The product of two consecutive positive integers is 110. Find the value of the lesser
integer.
Answers
Related Questions
how do you simplify 10+6x
Answers
Step-by-step explanation:
To simplify this problem, you would have to factor the expression first:
(factor 2 out)
10 + 6x would now be:
2 ( 5 + 3x)
your friend would like to play a betting game with you and pulls out a bag of red and green candies. your friend tells you to cover your eyes and randomly pull a piece of candy from the bag. they tell you they will give you $2.00 if you pull a red candy, but if you pull a green candy you will have to pay them $1.00. there is a .4 probability that you pull a green candy and .6 probability that you pull a red candy. what is your expected value for this game?
Answers
The expected value for this game is $0.80.
What is your expected value for this game?The expected value for this game is calculated using the formula below:
Expected value = (probability of winning * amount won) + (probability of losing * amount lost)Data given:
If you pull a green candy you will have to pay them $1.00 and there is a 0.4 probability that you pull a green candy
If you pull a red candy you will have to pay them $2.00 and there is a 0.6 probability that you pull a red candy.
Expected value = (0.6 * $2.00) + (0.4 * -$1.00)
Expected value = $1.20 - $0.40
Expected value = $0.80
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Find the measure (in degrees, not equal to the given measure) of the least positive angle that is coterminal with A.
A=343
Answers
The smallest positive angle that is equivalent to A=343 degrees is 703 degrees.
To find the measure of the least positive angle that is coterminal with A, we need to determine the equivalent angle within one full revolution (360 degrees) of A.
A is given as 343 degrees. To find the coterminal angle within one revolution, we can subtract or add multiples of 360 degrees until we obtain a positive angle.
Let's subtract 360 degrees from A:
343 - 360 = -17
The result is a negative angle, so we need to add 360 degrees instead:
343 + 360 = 703
Now, we have a positive angle of 703 degrees, which is coterminal with 343 degrees.
The measure of the least positive angle that is coterminal with A is 703 degrees.
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Quadrilateral ABCD is inscribed in this circle
What is the measure of angle b?
Answers
Answer: 132 degrees
Step-by-step explanation:
The point P = (-5/3 squared, y) lies on the unit circle shown below. What is the value of
y in simplest form?
Answers
The required value of y for the unit circle is: 2/3
How to find the point on the unit circle ?The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).
The equation of the circle is given by:
(x - h)² + (y - k)² = r²
where:
h, k is the coordinate of the center of the circle on coordinate plane.
r is the radius of the circle.
Here,
Equation of the unit circle is given as,
x² + y² = 1
Now substitute the given value in the equation,
5/9 + y² = 1
y² = 1 - 5/9
y² = 4/ 9
y = √(4/9)
y = 2/3
Thus, the required value of y for the unit circle is 2/3
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Lef f{(-1,2), (0,3),(1,5),(-1,3)} and g={(-2,1),(0,3),(1,5),(-1,3),(3,0)} find 2f + 4g and 2g/h
Answers
The value of the functions 2f + 4g is {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)} and the value of 2g/h is (1,2.5)
In particular, a function maps each element of a set (called the domain) to a unique element of another set (called the range). In this context, we'll look at two functions, f and g, and explore how we can perform arithmetic operations with them.
We can think of these pairs as points on a Cartesian plane, where the x-coordinate represents the input and the y-coordinate represents the output.
Now, let's move on to the arithmetic operations with functions. The first operation we're asked to perform is 2f + 4g. To do this, we need to apply the following steps:
Multiply each ordered pair in f by 2, and multiply each ordered pair in g by 4. This means that the inputs stay the same, but the outputs are multiplied by their respective constants.
Simplify the resulting set by removing any duplicate ordered pairs.
Let's work through this process step by step for our given functions:
Multiplying f by 2 gives us: {(-2,4), (0,6), (2,10), (-2,6)}
Multiplying g by 4 gives us: {(-8,4), (0,12), (4,20), (-4,12), (12,0)}
Taking the union of these sets gives us: {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}
Simplifying this set by removing duplicates gives us: {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}
So, 2f + 4g is the function represented by the set {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}.
For the ordered pair (1,5) in g, the corresponding ordered pair in h is (5,4). So, we can compute 2g(1)/h(5) as follows:
2g(1) = 2 * 5 = 10
h(5) = 4
2g(1)/h(5) = 10/4 = 2.5
Therefore, the ordered pair (1,2.5) is in the result set.
