Answer:
( - ∞, 1] U [3, ∞)
In other words,
\(x\le1,x\ge3\)Explanation:
To solve the system given, we first get rid of the absolute value sign and decompose the inequality into two
\(\begin{gathered} |4x-8|\ge4 \\ \rightarrow4x-8\ge4 \\ 4x-8\le-4 \end{gathered}\)Let is solve the two inequalities
\(\begin{gathered} 4x-8\ge4 \\ \end{gathered}\)add 8 to both sides to get
\(4x\ge12\)finally, divide both sides by 4 to get
\(\boxed{x\ge3}\)Now for the second inequality
\(4x-8\le-4\)adding 8 to both sides gives
\(4x\le4\)Finally, dividing both sides by 4 gives
\(\boxed{x\le1.}\)Hence, the solution to the system is
\(x\le1,x\ge3\)which can be written as
\(\mleft(-\infty,1\rbrack\cup\lbrack3,\infty\mright)\)find the product in lowest terms 24/18x2/17x34/3
Answer:
Step-by-step explanation:
To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:
(24/18) * (2/17) * (34/3)
First, we can simplify the fractions by reducing any common factors in the numerators and denominators:
24/18 = (212)/(29) = 12/9 = 4/3
2/17 = 2/17
34/3 = (2*17)/3 = 34/3
Now we can multiply the simplified fractions:
(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153
The product of the given fractions in lowest terms is 272/153.
The populations of 2 cities grow according to the exponential functions. Pi(t) = 120 e 0.011 t P2(t)= 125 e 0.007 t Where, P₁ and P2 are the populations (in thousands) of cities A and B respectively. t is the time in years such that t is positive and t = 0 corresponds to the year 2004. When were the populations of the two cities equal and what were their populations?
Hello,
I hope you and your family are doing well!
To find when the populations of the two cities are equal, we can set P1(t) = P2(t) and solve for t:
120 e 0.011 t = 125 e 0.007 t
Dividing both sides by e 0.007 t:
120 = 125 * (e 0.011 t / e 0.007 t)
Using the property that e^(a+b) = e^a * e^b, we have:
120 = 125 * e^(0.011 t - 0.007 t)
120 = 125 * e^(0.004 t)
Dividing both sides by 125:
1.2 = e^(0.004 t)
Taking the natural logarithm of both sides:
ln 1.2 = ln e^(0.004 t)
ln 1.2 = 0.004 t
t = ln 1.2 / 0.004
t = approximately 8.44 years
Therefore, the populations of the two cities were equal approximately 8.44 years after 2004, or in the year 2012. To find the population of the two cities at this point in time, we can substitute t = 8.44 into either of the exponential functions:
P1(8.44) = 120 e 0.011 * 8.44 = approximately 123.88 thousand
P2(8.44) = 125 e 0.007 * 8.44 = approximately 123.88 thousand
Therefore, the populations of the two cities were equal to approximately 123.88 thousand when they were equal.
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Happy Holidays!
9. Find m DF
m
140°
DF:
=
E
44°
20. Find
mZPQR.
131*
m/POR=
Need done asap please show work
According to the angles between intersecting secant and tangent, the value of
angle DF is 52 degrees
angle PQR = 49 degrees
How to solve for angle DFThe value of angle DF is solved using the angles of intersecting secant out side the circle
The theorem give the formula in the form
44 = 1/2 (140 - DF)
88 = 140 - DF
DF = 140 - 88
DF = 52 degrees
Using intersection of tangents, for the second figure
exterior angle = 1/2 (major arc - minor arc)
major arc = 360 - 131 = 229
PQR = 1/2 (229 - 131)
PQR = 49 degrees
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G= 2f/A please help find F
Find F
Answer:
f= G×A/2
Step-by-step explanation:
\(\sf{}\)
hope it's helpful to you ☺️
A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally
distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what percentage of cars
are driving less than 65 mi/hr? Use the empirical rule to solve the problem. (Round to the nearest tenth of a
percent)
The solution is : the percentage of cars that are driving less than 45 mi/hr is 2.3%
Here, we have,
Since the speeds of cars are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = speeds of cars
µ = mean speed
σ = standard deviation
From the information given,
µ = 55 mi/hr
σ = 5 mi/hr
The probability that a car is driving less than 45 mi/hr is expressed as
P(x < 45)
For x = 45
z = (45 - 55)/5 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
Therefore, the percentage of cars that are driving less than 45 mi/hr is
0.023 × 100 = 2.3%
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Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145 millimeters, and a standard deviation of 7 millimeters. If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be less than 141.5 millimeters? Round your answer to four decimal places.
Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).
What is probability?Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is expressed as a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.
According to question:To solve this problem, we can use the formula for the standard deviation of the sample mean:
Standard deviation of sample mean = standard deviation / √(sample size)
Plugging in the given values:
Standard deviation of sample mean = 7 / √(31)
Next, we can calculate the z-score, which is the number of standard deviations the sample mean is below the population mean:
z-score = (sample mean - population mean) / standard deviation of sample mean
Plugging in the given values:
z-score = (141.5 - 145) / (7 / √(31))
Using a calculator, we find that the z-score is approximately -2.22.
Finally, we can use a standard normal distribution table or a calculator to find the probability that a z-score is less than -2.22.
Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).
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What is the total weight of the bags that weighed /8 pound each?
The total weight of Rice that Mark buys is given as follows:
2.5 pounds.
How to obtain the total weight?The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.
The weight of each bag is given as follows:
5/8 pounds = 0.625 pounds.
The number of bags is given as follows:
4 bags.
Hence the total weight of Rice that Mark buys is given as follows:
4 x 0.625 = 2.5 pounds.
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PLEASE HURRY!!!!
MGSE6.NS.5: Mrs. Smith had the following transactions during the week:
What is the sum of all of the transactions for the week?
346 I think
Step-by-step explanation:
750-348=402
402-201=201
201+145=346
What is the area of the quadrilateral?
Answer:
\( 16 \: {m}^{2} \)
Step-by-step explanation:
Area of the quadrilateral
\( = \frac{1}{\cancel 2} \times 8 \times \cancel 2 + \frac{1}{\cancel 2} \times 8 \times \cancel 2 \\ \\ = 8 + 8 \\ \\ = 16 \: {m}^{2} \)
What is the value of n?
Enter your answer in the box.
n = __ cm
The value of the missing segment n using the product of intersecting chord theorem is 14cm
Using the product of intersecting chord principleThe product of the segments of two intersecting chords are equal.
The segments of the chords ;
Chord 1 = 4 and n
Chord 2 = 7 and 8
The principle can be related Mathematically thus ;
4 × n = 7 × 8
4n = 56
Divide both sides by 4
4n/4 = 56/4
n = 14
Therefore, the value of n in the question is 14cm
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a car park charges 1.20 for each car entering.
the payment station only accepts 1 pound and 20 coins.
here are the coins that were collected a number of 1 176
number of20 320 Assuming each driver pays the exact amount work the percentig of people that payd withe six 20
65.986% of the people paid with six 20 coin
To determine the percentage of people who paid with six 20 coins, we need to calculate the total amount collected from those coins and compare it to the total amount collected overall.
Given that each car entering the car park pays 1.20, we can assume that for every 1 pound paid, there is one 20 coin. Let's represent the number of people who paid with six 20 coins as "x."
The total amount collected from the 20 coins is calculated by multiplying the number of 20 coins (320) by 20, which gives us 320 * 20 = 6,400 pence.
Since each car pays 1 pound and 20 coins, which is equal to 120 pence, the total amount collected from all the cars can be calculated by multiplying the total number of cars by 120. We can represent the total number of cars as "y."
The equation representing the total amount collected from all the cars is:
120 * y = 1176 * 100 (since 1 pound is equal to 100 pence)
By solving this equation, we find:
y = (1176 * 100) / 120
Now, we can calculate the total amount collected from the 20 coins as a percentage of the total amount collected overall.
