The standard deviation of a binomial distribution with n trials and a probability of success of p is given by the formula:
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]From the problem, we identify:
[tex]\begin{gathered} n=450 \\ p=0.3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sigma=\sqrt[]{450\cdot0.3\cdot(1-0.3)}=\sqrt[]{450\cdot0.3\cdot0.7} \\ \sigma\approx9.72 \end{gathered}[/tex]20. A sequence is defined recursivelybelow:+4a, = 8,-1a, = -3Which function can be used to find the nthsequence?
A)
1) Let's insert the Recursive formula for a:
[tex]\begin{gathered} a_n=a_{n-1}+4 \\ a_1=-3 \\ f(n)=-3\text{ +(n-1)4} \\ f(n)=-3\text{ +4n-4} \\ f(n)=4n-7 \end{gathered}[/tex]When we apply the General formula f(n) we'll need the first term. for that sequence, and then rearrange it we find the function for the nth term of that Arithmetic Sequence.
All we need now is to plug into the formula the nth term we want to find out.
Hi,I need help with this I tried and I can’t get the answer
Given
[tex]12000\div300[/tex]We can decompose the above expression below
Explanation
300 can be decomposed into
[tex]300=100\times3[/tex]Therefore,
Answer:
[tex]12000\div100\div3[/tex]Draw a graph of a parabola that has the followinsignificant features:a > 0one X - intercepty - intercept at 4Write the equation to your parabola:
Saira is using the formula for the area of a circle to determine the value of .
For this problem, we just have to use the values we're given to calculate the approximate value of pi.
The formula presented is
[tex]\pi=Ar^{-2}[/tex]When you have a negative exponent, we can use the following property
[tex]a^{-b}=\frac{1}{a^b}[/tex]Using this property, our problem turns out to be
[tex]\pi=\frac{A}{r^2}[/tex]Now, we just need to plug the given values on this equation
[tex]\pi=\frac{50.265}{4^2}=3.1415625\approx3.142[/tex]The approximated value for pi is 3.142.
which methods correctly solve for variable x in the equation 3/4 (x - 8)=6?
SOLUTION
The equation given is
[tex]\frac{3}{4}(x-8)=6[/tex]Step1
Multiply both sides by
[tex]\frac{4}{3}[/tex]We have
[tex]\begin{gathered} \frac{4}{3}\times\frac{3}{4}(x-8)=\frac{4}{3}\times6 \\ \\ x-8=8 \end{gathered}[/tex]Step2
Add 8 to both sides of the equation
[tex]\begin{gathered} x-8+8=8+8_{} \\ x=16 \end{gathered}[/tex]Therefore, the correct method that solves the equation is
5. Multiply both sides by 4/3 and then add 8 to both sides of the equation
similarly,
Distribute 3/4 to (x-8)
[tex]\begin{gathered} \frac{3}{4}(x-8)=6 \\ \frac{3}{4}x-6=6 \end{gathered}[/tex]Then add 6 to both sides
[tex]\begin{gathered} \frac{3}{4}x-6=6 \\ \\ \frac{3}{4}x-6+6=6+6 \\ \frac{3}{4}x=12 \end{gathered}[/tex]Then multiply both sides by 4/3
[tex]\begin{gathered} \frac{3}{4}x\times\frac{4}{3}=12\times\frac{4}{3} \\ \\ x=16 \end{gathered}[/tex]Hence
2. Distribute 3/4 to (x-8), then add 6 to both sides and finally multiply both sides by 4/3
Therefore
Distribute 3/4 to (x-8), then add 6 to both sides and finally multiply both sides by 4/3
and
Alan bought 36 gallons of gas for $2.05 per gallon. How much did he spend ongas? *
Alan bought 36 gallons of gas for $2.05 per gallon.
total amount of gas = 36 gallons
Price of one gallon = $2.05
So, for the price of 36 gallons : Multiply the amount of 1 gallon with the the number of gallon
Price of 36 gallons = 36 x 2.05
Price of 36 gallons = $73.8
Alan spend an amount of $73.8 on the gas of 36 gallons
Answer : $73.8
Are these triangles congruent? If they are, justify it which congruence statement. If not, say cannot be determined. *
According to the figure given
We are given triangle GFH and EFH
[tex]\begin{gathered} <\text{ H }\cong\text{ < F} \\ FE\text{ }\cong\text{ GH} \end{gathered}[/tex]Line FE is parallel to line GH
Therefore, the triangles are congruent by side and angle
You earn a salary of $40000 per year and decide to save 20% of your gross pay. You then set a goal of creating $16000 and emergency fund. How long will it take you to achieve your goal?
