Answer:
x > 2 or x < −4
Step-by-step explanation:
Let's solve your inequality step-by-step.
|3x + 3| −5 > 4
Step 1: Add 5 to both sides.
|3x + 3| −5 + 5 > 4 + 5
|3x + 3| > 9
Step 2: Solve Absolute Value.
|3x + 3| > 9
We know either3x + 3 > 9 or 3x + 3 < −9
3x + 3 > 9(Possibility 1)
3x + 3 −3 > 9 −3(Subtract 3 from both sides)
3x > 6
3x > 6 (Divide both sides by 3)
3 3
x > 2
3x + 3 < −9(Possibility 2)
3x + 3 −3 < −9 −3(Subtract 3 from both sides)
3x < −12
3x < -12 (Divide both sides by 3)
3 3
x < −4
FOR MY LAST QUESTION I forgot to add the screenshot so, help please! 25 points
Answer: c. P=43
d. P=3x^2+5x+8
Step-by-step explanation:
c. P=12x+19 ==> See how I got this formula in my previous answer to parts a and b
P=12(2)+19
P=24+19
P=43
d. P=a+b+c+d
P=x^2 +4x+8+2x^2 +x
P=x^2 +2x^2 +4x+x+8
P=3x^2+5x+8
your bedroom sock drawer contains 4 green socks and 6 yellow socks that are mixed together. the light in your room is broken so you must select your socks in the dark. what is the probability you will select two socks of the same color on your first try?
The probability of selecting two socks of same color is 0.96.
According to the given question.
Total number of green socks = 4
Total number of yellow socks = 6
So, the total number of socks in a drawer = 4 + 6 = 10
Since as we know that, the probability of an event is computed as: P(E) = Number of favourable outcome /Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.
So, the probability of selecting a green scoks = 4/10 = 2/5
And the probability of selecting a yellow socks = 6/10 = 3/5
Therefore, the probability of selecting two socks of same color
= probability of selecting both the green socks or probability of selecting both the yellow socks
= [( 2/5) + (2/5)] × [(3/5)+(3/5)]
= (4/5) × (6/5)
= 24/25
= 0.96
Hence, the probability of selecting two socks of same color is 0.96.
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I need help solving. Im stuck please help me.
A bag has 1 red, 3 blue, and 4 green marbles. Outcome A is drawing a green marble on the first draw. Outcome B is drawing a green marble on the second draw without replacing the first marble.
The Probability that Outcome B is drawing a green marble on the second draw without replacing the first marble is
P(B|A) = 3/7.
What is probability ?The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.
Probability is another word for possibility. It is a field of mathematics that examines the occurrence of a random event. The value is given as a number between 0 and 1. To determine how likely an event is to occur, probability has been introduced in mathematics.
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natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. a radio tracker costs $650 and a gps tracker costs $1400. natalie wants to buy at least 9 radio trackers and more than 3 gps trackers. the following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of gps trackers. x ≥ 9 y > 3 650x 1400y ≤ 15000 which yellow shaded region corresponds to natalie's possible choices?
Natalie will choose 7 and 8 as the yellow-shaded region corresponds to Natalie's possible choices.
What do you mean by GPS?Even though it appears complex, 3-dimensional trilateration is a straightforward mathematical process that underlies GPS. It's critical to have a fundamental understanding of 2-D Trilateration, which is necessary to completely comprehend 3-D Trilateration. Similar principles apply to three-dimensional trilateration, however, spheres rather than circles are used. Here is how the Global Positioning System uses 3-D trilateration to pinpoint an object's precise location. When the first satellite sends a signal, the GPS receiver measures the distance between the two. Say the distance between the receiver and the satellite is 20 000 miles. This implies that the receiver might be located anywhere on the 20 000 km diameter green sphere's surface and in any direction.
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brainliest to coorrrect answer
The measures of angles q, r and s are 100°, 135° and 125° and the sum of the three angles equals 360°.
What are the measures of missing angles of a geometric system?
