Answer:
Part A : $6.23
Part B : $6.48
Step-by-step explanation:
Let's apply the Simple Interest Formula, which is :
Simple Interest = Principal Amount x Interest rate x Time Period
In one year :
I = 5.99 x 4% x 1I = $0.24Cost = $5.99 + $0.24Cost = $6.23In 2 years :
I = $6.23 x 4% x 1I = $0.25Cost = $6.23 + $0.25Cost = $6.48A certain car was purchased for $22,500. The car
has a resale value of $14,500 after a useful life of 6
years. What is the annual depreciation expense for
this car?
Annual depreciation expense = $ [?]
Round to the nearest hundredth.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\$14500\\ P=\textit{initial amount}\dotfill &\$22500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6\\ \end{cases}[/tex]
[tex]14500=22500(1 - \frac{r}{100})^{6}\implies \cfrac{14500}{22500}=\left( \cfrac{100-r}{100} \right)^6\implies \cfrac{29}{45}=\left( \cfrac{100-r}{100} \right)^6 \\\\\\ \sqrt[6]{\cfrac{29}{45}}=\cfrac{100-r}{100}\implies 100\sqrt[6]{\cfrac{29}{45}}=100-r \\\\\\ r=100-100\sqrt[6]{\cfrac{29}{45}}\implies r\approx \stackrel{\%}{7.06}[/tex]
Meghan’s bank account is charged $9.95 per month for an online newspaper subscription. How could you represent the change in her account balance after three months of charges?
·⎯.=
After three months, the change in her account balance is $.
A number line from negative 30 to 0, split into 3 equal sections of negative 9.95.
Convince Me!
Meghan’s bank account is charged 3 times. Without calculating, how can you determine whether this would be a negative or positive change to her account? Explain.
The expression for the amount of Meghan's newspaper for three months will be T = C - (9.95 x 3).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, expansion and division.
The account balance total can be calculated with the following equation where the variable T represents the final balance while the variable C represents her current balance before the three months.
T = C - (9.95 * 3)
The monthly charge is multiplied by the three months that Megan will be charged and then discounted from her current balance in order to give the new Total Balance after paying the subscription for the three months.
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meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.
The probability that it will not rain on both Saturday and Sunday will be 0.2268.
How to calculate probability?From the information, meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.
The probability that it will not rain on both Saturday and Sunday will be:
= (1 - 42%) × (1 - 54%)
= 0.58 × 0.46
= 0.2268
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PLEASE HELP ME ANSWER THIS PROBLEM
Answer:
9
Step-by-step explanation:
because 3*4=12 then divide 108 by 12 giving you 9
Does anyone know how to do this Venn diagram question?
Answer:
[tex]\frac{8}{30}[/tex]
Step-by-step explanation:
Card(AUBUC)= Card(A)+card(B)+card(C)-Card (A∩B) -Card( A∩C)-Card(B∩C) +Card(A∩B∩C)
= 21 + 14 + 15 - 10 - 8 - 4 + 2
= 30
Then
Card(AUBUC) = 30
Card( A∩C) = 2 + 6 = 8
[tex]p\left( A\cap C\right) =\frac{card\left( A\cap C \right) }{card\left( A\cup B\cup C \right) }[/tex]
[tex]=\frac{8}{30}[/tex]
What is the probability of randomly selecting a bird
At a local market, Vijay buys two spice blends.
• Tandoori Seasoning: 3.5 ounces for $3.60 an ounce
• Garam Masala: 4 ounces for $2.75 an ounce
He calculates the total cost for the spice blends using the steps shown below.
Use the drop-down menus to explain Vijay's error.
Vijay's Calculation
Garam
Masala
Tandoori
Seasoning
Total Cost
of Tandoori
Seasoning
Total Cost
of Garam
Masala
Total Cost
of Both
Spices
2.88
3.60
x 3.5
2.75
4
+ 11.00
13.88
11.00
1800
+1080
2.880
Click the arrows to choose an answer from each menu.
The total cost of Choose.....
is incorrect. Vijay
Choose...
▼
when multiplying Choose...
cost of both spice blends is actually Choose...
x
Y
The total
Answer:
Step-by-step explanation:
The total cost of Tandoori Seasoning is incorrect.
Vijay made an error when multiplying 3.5 ounces by $3.60 .
Cost of both spice blends is actually $23.6.
What is a error?
it is defined as the deviation of an entitiy from its corrected value while calculating.
