Answer:
a). r = [tex]\frac{6}{7}[/tex]
b). At least 5 terms should be added.
Step-by-step explanation:
Formula representing sum of infinite geometric sequence is,
[tex]S_{\inf}=\frac{a}{1-r}[/tex]
Where a = first term of the sequence
r = common ratio
a). If the sum is seven times the value of its first term.
[tex]7a=\frac{a}{1-r}[/tex]
[tex]7=\frac{1}{1-r}[/tex]
7(1 - r) = 1
7 - 7r = 1
7r = 7 - 1
7r = 6
r = [tex]\frac{6}{7}[/tex]
b). Since sum of n terms of the geometric sequence is given by,
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]
If the sum of n terms of this sequence is more than half the value of the infinite sum.
[tex]\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}[/tex] > [tex]\frac{7a}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{1}{2}[/tex]
[tex]-(\frac{6}{7})^{n}> -\frac{1}{2}[/tex]
[tex](\frac{6}{7})^{n}< \frac{1}{2}[/tex]
[tex](0.85714)^{n}< (0.5)[/tex]
n[log(0.85714)] < log(0.5)
-n(0.06695) < -0.30102
n > [tex]\frac{0.30102}{0.06695}[/tex]
n > 4.496
n > 4.5
Therefore, at least 5 terms of the sequence should be added.
What single decimal multiplier would you use to increase by 7% followed by a 4% decrease?
Answer: To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93
Step-by-step explanation:
Help! Please do a,b,c and d with explanation
Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
__
b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
__
c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
__
d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
A 40-foot ladder leans against a building. If
the base of the ladder is 6 feet from the
base of the building, what is the angle
formed by the ladder and the building?
Answer:
Step-by-step explanation:
draw it out and use trig function to solve for the angle. Keep in mind, after getting trig, need to do inverse
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a gender selection method used to increase the likelihood of a baby being born a girl, 1936 users of the method gave birth to 950 boys and 986 girls. There is about a 21% chance of getting that many girls if the method had no effect.
Answer:
Due to the fact that there is 21% chance of getting that many girls by chance and also In conjunction to that; there is no test involved as well , we can conclude that the method does not have statistical significance.
The result does not appear to have a practical significance.
Step-by-step explanation:
Given that:
In a random selection 1936 users, we observed that the method gave birth to 950 boys and 986 girls
There is about a 21% chance of getting that many girls if the method had no effect.
Due to the fact that there is 21% chance of getting that many girls by chance and also In conjunction to that; there is no test involved as well , we can conclude that the method does not have statistical significance.
Given that:
The number of girls = 986
Number of boys = 950
Number of babies born = 1936
The percentage of girls = number of girls born/ number of babies born
The percentage of girls = 986 /1936
The percentage of girls = 0.5093
The percentage of girls = 50.93%
We can infer that this method does not have a practical significance because most couples would not prefer to use a method that raise the likelihood of a girl from the approximately 50% rate expected by chance to the 50.93% .
Given A triangle with sides x=6.35 cm and Y=12.25 cm with an angle of 90 degrees between them, find the length of the hypotenuse and the size of the other two angles.
Answer:
Hypotenuse = 13.798 cm, Angle1 = 27.4° and Angle2 = 62.59°
Step-by-step explanation:
The first step to help us understand the question would be to draw it out.
A right angled triangle, with the two sides that make the right angle being x and y (it does not matter which way you put x and y).
I have attached the quick sketch I will refer to.
To find the length of the hypotenuse (lets call it H) we can use Pythagoras theorem as shown below
[tex]{x^{2}+y^{2}} = H^{2}[/tex]
Substitute in our values for x and y, and solve for H
[tex]{6.35^{2}+12.25^{2}} = H^{2}[/tex]
[tex]190.385 = H^{2}[/tex]
[tex]\sqrt{190.385} = H[/tex]
H = 13.79 cm
To find the other two angles of the triangle we will use trigonometry
I will first look for angle ∅. Since we have all three sides of the triangle we can use any of the three trig functions, I chose to use Tan
Tan ∅ [tex]= \frac{opposite}{adjacent}[/tex]
Substitute in our values for x and y, and solve for ∅
Tan ∅ = [tex]\frac{6.35}{12.25}[/tex]
∅ = [tex]tan^{-1} \frac{6.35}{12.25}[/tex]
∅ = 27.4°
Now do the same for angle β. I chose to use Tan again
Tan β [tex]= \frac{opposite}{adjacent}[/tex]
Substitute in our values for x and y, and solve for β
Tan β = [tex]\frac{12.25}{6.35}[/tex]
β = [tex]tan^{-1} \frac{12.25}{6.35}[/tex]
β = 62.59°
An internet story that goes viral has a number of readers that is increasing exponentially, with number of readers in millions represented by 2x, where x is the time, in days. Find the time when the number of readers reaches 9 million.
