The possible values of the number x are any real number that is less than or equal to 103.2. This can be written as: x <= 103.2
Let's call the number "x".
The sum of 4.5 and one-third of x can be written as:
4.5 + (1/3)x
The inequality to represent the statement "the sum is equal to at most 38.9" would be:
4.5 + (1/3)x <= 38.9
To solve for x, we can isolate x by subtracting 4.5 from both sides:
(1/3)x <= 34.4
And finally, multiplying both sides by 3:
x <= 103.2
So, all the possible values of the number x are any real number that is less than or equal to 103.2. This can be written as:
x <= 103.2
or
-∞ < x <= 103.2
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A rectangle has an area of 24 square inches. The rectangle is reduced by a scale factor of 1/2. What is the area of the new triangle?
Answer:
12
Step-by-step explanation:
i hope this is right I suggest you double check
Let △ABC be a right triangle with m∠C = 90°. Given tan ∠B = 0.25, find tan ∠A. tan ∠A =
The solution of the given problem of triangle comes out to be tan ∠A = 0.25.
What exactly does a triangle mean?Triangles are called polygons if they have four quadrants or more. Its form is a simple geometric figure. When put together, the characters ABC create a right-angled triangle. When the boundaries are incompatible, Euclidean geometry generates a new rectangle with square corners. Triangles are regarded as polygons because they have three edges and three corners.
Here,
Since △ABC is a right triangle with m∠C = 90°, we know that m∠A + m∠B = 90°.
Using the fact that tan ∠B = opposite/adjacent, we can set up a ratio using a common factor, x, for the opposite and adjacent sides of ∠B:
tan ∠B = 0.25 = opposite/adjacent = x/4x
Simplifying the right side, we get:
0.25 = x/4x = 1/4
Multiplying both sides by 4x, we get:
x = 4
So the opposite side of ∠B has length x = 4, and the adjacent side has length 4x = 16.
Using the Pythagorean theorem, we can find the length of the hypotenuse of △ABC:
c² = a² + b²
c² = 4²+ 16²
c² = 256
c = √256
c = 16
Now, we can use the fact that tan ∠A = opposite/adjacent to find tan ∠A:
tan ∠A = opposite/hypotenuse = 4/16 = 1/4
Therefore, tan ∠A = 0.25.
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what is the slope of the line shown below? (-2,5) (3,-5)
Answer: -2
Step-by-step explanation: use the slope formula.
THREE QUESTIONS 21POINTS HELP!!!
8. Six boys have heights of 1.53 m, 1.49 m, 1-60 m, 1.65 m, 1.90 m and 1.43 m. (a) Find the mean height of the six boys. (b) Find the mean height of the remaining five boys when the shortest boy leaves.
9. In a maths test the marks for the boys were 9, 7, 8, 7, 5 and the marks for the girls were 6, 3, 9, 8, 2, 2. (a) Find the mean mark for the boys. (b) Find the mean mark for the girls. (c) Find the mean mark for the whole class.
10. Five different drinks have an average (mean) price of £1.50. When a sixth drink is added the new average price is £1.60. How much did the sixth drink cost?
I'll do problem 8 to get you started.
Part (a)
To find the mean, we first add up the values
1.53+1.49+1.60+1.65+1.90+1.43 = 9.6
Then divide over 6 since this is the number of values in the set.
9.6/6 = 1.6
Answer: 1.6 meters==================================================
Part (b)
The shortest boy is 1.43 meters tall. If he leaves the group, then we have these heights leftover
1.53, 1.49, 1.60, 1.65, 1.90
Adding them up gets us
1.53+1.49+1.60+1.65+1.90 = 8.17
Then divide by 5
8.17/5 = 1.634
Answer: 1.634 metersFind the value of x [6x-1] [10x+5]
Answer:
x = 6
Step-by-step explanation:
You want the value of x in the geometry where an angle bisector has divided a triangle into sides 42 and (6x-1), and corresponding sides 78 and (10x+5).
