The center of gravity of the distribution center is located at (14.84, 12.84)
What is the center of gravity?The center of gravity is a point at which the total weight of a body can be thought to be located for calculation purposes.
The coordinates of the five distribution centers using the x and y coordinates are;
A(20, 15) 75, B(10, 12) 50, C(15, 10) 60, D(15, 20) 80, E(12, 12) 50
The center of gravity is found using the formula;
[tex]x = \dfrac{m_1\cdot g\cdot x_1+ m_2\cdot g\cdot x_2 + m_3\cdot g\cdot x_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]
[tex]y = \dfrac{m_1\cdot g\cdot y_1+ m_2\cdot g\cdot y_2 + m_3\cdot g\cdot y_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]
Coordinates of the center of gravity of the distribution center is therefore;
[tex]x = \dfrac{75\times 20+ 50\times 10+ 60\times 15+80\times 15+50\times 12}{75+50+60+80+50} \approx 14.92[/tex]
[tex]y = \dfrac{75\times 15+ 50\times 12+ 60\times 10+80\times 20+50\times 12}{75+50+60+80+50} \approx 12.84[/tex]
The coordinates of the center of gravity of the distribution center is; (14.92, 12.840
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Standard automobile license plates in a country display one number, followed by three letters, followed by three numbers. How many different standard plates are possible in the system ? ( assume repetition of letters and numbers are allowed)
Answer:
175760000
Step-by-step explanation:
There are 10 possibilities for each number and 26 possibilities for each letter.
Using the multiplication principle, the answer is [tex](10)(26^3)(10^3)=175760000[/tex]
Need help please?????
Answer:
Q1: 13 :)
Q2: 9 :)
Q3: 5 :)
Q4: 1 :)
Step-by-step explanation:
For functions, we must replace the x with the value given in the table and solve from there! :D
Question 1:
y = -2(-2) + 9
y = 4 + 9
y = 13
Question 2:
y = -2(0) + 9
y = 0 + 9
y = 9
Question 3:
y = -2(2) + 9
y = -4 + 9
y = 5
Question 4:
y = -2(4) + 9
y = -8 + 9
y = 1
Have an amazing day!!
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 8. If there were 8918 total votes, how many yes votes were there?
Find the value of x.
(6x + 1)°
(9x - 23)°
geometry
The value of x using the F.O.I.L method can be determined by the expression: [tex]54x^2-129x-23[/tex]
What is FOIL Method?
FOIL is a mnemonic for the standard method of multiplying two binomials, hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product:
First (“first” terms of each binomial are multiplied together)
Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second)
Inner (“inside” terms are multiplied—the second term of the first binomial and the first term of the second)
Last (“last” terms of each binomial are multiplied)
In the question, It is given:
(6x + 1)°
(9x - 23)°
Now Apply the F.O.I.L Method, to find the value of x;
⇒(6x + 1) (9x-23)
Remove parenthesis and multiply;
⇒6x×9x+6x×(-23)+1×9x+1×(-23)
⇒6x x 9x+6 x 23x + 1 x 9x + 1 x 23
Now, we have to simplify the terms,
⇒6x x 9x + 6 x 23x + 1 x 9x + 1 x 23
So after simplification, we get:
[tex]54x^2-129x-23[/tex]
Hence,
The value of x can be determined by the expression: [tex]54x^2-129x-23[/tex]
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Rewrite the expression as an equivalent expression with fewer terms:
3x4 (5x + 7)
The equivalent expression to the given expression 3x - 4 - (5x + 7) with fewer terms is - 2x - 11.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
3x - 4 - (5x + 7)
Open the bracket
3x - 4 - (5x + 7) = 3x - 4 - 5x - 7
Take likely terms together
3x - 4 - (5x + 7) = 3x - 5x - 4 - 7
Solving to get.
3x - 4 - (5x + 7) = - 2x - 11
Hence "The equivalent expression to the given expression 3x - 4 - (5x + 7) with fewer terms is - 2x - 11".
