The solution set to inequality |x + 2| > 2 is equal to x < - 4 or x > 0, whose interval notation is x ∈ (- 4, 0).
How to solve an inequality involving an absolute value
In this problem we find the definition of the following inequality, whose solution set must be found:
|x + 2| > 2
First, use the definition of absolute value to eliminate bars:
x + 2 < - 2 or x + 2 > 2
Second, clear x on each expression:
x < - 4 or x > 0
Third, write the solution set in interval notation:
x ∈ (- 4, 0)
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Alex Murphy purchased a TV with surround sound and remote control on an installment plan with a 60 down payment and 12 payments of $104.63. Find the installment price of the TV.
The installment price of the TV is $1,195.56.
To find the installment price of the TV, we need to calculate the total amount paid over the installment period.
The down payment is $60, and there are 12 monthly payments of $104.63 each.
Total amount paid over 12 months = Monthly payment x Number of payments
= $104.63 x 12
= $1,255.56
Now, we can calculate the installment price by subtracting the down payment from the total amount paid:
Installment price = Total amount paid - Down payment
= $1,255.56 - $60
= $1,195.56
Therefore, the installment price of the TV is $1,195.56.
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( MAKE YOUR OWN COMIC AND SOLVE IT SHOWING WORK) THE COMIC HAS TO BE ALIKE TO THE EXAMPLE NOT THE SAME THING BUT DIFFERENT CHARATER DIFFERENT TRIG PROBLEMS
To create another comic out of the scenario is as follows: An eagle is chasing a bird and spots it on top of a 10ft tree and is looking at it at an angle of elevation of 30° degrees.
How to calculate the distance the eagle needs to catch the bird?To calculate the distance, the trigonometric sine law needs to be obeyed and the formula is written below as follows.
a/sinA = b/sinB
where;
a= 10ft
A= 30°
b= ?
B= 90°
That is;
10/sin30° = b/sin90°
make b the subject of formula;
b = 10×sin90°/sin30°
= 10×1/0.5
= 20ft
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-1
-2
The lengths of movie files that are available for streaming are modeled using the normal distribution shown below.
The mean of the distribution is 170.8 min and the standard deviation is 19.7 min.
100
in the figure, Vis a number along the axis and is under the highest part of the curve.
And, U and Ware numbers along the axis that are each the same distance away from V.
Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W.
Continue
3
0
U
120
Percentage of total area shaded: (Choose one)
140
160
180
V
Time (in min)
200
220
0 240
W
3
Answer:
the best value for the percentage of the area under the curve that is shaded is 68%.
Step-by-step explanation:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean is 170.8 min and the standard deviation is 19.7 min, we can calculate the values of U, V, and W.
U: U is one standard deviation below the mean.
U = Mean - 1 * Standard Deviation
U = 170.8 - 1 * 19.7
U ≈ 151.1
V: V is the mean.
V = Mean
V = 170.8
W: W is one standard deviation above the mean.
W = Mean + 1 * Standard Deviation
W = 170.8 + 1 * 19.7
W ≈ 190.5
Now, let's determine the best value for the percentage of the area under the curve that is shaded. Based on the empirical rule, the highest percentage that can be shaded is approximately 68% since it represents the data within one standard deviation of the mean.
Therefore, the best value for the percentage of the area under the curve that is shaded is 68%.
A point (3, 4) is the point of intersection of the diagonals of the parallelogram, two of whose consecutive corners are at the points (3, 2) and (5, 10). Find the co-ordinates of the remaining corners
The coordinates of the remaining corners are (2, 2) and (2, 10).
To find the coordinates of the remaining corners of the parallelogram, we can use the fact that the diagonals of a parallelogram bisect each other.
Let's call the point of intersection of the diagonals as (3, 4). The midpoint of one diagonal is the same as the midpoint of the other diagonal.
First, let's find the midpoint of the diagonal connecting (3, 2) and (5, 10). The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Applying this formula, we find the midpoint as (4, 6).