ProportionThe angle bisector divides the sides of the triangle proportionally:
(6x -1)/42 = (10x +5)/78
13(6x -1) = 7(10x +5) . . . . . . . . multiply by 546
78x -13 = 70x +35 . . . . . . . simplify
8x = 48 . . . . . . . . . . . . . . add 13-70x
x = 6 . . . . . . . . . . . . . . divide by 8
Doris and Miguel are saving money weekly but at different rates. Doris
and Miguel both write and graph equations to represent their savings. In
both equations y represents the amount in savings account after x
number of weeks. When the equations are graphed, the lines intersect at
the point (6,114). Which statement best explains the point of
intersection?
Miguel will have $114 more than Doris after 6 weeks.
Doris will have $114 more than Miguel after 6 weeks.
Doris and Miguel will have the same amount after 6 weeks.
Doris and Miguel will have the same amount after 114 weeks.
Answer:
Doris and Miguel will have the same amount after 6 weeks.
Step-by-step explanation:
if 6 is the amount of weeks and 114 is the savings, then the point that the lines will cross at represents 114 dollars after 6 weeks. this means that after six weeks, both doris and miguel will have 114 dollars.
15 more than twice a number is 37. Wht is the number
A number which is 15 more than twice a number is 37 is 11.
Let the number be N.
Let's set up the equation.
A number is 15 more than twice a number is 37,
2N + 15 = 37
Let's subtract 15 from both sides.
2N = 22
Divide both sides by 2, and you get
N = 11
So the number which is 15 more than twice a number is 37 is 11.
A number system is a means of representing numbers. It is a method of representing numbers in a set of numbers consistently by using digits or other symbols. Each number receives a unique representation as well as information about the arithmetic and algebraic structure of the numbers. Addition, subtraction, multiplication, and division are just a few of the mathematical operations we may carry out using it.
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If 6 Gardner's can now the grass of a soccer field in 2 hours how many gardeners can mow the same field in 3 hours
The same field can be mowed in 3 hours by 2 gardeners.
A soccer field may be mowed by 6 gardeners in 2 hours, meaning each one works at a rate of 1/6 of the field per hour.
We must ascertain the rate at which the field can be mowed in 3 hours, which is 1/3 of the field every hour, in order to establish the number of gardeners required to mow the same field in that amount of time.
We divide this rate by the rate of each gardener, which is 1/6 of the field each hour, to determine the required number of gardeners, resulting in the equation 1/3 / 1/6 = 2.
Hence, 2 gardeners can mow the same field in 3 hours.
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I need some help please
Answer:
( 11 )y + ( 1 )z
Step-by-step explanation:
8y + 3y
5z - 4z
a sequence can be defined by an = an-1 + an-2 where a0 = 0 and a1 = 1. What are the first 6 terms of the sequence?
The first six terms of the sequence are 1, 1, 2, 3, 5 and 8. The solution has been obtained by using arithmetic progression.
What is arithmetic progression?
In an arithmetic progression (AP) sequence of numbers, there is always the same amount of difference between any two subsequent integers. Arithmetic Sequence is another name for it.
We are given a sequence as a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + a[tex]_{n-2}[/tex] where a₀ = 0 and a₁ = 1.
So, the first term is a₁ = 1
The second term is
a₂ = a₂₋₁ + a₂₋₂
a₂ = a₁ + a₀
a₂ = 1
The third term is
a₃ = a₃₋₁ + a₃₋₂
a₃ = a₂ + a₁
a₃ = 1 + 1
a₃ = 2
The fourth term is
a₄ = a₄₋₁ + a₄₋₂
a₄ = a₃ + a₂
a₄ = 2 + 1
a₄ = 3
The fifth term is
a₅ = a₅₋₁ + a₅₋₂
a₅ = a₄ + a₃
a₅ = 3 + 2
a₅ = 5
The sixth term is
a₆ = a₆₋₁ + a₆₋₂
a₆ = a₅ + a₄
a₆ = 5 + 3
a₆ = 8
Hence, the first six terms of the sequence are 1, 1, 2, 3, 5 and 8.
