Answer:
In set-builder notation, the set of solutions is:
[tex]\left \{u|-3<u<7\right\}[/tex]
Step-by-step explanation:
Let's start by isolating the absolute value expression on one side of the inequality:
8 | u - 2 | - 7 < 33
add 7 on both sides:
8 | u - 2 | < 40
divide both sides by 8:
| u - 2 | < 5
Now, in order to remove the absolute value symbols, we need to consider two different cases:
1) what is inside the absolute value symbols is larger than or equal to zero, so in such case when we remove the absolute value we get exactly what was inside:
u - 2 < 5
u < 5 + 2
u < 7
Now the other case;
2) what is inside the absolute value is smaller than zero, then when removing the symbols we get:
2 - u < 5
2 - 5 < u
-3 < u
Then the set of solutions of this inequality are the set of u values such that u is larger than -3 (to the right of -3 on the number line, and smaller than 7 (to the left of the number 7 on the number line.
In graph form this should look like a highlighted segment on the number line that starts at -3 on the left, ends at 7 on the right, and doesn't include the endpoints -3 and 7.
in set builder notation, the set of solutions is given by:
[tex]\left \{u|-3<u<7\right\}[/tex]
A 6- foot roll of waxed paper costs $3.60. What is the price per inch?
Step-by-step explanation:
hope this helps
20 cent per inch
gordon drives 220 miles from new york to boston in 4 hours. what is his car's average speed?
Answer:
55 mph
Because he drives to new york to boston in 4 hours and its 220 miles so 220 is the miles and you divide by the hours so 4 hours so he drove 55 mph
2.5 8.7 *** 9.6 4.6 *** 5.1 9.9 *** 10.0 6.0 10.3 *** 10.5 6.5 *** 6.6 11.6 8.5 12.0
Consider the sample of n = 20 scores. Notice that they are listed in order from 2.5 to 12.0,
but that some of the scores are obscured by ***. The mean, M, of these scores is 8.0. Suppose you are asked for the sample standard deviation of these scores. Since you don't have all of them, you cannot calculate it. Which of the following is the best estimate of the sample standard deviation?
a. 9.5
b. 0.5
c. 6.4
d. 2.7
Answer:
D. 2.7
Step-by-step explanation:
Given
[tex]Mean = 8.0[/tex]
[tex]n = 20[/tex]
[tex]Range = 2.5\ to\ 12.0[/tex]
Required
Estimate the standard deviation
Since, the given data has incomplete parameters, we can apply the range rule to estimate the standard deviation;
This is done as follows;
[tex]S.D = \frac{1}{4}(Max - Min)[/tex]
In this case:
[tex]Max = 12.0[/tex]
[tex]Min = 2.5[/tex]
So:
[tex]S.D = \frac{1}{4}(Max - Min)[/tex]
[tex]S.D = \frac{1}{4}(12.0 - 2.5)[/tex]
[tex]S.D = \frac{1}{4}(9.5)[/tex]
[tex]S.D = 2.375[/tex]
From the list of given option, the closest to 2.375 is 2.7;
Hence, the best estimate is 2.7
The correct option is D. 2.7
Given that,
The mean is 8.0.the n = 20.The range is from 2.5 to 12.0The calculation is as follows:The standard deviation should be
[tex]= \frac{1}{4} (12 - 2.5)\\\\ = \frac{1}{4} (9.5)[/tex]
= 2.375
= 2.7
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An angle measuring 32 degrees has a complement that measures (2x - 16)degrees. What is the value of x? (and the steps)
Answer:
37°
Step-by-step explanation:
32+2x-16=90
2x+16=90
2x=90-16
2x=74
x=37
which statement most accurately describes what can happen to jobs in a bad economy
Ansewern
I think you forgot the stament and please add it so i can helpyou out with it.
Step-by-step explanation:
For the function f(x)=-1/3x-2, find the value of x for which f(x)=x.
Step-by-step explanation:
f(x)=-1/3x-2=x
3x²-2x-1=o
(3x-1)(x+1)=o
x=1/3(or)x=-1
Point Tis on line segment SU. Given TU = 4x + 1, SU = 8, and ST = 3x,
determine the numerical length of TU.
Answer:
5 units
Step-by-step explanation:
If point T is on the line segment SU, then ST + TU = SU.
