Answer:
E(x) = 15 minutes
Step-by-step explanation:
The random variable X (waiting time) has a uniform distribution between the interval [0,30], because it is just as likely that you arrive in any time and then your waiting time is minimum 0 minutes and maximum 30 minutes
The expected value of a random variable uniform is:
E(x) = [tex]\frac{a+b}{2}[/tex]
Where a and b are the interval's extremes
Thus
E(x) = [tex]\frac{0+30}{2}[/tex]
E(x) = 15 minutes
Suppose the time that it takes a certain large bank to approve a home loan is Normally distributed, with mean (in days) μ μ and standard deviation σ = 1 σ=1 . The bank advertises that it approves loans in 5 days, on average, but measurements on a random sample of 500 loan applications to this bank gave a mean approval time of ¯ x = 5.3 x¯=5.3 days. Is this evidence that the mean time to approval is actually longer than advertised? To answer this, test the hypotheses H 0 : μ = 5 H0:μ=5 , H α : μ > 5 Hα:μ>5 at significance level α = 0.01 α=0.01 .
Test hypothesis :
[tex]H_0 : \mu =5\\\\ H_a: \mu >5[/tex]
Since alternative hypothesis is right-tailed and population standard deviation is known σ = 1 , so we perform a right-tailed z-test.
Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
[tex]\mu[/tex] = population mean
[tex]\sigma[/tex] =population standard deviation
n= Sample size
Substitute values, we get
[tex]z=\dfrac{ 5.3-5}{\dfrac{1}{\sqrt{500}}}[/tex]
[tex]z=\dfrac{ 0.3}{0.04472135955}\approx6.7[/tex]
Critical value for 0.01 significance level in z-table is 2.326.
Decision : Test statistic (6.7)> Critical value ( 2.326), it means we reject that null hypothesis.
i.e. [tex]H_a[/tex] is accepted.
We conclude that there is sufficient evidence that the mean time to approval is actually longer than advertised.
How many numbers in the set {3, 13, 23, 33, . . .} can be written as the difference of two primes?
Answer:
1
Step-by-step explanation:
An odd number will be the difference of an even and an odd number. The only even prime is 2, so the other prime must end in 5. There is only one such.
Only 3 = 5 -2 can be written as the difference of primes.
Answer:
1
Step-by-step explanation:
Notice that when we subtract two integers, the difference can only be odd if one integer is even and one integer is odd (even - even = even and odd - odd = even). If one integer is even, then that integer is divisible by 2 and thus not prime. The only exception is 2, the only even prime number. So one of the primes must be 2. If we add 2 to each number in the set to find the other prime, we end up with $\{5, 15, 25, 35, \ldots\}$. All of the numbers in the set are divisible by 5, which means the only prime number in the set is 5. So the only number in the set $\{3,13,23,33, \ldots\}$ that can be written as the difference of two primes is $5-2=3$. The answer is $\boxed{1}$ number.
Yes I copied and pasted the proper answer from a different site. I didn't want to write it out.
Put number 1 for the first image and number 2 for the second image. Thanks!
Answer:
Is below
Step-by-step explanation:
1.
b. x </= -7 OR x > 4
d. x >/= -7 AND x < 4
e. x >/= -7 OR x < 4
c. x </= -7 AND x < 4
a. x </= -7 OR x < 4
2.
( - the absolute sign
(d - 3.5) </= 1.5
d - 3.5 </= 1.5 (positive case)
d </= 5
(d - 3.5) >/= 1.5
d - 3.5 >/= -1.5 (negative case)
d >/= 2
D. Is the number line graph of the inequality.
Susie, Meg, and Jane drive together to visit their grandma. Audit drive for 65 miles,and Meg drives 2 times as far as Susie. Then Jane drives twice as far as Susie and Meg combined. How far did Jane drive
Answer:
Jane has drive 390 miles to visit Grandma.
Step-by-step explanation:
Given:
Number of miles Susie drive = 65 miles
Meg drives 2 times as far as Susie.
It means Number of miles Meg drive is equal to twice the number of miles driven my Susie.
