The standard deviation of the fitness center is larger than the standard deviation of the last shipment
Which distribution has the larger standard deviation?The given parameters are:
Distribution: Normal distribution
The last shipment
Mean weight = 2.7 grams
Standard deviation = 0.1 gram.
Fitness center
Mean weight = 100.2 pounds
Standard deviation = 0.1 pound
In the above parameters, we can see that the fitness center has a larger mean weight than the last shipment, while they both have the same standard deviation
This means that the standard deviation of the fitness center is larger than the standard deviation of the last shipment
And so, the distribution of the fitness center is more dispersed
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Suppose that a certain college class contains 51 students. Of these, 23 are freshmen, 30 are mathematics majors, and 7 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a freshman and a mathematics major?
(b) Given that the student selected is a freshman, what is the probability that he is also a mathematics major
Considering the definition of probability and its properties:
the probability that the student is both a freshman and a mathematics major is 3/17. given that the student selected is a freshman, what is the probability that he is also a mathematics major is 3/10.Definition of ProbabitityProbability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.
P(A)= number of favorable cases÷ number of total cases
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Conditional probabilityThe conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:
P(A|B) = P(A∩B)÷ P(B)
Probability that the student is both a freshman and a mathematics majorIn first place, let's define the following events:
F: The event that the student is a freshman.M: The event that the student is a mathematics major.You know:
A certain college class contains 51 students. 23 students are freshmen. → P(F)= 23÷51 → P(F)= 23/5130 students are mathematics majors. → P(M)= 30÷51 → P(M)= 30/517 students are neither a freshman or a mathematics mayor → P [(F∪M)']= 7÷51= 7/51The probability that a student is a freshman or a mathematics mayor is:
P [(F∪M)']= 1- P(F∪M)
7/51= 1 - P(F∪M)
7/51 - 1= -P(F∪M)
-44/51= -P(F∪M)
44/51= P(F∪M)
So, the probability that the student is both a freshman and a mathematics major is calculated as:
P(F∪M)= P(F) + P(M) -P(F∩M)
44/51= 23/51 + 30/51 - P(F∩M)
44/51- 23/51 - 30/51= - P(F∩M)
-3/17= - P(F∩M)
3/17= P(F∩M)
Finally, the probability that the student is both a freshman and a mathematics major is 3/17.
Probability that a student is a mathematics major being a freshmanThe probability that a student is a mathematics major, knowing that he is also a freshman, is calculated as:
P(M|F) = P(M∩F)÷ P(M)
So:
P(M|F) = 3/17÷ 30/51
P(M|F) = 3/10
Finally, given that the student selected is a freshman, what is the probability that he is also a mathematics major is 3/10.
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⦁ Sally and Mary are best friends. Their families both went to the beach on June 1st to celebrate the start of summer vacation. After that day Sally’s family continues to go to the beach every 4 days. Mary’s family only goes to the beach every 14 days.
⦁
⦁ Would you use Greatest Common Factor or Least Common Multiple to help solve this problem?
Based on the fact that Mary's family goes every 14 days and Sally's family goes every 4 days, the method of solving this problem is the Least Common Multiple.
When to use Least Common Multiple?The Least Common Multiple is used to find out when two or more events will occur at the same time if those events occur at fixed intervals that are different from each other.
Sally's family goes to the beach every 4 days and Mary's family goes every 14 days.
You can therefore solve for the day that they will next meet on the beach using their Least Common Multiple which is 28. They will next be at the beach on the same day after 28 days.
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Question 6 of 25
The table below shows the cost of sending packages of various weights.
What is the cost of mailing a 6-ounce package?
Weight
(ounces)
1
2
3
4
50
6
7
Cost
(dollars)
.32
.64
.96
1.28
1.60
1.92
2.24
Answer here
dollars
PLEASE HELP FAST
Answer:
$1.92
Step-by-step explanation:
The corresponding row to 6 ounces is this
3y is greater than or equal to 9
[tex]3y \geqslant 9 \\ y \geqslant \frac{9}{3} \\ y \geqslant 3[/tex]
Answer: y > 3
Step-by-step explanation: 3y > 9
3y/3 > 9/3
y > 3
Parts of algebraic expressi
Consider the expression x² + x + 7.
