Fill in the blank: Some of the most common symbols used in formulas include
(addition), - (subtraction), * (multiplication), and / (division)
These are called _____.
a. 1 point domains.
b. References.
c. Operators.
d. Counts
Answers
These symbols are called operators.
Mathematics is the science that relates everyday practices and nature to human reasoning and numerical logic.
Math OperationsThe four basic math operations are present in your day-to-day life, for example: when you pay your bills. The math operations are:
addition - represented by symbol "+"subtraction - represented by symbol "-"multiplication - represented by symbol "x"division - represented by symbol "÷"These symbols, also, are known as arithmetic operators.
Note that in math expressions, it is necessary to apply the rule of operations: parentheses, exponents, multiplication/division, and addition/subtraction.
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Related Questions
In general, which of the following is the least appropriate measure of central tendency for data sets that contain outliers?
a. mean
b. median
c. mode
Answers
The mean is the least appropriate measure of central tendency for data sets that contain outliers.
The correct option is a.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
These numbers, which were determined from the ranking data, are not affected by outliers.
In contrast, the mean is determined by utilizing all the data.
Additionally, mean is sensitive to outliers.
Therefore, if the data set contains outliers, the mean is the least suitable measure of central tendency.
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a state had three letters followed by three digits as the format for license plates. in order to increase the number of plates available, the state changed the format to four letters followed by two digits. what is the positive difference between the number of plates available with the new format and the number of plates available with the old format?
Answers
The positive difference is 10,000. The old format had 26^3 = 17,576 possible combinations, while the new format has 26^4 = 456,976 possible combinations. The difference is 456,976 - 17,576 = 439,400, or 10,000 times the original amount.
The old format for license plates used three letters followed by three digits, which provided 26^3 = 17,576 possible combinations. The state changed the format to four letters followed by two digits, offering 26^4 = 456,976 possible combinations. This gives us a positive difference of 10,000 times the original amount, or 456,976 - 17,576 = 439,400. This increase in the number of combinations greatly increases the number of license plates available in the state.
The old license plate format of three letters followed by three digits provided an initial total of 17,576 combinations. This limits the amount of license plates available, as well as the individuality of the plates. In order to increase the number of plates and provide more individuality, the state changed the format to four letters followed by two digits. This new format increases the total number of combinations to 456,976, which is a positive difference of 439,400, or 10,000 times the original amount. This allows for more license plates to be available, as well as more individuality, as there are now 456,976 unique combinations to choose from.
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Solve for x 70=-8x+38
Answers
Answer:
hope it helps you.......
Given ∠2 and ∠4 are vertical
Prove ∠2 ≅ ∠4
Assemble the proof by dragging tiles to the Statements and Reasons columns.
Answers
We proved that \(\angle2\cong\angle4\).
Given: \(\angle2\) and \(\angle4\) are vertical.
We have to prove \(\angle2\cong\angle4\)
The \(\cong\) means congruence which means \(\angle2\) and \(\angle4\) both have same size and angle. We have to show that they both have same size or angle to prove them congruence.
As we know that the value of straight line is \(180^{o}\).
From the given figure we can see that
\(\angle1+\angle2=180^{o}\)
\(\angle3+\angle4=180^{o}\)
\(\angle1+\angle4=180^{o}\)
\(\angle2+\angle3=180^{o}\)
To prove the \(\angle2\cong\angle4\) we subtract \(\angle1+\angle2=180^{o}\) and \(\angle1+\angle4=180^{o}\)
\(\angle1+\angle2-(\angle1+\angle4)=180^{o}-180^{o}\)
We first simplify bracket. When we multiply with the subtraction sign then the sign under the bracket will changed.
\(\angle1+\angle2-\angle1-\angle4=0\)
There have \(\angle1\) in addition and subtraction then there only remains
\(\angle2-\angle4=0\)
We can write that notation as
\(\angle2=\angle4\)
Since \(\angle2=\angle4\), that means they both have same angle.
So we proved that \(\angle2\cong\angle4\).
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Suppose you have an outdoor pool measuring 25 ft by 10ft . You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 ft³ of cement, how wide should the walkway be?
Answers
The area covered by the pool and the cement walkway is 304 square feet. The width of the walkway would be 5 feet
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Let x be represent the width of the walkway.
The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway = 25+ x + x = 25 + 2x
The total width of the pool and the walkway = 10 + x + x = 10 + 2x
The area covered by the pool and the cement walkway is 304 square feet. This means that;
(25 + 2x)(10 + 2x) = 304
250 + 50x + 20x + 4x^2 = 304
4x^2 + 70x + 250 - 304 = 0
4x^2 + 70x - 54 = 0
x(x + 20) - 5(x + 20) = 0
(x - 5)(x + 20) = 0
x = 5 or x = - 20
Thus The width cannot be negative.
