The difference of 30000 and 6985 using compensation is 23015
The method of compensation refers to calculating mentally without any paper work.
Here, we are asked to find the difference of 30000 and 6985 which are comparatively large numbers. Everyone would prefer using pen and paper to calculate this. But we can do this by compensation within a few steps.
Add 15 to 6985 [Addition is simpler than subtraction]. We get 7000.Now subtract 7000 from 30000 [ more zeros in the numbers make the mental calculation easy]. We just have to subtract 7 from 30 and adjoin 3 zeros in 7000. So we get 23000.Lastly add the 15 from the first step again to 23000.So the final answer is 23015.
i.e., 30000-6985 = 23015
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Help please!
The area of a square is 9 square feet. What is the length of one side of the square?
Answer:
the length of one side of square is 3
which row of pascal’s triangle would you use to expand (2x 10y)15? row 10 row 12 row 15 row 25 how many terms are in this expansion? 3 terms
15th row of the Pascal's Triangle is used to expand [tex](2x+10y)^{15}[/tex]. There will be 16 terms in the expansion.
Pascal's Triangle is used to find the co-efficient for binomial expansions.
The nth row of the Pascal's Triangle gives the coefficients in the expansion of binomial expressions of degree n. For example, in the expansion of [tex](x+y)^2[/tex] , the binomial coefficients are 1,2,1 which is given in the 2nd row of Pascal's Triangle. Also the expansion has three terms, therefore. The Pascal triangle starts with 0th row consisting of only 1.
Here the given expression is [tex](2x+10y)^{15}[/tex] of degree 15. So its binomial coefficient is given in the 15th row of Pascal's triangle.
The number of terms in the binomial expansion of degree n will be n+1 because the coefficients in nth row will n+1 in number.
Hence there will be 16 terms in the expansion of [tex](2x+10y)^{15}[/tex].
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Answer:
The person above helped, and below I've attached a ss with all of the parts of this question answered - Hope it helps!
Step-by-step explanation:
Brainliest would be very much appreciated :) - hope you have a good day!
Find two consecutive even integers such that 6 times the smaller integer is 36 more than 3 times the larger integer. Please Help me!
The integers are 14 and 16.
How to calculate the value?Let the integers be represented by x and x+2.
It was stated that the consecutive even integers such that 6 times the smaller integer is 36 more than 3 times the larger integer.
This will be:
6(x) = 3(x + 2) + 36
6x = 3x + 6 + 36
6x = 3x + 42
6x - 3x = 32
3x = 42
Divide
3x/3 = 42/3
x = 14.
The larger number will be:
= x + 2
= 14 + 2
= 16
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A restaurant earns $1073 on friday and $1108 on saturday. Write and solve an equation to find the amount x(in dollars) the restaurant needs to earn in Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
The amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.
What is average ?
The average is the ratio of the sum of the number of a given set of values to the total number of values present in the set.
It is given that restaurant earns $1073 on Friday and $1108 on Saturday.
The amount which restaurant needs to earn on Sunday to average $1000 per day over the three-day period can be calculated by finding the average.
The average is given by ratio of sum of amount on each day from Friday to Sunday and divide it by number of days.
Let's assume amount earn on Sunday is $x.
So ,
[tex]\frac{1073 + 1108 + x}{3}[/tex] = 1000
1073 + 1108 + x = (1000 × 3)
2181 + x = 3000
Let's solve this equation to get the value of x.
x = 3000 - 2181
x = $819
So , amount earn by restaurant is $819.
Therefore , the amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.
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work out the volume of cylinder B
Answer:
720cm³
Step-by-step explanation:
Volume of a cylinder is given by Base Area (A) x Height (h)
or V = Ah
Volume of cylinder A = 18 x 5 = 90 cm³
Base Area A = πr² where r is the radius of the base
For cylinder A, if radius = rₐ
Area = π x (rₐ)² = 18
We can see that cylinder B has twice the height of cylinder A. That means cylinder B radius is twice the radius of cylinder A
So radius of cylinder B = 2 x rₐ = 2rₐ
Base Area of Cylinder B = π x (2rₐ)² = 4π(rₐ)² = 4 x Base Area of cylinder A = 4 x 18 = 72
So while the heights are in the ration 1:2, the base areas are in the ratio 1:4 because the areas are directly proportional to the square of the radius
Hence Volume of Cylinder B = 72 x 10 = 720 cm³
Another way to look at this is that the volume of cylinder B = 8 (2 x 2 x2) times the volume of cylinder A = 8 x 90 = 720cm³
a real-valued function f (x) is said to be increasing on the closed interval [a, b] if for all x1, x2 ∈ [a, b], if x1 < x2, then f (x1) < f (x2) write the negation of this definition
A real valued function f(x) is said to be decreasing on the interval [a,b] for all x1,x2 if x1 < x2, And f(x1) > f(x2)
What are increasing and decreasing function ?A function is said to be increasing if we increase the value of the independent variable the function also increases and a function is said to be decreasing if we increase the value of the independent variable the function decreases.