What is the exact solution written as a logarithm?
What is an approximate solution rounded to the nearest thousandth?
Answer:
a) [tex]x = \log_{2} 9,000,000[/tex], b) [tex]x \approx 23.101\,days[/tex]
Step-by-step explanation:
The number of readers as a function of time is:
[tex]n = 2^{x}[/tex]
Where:
[tex]x[/tex] - Time, measured in days.
[tex]n[/tex] - Number of readers, dimensionless.
a) The time when the number of readers reaches 9 million is:
[tex]x = \log_{2} n[/tex]
[tex]x = \log_{2} 9,000,000[/tex]
b) The approximate solution rounded to the nearest thousandth is:
[tex]x \approx 23.101\,days[/tex]
Duke takes a car in for basic service. The service agent says a few extra repairs are needed, so Duke adds the cost of those repairs mentally, rounding to the nearest 10. What is Duke's total estimate for the repairs? The costs are as follows: Wheel alignment: $82 Transmission fluid flush: $157 Cabin air filter: $58 Note: 4 or less rounds down, 5 or more rounds up. For example, 14 becomes 10, while 15 becomes 20.
Answer:
The total repair cost was around $300 .
Step-by-step explanation:
I wasn't sure when you were saying to round, so here are two options.
(For rounding at the end) :
82+157+58 = 297
Rounds to 300.
(For rounding as he's adding everything up) :
80+160+60= 300.
So either way it's 300!
Hope this helped!
What’s the correct answer for this question?
Answer:
C:
Step-by-step explanation:
Both angles add up to 180°
<BCG + <BFG = 180°
2x+146+4x+238=180
6x+384 = 180°
6x = 180-384
6x = -204
Dividing both sides by 6
x = -34
A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of these 25 are selected at random to be checked by a particular technician, what is the probability that exactly 3 of those selected are laser printers (so that the other 3 are inkjets)
Answer:
The probability is 0.31
Step-by-step explanation:
To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.
In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is [tex]\binom{25}{6}[/tex], where [tex]\binom{n}{k} = \frac{n!}{(n-k)!k!}[/tex]. We have that [tex]\binom{25}{6} = 177100[/tex]
Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in [tex]\binom{10}{3}\cdot \binom{15}{3} = 54600[/tex]
So the probability of having 3 laser printers and 3 inkjets is given by
[tex] \frac{54600}{177100} = \frac{78}{253} = 0.31[/tex]
The lines shown below are parallel if the green line has a slope of 8 what is the slope of the redline?
Answer:
Option D
Step-by-step explanation:
If these lines are parallel, they should have the same slope. How so? Well slope is the change in axis, y / x more specifically. If the lines are parallel they should change at a similar rate so that they don't intersect, and hence are, by definition, ║;
[tex]Green Line's Slope = Red Line's Slope,\\8 = Red Line's Slope,\\Red Line's Slope = 8 units\\\\Solution - Option D[/tex]
Hope that helps!
Which equation can be used to determine the distance between the origin and (–2, –4)? d = StartRoot ((0 minus 2) + (0 minus 4)) squared EndRoot d = StartRoot (0 minus (negative 2)) squared + (0 minus (negative 4)) squared EndRoot d = StartRoot ((0 minus 2) minus (0 minus 4)) squared EndRoot d = StartRoot (0 minus (negative 2)) squared minus (0 minus (negative 4)) squared EndRoot
Answer:person up top is right it’s B
Step-by-step explanation: on edg 2020
Answer:
The answer is B
Step-by-step explanation:
lol yw guys
The combined SAT scores for the students at a local high school are normally distributed with a mean of 1527 and a standard deviation of 291. The local college includes a minimum score of 1207 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement? P(X > 1207) =
Answer:
Step-by-step explanation:
Let x be the random variable representing the SAT scores for the students at a local high school. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 1527
σ = 291
the probability to be determined is expressed as P(x > 1207)
P(x > 1207) = 1 - P(x ≤ 1207)
For x < 1208
z = (1207 - 1527)/291 = - 1.1
Looking at the normal distribution table, the probability corresponding to the z score is 0.16
P(x > 1207) = 1 - 0.16 = 0.84
Therefore, the percentage of students from this school earn scores that satisfy the admission requirement is
0.84 × 100 = 84%
An aeroplane X whose average speed is 50°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then changes its course and flies on a bearing 1200 to an airstrip A. Another aeroplane Y leaves kano airport at 10.00am and flies on a straight course to the airstrip A. both planes arrives at the airstrip A at 11.30am. calculate the average speed of Y to three significant figures. the direction of flight Y to the nearest degree
Answer:
(a)123 km/hr
(b)39 degrees
Step-by-step explanation:
Plane X with an average speed of 50km/hr travels for 2 hours from T (Kano Airport) to point U in the diagram.
