The account balance at the end of two years (eight quarters) is $866.24.
Suki earned $66.24 interest during that time.
What do you mean by interest rate?
The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.
According to data in the given question,
We have:
Placed amount= A= $800
Interest rate (quarterly)= r= 4%
Time= t = 2 years
Now, we will using the formula below:
[tex]A=P(1+\frac{r}{n} )^{nt}\\=800(1+\frac{0.04}{4} )^{4*2}\\=800(1+0.01 )^{8}\\=800(1.0828)\\=866.24[/tex]
So, the account balance at the end of two years (eight quarters) is $866.24.
Then, we have to determine the earned interest during that time,
Earned interest= A-P
= 866.24 - 800
= 66.24
Therefore, she earned $66.24 interest during that time.
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Manny and Ada pool their money from a fundraiser. Manny raised 7 dollars less than twice what Ada raised.
Manny made $45 more than Ada. If the amount that Ada raised is represented by a then which of the following equations correctly models the information given?
(1) 2a-7-a=45
(2) 7-2a + a = 45
(3) 2a -7+ a = 45
(4) 2a-7+45=a
Identify the slope and y-intercept of the function y = -2x + 3.
OA. The slope is 2.
The y-intercept is (0, 3).
OB. The slope is 3.
The y-intercept is (0, -2).
OC. The slope is 3.
The y-intercept is (0, 2).
OD. The slope is -2.
The y-intercept is (0, 3).
The slope and the y-intercept of the function y = -2x+3 is -2 and (0,3).
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. The slope is constant (the same) anywhere on the line.
Slope is calculated as (change in y divided by change in x). i.e.
slope=dy/dx
What is y-intercept?The y- intercept of a graph is the point where the graph intersects the y-axis.
The x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.
So the y-intercept of the function y = -2x+3 is y= 3 i.e. (0,3).
slope = dy/dx = d/dx(-2x) + d/dx(3) = -2
⇒slope = -2.
Therefore slope of y = -2x+3 is -2 and y-intercept is (0,3).
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Write the Parabola in standard form
Y=-x² + 4x-1
Hair alon increaed it price for a hair cut from $25 to $50, what might happen to demand for that ervice? What hould happen if the oppoite occurred - if the price wa reduced from $50 to $25? What other factor could influence conumer demand in thee ituation? EXPLAIN
If the price is increased from $25 to $50 the demand will fall whereas when the price is decreased from $50 to $25 the demand for haircut will increase.
The price has the greatest influence on a product's demand. The cost of a thing and the demand for it generally go hand in hand. Demand of a product is inversely proportional to its price.
Lower prices increase demand, while higher prices decrease it. This is a result of consumer satisfaction levels.
The other factors influencing consumer demand are:-
Tastes and preferences.Consumer's income.Availability of substitutes.Number of consumers in the market.Consumer's expectations.Elasticity vs. inelasticityTo study the demand in detail visit;
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PLEASE HELP ME!!
Amelia needs to buy some cat food. At the nearest store, 2 bags of cat food cost $9.50 . How much would amelia spend on 3 bags of cat food?
Answer:
$14.25
Step-by-step explanation:
2 bags of cat food costs $9.50. To calculate the price of one, divide $9.50 in half.
$9.50/2 = $4.75
Now, to calculate how much she'd have to spend on 3 bags, you need to multiply $4.75 by 3
$4.75 x 3 = $14.25
by using division, we can find what 1 bag of cat food is worth. Then, we can use multiplication to find what 3 bags of cat food are worth
Process:Worth of One Bag
where w is the worth of one bag
Set up equation w = 9.50/2
Solve w = $4.75
Worth of Three Bags
where w is the worth of 3 bags
Set up equation w = 4.75(3)
Solve w = $14.25
Answer: $14.25Why is the area of a triangle 1/2 Bxh?.
By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).
Some properties of rectangle are ?The opposite sides are parallel and equally spaced apart, and each internal angle is 90 degrees.360 degrees are equal to the total of all internal angles.Both of the diagonals are identical in length and parallel to one another.A rectangle's perimeter is equal to 2a+2b units if its sides are of lengths a and b.A rectangle with sides that are a and b long has an area that is equal to ab sin 90 square units.Diagonally is the diameter of the circumference of a rectangle.To Prove:- Area of a triangle= 1/2 (base×height)
Diagonals of the rectangle divide it into two parts of equal areas.
Let ABCD be a rectangle.
In ΔABC and ΔADC,
AC=AC
By Alternate Interior Angles:
∠BAC=∠CAD
∠BCA=∠CDA
Hence, ΔABC≅ΔACD
∴ar(ΔABC) =ar(ΔACD)
Let ΔABC,
We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.
