Answer:
9 batches of tarts.
Step-by-step explanation:
This is 8 / (8/9)
= 8 * 9/8
= 9 batches of tarts.
The American Veterinary Association claims that the annual cost of medical care for dogs averages $100, with a standard deviation of $30, and for cats averages $120, with a standard deviation of $35.
a) What's the expected difference in the cost of medical care for dogs and cats?
b) What's the standard deviation of that difference?
c) If the costs can be described by Normal models, what's the probability that medical expenses are higher for someone's dog than for her cat?
d) What concerns do you have?
Answer:
a)20$
b)46,1$
c)0,3336
d)No concerns
Step-by-step explanation:
A) To find expected difference of cost of medical care for dogs and cats we can simply subtract average costs of cats and dogs.
[tex]120-100=20[/tex]
Expected difference will be 20$.
B) To find the standard deviation of that difference, we need to square deviations and add them and square root it again.
[tex]\sqrt{(30^2+35^2)} =46,1[/tex]
Expected difference will be 46,1$.
C)We need to find the Z value to find the probability of more expensive dogs than cats in a Vet vise.[tex]Z=(0-20)/46,1=-0,434[/tex]
Z value of the function is -0,434
From the Z table that you can find at the attachment. The probability is %33,36 or 0,3336
D) This is a subjective part. I don't have any concerns
If the lengths of two sides of a certain triangle are 5 and 10, what is the length of the third side of the triangle?
Answer:
Step-by-step explanation:
let x be the length of third side.
10-5<x<10+5
or 5<x<15
so third side is between 5 and 15 .
Answer: The length of the third side is greater than 5 and less than 15 units.
Step-by-step explanation: Given that the lengths of two sides of a certain triangle are 5 and 10 units.
We are to find the length of the third side of the triangle.
Let x represents the length of the third side of the given triangle.
We know that the sum of the lengths of two sides of a triangle is always greater than the length of the third side, so we must have
[tex]5+10>x\\\\\Rightarrow x<15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
[tex]5+x>10\\\\\Rightarrow x>5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
and
[tex]x+10>5\\\\\Rightarrow x>-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From inequalities (i), (ii) and (iii), we get
[tex]5<x<15.[/tex]
Thus, the length of the third side is greater than 5 and less than 15 units.
Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Given is the probability distribution if we ignore the few households that own more than 5 cars. Number of cars 0 1 2 3 4 5 Probability 0.09 0.36 0.35 0.13 0.05 0.02 About what percentage of households have a number of cars within 2 standard deviations of the mean?
Final answer:
About 95% of households would typically be expected to have a number of cars within 2 standard deviations of the mean, as per the empirical rule for a normal distribution.
Explanation:
The question, in a broad sense, relates to the concept of a probability distribution, specifically to the normal distribution and the empirical or 68-95-99.7 rule. To answer the question about the percentage of households with a number of cars within 2 standard deviations of the mean, one needs to apply the properties of the normal distribution. Typically, about 95% of observations can be found within 2 standard deviations of the mean on a normal distribution. However, to be precise for this case, one would calculate the mean (μ) and standard deviation (σ) of the given probability distribution, then sum the probabilities of the random variable X falling between μ - 2σ and μ + 2σ to find the desired percentage of households.
About 93% of households have a number of cars within 2 standard deviations of the mean.
To determine the percentage of households that have a number of cars within 2 standard deviations of the mean, we need to perform the following steps:
Calculate the mean (μ) of the probability distribution:[tex]\mu = \sum xP(X=x)[/tex]
[tex]\mu = 0(0.09) + 1(0.36) + 2(0.35) + 3(0.13) + 4(0.05) + 5(0.02) = 1.75[/tex]
Calculate the variance (σ²) of the distribution:[tex]\sigma^2 = \sum (x - \mu)^2 P(X=x)\\\sigma^2 = (0 - 1.82)^2(0.09) + (1 - 1.82)^2(0.36) + (2 - 1.82)^2(0.35) + (3 - 1.82)^2(0.13) + (4 - 1.82)^2(0.05) + (5 - 1.82)^2(0.02) = 1.1675[/tex]
Calculate the standard deviation (σ):[tex]\[\sigma = \sqrt{1.0764} \approx 1.0805[/tex]
Determine the range within 2 standard deviations of the mean.The range is from μ - 2σ to μ + 2σ.
