After 34 hours, there are approximately 29 bacteria(to the nearest hundred) in the culture.
What is meant by multiplication?Combining two or more bacterium streptococcus to create a new number is the mathematical action known as multiplication. It is frequently represented by the letter "x" or an asterisk (*), and is also referred to as the "times" operation. Since multiplication may be regarded of as a shortcut for repeatedly adding a number to itself, it is closely connected to addition. For instance, multiplying two by three is identical to adding two plus two plus two, which equals six. Division and multiplication are connected because dividing one number by another is equivalent to multiplying the first number by the reciprocal of the second number. For example, 3 x 1/2 is equivalent to dividing 3 by 2, which equals 1.5.
How to solve?
N(t) = N0 * 2^(t/tau)
N(34) = 9 * 2^(34/1.6) = 9 * 2^(21.25)
To round this number to the nearest whole number, we can first calculate 2^(21.25) and then multiply it by 9. Since 2^(21.25) is approximately 3.2, the final answer is approximately 29. This means that after 34 hours, there are approximately 29 bacteria in the culture.
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a pile of bricks weight 22kg.18759grams of bricks are removed.what weight is left?
The weight that is left when 18759 grams of bricks are removed is 3.241 kg
How to determine the remaining weight?From the question, we have the following parameters that can be used in our computation:
Pile of bricks = 22 kg
The weight removed from the pile = 18759 grams
The remaining weight can be calculated using the following subtraction equation
Remaining weight = Pile of bricks - The weight removed from the pile
Substitute the known values in the above equation, so, we have the following representation
Remaining weight = 22 kg - 18759 grams
Convert grams to kg
This gives
Remaining weight = 22 kg - 18.759 kg
Evaluate the difference in the above equation
Remaining weight = 3.241 kg
Hence, the remaining weight is 3.241 kg
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What is the product of 10 numbers?.
Product of first 10 natural numbers is 3628800.
What is natural numbers?
In arithmetic, the natural numbers are those numbers used for enumeration and ordering. Numbers used for enumeration are referred to as cardinal numbers, and numbers used for ordering are referred to as ordinal numbers
Main body:
The first ten natural numbers are 1,2,3,4,5,6,7,8,9,10.
The product is the multiple all numbers.
Product of first 10 natural numbers is given by,
P = 1*2*3*4*5*6*7*8*9*10
P =3628800.
Therefore, Product of first 10 natural numbers is 3628800.
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mr. imani wants to purchase paper and notebooks for his classroom. at dollar discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. this is modeled by 1.25p + 2.50n. evaluate for p = 10 and n=30 to find how much it will cost mr. imani to purchase 10 packs of paper and 30 notebooks.
1.$450.00
2.$62.50
3.$43.75
4.$87.50
The total cost for buying 10 packs of paper and 30 notebooks is $87.50.
What is equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Mr. Imani wants to purchase paper and notebooks for his classroom. at dollar discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. this is modelled by 1.25p + 2.50n. evaluate for p = 10 and n=30
Putting p = 10 and n = 30, we get,
1.25*10+2.50*30 = 87.50
Hence, The total cost for buying 10 packs of paper and 30 notebooks is $87.50.
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what is the probabiluity that in a random sample of 500 adults more than 30 percent do not own a credit card
Using p-hat formula and probability,
we get
a) Sampling distribution of p-hat = 0.02029286
b)The probability that in a random sample of 500 adults more than 30% do not own a credit card is
=0.3121
c) The probability that in a random sample of 500 adults between 25% and 30% do not own a credit card is 0.6635
We have given that
29% of adults do not own a credit card according to creditcard.com.
a) Sample size (n) = 500 of adults have own credit card
sample proportion, for the adults do not own a credit= 29% = 0.29
Normal distribution exits here with p
= 1-0.29=0.71 and
Standard error (p-hat) =sqrt(p(1-p)/n)
=sqrt(0.71× 0.29/500)
p-hat = 0.02029286
b) Now, more than 30% do not have own credit card.