Now it is given that,
Tandoori Seasoning = 3.5 ounces for $3.60 an ounce
Garam Masala = 4 ounces for $2.75 an ounce
Hence, total cost of Tandoori Seasoning = 3.5*$3.60
⇒ total cost of Tandoori Seasoning = $12.6
and total cost of Garam Masala = 4*$2.75
⇒ total cost of Garam Masala = $11
Therefore, total cost for the spices =cost of Tandoori Seasoning + cost of Garam Masala
⇒ total cost for the spices = $12.6 + $11
⇒ total cost for the spices = $23.6
Hence, we conclude that,
The total cost of Tandoori Seasoning is incorrect.
Vijay made an error when multiplying 3.5 ounces by $3.60 .
Cost of both spice blends is actually $23.6.
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Find the fourth derivative of f(x)=3^x+ln(x)-108x. f(4)(x)=
[tex]f(x) = 3^x + \ln x -108 x\\\\f'(x) = 3^x \ln 3 + \dfrac 1x - 108\\\\f''(x) = 3^x \cdot 0+ \ln 3\cdot 3^x\cdot \ln (3)-x^{-1-1}-0= 3^x \cdot \ln^2 3 -x^{-2}\\ \\f'''(x) = 3^x \cdot 0 + \ln^2 (3) \cdot 3^x \cdot \ln (3) +2x^{-2-1} = 3^x \ln^3 (3)+2x^{-3}\\\\f''''(x) = 3^x \cdot 0 + \ln^3 (3) \cdot 3^x \ln(3) -3\cdot 2 x^{-3-1} = 3^x\ln^4 (3)-6x^{-4} \\\\\text{Hence the fourth derivative of f(x) is}~~ 3^x\ln^4 (3)-6x^{-4}.\\\\[/tex]
[tex]\textbf{Note:}\\\\\dfrac{d}{dx}(uv) = u \dfrac{dv}{dx} + v\dfrac{du}{dx}\\\\\dfrac{d}{dx} \ln (x) = \dfrac 1x\\\\\dfrac{d}{dx} a^x = a^x \ln a\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} (\text{Constant}) = 0[/tex]
In a popular online role playing game, players can create detailed designs for their
character's "costumes," or appearance. Gabriella sets up a website where players can
buy and sell these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
27 visitors purchased no costume.
75 visitors purchased exactly one costume.
11 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
more than one costume as a fraction in simplest form.
Probability that the next person will purchase more than one costume as a fraction in simplest form is; 11/113
How to find probability?
We are given the data for number of people who visited the website and the number of costumes purchased in a single day as;
Number of visitors that purchased no costume = 27 visitors
Number of visitors that purchased exactly one costume = 75
Number of visitors that purchased more than one costume = 11
Total number of visitors = 27 + 75 + 11 = 113
Thus;
Probability that the next person will purchase more than one costume as a fraction in simplest form is;
P(purchase more than one costume) = 11/113
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Find the surface area and volume of the figure below. Round your answers to the nearest tenth. (50 pts)
Answer:
Surface Area = 188.4 square yardsVolume = 216 cubic yardsStep-by-step explanation:
Finding the hypotenuse of the triangular side :
Applying Pythagorean theorem√6² + 6²√2 x 6²6√2Finding Surface Area :
Area (2 triangles) + Area (2 smaller rectangles) + Area (larger rectangle)2 x 1/2 x 6 x 6 + 2 x 12 x 6 + 12 x 6√236 + 144 + 6√2180 + 6√26 (30 + √2)6 (30 + 1.4)6 (31.4)188.4 square yardsFinding Volume :
1/2LWH1/2 x 12 x 6 x 66³216 cubic yardshelp me please i need help
Answer:
B. 11
Step-by-step explanation:
Hope this helps! ;-)
Answer:
11
Step-by-step explanation:
15-12/3
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
15-4 = 11
A study of the impact of caffeine consumption on reaction time used 24 subjects and divided them into 12 pairs based on the average hours of sleep they got. One randomly assigned member of each pair drank two cups of caffeinated coffee, and the other drank two cups of decaf. Each subject's performance on a standard reaction time test was recorded. The difference for each pair is calculated (caffeinated - decaf). A 95% confidence interval for the mean difference in reaction times is (-1.2, 0.75).
What is a valid conclusion they can make?
a. Because the confidence interval includes more negative numbers than positive, we have convincing evidence that caffeine decreases reaction time.
b. Because the confidence interval includes 0, we don't have convincing evidence that there is a difference in reaction time.
c. Because the center of the interval is -0.225, we have convincing evidence that decreases reaction time.
d. Because the confidence interval includes 0, we have convincing evidence that the true mean difference is 0.
Using the confidence interval, it is found that the correct option regarding the valid conclusion they can make is given by:
b. Because the confidence interval includes 0, we don't have convincing evidence that there is a difference in reaction time.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not a difference in reaction times, that is:
[tex]H_c - H_d = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference, that is:
[tex]H_c - H_d \neq 0[/tex]
The interval contains 0, hence there is not enough evidence to reject the null hypothesis, which means that option B is correct.
