There are 1960 different ways to distribute 8 identical pieces of candy to the five children, where the twins get an equal amount of candy.
First, distribute the candy to the twins.
Split the 8 pieces of candy into two equal parts for the twins using combinations:
C(8, 4)
This means selecting 4 pieces of candy from the 8 identical pieces for one twin, and the remaining 4 pieces will automatically go to the other twin.
C(8, 4) is calculated as:
[tex]^8C_4 = \dfrac{8!}{4!(8-4)!}[/tex]
= 8! / (4! * 4!)
= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
= 70
Now, you have distributed 4 pieces of candy to each of the twins. Y
In this case, you have 6 pieces of candy to distribute among 3 children, and you can use two dividers (bars) to separate the candy for each child.
This can be represented as:
OO|OO|OO
The two bars split the 6 pieces of candy into three sections for the three children.
So, you have C(6 + 2, 2) ways to distribute the remaining candy:
[tex]^{6+2}C_2 = \dfrac{8!}{2!(8-2)!}[/tex]
= 8! / (2!(8 - 2)!)
= 8! / (2! * 6!)
= (8 * 7) / (2 * 1)
= 28
Now, the total number of ways to distribute the candy
Total ways = C(8, 4) * C(8, 2) = 70 * 28 = 1960
So, there are 1960 different ways to distribute.
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a quality control inspector has drawn a sample of 11 light bulbs from a recent production lot. suppose that 60% of the bulbs in the lot are defective. what is the standard deviation of the number of defective bulbs in the sample? round your answer to two decimal places.
The standard deviation of the number of defective bulbs in a sample of 11 light bulbs, where 60% are defective, is 1.53, rounded to two decimal places.
The number of defective bulbs in a sample of 11 light bulbs follows a binomial distribution with parameters n = 11 and p = 0.6, where n is the sample size and p is the probability of a defective bulb.
The standard deviation of the binomial distribution is given by the formula:
σ = sqrt(np(1-p))
where σ is the standard deviation, n is the sample size, p is the probability of success (defective bulb), and (1-p) is the probability of failure (non-defective bulb).
Substituting the values into the formula, we get:
σ = sqrt(11 * 0.6 * 0.4) = 1.53
Therefore, the standard deviation of the number of defective bulbs in the sample is 1.53, rounded to two decimal places.
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Can anyone please help 10 points
The value of x using similar triangles theorem is = 13/3.
What are similar triangles?Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles.
When two objects have the same shape but different sizes, they can be said to be comparable.
This indicates that comparable shapes superimpose one another when amplified or de-magnified.
The term "Similarity" refers to this characteristic of like shapes.
Now in the given figure,
the proportion of the triangles' side is same.
So, 12/4 = 13/x
x = 13/3
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if the answer to our three questions for this particular limit is affirmative, what can you say about the continuity of the logarithm function? what would be its derivative? what would be r12 ln x dx?
Yes
The logarithm function is continuous for all x>0. Its derivative is 1/x and r12 ln x dx = x ln x - x + c.
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The school cafeteria has 150 cups of strawberries and 450 cups of blackberries. How many total cups of berries does the school cafeteria have?
Total number of cups of berries does the school cafeteria have is 600
Addition is a basic mathematical operation that involves combining two or more numbers or quantities to find a total or sum. In other words, it is the process of finding the total amount when two or more numbers are added together.
To find the total number of cups of berries in the school cafeteria, you can add the number of cups of strawberries and blackberries.
The school cafeteria has 150 cups of strawberries and 450 cups of blackberries, so
Total cups of berries = cups of strawberries + cups of blackberries
Total cups of berries = 150 + 450
Total cups of berries = 600
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if the matrix product a1b is known, how could you calculate b1a without necessarily knowing what a and b are?
We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.
To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.
Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
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a children's liquid medicine contains 100 mg of the active ingredient in 5 ml . if a child should receive 300 mg of the active ingredient, how many milliliters of the medicine should the child be given? for the purposes of this question, assume that these numbers are exact.
