The lower bound for the weight 21.58 g correct to 2 decimal places is 21.57 g. This is because the next smallest value based on the rounding is obtained rounding down the number in second decimal place, which is 5.
To find the lower bound for the weight 21.58 g correct to 2 decimal places, we need to consider the next smallest number that can be represented to 2 decimal places.
Since the second decimal place is 8, the next smallest number is obtained by rounding down the number in the second decimal place, which is 5. Therefore, the lower bound for 21.58 g correct to 2 decimal places is: 21.57g
Note that the weight could be more precise than what we are given, but to represent it to 2 decimal places we have to make an assumption about the last digit.
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Three marbles are chosen from the bag below. What is the probability that all marbles chosen will be red? Write your answer as a fraction.
The probability that all marbles chosen are red is obtained using the hypergeometric distribution, which is presented during the answer.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The meaning of each parameter for this problem is given as follows:
N is the total number of marbles.k is the total number of red marbles in the bag.n = 3 is the number of marbles that will be chosen.x = 3 is the desired number of red marbles.More can be learned about the hypergeometric distribution at https://brainly.com/question/14741653
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Once a month, the cafeteria has each student pick a card from a standard deck of cards. Students who pick an ace get a free lunch. Last month 26 of the 280 students won a free lunch. As a percent to the nearest tenth, what is the experimental probability of winning?
Last month 26 of the 280 students won a free lunch. The experimental probability of winning will be 13/140
Probability is the occurence of the events. Some of the events cannot be predicted with certainty. Probability of any event can be defined as P(A) , and there are many types of probability density functions.
Once a month, the cafeteria has each student pick a card from a standard deck of cards. From the deck of cards, each student has to pick a card for every one month.
Students who pick an ace get a free lunch
Given that,
Last month 26 of the 280 students won a free lunch and the percentage of winning is near to 9.2% approximately and it is very near to the 10%.
The experimental probability of winning is the ratio of number of possible outcomes to the total number of outcomes.
So, the experimental probability of winning is 26/280 = 13/140
Therefore, the experimental probability of winning is 13/140
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the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase
The formula to calculate the new value after an increase is to multiply the original value by the percentage of the increase.
The formula to calculate the new value after an increase is to multiply the original value by the percent of the increase. For example, if the original value is $100 and the increase is 10%, the new value would be $100 x 1.10 = $110. This formula can be applied to any original value and any percentage increase. It is useful for calculating the new value after applying a percentage increase, such as when calculating a pay raise or the cost of goods after a price increase. The formula can also be applied to calculate the new value after a percentage decrease, by multiplying the original value by 1 minus the percentage of the decrease.
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The complete question is
the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase by multiplying the original value by the percent for a new value?
1. The distance d through which a stone falls from rest is proportional
to the square of the time taken t. If the stone falls 45 m in 3 seconds,
how far will it fall in 6 seconds? How long will it take to fall 20 m?
Answer:
In 6 seconds: 180 m
20 m: in 2 seconds
Step-by-step explanation:
y = distance
x = time
y is proportional to x:
y = kx
y is proportional to the square of x:
y = kx²
We are given: (3, 45)
45 = k × 3²
45 = 9k
k = 5
The equation is:
y = 5x²
When x = 6,
y = 5(6²)
y = 180
180 m in 6 seconds
When y = 20,
20 = 5x²
x² = 4
x = 2
2 seconds for 20 m
a garden is in the shape of a rectangle with a perimeter of 18 meters. the length is 3 meters more than twice the width. find the length of the garden
The length of the garden which is in the shape of a rectangle with a perimeter of 18 meters and whose length is 3 meters more than twice the width, is 7 metres.
Let's name the width "w" and the length "l" of the rectangle.
We know from the problem description that the rectangle's perimeter is 18 metres, thus we can formulate an equation:
2l + 2w = 18
We also know that the length is 3 metres longer than the breadth, thus we can solve the following equation:
l = 2w + 3
We may plug the second equation into the first to remove the letter "l" and get an equation with only one variable:
2(2w + 3) + 2w = 18
When we simplify this equation, we get:
6w + 6 = 18
When we subtract 6 from both sides, we get:
6w = 12
When we divide both sides by 6, we get:
w = 2
We can use the second equation to get the length now that we know the width is 2 metres:
l = 2w + 3 = 2(2) + 3 = 7
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If 10,000 is deposited into a savings account that pays 2. 3% annual interest, how much more would the
The account would contain 10,230.00 after 1 year.the amount in the account after 1 year, we can use the formula: [tex]P (1 + r/n)^nt[/tex]
To find the amount in the account after 1 year, we can use the formula:[tex]P (1 + r/n)^nt[/tex]
Where,
P = Principal Amount
r = Rate of Interest
n = Number of times the interest is compounded per year
t = Time in years
For this question,
P = 10,000
r = 2.3%
n = 1
t = 1
Therefore,
[tex]10,000 (1 + 0.023/1)^1*1\\10,000 (1.023)^1[/tex]
10,000 x 1.023
= 10,230.00
The complete question is:
If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account contain after 1 year?