μ - 2σ = 1.75 - 2(1.0805) ≈ -0.411
μ + 2σ = 1.75 + 2(1.0805) ≈ 3.911
Since the number of cars cannot be negative, the range is from 0 to 3.911 (practically up to 3 cars).
Sum the probabilities of households owning within 0 to 3 cars.0.09 + 0.36 + 0.35 + 0.13 = 0.93
Thus, about 93\% of households have a number of cars within 2 standard deviations of the mean.
Complete question:
Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Given is the probability distribution if we ignore the few households that own more than 5 cars.
Number of cars: 0\\ 1 \\ 2\\ 3 \\ 4\\ 5
Probability: 0.09 \\ 0.36\\ 0.35\\ 0.13\\ 0.05\\ 0.02
About what percentage of households have a number of cars within 2 standard deviations of the mean?
Use synthetic division with the factor x + 1 to completely factor LaTeX: x^3+2x^2-5x-6x 3 + 2 x 2 − 5 x − 6.
Answer:
[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex].
Step-by-step explanation:
To find [tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}[/tex] using synthetic division you must:
Write the problem in a division-like format. To do this:
Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right.
[tex]\begin{array}{c|cccc}&x^{3}&x^{2}&x^{1}&x^{0}\\-1&1&2&-5&-6\\&&\\\hline&\end{array}[/tex]
Step 1: Write down the first coefficient without changes:
[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\\\hline&\1\end{array}[/tex]
Step 2:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\left(-1\right) \cdot 1=-1\\\hline&{1}&{2}+\left({-1}\right)={1}\end{array}[/tex]
Step 3:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}{-1}&1&2&{-5}&-6\\&&-1&\left({-1}\right) \cdot {1}={-1}\\\hline&1&{1}&\left({-5}\right)+\left({-1}\right)={-6}\end{array}[/tex]
Step 4:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}{-1}&1&2&-5&{-6}\\&&-1&-1&\left({-1}\right) \cdot \left({-6}\right)={6}\\\hline&1&1&{-6}&\left({-6}\right)+{6}={0}\end{array}[/tex]
We have completed the table and have obtained the following resulting coefficients: 1, 1, −6, 0.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is [tex]x^{2}+x-6[/tex], and the remainder is 0.
[tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}=x^{2} + x - 6+\frac{0}{x + 1}=x^{2} + x - 6[/tex]
Now, we factor [tex]x^{2}+x-6[/tex]
[tex]\left(x^2-2x\right)+\left(3x-6\right)\\x\left(x-2\right)+3\left(x-2\right)\\\left(x-2\right)\left(x+3\right)[/tex]
Therefore,
[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex]
Paul has 2/3 as many postcards as Shawn. The number of postcards Shawn has is 3/5 of the number of postcards Tim has. If the three boys have 280 postcards altogether, how many more postcards does Tim have than Paul
Tim has 84 more postcards than Paul.
Step-by-step explanation:
Given,
Total number of postcards = 280
Let,
Tim's share of postcards = x
Shawn's share of postcards = [tex]\frac{3}{5}\ of\ Tim's\ share[/tex] = [tex]\frac{3}{5}x[/tex]
Paul's share of postcards = [tex]\frac{2}{3}\ of\ Shawn's=\frac{2}{3}(\frac{3}{5}x)=\frac{2}{5}x[/tex]
According to given statement;
[tex]x+\frac{3}{5}x+\frac{2}{5}x=280[/tex]
Taking LCM
[tex]\frac{5x+3x+2x}{5}=280\\\\\frac{10x}{5}=280\\\\2x=280[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{280}{2}\\x=140[/tex]
Paul's share = [tex]\frac{2}{5}x=\frac{2}{5}(28)=56[/tex]
Difference = Tim's share - Paul's share
Difference = 140 - 56 = 84 cards
Tim has 84 more postcards than Paul.
Keywords: addition, fraction
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In the parallelogram below, y = ?
Answer:
y = 33°
Step-by-step explanation:
The left side and the right side are parallel, so the angles marked y and 33° are alternate interior angles, hence congruent.
y = 33°
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.9 with a standard deviation of 2.2.
(a) What response represents the 92nd percentile?
(b) What response represents the 62nd percentile?
(c) What response represents the first quartile?