- 22
Complete 2 descriptions of the parts of the expression.
1. The entire expression is a sum with
2. The coefficients are
The terms in the expression x² + x + 7 + 22 are x², x, 7 and 22.
What is an expression?
The value of anything is represented by a group of numbers, symbols, and operators called an expression.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.
The terms in the given expression are x², x, 7 and 22.
The coefficient of x² is 1 and coefficient of x is also 1.
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SOME ONE PLEASE ANSWER ASAP NEED EXPLAIN FULL STEPS
Answer:
[tex]{ \tt{( \frac{ - 4}{9} \times \frac{63}{28}) - ( \frac{33}{66} \times \frac{ - 51}{17} ) + ( \frac{5}{8} \times \frac{4}{10)} }} \\ \\ = { \tt{( \frac{ - 4}{28} \times \frac{63}{9}) - ( \frac{1}{2} \times \frac{ - 3}{1} ) + ( \frac{5}{10} \times \frac{4}{8} )}} \\ \\ { \tt{ = ( - 1) - ( - \frac{3}{2} ) + ( \frac{1}{4}) }} \\ \\ = { \tt{ \frac{3}{4} }}[/tex]
Answer:
[tex]\sf \dfrac{3}{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\implies \sf \left(\dfrac{-4}{9} \times \dfrac{63}{28}\right)-\left(\dfrac{33}{66} \times \dfrac{-51}{17}\right)+\left(\dfrac{5}{8} \times \dfrac{4}{10}\right)[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{a \times b}{c \times d}:[/tex]
[tex]\implies \sf \left(\dfrac{-4\times63}{9\times28} \right)-\left(\dfrac{33 \times -51}{66 \times 17}\right)+\left(\dfrac{5\times4}{8\times10} \right)[/tex]
Multiply the numbers:
[tex]\implies \sf \left(\dfrac{-252}{252} \right)-\left(\dfrac{-1683}{1122}\right)+\left(\dfrac{20}{80} \right)[/tex]
Reduce the fractions:
[tex]\implies \sf -1-\left(\dfrac{-3}{2}\right)+\left(\dfrac{1}{4} \right)[/tex]
[tex]\textsf{Apply rule}\quad \:a-\left(-b\right)=a+b:[/tex]
[tex]\implies \sf -1+\dfrac{3}{2}+\dfrac{1}{4}[/tex]
Adjust the fractions based on the LCM of 4:
[tex]\implies \sf \dfrac{-4}{4}+\dfrac{6}{4}+\dfrac{1}{4}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \sf\dfrac{-4+6+1}{4}[/tex]
Add the numbers in the numerator:
[tex]\implies \sf \dfrac{3}{4}[/tex]
What is 31 lb to g (Convert from on to kg, then kg to g).
Answer:
The answer would be 14061.364 grams.
Lorie ordered a shed to hold her gardening supplies. The shed had a length of 18.25 ft, a width of 15 ft, and a height of five and one fifth ft.
Determine the volume, V, using the formula V = lwh.
1,423.5 cubic ft
1,373.5 cubic ft
142.35 cubic ft
38.45 cubic ft
The volume of the shed ordered by Lorie to hold her gardening supplies is (option a) 1423.5 cubic ft.
Given,
Lorie ordered a shed to hold her gardening supplies.
The length of the shed, l = 18.25 feet
The width of the shed, w = 15 feet
The height of the shed, h = 5 1/5 feet = 26/5 = 5.2 feet
We have to determine the volume of the shed:
From the given data we can assume that the shed is like a cuboid. So to determine the volume, we can use the cuboidal formula.
That is,
Volume = length × width × height
V = l × w × h
V = 18.25 × 15 × 5.2
V = 1423.5 feet
Therefore, the volume of the shed ordered by Lorie to hold her gardening supplies is 1423.5 feet.
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5. What is the monthly periodic rate on a loan with an APR of 19.5%? Provide answer in thre
decimal places.
Answer:
Step-by-step explanation:
0.195/12 = 0.0163 = 1.63%
Hence, the monthly periodic rate is [tex]1.63[/tex]%.
What is the periodic rate?
A periodic interest rate is a rate that can be charged on a loan, or realized on an investment over a specific period of time.
