The inequality is (3,∞) < x < 4.
What is an inequality?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Given Data
x is a number less than 4
x<4
Numbers which are less than 4 are 3 to infinity
So,
The inequality is:
(3,∞) < x < 4
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1. What is the equation of an ellipse with center, (h, k) that is elongated in the x-direction?
The equation of an ellipse with center, (h, k) that is elongated in the x-direction is: (x - h)²/a² + (y - k)²/b² = 1.
What is defined as the ellipse?In aspects of locus, an ellipse is the collection of every point on an XY-plane with whom the distance from 2 fixed points (called foci) adds up to the a constant value.
Ellipse does have two focal points, which are also known as foci.A fixed distance is referred to as a directrix.The eccentricity of an ellipse ranges from 0 to 1.The total sum of every distance from an ellipse's locus to its two focal points is constant.Ellipse contains a single major and one minor axis, as well as a center.The standard form of equation of ellipse with centres (h, k) that is elongated in the x-direction is given as;
(x - h)²/a² + (y - k)²/b² = 1
Now, when the centre of the ellipse coincides with the origin of coordinates axis, the becomes;
x²/a² + y²/b² = 1
Thus, the equation of ellipse of obtained.
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for a certain company, a train coming from new york to washington dc takes 3 hours to travel 228 miles. a new train company is able to complete the same journey in only 2.5 hours. how much faster is the new company’s train in terms of miles per hour?
A.) 7.5
B.) 11.7
C.) 15.2
D.) 17.3
E.) 21.4
Answer:
The new company’s train is C. 15.2 miles faster.
Step-by-step explanation:
Train A: 228/3 = 76 miles per hour
Train B: 228/2.5 = 91.2 miles per hour
91.2 - 76 = 15.2
How many square feet of outdoor carpet will
we need for this hole?
36ft^2 square feet of outdoor carpet we will need for this hole.
How to find the square feet of carpet needed?Big square: Length = 6 ft ; Width = 4 ft
Small square: Length = 6 ft ; Width = 2 ft
Area = L x W
Big square: 6 * 4 = 24 ft^2
Small square: 6 * 2 = 12ft^2
On adding both, we get
Total area = 24 + 12 = 36ft^2
36ft^2 square feet of outdoor carpet we will need for this hole.
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Use the equation below to find p, if a=16,b=9, and c=13
The value of p when a = 16, b = 9 and c = 13 is 38
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Given that:
p = a + b + c
Substituting the values of a, b and c:
p = 16 + 9 + 13
p = 38
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?:12 =7:14 what is the answer
Answer:
I believe the answer is 6:12. . .
Step-by-step explanation:
I think that 7:14 equals 1:2 in its simplest form. 6:12 also is equivalent to 1:2. 1:2 = 1:2.
A triangle is dilated by a factor of 2 and then rotated clockwise. Which statement about the triangle's image and pre-image is correct?
The correct statement about the triangle's image and pre-image is 'the image and pre-image are not congruent because one of the transformation is rigid transformation and the other is not.'
The correct answer is an option (1)
In this question, a triangle is dilated by a factor of 2 and then rotated clockwise.
We need to select the correct statement about the triangle's image and pre-image.
We know that rotation is a rigid transformation but dilation is not a rigid transformation.
Dilation does not preserve the size of the image.
Also, the image and pre-image are not congruent as the corresponding sides of triangle's image and pre-image are not equal.
Therefore, the correct statement about the triangle's image and pre-image is 'the image and pre-image are not congruent because one of the transformation is rigid transformation and the other is not.'
The correct answer is an option (1)
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What value of c in the equation cx+4y=12 would give the equation a slope of 8?
Please provide all work and steps you used to find your answer, or the answer is pretty much useless. Thank you!
The value of c in the equation cx+4y=12 would give the equation a slope of 8 would be 32.
What is the slope of a straight line?A straight line of the form y = MX + c has its slope as 'm'
It is constant for a line. The more the slope is, the steeper the line is.
Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have a negative slope. The horizontal line has 0 slopes and the vertical line has an infinite slope, as it is now at maximum steepness.
We have been given the equation cx+4y=12 which has a slope of 8.
Also cx+4y=12
4y = 12 - cx
y = 12/4 - cx/4
y = 3 - cx/4
Then we know that straight line of the form y = mx + c
By comparing the formula;
y = 3 - cx/4
Slope = c/4 = 8
c/4 = 8
c = 8(4)
c = 32
Therefore, the value of c in the equation cx+4y=12 would give the equation a slope of 8 would be 32.
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A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is purple.
Answer: 32/139
Step-by-step explanation:
42+45+20+32=139
32/139
Dad is getting food ready for my birthday party! Including me, there will be 18 people at the party. Dad is baking cookies for us! He can bake 24 cookies per batch. How many batches should should I tell dad to make so we can have 4 cookies?