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WILL GIVE BRAINLIEST 25 POINTS
Congruent?
If so, what property?
Answer:
Yes, by ASA congruence.
Step-by-step explanation:
Solving :
∠DAB = ∠BCD (indicated in diagram)∠ADB = ∠DBC (indicated in diagram)BD = BD (common side)ΔABD ≅ ΔCDBHence, as 2 angles and a side of the triangles are equal, we can say they are congruent by ASA congruence.
[tex]\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Let's check if the two triangles are } [/tex][tex] \textbf{congruent} [/tex] ~
[tex] \large\textsf{Given information } [/tex]:
[tex] \textsf{Two angles of a triangle is equal to corresponding} [/tex] [tex] \textsf{two angles of another triangle, and they} [/tex][tex] \textsf{have one side in common (should be equal} [/tex][tex] \textsf{for both) } [/tex]
[tex] \textsf{So, after analyzing this information, we can } [/tex][tex] \textsf{conclude that the two triangles are congruent by} [/tex][tex] \textsf{AAS congruency criteria.} [/tex]
[tex] \texttt{[ since two angles are equal and one} [/tex][tex] \texttt{non included side is common/equal ]} [/tex]
Select the reason that best supports Statement 8 in the given proof.
A. Addition Property of Equality
B. Division Property of Equality
C. Substitution
D. Subtraction Property of Equality
Given: Ray BV bisects
Statement 8 (x = 10/5 or x = 2) is given by the division property of equality. Then the correct option is B.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Suppose that we're taking about
It means, we divide p into q equal parts.
And each part is of value p/q
Statement 7 is given below.
5x - 10 = 0
Then statement 8 is given by the division property of equality.
5x = 10
x = 10/5
x = 2
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In which quadrants is tangent positive?
A. II and IV
OB. I and III
OC. I and II
OD. I and IV
The quadrants in which the tangent is positive are I and III.
Option B is the correct answer.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
Tangent is defined as the ratio of the opposite side to the adjacent side of a right triangle.
It is positive when the opposite side and the adjacent side are both positive or both negative.
In the first quadrant (I), both the opposite and adjacent sides are positive, so the tangent is positive.
In the second quadrant (II), the opposite side is positive and the adjacent side is negative, so the tangent is negative.
In the third quadrant (III), both the opposite and adjacent sides are negative, so the tangent is positive.
In the fourth quadrant (IV), the opposite side is negative and the adjacent side is positive, so the tangent is negative.
Therefore,
The quadrants in which the tangent is positive are I and III.
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What is this a picture of
Answer:
inscribed angle
Step-by-step explanation:
That is an inscribed angle in a circle ....
Answer:
inscribed angle
Step-by-step explanation:
The vertex (point, corner) of the angle is ON the circle, this is an inscribed angle.
Simplify 4 – 8 × 2. Question 9 options: A) –4 B) –8 C) –10 D) –12
Answer:
b
Step-by-step explanation:
4 - 8 = -4 times 2 = -8
What’s the definition of decreasing function?
Answer:a function whose value decreases as the independent variable increases over a given range.
Step-by-step explanation:
Hey:This is super easy!!
3x+4=10
Answer:
x = 2
Step-by-step explanation:
We can find this by doing the short (and wildly incorrect way, according to teachers) way and input two in. The way the teachers want you to do it is this way:
3x + 4 = 10
3x + 4 (-4) = 10 (-4)
3x = 6
3x = 6/3
x = 2
2 is your answer.
Select the correct vocabulary word from each drop-down menu to correctly complete the sentences.
A(n)
Choose...
is a chore, but it is not a game.
A(n)
Choose...
is a bond, but it is not a separation.
An ERRAND is a chore, but it is not a game and A CONNECTION is a bond, but it is not a separation.
What is Errand?An ERRAND is a chore, but it is not a game.
The correct vocabulary word from each drop-down menu that correctly complete the first sentences is errand.
What is Connection?A CONNECTION is a bond, but it is not a separation
The correct vocabulary word from each drop-down menu that correctly complete the second sentences is connection.
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Determine the equation of the line passing through the points (-1, 1) and (1, 7).
Write the line in standard form Ax+By=C
Answer:
[tex]3x + y = -4[/tex]
Step-by-step explanation:
We were given to points on the line we are trying to find, hence we are able to determine the slope/gradient.
[tex]( - 1, \: 1) \: and \: (1, \: 7) \\ slope = \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \\ \\ s = \frac{7 - 1}{1 - ( - 1)} \\ s = \frac{6}{2} [/tex]
Slope is equal to 3.
