The resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
What is roster form?In the set-builder form, a short, statement, or formula is written inside a pair of curly braces, as opposed to the roster form, where the listed items are enclosed in a pair of curly braces and separated by commas.
Roster or tabular form: In roster form, all of the components of a set are listed, with commas used to divide them and braces used to enclose them.
For instance, Z = the set of all integers = {…,−3,−2,−1,0,1,2,3,…}.
So, we have:
B = {x:x is an integer and -4 < x < 6}
B has numbers from -4 and 6.
Now, write B in roster form as:
B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}
Therefore, the resultant answer in roster form is B = {-3, -2, -1, 0, 1, 2, 3, 4, 5}.
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Complete question:
Write the following sets in roster form:
B = {x:x is an integer and -4 < x < 6}
If D is the Midpoint of AC and E is the midpoint of BC find the value of X
D is the midpoint of AC, and E is the midpoint of BC, hence the value of x for the given problem will be 9 units.
What is similar triangle?If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.
Here,
Since these are similar triangle,
BE=EC
BC=BE+EC
BC=2BE
6/(3x-15)=1/2
12=3x-15
3x=27
x=9
The value of x for the given problem where D is the Midpoint of AC and E is the midpoint of BC will be 9 units.
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You are considering taking out a loan of $8,000.00 that will be paid back over 8 years with quarterly payments of $320.19. If the interest rate is 6.3% compounded quarterly, what would the remaining balance be immediately after the fourteenth payment?
The remaining balance would be $___________. (Round to 2 decimal places.)
Answer:
78.8
Step-by-step explanation:
For the following word problems, first write a system of equations then solve for full marks.
3. The perimeter of a rectangle is 64 cm. Twice the width is 4 cm more than the length.
Find the dimensions of the rectangle.
The length of rectangle is 20cm and width is 12cm.
Let the length is x cm and width is y cm.
then perimeter 2(x+y) =64 cm
=> x+y = 64/2 = 32
=> x + y = 32 .............(1)
and according to question twice the width is 4cm more than length so,
2y = x + 4
=> 2y -x = 4 .............(2)
now we add these two equation to find the value of x and y.
3y = 36
=> y = 12
now put the value of y on any equation to find value of x ,
x +12 = 32
=> x = 32 -12 = 20
so, the length of rectangle is 20cm and width is 12cm.
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The perimeter of a square is 56. Express the length of a diagonal of the square in simplest radical form.?
The length of the diagonal of a square with a perimeter of 56 is 14√2.
What is a diagonal?A diagonal is the longest line that divides a plane shape into two equal parts.
To calculate the length of the diagonal of the square, first we need to find the length of the square using the perimeter formula.
Formula:
P = 4a............ Equation 1Where:
P = Perimeter of the squarea = Length of the squareFrom the question,
Given:
P = 56Substitute the value into equation 1 and solve for a
56 = 4aa = 56/4a = 14Finally to find the length of the diagonal of the square, we use the formula below
d = √(2a²)................... Equation 2Where:
d = Lenght of the diagonal of the squarea = Length of the square = 14Substitute into equation 2
d = √(2×14²)d = 14√2Hence, the length of the diagonal is 14√2.
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Answer:
qfewwqeffwqfefewqwqreg
Step-by-step explanation:
What is the measure of angle x? (5 points)
A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 45 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 45 degree angle, is labeled as x.
Question 2 options:
1)
45 degrees
2)
90 degrees
3)
135 degrees
4)
140 degrees
Answer:
idek
Step-by-step explanation:
What are the measures of 21 and Z2? Explain.
I need help please help me
The measure of [tex]\angle 1[/tex] is [tex]60^{\circ}[/tex] because it is related to one of the angles of the triangle by the alternate interior angles theorem.
The measure of [tex]\angle 2[/tex] is [tex]120^{\circ}[/tex] because it is adjacent to one of the angles in the triangle.
If four times my age is
increased by 20, the result is 80.
How old am I?
Solve for x:
4(x-5)
8
= 9y
X =
= [?]y + []
Enter
1. A mass of 30kg is suspended from a massless rope on one side of a massless, frictionless pulley. A mass of 10kg is connected to the rope on the other side of the pulley and is sitting on a ramp with an angle of inclination of 30. The system is shown in the following diagram.
a. The coefficient of friction is } 0.10. What is the acceleration of the system?
b. What is the tension in the rope?
a. Acceleration of the system (a) = 6.125 m/s^2
b. The tension in the rope (T) = 110.25
What is the definition of acceleration ?