Gross pay amount = $40,000
Percentage of the gross pay saved = 20%
Amount of gross pay saved per year = 20% of 40,000
Amount of gross pay saved per year = 20/100 * 40,000
Amount of gross pay saved per year = 20*400 = $8000
This means that $8000 is saved per year.
Next is to calculate the number of years it will take to save $16,000
Let us use the equality postulate;
1 year = $8,000
x year = $16,000
cross multiply
8000x = 16000
x = 16000/8000
x = 2
This means that it will take 2 years for me to achive my goal.
Write the nth rule for each geometric sequence.5) 7, 14, 28, 56...
We have the next numbers
[tex]7,14,28,56[/tex]as we can see we have double of the previous number, so the rule is
[tex]a_n=a_{n-1}\cdot2[/tex]we need to prove the rule
[tex]a1=7[/tex][tex]a2=7\cdot2=14[/tex][tex]a3=14\cdot2=28[/tex][tex]a4=28\cdot2=56[/tex]as we can see the rule is appropriate for the geometric sequence
-help me please!!!!!
Answer: 3/16
Step-by-step explanation:
You need a common denominator to add those three. It’s easiest to multiply rather than divide so multiply 1/4 times 4 to get 4/16 and then multiply 3/8 times 2 to get 6/16. 6+4+3=13. 16/13=3, add the denominator and you get 3/16 as the remaining amount.
What equation represents a line which is parallel to the line y=5/4x - 7
A characteristic of parallel lines is that they have the same slope.
So for the line
[tex]y=\frac{5}{4}x-7[/tex]The slope is
[tex]m=\frac{5}{4}[/tex]Any line parallel to this one will have the same slope:
[tex]y=\frac{5}{4}x+b[/tex]Foe example, let's say that the parallel line has to pass through the point (2,3)
Using the point slope form you can determine the equation as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{5}{4}(x-2) \\ y-3=\frac{5}{4}x-\frac{5}{2} \\ y=\frac{5}{4}x-\frac{5}{2}+3 \\ y=\frac{5}{4}x+\frac{1}{2} \end{gathered}[/tex]The line
[tex]y=\frac{5}{4}x+\frac{1}{2}[/tex]is parallel to
[tex]y=\frac{5}{4}x-7[/tex]how do you solve the system of linear equation y=2x-3y=x^2-3A. (0,3) and (2,0)B. (-1,-5) and (4,5)C. (3,6) and (-1,6)D. (0,-3) and (2,1)
SOLUTION:
We want to solve the system of equations;
[tex]\begin{gathered} y=2x-3 \\ y=x^2-3 \end{gathered}[/tex]Substituting, we have;
[tex]\begin{gathered} 2x-3=x^2-3 \\ x^2=2x\text{ \lparen x=0 is a solution \rparen} \\ divide\text{ both sides by x} \\ x=2 \end{gathered}[/tex]Inserting the values, we have;
[tex]\begin{gathered} when\text{ x = 0;} \\ y=2(0)-3 \\ y=-3 \end{gathered}[/tex][tex]\begin{gathered} when\text{ x = 2} \\ y=2(2)-3 \\ y=1 \end{gathered}[/tex]Thus, the solutions are;
[tex](0,-3)\text{ }and\text{ }(2,1)[/tex]I need help with solving propotional segments in right triangles. I need help with number 4.