Since the point (3, 4) is the midpoint of the other diagonal, we can use this information to find the coordinates of the remaining corners.
If we reflect the point (4, 6) across the point of intersection (3, 4), we will obtain the coordinates of the remaining corners.
Reflecting (4, 6) across (3, 4), we get:
(4 - 2, 6 - 4) = (2, 2)
Therefore, the remaining corners of the parallelogram are (2, 2) and (2, 10).
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Find the coordinates for the midpoint of the segment with the endpoints given.
(5, 6) and (8, 2)
A bag contains 7 red, 12 white and 4 green balls. Three balls are drawn randomly. What probability that (a) 3 balls are all white (b) 3 balls are one of each color (c) 3 balls are same color
(a) Probability that 3 balls are all white:
Step 1:
Total balls = Number of red balls + Number of white balls + Number of green balls = 7 + 12 + 4 = 23.
Step 2:
Total ways to choose 3 balls = C(23, 3) = 23! / (3 * (23-3) ) = 23 / (3 * 20) = (23 * 22 * 21) / (3 * 2 * 1) = 1771.
Step 3: Calculate the number of ways to choose 3 white balls out of 12:
Number of ways to choose 3 white balls = C(12, 3) = 12 / (3 * (12-3) ) = 12 / (3 * 9) = (12 * 11 * 10) / (3 * 2 * 1) = 220.
Step 4: Calculate the probability of selecting 3 white balls:
Probability = Number of ways to choose 3 white balls / Total ways to choose 3 balls = 220 / 1771 ≈ 0.1241.
Therefore, the probability that 3 balls drawn are all white is approximately 0.1241.
(b) Probability that 3 balls are one of each color:
Step 1: Calculate the total number of balls in the bag (same as above): Total balls = 23.
Step 2: Calculate the total number of ways to choose 3 balls out of 23 (same as above): Total ways to choose 3 balls = 1771.
Step 3: Calculate the number of ways to choose 1 ball of each color:
Number of ways to choose 1 red, 1 white, and 1 green ball = Number of red balls * Number of white balls * Number of green balls = 7 * 12 * 4 = 336.
Step 4: Calculate the probability of selecting 3 balls of different colors:
Probability = Number of ways to choose 1 ball of each color / Total ways to choose 3 balls = 336 / 1771 ≈ 0.1899.
Therefore, the probability that 3 balls drawn are one of each color is approximately 0.1899.
(c) Probability that 3 balls are of the same color:
Step 1: Calculate the total number of balls in the bag (same as above): Total balls = 23.
Step 2: Calculate the total number of ways to choose 3 balls out of 23 (same as above): Total ways to choose 3 balls = 1771.
Step 3: Calculate the number of ways to choose 3 balls of the same color:
Number of ways to choose 3 red balls = C(7, 3) = 7 / (3 * (7-3) ) = 7 / (3 * 4 ) = (7 * 6 * 5) / (3 * 2 * 1) = 35.
Number of ways to choose 3 white balls = C(12, 3) = 220.
Number of ways to choose 3 green balls = C(4, 3) = 4.
Step 4: Calculate the probability of selecting 3 balls of the same color:
Probability = (Number of ways to choose 3 red balls + Number of ways to choose 3 white balls + Number of ways to choose 3 green balls) / Total ways to choose 3 balls = (35 + 220 + 4) / 1771 ≈ 0.1416.
Therefore, the probability that 3 balls drawn are of the same color is approximately 0.1416.
Answer:
12 white balls2323Step-by-step explanation:
(a) Probability that 3 balls are all white:
Total number of balls = 7 red + 12 white + 4 green = 23
Number of favorable outcomes = 12 white balls
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 12 / 23
(b) Probability that 3 balls are one of each color:
Total number of balls = 7 red + 12 white + 4 green = 23
Number of favorable outcomes = 7 red balls * 12 white balls * 4 green balls
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (7 * 12 * 4) / (23 * 22 * 21)
(c) Probability that 3 balls are the same color:
Total number of balls = 7 red + 12 white + 4 green = 23
Number of favorable outcomes = (7 red balls * 6 red balls * 5 red balls) + (12 white balls * 11 white balls * 10 white balls) + (4 green balls * 3 green balls * 2 green balls)
Which graph represents the function f(x) = −|x − 2| − 1?