Lenders typically quote interest rates on an annual basis, but the interest compounds more frequently than annually in most cases.
Here given that,
Loan with an APR of [tex]19.5[/tex]%
So, [tex]19.5[/tex]% is
[tex]\frac{19.5}{100}=0.195[/tex]
Annual periodic rate means [tex]12[/tex] months.
then,
[tex]{0.195}{12}=0.0163\\[/tex]
[tex]=1.63[/tex]%
Hence, the monthly periodic rate is [tex]1.63[/tex]%.
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At a baseball game, 56% of people attending were supporting the home team, while 44% were supporting the visiting team. If the total number of people attending the game was 3000, how many people attending were supporters of the home team?
Answer: 1680
Step-by-step explanation:The answer is 1680 because 56 percent of 3000 is 1680 people and 44 percent of 3000 is 1320 people
Solve and check: 3m + 1 = 100
Answer:
m=33
Step-by-step explanation:
Step 1: Subtract 1 from both sides.
3m+1−1=100−1
3m=99
Step 2: Divide both sides by 3
m=33
Step-by-step explanation:
solve:
3m+1=100
3m=99
99/3=33
m=33
check:
m= 33
33*3=99
99+1=100
d) $39,950
8. The car is $39,950. Interest is 10.25% and you finance for 7 years.
Figure the payments if you put down a) $0 b) $2,000 c) $3,000 d)
$5,000
[tex]\frac{10.25}{100}[/tex]Answer:
Step-by-step explanation:
The formula for simple interest is: A= P(1+in)
The formula for compound interest is: A=P[tex](1+i)^{n}[/tex]
A= amount after added interest
P= initial amount invested
i= interest rate
n= number of periods (in this case its 7 years)
*REMEMBER THIS FORMULA
a) A=0
P=?
i=10,25
n=7
(simple interest)
a) A= 0 (1 +[tex]\frac{10.25}{100}[/tex] ×7)
=0
b) A=2 000 (1 + [tex]\frac{10.25}{100}[/tex] ×7)
A=3435
c) A= 3 000( 1 + [tex]\frac{10.25}{100}[/tex] ×7)
A= 5152.5
d) 5000(1 + [tex]\frac{10.25}{100}[/tex] ×7)
= 8587.5
It's just a matter of substitution. I hope this helped.
Answer:
(a) $668.39
(b) $634.93
(c) $618.20
(d) $584.74
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]
where:
PMT = monthly payment.P = loan amount.i = interest rate per month (in decimal form).n = term of the loan (in months).Given:
P = $39.950 less any down payment.i = 10.25% / 12 = 0.1025/12n = 7 years = 7 × 12 = 84 monthsPart (a)Down payment = $0
⇒ P = $39,950
[tex]\implies \sf PMT=\dfrac{39950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 668.3892086[/tex]
Therefore, the monthly payment is $668.39.
Part (b)Down payment = $2,000
⇒ P = $39,950 - $2,000 = $37,950
[tex]\implies \sf PMT=\dfrac{37950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 634.9279215[/tex]
Therefore, the monthly payment is $634.93.
Part (c)Down payment = $3,000
⇒ P = $39,950 - $3,000 = $36,950
[tex]\implies \sf PMT=\dfrac{36950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 618.197278[/tex]
Therefore, the monthly payment is $618.20.
Part (d)Down payment = $5,000
⇒ P = $39,950 - $5,000 = $34,950
[tex]\implies \sf PMT=\dfrac{34950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]
[tex]\implies \sf PMT = 584.735991[/tex]
Therefore, the monthly payment is $584.74.
Find the value of x.
Answer:
250°Step-by-step explanation:
360° - the know angles
360 - 20 - 70 - 20 = 250°
Step-by-step explanation:
Well this is a full circle, and in a full circle, theres 360 degrees.
So if we add up 20, 70 and 20 degrees, it comes to a total of 110 degrees.
If we subtract 110 d from 360 d, we get 250 degrees. Therefore,
X = 250 degrees
Hope this helped
Formulate 600lbs of a 13% cp ration using alfalfa hay (18%cp) and clover 4%cp)
The amount of Alfalfa hay is 385.71 lbs
The amount of Clover is 572.45 lbs.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
We have,
Alfalfa hay = 18 % CP
Clover = 4% CP.