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Group 4: A drive in movie charges $15 per car, plus $2 per person as an
admission fee. The total charged for a car with x people is m(x) = 2x + 15.
How will the graph of this function change if the per car charge is changed
to $20 per car?
O
The line will shift vertically down by $5.
O The line will shift vertically up by $5.
O The line will shift horizontally left by $5.
O The line will shift horizontally right by $5.
Answer:
The graph of the function will shift vertically up by $5.
Step-by-step explanation:
The original function is m(x) = 2x + 15, where x is the number of people in the car. If the per car charge is changed to $20 per car, the new function becomes m(x) = 2x + 20, because the charge per car has increased by $5.
This means that the y-intercept of the new function is 20 instead of 15, which represents the minimum cost for a car, regardless of the number of people inside. So the graph of the new function will be shifted vertically up by $5 from the graph of the original function.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Daniel is working two summer jobs, making $8 per hour babysitting and making $15 per hour lifeguarding. In a given week, he can work a maximum of 18 total hours and must earn no less than $200. If Daniel worked 3 hours babysitting, determine the minimum number of whole hours lifeguarding that he must work to meet his requirements
The minimum number of hours life guarding that Daniel must work to meet his requirements = 12 hours
To the nearest whole number approximately:
If the digit following the decimal is less than 5, only the number preceding the decimal should remain unchanged.
Add one to the number before the decimal and eliminate the decimal part if the digit following the decimal is five or greater.
Given the information,
Babysitting pays Daniel $8 per hour, and life guarding pays him $15 per hour.
Daniel can only work a total of 18 hours per week and must make at least $200.
Daniel has been babysitting for three hours.
Daniel thus makes 3 x 8 = 24 dollars.
He has earned $200 - 24 = 176 dollars from the original $200.
Let's say Daniel was a lifeguard for m hours.
He therefore made m x 15 = 176.
15 × m = 176
m = 11.73
m ≈ 12 hours
So, the minimum number of whole hours = 12
This means, Daniel must work 12 hours lifeguarding to meet his requirements.
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for the histogram on the right determine whether the mean is greater​ than, less​ than, or approximately equal to the median. justify your answer.
The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.
The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.
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What is the distance between these two points?
(2,0) and (2,−5)
The distance between these two points (2,0) and (2,−5) is 5 unit.
The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.
d=√((2 – 2)² + (-5 – 0)²)
d = √(0+25)
d = 5 unit
if the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:
PQ = |x2 – x1|
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The instructions on a carton of chemicals call for mixing 144 fl oz of water, 24 fl oz of chemical No. 1, and 56 fl oz of chemical No. 2. How many quarts are
contained in the final mixture?
The final mixture contains 7 quarts.
What is Mixture?
A mixture is generated when more than one chemical is mixed. A mixture can be created in a variety of ways, including using a liquid, solid, or gaseous medium.
First, let's add up the amount of the three ingredients to find the total volume of the mixture:
144 fl oz + 24 fl oz + 56 fl oz = 224 fl oz
Now, we can convert fluid ounces to quarts:
1 quart = 32 fluid ounces
So, we can divide the total volume in fluid ounces by 32 to find the total volume in quarts:
224 fl oz / 32 fl oz/quart = 7 quarts
Therefore, The final mixture contains 7 quarts.
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jeremy's average for 11 math tests is 80. His teacher announced that the students could eliminate any one of their test grades then recompute their average. Jeremy eliminated 30 on his first test. what is his average now?
Answer: His average is 85 now.
Step-by-step explanation:
Average is the sum of all his math tests divided by the number of the math tests he took, so we get:
[tex]\frac{sum }{11}=80[/tex]
sum = 11 x 80
sum = 880
880 - 30, we get 850, which becomes the new sum of the 10 math test scores, because he eliminated one test score.
[tex]\frac{850}{10} =85[/tex]
His average is 85 now.
QUESTION FOR FOR LIH04
write the equation for the given graphs. How do we find the "a" value?
