Answer:
47
Step-by-step explanation:
We know, that the angle at the vertex of a rectangle is 90 degree
So, if a line drawn divides it into two angles, then one of them is complementary to the other.
Hence, ADB = 90 - EDC
= 90 - 43
= 47
You made it onto the game show Let's Make a Deal! You are chosen for the opportunity to win some cash! You are
presented with a bag that contains 5 $100 bills, 8 $20 bills, 18 $5 bills, and 35 $1 bills. (write probabilities in
simplified fraction / ratio form)
Wayne says you can draw three bills randomly from the bag for your prize (you keep each bill you draw). What is
the probability of winning $300?
Unfortunately, you draw three $1 bills! Wayne feels for you and says you can put two of the bills back into the bag
(replace the bills). What is the probability of winning $201?
So the probability of winning $300 is 1/1315 & the probability of winning $201 is 7/196.
Why would you say so ?The probability of winning $300:
There are a total of 5 $100 bills + 8 $20 bills + 18 $5 bills + 35 $1 bills = 66 bills in the bag.
The probability of winning $300 by drawing 3 bills is the number of ways to select 3 $100 bills divided by the total number of possible combinations of 3 bills, which is:
(5 choose 3) / (66 choose 3) = (5! / (3! * (5-3)!) ) / (66! / (3! * (66-3)!)) = 10 / 13,145 = 1/1315
So the probability of winning $300 is 1/1315.
The probability of winning $201:
We can win $201 by drawing a $100 bill, a $50 bill (which can be achieved by drawing two $20 bills and putting back one), and a $1 bill.
The probability of winning $201 is the number of ways to select 1 $100 bill, 2 $20 bills (which can be rearranged into 1 $50 bill), and 1 $1 bill divided by the total number of possible combinations of 3 bills, which is:
(5 choose 1) * (8 choose 2) * (35 choose 1) / (66 choose 3) = (5 * 28 * 35) / 13,145 = 4900 / 13,145 = 7/196
So the probability of winning $201 is 7/196.
What is probability ?Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur. A probability of 0.5, for example, indicates that an event is equally likely to occur or not occur.
Probabilities can be calculated based on the number of favorable outcomes divided by the number of possible outcomes in a given scenario. For example, if you roll a die, the probability of rolling a 6 is 1/6 because there is only 1 favorable outcome (rolling a 6) out of 6 possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
Probability is a key concept in statistics and is used to make predictions and decisions in fields such as finance, insurance, engineering, and more.
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For each ordered pair (x,y), determine whether it is a solution to the inequality y>2?
For each ordered pair (x,y),
the solution is (-8, 7).
The correct option is D.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
We have an inequality:
y > 2.
From the given choices of ordered pair (x, y):
Substituting the values to the inequality.
And then,
7 > -8.
Therefore, the solution is (-8, 7).
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Which graph represents the proportional equation y 125m?
The graph for the proportional equation y = 125m is shown in image by red line.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
We have to given that;
The proportional equation is,
⇒ y = 125m
Clearly, The equation shows the equation of line.
Hence, The graph for the proportional equation y = 125m is shown in image by red line.
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each player rolls a six-sided die . they cannot see their own outcome but they can see the outcome of the other player. they must submit a guess of their own roll what is the maximum probability of victory?
The maximum probability of victory in this scenario is 50%.
Each player has an equal chance of rolling any number from 1 to 6, so the probability of rolling a specific number is 1/6.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favourable outcomes/Total number of outcomesSince the players cannot see their own outcome but can see the outcome of the other player, they must guess their own roll based on the observed roll of the other player. If the two players roll different numbers, one of them will have the correct guess, and their probability of winning is 1/6.
If the two players roll the same number, then both players have the same information and the probability of either player winning is still 1/6.
The maximum probability of victory is (1/6) + (1/6) = 1/3 + 1/3 = 2/3 = 50%.
Therefore, the probability is 50%.