The total amount of ration is 600 lbs of a 13% CP.
Let x pounds of alfalfa hay have been used.
The amount of clover will be 600 - x lbs.
The CP amount in 600 lbs mixture will be equal to the sum of CP amounts in x lbs alfalfa and (600 - x) lbs clover.
13% of 600 = 18% of x + 4% of (600 - x)
We need to find x.
13/100 x 600 = 18/100 x (x) + 4/100 x (600 -x)
78 = 18x / 100 + 24 - 4x/100
78 - 24 = 18x/100 - 4x/100
54 = 14x / 100
14x = 54 x 100
x = 5400/14
x = 385.71 lbs
Thus,
The amount of Alfalfa hay= 385.71 lbs
The amount of Clover = 600 - 385.71 = 572.45 lbs.
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HELP 65 POINTSS!! Answer BOTH parts of the question by drawing on the following coordinate plane. For each of the transformations, use the ORIGINAL pre-image to make the new image.
(a) Draw the image of ∆PQR after a rotation of 90° clockwise about the origin. Label the image ∆P'Q'R'.
(b) Draw the image of ∆PQR after a reflection across the y-axis. Label the image ∆P''Q''R''.
Using translation concepts, the transformed triangles are given in the graph at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.
For this problem, the coordinates of triangle PQR are given as follows:
P(-1,-1), Q(-3,-2), R(-3,-4).
The rule for a 90º clockwise rotation around the origin is given by:
(x,y) -> (y,-x).
Hence the coordinates of triangle P'Q'R' are given by:
P': (-1,-1) -> (-1,1).Q': (-3, -2) -> (-2, 3).R' : (-3, -4) -> (-4, 3).The rule for a reflection over the y-axis is:
(x,y) -> (-x,y).
Hence the coordinates of triangle P''Q''R'' are given by:
P'': (-1,-1) -> (1,-1).Q'': (-3, -2) -> (3, -2).R'' : (-3, -4) -> (3, -4).Both triangles are given in the graph at the end of the answer.
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PLEASE HELP! DUE IN LESS THAN 2 HOURS! IM STUCK! I THINK THEY ARE ALL TRUE! WHAT ONE IS FALSE AND WHY! PLEASE HELP ME! YOU WILL GET 50 POINTS! THANKS QUESTION DOWN BELOW!!!
=====================================================
Reason:
Let's go through the four answer choices to see which are true and which are false. We'll rule out the ones that are true.
A) This is true. We can use inductive reasoning to form a conjecture. A conjecture is basically a generalized guess. For example, a guess would be something like "the sum of the first n odd numbers is n^2". So 1+3 = 4, 1+3+5 = 9, 1+3+5+7 = 16, 1+3+5+7+9 = 25, and so on. Does the pattern go on forever? Or does it stop at some point? That's why a proof is needed.B) This is true. See choice A.C) This is true. Some conjectures have been proven (such as the example I mentioned in choice A) while others have not. A famous unproven conjecture is Goldbach's Conjecture. D) This is false. Inductive reasoning helps form a conjecture, but it does not lead to definitive proof. We would need deductive reasoning.Mr. and Mrs. Rodriguez hope to send their son to college in thirteen years. How much money should they invest now at an interest rate of 9% per year, compounded continuously, in order to be able to contribute $8000 to his education?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
$2,482.94
Step-by-step explanation:
[tex]p {e}^{.09 \times 13} = 8000[/tex]
[tex]p = \frac{8000}{ {e}^{.09 \times 13} } = 2482.94[/tex]
∠A and \angle B∠B are supplementary angles. If m\angle A=(2x-4)^{\circ}∠A=(2x−4) ∘ and m\angle B=(4x-14)^{\circ}∠B=(4x−14) ∘ , then find the measure of \angle A∠A.