Therefore, the width of the walkway is 5 feet.
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what is the value of the following expression? true && !false
Answers
The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.
1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".
2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".
Therefore, the value of the expression "true && !false" is "true".
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Solve the system.
0.2x + 0.5y = 4
-0.1x + 0.3y = -2
A)
(20,0)
B)
(-2,5)
C
(-5, 10)
D)
(50, 10)
HELP
Answers
Answer:
A
Step-by-step explanation:
when plotted this is 20,0
2 trains run from London to Cambridge by 2 routes. The probability that 2 trains are late is 0.1 and 0.15.
Work out the probability that 1 is late.
Answers
Thus, probability that either one of the two trains from London to Cambridge is late : 0.22.
Explain about the total probability?A fundamental statistician's rule governing conditional versus marginal probabilities is the total probability rule, commonly referred to as the law of total probability.
According to the rule, if the chance of an event is uncertain, it can be determined using the probabilities of numerous different occurrences that have already occurred.
For the given question:
The probability for 1 st train arrive late P(E) = 0.1.
Then, probability for 1 st train not arrive late P(E') = 1 - 0.1 = 0.9.
Now,
The probability for 2nd train arrive late P(F) = 0.15.
Then, probability for 2nd train not arrive late P(F') = 1 - 0.15 = 0.85
So,
probability that either 1 is late = P(E)*P(F') + P(E')*P(F)
probability that either 1 is late = 0.1*0.85 + 0.9*0.15
probability that either 1 is late = 0.22
Thus, probability that either one of the two trains from London to Cambridge is late : 0.22.
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Complete question:
2 trains run from London to Cambridge by 2 routes. The probability that 2 trains are late is 0.1 and 0.15. Work out the probability that 1 is late?
Franklin Middle School's spring concert is next week. The music teacher chose students from the choir and the orchestra to perform solos. There are 25 choir students, and 5 of them have a solo. There are 20 orchestra students, and 4 of them have a solo. Do the two groups have the same ratio of students with a solo to total students?
Answers
The two groups have the same ratio of students with solo to total students.
How to solve for ratios?We should know that ration is the quotient of two numbers. In mathematics ration is defined as as the number of times one number contains another number
The given parameters are
25 choir students
5 solo students from the choir
20 Orchestra students
4 solo orchestra students
Expressing the ratio of total choir students to total orchestra students and solo choir students to solo orchestra students we have
25:20 = 5:4
Dividing the left hand side by 5
5:4 = 5:4
In conclusion the ratio of total choir students to total orchestra students and solo choir students to solo orchestra students are the same = 5:4
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Tanya wants to sew her own jean jacket. She found a sewing pattern for her size and realized she
needs 4 yards of fabric. She goes to the store and finds the denim fabric she likes, which is priced
at $7.50 per yard. She also needs to buy buttons to put on the jean jacket. She finds a pack of
buttons priced at $6.99. How much will Tanya spend at the store on her fabric and buttons?
Answers
Answer:
$36.99
Step-by-step explanation:
Fabrics per yard = $7.50
Pack of buttons = $6.99
Fabrics needed = 4 yards
How much will Tanya spend at the store on her fabric and buttons?
Total cost of fabric and button = cost of 4 yards of fabric + pack of buttons
= 4(7.50) + 6.99
= 30 + 6.99
= 36.99
Total cost of fabric and button = $36.99
Simplify: ( -16 - 8)/2 + 25 / 5 + 1
Answers
-6
-24/2 + 25/5 + 1
-24/2+25/5+1
-12+25/5+1
-12 + 5 + 1
-7+1
-6
Use the trigonometric functions to find the value of x.
Write your answer as a decimal rounded to the nearest tenth.
Answers
Answer:
57.8
Step-by-step explanation:
Use Sine
Sin x°=11 ÷13
x°=sin inverse of 11÷13
x°= 57.8°
One of the legs of a right triangle measures 2 cm and its hypotenuse measures 18 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Answer:
17.9
Step-by-step explanation:
Florence works in the shipping department of a toy factory that makes radio-controlled helicopters. Small helicopters weigh 3 kilograms each, and are shipped in a container that weighs 20 kilograms. Large ones, on the other hand, weigh 4 kilograms apiece, and are shipped in a container that weighs 10 kilograms. If these boxes can hold a certain number of helicopters each, all of the packed containers will have the same shipping weight. What would the total weight be?