Framing equation we get;
Number of miles Meg drive = 2 × Number of miles Susie drive = [tex]65 \times 2=130\ miles[/tex]
Also Given:
Jane drives twice as far as Susie and Meg combined.
Number of Miles Driven by Jane is equal to twice the sum of Number of miles Susie drive and Number of miles Meg drive.
Framing equation we get;
Number of miles Meg drive = 2 × (Number of miles Susie drive + Number of miles Meg drive) = [tex]2\times (65+130) = 2\times 195 = 390\ miles[/tex]
Hence Jane has drive 390 miles to visit Grandma.
The binary value of the ASCII letter "c" is 0110 0011. Using the handy chart that we learned in the lesson, convert this number to its decimal value. You'll need to use some math for this question.
Answer:
The decimal value is 99.
Step-by-step explanation:
We want to convert 01100011 to decimal.
We start counting the digit from the rightmost digit using zero-index system:
0 = 7
1 = 6
1 = 5
0 = 4
0 = 3
0 = 2
1 = 1
1 = 0
We multiply each digit by 2 having the index as power:
[tex]= (0 * 2^{7} ) + (1 * 2^{6} ) + (1 * 2^{5} ) + (0 * 2^{4} ) + (0 * 2^{3} ) + (0 * 2^{2} ) + (1 * 2^{1} ) + (1 * 2^{0} )\\= (0 * 128) + (1 * 64) + (1 * 32) + (0 * 16) + (0 * 8) + (0 * 4) (1 * 2) + (1 * 1)\\= 0 + 64 + 32 + 0 + 0 + 0 + 2 + 1\\= 99[/tex]
Therefore, the decimal value of "c" is 99.
The decimal value of the given binary value 0110 0011 is 99.
Given information:
The binary value of the ASCII letter "c" is 0110 0011.
It is required to convert the given binary value into a decimal number.
So, to convert a binary code to a decimal code, it is required to multiply the binary numbers with indices of 2.
The code can be converted to decimal number as,
[tex]d=2^0\times 1+2^1\times1+2^2\times0+2^3\times0+2^4\times0+2^5\times1+2^6\times1+2^7\times0\\d=1+2+0+0+0+32+64+0\\d=99[/tex]
Therefore, the decimal value of the given binary value 0110 0011 is 99.
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John is planning to go to graduate school in a program that will take three years. John wants to have available $10,000 available each year for his school and living expenses.
If he earns 6% on his investments, how much must be deposited at the start of his studies for him to withdraw $10,000 a year for three years?
a) $10,000
b) $29,100
c) $30,000
d) $18,390
Answer:
d) $18,390
Step-by-step explanation:
Let X be the amount of money he deposited on the first year of his study.
The question says that he earns 6% on his investment without specifying the investment return time. However, normally it's annually, so let's assume his earning is 6% per annum.
Given that he did not make any withdrawal until the end of the first year, in 2nd year, he'll get the earning of his investment minus 10,000 to pay for his first year study
2nd year Y = X(1.06 ) - 10000
The same goes with 3rd year
3rd year Z = Y(1.06) - 10000
In worst case scenario, let's assume all of the money is used up at the end of third year
Z = 0
Y(1.06) - 10000 = 0
Substitute the first year into the equation:
Y(1.06) - 10000 = 0
(X(1.06)-10000)1.06 -10000 = 0
(1.06^2)X -1.06(10000) - 10000 = 0
X = (10000+10600)/1.06^2 = 18333.92
So the minimum deposit he needs to make to survive for the whole 3 years is $18333.92.
From the answer selection, the nearest value is d) $18,390
what is the difference between dependent variable independent variable vs response variable explanatory variable?
Answer:
Step-by-step explanation:
we are to distinguish between
dependent variable independent variable
vs
response variable explanatory variable
An independent variable is one which is not affected by any other variable for example, the amount we spend, the time we study ,etc.
An explanatory variable is a type of independent variable but not fully independent but depends on some factors.