Percentage = (Amount from 20 coins / Total amount collected) * 100
Percentage = (6400 / ((1176 * 100) / 120)) * 100
Simplifying the equation, we get:
Percentage = (6400 * 120) / 1176
By evaluating this expression, we find that the percentage of people who paid with six 20 coins is approximately 65.986%.
In summary, approximately 65.986% of the people paid with six 20 coin
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Write a word problem for (12X2) + (4X3)
Answer:
My friend David bought 2, $12 pairs of jeans and 4, $3 bracelets. How much did David spend in total?
Step-by-step explanation:
Since, David is buying 2, $12 items and 4, $3 items and since were finding the total, we want to multiply (12×2) + (4×3)!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
If one picture frame costs $15, and i have $50. How many pucture frames can i buy?
Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system.
y < 6
y ≥ –3x – 1
Answer:
solution is D 6,0
Step-by-step explanation
The variables x and y vary inversely, and y=6 when x=2. Write an equation that relates x and y. Then find y when x = 3
Answer:
\(y = \frac{12}{x} \)
y= 4
Step-by-step explanation:
Since x and y are inversely proportional to each other,
\(y = \frac{k}{x} ,where \: k \: is \: a \: constant.\)
Let's find the value of k.
When y= 6, x= 2,
\(6 = \frac{k}{2} \)
k= 6(2)
k= 12 (×2 on both sides)
Substitute the value of k back into the equation:
\(y = \frac{12}{x} \)
When x=3,
\(y = \frac{12}{3} \)
y= 4
Two bicycle trails were developed in a new housing development. One trail is
3 1/2 miles long. The other trail is 3/4 as long. How long is the second trail?
The length of the second trial will be equal to 2(⁵/₈) miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.
The length of the second trial will be calculated as,
Length = 3/4 x ( 3¹/₂ )
Length = 2(⁵/₈)
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I think the answer is A. Can you check if I am correct in my thinking? Thanks!
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
\(\begin{gathered} Given\text{ the function,} \\ f(x)\text{ = x}^3-20x^2\text{ + 123 x - 216} \\ Using\text{ Rational Root theorem, we have that:} \\ f(x)\text{ =}\frac{x^3-20\text{ x}^2+\text{ 123x - 216}}{x-\text{ 3}}=\text{ x}^2-\text{ 17 x + 72} \\ Now,\text{ factorizing x}^2-17x\text{ + 72 , we have that:} \\ \end{gathered}\)\(\begin{gathered} x^2\text{ -17 x+ 72 = \lparen x- 8 \rparen \lparen x - 9 \rparen} \\ Hence,\text{ we can see that:} \\ x^3-20x^2+\text{ 123 x - 216 = \lparen x- 3\rparen \lparen x - 8 \rparen \lparen x - 9 \rparen} \\ Hence,\text{ we have zero imaginary roots and 3 real roots} \end{gathered}\)CONCLUSION:
The final answer is:
\(zero\text{ imaginary , 3 real roots \lparen OPTION A \rparen}\)1) Consider that lines A and B are parallel Which equation models the relationship between 21 and 25? es A) 41=25 B) 41+25= 90° 921+25=180° D) Z1+25=100⁰ 5 2
Answer: C
Step-by-step explanation:
First, we will use the fact that corresponding angles are congruent. This means that ∠1 and ∠6 are congruent, and ∠5 and ∠8 are congruent.
Next, we know that a straight line is equal to 180°.
Using this information, we can confirm that the answer is option C,
∠1 + ∠5 = 180°
See attached for a basic drawing showing the angles.
\( \sf{\qquad\qquad\huge\underline{{\sf Answer}}} \)
In the given figure, Angle 1 and Angle 5 are angles formed between the parallel lines and are on same side of the transversal therefore we can conclude that the given pair of angles form Co - Interior Angles.