Answer:
a) A response of 8.9 represents the 92nd percentile.
b) A response of 6.6 represents the 62nd percentile.
c) A response of 4.4 represents the first quartile.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 5.9
Standard Deviation, σ = 2.2
We assume that the distribution of response is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) We have to find the value of x such that the probability is 0.92
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.92[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<1.405) = 0.92[/tex]
[tex]\displaystyle\frac{x - 5.9}{2.2} = 1.405\\x = 8.991 \approx 8.9[/tex]
A response of 8.9 represents the 92nd percentile.
b) We have to find the value of x such that the probability is 0.62
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.62[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<0.305) = 0.92[/tex]
[tex]\displaystyle\frac{x - 5.9}{2.2} = 0.305\\x = 6.571 \approx 6.6[/tex]
A response of 6.6 represents the 62nd percentile.
c) We have to find the value of x such that the probability is 0.25
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.25[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<0.305) = -0.674[/tex]
[tex]\displaystyle\frac{x - 5.9}{2.2} = -0.674\\x = 4.4172 \approx 4.4[/tex]
A response of 4.4 represents the first quartile.
The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides. Your company claims that the average waiting time is seven minutes at the busiest times, 8 a.m. to 10 a.m., Monday through Thursday. One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds seven minutes. You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes. If the value of your test statistic is less than the critical value, the correct decision is to _____.
A. increase the sample size
B. reduce the sample size
C. fail to reject the seven-minute average waiting time claim
D. maintain status quo
E. reject the seven-minute claim
Answer:
A. increase the sample size
Step-by-step explanation:
By increasing sample size, the amount of data included in the statistical calculation is more. As the size increases, the uncertainty decreases, hence the confidence level on our estimate is higher. By having more sample, we have more accurate analysis, and our margin of error can be reduced as well.
PLEASE PLEASE HELP!!!
Which of the following is the graph of f(x) = x2 + 3x − 4?
Answer:
lt is the graph of x2+3x-4
Answer:
See Graph
Step-by-step explanation:
Find the Solution for
1x2+3x−4=0
using the Quadratic Formula where
a = 1, b = 3, and c = -4
x=−b±sqrtb^2−4ac/2a
x=−3±sqrt3^2−4(1)(−4/2(1)
x=−3±sqrt9−−16/2
x=−3±sqrt25/2
Simplify the Radical:
x=−3±sqrt5/2
We get x=22x=−82
which becomes
x=1
x=−4
Here is the graph:
3 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a red card?
Answer: [tex]\dfrac{15}{17}[/tex]
Step-by-step explanation:
Total number of cards in a deck = 52
Number of red cards = 26
Number of cards not red =
Number of ways to draw not red cards = [tex]^{26}C_3[/tex]
Total ways to draw 3 cards = [tex]^{52}C_3[/tex]
The probability that none of three cards are red = [tex]\dfrac{^{26}C_3}{^{52}C_3}[/tex]
[tex]=\dfrac{\dfrac{26!}{3!(26-3)!}}{\dfrac{52!}{3!(52-3)!}}[/tex] [∵ [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
[tex]=\dfrac{\dfrac{26\times25\times24\times23!}{(23)!}}{\dfrac{52\times51\times50\times49!}{3!(49)!}}=\dfrac{2}{17}[/tex]
Now , the probability that at least one of the cards drawn is a red card = 1- Probability that none cards are red
[tex]=1-\dfrac{2}{17}=\dfrac{17-2}{17}=\dfrac{15}{17}[/tex]
Hence, the required probability = [tex]\dfrac{15}{17}[/tex]
One apple and two plums cost $1.11. Two apples and 2 plum cost $1.38. How much does 1 apple and 1 plum cost?
answer: 0.69
answer explanation:
to start take 1.38 and 1.11 and subtract to find a price of a plum which is 0.27 since 1.38 have a extra plum then take 1.11 and take away 0.27 from 1.11 and get 0.84 then divide by 2 and get 0.42 so a apple cost 0.42 and a plum cost 0.27 together cost 0.69 which is nice
To find the cost of 1 apple and 1 plum, set up and solve a system of equations based on the given costs of different fruit combinations.
To solve this problem, we need to set up a system of equations:
Let x be the cost of one apple and y be the cost of one plum.From the given information, we have the equations: x + 2y = 1.11 and 2x + 2y = 1.38.Solve the system of equations to find the cost of 1 apple and 1 plum, which is $0.47.
