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How is solving a compound inequality in compact form similar to solving a simple inequality? How is it different?
Answer: Solving a compound inequality in compact form is similar to solving a simple inequality in the sense that both involve isolating the variable on one side of the inequality and then using the same rules of inequality to find the solution set. Both compound and simple inequalities can be graphed as a line on a number line or coordinate plane, with the solution set being either all the numbers less than, greater than, or between two values, depending on the inequality sign.
However, solving a compound inequality in compact form is different from solving a simple inequality in that a compound inequality has two or more inequality statements combined using "and" or "or" connectors. When solving a compound inequality, we have to consider both inequalities together to find the final solution set. For example, when solving the inequality 3 < x < 5, we have to consider both 3 < x and x < 5, to find the range of x that satisfies both inequalities. And when we have a compound inequality with "or" connector like 3<x<5 or 6<x<8, we need to find the solution set for each inequality separately and then combine them.
So, the difference between solving a compound inequality and a simple inequality is that a compound inequality has multiple inequality statements that must be considered together to find the final solution set, while a simple inequality has only one inequality statement.
Step-by-step explanation:
1. Patrick Mahomes throws a 5kg football to Tyreek Hill at 25m/s to win Super
Bowl LV. What was the Kinetic Energy of the football as it was traveling down the
field? PE = mxgx h PE = wxh KE =. 5 xm xv^2 g = 9. 8 m/s *
1225 J is the Kinetic Energy of the football as it was traveling down the
field.
Calculate the Kinetic Energy (KE) of the football.
KE = 0.5 x 5 kg x (25 m/s)^2
Calculate the Kinetic Energy of the football in Joules (J).
KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2
Calculate the Kinetic Energy of the football in Joules (J).
KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2 = 1225 J
The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.
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out of the 33 costumes for the school play, 17 need to be altered to fit an actor. 15 costumes need to be shortened and 11 costumes need to be taken in. what is the probability that a randomly selected costume needs both shortened and taken in?
The probability that randomly selected costume needs both shortened and taken in is 9/33
There are a total of n(T) = 33 costumes. Of these n(A) = 17 require alteration. The two sorts of change are shortening and taking in. n(S) = 15 costumes require shortening, and n(I) = 11 costumers require being taken in.
We are to determine the probability that a randomly selected costume requires both shortening and taken in.
The following is the formula for the union of sets.
P(S ∪ I) = P(S) + P(I) - P(S ∩ I)
∴ S ∪ I = A
∴ P(A) = P(S) + P(I) - P(S ∩ I)
∴ [tex]\frac{n(A)}{n(T)} = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - P(S \cap I)[/tex]
∴ [tex]P(S \cap I) = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - \frac{n(A)}{n(T)}[/tex]
Substituting the values:
∴ [tex]P(S \cap I) = \frac{15}{33} + \frac{11}{33} - \frac{17}{33}[/tex]
∴ [tex]\frac{26}{33} - \frac{17}{33}[/tex]
∴ [tex]\frac{9}{33}[/tex]
Therefore the probability that randomly selected costume needs both shortened and taken in is 9/33
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Right now, our economy is just beginning to recover from a recession. Jobs are
hard to find and salaries are relatively low. How will you take this into account
when you make plans for what to do after high school?
When the economy is experiencing inflation, money is worth less and less over
time. What are three ways to protect yourself from the effects of inflation?
Plans for what to do after high school and three ways to protect yourself from the effects of inflation are mentioned below.
To take into account a recovering economy with scarce jobs and low salaries when making plans for after high school, one could consider the following:
Obtaining job skills or education in high-demand fields that are less likely to be affected by economic slowdowns.Pursuing opportunities for remote work or freelance work, which can provide flexibility and stability in a changing job market.Starting a side business or investing in stocks or real estate to generate additional income and build wealth over time.To protect oneself from the effects of inflation, one could consider the following:
Investing in assets that are expected to keep pace with or outgrow inflation, such as stocks, real estate, or commodities.Building an emergency fund to cover unexpected expenses and reduce the need to draw from investments during periods of high inflation.Keeping debt levels low and paying off high-interest debt to reduce financial stress during periods of rising prices.To learn more about inflation here:
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What reflections map the figure onto itself
A line of symmetry is the reflections map the figure onto itself.