Answers
Answer:
50 kg
Step-by-step explanation:
Given that:
SMALL HELICOPTERS:
Weight of small helicopters = 3kg
Weight of shipping container = 20kg
LARGE HELICOPTERS:
Weight of large helicopters = 4kg
Weight of shipping container = 10kg
Number of helicopters each shipping container can hold = s ; all of the packed containers will have the same shipping weight
Shipping weight :
(Weight per helicopter * number of helicopter) + weight of shipping container
Shipping weight of Small helicopters :
(3kg * s) + 20
Shipping weight Large helicopters :
(4kg * S) + 10
Shipping weight of Small helicopters = shipping weight of large helicopters
3s + 20 = 4s + 10
20 - 10 = 4s - 3s
10 = s
Hence, member of shipped helicopters = 10
Total shipping weight :
(4 * S) + 10
(4*10) + 10
40 + 10 = 50kg
Which characteristic is necessary for an extraneous variable to become a confounding variable? a. It must have no systematic relationship with the dependent variable. b. It must change systematically from one participant to the next. c. It must have no systematic relationship to the independent or dependent variables. d. It must change systematically when the independent variable is changed.
Answers
It must change systematically when the independent variable is changed for an extraneous variable to become a confounding variable that is option D.
This is because a confounding variable is a variable that is related to both the independent and dependent variables and affects the outcome of the study, making it difficult to determine the true effect of the independent variable. In order for a variable to be considered a confounding variable, it must change systematically with changes in the independent variable.
A confounding variable is a variable that affects the outcome of a study but is not the variable of interest. This can create ambiguity in the results and make it difficult to determine if the observed effect is due to the independent variable or the confounding variable. In order for a variable to be considered a confounding variable, it must change systematically with changes in the independent variable.
This means that as the independent variable changes, the confounding variable also changes in a predictable way. Without controlling for this variable, the study may not accurately reflect the true effect of the independent variable. Therefore, it is important to identify and control for confounding variables in a study to ensure that the results are valid and reliable.
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when sampling from a normal population such as sat scores, the distribution of the sample means will also have a normal distribution with the same mean; but, the variability in sample means will be less than the variability in individuals (similar to how variability in sample proportions will be less than the variability in individuals). there are mathematical formulas we can use to find the mean and standard deviation of the sampling distribution of the sample mean for samples of size : mean of the sampling distribution of the sample mean
Answers
When sampling from a normal population, such as SAT scores, the distribution of sample means will indeed have a normal distribution with the same mean as the population mean.
However, the variability in sample means will not necessarily be less than the variability in individuals. In fact, the variability in sample means is related to the sample size and the variability of the population.
To clarify, the mean of the sampling distribution of the sample mean is indeed equal to the population mean. This property is known as the expected value or the unbiasedness of the sample mean as an estimator of the population mean.
The standard deviation of the sampling distribution of the sample mean, also called the standard error of the mean, is determined by the population standard deviation (σ) and the sample size (n). The formula for the standard error of the mean is:
Standard Error of the Mean = (Population Standard Deviation) / sqrt(Sample Size)
In the case of SAT scores, if we know the population standard deviation and we take samples of a specific size, we can use the above formula to calculate the standard error of the mean. This standard error represents the average variability or dispersion of sample means around the population mean.
It's important to note that as the sample size increases, the standard error of the mean decreases, indicating that the sample means become more precise estimators of the population mean. This reduction in variability occurs due to the effect of sample size on reducing sampling error.
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Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. What is the balance after 5 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Answers
The amount of money in Lucia's account after 5 years will be $1,105.5.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,
A = $600 × (1 + 0.13)⁵
A = $600 × (1.13)⁵
A = $600 × 1.84
A = $1,105.5
The amount of money in Lucia's account after 5 years will be $1,105.5.
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a home improvement store has 11 unmarked holly plants for sale, 7 of which are female. if a homeowner buys 4plants at random, what is the probability that berries will be produced?
Answers
The probability that a plant will produce berries can be calculated as the proportion of female plants in the population, which is 7/11.
The probability that berries will be produced if the homeowner buys 4 plants at random can be calculated as the number of successful outcomes (i.e., buying 4 female plants) divided by the total number of possible outcomes (i.e., the number of ways to choose 4 plants from 11).
Since the plants are selected without replacement, this is equivalent to finding the number of combinations of 4 female plants out of 7. The formula for combinations is given by C(n,k) = n! / (k! (n-k)!).
So, the number of combinations of 4 female plants out of 7 is C(7,4) = 35. The total number of combinations of 4 plants out of 11 is C(11,4) = 330.
Therefore, the probability that berries will be produced is 35/330 = 7/66.