P(p-hat>0.3) = P((phat- p)/sqrt(p×(1-p)/n) >(0.3-0.29)/sqrt(0.29× (1-0.29)/500))
=P(Z>0.49) =0.3121 (from standard normal table)
c) Sample size (n) = 500 and p-hat lies between 25% to 30% .
P(0.25<phat<0.3)
= P((0.25-0.29)/sqrt(0.29*(1-0.29)/500) <Z< (0.3-0.29)/sqrt(0.29*(1-0.29)/500))
=P(-1.97<Z<0.49)
=0.6635 (from standard normal table)
Hence, we calculated all the required probabilities.
a) p-hat = 0.02029286
b) P(p-hat>0.3) =0.3121
c) P(0.25<phat<0.3) =0.6635
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Complete question:
According to creditcard.com, 29% of adults do not own a credit card.
a. Suppose a random sample of 500 adults is asked, "Do you own a credit card?" Describe the sampling distribution of p-hat, the proportion of adults who own a credit card.
b. What is the probability that in a random sample of 500 adults more than 30% do not own a credit card?
c. What is the probability that in a random sample of 500 adults between 25% and 30% do not own a credit card?
suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped. draw the adiabatic and isochoric processes on a p-v diagram.
The diagram of adiabatic and isochoric process on a pv diagram is given below.
In the given question we have to suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped the draw the adiabatic and isochoric processes on a p-v diagram.
The Adiabatic Process
A thermodynamic process known as adiabatic means that no heat is transferred into or out of the system. For an ideal gas, an adiabatic process is a reversible process with constant entropy. The adiabatic process is mathematically represented by the expression ∆Q=0.
The Isochoric Process
A thermodynamic process known as an isochoric process, also known as a constant-volume process, isovolumetric process, or isometric process, occurs when the volume of the closed system undergoing the process remains constant.
The diagram of adiabatic and isochoric process on a pv diagram is given below:
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Write a two column proof for the following statement.
“Given that 2( -x + 4) = 3 , prove that x = 5/2.
The two column proof for the statemen is as follows
Statement Reason
2(-x + 4) = 3 given
-2x + 8 = 3 Distributive property of multiplication
-2x = 3 - 8 Collection of similar terms
-2x = -5 Subtraction property of equality
-2x/-2 = -5/-2 Division property of equality
x = 5/2 Definition of equality
What is algebra?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.
In algebra, we utilize integers with fixed or definite values, such as 2, 13, 0.5, etc. combined with variables like x, y, and z
An instance of algebra is 2( -x + 4) = 3
What is distributive property of multiplication?The distributive property of multiplication is applied when there is multiplication over addition of terms like exemplified here
2(-x + 4)
= -2x + 4
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Is it a zero if it touches the x-axis?.
At the zero point the curve can either cross the x-axis or just touch it. The root of the function is the number c with f(c) = 0.
If the graph intersects the x-axis and looks nearly linear at the intersection, it is a single root. Even multiplicity zero if the graph touches the x-axis and bounces off the axis.
Different graphs with different x-intercepts. The graph may intersect the x-axis at the intersection. Otherwise, the graph touches the x-axis and bounces.
For example, suppose you plot a function.
f (x) = (x + 1) (x - 2)²
See the figure above to see how the function behaves differently for different x intercepts.
x intercept at x = -1 is the solution of the equation
x + 1 = 0 , graph goes straight through the x intercept at x= −1 . We call it a single zero because zero corresponds to a single factor in the function.
x intercept at x = 2 is the iterative solution of the equation ( x - 2 )= 0
The graph touches the axis at the intercept and changes direction. The coefficients are quadratic (order 2), so, (x-2)²= (x - 2 )(x - 2)
coefficients are repeated and appears twice. The number of times a given factor appears in the factored form of a polynomial equation is called its multiplicity. Zero associated with this factor, the factor is (x-2), occurs twice, and has a multiplicity of 2 .
thus, the behaviour of graph shows that any point of f(x) which touch or intersect x-axis is call zero of f(x).