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what is the area of the parallelogram
Answer:
9yd^2
Step-by-step explanation:
A = bh
You are given the height of 2yd and a base of 4.5 yd.
A = (2yd)(4.5yd)
= 9yd^2
Answer:
9yd
Step-by-step explanation:
3½²-2²= √8.25=2.8
4.5-2.87=1.63
½×2.87×2=2.87
½(4.5+1.63)2=6.13
6.13+2.87=9yd
Identify the like terms in the expression:
-12x +15y -17x +16y
Travis decided to make a frame for his birthday. The frame will be cut out of a piece of steel, and the final area of the frame should be 30in². The inside of the frame has to be 11in by 6 in The area of the piece of steel before cutting out the frame is A = (11+2x)(6+2x)in²
Answer:
To make a frame with an area of 30in², Travis needs to cut out a piece of steel with an area of A = (11+2x)(6+2x)in², where x is the width of the frame. The inside of the frame must be 11in by 6in, so the width of the frame must be x = (30 - 11*6)/4 = 2.25in. The total area of the piece of steel must therefore be A = (11+2*2.25)(6+2*2.25) = 30in².
Step-by-step explanation:
To determine the value of x that will result in a final area of the frame of 30in², we can use the equation for the area of the piece of steel before cutting out the frame:
A = (11 + 2x)(6 + 2x)
We can expand this expression to get:
A = 66 + 44x + 12x^2
Since the inside of the frame has to be 11in by 6in, the area of the frame is 11 * 6 = 66in². So, we want to find the value of x that will result in the area of the piece of steel being equal to the area of the frame plus 30in². This means we want to find the value of x that will satisfy:
66 + 44x + 12x^2 = 96
Expanding the left-hand side of this equation and collecting like terms, we get:
12x^2 + 44x = 30
Dividing both sides of the equation by 12, we get:
x^2 + 3.67x = 2.5
To solve for x, we can use the quadratic formula or factoring. Once we have found the value of x, we can use it to determine the dimensions of the piece of steel before cutting out the frame.
Help……………………………………..
The value of c for which the limit of the function does not exist is given as follows:
c = -2.
When does the limit of a function not exist?The limit of a function will not exist if a function has different lateral limits, that is, if the to the right of x = c the graph has a different numeric value than to the left of x = c.
For this problem, we look at the graph at x = -2, hence:
To the left of x = -2, the function assumes a value of 4.To the right of x = -2, the function assumes a value of 6.This means that the function has different lateral limits, hence the limit of the function does not exist for c = -2.
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At what point do the graphs of the lines below intersect?
�
=
9
�
+
2
y=9x+2
�
=
−
3
�
+
12
y=−3x+12
(
−
5
3
,
−
13
)
(−
3
5
,−13)
(
−
7
6
,
15
1
2
)
(−
6
7
,15
2
1
)
(
5
6
,
9
1
2
)
(
6
5
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17
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The solution of the equations y = 9x + 2 and y = - 3x + 12 will be (5/6, 19/2). Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equations are given below.
y = 9x + 2 ...1
y = - 3x + 12 ...2
From equations 1 and 2, then we have
9x + 2 = - 3x + 12
12x = 10
x = 5 / 6
Then the value of 'y' is given as,
y = 9(5/6) + 2
y = 15/2 + 2
y = 19 / 2
The solution of the equations y = 9x + 2 and y = - 3x + 12 will be (5/6, 19/2). Then the correct option is C.
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Mark also has a 1:40 model Phantom II plane.The real Phantom II has a wingspan of 465”. What’s the wing span of the model in inches.
“=inches
The wing span of the 1:40 model Phantom II is 18.31 inches.
What is unit conversion?
A unit conversion is a conversion with different units of measurements of same quantity. It is a process with multiple steps that involves multiplication or division by particular factor.
Wingspan of real Phantom II =465''(in millimeter)
1 inch = 2.54 cm⇒25.4 mm.