So, the relation between them is as :
\( \qquad \sf \dashrightarrow \angle1 + \angle5 = 180 \degree\)Then, the correct choice will be C
Elisa starts baking a pie at 11:25 a.m.
The pie needs to bake for 45 minutes.
What time will the pie be done?
Answer:
12.10 pm
Step-by-step explanation:
just take the 45 minutes she uses to bake and add to the time she starts
11.25 a.m+45
12.10 pm
A manufacturing machine has a 10% defect rate. If 3 items are chosen at random, what is the probability that at least one will have a defect
Answer:
0.271 = 27.1% probability that at least one will have a defect
Step-by-step explanation:
For each item, there are only two possible outcomes. Either they have a defect, or they do not. Items are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
A manufacturing machine has a 10% defect rate.
This means that \(p = 0.1\)
3 items are chosen at random
This means that \(n = 3\)
What is the probability that at least one will have a defect?
This is
\(P(X \geq 1) = 1 - P(X = 0)\)
In which
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{3,0}.(0.1)^{0}.(0.9)^{3} = 0.729\)
\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.729 = 0.271\)
0.271 = 27.1% probability that at least one will have a defect
Which of the following describes the transformations performed on the object shown above?
A.
The object was reflected across the y-axis and shifted -1 unit in the x direction and -7 units in the y direction.
B.
The object was reflected across the y-axis and shifted 1 unit in the x direction and -7 units in the y direction.
C.
The object was reflected across the x-axis and shifted 7 units in the x direction and -5 units in the y direction.
D.
The object was reflected across the x-axis and shifted 9 units in the x direction and -3 units in the y direction.
Answer:
B is the answer I believe
activity 7 circles and terms related to it☺
Answer:
Step-by-step explanation:
The pats of the circle R required are:
1. A circle - ABCD
2. Four radii - AR, BR, CR, and DR
3. Two diameters - AB and CD
4. Two tangents - GA and TB
5. A chord - BC
6. Two secant each containing a diameter - ARB and CRD
7. The longest chord - AC = DB
8. Two points of tangency - A and B
9. Four minor arcs - AC, CB, BD, DA
10. Four major arcs - AB, BA, CD, DC
5. The average age of men at the time of their first marriage is 24.8 years. Suppose the
standard deviation is 2.8 years. Forty-nine married males are selected at random and asked the
age at which they were first married. Find the probability that the sample mean will be more than 26.
Answer:
0.0013 = 0.13% probability that the sample mean will be more than 26.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average age of men at the time of their first marriage is 24.8 years. Suppose the standard deviation is 2.8 years.
This means that \(\mu = 24.8, \sigma = 2.8\)
Forty-nine married males are selected at random and asked the age at which they were first married.
This means that \(n = 49, s = \frac{2.8}{\sqrt{49}} = 0.4\)
Find the probability that the sample mean will be more than 26.
This is 1 subtracted by the pvalue of Z when X = 26. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{26 - 24.8}{0.4}\)
\(Z = 3\)
\(Z = 3\) has a pvalue of 0.9987
1 - 0.9987 = 0.0013
0.0013 = 0.13% probability that the sample mean will be more than 26.
Find the volume of a pyramid with a square base, where the side length of the base is
10.6
in
10.6 in and the height of the pyramid is
12.3
in
12.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
V = 460.68
Step-by-step explanation:
V=(lwh)/3
HELP (THE OPTIONS FOR CHOOSE IS yes no yes no yes no yes no) AND NO PUTTING FAKE ANSWERS OR PUTTING NOT CORRECT ANSWERS LIKE answer:e step by step explanation:e PLEASE NONE OF THAT
Yes, she did buy additional carrot seed. No, the total number of seeds was 1120. No, the total price is $171. She did buy more maize and beans than carrots.
What is multiplication?Multiplication is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and division. A product is the outcome of a multiplication operation. Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilize every day. When we multiply two numbers, the result is known as the product. The multiplicand is the number of items in each group, and the multiplier is the number of such equal groupings. In our situation, the multiplicand is, the multiplier is, and the product is 6.
