A reasonable exponent is one that is fractional. For instance, 412 4 1 2 can be used to represent the number 4.
What is meant by rational exponent?Exponents that are fractions with the denominator a root and the numerator a power are known as rational exponents. For instance, 813 is another method to write 38, while 1612 is another way to write 16. A fractional exponent is a rational exponent. For instance, the number 4 can be written as 412 4 1 2. Though they can be challenging to use at first, rational exponents can actually make some issues simpler.The ability to express rational exponents in pq form as opposed to irrational exponents in pq form is one of the key distinctions between the two types of exponents. Rational exponents are rational numbers, whereas irrational exponents are infinite or non-repeating decimals.Given,
[tex]$\left(\frac{4 y^2}{5}\right)^2[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$=\frac{\left(4 y^2\right)^2}{5^2}[/tex]
Simplify [tex]$\left(4 y^2\right)^2: 16 y^4$[/tex]
[tex]$=\frac{16 y^4}{5^2}[/tex]
The we get,
[tex]$& =\frac{16 y^4}{25}[/tex]
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I need help finding b
Step-by-step explanation:
You would find a the same way as finding B, just backwards
[tex]( {x}^{2} - 1)( {x}^{2} + 5)[/tex]
Distributing we get
[tex] {x}^{4} + 5 {x}^{2} - {x}^{2} - 5[/tex]
Simplifying it...
[tex] {x}^{4} + 4 {x}^{2} - 5[/tex]
here is a probability that a randomly selected 30-year-old male lives through the year. A life insurance company charges $154 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $ as a death benefit. Complete parts (a) through (c) below. Question content area bottom Part 1 a. From the perspective of the -year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? The value corresponding to surviving the year is $ negative 195. The value corresponding to not surviving the year is $ 99,805. (Type integers or decimals. Do not round.) Part 2 b. If the -year-old male purchases the policy, what is his expected value? The expected value is $ enter your response here.
Answer: a. From the perspective of the 30-year-old male, the monetary value corresponding to surviving the year is -$154 (the cost of the insurance policy). The monetary value corresponding to not surviving the year is $99,805 (the death benefit payout).
b. If the 30-year-old male purchases the policy, his expected value can be calculated using the formula:
Expected Value = (Probability of Event A) * (Value of Event A) + (Probability of Event B) * (Value of Event B)
In this case, the probability of surviving the year and not surviving the year can be assumed to be the same, as we don't have any specific information on the individual's health or life expectancy. Therefore, the probabilities can be assumed to be 0.5 each.
Plugging in the values, we get:
Expected Value = (0.5) * (-$154) + (0.5) * ($99,805) = ($50,326)
So, the expected value for the 30-year-old male purchasing the policy is $50,326.
Step-by-step explanation:
PLEASE HELP ASAP IF YOUHELP QUICK I WILL
GIVE BRANLIST In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is Predict how many times
36
the rolls will result in a sum greater than 10 if the experiment is repeated 108 times
OPTIONS
3
9
10
1&
The theoretical probability that a sum greater than 10 is obtained is given as follows:
p = 1/12.
Out of 108 trials, the expected number of trials with a sum greater than 10 is given as follows:
9.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The 36 total outcomes for the pair of dices is given as follows:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)Out of these outcomes, three of them, (5,6), (6,5) and (6,6) have a sum greater than 10, hence the probability is given as follows:
p = 3/36
p = 1/12.
Then the expected number is given as follows:
E(X) = 108 x 1/12
E(X) = 9.
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Answer:
9
Step-by-step explanation:
experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is Predict how many times.
Therefore the experement is 9
Can someone help with some algebra 2 questions?
The specified radical expressions in the questions are evaluated and presented in the simplest form as follows;
(2) [tex]\sqrt[3]{x^2\cdot y^2} \cdot \sqrt[4]{x^5\cdot y^3} = \sqrt[12]{x^{23}\cdot y^{17}}[/tex]
(3) f(g(x)) = √(6·x + 1) - 5
(4) x = (15 ± √(33))/2
(5) x = 126
What is a radical expression?A radical is a mathematical expression which contains the radical expression, '√', which represent a fractional indices of the form 1/n.
