Answer: 17+3x
Step-by-step explanation:
7(3 + x) - 4(x + 1)=
21+7*x-4x+(-4*1)= ==> Distribution Property
21+7x-4x+(-4)=
21+3x-4=
21-4+3x=17+3x
PLS HELP
Ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles. What fraction of those who were cast got major roles? Write your answer as a decimal.(1 point)
The fraction of those who were cast and got major roles is 1/5.
Number of the students who were cast
The number of the students who were cast out of the Ninety students auditioned for the school play is calculated as follows;
Total number of students = 90
Number of students who were cast = ¹/₃ x 90 = 30
Number of students who go major role = 6
The fraction of those who were cast and got major roles is calculated as follows;
fraction of students who got major role = 6/30
fraction of students who got major role = 1/5
Thus, the fraction of those who were cast and got major roles is 1/5.
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Answer:
Total number of students = 90
Number of students who were cast = ¹/₃ x 90 = 30
Number of students who go major role = 6
fraction of students who got major role = 6/30
fraction of students who got major role = 1/5
1/5 = 0.2
find the direction cosines and direction angles of the vector. (give the direction angles correct to the nearest tenth of a degree.)
The direction cosines and direction angles will be - [tex]\frac{x}{r},\frac{y}{r},\frac{z}{r}[/tex] and
cos⁻¹([tex]\frac{x}{r}[/tex]), cos⁻¹([tex]\frac{y}{r}[/tex]),cos⁻¹([tex]\frac{z}{r}[/tex]) respectively.
The direction cosines of a specified vector, m = xi + yj + zk, are the cosines of the angles it makes well with x, y, and z axes.
The direction cosines of m are cos a, cos b, and cos c in the x, y, and z axes, respectively, if a forms the angles a,b and c (which are the direction angles) with the x, y, and z axes, respectively.
Let us consider equation as = [tex]xi + yj +zk[/tex]
vector of the equation will be - (x,y,z)
r = length of vector = [tex]\sqrt{x^{2} +y^{2} +z^{2} }[/tex]
The direction cosines will be -
[tex]\frac{x}{r},\frac{y}{r},\frac{z}{r}[/tex]
angles will be - cos⁻¹([tex]\frac{x}{r}[/tex]), cos⁻¹([tex]\frac{y}{r}[/tex]),cos⁻¹([tex]\frac{z}{r}[/tex])
Let us consider an example,
If we have vector as (1,2,3)
= i + 2j + 3k
= r = [tex]\sqrt{1^{2} +2^{2} +3^{2} }[/tex]
= [tex]\sqrt{14}[/tex]
Direction cosines will be -
[tex]\frac{1}{\sqrt{14} } , \frac{2}{\sqrt{14} }, \frac{3}{\sqrt{14} }[/tex]
Angles will be -
cos⁻¹([tex]\frac{1}{\sqrt{14} }[/tex]), cos⁻¹([tex]\frac{2}{\sqrt{14} }[/tex]),cos⁻¹([tex]\frac{3}{\sqrt{14} }[/tex])
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The temperature was -6 f it rose to 0f what represents the change in temperature
1 Latisha and Maisha are twins. They have a brother who is eleven years younger than
them and an older sister who is four years older. The sum of the ages of all four siblings
is 73. Find Latisha's age.
You can earn 8 percent interest, compounded annually. how much must you deposit today to withdraw $10,000 in 6 years?
We must deposit (B) $6,301.70 today to withdraw $10,000 in 6 years.
What do we mean by compound interest?Compounding interest is an important concept in the financial sector that has a direct impact on the value of financial assets. According to this theory, received interest will be invested back in the initial investment. This will result in additional interest earnings on the initial interest.To find the amount:
Given -
Future account balance = $10,000N = 6I = 8%Estimate the initial deposit required to obtain $10,000 in 6 years:
Initial deposit = Balance/(1 + 1)ⁿInitial deposit = 10,000/(1 + 8%)⁶Initial deposit = 6,301.70Therefore, we must deposit (B) $6,301.70 today to withdraw $10,000 in 6 years.
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The correct question is given below;
You can earn 8 percent interest, compounded annually. How much must you deposit today to withdraw $10,000 in 6 years?
A. $5,402.69
B. $6,301.70
C. $6,756.76
D. $8,432.10
E. $9,259.26
find two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm.
Two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm is 12.3cm and 19.3cm.