Since we have the value for the slope, we can now use one of the points on the line to determine the equation of the line.
note that the coefficient of x is the slope. In this case the A from the standard form (Ax + By= C) is the slope.
[tex] \\ let \: us \: use \: the \: point \: ( - 1, \: 1) \\ a = 3 \: \: \: \: y = 1 \: \: \: x = - 1\\ ax + by = c \\ 3( - 1) + 1 = c \\ - 3 + 1 = c [/tex]
[tex] - 2 = c \\ therefore \: the \: equation \: of \: the \\ \: line \: is \\ ax + by = c \\ 3x + y = - 4[/tex]
The volume of a right cone is 3000π units^3. If its radius measures 15 units, find its height.
Answer:
40 unitsStep-by-step explanation:
In the question, it is given that a right cone has a radius of 15 units and volume of 3000π units³ and we have to find the height of the cone.
[tex] \: [/tex]
To Find the height of the cone, we must know this formula :
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi {r}^{2}h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]
Where,
r refers to the radius of the cone. h refers to the height of the cone.Now, we will substitute the values in the formula :
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times {(15)}^{2} \times h = 3000 \pi}}}}}}} \\ \\[/tex]
Cancelling π from both sides we get :
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times {(15)}^{2} \times h = 3000 \cancel\pi}}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times 225 \times h = 3000}}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{225}{3} \times h = 3000}}}}}}} \\ \\[/tex]
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf 75 \times h = 3000}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf h = \frac{3000}{75} }}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h =40 }}}}}}} \\ \\[/tex]
Therefore,
The height of the cone is 40 units .Solve for x. Round to the nearest tenth.
Answer:
x = 27.19
Step-by-step explanation:
Sin(54) =22/x
0.81=22/x
x0.81= 22
x = 27.19
Need help on this one please
Help!!! Please and thank you.
(HARD) Parallelogram MNOP is shown
Prove that MP and NO bisect each other. Drag the correct reason into each correct blank to complete the proof.
A diagram of parallelogram MNOP is attached below
We have side MN, || side OP, and side MP || NO
Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.
Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.
∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines
∠N+∠O=180° and ∠O+∠P=180°
∠N and ∠P are of equal size
we deduce further that ∠M and ∠O are of equal size
Hence, the correct statement to complete the proof is
∠M ≅ ∠O; ∠N ≅ ∠P
Which statement about the graphs is true?
O Graph A is a valid density curve because the part of
the graph from 2 to 6 is below the horizontal axis.
O Graph A is not a valid density curve because the
part of the graph from 1 to 2 is above the horizontal
axis.
O Graph B is not a valid density curve because part of
the horizontal axis has negative values.
O Graph B is a valid density curve because the curve
is above the horizontal axis, and the area under the
curve is 1.
The statement about the graphs is true is: Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
Statement about the graph that is trueGraph curve is above the horizontal axis.
Let determine the area under the curve using this formula
Base of left and right triangle
Left
Base = -3 - (-5)
Base= 2
Right
Base= 3 - (-3)
Base= 6
Right and left height
Height= 0.25
Hence:
Total area=(base× height)/2
Total area=[ (2×0.25)/2] + (6×0.25)/2
Total area=0.25+0.75
Total area=1
Therefore Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
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Given that circumference of a circle is 44m. Calculate it's area
Answer:
Area=154.062 [tex]m^{2}[/tex]
Step-by-step explanation:
As Circumference of a circle is given by;
[tex]C=2\times \pi\times r[/tex]
As the circumference is 44m so we can calculate the value of r by using the above formula.
[tex]44=2\times \pi \times r\\\\\frac{44}{2\pi} =r\\\\\implies r=\frac{22}{\pi} =7.003 m[/tex]
Now to Calculate the Area of a Circle.
As the area of a circle is,
[tex]Area =\pi \times r^{2}\\ Area=\pi \times (7.003)^{2} \\Area=\pi \times 49.039\\Area=154.062m^{2}[/tex]
if your 14 and you have a kid at 21 how old will your kid be when your 30
Answer:
Your kid will be 9 years old.
Step-by-step explanation:
It's not relevant, that you are 14 now.
Answer: 9
Step-by-step explanation: Regardless of if you are 14 or not, 30-21=9
b) In one year, Clara and Dave borrowed books from a library in the ratio 3:7. Dave borrowed 35 books. Work out the number of books borrowed by Clara.
3:7 =
3/7
3/7 = x/35
7x = 105
x = 15
answer : clara borrowed 15 books
I think it would be 15, because 3 doesn't go in evenly into 35. You might have the order of the ratio messed up.