Answer:
The graph representing the function f(x) = −|x − 2| − 1 is a downward-opening V-shaped graph that is shifted 2 units to the right and 1 unit downward from the standard absolute value function |x|.
Step-by-step explanation:
Here is a description of the graph and its key points:
The vertex of the graph is located at the point (2, -1), which represents the minimum point of the graph.
The graph approaches negative infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.
The graph is symmetric with respect to the vertical line x = 2.
Please note that I cannot display images directly, but you can search for "graph of f(x) = −|x − 2| − 1" on an online graphing tool or use a graphing calculator to visualize the specific graph.
The relation of a line graph is visualized by drawing
lines between all of the points on a grid.
The relation of a line graph is visualized by drawing lines between all of the points on a grid is false.
What is a line graph?A line graph is a type of graph that uses lines to connect data points. The points are typically plotted on a grid, but the lines do not need to connect all of the points. In fact, it is often more helpful to only connect the points that are relevant to the data that you are trying to visualize.
For example, when graphing temperature over time, there is only need to connect the points that represent the temperature at each hour. There is no need to connect the points that represent the temperature at midnight, 2am, 4am, etc.
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Complete question:
The relation of a line graph is visualized by drawing lines between all of the points on a grid. Is this true or false? Explain your answer.
the diameter of a circular hoop is 30 cm. What distance will it travel if it makes 80 revolutions? Take pie= 3.14
Answer ASAP
4,, and C represent three different numbers from 2 through 5. What is the SMALLEST possible value of the entire expression below?
Show your work.
10 - A B/C
The smallest possible value of the entire expression is 7.5, which occurs when A = 5, B = 2, and C = 4.
We are given the three different numbers 4, and C represent three different numbers from 2 through 5 and we have to find out the smallest possible value of the entire expression 10 - A B/C.
To find the smallest possible value, we need to take the greatest value of A, the smallest value of B, and the smallest value of C.
The given number 4 is in between 2 and 5, so it cannot be the greatest value.
Therefore, A must be 5. Now, the other two numbers must be chosen from the remaining three numbers 2, 3, and 4.
We need to choose the smallest possible value of B and C to make the entire expression the smallest. The smallest value of B is 2.
Now, we need to choose the smallest possible value of C. If C is 4, then the entire expression becomes:10 - 5(2/4) = 10 - 2.5 = 7.5If C is 5, then the entire expression becomes:10 - 5(2/5) = 10 - 2 = 8
Thus, the smallest possible value of the entire expression is 7.5.
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Write an algebraic expression to represent the given phrase. Use x as the variable to
represent the unknown quantity.
8. The sum of a number and 20
9. The product of a number and 20
10. The quotient of 20 and a number
11. The difference of a number and 20
Choices for 8-11:
A) 20-x
D) x + 20
B) 20x
20
X
E)
C) X-20
X
20
AB)
Answer:
8) x + 20
9) 20x
10) 20/x
11) x-20
Step-by-step explanation:
8) x + 20
9) 20x
10) 20/x
11) x-20
Solve 3x + 6 = 34
Answers:
−2
4
6
10
Answer:
To solve the equation 3x + 6 = 34, we need to isolate x on one side of the equation.
First, we can start by subtracting 6 from both sides of the equation to get:
3x + 6 - 6 = 34 - 6
Simplifying this, we get:
3x = 28
Next, we divide both sides by 3 to isolate x:
3x/3 = 28/3
Simplifying this, we get:
x = 28/3
This is not one of the answer choices listed. However, we can approximate the answer to the nearest integer. Using a calculator, we get:
x ≈ 9.333
Rounding to the nearest integer, we get:
x ≈ 9
Therefore, the answer closest to the solution of the equation 3x + 6 = 34 is 10.
A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
.
