0.262144 = 26.2% of getting all the 6 questions correctly.
What is Binomial probability ?
The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes.
This is a binomial distribution problem
Binomial distribution function is represented by :
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 6 multiple choice questions
x = Number of successes required = 6 (we want to get it all right.
p = probability of success = 0.8 (80% chance of getting any individual question right; 0.8 probability of getting each question correctly)
q = probability of failure = 1 - 0.8 = 0.2
P(X = 6) = ⁶C₆ (0.8)⁶ (0.2)⁶⁻⁶
= 1(0.262144)(1)
= 0.262
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3. Elena is ordering dried chili peppers and corn husks for her cooking class. Chilipeppers cost $16.95 per pound and com husks cost $6.49 per pound. Elenaspends less than $50 ond pounds of dried chili peppers and h pounds of cornhusks. Here is a graph that represents this situation.Scorn husks (pounds)4682dried chilis (pounds)
SOLUTION
3.a. From the question, we can know that chilli pepper cost $16.95 per pound and corn cost $6.49 per pound, and she has to spend less than $50 on d chilli pepper and h corn,
This means that d represents pepper and h represents the corn, So we have
[tex]\begin{gathered} (16.95\times d)+(6.49\times h)<50 \\ 16.95d+6.49h<50 \end{gathered}[/tex]Hence the inequality that represents this is
[tex]16.95d+6.49h<50[/tex]3.b. Now from the equation, we have that
[tex]\begin{gathered} 16.95d+6.49h<50 \\ so\text{ we will substitute d for 2 and h for 4} \end{gathered}[/tex]If we get less than 50, then the answer is yes. We have
[tex]\begin{gathered} 16.95d+6.49h \\ 16.95(2)+6.49(4) \\ 33.9+25.96 \\ 59.86\text{ } \end{gathered}[/tex]Hence the answer is No because based on our calculation, she will spend $59.86 which is greater than $50.
3.c. We will again substitute 1.5 for d and 3 for h into the equation and see if we get less than 50, we have
[tex]\begin{gathered} 16.95d+6.49h \\ 16.95(1.5)+6.49(3) \\ 25.425+19.47 \\ =44.895 \\ =44.90 \end{gathered}[/tex]Hence the answer is YES because based on our calculation, she will spend $44.90 which is less than $50.
Simplify [tex]5 \sqrt{11} - 12 \sqrt{11} - 2 \sqrt{11} [/tex] a) [tex] - 33 \sqrt{9} [/tex]b)[tex] - 11 \sqrt{9} [/tex]c)[tex] - 9 \sqrt{11} [/tex]d) [tex] - 9 \sqrt{33} [/tex]
In the given equation, the radical term is same in each term(radical is the being the square root of 11)
5sqrt(11)-12sqrt(11)-2sqrt(11)
Take the sqrt(11) common
sqrt(11){5-12-2}
sqrt(11){5-14}
sqrt(11){-9}
{-9}sqrt(11)
The correct answer is (c). -9Sqrt(11)
Rocco’s family is planning a reunion. Family members traveling from out of town have two options for airfare and hotels. As shown in the table, the cost of airfare for Option 2 is 0.75 times the cost of airfare for Option 1. For the same total cost, 12 family members can attend the reunion if they choose Option 2. Only 10 family members can attend if they choose Option 1. What is the cost of airfare for Option 1?
Option 1's airfare will set you back $2600.
The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired. See.
We have been given that
For option 1
Airfare = $x
Hotel = $600
For option 2
Airfare = $0.75x
Hotel = $800
Only 10 family members can attend if they choose Option 1.
10x + $600 .........eq 1.
12 family members can attend the reunion if they choose Option 2.
12(0.75)x + $800
9x + $800 ........eq 2.
By using Eq (1) and Eq (2)
10x + $600 = 9x + $800
10x - 9x = $800 - $600
x = $200
Put the value of x in the eq (1)
Then we get 10x + $600
= 10 x 200 + $600
= 2000 + $600
= $2600
Hence , the cost of airfare for Option 1 is $2600.