The function C(x) = 25.50x + 50 models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house. What is the average rate of change of the function between 3 hours and 9 hours? A. $17.00 per hour B. $25.50 per hour C. $31.05 per hour D. $42.15 per hour
Answer:
The average rate of change is $25.5 per hour, option B.
Step-by-step explanation:
Average Rate of Change
When we are explicitly given some function C(x), we sometimes need to know the rate of change of C when x goes from [tex]x=x_1[/tex] to [tex]x=x_2[/tex]. It can be computed as the slope of a line .
[tex]\displaystyle m=\frac{C(x_2)-C(x_1)}{x_2-x_1}[/tex]
The provided function is
[tex]C(x)=25.50x + 50[/tex]
We are required to compute the average rate of change between the points
[tex]x_1=3\ ,\ x_2=9[/tex]
Let's compute
[tex]C(3)=25.50(3) + 50=126.5[/tex]
[tex]C(9)=25.50(9) + 50=279.5[/tex]
[tex]\displaystyle m=\frac{279.5-126.5}{9-3}[/tex]
[tex]\displaystyle m=\frac{153}{6}=25.5[/tex]
The average rate of change is $25.5 per hour, option B.
A set of observations on a variable measured at successive points in time or over successive periods of time constitute aa. geometric series.
b. time invariant set.c. time series.
d. logarithmic series.
Answer:
time series
Step-by-step explanation:
A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time.
Help!plzzzzzzzzzzzzzzx
He used 86 pounds of type A coffee.
Step-by-step explanation:
Cost of type A coffee = $5.40 per pound
Cost of type B coffee = $4.05 per pound
Total blend made = 138 pounds
Total cost = $675.00
Let,
x represents the pounds of type A coffee
y represents the pounds of type B coffee
According to given statement;
x+y=138 Eqn 1
5.40x+4.05y=675 Eqn 2
Multiplying Eqn 1 by 4.05
[tex]4.05(x+y=138)\\4.05x+4.05y=558.90\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5.40x+4.05y)-(4.05x+4.05y)=675-558.90\\5.40x+4.05y-4.05x-4.05y=116.1\\1.35x=116.1\\[/tex]
Dividing both sides by 1.35
[tex]\frac{1.35x}{1.35}=\frac{116.1}{1.35}\\x=86[/tex]
He used 86 pounds of type A coffee.
Keywords: linear equation, elimination method
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Identify the conic that is formed by the intersection of the plane described and the double-napped cone.
The plane intersects both nappes and does not pass through the vertex.
What is the conic section formed?
Circle
Hyperbola
Ellipse
Parabola
If the cutting plane was parallel to the circular base of the cones, then we would have a circular cross section (assuming the plane doesnt cut through the vertex). However, we're told than the plane intersects both nappes, or cones, so it's not possible for the plane to be parallel to the base faces. We can rule out choice A.
We can rule out choice C and choice D for similar reasons. An ellipse only forms if the plane only cuts through one cone only, which is the same story for a parabola as well.
HELP ASAPPPPP
Given that 6 > –2, which statements are true? Check all that apply.
(2)(6) > (–2)(2)
6/2 < -2/2
(–2)(6) > (–2)(–2)
6/-2 < -2/-2
(2)(6) < (–2)(2)
6/2 > -2/2
Answer:
The Statements which are true are:
(2)(6) > (–2)(2)
6/-2 < -2/-2
6/2 > -2/2
Step-by-step explanation:
Given:
6 > –2
We need to check all options which are true,
Hence we will check for all 1 by 1.
(2)(6) > (–2)(2)
It means that when 2 is multiplied on both side we get the value as
12 > -4
Since 12 is greater than -4.
Hence this statement is true.
6/2 < -2/2
It means that when 2 is divided on both side we get the value as
3 < -1
Since 3 is greater than -1.
Hence this statement is false.
(–2)(6) > (–2)(–2)
It means that when -2 is multiplied on both side we get the value as
-12 > 4
Since -12 is less than 4.
Hence this statement is false.
6/-2 < -2/-2
It means that when -2 is divided on both side we get the value as
-3 < 1
Since -3 is lesser than 1.
Hence this statement is true.
5) (2)(6) < (–2)(2)
It means that when 2 is multiplied on both side we get the value as
12 < -4
Since 12 is greater than -4.
Hence this statement is False.
6/2 > -2/2
It means that when 2 is divided on both side we get the value as
3 > -1
Since 3 is greater than -1.
Hence this statement is True.