Though explanatory and independent variables are practically used interchangeably the main difference is explanatory variable is not independent but explains the variations in the response varaible.
In experimental research, the independent variable is manipulated to observe its effect on the dependent variable, which is subsequently measured. Control variables are kept constant to ensure valid results. The dependent variable depends on the independent variable, such as the growth of plants depending on the amount of fertilizer applied.
In the context of experimental research, an independent variable, also known as an explanatory variable, is the one that is changed or controlled by the experimenter to examine its effect on another variable. On the other hand, a dependent variable, also referred to as a response variable, is what is measured or observed in the experiment to determine the effect of the independent variable.
For instance, if a study is conducted to see how the amount of fertilizer affects the growth of plants, the amount of fertilizer would be the independent variable because it is what the experimenter varies during the study. The growth of the plants, typically measured in height or biomass, would be the dependent variable because it is the result that is measured in response to the manipulation of the independent variable.
The control variables are equally crucial as they answer the question "What do I keep the same?" They need to be maintained consistently to ensure that the results are due only to the manipulation of the independent variable and not to other extraneous factors.
The authors of a study analyzing the effect of marital status on support for a football team would manipulate the marital status (independent variable) to measure the change in support or opposition for the team (dependent variable).
F n is a natural number then√n is (a) always a natural number (b)always an irrational number (c)always a rational number(d) sometimes a natural number and sometimes an irrational number
Answer:
(d) sometimes a natural number and sometimes an irrational number
Step-by-step explanation:
Consider the natural numbers 3 and 4:
√4 = 2, a natural number
√3 ≈ 1.73205080756887729352744634150..., an irrational number
6(-3v+1)=5(-2v-2)(if there is no solution,type in ''no solution'')v= Answer
Answer:
v = 2
Step-by-step explanation:
Eliminate parentheses by using the distributive property.
-18v +6 = -10v -10
6 = 8v -10 . . . . . . . . . add 18v
16 = 8v . . . . . . . . . . . add 10
2 = v . . . . . . . . . . . . . divide by the coefficient of v
The answer is v = 2.
Answer:
v = 2
Step-by-step explanation:
6 (-3v + 1) = 5 (-2v - 2)
- 18v + 6 = - 10v - 10
- 18v + 10v = - 10 - 6
- 8v = - 16
- v = - 16/8
- v = - 2
v = 2
The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is (2w+8)(2w+10)=224, where w represents the width of the mat around the photo.
The required width of the mat around the photo is given as 3 inches.
Given that,
The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is (2w+8)(2w+10)=224, where w represents the width of the mat around the photo.
The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
here,
(2w + 8)(2w + 10) = 224
4w² + 16w + 20w + 80 = 224
4w² + 36w - 144 = 0
w² + 9w - 36 = 0
[w -3][w + 12] = 0
w = 3 and w = -12
Since the measure of width cannot be negative so -12 can be neglected.
w = 3 preferred,
Thus, the required width of the mat around the photo is given as 3 inches.
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A driver can be jailed up to one year and fined up to $5,000 if he or she _________________.A. dumps litter on any public or private property or any waters in Georgia B. refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer C. rides in a house trailer while it is being towed by a vehicle on a highway
A driver can be jailed up to one year and fined up to $5,000 if he or she refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.
Answer: Option B
Step-by-step explanation:
This Vehicle codes 2800.1 state a violation or avoidance of police. The rules as follows: "Any person who, while driving a motor vehicle and intentionally avoiding it, intentionally escapes or attempts to escape from a peace officer " Any driver who "intentionally fails or refuses to stop the vehicle or otherwise, an attempt to escape or prosecute the pursuing police officer when he receives a visual and audible signal to stop the vehicle.
"Visual and audible" signals include sirens, lights, hand signals and voice commands. You must have been able to hear and / or see these signals to be accused of escaping and attempting to escape from the police. This is a level II or level 3 crime, and any penalties for those fleeing or trying to avoid a police officer will depend on the scale of the crime they are suspected of.