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Help please!! Numbers 7-9
The value of the expression 7 - 9 using subtraction will be negative 2.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
7 and 9
Then the difference between the numbers 7 and 9 will be given by putting a minus sign between them. Then we have
⇒ 7 - 9
⇒ - 2
The value of the expression 7 - 9 using subtraction will be negative 2.
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What is the range of the points on the graph?
Answer:16
Step-by-step explanation:
Translate the following English phrases into algebraic equation and vice versa.
5(x+4)=6 Answer: ?
x-7=10 Answer: ?
suppose a similar survey will be given to vaccine-eligible people in canada by canadian health officials. a 99 percent confidence interval for the proportion of people who will have received flu vaccine is to be constructed. what is the smallest sample size that can be used to guarantee that the margin of error will be less than or equal to 0.02?
The sample size would need to be at least 1130 to guarantee a margin of error of 0.02 or less.
To calculate the sample size required to construct a 99 percent confidence interval for the proportion of people who will have received flu vaccine in Canada, the following formula can be used:
n = (Zα/2)2 * P * (1-P) / E2
Where n is the sample size, Zα/2 is the z-score for 99 percent confidence (2.58), P is the estimated proportion of the population that will receive the flu vaccine (assumed to be 0.5), and E is the margin of error (0.02).
Plugging in the values, we get:
n = (2.58)2 * 0.5 * (1-0.5) / (0.02)2 = 1130
Therefore, the sample size would need to be at least 1130 to guarantee a margin of error of 0.02 or less.
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you are visiting a tide pool and you measure the height and width of ten different sea anemones. you return one month later when the environmental conditions are the same as before but notice one of the anemones has changed such that it appears to have grown two inches in height. which answer option helps explain the difference in the size of the anemones that you observe?
How much water supporting the hydrostatic skeleton and the constriction of round muscles.
Hydrostatic skeletons (some of the time recently called "hydrostats") utilize a depression loaded up with water; the water is incompressible, so the organic entity can utilize it to apply power or change shape. Plants utilize osmotic pressure to compress the pit, while creatures do it with muscle layers in the hydrostat's walls.
The most widely recognized muscle game plan is to have a layer with longwise or longitudinal filaments and a layer with roundabout or circumferential strands.
Most hydrostatic skeletons are pretty much tube shaped, so longitudinal muscles will more often than not abbreviate them and furthermore enlarge them because of consistent volume, though circumferential muscles will generally do the inverse. The longitudinal and circumferential muscles are in this manner antagonistic.
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If B (-8,3) is reflected across the line
y= -x and then translated by T < -1,5 > , then B’’ is
The point B'' after the transformation is (-4, 13).
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
A figure when undergoes reflection becomes it's mirror image.
A point (x, y) after a reflection across the line y = -x is (-y, -x).
Given point is B(-8, 3).
After the reflection, it changes to B'(-3, 8).
Then the point undergoes translation by (-1, 5).
B'(-3, 8) is translated to B''(-3 - 1, 8 + 5) = B''(-4, 13).
Hence the point B(-8, 3) after the reflection and translation gives the point B''(-4, 13).
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china and germany specialize in the production of silk and automobiles respectively. they are considered the best at their specializations. assume that china trades silk with germany in exchange for automobiles. which perspective is illustrated by this form of trade?
This form of number of trade illustrates an example of comparative advantage, where each country specializes in the production of goods that they are more efficient at producing and then trading those goods with each other.
Comparative advantage is a concept in economics that states that countries that specialize in goods they are more efficient at producing will be able to produce those goods at a lower cost than countries that do not specialize in that good. In this form of trade, China specializes in the production of silk, while Germany specializes in the production of automobiles. By trading these goods with each other, both countries are able to benefit from the number of specialization of each other, as they can produce silk or automobiles more efficiently and at a lower cost than the other country.
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Are these 2 lines parallel? Please help ASSP!
no is not a parrel is a standard line
Answer: No
Step-by-step explanation: Parallel lines have the same slope but different y-intercepts. By using the table, we find out that the slope of the second line is 1/2. the slope of the first one is -1/2 so they are not the same.