In space, a point is a precise position or location. It is possible to depict it in relation to a coordinate system and its origin. It has no length and is a zero-dimensional entity.
A line is made up of an unlimited number of points that form a straight line. One-dimensional objects like lines lack both thickness and width. It stretches forever in both directions. An endpoint and a beginning point define a line segment, which is a component of a line. A linear equation can be used to depict a line.
D is between C and E
_ _ _
C D E
CD =CE-DE
CD=15.8-3.5cm
CD=12.3 cm
E is between D and C
_ _ _
D E C
CD=CE+DE
CD=15.8+3.5cm
=19.3cm
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Find the inequality represented by the graph.
Answer: y<3x-4
Step-by-step explanation:
[tex](0,-4) \ \ \ \ \ \ (1,-1)[/tex]
The equation of the line
[tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
[tex]\displaystyle\\x_1=0\ \ \ \ x_2=1\ \ \ \ y_1=-4\ \ \ \ y_2=-1\\Hence,\\\frac{x-0}{1-0} =\frac{y-(-4)}{-1-(-4)} \\\\\frac{x}{1} =\frac{y+4}{-1+4} \\x=\frac{y+4}{3}[/tex]
Умножьте обе части уравнения на 3:
[tex]3x=y+4\\3x-4=y+4-4\\3x-4=y[/tex]
Thus, y<3x-4
andrew took a handful of change out of his picket adn noticed taht he was only holding dimes adn quarters in his hand. he counted that he had 22 coins that ammounted to $4. how many quarters and how many dimes does andrew have?
Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
What is a system of linear equations?A system of linear equations is a set of two or more linear equations. Linear equations refer to the equations that involve two or more variables in the form of "ax + b".
Given:
Number of coins = 22; only dimes and quarters.Amount of coins = $4To find: Number of dimes and quarters.
Finding:
Now, 1 dime = 10 cents and 1 Quarter = 25 centsAlso, 100 cents = $1=> By unitary method, $4 = 4(100) = 400 cents
Let the number of dimes be d and number of quarters be q.Now, According to question, a system of linear equations follows:d + q = 22 (Number of coins) => d = 22 - q (eqn1)
and 10d + 25q = 400 (amount of coins)
=> 10 ( 22 - q ) + 25q = 400
=> 220 - 10q + 25q = 400
=> 15q = 400 - 220 = 180
=> q = 12, i.e., number of quarters = 22 upon the solving of this system of linear equations.
On substituting the value of q in eqn1, we get: d = 22 - 15 = 7, i.e., number of dimes = 7.
Hence, Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
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in a month, carlos can produce a maximum of either 60 bushels of pears or 30 bushels of apples, or any linear combination in between. similarly, diane can produce a maximum of either 20 bushels of pears or 5 bushels of apples, or any linear combination in between.
Thus 3 bushels of pears can be acceptable term of trade for bushels of pears.
Opportunity cost of 1bushel of apple for Carlos=2pears
Opp. Cost of 1 bushles of apple for Donna=4pears
Thus ,
Term of trade acceptable to both for one bushels of apple is 2-4 bushels of pears
Ryan bought 6 apples and 9 peaches for a total of $9.75. Madi bought 4 apples and 5 peaches for $5.75. How much are apples and peaches?Define the variables.▪ Write 2 equations that model the situation.▪ Solve the system by either graphing, substitution or linear combinations.▪ Answer the question that was asked.▪ Plug in both answers and check your worka. The required equations are 6a+9p = 9.75 and 4a+5p = 5.75 .
b. The solution is given in the attached picture.
c. Apples are 1/2 and Peaches are 0.75
d. Solving the equations by putting the values
Let's take equation 1
6a+9p = 9.75
6 (1/2) + 9 (0.75) = 9.75
So equation satisfies both sides
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Which statement about this figure is true?
It has reflectional symmetry with one line of symmetry.
It has point symmetry.
It has no reflectional symmetry.
It has rotational symmetry with an angle of rotation of 180°.
Please explain all the steps you used to get the answer.
The complete compound inequality is 9 <= 1.5x <= 12
How to complete the compound inequality?From the given figure, we have'
Height = x
Base = 3
The area of a triangle is
Area = 0.5 * Base * Height
So, we have
A = 0.5 * 3 * x
Evaluate
A = 1.5x
The compound inequality is given as
9 <= A <= 12
Substitute A = 1.5x in 9 <= A <= 12
9 <= 1.5x <= 12
Hence, the complete compound inequality is 9 <= 1.5x <= 12
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The mean exam score for the first group of twenty examinees applying for a security
job is 35.3 with a standard deviation of 3.6.