Given
TU = 4x + 1
SU = 8
ST = 3x
To get TU, we need to get the value of x first. To get x, we will substitute the given parameters into the formula;
3x+4x+1 = 8
7x+1 = 8
subtract 1 from both sides
7x+1-1 = 8-1
7x = 7
divide both sides by 7
7x/7 = 7/7
x = 1
Substitute x = 1 into the length TU
Since TU = 4x+1
TU = 4(1)+1
TU = 5
Hence the numerical length of TU is 5 units
What is the relative size of (how many times as large) a circle's' circumference C to its diameter, d
Answer:
The circumference is pi times larger than the diameter of a circle.
Step-by-step explanation:
The formula of the circumference of a circle is
C = 2(pi)r = (pi)d
C = (pi)d
To find the ratio of the circumference to the diameter, divide both sides of the equation by d.
C/d = pi
The circumference is pi times larger than the diameter of a circle.
2. What fractional part of the quadrilateral is not shaded?
Answer:
plz show the pic so I can understand
Write an equation in slope intercept form that is parallel to y = 3x + 4 and goes through the point (-1,5)
Answer:
Step-by-step explanation:
y - 5 = 3(x + 1)
y - 5 = 3x + 3
y = 3x + 8
answer is C
Sonia wants to sew ribbon along each side of a square pillow if the pillow has an area of 144 in² how much ribbon must she by to have the exact amount that she needs
Answer:
12 in
Step-by-step explanation:
she has square pillow, so 12*12=144 sq in
What is the value of x (3x-10)° 149
Steps to solve:
(3x - 10) = 149
~Add 10 to both sides
3x = 159
~Divide 3 to both sides
x = 53
Best of Luck!
Write the equation of a line that is parallel to y = 1/2 x + 5
that passes through the point (2,6).
Answer:
y = 1/2x + 5
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
When 2 lines are parallel, they have the same slope.
Step 1: Define variables
Random point (2, 6)
m = 1/2
y = 1/2x + b
Step 2: Find b
6 = 1/2(2) + b
6 = 1 + b
5 = b
Step 3: Rewrite parallel linear equation
y = 1/2x + 5
how would you solve for 5x=13 for x
Answer:
divide by 5: x = 13/5 = 2.6
Step-by-step explanation:
Make use of the properties of the multiplicative inverse and the multiplication identity element. Multiplying both sides of the equation by the multiplicative inverse of the coefficient of x makes the result be 1x on the left side.
(1/5)(5x) = (1/5)(13)
1x = 13/5
The multiplicative identity element (1) does not change the value of what it multiplies, so this simplifies to ...
x = 13/5
_____
Effectively, we divide (both sides) by 5.
If it is an addition problem with different signs what do you do
Answer:
To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.
plz give brainlist
hope this helped
Evaluate the expression and write your answer in the form a + bi. 1) (2-6i)+(4+2i)2) (6+5i)(9-2i)3) 2/(3-9i)4) (3 − 5i)(7 − 2i)
Answer:
Step-by-step explanation:
Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.
1) (2-6i)+(4+2i)
open the parenthesis
= 2-6i+4+2i
collect like terms
= 2+4-6i+2i
= 6-4i
2) (6+5i)(9-2i)
= 6(9)-6(2i)+9(5i)-5i(2i)
= 54-12i+45i-10i²
= 54+33i-10i²
In complex number i² = -1
= 54+33i-10(-1)
= 54+33i+10
= 54+10+33i
= 64+33i
3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i
= 2/3-9i*3+9i/3+9i
=2(3+9i)/(3-9i)(3+9i)
= 6+18i/9-27i+27i-81i²
= 6+18i/9-81(-1)
= 6+18i/9+81
= 6+18i/90
= 6/90 + 18i/90
= 1/15+1/5 i
4) For (3 − 5i)(7 − 2i)
open the parenthesis
= 3(7)-3(2i)-7(5i)-5i(-2i)
= 21-6i-35i+10i²
= 21-6i-35i+10(-1)
= 21-41i-10
= 11-41i
Simplified form of the given expressions will be,
1). 6 - 4i
2). 64 + 33i
3). [tex]\frac{1}{15}+\frac{1}{5}i[/tex]
4). [tex]\frac{31}{53}-\frac{31}{53}i[/tex]
1). In a complex number (a + bi),
a = Real part of the complex number
bi = Imaginary part
Expression given in the question → (2 - 6i) + (4 + 2i)
Rule to solve the given expression,
"Add real part and imaginary part of two complex numbers separately"
(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)
= 6 + (-4i)
= 6 - 4i
Therefore, simplified form of the given expression will be (6 - 4i).