What reflection map the figure onto itself?A line of symmetry is, in other words, a line that splits a figure into two mirror representations. This line's reflection maps the figure onto itself. While some figures lack symmetry, others do feature one or more lines of symmetry. An example of a form having reflection symmetry is a rectangle.
The symmetry axes are shown and given the letters m and n. The figure will map to itself when reflected across either (or both) of the symmetry axes. It seems like you want to call those reflections...
Ra, where
a = m, and
Rb, where
b = n
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Robel' father i 4 time a old a Robel. After 5 year, father will be three time a old a Robel. Find their preent age.
Robel's age will be 15 and Father's age will be 45, which is three times as old as Robel.
Robel's current age = x
Father's current age = 4x
After 5 years,
Robel's age = x + 5
Father's age = 4x + 5
After 5 years, father will be three times a old a Robel
4x + 5 = 3(x + 5)
4x + 5 = 3x + 15
x = 10
Therefore, Robel's current age is 10 years and father's current age is 40 years.
Let x represent the current age of Robel and 4x represent the current age of Robel's father.
We can use the formula 4x + 5 = 3(x + 5) to solve for x.
We rearrange the equation to get x = 10.
Robel's current age is 10 years and father's current age is 40 years.
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how can you write prime factorization and find the greatest common factor and least common multiple of two numbers
Answer:
Step-by-step explanation:
Prime factorization is the process of expressing a number as the product of its prime factors. To find the prime factorization of a number, you can use the following steps:Divide the number by the smallest prime factor (2) and write the result.Divide the quotient from step 1 by the next smallest prime factor (3) and write the result.Repeat step 2 with each successive prime factor until the quotient is 1.For example, to find the prime factorization of 60:60 / 2 = 30 -> 2
30 / 2 = 15 -> 2 * 2 = 4
15 / 3 = 5 -> 4 * 3 = 12
5 / 5 = 1 -> 12 * 5 = 60The prime factorization of 60 is 2 * 2 * 3 * 5To find the greatest common factor (GCF) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the GCF as the product of the prime factors that are common to both numbers, each raised to the lowest power that occurs in both factorizations.For example, to find the GCF of 24 and 40:Prime factorization of 24 = 2^3 * 3
Prime factorization of 40 = 2^3 * 5The GCF is 2^3 = 8To find the least common multiple (LCM) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the LCM as the product of the prime factors of each number, each raised to the highest power that occurs in either factorization.For example, to find the LCM of 24 and 40:Prime factorization of 24 = 2^3 * 3
Prime factorization of 40 = 2^3 * 5The LCM is 2^3 * 3 * 5 = 120Alternatively, you can use the formula LCM(a, b) = (a * b) / GCF(a, b)Please note that this is a method for finding the prime factorization and GCF/LCM of small numbers. For larger numbers, it is more efficient to use a specific algorithm or software.
(WILL GIVE BRAINLIEST)
The following table shows the number of goals that the Texas Sharpshooters scored in each of their 8 hockey games this season.
(Table with 3, 4, 1, 4, 1, 1, 2, 1)
Based on this data, what is a reasonable estimate of the probability that the Texas Sharpshooters score exactly 1 goal next hockey game?
Choose the best answer.
Choose 1 answer:
(Choice A)
A
0. 13
(Choice B)
B
0. 24
(Choice C)
C
0. 50
(Choice D)
D
1. 0
The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5
The following figure accurately depicts the table.
Experimental probability is the likelihood of a future event based on past happenings.
Experimental probability is equal to the ratio of good results to all possible results.
To calculate the likelihood that the Texas Sharpshooters will score precisely
Next hockey game: 1 goal
As displayed in the table:
a successful outcome is repeated four times.
So, positive results equal 4
8 total results
likelihood = 4/8 = 0.5
So, The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5
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Answer:
0.50 (Choice C)
Step-by-step explanation:
Khan Academy told me.
The mangum public school professional development committee is planning the schedule for the next school year. They would like to send teachers to a summer training on mentor groups. The advanced payment for the training is $1,250 to send as many teachers as you want. The cost at registration is $175 per teacher. The school board paid $1,250 for early registration. How many teachers must attend for this to be a good decision?
This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.
What is an algebraic manipulation?
Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.