Second-Degree Misdemeanour - in jail maximum of 2 years and fine max. of $5,000 Third-Degree Felony - in jail maximum of 7 years and fine max. of $15,000.A driver can be jailed up to one year and fined up to $5,000 if he or she refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.
Explanation:The correct answer is B. refuses to bring his or her vehicle to a stop when given a visual or an audible signal by a police officer.
Under Georgia law, a driver can be jailed up to one year and fined up to $5,000 if they refuse to stop their vehicle when signaled by a police officer. This is considered a serious offense because it puts both the driver and other people's safety at risk.
Examples of situations where a driver may refuse to stop include fleeing from law enforcement, attempting to evade arrest, or engaging in dangerous driving behaviors that necessitate a traffic stop.
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Find the APY corresponding to the following nominal rate. 7​% compounded semiannually.
Answer:
7.23%.
Step-by-step explanation:
We are asked to find APY (Annual Percentage Yield) to the nominal rate of 7% compounded semiannually.
We will use annual percentage yield formula to solve our given problem.
[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
Let us convert 7% into decimal form.
[tex]7\%=\frac{7}{100}=0.07[/tex]
Semiannually means two times per year.
[tex]APY=(1+\frac{0.07}{2})^{2}-1[/tex]
[tex]APY=(1+0.00583333)^{12}-1[/tex]
[tex]APY=(1.00583333)^{12}-1[/tex]
[tex]APY=1.0722900804298071-1[/tex]
[tex]APY=0.0722900804298071[/tex]
[tex]APY\approx 0.0723[/tex]
Let us convert 0.0723 into percentage by multiplying with 100.
[tex]0.0723\times 100=7.23\%[/tex]
Therefore, annual percentage yield would be 7.23%.
The APY for a 7% nominal rate compounded quarterly is approximately 7.19%.
To find the APY (Annual Percentage Yield) for a nominal rate of 7% compounded quarterly, we use the following formula:
APY = (1 + r/n)ⁿ - 1
where r is the nominal interest rate and n is the number of compounding periods per year.
Convert the nominal rate from a percentage to a decimal: 7% = 0.07.
Identify the number of compounding periods per year: quarterly means n = 4.
Plug the values into the formula:
APY = (1 + 0.07/4)⁴ - 1
Calculate inside the parenthesis first: 0.07/4 = 0.0175.
Add 1: 1 + 0.0175 = 1.0175.
Raise to the fourth power: (1.0175)⁴ ≈ 1.071889
Subtract 1: 1.071889 - 1 ≈ 0.071889
Convert the decimal back to a percentage to get the APY: 0.071889 × 100 ≈ 7.19%.
Therefore, the APY corresponding to a 7% nominal interest rate compounded quarterly is approximately 7.19%.
Complete Question :
Find the APY corresponding to the following nominal rate 7% compounded quarterly The APY is %. (Type an integer or a decimal. Round to the nearest hundredth as needed. Do not round until the final answer)
Please help me with this problem
Answer:
domain: [0, 7]range: [-2, 4]is a function? YESStep-by-step explanation:
The domain is the horizontal extent, which is from x=0 to x=7.
The range is the vertical extent, which is from y=-2 to y=4.
The curve passes the vertical line test, so the relation IS A FUNCTION.
_____
The vertical line test asks whether any vertical line intersects the curve at more than one point. If so, the relation is NOT a function.
The output of a process is stable and normally distributed. If the process mean equals 23.5, the percentage of output expected to be less than or equal to the mean: a. is 50%. b. is greater than 75%. c. cannot be determined without knowing the standard deviation value. d. is less than 25%
Answer:
Option a) 50% of output expected to be less than or equal to the mean.
Step-by-step explanation:
We are given the following in the question:
The output of a process is stable and normally distributed.
Mean = 23.5
We have to find the percentage of output expected to be less than or equal to the mean.
Mean of a normal distribution.
The mean of normal distribution divides the data into exactly two equal parts.50% of data lies to the right of the mean.50% of data lies to the right of the meanThus, by property of normal distribution 50% of output expected to be less than or equal to the mean.
