To prove angle abd and angle cbd are congruent using a proof by contradiction, the assumption statement that starts the proof is Angle abd and angle cbd are not congruent.
What is proof by contradiction?Proof by contradiction is a technique used in logic and mathematics to verify the truth or validity of a claim by demonstrating how presuming the proposition to be incorrect results in a contradiction.
A proof by contradiction first starts with the negation, or opposite of the hypothesis.
In context of the problem, the proof by contradiction will start by the opposite . Since we are to prove that angle abd and angle cbd are congruent, the opposite is Angle abd and angle cbd are not congruent.
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9x + 2 = 10x +7
solve for x
Answer:
The value of x is (-5)
Step-by-step explanation:
9x + 2 = 10x + 7
9x - 9x + 2 - 7 = 10x - 9x + 7 - 7
(-5) = x
x = (-5)
Thus, The value of x is (-5)
What is v equal to?
v-(-12)>23
Answer:
V>11
Step-by-step explanation:
the amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 110 minutes and a standard deviation of 11 minutes. what is the probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes?
The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes is 0.0474 or 0.033.
Given,
In a normal random variable
Mean , [tex]\mu[/tex] = 110 minutes
Standard deviation , [tex]\sigma[/tex] = 11 minutes
then
The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes will be
a)
To find the Probability that a randomly selected product will be assembled in less than 91.630 minutes, first calculate the z-score at 91.360 minutes
[tex]z-score = \frac{x-\mu}{\sigma}\\\\z-score=\frac{91.63-110}{11}\\\\z-score=\frac{-18.37}{11}=-1.67\\[/tex]
from z-score table , [tex]p(x < -1.67)=0.04746[/tex]
b)
To find the Probability that a randomly selected product will be assembled in more than 130.35 minutes, first calculate the z-score at 130.35 minutes.
[tex]z-score = \frac{130.35-110}{11}\\\\z-score=\frac{20.35}{11}=1.85[/tex]
From z-score table,
[tex]p(x > 1.85)\\\\=1-p(x < 1.85)\\\\=1-0.967\\\\=0.033[/tex]
Thus, the probability for product assembled in more than 130.35 minutes is 0.033
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I need an answer to this asap!! Lotos of points!!!
A- The red triangle is the image of the blue triangle. What kind of transformation occurred? How do you know?
Determine the scale factor of the transformation.
^Question 1
Answer: Ask three before me!
Step-by-step explanation: Ask three before me!
Solve for e.
2e + 3 + 7 = 2
e = [?]
a memory researcher is testing an experimental behavioral treatment to see if it helps or hurts the memory of alzheimer's syndrome patients. after 3 months of treatment, she tests the patient's memories using a standardized test, and the data is presented below. the population mean for this test is 50. did the treatment affect the patients' memories? use .01 as the level of significance. 43 56 78 76 58 54 44 38 44 71 83 90 the appropriate alternative hypothesis will be .
H1: The treatment affected the patients' memories.The alternative hypothesis, H1, states that the treatment affected the patients' memories.
To test this hypothesis, the researcher needs to compare the test scores to the population mean of 50. The researcher will use a one-tailed t-test with a .01 level of significance. If the calculated t-value is greater than the critical value, then the null hypothesis will be rejected and the alternative hypothesis will be accepted.
To conduct the t-test, the researcher will need to calculate the mean of the patient's test scores, the standard deviation, and the t-value. The mean is calculated by taking the sum of the test scores and dividing by the number of test scores. The standard deviation is calculated by taking the square root of the sum of the squared deviations from the mean divided by the number of test scores minus one. The t-value is calculated by taking the difference between the mean of the patient's test scores and the population mean, divided by the standard deviation of the patient's test scores, multiplied by the square root of the number of test scores. If the calculated t-value is greater than the critical value, then the null hypothesis can be rejected and the alternative hypothesis can be accepted, indicating that the treatment did affect the patient's memories.
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The average height of the five players on the basketball team was 77 inches. One of the players was 71 inches tall. Another was 74 inches tall, and two were each 78 inches tall. How tall was the tallest player on the team?
How to solve this question
Answer:
The tallest player on the team was 78 inches tall
Step-by-step explanation:
luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
Luka will require 24 cups of water to make lemonades as calculated from the data given.
The quantity of sugar which he use is twice the amount of lemon which he us ,
= 2 x 3 = 6
and ,
as we know the amount of water is 4 times as much as lemon juice
Therefore, amount of water
= 4 * 6
= 24
A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.
A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.
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2. Divide. Write the answer in simplest
form.
6 2/3 divided by 4 1/5
Answer:
100/63
Step-by-step explanation:
6 2/3 ÷4 1/5
20/3÷21/5
20/3×5/21
1 37/63 or 100/63 or 1.587301587
so the answer is one (whole number) thirty seven over sixty three
The sum of the digits of a certain two digit number is 13. Twice the tens digit exceeds the unit digit by 2. What is the number?
