Answer:
5 years
Step-by-step explanation:
We are given;
Initial value of the car = $12,500 Rate of Depreciation = 13% per year New value (after depreciation) = $6,250 (half the initial value)We are required to determine the time taken for the value of the car to depreciate to half the original value.
We need to know the depreciation formula;New value = Initial value ( 1 - r/100)^nTherefore;
$6,250 = $12,500(1 - r/100)^n
0.5 = (1 - 13/100)^n
0.5 = 0.87^n
Introducing log on both sides;
log 0.5 = n log 0.87
Therefore;
n = log 0.5 ÷ log 0.87
= 4.977
= 5 years
Therefore, it takes 5 years for the value of the car to depreciate to half the initial value.
There are 6 students that like milk. There is one student who likes water. How many fewer students like water than milk?
Answer:
5
Step-by-step explanation:
If 5x - 3y = 1 and x = 2y - 4, then x • y = ?
I don’t need an explanation of the answer since it’s multiple choice, but feel free to give an explanation if you want :) thank you and please answer quickly this is due tomorrow!!
Answer:
x = 2, y = 3
Step-by-step explanation:
i) It is given that 5x - 3y =1
ii) It is also given that x = 2y - 4
iii) we can substitute the value of x from ii) in the equation in i) and we will get 5(2y - 4) - 3y = 1 ⇒ 10y - 20 -3y = 1 ⇒ 7y = 21 ∴ y = 3
iv) substituting the value of y obtained in ii) we get x = (2 × 3) - 4 = 6 - 4 = 2.
v) Therefore x = 2.
PLEASE HELP ME
Describe the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z”.
Answer:
the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z” are
i) reflect the the triangle about the x- axis.
ii) shift the result of i) by 1 upwards
iii) shift the result of ii) by 5 to the left
Step-by-step explanation:
the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z” are
i) reflect the the triangle about the x- axis.
ii) shift the result of i) by 1 upwards
iii) shift the result of ii) by 5 to the left
The sum of two numbers is 15. The first number is half of the second number. What are the two numbers?
Answer:
10 5
Step-by-step explanation:
10 ÷ 2 = 5 and 5 + 10 = 15
Answer:
5 and 10
Step-by-step explanation:
X×Y=15
X=15-Y
X=Y/2
Y/2=15-Y
Add Y to both sides
3Y/2=15
3Y=30
Y=10
X=5
If the arc length shown in blue is 21.3 inches, then 0 to the nearest hundredth of a
radian is
Answer: [tex]\theta\approx1.78\ rad[/tex]
Step-by-step explanation:
By definition, the Arc lenght can be calculated with the following formula:
[tex]s=r\theta[/tex]
Where "s" is the Arc lenght, "r" is the radius and [tex]\theta[/tex] is the central angle measured in radians.
From that equation you can solve for [tex]\theta[/tex] dividing both sides of the equation by the radius "r", then:
[tex]\frac{s}{r}=\frac{r\theta}{r}\\\\\theta=\frac{s}{r}[/tex]
According to the information given in the exercise:
[tex]s=21.3\ in[/tex]
And you can identify in the figure that the radius of the circle is:
[tex]r=12\ in[/tex]
Therefore, you can substitute values into the equation:
[tex]\theta=\frac{21.3\ in}{12\ in}[/tex]
Finally, evaluating, you get the following result:
[tex]\theta=1.775\ rad[/tex]
Rounded to the nearest hundredth of a radian:
[tex]\theta\approx1.78\ rad[/tex]
Help please time limit...Amanda is choosing between two exercise routines.
In Routine #1, she does only running, 15.5 burning calories per minute.
In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 12.75 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
Use t for the number of minutes spent running, and solve your inequality for ..
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Step-by-step explanation:
Routine # 1;
Calories burned in running = 15.5 per minute
Let,
t be the minutes spent running.
T = total calories burned
T = 15.5t
Routine # 2;
Calories burned while walking = 22 calories
Calories burned while running = 12.75 per minute
T = 12.75t + 22
For burning more calories in Routine 1;
Routine 1 > Routine 2
[tex]15.5t>12.75t+22\\15.5t-12.75t>22\\2.75t>22\\[/tex]
Dividing both sides by 2.75
[tex]\frac{2.75t}{2.75}>\frac{22}{2.75}\\t>8[/tex]
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Keywords: linear inequality, division
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If 24 people have the flu out of 360 people, how many would have the flu out of
900?
If 24 people have the flue out of 360 people then out of 900, 60 people would have flue if solved through percentage.
What is a percentage?It is a ratio expressed as a fraction of 100. it's expressed using the sign %.
