percent, [? ]%
Answer:
people who ordered a cold drink=
[tex]8+12+5=25[/tex]
people who ordered a large cold drink= 5
[tex]probability= \frac{5}{25}[/tex] [tex]=\frac{1}{5}[/tex]
[tex]=\frac{1}{5} \times100=20~\%[/tex]
[tex]Answer: 20\%[/tex]
-----------------------
Hope it helps...
Have a great day!!
The probability that the customer ordered a large given that he or she ordered a cold drink is 5%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given the order of the first 100 customers in a coffee shop.
Number of customers who ordered a large which is also a cold drink = 5
Total number of customers = 100
Probability = Number of desired outcomes / Total number of outcomes
Substituting,
Probability = 5 / 100 = 0.05 = 5%
Hence the required percent is 5%.
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