The solution for the equation 2.3p - 10.1 = 6.5p - 4 - 0.01p is p = -4.19/6.1
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
2.3p - 10.1 = 6.5p - 4 - 0.01p
Solve for p.
2.3p - 10.1 = 6.5p - 4 - 0.01p
Combining the like terms.
2.3p - 10.1 = 6.49p - 4
4 - 10.1 = 6.49p - 2.3p
-6.1 = 4.19p
p = -4.19/6.1
Thus,
The solution is p = -4.19/6.1
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Ethan's wallet contains 19 bills totaling to
$114. If Ethan's wallet only contains $20-
bills and $1-bills, how many $20 bills are in
Ethan's wallet?
Systems of linear equations applications
When the function f(x) is divided by 2x + 1, the quotient is x² - 8x + 8 and the
remainder is 5. Find the function f(x) and write the result in standard form.
Please help
The expression for the function f(x) in standard form if the function f(x) is divided by x-2 is f(x) = 3x³ + 2x² - 20x + 17.
What will be the function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5?The function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5 is determined as follows:
f(x) = (2x + 1)(x² - 8x + 8) + 5
Simplifying the above gives the following:
f(x) = 2x³ - 16x² + 16x + x² - 8x + 8 + 5
f(x) = 3x³ - 15x² + 8x + 13
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please show solution thank you<3
The university of California health services committee has five members. two members are chosen to serve as the committee chair and the vice chair. each committee member is equally likely to serve in either of the positions. What is the probability of randomly selecting the chair and the vice chair?
Answer:
the probability of randomly selecting the chair and the vice chair is 10%.
Step-by-step explanation:
There are a total of 5 members on the health services committee, and 2 of them will be chosen to serve as the chair and vice chair, respectively.
The probability of randomly selecting the chair out of the 5 members is 2/5, or 40%.
Once the chair is selected, there are 4 members remaining, and only one of them can serve as the vice chair. Therefore, the probability of randomly selecting the vice chair out of the remaining 4 members is 1/4, or 25%.
To find the probability of randomly selecting the chair and the vice chair, we need to multiply the individual probabilities of selecting each position, which is (2/5) * (1/4) = 2/20 = 1/10 = 10%.
So, the probability of randomly selecting the chair and the vice chair is 10%.
Write an expression to represent:
3 minus the product of 2 and x
.
Answer: 3 - 2x
Step-by-step explanation:
Product = Multiplication
Product of 2 and x = 2*x
3 minus 2x
3-2x
Answer:
3−2×x or 3-(2xx)
5 math teachers, 6 science teachers, and 5 social studies teachers attending a conference break for lunch at the same time. During the lunch break, they randomly finish and return to the conference individually. Find the probability that the first two people to leave are science teachers.
The probability that the first two people to leave are science teachers is; 2/15
What is the probability of selection?The parameters about the subject teachers are;
Number of maths teachers = 5
Number of Science Teachers = 6
Number of Social Studies Teachers = 5
Total number of teachers = 5 + 6 + 5
Total teachers = 16
Thus;
Probability that first to leave is a science teacher = 6/15
Probability that after the first leaves, the second to leave will be a science teacher = 5/15
Thus;
P(first two to leave are science teachers) = (6/15) * (5/15)
= 2/15
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Hame:
Date:
Per.
3. The distance between Venice and Florence is 171 miles. It takes 2% hours
to travel from Venice to Florence by train. Write an equation that
represents the distance travelled, d, and the time, t.
The equation that relates velocity, distance and time is given as follows:
v = 171/2.
How to obtain the equation?The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:
v = d/t.
In which:
v is the velocity.d is the distance.t is the time.The parameters for this problem are given as follows:
d = 171, t = 2.
Hence the equation that gives the velocity in miles per hour is of:
v = 171/2.
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find examples that contradict the conclusions of proposition 2.4.10 if a and b are not coprime (i.e. share a factor greater than ).
The conclusion of the proportion is if a and bare not coprime, when it share a factor greater than 1
Here we have given that if and are not coprime that is share a factor greater than.
And we need to find the examples that contradict the conclusions of proposition.
While we looking into the given question, we have identified that if and are not coprime.
In order to find the conclusion to this one, we must know the definition of co prime.
The term co prime is referred as those umbers that do not have any common factor other than 1.
As per the definition, we have clearly know that if the two number has the factor greater than one then it will not a co prime to each other.
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Find the product of the complex number and its conjugate. 1/3 + 2i
Answer:
Step-by-step explanation:
1/3 + 2i is a complex number, with the real part equal to 1/3 and the imaginary part equal to 2i. It can be represented in a Cartesian coordinate system as a point (1/3, 2)
1. If m angle ABD = 60°, find m angle
BDC.