Kayla works in the marketing team for Apple. She has been asked by her manager to create a marketing campaign through TV advertisement to increase the number of people which enter the apple store in London every day.
380 is double the difference between, the target amount of people which apple want to visit the store everyday and 100, the current amount of people which enter the store every day.
How many people does Apple want to visit the store every day after Layla’s marketing campaign? Let X be Apple’s target amount of people and find the answer.
290 people Apple wants to visit the store every day after Layla’s marketing campaign.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given Apple wants to increase the number of people who enter in stores in London every day,
let X be Apple’s target amount of people,
380 is double the difference between, the target amount of people which apple wants to visit the store every day and 100
difference between the target amount of people and 100 is
X - 100
double the equation = 2(X - 100)
the equation is equal to 380
2(X - 100) = 380
divide both sides by 2
X - 100 = 380/2
X - 100 = 190
X = 190 + 100
x = 290
Hence Apple’s target amount of people is 290.
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negative one-third divided by five-fourths divided by negative two-fifths equals?
The solution of the division of the fraction is expressed as; -⁴/₁₅
How to divide fractions?When dividing fractions, what will carry out first is to turn it into multiplication. Thereafter, we will make use of the multiplicative inverse (reciprocal) to multiply.
We have the expression as;
-¹/₃ ÷ ⁵/₄
By the method described above, we can say that the solution is;
-¹/₃ × ⁴/₅
= -⁴/₁₅
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P (-6,0), Q (-3,-4) and R (-3,1) are three points. Show that PQ=QR
Answer:
see below
Step-by-step explanation:
basically it's asking you the triangle long side if they r the same
PQ length: need to know the diff b/w 2 x's n 2y's
-3+6 = 3
-4-0=-4
so 3²+4² =5² - you should memorize this.
QR length - same thing
-3+3=0
1+4=5
so 0²+5² =5²
Same. done.
Theodore wants to exchange £350 for dollars ($).
How many more dollars would he get in the bank than in the travel agent?
Travel agent
Bank
Travel
LOCAL BANK
£1= $1.27
£1= $1.32
Theodore will have $17.5 more from the bank than the travel agent.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Theodore wants to exchange £350 for dollars ($).
Bank's exchange rate is £1 = $1.32.
So, £350 = $1.32×350.
= $462.
Travel agent's exchange rate is £1 = $1.27.
So, £350 = $1.27×350.
= $444.5.
Therefore, He will get $(462 - 444.5) = $17.5 more.
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PLEASE HELP I NEED IT QUICKLY
The solution of the equations are as follows:
A. x = 11
B. No solution
C. Many solution
D. x = 0
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The solution of the following variables can be found as follows:
A variable is a number represented with letter in an equation. Hence, let's find the variables of the equations.
x - 4 = 1 / 2 (x + 3)
x - 4 = 1 / 2 x + 3 / 2
x - 1 / 2x = 3 / 2 + 4
1 / 2 x = 11 / 2
cross multiply
2x = 22
x = 22 / 2
x = 11
-4x = 1 / 2 (-8x + 2)
-4x = -4x + 1
-4x + 4x = 1
0 = 1
No solution
3 - 2(-3x + 1) = 6x + 1
3 + 6x - 2 = 6x + 1
1 + 6x = 6x = 1
1 - 1 = 6x - 6x
0 = 0
Many solutions
0.5(x + 3) = -3(x - 0.5)
0.5x + 1.5 = -3x + 1.5
0.5x + 3x = 1.5 - 1.5
3.5x = 0
x = 0
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find the slope of the line that passes through each pair of points. (2,4) and (9,12)
Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.
What is Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:
m= (y₂ - y₁)÷ (x₂ - x₁)
Slope of the line in this caseIn this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:
m= (12 -4)÷ (9 -2)
Solving:
m= 8÷ 7= 8/7
Finally, the slope of the line is 8/7.
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Select the trigonometric equation that can be used to find x.