Answer:
A,D,F
Step-by-step explanation:
I got these correct!
You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. find the probability that both cards are black. express your answer as a simplified fraction.
Answer:
[tex]\frac{25}{102}[/tex].
Step-by-step explanation:
Total number of cards in a deck = 52
number of black cards in a deck = 26
Find the probability that both cards are black (without replacement).
Therefore, both events are dependent.
The probability of first card is black = [tex]P_{1}=\frac{26}{52}[/tex]
the probability of second card is black = [tex]P_{2}=\frac{25}{51}[/tex]
[tex]P=\frac{26}{52}[/tex] × [tex]=\frac{25}{51}[/tex]
= [tex]\frac{1}{2}[/tex] × [tex]\frac{25}{51}[/tex]
= [tex]\frac{25}{102}[/tex]
The probability that both cards are black is [tex]\frac{25}{102}[/tex].
The probability that both cards picked without replacement are black is [tex] \frac {25}{102}[/tex]
Number of black cards in deck = 26
Total number of cards = 52
Recall :
Probability = (required outcome / Total possible outcomes)
Therefore,
Ist pick :
P(black card) = 26/52
Number of black cards left = 26 - 1 = 25
Total number of cards left = 52 - 1 = 51
2nd pick:
P(black card) = 25 / 51
Therefore, probability that both cards are black is ;
[tex]P(Both \: black) = \frac{26}{52} \times \frac{25}{51} = \frac {25}{102}[/tex]
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can someone help me with this question?
it's pretty difficult.
Answer:
C
Step-by-step explanation:
One angle is larger than other from the SAS Inequality Theroem that state that if two congruent sides are congruent, then one of the included angle is greater than the other
Answer
m< 1 > m < 2.
Step-by-step explanation:
< 1 is opposite the longer side.
A researcher interested in language development obtains a sample of 25 three-year-old girls and a sample of 25 three-year-old boys. Each child is given a vocabulary test and the researcher computes the mean score for each sample. The difference between the two sample means is an example of a
a. statistic
b. variable
c. constant
d. parameter
Answer:
(a) statistic
Step-by-step explanation:
The researcher conducted the research using sample space of 25 three-year-old girls and 25 three-year-old boys. This sample space is subjected to test with an expected outcome. The test allows the research to perform analysis on the event base on data he has collected. The collection, analysis and interpretation of data is called statistics.
On monday,a local hamburger shop sold a total of 330 hamburgers and cheeseburgers.The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on monday?
Answer:
165 Hamburgers
Step-by-step explanation:
330 divided by 2 is 165
What does an increase in taxes and decrease in the money supply do to the supply and demand curves?
Answer:
The supply and demand curves will shift to the left i.e. there will be a decrease in demand and supply.
Step-by-step explanation:
First: Tax is a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.
Secondly: Money supply is the total amount of monetary assets available in an economy at a specific time.
When tax is increased, this means individuals and businesses have to contribute more to the state revenue leaving both categories with lesser income or profit i.e. lesser to spend.
In the same way, when money supply decreases, there is lesser money available to both individuals and businesses
What this implies is that demand will decrease because income has decreased. Supply will also decrease because producers will not make as much profit given the increase in tax (tax is considered cost of production).
As a result of this, the demand curve shifts to the left, the supply curve also shift to the left because both demand and supply will decrease.
Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 4%, the intermediate-term bonds pay 5%, and the long-term bonds pay 6% simple interest per year. Mark wishes to realize a total annual income of 5.25%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?
Answer:
Short-Term investment: 5000$
Intermediate-Term investment: 65000$
Long-Term investment: 30000$
Step-by-step explanation:
To construct our first equation lets define sort-term bond investment as x, long-term investment as y.
So the equation is:
[tex]x*0,04+(100000-x-y)*0,05+y*0,06=5250[/tex]
From the equation it is found that:
[tex]y=25000+x[/tex]
Instead of y, if we put 25000+x the equation will be as following:
[tex]x*0,04+75000*0,05+(25000+x)*0,06=5250[/tex]
From the equation it is found that:
[tex]x=5000[/tex]
Short-Term investment is 5000$
[tex]x+25000=y[/tex]
Long-Term investment is 30000$
Rest of the money is Intermediate-Term investment 65000$
Question 8 options:
The graph of the line below has a slope of 34, and a y-intercept of 8.