The child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
The given problem requires us to determine the number of milliliters of a liquid medicine that a child should receive in order to obtain a specific dosage of the active ingredient. We are given that the medicine contains 100 mg of the active ingredient in 5 ml.
The child needs to receive 300 mg of the active ingredient, and there are 100 mg of the active ingredient in 5 ml of the medicine. Therefore, the child should be given:
[tex]\frac{300 mg}{100mg/5ml} = \frac{300\text{ mg} \times 5\text{ ml}}{100\text{ mg}} = 15\text{ ml}$$[/tex]
So the child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
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The associative property works with expressions that use
A
division and subtraction. B
addition and subtraction. C
multiplication and division. D
multiplication and addition
The associative property works with expressions that use multiplication and addition. The correct option is (D).
The associative property is a rule in mathematics that allows us to change the grouping of the numbers or variables in an expression without changing the result. This property only applies to addition and multiplication, and not to subtraction and division.
The associative property of addition tells us that we can add a group of numbers in any order, and the result will be the same. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). The associative property of multiplication tells us that we can multiply a group of numbers in any order, and the result will be the same. For example, (2 × 3) × 4 is the same as 2 × (3 × 4).
However, the associative property does not work with subtraction and division. For example, (10 - 3) - 2 is not the same as 10 - (3 - 2). Similarly, (12 ÷ 2) ÷ 3 is not the same as 12 ÷ (2 ÷ 3). Therefore, the correct answer to the question is D - the associative property works with expressions that use multiplication and addition.
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Use the situation below to answer questions 1 - 3.
A new Microsoft Surface computer costs $1275, but depreciates 16.5% each year as new
technology comes out.
1. Is this situation exponential growth or decay?
2.
Two students, Josh and Eve were debating how to represent a function to model
the value, V, after x years. Both of their functions are below. Explain who you
agree with and why.
Josh
V(x) = 1275 (0.835)*
Eve
V(x) = 1275(1.165)*
3. Write the correct function that models the context using both forms.
V(x) = a(b)*
V(x) = a(1+r)*
1. Exponential decay 2. Josh's function represents the situation correctly 3. V(x) = 1275(0.835)ˣ, V(x) = 1275(1-0.165)ˣ
Describe Exponential decay function ?An exponential decay function is a mathematical function that describes the decrease in value of a quantity over time or through a series of events. It is often used to model natural phenomena such as radioactive decay or the spread of diseases.
In an exponential decay function, the value of the quantity decreases exponentially over time. This means that the rate of decrease is proportional to the value of the quantity at any given time.
The exponential decay function is characterized by a decreasing graph that approaches zero but never touches the x-axis. The rate of decay slows down over time, but the quantity never completely disappears. The function is used in various fields such as physics, chemistry, biology, finance, and economics, to name a few.
1. This situation represents exponential decay because the value of the computer decreases by 16.5% each year.
2. Josh's function represents the situation correctly because it involves the decay factor (0.835) which is less than 1, reflecting the decrease in value each year. Eve's function represents exponential growth which is not consistent with the situation where the value of the computer decreases each year.
3. V(x) = 1275(0.835)ˣ represents the function using the form V(x) = a(b)ˣ where a = 1275 and b = 0.835.
Alternatively, V(x) = 1275(1-0.165)ˣ represents the function using the form V(x) = a(1-r)ˣ where a = 1275 and r = 0.165.
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Help me with these please!!
The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.
What in mathematics is an angle?An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.
Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.
Angle ABC = Angle ABD + Angle ACD
replacing the specified values:
110° = Angle ABD + 75°
Simplifying:
Angle ABD = 110° - 75°
Angle ABD = 35°
Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:
AC / CD = AB / BD
replacing the specified values:
AC / 10 = 16 / 8
Simplifying:
AC = 20
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Complete Question:
Find the angle ∠ABD jn the given figure
true/false. the null hypothesis predicts there is a relationship between the variable and a significant difference between the groups.
The given statement " the null hypothesis predicts there is a relationship between the variable and a significant difference between the groups." is False because the null hypothesis predicts that there is no relationship between the variables and no significant difference between the groups.