The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11
How to determine the equations of the graphsFrom the question, we have the following parameters that can be used in our computation:
The graphs
The lines are absolute function graphs, and they can be represented as
y = a|x - h| + k
Where
Vertex = (h, k)
For the blue line, we have
(h, k) = (2, -5) and (x, y) = (0, -4)
So, we have
-4 = a|0 - 2| - 5
2a = 1
a = 1/2
So, the equation is y = 1/2|x - 2| + 5
For the red line, we have
(h, k) = (-2, 3) and (x, y) = (0, -11)
So, we have
-11 = a|0 + 2| + 3
2a = -14
a = -7
So, the equation is y = -7|x + 2| - 11
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2x(x) + 28 = (2x + 2)(x + 2)
Answer:
x = 4
Step-by-step explanation:
2x(x) + 28 = (2x + 2)(x + 2) ← expand factors using FOIL
2x² + 28 = 2x² + 6x + 4 ( subtract 2x² from both sides )
28 = 6x + 4 ( subtract 4 from both sides )
24 = 6x ( divide both sides by 6 )
4 = x
A wholesaler sells 1 kg of green tea leaves for $8 and 600 g of assam black tea leaves for $7.20. A tea merchant wants to mix these two types of tea leaves to form 100 kg of classic blend. Determine the amount of each type of tea leaves he should order from the wholesaler such that his cost price is $10/kg.
Answer:
50 kg of green tea leaves and 50 kg of assam black tea leaves.
Step-by-step explanation:
Let x kg be the amount of green tea and y kg be the amount of Assam tea.
x+y=100 (1) [mass]
price for 1 kg of assam tea= 7.20/600×1000g
= $12/kg
total cost= 100×10
= $1000
8x+12y= 1000 (2) [cost]
(1)×8: 8x+8y= 800 (3)
(2)-(3): (8x+12y)-(8x+8y)= 1000-800
4y= 200
y= 50 (4)
sub (4) into (1):
x+50= 100
x= 50
Heeeeeloepepepelelelelelelelelelloeoepeoepwp
Answer:
C) E = 118°; T = 118°
-----------------------------------
The given figure is a kite since it has two pairs of congruent sides as marked.
Its one pair of opposite angles are congruent. That is:
∠E ≅ ∠TSum of all interior angles of a quadrilateral is 360°:
m∠W + m∠E + m∠S + m∠T = 36029 + x + 95 + x = 3602x + 124 = 3602x = 360 - 1242x = 236x = 118Both the missing angles are 118°.
Todd and Amani started savings accounts. Todd started with
$10 and deposits $4 each week. Amani started with $10 and
makes two $2 deposits each week. Complete the table. Will
Todd and Amani ever have the same amount in their
accounts? Why or why not? Write an equation to represen-
the total amount in each of their accounts at any
given time.
a) Since Todd and Amani started with the same initial deposit, they will never have the same amount in their accounts if they keep to their weekly savings plans because Todd's weekly savings are two times that of Amani.
b) An equation to represent the total amount in each of their accounts at any given time or weeks is as follows:
Todd, t = 10 + 4wAmani, a = 10 + 2w.What is an equation?An equation is a statement of equality or equivalence of two or more mathematical expressions.
Mathematical expressions combine values, variables, and numbers or constants without the equation symbol (=), which differentiates them from equations.
Todd Amani
Initial deposit in account $10 $10
Weekly deposits $4 $2
Let the number of weeks of deposits = w
Let the total deposit in Todd's account in w weeks = t
t = 10 + 4w
Let the total deposit in Amani's account in w weeks = a
a = 10 + 2w
For Todd's and Amani's account to be equal, 10 + 4w = 10 + 2w
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A store charges a restocking fee for any returned item based upon the item price. An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. If you return an item that has an original price of $180, how much is the restocking fee?
An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. The restocking fee for an item priced at $180 is $10.
To solve this problem, we need to use a proportion to relate the item price to the restocking fee. The problem provides two pairs of corresponding item prices and restocking fees: $200 and $12, and $150 and $9. We can set up a proportion using these pairs:
$200/$12 = $150/$9
We can simplify this proportion by dividing both sides by 3:
$200/$4 = $150/$3
Now we can use the simplified proportion to find the restocking fee for an item priced at $180. We'll use cross-multiplication:
$200 x $3 = $150 x $4
$600 = $600
This tells us that the ratios are equivalent, and the restocking fee for an item priced at $180 is $10.
In other words, the restocking fee is proportional to the item price, and we can use the given pairs of prices and fees to find the fee for any given price using a proportion.
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please help with this
Answer: the initial points is 30.
and per pair of shoes is 15.
Step-by-step explanation:
Points: 0 of 1
A student wants to simulate 28 birthdays, but she does not have a calculator or software program available, so she makes up 28 numbers between 1 and 365
it okay to conduct the simulation this way? Why or why not?
Choose the correct answer below.
OA. Yes. People are capable of randomly making up numbers between two values.
OB. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
OC. No. Simulations must be performed with either a calculator or a statistical program.
OD. Yes. People are better at picking birth dates than computers, since they can base the numbers on the birth dates of people they know.
Save
From the given choices, we get:
No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
The correct option is D.
What is simulation?A computer experiment in which you can select a random sample from the given probability distributions is called a simulation.
Given:
A student wants to simulate 28 birthdays,
but she does not have a calculator or software program available,
so she makes up 28 numbers between 1 and 365.