Distance = Speed X Time
Therefore: Distance from T to U =50km/hr X 2 hr =100 km
It moves from Point U at 9.00 am and arrives at the airstrip A by 11.30am.
Distance, UA=50km/hr X 2.5 hr =125 km
Using alternate angles in the diagram:
[tex]\angle U=110^\circ[/tex]
(a)First, we calculate the distance traveled, TA by plane Y.
Using Cosine rule
[tex]u^2=t^2+a^2-2ta\cos U\\u^2=100^2+125^2-2(100)(125)\cos 110^\circ\\u^2=34175.50\\u=184.87$ km[/tex]
Plane Y leaves kano airport at 10.00am and arrives at 11.30am
Time taken =1.5 hour
Therefore:
Average Speed of Y
[tex]=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)[/tex]
b)Flight Direction of Y
Using Law of Sines
[tex]\dfrac{t}{\sin T} =\dfrac{u}{\sin U}\\\dfrac{125}{\sin T} =\dfrac{184.87}{\sin 110}\\123 \times \sin T=125 \times \sin 110\\\sin T=(125 \times \sin 110) \div 184.87\\T=\arcsin [(125 \times \sin 110) \div 184.87]\\T=39^\circ $ (to the nearest degree)[/tex]
The direction of flight Y to the nearest degree is 39 degrees.
Consider the following numbers Which of these numbers are counting numbers?
{9 ,1, 4/5, √16 , 0.7 , -1, -√2 , π , 0}
The counting number(s) is/are _______(Use a comma to separate answers as needed Do not simplify.)
Answer:
9, 1
Step-by-step explanation:
Counting numbers are numbers that can be used for counting purposes. This group of numbers does not include negative numbers, fractions, zero, decimal numbers etc. They are positively directed whole numbers.
From the question, given the condition not to simplify, then the counting numbers are:
9, 1
others numbers can not be referred to as counting numbers.
Aisha needs to be at least 48 inches tall to ride the colossal coaster at the amusement park. If she grows 5 inches during the next year, Aisha will still not be tall enough to ride. In the context of this situation, what does the inequality x less-than 43 represent?
Answer:
Aisha is shorter than 43 inches.
Step-by-step explanation:
[tex]x+5=48[/tex]
[tex]x=48-5[/tex]
[tex]x=43[/tex]
[tex]x >43[/tex]
Answer:
The answer is B!
Step-by-step explanation:
Test taking! <3
Suppose that a random number generator randomly generates a number from 1 to 65. Once a specific number is generated, the generator will not select that number again until it is reset. If a person uses the random number generator 65 times in a row without resetting, how many different ways can the numbers be generated?
Answer:
65!
65! = 8. 2547650592 * 10^ 90 approximately
Step-by-step explanation:
A random number generator randomly generates a number from 1 to 65.
Once a specific number is generated, the generator will not select that number again until it is reset.
The number of ways it can be used is = 65!
65! = 8. 25476505* 10^ 90 approximately
What statement best explains The relationshipBetween numbersDivisible by 5 and 10
Answer:
a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Step-by-step explanation:
Given : Statement 'The relationship between numbers divisible by 5 and 10'.
To find : What statement BEST explains the statement?
Solution :
First we study the divisibility rules,
Rule for the number divisible by 5 is that number must end in 5 or 0.
Rule for the number divisible by 10 is that number need to be even and divisible by 5, as the prime factors of 10 are 5 and 2 and the number to be divisible by 10, the last digit must be a 0.
According to the divisibility rules Option D is correct.
Therefore, The correct statement explains the relationship between numbers divisible by 5 and 10 is a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14. Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16. Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Answer:
Due to the higher z-score, Norma should be offered the job
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Whoever has the higher z-score should get the job.
Norma:
Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14.
This means that [tex]X = 84.2 \mu = 67.4, \sigma = 14[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{84.2 - 67.4}{14}[/tex]
[tex]Z = 1.2[/tex]
Pierce:
Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16.
This means that [tex]X = 276.8, \mu = 264, \sigma = 16[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{276.8 - 264}{16}[/tex]
[tex]Z = 0.8[/tex]
Reyna:
Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8.