Acceleration defines that the rate at which velocity changes with time, in terms of both speed and direction.
For 30 kg mass
m . g - T = m . a
30 x 9.8 - T = 30. a ⇒ (1)
For 10 kg mass
T - m base 2 g Sin θ = m base 2 a
T - 10 x 9.8 Sin 30° = 10 x a ⇒ (2)
a. Adding equation (1) and (2)
294 - 49 = 30 a + 10 a
245 = 40 a
a = 245/40
a = 6.125 m/s^2
Therefore, acceleration = 6.125 m/s^2
b. Sub a value in equation (1) we get,
T = 110.25
Therefore , tension in the role = 110.25
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Use the unique factorization for the integers' theorem (Section 4.3) and the definition of logarithm to prove that log3 (7) is irrational.
It is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
Explain the term unique factorization theorem?Every integer bigger than 1 is either a prime number by itself or the result of a singular combination of prime numbers, based on the fundamental theorem of arithmetic (FTA), Often known as the unique factorization theorem or even the unique-prime-factorization theorem.If a contradiction is rational, then log3(7) = a/b for some a,b∈R .
In which, b≠0 will be true.
As a result, 7 = 3ᵃ/ᵇ according to the definition of logarithms.
7 = 1*7 is unique according to the unique factorization theorem.
Thus, it is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
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Jazzmen's heart rate is 47 beats per minute. If this is her average heart rate, how
many times will her heartbeat in 50 years?
Answer:1235160000 beats
Step-by-step explanation:
There are 525600 minutes in a year
47*525600= 24703200
24703200*50= 1235160000
In a raffle, one ticket will win a $560 prize, one ticket will win a $490 prize, one ticket will win a $270 prize, one ticket will win a $180 prize, and the remaining tickets will win nothing. There are 500 in the raffle. If you have a ticket, what is the expected payoff?
The expected payoff from the raffle is given as follows:
$3.
How to obtain the expected payoff?The payoff is modeled by a discrete distribution, hence the expected payoff is the expected value of the said discrete distribution.
There are 500 tickets in the raffle, hence the probabilities are given as follows:
P(X = 560) = 1/500.P(X = 490) = 1/500.P(X = 270) = 1/500.P(X = 180) = 1/500.P(X = 0) = 496/500.The expected value of a discrete distribution is calculated as the sum of all outcomes multiplied by it's respective probability, hence:
E(X) = 560 x 1/500 + 490 x 1/500 + 270 x 1/500 + 180 x 1/500 + 0 x 496/500 = $3.
(all the outcomes and their probabilities are taken from the distribution built in this problem).
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4+2p=10( 5 3 p−2) i really need help ASAP!!
Answer:
p=24/528
Step-by-step explanation:
4+2p=10(53p-2)
4+2p=530p-20
24+2p=530p
24=528p
24/528=p
Poison Ivy received a total piecework paycheck of $465.47. She receives 89 cents per unit produced. How many units did she produce?
There are 523 units did she produced.
What is paycheck?
Traditionally, an employer would issue a paper document known as a paycheck—also spelled pay cheque, pay check, or pay cheque—to pay an employee for services rendered.
Businesses pay their employees for their work through paychecks. Bi-weekly and semi-monthly delivery schedules are the most typical ones, though this can change depending on the employer's preferences and any applicable state laws and regulations.
Given that:
Piecework pay = $465.47
Price per unit = 89 cents = $0.89
Number of units=$x
Let,
Total piecework pay = Price per unit x number of items sold
$465.47 = 0.89 x x
x = 523
Hence, there are 523 units did she produced.
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7 people equally share 1/2 a pan of macaroni and cheese how much of the whole pan each person get
Answer:
1/14
Step-by-step explanation:
If 7 people equally share 1/2 a pan of macaroni and cheese, each person will get 1/2 / 7 = 1/14 of the pan.
To find the fraction of the pan that each person gets in terms of the whole pan, we can multiply the fraction 1/14 by the denominator of the fraction representing the whole pan. If the whole pan is represented by 1 pan, the fraction representing each person's share would be 1/14 * 1 = 1/14 of a pan.
So, each person would get 1/14 of a pan of macaroni and cheese.
Answer: 1/14
Step-by-step explanation:
1/2 / 7 = 1/14≅ 0.07142857
In circle R, RS= 15 and the length of ST =6pi Find angleSRT
Step-by-step explanation:
you can find it by using the arc formula?
Dontrell bought 5 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
____________________
Step-by-step explanation:
y = 3.52x
This equation states that the total amount paid, y, is equal to 3.52 multiplied by the number of pounds of potatoes, x.
