The error was made in the Step 1 as Distributive property of multiplication was not used correctly .
In the question ,
it is given that
the equation is 2x -(1/4)(12x+4)= 3
Step 1 : by using the distributive property of multiplication ,
we get
2x - (1/4)*12x -(1/4)*4 = 3
2x - 3x - 1 = 3
So , after the first step the equation should be 2x - 3x - 1 = 3
we see that the Distributive property of multiplication , was not used properly as the negative sign was not distributed to both the terms .
So , Step 1 is wrong.
Step 2 : Adding like terms
we get ,
-x - 1 = 3
Step 3 : Adding 1 to both the sides ,
we get
-x - 1 [tex]+[/tex] 1 = 3 + 1
Step 4:
-x = 4
x = -4
Therefore ,The error was made in the Step 1 as Distributive property of multiplication was not used correctly .
The given question is incomplete , the complete question is
An equation and the steps to solve it are shown below:
2x -(1/4)(12x+4)= 3
Step 1: 2x + 3x + 1 = 3
Step 2: 5x+1=3
Step 3: 5x+1-1=3-1
Step 4: 5x = 2
In which step was the error made and why?
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PLEASE HELP!
Find the y-intercept of the line on the graph.
Enter the correct answer.
008
Clear all
7
DONE
Answer: y intercept is -1
Step-by-step explanation:
what is the slope intercept form of 4y+x=-1
Answer:
[tex]y=-\frac{1}{4}x-\frac{1}{4}[/tex]
Step-by-step explanation:
To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]4y+x=-1 \\ \\ 4y=-x-1 \\ \\ y=-\frac{1}{4}x-\frac{1}{4}[/tex]
What is the slope of the line that passes through the points (-4,6) and (-4,18 Write your answer in the simplest form.
(X^2 + 9) / (x-3)
Synthetic Division
Pls show work
The synthetic division (x²+9) by (x-3) has a quotient of x+3 and the remainder of 18
How to use synthetic division to solve polynomials?
Synthetic division is a way of performing the division of polynomials, with less writing and fewer calculations than the long division method
Given: (x²+9) ÷ (x-3)
The numerator can be written as p(x)= x²+9
The zero of the denominator g(x) is 3 (Note: the sign changed)
The coefficients of p(x) are arranged as follows, with the zero of g(x) on the left:
3 | 1 0 9
|________
The first coefficient after the bar is "dropped" to the last row.
3 | 1 0 9
|___________
| 1
The dropped number is multiplied by the number before the bar, and placed in the next column
3 | 1 0 9
| 3
|___________
| 1
An addition is performed in the next column
3 | 1 0 9
| 3
|___________
| 1 3
The previous two steps are repeated and the following is obtained:
3 | 1 0 9
| 3 9
|___________
| 1 3 18
Here, the last term (18) is the remainder while the rest are the coefficients of the quotient
The terms are written with increasing degree from right to left beginning with degree zero for the remainder and the result
1x + 3 | 18
Where the quotient q(x) = x+3 and the remainder r(x) = 18
Therefore, the quotient is x+3 and the remainder is 18
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6) There are 11 marbles in a bag. Two are yellow, five are pink and four are green. Suppose you pull out one
marble, record its color, put it back in the bag and then pull out another marble. Find the probability that
when selecting 3 marbles, you have selected a yellow first, green second and pink last.
The probability is 0.1.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.acc to our question-
total marbles= 11yellow marbles=2pink marbles=5green marbles=30.01 + 0.04 + 0.05Hence,The probability is 0.1.
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pens cost 20p each and pencils cost 12p each if i buy 6 pens and 5 pencils what will be the total cost
Answer:
$1.80
Step-by-step explanation:
A square painting has a side length of 17 inches.
What is the area of the painting?
The area of the painting is 289 [tex]inches^{2}[/tex].
Given:
A square painting has a side length of 17 inches.
we know that,
Area of square = side * side.
= 17 inches * 17 inches
= 289 [tex]inches^{2}[/tex].