How to calculate percentage?The percentage of individuals gets affected from flue out of 360 is 24*100/360
=2400/360
=6.67%
Then per 6.67% out of 900 approx 60 (900*6.67%) people would be affected from flue.
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Picture attached please help!! I don't understand these questions.
Answer:
a, e
Step-by-step explanation:
a. function A has a slope of -2/3. the negative means it goes down. function B is going down on the graph so both functions have neg. rates of change.
b. function A's slope is -2/3. function b has a slope of -1.
c. since both functions slopes aren't the same they are not parallel.
d. 2/3 is a lesser rate of change than 1.
e. looking at the graph, function b is linear. A is linear since the "x" is not squared, cubed, etc.
The bodega offers two deals on chicken nuggets. In deal #1 you can buy 5 chicken nuggets for $7.50. In deal #2 you can buy 8 chicken nuggets for $10.00. In which deal is each chicken nugget cheaper.
Answer:
The 2nd deal is better
Step-by-step explanation:
First you divide the chicken nuggets by the price and then find how much one chicken nugget costs. In this case $10 divided by 8 is $1.25 while $7.50 divided by 5 is $1.50. The first deal costs more for one chicken nugget so deal 2 is better
Answer:
deal 2 is better the chicken nuggets are cheaper and you could have more chicken nuggets even though it cost more then deal 1, 1 chicken nugget is cheaper in deal 2 than it is in deal 1 so I think you should go for deal 2 Hope I Helped :)
Step-by-step explanation:
what of the following is not a characteristic of all parallelograms diagonals bisect each other be opposite angles are congruent C diagonals are angle bisectors deep is the sides are congruent
The correct option that is not a characteristic of all parallelograms is C, 'diagonals are angle bisectors,' as it does not apply to every parallelogram, unlike the other options listed.
Explanation:The question is related to the properties of parallelograms, and specifically, it asks which option is not a characteristic of all parallelograms. To answer this, we must review the properties of parallelograms:
Diagonals bisect each other.Opposite angles are congruent.The sides are parallel, but not necessarily congruent.Option A (Diagonals bisect each other) and Option B (Opposite angles are congruent) are indeed true characteristics of parallelograms. However, diagonals being angle bisectors is not a general characteristic of all parallelograms, making it incorrect for Option C. Finally, Option D (The sides are congruent) describes a property specific to a rectangle or a rhombus rather than all parallelograms. Thus the correct answer is C, diagonals are angle bisectors, as it is not a defining feature for all parallelograms. Parallelograms have diverse shapes like rectangles, squares, and rhombi, and this property doesn't apply universally.
PLEASE HELP ME
Describe the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z”.
Answer:
The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.
Explanation:
By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.
You can check that analitically
Departing from the triangle: XYZ
Translation 5 units to the left: (x,y) → (x - 5, y) Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)Translation 1 unit down: (x,y) → (x, y-1)
(-11,2) → (-11, 2 - 1) = (-11, 1)(-9,7) → (-9, 7 - 1) = (-9, 6)(-7, 2) → (-7, 2 - 1) = (-7, 1)Reflextion accross the x-axis: (x,y) → (x, -y)
(-11, 1) → (-11, -1), which are the coordinates of vertex X"(-9, 6) → (-9, -6), which are the coordinates of vertex Y""(-7, 1) → (-7, -1), which are the coordinates of vertex Z"
Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.
1/4 of 1% expressed as a decimal
Answer:
0.0025
Step-by-step explanation:
:)
1/4 of 1%, when expressed as a decimal, is equal to 0.0025
What do we mean by percentage?A percentage is a ratio with the second part always equal to 100. It represents parts per hundred.
How do we solve the given question?We have been given 1%.
We replace percentage in fraction, and then fraction to decimal.
1% = 1/100 = 0.01
Now, we need to calculate 1/4th of this value, that is, 0.25 multiplied by the above value,
= 0.25 * 0.01 = 0.0025
So, our answer is 0.0025.
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If the base angles of an isosceles triangle each measure 37° then the vertex angle measures 106°
Answer:
the given statement is true.
Step-by-step explanation:
i) It is given that the base angles of an isosceles triangle each measure 37°.
ii) Adding the values of the base angles is = 37° + 37° = 74°
iii) from the property of triangles we know that the sum of all the angles in a triangle is equal to 180°
iv) let the vertex angle be = y°
v) Therefore we can say from ii), iii) and iv) above that
74° + y° = 180°
vi) therefore the vertex angle y = 180° - 74° = 106°
Hence the given statement is true.
Show work please I don’t understand it.