The measure of angle A is 62 degrees
Supplementary anglesSupplementary angles are angles that sunset up to 180 degrees. For instance, if A+B = 180, then A and B are supplementary
The sum of supplementary angles is 180 degrees such that;
<A + <B = 180
Given the following parameters
<A = 2x-4
<B = 4x-14
Substitute
2x-4 +4x-14 = 180
6x - 18 = 180
6x = 198
x = 198/6
x = 33
<A = 2x - 4
<A = 2(330 - 4
<A = 62 degrees
Hence the measure of angle A is 62 degrees
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convert 3/7 to percent
The percentage is 42.8571%.
what is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given fraction:
3/7
To convert the fraction into percentage we have multiply 100
3/7*100
=300/7
= 42.8571%
Hence, the percentage of fraction 3/7 is 42.8571%.
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If m = 8 and n = 4, all of the following represent the same value except
Correct answer is D. For the numerical equation, If m = 8 and n = 4, all of the following represent the same value except mn.
What is a numerical equation?Numbers and their operations are used to represent a numerical equation. Statements can also be used to create mathematical expressions.
On calculating, the following values,
If m = 8 and n = 4;
For 1/2m, the value will be -
1/2 × 8 = 4 .......(1)
For n/1 the value will be -
4/1 = 4 .......(2)
For m-n the value will be -
8 - 4 = 4 .......(3)
For mn, the value will be -
8 × 4 = 32 ......(4)
From (1), (2), (3), (4) it can be seen that the value is same instead for mn.
Complete question -
If m = 8 and n = 4, all of the following represent the same value except _____.
1/2 m
n/1
m-n
mn
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A piece of gravel is kicked from the roof of a building, 240 feet above the ground. After t seconds, the piece of gravel has fallen 16t^2 feet. how far from the ground is it after 3 seconds?
Using substitution method, the ground will be 96 feet far after 3 seconds.
What is substitution method?Finding the value of any variable from one equation in terms of another variable is the first step in the substitution technique. For instance, if there are two equations, x+y=7 and x-y=8, we may deduce that x=7-y from the first equation. Applying the replacement approach begins with this.
240-16 t² {t = 3, Substitution method}
=240 - 16×32
=240 - 16x9
=240-144
= 96 feet
96 feet from the ground.
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The circumference of a circle is 9.36cm.
Find the length of the diameter.
Give your answer rounded to 2 DP.
Answer:
The circumference of a circle with diameter 9.36 is 29.41
Step-by-step explanation:
the circumference of a circle is
2×pi×r
with r being the radius and therefore, 2×r being the diameter.
2×pi×r = 9.36 cm
2r = diameter = 9.36/pi = 2.979380535... ≈ 2.98 cm
Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
The point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
In this question we have been given a graph of Skateboards vs. Bikes.
We need to find the point that represents an INEFFICIENT point of production.
Inefficient production means the economy can be producing more goods without using any additional resources.
In given production possibility curve, an INEFFICIENT point of production is point A.
Therefore, the point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
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please help will give more points in a separate question if all correct i will give 200 points
Answer:
true for the first one and also true for the other one.
Este diagrama de puntos muestra la edad, en años, de 29 perros en un parque para perros
Answer:
3
Step-by-step explanation:
3 seeing as most dogs (5 dogs) are at the age of 3
For distinct complex numbers [tex] \rm z_1,z_2, \cdots, z_{673},[/tex] the polynomial
[tex] \rm(x - z_1 {)}^3(x - z_2 {)}^3 \dots(x - z_{673} {)}^3[/tex]
can be expressed as
[tex] \rm {x}^{2019} + 20 {x}^{2018} + {19}x^{2017} + g(x),[/tex]
where g(x) is a polynomial with complex coefficients and with degree at most 2016.
[tex] \rm The \: value \: of \left | \sum \limits_{1 \leq j < k \leq673 }z_{j} z_k\right| [/tex]
can be expressed in the form m/n, where m and n are relatively prime positive integers. Find m+n.
