So, we have a total of 11 light bulbs. 5 are green, 4 are yellow and two are red. In cases in which the light bolbs are considered identical, we use the following math formula:
[tex]N=\frac{n!}{n_g!n_{y!}n_r!}[/tex]In which n is the total, 11. ng is thee number of green lightbulbs, ny the number of the yellow ones, and nr the number of the reds. So:
[tex]\begin{gathered} N=\frac{11!}{5!4!2!} \\ N=\frac{11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!\cdot24\cdot2} \\ N=11\cdot10\cdot9\cdot7 \\ N=6,930 \end{gathered}[/tex]So, Ahmad has 6,930 distinct orders
Simplify and then evaluate the equation when x=4 and y =2
We need to plug in
x = 4
y = 2
into the expression and simplify/evaluate.
Let's evaluate:
[tex]\begin{gathered} 5x+2(9y-x)-y \\ x=4,y=2 \\ So, \\ 5(4)+2(9(2)-(4))-(2) \\ =20+2(18-4)-2 \\ =20+2(14)-2 \\ =20+28-2 \\ =46 \end{gathered}[/tex]Answer46When a positive number x is divided by 7, the remainder is 4. What is
the remainder when x is divided by 4?
When a positive number x is divided by 7, the remainder is 4. The remainder when x is divided by 4 is 7.
What is a remainder?
The quantity "leftover" after executing a computation in mathematics is referred to as the remainder. The remainder is the integer that remains after dividing two integers to get an integer quotient in mathematics.
The remainder operator (%) returns the amount of one argument that is left over after dividing it by another operand. For instance, when 41 is divided by 7, the remaining is 6 and the quotient is 5.
Solution Explained:
A/Q
x / 7 = 4
Solving this equation
x = 4 X 7 = 28
Now putting the value of x in the equation
x / 4
= 28 / 4 = 7
Therefore, the remainder when x is divided by 4 is 7.
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I need help I am a teacher and have to explain this to my students
Solve the given inequality as shown below
[tex]\begin{gathered} r+6\ge11 \\ \Rightarrow r+6-6\ge11-6 \\ \Rightarrow r\ge5 \end{gathered}[/tex]Therefore, any number equal to or greater than 5 is a solution to the given inequality.
The correct answers are 5, 6, and, 7.
What is the mean absolute deviation (MAD) of the dada set? 2, 5, 6, 12, 15 Enter your answer as a decimal in the box.
To get the mean absolute deviation, we first need the mean of the set. The mean is calculated by the sum of the values divided by the number of data:
[tex]\begin{gathered} \mu=\frac{2+5+6+12+15}{5} \\ \mu=\frac{40}{5} \\ \mu=8 \end{gathered}[/tex]To get the means absolute deviation, we have to get the absolute difference between each data and the mean, sum them up and divide by the number of data:
[tex]\begin{gathered} d_1=|2-8|=|-6|=6 \\ d_2=|5-8|=|-3|=3 \\ d_3=|6-8|=|-2|=2 \\ d_4=|12-8|=|4|=4 \\ d_5=|15-8|=|7|=7 \\ MAD=\frac{6+3+2+4+7}{5}=\frac{22}{5}=4.4 \end{gathered}[/tex]Select the correct answer.Solve the equation using the method of completing the square.A. B. C. D.
Answer:
C. -4 ± 2√6
Explanation:
The given equation is
3x² + 24x - 24 = 0
First, add 24 to both sides
3x² + 24x - 24 + 24 = 0 + 24
3x² + 24x = 24
And factorize 3 on the left side
3(x² + 8x) = 24
Then, to complete the square, we need to add and substract (b/2)² to the expression in parenthesis. In this case, b = 8, so
(b/2)² = (8/2)² = 4² = 16
Then, add and subtract 16 as follows
3(x² + 8x + 16 - 16) = 24
3(x² + 8x + 16) - 3(16) = 24
3(x² + 8x + 16) - 48 = 24
Finally, we can factorize and solve for x
3(x + 4)² - 48 = 24
3(x + 4)² - 48 + 48 = 24 + 48
3(x + 4)² = 72
3(x + 4)²/3 = 72/3
(x + 4)² = 24
Solving for x, we get
[tex]\begin{gathered} x+4=\pm\sqrt{24} \\ x+4-4=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{4\cdot6} \\ x=-4\pm2\sqrt{6} \end{gathered}[/tex]Therefore, the answer is
C. -4 ± 2√6
Given: AB - BC, ZA ZC and BD bisects ABC. Prove: A ABD ~ ACBD.