A worker will waterproof 4 commercial roofs if he spends 1 1/4 of waterproofing for each roof.
How many liters does he need to do the job?
If you already had 2 1/4 liters, then how much waterproofing do you need?
is fractions with procedure
-First question:
To calculate the number of liters, the number of roofs must be multiplied by the amount of waterproofing used for each roof.
To multiply the fractions, transform the mixed fractions to improper:
[tex]\begin{gathered} \sf1 \frac{1}{4} \times 4 = \\ \\ \sf \frac{4 \times 1 + 1}{4} \times \frac{4}{1} = \\ \\ \sf \frac{4 + 1}{4} \times \frac{4}{1} = \\ \\ \sf\frac{5}{4} \times \frac{4}{1} = \\ \\ \sf \frac {5 \times 4}{4 \times 1} = \\ \\ \boxed{ \sf \frac{ \red{20}}{ \red4}} = \sf \blue5\end{gathered}[/tex]
So you need five liters of waterproofing to get the job done.
-Second question:
To calculate the number of liters; It must be subtracted from the number of liters you need in total, which you already had or had:
[tex]\begin{gathered} \sf5 - 2 \frac{1}{4} = \\ \\ \sf \frac{5}{1} - \frac{4 \times 2 + 1}{4} = \\ \\ \sf\frac {5}{1} - \frac{8 + 1}{4} = \\ \\ \sf \frac{5}{1} - \frac{9}{4} = \\ \\ \sf\frac{4 \div 1 \times 5 - 4 \div 4 \times 9}{4} = \\ \\ \sf \frac{20 - 9}{4} = \\ \\ \boxed{ \sf \frac{11}{4}} = \boxed{ \sf \blue2 \: \: \blue{\sf\frac{3 }{4} }}\end{gathered}[/tex]
So, you need two whole and three quarter liters of waterproofing.
An employee earns $175 for 15 hours work. Do these quantities (salary and time) vary indirectly or directly?
Based on the information given the constant of variation is 11.67.
What is the rate of change?
The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time
by using this formula
Constant of variation = Amount earned/Time
Where:
Amount earned=$175
Time=15 hours
Let's plug in the formula
Constant of variation=$175/15
Constant of variation=11.66
Constant of variation=11.67 (Approximately)
Hence, the constant of variation is 11.67.
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While catching tadpoles, you and your friend decide to have a competition. After m minutes, you have (5m + 7) tadpoles and your friend has (3m+ 18) tadpoles. Select any expressions that could represent the total number of tadpoles that you and your friend can catch.
Answer:
TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)
Step-by-step explanation:
They ask you "elect any expressions that could represent the total number of tadpoles that you and your friend can catch."
then you need the SUM of both.
TOTAL NUMBER OF TADPOLES = (5m + 7) + (3m+ 18)
Tami rolled a die 20 times. 14 times it landed on an even number; 6 times it landed on an odd number. How does the experimental and theoretical probability compare, for rolling an odd number?
A)
The theoretical probability is higher.
B)
The experimental probability is higher.
C)
The experimental and theoretical probability are equal.
The answer is the Theoretical probability is higher than the Experimental probability.
Experimental and Theoretical Probabilities:Experimental probability:
The basis for experimental probability is what actually happens. It is dependent on the outcomes of several tests or experiments.
It is calculated by repeatedly recreating the event, recording the outcomes, and then converting the outcomes into a ratio or decimals.
Experimental probability = No of times event occurs/ No of trials
Theoretical Probability:
Theoretical probability is derived from a theory or what is predicted to occur. It is based on information and math.
It is determined by dividing the total number of outcomes by the proportion of favorable results. Either convert it to decimal form or leave it as a ratio or fraction.
Theoretical probability = No of favorable outcomes/ No of outcomes
Here we have
Tami rolled a die 20 times
14 times it landed on an even number;
6 times it landed on an odd number.
The die rolled for an odd number
As we a die will have 6 faces
Number of odd numbers = 3 [i.e 1, 3, 5 ]
Number of even numbers = 3 [ i.e 2, 4, 6 ]
⇒ Theoretical probability = 3/ 6 × 100 = 50%
The die is rolled 20 times, 6 times it landed on an odd number.
⇒ Experimental probability = 6 / 20 = 30%
As we can see,
The theoretical probability is higher than the Experimental probability.
Therefore,
The answer is the Theoretical probability is higher than the Experimental probability.