We have
AD=9 in
DB=4 in
find DC,AC and BC
we can do the next equivalences
[tex]\frac{AD}{DC}=\frac{DC}{DB}[/tex][tex]\frac{9}{DC}=\frac{DC}{4}[/tex]then we clear DC
[tex]\begin{gathered} DC=\sqrt[]{36} \\ DC=6 \end{gathered}[/tex]For AC we use the Pythagorean theorem
[tex]AC=\sqrt[]{9^2+6^2}=10.81[/tex]For BC we use the Pythagorean theorem
[tex]BC=\sqrt[]{6^2+4^2}=7.21[/tex]PLEASE HELP!! ALGEBRA 1 HW I WILL GIVE BRAINLYEST
Answer:
answer Is -5/2 becouse if the line Is horizontal his equation Is y=k and in this case k= -5/2
If a card is drawn from an ordinary deck of 52 cards, find the probability of getting a heart or a face card?
Given:
Total number of cards = 52
Number of face cards = 12
Number of heart cards = 13
Required: Probability of getting a heart or a face card
Explanation:
Number of cards that is both face cards and heart cards = 3
Number of cards that are either heart or face card
= 12 + 13 - 3
=22
Probability of getting a heart or face card = Number of favorable cases/ Total number of cases
[tex]=\frac{22}{52}=\frac{11}{26}[/tex]Final Answer: The probability of getting a heart or face card is 11/26.
donuts at Krispy Kreme are always perfectly round. The diameter of the circular donut is 6 inches. Which of the following is closest to the circumference of the donut?
The circumference of a donut is computed as follows:
[tex]C=\pi\cdot D[/tex]where D is the diameter of the donut. Substituting with D = 6,
[tex]\begin{gathered} C=\pi\cdot6 \\ C=18.85\text{ in} \end{gathered}[/tex]At what value of w does the graph have a vertical asymptote? Explain how you know and what this asymptote means in the situation.
Vertical asymptote are vertical lines which corresponds to the zeros of the denominator of our rational function. Then, the zeros of T(w) ocurr when
[tex]530-w=0[/tex]which gives
[tex]w=530[/tex]Therefore, the vertical asymptote is w = 530.
The asymptote is a line that the graph function approaches but never touches. In our case, this means that the speed of the wind is very close to 530 mph but never touches this value.
find the value of X thy would prove j || k. state the converse that justifies your answer.
Given two parallel lines and a transversal
The given angles: (2x-8) and (9x-10) are supplementary angles
So, the sum of the angles = 180
So,
[tex](2x-8)+(9x-10)=180[/tex]Solve the equation to find x :
[tex]\begin{gathered} 2x-8+9x-10=180 \\ 11x-18=180 \\ 11x=180+18 \\ 11x=198 \\ \\ x=\frac{198}{11}=18 \end{gathered}[/tex]So, the answer will be x = 18
The converse of the solution:
when x = 18
So, the measure of the angles will be:
2x - 8 = 2 * 18 - 8 = 36 - 8 = 28
9x - 10 = 9 * 18 - 10 = 162 - 10 = 152
The sum of the angles are = 28 + 152 = 180
So, the sum of the angles = 180
So, the angles are supplementary angles
So, the lines J and K are parallel lines
so, J || K
An 8-pack of batteries cost $9.44.what is the price, in dollars , of one battery?A)- $0.85B)- $1.18C)- 1.44D)- 2.36
In order to determine the cost of only one battery, calculate the quotient in between the cost of 8 batteries over 8:
$9.44/8 = $1.18
Hence, one battery costs $1.18
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.0.50 : 0.25
Answer:
2/1
Explanation:
Given the ratio:
[tex]0.50\colon0.25[/tex]Divide both sides by 0.25
[tex]\begin{gathered} \frac{0.50}{0.25}\colon\frac{0.25}{0.25} \\ =2\colon1 \\ =\frac{2}{1} \end{gathered}[/tex]Thus, the ratio as a fraction in simplest form is 2/1.
PLEASE just give me the answers and not a whole defintion of every single word. I just want quick answers so I can check my work. *don't worry, this is just a math practice
7. m and n are parallel because both alternate interior angles are equal.
8.m and n are parallel because Alternate exterior angles are equal.
9.m and n are parallel Because corresponding angles are equal.
10. m and n are parallel because corresponding and consecutive angles are equal.
11. m and n are parallel because alternate exterior angles are equal.
12.m and n are parallel because vertical (opposite) angles are equal.
