Answer:
180
Step-by-step explanation:
Find the LCM of 12, 18, and 20
[tex]12 = 2 \times 2 \times 3[/tex]
[tex]18 = 2 \times 3 \times 3[/tex]
[tex]20 = 2 \times 2 \times 5[/tex]
LCM = 2 × 2 × 3 × 3 × 5 = 180
In a recent year (365 days), a hospital had 5705
births.
a. Find the mean number of births per day.
b. Find the probability that in a single day, there are 17
births.
c. Find the probability that in a single day, there are no births. Would 0 births in a single day be a significantly low number of births?
Using the Poisson distribution, it is found that:
a) The mean is of 15.63.
b) The probability is of 0.0911 = 9.11%.
c) The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes.e = 2.71828 is the Euler number.[tex]\mu[/tex] is the mean in the given interval.Item a:
The mean is given by:
[tex]\mu = \frac{5705}{365} = 15.63[/tex]
Item b:
The probability is P(X = 17), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 17) = \frac{e^{-15.63}(15.63)^{17}}{(17)!} = 0.0911[/tex]
The probability is of 0.0911 = 9.11%.
Item c:
The probability is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-15.63}(15.63)^{0}}{(0)!} = e^{-15.63}[/tex]
The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
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Using the Poisson distribution, it is found that
a) The mean is 15.63.
b) The probability is[tex]e^{-15.63}[/tex] of 0.0911 = 9.11%.
c) The probability is, which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P\left(X=x\right)=\frac{e^{-\mu }\mu ^x}{x!}[/tex]
The parameters are
x is the number of successes.
e = 2.71828 is the Euler number.
[tex]\mu[/tex] is the mean in the given interval.
Item a:The mean is given by:
[tex]\:\mu =\frac{5705}{365}[/tex]
Item b: The probability is P(X = 17), hence:
[tex]P\left(X=17\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{17}}{17!}=0.0911[/tex]
The probability is of 0.0911 = 9.11%.
Item c:The probability is P(X = 0), hence:
[tex]P\left(X=0\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{0}}{0!}=e^{-15.63}[/tex]
The probability is,[tex]e^{-15.63}[/tex] which is less than 0.05,
hence 0 births in a single day would be a significantly low number of births.
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I have a geometry question thank you!
Answer:
The answer is 1.5.
Step-by-step explanation:
I don't have one
? Question
Write an expression to represent the perimeter of Melissa's garden in terms of x.
Type the correct answer in each box. Use numerals instead of words.
Perimeter:
Question 3
? Question
x +
The expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.
l=3x+2
b=x+5
The linear equation is the equation where the highest degree of the variables is 1.
Here given that the garden is rectangular in shape and the tomato patch is square in shape.
the length of the side of the square tomato patch is x.
Asuume the length of the rectangle garden is l
and the breadth of the rectangle garden is b.
Given that
the length of the garden is greater than the 3 times of the length of the rectangular garden by 2 feet.
3 times of the length of the rectangular garden is 3x
2 feet greater than 3 times of the length of the rectangular garden= 3x+2
so from above, it is clear that l=3x+2
similarly, the breadth of the garden is greater than the length of the rectangular garden by 5 feet.
then the breadth of the garden = b= x+5
Therefore the expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.
l=3x+2
b=x+5
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Four students were asked to write an expression which has terms that have a greatest common factor of ab. The
expressions provided by the students are shown below.
Olivia
20ab-14abc
Michelle
16a+3b
Michelle
Naomi
Which student wrote the correct expression?
O Olivia
O Peyton
Naomi
18abc-13abc
Peyton
15abc+ 14ab
Answer: Peyton
Step-by-step explanation:
Michelle: Greatest common factor is 1
Naomi: Greatest common factor is abc
Olivia: Greatest common factor is 2ab
Peyton: Greatest common factor is ab
Please I need help on Fundametal Trigonometric Identities?
Fundamental Trigonometric Identities are listed below:
[tex]sin^{2}[/tex]Θ + [tex]cos^{2}[/tex]Θ = 1[tex]sec^{2}[/tex]Θ - [tex]tan^{2}[/tex]Θ = 1[tex]cosec^{2}[/tex]Θ - [tex]cot^{2}[/tex]Θ = 1sinΘ = 1 / cosec Θ cos Θ = 1 / sec Θ tan Θ = 1 / cot Θ tan Θ = sinΘ / cosΘ cotΘ = cosΘ / sinΘMeaning of Fundamental Trigonometric IdentitiesFundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.
In conclusion, A few Fundamental Trigonometric Identities are listed above.
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Consider the function f(x)=3^x and the translation if f(x) named g(x). Janeen created a table for select values of x. What can be concluded about the relationship between two functions?