A null hypothesis is a statement that suggests that no relationship exists between two variables. It serves as the baseline assumption and a starting point for researchers to test their alternative hypothesis.
Null hypothesis testing is a statistical method used to compare two mutually exclusive propositions: the null hypothesis and the alternative hypothesis.
In hypothesis testing, the null hypothesis states that there is no significant difference between two groups, while the alternative hypothesis suggests that there is a significant difference between the two groups.
If the observed data deviates significantly from what we would expect under the null hypothesis, we reject it in favor of the alternative hypothesis.
If the observed data does not significantly deviate from what we would expect under the null hypothesis, we fail to reject it.
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you and a friend are in school and are trying to figure out where to eat. she told you that she would like to go to her favorite pizza place that is 7 miles away from her home. both of you know that her home is 8 miles away from school. approximately how far is the pizza place from the school?
After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.
What is expressiοn ?In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.
Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.
If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:
distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp
8 miles minus 7 miles = distance frοm pizza place tο schοοl
1 mile frοm the pizza place tο the schοοl
As a result, the pizza place is abοut a mile away frοm the schοοl.
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Noah was at home. He got on his bike and rode to his friends
Answer:
what's your exact question
Answer:
can u pls type the full question
Neal buys a board game. He pays for the board game and pays
$
1.54
$1.54dollar sign, 1, point, 54 in sales tax. The sales tax rate is
5.5
%
5.5
Proportionately, the cost of the board game without the sales tax is $28.00.
What is the sales tax?The sales tax is the levy imposed by the government on the consumption and production of certain goods and services.
The purposes of imposing sales taxes are to discourage consumption and to increase governmental revenue.
Proportion refers to the equation of two ratios.
In this situation, we can equate the value of the sales tax with its percentage to determine the cost of the board game.
The sales tax in dollars = $1.54
The sales tax rate = 5.5%
Proportionately, the value of the board game without the sales tax = $28.00 ($1.54/5.5%).
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Question Completion:How how is the cost?
if a water bottle contains 375 ml, what is the volume in quarts? group of answer choices 1.21 qt 355,000 qt 0.396 qt 0.826 qt 2.52 qt
If a water bottle contains 375 ml, So the volume in quarts is 0.396 qt.
The volume of a water bottle containing 375 ml can be converted into a quart using the conversion formula.
One can use the following conversion formula to convert a given volume in ml to quarts.
The conversion formula for ml to quarts is given as;
1 ml = 0.00105669 quarts
Volume in quarts = Volume in ml × 0.00105669
Now, to calculate the volume of 375 ml of the water bottle in quarts,
We will substitute the given volume in the above conversion formula as follows,
Volume in quarts = 375 ml × 0.00105669
= 0.396 qt
Hence, the volume of the water bottle containing 375 ml is 0.396 qt.
Therefore, the correct option is C. 0.396 qt.
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76. cash to find work? (4.2) will cash bonuses speed the return to work of une,ployed people? the illinois department of employment security designed an expierment to find out. the subjects were 10,065
The experiment by the Illinois Department of Employment Security found that cash bonuses can be an effective way to incentivize unemployed people to return to work.
The experiment conducted by the Illinois Department of Employment Security provides evidence on whether cash bonuses can speed up unemployed people's return to work. The results of the experiment suggest that offering cash bonuses can be an effective way to incentivize people to find work.
Specifically, the experiment found that the group of individuals who were offered a $500 cash bonus for finding a job within 11 weeks and holding it for at least 4 months were more likely to find employment than the control group. Additionally, the group that could tell potential employers that the state would pay the employer $500 for hiring them also had a higher likelihood of finding work compared to the control group.
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The given question is incomplete, the complete question is:
The Illinois Department of Employment Security designed an experiment to find out. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held for at least 4 months. Others could tell potential employers that the state would pay the employer$500 for hiring them. A control group got neither kind of bonus. Will cash bonuses speed unemployed people's return to work?
is there a significant difference in the mean amount of e. coli bacteria detected by the two methods for this type of beef? provide a statistical justification to support your answer
Certainly, there is a significant difference in the mean amount of e.coli bacteria detected by the two methods for this type of beef. This can be supported statistically by conducting a hypothesis test.