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How do you list all rational roots using rational root theorem?.
The rational root theorem says that if you take all the factors of the constant term in a polynomial and divide by all the factors of the leading coefficient
The rational root theorem is also known as the rational zero theorem (or) the rational zero test (or) rational test theorem and is used to determine the rational roots of a polynomial function.
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the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s. when the length is 15 cm and the width is 13 cm, how fast is the area of the rectangle increasing (in cm2/s)?
If the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s. The area of the rectangle increasing is: 114 cm2/sec.
How to find the area of the rectangular?Using product rule formula
(dA / dt) = L× (dW / dt) + W × (dL / dt)
Where:
dA/dt = Rate that the area of the rectangle is increasing
dL/dt = 3 cm/s
L = 15 cm
dW/dt = 5 cm/s
W = 13 cm
Let plug in the formula
(dA / dt) = (15) × (5) + (13) × (3)
(dA / dt) = 75 + 39
(dA / dt) = 114 cm2/sec
Therefore 114 cm2/sec is the area of the rectangular.
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what is the exact difference from (-4, 2) to (4, 6)
A) sqrt 24 units
B) sqrt 86 units
C) sqrt 100 units
D) sqrt 128 units
The exact difference from (-4, 2) to (4, 6) is √80 units
How to determine the exact difference?From the question, we have the following points that can be used in our computation:
(-4, 2) to (4, 6)
These points can be rewritten as
(x, y) = (-4, 2) to (4, 6)
The exact difference can be calculated using the distance formula
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where
(x, y) = (-4, 2) to (4, 6)
Substitute the known values in the above equation, so, we have the following representation
distance = √[(-4 - 4)² + (2 - 6)²]
Evaluate
distance = √80
Hence, the distance is √80 units
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please help!!!!!! UrGenT
Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
The difference between any two successive integer squares is equal to the total of all these two integers, as demonstrated by the completed proof.
What exactly is meant by consecutive integers?Sequentially succeeding numbers are referred to as consecutive numbers.There is always a 1 difference when there are two numbers.A series of numbers has an equal mean and median.It concludes that n, n+1, and n+2 are all numbers if n is just a number.Let x represent any integer to prove algebraically.
This means that x+1 should be the following integer.
The claim demands evidence;
(x+1)² - x² = x+(x+1)
Consider the left hand side;
= x² + x + x + 1² - x²
= 2x+1 (Left Hand Solution)
Similarly, the right side.
= x + (x + 1)
= 2x + 1
Thus, subtracting the difference between two consecutive squared integers equals adding the two integers that since LHS=RHS equality is clear.
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What other pair of corresponding congruent parts is needed to prove that the two triangles are congruent by ASA congruence postulate?.
Two triangles if the side between any two corners of one triangle cornor corresponds to the side between the corresponding two angles of the second triangle corner are said to be congruent by the ASA rule.
Create a point F' on ray AC such that BF' is equal to DE.
Angle BAF' = angle BAC, which equal to
angle EDF, AB = DE (given), so ∆ DEF
= ∆ ABP
Point F' has two possibilities: F' is equal to point C please.
If F' is not on C, line AC and ray BC intersect only at C, so F' is not on ray BC. Therefore the angle ABF' is not = the angle ABC. But this is a contradiction. Because angle ABF' = angle DEF (because ∆ DEF = ∆ ABF') and angle DEF = angle ABC (given). So, this case does not occur.
Therefore, F' = C must be true.
∆ABC = ∆ABF' = ∆DEF.
The reasonwe only need some parts to
prove congruence of triangles is that from these parts we can (in Euclidean geometry) derive other parts. This is because the basic axioms and definitions allow us to make "guesses" that turn out to be true every time.
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Solve x^2-3x=-8. Please explain
Answer:
No solution.