The conclusion about the relationship is
The functions have the same base.The functions have the same range.The functions have the same domain.g(x) is a translation left 1 unit.What is function?The complete question is:
Consider the function f(x) = 3x and a translation of f(x) named g(x). Janeen created a table for select values of x. Her table is shown below. What can be concluded about the relationship between the two functions? Check all that apply.
The functions have the same base.
The functions have the same range.
The functions have the same exponent.
The functions have the same domain.
g(x) is a translation left 1 unit.
g(x) is a translation right 2 units.
g(x) is a translation up 2 units.
Given function is:
f(x) = [tex]3^{x}[/tex]
g(x) = [tex]3^{x+1}[/tex]
Firstly, the functions have the same base i.e., base 3.
second, the functions have the same range.
As the range of f are all the values that f can assume. i.e., positive numbers and the range of g are all the values that g can assume. i.e., positive numbers.
third, both functions have the same domain as x = {0,1,2,3}.
Fourth, g(x) = f(x+1). So, g(x) is a translation left 1 unit.
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A manufacturer makes two type if products X and z at each if two different locations A and B. the materials used to make each if the products are steel, glass and plastic. suppose it takes three units of steel, one unit of glass and two units of plastic to make one unit of product X and four units of steel and one half units of glass and three units of plastic to make one unit of product Z. suppose further that steel, glass and plastic cost birr 10, 2, and 3 per unit respectively at location A. at location B steel, glass abd plastic cost 9,3 and 4 per unit respectively. using matrix algebra. find the material cost of making one of each product at each of the two locations.
Using matrix algebra, the material cost of making one of each product at each location is as follows:
Product X Product Z
Location A birr 38 birr 50
Location B birr 38 birr 49.5
What is matrix algebra?Matrix algebra involves the arrangement of numbers in a rectangular array.
Matrices are arranged in columns and rows to express some mathematical values.
Data and Calculations:Matrix O: Materials Requirement Per UnitSteel Glass Plastic
Product X 3 1 2
Product Z 4 0.5 3
Matrix P: Materials Cost Per UnitSteel Glass Plastic
Location A 10 2 3
Location B 9 3 4
Matrix R: (O x P) Material Cost of Product XSteel Glass Plastic Total
Location A 30 2 6 38
Location B 27 3 8 38
Matrix R: (O x P) Material Cost of Product ZSteel Glass Plastic Total
Location A 40 1 9 50
Location B 36 1.5 12 49.5
Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.
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find the slope of the line that passes through the points (2,1) and (-7,4)
Answer:
[tex]-\frac13[/tex]
Step-by-step explanation:
Just the slope, so we can simply apply the definition, as variation in y over the variation in x
[tex]m= \frac{\Delta y}{\Delta x} = \frac{1-4}{2-(-7)} = \frac {-3}{9} = -\frac13[/tex]
Answer:
0.222
Step-by-step explanation:
Y2-Y1 ÷ X2-X1
4-2 ÷ -7-2
2÷-9
0.222
What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)? The equation of the line in slope-intercept form is y =-5/3 x + ____
Substituting into point-slope form,
[tex]y+5=-\frac{5}{3}(x-15)\\\\y+5=-\frac{5}{3}x+25\\\\\boxed{y=-\frac{5}{3}x+20}[/tex]
If two triangles are congruent, which of the following statements must be true? Check all that apply. A. The corresponding sides of the triangles are congruent. B. The triangles have the same shape and size. C. The corresponding angles of the triangles are congruent. D. The triangles have the same shape, but not the same size. If two triangles are congruent , which of the following statements must be true ? Check all that apply . A. The corresponding sides of the triangles are congruent . B. The triangles have the same shape and size . C. The corresponding angles of the triangles are congruent . D. The triangles have the same shape , but not the same size.
Answer:
Step-by-step explanation:
A. Correct
B. Correct
C. Correct
D. False
2.
A. Correct
B. Correct
C. Correct
D. False
Hope I helped!
(x³ + ³) / (x - y)
Do not include parentheses in your answer.
The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
Complete questionSimplify the expression: (x³ + (-y)³) / (x - y)
Do not include parentheses in your answer.
How to simplify the expression?The expression is given as:
[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]
Open the inner bracket
[tex]\frac{x^3 -y^3}{(x - y}[/tex]
Apply the difference of two cubes to the numerator
[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]
Cancel out the common factors
[tex]x^2+xy+y^2[/tex]
Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
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Managerial Accounting
Answer:
1400 units
$26,600
1700 units
$32,300
Step-by-step explanation:
yw :))
pls help me solve for x in this equation
Answer:
x = 9/2
Step-by-step explanation:
√2x + √2x = 6
2√2x = 6
2√2x/2 = 6/2
√2x = 3
(√2x)² =( 3)²
2x = 9
x = 9/2
Answer:
x = 4.5
Explanation:
[tex]\rightarrow \sf \sqrt{2x} + \sqrt{2x} = 6[/tex]
add following
[tex]\rightarrow \sf 2\sqrt{2x} = 6[/tex]
divide both sides by 2
[tex]\rightarrow \sf \sqrt{2x} = 3[/tex]
square both sides
[tex]\rightarrow \sf 2x = 3^2[/tex]
simplify the following
[tex]\rightarrow \sf 2x = 9[/tex]
divide both sides by 2
[tex]\rightarrow \sf x = 4.5[/tex]
3. College Students (10 points)
In Fall 2019, there were approximately 16.6 million undergraduate students in degre
granting postsecondary institutions. This represents a 5% decrease from the Fall 200
number of students. How many undergraduate students were there in 2009?