The null hypothesis ([tex]H_0[/tex]) is that there is no significant difference in the mean amount of E. coli bacteria detected by the two methods. The alternative hypothesis ([tex]H_a[/tex]) is that there is a significant difference in the mean amount of e.coli bacteria detected by the two methods.
The two-sample t-test can be used to test the hypothesis. The t-test compares the means of two independent groups and determines whether they are significantly different. The t-test assumes that the two samples are normally distributed and have equal variances.
If the sample sizes are large, then the t-test can still be used even if the samples are not normally distributed.
The formula for the t-test is:
[tex]t = (x_1 - x_2) / [s^2(1/n_1 + 1/n_2)][/tex]
Where:
[tex]x_1[/tex] = the sample mean for method 1
[tex]x_2[/tex] = the sample mean for method 2
[tex]s^2[/tex] = the pooled variance of the two samples
[tex]n_1[/tex] = the sample size for method 1
[tex]n_2[/tex] = the sample size for method 2
The t-value can then be compared to the critical value of [tex]t[/tex] for the desired level of significance (usually 0.05).
If the t-value is greater than the critical value of [tex]t[/tex], then the null hypothesis can be rejected and it can be concluded that there is a significant difference in the mean amount of E. coli bacteria detected by the two methods.
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use excel to find the critical value of z for each hypothesis test. (negative values should be indicated by a minus sign. round your answers to 3 decimal places.) (a) 2 percent level of significance, two-tailed test.
The critical value of z for each hypothesis test is 2.326
In this question, we are asked to use Excel to find the critical value of z for each hypothesis test. We are given a 2 percent level of significance for a two-tailed test. To find the critical value, we can use the NORM.S.INV function in Excel. The syntax for this function is =NORM.S.INV(probability).
We can enter the probability as 1 - (alpha / 2) for a two-tailed test, where alpha is the level of significance. We can then round the result to three decimal places.
To find the critical value for a 2 percent level of significance, two-tailed test, we can follow these steps:
Step 1: Calculate the value of alpha
Alpha = 2% = 0.02
Step 2: Calculate
1 - (alpha / 2)1 - (alpha / 2)
= 1 - (0.02 / 2)
= 0.99
Step 3: Use the NORM.S.INV function in Excel=NORM.S.INV(0.99)
This gives us a critical value of z = 2.326.
Therefore, the critical value of z for the hypothesis test with a 2 percent level of significance and a two-tailed test is 2.326.
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if the odds on a bet are 16:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).
The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.
To express this probability as a fraction, we can use the formula:
Probability of winning = 1 / (odds + 1)
Plugging in the given odds, we get:
Probability of winning = 1 / (16 + 1)
Probability of winning = 1/17
In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.
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which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. the sample sizes are greater than 30.
The following conditions must be met to conduct a two-proportion significance test:
the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.
To conduct the two-proportion significance test, the following conditions must be met:
Populations must be independent.
Sample sizes are greater than 30.
The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.
The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.
In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
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Can anyone help me with this? i have 6 problems like this and I don't know how to solve them.
1. y=x+4
y = 3x
2. x=-2y+1
x-y=-5
3. y=x-7
2x+y=8
4. y=3x-6
-3x+y=-6
5. x+2y=200
x=y+50
6. 4x+3y=1
x=1-y
Its Solving Using Substitution. It's also due tomorrow so please help.
Answer:
Sure, I can help you solve these problems using substitution. Let's start with problem 1:1. y=x+4 y=3x To solve this system of equations, we need to substitute one of the variables from one equation into the other equation. We can solve the second equation for y:y=3x Now we can substitute this expression for y into the first equation:y=x+4 3x=x+42x=4x=2 Now we can substitute this value for x into either equation to solve for y:y=x+4 y=2+4y=6 So the solution to this system of equations is x=2, y=6. You can follow the same procedure to solve the rest of the problems. 2. x=-2y+1 x-y=-53. y=x-7 2x+y=84. y=3x-6 -3x+y=-65. x+2y=200 x=y+506. 4x+3y=1 x=1-y Let me know if you need any further assistance.