Answer:
Step-by-step explanation:
6.5
cross-tabulation can only be used for two variables; each variable must have well-defined labels. true false
The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false
The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that that present the results of the entire group of respondents
The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "
The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables
The cross tabulation can be used for two or more variables
Therefore, the the given statement is false
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Madison bought a bike that was marked down by $25.00. If the percent it was marked
down was 20%, what did the bike originally cost
The original cost of the bike is $20
What is percentage ?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," the percent sign, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
A fraction of 100 is represented as a number or ratio known as a percentage. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
Let x be the discount
20/100 = x / 25
1/5 = x/25
x = 25/5
x = 5
The discount is 5
The original cost is
$25 - $5
= $20
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Lisa paid $46.58 for 16.7 gallons of gasoline. What was the cost per gallon, rounded to the nearest hundredth?
Compare the landscaping cost’s between company A and company B. Let “c”represent landscaping cost in dollars, and “s” the yard size,in square feet.
The equation to the model is c = 0.0255s
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
c = ms + b
m = 17 / 680
7.5 = 17 / 680 (300) + b
7.5 = 7.5 + b
b = 0
c = 17 / 680 s
= 0.0255s
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Distributed property 9(x + 4) = 9x+4
These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two yellow marbles if the first one is placed back before the second draw. Write your answer as a ratio. Reduce to simplest terms
The probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
Explain the term probability with replacement?For queries where the results are repeated in the sample space, probability with replacement is utilized. This indicates that the item is replaced with in sample space after being picked, keeping the sample space's total number of items constant.The formula for the probability;
probability = favourable outcome/total outcome
The bag contains the marbles as;
yellow marbles: 2pink marble: 3blue marble: 5Total marble: 10Thus, probability of drawing 1st yellow marble.
probability(1st yellow) = 2/10 = 1/5
As the ball is placed again in the bag.
probability(2nd yellow) = 2/10 = 1/5
So, probability of drawing two yellow marble = 1/5 x 1/5 = 1/25.
Thus, the probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
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What is the area for 9 ft? Use 3.14 for pi.
Answer: 14.13
Step-by-step explanation:
3.14 x Radius
The radius is half of the diameter which is 4.5
the Equation is 3.14 x 4.5=14.13
GEOMETRY
The solid portion of the graph represents the relationship between the width of a rectangle in centimeters x and the area of the rectangle in centimeter squared y. Find and interpret any symmetry in the graph of the function
I need some with this I would really appreciate if you could be able to help me with this.
I don't see the picture. Can you send it in the message.
Given that there are 4 different trails to the top of a mountain.
We need to determine in how many different ways a person can hike up and down the mountain if:
a. He must take the same train both ways
b. He can, but need not, take the same train both ways
c. He does not want to take the same trail both ways.
For case (a), the person can hike up and down the mountain in 4 different ways. For case (b), the person can hike up and down the mountain in 15 different ways. For case (c), the person can hike up and down the mountain in 12 different ways.
In case (a), the person must take the same trail both ways, so there are only 4 different options available, one for each of the 4 trails.
In case (b), the person can take the same trail both ways if they choose, but they are not required to do so. This means that they have 4 different options for the trail they take on the way up, and then 4 different options for the trail they take on the way down. This results in a total of 4 x 4 = 16 different possibilities.
However, one of these possibilities is the case where the person takes the same trail both ways, which has already been counted in case (a), so we need to subtract this possibility to avoid double counting. This results in a total of 16 - 1 = 15 different possibilities.
In case (c), the person does not want to take the same trail both ways, so they have 4 different options for the trail they take on the way up, and then 3 different options for the trail they take on the way down (since they cannot take the same trail they took on the way up). This results in a total of 4 x 3 = 12 different possibilities.
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Find the volume of the pyramid.
Answer:
180 ft^3
Step-by-step explanation:
volume of the pyramid = (1/3)(area of base) (height)
v= 1/3×(10×12÷2)×(9)
= 180 ft^3
Answer:
answer on the picture.....
Find two consecutive positive integers such that the square of the first decreased by 21 equals 6 times the second
The given two consecutive positive integers are 9 and 10.
What is an integer?It is a whole number that can be positive, negative, or zero.
Let consider x and x+1 as two consecutive positive integers.
Given that,
[tex]x^{2} -21=6(x+1)[/tex]
[tex]x^{2} -6x-27=0[/tex]
It can be written in fractional form like,
(x-9)(x+3)=0
so the values of x are 9 and -3.
Here, only positive integers are considered.
Hence 9 and 10 are the two consecutive positive integers.
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The first 5 terms of a sequence are shown.
–3, –2.5, –2, –1.5, –1, ...
Write a function to describe the sequence. Explain your function.
The first 5 terms of a sequence are shown are called arithematic sequence.
What is arithmetical sequence?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is.
A collection of numbers that follow a pattern is called a sequence.
As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulas for arithmetic sequences.
The equation to determine the nth term in an arithmetic sequence
The formula for calculating the sum of an arithmetic sequence's first n terms
The arithmetic sequence formula can be used to discover any term in the arithmetic sequence.