Here,
Beans=12*40
=480
cost of beans=12*5
=$60
Carrot=15*36
=540
cost of carrot=15*7
=$105
Corn=2*50
=100
cost of corn=2*3
=$6
Total seeds=1120
Total cost=$171
Yes she bought more of carrot seed. No the total seeds was 1120. No the total cost is $171. Yes she bought more corn and beans than carrot.
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A 11-inch candle is lit and burns at a constant rate of 1.1 inches per hour. Let t represent the number of hours since the candle was lit, and suppose R
is a function such that R (t) represents the remaining length of the candle (in inches) t
hours after it was lit.
- What is the domain of R^−1 relative to this context? Enter your answer as an interval.
- What is the range of R^−1 relative to this context? Enter your answer as an interval.
Therefore, in response to the given query, we can state that R(-1)'s inequality possible spectrum is thus: [0, 10]
What is inequality?A connection between two expressions or numbers that is not equivalent in mathematics is referred to as an inequality. Thus, disparity results from inequity. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and disparity are not the same. Use the not equal sign most frequently when two numbers are not identical. (). Values of any size can be contrasted using a variety of disparities. By changing the two sides until only the factors are left, many straightforward inequalities can be answered. However, a number of factors support inequality: Both parts' negative numbers are divided or added. Exchange the left and the right.
The equation can be used to describe the candle's length, R(t):
R(t) = 11 - 1.1t
where t represents how long the light has been burning, in hours.
We must determine t in terms of R in order to determine the negative of R(t):
R = 11 - 1.1 t = (11 - R)/1.1 t = (11 - R)
R(t)'s inverse function is thus:
\(R^{(-1)}(R) = (11 - R)/1.1\)
0 ≤ R ≤ 11
So, R(-1)'s scope is as follows:
[0, 11]
0 ≤ R ≤ 11
Inputting these limits into the equation for R(-1) yields the following results:
\(R^{(-1)}(0) = 11/1.1 = 10\\R^{(-1)}(11) = 0/1.1 = 0\)
R(-1)'s possible spectrum is thus:
[0, 10]
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5. Brandon says 4 x 800 is greater than 8 x 4,000. Renee says 4 x 800 is less than 8 X 4,000. B. A. Without calculating the answer, explain how to use place-value strategies or the Associative Property to find which is greater
Answer:
a is greater
Step-by-step explanation:
Place value is the system in which the position of a digit in a number determines its value.
Using place-value strategies without calculating we find that,
Renee says 4 x 800 is less than 8 x 4,000 is correct.
What is a place value of a number?It is the system in which the position of a digit in a number determines its value.
Example:
135789
9 - ones
8 - tens
7 - hundreds
5 - thousands
3 - ten thousands
1 - hundred thousands
We have,
4 x 800:
Here we are multiplying a hundred-place value number.
= 3200
This can be said to be in place value of thousands.
8 x 4000:
Here we are multiplying a thousand-place value number.
= 32000
This can be said to be in place value of ten thousands.
We can say that,
8 x 4000 is greater than 4 x 800
Thus,
Renee says 4 x 800 is less than 8 X 4,000 is correct.
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arun is older than suav. their ages are consecutive integers. find arun's age if the sum of the square of arun's age and 4 times suav's age is 92.
If the ages of Arun and Suav are consecutive integers than the Arun's age is 8 years .
In the question ,
it is given that ,
Arun is older than Suav ,
and their ages are consecutive integers ,
Let the Suav's age be = "x"
So , the Arun's age be = "x+1" .
it is given that , the sum of the square of Arun's age and 4 times Suav's age is 92.
that means ;
(x+1)² +4x = 92
x² +6x + 1 = 92
x² + 6x - 91 = 0
Solving the quadratic equations ,
we get ,
x = 7 and x = -13 .
age cannot be negative , So ,
x = 7 ,
thus, the Arun's age will be = 7 + 1 = 8 years.
Therefore , the age of Arun is 8 years .
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