In rectangle ADBE,
we get,
ar(ΔABE)=ar(ΔADB)
Similarly, in rectangle ADCF,
ar(ΔADC)=ar(ΔACF)
Now, area of rectangle BCFE, from axiom,
=(length)⋅(breadth)
=AB⋅BC
=AD⋅BC
Also,
ar(BCFE)
=ar(ADBE) + ar(ADCF)
=2⋅ar(ΔADC) + 2⋅ar(ΔADB)
=2(ar(ΔADC) + ar(ΔADC)
=2(ar(ΔABC))
From (1) and (2),
2(ar(ΔABC)) = AD⋅BC
ar(ΔABC) = 1/2AD⋅BC
ar(ΔABC) = 1/2(base)⋅(height)
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2b - 15 = 33
What is the answer?
Answer:
Step-by-step explanation:
2b - 15 = 33
+15 +15
2b = 48
b = 24
Daiy i given a cale drawing with the route to her campite. The route to the campite i 28 cm on the drawing. The cale on the drawing i 1 : 300. What i the actual length of the route?
metre
According to scale drawing, the actual length of route is 84 metres.
The calculations will be based on the concept of ratio and proportion -
Ratio in real :: Ratio of scale drawing
Let us assume the actual length of route be x.
28 : x :: 1 : 300
Writing the ratio as fraction
28/x = 1/300
Cross multiplying the fraction
x = 28 × 300
Performing multiplication on Right Hand Side of the equation
x = 8400 cm
Converting centimetres to meters. As per the known fact, 100 cm = 1 metre
8400 cm = 84 meters
Thus, the actual length is 84 meters.
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△KIX can be mapped onto \triangle REM△REM by a rotation. If \text{m}\angle X = 117^{\circ}m∠X=117
∘
and \text{m}\angle I = 2^{\circ}m∠I=2
∘
, find \text{m}\angle Rm∠R.
\text{m}\angle Rm∠R
can
be determined. \text{m}\angle R =m∠R=
The measure of angle R, found through the angle sum property of a triangle and corresponding angles in ΔKIX and ΔREM is m∠R = 61°
What are corresponding angles?Corresponding angles are angles in two congruent or similar triangles, located between a pair of segments in one triangle that are congruent to a pair of segment in the other triangle
The details of the question are;
The transformation that maps triangle ΔKIX unto triangle ΔREM is a rotation.
Please see attached the example drawing of ΔKIX and ΔREM created with MS Excel.
A rotation transformation is a rigid transformation, therefore, the side lengths and shape of triangle ΔKIX is preserved in the image of the triangle, ΔREM
The measure of angle ∠X in triangle ΔKIX is ∠X = 117°
The measure of angle ∠I in ΔKIX is ∠I = 2°
∠K + ∠I + ∠X = 180° (angle sum property of a triangle)
The measure of angle ∠K = 180° - (∠X + ∠I)
Therefore;
m∠K = 180° - (117° + 2°) = 61°
m∠K = 61°
Based on the naming of the triangles ΔKIX and ΔREM, we have;
∠K corresponds to ∠R, ∠I corresponds to ∠E, and ∠X corresponds to angle ∠R, therefore;
∠K ≅ ∠R, ∠I ≅ ∠E, ∠X ≅ ∠R, which by the definition of congruency indicates;
∠K = ∠R, ∠I = ∠E, ∠X = ∠R
m∠R = m∠K = 61°
m∠R = 61°
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Evaluate 23x-1 for x = 1.
A: 4
B: 1
C: 7
D: 8
Answer:
23-1=22
Step-by-step explanation:
The average class size at Lexington Middle School is 21 students, which is 5% larger than it was a decade ago. What was the average class size then?
Proportionately, the average class size at Lexington Middle School a decade ago was 20.
What is the proportion?Proportion is the ratio or relative numerical relationship of two or more values equated to one another.
Proportions are fractional values, showing how much of a number is contained in another or the whole.
Proportions are depicted as decimals, fractions, or percentages.
The current average class size at Lexington Middle School = 21 students
The percentage increase in class size = 5%
Let the current average class size = 105% (100 + 5)
The previous decade's average class size = 21/105% = 20
Thus, a decade ago, the average class size was 20, proportionately increasing by 5%.
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Factor [tex]6x^{2} -2x=0[/tex]
6x^2 - 2x = 0
-> 2x ( 3x - 1 ) = 0
For this equation to hold true, either 2x or 3x-1 must be equal to 0.
-> 2x = 0 - > x = 0
-> 3x - 1 = 0 -> x = 1/3
What is the sum
of the solutions to
x² - 7 = 6x?