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hello I need help understanding a slope and y-intercept math problem I need a tutor that will please allow me to ask for the question so I can better understand what I'm working on thank you
ANSWER
EXPLANATION
Slope is defined as the numerical value that determines the steepness of a line
Mathematically, slope is expressed below as
[tex]\text{ Slope = }\frac{\text{ rise }}{\text{ run}}[/tex]what is the measure of the third angle in right triangle if one angle measures 28 degrees?
In a right triangle, two of the sides meet at 90 degrees
This means that one of its angles is 90 degrees
we have also been told that another angle is 28 degrees
To get the third angle:
The Sum of angles in a triangle is 180 degrees
let the unknown side be represented by y
y + 28 + 90 = 180
y + 118 = 180
y = 180 - 118
y = 62
The third side is 62 degrees
The number of bacteria in a culture is given by the function n(t)=985e^.2twhere t is measured in hours.(a) What is the relative rate of growth of this bacterium population?(b) What is the initial population of the culture (at t=0)(c) How many bacteria will the culture contain at time t=5
Answer:
(a) The relative rate of growth is 0.2
(b) The initial population is 985
(c) The amount of bacteria at time t = 5 is 2677.5
Explanation:
An exponential equation to model exponential growth is:
[tex]G(t)=Ie^{rt}[/tex]Where:
• I is the initial population
,• r is the rate of relative growth
,• t is the time
We have in this problem:
[tex]n(t)=985e^{0.2t}[/tex]Then:
(a) The relative rate is 0.2
(b) The initial population is 985
(c) To find the population at t = 5, we evaluate the equation:
[tex]n(5)=985e^{0.2\cdot5}=985e^1=985e\approx2677.5[/tex]
Rewrite (108 +224) using factoring.
A. 2(106 + 112)
B. 4(27 +56)
C. 6(17+6)
D. 12(8+27)
Answer:
B
Step-by-step explanation:
108/4 = 27
224/4 = 56
The other ones don't work if you distribute the outside numbers.
The solution of the expression after factoring is,
⇒ 4 (27 + 56)
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The expression is,
⇒ 108 + 224
Now, We can factor as;
⇒ 108 + 224
⇒ 4 × 27 + 4 × 56
⇒ 4 (27 + 56)
Thus, The solution of the expression after factoring is,
⇒ 4 (27 + 56)
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What is the next number??49,66,83,100 __
I need help with this problem
we know that
In this problem the answer is true
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
If F is similar a G and G is similar a H , then F is similar a H
answer is true
Problem N 2
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem we have that
triangle CAS is similar to triangle TEC
that means
and
CA/TE=AS/EC=CS/TC
so
Its not always trueFind (f • g) (0) when f(x) = 4x + 7 and g(x) = 1/x.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Given\text{ that:} \\ (f\text{ o g \rparen \lparen x \rparen = f\lparen g\lparen x\rparen\rparen} \\ But\text{ g\lparen x\rparen = }\frac{1}{x} \\ Then,\text{ we have that:} \\ f(\frac{1}{x}) \\ But\text{ f\lparen x\rparen = 4 x + 7} \\ Then\text{ f\lparen}\frac{1}{x})\text{ = 4\lparen}\frac{1}{x})\text{ + 7}_ \\ This\text{ means that: } \end{gathered}[/tex][tex]\begin{gathered} (f\text{ o g\rparen \lparen x\rparen = f\lparen g\lparen x\rparen \rparen = f\lparen}\frac{1}{x})\text{ =4\lparen}\frac{1}{x}\text{ \rparen + 7} \\ Then,\text{ we have that:} \\ (f\text{ o g \rparen \lparen 0 \rparen = 4 \lparen}\frac{1}{0})\text{ + 7 = undefined \lparen OPTION A \rparen} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]undefined\text{ \lparen OPTION A \rparen}[/tex]Ciara budgeted $30 per month for entertainment. Movies cost $7 and sports games cost $5.
Let x represent the number of movies she attended in a given month and let y represent the number of sports games she attended in the same month.