Step-by-step explanation:
1. Move terms to the left side
x² - 3x = -8
x² - 3x - (-8) = 0
2. Use the quadratic formula
x = [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x² - 3x + 8 = 0
a = 1
b = -3
c = 8
x = [tex]\frac{-(-3) + \sqrt{(-3)^2 - 4 * 1 * 8} }{2*1}[/tex]
3. Simplify
After simplifying:
x = [tex]\frac{3 + \sqrt{-23} }{2}[/tex]
4. No real solutions because the discriminant is negative.
The square root of a negative number is not a real number.
d = -23.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
b. in the below figure, the system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks, what is the daily demand?
The system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks, so the daily demand is 2700 units / day.
In the given question, the system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks.
We have to find the daily demand.
The figure is given below:
Total operating time of the facility = 8 hours - 2 breaks of 15mins each
Total operating time of the facility = 480 mins - (2*15 mins)
Total operating time of the facility = 480 mins - 30 mins
Total operating time of the facility = 450 minutes.
Time taken for 1 output = Cycle time of system = Bottleneck of the supply-demand matched process = 10 seconds.
Total output = Total operating time / Time taken for 1 output
Total output = 450 minutes / 10 seconds
Total output = 2700 units / shift.
Since the market's demand and operational time are in balance, all production is created using the pull principle.
That means; Supply = demand.
Therefore the market demand for the product = 2700 units / day.
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I got 2+12s<50a but it says its wrong
The inequality to represent the number of album and song Jorge can download is 2s + 12a ≤ 50
How to use inequality to represent a situation?It cost 2 dollars to download a song and 12 dollars to download an entire album. Jorge has 50 dollars to spend on downloading music.
The inequality that represents the number of songs(s) and album(a) that Jorge can download can be represented as follow:
Therefore,
a = number of albumss = number of songsHence, the inequality is as follows:
2s + 12a ≤ 50
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Why is partitioning a directed line segment into a ratio of 1/2 is not the same as finding half the length of the directed line segment?.
The difference between partitioning into a ratio of 1/2 and finding half of a line segment is that partitioning in that ratio means one part is longer than the other, whereas finding half the length means both parts are the same length.
What is the partition of the line?
Partition means to separate or to divide. A line segment can be partitioned into smaller segments which are compared as ratios.
When we say we want to partition a line into a ratio of say x/y, it means that the line has been divided in that ratio and as such, the total number of parts is x + y.
Similarly, when we partition a line in the ratio 1/2, it implies that the total number of parts of the line segment is 1 + 2 = 3.
This means one part of the divided segment is bigger than the other one.
In contrast, half of the line segment means that the line segment is divided into two equal parts.
Thus, the fundamental difference between partitioning into a ratio of 1/2 and finding half of the line segment is that partitioning in that ratio means one part is longer than the other while half the length means that both parts are the same length.
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Because 1:2 is not a fraction while 1/2 is, you cannot assume that 1:2 is one-half of a line or anything that is being delt with in fact. The length of the line might be 18 units, and if it says that there needs to be some sort of action with a ratio of 1:2, you are not splitting that length in half, you are taking one unit from the left side, and two from the right, which does not equal the length of half of 18 units.
What is 2 multipled by 6 ?
Answer:
12
Step-by-step explanation:
2 * 6
6 + 6 = 12
Answer:
12
Step-by-step explanation:
Find an explicit formula for a sequence of the form
a1, a2, a3,
with the initial terms given below.
5, 10, 20, 40, 80, 160, 320
an =
The explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then aₙ = 5 × 2ⁿ⁻¹.
As given in the question,
Given initial terms of the sequence are as follow:
5, 10, 20, 40, 80, 160, 320
a₁ , a₂ , a₃ representing initial terms
a₂ / a₁ = 10 /5
= 2
a₃ / a₂ = 20 /10
= 2
a₄ /a₃ = 40 / 20
= 2
Common ratio 'r ' = 2
First term a₁ = 5
Given sequence is representing the geometric sequence
Explicit formula for nth of the geometric sequence is given by :
aₙ = a₁ × rⁿ⁻¹
= 5 × 2ⁿ⁻¹
Therefore, the explicit formula for a sequence given in the form of a₁ , a₂ , a₃ representing initial terms 5,10,20, 40 , 80 , 160 , 320 then
aₙ = 5 × 2ⁿ⁻¹.