(2) The specified radical expression is presented as follows;
∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex]
Expressing the above radical expression in index form, we get;
∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}}[/tex]
Adding the index of like variable terms, we get;
[tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}} = x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} }[/tex]
(2/3) + (5/4) = (2×4 + 5×3)/12 = 23/12 = 1 11/12
Therefore; [tex]x^{\frac{2}{3} + \frac{5}{4} } = x^{\frac{23}{12} }[/tex]
2/3 + 3/4 = (2 × 4 + 3 × 3)/(12) = 17/12 = 1 5/12
Therefore; [tex]y^{\frac{2}{3} + \frac{3}{4} } = y^{\frac{17}{12} }[/tex]
Which indicates that we get; [tex]x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} } = x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]
Therefore; ∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]
In radical form, we get; [tex]x^{\frac{23}{12} } \times y^{\frac{17}{12} } = \sqrt[12]{x^{23} \cdot y^{17}}[/tex](3) The functions, f(x) = √(3·x + 4) - 5, g(x) = (2·x - 1)
The composite function, f(g(x)) can be found as follows;
f(g(x)) = √(3·g(x) + 4) - 5 = √(3·(2·x - 1) + 4) - 5
f(g(x)) = √(3·(2·x - 1) + 4) - 5 = √((6·x - 3) + 4) - 5 = √(6·x + 1) - 5
The composite function, f(g(x)) is therefore; f(g(x)) = √(6·x + 1) - 5(4) (√(x - 1)) = x - 7
Squaring both sides, we get;
(√(x - 1))² = (x - 7)²
(√(x - 1))² = x - 1(x - 7)² = x² - 14·x + 49Therefore;
(√(x - 1))² = x - 1 = (x - 7)² = x² - 14·x + 49
x - 1 = x² - 14·x + 49
x² - 14·x + 49 - (x - 1) = 0
x² - 15·x + 48 = 0
The quadratic formula can be used to solve the above equation to get;
x = (-(-15) ± √((-15)² - 4×1×48))/(2 × 1) = (15 ± √(33))/2
x = (15 ± √(33))/2(5) 2·∛(x - 1) + 6 = 16
2·∛(x - 1) + 6 = 16
Subtracting 6 from both sides, we get;
2·∛(x - 1) + 6 - 6 = 16 - 6 = 10
2·∛(x - 1) = 10
∛(x - 1) = 10/2 = 5
∛(x - 1) = 5
∛(x - 1)^3 = 5^3
∛(x - 1)^3 = x - 1
5^3 = 125
∛(x - 1)^3 = x - 1 = 125
x = 125 + 1 = 126
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If you toss 10 fair coins, in how many ways can you obtain at least one head and one tail?
Answer:1/2 head and 1/2 tails
Step-by-step explanation: no.of experiments for heads = 5
total no of experiments=10
probability=5/10=1/2
no.of experiments for = 5
total no of experiments=10
probability=5/10=1/2
A ball bounces to a height of 5.2 feet on the first bounce. Each subsequent bounce reaches a height that is 83% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to thousandths place.
1.680 ft
2.048 ft
2.468 ft
4.316 ft
Answer:
Below
Step-by-step explanation:
5.2 * .83 second
(5.2 * .83) * .83 = 5.3 * .83^2 third
.
= 5.2 ( .83)^4 Fifth = 2.468 ft
Find the length of the dashed line in the
circle.
The length of the dashed line in the circle is
ft.
4.893 ft
9
17.708 ft →
4.893 f
The length of the dotted line would be 7.922 ft.
What is the diameter of the circle?A circle's diameter is measured from the center of the circle outward. It is equivalent to twice the radius, or the distance a circle's radius is measured from its center to any other point on the circle.
The mathematical formula for a circle's diameter is d = 2r if d is the circumference and r is the radius.