Since BD bisects ABC, then angles ADB and BDC are congruent. Now that we have that both triangles ABD and CBD have the same two sides and angle, we have that they are congruent (because the side-angle-side postulate)
Once Farid spends 15 minutes on a single level in his favorite video game, he loses a life. Hehas already spent 10 minutes on the level he's playing now.Let x represent how many more minutes Farid can play on that level without losing a life.Which inequality describes the problem?
If he spends 15 minutes on a single level, he loses his life.
He has already spent 10 minutes on the level he is playing now.
x = the number of minutes he can play without losing a life.
The inequalities that can be use to represent this scenario will be
[tex]10+x<15[/tex]answer choices:454ft square inches, 252ft square inches, 156ft square inches
Tp fint the total area of the figure start by calculating the area of the square and the triangle separately.
Area of the square is calulated by mutiplying the side by the side
[tex]\begin{gathered} A=(14ft)\cdot(14ft) \\ A=196ft^2 \end{gathered}[/tex]Area of the triangle follows the formula:
[tex]A=b\cdot\frac{h}{2}[/tex]The base of the triangle is the same as the length of the square's side.
[tex]\begin{gathered} A=\frac{(14ft)\cdot(8ft)}{2} \\ A=56ft^2 \end{gathered}[/tex]Add both sides to find the total area
[tex]\begin{gathered} A_t=56ft^2+196ft^2 \\ A_t=252ft^2 \end{gathered}[/tex]Factor. x2 − x − 72 (x − 8)(x + 9) (x − 6)(x + 12) (x + 8)(x − 9) (x + 6)(x − 12)
The solution of the given equation are; (x + 8)(x − 9)
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We have been given the quadratic equation as;
x² − x − 72
Solving;
x² − (9-8)x − 72
x² − 9x +8x− 72
The factors are;
(x + 8)(x − 9)
Therefore, the solution of the given equation are; (x + 8)(x − 9)
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The circle at the right represents a planet. The radius of the planet is about 6600 km. Find the distance to the inizon that a person can seeon a clear day from the following heighth above the planeth 7 km
Which answer choice represents a simplified form of the expression 2.5 + 7 1 - 2.3 - 4?* O (2.5 + 2.3) - 7-4 0 (2.5 - 2.3) - (7-4) O (2.5 - 2.3) + (7 - 4) 4 + 7 + (2.5 - 2.3)
Solve the equation, give the exact solution then approximate the solution to the nearest hundredth
Given the expression:
[tex]10-3x^2=4[/tex]We can find its solution by solving like a linear equation up until the exponent:
[tex]\begin{gathered} 10-3x^2=4 \\ \Rightarrow-3x^2=4-10 \\ \Rightarrow-3x^2=-6 \\ \Rightarrow x^2=\frac{-6}{-3}=2 \\ x^2=2 \end{gathered}[/tex]now, we can apply the square root on both sides to get the following:
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt[]{2} \\ \Rightarrow x=\pm\sqrt[]{2=} \\ x=\pm1.41 \end{gathered}[/tex]therefore, the solutions of the equation are x=1.41 and x=-1.41
2. Write the equation of the graph shown below. 3 1 -2 0 2 1-
The function in the graph is V shaped, this indicates that it corresponds to a function of an absolute value of x:
[tex]f(x)=|x|[/tex]The V opens downwards, which means that the coefficient that multiplies the module (a) is negative:
[tex]f(x)=-|x|[/tex]→ This means rthat when we calculate the value of "a", this value has to be negative
As you can see in the graph, the vertex of the function is (0,3)
Following the vertex form:
[tex]f(x)=a|x-x_v|+y_v[/tex]Where xv represents the x-coordinate of the vertex and yv represents the y-coordinate of the vertex. Replace them in the formula and we get that:
[tex]\begin{gathered} f(x)=a|x-0|+3 \\ f(x)=a|x|+3 \end{gathered}[/tex]Now all we need to do is determine the value of "a", for this we have to use one point of the function and replace it in the formula, this way "a" will be the only unknown.