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Select the correct answer. Simplify (8x + 5) + (4x+6) A. 4x - 11 B. 12x-1 C. 12x + 11 D 4x + 1
Answers
we are given the following expression:
\(\mleft(8x+5\mright)+(4x+6)\)First, we will associate like terms, that is terms that have the same variable elevated to the same exponent:
\((8x+4x)+(5+6)\)Adding like terms:
\(12x+11\)Since we can't simplify any further, this is the final answer.
a diver begins at sea level and dives down 200 feet he ascends at a steady rate 12 1/3 for 4.5 minutes which of the following numerical expressions represents the final depth of the diver
A. 200 + 12 1/3 (4.5)
B. 200 - 12 1/3 (4.5)
C. -200 + 12 1/3 (4.5)
D. -200 - 12 1/3 (4.5)
Answers
The numerical expressions represent the final depth of the diver will be the negative 200 + 12 1/3 (4.5). Then the correct option is C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A diver begins at sea level and dives down 200 feet.
He ascends at a steady rate of 12 1/3 for 4.5 minutes.
Then the numerical expressions represents the final depth of the diver will be
Let the negative sign for the downward and the positive sign for upward.
Then we have
⇒ - 200 + 12 1/3 (4.5)
Then the correct option is C.
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Test the validity of the equation: x=x
0
+v
0
t+
2
1
at
2
where, x : displacement at time t,x
0
: displacement at time t=0,v
0
: velocity at time t=0 and a : acceleration due to gravity. 5- Using the dimensional analysis technique, find the relationship of the periodic time T of a simple pendulum if you know that the factors affecting are: mass of the bob (m), length (L) of the pendulum and the acceleration due to gravity (g). 1- Using the dimensional analysis, test the validity of the equation: T=2π
g
L
where T is periodic time, π is constant, L is length and g is acceleration due to gravity.
Answers
The equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.
To test the validity of the equation x = x₀ + v₀t + (1/2)at², we can check if the dimensions on both sides of the equation are consistent.
Breaking down the dimensions of each term:
x: Displacement has dimensions of length (L).
x₀: Initial displacement has dimensions of length (L).
v₀t: Velocity times time has dimensions of (L/T) * T = L.
(1/2)at²: Acceleration times time squared has dimensions of (L/T²) * T² = L.
Since the dimensions on both sides of the equation are consistent (L = L), the equation x = x₀ + v₀t + (1/2)at² is valid.
Now, let's use dimensional analysis to find the relationship of the periodic time T of a simple pendulum using the factors affecting it: mass of the bob (m), length (L) of the pendulum, and acceleration due to gravity (g).
The factors affecting the periodic time T of a simple pendulum are:
Mass (m): Denoted by [M].
Length (L): Denoted by [L].
Acceleration due to gravity (g): Denoted by [LT⁻²].
The periodic time T of a simple pendulum is expected to depend on these factors in some way.
By applying dimensional analysis, we can determine the relationship between these factors. The equation is given as T = 2π √(L/g), where T is the periodic time, π is a constant, L is the length, and g is the acceleration due to gravity.
Breaking down the dimensions of each term:
T: Periodic time has dimensions of time (T).
2π: A constant, so it is dimensionless.
√(L/g): The square root of the ratio of length to acceleration due to gravity has dimensions of √([L]/[LT⁻²]) = √(T²) = T.
Therefore, the equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.
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find all the expressions that are equal to 4*10^-3
Answers
Answer:
Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)
Write 14/5 as a mixed number
Answers
Answer:
2 4/5
Step-by-step explanation:
14 = 10 + 4
10/5 = 2
4/5
Given ABC, what is the value of x?
HELP ME PLS THIS IS URGENT
Answers
Answer:
x=35
Step-by-step explanation:
We know that sum of angles in a triangle=180
120
o
+25
o
+x=180
145
o
+x=180
o
x=35
o
Evaluate each determinate . |5 1||-4 0||-2 37. -1||9. -83. -2||10. 512. -8|
Answers
Number 1
Given
\(\begin{bmatrix}{5} & {1} \\ {-4} & {0}\end{bmatrix}\)Solution
The determinant formula
\(\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix}=ad-bc\)Now apply the determinant formula
\(\begin{gathered} \begin{bmatrix}{5} & {1} \\ {-4} & {0}\end{bmatrix}=(5\times0)-(1\times-4) \\ \\ \begin{bmatrix}{5} & {1} \\ {-4} & {0}\end{bmatrix}=0-(-4) \\ \\ \begin{bmatrix}{5} & {1} \\ {-4} & {0}\end{bmatrix}=0+4 \\ \\ \begin{bmatrix}{5} & {1} \\ {-4} & {0}\end{bmatrix}=4 \end{gathered}\)The final answer
\(\begin{bmatrix}{5} & {1} \\ {-4} & {0}\end{bmatrix}=4\)A small town has 35003500 inhabitants. At 8AM,2808AM,280 people have heard a rumor. By noon half the town has heard it. At what time will 9090% of the population have heard the rumor?(Do not round kk in your calculation. Round your final answer to one decimal place.)
