The mean height of plants is 44.07cm.
Given that a raj measures the height of 70 plants which is shown in the table in the image attached below.
The mean is defined as the mean value equal to the ratio of the total number of a given set of values to the total number of values contained in that set.
Firstly, we will find the midpoint of the height by using the formula
(upper limit +lower limit)/2
When h is 10<h<20 then the midpoint is
x₁=(10+20)/2
x₁=15
When h is 20<h<0 then the midpoint is
x₂=(20+40)/2
x₂=30
When h is 40<h<50 then the midpoint is
x₃(40+50)/2
x₃=45
When h is 50<h<60 then the midpoint is
x₄=(50+60)/2
x₄=55
When h is 60<h<90 then the midpoint is
x₅=(60+90)/2
x₅=75
Now, we will find the mean height by using the formula
x=(f₁x₁+f₂x₂+f₃x₃+f₄x₄+f₅x₅)/(Σfi)
Here, f₁=7,f₂=15,f₃=27,f₄=13,f₅=8
and Σfi=7+15+27+12+8=70
Substitute these values in the formula, we get
x=(7×15+15×30+27×45+12×55+8×75)/70
x=(105+450+1215+715+600)/70
x=(3085)/70
x=44.07
Hence, the estimate of the mean height of the plants when raj measures the height of 70 plants is 44.07cm.
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What's the explicit rule for the sequence 3, -6, 12, -24, 48, ...?
Answer:
[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
- 6 ÷ 3 = 12 ÷ - 6 = - 24 ÷ 12 = 48 ÷ - 24 = - 2
this indicates the sequence is arithmetic with explicit rule
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 3 and r = - 2 , then
[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]
Answer:
[tex]\sf \dfrac{-3}{2}(-2)^n[/tex]
Step-by-step explanation:
Explicit formulas are used to represent all the terms of the geometric sequence with a single formula.
[tex]\sf \boxed{\bf t_n = ar^{n-1}}[/tex]
a is the first term.
r is the common ratio.
r = second term ÷ first term.
3 , - 6 , 12, - 24, 48 ,........
a = 3
r = -6 ÷ 3 = -2
[tex]\sf t_n = 3*(-2)^{(n-1)}\\\\[/tex]
[tex]\sf = 3*(-2)^{n}*(-2)^{-1}\\\\ =3*(-2)^n*\dfrac{-1}{2}\\\\= \dfrac{-3}{2}(-2)^n[/tex]
Check:
[tex]\sf t_1 =\dfrac{-3}{2}*(-2)^1=\dfrac{-3}{2}*(-2) = 3\\\\\\t-2 = \dfrac{-3}{2}*(-2)^2 = \dfrac{-3}{2}*4=-6\\\\\\t_3=\dfrac{-3}{2}*(-2)^3=\dfrac{-3}{2}*(-8)=12[/tex]
The revenue earned from tourists in Florida was:
2018 – $4 381 million
2019 – $3 607 million
What is the percentage decrease in revenue from tourists to Florida?
Select one answer
A) 17.67%
B) 21.46%
C) 82.33%
D) 121.46%
The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of each side is 10.4 inches and the length of each side is 12 inches.
The are of the triangle is mathematically given as
a=62.4in^2. This is further explained below.
What is the area of the triangle?Generally, the equation for the area is mathematically given as
a= 0.5(base X height)
Therefore
a= 0.5 (10.4 x 12)
a=62.4in^2
In conclusion, The area of the triangle is
a=62.4in^2
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Carla left the bookstore traveling 12 mph. Then, 3 hours later, Zari left traveling the same direction at 18 mph. How long does Zari have to travel before catching up with Carla
Answer:
6 hours.
Step-by-step explanation:
Speed = distance / time.
Carla travels 3 * 12 = 36 miles before Zari leaves the shop.
So Zari travels x miles in the same time as Carla travels x- 36 miles.
So 18 = x/t and 12 = (x - 36)/t
From first equation x = 18t so we have the equation
12 = (18t - 36/t
18t - 36 = 12t
6t = 36
t = 6 hours.
What is the simplified form of startroot startfraction 48 over 192 endfraction endroot?
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
How to simplify rational numbers
In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:
(a · c)/(b · c) = a/b, where a, b, c are natural numbers. (1)
Along with power properties.
Now we proceed to simplify the rational number:
48/192 = (2⁴ × 3) / (2⁶ × 3)
48/192 = 1 / 2²
48/192 = 1 / 4
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
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Answer:
4
Step-by-step explanation:
Subtract.
3 x - z + 9
3 x - 16 y - z + 9
3 x + z + 9
Answer:
1)3×-8
-24
Step-by-step explanation:
2)bshejejnenenejejkejehrh
Which values of x would make a polynomial equal to zero if the factors of the
polynomial were (x-5) and (x-6)?