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Your friend just returned to the United States from their trip to Nepal and wants to exchange their 10,323 Nepalese rupees for U.S. dollars. How many dollars will they receive if the current exchange rate is 1 U.S. dollar to 124 Nepalese rupees? $103.23 $90.83 $83.25 $14.89
Answer: C) $83.25
Step-by-step explanation: First you multiply 124 by whatever amount equivocates to 10,323 then multiply 1 by that same amount and you get the answer, 124 x 83.25 = 10,323, and 1 x 83.25 = 83.25
Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of work hours. How much will they have earned?
The number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Eliza has = 14 + 7x
x is the number of weeks
For Sahana:
y - 8.40 = (16.80-8.40)/(2-1)[x - 1]
y = 8.4x - 8.4 + 8.4
y = 8.4x
14 + 7x = 8.4x
x = 10 hours
Thus, the number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.
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You have a whole pizza in the refrigerator. On your first trip you eat half of it. On each other trip you eat another half of what is left. After five trips what fractional part of the pizza have you ate?
Answer: You would have eaten 31/32 of the pizza.
Step-by-step explanation:
1/2 + 1/2^2+1/2^3+1/2^4+1/2^5 =
1/2(1-(1/2)^5)/1-1/2 =
1-1/32=
31/32
good question.
Convert 3 pints into liters. Round your answer to the nearest hundredth
Answer:
1.42 liters is the correct answer
Writing Equations of lines
Write the equation of each line with the given information
Slope = 7, y-intercept = -3
Simplify Tan A + Cot A
Tan A + Cot A = 2 Cosec 2A.
It is a simple TRIGNOMETRY question, which is directly based on their formulas.
In this question we have one side of formula either LHS or RHS and we have to find other,
Tan A + Cot A
we know Tan A = sin A /Cos A and Cot A = cos A / sin A
So by putting this in place of Tan A + Cot A we get,
⇒ (sin A / cos A) + (cos A / sin A)
⇒ (sin∧2 A + cos∧2 A) / cos A sin A
⇒1/ cos A sin A
⇒2/2cos A sin A
⇒ 2/Sin 2A
⇒ 2 Cosec 2A
Hence, the question is simplified.
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doreen schmidt is a chemist. she needs to prepare 36 ounces of a 11%
The answer to Question based on Conversion of Units is 1008gm
What is Conversion OF Units?
It is a method to convert units from one version from another.
Solution:
Here in this Question we must know the conversion that 1 ounce is nearly equal to 28gms
Hence if Doreen Schmidt needs to prepare 36 ounces of 11% solution he needs to have exact measurement of chemicals
Hence we can say must have that 36 ounces of chemicals to make that
Hence by unit conversion 36 multiplied by 28 which comes out to be 1008gm of chemical he needs to have
to make 11% solution
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A ship is tied to a dock with a rope
length 10 m. At low tide, the rope is
stretched tight, forming an angle of 45⁰ with the horizontal. At high tide, the stretched rope makes an angle of 30° with the horizontal. How much closer to the dock, horizontally, is the ship at low tide than at high tide?
1 meter and 59 centimeters.
Describe the hypotenuse.The longest side in a right triangle is called the hypotenuse. In other terms, the hypotenuse is the side that faces the right angle.
theorem of Pythagoras
[tex]a^{2} +b^{2} = c^{2}[/tex]
A is a right triangle's side.
B is the right triangle's side.
c = hypotenuse
Think of a right triangle where the height and distance are the legs and the hypotenuse is the rope.
We are aware that:
cos(45°) =x/10
cos(30°) =y/10,
where x represents the distance between the ship and the dock at low tides and y represents the distance during high tides.
We are searching for the y-x distance difference (since it will be farther away during high tides).
Using the previous equations:
x=cos(45°) and y=cos(30°)
Hence:
y - x = 10(cos(30°) - cos(45°))
Hence, the exact value of the distance is 10(cos30° - cos45°)
Using a calculator, this is approximately 1.59 meters.
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If 20% of a number is 40, find 2% of that number.
Answer:
4
Step-by-step explanation:
20% = 40
10% = 20
100% = 200
200 * .02 = 4
The value of 2% of that number is,
⇒ 4
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
20% of a number is 40.
Let the number = x
Hence, We get;
⇒ 20% of x = 40
⇒ 20/100 × x = 40
⇒ 1/5 × x = 40
⇒ x = 200
Thus, The value of 2% of that number is,
⇒ 2% of 200
⇒ 2/100 x 200
⇒ 4
Thus, The value of 2% of that number is,
⇒ 4
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