The maximum number of tables the restaurant can have is 37. This ensures that the total number of people seated at the tables (37 * 4 = 148) is less than the legal limit of 150 people in the restaurant at one time.
To find the maximum number of tables the restaurant can have, we need to solve the inequality 4t < 150.
Dividing both sides of the inequality by 4, we have:
t < 150/4
Simplifying the right side, we get:
t < 37.5
Since the number of tables must be a whole number, we can conclude that the maximum number of tables the restaurant can have is 37.
Let's verify this by substituting t = 37 into the original inequality:
4t < 150
4(37) < 150
148 < 150
Since 148 is less than 150, the inequality holds true. However, if we increase the number of tables to 38, we get:
4(38) < 150
152 < 150
In this case, 152 is not less than 150, so the inequality is no longer satisfied.
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What is the length of side s of the square shown below?
45
90°
OA. 1
OB. 2
OC. 2.2
OD. 4
OE. E
F. 4.2
Answer:
E
Step-by-step explanation:
using Pythagoras' identity on the lower right triangle , with legs s and hypotenuse 2 , then
s² + s² = 2²
2s² = 4 ( divide both sides by 2 )
s² = 2 ( take square root of both sides )
s = [tex]\sqrt{2}[/tex]
Rewrite each fraction with a denominator of 12.
3
4
5
3
The equivalent fractions with a denominator of 12 are
3/4 = 9/125/3 = 20/12How to rewrite the fractionsTo rewrite each fraction with a denominator of 12, we need to find an equivalent fraction that has 12 as its denominator.
3/4 can be rewritten as (3/4) * (3/3) = 9/12.
5/3 can be rewritten as (5/3) * (4/4) = 20/12.
Therefore, the fractions with a denominator of 12 are:
3/4 = 9/12
5/3 = 20/12
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complete questions
Rewrite each fraction with a denominator of 12.
3/4
5/3
PLEASE HELP!
See the image below!
Answer:
A ≈ 199.98
Step-by-step explanation:
the area (A) of Δ ABC can be calculated as
A = [tex]\frac{1}{2}[/tex] ab sinΘ ( substitute values for a, b and Θ )
= [tex]\frac{1}{2}[/tex] × 25 × 33 × sin29°
= 12.5 × 33 × sin29°
≈ 199.98 ( to 2 decimal places )
please see photo thank you
Answer:
look below
Step-by-step explanation:
formula A=1/3 Bh
1/3 ×8×5×5
8x5x5=200
200/3=66.66666 round to 66.77cubic metets
Find the enclosed area within the boundaries defined by the equations
x = 2y^2− 6, x = 2 − 1/3y, y= 7 and y= −3. Can someone help me plss
Answer: sorry I can't help you
Step-by-step explanation:
The enclosed area can be found by plotting the given equations, finding the points of intersection, establishing the boundaries, and then calculating the integral of the difference between the two functions within these boundaries.
∫7-3[ (2-1/3*y) - (2y² - 6) ] dy
Explanation:
To find the enclosed area within the boundaries defined by the equations x = 2y²- 6, x = 2 – 1/3y, y= 7 and y= -3, you would firstly have to plot these equations on a plane, observe their intersection points and identify the boundaries of the area enclosed.
Then, the enclosed area can be calculated by integrating the difference between the two functions within those points where y = -3 to y = 7. Once you've done that, you calculate the definite integral of each of the functions separately from y = -3 to y = 7 and subtract the results. Here's the computation:
∫7-3[ (2-1/3*y) - (2y² - 6) ] dy
Calculating this integration will give you the area enclosed within the boundaries defined by these equations.
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The area of a kindergarten classroom is 972 square feet. How many square yards is that? (There are 9 square feet in a square yard.)
Answer:
972 ft²(1 yd²/9 ft²) = 108 yd²
Simplify and then evacuate by plugging in the vaules of A, B, C, and/or D
A = 8
B = 10
C =16
D = 11
Evaluating the expression results to
A - 2(B - A) - 3B simplifies to --18C(4 - D) + 2CD simplifies to 240How to evaluate the expressionsTo simplify the given expressions, we substitute the values of A, B, C, and D into the expressions and perform the necessary calculations.