465''=[tex]\frac{465}{25.4}[/tex]
= 18.31 inches.
Hence, wingspan of the model 1:40 model Phantom II in inches is 18.31.
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A group of volunteers tagged and released 29 owls as part of a research project. Later, the researchers counted 902 owls, 11 of which had tags. To the nearest whole number, what is the best estimate for the owl population?
Based on the given information, the best estimate for the owl population is 891.
The team of volunteers released 29 owls, and later the researchers counted 902 owls, 11 of which had tags. This means that 891 owls were not tagged, so the total owl population is 891 + 29 = 920. However, the question is asking for an estimate to the nearest whole number, so the best estimate for the owl population is 891.
To further understand the owl population, researchers can look at several factors. These include the types of habitats that owls inhabit, the availability of food in those habitats, the presence of predators or other threats, and the overall health of the owl population.
Researchers can also use various methods to monitor the population and determine if it is increasing or decreasing over time.
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Write the equation of a circle whose center is at (-11,15) and whose radius is 9
Your answer must be in Standard Form AND simplified
Answer:
[tex]\textsf{Standard form}: \quad (x+11)^2+(y-15)^2=81[/tex]
[tex]\textsf{Simplified form}: \quad x^2+22x+y^2-30y+265=0[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Equation of a circle in standard form}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given the center is (-11, 15) and the radius is 9:
a = -11b = 15r = 9Substitute the values of a, b and r into the equation of a circle:
[tex]\implies (x-(-11))^2+(y-15)^2=9^2[/tex]
[tex]\implies (x+11)^2+(y-15)^2=81[/tex]
To write the equation in simplified form, expand the brackets:
[tex]\implies x^2+22x+121+y^2-30y+225=81[/tex]
Collect like terms:
[tex]\implies x^2+22x+y^2-30y+225+121-81=0[/tex]
[tex]\implies x^2+22x+y^2-30y+265=0[/tex]
PLEASE HURRY! You encounter the following statement and explanation when reviewing a report at your finance job: (14^0/14^3)^1/3=14^-2/3 They are equivalent because (14/14^3)^1/3=(14^-2)^1/3
You notice this statement and explanation in the report are wrong. explain why it is wrong and give the correct answer.
The expressions are not equal and the explanation is wrong because the index forms have different exponential values.
The correct answer is 14^-1/3
How to determine the correct optionEquivalent expressions are known as expressions that are the same solution but differ in the mode of their arrangement.
From the information given, we have the index forms;
(14^0/14^3)^1/3=14^-2/3
It is important to note that exponents with zero equals 1.
Then, we have that;
1/14^1/3 = 14 ^-2/3
Take the inverse of the exponent
14^-1/3 is not equal to 14^-2/3
Hence, the correct answer is 14^-1/3
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There are 5,280 feet in a mile. Round answers to the nearest unit. a. How many miles does a car traveling at 42 mi/h go in one hour
The answers for questions G, H, K, and L are the same as questions C, D, K, and L, respectively, because the speed (65mi/h) remains constant.
A. 65 miles in one hour: If a car is traveling at 65 miles per hour (mi/h), then in one hour it will travel 65 miles.
B. 340,800 feet in one hour, 65 miles is equal to 5,280 x 65 = 340,800 feet.
C. 5,680 feet in one minute, 340,800 feet ÷ 60 = 5,680 feet in one minute.
D. 94.67 feet in one second, 5,680 feet ÷ 60 = 94.67 feet in one second.
E. 42 miles in one hour: If a car is traveling at 42 miles per hour, then in one hour it will travel 42 miles.
F. 221,760 feet in one hour, 42 miles is equal to 5,280 x 42 = 221,760 feet.
G. 5,680 feet in one minute.
H. 94.67 feet in one second.
I. x miles in one hour.
J. 5,280 x x feet in one hour:
K. (5,280 x x) ÷ 60 feet in one minute.
L. ((5,280 x x) ÷ 60) ÷ 60 feet in one second.
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There are 5,280 feet in a mile. Round answers to the nearest unit.