Answer:
2<6
Step-by-step explanation:
2(n+3)-4
(2n + 6)-4
2n + 2
--------(both can be divided by 2)
2 2
n=2
2<6
the second line the the last i believe im not so sure about the graphing but i hope starting you off with 2<6 helps
What is the they answer for
5+4(n+9)=-3
Answer:x=-11
Step-by-step explanation:
a principal that will amout to 150000 for 8 years at 9/1/2 %
The principal amount is 85227.27 and the interest is 64772.73.
Solution:
Given:
Amount (A)= 150000
Number of years (n)= 8
Rate of interest (r)= [tex]9\frac{1}{2}\%=\frac{19}{2}\%[/tex]
To find: The principal (P)
We know that the principal is the sum of amount and interest. That is, [tex]\bold{P+I=A}[/tex]
This can be written as [tex]\bold{I=A-P \rightarrow(1)}[/tex]
The formula of simple interest is [tex]\bold{I=\frac{Pnr}{100} \rightarrow(2)}[/tex]
On equating (1) and (2) we get,
[tex]\Rightarrow\bold{A-P=\frac{Pnr}{100}}[/tex]
On substituting the values we get,
[tex]\Rightarrow\bold{150000-P=\frac{P\times8\times19}{100\times2}}[/tex]
On solving we get,
[tex]\bold{\Rightarrow 150000-P=0.76P}[/tex]
On grouping the like terms together we get,
[tex]\bold{\Rightarrow 150000=0.76P+P}[/tex]
[tex]\bold{\Rightarrow 150000=1.76P}[/tex]
[tex]\bold{\Rightarrow P=\frac{150000}{1.76}}[/tex]
[tex]\bold{\Rightarrow P=85227.2727\approx85227.27}[/tex]
If principal is 85227.27, then the interest will be [tex]\bold{I=150000-85227.27\rightarrow64772.73}[/tex]
Tavon has a gift card for $ 155 that loses $ 3.50 for each 30-day period it is not used. He has another gift card for $ 135 that loses $ 3 for each 30-day period it is not used.
a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal value?
Answer:
A) 40
B) $ 15
Step-by-step explanation:
A)An equation for the number of 30-day periods until the value of the gift cards will be equal
Let x be the number of time periods for which the gift card is not used, then
For the gift card $ 155 if it is not used for x periods, then the amount that will be lost is
155 - 3.50 x---------------------(1)
For the gift card $ 135 if it is not used for x periods, then the amount that will be lost is
135 - 3x---------------------- (2)
Now when both the amount lost is equal
[tex]155 - 3.50x = 135 - 3x[/tex]
solving the equation, we get
[tex]155 -135 = -3x + 3.50x[/tex]
20 = 0.5x
[tex]x = \frac{20}{0.5}[/tex]
x = 40
Thus the value of gift cards will be equal for 40 ,30 day periods.
B)The value of each card be when they have equal value
The two cards will have equal value after 40 30 day periods, this denotes that at this time, the value of each card will be equal.
Then
[tex]155 - 3.50x = 135 - 3x[/tex]
substituting x = 40, we get
[tex]155 - 3.50(40)= 135 - 3(40)[/tex]
[tex]155 - 140= 135 - 120[/tex]
[tex]15 =15[/tex]
when they have equal value, the value of each card will be $15
if a=(-2 -4) and b=(-8 4) what is the length of AB
Use the distance formula Sqrt ( (x2-x1)^2 +(y2-y1)^2)
Distance = sqrt ( (-8 - -2)^2 +(4- -4)^2)
Distance = sqrt(-6^2 + 8^2)
Distance = sqrt ( 36 + 64)
Distance = sqrt(100)
Distance = 10
The length is 10
Answer: 10 units
Step-by-step explanation: took test hope this helps
How do you solve 9+x/9=7/3
Answer:
-60
Step-by-step explanation:
9+x/9=7/3
x/9=7/3-9
x/9=7/3-27/3
x/9=-20/3
x=(-20/3)(9)
x=-180/3
x=-60
A square table has an area of "2116" square inches. A tablecloth hang 3 inches over each end of the table, What is the area of the part of the tablecloth that hangs over the table?
The area of the part of the tablecloth that hangs over the table is 285 square inches
Step-by-step explanation:
In order to find the area of table cloth that hangs over the table, we have to find the area of table and the total area of table cloth.
Given
Area of table = [tex]A_t = 2116\ in^2[/tex]
To find the side of the square
[tex]A_t = s^2\\s^2 = 2116[/tex]
Taking Square root on both sides
[tex]\sqrt{s^2} = \sqrt{2116}\\s = 46\ inches[/tex]
When the table cloth is hanged, 3 inches are left to hang over this means that the side will now be: 46+3 = 49 inches
The area of table cloth = [tex]A_c = 49*49 = 2401\ in^2[/tex]
The area of table cloth that will be hung over the table is:
[tex]A_c-A_t\\= 2401-2116\\= 285\ in^2[/tex]
Hence,
The area of the part of the tablecloth that hangs over the table is 285 square inches
Keywords: Square, side
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y
=
−
2
x
2
+
113
x
−
497
y=−2x
2
+113x−497
The company should sell each widget for $28.25, to the nearest cent.