A - 2(B - A) - 3B:
Substituting the values:
8 - 2 * (10 - 8) - 3 * 10
Simplifying the expression inside parentheses
8 - 2(2) - 3 * 10
8 - 4 - 30
Performing subtraction
8 - 4 - 30
-18
Therefore, A - 2(B - A) - 3B simplifies to --18
evaluate the second expression C(4-D)+2CD:
C = 16
D = 11
Substituting the values:
16(4 - 11) + 2(16)(11)
Simplifying
16(-7) + 2(16)(11)
-112 + 352
240
Therefore, the value of the expression C(4-D)+2CD, when C = 16 and D = 11, is 240.
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Dilation D was performed on a rectangle. How does the image relate to the pre-image? Select three options
v.²/
The image is a reduction because 0
The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.
The angles of the image are two-fifths the size of the angles of the pre-image.
O The center of dilation is at point Q.
The base of the image is two-fifths the size of the base of the pre-image.
The true statements are
The base of the image is two-fifths the size of the base of the pre-image.The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The image is a reduction because 0 < n < 1How to get the true statementsDilation was performed on a rectangle with a center of dilation at point V. We will evaluate the given options to determine their accuracy:
Option 1: The image is a reduction because 0 < n < 1 (True)
Explanation: Since the dilation factor is 2/5, this is less than 1, the resulting image will be smaller than the original rectangle. Therefore, this option is true.
Option 2: This is true. Dilation preserves the proportional relationship between corresponding sides of similar shapes. Since the dilation factor is 2/5, the side lengths of the image will be two-fifths the length of the corresponding side lengths of the pre-image. Therefore, this option is true.
Option 5: is true Since the dilation factor is 2/5, the base of the image will be two-fifths the length of the base of the pre-image. This is in line with the proportional relationship preserved by dilation. Therefore, this option is true.
In summary, options 1, 2, and 5 are true, while options 3 and 4 are false.
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question
Dilation D Subscript V, two-fifths was performed on a rectangle. How does the image relate to the pre-image? Select three options. The image is a reduction because 0 < n < 1. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The angles of the image are two-fifths the size of the angles of the pre-image. The center of dilation is at point Q. The base of the image is two-fifths the size of the base of the pre-image.
Which description does NOT guarantee that a quadrilateral is a parallelogram?
a quadrilateral with consecutive angles supplementary
a quadrilateral with the diagonals bisecting each other
a quadrilateral with both pairs of opposite sides congruent
quadrilateral with two opposite sides parallel
The description that does NOT guarantee that a quadrilateral is a parallelogram is:
a quadrilateral with consecutive angles supplementary.Why the statement is not a guaranteeWhile it is true that consecutive angles in a parallelogram are supplementary (their sum is 180 degrees), the converse is not true. In other words, having consecutive angles that are supplementary does not necessarily imply that the quadrilateral is a parallelogram.
There are other types of quadrilaterals, such as trapezoids or irregular quadrilaterals, that can also have consecutive angles that are supplementary.
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Please help me with this
he square of 9 less than a number is 3 less than the number. What is the number? –12 or 7 –12 or –7 –7 or 12 7 or 12
Answer:
I thing its 7- 12 sorry if wrong
Step-by-step explanation:
Please help with the attached math problem.
{-2, 3, 2, 4, -3} what is the range?
Answer: 7
Step-by-step explanation:
The range of a set of numbers is the difference between the highest and lowest numbers in that set.
For the given set, the highest number is 4 and the lowest number is -3.
So, the range is 4 - (-3) = 7.
A rectangular piece of paper measures 280 cm by 140 cm . How many circles of radius 7 cm can be cut out from it?