Step-by-step explanation:
x² - 7 = 6x
x² - 6x - 7 = 0
the generation solution to such a quadratic ratatouille
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a) =
= (6 ± sqrt((-6)² - 4×1×-7))/(2×1) =
= (6 ± sqrt(36 + 28))/2 = (6 ± sqrt(64))/2 =
= (6 ± 8)/2 = (3 ± 4)
x1 = 3 + 4 = 7
x2 = 3 - 4 = -1
the sum of both solutions is : 7 + -1 = 7 - 1 = 6
math pls help!!!!! rewarding points
Answer:
x=90. 3x=270
Step-by-step explanation:
120•6=45•2+135•2+4x
X=90
3X=270
Rebecca is x years old.
Mary is 8 years older than Rebecca. Jill is three times older than Mary. The sum of their ages is 67.
(a) Form an equation in terms of x
(b) Solve the equation and work out Rebecca’s, Mary’s and Jill’s ages.
Given that Rebecca is x years old and Mary is 8 yrs older than her , so the age of Mary will be;
[tex]\longrightarrow Age_{Mary}= x+8 [/tex]
Again Jim is 3 times older than Mary, so the age of Jim will be,
[tex]\longrightarrow Age_{Jim}= 3(x+8) [/tex]
Now we are given that the sum of their ages is 67. So that ;
Equation in terms of x :-
[tex]\longrightarrow x + (x+8) +3(x+8)=67 [/tex]
Solving the equation,
[tex]\longrightarrow x + x +8+3x+24=67\\ [/tex]
[tex]\longrightarrow 5x + 32 =67\\ [/tex]
[tex]\longrightarrow 5x = 67-32 \\ [/tex]
[tex]\longrightarrow 5x = 35\\ [/tex]
[tex]\longrightarrow x = 7 [/tex]
So ,
Age of Rebecca= x = 7 yrs Age of Mary = x+8 = 15yrsAge of Jim =3(x+8) = 45 yrs .And we are done!
find the sum of the interior angles of a polygon with 28 sides
The sum of the interior angles of a polygon with 28 sides is 4680°.
According to the question,
We have the following information:
The number of sides of a polygon = 28
We know that the following formula is used to find the sum of the interior angles of a polygon:
(n-2)*180 where n is the number of sides
Putting the value of n in this formula for the given polygon:
(28-2)180
We will first solve the bracket and then we will multiply the obtained result by 180:
26*180
4680°
Hence, the sum of the interior angles of a polygon with 28 sides is 4680°.
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The distance traveled by a cruise ship varies directly with the number of hours it travels. After 2 hours, a cruise ship travels 30 miles. After 4 hours, a cruise ship travels 60 miles. Determine the time it would take the cruise ship to travel 75 miles.
It will take the ship 5 hours to travel 75 miles
What is variation?A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
if it takes 2 hours to cover 30 miles by the ship and 4 hours to cover 60 miles.
let d be the distance covered in miles and t time taken in hours
The d ∝ t
introducing a constant
d = kt
when d = 30, t = 2
30 = 2k
k = 30/2
k = 15
The equation relating d and t is
d = 15t
to find t when d = 75, making t the subject of the equation
t = d/15
t = 75/15
t = 5 hours
In conclusion, 5 hours is the time taken to cover 75 miles.
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Find the 97th term of the arithmetic sequence -16, 2, 20, ...
Answer: 1712
Step-by-step explanation:
[tex]a_{n} = a_{1} + d(n -1)[/tex]
[tex]a_{1} = -16[/tex]
[tex]d = 2 - (-16) = 18\\[/tex]
[tex]20 - 2 = 18[/tex]
[tex]-16 + 18(n+1)[/tex]
[tex]-16 + 18(97+1)[/tex]
[tex]-16 + (1728)\\[/tex]
[tex]1712[/tex]
I need help with this problem asap
Answer:
bro that question is absolute whack
select all that apply. in a population of 250 students, 60% are whites, 20% are latinos, 15% are blacks, and 5% others. in a proportionate stratified random sample of 120, group of answer choices the number of whites selected is 72. the number of blacks selected is 50. the number of latinos selected is 37. the number of other racial and ethnicity background selected is 6.
In proportionate stratified random sample of 120, 72 are Whites, 24 are latinos, 18 are blacks, and 6 are others.
From the question, we have
In a population of 250 students, 60% are whites, 20% are latinos, 15% are blacks, and 5% others.
sample = 120
Number of whites = 60% of 120
= 0.6 × 120
=72
Number of latinos = 20% of 120
= 0.2 × 120
=24
Number of blacks = 15 % of 120
= 0.15 × 120
= 18
Number of others = 5% of 120
= 0.05 × 120
= 6
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. We frequently do one of the fundamental mathematical procedures. Using multiplication tables is the most obvious application. To represent the repetitive addition of one number to another, mathematicians multiply two numbers. Natural numbers, fractions, integers, whole numbers, and other types of numbers can be included. When M is multiplied by n, M is either added to itself 'n' times or subtracted from itself.