Sarah sent half of the Christmas cards to her friends,and Richard sent three eights of them to his friends. If there are 32 cards in all and Sarah and Richard want to send an even number of cards to their families. How many cards would Sarah's family get.
Answer:
Sarah family will get 2 cards
Step-by-step explanation:
The total number of cards is 32
Sarah sent half of the Christmas cards to her friends,= 1/2 *32= 16 cards for Sarah's friends
Richard sent three eights of them to his friends.
3/8 *32=12 cards for Richards friends
Total = 12+16= 28
Card left= 32-28=4
Since Sarah and Richard want to send an even number of cards to their families. Then Sarah's family and Richard's family will receive 2 apiece.
Sarah's family would receive 2 cards after accounting for the cards Sarah and Richard sent to their friends from the total of 32 cards.
Explanation:To solve how many Christmas cards Sarah's family will get, first calculate how many cards Sarah and Richard sent to their friends. Sarah sent half of 32, which is 16 cards. Richard sent three eights of 32, which can be calculated as (3/8) * 32 = 12 cards. Together, they sent 28 cards to their friends. Since there are 32 cards in total, the remaining cards for their families would be 32 - 28 = 4 cards. If these 4 cards are to be distributed evenly, both families would get 2 cards each. Thus, Sarah's family would get 2 cards.
HELPPP ME PLEASE I'LL GIVE YOU 60 POINTS IF YOU HELP ME AND IF IT'S THE RIGHT ANSWER
Good evening
Answer:
f(-3) = -4
Step-by-step explanation:
just using the calculator replace x by -3
f(-3) = 4(-4-(-3)) = 4(-4+3) = 4×(-1) = -4.
:)
Answer:
-4
Step-by-step explanation:
How you start the equation is by plugging -3 into both of the x's in the problem to make it:
f(-3) = 4(-4 - (-3))
f(-3) = 4(-4 + 3)
f(-3) = 4(-1)
f(-3) = -4
The answer would be written as:
f(-3) = -4
I hope this helps!
p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right ) P is the product, indicated above, of all the numbers of the form 1 – \frac{1}{k}, where k is an integer from 2 to 50, inclusive. What is the value of P
Answer:
The value of p would be [tex]\frac{1}{50}[/tex]
Step-by-step explanation:
Given,
[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right )[/tex]
[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{49} \right )\left ( 1 - \frac{1}{50} \right )[/tex]
[tex]p=\frac{2-1}{2}.\frac{3-1}{3}.\frac{4-1}{4}......\frac{49-1}{49}.\frac{50-1}{50}[/tex]
[tex]p=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{48}{49}.\frac{49}{50}[/tex]
[tex]p=\frac{1.2.3.4.........48.49}{2.3.4........49.50}[/tex]
[tex]p=\frac{1}{50}[/tex]
Hence, the value of p is 1/50.
P is the product, indicated above, of all the numbers of the form , where k is an integer from 2 to 50, inclusive. Value of P is 2) 1/50.
To find the value of [tex]\( P \)[/tex], we can simply multiply all the terms together:
[tex]\[ P = \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \ldots \left(1 - \frac{1}{50}\right) \][/tex]
We start with [tex]\( k = 50 \)[/tex]. and go up to [tex]\( k = 50 \)[/tex]. Let's calculate it:
[tex]\[ P = \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \ldots \left(1 - \frac{1}{50}\right) \][/tex]
[tex]\[ P = \left(\frac{1}{2}\right)\left(\frac{2}{3}\right)\left(\frac{3}{4}\right) \ldots \left(\frac{49}{50}\right) \][/tex]
[tex]\[ P = \frac{1}{50} \][/tex]
So, the value of [tex]\( P \) is \( \frac{1}{50} \).[/tex]
[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right[/tex]) P is the product, indicated above, of all the numbers of the form [tex]1 – \frac{1}{k}[/tex], where k is an integer from 2 to 50, inclusive. the value of P is [tex]\( P \) is \( \frac{1}{50} \).[/tex]
Question:-
[tex]p = \left ( 1 - \frac{1}{2} \right )\left ( 1 - \frac{1}{3} \right )\left ( 1 - \frac{1}{4} \right )...\left ( 1 - \frac{1}{50} \right )[/tex]
P is the product, indicated above, of all the numbers of the form [tex]1 – \frac{1}{k}[/tex], where k is an integer from 2 to 50, inclusive. What is the value of P ?