2). Given expression → (6 + 5i)(9 - 2i)
Rule to solve the expression → i² = -1
(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)
= 54 - 12i + 45i - 10i²
= 54 - 12i + 45i + 10 [Since, i² = -1]
= (54 + 10) + (45i - 12i)
= 64 + 33i
Therefore, simplified form of the given expression will be (64 + 33i).
3). Given expression → [tex]\frac{2}{3-9i}[/tex]
Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).
[tex]\frac{2}{3-9i}= \frac{2(3+9i)}{(3-9i)(3+9i)}[/tex]
[tex]=\frac{2(3+9i)}{3^2-(9i)^2}[/tex]
[tex]=\frac{6+18i}{9-81(-1)}[/tex]
[tex]=\frac{6+18i}{9+81}[/tex]
[tex]=\frac{6+18i}{90}[/tex]
[tex]=\frac{6(1+3i)}{90}[/tex]
[tex]=\frac{1}{15}+\frac{1}{5}i[/tex]
Therefore, simplified form of the given expression will be [tex]\frac{1}{15}+\frac{1}{5}i[/tex]
4). Given expression → [tex]\frac{(3-5i)}{(7-2i)}[/tex]
Multiply numerator and denominator with the conjugate of the denominator.
[tex]\frac{(3-5i)}{(7-2i)}=\frac{(3-5i)(7+2i)}{(7-2i)(7+2i)}[/tex]
[tex]=\frac{3(7+2i)-5i(7+2i)}{7^2-(2i)^2}[/tex]
[tex]=\frac{21+4i-35i-10i^2}{49-4(-1)}[/tex]
[tex]=\frac{21-31i+10}{53}[/tex]
[tex]=\frac{31-31i}{53}[/tex]
[tex]=\frac{31}{53}-\frac{31}{53}i[/tex]
Therefore, simplified form of the given expression will be [tex]\frac{31}{53}-\frac{31}{53}i[/tex].
Learn more,
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write the number 3/100 as a decimal.
Answer:
Step-by-step explanation
0.03.
Sin(x)=x- x3/3!+x5/5!-x7/7!+....The percentage relative approximate error in using three terms to find sin(4.1) is ______percent.
Answer:
The answer is "239.62%".
Step-by-step explanation:
Given value:
[tex]\bold{\sin(x)=x- \frac{x^3}{3!}+\frac{x^5}{5!} - \frac{x^7}{7!}+....}[/tex]
Solve the first three values:
[tex]\sin(x)=x- \frac{x^3}{3!}+\frac{x^5}{5!}[/tex]
put the value of sin(4.1):
[tex]\to \sin(4.1)=(4.1)- \frac{(4.1)^3}{3!}+\frac{(4.1)^5}{5!} \\\\[/tex]
[tex]=(4.1)- \frac{(4.1)^3}{3!}+\frac{(4.1)^5}{5!} \\\\=(4.1)- \frac{68.92}{3 \times 2\times 1}+\frac{1158.56}{5\times 4 \times 3 \times 2 \times 1}\\\\[/tex]
[tex]=(4.1)- 11.48+9.65\\\\= 2.27[/tex]
The actual value of [tex]\sin(4.1) = -1.59[/tex]
Calculating the percentage relative approximate error value:
Formula:
[tex]=\frac{actual \ value - \ approx \ value }{actual \ value} \times 100\\\\[/tex]
[tex]=\frac{-1.59 - 2.27 }{-1.59} \times 100\\\\= \frac{-3.81}{-1.59} \times 100\\\\= \frac{3.81}{1.59} \times 100\\\\=239.62 \ \%[/tex]
Negotiating in trade means you are ________
A. coming to an agreement on an item's value
B. discussing how to get to market
C. calculating your total cost
D. exchanging a damaged good
Negotiating in trade means you are coming to an agreement on an item's value option (A) is correct.
What is negotiation?The goal of negotiation is to obtain an agreement on one or more contentious issues between two or more parties.
As we know,
On the other hand, trade negotiation is a procedure whereby countries come together to talk about the potential for trade with the aim of arriving at a trade agreement.
When you bargain in trade, you're settling on a price for a product.
