The day of the month that was 75% of the pond algae-free is: on day 28 or third day.
75% of the pond algae-freeSince we were told the algae doubled every day until it was covered in algae on day 30 of the month.
Hence:
Day 30 (First day)= It was 100% covered.
Day 29 (Second day)=It was 50% covered.
Day 28 (Third day )=it was 25% covered, which will be the same as 75% pond algae-free.
Therefore the day of the month that was 75% of the pond algae-free is: on day 28 or third day.
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The complete question is:
amount of algae covering the Smith's backyard pond doubled every day until it was completely covered in algae on day 30 of the month. On what day of that month was 75% of the pond algae-free?
huang bought 12 boxes of floor tiles that weight 288 pounds each. how much is this in kilograms
[tex]in \: pounds \\ 12 \times 288 = 3456 \: pounds[/tex]
[tex]1 \: kilo = 2.2046 \: pounds[/tex]
[tex]x \: kilos = 3456 \: pounds[/tex]
[tex]x = \frac{3456}{2.2046} = 1567.61 \: kilos[/tex]
What is the area of a rectangle with side lengths of 6/8 meter and 4/10 meter?
Enter your answer as a fraction in simplest form by filling in the boxes.
$$
m²
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is,
Area of rectangle = 6/8 meter × 4/10 meter
= 24 / 80 meters²
= 6 /20 meters²
= 0.3 meters²
Hence, The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².
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Consider parallelogram PQRS, where PQ ≅ RS and QR ≅ PS. Construct diagonal PR and diagonal QS. By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ. Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.
What statement is proven by the given steps?
A.
A quadrilateral with congruent consecutive angles is a parallelogram.
B.
Consecutive angles of a parallelogram are congruent.
C.
Opposite angles of a parallelogram are congruent.
D.
A quadrilateral with congruent opposite angles is a parallelogram.
The correct answer would be option(C) opposite angles of a parallelogram are congruent.
What is Parallelogram?A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.
Given that PQRS is a parallelogram.
PQ ≅ RS
QR ≅ PS
By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.
Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.
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Answer:
"B"
Step-by-step explanation:
What would x be? (giving 50 points!)
Using the following image, solve for x.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: CD + DE = CE[/tex]
[tex]\qquad \tt \rightarrow \: x + 10 + x + 4 = 8[/tex]
[tex]\qquad \tt \rightarrow \: 2x + 14 = 8[/tex]
[tex]\qquad \tt \rightarrow \: 2x =8 - 14[/tex]
[tex]\qquad \tt \rightarrow \: 2x = - 6[/tex]
[tex]\qquad \tt \rightarrow \: x = - 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
[tex]\huge \boxed{\sf x=-3}\\\\\\\displaystyle \sf CD+DE=8 \\\\x+10+x+4=8\\\\2x+14=8\\\\Subtracting\ 14\ from\ each\ side\\\\ 2x+14-14=8-14\\\\2x=-6\\\\ Dividing\ each\ side\ by\ 2 \\\\ \frac{2x}{2} =\frac{-6}{2} \\\\x=-3[/tex]
6+x= 34 how do you solve for x?
Which statements about the local maximums and minimums for the given function are true? Choose three options.
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Over the interval [3, 5], the local maximum is 0.
The statements about the local maximums and minimums for the given function which are true include:
Over the interval [2, 4], the local minimum is –8.Over the interval [3, 5], the local minimum is –8.Over the interval [1, 4], the local maximum is 0.What is Function?This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.
According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.
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if −x+5y=7 is a true equation, what would be the value of -2(-x+5y)
Answer:
-14
Step-by-step explanation:
Given -x+5y=7
Now we substitute x+5y into -2(-x+5y)
-2(-x+5y) = (-2)(7)
= - 14
A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 98% confidence if
The sample size required is 1725.
(A) Sample size calculation
p=0.15
For 98%, z=2.326
d=0.02
Sample size = (z^2*p*(1-p))/d^2
= (2.326^2*0.15*0.85)/0.02^2
=1724.5
The sample size required= 1725
(B) Sample size calculation
p=0.5
For 98%, z=2.326
d=0.02
Sample size = (z^2*p*(1-p))/d^2
= (2.326^2*0.5*0.5)/0.02^2
= 3381.4
The sample size required= 3382
In records, the pattern size is the degree of the variety of character samples utilized in a test. For example, if we're testing 50 samples of folks that watch television in a town, then the pattern length is 50.
Sample size willpower is the act of selecting the range of observations or replicates to consist of in a statistical pattern. The sample size is a crucial function of any empirical look at in which the intention is to make inferences about a populace from a sample.