To determine if sending teachers to the summer training on mentor groups is a good decision, the committee needs to calculate the break-even point. This is the point at which the cost of sending the teachers is equal to the cost of not sending them. The break-even point can be calculated by dividing the advanced payment by the difference between the cost at registration and the advanced payment.
In this case, the break-even point is: $1,250 ÷ ($175 - $1,250) = $1,250 ÷ -$1,075 = 7 teachers.
Hence, This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.
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7. A fundraising dinner was held on two
consecutive nights. On the first night,
100 adult tickets and 175 children's tickets
were sold for a total of $937. 50. On the
second night, 200 adult tickets and 316
children's tickets were sold for a total
of $1790. What was the price for a
children's ticket?
so
The price for a children's ticket is $2.50
Now, According to the question:
A fundraising dinner was held on two consecutive nights.
Let the number of children's tickets be x.
Let the number of adults' tickets be y.
The total number of tickets sold is 937.50
On the first night, 100 adult tickets and 175 children's tickets
Therefore,
100x + 175y = $937.50
On the second night, 200 adult tickets and 316 children's tickets were sold for a total of $1790.
200x + 316y = $1790
Now, we have two simultaneous equations:
100x + 175y = $937.50 ----(1)
200x + 316y = $1790----(2)
Divide by 2 equation (2)
100x + 158y = $895----(3)
From the first equation, make y the subject of the formula:
100x = 937.50 - 175y
Put the value of 100x in equation (3)
937.50 -175y + 158y = $895
937.50 - 17y = $895
-17y = -42.5
y = 2.50
Hence, the price for a children's ticket is $2.50
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get more math . please help
She will lay sod over area of 925.02 square feet of 3/4 of circle and triangle.
What is a circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The equation of circle in the plane is given as:
(x-h)^2 + (y-k)^2 = r^2
where (x, y) are the coordinate points
(h, k) is the coordinate of the center of a circle
and r is the radius of a circle.
and Area of circle = πr²
Now,
Sod will be laid over=3/4*circle + on triangle
=3/4*πr^2+1/2*base*height
=3/4*3.14*18*18+1/2*18*18
=763.02+162
=925.02 square feet
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There are 5 girls, 6 boys and some adults in a room. Jenny selects at random one of these people
If there are 5 girls, 6 boys and some adults in a classroom and probability that a girl is chosen is 1/3 , then the probability of an adult being chosen is 4/15 .
The number of adults in unknown .
So let "n" denote the number of adults.
the number of girls in the room is = 5 girls ;
the number of boys in the group is = 6 boys ;
So , the total number of people to choose from will be = 5 + 6 + n ;
= 11 + n ;
The probability of picking the girl from this group will be = 5/(11+n) ;
the probability of girl being selected is = 1/3,
Equating both the probabilities ,
we get ; 5/(11+n) = 1/3
On Cross multiplying we have : 11 + n = 15
which means ⇒ n = 4 and number of adults is = 4 ;
So ,the total number of people is = 11 + 4 = 15.
So , The probability of picking adult is = 4/15.
The given question is incomplete , the complete question is
There are 5 girls, 6 boys and some adults in a classroom. The probability that a girl is chosen is 1/3. What is the probability of an adult being chosen ?
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Solve this equation in the
given domain: 0
*give answer in radians*
3 sin (2x-4)=2
There should be 4 answers.
look at attached photo
The solution to the equation in the given interval is 2.365
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
3sin(2x - 4) = 2
Divide both sides of the equation by 3
So, we have the following representation
sin(2x - 4) = 2/3
Take the arcsin of both sides
This gives
2x - 4 = 0.73
Evaluate the like terms
2x = 4.73
Divide by 2
x = 2.365
Hence, the value of x is 2.365
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9 thousands 2 tens x10 =
Answer: 90200
Step-by-step explanation:
9020 x 10 = 90200.
Just add one more zero when multiplying by ten.
Please Help I Need Help With This Problem.
The equation can be written as 6 + (-6y) = -6y - 1 + (7).
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
The given is an equation with missing parts.
The left hand side of the equation does not contain a term with variable, but the right hand side contains it.
Adding that term in the left hand side, we get, 6 + (-6y) in the left hand side.
So the right hand side must be equal.
So the expression in the right hand side is -6y - 1 + (7).