I need help with this 6-9 should be matched with either A-H
Explanation
To answer the question, we will make use of some of the properties of a parallelogram
These are
The opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary.
Each diagonal of a parallelogram separates it into two congruent triangles.
The diagonals of a parallelogram bisect each other.
Therefore
For question 6
[tex]\begin{gathered} mTherefore, the answer to question 6 is AQuestion 7
[tex]mThe answer to question 7 is EQuestion 8
[tex]\begin{gathered} DF=FB \\ Diagonals\text{ bisect each other} \\ DF=17 \end{gathered}[/tex]The answer to question 8 is C
Question 9
[tex]\begin{gathered} mThe answer to question 9 is FFor what values of k will the sum of the solutions of x^2 - (k^2 - 3k)x + 24=0 be 10?
The Solution:
Given the equation below:
[tex]x^2-(k^2-3k)x+24=0[/tex]We are required to find the value of k that will make the sum of the solutions to be 10.
Step 1:
Let:
[tex]\begin{gathered} k^2-3k\text{ be represented with b} \\ \text{ So that we have} \\ k^2-3k=b\ldots eqn(1) \end{gathered}[/tex]So, the given equation becomes:
[tex]x^2-bx+24=0[/tex]We shall the Quadratic Formula Method to solve for x in terms of b.
In this case,
[tex]\begin{gathered} a=1 \\ b=-b \\ c=24 \end{gathered}[/tex]Substituting, we get
[tex]x=\frac{-b\pm\text{ }\sqrt[]{(-b)^2-(4\times1\times24)}}{2(1)}[/tex][tex]x=\frac{-b\pm\text{ }\sqrt[]{b^2-96}}{2}[/tex]So, the solutions to the given equation are:
[tex]\begin{gathered} x=\frac{-b+\text{ }\sqrt[]{b^2-96}}{2} \\ \text{ or} \\ x=\frac{-b-\text{ }\sqrt[]{b^2-96}}{2} \end{gathered}[/tex]Equating their sum to 10.
[tex]\begin{gathered} \frac{-b+\text{ }\sqrt[]{b^2-96}}{2}+\frac{-b-\text{ }\sqrt[]{b^2-96}}{2}=10 \\ \\ \\ \frac{-b+\text{ }\sqrt[]{b^2-96}+-b-\text{ }\sqrt[]{b^2-96}}{2}=10 \end{gathered}[/tex]Simplifying, we get
[tex]\begin{gathered} \frac{-2b}{2}=10 \\ \\ -b=10 \end{gathered}[/tex]Substituting for b, we get
[tex]\begin{gathered} -(k^2-3k)=10 \\ k^2-3k=-10 \\ k^2-3k+10=0 \end{gathered}[/tex]Solving for k by the Quadratic Formula method of solving quadratic equation, we get
[tex]k=\frac{-b\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]Where
[tex]a=1,b=-3\text{ and c=10}[/tex]Substituting, we get
[tex]k=\frac{-(-3)\pm\text{ }\sqrt[]{(-3)^2-(4\times1\times10)}}{2(1)}[/tex][tex]k=\frac{3\pm\text{ }\sqrt[]{9^{}-40}}{2}=\frac{3\pm\text{ }\sqrt[]{-31}}{2}[/tex][tex]\begin{gathered} k=\frac{3+\text{ }\sqrt[]{-31}}{2}\text{ or }k=\frac{3-\text{ }\sqrt[]{-31}}{2} \\ \end{gathered}[/tex]Therefore, the correct answer is
[tex]k=\frac{3+\text{ }\sqrt[]{-31}}{2}\text{ or }k=\frac{3-\text{ }\sqrt[]{-31}}{2}[/tex]Alternatively,
We can use the sum of roots formula below:
[tex]\begin{gathered} \text{ Sum of roots = }\frac{-b}{a} \\ \text{if given a quadratic equation of the form ax}^2+bx+c=0 \end{gathered}[/tex]So, we get
[tex]\begin{gathered} a=1 \\ b=-(k^2-3k) \\ c=24 \end{gathered}[/tex]So,
[tex]\begin{gathered} \text{ Sum=}\frac{--(k^2-3k)}{1}=10 \\ \\ k^2-3k=10 \\ \\ k^2-3k-10=0 \end{gathered}[/tex]Then you can now solve from here as have done in the previous method.