What inequality models this problem?
_____x + y ≥ ________
The inequality that models the given problem is:
7x + 5y ≥ 30
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The budgeted amount for the month = $30
Cost of the movie = $7
Cost of sports games = $5
x = represent the number of movies she attended.
y = represents the number of sports games she attended.
The inequality that models the situation above is:
7x + 5y ≥ 30
Thus,
The inequality that models the situation above is:
7x + 5y ≥ 30
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Consider the following graph of two functions(2) + (-1)Step 2 of 2 Hind/(?) + (-1)Enable Zoom/Pan8(x) = x? - 2 - 1(0) --10Submit Ar
Okay, here we have this:
Considering the provided graph, we are going to perform the requested operation, so we obtain the following:
So to find the values at which the functions are evaluated we will look at the graph to see what value y takes when it is at the given value of x, then we have:
f(2)+g(-1)
=-1+2
=1
Finally we obtain that the requested operation is equal to 1.
Solve the equation. 5x – 2 (2x + 6) = 15
ANSWER:
The value of x is 27
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]5x-2\cdot(2x+6)=15[/tex]solving for x:
[tex]\begin{gathered} 5x-4x-12=15 \\ x=15+12 \\ x=27 \end{gathered}[/tex]If g(x) = x2 + 3, find g(4).
11
19
16
8
Find the area of the following regular polygons. Round all answers to nearest 10th
Step 1
Draw the regular polygon to find out how many triangles are in it.
We can, therefore, conclude the regular polygon has 5 triangles in it
Step 2
Find the area of 1 triangle
[tex]\begin{gathered} \text{The angle at the center = 360}^o \\ \text{But since they are 5 triangles, each will have an angle of }\frac{360}{5}=72^o \end{gathered}[/tex]Since the two sides of each triangle are radius, then they share the same angle. Hence,
[tex]\begin{gathered} \text{The angle at the base of each triangle is given by} \\ 180=72+x+x \\ 180-72=2x \\ \frac{2x}{2}=\frac{108}{2} \\ x=54^o \end{gathered}[/tex]We can then find the k and y thus
[tex]\begin{gathered} \sin 54=\frac{k}{6} \\ k=\text{ 6sin54} \\ k=\text{ 4.854101966 units} \\ \cos 54=\frac{y}{6} \\ y=6\cos 54 \\ y=3.526711514\text{ units} \\ 2y=7.053423028 \end{gathered}[/tex]The area of one of the triangles is
[tex]\begin{gathered} A=\frac{1}{2}\times base(2y)\times height(k) \\ A=\frac{1}{2}\times7.053423028\times\text{4.854101966} \\ A=17.11901729\text{ units} \end{gathered}[/tex]The area of the 5 triangles will be
[tex]17.11901729\text{ }\times5=85.59508647unit^2[/tex]Hence the area of a regular polygon to the nearest tenth is given as;
[tex]85.6units^2[/tex]Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.(-15. **)
Given: The polar coordinate below
[tex](-1.5,\frac{3\pi}{4})[/tex]To Determine: The position of the point given in the circular grid shown
Solution
Note that the each of the circular grid line is 0.5 units apart
The point of the coordinate given is as shown below
It can be observed from the graph above that point is located between the 5th and 6th circular grid as counted from the center (that is between the red and the blue circular grid) above.
the equation of line v is y= 9/2x + 5. line w is perpendicular to v. What is the slope of line w? Simplify your answer
Answer:
-9/2x
Step-by-step explanation:
if its perpendicular to it then you just add a negative sign
Kathy and Mark Smith believe investing in retirement is critical. Kathy begin investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than mark who begin saving when he was 25 if there total retirement savings equals 1,450,000 how much are Kathy’s and Mark’s investments worth
Kathy’s retirement savings is $11,60,000
Mark’s retirement savings is $2,90,000
Total retirement savings amount is $1,450,000
Kathy’s investment is 4 times more than Mark
Calculation of future value at the end of 6 years:
Particulars Values
Total retirement savings $1450000
Mark investment (times) 1
Number of times kathy's investment is more B3x4 = 4
Total B34 = B3+B4 = 5
Kathy's retirement savings (B2*B4)/B5 = $11,60,000
Mark's retirement savings B7/B4 = $2,90,000
What is investment ?Investing is holding assets with the goal of achieving value over a period of time. Investing requires the sacrifice of some current asset, such as time, money, or effort. The purpose of financial investments is to obtain income from the invested property. Investments typically fall into three main categories: stocks, bonds, and cash. Each group has many different rankings. Here are six types of investments you can consider for long-term growth, and what you should know about each
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line shown in simplest form is 3.