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What is the most positive number?.
Integers greater than 0 are positive number.
What is rational number?
A rational number could be a number that may be expressed as the quotient or fraction p/q of 2 integers, a dividend p and a non-zero divisor letter.
Main body:
The definition of positive integers in math states that "Integers that are larger than zero are positive integers". Integers may be classified into 3 types: negative integers, zero, and positive integers. examine the quantity line given below to know the position and worth of positive integers.
1 is that the smallest positive whole number and therefore the greatest positive whole number isn't referred to as the list is endless.
Therefore the definition of positive integer is such as.
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I don’t understand this
Answer:
find the tan inverse
[tex] { \tan(?) }^{ - 1} [/tex]
of the value to get the angle.
1d.p = 29.2°
The marketing group and Rings Are Us is trying to predict if undergraduate or graduate students are more inclined to purchase (y = 1) or not purchase (y=0) a class ring at graduation. Using the following count on the training data set, calculate the conditional probability of both to determine which should be classified to the purchase group. Undergraduate (x = 1) 70 Graduate (x = 0) 100 Purchase (y = 1) No Purchase (y = 0) 30 110 Multiple Choice Undergraduate 0.70 > 0.272; Graduate 0.428 <0.272. The undergraduate is assigned to the purchaser group. Undergraduate 0.30 <0.20; Graduate 0.524 > 0.476. The graduate is assigned to the purchaser group. Undergraduate 0.70 > 0.30; Graduate 0.476<0.524. The undergraduate is assigned to the purchaser group. Undergraduate 0.303 > 0.272; Graduate 0.476< 0.524. The undergraduate is assigned to the purchaser group.
The correct option is that Undergraduate is assigned to the purchaser group.
P ( purchase | Undergraduate ) = [tex]\frac{70}{70 + 30}[/tex] = 70 / 100 = 0.70 ,
⇒ P ( y = 0 | Undergraduate ) = 0.3
P ( purchase | Graduate ) = [tex]\frac{100}{100 + 110}[/tex] = 0.476
⇒ P ( y = 0 | Graduate ) = 0.524
Therefore,
as P ( y = 1 | undergraduate ) = 0.707 > 0.30 and
0.476 > 0.524,
Undergraduate group is assigned to the purchase group.
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at one school, the average amount of time that tenth-graders spend watching television each week is 20.8 hours. the principal introduces a campaign to encourage the students to watch less television. one year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased from the previous mean of 20.8 hour
the average amount of time spent watching television per week has decreased from the previous mean of 20.8 hour then the test is left tailed
In two tailed hypothesis, the alternative hypothesis is when mean can either be lesser or greater than the given value. Usually uses the symbol ≠.
In right tailed, the alternative hypothesis is when the mean is greater than the given value.
In left tailed, the alternative hypothesis is when the mean is lesser than the given value.
In this question, the hypothesis test to be performed is to determine if the average amount of time spent watching television per week has decreased from the given value of 20.8 hours.
Thus, it is left tailed test.
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choose the inequality shown by this diagram
The inequality shown in the diagram is the one in option C.
-2 < x ≤ 7
Which is the inequality on the diagram?On the number line we can see that our variable is x, the graph of the solution set of the inequality starts with an open circle at x = -2.
The open circle means that x = -2 is not a solution of the inequality, then we start with:
-2 < x
Then we can see a closed circle at x = 7, a closed cirlce means that the value is a solution, so x can be equal to 7, and the inequality is:
-2 < x ≤ 7
So the correct option is C.