In this problem we find a geometric system generated by three lines no collinear to each other, which generate the triangle DEF. In accordance with the Euclidean geometry, the sum of the measures of internal angles in a triangle equals 180°:
m ∠ FDE + m ∠ DEF + m ∠ DFE = 180° (1)
If m ∠ FDE = 80° and m ∠ DEF = 45°, then the measure of the angle DFE is:
m ∠ DFE = 55°
Finally, we find the values of the angles q, r and s by definition of supplementary angles:
q = 180° - 80°
q = 100°
r = 180° - 45°
r = 135°
s = 180° - 55°
s = 125°
The sum of the measures of angles q, r and s is:
q + r + s = 360°
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Find the surface area of a cube with side length og 6 1/2 inches.
PLEASE SHOW WORK
The surface area of a cube with side length of 6 1/2 inches is 253.5 square in
Surface area of cubeThe formula for calculating the surface area of cube is expressed as:
Surface area = 6L^2
where
L is the side length of the cube
Substitute
SA = 6(13/2)^2
SA = 6 * 169/4
SA = 3 * 169/2
SA = 253.5 square in
Hence the surface area of a cube with side length of 6 1/2 inches is 253.5 square in
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What transformation is represented by the rule
(1, y) → (1, y+3)?
O translation 3 units down
O translation 3 units right
O translation 3 units up
O translation 3 units left
X
. You deposit money in an account that earns Simple interest at an annual rate of 6%. After 8 years.
Y
the account earns $360 in interest. How much money did you deposit in the account?
Answer:
$750
Step-by-step explanation:
I = interest
p = principle
r = rate
t = time
I = prt Plug in what you know and solve for p
360 = p (.06)(8)
360 =p.48 Divide both sides by .48
750 = p
The principal is deposited in the account is $750.
Given that, rate of interest =6%, time period = 8 years and simple interest = $360.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Now, 360 = (P×6×8)/100
⇒ 360 = 48P/100
⇒ 48P = 36000
⇒ P = 36000/48
⇒ P = $750
Therefore, the principal is deposited in the account is $750.
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A pharmacist mixes 5g of a power with 45cm of water to make a prescription medicine . how much powder should she mix with 81cm of water to make a larger amount of the same medicine.
The pharmacist should mix 9 g of a power to make a larger amount of the medicine
To solve this problem, we have to state the equation using the information of the problem
Information about the problem:
mass(1) = 5gvolume(1) = 45 cm3volume(2)= 81 cm3mass(2) = ?Calculating the rate of the medicine with the 1st mixed:
rate = mass(1)/ volume(1)
rate = 5g / 45cm3
rate = 0.11 g/cm3
Calculating how much power the pharmacist needs for the volume(2):
mass(2) = rate * volume(2)
mass(2) = 0.11 g/cm3 * 81 cm3
mass(2) = 9 g
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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a tripod has three legs each of length 5 feet. when the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground. in setting up the tripod, the lower 1 foot of one leg breaks off. let $h$ be the height in feet of the top of the tripod from the ground when the broken tripod is set up. then $h$ can be written in the form $\frac{m}{\sqrt{n}}$, where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. find $\lfloor m \sqrt{n} \rfloor$. (the notation $\lfloor x \rfloor$ denotes the greatest integer that is less than or equal to $x$.)
The value of [m + √n] is 183.
We note that AO=3. From this we can derive that the side length of the equilateral is 3√3. We now use 3D coordinate geometry.A is (0, 0, 0), B is (3√3, 0, 0), C is ((3√3)/2, 9/2, 0), T is ((3√3)/2, 3/2, 4), and S is ((3√3)/10, 3/10, 4/5).We know three points of the SCB plane, so we can write out the equation for the plane. Plane SCB can be expressed as (4√3)x + 4y + 39z - 36 = 0.Applying the distance between a point and a plane formula(ax + by + cz + d)/(√(a² + b² +c²)Put T's coordinates in this in (x, y, z), and replace the values of a, b, c, and d with plane equation coefficients.We get the distance equal to 144/(√1585).A distance of the form m/(√n) is given to us.We have to calculate [m + √n] = [144 + √1585] = 183.To learn more about plane, visit :
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Which of the following is not a rational number?