Therefore the area of the painting is 289 [tex]inches^{2}[/tex].
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pythagorean theorem digital escape puzzle 2 HELPPPP
Answer:
EGFB
Step-by-step explanation:
PQ= (105)^2 + (208)^2
PQ=233
Area = b*h
Area = 21840
RS = (210)^2 + (120)^2
RS = 241.87
Area = 1/2bh
Area = 1/2 (210)(120)
Area = 12600
for a binomial experiment, how many outcomes are possible for each trial? what are the possible outcomes? one; success three; success, failure, or neither two; success or failure one; failure
In a binomial experiment, there are two possible results for each trial, which are referred to as "success" and "failure," respectively.
Define the term binomial experiment?If the following criteria are satisfied, a statistical experimentation can be categorised as a binomial experiment:
There are n trials in a given number.For each trial, there are simply the two outcomes "success" and "failure." The letters p and q stand for the likelihood of success with one trial and the likelihood of failure on one trial, respectively.The n separate trials are repeated under the same circumstances.The binomial probability distribution describes how a binomial experiment's results will turn out. The proportion of successes attained there in n independent trials is the random variable X. The formula μ=np gives the standard deviation and can be used to compute the mean of X; σ = √npqThus, in a binomial experiment, there are two possible results for each trial, which are referred to as "success" and "failure," respectively.
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What is the domain of the function?
A XER
B x≤5
C y≤ 5
D y≥5
Answer:
A
Step-by-step explanation:
Domain is the set of x values, so we can cross off C and D as answer choices as those would be possible answer choices for range. Looking at the graph, you can see the graph continues infinitely. The domain of the function is all real numbers, or A.
Halima either travels by bus or walks when she visits the town centre.
The probability that she catches the bus to town is 0.4.
The probability that she catches the bus from town is 0.9
b) Work out the probability that Halima
walks at least one way.
The probability that Halima walks at least one way is 0.64
Calcualting Probability:
Probability is a branch of mathematics which is deals with the occurrence of a random event. The value of probability is expressed from zero to one but not more than 1. It is used to predict how likely events are to happen. The probability of an event 'E' is denoted by P(E).
Here we have
Halima either travels by bus or walks when she visits the town center
The probability that she catches the bus to town = 0.4
The probability that she catches the bus from town = 0.9
Let A and B be the events that she catches the bus to the town and the event that she catches the bus from the town respectively
=> P(A) = 0.4
=> P(B) = 0.9
The above events P(A) and P(B) are two independent events
Then the probability that she catches the bus to and from the town
=> P(A∩B) = 0.4 × 0.9 = 0.36
Therefore,
The Probability she walks at least one way P(A ∪ B) = 1 - P(A∩B)
=> P(A∪B) = 1 - 0.36
=> P(A∪B) = 0.64
Hence,
The probability that Halima walks at least one way = 0.64
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Find the equation of a line parallel to 3x+3y=6 that passes through the point (7,-1)
The equation of the line parallel to 3x+3y=6 that passes through the point (7,-1) is y = -x + 8
How to find equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe lines that are parallel have the same slopes.
Therefore, let's find the slope of the equation 3x+3y=6.
3x + 3y = 6
3y = - 3x + 6
divide through by 3
y = - x + 2
Therefore, the slope is - 1.
Let's find the y-intercept of the equation using (7, 1)
y = - x + b
1 = - 7 + b
b = 8
Therefore, the equation of the line is y = -x + 8
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stackoverflow the sum of three numbers is $96$. the first number is $6$ times the third number, and the third number is $40$ less than the second number. what is the absolute value of the difference between the first and second numbers?
The absolute value of the difference between the first and second numbers is 5.
Here we have to find the difference between the first and the second numbers.
There are three statements.
Let a, b, and c be the first, second, and third numbers respectively.
The first statement is that the sum of the three number is 96.