This means that [tex]X = 7.62, \mu = 7.3, \sigma = 0.8[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.62 - 7.3}{0.8}[/tex]
[tex]Z = 0.4[/tex]
Due to the higher z-score, Norma should be offered the job
Match each equivalent expression with the property that it represents.
Associative Property of Multiplication
3 + (5 + 7) = (3 + 5) + 7
Identity Property of Multiplication
3 + 5 = 5 + 3
Identity Property of Addition
5(1) = 5
Commutative Property of Addition
(3 + 5) + 0 = (3+5)
Associative Property of Addition
[ 3(5) (4) = (3) 5(4)]
Answer:
Associative Property of Multiplication: [ 3(5) (4) = (3) 5(4)]Identity Property of Multiplication: 5(1) = 5Identity Property of Addition: (3 + 5) + 0 = (3+5)Commutative Property of Addition: 3 + 5 = 5 + 3Associative Property of Addition: 3 + (5 + 7) = (3 + 5) + 7Step-by-step explanation:
The associative property lets you move parentheses in a sum or product. That is, it doesn't matter which sum or product you compute first.
The commutative property lets you swap the order of operands in a sum or product.
The identity property says the operation using the identity element gives the original value, unchanged.
Answer:
Step-by-step explanation:
I would like to purchase 20 products at a cost of $65 per product. What would be my total with 3.5 sales tax
Answer:
Answer:
The total is: $ 1345.5
Step-by-step explanation:
It is given that:
I would like to purchase 20 products at a cost 65.00 per product.
This means that the cost of 20 products will be:
Also, there is a sales tax of 3.5%
This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.
i.e. he need to pay 3/5% on $ 1300
This means that the amount of tax he need to pay is: 3.5% of 1300
= 3.5%×1300
= 0.035×1300
= $ 45.5.
Hence, the total cost is: $ 1300+$ 45.5
This means that the total cost is: $ 134.5
hence of other wise find the radius of a circle when A= 88/63 leave your answer as a fraction in its simplest form
Answer:
Step-by-step explanation:
A=πr^2
But A=88/63
88/63=πr^2
88/63π=r^2
√88/63π=r
Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137 ft from camera 3. Cameras 1 and 3 were 158 ft apart. Which camera had to cover the greatest angle
Answer:
Camera 2nd has to cover the maximum angle, i.e. [tex]78.70^\circ[/tex].
Step-by-step explanation:
Please have a look at the triangular park represented as a triangle [tex]\triangle ABC[/tex] with sides
a = 110 ft
b = 158 ft
c = 137 ft
1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.
We can use law of cosines here, to find out the angles [tex]\angle A, \angle B, \angle C[/tex]
As per Law of cosine:
[tex]cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}[/tex]
Putting the values of a,b and c to find out angles [tex]\angle A, \angle B, \angle C[/tex].
[tex]cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ[/tex]
[tex]cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ[/tex]
[tex]cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ[/tex]
Camera 2nd has to cover the maximum angle, i.e. [tex]78.70^\circ[/tex].
WILL MARK BRAINLIEST PLEASE HELP
Answer:
1) h = -1/2t^2 +10t
2) h = -1/2(t -10)^2 +72
3) domain: [0, 20]; range: [0, 50]
Step-by-step explanation:
1.) I find it easiest to start with the vertex form when the vertex is given. The equation of the presumed parabolic path for Firework 1 is ...
h = a(t -10)^2 +50
To find the value of "a", we must use another point on the graph. (0, 0) works nicely:
0 = a(0 -10)^2 +50
-100a = 50 . . . . . . subtract 100a
a = -1/2 . . . . . . . . . divide by -100
Then the standard-form equation is ...
h = (-1/2)(t^2 -20t +100) +50
h = -1/2t^2 +10t
__
2.) The path of Firework 2 is translated upward by 22 units from that of Firework 1.
h = -1/2(t -10)^2 +72
__
3.) The horizontal extent of the graph for Firework 1 is ...
domain: 0 ≤ t ≤ 20
The vertical extent of the graph for Firework 1 is ...
range: 0 ≤ h ≤ 50
Which of the following sequence of transformations takes point J(9, 1) to J'(-3, 7)?
Answer:
Translate point J 12 units down and 6 units right.
You received your monthly bank statement and you are reconciling your account balance using the information below. What is the true balance of your checking account? Check Register Balance $314.97 Bank Statement Balance $423.68 Outstanding Checks $123.71 Service Charge $15.00
Answer:
299.97 is the actual answer
Step-by-step explanation:
I took the test.
James makes fruit punch by mixing fruit jucie and lemonade in the ratio 1:4 she needs to make 40 liters of punch for a party How much of each ingredient does she need? Fruit juice ? Liters Lemonade ?liters
Part 2
During the party Josie decides to make some more.