Hence the expressions are 6 + (-6y) on the left hand side and -6y - 1 + (7) on the right hand side.
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The value of a house increased by 30% to $156,000.
What was the original price of the house?
The original price of the house is 156,000
How to calculate the original price of the house?
From the question,
The house was increased by 30% which leads to an increase to 156000
To get the original price of the house
Let the value of the house be x
We then multiply the original price of the house(x) by 30%
we have 0.30*x
0.30x = 156000
Divide both sides by 0.30
x = 520,000
Hence, 520000 is the original price of the house
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Roger received $200 for his birthday. He wants to use the money to buy new clothes for work. He can buy pants
for $30 and shirts for $20. He wants at least 6 new items. Determine the shirt and pants combination Roger
can buy.
Answer: He can buy 4 pants for $120 and 4 shirts for $80
Answer: Roger wants to buy at least 6 items, so he needs to buy at least 6 pants or 6 shirts or a combination of both.
Step-by-step explanation:
The cost of 6 pants is $30 x 6 = $180.
The cost of 6 shirts is $20 x 6 = $120.
If Roger wants to buy both pants and shirts, he can buy 3 pants and 6 shirts for a total cost of $90 + $120 = $210.
Another option would be 4 pants and 5 shirts for a total cost of $120 + $100 = $220.
Thus, Roger can buy either 6 pants, 6 shirts or a combination of 3 pants and 6 shirts or 4 pants and 5 shirts with his $200.
:>>>>>>>>>>>>>>>>>>>>
Stanley feeds each of his dogs 1/6 of a can of food each day. He uses a total of 1/2 of a can of food each day. How many dogs does Stanley have?
Answer: 3 dogs
Step-by-step explanation:
Each dog eats 1/6 cans of food
Stanley uses a total of 1/2 cans of food
[tex]\frac{1}{2}[/tex] / [tex]\frac{1}{6}[/tex] = 1/2 * 6
= 3 dogs
Jordan spent 5 hours over the weekend studying for 3 tests. He spent an equal amount of time studying for each test.
How long did Jordan spend studying for each test?
134 hours
35 hour
15 hour
123 hours
As per the concept of fraction, the amount time spend for each test is 1.67 hours
In math the term called fraction is known as the number is expressed as a quotient in which the numerator is divided by the denominator.
Here we have know that Jordan spent 5 hours over the weekend studying for 3 tests.
In order to find the amount of time spend for each test, we have to divide the total number of subject by the time spend by him.
Here the value of total subjects = 5 and the amount of time spend by him is 3.
Then the amount of time time spend for each test is calculated as,
=> 5/3
=> 1.67 hours
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solve these proportion for the variable x. Use the reasoning of scalling to solve
Answer:
x = 200
Step-by-step explanation:
[tex]\frac{x}{5} = \frac{120}{3}[/tex]
so you cross multiply
5 × 120 = 600
x × 3 = 3x
so
3x = 600
x = 200
Please help with the math and explain every step ty and *40 points* will mark brainless
Answer:
see below
Step-by-step explanation:
5000
60% = 3000 in stocks
year 1 gain 9% = 3000*1.09 =3270
year 2 loss 4% = 3270*(1-4%) =3139.2
40% = 2000 in savings
year 1 earn 4.9% = 2000*1.049 = 2098
year 2 earn 4.9% = 2098*1.049=2200.8
TOTAL in 2 years = 3139.2+2200.8 = 5340
so gain = 5340-5000 =340
if all only in savings:
5000*(1.049)² = 5502
Read each question and find the correct answer in the wheel. the letter that matches the answer on the wheel is what will go in the code.
1. The probability of getting heads on the first two and then a tail on the third is 1/8.
2. The probability of not getting a clay pot or a cactus is 1/2.
3. The probability of getting the same number twice is 1/36.
4. The probability of getting at least two heads is
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
1. The probability of getting a head P(H) = 1/2 and the probability of getting a tail P(T) = 1/2.
Therefore, The probability of getting heads on the first two and then a tail on the third is,
= (1/2)×(1/2)×(1/2).
= 1/8.
2. The probability of getting a clay pot is 1/4 and the probability of getting a cactus is 1/4.
So, The probability of getting a clay pot or a cactus is 1/4 + 1/4.
= 2/4.
= 1/2.
