Answer:
y^2
Step-by-step explanation:
a^m/a^n = a^(m - n)
y^5/y^3 = y^2
The sum of three numbers is 23.
Three times the smallest is 4 less than the largest, while the sum of the largest
and smallest is 16. Use a linear system in three variables to find the three numbers.
The three numbers are __ , __
and __
Answer:
The three numbers are 3, 7 and 13
Step-by-step explanation:
Considering the 3 numbers: x, y and z
x + z = 16
z=16-x
3x=z-4
3x=16-x-4
4x=12
x=3
3+z=16
z=16-3
z=13
3+13+y=23
y=23-13-3
y=7
Hope this helps :)
Tell whether the expression is positive or negative without evaluating it. -3/10 X (-8/15)
The expression -3/10 X (-8/15) is positive
Expression
Expression in mathematics has two or more variables, terms and constants. Also, arithmetic expression contains only numbers and mathematical operators and algebraic expression
The expression has negative sign and from mathematical calculation we already know the following relation:
+ x + = +
positive multiply by positive equals Positive
- x - = +
Negative multiply by Negative equals Positive
+ x - = -
Positive multiply by Negative equal Negative
hence, - [tex]\frac{3}{10}[/tex] x - [tex]\frac{8}{15}[/tex]
The negative sign multiply by -3/10 X (-8/15) sign will give positive.
Therefore, the expression -3/10 X (-8/15) is positive.
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➤ Solve the inequalities.
T -3 is less than or equal to 2
-3 is less than 2
< is the symbol
An 80% confidence interval for a proportion is found to be (0. 27 , 0. 33). What is the sample proportion?
A. 0. 29
B. 0. 30
C. 0. 31
D. 0. 33
If an 80% confidence interval for a proportion is found to be (0.27, 0.33), then the sample proportion would be 0.30
What do you understand by sample proportion?Sampling is frequently used to estimate the proportion of a population that has a given attribute, such as the proportion of all faulty goods coming off an assembly line or the proportion of all individuals visiting a retail store who make a purchase before leaving. The percentages for the population and sample are written as p and p, respectively. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.
The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance.
How to solve?
For this case the confidence interval is given by:
(0.27; 0.33)
We can find the estimaed proportion in the following way:
p = (0.27 + 0.33)/2 = 0.30
then the sample proportion would be 0.30
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prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
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determine the zeros of f(x)=28x^2−7
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The function is given below.
f(x) = 28x² - 7
For the zeroes of the function, put f(x) = 0, then we have
f(x) = 0
28x² - 7 = 0
x² = 1/4
x = ± 1/2
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
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8. Divide-2x³-4x² + 3x + 2 by x-3. (1 point)
-2x²10x-27, R-79
-2x²10x-27
-2x²10x - 27, R 83
-2x²10x + 27, R 83
The value of the quotient of the polynomial is 2x^2 + 2x + 10 and the remainder is 28
What does it mean to divide polynomials?A method for solving a rational number that represents a polynomial divided by a monomial or another polynomial is called "dividing polynomials." In order to divide normally, we place the dividend and the divisor in the exact same manner.
How do you divide polynomials?Divide the first term of the dividend by the highest term of the divisor, which in this case is x (i.e., the term with the highest power of x).
Divide the divisor by the outcome you just got (the first term of the eventual quotient).
By following the above rules where
2x3-4x2+3x+2 is divided by the x-3, We get the following equation
where
quotient is 2x2+2x+10
and the remainder is 28
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at the beginning of the day, the stock market goes up 30 1/2 points. At the end of the day, the stock market goes down 120 1/4 points. What is the total change in the stock market from the beginning of the day to the end of the day?
The total change in the stock market from the beginning of the day to the end of the day is 89.75
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
At the beginning of the day, the stock market goes up 30 1/2 points.
At the end of the day, the stock market goes down 120 1/4 points.
The total change in the stock market from the beginning of the day to the end of the day.
= 120(1/4) - 30(1/2)
= 481/4 - 61/2
= 120.25 - 30.5
= 89.75
Thus,
The total change in the stock market from the beginning of the day to the end of the day is 89.75
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What is the y-intercept, b, of the additive relationship represented by this table?
Enter your answer as an integer in the box.
b = ?
Answer:
3
Step-by-step explanation:
State the domain and range of the graph below
Answer:
For the first graph:
Domain: -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞
Range: y [tex]\geq[/tex] 3
For the second graph:
Domain: 0 [tex]\leq[/tex] x [tex]\leq[/tex] 4
Range: y [tex]\leq[/tex] 64
Step-by-step explanation:
For the second graph, I'm assuming that that point are stopping at (0,0) and (4,0) that's why I wrote that for the domain. If it doesn't stop, then the domain would be the same and the first graph.
Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, Upper R left parenthesis x right parenthesis, andcost, Upper C left parenthesis x right parenthesis, of producing x units are in dollars. R(x)=3x, C(x)=0.05x^2+0.04x+10
To maximize the profit 29.6 units must be produced.
What is the maxima or minima?
The maxima and minima of a function collectively referred to as extrema in mathematical analysis, are the highest and lowest values of the function, either on the whole domain or within a specific range.
We have given,
The revenue function is,
R(x)=3x
Cost function,
C(x)=0.05x^2+0.04x+10,
Where
x = number of units produced.
Thus, profit = revenue - cost
P(x) = 3x - (0.05x^2+0.04x+10)
= -0.05x^2 + 2.96x - 10
Differentiating with respect to x,
P'(x) = -0.1x + 2.96
Again differentiating with respect to x,
P''(x) = -0.1
For maxima or minima,
P'(x) = 0,
0 = -0.1x + 2.96
-0.1x = -2.96
x = 2.96/0.1
For x = 29.6,
P''(x) = negative,
Hence, to maximize the profit 29.6 units must be produced.
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A random sample of 64 sat scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. the 95onfidence interval for the population mean sat score is: ________
a. 1.96. b. 1.998.
c. 1.645. d. 1.28.
The 95% confidence interval for the population mean SAT score is given as follows:
(1340, 1460).
How to calculate the confidence interval?The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.
The bounds are obtained according to the equation defined as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 1400, n = 64, s = 240[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.
Then the lower bound of the interval is of:
1400 - 1.998 x 240/sqrt(64) = 1340.
The upper bound of the interval is of:
1400 + 1.998 x 240/sqrt(64) = 1460.
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A candidate for office claims that "there is a correlation between television watching and crime." Criticize this statement on statistical grounds.
There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.
What is correlation?Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).
What are qualitative and quantitative variables?
The variables are classified as qualitative or quantitative as follows:
Qualitative variables assume labels as values.
Quantitative variables assume numbers as values.
The relevance of the variables according to association and correlation are given as follows:
Qualitative variables can have association.
Quantitative variables can have correlation.
The variables in this problem are given as follows:
Television watching -> yes/no -> qualitative.
Crimes committed -> yes/no -> qualitative.
As they are qualitative variables, they can have association, and thus there is no correlation between the two variables
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The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
Answer:
hi do you mind making the question a bit clear? where is the table?
Step-by-step explanation:
Vocabulary Use the terms divisor,
dividend, quotient, and remainder to
describe how to divide.
The divide rule will be;
⇒ Divisor = (Dividend - Remainder) / Quotient
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Vocabulary Use the terms divisor, dividend, quotient, and remainder.
Now,
If we have to find the divisor , then we can use the divide rule as;
⇒ Divisor = (Dividend - Remainder) / Quotient
Thus, The divide rule will be;
⇒ Divisor = (Dividend - Remainder) / Quotient
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Which polygon appears to be regular?
Answer:
Figure b
Step-by-step explanation:
the sides are equal
A mountain climber found that the relationship between his altitude and the surrounding air temperature is linear. The function
represents this relationship, where is the altitude in meters and is the temperature in degrees Fahrenheit. According to this function, by how much is the temperature decreasing for every meter that the mountain climber’s altitude increases?
The temperature decrease for every meter that the mountain climber's altitude increases is given by:
-100 ºF.
What is the temperature decrease?The function that models this situation is a linear function, which has the format defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope of the function, representing by how much y changes when x is increased by one.b is the y-intercept of the function, representing the numeric value of y when x = 0.In the context of this problem, the function is defined as follows:
f(a) = -100a + 75.
Hence the slope of the function is of:
-100.
Representing the temperature decrease for each meter of altitude increase of the climber.
Missing InformationThe function is defined as:
f(a) = -100a + 75.
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ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
Calculate how far each of the following travels. A helicopter flies at a speed of 72miles per hour for 10 minutes
Answer:
12 miles
Step-by-step explanation:
72 x [tex]\frac{10}{60}[/tex] = 12
The bill for two book came to $28. 48. One book cot $7. 44. What wa the cot of the other one
Answer:
Step-by-step explanation:
Ok:
If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price
2. 28.45-7.44=$21.01
3. Answer: The cost of the other one is $21.01
Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
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Please help again 10 points again to first one
Answer: it would be 18 candies that are left
Step-by-step explanation:
I did the math
Find the exact value of sin(u + v) given that sinu = 5/3 and cos v =-4/5. (Both u and v are in Quadrant I.)
