Answer:
23
Step-by-step explanation:
We can check all the possibilities.
It is not necessary to consider y>16, because in this case, 16#y=16 as 16 is too small to be split in y parts.
Now, 1,2,4, 8 and 16 are factors of 16. When you divide 16 by any of the previous integers, the remainder is zero so we discard these.
When y=3, 16=5(3)+1, 16#3=1 so we add y=3. From this, 16=3(5)+1 thus 16#5=1 and we add y=5.
We discard y=6 as 16#6=4 (using that 16=6(2)+4). We also discard y=7 because 16=2(7)+2 then 16#7=2.
For y=9,10,11,12,13,14, when dividing the quotient is one so 16#y=16-y>1 and these values are discarded. However, we add y=15 because 16=15(1)+1 and 16#15=1.
Adding the y values, the sum is 3+5+15=23.
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!
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).
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 telephone pole is _____ feet tall. (Round to the nearest whole number)
14 ft
42 ft
33 ft
85 ft
Answer:
33 ft
Step-by-step explanation:
sin( angle ) = opposite / hypotenuse
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.
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
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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A woman went shopping. First she spent 4/5 of all the money she had in her purse and then she lost 2/3 of what was remaining. Now she has $10 left. How much money did she spend?
Answer:
$120
Step-by-step explanation:
Suppose the woman had x dollars in her purse at the beginning of the shopping.
First, she spent 4/5 of all the money she had, therefore she had 1-4/5=1/5 left
1/5 of x = (1/5)x or 0.2x
Then she lost 2/3 of what was remaining, which is 2/3 * (1/5)x= (2/15)x
What will be left will be (1-2/3) or 1/3 of that 1/5x left after shopping.
This will be 1/3*(1/5)x=(1/15)x
It is given from the problem statement that this is $10 left.
Therefore, (1/15)x= 10
Multiplying through by 15 and simplifying,
x= $150.
Now she spent 4/5 of this $150, which is
(4/5)*150=$120
To find out how much money the woman spent, we need to determine the amount she had in her purse and then calculate the difference after spending and losing some. We can solve this using a step-by-step approach.
Explanation:To calculate how much money the woman spent, we need to follow these steps:
First, she spent 4/5 of all the money she had in her purse. Let's call this amount X.After spending 4/5 of X, she lost 2/3 of what was remaining. This means she has 1/3 of what was remaining left. Let's call this amount Y.We know that Y is equal to $10. So, we can set up the equation Y = $10 and solve for X.Once we find X, we can calculate how much money the woman spent by subtracting X from the original amount she had in her purse.Let's solve this step-by-step:
Step 1: X = Amount she had in her purse
Step 2: Y = (4/5) * X * (1/3)
Step 3: Y = $10
Step 4: Calculate X - Y to find how much money she spent.
Given the following triangle, solve for angle X
A. 41.77
B. 40.46
C. 40.15
D. 39.69
Cos(Angle) = Adjacent leg / Hypotenuse
Cos(X) = 3.5/4.6
X = arccos(3.5/4.6)
X = 40.46 degrees.
I NEED THE ANSWER FOR THIS TOO PLEASE
Answer:
Translated in numerical form: x - 2 ≤ 33.
The solution graph on a numbered line is shown in figure a.
The solution in a set notation: {x|x ≤ 35}
The solution in interval notation: (-∞, 35]
Step-by-step explanation:
"two less than a number is less than or equal to thirty three".
let's say the number is x.
Translated in numerical form: x - 2 ≤ 33.
Lets solve it:
x - 2 ≤ 33
x ≤ 33 + 2
x ≤ 35
The solution graph on a numbered line is shown in figure a.
The solution in a set notation: {x|x ≤ 35}
The solution in interval notation: (-∞, 35]
Keywords: inequality, graph
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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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Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).
Answer:
p(0) = 35
Step-by-step explanation:
-3, √7 and 1-√6 are all roots, hence, we can factorize (x-(-3)) = (x+3), (x-√7) and (x- (1-√6)) = (x-1+√6) from p. Since p has rational coefficients, then we need to cancel out both √7 and √6. To do so we should multiply by the rational conjugate, of the expressions (x-1+√6) and (x-√7), that means, where a square root of a non square positive number appears, place the opposing sign there.
The rational conjugate of (x-√7) is (x+√7), and
(x-√7)*(x+√7) = x²-7
On the other hand, the rational conjugate of (x-1+√6) is (x-1-√6), and
(x-1+√6) * (x-1-√6) = ( (x-1) + √6) * ((x-1) -√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5.
Thus, both x²-7 and x²-2x-5 are factors of p. The polynomial has the form
[tex]P(x) = c(x+3)(x^2-7)(x^2-2x-5)[/tex]
Where c is a constant. To determine c, we need to use the other piece of information given: p(-1) = 8
When we evaluate in -1, we get
[tex]p(-1) = c*(-1+3)((-1)^2-7)((-1)^2-2(-1)-5) = c* 2*(-6)*(-2) = c*24 = 8[/tex]
Thus, c = 8/24 = 1/3.
