The probability of selecting a female student with long hair is 45%
Let there be a total of 100 students in the class
Since 60% of the students are female, therefore out of 100 students 60 will be female students
Now, out of these 60 students, 75% have long hair, As a result, = 75% of 60 = 45 female students will have long hair
Probability of selecting female student with long hair = Number of female students with long hair/ Total number of students in the class
= 45/100
So, there is a 0.45 or 45% chance that a female student with long hair is selected
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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.
can someone help please?
∠1 and ∠4 are vertical interior angle.
∠1 ≅ ∠5 follows Transitive property of congruence
g ║h by corresponding angle theorem
How to find angles ?The diagram is to prove alternate interior angles converse.
Therefore,
∠4 ≅ ∠5 (Alternate interior angles)
By, the vertical interior angle congruence, ∠1 ≅ ∠4
Vertically opposite angles are congruent. Vertically opposite angles share the same vertex.
Then by the Transitive property of congruence, ∠1 ≅ ∠5.
So, by the corresponding angles theorem, g ║h
Corresponding angles are usually congruent.
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Finish solving the equation 5p + 7 - 3p = 3(2 - p)+1 using the steps that are partially below.
Answer:
p = 0
Steps shown below
Step-by-step explanation:
5p + 7 - 3p = 3(2 - p) + 1
5p + 7 - 3p = 6 - 3p + 1 (Distributive Property of Equality)
2p + 7 = 7 - 3p (Combine Like Terms)
2p + 7 + 3p = 7 - 3p + 3p (Addition Property of Equality)
5p + 7 = 7 (Simplify)
5p + 7 - 7 = 7 - 7 (Subtraction Property of Equality)
5p = 0 (Combine Like Terms)
5p/5 = 0/5 (Division Property of Equality)
p = 0 (Simplify)
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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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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Use the following function rule to find g(-p). Simplify your answer.
g(x) = 9W + 4
g(-p) =
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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Guys please explain how you get this I have an exam in half an hour sobs
Answer:
0.62853934
Step-by-step explanation:
Use a calculator.
I didn't get very far by hand. I've attached my partial solution.
Please help!! 15 points
Can u pls help me! I need this answers ASAP
Answer:
y=mx+b so the answer is 28980/420 which equals 69 lol
Step-by-step explanation:
Help ASAP please! Thank you
evaluate the function when x = -2, 0, and 5
1) f(x) = 1.5x + 1
2) g(x) = 11 - 3x + 2
3) h(x) = - 3 - x - 2
1) At x = -2, 0, and 5, the solutions are; f(-2) = -2, f(0) = 1 and f(5) = 8.5
2) At x = -2, 0, and 5, the solutions are; g(-2) = 18, g(0) = 13, g(5) = -2
3) At x = -2, 0, and 5, the solutions are; h(-2) = -3, h(0) = -5 and h(5) = -10
How to solve Linear Functions?
We want to evaluate each of the given functions when x = -2, 0, and 5.
1) f(x) = 1.5x + 1
At x = -2, we plug in -2 for x in the linear equation to get;
f(-2) = 1.5(-2) + 1
f(-2) = -2
At x = 0, we plug in 0 for x in the linear equation to get;
f(0) = 1.5(0) + 1
f(0) = 1
At x = 5, we plug in 5 for x in the linear equation to get;
f(5) = 1.5(5) + 1
f(5) = 8.5
2) g(x) = 11 - 3x + 2 = 13 - 3x
At x = -2, we plug in -2 for x in the linear equation to get;
g(-2) = 13 - 3(-2)
g(-2) = 18
At x = 0, we plug in 0 for x in the linear equation to get;
g(0) = 13 - 3(0)
g(0) = 13
At x = 5, we plug in 5 for x in the linear equation to get;
g(5) = 13 - 3(5)
g(5) = -2
3) h(x) = -3 - x - 2 = -5 - x
At x = -2, we plug in -2 for x in the linear equation to get;
h(-2) = -5 - (-2)
h(-2) = -3
At x = 0, we plug in 0 for x in the linear equation to get;
h(0) = -5 - 0
h(0) = -5
At x = 5, we plug in 5 for x in the linear equation to get;
h(5) = -5 - 5
h(5) = -10
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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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What is 9792381 ÷ 13 with the remainder? How do you solve for that?
The value of 9792381 ÷ 13 with the remainder will be 753260 remainder 1.
What is division?In contrast to multiplication, division is the process of dividing a given sum into equal pieces.
To solve the division will be illustrated as thus;
The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder.
Calculate the division as usual using your calculator. Once you have the result in decimal form, take the entire number out and multiply the decimal value that remains by the original problem's divisor. The outcome is your remainder.
In this case, the value when we divide 9792381 by 13 is 753260 remainder 1.
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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)=
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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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
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!
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
how do you solve 5 ( square root of 164)?
The number obtained by multiplying 5 and square root 164 is 64.
What is square root operator in mathematics?The square root operator in mathematics can be defined as a factor of a number that, when multiplied by itself, gives the original number.
The square root operator in mathematics is denoted by the symbol "√".
The problem 5 (square root of 164) is calculated as follows;
5 ( square root of 164) = 5√164
5√164 = 5(12.8) = 5 x 12.8 = 64
Thus, we can conclude that using the mathematics operator "√", the number obtained from 5 (square root of 164) will be greater than 5 but less than 164.
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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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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).
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 }
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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Why is 1/8 rational?
Answer:
The decimal terminates and does not repeat
Step-by-step explanation:
1/8 = .125
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
ian scores 44 out of 60 what is his score as a 1 decimal point
When Ian scores 44 out of 60, his score as a 1 decimal point is 0.3.
How to calculate the decimal?From the information, Ian scores 44 out of 60. This will be illustrated as:
Ian's score = 44
Total score = 60
The decimal will be illustrated as:
= Ian's score / Total score
= 44 / 60
= 4 / 15
= 0.3
Therefore, the score is 0.3
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If PQ QR, QR= 8, and RS = 11, what is the length of PS?
Answer:i don't know if right but 19
Step-by-step explanation:
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 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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Please help me Please help me
The answers of the given question are a followed
2. Same side interior angle theorem
3. Same side interior angle theorem
4. Vertical angle theorem
5. Vertical angle theorem
6. Substitution
What is vertical angle theorem?
The Vertical Angle Theorem states that two intersecting lines' opposing angles must be congruent, or of equal value. The angles opposite to each other will always be congruent, or equal in value, regardless of the manner in which or the location at which two straight lines intersect one another:
Two straight lines that cross each other create two linear pairs, according to the Vertical Angle Theorem. As a result, the adjacent angles created by the intersection of two lines are supplementary angles, meaning that their angles sum to 180 degrees:
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