Α. 0
B. √2
C. 3/4
D. √4
Answer: B
Step-by-step explanation: the square root of 2 cannot really be expressed as a fraction where both the numerator and the denominator are integers.
Answer:
B
Step-by-step explanation:
What is the student error in the multiplication below?
Multiply the ones: 957 times 23 = 2871. Above the 9 in 957 is 1, above the 5 in 957 is 2.
Multiply the tens: 957 times 23 = 2871. 2871 + 1914 = blank. Above the 9 in 957 is 1, above the 5 in 957 is 1.
Answer:
When multiplying the tens, the student didn't use the 0 place holder for the ones place.
Step-by-step explanation:
When using or doing long multiplication the answer was correct (2871) BUT before multiplying the tens, a zero should be placed in the ones place of the results. So, the tens should be 19140
2871+19140=22011
Answer: 1) When multiplying the ones, the student did not carry over a ten to the next place in the first multiplication.
2) When multiplying the ones, the student should have calculated 3 times 2 plus 5 as 11 and placed a 1 in the tens place.
3) When multiplying the tens, the student did not use the 0 place holder for the ones place.
4) When multiplying the tens, the student should have calculated 2 times 1 plus 9 as 11 and used a 1 should in the hundreds place.
Answer:
The correct option is;
4) When multiplying the tens, the student did not use the 0 place holder for the ones place
Step-by-step explanation:
Here we have when doing long multiplication, the student correctly multiplies the ones as 2871, however, before commencing multiplication of the tens, a 0 should be placed in the ones place of the result as a place holder such that the outcome of the multiplication of the tens should be;
19140
Hence, the correct result should be 2871 + 19140 = 22011
The correct option is therefore, that "When multiplying the tens, the student did not use the 0 place holder for the ones place."
Step-by-step explanation:
I need help with this one
Answer:
c) -66%, -0.45, -1/3, 1.8
Step-by-step explanation:
Numbers provided:
-66%-1/3-0.451.8Rewrite them in decimals:
-66% = -0.66-1/3 = -0.33-0.45 = -0.451.8 = 1.8In ascending order (from least to greatest):
-0.66 < -0.45 < -0.33, 1.8-66% < -0.45 < -1/3 < 1.8Solution: -66%, -0.45, -1/3, 1.8
Calculus help please
Step-by-step explanation:
THE POINT WHERE
[tex]f( - 4) = ( { - 4})^{2} + 1 \\ f( - 4) = 16 + 1 \\ f( - 4) = 17[/tex]
Now we have point (-4,17)
the gradient of the tangent line at that point of f(x) is the first derivative f'(x)=2x at that point
f'(x) =m
f'(-4)=2(-4)
f'(-4)=-8
The gradient therefore is -8
the general equation of a straight line is given by
[tex]y = mx + c \\ 17 = ( - 8)( - 4) + c \\ 17 = 32 + c \\ c = 17 - 32 \\ c = - 15 \\ \\ y = - 8x - 15[/tex]
HOPE THIS HELPS!!
can anyone answer this for me
Answer:
{-9, 3, 10}
Step-by-step explanation:
Place the elements (the numbers marked by red) within curly brackets.
write a ratio and sentence comparing the number of jeans bought to the cost
In words, the ratio of the number of jeans bought to the cost is four to thirty two.
How to write a ratio?
We are told that you just bought 4 pairs of jeans for $32.
Now, since you bought 4 pairs for a cost of $32, then we can say that the ratio to represent the number jeans per dollars is;
4 :32
Thus, writing this in words we can say that the ratio of the number of jeans bought to the cost is four to thirty two.
Alternatively, we can also express it as a fraction with numerator and denominator as 4/32.
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Complete question is;
You just bought 4 pairs of jeans for $32. write a ratio and sentence comparing the number of jeans bought to the cost
What are the leading coefficient and degree of the polynomial -u^8+18+10u^3
Answer:
Step-by-step explanation:
The variable here is u, and the highest power of u is u^8. The first term is thus -u^8, and the coefficient of this is -1. Thus, the leading coefficient of the polynomial is -1. The degree is 8.
In a week, a man received a paycheck for $826.60. The withholding for taxes was $91.40. If he worked 34 hours in that week, what is his hourly pay rate?