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The Wagner Corporation has a $22 million bond obligation outstanding, which it is considering refunding. Though the bonds were initially issued at 12 percent, the interest rates on similar issues have declined to 10 percent. The bonds were originally issued for 20 years and have 16 years remaining. The new issue would be for 16 years. There is a 7 percent call premium on the old issue. The underwriting cost on the new $22 million issue is $680,000, and the underwriting cost on the old issue was $530,000. The company is in a 40 percent tax bracket, and it will allow an overlap period of one month ( 1/12 of the year). Treasury bills currently yield 5 percent. (Do not round intermediate calculations. Enter the answers in whole dollars, not in millions. Round the final answers to nearest whole dollar.) a. Calculate the present value of total outflows. Total outflows b. Calculate the present value of total inflows. Total inflows $ c. Calculate the net present value. Net present value $ d. Should the old issue be refunded with new debt? Yes No
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The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes
To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.
Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.
Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax. Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.
Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows. If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.
Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,
CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080. NPV ≈ $824,179. Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.
Therefore, the answers are:
a. Total outflows: $2,007,901
b. Total inflows: $827,080
c. Net present value: $824,179
d. Should the old issue be refunded with new debt? Yes
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Which expression is equivalent?
Answers
Answer:
Option one is correct
Step-by-step explanation:
Hope it's helpful... :)
Half of 1/2 cake = ____ cake.
Answers
Answer:
0.5
Step-by-step explanation:
PLEASE URGENT HELP NEEDED
Answers
Answer:
l think the answer is A. 20 sorry lf I am wrong
ninety percent of the people who have a particular disease will have a positive result on a given diagnostic test. ninety percent of the people who do not have the disease will have a negative result on this test. if 5 percent of a certain population has the disease, what percent of that population would test positive for the disease? responses 4.5%
Answers
The total probability that the result of a test will be positive is
P(A) = 14%.
Now, According to the question:
We have following the some steps for the solving question:-
Step 1. Give algebraic names to various events described:
Let the event A represent the event that the diagnostic test gives a positive result, the event \(E_1\) represent the event that a person has the particular disease, and, the event \(E_2\) = not \(E_1\) represent the event that a person does not have the particular disease.
Step-2: Evaluate the given situation mathematically.
It is given that ninety percent of the people who have the disease will have a positive result on a given diagnostic test.
In other words, the conditional probability of the event that the diagnostic test gives a positive result (A) given that the tested person has the disease (\(E_1\)), is given to be 90%. Thus, P(A|\(E_1\)) = 90%
In other words, the conditional probability of the event that the diagnostic test gives a negative result (Not A), given that the tested person does not have the disease ( \(E_2\) = not \(E_1\)), is given to be 90%.
Thus, P(not A|\(E_2\)) = 90%.
Further, it is given that five percent of the population has the disease. In other words, the event that a person has the disease (\(E_1\)) has the probability of 5% .
Thus, P(\(E_1\)) = 5%.
It is needed to find what percent of that population would test positive for the disease.
Thus, the probability that a person will have a positive result when tested,
P(A), is to be determined.
Step-3: Determine an expression for the required probability in terms of known quantities:
Recall that the Theorem of Total Probability states that if \(E_1\), and \(E_2\) are mutually exclusive and exhaustive events, then the total probability of another event A can be written as
P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(E_2\))P(A|\(E_2\)) in terms of the conditional probabilities of A.
Note that the events \(E_1\) and \(E_2= not E_1\) are exhaustive events because a person will either have the disease (\(E_1\)), or not have the disease (\(E_2\)) , there is no third possibility. Also, note that the events \(E_1\) and \(E_2= not E_1\) are mutually exclusive events because a person cannot both have the disease (\(E_1\)), and not have the disease (\(E_2\)) at the same time. Thus, \(E_1\) , and \(E_2\) are mutually exclusive and exhaustive events.
Hence, by the theorem of total probability, the probability that a person will have a positive result when tested is given by
P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(E_2\))P(A|\(E_2\))
P(\(E_1\)) = 5% , P(A|\(E_1\)) = 90% , P(A|\(E_2\)) =90%
P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(E_2\))P(A|\(E_2\))
P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(not E_1\))P(A|\(E_2\)) [Since \(E_2\) = not \(E_1\)]
P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}P(A|\(E_2\))
P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}{1 - P(not A|\(E_2\))}
Thus, P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}{1 - P(not A|\(E_2\))}
Step-4: Evaluate the required probability.