Take pie = 22/7
Answer ASAP
Work Shown
rectangle area = length*width = 280*140 = 39,200 square cm
circle area = pi*r^2 = (22/7)*(7)^2 = 154 square cm
Divide the two areas
39200/154 = 254.54545 approximately
That rounds down to 254
Rounding to 255 will not work because there won't be enough paper for that 255th circle
Is triangle fgh similar to triangle jkl? If so, identify the similarity postulate or theorem that applies. (Please help!!!)
The similarity of the triangles cannot be determined
How to identify if the triangles are similarFrom the question, we have the following parameters that can be used in our computation:
The triangles (see attachment)
The triangles are given as
FGH and JKL
Where we have
A pair of corresponding angle
Also, we have
A pair of similar side
There are no other parameters to determine if the triangles are similar or not
This means that the similarity cannot be determined
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A 450 ft by 280 ft land will be fenced; a roll of 5 ft fence has a length 60 ft and costs $60.00; tax is 9.5%; Dan will charge ¼ of the cost te credit card; how much will he pay in cash?
Dan will pay approximately $1231.87 in cash for the fence.
To determine how much Dan will pay in cash for the fence, we need to calculate the total cost of the fence, apply the tax, and then determine the portion that will be paid with a credit card.
Dimensions of the land to be fenced: 450 ft by 280 ft
Length of a roll of fence: 60 ft
Cost of a roll of fence: $60.00
Tax rate: 9.5%
Portion to be paid with a credit card: 1/4 (or 25%)
First, let's calculate the total perimeter of the land to determine how many rolls of fence are needed:
Perimeter = 2 [tex]\times[/tex] (Length + Width)
Perimeter = 2 [tex]\times[/tex] (450 ft + 280 ft)
Perimeter = 2 [tex]\times[/tex] 730 ft
Perimeter = 1460 ft
Since each roll of fence is 60 ft long, the number of rolls needed is:
Number of rolls = Perimeter / Length of a roll
Number of rolls = 1460 ft / 60 ft
Number of rolls ≈ 24.33 rolls
Since we can't purchase a fraction of a roll, we need to round up to the nearest whole number of rolls.
Thus, we need to purchase 25 rolls.
The total cost of the fence without tax is:
Total cost = Number of rolls [tex]\times[/tex] Cost per roll
Total cost = 25 rolls [tex]\times[/tex] $60.00 per roll
Total cost = $1500.00
Now, let's calculate the tax amount:
Tax amount = Total cost [tex]\times[/tex] Tax rate
Tax amount = $1500.00 [tex]\times[/tex] 9.5% (or 0.095)
Tax amount = $142.50
The total cost including tax is:
Total cost with tax = Total cost + Tax amount
Total cost with tax = $1500.00 + $142.50
Total cost with tax = $1642.50
Finally, let's calculate the portion to be paid with a credit card and the portion to be paid in cash:
Portion paid with credit card = Portion to be paid with a credit card * Total cost with tax
Portion paid with credit card = 25% [tex]\times[/tex] $1642.50
Portion paid with credit card = $410.63
Portion paid in cash = Total cost with tax - Portion paid with credit card
Portion paid in cash = $1642.50 - $410.63
Portion paid in cash = $1231.87
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See the attached two problems, one is consider the augmented matrix and the other is consider the matrix.
The row operations on the augmented matrix are
R₂ → 4R₂R₃ → R₃ + 3What is an augmented matrix?An augmented matrix is a matrix in which the coefficient matrix and the column matrix are written together.
Since we have the augmented matrix
[tex]\left[\begin{array}{ccc}1&3&5\\0&\frac{1}{4} &-1\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\1&\\10&\end{array}\right][/tex]
To determine the next row operations, we proceed as follows.
Since we want to convert the second element in the second row to 1, we multiply row 2 by 4,
So, R₂ → 4R₂
So, the augmented matrix becomes
[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\10&\end{array}\right][/tex]
Now, since we want to convert the first element in the third row to 0, the row operation we perform is we add 3 to row 3
So, R₃ → R₃ + 3
So, the augmented matrix becomes
[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\0&9&-8\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\13&\end{array}\right][/tex]
So, the row operations are
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