1.) [tex]\frac{1}{100}[/tex]
2.) [tex]\frac{1}{50}[/tex]
3.) [tex]\frac{1}{49}[/tex]
4.) [tex]\frac{49}{50}[/tex]
5.)[tex]\frac{99}{100}[/tex]
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Answer:
maybe
Step-by-step explanation:
If p is prime, then answer is NO. If p is not prime, the answer is YES.
__
Some positive integers are prime; some are not. We need to know more about p before we can give a better answer than this.
Select one of the factors of x3y2 + 8xy2 + 5x2 + 40.
a) (xy2 + 5)
b) (x2 + 4)
c) (xy2 − 5)
d) (x2 − 8)
Answer:
Option a - [tex]xy^2+5[/tex]
Step-by-step explanation:
Given : Polynomial [tex]x^3y^2+8xy^2+5x^2+40[/tex]
To find : Select one of the factors of polynomial ?
Solution :
The polynomial [tex]x^3y^2+8xy^2+5x^2+40[/tex]
We factor of above polynomial by taking common terms,
[tex]xy^2(x^2+8)+5(x^2+8)[/tex]
[tex](xy^2+5)(x^2+8)[/tex]
From the given options,
[tex]xy^2+5[/tex] is one of the factors of polynomial.
Therefore, option a is correct.
For each recipe, write a ratio that compares the number of parts of lemonade to the total number of parts.
Answer: Samantha's Recipe:
Ratio of lemonade = 2 1/2 : 6
Caden's Recipe:
Ratio of lemonade = 15 : 32
Step-by-step explanation:
Samantha's Recipe
3 1/2 parts cranapple juice
2 1/2 parts lemonade
Caden's Recipe
4 1/4 parts cranapple juice
3 3/4 parts lemonade
For each recipe, write a ratio that compares the number of parts of lemonade to the total number of parts.
Solution:
For Samantha's Recipe:
Total number of parts = cranapple juice parts + lemonade parts = 3.5 + 2.5 = 6.0
Ratio of lemonade to total number of parts = (2.5)/(6.0) = 2 1/2 : 6
For Caden's Recipe:
Total number of parts = cranapple juice parts + lemonade parts =(17/4)+(15/4) = (32/4) = 8
Therefore, Ratio of lemonade to total number of parts = (15/4) / (8) =(15)/(32) = 15:32
Shelby Middle School is thinking of changing its dress code. What would be the best way to collect data? A) Survey 100 randomly chosen students. B) Survey 100 athletes and cheerleaders. C) Survey 100 randomly chosen 8th graders. D) Survey 100 students who have had dress code violations.
Answer:
it would be A if you choose 100 random people then they would give you some explanation of why you should or shouldn't change the dress code.
Given the following triangle, solve for angle B.
A. 52.56
B. 51.34
C. 50.12
D. 49.34
Tan(Angle) = Opposite leg / Adjacent leg
Tan(B) = 4/5
B = arctan(4/5)
B = 51.34 degrees.
Solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain a decimal approximation for the solution.e^x = 22.8
Answer: x = ln 22.8; 3.13
Step-by-step explanation:
Given the exponential equation
e^x = 22.8
We apply ln to both sides since only natural logarithm can cancel out exponents.
lne^x = ln 22.8
x = ln 22.8
x = 3.13
Cara grew 4inches in second grade and 3 inches in third grade. If Cara was 44 inches tall at the start of second grade, how tall is she at the end of third grade?
Answer:
Height of Cara at the end of the Third grade is 51 inches.
Step-by-step explanation:
Given:
Height of Cara at the start of second grade = 44 inches
In second grade she grew = 3 inches.