Substitute P(\(E_1\)) = 5% , P(A|\(E_1\)) = 90% , P(A|\(E_2\)) =90% in
P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}{1 - P(not A|\(E_2\))} .
= (5%) × (90%) + {1 - 5%} × {1- 90%}
= (5/100) × (90/100) + {1- 5/100} × {1 - 90/100}
= (450/10000) + {(100 -5)/100} × {(100 - 90)/ 100}
= 450/10000 + 95 × 10 / 10000
= 45/1000 + 95/1000
= 45 + 95 / 1000
= 140/ 1000
= 14/100
= 14%
Thus, the total probability that the result of a test will be positive is
P(A) = 14%.
Hence, 14% of the population would test positive for the disease.
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What is f(x) = - 2x + 7 where x = - 5?
A) -3
B) 3
C) -7
D) 17
Answers
Answer:
answer is D
Step-by-step explanation:
f(x) = -2(-5) + 7
f(x) = 10 + 7 = 17
the solution is 17
It is a straight path that goes on without end in two directions. What is it?
A. line
B. plane
C.ray
D. triangle
Answers
The correct answer is A. line. A line is a straight path that extends infinitely in both directions. It has no endpoints and continues indefinitely.
A line is a basic geometric object that is defined by two points or can be represented by a single equation. It is characterized by its straightness and infinite length, extending in both directions without any boundaries or endpoints. A line can be represented by a straight line segment with two distinct points or by an equation such as y = mx + b in a coordinate system.
On the other hand, a plane refers to a two-dimensional flat surface that extends infinitely in all directions. It is not a straight path but rather a flat, continuous surface. A ray, is a part of a line that has one endpoint and extends infinitely in one direction. It is not a straight path that continues indefinitely in both directions like a line.
A triangle is a closed geometric shape with three sides and three angles. It is not a straight path but rather a closed figure formed by connecting three non-collinear points.Therefore ,the correct answer is A.
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A(n) _____ can be used to establish a cause and effect relationship between the explanatory and response variables.
Answers
A(n) experiment can be used to establish a cause and effect relationship between the explanatory and response variables.
In an experiment, researchers actively manipulate the explanatory variable (also known as the independent variable) to observe its effect on the response variable (also known as the dependent variable). By controlling and manipulating the conditions of the experiment, researchers can establish a cause and effect relationship between the variables.
The key characteristic of an experiment is the ability to assign participants or subjects randomly to different treatment groups. This random assignment helps ensure that any observed effects on the response variable are due to the manipulation of the explanatory variable and not due to other confounding factors.
By conducting experiments, researchers can gather strong evidence to support or refute hypotheses about causal relationships. The experimental design allows for rigorous control over potential sources of bias and provides a foundation for drawing conclusions about cause and effect.
It is important to note that while experiments are powerful in establishing causality, they may not always be feasible or ethical for certain research questions. In such cases, other study designs, such as observational studies, can provide valuable insights, but establishing causal relationships becomes more challenging.
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Please solve this is a not a test or quiz it is a question by my teacher as how to solve the problem
Answers
Answer:
0
Explanation:
Consider the diagram below:
Point P divides segment CD in the ratio 3:2.
To find the coordinate of P, we use the formula for the internal division of a line segment given below:
\(P(x,y)=\mleft(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\mright)\)Thus, the x-coordinate of P is:
\(\begin{gathered} \dfrac{mx_2+nx_1}{m+n}=\frac{3(4)+2(-6)}{3+2}\text{ where }\begin{cases}m\colon n=3\colon2 \\ x_1=-6,x_2=4\end{cases} \\ =\frac{12-12}{5} \\ =\frac{0}{5} \\ =0 \end{gathered}\)The x-coordinate of P is 0.
Extra
The y-coordinate of P is:
\(\begin{gathered} \dfrac{my_2_{}+ny_1}{m+n}=\frac{3(5)+2(0)}{3+2}\text{ where }\begin{cases}m\colon n=3\colon2 \\ y_1=0,y_2=5\end{cases} \\ =\frac{15+0}{5} \\ =\frac{15}{5} \\ =3 \end{gathered}\)The y-coordinate of P is 3.