Your question is incomplete. Please find the complete question below.
A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with98% confidence if
(a) Does he use a 2006 estimate of 15% obtained from a Coinstar National Currency Poll?
(b) he does not use any prior estimate?
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please help me answer this!!
The value of x from the given expression is 5/6
Expansion of equation
Given the expression to expand expressed as:
15 = 3/5(6x + 20)
We are to determine the value of x
15(5) = 3(6x + 20)
Expand
75 = 18x +60
Collect like terms
18x = 75 - 60
18x = 15
x = 15/18
x = 5/6
Hence the value of x from the given expression is 5/6
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find the sine of y. write your answer in simplified, rationalized form. do not round.
Answer:
[tex]\frac{\sqrt{61} }{\sqrt{97} }[/tex]
Step-by-step explanation:
Sin(y) = opposite over hypotenuse
opposite side is [tex]\sqrt{61}[/tex]
hypotenuse is [tex]\sqrt{97}[/tex]
For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.
35. f(x) = 3x + 2, g(x) = 5 − 6x
Answer:
The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.
Step-by-step explanation:
It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.
It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].
To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.
To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.
Step 1 of 2
Substitute g(x) for x in f(x) and simplify the expression.
[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]
Step 2 of 2
Substitute f(x) for x in g(x) and simplify the expression.
[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]
tion
If a soccer team made 19 penalty shots out of 100, what fraction and what
percentage of penalty shots did the team miss? Choose two answers.
A.
B. 19%
C.
19
100
D.
81
100
80
100
E. 81%
OF. 0.19%
A number in a fraction implies the part of a number in another given number. While percentage relates a given number to 100%. Thus the answers to the given question are:
a. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]
b. percentage of penalty shots missed = [tex]\frac{81}{100}[/tex] x 100%
= 81%
A fraction is a part of a given number stated in a quotient form. Generally, all numbers can be expressed in form of fractions, even whole numbers.
The percentage is an expression that shows the part of a number in a given number with respect to 100%. An example is 10%([tex]\frac{10}{100}[/tex]).
From the given question, let;
n, number of penalty shots made = 19
T, the total number of penalties taken = 100
Thus, the number of penalties missed = T - n
= 100 - 19
= 81
Thus,
i. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]
ii. percentage of penalty shots missed = [tex]\frac{81}{100}[/tex] x 100%
= 81%
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CNA SOMEONE HELP ME
measure of
angle C = 48 degrees, a = 5, b = 9. What is the length
of c to the nearest tenth?
Answer: 6.8
Step-by-step explanation:
By the Law of Cosines,
[tex]c^2 = 5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}\\\\c=\sqrt{5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}}\\\\c \approx 6.8[/tex]
According to the fundamental theorem of algebra, how many roots exist for the polynomial function? (9x 7)(4x 1)(3x 4) = 0
3 roots are exist, since the polynomial is of third degree.
According to statement
This follows immediately from the zero product property: if ab=0, then either a=0 or b=0. We have3 roots are exist, since the polynomial is of third degree.
(9x+ 7)(4x +1)(3x+ 4) = 0
from which it follows that each of which admits only one solution.
AND
using the fundamental theorem of algebra, expanding we have a polynomial that is of third degree:
(9x+ 7)(4x +1)(3x+ 4) = 0
108x^3 + 255 x^2 +169x + 28 =0
The theorem states that a polynomial will have up to n distinct roots. In this case, it follows that there are exactly 3, since the solutions to the system above are all distinct.
So, 3 roots are exist, since the polynomial is of third degree.
DISCLAIMER : The question was incomplete. Please find the full content below.
QUESTION
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots
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what is the rule of the reflection?
The rule of reflection in the image shown is: (x, -y).
What is Reflection?Reflection is a transformation which creates a new image by flipping over a line of reflection. The new image is congruent to the original image after reflection. The rule of reflection over an x-axis is given as, (x, -y).
In the image given we can see that rotating triangle LMN over the x-axis gave us:
M(-5, 4) → M'(-5, -4)
L(-4, 2) → L'(-4, -2)
N(-2, 3) → N'(-2, -3)
Therefore, the rule of reflection is: (x, -y).
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Describe the transformations necessary to transform the blue graph of f(x) into the red graph of g(x)
Transformation is a process that involves either increasing, or decreasing the size of a given object, or changing its orientation to produce an image.
The required transformations are:
i. For graph a - translation.
ii. For graph b - dilation.