According to the given question real-valued function f (x) is said to be increasing on the closed interval [a, b] if for all x1, x2 ∈ [a, b], if x1 < x2, then f (x1) < f (x2).
A real valued function f(x) is said to be increasing on the interval [a,b] if a < b, And f(a) < f(b).
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I WILL GIVE BRAINLIEST Juan writes 3^2 ∙9^4 = 27^6 and the teacher marked it wrong. Explain Juan’s error.
Juan multiplied the bases together, and added the power together, therefore, his solution is wrong.
What is power?Power is the result of multiplying same number for n number of times. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.
The correct solution,
3² ∙ 9⁴
= 3² ∙ (3²)⁴
= 3² ∙ 3⁸
= 3¹⁰
Hence, Juan multiplied the bases together, and added the power together, therefore, his solution is wrong.
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перший завод виготовляє 6000 деталей з них 2% бракованих а в другого 6% бракованих скільки деталей робить другий завод якщо разом в них 3%
Answer:
18000
Step-by-step explanation:
18 000, тому що якщо ви заробляєте 6 000 і маєте 2% дефектних деталей, помножте на 3, щоб отримати 6% дефектних деталей, які дають вам 18 000
Information about five planets is shown in the table below.
Diameter (km)
4.88 × 10³
1.43 x 105
1.28 x 10¹
6.78 × 10³
1.21 x 105
Planet
Mercury
Jupiter
Earth
Mars
Saturn
Mass (kg)
3.3 x 1023
1.898 × 1027
5.97 x 1024
6.42 x 1023
5.68 × 1026
a) Write down the name of the planet with the greatest mass.
b) Work out the radius of Mercury giving your answer as an ordinary number.
Answer:
Mass is the property of a body that measure its inertia. It is taken as the measure of the amount of material it contains and have weight in gravitational field
Mass is also refers as the weight of an object. It is measured in grams (g) and kilograms (kg)
Radius of an object is defined as a straight line from the centre of a circular object to the circumference of the circular object
According to the data given of five planets
(a) The planet which has greatest mass is Mars that is 6.42 x 1023 kg
Radius of a given object can be calculated by dividing the diameter of the given object by 2.
(b) Radius of the mercury = Diameter given in kilometers / 2
= 4.88 × 10³ / 2
= 2.44 x 103 km
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how to find the rise and run on the graph
rise: 1 run: 2
slope: 1/2
you can start from any point on the slope. if i picked point (-5,0) i go up 1 square and right 2 squares to get to point (-3, 0). thats basically the rise and run, and the slope is always rise over run
how do you find the y-intercept from vertex form
It is found that the intercepts can be found from vertex form, if the graph is hovering above the x axis (k<0).
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x) At y-axis, we've got x = 0, so putting it will give us the y-intercept. Thus, y-intercept of y = f(x) is y = f(0)
If a quadratic equation is written in the form y=a(x-h)² + k
therefore it is called to be in vertex form. It is called so because when you plot this equation's graph, we will see vertex point(peak point) is on (h,k)
To convert the given equation to vertex form, We will take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
To find the intercepts, if the graph is hovering above the x axis (k<0) then there will be no real solutions for the x intercept.
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if the length of a rectangle is increased by 30 percentage and the width of the same rectangle is decreased by 30 what is the affect on the area
Answer:
The area will decrease by 9%.
Step-by-step explanation:
The area of a rectange is given by the formula below.
[tex]\boxed{\text{Area of rectangle}= \text{length}×\text{width}}[/tex]
Let the original length and width of the rectangle be L and W respectively.
Start by finding the original area:
Original dimensions
Length= L= 100%L
Width= W= 100%W
Original area= LW
Let's find the dimensions of the new rectangle in terms of L and W.
New dimensions
Length= (100% +30%)L= 130%L
Width= (100%-30%)W= 70%W
New area
[tex] = \frac{130}{100} L \times \frac{70}{100} W[/tex]
[tex] = \frac{91}{100} LW[/tex]
= 91% LW
Comparing the new area with the original area:
100% LW- 91% LW= 9% LW
∴ The area will decrease by 9%.