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. X y 11 7.31 9 6.56 12 13.36 10 12 7.197.64 14 9.22 5 6.33 4 5.54 13 8.52 8 6.11 5 5.91 Create a scatterplot of the data. Choose the correct graph below. OA OB. OC. O O .............. Lullulilu 5 :50 O CODOO 5f0 OTT 0 5 10 15 20 25 OTT 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 Find the equation of the regression line. ŷ = + x (Round the constant two decimal places as needed. Round the coefficient to three decimal places as needed.) Identify a characteristic of the data that is ignored by the regression line. O A. The data has a pattern that is not a straight line. OB. There is no trend in the data. OC. There is an influential point that strongly affects the graph of the regression line. OD. There is no characteristic of the data that is ignored by the regression line.
Answers
The equation of the regression line is y = 0.430x + 3.59.
A characteristic of the data that is ignored by the regression line is that: A. The data has a pattern that is not a straight line.
How to find an equation of the regression line?In order to determine a linear equation for the regression line (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatterplot).
In this scenario, the x-values would be plotted on the x-axis of the scatterplot while the y-values would be plotted on the y-axis of the scatterplot.
On the Excel worksheet, you should right click on any of the data point on the scatterplot, select format trend line, and then tick the box to display an equation for the regression line (trend line) on the scatter plot.
By critically observing the scatterplot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the regression line (trend line) is given by:
y = 0.430x + 3.59
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PLS HELPPP TIME LIMIT!!!!
Answers
58º + 56º = 114º
180º - 114º = 66º
9/4 divided by 3/8 with quotient
Answers
Answer:hey hunny boo it’s 61!✨ hope I helped :)
Step-by-step explanation:
The quotient of the given fractions is 6.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, 9/4 divided by 3/8.
When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction reversing its numerator and denominator is the first step in dividing fractions. Multiply the two numerators after that. Multiply the two denominators after that.
Here, 9/4 ÷ 3/8
= 9/4 × 8/3
= 3 × 2
= 6
Therefore, the quotient is 6.
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which value of C would not make the following expression factorable: 6x^2-13x+c
Answers
Answer:
1
Step-by-step explanation:
Estimate a 15% tip on a dinner bill of $43.27 by first rounding the bill amount to the nearest ten dollars.
Answers
Answer:
6.00$
Step-by-step explanation:
43.27 rounds down to 40.00.
15% of 40.00 is 6.00
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The graph of 2x + y =8 is shown on the graph below. Graph the equation y= 1/3x - 6 on the same coordinate plane below. Plot the point that represents the solution to the system considering of the two equations.
Answers
Answer:
See graph below. The point is (6,-4)
Step-by-step explanation:
I used a scale of 1 for the x and y axis. Your graph uses a scale of counting by 2's
Please helpppp.I need to get my grade up and this will get it up!!
Answers
Answer:
It should be 15 weeks
Step-by-step explanation:
if you look at the graph you can see every two weeks it goes down by 100, go to the end of the graph and continue from there. you should get 15 weeks till 300 tickets
A rectangle price of lawn i 55 m 98 m long find the length of the fence around it
Answers
Answer:
306m
Step-by-step explanation:
someone else asked the same question here! https://brainly.com/question/30091724
there are better explainations there :)
you're looking for the perimeter, so you need to add all the sides. that's 55+55+98+98, which is 306.
[3 + 3 + 3 + 3 pts) In this exercise you will generalize the binomial distribution.
(a) Show that the number of possible ways in which a set A with cardinality |A| = n can be partitioned into r subsets A1,..., A, with cardinalities n1,..., nr such that ni +...+ nor = n is equal to n! / ni!...n!
Answers
The number of possible ways to partition a set A with cardinality n into r subsets with varying cardinalities is given by n! / (n1! * n2! * ... * nr!).
How can a set A be partitioned into subsets of different sizes?Partitioning a set A into subsets of varying sizes involves calculating the number of possible ways to arrange the elements in the subsets. The formula n! / (n1! * n2! * ... * nr!) accounts for the total number of permutations while considering the specific sizes of each subset.
To understand why this formula works, let's break it down step by step.
Step 1: Counting permutations
The numerator n! represents the total number of permutations of the elements in set A. This is because when we partition a set, the order in which we choose the elements for each subset matters. So, we start with n choices for the first element, (n-1) choices for the second element, and so on, resulting in n! permutations.