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
The equation of a line in slope intercept form is:
y = mx + b
Where m is the slope and b is the y intercept
The slope of a line is the ratio of rise to run. It is given by:
Slope = rise / run
For the line, using the point (0, -5) and (3, 4), the slope is:
Slope = rise / run
Substituting:
Slope = [4 - (-5)] / (3 - 0) = 9/3 = 3
Slope = 3
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Ms. Frank made some costumes. The table shows the fabric she used. Color of Fabric Blue Gold Red Amount of Fabric (in yards) LOLO 3 4. moo Part A Did she use more blue fabric or red fabric? Use a number line and words to prove your answer.
Hence, she used more blue fabric
B)
[tex]\text{Amount of Gold fabric = }\frac{3}{4}=\frac{3\times2}{4\times2}=\frac{6}{8}[/tex]Therefore,
[tex]\text{Amount of Gold fabric = }\frac{6}{8}>\frac{3}{8}=Amount\text{ of Red fabric}[/tex]That is
[tex]\text{Amount of Gold fabric > Amount of Red fabric}[/tex]C)
Hence,
the equivalent fractions are:
[tex]\begin{gathered} \frac{1}{4}=\frac{2}{8} \\ \frac{2}{4}=\frac{4}{8} \\ \frac{3}{4}=\frac{6}{8} \\ \end{gathered}[/tex](-26, -11) and (39, 34).
Answer:
Sorry I don't get the question but have a good day!
Step-by-step explanation:
The sum of 5 and a number, where n represents the unknown number
Answer:
5+n
Step-by-step explanation:
question didnt specify what was needed so this was the equation
A bird spots a worm on the ground. The bird is 36 feet above the ground and with a horizontal distance of 45 feet to the worm. What is the angle of the bird's view on the worm? Round your answer to the nearest hundredth.
Let's take a look at the situation:
We know, because of the Pythagorean theorem, that:
[tex]\begin{gathered} d^2=45^2+36^2\rightarrow d=\sqrt[]{45^2+36^2} \\ \rightarrow d=57.63 \end{gathered}[/tex]Thereby, using the law of sines:
[tex]\begin{gathered} \frac{d}{\sin90}=\frac{45}{\sin a} \\ \rightarrow d\sin a=45\sin 90\rightarrow\sin a=\frac{45}{d} \\ \rightarrow a=\arcsin (\frac{45}{57.63}) \\ \rightarrow a=51.34 \end{gathered}[/tex]The angle of the bird's view on the worm is 51.34°
using question 1, what is the answer to question 9?
The daily cases parabola peaks at T:
[tex]T=\frac{1}{r}\ln \frac{N_{\infty}-N_0}{N_0}[/tex]r in the first page is:
[tex]r=\frac{\ln 2}{3}[/tex]Given data:
[tex]\begin{gathered} N_{\infty}=3.3M \\ N_0=10 \end{gathered}[/tex]Calculate T with the given data.
[tex]\begin{gathered} T=\frac{1}{\frac{\ln2}{3}}\ln \frac{3.3M-10}{10} \\ \\ T=\frac{3}{\ln2}\ln \frac{3299990}{10} \\ \\ T=\frac{3}{\ln2}\ln 329999 \\ \\ T\approx55 \end{gathered}[/tex]Then, the daily cases peak is at T=55 (approximately)
Calculus question need help asap
The first derivative of the given function is :
g'(x) = 24x²-24x-288
The second derivative of the function is:
g''(x) = 48x-24
The value of g''(-3) is:
-168
At x=-3 the graph of g(x) is concave down.