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shoe store a is having a sale in which every pair of shoes is 40% off. shoe store is having a sale in which $40 is deducted from the regular price. gwen buys 3 identical pairs of shoes at store a. because of the sale, she saves 73.50. what is the regular price of each pair
The percentage discount of 40% from the regular price of shoes and the $73.5 Gwen saves indicates that the regular price of each pair of shoe she buys is $61.25
What is a percentage in mathematics?A percentage is the expression of a proportion based on a scale of 100. A percentage can be described as a fraction that has 100 as the denominator.
The percentage discount = 40%
The amount Gwen saves = $73.50
The number of shoes she buys = 3
The discount on each shoe = $73.5 ÷ 3 = $24.5
Let x represent the regular price of each shoe, from the information in the question, we have;
40% of x = $24.5
40% × x = $24.5
The regular selling price is therefore the ratio of $24.5 and 40% as follows;
The regular selling price = $24.5 ÷ 40% = $61.25
Each pair of shoe regularly costs $61.25
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what are the rules for atom moluclue elements and compound
For an atom to be considered as such it needs to be composed of subtatomic particle (neutrons, electrons, protons), an molecule includes two or more atoms, an element has defined properties and a compound includes two or more element.
What are the rules for an atom?It is made up of neutrons, electrons and protons.Electrons move around the nucleus composed of neutrons and protons.What are the rules for an element?They have a define atomic numberThey have defined melting point, boiling point, state, condutivity, among others.What are the rules for a molecule?It includes at least two atoms, these atoms can be from the same element or from different element.It has a defined molecular weight and properties based on its components.What are the rules for a compound?It includes two or more elements.It has defined properties.The elements can be separated chemically.Learn more about atoms in: https://brainly.com/question/1566330
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What is the sum of this geometric series?
A store purchases baseball hats from two different manufacturers in 3 different colors, summarized below. One hat is chosen at random. Give your answer as a decimal out to at least 4 places.
Black Blue Red Total
Manufacturer A 30 19 13 62
Manufacturer B 21 25 28 74
Total 51 44 41 136
a) Find the probability that the hat was was Blue or was from Manufacturer B.
b) Find P(RedC).
c) Find P(Manufacturer B and Red).
d) Find P(Manufacturer B or Red).
The probability that the hat was blue or was from Manufacturer B is 0.8677.
The P[tex](red)^{c}[/tex] is 0.6985.
The P(manufacturer B and Red) is 0.1640.
The P(Manufacturer B or Red) is 0.8456.
What are the probabilities?Probability is used to determine the odds that a random event would happen. The odds that the random event happens range from 0 to 1.
The probability that the hat was blue or was from Manufacturer B = (number of blue hats / total number of hats) + (number of hats from manufacturer B / total number of hats)
The probability that the hat was blue or was from Manufacturer B = (44 / 136) + (74 / 136) = 118/136 = 0.8677
The P[tex](red)^{c}[/tex] = complement of red = hats that are not red = (number of black hats + number of blue hats) / total number of hats
The P[tex](red)^{c}[/tex] = (51 + 44) / 136
The P[tex](red)^{c}[/tex] = 95 / 136
The P[tex](red)^{c}[/tex] = 0.6985
The P(manufacturer B and Red) = (number of hats produced by manufacturer B / total number of hats) x (number of red hats / total number of hats)
(74 / 136) x (41 / 136) = 0.1640
The P(Manufacturer B or Red) = (number of hats produced by manufacturer B / total number of hats) + (number of red hats / total number of hats)
(74 / 136) + (41 / 136) = 115 / 136 = 0.8456
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tan 20 degrees + tan 40 degrees/1-tan 20 degrees tan 40 degrees
The value of (tan20° + tan40°)/(1 - tan20°tan40°) is √3.
What is the formula for tan(A + B)?tan(A + B) = (tanA + tanB)/(1 - tanA.tanB).
Given, tan 20 degrees + tan 40 degrees/1-tan 20 degrees tan 40 degrees
which is,
= (tan20° + tan40°)/(1 - tan20°tan40°).
= tan(20 + 40)°.
= tan60°.
= √3.
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Felix and Latisha completed different versions of an IQ test. Felix earned a score of
130 with a mean of 105 and std dev of 10. Latisha earned a score of 120 with a
mean of 95 and a std dev of 5.
Who earned a higher IQ score?
