Answer:
x alpha 1/y
: Introducing a constant k
x = k/y
where x = 7, y= 6
7 = k / 6
Cross Multiply
K ( constant) = 42
Answer: k = 42
Step-by-step explanation:
Formula = [tex]y = \frac{k}{x}[/tex]
plug in values:
6 = [tex]\frac{k}{7}[/tex]
multiply both sides by 7
k = 42
A 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]
Please help I will give you so much points
Answer:
∠[tex]DEC[/tex]
Step-by-step explanation:
vertical angles are opposite angles that are made by 2 intersecting lines
please help!!!
Events A and B are mutually exclusive. Find the missing probability.
11
17
6) P(B) = P(A or B) =
P(A) = ?
20
20
17
A) 1/15
B)
C)
E) None of these
5/6 0/-
D)
2014
The missing probability for the given mutually exclusive event is 3/10
What is Mutually Exclusive Event?Mutually exclusive events are those events that do not occur at the same time.
Here, Let P(A) be x,
P(B) = 11/20, P(A or B) = 17/20, P(A and B) = 0
By Addition theorem of Probability,
P(A or B) = P(A) + P(B) - P(A and B)
17/20 = x + 11/20 - 0
x = [tex]\frac{17}{20} - \frac{11}{20}[/tex]
x = 6/20
x = 3/10
Thus, The missing probability for the given mutually exclusive event is 3/10
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Answer:
C) 3/10
Step-by-step explanation:
Applying the Addition Theorem of Probability :
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Here :
P(A ∪ B) = 17/20P(B) = 11/20P(A ∩ B) = 0 (as they are mutually exclusive)Solving :
17/20 = 11/20 + 0 + P(A)P(A) = 17/20 - 11/20P(A) = 6/20 = 3/10Help!!! Please and thank you.
Question 2(Multiple Choice Worth 1 points)
(06.01 MC)
Classify the expression: −2x
A: Quadratic expression
B: Linear expression
C: Cubic expression
D: Exponential expression
Answer:
it is a linear expression
Answer:
B. Linear expression
Step-by-step explanation:
your friend wants to sell his car toyota suv your friend did some online research on similar cars and found the following prices 13500, 12900,15300,13700,12000,. What do you think would be a reasonable price for your friend to sell the car? how did you come up with this price
1. A reasonable price for my friend to sell the car is $13,480.
2. This price is determined as an average of the prices of similar cars.
What is an average?An average is a typical value in a dataset.
An average is the mean of a set of numbers.
The average value can be computed by summing the set of numbers and dividing the result by the number of items.
Data and Calculations:Prices of similar cars:
A. 13,500
B. 12,900
C. 15,300
D. 13,700
E. 12,000
Sum = $67,400
Average = $ 13,480 ($67,400/5)
Thus, a reasonable price for my friend to sell the car is $13,480, which is the average price of similar cars.
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Audrey deposited $80 in an account earning 10% interest compounded annually.
To the nearest cent, how much will she have in 3 year Use the formula 8-p(1 + r), where B is the balance (final amount) p is the principal (starting amour.), ris the interest rate expressed as a decimal, and t is the time in years.
$?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$80\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=80\left(1+\frac{0.10}{1}\right)^{1\cdot 3}\implies A=80(1.1)^3\implies A=106.48[/tex]
How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
Answer:
haha kala mo ba maiinit
Step-by-step explanation:
[tex]\green{ \rule{500pt}{999999pt}}[/tex]
Find the area of a piece of
carpet that measures 14 feet by 3
feet. Write your answer as a mixed
number.
Answer:
42 ft ^ 2
Step-by-step explanation:
All we have to do is multiply 14 and 3. That gives us 42.
Answer:
3/4 sq ft
Step-by-step explanation:
1/4*3=3/4
im pretty sure u meant 1/4 not 14 bc it says "mixed number"
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.
(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
Aisha estimates the product of 12 and 2.4 by rounding 2.4 to the nearest whole. She rounded 2.4 to
then she multiplied it by 12. Her estimation was
. Next, she multiplied 12 x 2.4 =
Answer: estimation=24
Step-by-step explanation:
2.4 is rounded down to 2
so she would do 2×12=24
A student tosses a coin and then draws a card from a stack of 4 cards labeled 1 through 4
What is the sample space for this compound event?
{H, T, 1, 2, 3, 4}
{H1, T1, H4, T4}
{HT1, HT2, HT3, HT4}
{H1, T1, H2, T2, H3, T3, H4, T4}
Answer:
The answer is the longest one <3
Step-by-step explanation:
I took the test:
If the coin is tossed and a card is chosen from 1 to 4, then the total sample will be 8. Then the correct option is D.