The second statement is that the first number is 6 times the third number.
a = 6c
The third statement is that the third number is 40 less than the second number.
c = b - 40
b = c + 40
The sum of the three numbers is 96.
a + b + c = 96
6c + c + 40 + c = 96
8c = 96 - 40
8c = 56
c = 7
As a = 6c and b = c + 40
Now put the value of c as 7 we have:
a = 6 × 7
= 42
b = 7 + 40
= 47
Difference between the first and second numbers= 47 - 42
= 5
Therefore the difference is 5.
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A truck driver is driving from Nome, Alaska, I
Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs
check
the weather continuously to make sure the gas
his truck remains in liquid form. The
gas he uses freezes at -40° F and evaporates at 140° F.
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.
(2 points)
Part B: Describe the
graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to
the inequality represent. (4 points)
Part C: In January 1989, the temperature in Nome, Alaska, dropped to -49° F. Would the gas in
the driver's truck have
remained in liquid form so he could have
driven on this day? Why or why not? (4 points)
The inequality of the change of state of the gas in the driver's truck indicates;
Part A: The inequality that represents the temperature at which the gas in the truck will be in liquid form is; -40 ≤ T ≤ 140
Part B: The graph is a shaded region bounded by two solid vertical lines at t = -40 and t = 140
Part C: The gas will be frozen because the temperature is below the freezing point temperature of the gas.
What is an inequality?An inequality indicates the relationship between two expressions that are not equal
The temperature at which the gas freezes = -40 °F
Temperature at which the gas evaporates = 140 °F
Part A: The inequality that represents the temperature at which the gas in the truck will remain in liquid form, t is; -40 ≤ t ≤ 140
Part B: The description of the graph of the inequality is a region on the coordinate plane bounded by two solid vertical lines at x = -40 and x = 140, the region between the two solid vertical lines is shaded/.
Part C: The temperature of -49 °F obtained in January 1989 in Nome, Alaska is not in the feasible region of the graph of the inequality, therefore, the gas in the driver's truck will not remain in liquid form, and would freeze, such that the driver would not drive on the specified date.
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a nurse researcher conducted an in-depth study of anxiety in patients undergoing chemotherapy. the researcher coded data from interviews with 20 patients, and a coinvestigator independently coded 8 of the 20 interviews. the coding of the two researchers was then compared. which quality-enhancement strategy was the researcher using?
The researcher was using Investigator triangulation quality-enhancement strategy.
The Investigator triangulation strategy make use of more than one researcher, investigator or interviewer to study the data.This research strategy can help you improve the credibility and the validity of your findings.
Including the Investigator triangulation strategy , there are basically four types of triangulation strategies . The other three are listed below :
- Data Triangulation
- Theory Triangulation
- Methodological Triangulation
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An uber charge a flat rate of $20 plu $2 per mile. Lyft charge a flat rate of $15 plu $4 per mile. Write an equation to find the number of mile m for which uber and lyft would cot the ame amount
The required equation is 20 + 2m = 15 + 4m. The number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.
Uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. We need to find out the equation and the number of miles for which Uber and Lyft would charge the same amount for the ride.
Let the charge of Uber and Lyft be represented by the variables C1 and C2. We can write the equations given below.
C1 = 20 + 2m
C2 = 15 + 4m
We need the charge for both companies to be equal.
C1 = C2
20 + 2m = 15 + 4m
Hence, the required equation is 20 + 2m = 15 + 4m. Now we will solve this equation to find the number of miles.
2m = 5
m = 2.5
Hence, the number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.
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snoopy brown is interested in the number of businesses that do not allow dogs in st. paul, mn. to conduct his study, he randomly selects 100 businesses listed in the st. paul phone book, calls them and asks their policy. what is the sample of this study?
The sample of study is 100 business.
Define sample.An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values. A sample is that precise value. The probability distribution of the random variable determines the possible values and the likelihood of each. A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.
Given,
Snoopy brown is interested in the number of businesses that do not allow dogs in st. paul, mn. to conduct his study, he randomly selects 100 businesses listed in the st. paul phone book, calls them and asks their policy.