A. -5 and 6
B. 5 and 6
C. 5 and -6
D. -5 and -6
If the factors of the polynomial were (x-5) and (x-6), the values of x that would make the polynomial equal to zero would be 5 and 6.
5 - 5 = 0
6 - 6 = 0
Assuming the polynomial is (x-5)(x-6), if one factor is 0 then anything multiplied by 0 is still 0.
Hope this helps!
Find the product -2/9(-5/3) I-Ready math
The product of the given fractions, -2/9(-5/3), is: 10/27.
How to Find the Product of Two Fractions?Given the fractions, -2/9(-5/3), recall that minus multiplied by minus equals plus.
So therefore, the product of the two fractions would be a positive number. Thus:
-2/9(-5/3) = (-2 × -5)/(9 × 3)
-2/9(-5/3) = 10/27
Therefore, the product is: 10/27.
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On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.
Which linear inequality is represented by the graph?
y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1
The graphed inequality is:
[tex]y \geq \frac{1}{3}*x - 1[/tex]
Which linear inequality is represented by the graph?We know that the line is solid, and the region above and to the left is shaded, then the inequality is of the form:
y ≥ line.
Now we need to get the linear equation.
It is of the form;
y = a*x + b
Where a is the slope and b is the y-intercept. Because it passes through (0, -1), we know that the y-intercept is -1.
And knowing that the line passes through (0, -1) and (3, 0), the slope is:
[tex]a = \frac{- 1 - 0}{0 - 3} = \frac{1}{3}[/tex]
Then the inequality is:
[tex]y \geq \frac{1}{3}*x - 1[/tex]
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mann
On a map, 2.5 inches represents 52 miles. What is the actual distance represented by 5 inches on the map?
2.5 5
52 x
Answer:
104 miles.
Step-by-step explanation:
5 inches is 2 * 2.5 inches so the distance required is 2*52 = 104 miles.
Find the lateral area of this pyramid whose
base is a regular hexagon with a side length of
3 cm and whose slant height is 12 cm.
12 cm
3 cm
[ ? ] cm2
The lateral area of the given pyramid is 108 cm².
Any three-dimensional figure's lateral surface area is its side surface area.
In the question, we are asked to find the lateral area of the given pyramid, whose base is a regular hexagon, with a side length of 3 cm, and the slant height of the pyramid is 12 cm.
To determine the lateral area, we determine the area of one lateral face, and then multiply it by the number of lateral faces in the pyramid.
The number of lateral faces = sides of the base = 6 {Since the base is a regular hexagon}.
Area of a lateral face = (1/2)*base*height {Since its a triangle},
or, area of a lateral face = (1/2)*3*12 {Since the base is the side length of the base, and the height is the slant height},
or, area of a lateral face = 18 cm².
Thus, the lateral area of the pyramid = 6 * 18 cm² = 108 cm².
Thus, the lateral area of the given pyramid is 108 cm².
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A boat with some water at its bottom was found leaking again. Assume that water goes into the boat at a constant rate. 3 hours are needed to get all the water out of the boat when 10 people work together. It takes 8 hours to get all the water out if 5 people work together. How many people are needed to get all the water out in 2 hours
The Number of people is 12 when time taken is 2 hours.
According to the statement
Time taken when 10 people works is 3 hours
Time taken when 5 people works is 8 hours
Then we have to find the number of peoples when time taken is 2 hours.
So, average time that for which single person works is 180 min/ 10 = 18 min.
It means the average time for single person works is 18 min in case of 10 people.
and one thing is clear that the number of people is greater than 10 people when time taken is 2 hours.
So, The Number of people is 12 when time taken is 2 hours.
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Need help with this problem
put into quadratic formula
Answer: [tex]\frac{-7+\sqrt{49-4(15)(-12)} }{30}[/tex]
Step-by-step explanation:
Use the quadratic formula:
[tex]\frac{-b+-\sqrt{b^{2}-4(ac) } }{2a}[/tex]
Substitute the values, A = 15, b = 7, c = -12
[tex]\frac{-7+-\sqrt{7^{2}-4*(15*-12) } }{2*15}[/tex]
Simplify to answer:
[tex]\frac{-7+49-4(15)(-12)}{30}[/tex]
I hope this helps!
PLEASE HELP ME! FAST
The quadrants in which all the coordinates given are located is; As explained below.
How to Identify Quadrants in coordinates?1) (2, 4) is located in Quadrant I where both x and y-values are positive.
2) (0, -3) is located in Quadrant II where x - values are positive but y-values are negative.
3) (-1, 1/2) is located in Quadrant IV.
4) (-2 1/2, -7) is located in Quadrant III where x and y values are both negative.
5) (0, 6) is located in Quadrant I where both x and y-values are positive.