Source: https://nces.ed.gov/fastfacts
The number of students is 33.2 million
What is percentage decrease?Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.
Given:
In 2019= 16.6 million
% decrease = 5%
So,
% decrease= x - 16.6/ x
5% = x- 16.6/x
0.05= (x-16.6)/x
0.05x = x-16.6
-0.05 x = -16.6
x= 16.6/0.05
x= 16600000/0.05
x= 332,000,000
x= 33.2 million.
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(x) = x + 0.14x, then find the value of T(290).
A. 300.45
B. 351.2
C. 325.8
D. 330.6
Answer:
D. 330.6
Step-by-step explanation:
To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.
__
T(x) = x +0.14x . . . . . given function definition
T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x
T(290) = 330.6
The value of T(290) will be 330.6.The relation between them is shown as T(x) is dependent and x is the independent variable. Option D s correct.
What is a function?A connection between independent variables and the dependent variable is defined by the function.
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
Given relation;
T(x) = x +0.14x
Substitute the value of x we get;
T(290) = 290 +0.14×290
T(290) = 330.6
Hence, option D s correct.
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Find the equation of the line that
3
is perpendicular to y ===x+1
and contains the point (9,12).
4
4
Y = 3 x + [ ? ]
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!what type of expression is 3+7-1/2
Numerical Expression
The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.
find the common denominator and thin combine the numerators over the common denominator trhin simplify each term thin simplify by adding subtracing thin the result can be shown in multiple forms
exact form 19/2
decimal form 9.5
mixed number form 9 1/2
The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?
Applying the negative exponent, the equivalent expression [tex]3^{-3}[/tex] is 1/27.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator.
Hence, the equivalent expression is:
[tex]3^{-3} = \dfrac{1}{3^3} = \dfrac{1}{27}[/tex]
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find sin(x/2), cos (x/2), and tan(x/2) from the given information.
Sin(x)= 15/17, 0 < x <90
sin(x/2)= ?
cos(x/2)=?
tan(x/2)= 0.6
I need help with sin and cos. I know what tan is.
Step-by-step explanation:
sin(x/2) = sqrt((1 - cos(x))/2)
cos(x/2) = sqrt((1 + cos(x))/2)
tan(x/2) = sin(x/2)/cos(x/2)
sin(x) = 15/17
so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.
via Pythagoras we get the 3rd, horizontal side :
17² = 15² + side²
289 = 225 + side²
64 = side²
side = 8
cos(x) = 8/17
sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =
= 0.514495755...
cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =
= 0.857492926...
tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =
= 3/5 = 0.6
Sarah conducted an experiment regarding the effectiveness of two mathematics tutoring programs: Math Master and Excel. She randomly selected 20 students from her high school and assigned 10 students to the Math Master program. Sarah then assigned the remaining 10 students to the Excel program.
Finding the percent increase, it is found that the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
What is the percent increase?The percent increase is given by the difference between the final and the initial score, divided by the initial score and multiplied by 100%.
Researching the problem on the internet, we have that:
In the Master program, the average score increased from 75 to 87.In the Excel program, the average score increased from 73 to 81.The percent increases are given as follows:
M = 12/75 x 100% = 16%,E = 8/73 x 100% = 10.96%.Hence the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
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Determine whether it is a function
Answer:
Relation 3 is not a function, as s has two outputs: tree and desk. Relation 4 is not a function for the same reason. -1 has three outputs: -2, -4, and -7.
Find the measure of the indicated angle to the nearest degree.
?
58
30
\frac{7}{4x}+\frac{5}{4x^2}
4x
7
+
4x
2
5
The expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]
What is Expression ?Expression is a mathematical statement consisting of variables , constants and mathematical operators .
It is given in the question to solve the expression
[tex]\rm \dfrac{4x}{7} + \dfrac{5}{4x^2}[/tex]
Taking LCM , LCM = 28x²
[tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]
Therefore the expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]
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Match each quadratic equation with its roots.
a2-a+11=0
a2-2a+15=0
a = 1ti√14
1± √47
a= 2
a=
1+√43
2
a=1+3i
a2-2a+10=0
a2-a+12=0
30
Answer:
wrong question please place correctly thanks
1. Given GH = 7x + 3, HI= 3x - 5,
and GI= 9x + 5.