When we subtract the circle's thickness from its outer diameter to determine the provided circle's inner diameter, we obtain q = 17.708 - 4.893 - 4.893.
We can solve this for q = 7.922
The dotted line would be 7.922 feet long as a result.
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Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 80 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.33?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's
approach and calculations.
(Enter your answer as a number accurate to 4 decimal places.)
The probability that the sample proportion is less than 0.33 is approximately 0.7422.
How to model sample proportion?The sample proportion of first-time customers can be modeled by a normal distribution with mean p, the true proportion of first-time customers, and standard deviation [tex]\sqrt{\frac{p(1-p)}{n}}[/tex], where n is the sample size.
In this case, p = 0.32, n = 80, and we want to find [tex]P(\hat{p} < 0.33)[/tex].
The standardized version of [tex]\hat{p}[/tex] is given by:
[tex]z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Substituting the values, we get:
[tex]z = \frac{0.33-0.32}{\sqrt{\frac{0.32(1-0.32)}{80}}} \approx 0.6579[/tex]
Using a standard normal distribution table (or a calculator or statistical software), we find that the probability of z being less than 0.6579 is approximately 0.7422.
Therefore, the probability that the sample proportion is less than 0.33 is approximately 0.7422.
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2.63 divied by 0.5 standard way
Answer: 5.26
Step-by-step explanation:
Answer:
= 0.190
Solution:
Change the divisor 2.63 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
50 ÷ 263 = 0.190
and therefore:
0.5 ÷ 2.63 = 0.190
Both calculated to 3 decimal places.
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Which of the following WAS NOT an impact of the crusades?
A. Change in culture in Europe
B. End of the Roman Empire
C. Monarchs grew more powerful
D. Many Christians were killed or badly injured
The option that was not an impact of the crusades is B. End of the Roman Empire.
What is the impact of the crusades?The Crusades were a series of religious wars fought between Christians and Muslims in the Middle East during the medieval period. The Crusades had a significant impact on European society and culture, including:
Monarchs grew more powerful: The Crusades helped to strengthen the power of monarchs in Europe, as they became more involved in financing and organizing the Crusades.
However, the Crusades did not bring about the end of the Roman Empire. The Roman Empire had already collapsed centuries earlier, in the 5th century AD, and the Crusades took place in the 11th-13th centuries AD, during the medieval period.
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Mark bought 4 pounds of bananas for $2.36 this week. Last week he paid $1.83 for 3 pounds of bananas. Which was the lower unit price?
Answer:
4 pounds
Step-by-step explanation:
2.36/4 = 0.59 cents a banana
1.83/3 = 0.61 cents a banana
estimate the population in the year 2040
The population in the year 2040 is 31800.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 4 is an equation.
We have,
The exponential equation is y = m[tex]a^t[/tex].
Where t is a variable
Now,
In 2007 (t = 0). the population was 12,000.
y = 12000
This means,
12000 = m[tex]a^0[/tex]
12000 = m
And,
In 2019 (t = 12). the population was 23,000.
y = 23000
23000 = m[tex]a^{23}[/tex]
23000 = 12000 [tex]a^{23}[/tex]
23000/12000 = [tex]a^{23}[/tex]
1.92 = [tex]a^{23}[/tex]
[tex]1.036^{23}[/tex] = [tex]a^{23}[/tex]
a = 1.03
Now,
y = 12000 [tex]1.03^t[/tex]
The population in the year 2040.
i.e
t = 33
y = 12000 x [tex]1.03^{33}[/tex]
y = 12000 x 2.65
y = 31800
Thus,
31800 is the population in the year 2040.
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2x = 32 in y= mx +b form
Counting back from 18, what number follows 17?
Answer:
16
Step-by-step explanation:
As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16
18) Solve for side AC.