The mean exam score for the second group of twenty examinees is 34.1 with a
standard deviation of 0.5. Both distributions are close to symmetric in shape.
a. Use the mean and standard deviation to compare the scores of the two groups.
b. The minimum score required to get an in-person interview is 33. Which group
do you think has more people get in-person interviews?
The mean exam score of the first group is [tex]35.3[/tex]
The mean exam score for the second group is [tex]34.1[/tex]
but [tex]35.3[/tex] is greater than [tex]34.1[/tex]
Standard deviation of the first group is [tex]3.6[/tex]
Standard deviation of the second group is [tex]0.5[/tex]
but [tex]3.6[/tex] is greater than [tex]0.5[/tex].
(a) We can draw a conclusion that the score of the second group is more evenly distributed.
(b) The second group has more people get in - person interviews because [tex]3.6\geq 0.6[/tex], so the scores of the exam for the second group are all close to 34.1. On the contrary, the score of exams for the first group is extreme polarization.
Mean: The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.Standard deviation: The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a database is in relation to its mean.To learn more about mean and standard deviation, click on the link given below:
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Round 2798.01 to 2 significant figure
The approximation of 2798.01 to 2 significant figures is 2800
How to round the expression to 2 significant figures?The expression is given as
2798.01
The approximation is given as
2 significant figures
The above means that we approximate the given expression such that only 2 significant figures are left
In this case, the 2 significant figures in the expression 2798.01 are 2 and 7
So, we start the approximation from 9
When 9 is approximated, the expression becomes
2798.01 = 2800
Hence, the approximation of 2798.01 to 2 significant figures is 2800
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Find a counterexample to show that the given conjecture is false.
If n is a real number, then n³>n.
Let [tex]n=0[/tex]. Then [tex]0^3 = 0[/tex] but 0 > 0 is a false statement.
Given y = x² + 3x - 2, find y when x = -2
Answer: - 10
Step-by-step explanation: -2 to the 2nd power is - 4. And 3 * - 2 is -6. So -4 + -6 = - 10.
I hope I have helped and I hope you have a wonderful day!
5) At West High School, 362 students take
Spanish. This number has been increasing
at a rate of 20 per year. The number of
students taking French is 259 and has been
decreasing at a rate of 3 per year. At these
rates, when will there be two times as
many students taking Spanish as taking
French?
Please help
Answer:
Step-by-step explanation:
In 6 years, because I subtracted 3 from 259 6 times and added 20 to 362 6 times.
Please help i will give out brainlist
Answer:
x = 16
Step-by-step explanation:
[tex]\frac{3x}{4}[/tex] + 3 = 15 (subtract 3 from both sides )
[tex]\frac{3x}{4}[/tex] = 12 ( multiply both sides by 4 to clear the fraction )
3x = 48 ( divide both sides by 3 )
x = 16
that is
subtraction / multiplication / division
Answer: ( not totally sure but I hope this helps)
Step-by-step explanation:
1. Given
2. Multiplication property of equality
3. Subtraction
4. Division property of equality
1. f(3)=2x-5 (show work)
Answer:
The answer is 1
Step-by-step explanation:
On a graph, it would be at the plot point (3,1)
15, 10, 20/3
Find the 9th term.
Answer:
15*2/3=10
10*2/3=20/3
20/3*2/3=40/9
40/9*2/3=80/27
80/27*2/3=160/81
160/81*2/3=480/243
480/243*2/3=960/729
960/729*2/3=1920/2187.
=1920/2187
The 9th term of the geometric sequence will be 1280 / 2187.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The sequence is given below.
15, 10, 20/3
The first term is 15. And the common ratio is given as,
r = 10 / 15
r = 2 / 3
The 9th term of the geometric sequence is given as,
a₉ = 15 · (2/3)⁹⁻¹
a₉ = 15 · (2/3)⁸
a₉ = 15 · 256/6561
a₉ = 1280 / 2187
The 9th term of the geometric sequence will be 1280 / 2187.
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Find the equation of a line parallel to 3x + 3y = 21 that passes through the point
(8,-2).