The measure of the value of 'x' from the expression is 8.8712
Solving triangles using trigonometry identityThe given image is a triangle with the following parameters:
Opposite = 8
Hypotenuse = x
acute angle = 46 degrees
Required
The measure of the angle 'x'
Applying the rule of trigonometry
sin theta = opposite/hypotenuse
sin 46 = 8/x
x = 8/sin46
x = 8.8713
Hence the value of x from then given triangle is 8.8712
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a university found that 40% of its students withdraw without completing the introductory statistics course. assume that students registered for the course. a. compute the probability that or fewer will withdraw (to 4 decimals).
The probability that 0 or fewer students will withdraw from the course is 26.68%.
Let x be the number of students that withdraw from the introductory statistics course.
We can use a binomial distribution to solve this problem. The binomial distribution formula is:
P(x) = nCx * p^x * (1-p)^(n-x)
Where n is the number of trials, p is the probability of success, and x is the number of successes.
In this case, n = 100 (the number of students registered for the course), p = 0.4 (the probability of a student withdrawing from the course), and x = 0, 1, 2, ..., 100 (the number of students that withdraw from the course).
We want to calculate the probability that 0 or fewer students will withdraw from the course. This can be calculated by summing all the probabilities of x = 0, 1, 2, ..., 100:
[tex]P(x ≤ 0) = P(x = 0) + P(x = 1) + P(x = 2) + ... + P(x = 100)\\P(x ≤ 0) = nCx * p^x * (1-p)^(n-x)\\P(x ≤ 0) = 100C0 * 0.4^0 * (1 - 0.4)^100\\P(x ≤ 0) = 0.2668 = 26.68%[/tex]
The probability that 0 or fewer students will withdraw from the course is 26.68%.
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i really really really need help with this one two
Answer:
-2x+24
Step-by-step explanation:
Distribute the -3 into 2x and -8, which gives you -6x+24+4xAdd like terms, which gives you -2x+24, since -6x and 4x are like termsSolved! -2x+24Express each ratio in simplest form
a 6:8
The ratio of 6:8 in the simplest form is 3:4. The result is obtained by dividing the ratio by the same number.
What is ratio?A ratio is a comparison between two quantities with the same units. The ratio is generally expressed as
a:b (read: a is to be)
Where
a is antecedentb is consequentThe antecedent and consequent of ratio can be multiplied or divided by the same number. It will make the same value of the ratio. The simplest form of the ratio is when the antecedent and consequent cannot be divided by any positif whole number anymore.
We have 6:8. Find the simplest form!
6 and 8 can be divided by 2.
6:8 = 6/2 : 8/2
6:8 = 3:4
Hence, the simplest form of the expression 6:8 is 3:4.
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An irregular pentagon is shown below.
Calculate the size of the angle marked n.
Give your answer in degrees (°).
39°
72°
n
85°
The angle measure of n is 74°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
An irregular pentagon is shown below.
The sum of the exterior angles of a polygon is 360°.
So,
n + 72 + 39 + 85 + 90 = 360
n = 360 - 286
n = 74°
Therefore, the angle measure of n is 74°.
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If 81 visit a store and five nineths of them buy gardening tools how many bought gardening tools
Answer: 45
Step-by-step explanation:
We can label 5/9 of 81 as Numerator/Denominator of a whole number.
To solve the problem, we multiply the Numerator by the whole number and leave the Denominator as is:
(5 x 81) / 9 = 405/9 = 45
Therefore, the answer to 5/9 of 81 in its lowest form is:
1. Quadrilateral ABCD has angles measuring 160° and 85°. What are the other 2
angles at a 3:20 ratio?
The measure of the angles of a quadrilateral in ratio 3:20 is 15 and 100 degrees.
What are quadrilateral?A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are A, B, C, and D. A quadrilateral has the following sides: AB, BC, CD, and DA.
Given that the 2 angles are in the ratio 3 : 20, then the measure of the angle can be taken as 3x and 20x.
We know that the sum of the internal angles of a quadrilateral is 360 thus:
160 + 85 + 3x + 20x = 360
23x = 115
x = 5
The measure of the angles are:
3x = 3(5) = 15
20x = 20(5) = 100
Hence, the measure of the angles of a quadrilateral in ratio 3:20 is 15 and 100 degrees.
