John measured two pieces of string. One piece measured \dfrac7{12}\text{ m}127 mstart fraction, 7, divided by, 12, end fraction, start text, space, m, end text and the other measured \dfrac47\text{ m}74 mstart fraction, 4, divided by, 7, end fraction, start text, space, m, end text.
Write the exponential equation y^6 = 30 in logarithmic form.Show your work here
We have the expression:
[tex]y^6=30[/tex]If we apply the logarithm with base 30 to both sides, we obtain:
[tex]\begin{gathered} \log_{30}(y^6)=\log_{30}(30) \\ 6\log_{30}y=1 \\ \log_{30}y=\frac{1}{6} \end{gathered}[/tex]Answer: an equivalent logarithmic expression is log_30(y) = 1/6
What is the range of y =
1
2
3
4
Answer:
y ≥ 5
Step-by-step explanation:
y ≥ 5
domain
x ≥ -7
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain: [ − 7 , ∞ ) , { x | x ≥ − 7 }
Range: [ 5 , ∞ ) , { y | y ≥ 5 }
The quotient of 1 and the square of a number written as a algebraic expression?
The algebraic expression for the quotient of 1 and the square of a number is written as 1/y²
What is an algebraic expression?An algebraic expression can best be defined as an arithmetic or mathematical expression that is known to consist of variables, coefficients, constants, factors as well as terms.
These expressions also said to be made up of numerous mathematical or arithmetic operations, which includes;
ParenthesesAdditionSubtractionMultiplicationBracketDivision, among othersFrom the information given, we have that;
The quotient of 1 and the square of a number
Now, let the number in this case be y
This expression can be represented as;
1/ (y)²
expand the bracket
1/y²
Hence, the expression is 1/y²
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0.5(x+6)=1+0.25(x-4)
Answer: -12
Step-by-step explanation:
0.5(x+6) = 1 + 0.25(x-4)
0.5x + 0.5×6 = 1+ 0.25x - 0.25×4
0.5x - 0.25x = 1 - 1 -3
0.25x = -3
x = -12
Find the value of x for which r || s. Then find m∠1 and in∠2.
m∠1=75-2x
mZ291-3x
The value of x for which r || s is
mt=1
m<2=□
Answer:
Since r and s are parallel lines, angle 1 = angle 2 (corresponding angles)
75 - 2x = 91 - 3x
x = 16
Angle 1 = 75 - 2(16) = 43°
Angle 2 = Angle 1 = 43°
Anthony finds some nickels and pennies in his change purse. How much money (in dollars) does he have if he has 100 nickels and 60 pennies? How much money (in dollars) does he have if he has xx nickels and yy pennies?
Total value, 100 nickels and 60 pennies (dollars):
Total value, xx nickels and yy pennies (dollars):
Answer:
Nickels are equal to 5 cent and pennies are equal to 1 so:
5 times 100 = 500
1 times 60 = 60
500 + 60 = 560
560 converted to dollars would be $5.60!
Step-by-step explanation:
Hope it helps! =D
After seventy seven failed attempts the hockey team finally won the championship. now one half of the fans think the city should name a street after the winning coach and 1/12 of those believed he should also be appointed mayor.what fractions of the fans believe the coach should be appointed mayor as well as have a street name after him. make sure ur answer is fully reduced
Answer: 1/24
Step-by-step explanation:
1/2 * 1/12 = 1/24
what is 12 root divided by 3 root (simplify)
Answer:
Дсдслсьмтстстсьсьалалла =4
Answer: 2
Step-by-step explanation:
1. Simplify the expression
[tex]sqrt(12)/sqrt(3)\\3.464/sqrt(3)\\3.464/1.732[/tex]
2. Perform any multiplication or division, from left to right:
[tex]3.464/1.732[/tex]
[tex]2[/tex]
1. ERROR ANALYSIS
Your friend is trying to find the maximum value of P = -x + 6y subject to the
following four constraints.
y ≤−2x +4
y≤x+1
x ≥ 0
y20
a. Explain what error your friend made in the graph below? (1 point)
b. Edit the graph below or paste a screenshot of your corrected graph from
Desmos. (1 point)
List the vertices of the feasible region. (1 point)
d. Use all vertices as you calculate and prove how to maximize the objective
function P? (2 points) to
Answer:
a. See below.
b. See attachment.
c. (1, 2) (2, 0) (0, 0) (0, 1)
d. The maximum value of P is 11.
