3/4
Explanation:First box:
number of pencils = 1
number of pens = 3
Probability of picking pen in the first box = number of pens /total number in the box
Total = 1 + 3 = 4
probability of picking pen in the 1st box = 3/4
2nd box:
number of color pencils = 2
number of crayons = 6
Total = 2 + 6 = 8
Probability of picking crayons in the 2nd box = number of crayons/total number in the box
Probability of picking crayons in the 2nd box = 6/8 = 3/4
Probability of picking a pen from the first box and a crayon from the second box = probability of picking pen in the 1st box × Probability of picking crayons in the 2nd box
Probability of picking a pen from the first box and a crayon from the second box = 3/4 × 3/4
Probability of picking a pen from the first box and a crayon from the second box = 9/16
solve the rational equation, State the excluded values -2/x-8 = x-1/x+2
Answer::
[tex]\begin{gathered} x=3\text{ or 4} \\ x\neq8,x\neq-2 \end{gathered}[/tex]Explanation:
Given the rational function:
[tex]\frac{-2}{x-8}=\frac{x-1}{x+2}[/tex]Step 1: Cross-multiply
[tex]-2(x+2)=(x-1)(x-8)[/tex]Step 2: Expand and simplify
[tex]\begin{gathered} -2x-4=x^2-8x-x+8 \\ -2x-4=x^2-9x+8 \\ x^2-9x+2x+8+4=0 \\ x^2-7x+12=0 \end{gathered}[/tex]Step 3: Solve the quadratic equation for x.
[tex]\begin{gathered} x^2-7x+12=0 \\ x^2-4x-3x+12=0 \\ x(x-4)-3(x-4)=0 \\ (x-3)(x-4)=0 \\ x-3=0\text{ or }x-4=0 \\ x=3\text{ or }x=4 \end{gathered}[/tex]Step 4: Find the excluded values
The excluded values are the values at which the function is undefined.
Set the denominators equal to zero.
[tex]\begin{gathered} x-8=0\text{ or x+2=0} \\ x=8,x=-2 \end{gathered}[/tex]Thus the solution of the function is:
[tex]\begin{gathered} x=3\text{ or 4} \\ x\neq8,x\neq-2 \end{gathered}[/tex]Sarah took the advertising department from her company on a road trip to meet with a potential client . Including Sarah a total of 13 people took the trip. She was able to purchase coach tickets for $190 and first class tickets for $990. She used her total budget for airfare for the trip, which was $6470 . How many first class tickets did she buy. How many coach tickets did she buy?
Data is
Coach tiquet price= 190
First class tiquet price= 990
X= number of coach
Y= first class ticket
People on board trip= 13
Total spent = 6470
Then , equations are
X+ Y = 13
190X + 990Y = 6470
Now find solution, for this 2x2 system
Method of substitution
Substitute Y= 13 - X
190X + 990 (13-X) = 6470
Group in two blocks
190X - 990X = 6470 - 990•13
-800X = - 6400
Then
X= -6400/-800 = 8
Now find Y
Y= 13 - X = 13-8= 5
Then finally answers are
She buyed 5 first class tickets
and 8 c
Miriam has 3 packages of pencils. Each
package has 6 pencils. She needs an
eraser for each pencil. How many erasers
will she need to buy?
Tell which OPERATIONS you will use. Then
solve the problem. (Very important) Grade 3 common core. Think it requires 2 operations or 2 equations.
From this question, we can deduce the following:
Number of packages she has = 3
Number of pencils in each package = 6
She needs an eraser for each pencil. Let's find how many erasers she will need to buy.
Let's first find the total number of pencils.
Here, we are to use the multiplication operation
We have:
Total number of pencils = Number of packages x Number of pencils in each package.
Total number of pencils:
3 packages × 6 pencils = 18 pencils..................................equation 1
Mariam has a total of 18 pencils.
Since she needs an eraser for each pencile, she will need 18 erasers for the 18 pencils.
18 pencils × 1 eraser = 18 erasers............................................equation 2.
