Answer:
x > 22
Step-by-step explanation:
Hey there!
Well to solve,
52 - 3x < -14
we need to single out x
52 - 3x < -14
-52 to both sides
-3x < -66
Divide both sides by -3
x > 22
The < changes to > because the variable number is a - being divided.
Hope this helps :)
Answer:
x > 22
Step-by-step explanation:
First, rearrange the equation
52 - 3 × x - (-14) < 0Then, pull out the like terms:
66 - 3xNext, apply algebra to the equation by dividing each side by -3. It should now look like this: x > 22.
Therefore, the solution set of the inequality would be x > 22.
I don't understand word problems can someone please answer it for me and I need it ASAP.
Answer:
Inequality: 3 + 1.2c
What you'd put on graph: 1 ≥ 13.50
What is the area of a parallelogram if the coordinates of its vertices are (0, -2), (3,2), (8,2), and (5, -2)?
Answer: 20 sq. units .
Step-by-step explanation:
Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.
First we plot these points on coordinate plane, we get parallelogram ABCD.
By comparing the y-coordinate of B and C with A and D , we get
height = 2+2 = 4 units
Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units
Area of parallelogram = Base x height
= 5 x 4 = 20 sq. units
Hence, the area of a parallelogram ABCD is 20 sq. units .
Consider the following. x = t − 2 sin(t), y = 1 − 2 cos(t), 0 ≤ t ≤ 2π Set up an integral that represents the length of the curve. 2π 0 dt Use your calculator to find the length correct to four decimal places.
Answer:
L = 13.3649
Step-by-step explanation:
We are given;
x = t − 2 sin(t)
dx/dt = 1 - 2 cos(t)
Also, y = 1 − 2 cos(t)
dy/dt = 2 sin(t)
0 ≤ t ≤ 2π
The arc length formula is;
L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt
Where α and β are the boundary points. Thus, applying this to our question, we have;
L = (0,2π)∫√((1 - 2 cos(t))² + (2 sin(t))²)dt
L = (0,2π)∫√(1 - 4cos(t) + 4cos²(t) + 4sin²(t))dt
L = (0,2π)∫√(1 - 4cos(t) + 4(cos²(t) + sin²(t)))dt
From trigonometry, we know that;
cos²t + sin²t = 1.
Thus;
L = (0,2π)∫√(1 - 4cos(t) + 4)dt
L = (0,2π)∫√(5 - 4cos(t))dt
Using online integral calculator, we have;
L = 13.3649
Solve 5(2x + 4) = 15. Round to the nearest thousandth.
[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]
Answer:
[tex]\huge\boxed{x=-0.5}[/tex]
Step-by-step explanation:
[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]
Fiona wrote the linear equation y = y equals StartFraction 2 over 5 EndFraction x minus 5.x – 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s? x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 2 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 2 EndFraction.y =
Answer:
D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{2}{5}x - 5[/tex]
Required
Determine its equivalent
From the list of given options, the correct answer is
[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]
This is shown as follows;
[tex]y = \frac{2}{5}x - 5[/tex]
Multiply both sides by [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]
Open Bracket
[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]
[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]
Subtract x from both sides
[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]
[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]
Multiply both sides by -1
[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]
[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]
Reorder
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Hence, the correct option is D
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Answer:
The 4th option
Step-by-step explanation:
Given below are descriptions of two lines. Line 1: Goes through (-2,10) and (1,1) Line 2: Goes through (-2,8) and (2,-4)
Answer:
Option (2)
Step-by-step explanation:
1). If two lines have the same slope, lines are defined as parallel.
m₁ = m₂
2). If the multiplication of the slopes of two lines is (-1), lines will be perpendicular.
m₁ × m₂ = (-1)
Line 1 : It passes through two points (-2, 10) and (1, 1).
Slope of the line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{1+2}{10-1}[/tex]
= [tex]\frac{3}{9}[/tex]
m₁ = [tex]\frac{1}{3}[/tex]
Line 2 : It passes through two points (-2, 8) and (2, -4).
Slope of the line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{8+4}{-2-2}[/tex]
= [tex]-\frac{12}{4}[/tex]
m₂ = -3
Since, m₁ × m₂ = [tex]\frac{1}{3}\times (-3)[/tex]
= (-1)
Therefore, given lines are perpendicular to each other.
Option (2) is the correct option.
Five more than the square of a number Five more than twice a number Five less than the product of 3 and a number Five less the product of 3 and a number Twice the sum of a number and 5 The sum of twice a number and 5 The product of the cube of a number and 5 The cube of the product of 5 and a number. 5 + x2 5 + 2x 5 - 3x 3x - 5 2x + 5 2(x + 5) 5x3 (5x)3 WILL MARK BRAINLIEST AND DON'T PUT A FAKE ANSWER TO GET POINTS EITHER CUS I NEED HELP
Answer:
BelowStep-by-step explanation: Let all unknown no be x
Five more than the square of a number
= [tex]5 + x^2[/tex]
Five more than twice a number ;
[tex]5+2x\\= 2x+5[/tex]
Five less than the product of 3 and a number ;
[tex]5- 3x\\= 3x-5[/tex]
Twice the sum of a number and 5 ;
[tex]2(x+5)\\[/tex]
The sum of twice a number and 5 ;
[tex]2x+5[/tex]
The product of the cube of a number and 5;
[tex]x^3 \times 5\\=5x^3[/tex]
The cube of the product of 5 and a number ;
[tex](5\times x)^3\\(5x)^3[/tex]
A soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification. Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration. What is the probability that the assembly line will be shut down, given that it is actually calibrated correctly? Use Excel to find the probability. Round your answer to three decimal places.
Answer:
The probability that the assembly line will be shut down is 0.00617.
Step-by-step explanation:
We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.
Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.
Let X = Number of bottles in the sample that are not within specification.
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 12 bottles
x = number of success = 2 or more bottles
p = probabilitiy of success which in our question is probability that
bottles are not within specification, i.e. p = 0.01
So, X ~ Binom (n = 12, p = 0.01)
Now, the probability that the assembly line will be shut down is given by = P(X [tex]\geq[/tex] 2)
P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)
= [tex]1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}[/tex]
= [tex]1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})[/tex]
= 0.00617
Jasmine is making 150 bracelets and she needs 26 cm of silver wire for each bracelet. She will buy either the 3.7 metre or the 10.5 metre packs. She wants to pay as little as possible for the silver wire. How much will she have to pay for the silver wire to make 150 bracelets? £
Answer:
The least possible price is p = £110
Step-by-step explanation:
From the question we are told that
The number of bracelets to be made is [tex]n = 150[/tex]
The length of silver require for on bracelet is [tex]x = 26 \ cm = 0.26 \ m[/tex]
The option of silver length packs that she buys is a = 10.5 m packs
b = 3.7 m packs
Generally
1 bracelet [tex]\to[/tex] 0.26 m
150 bracelet [tex]\to[/tex] z
=> [tex]z = \frac{150 * 0.26}{1}[/tex]
=> [tex]z = 39 \ m[/tex]
Now for option a i.e 10.5 m per pack
The number of packs require is
[tex]v = \frac{z}{a}[/tex]
=> [tex]v = \frac{39}{ 10.5}[/tex]
=> [tex]v = 3.7 1[/tex]
given that the number of packs cannot be a fraction but an integer hence she needs to purchase v = 4
and that 4 packs would equal t = 4 * 10.5 = 42 meters of silver
Now for option d i.e 3.7 meters per pack
The number of packs requires is
[tex]w = \frac{z}{b}[/tex]
=> [tex]w = \frac{39}{3.7}[/tex]
=> [tex]w = 10.54[/tex]
given that the number of packs cannot be a fraction but an integer hence she needs to purchase w= 11
and that 11 packs would equal t = 11 * 3.7 = 40.7 meters of silver
So the comparing the option and option b we see that for her to pay as little as possible she needs to go for option b since option be will produce the 150 bracelet with a little excess while option a will produce the 150 bracelet with much excess
Assuming the price for the 3.7 m pack is £10
And the price for the 10.7 pack is £30
The least possible amount she would pay is
[tex]p = 10 * 11[/tex]
p = £110
In which set(s) of numbers would you find the number -832 a. whole number b. irrational number c. integer d. rational number e. real number f. natural number
Answer:
integer of course
Step-by-step explanation:
an integer can either be negative or positive.
Henry is investing at a continuously compounded annual interest rate of 4.5%. How many years will it take for the balance
to triple? Round your answer up to the nearest whole number, and do not include the units in your answer.
Answer:
1 year
Step-by-step explanation:
Hello,
Continuously compounding with an annual interest rate of 4.5% means multiplying the initial investment by (for t tears).
[tex]\displaystyle e^{(1+4.5\%)t}=e^{\left( 1.045\cdot t \right) }[/tex]
So we need to find t so that:
[tex]\displaystyle e^{\left( 1.045\cdot t \right) }=3\\\\1.0.45t=ln(3)\\\\t=\dfrac{ln(3)}{1.045}=1.051304...[/tex]
Rounding to the nearest whole number gives 1 year.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
25
Step-by-step explanation:
Trust me
. In statistics, a data set has the following characteristics: (Choose all that apply) A:A data set is a collection of similar data. B:A data set can contain only quantitative data. C:A data set is any piece of descriptive or quantitative information on any object of study. D:A data set contains data all of which have some common characteristic.
Answer:
A. A data set is a collection of similar data.
D. A data set contains data all of which have some common characteristic.
If the occurrence of one event does not influence the outcome of another event, then two events are:
A. conditional
B. disjoint
C. independent
D. interdependent
Answer:
C. Independent
Step-by-step explanation:
Independent events are events that have no impact on each other.
So, if the occurrence of an event doesn't influence the outcome of another, this means that they are independent because they do not impact each other.
This must mean C is correct because the two events have to be independent.
PLS HELP ASAP Solve the inequality and enter your solution as an inequality in the box below 8>4-x>6
Answer:
−4<x<−2
Step-by-step explanation:
8 > 4 − x > 6
8 > −x + 4 > 6
8 + −4 > −x + 4 + −4 > 6 + −4
4 > −x > 2
Since x is negative we need to divide everything by -1 which gives us...
−4 < x < −2
A technician is testing light bulbs to determine the number of defective bulbs. The technician records the table below to show the results. Result of Light Bulb Test Number of Bulbs Tested 14 28 84 336 Number of Defective Bulbs Found 1 2 6 ? The technician expects to find 24 defective bulbs when 336 are tested. Which statement explains whether the technician’s reasoning is correct, based on the information in the table?
Answer:
He should find 24 defective lightbulbs.
Step-by-step explanation:
1. Divide the number of defective bulbs by the total number of bulbs for each section.
2. Make sure the number you get is the same each time.
3. Divide the guessed number of bulbs (24) by the total number of bulbs (336)
4. If the number you got for step 4 matches the number you got for step 3, then he is right
Answer:
The answer is A
Step-by-step explanation:
on NCCA
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
Assume that women's heights are normally distributed with a mean given by mu = 64.3 inches, and a standard deviation given by sigma= 2.2 inches.
A) If a woman is randomly selected, find the probability that her height is less than 65 inches.
B) If 34 women are randomly selected, find the probability that they have a mean height less than 65 inches.
Answer:69
Step-by-step explanation:
Armando is baking 36 batches of brownies for the bake sale. Each batch of brownies takes cups of flour. What is a reasonable estimate of the amount of flour that he will need to bake all thirty-six batches of brownies?
Answer:
Well, let's assume that "cups" = 3 cups of flour.
Step-by-step explanation:
First, multiply 3x36.
If for some reason this is incorrect, try 2 cups instead of 3. Both are reasonable measurements when it comes to baking.
g a video game claims that the drop rate for a certain item is 5% according to the game publisher. in online forums, a number of players are complaining that the drop rate seems to be low. in order to test the drop rate claim, 100 players agree to attempt to get the drop, each attempting 10 times. of the 1000 tries, the item only drops 40 times state the null hypothesis needed to test this claim group of answer choices
Answer:
p0 = 0.05
Step-by-step explanation:
How many different sets of polar coordinates can be given for a point, within one rotation? I thought it was infinite, but the given options are 1, 2, 3, and 4.
Answer:
the answer is 4
Step-by-step explanation:
so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get
Answer:
Solution : 4
Step-by-step explanation:
The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,
( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )
Respectively if theta was q say,
( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )
Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.
Which of the following is the correct set notation for the set of perfect squares between 1 and 100 (including 1 and 100)?
Select the correct answer below:
{p2∣p∈ℤ and 1≤p≤10}
{p2∣p∈ℤ and 1
Answer:
[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]
Step-by-step explanation:
Given
Range: = 1 to 100 (Inclusive)
Required
Determine the notation that represents the perfect square in the given range
Represent the range with P
P = 1 to 100
Such that the perfect squares will be P² and integers
In set notation, integers are represented with Z
The set notation becomes
[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]
The [tex]\leq[/tex] shows that 1 and 100 are inclusive of the set
In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find m∠NMC.
Answer:
∠NMC = 50°
Step-by-step explanation:
The interpretation of the information given in the question can be seen in the attached images below.
In ΔABC;
∠ A + ∠ B + ∠ C = 180° (sum of angles in a triangle)
∠ A + 70° + 50° = 180°
∠ A = 180° - 70° - 50°
∠ A = 180° - 120°
∠ A = 60°
In ΔAMN ; the base angle are equal , let the base angles be x and y
So; x = y (base angle of an equilateral triangle)
Then;
x + x + 60° = 180°
2x + 60° = 180°
2x = 180° - 60°
2x = 120°
x = 120°/2
x = 60°
∴ x = 60° , y = 60°
In ΔBQC
∠a + ∠e + ∠b = 180°
50° + ∠e + 40° = 180°
∠e = 180° - 50° - 40°
∠e = 180° - 90°
∠e = 90°
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
∠i = 50° - 40° = 10°
In ΔNQC
∠f + ∠i + ∠j = 180°
90° + 10° + ∠j = 180°
∠j = 180° - 90°-10°
∠j = 180° - 100°
∠j = 80°
From line AC , at point N , ∠y + ∠c + ∠j = 180° (sum of angles on a straight line)
60° + ∠c + ∠80° = 180°
∠c = 180° - 60°-80°
∠c = 180° - 140°
∠c = 40°
Recall that :
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
Then In Δ NMC ;
∠d + ∠h + ∠c = 180° (sum of angles in a triangle)
∠d + 90° + 40° = 180°
∠d = 180° - 90° -40°
∠d = 180° - 130°
∠d = 50°
Therefore, ∠NMC = ∠d = 50°
a radion station usa 1\6 of its time for the news. in a 12 hour day, how many hours are used for music & entertainment?
Answer:
10 hours
Step-by-step explanation:
In order to answer this question, you must assume that all air time not spent on news is spent on music & entertainment. That would usually not be the case, as there would usually be advertisements and public service programming along with everything else.
The time spent on news is ...
(1/6)(12 hours) = 2 hours
If the rest is spent on music and entertainment, then ...
12 -2 = 10 . . . hours are used for music and entertainment
How would you simplify and rationalize this expression? [tex]\frac{5\sqrt[4]{2}}{4\sqrt[4]{162} }[/tex]
Answer:
5/12
Step-by-step explanation:
(5 * 2^1/4)/4 * 162^1/4) = (5 * 2^1/4)/4 * 3 *2^1/4)
multiply top and bottom by 2^3/4
(5 * 2)/4 * 3 * 2) = 10/24 = 5/12
round 38562 to one significant figure
Answer:
plz refer the attachment
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
ROUND 38562 to ONE significant figure.
Answer:
= 4000
Rounding Significant Figures Rules
~ ↓↓↓↓↓↓↓ ~
Non-zero digits are always significant
Zeros between non-zero digits are always significantLeading zeros are never significantTrailing zeros are only significant if the number contains a decimal pointExamples of Significant Figures❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
❀*May*❀
somebody please help
Find the sum (x^3+5x^2+3x-7)+(8x-6^2+6)
Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)
Answer:
x^3 - x^2 + 11x - 1
-x^3 - 8x^2 + 5x + 7
Step-by-step explanation:
Find the sum
(x^3+5x^2+3x-7)+(8x-6x^2+6)
=x^3+5x^2+3x-7+8x-6x^+6
Collect like terms
=x^3 +5x^2-6x^2+3x+8x-7+6
Add the like terms
= x^3 - x^2 + 11x - 1
Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)
(7x-3x^2+2)-(x^3+5x^2+2x-5)
= 7x-3x^2+2-x^3-5x^2-2x+5
Collect like terms
= -x^3-3x^2-5x^2+7x-2x+2+5
Add the like terms
= -x^3 - 8x^2 + 5x + 7
If 7time the 7th of Ap. Is equal of 11 tomes its 11th term find 18th term
0 0
,
---------------
What value of x makes this equation true?
17 5 - 7 = -4
x=
y Su
What value of x makes this equation true? X/6-7=-4
Answer:
x=18
Step-by-step explanation:
x/6 - 7 = -4
x/6 = 3
(x/ 6) * 6 = 3*6
x = 18
what number has 7 ten thousands, 1 thousand, 1 hundred, and no ones?
Answer:
[tex]71,100[/tex]
Step-by-step explanation:
If you are trying to find a number that is written in word form, we can just use place values to find what goes where.
A number is broken down into this:
Ten thousands, thousands, hundreds, tens, ones.
If they have 7 ten thousands, the first digit will be a 7.
If they have 1 thousand, the second digit will be a 1.
If they have 1 hundred, the third digit will be a 1.
Since nothing is stated about tens, we assume it's value is 0.
And since there are no ones, it's value is 0.
So:
71,100.
Hope this helped!