*Note that percentage is equivalent to dividing a number by 100.
a survey indicated that the vast majority of college students own their own personal computers what information would you want to know before you accepted the results of this survye
The required information is (B), (C), (D), and (I).
What is a survey?A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people. Surveys can be conducted over the phone, by mail, on the internet, or even on street corners or in shopping malls. In fields such as social research and demography, surveys are used to gather or gain knowledge.Survey research is frequently used to assess people's thoughts, opinions, and feelings.So,
A. Who paid for the survey? It is not required.
B. Who made up the population from which the sample was drawn? Needed.
We need to know if the sample is representative of the "college students" population, on which we are basing our conclusions.
C. What sampling strategy was used? Needed.
We want to know if the sample was chosen at random.
D. How large was the sample size? Needed.
This information is required to determine the accuracy of the results.
E. What are the colleges represented in the sample?
It's not necessary if we already know "B."
F. How many survey questions were there? It is not required.
G. How many people participated in the survey? It is not required.
H. What were the questions? It is not required.
I. Is the language in the questions clear, accurate, unbiased, and valid? Needed.
We want to know if the answer was unbiased and clear so that we can determine if the conclusions are also unbiased.
J. What day of the week was the survey held? It is not required.
Therefore, the required information is B, C, D, and I.
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The correct question is given below:
A survey indicates that the vast majority of college students own their own personal computers. What information would you want to know before you accepted the results of this survey? Select all that apply. A. Who funded the survey? B. What was the population from which the sample was selected? C. What sampling design was used? D. What was the sample size? E. What are the names of the colleges included in the sample? F. How many questions were asked in the survey? G. How many people conducted the survey? H. What questions were asked? I. Were the questions clear, accurate, unbiased, and valid? J. On what day of the week was the survey conducted? g
Can someone tell me what 17-6+2 is please?
Answer:
[tex]\frac{3}{x-1}+\frac{2}{x+1}=\frac{5}{x}[/tex]
Can somebody please help me?
Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched. What is the change in elevation?
The change in elevation will be 0.
What is the change in elevation?It should be noted that from the information, Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched.
Therefore, when it flew, the expression will be +168.
When it came down, the expression will be -168.
Therefore, the change in elevation will be:
= +168 - 168.
= 0
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Given f(x) = 5x squared of 2 + 2 and g(x) = 8 - 3x, find the following.
12. Find g[f(-2)].
11. Find flg(x)).
what is the diffrence between irregular and irrational numbers?
Answer:
Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.
Step-by-step explanation:
please make my answer as brainelist
If point A (–1, 0) is the midpoint of segment CT, and T is located at (1, 2), what are the coordinates of point C?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad T(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +x}{2}~~~ ,~~~ \cfrac{ 2 +y}{2} \right) ~~ = ~~ \stackrel{\textit{\LARGE A}}{(-1~~,~~0)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+x}{2}=-1\implies 1+x=-2\implies \boxed{x=-3} \\\\\\ \cfrac{2+y}{2}=0\implies 2+y=0\implies \boxed{y=-2}[/tex]
Which equation represents the line with slope −2/3 that passes through (3, 0)?
The following equation [tex]y=\frac{-2x}{3}+2[/tex] represents the given line.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=3x+1. Where:
a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex].
b= the constant term that represents the y-intercept.
For solving linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.
For the given example: a=3 and b=1
The question gives:
the value of the slope (a) = -2/3the coordinates of a point = (3,0)Thus, you can write from the question information :
y=ax+b
0= -2/3*(3)+b
0= -2 + b
b=2
Now, you know the value of the slope and the constant term.
Therefore, the standard form for the linear equation is:
[tex]y=\frac{-2x}{3}+2[/tex]
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f(a) = a + 3. Find f(7)
Answer: a=1/2=0.5
Step-by-step explanation:
7(a)=a+3
Subtract a from both sides.
7a−a=3
Combine 7a and −a to get 6a.
6a=3
Divide both sides by 6.
a= 63
Reduce the fraction
63
to lowest terms by extracting and canceling out 3.
a= 21
Maria purchased 1,000 shares of stock for $35.50 per share in 2003.
share. Express her capital gain
She sold them in 2007 for $55.10 per
as a percent, rounded to the nearest tenth of a percent.
Maria's capital gain is 55.2%.
Here, we are given that Maria purchased 1,000 shares of stock for $35.50 per share in 2003.