Lets take for example one of the roots (points where the function crosses the x-axis)
Point (1, 0)→ replace it in the formula
[tex]\begin{gathered} 0=a|1|+3 \\ 0=a+3 \\ a=-3 \end{gathered}[/tex]Now that we know the value of a, we can determine the wquation of the function as
[tex]f(x)=-3|x|+3[/tex]_+_=10.5 _-3.25=_help me pls
These questions can have multiple answers
for instance,
a)
_+_=10.5
8.5 + 2 = 10.5
5.5 + 5 = 10.5
3.5 +7 = 10.5
5.25 + 5.25 = 10.5
b)
_-3.25 =_
7 - 3.25 = 3.75
7.25 - 3.25 = 4
10. 5 - 3.25 = 7.25
c)
if each _ have the same value
x + x = 10.5
2x= 10.5
x= 5.25
d)
if each _ have the same value
_-3.25 =_
x -3.25= x
x-x = 3.25
0= 3.25
In this case, each x cannot be the same, it would have to be a number that you subtract 3. 25 and it remains the same number. That is not possible.
but if i use x= 5.25
5.25- 3.25= 2
need help converting point slope form equation to slope intercept form(y+10)=1/3(x+9)
The slope-intercept form is
→ y = m x + b
→ m is the slope
→ b is the y-intercept
∵ The given equation is
[tex]y+10=\frac{1}{3}(x+9)[/tex]First, multiply the bracket (x + 9) by 1/3
[tex]\begin{gathered} \because y+10=\frac{1}{3}(x)+\frac{1}{3}(9) \\ \therefore y+10=\frac{1}{3}x+3 \end{gathered}[/tex]Subtract 10 from both sides
[tex]\begin{gathered} \because y+10-10=\frac{1}{3}x+3-10 \\ \therefore y+0=\frac{1}{3}x-7 \\ \therefore y=\frac{1}{3}x-7 \end{gathered}[/tex]The equation in the slope-intercept form is y = 1/3 x - 7
Use a proportion to find the missing side length, x.
Answer:
The measure of angle ABC is;
[tex]m\measuredangle ABC=72^0[/tex]Explanation:
Given the triangle ABC.
Recall that the sum of angles in a triangle is 180 degrees;
[tex]8x+6x+6x=180[/tex]solving for x, we have;
[tex]\begin{gathered} 8x+6x+6x=180 \\ 20x=180 \\ x=\frac{180}{20} \\ x=9 \end{gathered}[/tex]From the diagram,
[tex]\begin{gathered} \measuredangle ABC=8x \\ \measuredangle ABC=8(9) \\ \measuredangle ABC=72^0 \end{gathered}[/tex]Therefore, the measure of angle ABC is;
[tex]m\measuredangle ABC=72^0[/tex]find the total and the interestprincipal $3200rate 5 1/2 yearscompounded semiannually for 6 years
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$3,200
r=5 1/2 %=5.5%=0.055
t=6 years
n=2
substitute the given values
[tex]A=3,200(1+\frac{0.055}{2})^{2\cdot6}[/tex]A=$4,431.31 ------> the totalFind out the interest
I=A-P
I=4,431.31-3,200
I=$1,231.31 -----> interestSimplify (3^z)^6 leave your answer in exponential notation
[tex](3^z)^6[/tex][tex]3^{6z}[/tex]
what is the value of x and y ?2x+3=Y
There can be infinite solutions for x and y, this is because if we look at the equation like a slope intercept equation
[tex]\begin{gathered} 2x+3=y \\ y=2x+3 \end{gathered}[/tex]we can see that this is the equation for a straight line.
if we graph it
All values of x and y that are obtain by the line can be a solution to the equation given.
The sum of sixteen times a number and twelve is 172. Find the number.
Answer:
Step-by-step explanation:
1. (16 · x) + 12 = 172
2. x= 172-12/16
3. x = 10
4. The number is 10.
Which expression is equivalent to (3x^5+ 8x^3) – (7x^2 - 6x^3)?3x^5 +14x^3 – 7x^23x^5+ 2x^3 – 7x^2- 4x^5+ 14x^3- 4x^3 + 14
so the answer is option #1
2) Coefficient of u^2v^2 in expansion of (2u - 3v)^4
Answer
Step-by-step Explanation
In the expansion of variables in a bracket raised to a particular power, we either use the Binomial theorem or the Pascal's triangle.
The Binomial theorem teaches how to use permutaion and combination to obtain the coefficients of each term while the Pascal's triangle presents the coefficient of each term for different integer powers of the variables in a triangular form where the next line of the triangle can be obtained from the previous line just by starting with a 1 and adding two consecutive terms of that previous line and ending with 1.
the sum of 1/3 and 3/8
Answer:
17/24
Explanation:
To add the fractions
[tex]\frac{1}{3}+\frac{3}{8}[/tex]we first find their common denominators.