ANSWER:
18 erasers
Y=cosx Can you please give a graph use color for function, asymptotes, etc.A short table of easy pointsThe domain and rangePlease identify and label the asymptotes (Please work this as if you didn’t have a calculator)
We will have the following:
We are given:
[tex]y=\cos (x)[/tex]We will construct a table from 0 to 10, that is:
[tex]\begin{cases}f(0)=\cos (0)\Rightarrow f(0)=1 \\ \\ f(1)=\cos (1)=0.5403023059\ldots \\ \\ f(2)=-0.4161468365\ldots \\ \\ f(3)=-0.9899924966\ldots \\ \\ f(4)=-0.6536436209\ldots \\ \\ f(5)=0.2836621855\ldots \\ \\ f(6)=0.960101702867\ldots \\ \\ f(7)=0.7539022543\ldots \\ \\ f(8)=-0.1455000338\ldots \\ \\ f(9)=-0.9111302619\ldots \\ \\ f(10)=-0.8390715291\ldots \\ \end{cases}[/tex]From this we can see that the function is periodic in nature and fluctuates between the values of y = 1 and y = -1, this can be seing as follows:
Now, from this we can obtain the domain and range:
[tex]\text{Dom}_f=(-\infty,\infty)[/tex][tex]\text{Ran}_f=(-1,1)[/tex]There are not asymptotes, but the maximum and minimum values the function will ever reach are y = 1 & y = -1 respectively.
Two rovers are exploring a planet. The system of equations below show each rover's elevation y at time x. Without graphing these equations, what conclusion can you make about the system of equations?Rover A: y = 1.6x - 4Rover B: 3y = 4.8x - 12What conclusion can you make about the system of equations?A. The system has infinity many solutions.B. The system has no solution.C. The system has exactly one solution.
A. The system has infinity many solutions.
we can conclude both rovers have the same road, and they started at the same time
Explanation
[tex]\begin{gathered} y=1.6x-4\text{ Equation(1)} \\ 3y=4.8x-12\text{ Equation(2)} \end{gathered}[/tex]
Step 1
Let
y represents the elevation
x represents the time
to solve for x, multiply equation(1) by -3 and then add the result to Equation (2)
[tex]\begin{gathered} y=1.6x-4\text{ Equation(1) by -3} \\ -3y=-4.8+4\text{ Equation(3)} \\ \text{now, add equation (3) and equation(2)} \\ \\ -3y=-4.8x+12 \\ 3y=4.8x-12 \\ ----------- \\ 0=0+0 \\ 0=0 \end{gathered}[/tex]when you get a solution like this
[tex]0=0[/tex]it means the system has infinite solutions,so the answer is
A. The system has infinity many solutions.
we can conclude both rovers have the same road, and they started at the same time.
I hope this helps you
What type of polar curve is the polar equation r = 3- 3 sin (O)?O limaconO lemniscateO roseO cardiod
The polar curves with the form:
[tex]\begin{gathered} r=a\pm b\sin (\theta) \\ r=a\pm b\cos (\theta) \end{gathered}[/tex]are limacons. where a and b are constants. But when a and b are the same values, the polar curve is a cardioid.
So, the polar curve with the equation:
[tex]r=3-3sin(\theta)[/tex]the polar curve is a cardioid because a and b are equal to 3.
Determine the correct equation used in order to solve the problem "The number 24 is what percent of the number 40?"
The correct equation that represents the expression "The number 24 is what percent of the number 40?" is as shown below;
The the unknown number in percent be 'x'
x percent of number 40 is expressed as;
x% of 40
x/100 of 40
If 24 is equal to the expression above, then the final equation will be expressed as;
24 = x/100 of 40
24 = 40x/100
24 = 0.4x
Rearrange
0.4x = 24
Hence the correct equation used to solve the problem is 0.4x = 24
In polar coordinates, which point is in the same location as (4, 120°)(4, −240°)(12, 40°)(−4, 480°)(−4, 120°)
The radius has to stay the same length so we can eliminate 12
- just changes the direction
To go negative, we add 180 or subtract 180
120+180 = 300
We could add 360 or subtract 360 and end up at the same point
120+360 = 480
120 - 360 =-240
(4,-240) is the same point
(-4,480) is in the opposite direction because of the negative sign
Skylar repairs washing machines. Her revenue, in dollars, can be modeled by theequationy = 80+ 24x, where x is the number of hours spent repairingmicrowaves. Her overhead cost, in dollars, can be modeled by the equationy=x2 – 100, where x is the number of hours spent repairing washingmachines.After how many hours does she break even?Note: The phrase break even refers to the value where the two functions areequivalent.