Okay so we have 18 ppl we want 4 cookies per person
in one batch we can make 24
first multiple 18 by 4 or vice versa
answer is 72
now divide 72 by 24
answer is 3
we need 3 batches to make 4 cookies per person
assume that the traffic to the web site of smiley’s people, inc., which sells customized t-shirts, follows a normal distribution, with a mean of 4.56 million visitors per day and a standard deviation of 720,000 visitors per day. (a) what is the probability that the web site has fewer than 5 million visitors in a single day? if needed, round your answer to four decimal digits
The probability that the web site has fewer than 5 million visitors in a single day is 0.7293.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 5 million
μ = mean = 4.56 million
σ = standard deviation = 720,000
z-score = (5 million - 4.56 million) / 720,000
z-score = 440,000 / 720,000
z-score = 0.6111
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0.6111
Using interpolation of values,
probability = 0.7293
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PLEASE HELP ASAP!!!!!!!!
(03.03 MC)
The table represents a continuous exponential function f(x). XE 2 3 4 5 f(x) 9 3 1 Graph f(x) and identify the y-intercept.
A.9
B.15
C.36
D.3
E.81
Answer: B. (15)
Y= -[tex]\frac{3}{1}[/tex]x + 15
Step-by-step explanation:
In the Table we see a f(x) decreasing by 3 for every 1 (x)
So we Have a Slope of -3(y) over 1(x)
Use the equation below to find a, if b=3 and h=4
A= bh
PLS HELP :(
Ed buys a vase for £24 and adds 25% onto price before putting it into his shop window
What price does the price tag say in the window
Answer:
£30
Step-by-step explanation:
Percentage = Division
24 × 25% or 24 ÷ 4
= 6
6 + 24
= 30
Please help me with this please
Answer:
Shark 4
Step-by-step explanation:
It has the lowest value
is 3/10 = 15/60 a equivalent ratios?
Answer: No.
Step-by-step explanation:
3 x 5 = 15,
but 10 x 5 = 50.
In order for the ratios to be equivalent, they would have to be written like this:
3/10 = 15/50
Therefore, it is not equivalent.
Hope this helps!
The cost to rent skis is $30 per hour plus a nonrefundable $25 deposit
A) Write an expression to rent skis for H hours
B)use the expression in part a to find the cost of renting skis for four hours
Answer:
A) 30 x ? = ? + 25 = ?.
B) 30 x 4 = 120. 120 + 25 = 145.
Answer: The answer is $145 to rent the skis for four hours.
which property is represented below
Answer : Transitive Property
If that's not correct, try Symmetric or substitution cause I know it's not reflexive
What ratio is equivalent to 7:6
Answer: 14 : 12
Step-by-step explanation:
Answer: 14:12
Step-by-step explanation: To find the ratio, you would either multiply or divide the two numbers by the same number, and you would get a simplified ratio or an equivalent one. Because 7:6 is simplified, we have to find an equivalent ratio, meaning we multiply. If we multiply 7 by two, we get 14. Multiply 6 by two to get 12. So, the answer is 14:12. Divide both 14 and 12 by two to get back to 7:6.
Automated manufacturing operations are quite precise but still vary, often with distribution that are close to Normal. The width in inches of slots cut by a milling machine follows approximately the N(0.97,0.001)
N(0.97,0.001) distribution. The specifications allow slot widths between 0.9698
0.9698 and 0.9702
What proportion of slots meet these specifications?
The proportion of slots who meet these specifications is 15.86%.
We are given that the width in inches of slots cut by a milling machine follows approximately the N(0.97,0.001) distribution.
Also, the specifications allow slot widths between 0.9698 and 0.9702
Let X = width in inches of slots cut by a milling machine
The z-score probability distribution for normal distribution is given by;
Z = (X - μ) /σ ~ N(0,1)
where, μ = population mean width = 0.97
σ = standard deviation = 0.001
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
Now, Probability that the specifications allow slot widths between 0.9698 and 0.9702 is given by = P(0.9698 < X < 0.9702)
= P(0.9698 < X < 0.9702) = P(X < 0.9702) - P(X 0.9698)
P(X < 0.9702) = P [(X - μ) /σ < [tex]\frac{0.9702 - 0.97}{0.001}[/tex]] = P (Z < 0.2) =
P(X ≤0.9698) = P [(X - μ) /σ ≤ [tex]\frac{0.9698 - 0.97}{0.001}[/tex] ] = P (Z ≤ -0.2) = 1- P(Z < 0.2)
= 1 - 5793 = 0.4207
So, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.2 in the z table which has an area of 0.5793.
Therefore, P(0.9698 < X < 0.9702) = 0.5793 - 0.4207 = 0.1586
Hence, the proportion of slots who meet these specifications is 15.86%.