Find the values of A and C
Answer:
Step-by-step explanation:
Based on what you have here as the slope we can set the slope formula equal to 34 using the points (0, 8) and (8, c) to solve for c, then use the points (0, 8) and (a, 5) to solve for a.
c first:
[tex]\frac{c-8}{8-0}=34[/tex] and
[tex]\frac{c-8}{8}=34[/tex] and
c - 8 = 272 s0
c = 280
For a:
[tex]\frac{5-8}{a-0}=34[/tex] and
[tex]\frac{-3}{a}=34[/tex] and
-34a = 3 so
[tex]a=-\frac{3}{34}[/tex]
That seems a little weird, but when you plug those points into the slope formula to solve for the slope, it works out the way it should.
What is the slope of this line? y = 2x + 4
-1/2
2
1/2
-2
Answer: the slope of the line is 2
Step-by-step explanation:
The equation of a straight line is represented in the slope intercept form as
y = mx + c
Where
m = slope
c = intercept
The given equation is y = 2x + 4
Comparing it with the slope intercept form given above,
m = 2. Therefore, the slope of the line is 2
Myriah wants to use dimensional analysis to find out how many centimeters (cm) are in 1.4 meters (m). Which of these equalities will be useful for this calculation?
Answer:
Option (4) is the answer.
Step-by-step explanation:
The given question is without options ; here is the complete question.
Myriah wants to use dimensional analysis to find out how many centimeters (cm) are in 1.4 meters (m). Which of these equalities will be useful for this calculation?
2.54 cm = 1 in.
1 m = 39.37 in.
1 cm = 10 mm
100 cm = 1 m
During the dimensional analysis Myriah wants to convert the dimension from meter to centimeter.
Option (1), In this option given equality is to convert centimeter to inch. which is not required.
Option (2), In this option equality is to convert meter to inch which is not required.
Option (3) the equality given will convert cm to mm, which is not required.
Option (4) equality given in this option will convert meter to centimeter which is the required equality.
Therefore, Option (4) will be the answer.
A pair of boots and a pair of tennis shoes cost $196.12. The difference in their cost is $44.38. Determine the cost of each type of footwear Write and solve using system of equations
Answer: A pair of boots costs $120.25. A pair of tennis shoes costs $75.87✔️
Step-by-step explanation:
Let B the cost of a pair of boots and let T the cost of a pair of tennis shoes.
Then we know:
A pair of boots and a pair of tennis shoes cost $196.12:
B + T = $196.12 } Equation 1
We also know:
The difference in their cost is $44.38:
B - T = $44.38 } Equation 2
From the equation 1 we know T:
T = $196.12 - B
Now we can substitute this value in equation 2:
B - ($196.12 - B) = $44.38
B - $196.12 + B = $44.38
2B = $44.38 + $196.12 = $240.5
B = $240.5/2 = $120.25◄cost of a pair of boots
Since we know the value of T from the equation 1:
T = $196.12 - B = $196.12 - $120.25 = $75.87◄cost of a pair of tennis shoes
Answer: A pair of boots costs $120.25. A pair of tennis shoes costs $75.87✔️
VerifyWe can substitute these values in equations 1 and 2 and check the results:
B + T = $196.12 } Equation 1
$120.25 + $75.87 = 196.12 ✔️check!
B - T = $44.38 } Equation 2
$120.25 - $75.87 = $44.38 ✔️check!
Spymore
The cost of a pair of boots is $120.25 and the cost of a pair of tennis shoes is $75.87.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, a pair of boots and a pair of tennis shoes cost $196.12.
Let the cost of a pair of boots be b and the cost of a pair of tennis shoes be t.
Now, b+t=196.12 --------(I)
The difference in their cost is $44.38.
b-t=44.38 --------(II)
Add equation (I) and (II), we get
b+t+b-t=196.12+44.38
2b=240.5
b=240.5/2
b=$120.25
Substitute b=$120.25 in equation (I), we get
b+t=196.12
t=196.12-120.25
t=$75.87
Therefore, the cost of a pair of boots is $120.25 and the cost of a pair of tennis shoes is $75.87.
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
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An investor just purchased a rectangular 2-acre retail lot for $250 a frontage foot. If she paid $100,000 total, what was the depth of the lot?
a. 400’ b. 250 c. 871’ d. 218’
Answer:
[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]
So for this case the best answer would be:
d. 218’
Step-by-step explanation:
Previous concepts
Foot front : "Is a foot measured along the front of a piece of property".