She has 4 litres of fruit juice left and plenty of lemonade.
How much extra punch can she make?
Part 3
To make the second batch of punch go further Josie adds 2 more litres of lemonade.
What is the ratio of fruit juice to lemonade in the second batch?
Answer:
Part 1.
Juice = 8 L.
Lemonade = 32 L.
Part 2.
20 L punch Josie can make.
Part 3.
New ratio juice : lemonade = 2 : 9
Step-by-step explanation:
Part 1.
1+4 = 5 parts altogether, 1 parts for juice and 4 parts for lemonade.
40 : 5 = 8 L is 1 part.
Juice - 1 part - 8 L.
Lemonade - 4 parts - 4*8 = 32 L.
Part 2.
1 parts of juice needs 4 parts of lemonade
4 L of juice needs x L of lemonade
1 : 4 = 4 : x
x = 4*4/1 = 16 L lemonade
4+ 16 = 20 L punch Josie can make
Part 3.
It was 4 L of juice and 16 L of lemonade.
After 2 L lemonade was added, we have 4 L of juice and (16+2) = 18 L of lemonade.
4 L juice : 18 L lemonade = 4/2 L juice : 18/2 L lemonade =
= 2 L juice: 9L lemonade
New ratio juice : lemonade = 2 : 9
4. The 92 million Americans of age 50 and over control 50% of all discretionary income. AARP estimates that the average annual expenditure on restaurants and carryout food was $1,873 for individuals in the age group. Suppose this estimate is based on a sample of 80 persons and that the sample standard deviation is $550. a. At 95% confidence, what is the margin of error
Answer:
$120.52
Margin of error M.E = $120.52
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
Where M.E = margin of error
M.E = zr/√n
Given that;
Mean x = $1,873
Standard deviation r = $550
Number of samples n = 80
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
M.E = (1.96 × $550/√80) = 120.5240639872
M.E = $120.52
Margin of error M.E = $120.52
What is the equation of the exponential graph shown?
Answer:
[tex]100(0.5)^{x}[/tex]
Step-by-step explanation:
According to the graph, the y int is at 100
so that is the starting point
Then at 1 it is at 50
[tex]\frac{100}{50}[/tex] is 2 so that means it is reduced by half
Just to make sure, [tex]\frac{50}{25}[/tex] is also /2 so that means it is the slope
Since it is a decay, the slope has to be less than one so you get the reciprecol of 2 to get....
[tex]\frac{1}{2}[/tex]
Answer:f(x)=100(2^x)
Step-by-step explanation:
The top and bottom margins of a poster are each 15 cm and the side margins are each 10 cm. If the area of printed material on the poster is fixed at 2400 cm2, find the dimensions of the poster with the smallest area.
Answer:
the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
Step-by-step explanation:
From the given question.
Let p be the length of the of the printed material
Let q be the width of the of the printed material
Therefore pq = 2400 cm ²
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
To find the dimensions of the poster; we have:
the length of the poster to be p+30 and the width to be [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex]
The area of the printed material can now be: [tex]A = (p+30)(\dfrac{2400 }{p} + 20)[/tex]
=[tex]2400 +20 p +\dfrac{72000}{p}+600[/tex]
Let differentiate with respect to p; we have
[tex]\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}[/tex]
Also;
[tex]\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}[/tex]
For the smallest area [tex]\dfrac{dA}{dp }=0[/tex]
[tex]20 - \dfrac{72000}{p^2}=0[/tex]
[tex]p^2 = \dfrac{72000}{20}[/tex]
p² = 3600
p =√3600
p = 60
Since p = 60 ; replace p = 60 in the expression q = [tex]\dfrac{2400 \ cm^2}{p}[/tex] to solve for q;
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
q = [tex]\dfrac{2400 \ cm^2}{60}[/tex]
q = 40
Thus; the printed material has the length of 60 cm and the width of 40cm
the length of the poster = p+30 = 60 +30 = 90 cm
the width of the poster = [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex] = [tex]\dfrac{2400 \ cm^2}{60} + 20[/tex] = 40 + 20 = 60
Hence; the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
Which ordered pair is the best estimate for the
solution of the system of equations?
y =
3x + 6
y = 1x – 2
Answer:
-4, -6
Step-by-step explanation:
3x+6= 1x-2
2x+6= -2
2x= -8
x= -4
Now that you have your x variable, you can go back and plug it in to your original equations:
y= 3(-4)+6,
y= (-12)+6 therefore y= -6
y=1(-4) -2,
y= (-4) -2 therefore y = -6