The overall algebraic expression will be: [tex]\frac{5(x+11)}{3(x+8)}[/tex]
Definition of algebraic expression -
An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
Five times the sum of a number and eleven, divided by three times the sum of the number and eight.
Let the number be x.
Five times the sum of a number and eleven means 5 multiplied to the sum of x and 11. In expression this will be written as:
5(x + 11)
Three times the sum of the number and eight means 3 multiplied to the sum of x and 8. In expression this will be written as:
3(x + 8)
So, the overall algebraic expression will be: [tex]\frac{5(x+11)}{3(x+8)}[/tex]
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Roger owns a one-acre piece of land. the length of the land is 484 feet. what is the width of his property? (hint: one acre = 43,560 square feet)
Answer:
90ft
Step-by-step explanation:
43,560ft² = L × l
43,560ft² = 484ft × l
43,560ft² ÷ 484ft = l
l = 90ft
To the nearest foot what is the length of a pendulum that makes one full swing in 1.9s
A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.
What is the length of a pendulum?A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.
Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".
Given the equation:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
where L is the length in feet and T is the time in seconds.
Given that T = 1.9sec,
Hence:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
L = 2.93 feet
A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.
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A train to new york city leaves every 7 minutes. another train to boston leaves the station every 6 minutes. suppose it is 6:30 am right now. at what time will both trains leave the station together again if both of them left the station together at 6:30 am?
Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
What is LCM?The lowest integer that is a multiple of two or more numbers is known as the LCM. For instance, the LCM of 4 and 6 is 12, and the LCM of 10 and 15 is 30. There are numerous ways for determining the least common multiples, just as there are for computing the greatest common divisors. One approach is to divide both numbers by their primes.To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:
If a train to New York City departs every 7 minutes and another to Boston departs every 6 minutes,The two trains then depart together after a time equal to the LCM of their individual intervalsLCM (7,6) = 42As a result, if they begin at the same time, they will depart at the same time every 42 minutes.If both trains left the station at 6.30 a.m., they will leave together again 42 minutes later, at 7.12 am.
Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
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A softball pitcher has a 0. 431 probability of throwing a strike for each pitch. if the softball pitcher throws 22 pitches, what is the probability that exactly 12 of them are strikes?
The probability that exactly 12 of them are strikes is 0.09.
In this question,
Number of pitches, n = 22
Probability of throwing a strike for each pitch, p = 0.431
Then, q = 1 - p
⇒ q = 1 - 0.431
⇒ q = 0.569
Number of strikes, x = 12
The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,
[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]
⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]
⇒ P(X=12) = (646646)(0.000041)(0.00355)
⇒ P(X=12) = 0.09431 ≈ 0.09
Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.
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16. a) In the given figure, OB bisects ABC and OC bisects ACB, prove that BOC - BAC = ABO+ACO.
Answer:
Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.
Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.
m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB
m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO
m<ABO + m<ACO = m<BOC - m<BAC
A cylinder has a radius of 1 inch and height of 1 inch.what is the approximate volume of the cylinder? round to the nearest hundredth. use 3.14 for π.1.05 cubic inches1.57 cubic inches3.14 cubic inches6.28 cubic inches
The volume of the cylinder is [tex]3.14 inch^3[/tex]
Given that
radius = 1 inch
height = inch
we know that volume =[tex]V = \pi \times r^2 \times h[/tex]
now put the value in the above equation we get
[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]
What is Volume?Volume is a measurement of three-dimensional space that is occupied.Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes.If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects with dimensions of zero, one, and two have no volume;To know more about volume with the given link
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Solve for P : p/10 = 7.2/3
P/10 = 7.2/3
P = 7.2x10/3
P=72/3
P= 24
Use the function, f(x)=50(1.02)^x to identify if it's growth or decay & the percentage of the growth or decay.
The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.
What is the growth rate in the function?The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
In this case, the function is given as:
f(x)=50(1.02)^x
It should be noted 1 + 2% = 1.02 which us the value in the parentheses.
In conclusion, the growth rate is 2%.
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Use a left-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
Answer:
25 / 4
Step-by-step explanation:
To find the left sum, you need to....
1.) Find Δx
2.) Find [tex]x_{k-1}[/tex]
3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx
4.) Solve for the left sum
Write as a single term from Pascal's Triangle in the form t_nr(1 mark)
t_13,8 + t_13,9
¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
What is Pascal's triangle?
Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.
What is combination?Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!
How to write a single term from Pascal's Triangle in the form t_nr = t_13,8 + t_13,9.Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that
¹³C₈ = 13!/8!(13 - 8)! = 13!/8!5! and ¹³C₉ = 13!/9!(13 - 9)! = 13!/9!4!So, ¹³C₈ + ¹³C₉ = 13!/8!5! + 13!/9!4!
= 13!/(8! × 5 × 4!) + 13!/(9 × 8! × 4!)