Therefore, The probability of not getting a clay pot or a cactus is,
= 1 - 1/2.
= 1/2.
3. Suppose we get a number 1 on the first throw and we know its probability is 1/6,
Therefore, The probability of getting 1 again is also 1/6.
So, The probability of getting the same number twice is,
= (1/6)×(1/6).
= 1/36.
4. The probability of getting at least two heads is,
P(HHT) + P(HHH).
= (1/2)×(1/2)×(1/2) + (1/2)×(1/2)×(1/2).
= 1/8 + 1/8.
= 2/8.
= 1/4.
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Quadrilateral ABCD and its dilated image A′B′C′D′ are shown in the figure.
Which of the points E, F, G, or H is the center of dilation?
The points G and H is the center of dilation from the points E, F, G, or H
What is Center of Dilation ?
The middle of a dilation is a hard and fast point inside the aircraft about which all points are increased or reduced in size. The middle is the handiest invariant (now not changing) factor below a dilation (k ≠1), and may be positioned inside, outdoor, or on a parent.
Given ,
In the Quadrilateral ABCD and its dilated image A′B′C′D′ are shown in the figure.
The points E, F, G, or H.
So, The center of dilation could be G and H .
Therefore, The points G and H is the center of dilation from the points E, F, G, or H
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What are these fashions are called?
the second hand of a clock is 8 centimeters long. find the linear speed of the tip of this second hand as it passes around the clock face.
The linear speed of the tip of this second hand as it passes around the clock face is 0.84 cm/ seconds
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
speed = x /tLength of a circle = 2*pi*rWhere:
x = distancet = timespeed = velocityr = radiusInformation about the problem:
pi = 3.14r = 8 cmt = 60 secondsv = ?As the distance in the problem will be the circumference of the circle that second-hand makes in one complete revolution, we have:
Length of a circle = 2*pi*r
Length of a circle = 2*3.14*8
Length of a circle = 50.24 cm
The time it takes to complete one full revolution by second hand is 60 seconds, so applying the velocity formula with this time, we get:
speed = x /t
speed = 50.24 cm/ 60 seconds
speed = 0.84 cm/ seconds
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Rewrite in simplest terms: -4(-3t-10t-7)-t
Answer:The mathematical expression -4(-3t-10t-7)-t can be simplified to -4( -13t - 7 ) - t . This can be simplified even further by combining like terms to -4( -13t - 7) - 1t .
Step-by-step explanation:
Which of the following is equivalent to
O A 1 + √5
2
OB. 1-√√5
2
O C. √5-1
2
OD √5-2
2
1 + √5
2
The equivalent expression is (a) 1 + √5
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
√5 + 1
The additive property of equality states that
a + b = b + a
using the above as a guide, we have the following:
√5 + 1 = 1 + √5
This means that the equivalent of √5 + 1 is 1 + √5
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Complete question
Which of the following is equivalent to √5 + 1
O A 1 + √5
OB. 1-√√5
O C. √5-1
OD √5-2
ariel bought several bags of caramel candy and several bags of taffy. the number of bags of taffy was more than the number of bags of caramels. taffy bags weigh ounces each, and caramel bags weigh ounces each. the total weight of all the bags of candy was ounces. how many bags of candy did she buy?
She buys 15 bags of candy.
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
Given that the number of bags of taffy was 5 more than the number of bags of caramels.
The Taffy bags weigh 8 ounces each, and the caramel bags weigh 16 ounces each.
The total weight of the bags of candy was 400 ounces.
Consider c be the total number of Carmel candy bags and t the total number of taffy bags that Ariel bought.
t = 5 + c
Then, we have:
8t + 16c = 400
8(5 + c) + 16c = 400
40 + 8c + 16c = 400
24c = 360
c = 15.
Hence, she buys 15 bags of candy.
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Complete the rule that describes the translation.
Answer:
(2,4)
Step-by-step explanation:
The point that's on the origin (0,0) goes to the right by 2 which is your x-axis and goes up 4 which is your y-axis.
Answer:
Translation: (2,4)
Step-by-step explanation:
The dot/point that's in the middle which is always (0,0) goes to the right by 2 (x-axis) meaning that the first coordinate would be 2. It then goes up 4 (y-axis) meaning that the second coordinate would be 4.