Use the multiplication method to increase £88 by 14%
To increase £88 by 14%, we can use the multiplication method, which involves multiplying the original amount by the decimal equivalent of the percentage increase.
The multiplication method is a mathematical technique used to solve problems involving multiplication. It involves breaking down numbers into their constituent parts and then multiplying those parts together to arrive at the final answer.
To find the decimal equivalent of 14%, we divide the percentage by 100:
14% ÷ 100 = 0.14
This tells us that a 14% increase is equivalent to multiplying the original amount by 1.14 (1 + 0.14).
To increase £88 by 14%, we can multiply it by 1.14:
£88 x 1.14 = £100.32
Therefore, the increased amount is £100.32.
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a spinner with the letters a, b, c, and d is spun. what is the theoretical probability of landing on the letter c?
The probability of the spinner landing on the letter C is 1/4
To understand the probability of the spinner landing on the letter C, we need to start by looking at the total number of possible outcomes. In this case, there are four possible outcomes, corresponding to the four letters A, B, C, and D.
Since each of the four quadrants on the spinner is equal in size, each of the four letters has an equal chance of being landed on. Therefore, the probability of the spinner landing on the letter C is the number of ways that the spinner can land on C, divided by the total number of possible outcomes.
Since there is only one way for the spinner to land on C, and there are four possible outcomes in total, the probability of the spinner landing on the letter C is 1/4
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The given question is incomplete, the complete question is:
A spinner with four equal quadrants labeled A, B, C, and D is spun. What is the theoretical probability of the spinner landing on the letter C
what is the radical equivalent to s^3/2
Answer:
√1.5
Step-by-step explanation:
As a fraction, the square root of 3/2 can be expressed as √1.51 or just as √1.5.
An empty shipping box has a mass of 2. 75 kilograms. An electronics store is packing 5 identical laptops in the shipping box. Each laptop has a mass of 1. 65 kg. The cost to ship the box was $40. 00 for the first 5 kg and $3. 15 for each kilogram over 5 kg. What was the cost to ship the packed box?
The cost to ship a box containing 5 laptops, weighing a total of 11 kg (including the empty box), is $58.90, with a cost of $40.00 for the first 5 kg and $3.15 for each additional kilogram.
The total mass of the packed shipping box can be found by adding the mass of the laptops (5 * 1.65 kg = 8.25 kg) to the mass of the empty box (2.75 kg) for a total mass of 11 kg.
Since the cost to ship the box is $40.00 for the first 5 kg and $3.15 for each additional kilogram over 5 kg, we can split the total mass into two parts: the first 5 kg and the additional weight above 5 kg.
The cost to ship the first 5 kg is $40.00, and the remaining weight is 11 kg - 5 kg = 6 kg.
The cost to ship the additional 6 kg is $3.15 per kilogram, so the total cost to ship the packed box is:
$40.00 + $3.15 * 6 kg = $58.90
Therefore, the cost to ship the packed box is $58.90.
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Describe each number at least one other way. A)35. 8 million
b)115. 2 thousands
c)97. 8 ten millions
A) 35. 8 million; thirty-five million eight hundred thousand, or thirty-five million eight hundred thousand dollars ,(b)115. 2 thousand; one hundred and fifteen thousand two hundred.(c) 97.8 million eight hundred thousand; 97.8 million eight hundred thousand. or 978 million.
What significance do numbers have?
We need good numeracy skills as parents to assist our children to develop, as patients to grasp healthcare information, and so as politicians to make sense of numbers and economic news. Selections in life were frequently based upon numerical data; in order to arrive at optimal decisions, we must be good at maths.
How are numbers used in everyday life?
Numbers are utilized in a variety of mathematical operations such as summation, subtraction, multiplication, division, percentage, and so on, that we employ in the everyday companies and exchanges. Quantities are numerical symbols representing integers that may be used for numbering, estimating, and doing other arithmetic operations.