A. How many miles does a car traveling at 65mi/h go in one hour?
B. How many feet does a car traveling at 65mi/h go in one hour?
C. How many feet does a car traveling at 65mi/h go in one minute?
D. How many feet does a car traveling at 65mi/h go in one second?
E. How many miles does a car traveling at 42mi/h go in one hour?
F. How many feet does a car traveling at 42mi/h go in one hour?
G. How many feet does a car traveling at 65mi/h go in one minute?
H. How many feet does a car traveling at 65mi/h go in one second?
i. How many miles does a car traveling at x mi/h go in one hour?
J. How many feet does a car traveling at x mi/h go in one hour?
K. How many feet does a car traveling at x mi/h go in one minute?
L. How many feet does a car traveling at x mi/h go in one second?
HELP ME PLEASE!!! 15 POINTS
In the diagram, KG, JF, AE and AH intersect at point A. Use this diagram for problems 1-3.
1. Describe the relevant angle relationships in the diagram.
2. Write and solve an equation to find the value of x.
3. What are the measures of ZJAH and ZGAH?
The relevant angle relationship in the diagram is that the total angle of line JKEF = the total angle on line JHGF.
The value of X = 20
The measures of ZJAH and ZGAH = 60° and 100° respectively.
How to solve the equation used to fine the missing value of X?To find the value of X, the angle of the straight line = 180°
Therefore, 3x+5x+X = 180
180 = 9x
X = 180/9
X = 20
Therefore the measures of <JAH = 3 × 20 = 60°
the measure of <GAH = 5×20 = 100°
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a random variable x is exponentially distributed with a mean of 25. what is the probability that x is between 25 and 30?
The probability that x is between 25 and 30 is 0.087.
The cumulative distribution function (CDF) of an exponential distribution with mean 25 is given by:
F(x) = 1 - exp(-x/25)
The probability that x is between 25 and 30 can be found by evaluating the CDF at x = 30 and x = 25 and subtracting the two values:
P(25 < x < 30) = F(30) - F(25) = (1 - exp(-30/25)) - (1 - exp(-25/25))
= (1 - exp(-1.2)) - (1 - exp(-1))
= 0.255 - 0.368
= 0.087
So, the probability that x is between 25 and 30 is 0.087.
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ASAP pls
The graph shows two accounts with the same principal and annual interest rate. Use the graph to estimate the answer to each question. Show your workAbout how much more compound interest than simple interest is earned after 35 years? Remember to show your work. About how much more compound interest than simple interest is earned after 45 years? Remember to show your work.
About $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.
What is a graph ?
A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.
Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.
Since the graph shows the balance for two accounts with the same principal and annual interest rate, we can assume that one account is earning simple interest while the other is earning compound interest.
To estimate the amount of compound interest earned after 35 years, we can look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 35 years is approximately $4,000, while the balance for the compound interest account is approximately $10,000. Therefore, the amount of compound interest earned after 35 years is approximately:
$10,000 - $4,000 = $6,000
To estimate the amount of compound interest earned after 45 years, we can again look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 45 years is approximately $5,500, while the balance for the compound interest account is approximately $18,000. Therefore, the amount of compound interest earned after 45 years is approximately:
$18,000 - $5,500 = $12,500
Therefore, about $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.
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In the figure, the octagon is formed by two overlapping squares. The overlapping region is also a square. The larger square has a length of 6cm. The smaller square has one corner at the center of the larger square and the smaller square has a length of 4cm. How many centimeters is the permeter of the octagon?
So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).
What is perimeter ?In geometry, a shape's perimeter is sometimes referred to as its total length. By adding up the lengths of all of an object's sides and borders, one can determine the circumference of something such as a form. The perimeter of a form can be calculated by adding up all of the edges' lengths. For instance, a rectangular with dimensions of 24 yards long as well as 15 yards wide will have a 78 yard perimeter.