Answer:
Step-by-step explanation:
The Clear-Bell Cell phone company has a plan that costs
customers $29.99 for a monthly service fee plus 3¢ per minute used.
a. Write a linear equation to model this situation.
b. Identify the slope and the y-intercept. Interpret the slope and y-intercept in the context of this problem.
c. If Polly talks for 136 minutes, how much would her cell phone bill be (excluding taxes)?
Answer: a. y=0.03x+29.99
b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.
y-int: (0, 29.99). Total cost per month when phone isn't being used.
c. $34.07
Step-by-step explanation:
a. p=Cell phone plan. m=minutes used for phone.
3¢=$0.03
p=29.99+0.03m
y=0.03x+29.99
b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.
y=0.03(0)+29.99
p=29.99 ==> y-int: (0, 29.99). Total cost per month when phone isn't being used.
c. y=0.03(136)+29.99
y=4.08+29.99
y=$34.07
two third of a number minus 5 gives 11
what is the number?
Answer: n=24
Step-by-step explanation:
n=number
2/3 * n - 5=11
2n/3=16
2n=48
n=24
If M is a midpoint of segment AB and AM=3x+1, if AB=20 cm what is the value of x?
Answer:
x = 3
Step-by-step explanation:
AB is the line segment and is 20 cm
Since M is the midpoint, AM = MB = 20/2 = 10
3x + 1 = 10
==> 3x = 10- 1 = 9
==> x = 9/3 = 3
Answer:
AB=20 then AM =10
now,
[tex]3x + 1 = 10 \\ 3x = 10 - 1 \\ 3x = 9 \\ x = 3 [/tex]
Find the perimeter and area of the
polygon with the given vertices.
W(5, — 1), X(5, 6), Y(2, — 1), Z(2, 6)
The perimeter is units. The area is
squareunits.
The perimeter of the polygon will be 20 units and the area will be 21 square units.
From the given vertices a rectangle will be formed. A rectangle is a closed figure in which each interior angle is a right angle. The Perimeter of the rectangle can be given by formula 2(l + b) and the area is given by l×b where l is the length and b is breadth of rectangle. Now from the given points the dimensions of rectangle will follow the order W (5, -1), X (5, 6), Z (2, 6) and Y (2, -1).
The length of the rectangle is given by l = √ (6 + 1) ² + (5 - 5) ²
l = √49
l = 7 units
The breadth of the rectangle is given by b = √ (6 - 6) ² + (2 - 5) ²
b = √9
b = 3 units
Now, the perimeter of rectangle = 2 (l + b)
P = 2(7 + 3)
P = 20 units
Area of the rectangle = l×b
A = 7×3
A = 21 square units.
Thus, the perimeter and area are 20 units and 21 square units respectively.
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Identify the rule(s) of algebra illustrated by the statement. (Select all that apply.) 1 · (1 + x) = 1 + x
The rule(s) of algebra illustrated by the statement is the identity property of algebra
How to identify the rule(s) of algebra illustrated by the statement.?The statement is given as:
1 · (1 + x) = 1 + x
The identity property of algebra states that:
1 * a = a or a * 1 = a
In the above (given) statement, we can see that the expression 1 + x is multiplied by 1 to given 1 + x
This can be illustrated as
1 * a = a
The rule(s) of algebra that illustrates the above equation is the identity property of algebra
Hence, the rule(s) of algebra illustrated by the statement is the identity property of algebra
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Interest earned: $39.60
Principal: ?
Interest rate: 11%
Time: 6 months
The principal amount is calculated as $720.
What is defined as the simple interest?Simple interest is a simple and quick method to calculate the interest on a loan.
Consumers who charge their loans on time as well as early each month benefit from simple interest.Auto loans as well as short-term personal loans have been typically interest-only loans.Simple interest is calculated by multiplying the daily interest rate by the principal multiplied by the number of days between payments.The formula for calculating the simple interest is;
SI = PRT/100
Where,
SI = simple interest
P = principal amount
R = rate of interest (%)
T = time period in years
For the given values in the question
Simple Interest earned: $39.60Interest rate: 11%Time: 6 months = 0.5 years.Substitute the given values in the question;
39.60 = (P×11×0.5)/100
P = 39.60×100/(11×0.5)
P = 720
Therefore, the value of the principal amount is estimated as $720.
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Lynden's first two, 100-meter-dash times are 13.075 seconds and 12.55 seconds. what are her mean (average) time? round your answer to the thousandths place.
The average time of Lynden's first two, 100-meter-dash is 12.813 seconds.
We are given the 100-meter-dash times of Lynden in first two races. So, the average time for first two races will be calculated using the formula -
Average = sum of all observations ÷ total number of observations
Sum of all observations here will be the sum of time of race.
Sum of observations = 13.075 + 12.55
Performing addition
Sum of observations = 25.625 seconds
Number of observations is the number of races whose time is taken in calculation.
Number of observations = 2
Keep the values in formula to find the average time.
Average time = 25.625 ÷ 2
Average time = 12.8125 seconds.
Rounding to nearest thousands place : 12.813 seconds
Hence, the average time of Lynden's first two, 100-meter-dash is 12.813 seconds.
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how to solve 233.91/3.45
Answer:if it is division it is:
Divide
233.91
by
3.45
=
67.8
Step-by-step explanation:
A particular antibiotic is eliminated from the blood with a half-life of 16 hours. how many hours does it take for 100-milligram dose to decrease to 30-milligrams in the blood?
Using the decay formula, the particular antibiotic with half-life of 16 hours, will decrease to 30-milligrams in the blood after 27.79 hours.
We can use the decay formula to solve the problem:
A(t) = A(0) . (0.5)^(t/T)
Where:
A(t) is the remaining quantity at time t
A(o) is the initial quantity
t is the time interval
T is the half-life rate
In the given problem:
A(0) = 100 milligram
T = 16 hours
A(t) = 30 milligram
We need to find t such that the remaining quantity of this antibiotic is 30 mg.
Substitute the given parameters into the formula:
A(t) = A(0) . (0.5)^(t/T)
30 = 100 . (0.5) ^(t/16)
Taking the logarithm:
log (30) = log [100 . (0.5) ^(t/16)]
Use the logarithm property, log(A.B) = log A + log B
log (30) = log (100) + log [(0.5) ^(t/16)]
Use the logarithm property, log(Aⁿ) = n.log A
log (30) = log (100) + (t/16) . log (0.5)
log (30) = 2 + (t/16) . log (0.5)
(t/16) . log (0.5) = log (30) - 2
t/16 = 1.737
t = 1.737 . (16) = 27.79 hours
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Need help rn pleas e
Answer:
659
Step-by-step explanation: Divishion of practice
Answer:
Area : 63.6 square inches.
Cost: Cost per square inch = 18.60 / 63.6 = $0.29 (rounded to the nearest cent)
Step-by-step explanation:
29) A company planned to donate 640 bags of groceries, 320 cases of bottled water, and 800 small toys to a
local relief center. Suppose that the number of bags of groceries, cases of bottled water, and small toys are to be
placed in boxes with the same number of each good in each box. For instance, you could place 10 bags of
groceries and 5 cases of water in each of 64 boxes, but that would require 12.5 toys per box-oops! To be as
efficient as possible, assume that the company wants to use as few boxes as possible and must have a whole
number of groceries, water, and toys in each box.
a) How many boxes are needed? b) What are the contents of each box?
160 boxes needed to pack these items
Therefore contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.
Given no of groceries bags = 640
number of cases of bottled water = 320
number of small toys = 800
We have to find out how many boxes are needed and the contents of each box.
(i) How many boxes are needed:
To do this we need to find the greatest common factor of these three items
as
640 - 2⁷ * 5
320 - 2⁶ * 5
800 - 2³ * 5²
GCF = 2⁵ * 5 = 160
Therefore 160 boxes needed to pack these items
(ii) Contents of each box:
No of bags of groceries in each box = 640 / 160 = 4
No of cases of bottled water = 320 / 160 = 2
No of toys in each box = 800 / 160 = 5
Therefore, contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.
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