The company breaks even when the revenue and cost are equal, then we have to solve the equation:
[tex]80+24x=x^2-100[/tex]Let's solve the equation:
[tex]\begin{gathered} 80+24x=x^2-100 \\ x^2-24x-100-80=0 \\ x^2-24x-180=0 \\ (x-30)(x+6)=0 \\ then \\ x=30 \\ or \\ x=-6 \end{gathered}[/tex]Since we can't have a negative number of hours we conclude that the company will break even when x=30, that is after 30 hours.
find the slope for the following two points of (6,6) (7,-7)
Slope = -13
Explanations:The slope of a line passing through two points with coordinates (x₁ , y₁ ) and (x₂ y₂) is calculated using the formula:
[tex]\text{Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex]Since the points are (6, 6) and (7, -7):
x₁ = 6, y₁ = 6, x₂ = 7, y₂ = -7
Substituting these into the formula:
[tex]\begin{gathered} \text{Slope = }\frac{-7-6}{7-6} \\ \text{Slope = }\frac{-13}{1} \\ \text{Slope = -13} \end{gathered}[/tex]0.8(10-x)=36 I understand just not fully
Step 1
Given;
[tex]0.8(10-x)=36[/tex]Required; To find the value of x
Step 2
Use the distributive law to expand the bracket
[tex]a(b+c)=(a\times b)+(a\times c)[/tex][tex](0.8\times10)+(0.8\times(-x))=36[/tex][tex]\begin{gathered} 8+(_{}-0.8x)=36 \\ Bring\text{ like terms together} \\ -0.8x=36-8 \\ -0.8x=28 \\ \frac{-0.8x}{-0.8}=\frac{28}{-0.8} \\ x=-35 \\ \end{gathered}[/tex]Hence, the value of x = -35
I have a problem. I have a picture of it because I can't type it
we have the next equation
[tex]5x^2-36x+36=0[/tex]we will use the formula to find the values of x of a second-grade equation
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where
a=5
b=-36
c=36
we substitute the values in the formula
[tex]x_{1,2}=\frac{36\pm\sqrt[]{36^2-4(5)(36)}}{2(5)}=\frac{36\pm\sqrt[]{576}}{10}=\frac{36\pm24}{10}[/tex][tex]x_1=\frac{36+24}{10}=\frac{60}{10}=6[/tex][tex]x_2=\frac{36-24}{10}=\frac{6}{5}[/tex]the values of x are
x=6 and x=6/5
Alternate interior angles are congruentTransitive property of congruenceCorresponding angles are congruentConverse of the corresponding angles postulate
Recall that the transitive property of congruence states that:
[tex]If\text{ }a\cong b\text{ and a}\cong c\text{ then b}\cong c.[/tex]Since
[tex]\angle1\cong\angle2\text{ and }\angle1\cong\angle4[/tex]then by the transitive property of congruence we get:
[tex]\angle2\cong\angle4.[/tex]Answer: Transitive property of congruence.
Use interquartile range to identify any outliers in the data set.49, 53, 38, 51, 54, 48, 59
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
49, 53, 38, 51, 54, 48, 59
Step 02:
outliers:
38, 48, 49, 51, 53, 54, 59
an outlier is a value that is much larger or smaller in a set of data
The answer is:
There are no outliers
Which graph is generated by this table of values? Х -4 0 3 y у 1 2 3 y เสี 4 3 1 5 4 3 2 1 IN 3 4 5 x -2 -5
Observe the table carefully.
The values (-4,1), (0,2) and (3,3).
Only the first graph marks these points correctly.
So the first option is the correct choice.
What equation results from completing the square and then factoring? X^2+22x=31
To answer this question we need to recall the expression for the square of a binomial:
[tex](a+b)^2=a^2+2ab+b^2[/tex]We are given the following expression
[tex]x^2+22x=31[/tex]Comparing to the general formula, we note the first term is similar to the term a^2
This means we already have the square of the first term, i.e. a = x
Now we focus on the second term 22x. It must be equal to the expression 2ab, that is
22x = 2ab
Since we already know a = x, then
22x = 2xb
Simplifying by x, we get
22 = 2b
Dividing by 2:
b = 11
It means the second term of the square is 11 and it's missing from the expression on the left side of the equation.
Completing square means we must add the exact number to form the square of the binomial as needed.
Note the missing term is b^2, the square of 11. Since 11 * 11 = 121, we add 121 to both sides of the equation:
[tex]x^2+22x+121=31+121=152[/tex]The left side is already formed as the square of (x+11), thus the required expression is
[tex](x+11)^2=152[/tex]Correct option: D.
Hello would like to see if you can help me with question 2?
Answer:
P(A or B) = 3/5
Explanation:
An independent event is an event that has no connection to another event's chances of happening. For A and B to be an independent event;
P(A or B) = P(A) + P(B)
Given the following parameters
P(A) = 1/5
P(B) = 2/5
Substituting the given parameters into the formula:
P(A or B) = 1/5 + 2/5
P(A or B) = 3/5
Hence the value of P(A or B) is 3/5
for the function whose graph is shown below, which is the correct formula for the function. please give me the answer for my daughter
From the graph notice that, the y-intercept is (0,3).