Thus, negotiating in trade means you are coming to an agreement on an item's value option (A) is correct.
Learn more about the negotiations here:
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!Need help!
Solve using Substitution Method
2x + 5y = 7
x = 2 - 4y
Answer:
x = 6y = - 1Step-by-step explanation:
2x + 5y = 7 ......... Equation 1
x = 2 - 4y .......... Equation 2
Substitute x that's equation 2 into equation 1 and solve for y
That's
2( 2 - 4y ) + 5y = 7
4 - 8y + 5y = 7
- 3y + 4 = 7
- 3y = 7 - 4
- 3y = 3
Divide both sides by - 3
y = - 1
Substitute the value of y into equation 1
That's
x = 2 - 4(-1)
x = 2 + 4
x = 6
Therefore the solutions are
x = 6y = - 1Hope this helps you
Give two points with integer coordinates that have a slope of 5/7 between them.
Answer:
(2,3) and (7,10)
Step-by-step explanation:
Use the slope 5/7 to get to a new point by moving up 5 units and moving to the right 7 units.
If the coordinate point is (x, y) then the coordinate of the other point will be (x + 5, y + 7).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The slope is the ratio of the rise or fall and run.
The slope is 5/7. The rise is 5 and the run is 7.
If the coordinate point is (x, y) then the coordinate of the other point will be (x + 5, y + 7).
More about the coordinate geometry link is given below.
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which statement correctly describes the expression
Answer:
c
Step-by-step explanation:
choice A means
[tex]11 - 2 {m}^{3} [/tex]
choice B means
[tex]2m - 11[/tex]
choice C means which is the answer
[tex] {2m}^{3} - 11[/tex]
choice D means
[tex] {(2m)}^{3} - 11[/tex]
hope it helps ❤❤❤
For any question comment me
Multiply the polynomial expressions below.
(7x + 5)(2x^3 - 4x^2 + 9x - 3)
Answer:
14x^8-18x^3+43x^2+24x-15
what is 3.825 as a fraction with a guide?
Answer:
3 33/40 or 153/40
Step-by-step explanation:
For first answer change the decimal .825 into fraction by making it over 1000. Then Simplify. For the second answer, take the first answer, multiply 3 with 40 and add 33. In the end both answers are equivanlent.
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknownA) 1116B) 2115C) 1939D) 2223
When looking at the Cov-19 data globally, it shows that 34 out of 50 (which is 68%) confirmed cases of infected people have recovered already. If that 68% holds true everywhere, answer the following: If a US state had about 56,000 confirmed cases, about how many people should have recovered?
Answer:
____________________
68% of 56000 is 38080.
I guess that'd be the amount of people that recovered.
____________________
!!!URGENT!!! Read Image Below.
Answer:
[tex] x = \frac{6 \pm \sqrt{(-6)^2 - 4(3)(8)}}{2(3)} [/tex]
Step-by-step explanation:
Given the equation, [tex] 3x^2 - 6x + 8 = 0 [/tex], the quadratic formula for solving this equation is given as:
[tex] x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
Where,
a = 3
b = -6
c = 8
Plug in the above values into the quadratic formula.
[tex] x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(3)(8)}}{2(3)} [/tex]
[tex] x = \frac{6 \pm \sqrt{(-6)^2 - 4(3)(8)}}{2(3)} [/tex]
A teacher raised a total of $135 for school supplies. He divides the money evenly among his 10 students.
Answer:
Each gets $13.5
Step-by-step explanation:
135/10= 13.5
The scale of a map is 1 in = 11.9 miles. How many inches will be drawn on the map to represent 30.9 miles?
Answer:
2.60 inches
Step-by-step explanation:
Map and actual distances are proportional. So the map distance m for 30.9 miles will be related to the actual distance in the same way the scale is:
m/30.9 = 1/11.9
m = 30.9/11.9 ≈ 2.5967
The length on the map is about 2.60 inches.
Give EG = 5x+7 EF =5x and FG=2x-7
Answer:
x = 7
42, 35, 7
Step-by-step explanation:
EG = 5x+7 EF = 5x FG = 2x-7Point F is on line segment of EG, therefore EG = EF + FG
5x + 7 = 5x + 2x - 72x = 14x = 7Then
EG = 5*7 + 7 = 42EF = 5*7 = 35FG = 2*7 - 7 = 7