Complete question:
select all that apply. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. In a proportionate stratified random sample of 120, ______.
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HELLPPPPPP I DONT UNDER
Answer:
y=16
Step-by-step explanation:
Notice that the first equation was multiplied by 4, so you have to multiply the result by 4 to keep it as a true equation
3.
How many times the value of the 7 in 107 is the value of the 7 in 170?
Answer:
14
Step-by-step explanation:
Work out an estimate for
√4.98 +2.16×7.35
The estimated value of √4.98 +2.16×7.35 = 18.1075
Mathematical Operations:Operators are Mathematical methods that emphasize particular actions like adding, dividing, and adding multiple times are known as Mathematical Operations. The basic mathematical operations are 4 types they are Addition, Subtraction, Multiplication, and Division.
While we use mathematical operations to solve a problem we will use the BODMAS rule as given below
B - Brackets (Calculating numerical parts in brackets comes first )
O - Orders (Simplify powers and square roots)
D - Division (Complete division parts )
M - Multiplication (complete multiplication)
A - Addition (complete additions part )
S - Subtraction ( End with subtractions )
Here we have
√4.98 +2.16×7.35
Here the value of √4.98 = 2.2315 (approximately)
From above value
=> √4.98 +2.16×7.35
=> 2.23 + 2.16 × 7.35
By using the BODMAS rule
=> 2.23 + 15.876 [ Do multiplication ]
=> 18.106 [ Do adding ]
Therefore,
The estimated value of √4.98 +2.16×7.35 = 18.106 (approx)
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w/5=3
can someone please help me on this asap
Reason:
Multiply both sides by 5 to undo the division.
w/5 = 3
5*(w/5) = 5*3
w = 15
As a way to check, plug in w = 15
w/5 = 3
15/5 = 3
3 = 3
We get a true statement at the end to confirm w = 15 is indeed the answer.
a local ice cream shop has a special deal on thursdays. buy a waffle cone for $3 and get each scoop for $1.50. what would be the rate of change in this word problem?
Answer: the rate change in this problem would be by 1.50
Step-by-step explanation:
The rate of change in this word problem will be 2.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A local ice cream shop has a special deal on Thursdays. buy a waffle cone for $3 and get each scoop for $1.50.
Now,
The rate of change will be find as;
The rate of change = $3 / $1.50
= 2
Thus, The rate of change in this word problem will be 2.
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John was setting up nametags for a business meeting. His supervisor placed the first three rowsthe first row has 3 nametags, the second row has 5 nametags, and the third row has 8 nametags.
How many nametags should be in the fourth row?
The number of nametags that should be in the fourth row is 12
How to calculate the value?It should be noted that this information illustrates sequence.
In this case, the supervisor placed the first three rowsthe first row has 3 nametags, the second row has 5 nametags, and the third row has 8 nametags.
The difference will be:
5 - 3 = 2
8 - 5 = 3
Therefore, the next one will have a difference of 4. This will be:
= 8 + 4
= 13
Check: 12 - 8 = 4
Therefore, the nametags should be 12.
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solve for X in the angle diagram
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees.
So we have [tex]108+47+(2x+11)=180[/tex]
Solve for x.
[tex]47+(2x+11)=72[/tex]
[tex]2x+11=25[/tex]
[tex]2x=14[/tex]
[tex]x=7[/tex]
Answer:
7
Step-by-step explanation:
108+47=155
180-155=25
25-11=14
14/2=7
Graph the equation y+4=x
Answer:
here you go..
Step-by-step explanation:
please mark brainliest...
Line SD is a line of symmetry for figure ASMHZDPX. Tyler says that ASDPX is congruent to SMHZD because side
Tyler's statement is incorrect , SMHZD and SAXPD are correct congruence for the given pentagons.
a.
Tyler's congruence is incorrect because line SD is a line of symmetry for ASMHZDPX so ASDPX and SMHZD are about SD symmetry therefore the figure division must be start from S or D.
b.
SMHZD And SAXPD are correct congruence for the given pentagons because they both start with the letter S which is in the line of symmetry SD.
Therefore Tyler's statement is incorrect , SMHZD and SAXPD are correct congruence for the given pentagons.
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Write the following expression in simplest form. the expression quantity negative three fifths times x minus 7 end quantity minus quantity negative 12 plus three tenths times x end quantity
Answer:
[tex]-\frac{9}{10} x+5[/tex]
Step-by-step explanation:
[tex](-\frac{3}{5} x-7)-(-12+\frac{3}{10} x)\\\\-\frac{3}{5} x-7+12-\frac{3}{10} x\\\\-\frac{3}{5} x+5-\frac{3}{10} x\\\\-\frac{6}{10} -\frac{3}{10}x+5\\\\-\frac{9}{10} x+5[/tex]