The sample of study is 100 business.
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Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answer:
Domain: {7, 8, 9} Range: {2, 3, 4, 5}
Step-by-step explanation:
This relationship is not a function because one input (7) gave two different outputs (2 and 4)
Please help me I WILL GIVE BRAINLY IF CORRECT!!<3 Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions LC)
Rewrite 30 - 6x³ using a common factor.
O2(15-3x³)
O 2x(15-3x²)
O6(5-6x³)
O6x(5-x²)
By factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])
The expression is given,
30 - [tex]6x^3[/tex]
The expression is the mathematical sentence that consist of different types of variables, numbers and the mathematical operators. The mathematical operators will be addition, subtraction, division and multiplication. The expression does not contains a equal sign or inequality signs
The expression is given,
30 - [tex]6x^3[/tex]
Take a common term outside
Here the common term is 2
30 - [tex]6x^3[/tex] = 2((30/2) - [tex]6x^3[/tex] /2)
= 2(15 - [tex]3x^3[/tex])
Hence, by factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])
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im struggling fr help me
Sophia spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -2.1°F. Between 9am and noon, the temperature increased by 10.8°F. Between noon and 3pm, the temperature decreased by 13°F. Between 3pm and 6pm, the temperature dropped 18.4°F. What was the temperature at 6pm?
PLEASE HURRY I NEED IT FAST
Using mathematical operations, we know that temperature after 6 p.m. will be -22.7°F.
What exactly are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, the temperature after 6 p.m. will be:
The temperature at different times:
At 9 a.m. = -2.1°FBetween 9 - 12 = +10.8°FBetween 12 - 3 = -13°FBetween 3 - 6 p.m. = -18.4Now, calculate to get the temperature after 6 p.m. as follows:
= -2.1 + 10.8 - 13 - 18.4 = -22.7°FTherefore, using mathematical operations, we know that the temperature after 6 p.m. will be -22.7°F.
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Write a polynomial f (x) that satisfies the given conditions.
Degree 3 polynomial with integer coefficients with zeros 7i and 9/5
If the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]
The zeros of the polynomial = 7i and 9/5
Here the degree of polynomial is 3, therefore there will be three zeros in polynomial, here only 2 zeros are given. We have to find the third zero of the polynomial.
Here one of the polynomial is complex number, therefore another zero will be the conjugate of the complex zero
Therefore the equation will be
(x+7i)(x-7i)(5x-9) = 0
We have to solve the equation
([tex]x^2[/tex] -7ix+7ix+49)(5x-9) = 0
([tex]x^2[/tex] + 49)(5x - 9) = 0
[tex]5x^3-9x^2+245x-441 =0[/tex]
Therefore
f(x) = [tex]5x^3-9x^2+245x-441[/tex]
Hence, if the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]
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What is the mode of the following numbers?
9,8, 7, 1,1
Answer:
Step-by-step explanation: 1 is the mode it has the most numbers that repeat
Answer:
The mode is 1.
Step-by-step explanation:
The mode is the number that occurs in a set the most. You can remember this as the word "most" and "mode" sounding similar.
a family has 5 natural children and has adopted 2 girls. each natural child has equal probability of being a girl or a boy, independent of the other children. find the pmf of the number of girls out of the 7 children.
PMF probability mass function:
2 - 0.03125, 3 - 0.15625, 4 - 0.3125, 5 -0.3125, 6 - 0.15625, 7 - 0.03125.
Define the term Probability?The probability of such a function is the degree to which an event will occur as a rational number.
A family has 2 adopted girls and 5 biological daughters.
Each naturally occurring child does have an equal chance of being a boy or a girl.
Out of the seven offspring, the probability mass function for girls is as follows:
B should stand for Boy, and G should stand for G.