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Numbers in front of variables
4a - 8b+ C
What's the coefficient for b in the above expression?
Answer
Submit
Answer:
- 8
Step-by-step explanation:
the coefficient is the numeric value, including the sign, in front of the variable.
4a - 8b + c
the coefficient of b is - 8
justina needs to dilate traiangle ABC using a scale factor of 1.5
Using the rule for a dilation, it is found that:
1. The table with the coordinates is given by the first image.
2. The graph of the dilated triangle is given by the second image.
3. The rule is: (x,y) -> (1.5x, 1.5y).
What is the effect of a dilation of a figure?When a figure is dilated by an scale factor of a, each vertex of the figure is multiplied by the scale factor of a, hence the rule is given by the following vector:
(x,y) -> (ax, ay).
The coordinates of the vertices of the pre-image are given as follows:
A(-2, -2), B(2,2), C(4, -2).
The dilation has a scale factor of 1.5, hence the rule for the calculation of each vertex of the image, considering the pre-image, is given as follows:
(x,y) -> (1.5x, 1.5y).
Then the vertices of the image will be given as follows:
A'(-3, -3), B'(3,3), C'(6, -3).
Each coordinate of A, B and C was simply multiplied by 1/2, and the triangle with these vertices is given by the second image at the end of the answer.
What is the missing information?The problem is incomplete, and is given by the first image at the end of the answer.
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solve for x 7 x + 6 / 4 = 2 x − 3 / 5 Give your answer as an improper fraction in its simplest form.
x = -14/9 is the solution to the equation ( 7x + 6 )/4 = ( 2x − 3 )/5 in a simplified improper fraction form.
What is the value of x in the given equation?Given the data in the question;
( 7x + 6 )/4 = ( 2x − 3 )/5x = ?To solve for x, first we cross multiply
( 7x + 6 )/4 = ( 2x − 3 )/5
5( 7x + 6 ) = 4( 2x − 3 )
Remove the parenthesis using distributive property
7x×5 + 6×5 = 2x×4 − 3×4
35x + 30 = 8x - 12
Collect like terms by moving all terms containing x to the left and all constant terms to the right side of the equation.
35x - 8x = -12 - 30
27x = -12 - 30
27x = -42
Divide both sides by 27
27x/27 = -42/27
x = -42/27
x = -14/9
Therefore, the value of x in the given equation ( 7x + 6 )/4 = ( 2x − 3 )/5 is -14/9.
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Answer:
2/3
Step-by-step explanation:
c(4+3c)-0.75(c+3)
PLEASE EXPLAIN NEED TO SHOW MY WORK ALREADY GOT IT RIGHT JUST NEED TO SHOW MY WORK
Answer:
3.25c + 3c^2 - 2.25.
Step-by-step explanation:
c(4+3c) - 0.75(c+3)
Distribute “c” through the parentheses
4c + 3c^2 - 0.75(c+3)
Distribute “-0.75” through the parentheses
4c + 3c^2 - 0.75c - 2.25
Collect like terms and your answer is
3.25c + 3c^2 - 2.25.
amanda wants to send her dresses to the laundry downstairs, and she wants to keep her cleaning within a budget of . the laundry charges for washing one dress and for ironing one. write an inequality to describe the possible number of dresses that amanda can send to be washed and send to be ironed. if amanda has dresses to be washed, what is the maximum number of dresses that she can send to be ironed? dresses (amanda can send to be ironed).
The maximum number of dresses that Amanda can send to be ironed is 8.
What is defined an inequality?An inequality compares two values to determine whether one is less than, greater than, or merely not equal to the other.a ≤ b shows that a is less than or equal to ba ≥ b shows that a is greater than or equal to b.For the given question;
Total budget of Amanda = $100.
Price of washing = $8 per dress.
Price of ironing = $5 per dress.
Total number of dress to be washed = 7.
Let x be the number of dress to be send for ironing.
The inequality becomes.
5x + 7×8 ≤ 100
5x + 56 ≤ 100; is the required inequality.
For finding the x, equate the value.
5x + 56 ≤ 100
5x ≤ 44
x ≤ 8.8
But x must be less, then.
x = 8 dress.
Thus, the maximum number of dresses that Amanda can send to be ironed is 8.
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The complete question is-
Amanda wants to send her dresses to the laundry downstairs, and she wants to keep her cleaning within a budget of $100 . the laundry charges $8 for washing one dress and for ironing one $5. write an inequality to describe the possible number of dresses that amanda can send to be washed and send to be ironed. if amanda has 7 dresses to be washed, what is the maximum number of dresses that she can send to be ironed? dresses (amanda can send to be ironed).
For every 3 lemons Chrissy buys at a farm stand,
the total cost increases by $1.80.
The constant of proportionality is ?