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What is the total number of proper subsets of a set consisting of n elements?
The total number of proper subsets of a set consisting of n elements is 2^n - 1.
How to find number of proper subsets?A proper subset of a set is a subset that contains fewer elements than the original set. The total number of proper subsets of a set consisting of n elements is given by 2^n - 1.
This is because each element in the set can either be included or excluded in a subset, leading to 2^n possible combinations. However, the empty set (i.e., the subset with no elements) is not considered a proper subset, hence the total number of proper subsets is 2^n - 1.
According to question:For example, if n = 3, then the set has 8 possible subsets: {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}. Out of these, only 7 are proper subsets. Hence,
the total number of proper subsets of a set consisting of 3 elements is 2^3 - 1 = 7.
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What is the probability that a standard normal random variable will be between 0.3 and 3.2?
A standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.
What is probability?The probability is calculated by dividing the total number of outcomes by the total number of events.
Odds and probability are two different concepts.
Divide the probability of an event occurring by the probability that it won't happen to calculate chances.
The four main types of probability that mathematicians study are axiomatic, classical, empirical, and subjective.
So, the probability that a standard normal random variable will occur with a probability ranging from 0.3 to 3.2 must therefore be calculated.
First, a mean and standard deviation are introduced for a standard normal random variable.
The probability that a standard normal random variable will fall between 0.3 and 3.2 needs to be calculated.
Therefore, it should be more likely that:
P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)
Using the usual value of z:
P(0.3<z<3.2)=0.9993−0.6179
Justify by saying:
P(0.3<z<3.2)=0.3814
Therefore, a standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.
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The diagrams below show measurements of Special right triangles. Select the correct measure from each pulldown menu to label selected measures.
The first special right triangle with angle 45° has the adjacent side equal to 16. The second special right triangle has the third angle equal to 60°, and the opposite and adjacent sides equal to 5 and 5√3 respectively, using the trigonometric ratios of sine and cosine.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
cos45 = adjacent/8√2 {adjacent/hypotenuse}
recall cos45 = √2
so;
adjacent = √2 × 8√2 {cross multiplication}
adjacent = 8 × 2
adjacent side = 16
The third angle for the second right triangle is derived as;
180° - (30 + 90)° = 60°
considering the angle 30°;
sin30 = opposite/10
recall sin30° = 1/2
opposite = 10/2 {cross multiplication}
opposite side = 5
cos30 = adjacent/10 {adjacent/hypotenuse}
recall cos30 = √3/2
adjacent = 10 × √3/2 {cross multiplication}
adjacent side = 5√3
Therefore, the first special right triangle with angle 45° has the adjacent side equal to 16. The second special right triangle has the third angle equal to 60°, and the opposite and adjacent sides equal to 5 and 5√3 respectively, using the trigonometric ratios of sine and cosine.
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Mindset: This discussion topic is about the impact of challenges on personal growth... Think of a time when you were challenged by a math assignment. What was the topic? Did you end
up successfully completing it? If you can not think of a challenge that you encountered in math class, think of one from another aspect of your life. Share what the challenge was and what
the outcome was. In either scenario, did you find yourself saying any negative self-talk ("There's no way I can do this." "I've never done this before." "I'm never going to get better at
this.")?
How can working through challenges in your math class influence how you see yourself as a math student? What are some strategies you can use (or are already using) to confidently approach
challenges in math?
Answer:
One time I was challenged by a math assignment was when I was performing rotations, and reflections. It was confusing to know what coordinates needed to change based on each rule. After studying and asking for help, I was able to complete this assignment. At time, I thought I didn't know enough to complete the assignment, but I am happy to say that I improved. Working through your problems can help you succeed and have more confidence in yourself as a student.
If you fit a slope and intercept at the same time, then their errors will be correlated. True or False?
The given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.
What is the intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.
This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.
These points satisfy x = 0 because of this.
The errors of a slope and an intercept will be connected if you fit them simultaneously.
By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept.
Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.
Therefore, the given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.
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