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Please help it’s urgent!!! Pls help!!! Will give brainliest!!Tina purchased a new refrigerator
on a payment plan. Four months after purchasing the refrigerator, the balance was $630. Six months after purchasing the refrigerator,
the balance was $520.
Write an equation that models the balance y after t months.
y = _t + _
Answer:
We can use the slope-intercept form of a linear equation to model the balance y after t months, where the slope represents the rate of change of the balance and the y-intercept represents the initial balance.
The initial balance (y-intercept) is the amount Tina borrowed to buy the refrigerator, which we don't know. But we can find the slope using the two data points provided:
Four months: balance = $630
Six months: balance = $520
The change in the balance over the two-month period is:
$520 - $630 = -$110
The slope of the line is the rate of change of the balance per month, which is:
slope = Δy/Δt = (-$110)/(6-4) = -$55/month
Using the point-slope form of a linear equation, we can plug in one of the data points to find the y-intercept:
y - 630 = -$55(t - 4)
y - 630 = -$55t + 220
y = -$55t + 850
Therefore, the equation that models the balance y after t months is:
y = -$55t + 850.
Help please, Which value of x satisfies the equation 7/3(x+9/28)=20
Answer:
Step-by-step explanation:
[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]
[tex]7 (x+\frac{9}{28} )=60[/tex] (multiplied both sides by 3)
[tex]x+\frac{9}{28} =\frac{60}{7}[/tex] (divided both sides by 7)
[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex] (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)
13. security y has the following returns over five years: 3%, 6%, 0%, 6%, and 3%. what is the arithmetic mean (average) return and the standard deviation (sample) for security y?
The arithmetic mean return is 3.6%, and the standard deviation is 2.14%.
To find the arithmetic mean, we add up the five returns and divide by the number of returns (in this case, 5):
(3% + 6% + 0% + 6% + 3%) / 5 = 3.6%
To find the standard deviation, we first need to find the variance. We can do this by taking each return, subtracting the mean return (3.6%), squaring the result, summing these values, and dividing by the number of returns minus 1 (4 in this case):
((3% - 3.6%)^2 + (6% - 3.6%)^2 + (0% - 3.6%)^2 + (6% - 3.6%)^2 + (3% - 3.6%)^2) / 4 = 0.046
The standard deviation is the square root of the variance:
√0.046 = 0.214 or 2.14%
Therefore, the arithmetic mean return for security y is 3.6%, and the standard deviation (sample) is 2.14%.
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A penny is 19 mm wide. What is the area of the front side of the penny? Use 3.14 for π. Round to the nearest hundredth if necessary.
HELP ME QUICK PLEASE!
Answer:
≈283,39 mm^2
Step-by-step explanation:
The diameter is 19 mm, so the radius is half diameter (9,5 mm)
[tex]a = \pi \times {r}^{2} = 3.14 \times {9.5}^{2} = 3.14 \times 90.25 ≈ 283.39[/tex]
Ally chooses a whole number
Write a number that Ally could have started with
Ally could have started with any whole number, including 0, 1, 2, 3, 4, etc. Whole numbers are numbers that don't contain any fractions, decimals, or negative numbers.
For example, 1/2 is not a whole number, but 2 is a whole number. When Ally chooses a whole number, she could choose any number that fits this criteria. For example, she could choose 0, 1, 4, 17, 100, or any other whole number.
Ally chooses a whole number. The whole numbers are integers that are greater than zero. It includes all the natural numbers (1, 2, 3, ...) and zero. Let's assume Ally selected a whole number as the question mentioned, we will have to determine the possible number options that Ally could have chosen.One whole number that Ally could have chosen could be 1. Since 1 is the first natural number, it is the smallest whole number. The other whole numbers are greater than 1. The next smallest whole number is 2, followed by 3, then 4, and so on.
There are an infinite number of whole numbers since they continue infinitely in both positive and negative directions. There is no limit to the largest or smallest whole number; therefore, Ally could have begun with any whole number.
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