6) (-5, 0) is located in Quadrant IV where x is negative but y is positive.
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Approximately ___% of a district’s students that are eligible for free and reduced meals are homeless at any given time.
Percentages are used to show the fraction of a thing. For example, if 5 students out of 20 like math, the percentage is 5/20 x 100= 25%
What is a Percentage?This refers to the number of ratios that is described as a fraction of 100 and is denoted by the sign %.
Hence, we can see that although your question is incomplete, I gave you a general overview of percentages for a better understanding of the concept.
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Activity in this activity, you will first find the squares of positive and negative numbers. then you will determine whether the solution to an equation is a perfect square. question 1 part a complete the table by squaring each positive x-value listed.
The complete table is shown below.
What is square root?A number's square root is the factor that can be multiplied by itself to yield that number. The square root of, the end square root is the symbol for the square root. Finding an integer's square root is the inverse of squaring a number.Complete the table as follows:
[tex]2^{2} = 2*2 = 4\\3^{2} = 3*3 = 9\\4^{2} = 4*4 = 16\\5^{2} = 5*5=25\\6^{2} =6*6=36\\7^{2} =7*7=49\\8^{2} =8*8=64\\9^{2} =9*9=81\\10^{2} =10*10=100\\11^{2} =11*11=121[/tex]
Therefore, the complete table has been shown.
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The question you are looking for is here:
Complete the table by squaring each positive x-value listed 2, 3,4,5,6,7,8,9,10,11.
Petra opens her mail one day to find that an anonymous donor has given her $3000 cash. (woohoo!) she sets aside $1000 to refurnish her apartment, and decides to invest the other $2000. unfortunately, the value of the stock swhe invested in started going down almost as soon as she invested her money. if the stock decreases at a rate of 15% per year for eight years, how much is the stock worth when she sells it eight years later?
The stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.
According to the question,
Petra opens her mail one day to find that an anonymous donor has given her $3000 cash. She sets aside $1000 to refurnish her apartment, and decides to invest the other $2000.
If the stock decreases at a rate of 15% per year for eight years. In order to find the stock worth when she sells it eight years later we have the formula
Value of stock after 'n' years = Principal[1-Rate/100]ⁿ
Value of stock after '8' years = 2000[1-15/100]⁸
= 2000[1-0.15]⁸
=2000[0.85]⁸
=2000[0.2725]
=545$
Hence, the stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.
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Question 1 of 21
Which of the following steps would you perform to the system of equations
below so that the equations have equal x-coefficients?
4x+2y = 4
12x+y = 22
O A. Divide both sides of the top equation by 3
B. Multiply both sides of the top equation by 3
C. Multiply both sides of the bottom equation by 3
OD. Divide both sides of the bottom equation by 2
A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.
A conditional probability of an event tells us that the event has already occured.
Given a _______ probability of an event is a ............. other event has already occurred.
We have to fill the blank with appropriate term or word associated with probability.
The right term is conditional.
Conditional probability of an event is a probability obtained with knowledge that some other event has already occured.
It is denoted as P(A I B).
It satisfies the following equation:
P(AIB)=P(A and B ) / P(B)
where P( A and B) is the probability of A and B together.
Hence conditional probability of an event is obtained with knowledge that some other event has already occured.
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Please help. was due 2 days ago
Answer:
[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]
Step-by-step explanation:
1) Split the second term in [tex]4{x}^{2}-8x-5[/tex] into two terms.
1- Multiply the coefficient of the first term by the constant term.
[tex]4\times -5=-20[/tex] to -8 and multiply to -−20?
2 and −10
3 - Split -8x as the sum of 2x and -10x.
[tex]4x^2+2x-10x-5[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]2x(2x+1)-5(2x+1)=0[/tex]
3) Factor out the common term [tex]2x+1[/tex].
[tex](2x+1)(2x-5)=0[/tex]
4) Solve for [tex]x[/tex].
1 - Ask: When will (2x+1)(2x-5) equal zero?
When 2x + 1 = 0 or 2x - 5 = 0
2 - Solve each of the 2 equations above.
[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]
What is the degree of the polynomial? 5x² + 8x³ + 4- 6x² - 3x5
Answer:
The degree of polynomial is 5.
Step-by-step explanation:
I suppose the polynomial is [tex]\displaystyle{5x^2+8x^3+4-6x^2-3x^5}[/tex]. To find the which degree this polynomial is, we consider the highest exponent of the term which is [tex]\displaystyle{3x^5}[/tex], the 5 is our highest degree of the term and thus, 5 is our highest degree of polynomial.
Answer:
5
Step-by-step explanation:
I'm assuming that the 5 in "3x5" is supposed to be a exponent. The degree of the polynomial is the greatest of the exponents (powers) of its various terms.