What is a sample?A sample is a collection of well-defined elements. A sample is represented by a capital letter symbol and the number of elements in the finite set is shown as a curly bracket {..}.
A student tosses a coin and then draws a card from a stack of 4 cards labeled 1 through 4.
Then the total number of the sample will be
Total sample = 2 × 4
Total sample = 8
Then the sample is given below.
[tex]\rm Sample = \begin{Bmatrix}(H,1) & (H,2) & (H,3) & (H,4) \\\\(T,1) & (T,2) & (T,3) & (T,4) \\\end{Bmatrix}[/tex]
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what principle will amount to $4000 if invested at 8.5% compounded quarterly for 5 years?
Answer:
$2626.75
Step-by-step explanation:
First, let's set up the equation for this: [tex]4000 = P(1 + \frac{0.085}{4})^{4(5)}[/tex]
Now, we can simply divide [tex]\frac{4000}{(1+\frac{0.085}{4})^{20} }[/tex]
and we get P ≈ $2626.75
PLEASE HELP ME ANSWER THIS PROBLEM
Answer:
9
Step-by-step explanation:
because 3*4=12 then divide 108 by 12 giving you 9
Rewrite √-9-6 in complex number notation.
A. −6 − 3i
B. −6 + 3i
C. √3i -6
D. -6 -√-9
Answer:
B) - 6 + 3i
Step-by-step explanation:
Complex number notation:
i² = -1
[tex]\sf \sqrt{-9}-6=\sqrt{3^2*i^2}-6[/tex]
[tex]\sf = 3i - 6[/tex]
Please answer as soon as possible as i need the answer fast
Answer:
[tex]\sf \dfrac{1}{4}[/tex]
Step-by-step explanation:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
From inspection of the diagram:
Total number of pawns = 16Total number of squares = 64[tex]\implies \textsf{P(landing on a pawn)} \sf = \dfrac{\textsf{Total number of pawns}}{\textsf{Total number of squares}}[/tex]
[tex]\implies \textsf{P(landing on a pawn)} \sf = \dfrac{16}{64}=\dfrac{1}{4}[/tex]
[tex]\sf probability : \bf 0.25[/tex]
Step-by-step explanation:The dimensions of a chess board is (8 × 8)There are 64 squares on a chess board.There are 8 black pawns and 8 white pawns.Total pawns in a chess board: (8 + 8) = 16 pawns on 16 squares.[tex]\sf Probability = \dfrac{favorable \ outcomes}{total \ outcomes}[/tex]
[tex]\dashrightarrow \ \sf probability : \ \bf \dfrac{16}{64}[/tex]
[tex]\dashrightarrow \ \sf probability : \ \bf \dfrac{1}{4} \ \ \approx \ \ 0.25 \ \ (as \ a \ decimal)[/tex]
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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What is the equation of the line that has a slope of
-3 and goes through the point (1, -2)?
Answer:
Step-by-step explanation:
y + 2 = -3(x - 1)
y + 2 = -3x + 3
y = -3x + 1
Jeremiah created a game where he flips a fair coin 3 times. Jeremiah wins the game if he flips heads at least 2 times. What are all the possible outcomes to win, based on the first two flips? What is the probability of winning, based on the first two flips? Move words and fractions to the table to answer the questions.
The probability of getting head at least two times will be 11%
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability will be:-
Sample outcomes are { H,H,H,T,T,T}
Favourable outcomes are { H }
So the probability of getting at least two times head will be:-
P = ( 1 / 3 ) x ( 1 / 3 ) = 0.11 = 11%
Therefore the probability of getting head at least two times will be 11%
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Answer:
The other persons explaition was difficult
Step-by-step explanation:
In November 2005, an international study to assess public opinion on the treatment of suspected terrorists was conducted (“Most in U.S., Britain, S. Korea, and France Say Torture is OK in at Least Rare Instances,” Associated Press, December 7, 2005). Each individual in random samples of 1000 adults from each of 9 different countries was asked the following question: “Do you feel the use of torture against suspected terrorists to obtain information about terrorism activities is justified?” Responses from Italy, Spain, France, the United States, and South Korea are summarized in the table below. Based on these data, is it reasonable to conclude that the response proportions are not the same for all five countries? Use a = 0.01 to test the appropriate hypotheses.
Based on the responses, the significance level, and the p-value, we can conclude that the response proportions are not the same for the countries.