= 13!/8!4![1/5 + 1/9]
= 13!/8!4! × [(9 + 5)/45]
= 13!/8!4! × 14/45]
= 13!/8!4! × 14/(9 × 5)]
= 14 × 13!/8! × 9 × 4! × 5)]
= 14!/9!5!
= 14!/9!(14 - 9)!
= ¹⁴C₉
So, ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
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Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)
The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.
In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.
In the given expression, a = 1, b = -4, and c = -21.
Thus, ac = -21.
The numbers having a product 21 are:
1*21 = 21,
3*7 = 21.
Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.
Thus, the expression can now be shown as:
x² - 4x - 21
= x² + (3 - 7)x - 21
= x² + 3x - 7x - 21
= x(x + 3) - 7(x + 3) {By taking common}
= (x - 7)(x + 3) {By taking common}.
Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
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a) The line y = 4 meets the line 2x + y = 8 at the point A
Fins the co-ordinates of A
b) The line 3x + y = 18 meets the x axis at the point B
Find the co-ordiantes of B
c) (i) Find the co-ordiantes of the mid-point M of the line joining A to B
(ii) Find the equation of the line through M parallel to 3x + y =18
answers :
a.
coordinates of A are (2,4)
b.
coordinates of B are (6,0)
i.
(4,2) is the midpoint
ii.
y = -3x + 18 is the parallel line
Step-by-step explanation:
a.
if two things are equal to the same thing then they are equal to each other
y = 4
2x + y = 8 is y = -2x +8 so
-2x +8 = 4
-2x = -4
x = 2
coordinates of A are (2,4)
b.
if two things are equal to the same thing then they are equal to each other
y=0
3x+y=18 is y = -3x+18 so
-3x+18=0
x = 6
coordinates of B are (6,0)
midpoint formula is
(X1+X2)/2 , (Y1+Y2)/2
(2,4) (6,0)
(X1+X2)/2 , (Y1+Y2)/2
(2+6)/2 , (4+0)/2
(4,2) is the midpoint
parallel line has the same x value
so for a line parallel to 3x+y=18 or y = -3x+18
the parallel line would be
y = -3x
point slope formula
point slope formulay - y1 = m (x - x1)
3x+y=18 or y = -3x+18 was 6,0 at y = 0
y - y1 = m (x - x1)
y - 0 = m (x - x1)
since it's a parallel line the m has to be the same
(6,0)
y - 0 = -3 (x - 6)
y = -3x + 18 is the parallel line
Pick the correct answer
Thanks so much :)
The linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
Line I is decreasing, hence it has a negative slope.Line K is constant, hence it has a slope of zero.Line J is increasing, hence it has a positive slope.Hence the linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
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Translate the triangle by
(-2 and -4)
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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dilate the line segment by a scale factor of 2 with a center of dilation at the origin. Draw the dilated segment on the provided graph.
Answer:
See attached
Step-by-step explanation:
Each point on the line segment moves to 2 times its previous distance from the origin.
Invariant pointThe center of dilation, the origin, is an invariant point. It doesn't move for any dilation factor. One end of the line segment is there, so it will not move.
Dilated pointsThe coordinates of each point are multiplied by the dilation factor. The other end of the line segment is (5, 5), so it moves to 2×(5, 5) = (10, 10).
The dilated line segment extends from (0, 0) to (10, 10). It is shown in red in the attached graph.
Charles used a chain which was 12.5 metres long, 12 times to measure the breadth of his garden. Stephen used a chain of different length 10 times to cover the breadth of Charles' garden and 18 times to cover its length. What is the area of Charles' garden to the nearest one tenth of a hectare?
A. 4.05 m^2
B. 5.4 m^2
C. 3.6 m^2
D. 4.1 m^2
The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Length of Charles garden = 12.5 m * 12 = 150 m
Length of Stephen chain = 150 m /18 = 25/3 m
Breadth of Charles garden - 25/3 * 10 = 250/3 m
Area of Charles garden = 150 m * 250/3 m = 12500 m =
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Consider the line y equals 2 over 5 x plus 4.
Find the equation of the line that is parallel to this line and passes through the point left parenthesis 5 comma negative 1 right parenthesis.
the parallel linear equation is:
y = (2/5)*x - 3
How to find the parallel line?Two lines are parallel if the lines have the same slope but different y-intercept.
Here we know the line equation:
y = (2/5)*x + 4
Then a parallel line is of the form:
y = (2/5)*x + c
Where c is different than 4.
We want this line to pass through (5, -1), then:
-1 = (2/5)*5 + c
-1 = 2 + c
-1 - 2 = -3 = c
Then the parallel linear equation is:
y = (2/5)*x - 3
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There are 6 dogs and 5 cats. In how many different orders can these animals be placed in line if any animal can be next to any other animal?