The common multiple of 3 and 8 is 24 because 3 * 8 = 24; therefore,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{1\cdot8}{3\cdot8}+\frac{3\cdot3}{8\cdot3}[/tex][tex]=\frac{8}{24}+\frac{9}{24}[/tex]Adding the numerators gives
[tex]\frac{8}{24}+\frac{9}{24}=\frac{17}{24}[/tex]Hence,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{17}{24}[/tex]A shipment of 10 computers contains 4 with defects. Find the probability that a sample of size 4, drawn from the 10, will not contain a defective computer,The probability is:
ANSWER
[tex]P=\frac{81}{625}[/tex]EXPLANATION
There are 4 defects out of 10 total computers. This means that there are 6 computers without defects.
The probability that 1 computer selected will not be defective is the total number of non-defective computers divided by the total number of computers:
[tex]P(one-without-defect)=\frac{6}{10}[/tex]Therefore, if a sample of 4 computers is selected, the probability that the sample will not contain a defective computer is:
[tex]\begin{gathered} P=\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}=(\frac{6}{10})^4 \\ P=\frac{81}{625} \end{gathered}[/tex]how do i solve for d ?3(2d-4) = 6(d-2)
Solution:
Given the equation;
[tex]3(2d-4)=6(d-2)[/tex]SImplify:
[tex]6d-12=6d-12[/tex]Since the two sides of the equation are equal, d has infinitely many solutions.
Find the sales tax in total cost of espresso machine that cost $46.95 the tax rate is 4% rounding your answer to the nearest cent
Given:
The total cost of espresso machine costs $46.95. and the tax rate is 4%.
To find:
Find the sales tax?
Explanation:
[tex]Sale\text{s tax=Sales tax percenatge}\times pre-tax\text{ cost}[/tex][tex]Total\text{ cost=Pre-tax value +Sales tax}[/tex]Solution:
We will start by converting sales tax percentage into a decimal by moving
the point two spaces to the left.
6%=0.06
Now, we need to multiply the pre-max cost of this item by this value
in order to calculate the sales tax cost
[tex]\begin{gathered} Sales\text{ tax=}0.04\times46.95 \\ Sales\text{ tax=1.878} \end{gathered}[/tex]Round to two decimal places
[tex]Sales\text{ tax=\$1.88}[/tex]Last, add this value of the pre-tax value of the item to find the total cost.
[tex]\begin{gathered} Total\text{ cost=Pre tax value + Sales tax} \\ Total\text{ Cost=46.95+1.88} \\ Total\text{ cost=}48.83 \end{gathered}[/tex]Hence, these are the required values.
Ben earned $400 dollars last month.He worked 3 days in the first week andalso worked 2 days in the secondweek. How much does he earn eachday?
Given Data:
Ben earned $400 last month.
Since in the academic calendar the last month was July consisting of 31 days.
Therefore the amount earned per day can be calculated as
[tex]\frac{400}{31}[/tex]Now, He worked 3 days in the first week and 2 days in the second week.
So the total number of working days is 5.
Therefore the amount earned for 5 days will be
[tex]\frac{400}{31}\times5=64.51[/tex]Therefore the amount for 6 days is approximate $65.
And Hence for each day it is $13.
5.) Figure 10.85 shows a method for constructing isosceles triangles. A. use the method of figure 10.85 to drawl two different isosceles triangles B. use the definition of circles to explain why this method will always produce an isosceles triangle.
You first draw two circles when different radii.
When you select two point over the circumference, and you connect a line in between these points and the center of the circle, you will always obtain two sides with the same length. It is because the length of these sides coincides witht the ratio of the circle.
Then, when you connect the points over the circumference between them, you have a side that can have a different length compared with the lengths of the lines connected to the center. Thus, you obtain an isosceles triangle; you have two sides with the same length (remember, it's the same as the radius) and one side with another length.
The key concepts used to convert units between different systems of measurement are shown without the final twosteps.1. Identify the units of measure to be converted,2. Write conversion factors,3. Cancel units.4.5.Which two steps will complete the list correctly?4. Divide the original measurement by the conversion factors.5. Check for reasonableness,4. Multiply the original measure by the conversion factors.5. Simplify the answer.4. Multiply the original measure by the conversion factors.5. Check for reasonableness,4. Divide the original measure by the conversion factors.
Here, we want to select from the options, the two best statements that completes the steps
The two steps are;
Multiply the origi
Can someone please help me do #6 and #8 please
#6:
As it's a rhombus, the diagonal is a bisector, so:
med 2 = 27
med 3 = 27
and
med 5 = 27
med 4 = med 1
Also, the sum of interior angles of a triangle is 180 degrees. Then:
27 + 27 + med 1 = 180
med 1 = 126
med 4 = 126