Step-by-step explanation:
[tex]\textsf{Maximize}: \quad P=-x+6y[/tex]
[tex]\textsf{Subject to}:\begin{cases}\begin{aligned} \quad y &\leq -2x+4\\y&\leq x+1\\x&\geq 0\\y & \geq 0\end{aligned}\end{cases}[/tex]
Graph the lines:
[tex]\textsf{Draw the line } \;\;y=-2x+4 \;\;\textsf{and shade under the line}.[/tex]
[tex]\textsf{Draw the line } \;\;y=x+1 \;\;\textsf{and shade under the line}.[/tex]
[tex]\textsf{Draw the line } \;\;x= 0 \;\;\textsf{and shade above the line}.[/tex]
[tex]\textsf{Draw the line } \;\;y=0\;\;\textsf{and shade above (to the right of) the line}.[/tex]
Therefore, the feasible region is bounded by the vertices:
A = (1, 2)B = (2, 0)C = (0, 0)D = (0, 1)Determine the value of P at the vertices by substituting the x and y values of the points into the equation for P:
[tex]\textsf{Value of $P$ at $A(1, 2)$}: \quad -(1)+6(2)=11[/tex]
[tex]\textsf{Value of $P$ at $B(2, 0)$}: \quad -(2)+6(0)=-2[/tex]
[tex]\textsf{Value of $P$ at $C(0, 0)$}: \quad -(0)+6(0)=0[/tex]
[tex]\textsf{Value of $P$ at $D(0, 1)$}: \quad -(0)+6(1)=6[/tex]
Hence, the maximum value of P is 11 at vertex (1, 2).
You are selling concessions at a local swim meet. Hot dogs are being sold for $1.00 and soda is being sold for $0.50. At the end of the day you made $150. Let x represent the number of hotdogs sold and y represent the number of sodas sold. Write an equation that can be used to find the number of hotdogs and sodas sold at the swim team.
A) Standard Form:
B) Slope-Intercept Form:
C) If you sold 40 hot dogs how many sodas did you sell?
D) Using the Standard Form, identify the x-intercept of the graph and explain how the x-intercept relates to the number of hot dogs and sodas sold.
E) Using Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the number of hot dogs and sodas sold.
A. The equation in standard form: x + 0.50y = 150
B. The equation in slope-intercept from: y = -2x + 300.
C. y = 220 sodas
D. x-intercept is (150, 0)
E. y-intercept is (0, 300).
What is the Standard Form and Slope-intercept Form of a Linear Equation?The standard form for an equation is: Ax + By = C, where C is a constant and A and B are integers.
The slope-intercept form is, y = mx + b, here, m = slope or unit rate, and b = y-intercept.
A. x = number of hotdogs
y = number of sodas
Cost of one hotdog = $1.00
Cost of one soda = $0.50
Total cost = $150
To write the equation in standard form, substitute A = 1, B = 0.5, and C = 150 into Ax + By = C:
x + 0.50y = 150
B. Rewrite x + 0.50y = 150 in slope-intercept form:
x + 0.50y - x = -x + 150
0.50y = -x + 150
Divide both sides by 2
y = -2x + 300 [slope-intercept form]
C. Substitute x = 40 into x + 0.50y = 150:
40 + 0.50y = 150
0.5y = 150 - 40
0.5y = 110
y = 220 sodas
D. Substitute y = 0 into x + 0.50y = 150:
x + 0.50(0) = 150
x = 150
The x-intercept is 150, it means when 0 number of soda is sold, 150 hot dogs is sold.
E. Substitute x = 0 into x + 0.50y = 150:
0 + 0.50y = 150
y = 150/0.5
y = 300
The y-intercept is 300, it means when 0 number of hot dog is sold, 150 sodas are sold.