Based on the z-score value, Latisha earned a higher IQ score.
How to determine who earned a higher IQ score?In order to determine the person who earned a higher IQ score, we would have to calculate the z-score for the two IQ tests that Felix and Latisha took.
Mathematically, the z-score of a given sample score can be calculated by using this formula:
Z-score = (x - μ)/σ
Where:
σ represents the standard deviation.x represents the sample score.μ represents the mean score.For Felix, we have the following:
Z-score = (130 - 105)/10
Z-score = 25/10
Z-score = 2.5.
For Latisha, we have the following:
Z-score = (120 - 95)/5
Z-score = 25/5
Z-score = 5.0.
Therefore, Latisha had the higher score because she has a higher z-score than Felix.
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$1,300 at 5% for 6 years
Answer:
$1742.12
Step-by-step explanation:
I'm assuming it would be compounded annually so,
A = 1300(1 + 0.05)^6
A = 1742.12
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −52, ordered pair: (−1,3)
Answer:
[tex] \huge{ \boxed{y = - 52x - 49}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = -52
In order to find c we substitute the points (−1,3) into the equation and find c
We have
[tex]3 = ( - 52)( - 1) + c \\ 3 = 52 + c \\ c = 3- 52 \\ c = -49[/tex]
We have m and c now so we substitute it into the main equation
We have the final answer as
[tex] \bold{y = - 52x - 49}[/tex]
Hope this helps you
3. The half-life of a certain radioactive substance is 14 days and there are 6.58 g
present initially. When will there be 1 gram remaining?
Using the initial amount of the radioactive substance, in 1 gram 913.28 hours remaining.
In the given question;
The half- life of the radioactive substance is
[tex]t_{1/2}[/tex]=14days
For changing this into hours we have to multiply 24 in 14 because in 1 day have 24 hours.
[tex]t_{1/2}[/tex]=14*24
[tex]t_{1/2}[/tex]=336 hours
Initial amount of the radioactive substance is:
N(0)=6.58g
Now here we use the radioactive substance formula
[tex]N(t)=N(0)(\frac{1}{2})^{t/t_{1/2}}[/tex]
Where; N(t)= the radioactive substance after t hours
N(0)= Initial amount of the radio active substances
[tex]t_{1/2}[/tex] = Half lie
t=time (in hours)
Now put the value in formula
N(t)=6.58[tex](\frac{1}{2})^{t/336}[/tex]
N(t)=6.58[tex](0.5)^{t/336}[/tex]
By the question we know
N(t)=1
1=6.58[tex](0.5)^{t/336}[/tex]
Divide by 6.58 on both side, we get
1/6.58=[tex](0.5)^{t/336}[/tex]
[tex](0.5)^{t/336}[/tex]=1/6.58
Now taking the log on both side:
log [[tex](0.5)^{t/336}[/tex]]=log [1/6.58]
t/336 log[0.5]=log[1/6.58]
The formula of log used here, is as follows: Log(m^b)=blog(m)
Multiply by 336 on both side,we get
t*log[0.5]=336 log[1/6.58]
t=(336 log[1/6.58])/ log[0.5]
t=913.28hours
Hence, In 1 gram 913.28 hours remaining.
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IXL Please Help Fast!
Step-by-step explanation:
from the first line s
y - 7 = 9/10 × (x - 4)
we only need the slope, which is 9/10.
the -7 did not disturb this. only if y had a factor different to 1, we would have to re-simplify the equation to get the slope.
remember, a slope expresses the ratio (y change / x change).
a perpendicular slope note turns the y/x ratio upside-down and flips the sign.
so, 9/10 turns into -10/9, which is the slope of the new line t.
we can use the point-slope form to incorporate the given point and get the y-intercept for the final slope-intercept equation :
y - 6 = -10/9 × (x - -6) = -10/9 × (x + 6) =
= -10/9 × x - 60/9 = -10/9 × x - 20/3
y = -10/9 × x - 20/3 + 6 = -10/9 × x - 20/3 + 18/3 =
= -10/9 × x - 2/3
the line t is
y = -10/9 × x - 2/3
Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the amount of taxes owed on a taxable income of $38,520.