Answer:
If angle ABD = 60°, then angle BDC can be found using the fact that the measures of the angles in a triangle add up to 180°.
So, m(angle BDC) = 180 - (m(angle ABD) + m(angle BDA))
Therefore, m(angle BDC) = 180 - (60 + m(angle BDA))
So the measure of angle BDC is not fixed, it depends on the measure of angle BDA.
paula used these steps to solve an equation
We can conclude that the division property of equality was done between step 4 and step 5.
What is linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then
a/c = b/c
At step 4: The equation was -6x = 57
To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below
-6x = 57
---- Divide both sides by -6 (Step 4)
-6x / -6 = 57 / -6
---- (Intermediary between step 4 and 5)
x = -9.5
----- Step 5
Hence, we can conclude that the division property of equality was done between step 4 and step 5
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What are the explicit equation and domain for an arithmetic sequence with a first term of 9 and a second term of 1?
Group of answer choices
an = 9 − 1(n − 1); all integers where n ≥ 1
an = 9 − 1(n − 1); all integers where n ≥ 0
an = 9 − 8(n − 1); all integers where n ≥ 0
an = 9 − 8(n − 1); all integers where n ≥ 1
The explicit equation and domain for an arithmetic sequence is a_{n}=9+(n-1)-8, the correct option is C
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given;
A first term of 9 and a second term of 1
a=9
D=1-9=-8
We know that the explicit equation of an AP is
a_{n}=a_{1}+(n-1)d
So, substituting the values
a_{n}=9+(n-1)-8
Therefore, the arithmetic sequence will be a_{n}=9+(n-1)-8.
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(A+7) (A+7) (A+7) (A+7)
Write the expression using exponential form
Answer:
(A+7)^4
Step-by-step explanation:
A heterozygous round pea is crossed with a purebred round pea. Predict the genotypic and phenotypic outcomes.
Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.
How do two heterozygous peas fare when they are bred?Punnet square analysis indicates that the progeny of two heterozygous pea plants (Yy) will be 75% (3/4) dominant and 25% (1/4) recessive. In the event that 1000 individuals are created, 750 will therefore be dominating.
Tt will be the genotype of a tall heterozygous plant. It will actually prevail over the recessive t allele because T is primarily the dominant allele. Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.
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Let F(s)=5s2+4s+4 F ( s ) = 5 s 2 + 4 s + 4 . Find a value of d d greater than 0 0 such that the average rate of change of F(s) F ( s ) from 0 0 to d d equals the instantaneous rate of change of F(s) F ( s ) at s=1. s = 1.
The required value of d for the given function is given as d = 2.
The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol
Here,
F(s) = 5s²+ 4s +4
F'(s) = 10s + 4
F'(1) = f(d) - f(0)/ d
10(1) + 4 = 5d² + 4d / d
14 = 5d +4
d = 2
Thus, the required value of d is given as d = 2.
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quantify the statement A(x) the square root of x raise to power 2 plus 4x plus 3 is a real number
A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic.
Which quadratic equation is the most fundamental?Quadratic equations or quadratic functions. A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic. Equations using quadratics is another name for it. The quadratic equation is expressed in its general form as ax2 + bx + c = 0.
For instance, 6x2 + 11x - 35 = 0, 2x2 - 4x - 2 = 0, 2x2 - 64 = 0, x2 - 16 = 0, x2 - 7x = 0, 2x2 + 8x = 0, etc. are examples of quadratic equations.
Three kinds of quadratics are frequently employed:
Standard Form: y = an x 2 + b x + c y = an x 2 + b x + c
y = a (x r 1, x r 2) is the factored form. y=a(x-r 1)(x-r 2) y=a(x−r1)(x−r2)
Vertex Formula: y=a (x h) 2 + k y=a (x-h)2 + k y=a (x-h) 2+k.
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Find the area of a window that measures 3 yards by 34 yard.
Answer:
102
Step-by-step explanation:
34x3=102
Moving vertically up from the origin is movement in the direction of positive z
The first hook will be hung at a point 4 feet east of the origin and 7.5 feet above the origin. The second hook will be hung at a point 5 feet east of the origin, 12
feet north of the origin, and 8 feet above the origin.
Provide the coordinates of the following points:
1. the first hook
2. the second hook
3.
the point on the string joining the hooks that is exactly halfway between the hooks
The coordinates of the hooks in three-dimensional space are found and the mid-point of the string is recognised as (4.5, 6, 7.75).
What is meant by three-dimensional space?
A three-dimensional space in geometry is a mathematical structure where a point's location depends on three different values.