A) 1.10
B) 8.24
C) 9.50
70
C
3
B
Step-by-step explanation:
tan0=opp/adj
where opposite =3,adjacent =x,=70
tan 70=3/x
2.7474=3/x
2.7474x=3
divide both sides by 2.7474
x=3/2.7474
x=1.0919
x=1.10 to 1 d.p
Every day, Austin packs his favorite sandwich in a plastic sandwich box. Austin's sandwich box is 13 centimeters long and 12 centimeters wide, but only 3 centimeters tall. What is the volume of Austin's sandwich box?
The volume of the rectangular sandwich box of Austin is given by the equation V = 468 cm³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular box be represented as V
Now , the equation will be
The length of the sandwich box = 13 cm
The width of the sandwich box = 12 cm
The height of the sandwich box = 3 cm
And , volume of the rectangular box V = Length x Width x Height
Substituting the values in the equation , we get
Volume of the rectangular box V = 13 x 12 x 3
On simplifying the equation , we get
Volume of the rectangular box V = 468 cm³
Hence , the volume of rectangular box is 468 cm³
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Complete the inequality to represent the following: 13 times a number x
is less than or equal to 200.
The value for the Inequality 13x ≤ 200 is x ≤ 15.384.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
13 times a number x is less than or equal to 200.
Now, Writing the Inequality Mathematically
13x ≤ 200
x ≤ 200 / 13
x ≤ 15.384
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A guy wire supporting a radio tower is positioned 145 feet up the tower. It forms a 45 angle with the ground. To the nearest tenth, about how long is the wire?.
The approximate length of the guy wire supporting the radio tower, as determined using trigonometry with the given information of a 45 degree angle and a height of 145 feet up the tower, is 145 feet.
We can use trigonometry to solve this problem. Let's call the length of the guy wire "x". The opposite side of the right triangle formed by the guy wire and the ground is 145 feet (the height of the tower where the guy wire is attached), and the angle opposite the guy wire is 45 degrees.
Using the trigonometric function tangent, we can set up the following equation:
[tex]tan(45)[/tex] = opposite / adjacent
where "opposite" is 145 feet and "adjacent" is the length of the guy wire, x. Simplifying this equation, we get:
1 = 145 / x
Multiplying both sides by x, we get:
x = 145
Therefore, the length of the guy wire is approximately 145 feet to the nearest tenth.
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I need help on my homework! Answer number 15, please :)
15) Evaluating the mathematical expression -10 -144/(-12) shows that 144 is being divided by 12 before subtracting 10, following the application of PEMDAS.
16) The value of the algebraic expression is 2.
What is the evaluation of an expression?The evaluation of an expression is finding its value by substituting variables and applying the PEMDAS rule.
PEMDAS means the order of algebraic operations that applies parentheses, exponents, multiplication, division, addition, and subtraction.
-10 -144/(-12)
-10 + (144/12)
-10 + 12
= 2
Thus, we have evaluated the expression to have a value of 2.
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The width of a rectangle is 35 of a foot and the length is 8 feet. What is the area? Responses A 340 ft2 3 40 ft 2 B 445 ft2 4 4 5 ft 2 C 835 ft2 8 3 5 ft 2 D 725
The solution is Option B.
The area of the rectangle is given by the equation A = 4 4/5 feet²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the equation will be
Let the length of the rectangle be L = 8 feet
Let the width of the rectangle be W = ( 3/5 ) feet
Now , Area of Rectangle = Length x Width
Substituting the values in the equation , we get
Area of Rectangle = ( 3/5 ) x 8
On simplifying the equation , we get
Area of Rectangle = 24/5 feet²
Area of Rectangle = 4 4/5 feet²
Hence , the area of the rectangle is 4 4/5 feet²
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Solve for x, each figure is a trapezoid
From the given trapezoid the value of the x is 1.
What is the trapezoid?
The sum of all the angles in a trapezoid is equal to 360°. The sum of the angles on the same side is equal to 180°.
We have,
Since a Trapizode has 360 Degrees total and since the sides are equal we can say that
180 = 66 + ∠R
∠R = 180 - 66
∠R = 114
so,
180 = 66 + (-2 + 116x)
180 = 66 - 2 + 116x
180 = 64 + 116x
180 - 64 = 116x
116 = 116x
x = 1
Therefore, from the given trapezoid the value of the x is 1.