Here,
To find the perimeter of the octagon, we need to determine the length of each side of the octagon.
First, let's find the length of the diagonal of the smaller square. We can use the Pythagorean theorem:
d²=4² + 4²=
d² = 16+16 =32
d = √32
=> d = 4√2
This diagonal of the smaller square is also the side length of the overlapping square.
Next, let's find the length of one of the sides of the larger square that overlaps with the smaller square. Since the length of the larger square is 6cm, the side length of the overlapping region (part of the larger square that overlaps with the smaller square) is:
6 - 4√2
Finally, the length of one of the sides of the octagon is the sum of the side lengths of the two squares that overlap, minus the side length of the overlapping square (since this side is counted twice):
=> 6 + 6 - 4√2 - 4√2 - (6 - 4√2)
Therefore, the perimeter of the octagon is:
=>8 (12 - 6√2) = 96 - 48√2
So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).
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one half of three fourths of a number is 20 less than two fifths of the same number. what is the number?
We divided both sides of the equation by (3/8) to get x = (40/3), the number is 40/3.
Let the number be x.
Then one half of three fourths of x can be expressed as [tex](3/4)*(1/2)*x = (3/8)*x[/tex]
Two fifths of x can be expressed as[tex](2/5)*x[/tex]
Therefore, according to the given statement, [tex](3/8)*x = (2/5)*x - 20[/tex]
Solving for x, we get: x = (40/3)
Therefore, the number is 40/3.
To calculate this, we first wrote the given statement in terms of fractions. Then we used algebraic manipulation to solve for x. We multiplied both sides of the equation by the LCD, 40, to get [tex]40*(3/8)*x = 40*(2/5)*x - 20*40[/tex]. Then we combined like terms to get ([tex]3/8)*x + 20*(5/8)*x = 40[/tex]. Then we subtracted [tex]20*(5/8)*x[/tex] from both sides to get [tex](3/8)*x = 40 - 20*(5/8)*x[/tex]. Finally, we divided both sides of the equation by (3/8) to get x = (40/3). Therefore, the number is 40/3.
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An automat machine make good pieces with a probability 0,96. Wich are the chances that the two piece is wrong?
The given information states that the machine produces good pieces with a probability of 0.96, which means that there is a 0.04 probability of getting a bad piece.
To calculate the probability of getting two bad pieces in a row, we multiply the probabilities of each individual bad piece:
0.04 * 0.04 = 0.0016
So the chances of getting two bad pieces are 0.0016, or 0.16%. This means that out of 100 tries, you would expect to get two bad pieces in a row 0.16 times.
It's vital to remember that independent events, like obtaining two terrible pieces, have probabilities that are determined by multiplying the individual possibilities.
This is based on the idea of the multiplication rule of probability, which states that the likelihood of two unrelated events occurring simultaneously is the sum of the probabilities of each event occurring separately.
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Each month, a shopkeeper spends 7x+19 dollars on rent and electricity. If she spends 2x−7 dollars on rent, how much does she spend on electricity? Use pencil and paper. For which value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s).
Answer:
Step-by-step explanation:
7x + 19 = cost rent and electricity
2x - 7 = cost of rent only
cost of electricity only = (7x + 19) - (2x - 7) = 5x + 26
5x + 26 < 100
5x < 74
x < 74/5
x < $14.80
Which of the following expressions is equivalent to -1/4 - 5/3
Step-by-step explanation:
the first one because positive (+) x negative (-) = negative (-), so it give you the negative sign in the middle
How Much SAND lol
Please Help
Step-by-step explanation:
Volume.
[tex]v = lwh[/tex]
[tex]l = 20 \: w = 18 \: h = 0.5[/tex]
We just multiply these three numbers.
[tex](20)(18)(.5) = 180[/tex]
[tex]180 {ft}^{3} [/tex]
50 POINTS. PLS REFER TO PICTURE
The correct answer is:
Function f is translated to the right 7 units.
Function f is translated down 4 units