AP = –3, –2.5, –2, –1.5, –1,
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Triangle ABC is similar to triangle PQR. Select all angels that have a sine of 5/13.
Thus, the angles which have sine of 5/13 are ∠C and ∠R, hence option C and F are correct.
What is trigonometry?
Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
We know that, in trigonometry, sin Ф = perpendicular/hypotenuse
For triangle ABC,
sin ∠C = AB/BC
⇒ sin ∠C = 5/13
sin ∠B = AC/BC
⇒ sin ∠B = 12/13
For triangle PQR, PQ = 5, QR = 13, PR = 12
sin ∠Q = PR/RQ
⇒ sin ∠Q = 12/13
sin ∠R = PQ/QR
⇒ sin ∠R = 5/13
Thus, the angles which have sine of 5/13 are ∠C and ∠R, hence option C and F are correct.
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1. Find the measure of y.
110°
z
yº
100°
87°
Answer:
97.8263768112
Step-by-step explanation:
Geometric Mean is denoted as 'x'
x = √(110×87)
x = √9570
∴ x = 97.8263768112
Define Geometric MeanThe Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. For instance, the geometric mean for a given pair of numbers, say 3 and 1, is equivalent to (3 + 1) = 3 = 1.732.In other terms, the geometric mean is the product of n numbers divided by the nth root. The geometric mean differs from the arithmetic mean, as is noted. As a result of the fact that in arithmetic mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we multiply the provided data values before taking the root of the entire number of data values using the radical index. Take the square root, for instance, if there are two data points, the cube root if there are three, the fourth root if there are four, and so on.To learn more about Geometric Mean refer https://brainly.com/question/28347817
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ayden deposits $2000 into a savings account with an annual interest rate of 3%. If he makes no further deposits or withdrawals, which graph shows the growth of his account balance?
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
How to resolve our equation?Ayden deposits $2000 into a savings account with an annual interest rate of 3%.
To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest.
A = $2,060.00
I = A - P = $60.00
A is equal to P(1 + rt).
First, convert R percent to r a decimal; for example, R/100 is 3%/100, or 0.03 per year.
A = 2000(1 + (0.03 × 1)) = 2060 \sA = $2,060.00
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
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What is the sum of x + y for the system of equations
below?
y=-3x-1
y = -2/3x + 6
O-24
-3
O-11
O5
The sum of x and y is 5.
What is an equation?An equation is a statement of two expressions connected by equal sign.
Given that, the system of equations, y=-3x-1 and y = -2/3x + 6
Simplifying the equations,
-3x-1 = -2x/3+6
Multiplying the both sides by -3
9x +3 = 2x-18
7x = -21
x = -3
Put x = -3 in any one of the equations,
y = -3(-3)-1
y = 9-1
y = 8
Hence, the sum is 5
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ow many ways can you get exactly six heads and exactly six tails if after six tosses you have had three tails and three heads?
The number of possible combinations available as calculated from the given data is 259200.
Coin just has a head and a tail.
The potential configuration is (6! * 6!)/2.
Divide by two because each coin has two faces.
The potential configuration is (6! * 6!)/2.
The potential configuration is (( 720 x 720)/2
The potential configuration is 259200.
259200 different combinations are available.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data.
Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
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A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of
0.2
0.20, point, 2 meters per week. After
7
77 weeks, the sheet is only
2.4
2.42, point, 4 meters thick.
The function's formula for the ice sheet's thickness is S(t) = 0.2t + 1.02.
How to write a linear function for the ice sheet's thickness?Mathematically, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;
S(t) = mt + b
Where:
S(t) represents the ice sheet's thickness.m represents the rate of change (slope) per week.t represents the time (measured in weeks).b represents the y-intercept or initial amount.After a time of 7 weeks and a rate of decrease of 0.2, the y-intercept or initial amount of ice can be calculated as follows;
S(t) = mt + b
2.42 = 0.2(7) + b
2.42 = 1.4 + b
y-intercept, b = 2.42 - 1.4
y-intercept, b = 1.02.
Therefore, the required linear function is given by S(t) = 0.2t + 1.02.
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Complete Question:
A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.42 meters thick.
Let S(t), denote the ice sheet's thickness S (measured in meters) as a function of time t (measured in weeks).
Write the function's formula.
S(t) = ?
A school is arranging a field trip to the zoo. The school spends 755.16 dollars on passes for 40 students and 2 teachers. The school also spends 387.20 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The money was spent on a pass and lunch for each student will be $27.66.
How to illustrate the expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The school is arranging a field trip to the zoo. The school spends 755.16 dollars on passes for 40 students and 2 teachers. The pass for each person will be:
= $755.16 / 42
= $$17.98
The school also spends 387.20 dollars on lunch for just the students. The amount for Howavh students will be:
= $387.20 / 40
= $9.68
The money was spent on a pass and lunch for each student will be:
= $9.68 + $17.98
= $27.66
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