Answer:
awsome
Step-by-step explanation:
565
if h(x)=4-6x, find each of the following
h(-1)
h(10)
h(5)
Answer:
(-1)=10
(10)= -54
(5)= -26
Step-by-step explanation:
h(-1)=4-6(-1)
h(-1)=4 (-6*-1)
h(-1)=4+6
h(-1)=10
h(10)=4-6(10)
h(10)=4 (-6*10)
h(10)=4-60
h(10)=-54
h(5)=4-6(5)
h(5)=4 (-6*5)
h(5)=4-30
h(5)=-26
Hope this helps.
16 houses on 2 blocks = houses per block
Answer:
0.125
Step-by-step explanation:
A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 5) and (3, 2), what is the equation for a parallel street that passes through (2, −3)?
y = 3x + 11
y = 3x − 9
y equals negative 1 third times x plus 1
y equals negative 1 third times x minus 7 thirds
The equation for the parallel street that passes through (2, -3) is: B. y = 3x - 9.
How to Find the Equation of Parallel Lines?Two lines that lie parallel to each other will have a slope (m) that is of the same value. The equation can be written as y = mx + b in slope-intercept form.
Find the slope of the line that passes through (4, 5) and (3, 2):
Slope (m) = change in y / change in x = (5 - 2)/(4 - 3)
Slope (m) = 3/1
Slope (m) = 3
The slope of a parallel line would also be 3.
Substitute (a, b) = (2, -3) and m = 3 into y - b = m(x - a):
y - (-3) = 3(x - 2)
y + 3 = 3x - 6
Subtract 3 to both sides of the equation
y + 3 - 3 = 3x - 6 - 3
y = 3x - 6 - 3
y = 3x - 9
Therefore, the equation for the parallel street that passes through (2, -3) is: B. y = 3x - 9.
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8+3a+7b-5+2a-7b combine like terms means to add the coefficients (numbers) in front of like variables
The coordinates of the midpoint of GH¯¯are M(8, 0) and the coordinates of one endpoint are H(−2, 9)
Using the midpoint concept, the other endpoint of the segment is: G(18,-9).
What is the missing information?The problem asks for the coordinates of the other endpoint, given by point G.
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
Hence the x-coordinate of G is found as follows:
8 = (x - 2)/2
x - 2 = 16
x = 18.
The y-coordinate of G is found as follows:
0 = (y + 9)/2
y + 9 = 0
y = -9.
The other endpoint of the segment is: G(18,-9).
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For this exponential
function,
what is the output value (y),
when the input value (x) is O?
y = 10•5x
(0,[?])
The output value of (y) will be 1 .
In mathematics, an exponential function is a function of the form f(x) = ax. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. Exponential functions, as the name suggests, involve exponents. But note that the base of the exponential function has a constant and the exponent has a variable, not vice versa.We have given an exponential function [tex]y=10.5^x[/tex] ......(1)
It is given that input value is 0 which means that replace the x with the input value in the given function.
Putting x = 0 in the equation (1) , we get
[tex]y=10.5^0[/tex]
Value of any number raised to power zero is always one .
[tex]y=1[/tex]
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I WILL GIVE 25 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer: The answer is b
Step-by-step explanation: Simplify and expand it to determine it
Jordan can ride her skateboard 75 meters in 30 seconds. How long will it take Jordan to ride her skateboard 1500 meters.
Step-by-step explanation:
1500÷75= 20
30×20= 600 seconds
600÷60= 10 minutes
Help me with this problem please I am begging you
Answer:
32/40
Step-by-step explanation:
First divide 40 by 15
to check denominator, calculate 15 * the ans and for numerator as well
Simplify this algebraic expression completely.
10y - 3(y + 5)
O A. 7y+2
O B. 7y+ 5
© C. 7y- 15
• D. 7y- 5
The answer for the following algebraic expression [tex]10y-3(y+5)[/tex] is Option C [tex]7y-15[/tex].
According to the given question statement, We are supposed to simplify the given algebraic expression [tex]10y - 3(y + 5)[/tex]
Solution is as follows:
[tex]10y - 3(y + 5)\\= 10y-3(y)-3(5)\\\[/tex]
[tex]=10y-3y-15[/tex]
[tex]=7y-15[/tex]
Hence [tex]7y-15[/tex] is our final answer.
Algebraic expression: The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We get to know how to express an unknown value using letters like x, y, and z in the basics of algebra. Here, we refer to these letters as variables. Variables and constants, both can be used in an algebraic expression. A coefficient is a value that is added before a variable and then multiplied by it. These letters are called as variables here. Both constants and variables may be employed in an algebraic expression. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.To learn more about Algebraic expression, click on the link given below:
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