What can be concluded about the response proportions for these countries?The null hypothesis is that the response proportions are the same. The alternate hypothesis is that the response proportions are not the same.
The sample size is large enough for a Chi-Square test to be used because the expected counts are all greater than 5.
Running a Chi-Square analysis shows that the P-value to be 0.000.
The P-Value is less than the significance level of 0.01 so the null hypothesis is rejected. This means that the alternate hypothesis of the response proportions not being the same is true.
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i need this answer as fast and soon as possible
Answer:
1.732
Step-by-step explanation:
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 .On a field trip to the planetarium, three students rode with their parents and the rest were evenly distributed on four buses. If 119 students went to the planetarium, how many were on each bus.
Answer:
29
Step-by-step explanation:
You do 119-3 because 3 students rode with their parents so then you do 116÷4=29
Use the formula; SA= 2(L) + 2(w) + 2(h) to find the survface area for a rectangular prism.
Question: (length = 2.2) (width = 1.46) (Height = 6)
Please answer this because im not smart.
Answer:
The surface area is 19.32
Step-by-step explanation:
The solution in the image
let y= -11sin(4x-8)
what is the amplitude?
what is the period?
what is the phase shift?
If the equation is y = - 11sin(4x - 8). Then amplitude will be 11, the time period is 4, and the phase difference is 8.
What is a sinusoidal Function?It is a function that repeats itself in a particular time interval.
The sinusoidal function is given as
y= |A| sin(ωx - Φ) ...1
Where A is amplitude, ω is the time period, and Φ is the phase difference.
The equation is given below.
y = -11 sin(4x - 8) ...2
Comparing the equations 1 and 2, then we have
Amplitude will be 11, the time period is 4, and the phase difference is 8.
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can someone help me with this question that is attached?
The value of f(g(x)) in the form a + bxⁿ is 1 -5x⁻². Where a = 1, b = -5 and n = -2
Determining the value of a functionFrom the question, we are to determine the value of f(g(x)) in the form a + bxⁿ
From the given information,
[tex]f(x) = \frac{x}{x+5}[/tex]
and
[tex]g(x) = x^{2} -5[/tex]
Then,
[tex]f(g(x)) = \frac{(x^{2} -5)}{(x^{2} -5) +5}[/tex]
∴ [tex]f(g(x)) = \frac{x^{2} -5}{x^{2} }[/tex]
Simplifying
[tex]f(g(x)) = \frac{x^{2} }{x^{2} } -\frac{5}{x^{2}}[/tex]
[tex]f(g(x)) = 1 -\frac{5}{x^{2}}[/tex]
[tex]f(g(x)) = 1 -5x^{-2}[/tex]
Hence, the value of f(g(x)) in the form a + bxⁿ is 1 -5x⁻². Where a = 1, b = -5 and n = -2.
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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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A study is testing the effectiveness of a new allergy medication. Sixty people who reported they have allergies volunteered to be part of the study and were randomly assigned to one of two groups, as shown in the design web.
Which of the following accurately describes the benefit of comparison in the experiment shown in the design web?
A) The level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect.
B) The overall level of allergic symptoms can be used to determine if the new allergy medication had a significant effect.
C) The level of allergic symptoms in the group who received the medication can be used to determine if the medication had a significant effect.
D) The level of allergic symptoms in both groups cannot be compared to determine if the medication had a significant effect because one group only received a placebo.
Answer:
I'm pretty sure it is d
Step-by-step explanation:
me and my sister have the same allergies but we take different allergy medicine because it affects us differently meaning that not everyone has the same reaction to all medicines
The level of allergic symptoms in both groups cannot be compared to determine if the medication had a significant effect because one group only received a placebo accurately describes the benefit of comparison in the experiment shown in the design web. Thus option A is correct.
What is an experiment?A scientific experiment inside which you carry out a sequence of tasks and closely monitor their results to discover new information. An investigation is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that hasn't been tried before.
Although one sample only obtained a placebo inside the investigation depicted in the design web, it is difficult to compare the severity of allergic rhinitis in both groups to establish whether the drug had a substantial impact. This appropriately illustrates the advantage of comparison. Therefore, option A is the correct option.
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y = 6 ( x - 1/2 ) (x + 3) ?
Answer:y
=
6
(
x
+
5
4
)
2
−
147
8
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
6
h
=
−
5
4
k
=
−
147
8
Find the vertex
(
h
,
k
)
.
(
−
5
4
,
−
147
8
)
Step-by-step explanation: