[tex]10s = 1000 - 100[/tex]
i)WHEN GROUPING LIKE TERMS 100 WAS GROUPED WITH 1000 SINCE IT CHANGED PLACE IT ALSO CHANGED THE SIGN FRKM POSITIVE TO NEGATIVE.[tex]10s = 900[/tex]
NOW TO GET THE VALUE OF s it means we will have to divide both sides by the coefficient os s which is 10.Meaning 10 will divide 10s and also 900 we get:
[tex] \frac{10s}{10} = \frac{900}{10} \\ s = 90[/tex]
ii) WE ALSO HAVE TO GROUP TERMS HERE. IT MEANS -5 WILL BE GROUPED WITH 25 BUT WHEN IT CHANGES POISTION IT WILL ALSO CHANGE SIGN.[tex]12m = 25 + 5 \\ 12m = 30 \\ \frac{12m}{12} = \frac{30}{12} \\ m= \frac{30}{12} \\ m = \frac{15}{6} [/tex]
Three consecutive positive odd integers such that 5 times the square of the
middle integer exceeds the product of the other two by 488.
By letting the smallest integer equal x, set up and solve a quadratic equation
to find the middle integer.
A solution by trial and improvement will not be accepted.
An analogous equation can be created by factoring a quadratic equation. 5x^2 = (x-2) * (x+2) + 488 can give integers 9, 11,13.
What is a quadratic equation?In algebra, quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as
[tex]{ax^{2}+bx+c=0}[/tex]
where a 0 and x denotes an unknown and a, b, and c denote known numbers, Since there is no ax2 term, the equation is linear (and not quadratic) if a = 0 (and b 0). The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient, linear coefficient, and constant or free term, respectively.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation. There can only be two solutions to a quadratic problem. One claims that a problem is a double root if there is just one solution. There are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or two real solutions if all the coefficients are real values. If complex roots are included, a quadratic equation will always have two roots; a double root counts as two. An analogous equation can be created by factoring a quadratic equation.
According to the formula, if 5x2 = x2 - 4 + 488, then 5x2 = x2 + 484.
For 4x2 = 484, subtract x2 from each side, resulting in x2 = 121.
For x = 11, square root each side.
TEST: 5*121 = 9*13 + 488, so 605 is equal to 117 plus 488.
The middle odd number, x, is equal to 11.
The figures are 9, 11, and 13.
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what is the maximum number of balls of clay of radius 2 that can completely fit inside a cube of side length 7 assuming the balls can be reshaped but not compressed before they are packed in the cube?
Answer:
Number of balls of clay: 10
Step-by-step explanation:
The volume of the cube is [tex]$V_{\text{cube}}=7^3=343,$[/tex]
and the volume of a clay ball is: [tex]$V_{\text{ball}}=\frac43\cdot\pi\cdot2^3=\frac{32}{3}\pi.$[/tex]
Since the balls can be reshaped but not compressed, the maximum number of balls that can completely fit inside a cube is
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=\left\lfloor\frac{343}{\frac{32\pi}{3} }\right\rfloor.\][/tex]
Approximating with [tex]$\pi\approx3.14[/tex]
We have:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=10.23565228[/tex]
We simplify to get:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor\approx10[/tex]
So:
[tex]\boxed{number\ of\ balls = 10}.$[/tex]
if u know this please help
Answer:
alternate angles and corresponding angles.
and vertical opposite angles
Step-by-step explanation:
#G o o g l e
Name the reciprocal that you will use to multiply
(Equations in picture)
I only need the reciprocals
Answer: 9/4 and -2/1 (or -2)
Step-by-step explanation: Reciprocals are just the fraction flipped
12. Adam didn't sleep well the night before a big trip. He only slept 4 ½ hours. This is 3/5
of what he usually sleeps. How many hours does he usually sleep?
Answer:
seven and a half hours
Step-by-step explanation:
aa
How many sheets of metal are in a stack 4.00 in. high if each sheet is 0.0146 in. thick?
The number of metal sheets in the stack is
(Round to the nearest whole number as needed.)
The number of metal sheets in the stack is 274 metal sheets
Ratio and proportionFractions are written as a ratio of two integers. For instance a/b is a fraction.
Given the following parameters
Height of metal sheet = 4.00in
Height of each sheet= 0.0146 in
Number of metal sheet = height of metal sheet/height of each sheet
Substitute
Number of metal sheet = 4.00/0.0146
Number of metal sheet = 274 metal sheets
This gives the required number of sheets
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The Jules Server Scholarship Fund gives a graduation award of
$250.00 to a graduating senior at North End High School. Currently the
fund has a balance of $8300.00 in an account that pays 2.2% interest
compounded annually. Will the amount earned in annual interest be enough
to pay for the award?
The compound interest of $182.60 will not be enough to pay for the award.
What is compounding?Compounding is the process by which interest is added to both the principal balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns to interest are magnified over time, or the so-called "miracle of compounding." For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest.So, annual interest will be sufficient to serve the award:
Compound interest of $83020.00 at the annual interest of 2.2% for 1 year will be $182.60.The total amount after 1 year will be $8482.60.(Refer to the compound chart given below)
Interest will be $182.6 and the graduation award is $250.00, so the interest will not be enough to pay for the award.Therefore, the compound interest of $182.60 will not be enough to pay for the award.
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Fav Sport
volleyball (12)
Basketball (18)
Ping Pong (8)
Softball (10)
Football (24)
(#s in brackets are the frequencies of their individual sports)
It should be noted that the angle sector for each sport will be:
volleyball (12) = 60°
Basketball (18) = 90°
Ping Pong (8) = 40°
Softball (10) = 50°
Football (24) = 120°
How to illustrate the information?From the information given, the following can be illustrated:
volleyball (12) = 12/72 × 360° = 60°
Basketball (18)= 18/72 × 360° = 90°
Ping Pong (8) = 8/72 × 360° = 40°
Softball (10) = 10/72 × 360° = 50°
Football (24) = 24/72 × 360° = 120°
Total = 72
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Solve the following...
4x+10=-26
Answer:
x = -9
Step-by-step explanation:
the goal is to get x by itself, so subtract 10 from both sides: 4x=-36
divide both sides by 4: x = -9
|-----4x+10=-26 |
|ANSWER= x=-9-------|
happy fall!
explanation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we have questions like this, and the x is just THROWN in there, we have to "combine our like terms."
STEP ONE ✨: "How do we do that..if one is on the other side?"
We have to make it disappear. +10-10 equals zero, right? right! So do that!
4x+10=-26
-10
But what we do to one side, we do to the other! Subtract 10 from the numbers on the equal side.
4x+10=-26
-10 -10
-26-10
4x=-36
STEP TWO : What do we do when a number has an X beside it?
Since this number is being multiplied to the x, we have to DIVIDE the 4x by 4, so we just get the x alone. It always works like this. Don't doubt yourself!!
4x=-36
/4 /4
-36/4=-9
x=-9!
----------------
i hope this helped! || much love! <33
Which of the following situations can be modeled by the equation?
answer = a
formula; a(1 + r)^x
a = the initial amount - 7.71 [answer cannot be b or d]
! i think it's a as the decay factor is < 1, therefore, 100-.933333
(Laws of Exponents with Integer Exponents LC) Simplify (34)−1. one over three raised to the fourth power one over three raised to the power of negative four −34 33
The simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
In the question ,
the expression is given as (3⁴)⁻¹ ,
the rule of law of exponents states that a⁻ⁿ = 1/aⁿ .
Using the above mentioned law of indices , the expression (3⁴)⁻¹ can be written as ,
(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴
which can be expressed in words as one over three raised to the fourth power .
Therefore , the simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
The given question is incomplete , the complete question is
The Simplified value of (3⁴)⁻¹ is
(a) one over three raised to the fourth power
(b) one over three raised to the power of negative four
(c) −3 to the power of 4
(d) 3 to the power of 3
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Thực hiện phép tính -7x^2(3x-4y)
Answer: -21x^3 + 28x^2 y
I need help..........
Answer:
y=1.34x-3.22
Step-by-step explanation:
y=mx+b
find m/ gradient:
[tex]m = \frac{-3.94 - 2.4}{-4.75 - 0}[/tex]
∴[tex]m=1.34[/tex]
find b/ y-intercept:
sub (2.4,0)
0= 1.34 (2.4) +b
b=0-3.216
b= -3.216
∴ b=-3.22(2.d.p)
linear equation:
∴1.34x-3.22
The price of a math textbook can be modeled by the equation:
y = 2x + 76, where x is time in years and y is the price of
the textbook. This equation tells us that the textbook originally
cost $76 and each year the cost went up $2. How many years
will it take for the textbook to cost $100?
HELP!!!! HELP HELP HELP HELP
The matchings are:
3x - y = -5 ⇒ table C.
x - 3y = 12 ⇒ table A.
3x - y = -2 ⇒ table D.
2x - 3y = 9 ⇒ table B.
How to match each equation to the correspondent table?The first equation we have is:
3x - y = -5
Evaluating in x = 0, we have:
3*0 - y = - 5
y = 5
So we have the point (0, 5).
Evaluating in x = -2 we get:
3*-2 - y = -5
6 + y = 5
y = 5 - 6 = -1
So we have the point (-2, -1)
The only table with that point is table C, so we conclude that it is the correct option.
2) The second equation is:
x - 3y = 12
Evaluating in x = 0 we get:
0 - 3y = 12
y = 12/-3 = -4
So we have the point (0, -4)
if x = 3 we have:
3 - 3*y = 12
-3*y = 12 - 3 = 9
y = 9/-3 = -3
So we have the point (3, -3)
The only table with these two points is table A, so that is the correct one.
3) The next equation is:
3x - y = -2
The tables left are B and D.
Now, let's evalaute this equation in x = 3.
3*3 - y = -2
9 - y = -2
9 + 2 = y
11 = y
So we have the point (3, 11)
Notice that on table B,the value associated to x = 3 is y = -1, so we discard table B, and we conclude that this equation relates to table D.
Trivially, the last equation:
2x - 3y = 9
Matches table B.
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an elementary school is offering 3 language classes: one in spanish, one in french, and one in german. the classes are open to any of the 100 students in the school. there are 28 students in the spanish class, 26 in the french class, and 16 in the german class. there are 12 students that are in both spanish and french, 4 that are in both spanish and german, and 6 that are in both french and german. in addition, there are 2 students taking all 3 classes.
Using Venn diagram, if a student is chosen randomly, (a) the probability that he or she is not in any of the language classes is 0.5, (b) the probability that he or she is taking exactly one language class is 0.32, and (c) if 2 students are chosen randomly, the probability that at least 1 is taking a language class is 0.753.
Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)
Let A = students in the Spanish class = 28
B = students in the French class = 26
C = students in the German class = 16
Hence, the probability of each class is:
P(A) = 28/100 = 0.28
P(B) = 26/100 = 0.26
P(C) = 16/100 = 0.16
P(A ∩ B) = 12/100 = 0.12
P(B ∩ C) = 6/100 = 0.06
P(A ∩ C) = 4/100 = 0.04
P(A ∩ B ∩ C) = 2/100 = 0.02
(a) P(not A, B, C) = 1 - P(A ∪ B ∪ C)
P(not A, B, C) = 1 - [P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]
P(not A, B, C) = 1 - (0.28 + 0.26 + 0.16 - 0.12 - 0.06 - 0.04 + 0.02)
P(not A, B, C) = 1 - 0.5
P(not A, B, C) = 0.5
(b) P(A, B, C only) = P(A only) + P(B only) + P(c only)
P(A, B, C only) = [P(A) - P(A ∩ B) - P(A ∩ C) + P(A ∩ B ∩ C)] + [P(B) - P(A ∩ B) - P(B ∩ C) + P(A ∩ B ∩ C)] + [P(C) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]
P(A, B, C only) = (0.28 - 0.12 - 0.04 + 0.02) + (0.26 - 0.12 - 0.06 + 0.02) + (0.16 - 0.06 - 0.04 + 0.02)
P(A, B, C only) = 0.14 + 0.10 + 0.08
P(A, B, C only) = 0.32
(c) P = 1 - (50/100 x 49/99)
P = 1 - (49/198)
P = 149/198
P = 0.753
To complete the problem, here are the questions:
(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
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Dante buys candy that costs $7 per pound. He will spend at least $42 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Dante will buy. Write your answer as an inequality solved for p
Answer:
p [tex]\geq[/tex] 6
Step-by-step explanation:
If one pound costs $7 and he's going to spend at least $42, then he will buy at least as many pounds as what costs $42.
42 divided by 7 equals 6, so he will buy at least 6 pounds of candy.
How do you write 6% as a fraction or mixed number?
Answer:
As a fraction: 3/50
It cannot be turned into a mixed number
your pulse reflects the rate at which your heart beats. a healthy resting pulse rate in adults is between 60 and 100 beats per minute. in which of these two settings is a binomial distribution more likely to be at least approximately correct? explain your answer. (a) you select at random 10 times in the next 24-hour period to take your pulse. you then go about your usual activities, including exercising and sleep. the random variable ???? is the number of measurements that are less than 100 beats per minute. (b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.
The situation in which the binomial distribution can be approximated to the normal distribution is given by:
(b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The binomial distribution can be approximated to the normal distribution if there are at least 10 failures and 10 successes on the experiment, that is:
np ≥ 10, n(1 - p) ≥ 10.
Meaning that a large number of trials is usually required for the approximation.
In the context of this problem, to achieve the large number of trials needed for the approximation, multiple days are needed to take the observations, hence option b is correct.
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True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight. terms were 3/10, 2/30, n/60. true value pays the invoice on may 22. what amount does true value pay?
True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight true value pays the invoice on may 22. then true value pay amount is $4900
Invoice dated 08/may/2020. Amounting to $5,800 which includes $800 freight.
Terms:
3/10 ; 2/30 ; n/60
The term 3/10 means that True value can avail of 3% discount if it pays within 10 days from date of issuance. The 10th day would be 18/may/2020
The term 2/30 means that True value can avail of 2% discount if it pays from the 11th day up to the 30th day from the date of issuance.
may 22 is beyond the 10th day but within the 30 days discount period. True Value can avail of the 2% discount.
5,800 - 800 = 5,000 The freight can't be subjected to discount thus it is deducted from the total invoice amount.
5,000 * 2% = 100
5,000 - 100 = 4900 amount True Value has to pay.
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Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
Please hurry! :D
Answer:
736 - 155 = 581.
581 divided by 12 is 48.416.
that means the minimum number of sets of knives Kaj should buy is 49.
Step-by-step explanation:
The area and perimeter
Answer:
N/A
Step-by-step explanation:
the area and perimeter for what exactly?
Mang Efren is now 5 times as old as his son. Four years ago, the product of their ages was 52. Find Mang Efren's present age in years. (Just type in the numerical value of your answer)
Mang Efren's present age is 30 years.
Let's assume the present age of Mang Efren's son is x years.
Mang Efren is presently 5 times as old as his son.
So, Mang Efren's present age = 5x years
Four years ago,
Mang Efren's son's age = x - 4 years.
Mang Efren's age = 5x - 4 years
According to the question, four years ago, the product of their ages was 52.
From this information, we will create an equation.
(x - 4)(5x - 4) = 52
5x² - 4x - 20x + 16 = 52
5x² - 24x + 16 - 52 = 0
5x² - 24x - 36 = 0
Solving the quadratic equation to obtain the value of x,
5x² - 30x + 6x - 36 = 0
5x(x -6) + 6(x - 6) = 0
(5x - 6)(x - 6) = 0
x = 6
So, Mang Efren's present age is 5 × 6 = 30 years.
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Could you guys help a sista out? I’m struggling
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The answer is not D
Answer:
b
Step-by-step explanation:
Ella walks to the art store at 2mph, but returns home at 4 mph. If her total walking time is 1/2 an hour, how far away is the art store? Express your answer as a fraction.
The distance of art store from Ella's house is 2/3 miles or 0.67 miles.
It is a question of time, speed and distance.
It is given in the question that Ella walks to the art store at 2mph, but returns home at 4 mph.
Also, the total time taken by Ella to cover the journey is 1/2 an hour.
We have to find the distance of art store from Ella's house.
Let the distance from Ella's house to art store be d miles.
We know that,
Speed = distance/time
Time = distance/speed
Hence, we can write,
time = d/2 (walking to the art store from from)
Also,
time = d/4 (walking to home from the art store)
Hence,
d/2 + d/4 = 1/2
3d/4 = 1/2
d = 2/3 miles or 0.67 miles.
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How much hours does it take the robot to complete one task
Answer:
0.41
Step-by-step explanation:
Evaluate m + (n-1)^2 if m = 3 and n = -4
Answer:
Step-by-step explanation:Answer: using identity[(a+b)(a-b) = a^2 - b^2]. (m+n)(m-n) = m^2 - n^2. m^2 - n^2 = (3)^2 - (4)^2 = -7.
Select the correct answer from each drop down-menu.
Which are the best definitions for theorem, conjecture, and axiom?
A statement that is assumed to be true without proof is a(n)
. A statement that has been shown to be true by vigorous application of logic is a(n)
. A(n)
is a statement that is believed to be true but hasn't been proven.
A statement that is assumed to be true without proof is a(n) Theorem
A statement that has been shown to be true by vigorous application of logic is a(n) ---> Conjecture
A(n) Axiom is a statement that is believed to be true but hasn't been proven.
What's the big difference between a definition and a theorem?A definition is both a precise and a general statement of the significance of a mathematical term.
It does this by laying down all of the characteristics of the word together with the structures that need to be true.
This is how the meaning of the word is defined. A mathematical assertion that can be demonstrated using logically sound mathematical reasoning is called a theorem.
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Determine the angle of rotation
Answer: b
Step-by-step explanation:
:)