120=!3÷!6
!2-!5=!3
to 120 modes
A box is to constructed with a rectangular base and a height of 5cm. if the rectangular base must have a perimeter of 28cm, which quadratic equation best models the volume of the box ? a. y=5(28-8)(x) b.y=5(28-2x)(x) c. y=5(14-x)(x) d. y=5(14-2x)(x)
y=5(14-x)(x) quadratic equation best models the volume of the box .
What is volume of cuboid?
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape. The volume of a cuboid is found by multiplying the length by the breadth by the height.Perimeter = 2(width + length) =28
Let x=width of base, then length of base = (28/2)-x = 14-x
Volume of box = length*width*height
=x(14-x)*5 ⇒ 5x(14-x)(x)
Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .
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What is the area of the shape?
The area of the shape is 35 square units
How to determine the area of the shape?The given shape is a trapezoid, and it has the following side lengths
Parallel bases = 6 and 8
Height = 5
The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height
Substitute the known values in the above equation
A = 0.5 * (6 + 8) * 5
Evaluate the product
A = 35
Hence, the area of the shape is 35 square units
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The area of the given trapezoid is given as 35 square units
How to determine the area of a trapezoid?The given shape is quadrilateral known s a trapezoid. The formula for calculating the are of the trapezoid is expressed as;
A = 1/2(a+b)*h
where
a and b are parallel sides
h is the height of the trapezoid.
Given the following parameters
a =6units
b = 8 units
h - 5 units
Substitute to have:
A = 1/2(6 + 8) * 5
A = 1/2(14) *5
A = 7 * 5
A = 35 square units
Hence the area of the given trapezoid is given as 35 square units
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What is the probability that the battery life for an ipad mini will be at least 11 hours?
Answer:
0.2857
Step-by-step explanation:
We want to determine,
The probability that the battery life is at least 11 hours is 0.2857.
The odds of rolling a die and getting an even number is 50%. Write out the success set and the sample set to use the definition of probability to show that this is true.
Answer:
It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).
plsssss help w math functions
Answer:
The second option:
[tex]2\sqrt{x}[/tex]
Step-by-step explanation:
If you need work please ask!
Have a nice day!
What is a population parameter? a population parameter is a numerical descriptive measure of a population. give three examples. (select all that apply. )
Examples of population parameter are mentioned below .
According to the question
Population parameter :
A population parameter is a numerical descriptive measure of a population or a number that describes something about an entire group or population.
The examples of population parameter is
1. The average weight of all middle-aged female Americans. The population consists of all middle-aged female Americans, and the parameter is µ.
2. The average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.
3. The average height of a class X. This is a parameter because it is states something about the entire population of class X.
Hence, examples of population parameter will depend on the population .
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Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]
[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]
next,
g(f(-5)) represents value of y at x = f(-5) = 1
hence,
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\sf \:g(f( - 5)) = 5[/tex]Please help and explain.
Answer:
B
Step-by-step explanation:
It's B
Answer:
Option B
Step-by-step explanation:
The equation is:
[tex]y=10-2x[/tex]
when x=2
[tex]y=10-2(2)010-4=6[/tex]
When x = 3
[tex]y=10-2(3)=10-6=4[/tex]
When x=4
[tex]y=10-2(4)=10-8=2[/tex]
Hope this helps
Determine how the strategies are similar. Picture below
Answer: Look at stwp by step
Step-by-step explanation:
Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2
Research that analyzes a portion of an entire population is carried out on a(n):____.
a. sample.
b. population.
c. census.
d. survey
Option (a) Sample
Sample is the research that analyzes a portion of an entire population.
A sample is a condensed, controllable portion of a bigger group. It is a subgroup of people with traits from a wider population. When populations are too big for a statistical test to include every potential participant or observation, samples are utilized.
By permitting researchers to obtain the same results from a sample as they would from the population, sampling helps researchers save money. Non-random sampling is much less expensive than random sampling since it reduces the expense of locating participants and obtaining their data.
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Csn u please help me o have no idea
Answer:
D.= √29
Step-by-step explanation:
Greetings!The distance between the two complex numbers,
Z₁=a+bi and Z₂=c+di in the complex plane is
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is
[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]
To find the distance between the two complex numbers using the formula
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
where,
a=4b=3c=6d=-2[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]
solve for x: 5^x/5^14=1/5^5
Answer:
[tex] \frac{1 \\ }{3125} [/tex]
Answer:
x = 9
Step-by-step explanation:
Law of exponents:[tex]\sf \dfrac{a^m}{a^n}=a^{m-n}\\\\\\ \dfrac{1}{a^m}=a^{-m}[/tex]
[tex]\sf \dfrac{5^x}{5^{14}}=\dfrac{1}{5^5}\\\\5^{x -14} = 5^{-5}[/tex]
Base are same. Compare the exponents.
x - 14 = -5
x = -5 + 14 {Addition property of equality}
x = 9