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the area of the parallelogram is 78 in^2. calculate its perimeter
6in 6.5in
Perimeter= blank in
Answer: 39 in
Step-by-step explanation:
If their food and beverage cot $25. 30 and there i an 8% meal tax, how much i the bill? After adding a tip, the total lunch cot wa $32. 24. What percentage tip did they give? Enter your anwer to the nearet percentage
The percentage tip did they give is 18%
If their food and beverage cost $25. 30
There i an 8% meal tax
The tax will be
$25.30(0.08) = $2.024.
Then we add the tax to the price such that
The bill will be
$25.30 + 2.024 = $27.32
Tip = 32.24 - 27.32 = 4.92
percentage tip did they give
= tip given /total amount of the bill x 100
= 4.92/27.32 x 100
= 18%
Therefore, If their food and beverage cot $25. 30 and there i an 8% meal tax and after adding a tip, the total lunch cot wa $32. 24.the percentage tip did they give is 18%
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Simplify the expression. 7(6x – 4) 1 1. distribute the 7 through the parentheses. 2. combine like terms. what is the expression in its simplest form? 42x – 28 7 42x – 3 42x – 28 1 42x – 27
here is a hanger that is in balance. squares are worth 2 grams and circles are worth 3 grams, and triangles are x grams. write an equation to represent the hanger diagram.
The equation to represent the hanger diagram is 5x - 2x = 21 - 12 and weight of 1 triangle in the hanger is 3 gram. .
In the question ,
it is given that ,
the the weight of one square is = 2 gram
the weight of one circle is = 3 gram
and the weight of one triangle is is = x gram
When the hanger is balanced , then weight on Left side = weight on Right side
we see that left side have 2 triangles , 6 squares and 3 circles ,
and the Right side have 2 circle , 3 square and 5 triangle ,
So , the balanced equation for the hanger can be written as
2*x + 6*2 + 3*3 = 2*3 + 3*2 + 5*x
2x + 12 + 9 = 6 + 6 + 5x
2x + 21 = 12 + 5x
5x - 2x = 21 - 12
3x = 9
x = 3
Therefore , the equation is 5x - 2x = 21 - 12 and the weight of triangle is 3 grams .
The given question is incomplete , the complete question is
There is a hanger that is in balance. squares are worth 2 grams and circles are worth 3 grams, and triangles are x grams. write an equation to represent the hanger diagram and find the weight of 1 triangle .
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What are rational roots examples?.
An example of rational roots can be given as:
Let the polynomial be: 4x³ + 3x² + 6x + 9;
Then,
coefficient of the variable with the highest degree = 4
coefficient having the variable with degree 0 = 9
Factors of 4 are: 1, 2;
Factors of 9 are: 1, 3;
The possible rational roots for such an equation will be: 3, 1, 1/2, 3/2, -3, -1, -1/2, -3/2;
Rational roots are the roots or solutions of equations of any polynomial consisting of one variable of any power.
Where all the coefficients are integers.
Let the solution/root of a polynomial be p/q. Then the root would be rational if and only if the coefficient of the variable with the highest degree is divisible by 'q' , and the coefficient independent of the variable or having the variable with degree 0 is divisible by 'p'
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n this scenario, what is the test statistic? the website developer would like to test the claim that the percent of websites that have serious vulnerabilities is less than 30%. sample size
the test statistic z is 1.7
What is test statistic?
A test statistic may be a datum employed in applied math hypothesis testing. A hypothesis take a look at is often laid out in terms of a test statistic, thought of as a numerical outline of a data-set that reduces the info to at least one worth that may be wont to perform the hypothesis test.
Main body:
Calculate the test statistic using the formula:
z= [tex]p-p'[/tex]/[tex]\frac{p'(p-p')}{n}[/tex]
where:
p = sample proportion,
n = sample size, and
Po = population proportion under the null hypothesis
Sample size = 34 websites = n
Sample proportion = 0.20 = p'
z = (0.3 - 0.2)/ (0.2*0.1)/34
z = 0.1 *34/0.02
z = 1.7
Hence value of test statistic z is 1.7
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