Step 2: Accounting for subsets
However, in the numerator, we are overcounting because the order of elements within each subset doesn't matter. To correct for this, we divide by the factorials of the sizes of the subsets (n1!, n2!, ..., nr!). This ensures that each partition is counted only once, irrespective of the order in which the elements are chosen within each subset.
Step 3: Simplifying the formula
Dividing n! by the product of the factorials simplifies the formula, giving us the final result: n! / (n1! * n2! * ... * nr!).
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In the exponential function f(x) = 3^-x 2, what is the end behavior of f(x) as x goes to [infinity]?
Answers
For an exponential function \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.
We have been given an exponential function \(f(x) = 3^{-x}2\)
We need to check the end behavior of f(x) as x goes to infinity.
Consider,
\(\lim_{x \to \infty} f(x)\\\\= \lim_{x \to \infty} 3^{-x}2\\\\=2\times \lim_{x \to \infty} 3^{-x}\\\\=2\times 3^{-\infty}\\\\=2\times 0\\\\=0\)
This means, x \(\rightarrow\) infinity, f(x) goes to 0
As x goes to infinity, f(x) goes to zero.
Therefore, for an exponential function \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.
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Nick, Sarah and Gavyn share some sweets in the ratio 7:3:3. Nick gets 36 more sweets than
Gavyn. How many sweets are there altogether?
Answers
Gavyn receives 36 fewer candies than Nick. There are 117 candies in total.
Explain about the basic operations?When it comes to the four fundamental algebraic operations, functions perform exactly as one would expect (addition, subtraction, multiplication, and division).
The most fundamental operation in mathematics is addition. In its most basic form, addition adds two numbers—the addends or terms—to create a third, the total of the numbers (for example, 2 + 2 = 4 or 3 + 5 = 8).
In several contexts, including multiplication (repeated addition), division, and other operations, the fundamental operations of addition and subtraction are applied (repeated subtraction). These operations are used to model the word problems as mathematical expressions.
In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
7x -3x =36
4x =36
x = 36/4
x = 9
Hence 7 + 3 + 3 =13 and 13 x 9 = 117 sweets totally
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1.
(04.02 LC)
Which of the following is a common characteristic of a binomial distribution? (4 points)
There are more than two possible outcomes.
The probability of success is the same in all trials.
There are infinitely many observations.
You should perform x trials until you observe a success.
Each trial is dependent on the previous trial.
Answer: The probability of success is the same in all trials.
Answers
The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.
What is the independent probability?Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.
You should perform x trials until you observe a success.
We have given that,
There are exactly two possible outcomes success and failure.
We have to determine the following is NOT a common characteristic of a binomial distribution.
By process of elimination:-
A binomial experiment is a statistical experiment that must meet certain requirements
All trials are independent.
There are a fixed number of n trials.
The probability of success, p, is the same for each trial.
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Find the values of x and y in the equation below.
aby
08
y =
DONEM
Answers
Answer:
x=6
y=18
Step-by-step explanation:
I just took the assignment in edg ;)
need help with this I'm so confused :(:(
Answers
Step-by-step explanation:
We know that m∠1 is 110°. If we look at m∠7 closely, we can see that while m∠1 is an obtuse angle (greater than 90° but less than 180°), m∠7 is an acute angle (less than 90°).
Now, we can eliminate 110° and 180° since we know that m∠7 is an acute angle. There are only 2 choices now: 40° or 70°.
If you flip the image around, you can see that the angle is slightly less than 90°, so it has to be 70°.
Answer:
2) 70°
Which equation represents the line that passes through (- 6 7 and (- 3 6 )?.
Answers
The equation represents the line that passes through (- 6, 7) and (- 3, 6) is y = -1/3x +5
What is meant by slope-intercept form?The slope-intercept form is just a means of formulating a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are clearly visible. This form is frequently referred to as the y = mx + b form. This line form is one of the most prevalent in algebra classes.
A line's slope-intercept form is y = mx + b, where m is its slope and b is its y-intercept.
The equation of the line which is passing through two points is:
y₂-y₁ / x₂-x₁
(6-7)/(-3+6)=-1/3
A line's slope-intercept form is y =mx +b, where m is the slope and b is the y intercept.
y = -1/3 x +b. We must now calculate b, the y intercept. To find b, plug one of the given points into the previous equation and solve for b.
6 = -1/3(-3) + b
b = 5
y = -1/3x +5
Therefore, the equation represents the line that passes through (- 6, 7) and (- 3, 6) is y = -1/3x +5
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