Rigid transformation involves a change in the orientation of a given object or resizing of a given object to produce an image. The types of transformation are reflection, translation, rotation, and dilation.
i. Reflection is a type of transformation that requires flipping a given object about a reference point or line.
ii. Translation is a type of transformation that involves moving an object in a particular direction without a change in its size and orientation.
iii. Rotation is a type of transformation that involves turning an object at a given angle about a reference point.
iv. Dilation is a type of transformation that require increasing or decreasing the size of the object using a given factor.
Therefore the necessary transformation to transform the blue graph of f(x) into the red graph of g(x) is:
a. For graph a is translation.
b. For graph b is dilaton.
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The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) cm2 What is the relative error
The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.
Given that the circumference of a sphere is 76cm and error is 0.5cm.
The formula of the surface area of a sphere is A=4πr².
Differentiate both sides with respect to r and get
dA÷dr=2×4πr
dA÷dr=8πr
dA=8πr×dr
The circumference of a sphere is C=2πr.
From above the find the value of r is
r=C÷(2π)
By using the error in circumference relation to error in radius by:
Differentiate both sides with respect to r as
dr÷dr=dC÷(2πdr)
1=dC÷(2πdr)
dr=dC÷(2π)
The maximum error in surface area is simplified as:
Substitute the value of dr in dA as
dA=8πr×(dC÷(2π))
Cancel π from both numerator and denominator and simplify it
dA=4rdC
Substitute the value of r=C÷(2π) in above and get
dA=4dC×(C÷2π)
dA=(2CdC)÷π
Here, C=76cm and dC=0.5cm.
Substitute this in above as
dA=(2×76×0.5)÷π
dA=76÷π
dA=24.19cm².
Find relative error as the relative error is between the value of the Area and the maximum error, therefore:
[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]
As above its found that r=C÷(2π) and r=dC÷(2π).
Substitute this in the above
[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]
Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.
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please help!!! (if you can explain the answer that would be great too)
Answer:
Option A
Step-by-step explanation:
Equation of line:[tex]\sf Slope=\dfrac{Change \ in \ y}{Change \ in \ x}=\dfrac{rise}{run}[/tex]
We can find the equation of line, by comparing the slope of line segment AC and slope of AE.
Slope of AC = Slope of AE
[tex]\sf \dfrac{4}{3}=\dfrac{y +2}{x}[/tex]
Cross multiply
4*x = 3*(y +2)
4x = 3y + 3*2
4x = 3y + 6
Equation of the line in standard form:
4x - 3y - 6= 0
statements and reasons please
The lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.
What are the properties of a parallelogram?Properties of a parallelogram include;
Opposite sides are equalOpposite angels are equalThe angles are supplementary to each other The diagonals of a parallelogram bisect each otherFrom the figure, we have that lines YZ and WZ are equivalent because the diagonal bisects the parallelogram to two four of which they are of equal lengths.
Thus, the lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.
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MN= cm
Help me please!! Stuck on this thanks:)
Answer:
3π
Step-by-step explanation:
arc length = radius x central angle in radians
π = radius x π/3
radius = 3π
since OMN is an equilateral triangle, radius = MN
thus MN = 3π
sabbir arrived at dhaka train station at 9 30 pm write this time using the 24hr clock
Okay so a 24hr clock is very simple. We usually turn to "PM" when its 12:00 (day time).
In the 24hr clock we do not, we don't use PM or AM but its crucial to know when converting a standard clock time to military time (aka. 24hr).
9:30 PM in 24hr clock is 12:00 + 9:30 because 9:30 is past that first 12 hours.
So in 24hr clock time it is 21:30. You can also count backwards from midnight to figure it out, for example 12:00 AM (midnight), minus 9:30 is 2:30. Therefore 24:00-2:30=21:30.
Hopefully it helps, heart will help me alot too!
Answer:
21:30
Step-by-step explanation:
The 24hour clock uses 0:00 for midnite. 1am through noon are just 1:00 - 12:00. But the pm hours continue counting up, 13 - 23.
For example, 1pm is 13:00 and 2pm is 14:00.
To change to 24 hour clock, for pm hours, ADD 12.
So for your problem, 9:30 is:
9:30 + 12
= 21:30
What is the probability that a two-digit number selected at random has a tens digit less than its units digit
The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).
[tex]A=24B=90\\\\P=A/B\\\\P=24/90\\p=4/15[/tex]
There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.
The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.
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Maya, lute and aran are cousins. maya's age is 1/3 of lute's and aran is 1/4 of lute's age. if the sum of their agaes is 38, find the ages of each cousin
The ages of Lute, Maya and Aran are respectively; 24, 8 and 6 years old.