Consequently, this is the probability mass function:
P(GGBBBBB) = ⁵C₀ x (0.5)⁰ x (0.5)⁵
= 0.03125
P(GGGBBBB) = ⁵C₁ x (0.5)¹ x (0.5)⁴
= 0.15625
P(GGGGBBB) = ⁵C₂ x (0.5)² x (0.5)³
= 0.3125
P(GGGGGBB) = ⁵C₃ x (0.5)³ x (0.5)²
= 0.3125
P(GGGGGGB) = ⁵C₄ x (0.5)⁴ x (0.5)¹
= 0.15625
P(GGGGGGG) = ⁵C₀ x (0.5)⁵ x (0.5)⁰
= 0.03125
Thus, the probability mass function for girls out of the 7 children is obtained.
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someone please help me im begging u for points
The solution of the algebraic equation is x = -2. The proof is elaborated below.
The algebraic equation given to us is 14(x + 1) = -7(4 + x). An equation is a mathematical statement that proves the equality of two mathematical expressions. The first step is to simplify the brackets. The equation becomes 14x + 14 = -28 - 7x. Now, we will add 7x to both sides of the equation. The equation is modified as 21x + 14 = -28. Now, we will subtract 14 from both sides of the equation. The equation is modified as 21x = -42. Now, we will divide both sides of the equation by 21. The equation is modified as x = -2.
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Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of ?1/3
Oy + 2 = (x+3)
Oy -2=(x-3)
Oy+ 3 = (x + 2)
Oy-3=(x-2)
The equation which passes through (3,2) and slope 1/3 is:
y - 2 = 1/3 (x - 3)
Given, we have:
slope (m) = 1/3
Point = (3,2) = (x₁,y₁)
we are asked to determine the point slope form :
we know that:
point slope form:
y-y₁ = m(x-x₁)
substitute the above values in the formula:
y - 2 = 1/3 (x - 3)
Hence the correct option is B.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, -6) and (-8, 2)
The distance between the two points is 8.25 units
What is meant by the distance between two points?The distance between two points in a plane is the length of the line segment separating the two locations. Typically, the equation d=((x2 - x1)2 + (y2 - y1)2) is used to calculate the distance between two locations. You may use this formula to get the separation between any two points on an x-y plane or coordinate plane.
The following is the formula for the separation between two points:
d= √(x₁-x₂)²+(y₁-y₂)²
Points (x1, Y1) and (x2, Y2)
As given in the question, the points are (-6, -6) and (-8, 2)
The distance between the two points is,
d= √(-6+8)²+(-6-2)²
d=√4+64
d=√68 units= 8.25 units
Therefore, the distance between the two points is 8.25 units
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Given l||m and m∠1 = 60°, select all angles that are also equal to 60°. 8 2 6 7 5 4 3
Answer:
2 , 3 , 4
Step-by-step explanation:
Corresponding angles: When two parallel lines are intersected by a transversal, the angles on the same side and same position of the transversal are same.
∠3 = ∠1
Vertically opposite angles: When two lines intersect, the opposite angles are congruent.
∠2 = ∠1
∠4 = ∠3
So, ∠1 = ∠2 = ∠3 = ∠4 = 60°
Dan spends
3
4
of his wages on rent and
1
8
on food. If he makes £240 per week, how much money does he have left?
The money left with Dan is £30 .
In the question ,
it is given that
the amount of money earned by Dan in a week is = £240 .
amount of money spent by Dan on rent is = 3/4 wage
amount of money spent by Dan on food is = 1/8 of wage
So ,
the total amount spent = amount spent on food + amount spent on rent
Substituting the values ,
we get ,
= 3/4 + 1/8 = 7/8 of his wage = (7/8)*240
= 210
so , total amount spent is £210 .
Amount left = amount earned - amount spent
= 240 - 210
= 30
Therefore ,The money left with Dan is £30 .
The given question is incomplete , the complete question is
Dan spends 3/4 of his wages on rent and 1/8 on food. If he makes £240 per week, how much money does he have left?
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Please help thank u! I would appreciate it ASAP
Answer:
Step-by-step explanation:
can’t be determined