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For what value(s) of b does the equation x + 3 - 1 2 x = 3 4 (bx - 5) have exactly one solution?
The value of b could be 0 so that the equation x + 3 - (1/2)x = 3/4(bx - 5) has exactly one solution.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equations are:
x + 3 - (1/2)x = 3/4(bx - 5)
Let
b = 0
x + 3 - (1/2)x = 3/4(- 5)
x/2 = -15/4 - 3
x/2 = -27/4
x = -27/2
Thus, the value of b could be 0 so that the equation x + 3 - (1/2)x = 3/4(bx - 5) has exactly one solution.
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What are the coordinates of point A? x x x A (1.2, 3.5) B (2,4) C D (1.7. 3.8) (4.9. 3.9) 6 5 4 3 2 1 1 2 B 3 4 5 5 ◆m 7 FO 00 В 9 73
The coordinates of point A is (1.7,3.8)
What is coordinate plane ?A coordinate plane is a surface with two dimensions made up of two number lines. It is created when the origin, the point at which the X-axis and Y-axis cross, is reached. To locate points, one uses the numbers on a coordinate grid. A coordinate plane is useful for graphing points, lines, and many other things. It serves as a map and provides clear instructions for getting from one place to another.
Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there which is 1.7. To get the y-coordinate, repeat the previous step while adhering to a horizontal line you will get y coordinate as 3.8
The coordinates of point A is (1.7,3.8)
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a binomial probability experiment is conducted with the given parameters. use technology to find the probability of x successes in the n independent trials of the experiment. n
P(X < 4) = 0.8059
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
In which
P(X < 4) = 0.8059
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5. The Outdoors Club held a car wash to raise money. They washed cars for $5 each and vans for
$7 each. They washed a total of 45 vehicles and earned a total of $243.
a) Write two equations to represent this linear system. (Don't forget your let statements)
b) How many of each type of vehicle did they wash?
A. In the given question, we know that the Club washed cars and vans. They charge $5 for cars and $7 for vans. They earned a total of $243. Also, they washed a total of 45 vehicles. We have to find out the Equations for the Linear system
Let, the Number of Cars = 'c', and the Number of Vans = 'v', then the equation representing the total number of vehicles will be:
=> v + c = 45 => Equation (1)
Now, if the cost of washing 1 car is $5 and the van is $7 then,
Cost of washing 'c' car: 5c
Cost of washing 'v' van: 7v
then the equation representing total Earning will be:
=> 7v + 5c = 243 => Equation (2)
B. Now, we have to calculate the system of Linear equations to find out the number of cars and vans.
by equation (1) we get:
=> v + c = 45
=> v = 45 - c => Equation (3)
Putting this value in Equation(2) we get:
=> 7(45-c) + 5c = 243
=> 315 - 7c + 5c = 243
=> 2c = 72
=> c = 36
Put this value of c = 36 in Equation (3), and we get:
=> v = 45 - 36
=> v = 9
Hence, the system of equations is v + c = 45, and 7v + 5c = 243 and the number of Cars washed is 36 and vans is 9
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You can use this rule to work out the total cost, in pounds, of hiring a carpet cleaner. Multiply the number of days by 7.8 and then add 12
Andy hires a carpet cleaner.
The total cost is £82.20
(a) Work out the number of days Andy hires the carpet cleaner for.
Andy hired the carpet cleaner for 9 days, bringing the total cost to £82.20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Dependent variables depend on other variable while an independent variable .
Let y represent the amount of money paid to the carpet cleaner for working x days. Multiply the number of days by 7.8 and then add 12, Hence:
y = 7.8x + 12
For a total cost of 82.20
82.2 = 7.8x + 12x = 9.
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I need help quickly please
the answer would be C ( i am not 100% sure though) c= -36x-9
d);
12(3x) = 36x
-12(-3/4) = 9
Please help!! 15 points
Which inequality is represented by the graph?
The inequality that is represented by the graph is; y ≤ 1.5x - 3
How to Interpret Inequality Graphs?
Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region.
Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
Now, the given line is a dashed line and shaded below the line and as such we will use the inequality symbol ≤ .
The equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From the graph, we have that;
c = -3
m = 1.5
Thus, we have the inequality as y ≤ 1.5x - 3
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There are some beads in a box 4/5 of the beads are blue and the remaining beads are red there are 60 red red beads how many blue beads are there? What is the total number of beads in the box ?
Answer:
There are 240 blue beads and 300 total beads.
Step-by-step explanation:
We know that 60 beads are red, and that represents 1/5 of the total beads. To get the total number, multiply 60 by 5 to get 300. To find the number of blue beads, which we know is 4/5 of the total, we multiply 300 (total) by 4/5 (or .8) and get 240 beads.
Find the angle measures for each angle.
Based on angle relationship, the measures for each angle are:
m∠1 = 103°; m∠4 = 103°; m∠7 = 103°; m∠5 = 77°; m∠6 = 77°; m∠3 = 77°; m∠2 = 77°.
How to Find Angle Measures?The relationship between angles that are formed by two paralleled lines and a transversal can be used to determine the measures of each of the angles.
Using angles relationship, we have:
Angle 1 = 103° [corresponding angles are equal]
Angle 4 = 103° [alternate interior angles are equal]
Angle 7 = 103° [vertical angles are equal]
Angle 5 = 180 - 103 = 77° [supplementary angles]
Angle 6 = angle 5 = 77° [vertical angles are equal]
Angle 3 = angle 5 = 77° [alternate interior angles are equal]
Angle 2 = angle 5 = 77° [corresponding angles are equal]
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the daily useage time on the apple iphone is normally distributed with mean 5.4 hours and standard deviation 1.2 hours. what proportion of iphone owners use their iphone between 4 and 7 hours in a day? round your answer to three decimal places.
Solving for the probability using the z-table, the proportion of iPhone owners who use their iPhone between 4 and 7 hours in a day is 0.787.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value (4 and 7)
μ = mean = 5.4
σ = standard deviation = 1.2
z-score = (4 - 5.4) / 1.2 where x = 4
z-score = -1.4 / 1.2
z-score = -7/6 or -1.1667
z-score = (7 - 5.4) / 1.2 where x = 7
z-score = 1.6 / 1.2
z-score = 4/3 or 1.3333
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = -7/6 or -1.1667 probability = 0.12197
z-score = 4/3 or 1.3333 probability = 0.90853
To determine the proportion of iPhone owners who use their iPhone between 4 and 7 hours in a day is the difference between the probabilities of the two values.
proportion = 0.90853 - 0.12197
proportion = 0.787
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Evaluate f(x) = 7x+9 at each of the following values:
f(-1)=
f(6)=
f(a)=
f(a+h)=
f(-a)=
-f(a)=
Question 2 of 10
Question 2
"If two lines intersect, then the lines are coplanar."
Identify the following statements as the contrapositive, converse, or inverse of the
statement above.
• If two lines do not intersect, then the lines are not coplanar. inverse
+
• If two lines are coplanar, then the lines intersect. converse
• If two lines are not coplanar, then the lines do not intersect.
contrapositive
C
The inverse of the conditional statement is : if two lines do not intersect, then the lines are not coplanar.
Conditionals are commands used in programming languages to handle decisions.
Conditional statements are those that have both a hypothesis and a conclusion. It is also known as a "If-then" statement. If the conclusion and the hypothesis are both true, the conditional statement is untrue.They include conditional statements, conditional expressions, and conditional constructions. Particularly, conditionals carry out various calculations or actions according on whether a boolean condition set by the programmer evaluates to true or false. The decision is always made in terms of control flow by selecting changing the control flow based on some situation.The contrapositive statement is : If two lines are not coplanar, then the lines do not intersect.
The converse statement is : If two lines are coplanar, then the lines intersect.
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In the diagram below, (5, 2) is the midpoint of a segment with one endpoint (-1,8). What is the other endpoint of the segment? Show your work or explain how you find your answer.