Therefore,
[tex]p(0) = \frac{1}{3} * (0+3)(0^2-7)(0^2-2*0-5) = \frac{1}{3}*3*(-7)*(-5) = 35[/tex]
I hope that works for you!
A wheel of 0.5 m radius rolls without slipping on a horizontal surface. The axle of the wheel advances at constant velocity, moving a distance of 20 m in 5 s. The angular speed of the wheel about its point of contact on the surface is:
The angular speed of the wheel at its point of contact on the surface is 8 radians per second.
Given that:
A wheel is rolling on a horizontal surface.
The radius of the wheel, r = 0.5 m
The velocity of the axle of the wheel is constant.
Here, the linear velocity can be found by taking the ratio of the distance to the time taken to cover that distance.
So, the linear speed is:
[tex]\text{v}=\frac{20}{5}[/tex]
[tex]=4 \text{ m/s}[/tex]
Now, the relationship between the angular speed and the linear speed is:
[tex]\omega=\frac{v}{r}[/tex]
[tex]=\frac{4}{0.5}[/tex]
[tex]=8[/tex] rad/s
Hence, the angular speed is 8 radians per second.
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The angular speed of the wheel about its point of contact on the surface is 8 rad/s.
To find the angular speed of the wheel about its point of contact on the surface, we can use the relationship between linear and angular velocity.
The linear velocity of a point on the wheel is given by:
v = ω * r
Where:
v is the linear velocity
ω is the angular velocity (angular speed)
r is the radius of the wheel
In this case, we know that the wheel rolls without slipping, which means the linear velocity of the point of contact with the surface is equal to the velocity of the axle. Since the axle moves a distance of 20 m in 5 s, the linear velocity can be calculated as:
v = 20 m / 5 s = 4 m/s
Given that the radius of the wheel is 0.5 m, we can rearrange the equation to solve for ω:
ω = v / r
ω = 4 m/s / 0.5 m
ω = 8 rad/s
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A certain club has 20 members. What is the ratio of the number of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?
A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4
Answer:
C
Step-by-step explanation:
This is a combination question.
In the first instance, we select 5 from 20 and in the second case , we select 4 from 20.
The total number of ways to solve the first instance is 20C5 = 15504 ways
The total number of ways to solve the second instance is 20C4 = 4,845
The ratio of the first to the second scenario is 15,504/4,845 = 3.2 = 16 to 5
Captain salamander is collecting Christmas trees to sell to the market. He collects 31 trees. He sells all his trees to 3 of his friends. Frazer has 3 more trees than Sally. Sally has 7 fewer trees than Flame. How many trees do each of his friends each get
Answer:
Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.
Step-by-step explanation:
Given;
Total Trees = 31
Let the number of trees Flame has be 'x'.
Now given:
Sally has 7 fewer trees than Flame.
framing in equation form we get;
Number of trees Sally has = [tex]x-7[/tex]
Also Given:
Frazer has 3 more trees than Sally.
framing on equation form we get;
Number of trees Frazer has = [tex]x-7+3 = x-4[/tex]
Now We know that Captain salamander total trees in 3 friends.
Hence we can say that;
Total Number of trees is equal to sum of number of trees Flame has and Number of trees Sally has and Number of trees Frazer has.
framing in equation form we get;
[tex]x+(x-7)+(x-4)=31\\\\x+x-7+x-4=31\\\\3x-11=31\\\\3x=31+11\\\\3x = 42\\\\x = \frac{42}{3} = 14[/tex]
Hence Number of trees Flame has = 14 trees
Number of trees Sally has = [tex]x-7 = 14-7 =7 \ trees[/tex]
Number of trees Frazer has = [tex]x-4 = 14-4 = 10 \ trees[/tex]
Hence Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.
On a certain hot summer's day, 539539 people used the public swimming pool. The daily prices are $ 1.25$1.25 for children and $ 2.50$2.50 for adults. The receipts for admission totaled $ 1023.75 .$1023.75. How many children and how many adults swam at the public pool that day?
Answer:the number of children that swam at the public pool is 259
the number of adult that swam at the public pool is 280
Step-by-step explanation:
Let x represent the number of children that swam at the public pool that day.
Let y represent the number of adult that swam at the public pool that day.
On a certain hot summer's day,539 people used the public swimming pool. This means that
x+ y = 539
The daily prices are $ 1.25 for children and $ 2.50 for adults. The receipts for admission totaled $ 1023.75. This means that
1.25x + 2.5y = 1023.75 - - - - - - - - - -1
Substituting x = 539 - y into equation 1, it becomes
1.25(539 - y) + 2.5y = 1023.75
683.75 - 1.25y + 2.5y = 1023.75
- 1.25y + 2.5y = 1023.75 - 683.75
1.25y = 350
y = 350/1.25 = 280
Substituting y = 280 into x = 539 - y , it becomes
x = 539 - 280 = 259
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.
Two random samples are taken, with each group asked if they support a particular candidate. A summary of the sample sizes and proportions of each group answering ``yes'' are given below: Pop1: n1=92 p1=0.768 Pop2: n2=95 p2=0.646 Suppose that the data yields (-0.0313, 0.2753) for a confidence interval for the difference p1-p2 of the population proportions. What is the confidence level? (Give your answer in terms of percentages.)