Which measure represents the standard deviation of the sample means and is used in place of the population standard deviation when
the population parameters are unknown?
The measure represents the standard deviation of the sample means and is used in place of the population standard deviation when the population parameters are unknown is; t-test.
Which measure is used when the population parameters are unknown?A hypothesis test for a population mean when In the case that the population standard deviation, σ, is unknown, carrying out a hypothesis test for the population mean is done in similarly like the population standard deviation is known. A major distinctive property is that unlike the standard normal distribution, the t-test is invoked.
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Answer:
standard error of the mean
Step-by-step explanation:
Plato/Edmentum
which of the following is the product of the rational expression shown below
Answer:
B
Step-by-step explanation:
[tex]\frac{x}{x-3}[/tex] × [tex]\frac{2x}{x+5}[/tex] ( no factors cancel on numerator / denominator )
= [tex]\frac{x(2x)}{(x-3)(x+5)}[/tex]
= [tex]\frac{2x^2}{x^2+2x-15}[/tex]
I can find the 3 third side of the triangle
Answer:
15
Step-by-step explanation:
First side is 20
Second side is 20 * (3/2), as it is 1 and 1 half times longer than the first
Second side is 30(as calculated above)
65-20-30 = 15
Solve each of the following equations show the solution on a number line check your answers 5-|n-1|=-2
n=8
n=-6
What is a number line?A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered.
The numbers on the number line increase as one moves from left to right and decrease as one moves from right to left.
Solution for the above equation 5-|n-1|=-2What is the modulus?A modulus function is a function that returns the absolute value of a number or variable. It yields the magnitude of the number of variables. It is also known as an absolute value function. This function's output is always positive, regardless of the input.
Open modulus with a positive sign.
5-|n-1|=-2
-|n-1|=-2-5
n+1= 7
n= 8
Open modulus with a negative sign.
5-|n-1|=-2
-|n-1|=-2-5
n-1= -7
n= -6
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Which of the following represents the divisor and the dividend for the
synthetic division problem below?
-1)29 7
OA. x+1 and 2x² +9x+7
OB. x+1 and -2*² -9x-7
OC. x-1 and 2x² +9x +7
OD. x-1 and -2*² -9x-7
The dividend is [tex]2x^2+9x+7[/tex] while the divisor is x + 1
Option A is correct
Division of polynomial using synthetic divisionThe coefficient outside the division block is -1.
This means that the divisor = x + 1
Also, the coefficients of the dividend are:
2, 9, 7
The highest exponent is 2 since there are three terms in the polynomial. Three terms show that the expression is a quadratic expression
Therefore, the dividend is [tex]2x^2+9x+7[/tex]
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What is the y-value of point A? On a coordinate plane, point A is 6 units to the right and 1 unit up.
Answer:
1
Step-by-step explanation:
Points on a coordinate plane are written as (x,y) coordinates. The vertical axis is the y axis. If your point is "one unit up" its y-value is 1. (The horizontal axis is the x-axis. The x-value is 6.)
What is the height, x, of the equilateral triangle shown?
60°
60°
10 in.
60°
O A. 5in.
O B.
OC. 10in.
OD. 10√3in.
5√/3in.
Answer:
B
Step-by-step explanation:
Drop an altitude. Either of the two resulting right triangles with legs of length 5 and x and a hypotenuse of 10.
By the Pythagorean theorem, it follows that the answer is B.
what is x and y? i am having trouble finding what x and y are
Answer:
x = 10
y =10√2
Step-by-step explanation:
45° - 45° - 90° triangle:The ratio of the sides of 45°- 45° - 90° triangle is a : a : a√2
The side opposite to angle 45° is a
a = 10
⇒ x = a
[tex]\sf \boxed{\bf x = 10}[/tex]
The side opposite to 90° is a√2
y = a√2
= 10√2
[tex]\sf \boxed{\bf y= 10\sqrt{2}}[/tex]
Answer:
y = 14.1 or 10√2Step-by-step explanation:
is an isosceles right triangle, so x = 10
to find y we use pythagoras
y = √(10²+10²)
y = √200
y = 14.1 or 10√2
One circle has a circumference of 12x cm. Another circle has a circumference of 32 cm. What is the ratio of the
adius of the smaller circle to the radius of the larger circle?
O 3:8
O 8:3
O 1:3
O 3:1
56:23
21
The ratio of the radius of the smaller circle to the radius of the larger circle as required in the task is; 3:8.
What is the ratio of the radius of the smaller circle to the radius of the larger circle?It follows from the task content that the circumference of the smaller circle is; 12cm while that of the bigger circle is; 32cm.
Since, the circumference of a circle is directly proportional to the radius of the circle from the formula; C = 2πr.
The ratio is therefore; 12:32, in which case, when expressed in its simplest form is; 3:8.
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