To maximize profit, we need to find the vertex of the parabola represented by the profit equation y = -2x^2 + 113x - 497. Since the coefficient of x^2 is negative, the parabola opens downwards, and the vertex represents the maximum point. The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula -b/2a.
For the equation y = -2x^2 + 113x - 497, a = -2 and b = 113. Plugging these values into the formula gives us: x = -113 / (2 × -2) = -113 / -4 = 28.25. Therefore, to maximize profit, the company should sell each widget for $28.25, to the nearest cent.
How do you do inverse operation on a fraction ( y/3 ) = -6
[tex]\frac{-1}{18}[/tex]
Solution:
Given expression is [tex]\frac{y}{3}=-6[/tex]
To find the inverse of y.
⇒ [tex]\frac{y}{3}=-6[/tex]
Do cross multiplication.
⇒ y = –6 × 3
⇒ y = –18
Inverse of y means reverse the function.
We know that inverse of y is [tex]\frac{1}{y}[/tex].
⇒ [tex]\frac{1}{y}= \frac{-1}{18}[/tex]
Hence, inverse of y is [tex]\frac{-1}{18}.[/tex]
The sum of twice a number and half the number is 10.
how would i write the equation?
66pts
Hello there i hope you are having a good day :) Your question : The sum of twice a number and half the number is 10.
Answer would be : 2x + x/2 = 10
Hopefully that helps you ❤
Answer:
2x+x/2 = 10
Step-by-step explanation:
x is the unknown value.
2x would be used to represent the unknown value of twice that number.
/2 would be used to represent half the number.
Hope this helps you!
How do use distributive property for -2.5(4x-8)+1.2(5x-1)
Answer:
Step-by-step explanation:
whats the square root of 64
Answer:
The square root of 64 is 8. 8*8=64
Hope this helps,
:)
The surface area of a tabletop is 5760 square inches. Which expression shows this number in scirntific notation?
Answer:
Scientific notation = 5.76 x 10³ square inches
Step-by-step explanation:
Standard notation = 5,760 square inches
Scientific notation = 5.76 x 10³ square inches
any help would be great
Graph the equation by plotting three
points. If all three are correct, the line
will appear.
-3y = 2x - 7
Answer:
Step-by-step explanation:
there's your graphed line
credits to desmos graphing calculator
how to solve u/5+3=1
First subtract 3: u/5 = -2
Now, because u is divided by 5, we can multiply by 5 to get u on its own.
u = -10
To check, -10/5 + 3 = 1
-2 + 3 = 1
1 = 1
This leaves us with a true statement, so the answer is correct.
In 2004, about $38 out of every $100 spent on advertising was spent on television advertising. The amount spent on radio advertising was about 21% as much as was spent on television advertising. How much of every $100 spent on advertising was spent on radio advertising?
Answer:
$8
Step-by-step explanation:
Given: Television advertising= $38 out of every $100 spent on advertising.
Radio advertising= 21% as much as was spent on television ads.
As given there are $38 spent on television ads on every $100 of advertising.
∴ Amount spent on television ads= [tex]\frac{38}{100}[/tex]
Now, finding amount spent on radio advertising on every $100 spent on advertising.
We know, The amount spent on radio advertising was about 21% as much as was spent on television advertising.
∴ Amount spent on radio advertising= [tex]\frac{38}{100} \times \frac{21}{100}[/tex]
⇒ Amount spent on radio advertising= [tex]\$ 0.0798[/tex]
To know the amount spent on radio advertising on every $100 spending on advertising.
Amount spent on Radio advertising on every $100 spending= [tex]0.0798\times 100= \$ 7.98 \approx \$ 8[/tex]
Hence, $8 spent on radio advertising on every $100 spending.
About $7.98 out of every $100 spent on advertising was allocated to radio advertising, based on the information that $38 out of every $100 was used for television advertising and radio advertising accounted for 21% of the television advertising amount.
In 2004, about $38 out of every $100 spent on advertising was spent on television advertising. To find out how much of every $100 was spent on radio advertising, which was about 21% as much as was spent on television advertising, we apply the following calculation:
Amount spent on radio advertising = Television advertising amount × (Radio advertising percentage / 100)
Amount spent on radio advertising = $38 × (21 / 100)
Amount spent on radio advertising = $7.98
Therefore, $7.98 out of every $100 spent on advertising was spent on radio advertising.