Thus, the total cost price of these shares = 1000 × 35.5
= $35500
In 2007, she sold all of the stocks for $55.10 per share
Thus, the total selling price of these shares = 1000 × 55.1
= $55100
Now, absolute gain = selling price - cost price
Here, Maria's absolute gain will be-
= 55100 - 35500
= 19600
Now, her percentage gain will be given by-
Gain % = absolute gain/ initial value × 100
= 19600/35500 × 100
= 55.2
Thus, Maria's capital gain is 55.2%.
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3/11 x 3/4 x 4 Please help I have no idea how to do this
Answer:
[tex]\bold{\dfrac{9}{11}}[/tex]
Step-by-step explanation:
I will use the dot notation for multiplication
We have
[tex]\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4[/tex]
Convert 4 to a fraction:
[tex]4=\dfrac{4}{1}[/tex]
Therefore
[tex]\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4 \\\\= \dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \dfrac{\cancel {4}}{1}\\\\[/tex]
Cross-cancel common factor 4
[tex]=\dfrac{3}{11}\cdot \dfrac{3}{1}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{a}{b}\cdot \dfrac{c}{d}=\dfrac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\dfrac{3\cdot \:3}{11\cdot \:1}[/tex]
[tex]=\bold{\dfrac{9}{11}}[/tex]
Solve for x. 7x - 3 = 2x - 18
Answer:
x = -3Step-by-step explanation:
7x - 3 = 2x - 18
5x = -15
x = -15 : 5
x = -3
-----------------------------
check
7 * (-3) - 3 = 2 * (-3) - 18
-24 = -24
the answer is good
among cbc students, 50% of students are enrolled in less than three courses and 33% of students are taking a math class. if 71% of students are either enrolled in less than three courses or taking a math course, what percentage of students are enrolled in less than three courses and taking a math course? group of answer choices 38% 35.5% 17% 83% 12%
12% of students are enrolled in less than three courses and taking a math course
For given question,
50% of students are enrolled in less than three courses and 33% of students are taking a math class.
The probability that the students are enrolled in less than three courses is 0.5
P(A) = 0.5
The probability that the students are taking a math class is 0.33
P(B) = 0.33
if 71% of students are either enrolled in less than three courses or taking a math course.
P(A ∪ B) = 0.71
We need to find the percentage of students that are enrolled in less than three courses and taking a math course.
i.e., we need to find P(A ∩ B)
We know that, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∩ B) = 0.5 + 0.33 - 0.71
P(A ∩ B) = 0.12
So, 12% of students are enrolled in less than three courses and taking a math course.
Therefore, 12% of students are enrolled in less than three courses and taking a math course.
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Find the value of k if the line y = kx +4 goes through the point (2, -2). Thank you
The answer is in the screenshot.
a company makes widgets from three machines. machine m1 makes 3000/hour, and 80% are good. machine m2 makes 4000/hour, and 90% are good. machine m3 makes 3000/hour, and 60% are good. all widgets are mixed together. what is the probability that a widget drawn at random is good
If all the widgets from the three machines are mixed together, then the probability that a good widget will be drawn at random is 0.78 or 78%.
Probability is defined as how likely an event is to occur, or how likely it is that a proposition is true.
If machine 1 makes 3000/hour and 80% are good, then the chances of it being good is 80% also or, 2400 out of 3000.
80% of 3000 is 2400
If machine 2 makes 4000/hour and 90% are good, then the chances of it being good is 90% also or, 3600 out of 4000.
90% of 4000 is 3600
If machine 3 makes 3000/hour and 60% are good, then the chances of it being good is 60% also or, 1800 out of 3000.
60% of 3000 is 1800
Mixing together the widgets from the three machines, use the formula to calculate the probability of an event which is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Probability(good) = (2400 + 3600 + 1800)/(3000 + 4000 + 3000)
Probability(good) = 7800/10000
Probability(good) = 0.78 or 78%
Hence, the probability that a good widget drawn at random is 0.78 or 78%.
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(Adding and Subtracting Rational Numbers MC)
Solve negative four minus one and three fifths.
five and three fifths
one and three fifths
four fifths
negative five and three fifths
Answer:
negative 5 and 3/5
Step-by-step explanation:
-4-1&3/5
-5&3/5
negative 5 and 3/5(three fifths)
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Answer:
negative 5 and 3/5
Step-by-step explanation:
-4-1&3/5
-5&3/5
negative 5 and 3/5(three fifths)
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Step-by-step explanation:
Simplify. 5/4+4(3/4−12)2
Answer:-355/4
Step-by-step explanation:
Answer:
= -355/4
Step-by-step explanation:
= 5/4 + 4(3/4 - 12)(2)
= 5/4 + (-45)(2)
= 5/4 + -90
= -355/3
What is this 6/x-5/-7=11