Answer:
And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex[ or 98%
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]p_1[/tex] represent the real population proportion for 1
[tex]\hat p_1 =0.768[/tex] represent the estimated proportion for 1
[tex]n_1=92[/tex] is the sample size required for 1
[tex]p_2[/tex] represent the real population proportion for 2
[tex]\hat p_2 =0.646[/tex] represent the estimated proportion for 2
[tex]n_2=95[/tex] is the sample size required for 2
[tex]z[/tex] represent the critical value for the margin of error
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:
[tex]ME= \frac{0.2753-(-0.0313)}{2}=0.1533[/tex]
And we know that the margin of erro is given by:
[tex]ME=z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
We have all the values except the value for [tex]z_{\alpha/2}[/tex]
So we can find it like this:
[tex]0.1533=z_{\alpha/2} \sqrt{\frac{0.768(1-0.768)}{92} +\frac{0.646 (1-0.646)}{95}}[/tex]
And solving for [tex]z_{\alpha/2}[/tex] we got:
[tex]z_{\alpha/2}=2.326[/tex]
And we can find the value for [tex]\alpha/2[/tex] with the following excel code:
"=1-NORM.DIST(2.326,0,1,TRUE)"
And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex] or 98%
The confidence level is 95%. This conclusion is reached by converting the upper bound of the confidence interval into a standard z-score and comparing it to the z-scores for common confidence levels.
Explanation:To determine the confidence level of interval, we need to look at the proportion of the total area under the standard normal curve that falls within the interval when converted into a standard z-score. For instance, a 90% confidence interval corresponds to an area of 0.90 under the curve, with 0.05 in each tail, and a Z score of ±1.645. A 95% confidence interval corresponds to an area of 0.95 under the curve, with 0.025 in each tail, and a Z score of ±1.96. A 99% confidence level corresponds to an area 0.99 under the curve, with 0.005 in each tail, and a Z score of ±2.575.
In this case, with a confidence interval of (-0.0313, 0.2753) and the estimated proportions of p1=0.768 and p2=0.646, we find the estimated difference is 0.122 and its standard deviation is 0.0782.
Converting the upper bound of the confidence interval into a standard z-score: (0.2753 - 0.122) / 0.0782 = 1.959, which corresponds to a 95% confidence level. Thus, the inference can be that if we were to sample from these populations many times, in 95% of the cases, the true difference between p1 and p2 would lie within the interval (-0.0313, 0.2753).
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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.
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Max is stacking logs at his campground for firewood. After his first load of logs, he has 8 logs on the stack. After the seventh load, he has 62 logs on the stack. Use sequence notation to represent the arithmetic function.
A] an = 8 + 6(n - 1)
B] an = 62 + 6(n - 1)
C] an = 8 + 9(n - 1)
D] an = 62 + 9(n - 1)
Answer:
[tex]\displaystyle a_n=8+9(n-1)[/tex]
Correct option: C]
Step-by-step explanation:
Arithmetic Sequences
Each term in an arithmetic sequence is obtained as the previous term plus a constant number called the common difference. The general term is
[tex]\displaystyle a_n=a_1+(n-1).r[/tex]
We are given this information
[tex]\displaystyle a_1=8\ ,\ a_7=62[/tex]
Replacing those values in the formula
[tex]\displaystyle 62=8+(7-1).r[/tex]
Solving for r
[tex]\displaystyle r=\frac{62-8}{6}=\frac{54}{6}=9[/tex]
[tex]\displaystyle r=9[/tex]
The general term is, then
[tex]\displaystyle a_n=8+(n-1)9[/tex]
Or equivalently
[tex]\displaystyle a_n=8+9(n-1)[/tex]
Correct option: C]
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
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.
One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?
Answer:
Step-by-step explanation:
160+112n=180k
112n=180k-160
for k=1
180-160=20(not divisible by 112)
k=2
180*2-160=360-160=200(not divisible by 112)
k=3
180*3-160=540-160=380(not divisible by 112)
180*4-160=720-160=560(divisible by 112)
so number of sides=560/112 +1=5+1=6
or (n-2)180=720
n-2=720/180=4
n=4+2=6
Answer:
6
Step-by-step explanation:
The sum of interior angle of a polygon is (n - 2)180.
But in the convex polygon given in the question, we know that the sum of the interior angles is as follows: : 160 + 112(n - 1)
Equating both will yield the following:
180n -360 = 112n - 112 + 160
180n - 360 = 112n + 48
180n - 112n = 360 + 48
68n = 408
n = 408/68 = 6
Hence , the convex polygon has 6 sides
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
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
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)
Victor read a total of 12 books over 4 months. After belonging to the book club for 5 months ,how many books will Victor have read in all? Solve using unit rates.
Answer:
15 books
Step-by-step explanation:
Given that Victor read a total of 12 books over 4 months which means for 1 month he reads 12/4 = 3 books
Also given that he belongs to the book club for 5 months
We know that he reads 3 books in 1 month
So in 5 months he reads [tex]5\times3=15books[/tex]
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?
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
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.