How to solve algebra problems?Let Lute's age be x
Thus;
Maya's age = ¹/₃x
Aran's age = ¹/₄x
We are told the sum of their ages is 38. Thus;
x + ¹/₃x + ¹/₄x = 38
Multiply through by 12 to get;
12x + 4x + 3x = 456
19x = 456
x = 456/19
x = 24
Maya's age = ¹/₃ * 24 = 8 years
Aran's age = ¹/₄ * 24 = 6 years
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The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are
The appropriate hypothesis which is used to test the dropout rate are [tex]H_{0}:p > =0.081\\[/tex] and [tex]H_{1}: p < 0.081[/tex].
Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.
The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.
The parameter of interest is the proportion to high school drop outs is p.
Sample proportion=[tex]p^{1}[/tex]=0.065
The hypothesis can be formed as under:
[tex]H_{0}:p > =0.081[/tex] (null hypothesis)
[tex]H_{1}:p < 0.081[/tex] ( alternate hypothesis)
Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.
[tex]Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}[/tex]
=[tex]0.065-0.081/\sqrt{(0.081*0.0919)/1000}[/tex]
=-1.85
Hence the appropriate hypothesis are [tex]H_{0}:p > =0.081[/tex] and [tex]H_{1}:p < 0.081[/tex].
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Write the phrase as a mathematical expression. Use x as the variable.
4 times the sum of 2 times a number and 7
Answer:
4(2x+7) which is equal to 8x+28
If the expression (2+ 3+ 2i) is a factor of a polynomial, which expression below
must also be a factor?
A: -(x+3+2i)
B: (x-3-2i)
C:(x-3+2i)
D:(x+3-2i)
Step-by-step explanation:
180 250 300 H.C.F by division method
Select the correct answer from each drop-down menu.
Trapezoid PQRS
4650
be inscribed in a circle because the
Reset
115⁰
Next
65°
Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.
What is the Inscribed Quadrilateral Conjecture?The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.
From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.
Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.
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What is the smallest natural number in which its digits are only 1's and 2's and which is divisible by 3 and 8?
Look at the multiples of lcm(3, 8) = 24, each of which are divisible by both 3 and 8. Naturally, the number we're looking for must have at least two digits.
The last/ones digit of a number [tex]n[/tex] can be computed by evaluating [tex]n \pmod{10}[/tex]. Suppose the ones digit is 1. Then
[tex]n \equiv 24k \equiv 20k + 4k \equiv 4k \equiv 1 \pmod{10}[/tex]
but this has no solution since no multiple of 4 ends in 1. So our number ends with a 2.
If our number has two digits, then in order for it to be divisible by 3, the first digit must be 1, since 1 + 2 = 3. But 12 is not divisible by 24.
If our number has three digits, then it's either 111 (with digital sum 1 + 1 + 1 = 3) or 222 (digital sum 2 + 2 + 2 = 6), since no other triplet of 1s and 2s sums to a multiple of 3. But 111 = 3×37 and 222 = 2×111, so neither are divisible by 24.
Now suppose [tex]n[/tex] has four digits. Also suppose that the tens digit is 2. Then our number must be 1122 to uphold divisibility by 3, but 1122 = 2×3×11×17 is not divisible by 8. So the tens digit must be 1. This in turn leaves two remaining candidates, 1212 and 2112. We have 1212 = 12×(100 + 1) not divisible by 8, so our number must be [tex]\boxed{n=2112}[/tex]. And it is, since 2112 = 24×88.
Maina is thrice old as her daughter seven years ago the ratio of their ages was 5:1 Find the daughters age in six years
The daughter's age in 6 years time is 20
How to determine their ages?Let their current age be x and y
So, we have:
x = 3y
7 years ago, we have:
x - 7 : y - 7 = 5 : 1
Express as fraction
[tex]\frac{x - 7}{y - 7} = \frac 51[/tex]
Cross multiply
x - 7 = 5y - 35
This gives
x = 5y - 28
Substitute x = 3y in x = 5y - 28
3y = 5y - 28
Evaluate the like terms
2y = 28
Divide by 2
y = 14
In 6 years time, we have:
y + 6 = 20
Hence, the daughter's age in 6 years time is 20
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What is the area of this polygon? Enter your answer in the box. units?
Answer:
45units^2
Step-by-step explanation:
Break the polygon into two shapes. A rectangle and a triangle.
The area formula for a rectangle is A=L•W or
Area = Length x Width. Counting the units for length and width is 9 x 2. Which would equal 18units.
Now for the triangle, the formula is A=1/2 (b•h)
The base is 9 and Height is 6.
9 • 6 = 54
Since a triangle is half the area of a rectangle you divide 54 by 2. Area for triangle is 27.
Now add the rectangle area and triangle area.
18+27=45
Area=45 units ^2