The general form of the line equation with slope m and y -intercept (0,c) is
y=mx+c.
So, here c=3.
The equation will be y=mx+3.
To find slope m use any point on the line.
The point (1,1) is lies on the line.
Substitute x=1, y=1 in y=mx+3.
[tex]\begin{gathered} y=mx+3 \\ 1=m(1)+3 \\ 1-3=m \\ -2=m \end{gathered}[/tex]So, the required formula for the function whose graph is given by figure is
[tex]y=-2x+3[/tex]If f(x)=3x+4, find f(-5)
Answer
f(-5) = -11
Explanation
The question asks us to find f(-5) when the function is defined as
f(x) = 3x + 4
So, f(-5) just involves solving this defined equation for when x = -5
f(x) = 3x + 4
f(-5) = 3(-5) + 4 = -15 + 4 = -11
Hope this Helps!!!
Find seco, cote, and cos 0, where is the angle shown in the figure. Give exact values, not decimal approximations. seco VIS 13 8 7 cot 0 7 0 cos o П
step 1
Apply Pythagorean theorem to find out the horizontal leg
8^2=x^2+7^2
x^2=64-49
x^2=15
x=√15
the cosine is equal to
cos=√15/8 ------> adjacent side divided by the hypotenuse
use the graph the parabola to fill in the table
Looking at the graph
Part a
This is a vertical parabola that opens Upward
Part b
The equation of the axis of symmetry is equal to the x-axis of the vertex (in a vertical parabola)
The vertex is the point (-3,3)
so
the equation of the axis of symmetry is x=-3Part c
The vertex is (-3,3)Part d
Find out the intercepts
y-intercept --------> (0,7)
x-intercepts ------> DNE (does not exist)
can you help me with my work
Given expression for function :
[tex]f(x)=x^2+6x+8[/tex]The general form of equation is :
[tex]ax^2+bx+c=0[/tex]The axis of symmetry is define as : the line that divides the parabola into two equal halves,
i,e
[tex]\text{ Ax is of symmetry = }\frac{-b}{2a}[/tex]From the given expression we have a= 1, b =6, c=8
So,
Axis of symmtery = -6/2(1)
Axis of Symmetry = -3
i.e x = -3
Now for the vertex
Vertex : which is the minimum point of the parabola and the parabola opens upward.
for vertex
Substitute the x = -3 and solve for the valur of f(x)
[tex]\begin{gathered} f(x)=x^2+6x+8 \\ f(-3)=(-3)^2+6(-3)+8 \\ f(-3)=9-18+8 \\ f(-3)=-9+8 \\ f(-3)=-1 \end{gathered}[/tex]So the vertex will be (-3, -1)
Which of the following constants can be added to x2 - 3x to form a perfect square trinomail?
The constant that can be added to [tex]x^2[/tex] - 3x to form a perfect square trinomial is [tex]2\frac{1}{4}[/tex]
The given expression is
[tex]x^2[/tex] - 3x
To form a perfect square trinomial
[tex](a-b)^2 =a^2-2ab+b^2[/tex]
The given expression is
[tex]x^2[/tex] - 3x
first we have to add a constant term with it
[tex]x^2[/tex] - 3x + z
By comparing the given expression and the perfect square trinomial
[tex]a^2 =x^2[/tex]
a = x
Similarly
-2ab = 3x
where know a =x
Then,
-2b = 3
b = -3/2
Similarly
[tex]b^2 = z[/tex]
[tex](\frac{-3}{2})^2[/tex] = z
9/4 = z
Convert the simple fraction to mixed fraction
9/4 = [tex]2\frac{1}{4}[/tex]
Hence, the constant that can be added to [tex]x^2[/tex] - 3x to form a perfect square trinomial is [tex]2\frac{1}{4}[/tex]
The complete question is :
Which of the following constants can be added to x2 - 3x to form a perfect square trinomial?
[tex]1\frac{1}{2},2\frac{1}{4}[/tex] and [tex]4\frac{1}{2}[/tex]
Learn more about perfect square trinomial here
brainly.com/question/16615974
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Solving systems of equations using substitution. y=2x-12. y=-3x+18
we can replace the value of y from one equation to another
this time I want to replace the first value of Y in the second equation
then
[tex](2x-12)=-3x+18[/tex]we will put the values accompanied with x on one side and the numbers on the other side
[tex]2x+3x=18+12[/tex]do the operations
[tex]5x=30[/tex]solve for x dividing 5 on both sides
[tex]x=\frac{30}{5}=6[/tex]the value of x is 6, now I can replace x on any of the principal equations
I am replacing on the second
[tex]\begin{gathered} y=-3x+18 \\ y=-3(6)+18 \\ y=-18+18 \\ y=0 \end{gathered}[/tex]the vaku
Kristy went shopping and spent $27 on shorts. if she spent $38 total, what percentage did she spend on shorts? (Round to nearest percent)
It is given that Kristy spent $27 on shorts and total amount is $38.