The exact value of sin(u + v), obtained using trigonometric identities is for sine and cosine is 16/65
What are trigonometric identities?Trigonometric identities are equations that involve trigonometric functions that are valid for all values of the input variable.
The possible value of sin(u) obtained from a similar question posted online is; sin(u) = 5/13
Both u and v are in quadrant II
The trigonometric identity of the addition formula for the sine of the sum of two angles, indicates;
sin(u + v) = sin(u)·cos(v) + sin(v)·cos(u)
sin(u) = 5/13
cos(v) = -4/5
sin(v) = √(1 - (cos(v))²)
Therefore;
sin(v) = √(1 - (-4/5)²) = 3/5
cos(u) = √(1 - (sin(v))²)
Therefore;
cos(u) = √(1 - (5/13)²) = 12/13
Therefore;
sin(u + v) = (5/13) × (-4/5) + (3/5) × (12/13) = 16/65
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Graph the given sequence to help you answer the
questions.
19, 15, 11, 7, ...
Which point is found on the graph?
Is the sequence linear? Why?
What type of sequence is it?
Answer: the answer is A,B,E
Step-by-step explanation:
Answer: The answer is (four/seven)
Yes, because it forms a straight line.
Arithmetic; it's a linear function.
Step-by-step explanation:
2023 Edgen
The mean of 11 numbers is 7 one of the numbers, 13, is deleted. What is the mean of the remaining 10 numbers?.
If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4
The mean of 7 numbers = 11
We know,
Mean = Sum of the terms / Number of terms
Substitute the values in the equation
11 = Sum of the terms / 7
The sum of the terms = 11 × 7
= 77
Number 13 is deleted
Sum of the terms = 77 - 13
= 64
Number of terms = 11 - 1
= 10
The mean = Sum of the terms / Number of terms
Substitute the values in the equation
= 64 / 10
= 6.4
Hence, the mean of the remaining 10 numbers is 6.4
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Which of the following are essential elements of hypothesis testing?
-It uses probability theory to determine if a hypothesis is a reasonable statement.
-It makes use of sample data.
The following are crucial factors in hypothesis testing:
It employs probability theory to evaluate if a hypothesis is a valid claim.It employs sample data.Explain the term hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.
The type of data being used and purpose of the study will determine the methodology the analyst uses. A basic hypothesis can anticipate a causal relationship between variables, i.e., that one has an impact on the other. This is known as hypothesis testing, and it uses sample data to determine the plausibility of a hypothesis.It is a technique for analysis that evaluates presumptions and establishes the likelihood of something based on a predetermined level of accuracy. Testing hypotheses offers a technique to determine whether the outcomes of an investigation are reliable.Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.
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Tom and rosie are designing a game. In each turn, a player rolls five 666-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=51+1+1+1+1=51, plus, 1, plus, 1, plus, 1, plus, 1, equals, 5 points, and the highest is 6+6+6+6+6=306+6+6+6+6=306, plus, 6, plus, 6, plus, 6, plus, 6, equals, 30 points.
Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
Based on the expected value, Rosie's statement is correct.
The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.
Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.
On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.
In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
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The complete question:
Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.
They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.
Tom says, "A player will most likely get 17.5 points in any given roll."
Rosie says, "Over 100 turns, we can expect a total of about 175 points."
Whose statement is correct based on the expected value?
name the property used in the equations
A) 3x+9y-1 = 3(x+3y) -1, here distributive property is used the 3 is multiplied with each term inside the bracket.
What is algebraic operations?
Any of the common arithmetic operations, such as addi - tion, subtraction, multiplication, division, raising to a complete number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power). These operations could be applied to numerical data, in which case people are frequently referred to as arithmetic operations. Similar operations can be carried out on factors, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of the a set to the same set. The dot product is an example of an operation that can be described by compounding simple algebraic operations, and is referred to as an algebraic operation.
b) 7x+5y-5y = 7x
Here the Additive inverse of 5y is used which is -5y .
c) (x-4)(x+3) = 0
here distributive property of addition over multiplication is used.
d) 4x+5x = 5x+4x
here commutative property is used.
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What is the value of x? Show your work.
Is Figure B a scale copy of Figure A
Answer:
YES!!Step-by-step explanation:
First of all let's look at the side lengths of both figures.
Let's see how the corresponding sides relate:-
[tex]\sf 6*\cfrac{1}{3} =3[/tex]
[tex]\sf 3*\cfrac{1}{3} =1[/tex]
We can see that all sides scale by the same factor of 1/3.
Therefore, YES A is a scaled copy of Figure B.
______________________
Hope this helps!
Have a great day!