The effective tax rate for a taxable income of $75,400 is 24%.
What is the Marginal tax rate?The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate.
WE have Given that;
Marginal Tax Rate Chart Tax Bracket
$0 –$10,275 10%
$10,276 –$41,175 12%
$41,176 –$89,075 22%
$89,076 –$170,050 24%
$170,051 –$215,950 32%
$215,951 –$539,900 35%
> $539,901 37%
Hence, the effective tax rate for income of $95, 600 lies in the range of a marginal tax rate of; 24%.
thus, the effective tax rate;
= 72,026/ 95600
= 24 %
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Answer:
4,416.90
Step-by-step explanation:
12% tax bracket: $38,520 - 10,725 = 27795(0.12) = 3335.4
1027.50+3335.4 = 4416.90
Make the subject of
9x = u
What is the total surface area of the triangular prism in square centimeters?
A. 240 cm^2
B. 368 cm^2
C. 320 cm^2
D. 344 cm^2
Answer: option a
Step-by-step explanation:
Question 9(Multiple Choice Worth 2 points)
(Equivalent Algebraic Expressions MC)
Simplify (z9z−3)−2.
1 over z raised to the twelfth power
1 over z raised to the sixth power
−z12
−z6
Question 10(Multiple Choice W
The simplified exponential expression (z^9z^(-3))^(-2) is given as follows:
1 over z raised to the twelfth power.
How to obtain is the simplified expression?The expression for this problem is given as follows:
(z^9z^(-3))^(-2)
The parenthesis takes precedence, hence the first term to be simplified is:
z^9z^(-3)
We have the multiplication of two terms with the same base and different exponents, hence the base z is kept and the addition of the exponents 9 and -3 is of:
9 - 3 = 6.
Hence the simplified part is of:
z^6
Then the expression is:
(z^6)^(-2).
Now we have the power of power rule, in which the base z is kept and then the exponents 6 and -2 are multiplied, as follows:
6 x (-2) = -12.
Then the simplified expression is:
z^(-12).
A negative exponent means that the number can be written into the denominator with a positive exponent, hence:
1/(z^12) = 1 over z raised to the twelfth power.
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Mateo is looking at another company for invitations. Company D sells 80 invitations for $44. What is the unit rate?
Answer:
80/44 = 1.81
The unit rate is $1.81
Gordon Rosel went to his bank to find out how long it will take for $800 to amount to $920 at 8% simple interest. Calculate the number of years. (Round time in years to the nearest tenth.)
Answer:
1.875 years or 1.9 if rounded to nearest tenth
Step-by-step explanation:
8% simple interest of $800 is $64. you know that 1% will be $8 per year and that 2 years of 8% simple interest will be $128. If you subtract 8 from 128, it is $120. So it will take him 1.875 years or [tex]1\frac{7}{8}[/tex]
Graph the solution to the equation y=1/4+2 and y=–2x–7
Answer:
Step-by-step explanation:
y= 1/4x+2
y=-2x-7
Graphs below
The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?
Answer:
2 points: b, d
Step-by-step explanation:
Given the graph of a cubic function, you want to know the number of relative extreme points.
Relative extremeA point is a relative extreme if the points on either side of it are both less than or both greater than the extreme point. A relative extreme is a peak point or valley point on a graph, a point where the slope is zero, and changes sign from one side of the point to the other.
ApplicationThe relative extremes on the given graph are labeled 'b' and 'd'. There are two relative extremes.
__
Additional comment
Point 'b' is a relative minimum, where the slope changes from decreasing to increasing, and adjacent points are more positive. Point 'd' is a relative maximum, where the slope changes from increasing to decreasing, and adjacent points are more negative.
An "absolute extreme" is a relative extreme such that no points anywhere on the graph are more extreme.
The number of relative extremes a polynomial graph may have is 1 less than the degree of the polynomial. This can help you determine the degree from the number of extremes, or the number of extremes from the degree.
..