Percentage of money spent on shorts is given by:
[tex]\frac{27}{38}\times100=71.05263158\text{ percent}\approx71.0526\text{ percent.}[/tex]So Kristy has spent 71.0526% of her money on shorts. It is 71% rounded to the nearest percent.
What are some equivalent fraction 7/8
The given fraction is 7/8.
Equivalent fractions to 7/8 would be 14/16, 21/14, and 28/32.Remember that you have to multiply a number with the numerator and denominator to find an equivalent fraction.
Find the rate of change at(see picture)Write the exact answer. Do not round.
the Given:
The expression is given as,
[tex]y=\sqrt[]{x+7}\text{ . . . . . (1)}[/tex]The value of dx/dt is,
[tex]\frac{dx}{dt}=7\text{ . . . . . . (2)}[/tex]The objective is to find dy/dt at y = 6.
Explanation:
Substitute y = 6 in equation (1),
[tex]\begin{gathered} y=\sqrt[]{x+7} \\ 6=\sqrt[]{x+7}\text{ . . . . (3)} \end{gathered}[/tex]To find dy/dt:
Differentiate equation (1) for t.
[tex]\begin{gathered} \frac{dy}{d\text{t}}=\frac{dy}{d\text{x}}\times\frac{d\text{x}}{dt} \\ =\frac{d}{d\text{x}}\sqrt[]{x+7}\times\frac{d\text{x}}{\mathrm{d}t} \\ =\frac{1}{2\sqrt[]{x+7}}\times\frac{d\text{x}}{\mathrm{d}t}\text{ . . . . .(4)} \end{gathered}[/tex]Substitute the value of equations (2) and (3) in equation (4).
[tex]\begin{gathered} \frac{d\text{ y}}{d\text{ t}}=\frac{1}{2\sqrt[]{x+7}}\times\frac{d\text{ x}}{d\text{ t}} \\ =\frac{1}{2\times6}\times7 \\ =\frac{7}{12} \end{gathered}[/tex]Hence, the value of the rate of change is 7/12.
Find the length of a side of asquare with an area of 71 units².(a)≈8.43(b) ≈ 8.5(c) 7(d) 7.1
Solution:
[tex]\begin{gathered} Area\text{ of a square= \lparen length\rparen}^2 \\ 71=l^2 \\ l=\sqrt{71} \\ l=8.426 \\ l=8.43\text{ \lparen2 decimal places\rparen} \end{gathered}[/tex]Answer = option A
Question 5 For AMVL, MZV = 90°, mZL = 30°, and ML = 54. (Draw a picture to help.) What is the value of VL? Answer А B 183 27V3 18 27
The side VL can be obtained using sin rule
[tex]\begin{gathered} \frac{\sin\text{ 90}}{54}\text{ =}\frac{\sin \text{ 60}}{VL} \\ \\ \Rightarrow\frac{1}{54\text{ }}=\frac{\frac{\sqrt[]{3}}{2}}{VL} \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{54\text{ }}=\text{ }\frac{\sqrt[]{3}}{2VL} \\ \text{Cross Multiply} \\ 2VL\text{ = 54 }\sqrt[]{3} \\ VL\text{ =}\frac{54\sqrt[]{3}}{2} \\ VL\text{ = 27}\sqrt[]{3} \end{gathered}[/tex]Option B is correct
Tony observed the solution to a pair of linear equations graphed in the coordinate plane to be(-6,-5). Which method can be used to verify that (-6,-5) is the correct solution?
Given:
the solution to a pair of linear equations graphed in the coordinate plane to be(-6,-5).
We will find which option is correct.
To verify that (-6,-5) is the correct solution
So, the first two options are wrong because the substitution is wrong
The third option is wrong because when the substitution with x = -6 into the equation on the right-side the answer will be as follows:
[tex]\begin{gathered} y=\frac{-1}{2}x-2 \\ -5=\frac{-1}{2}(-6)-2 \\ -5=3-2 \\ -5=1\rightarrow\text{Wrong} \end{gathered}[/tex]So, the answer will be option 4
we must substitute with x = -6 and y = -5