H
G
A. Find x:
B. Find GH:
Answer:
[tex]\boxed{\bf x=7}[/tex]
[tex]\boxed{\bf GH= 52}[/tex]
Step-by-step explanation:
In the line segment..
[tex]\bf 7x+3+3x-5=9x+5[/tex]
Combine like terms.
[tex]\bf 10x-2=9x+5[/tex]Add -2 to both sides.
[tex]\bf 10x-2+2=9x+5+2[/tex][tex]\bf 10x=9x+7[/tex]Subtract 9x from both sides.
[tex]\bf 10x-9x=9x+7-9x[/tex][tex]\boxed{\bf x=7}[/tex][tex]\bf GH=7x+3[/tex]
[tex]\bf 7(7)+3[/tex][tex]\bf 49+3[/tex][tex]\boxed{\bf 52}[/tex]__________________Please help with this difficult one...
The composite function is given as follows:
[tex](f \circ g)(x) = \frac{2x + 6}{3x + 22}[/tex]
The domain of the composite function is: [tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]
What is the composite function of f(x) and g(x)?The composite function is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{2}{x + 3}[/tex].[tex]g(x) = \frac{13}{x + 3}[/tex].Hence the composite function is:
[tex](f \circ g)(x) = f\left(\frac{13}{x + 3}\right) = \frac{2}{\frac{13}{x + 3} + 3} = \frac{2(x + 3)}{13 + 3(x + 3)} = \frac{2x + 6}{3x + 22}[/tex]
For the domain, we have to remove the points outside the domain of both the primitive and the composite functions, that is, the zeroes of the denominators, hence:
[tex]x + 3 \neq 0 \rightarrow x \neq 3[/tex]
[tex]3x + 22 \neq 0 \rightarrow x \neq -\frac{22}{3}[/tex]
Hence the domain is:
[tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]
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833.30/
1-(1+0.00833)^-360
Answer:
833.25 or 877.59
Step-by-step explanation:
I solved this in two different ways because I wasn't sure on how the question was meant to be read.
Attempt 1:
(833.3/1)-(1+0.00833)^-360
(1+0.00833)^-360 = 0.0505
so:
833.3 - 0.0505 = 833.25
Attempt 2:
833.3/(1-(1+0.00833)^-360)
1- 0.0505 = 0.9495
833.3/0.9495 = 877.59
You invest $2100 in an account at 1.5% per year simple interest. The equation
that represents this scenario is:
A(n) = 2100 + (n-1)(0.0152100)
How much will you have in the account in year 6? Round your answer to the
nearest dollar.
OA. $2289
о C. $2258
D. $2132
B. $17,850
Answer:
My guess would be D
Step-by-step explanation:
Need some help. Urgently. Please explain and answer.
Find volume
πr²hπ(4)²(10)16π(10)160πDensity=12g/cm³
We know
mAss=Density ×Volume
12(160)π1920π6031gAnswer:
6032 g
Step-by-step explanation:
The battery can be modeled as a cylinder.
Volume of a cylinder
[tex]\sf V=\pi r^2 h[/tex]
where:
r is the radiush is the heightGiven:
r = 4 cmh = 10 cmSubstitute the given values into the formula and solve for v:
[tex]\begin{aligned}\textsf{Volume of a cylinder} & =\sf \pi r^2 h \\ \implies \textsf{Volume of the battery} & = \sf \pi (4)^2(10)\\ v& = \sf 160 \pi\:\:cm^3\end{aligned}[/tex]
Density equation
[tex]\rho =\dfrac{m}{v}[/tex]
where:
[tex]\rho[/tex] is densitym is massv is volumeGiven:
[tex]\rho = 12 \dfrac{\text{g}}{\sf cm^3}[/tex]
[tex]v=160 \pi \sf \:\:cm^3[/tex]
Substitute the given values into the Density equation and solve for m:
[tex]\begin{aligned}\rho & =\dfrac{m}{v}\\\implies 12 \dfrac{\text{g}}{\sf cm^3} & = \dfrac{m}{160 \pi \sf \:\:cm^3}\\m & = 12 \dfrac{\text{g}}{\sf cm^3} \cdot 160 \pi \sf \:\:cm^3\\m & = 12 \cdot 160 \pi \:\text{g}\\ m & = 1920\pi\:\text{g}\\ m & = 6031.857895...\:\text{g}\end{aligned}[/tex]
Therefore, the total mass of the battery to the nearest gram is 6032 g.
Help please confused
Answer:
AB : y=1/5x+12
CB : y=-3x+10
CD : y=1/2x-1
DA : y=-2x+1