At x=-3 there is local maximum.
Given the function is g(x) = 8x³-12x²-288x
The first derivative of the function is:
g'(x) = 8(3)x³⁻¹ - 12(2)x²⁻¹ - 288(1)x¹⁻¹
g'(x) = 24x₂-24x-288
g'(X) = 24(x²-x-12)
Now, the second derivative of the function is :
g'(x) = 24(x²-x-12)
or x²-x-12 = 0
x²-4x+3x-12=0
x(x-4)+3(x-4) = 0
(x-4)(x+3)
x=4 and x=-3
now, g''(x) =24(2)x²⁻¹ - 24(1)x¹⁻° - 12(0)
g''(x) = 48x-24
Now find the local maximum and local minimum.
for x=4
g''(x) = 48x-24
g''(x) = 48(4)-24
g''(x) =168
Since, g''(x)>0 sox=4 is local minimum.
for x=-3
g''(x) = 48x-24
g''(x) = 48(-3)-24
g''(x) = -168
Since, g''(x)<0,so x=-3 is the local maximum.
Hence at x=-3 the graph of g(x) is concave down.
Hence we get the desired results.
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Can anyone help me with #18?
Answer:
SubtractSquareSum(add)DivideSquare RootRoundStep-by-step explanation:
The standard deviation of a data set is computed using the formula:
[tex]\sigma = \sqrt{\dfrac{\sum_{i=1}^{n}(x_i - \mu)^{2}}{n}}[/tex]
where [tex]\sigma[/tex] is the standard deviation, [tex]x_i[/tex] are the individual data values, [tex]\mu[/tex] is the mean and [tex]n[/tex] is the number of observations
So we first subtract the mean from each data value
then we square the result
then we sum(add) up all these values
then divide by n
and finally find the square root
The round operation will occur after all the above calculations
An amusement park sells hats, T-shirts and stuffed toys. The table on the top gives the number of each type of souvenir sold during a two-week period. The table on the bottom gives the price of each souvenir. Find the total amount spent on souvenirs each week.
Hats
T-shirts
Toys
Week 1
128
240
58
Week 2
130
215
89
Item
Price
Hats
$14
T-Shirts
$18
Toys
$24
a.
Week 1: $426, Week 2: $434
b.
Week 1: $6048, Week 2: $6128
c.
Week 1: $7504, Week 2: $7826
d.
Week 1: $482, Week 2: $480
The total amount spent on souvenirs each week for an amusement park sells hats, T-shirts and stuffed toys is c. Week 1: $7504, Week 2: $7826
How to find the total amount spent each weekAmount of Hats per week
week 1
= 128 * $14
= $1792
Week 2
= 130 * 14
= $1820
amount of T-Shirts per week
week 1
= 240 * $18
= $4320
Week 2
= 215 * 18
= $3870
amount of Toys per week
week 1
= 58 * $24
= $1392
Week 2
= 89 * $24
= $2136
Total amount for week 1
= 1792 + 4320 + 1392
= $7504
Total amount for week 2
= 1820+ 3870+ 2136
= $7826
therefore option c is the correct option
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-5g - 6 for g = -2
04
O 16
O 10
O-13
Answer: A (4)
Step-by-step explanation: -5 (-2) - 6 = 4
Courtney ran at a rate of 6.5 miles per hour. At this rate, about how many kilometers can she run in 2 hours? 0 10.5 km O 13 km O 21 km 0 24.8 km
6.5 miles per hour
How many km in 2 hours ?
6.5 miles per hour in two hours would be 2(6.5) = 13 miles
13 miles in kilometers are 13(1.60934) = 20.92142 which is almost 21 Km
Answer:
21 Km
if f(x)=3x+2, find f(2)
f(x)=3x+2
To fin f(2) replace x by 2 and solve:
f(2) = 3(2)+2 = 6 +2 = 8