For this question, we are considering the east of origin as the positive x-axis, the above origin as the positive z-axis and the north of the origin as the positive y-axis.
a) For the first hook there is no y-axis, it is hung in the xz plane.
So the coordinates are (4,0,7.5)
b) The second hook coordinates are given as (5, 12,8)
c) The point on the string which joins the hook, which is halfway between the hooks can be found using the mid-point formula.
x= (x1 + x2)/2 = (4+5)/2 = 4.5
y = (y1 + y2) /2 = (0+12) / 2 = 6
z = (z1+z2) / 2 = (7.5 + 8) /2 = 7.75
Therefore the mid-point of the string is (4.5, 6, 7.75).
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What is 25% of R594180
Answer:
148545
Step-by-step explanation:
it's easy enough
A sum of £36000 is divided between ALex ,Bill and claire by the ratio of 2 ×3/4 : 1×1/2 : 2×1/4 what is the amount each individual gets
so hmm £36000 will be split, hmmm let's call the ratios "a,b and c", so the amount will be split in ratios of a : b : c, which means we'll be dividing the 36000 bucks by (a + b + c) and distribute accordingly, let's do that, hmm let's convert also all those mixed fractions to improper fractions.
[tex]\stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} ~\hfill \stackrel{mixed}{1\frac{1}{2}} \implies \cfrac{1\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{3}{2}} \\\\\\ \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} ~\hfill \boxed{\cfrac{11}{4}+\cfrac{3}{2}+\cfrac{9}{4}\implies \cfrac{13}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{36000}{~~ \frac{13 }{2 } ~~}\implies 36000\cdot \cfrac{2}{13}\implies \cfrac{72000}{13} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{Alex}{\cfrac{11}{4}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{3}{2}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Claire}{\cfrac{9}{4}\cdot \cfrac{72000}{13}}\implies \stackrel{Alex}{\cfrac{198000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{108000}{13}}~ : ~\stackrel{Claire}{\cfrac{162000}{13}} \\\\\\ ~\hfill \stackrel{Alex}{15230\frac{10}{13}}~~ : ~~\stackrel{Bill}{8307\frac{9}{13}}~ : ~\stackrel{Claire}{12461\frac{7}{13}}~\hfill[/tex]
14. Higher Order Thinking Lake Trail is 4 3/5ths miles long. Outlook Trail is 5 5/6ths miles long. Pinewoods Trail is 1 3/10ths miles longer than Lake Trail. Which trail is longer, Pinewoods Trail or Outlook Trail? Explain.
please help me :)
The Pinewoods Trail is longer than the Outlook Trail.
What are fractions?The definition of a fraction is a portion of a whole. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin.
Given the length of Lake Trail = 4 and 3/5 mile
length of Lake Trail = 23/5 miles
length of Outlook Trail = 5 and 5/6 mile
length of Outlook Trail = 35/6 miles
length of Pinewoods Trail = 1 and 3/10 miles longer than Lake Trail
length of Pinewoods Trail = 33/10 + 23/5
length of Pinewoods Trail = (33 + 46)/10
length of Pinewoods Trail = 79/10 miles
comparing the length of Outlook Trail and Pinewoods Trail,
which is 35/6 and 79/10 miles respectively,
the common denominator for both is 30,
35/6 = (35*5)/(6*5)
35/6 = 175/30
and 79/10 = (79*3)/(10*3)
79/10 = 273/30
here 273/30 > 175/30
Hence Pinewoods Trail is longer.
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Consider the following sample data.
14 9 19 18 5
8
Calculate the z-score for the following values.
a. 12
b. 6
c. 15
d. 13
The z-score for a-d are?
(Round to two decimal places as needed.)
Take the original data and divide it by the standard deviation to determine the z-scores. X is a symbol for the relevant data point. For the population from which you selected your sample, mu and sigma stand in for the mean and standard deviation.
What are z-scores?In terms of standard deviations above or below the mean, a data point's z-score quantifies this exact distance.
A z-score is calculated using the following formula:
data point = mean standard deviation
Data point means with standard deviation equal to z
The same equation is given below in symbol form:
z= x−μ / σ
Some significant z-score details are as follows:
An elevated z-score indicates that the data point is.
When a data point has a negative z-score, it is below average.
The data point is considered to be roughly average if the z-score is near to 0.00.
If a data point's z-score is higher or lower than 3 33 or 3 3minus, the data point is deemed uncommon.
At Almond, the average score on a history midterm is
= 85 = 85mu, which is equivalent to 85 with a standard deviation of
= 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2
On the test, Michael received a score of 86.866.668.
Calculate Michael's exam grade in Z-score form.
His Grade = Mean Grade Standard Deviation
= 86 − 85 / 2
= 1 /2 = 0.5 z z z
= standard deviation of his grade and mean grade.