An equation that relates the total cost, y, and the
number of lemons, x, is y = ? x.
Use the equation you wrote to complete the table.
Table:
Numbers of lemons(x) | Total cost(y)
4 | _?__
_?__ | $4.20
_?__ | $9.00
18 | _?__
Answer:
The constant of proportionality is $1.80
y = 1.80x
Step-by-step explanation:
The constant of proportionality is $1.80
An equation that relates the total cost, y, and the number of lemons, x, is
y = 1.80x
where,
y =Total cost
x = number of lemon
When x = 4
y = 1.80x
y = 1.80(4)
y = 7.2
y = $7.2
When y = $4.20
y = 1.80x
4.20 = 1.80x
x = 4.20 / 1.80
x = 2 1/3
x = 2 1/3
When y = $9.00
y = 1.80x
9.00 = 1.80x
x = 9.00 / 1.80
x = 5
x = 5
When x = 18
y = 1.80x
y = 1.80 × 18
y = 32.4
y = $32.4
Diego and Stacy can paint a doghouse in 5 hours when working together. Diego works twice as fast as Stacy. Let x be the number of hours it would take Diego to paint the doghouse and y be the number
of hours it would take Stacy to paint the doghouse. How long would it take Stacy
to paint the doghouse if she was working alone? How long would it take Diego to paint the doghouse if he was working alone?
Please show steps!
If Stacy works alone, it will take her 11 hours 40 minutes to paint the doghouse.
If Diego works alone, it will take him 5 hours 40 minutes to paint the doghouse.
How to find how long would it take Stacy and Diego to paint the doghouse while working alonegiven data
Diego and Stacy can paint a doghouse in 5 hours
Diego works twice as fast as Stacy
Let x be the number of hours it would take Diego to paint the doghouse and y be the number
Putting the given information mathematically
Diego and Stacy can paint a doghouse in 5 hours
x + y = 5hoursDiego works twice as fast as Stacy
x = 2yx + y = 5hours
Since x = 2y
2y + y = 5
3y = 5
y = 5/3
y = 1 1/3
from x = 2y
x = 2 * 5/3
x = 10/3
x = 3 1/3
1/3 hours is a fraction of hours. we convert it to minutes by multiplying by 60
= 1/3 * 60
= 20 minutes
Therefore it will take Diego 3 hours 20 minutes and Stacy 1 hour 20 minutes for them to complete a 5 hours work
If Diego works alone
Diego alone = 5 hours + Stacy's hours * 1/2
since Diego is twice faster than Stacy then Stacy's time will be halved
Diego alone = 5 hours + 80 minutes * 1/2
Diego alone = 5 hours + 40 minutes
Diego alone = 5 hours 40 minutes
if Stacy works alone
Stacy alone = 5 hours + Diego's hours * 2
Stacy alone = 5 hours + 3 hours 20 minutes * 2
Stacy alone = 5 hours + 6 hours 40 minutes
Stacy alone = 11 hours 40 minutes
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Shaniece took a taxi from her house to the airport. The taxi company charged a pick-up fee of $3.40 plus $3.50 per mile. The total fare was $80.40, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride.
Please help!!!!!!!!!
Answer:
f(-4) = 19
Step-by-step explanation:
Since -4 < 1, we need to use the bottom part of the function:
[tex]f( - 4) = {( - 4)}^{2} + 3 = 16 + 3 = 19[/tex]
Find irrational number, which is more than 0,6(3) and less than 0,64.
An irrational number that lies between the two given ones, 0.6333.... and 0.64 is:
√7 - 2.01 =0.63575...
How to find an irrational number between the two given ones?Remember that an irrational number is a number that can't be written as the quotient between two integers.
Here we want to find two numbers between 0.6333 (where the 3 repeats infinitely) and 0.64
So we cold try to find a number like:
6.3349412490184...
Such that there is no pattern (because if there were a pattern, it would not be an irrational number).
An example of this can be, for example:
√7 = 2.64575...
This is an irrational number.
Now, if we subtract 2.01 from that we will get:
√7 - 2.01 = 2.64575... - 2.01 = 0.63575...
This is an irrational number and lies between the two given ones, then we conclude that √7 - 2.01 =0.63575... is a correct option.
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please help me with question 19 please i really need the answer asap!! thanks!!
Answer:
D) 116
Step-by-step explanation:
Supplementary angles add up to 180°
∠CDE + ∠FDE = 180
3x + 10 + 6x + 8 = 180
3x + 6x + 10 + 8 = 180
Combine like terms,
9x + 18 = 180
Subtract 18 from both sides,
9x = 180 - 18
9x = 162
Divide both sides by 9
x = 162 ÷ 9
[tex]\sf \boxed{\bf x = 18}[/tex]
∠FDE = 6x + 8
= 6*18 + 8
= 108 + 8
= 116°