By comparing with the definition:
From the given choices, we get,
D. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
Hence, D is the correct option.
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Can someone please help me with this aleks
The measure of <E= 60, <F= 95 and <G= 25 degree.
What is similarity?In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.
Given:
The two triangles are similar.
In triangle JKL using Angle Sum Property
<J + <K + <L = 180
95 + 60 + <K = 180
155 + <K = 180
<K = 180- 155
<K = 25 degree
Thus, the measure <E= 60
and, the measure <F= 95
and, the measure of <G= 25.
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Triangles PQR and XYZ are equilateral triangles. The sides of PQR are
5 inches long. One side of XYZ is (2x - 3) inches. What value of x
makes the triangles congruent?
Answer:
x = 4
Step-by-step explanation:
2x - 3 = 5 Add 3 to each side
2x - 3 + 3 = 5 + 3
2x = 8 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]
x = 4
a millworker measures the width of a plank. the width is . what is the width in meters? write your answer as a decimal.
If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58
The width of the plank in decimeter = 15.8 dm
Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit
We have to find the width of the plank in meter
We know that,
1 decimeter = 0.1 meter
Convert the given decimeter to meter
15.8 decimeter = 15.8 × 0.1
Multiply the numbers
= 1.58 meters
Therefore, the width of the plank in meter is 1.58
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The given question in incomplete, the complete question is :
A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?
The three sides of a triangular fence have lengths 2x + 3, y − 6, and 4x − 3. What is the total perimeter?
2x + y − 6 feet
6x + y feet
6x + y + 6 feet
6x + y − 6 feet
A triangular fence having dimensions 2x + 3, y − 6, and 4x − 3, has a perimeter of Option D: 6x + y - 6 feet.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
A triangular fence has measurements -
a = (2x + 3) feet
b = (y - 6) feet
c = (4x - 3) feet
The formula for perimeter of a triangle is -
Perimeter = sum of all three sides
So the equation will be -
Perimeter = a + b + c
Substitute the values in the equation -
Perimeter = (2x + 3) + (y - 6) + (4x - 3)
Perimeter = 2x + 3 + y - 6 + 4x - 3
Perimeter = 6x + y - 6
Therefore, the value for perimeter is 6x + y - 6 feet.
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What is 3 5/12 - 8/12 equal to?
Answer:
Step-by-step explanation:
first, write down on paper 3 5/12 - 8/12 then convert the mixed fraction into a more straightforward form. so 3 5/12 equals 37/12. then you do 37 - 8 = 29 so then change it into a fraction and the answer is 29/12. if you what it as a mixed fraction then it would be 2 5/12
Need help fast!
Whats rhe radical aproximation of
7.07
7.21
7.93
Answer:
The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:
2.65
2.68
2.82
Step-by-step explanation:
Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:
Start by finding an approximate square root by making an educated guess or by using a calculator.
Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.
Refine the estimate by averaging the guess and the number divided by the guess.
Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.
Here's an example for 7.07:
An educated guess for the square root of 7.07 could be 2.7
Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.
To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.
Repeat steps 2 and 3 until the desired level of accuracy is achieved.
After several iterations, the square root of 7.07 is approximately equal to 2.65.
Similarly, you can find the approximate square roots of 7.21 and 7.93.
a wooden artifact from an ancient tomb contains 35 percent of the carbon-14 that is present in living trees. how long ago, to the nearest year, was the artifact made? (the half-life of carbon-14 is 5730 years.)
The wooden artifact was made approximately 3,183 years ago. The amount of carbon-14 present in an artifact can be used to determine how long ago the organism that the artifact came from died.
The half-life of carbon-14 is 5730 years, which means that every 5730 years, half of the carbon-14 in a sample will decay. Let's call the amount of carbon-14 in the living tree sample 100%. Since the artifact contains 35% of that amount, we can write:
0.35 x 100% = 100% x (1/2)^(t/5730)
where t is the number of years since the artifact was made.
Simplifying this equation, we get the following:
0.35 = 0.5^(t/5730)
Taking the logarithm of both sides, we get:
log(0.35) = (t/5730) x log(0.5)
Solving for t, we get:
t = (5730 x log(0.35)) / log(0.5)
Using a calculator, we get:
t ≈ 3,183 years
Therefore, the wooden artifact was made approximately 3,183 years ago.
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plssss helppppp
Factor the polynomial.
x³+3x²-x-3
Answer:
(x-1)(x+1)(x+3)
Step-by-step explanation:
[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]
If 65% of a number is 208 and 15% ofthe same number is 48, find 80% of that number.
Answer:
256
Step-by-step explanation:
65% is 208
15% is 48
15% + 65% is 80%
So, just add 48 and 208 together:
48 + 208 = 256
Therefore, 80% of that number is 256.
Answer:
256
Step-by-step explanation:
We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.