Hence height of Cara at the end of the second grade will be equal to sum of Height of Cara at the start of second grade and height she grew in second grade.
Framing the equation we get;
height of Cara at the end of the second grade = 44 + 4 = 48 inches
Also Given:
Height she grew in third grade = 3 inches
We need to find Height of Cara at end of third grade.
Hence height of Cara at the end of the Third grade will be equal to sum of Height of Cara at the end of second grade and height she grew in third grade.
Framing in equation form we get;
Height of Cara at the end of the Third grade = 48 + 3 = 51 inches
Hence Height of Cara at the end of the Third grade is 51 inches.
Answer:
51 inches
Step-by-step explanation:
44 + 4 + 3= 51
A set of five distinct positive integers has a mean of $1000$ and a median of $100$. What is the largest possible integer that could be included in the set?
Answer:
e = 4796
Step-by-step explanation:
given,
mean of five distinct positive number = 1000
median of the number = 100
100 is median means two number will be less than 100 and two number will be greater than 100.
let five number be
a , b, c, d, e
'e' should be the largest number
As 100 is median so 'c' = 100.
'a' and 'b' should be as small as possible and d should be the number nearest to 100.
As all the number are distinct so the least number be equal to 1 and 2
now d will be equal to 101 (nearest to 100)
now,
sum of the five number = 5 x 1000 = 5000
a + b + c + d + e = 5000
1 + 2 + 100 + 101 + e = 5000
e = 5000 - 204
e = 4796
hence, the largest number will be equal to e = 4796
The Long family spent $38.62 for school supplies and $215.78 for new school clothes. They paid sales tax on their purchases. If the Long family paid $269.07 total, determine if they paid the correct amount.
A. The Long family paid $2.63 too little for their purchases.
B. The Long family paid the correct amount for their purchases.
C. The Long family paid $1.61 too much for their purchases.
D. The Long family paid $2.63 too much for their purchases.
Answer:
A. The Long family paid $2.63 too little for their purchases.
Step-by-step explanation:
We have been given that the Long family spent $38.62 for school supplies and $215.78 for new school clothes. They paid 6.8% sales tax on their purchases.
First of all, we will add both amounts as:
[tex]\$38.62+$215.78=\$254.40[/tex]
Now, we will find 6.8% of 254.40.
[tex]\text{Amount of tax paid}=\$254.40\times \frac{6.8}{100}[/tex]
[tex]\text{Amount of tax paid}=\$254.40\times0.068[/tex]
[tex]\text{Amount of tax paid}=\$17.2992[/tex]
Upon adding $254.40 and $17.2992, we will get total amount paid by Long family.
[tex]\text{Total amount paid by Long family}=\$254.40+\$17.2992[/tex]
[tex]\text{Total amount paid by Long family}=\$271.6992[/tex]
Now, we will subtract $271.6992 from $269.07:
[tex]\$269.07-\$271.6992[/tex]
[tex]-\$2.6292\approx -\$2.63[/tex]
Since the long family paid $2.63 less than actual amount, therefore, the Long family paid $2.63 too little for their purchases and option A is the correct choice.
Answer:
A
Step-by-step explanation:
Diego said that the answer to the question "how many groups of 5/6?" are in one is 6/5 or 1 1/5. Do you agree with the same explain your explain or show your reasoning
Answer: I agree with 6/5 and with 1 1/5
Step-by-step explanation: okay, to find the value of the amount of 5/6 in 1, we simply just divide 1 by 5/6
Taking a similar problem with different numbers. Let's the the amount of 2s in 10, we do 10/2 which equals 5, so we have 5 2s in 10, you get? 2,4,6,8,10
So dividing 1 by 5/6
I / (5/6)
Change since to multiplication
1 * 6/5
= 6/5
Changing this to a mixed fraction, we get 1 whole number, 1 over 5 = 1 1/5
Answer:Answer: I agree with 6/5 and with 1 1/5
Step-by-step explanation:
Step-by-step explanation: okay, to find the value of the amount of 5/6 in 1, we simply just divide 1 by 5/6
Taking a similar problem with different numbers. Let's the the amount of 2s in 10, we do 10/2 which equals 5, so we have 5 2s in 10, you get? 2,4,6,8,10
So dividing 1 by 5/6
I / (5/6)
Change since to multiplication
1 * 6/5
= 6/5
Changing this to a mixed fraction, we get 1 whole number, 1 over 5 = 1 1/5
(copied from another user) so credit to her
Which statement best describes a solution to the system of equations 3x+Y=17 X+2y=49 A. It has no solution B. It has infinite solutions C. It has a single solution x=15 y=17 D. It has a single solution x=-3 y=26
Answer:
It has a single solution x=-3 y=26
Step-by-step explanation:
The ratios of coefficients of x and y are different, so the pair of equations has one solution. It is easy to tell the first offered solution (15, 17) does not satisfy the first equation, so that choice is eliminated.