Answers
It will take approximately 3.9 hours from noon for 90% of the population to hear the rumor, which means they will have heard it by approximately 3:00 PM.
By noon, half of the town's population, which is 3500/2 = 1750, has heard the rumor. This means that 1750 - 280 = 1470 people heard the rumor between 8AM and noon. Therefore, the number of people who have yet to hear the rumor is 3500 - 1750 = 1750.
To find out when 90% of the population will have heard the rumor, we can use the formula:
(people who have heard the rumor) / (total population) = 0.9
Solving for the number of people who need to hear the rumor, we get:
(0.9)(3500) = 3150
To find out how many people need to hear the rumor from noon onwards, we subtract the number of people who have already heard it:
3150 - 1750 = 1400
To find out how long it will take for 1400 more people to hear the rumor, we can use the ratio:
(number of people who hear the rumor per hour) / (total population) = (1400 / 1750)
Solving for the number of people who hear the rumor per hour, we get:
(number of people who hear the rumor per hour) = (1400 / 1750) * (1 / k)
where k is the number of hours it takes for 90% of the population to hear the rumor. Solving for k, we get:
k = (1400 / 1750) * (1 / (number of people who hear the rumor per hour))
Plugging in the value of 280 for the number of people who heard the rumor from 8AM to noon, we get:
\(k = (1400 / 1750) * (1 / ((1470 + 280) / 4))\)
k = 3.86
Therefore, it will take approximately 3.9 hours from noon for 90% of the population to hear the rumor, which means they will have heard it by approximately 3:00 PM.
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Factorise x^2+4x+3
Write your steps as well please
Answers
Step-by-step explanation:
x²+4+3x²+x+3x+3x(x+1)+3(x+1)(x+1)(x+3)hope it helps.
stay safe healthy and happy...Which function has the same graph as y= 5sin(x + 2)? Y=5cos x.
y=5cos(x-pie). Y=5cos(x- pie/2). Y=5cos(x+pie/2)
Answers
Answer:
y=5cosx
Step-by-step explanation:just took the test.
Will give brainliest!! I need these answers asap!!! Please show your work!!! (Please do all of the 21 questions)
Answers
Answer: this is gonna be kinda long here i wrote some on because it was to much
Step-by-step explanation:
5. 459 times 87 = 39933
6. 2,679 times 5 = 13395
987 times 23 = 22701
9. 64,897 divided by 47 = 1380
10. 687 times 9 = 6183
17. 987 divided by 97 = 10
Find the slope of the tangent line to the given polar curve at the point specified by the value of theta.
r = 6 cos(theta),
theta = ????/3
Answers
The slope of the tangent line to the given polar curve at the point specified by the value of theta is m= 1/√3.
What is meant by tangent line?A straight line that just touches a plane curve at a particular location is referred to as the tangent line (or tangent) to the curve in geometry. It was described by Leibniz as the line connecting two points on the curve that are endlessly near to one another. A line passes through the point (c, f(c)) on the curve and has a slope of f'(c), where f' is the derivative of f. This is more properly referred to as being a tangent of the curve y = f(x) at a point x = c. Curves in n-dimensional Euclidean space and curves in space have a comparable definition.
The tangent line is "passing" through the point of tangency—the intersection of the tangent line and the curve as it travels.
Given,
r=6cosθ
f'(θ)=-6sinθ
θ=π/3
dy/dx=(f'(θ)sinθ+f(θ)cosθ)/(f'(θ)cosθ-f(θ)sinθ)
dy/dx=( -6sinθsinθ+6cosθcosθ)/(-6sinθcosθ-6cosθsinθ)
=(6cos²θ-6sin²θ)/-12 sinθcosθ
=6(cos²θ-sin²θ)/-6(2sinθcosθ)
=6cos2θ/-6sin2θ
=-cos2θ/sin2θ
=-cot2θ
Slope of the given polar curve at θ=π/3 is
m=dy/dx
m= -cot(2(π/3))
m = cot(-2π/3)
m= 1/√3
Therefore, the slope of the tangent line to the given polar curve at the point specified by the value of theta is
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