Solution to the problem
For this case we need to begin finding the number of frontage feet, with the following formula:
[tex]Frontage fronts=\frac{Amount paid}{Unitary price}[/tex]
And for this case if we replace the values given we got:
[tex]Frontage fronts=\frac{100000}{250}=400 fromtage foot[/tex]
Now we need to convert the area to square feet. And we know that:
[tex] 1 acre= 43560 ft^2[/tex]
And converting we got: [tex]2 acre *\frac{43560 ft^2}{1 acre}=87120 ft^2[/tex]
Now we can divide the total area by the total of frontage feer and we got:
[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]
So for this case the best answer would be:
d. 218’
Can some one help me set up an equation out of these word problems? PLEASE HELP!!!1: sam is an accountant. He finds that he spends two-fifths of his work day answering emails. If he spent 3.6 hours answering emails yesterday ,how many hours did he work.2: elaina charged $83 on her credit card to buy groceries. If the balance is now $294, what was the balance before she bought groceries.3: Max spends three times as long on his math homework than he does on his science homework.If he spent a total of 64 minutes on math and science homework last night, how long did he spend on math homework.4 The gardenview hotel is seventeen less than twice the height of the Plaza Hotel .If their combined height is 361 feet,How tall is the gardenview hotel
Answer:
1. 9 hours 2. $377 3. 48 hours 4. 235 feet
Step-by-step explanation:
In all cases below, let x represent the variable sought for.
1: 2x/5=3.6,
x=5/2 *3.6=9 hours
2. x-83=294
x=83+294=377
3. x+x/3=4x/3=64
x=64*3/4=48 hours
4. If the gardenview hotel's height is x, then (x+17)/2 will be the height of the Plaza Hotel.
The combined height will be x + (x+17)/2 = 361 feet
Multiplying by 2 across board,
2x+x+17=722
3x+17=722
3x =722-17=705
x=705/3=235m
Answer:
It is A. my friend
Step-by-step explanation:
You go out to eat and your bill comes to $123. The GST is 5% and you leave a 15%
tip. How much would it cost altogether?
Final answer:
The total cost, including a 5% GST and a 15% tip on a bill of $123, would be $147.60, calculated by adding the GST and the tip amount to the original bill.
Explanation:
To calculate the total cost of the meal including tax and tip, we add both the Goods and Services Tax (GST) and the tip percentage to the original bill amount.
Calculate the GST by converting the percentage to a decimal and multiply by the bill amount: 0.05 × $123 = $6.15.Add the GST to the original bill: $123 + $6.15 = $129.15.Calculate the tip amount: Convert 15% to a decimal and multiply by the original bill amount: 0.15 × $123 = $18.45.Add the tip to the subtotal: $129.15 + $18.45 = $147.60.The total cost, including a 5% GST and a 15% tip on a bill of $123, would be $147.60.
answer plzzz 30 pointss for eachh
Answer:
D. [tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]
Step-by-step explanation:
Given:
Let us find the equations of the lines from the graph.
First let us determine the equation of the broken line.
The slope of the broken line is positive as 'y' values increases with increase in 'x'. The slope is the ratio of the absolute value of y-intercept to that of the x-intercept.
x-intercept = 6, |y-intercept| = |-4| = 4
So, [tex]m=\frac{4}{6}=\frac{2}{3}[/tex]
Now, equation of a line with slope 'm' and y -intercept 'b' is given as:
[tex]y=mx+b[/tex]
Here, [tex]m=\frac{2}{3},b=-4[/tex].So, equation of the broken line is:
[tex]y=\frac{2}{3}x-4[/tex]
Now, from the graph, the solution is below the broken line. So, the equality sign is replaced by the less than inequality sign. So,
[tex]y<\frac{2}{3}x-4[/tex]
Now, let us determine the equation of the other line.
y-intercept, [tex]b = 2[/tex], x-intercept = 1
Slope is negative as 'y' decreases with increase in 'x'. So,
Slope, [tex]m=-\frac{2}{1}=-2[/tex]
Now, equation is given as:
[tex]y=-2x+2[/tex]
From the graph, the solution region is to the left of the line. So, the 'equal to' sign is replaced by the 'greater than or equal to' sign' as the line is also included in the solution region. So, the inequality becomes:
[tex]y\geq-2x+2[/tex]
Therefore, the last option is correct.
[tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]