Fortunately, the second offered solution, (x, y) = (-3, 26), satisfies both equations.
The equations have a single solution: (x, y) = (-3, 26).
Answer: The equation has a single solution x = -3 , y = 26.
( -3, 26 )
Step-by-step explanation:
3x + y =17 ---------------------(1)
x + 2y = 49 -------------------(2)
Using substitution approach
From (2)
x = 49 - 2y --------------------(3)
Now put (3) in equation (1) and solve.
3(49 - 2y) + y = 17
Open the bracket and solve
3 x 48 - 3 x 2y + y = 17
147 - 6y + y = 17
Gather like terms
-5y = 17 - 147
-5y = -130
Multiple through by (-1)
5y = 130
Divide by 5
y = 130/5
y = 26.
Substitute for y now in equation (3) to get the value of x
3x + y = 17
3x + 26 = 17
3x = 17 - 26
3x = -9
Now , divide by 3
x = -3
The equation had a single solution of x = -3 , y = 26
Chech.
3 x -3 + 26
-9 + 26
= 17
The graph of which function passes through (0,3) and has an amplitude of 3? f (x) = sine (x) + 3 f (x) = cosine (x) + 3 f (x) = 3 sine (x) f (x) = 3 cosine (x)
Answer:
[tex]f(x)=3*cosine(x)[/tex]
Step-by-step explanation:
We are looking for a trigonometric function which contains the point (0, 3), and has an amplitude of 3.
We know that for a sine function [tex]f(x)=sin(x)[/tex], [tex]f(0)= 0[/tex]; therefore the function we a looking for cannot be a sine function because it is zero at [tex]x=0[/tex].
However, the cosine function [tex]f(x)=cos(x)[/tex] gives non-zero value at [tex]x=0:[/tex]
[tex]f(0)=cos(0)=1[/tex]
therefore, a cosine function can be our function.
Now, cosine function with amplitude [tex]a[/tex] has the form
[tex]f(x)=a*cos(x)[/tex]
this is because the cosine function is maximum at [tex]x= 0[/tex] and therefore, has the property that
[tex]f(0)=a*cos(0)= a[/tex]
in other words it contains the point [tex](0, a)[/tex].
The function we are looking for contains the point [tex](0, 3)[/tex]; therefore, its amplitude must be 3, or
[tex]f(x)=3cos(x)[/tex]
we see that this function satisfies our conditions: [tex]f(x)[/tex] has amplitude of 3, and it passes through the point (0, 3) because [tex]f(0)=3[/tex]
Answer:
D
Step-by-step explanation:
edge
The demand curve for original Iguanawoman comics is given by q = (400 − p)^2/100 (0 ≤ p ≤ 400) where q is the number of copies of the publisher can sell per week if it sets the price at $ pa) Find the price elasticity of demand when the price is set at $ 40 per copy.b) Find the price at which the publisher should sell the book in order to maximize weekly revenue. Hint: weekly revenue reaches its maximum value when the price elasticity of demand E = − dq/dp p/q , equals 1. Find the price such that E = 1c) What, to the nearest $ 1, is the maximum weekly revenue the publisher can realize from sales of Iguanawoman comics?