Find a third number so that the three numbers form a right triangle:
i)
9, 41
ii) 13, 85
The third number so that the three numbers form a right triangle,
1)40
2)84
Therefore, we can form a right triangle with 9,41,40 and 13,85,84
What is a Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
1) By applying Pythagorean theorem,
a²+b²=c²
x²+9²=41²
x²=41²-9²
x²=1681-81
x²=1600
x=√1600
x=40
Therefore, the third number is 40
2) x²+13²=85²
x²=85²-13²
x²=7225-169
x²=7056
x=√7056
x=84
Therefore, the third number is 84
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Write a function for the line with a slope of −14 that passes through the point (4, 5).
hint:Substitute the slope and the coordinates of the given point into the equation y=mx+b, then solve for b.
hint2: The slope is m in y=mx+b.
Answer:
y = -14x + 61
Step-by-step explanation:
You need the slope and the y-intercept to write the equation. They give us the slope. We will use the point given (4,5) to find the y intercept. A point is given in the form (x,y)
slope (m) = -14
y = 5 Given from the point (4,5)
x = 4 Given from the point (4,5)
y = mx + b Plug in what we know
5 = -14(4) + b
5 = -56 + b Add 56 to both sides of the equation
61 = b
y = -14x + 61
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about μ if the sample size, n, is 13. (b) Construct an 80% confidence interval about μ if the sample size, n, is 26. (c) Construct a 98% confidence interval about μ if the sample size, n, is 13. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
The confidence intervals for this problem, using the t-distribution, are given as follows:
a) 80% confidence level, n = 13: (106.24, 113.76).
b) 80% confidence level, n = 26: (107.42, 112.58).
c) 98% confidence level, n = 13: (102.56, 117.44).
d) These intervals could not be computed if the population had not been normally distributed, as the sample size is less than 30.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical values, using a t-distribution calculator, for the two-tailed 95% intervals, are given as follows:
80% confidence, n = 13, 12 df: t = 1.3562.80% confidence, n = 26, 25 df: t = 1.3163.98% confidence, n = 13, 12 df: t = 2.681.The mean and the standard deviation are given as follows:
[tex]\overline{x} = 110, s = 10[/tex]
For item a, with n = 13, the bounds of the interval are given as follows:
110 - 1.3562 x 10/sqrt(13) = 106.24.110 + 1.3562 x 10/sqrt(13) = 113.76.For item b, with n = 26, the bounds of the interval are given as follows:
110 - 1.3163 x 10/sqrt(26) = 107.42.110 + 1.3163 x 10/sqrt(26) = 112.58.For item c, with n = 13, the bounds of the interval are given as follows:
110 - 2.681 x 10/sqrt(13) = 102.56.110 + 2.681 x 10/sqrt(13) = 117.44.The Central Limit Theorem states that the intervals can be obtained for non-normal populations only if the sample size is equal or greater than 30.
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Which expression is equivalent to (3x4y5)-²?
Answer:Equivalent expressions Calculator Get detailed solutions to your math problems with our Equivalent expressions step-by-step calculator. Practice your math skills and learn step by step.
Answer:
Answer:Equivalent expressions Calculator Get detailed solutions so your math problems with ur Equivalent expressions
Step-by-step explanation:
Linda makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working in hours.
Determine the length of the line segment shown.
line segment from negative 10 comma 9 to 5 comma negative 1
4 units
18 units
19 units
21 units
The length of the line segment is 18 units. option B is the correct answer.
We know that
The distance(D) between two points (x₁ , y₁) and (x₂, y₂) is
D = √( y₂ - y₁)² + (x₂ - x₁)²
From the question, we have
Two endpoints of the line segment are (-10, 9) and (5, -1).
D = √( y₂ - y₁)² + (x₂ - x₁)²
D = √(-1 - 9)² + (5 - (-10))²
D = √100 + 225
D = √325
D = 18 units (approx.)
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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Answer: 18 units
Step-by-step explanation: I got it right on the quiz
Write the rate as a fraction in lowest terms.
6 persons for 40 dresses
The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]
What are fractions?
Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.
A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.
In the given question, we have:
6 persons for 40 dresses;
So, here
The numerator is 6;
and,
The denominator is 40;
So, The fraction that will be formed is: [tex]\frac{6}{40}[/tex]
In order to simplify to the simplest form, we have to divide it by the common divisor of 6 and 40.
So,
The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]
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