= 2 / 86−85
= 2 / 1 =0.5.
The z-score for Michael is 0.5, 0.50, and 5. He received a grade that was half a standard deviation higher than the mean.
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PLEASE HELP!!!!!!!! i dont understand this at all
Answer:
4
--
3
Step-by-step explanation:
Rate of Change via a table should be
f(x2)-f(x1)
-------------
x2 - x1
In this problem they indicated X2 is 36 and X1 is 18
At 36, F(X) is 61 and for 18, it's 37
Now to plug in...
61 - 37
----------
36 - 18
That boils down to
24
----
18
If we want to simplify it;
4
--. or. 1.333
3
y=3+4+369/2 plas helppppp
Answer:
191.5
Step-by-step explanation:
3 x 10 + 6 x1 + 1 + 8 x 1/1,000 in standred form
The expression in the standard form is 37.008
How to evaluate the expression in standard formFrom the question, we have the following parameters that can be used in our computation:
3 x 10 + 6 x1 + 1 + 8 x 1/1,000
Evaluate the products
This gives
30 + 6 + 1 + 8/1,000
Evaluate the quotients
30 + 6 + 1 + 0.008
Evaluate the sum
37.008
Hence, the number in standard form is 37.008
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Simplify. Need ASAP. show work
The simplified expressions that we have are;
a) 2∛16 - 12
b) (-375)^1/3x^8/3y^8/3
What is simplification?The term simplifications means that we have to write the expression is the easiest way that it can be written. In this case we have two expressions. We can be able to simplify them as we work through the steps that have been written below;
8) -2∛81 + 2∛16 - 2∛81
-4∛81 + 2∛16
-4(3) + 2∛16
2∛16 - 12
10) ∛-375x^8y^8
This simplifies to;
(-375)^1/3x^8/3y^8/3
This is the way that we can be able to simplify the expressions here.
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Mr. Jones invested a sum of money in 6% bonds. He invested $400 more than this sum in 4% bonds. If his total annual income was $116, how much did he invest in each kind of bond?
a = amount invested at 6%
how much is 6% of "a"? (6/100) * "a", namely 0.06a.
b = amount invested at 4%
how much is 4% of "b"? (4/100) * "b", namely 0.04b.
we also know that the yielded amount in interest or the annual income he's got from both is $116, so if we simply add their interest, that'd be 0.06a + 0.04b = 116.
We also know that he invested 400 more in "b" than in "a", so whatever "a" might be, we know that b = a + 400.
[tex]0.06a~~ + ~~0.04(\stackrel{b}{a+400})~~ = ~~116\implies 0.06a+0.04a+16=116 \\\\\\ 0.10a+16=116\implies 0.10a=100\implies a=\cfrac{100}{0.10} \\\\\\ \boxed{a=1000}\hspace{5em}\stackrel{1000+400}{\boxed{b=1400}}[/tex]
HELPPP PLEASEEE take your time , explanation please
Answer:
3 1/10 as a fraction
Step-by-step explanation:
3.3 as a fraction is 3 3/10. The first 3 is a whole number because it is to the left of the decimal point, and it represents 3 ''ones''. However, the second 3 to the right of the decimal point represents a decimal amount. Because this 3 is in the tenths place, we say it as ''3 tenths.
33 is repeating
When converting a percent in fraction form, you must know its place value of each number, and you can easily transform it to fraction.
EXAMPLE:3.3% - the place value is ones. It is a whole number and called as three.
3.3% - the place value is tenths. It is called as three-tenths.
ANSWER= 3 3/10 as this can't be simplified.PERCENT TO DECIMAL
When you convert a percent to decimal, you must divide it by 100.
SOLUTION (in the photo)3.3 ÷ 100
ANSWER= 0.33Question 15 (2 points)
The equation 5x-11 = 6x-x-11 has infinite solutions.
O True
O False
Reason:
The 6x-x on the right hand side simplifies to 5x
This means the right hand side turns into 5x-11, which is an identical copy of the 5x-11 on the left side.
The equation 5x-11 = 5x-11 has infinitely many solutions because we can replace x with any real number to end up with a true statement.
If using the method of completing the square to solve the quadratic equation x^2-16x-34=0, which number would have to be added to "complete the square"?
To complete the square, you would add (16/2)^2 = 64/4 = 16 to both sides of the equation.
What does a math quadratic equation mean?x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd polynomials equation, which is guaranteed by the algebraic fundamental theorem.
How can you tell whether or not an equation is quadratic?In other terms, you have a quadratic equation if a times the squares of the equation after b plus b twice that the same phrase not square plus c equals 0. The initial equation will change to a quadratic equation if the value in the () is replaced with such a variable like t.
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