Let
[tex]S = \displaystyle \sum_{1\le j<k\le673} z_jz_k[/tex]
and
[tex]p_{\mu,\nu}(x) = (x-z_1)^\mu (x-z_2)^\mu \cdots (x-z_\nu)^\mu[/tex]
The [tex]z_jz_k[/tex] terms occur in the coefficient of the [tex]x^{\mu\nu-2}[/tex] term, given by
[tex]\displaystyle \left[x^{\mu\nu-2}\right] p_{\mu,\nu} = \binom\mu2 \sum_{r=j}^\nu z_j^2 + \mu^2 \sum_{1 \le j < k \le \nu} z_jz_k[/tex]
(essentially due to Vieta's formulas)
With [tex]\mu=3[/tex] and [tex]\nu=673[/tex], we have
[tex]\displaystyle \left[x^{2017}\right] p_{3,673} = \binom32 \sum_{j=1}^{673} z_j^2 + 3^2 S \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \sum_{j=1}^{673} z_j^2 \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \left(\left(\sum_{j=1}^{673} z_j\right)^2 - 2 S\right) \\\\ ~~~~ \implies S = \frac{19}3 - \left(\sum_{j=1}^{673} z_j\right)^2[/tex]
The remaining sum on the right is the sum of the roots of [tex]\sqrt[3]{p_{3,673}(x)} = p_{1,673}(x)[/tex].
Recall that the sum of the roots of a polynomial
[tex]P_n(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_0[/tex]
is [tex]-\frac{a_{n-1}}{a_n}[/tex]. Then the sum of the roots of [tex]p_{3,673}(x)[/tex] is -20, which is 3 times the sum of the roots (counting multiplicity) of [tex]p_{1,673}[/tex], so
[tex]\displaystyle \sum_{j=1}^{673} z_j = -\dfrac{20}3 \\\\ ~~~~ \implies S = \frac{19}3 - \left(-\frac{20}3\right)^2 = -\frac{343}9 \\\\ ~~~~ \implies |S| = \frac{343}9, m=343, n=9 \implies m+n = \boxed{352}[/tex]
A researcher is studying the growth of bacteria.
He starts with 320 of the bacteria. It grows
continuously at a rate of 4% per hour. How
many bacteria will there be in 17 hours?
(Round to the nearest integer if necessary)
136000 many bacteria will there be in 17 hours at a rate of 4 percentage per hour.
What is an example of a percentage?
Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.given ,
rate = 4%
bacteria starts growing = 320
rate = 4%
4% = 320
1 = [tex]\frac{320 * 100}{4} = 8000[/tex]
bacteria will there be in 17 hours = 17 × 8000
= 136000
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what value of x makes 6e^4x = 14 true?
For the given equation 6e^4x = 14, the value of x is [tex]x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]
How to Find x's Value?Getting x alone on one side of the equation and everything else on the other side will be the first step towards solving for x. The golden rule of algebra states that everything done to one side of an equation must also be done to the other.
Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.
For the given equation,
6e^4x = 14
[tex]x = ln \frac{3^{3/4} * \sqrt[4]{7} }{3}\\ \\x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]
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The last of my points. Given the unit circle, what is the value of y? This my last question.
Answer:
y = - [tex]\frac{\sqrt{111} }{20}[/tex]
Step-by-step explanation:
using Pythagoras' identity in the right triangle formed by the radius 1 and the given point, then
y² + (- [tex]\frac{17}{20}[/tex] )² = 1²
y² + [tex]\frac{289}{400}[/tex] = 1
y² = 1 - [tex]\frac{289}{400}[/tex] = [tex]\frac{111}{400}[/tex] ( take square root of both sides )
y = ± [tex]\sqrt{\frac{111}{400} }[/tex] = ± [tex]\frac{\sqrt{111} }{20}[/tex]
since the point is in the third quadrant then y < 0
y = - [tex]\frac{\sqrt{111} }{20}[/tex]
Sarah bought snacks for her team's practice. She bought a bag of chips for $1.56 and a 20-pack of juice bottles. The total cost before tax was $33.96. Write and solve an equation which can be used to determine jj, how much each bottle of juice cost.
Cost of a bottle of juice is $ 1.62
Equation for determining the cost of juice is 1.56 + 20x = 33.96
Given,
The cost of a bag of chips = $ 1.56
Number of juice bottles bought by Sarah = 20 pack
Total cost before tax = $ 33.96
Cost of one bottle of juice = x
We have to find x:
Then the equation will be:
1.56 + 20x = 33.96
Add -1.56 to both sides:
1.56 + 20x - 1.56 = 33.96 - 1.56
We get,
20x = 32.4
Now find x,
x = 32.4 / 20
Then,
x = 1.62
That is, the equation for finding the cost of a bottle of juice is 1.56 + 20x = 33.96.
The cost of one bottle of juice is $1,62
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