The the coordinates of the other endpoint of a line segment with an endpoint of (-1,8) and a midpoint of (5, 2) is ( 11,-4 ).
How determine the a second endpoint from a point and a midpoint?A midpoint is simply a point that divides a line segment into two equal halves.
The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2
Given the data in the question;
Midpoint (5,2)
x = 5y = 2Endpoint 1 ( -1,8)
x₁ = -1y₁ = 8Endpoint 2 ( x₂,y₂)
x₂ = ?y₂ = ?To determine the coordinate of endpoint 2, plug the given points into the midpoint formula above and solve for x₂ and y₂.
First, we get the x-coordinate.
x = (x₁+x₂)/2
5 = ( -1 + x₂ )/2
( -1 + x₂ ) = 5 × 2
( -1 + x₂ ) = 10
x₂ = 10 + 1
x₂ = 11
Next, we get the y-coordinate
2 = ( 8 +y₂ )/2
8 +y₂ = 2 × 2
8 + y₂ = 4
y₂ = 4 - 8
y₂ = -4
Therefore, the coordinates of the other endpoint is ( 11,-4).
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Help with this
Please asap
Answer:
x = 3
Step-by-step explanation:
6 + 8x
--------- = 5x
2
6 + 8x
--------- = 5x (2)
2 (2)
6 + 8x = 10x
-8x -8x
------------------
6 = 2x
÷2 ÷2
-----------
3 = x
I hope this helps!
x f(x)
−2 4
−1 3
0 2
1 1
2 0
3 1
4 2
5 3
6 4
What are the vertex and range of the function?
Vertex (0, 2), Range: {y | 0 ≤ y < ∞}
Vertex (0, 2), Range: {y | 2 ≤ y < ∞}
Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
Vertex (2, 0), Range: {y | 2 ≤ y < ∞}
Examining the given function it could be found that
the vertex is (2, 0)the range is {y | 0 ≤ y < ∞}This makes the third option a more correct option
How to find the vertex and rangeThe term vertex is used most times when the graph discussed is a curve, I t represents the peak of the graph. It may be the lowest or highest value depending on where the graph opens
This graph opens up and the vertex is the least value in the y axis which is 0, that is (2, 0)
The range is in the y axis. It is all the values in the y direction, that is from least to the maximum values. making the value: {y | 0 ≤ y < ∞} correct
This tow values are seen in the third option
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Can anyone please help me?
Answer:
the answer is 60
Step-by-step explanation:
Why is 1/8 rational?
Answer:
The decimal terminates and does not repeat
Step-by-step explanation:
1/8 = .125
A new mobile device has a value of $256.25. It’s value changes by -22 1/2% each year. What is the value of the phone after two years?
If new mobile device has a value of $256.25 and its value changes by [tex]22\frac{1}{2}[/tex]% each year, then the value of phone after two years is $153.76
The value of new mobile device = $256.25
The percentage of value change = [tex]22\frac{1}{2}[/tex]%
Convert the mixed fraction to decimal form
[tex]22\frac{1}{2}[/tex]% = 22.5%
After one year mobile value = 256 - (256×22.5/100)
= 256-57.6
= $198.4
After two year the mobile value = 198.4-(198.4×22.5/100)
= 198.4-44.64
= $153.76
Hence, if new mobile device has a value of $256.25 and its value changes by [tex]22\frac{1}{2}[/tex]% each year, then the value of phone after two years is $153.76
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Which property could be used to solve the problem?
Erica rode her bike for 5 hours last week. This week, she did not ride her bike. How many hours did she ride her bike in the past two weeks?
a) additive inverse property
b) additive identity property
c) multiplicative inverse property
d) multiplicative identity property
The property that could be used to solve the problem when Erica rode her bike for 5 hours last week is B. additive identity property.
How to illustrate the information?From the information, Erica rode her bike for 5 hours last week and this week, she did not ride her bike.
It should be noted that the additive identity property illustrates that when a number is added to zero, the value is the same number.
In this case, the number of hours that she ride her bike in the past two weeks is:
= 5 + 0
= 5
In conclusion, the correct option is B.
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