Solve the quadratic equation above for k.
Find the equation of the line, in slope-intercept form, through (-4, 6)and parallel to y=-3x + 4. (Show work) (3 pts)
The given equation is
[tex]y=-3x+4[/tex]Notice that this equation represents a line in slope-intercept form, where its slope is -3.
Now, we have to find a new line parallel to the one above, which means the slope of the new line is also 3 because parallel lines have equal slopes.
Then, we use the given points (-4,6) and the slope -3 to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=-3(x-(-4)) \\ y-6=-3x-12 \\ y=-3x-12+6 \\ y=-3x-6 \end{gathered}[/tex]Therefore, the equation of the parallel line is y = -3x - 6.El producto de 2 por la diferencia de x y y
La diferencia de 'x' y 'y' se puede escribir asi:
[tex]undefined[/tex]In circle O, mPN= 131°. Solve for x if m
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: state the required theorem
The arc measure is equal to the angle at the center. Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc.
STEP 2: Get the equation
[tex]131^{\circ}=6x+26[/tex]STEP 3: Solve for x
[tex]\begin{gathered} 131=6x+26 \\ 131-26=6x \\ 105=6x \\ \frac{6x}{6}=\frac{105}{6} \\ x=17.5 \end{gathered}[/tex]Hence, the value of x is
Please help me if you could if you can't I understand. what fractions are equivalent to 2/3 and 7/12 using the least common denominator?
2/3 ---->8/12
7/12 ----> 7/12
1) Equivalent fractions have the same value proportionally, so let's find out equivalent fractions:
[tex]\frac{2}{3}+\frac{7}{12}[/tex]2) To find equivalent fractions and sum those fractions, let's factorize 3 and 12 dividing them only by Prime Numbers, when one of those numbers can't be divided then we repeat it below:
As we can see on the first line, 12 can be divided by 2 and 3 cannot.
So we repeat 3 on the line below.
We then picked 6 and divided by 2, and then repeated below 3.
Then divided3 by 3
3) Now we can rewrite 2/3 + 7/12 as:
So using the Least Common Denominator we have 2/3 (8/12) and 7/12 (7/12) as their equivalent fractions. Note that 7/12 in this case is equivalent to itself.
while free diving in the ocean, Tanya streeter once said a record by diving 525 ft and 3 and 1/2 minutes. how many feet per minute did she dive?
ok
length = 525 ft
time = 3.5 min Is that correct 3 and 1/2 minutes?
rate = 525/3.5
rate = 150 ft/min
For the school play, tickets cost $13.50 for adults and $5 for kids under 12. How
many total tickets would someone get if they purchased 6 adult tickets and 22 kids
tickets? How many total tickets would someone get if they purchased a adult tickets
and k kids tickets?
Total tickets, 6 adult tickets and 22 kids tickets:
Total tickets, a adult tickets and k kids tickets:
Answer
The adult-135 And the Kid-27:
Step-by-step explanation:
13.50 * 10=135
4.50 * 6 =27
question number 1 and 2 and find measure of. angle 1
Explanation
Step 1
vertical angles:
Vertical angles are pair angles formed when two lines intersect
[tex]m\measuredangle x=m\measuredangle y[/tex]so, we need to find a vertical angle in
a)
Figure 1:
blue angles are vertical, so
[tex]m\measuredangle HML\text{ and m}\measuredangle JMK[/tex]Figure 2:
hence, a pair of vertical angle is
[tex]\begin{gathered} \\ m\measuredangle LQM\text{ and m}\measuredangle\text{PQN} \end{gathered}[/tex]Step 2
pair of adjacent angles:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap
[tex]m\measuredangle x\text{ is adjacent to m}\measuredangle y[/tex]then
a)
for Figure 1
pair of adjacent angles
[tex]m\measuredangle HMJ\text{ and m}\measuredangle JMK[/tex]b) for Figure 2
pair of adjacent angles
[tex]m\measuredangle LQM\text{ and m}\measuredangle LQR[/tex]I hope this helps you