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When Cheryl's phone battery is 55% charged, she knows it will last for another 1.5 hours. If Cheryl's
phone battery loses its charge at a constant rate, how long, in hours, will it last when it is fully charged?
The battery will last 2.73 hours when it is fully charged
How to determine how long it will last when it is fully charged?The unit rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, the unit rate is one quantity divided by the other quantity
Since Cheryl's phone battery is 55% charged and it will last for another 1.5 hours. Thus, the rate will be:
rate = 1.5 hours/55% = 3/110 hour per %
When it is fully charged, that is 100%. Thus, it will take:
Time for 100% = (3/110) * 100% = 2 8/11 hours = 2.73 hours
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Help me with this question
Answer:
D.666 cubic centimeters
Step-by-step explanation:
Volume of cylinder is 3 time the volume of cone of the same radius.
Volume of cylinder= πr²h
Volume of cone = 1/3 x πr²h
help me find the measure
Answer:
= 60°
Step-by-step explanation:
Exterior angle =
[tex] = \frac{360}{n} [/tex]
[tex] = \frac{360}{6} \\ = {60}^{o} [/tex]
= 60°
helpppp geometry 8th grade
The length of the segment QV is 9.2 units
What is a square?
Regular quadrilaterals, such as a square, have four equal sides and four equal angles (right angles, 90-degree angles, or angles of /2 radian). It is also known as a rectangle with two neighbouring sides of identical length. It is the only regular polygon whose internal angle, central angle, external angle, and diagonal length are all equal (90°).
diagonal length, d=a√2 , where, d--> diagonal length , a= side length
So, d= 13* 1.4142 = 18.3847 units
Diagonals bisect each other
QV = d/2 = 18.3847/2 = 9.1923
Rounding to 1 decimal place
QV = 9.2 units
The length of the segment QV is 9.2 units
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find the value of each variable show proofs
Answer:
Answer is in the attached photo
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note for this question, Sine rule can be used to find both x and y as well instead of Pythagoras' Theorem.
x=18, y=9√3
There is a theorem with 30 degrees 30 degrees 90 degrees triangles, it is that the side opposite of 30 degrees angle is a, the hypotenuse is 2a, and the other leg opposite the 60 degree angle is a√3
So, since a=9, x=2a=18 and y=a√3=9√3
Together, Steve and Tom sold 125 raffle tickets for their school. Steve sold 17 more than three times as many raffle tickets as Tom. How many raffle tickets did each boy sell?
Tom sold 27 raffle tickets and Steve sold 98 raffle tickets.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
Together, Steve and Tom sold 125 raffle tickets for their school.
Steve sold 17 more than three times as many raffle tickets as Tom.
Let s be the number of raffle tickets sold by Steve and t be the raffle tickets sold by Tom.
So,
3t + 17 + t = 125
4t = 108
t = 27
And s = 98
Therefore, Steve sold 98 and Tom sold 27 tickets.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
Solution to the quadratic equation
The solution to the quadratic equation is determined as follows;
2x² + 12x - 3 = 0
2x² + 12x = 3
divide through by 2
x² + 6x = ³/₂
take half of coefficient of x, square it and add it both sides of the equation
(x + 3)² = ³/₂ + 3²
x² + 6x + 9 = 9 + ³/₂
2(x² + 6x + 9) = 18 + 3
Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
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The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest.) 865, 970, 985, 1005, 1015, 1035, 1055, 1080, 1095, 1095 Send data to calculator Suppose that one of the people moves. Her rent changes from $1095 to $1045. Answer the following.
The new list of rents, ordered from least to greatest, would be 865, 970, 985, 1005, 1015, 1035, 1055, 1080, 1045, 1095. The median rent would also be changed from $1095 to $1045.
Solve d+5/-2<=-3/2 please help I will give brainly
Answer:
Step-by-step explanation:
inequality form
d≤ 1
Interval Notation:
(−∞,1]
