Answer:
1)0.2502
2)0.475
3)0.003505
Step-by-step explanation:
Total No. of question n= 10
There are four choices in each question
So, Probability of success [tex]p = \frac{1}{4}[/tex]
Probability of failure q = [tex]1- \frac{1}{4}=\frac{3}{4}[/tex]
We will use binomial over here
[tex]P(X=x)=^nC_r p^r q^{n-r}[/tex]
1)
[tex]P(X = 3)=^{10}C_3 (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=\frac{10!}{3!7!} (\frac{1}{4})^3 (\frac{3}{4})^7\\P(X = 3)=0.2502[/tex]
2) [tex]P(X > 2)=1-P(X\leq 2)[/tex]
P(X>2)=1-(P(X=0)+P(X=1)+P(X=2))
[tex]P(X>2)=1-(^{10}C_0 (\frac{1}{4})^0 (\frac{3}{4})^{10}+(^{10}C_1 (\frac{1}{4})^1 (\frac{3}{4})^9+^{10}C_2 (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]
[tex]P(X>2)=1-((\frac{1}{4})^0 (\frac{3}{4})^{10}+(\frac{10!}{1!9!} (\frac{1}{4})^1 (\frac{3}{4})^9+\frac{10!}{2!8!} (\frac{1}{4})^2 (\frac{3}{4})^8)[/tex]
P(X>2)=0.475
3)
[tex]P(X\geq 7)=P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\P(X\geq 7)=^{10}C_7 (\frac{1}{4})^7 (\frac{3}{4})^{3}+(^{10}C_8 (\frac{1}{4})^8 (\frac{3}{4})^2+^{10}C_9 (\frac{1}{4})^9 (\frac{3}{4})^1+^{10}C_{10} (\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=\frac{10!}{7!3!} (\frac{1}{4})^7 (\frac{3}{4})^{3}+\frac{10!}{8!2!} (\frac{1}{4})^8 (\frac{3}{4})^2+\frac{10!}{9!1!} (\frac{1}{4})^9 (\frac{3}{4})^1+\frac{10!}{10!0!}(\frac{1}{4})^{10} (\frac{3}{4})^0\\\\P(X\geq 7)=0.003505[/tex]
what equation is modeled by the graph below?
Answer:
B. -5/12
Step-by-step explanation:
Answer:
B.5/12
Step-by-step explanations:
Solve and show the steps to the picture attached
Answer:
The image of point (2, 4) after transformation is (-2, 13) ⇒ D
Step-by-step explanation:
Let us revise some transformation
Translation right-left OR up-down
If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) ⇒ add x-coordinate of every point by hIf the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h) ⇒ subtract x-coordinate of every point by hIf the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k ⇒ add y-coordinate of every point by kIf the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k ⇒ subtract y-coordinate of every point by kA vertical stretching and a vertical compression (or shrinking)
If m > 1, the graph of y = m • f(x) is the graph of f(x) vertically stretched by factor m. ⇒ multiply every y-coordinate by mIf 0 < m < 1 (a fraction), the graph of y = m • f(x) is the graph of f(x) vertically shrunk (or compressed) by factor m ⇒ multiply every y-coordinate by mLet us use these rules to solve the question.
∵ Point (2, 4) lies on y = x²
∵ The image of y = x² is y = 3(x + 4)²+1
→ The rules of transformation is y = m(x + h)² + k
∵ m is the scale factor of a vertical stretched
∵ m = 3
→ By using the 5th rule above
∴ The y-coordinate of point (2, 4) should multiply by 3
∴ The image of the point is (2, 4 × 3) = (2, 12)
∵ h is the horizontal translation to the left
∵ h = 4
→ By using the 2nd rule above
∴ The x-coordinate of point (2, 12) should subtract by 4
∴ The image of the point is (2 - 4, 12) = (-2, 12)
∵ k is the vertical translation up
∵ k = 1
→ By using the 3rd rule above
∴ The y-coordinate of point (-2, 12) should add by 1
∴ The image of the point is (-2, 12 + 1) = (-2, 13)
∴ The image of point (2, 4) after transformation is (-2, 13)
Question 1 (2 points)
(03.04)
For the function f(x) = -(x + 1)2 + 4, identify the vertex, domain, and range. (2 points)
A-The vertex is (-1,4), the domain is all real numbers, and the range is y greater than4.
B-The vertex is (-1, 4), the domain is all real numbers, and the range is y less than4.
C-The vertex is (1,4), the domain is all real numbers, and the range is y greater than 4.
D-The vertex is (1.4), the domain is all real numbers, and the range is y less than4.
Answer:
The vertex is (-1, 4), the domain is all real numbers, and the range is y less than 4
Step-by-step explanation:
Given
[tex]f(x) = -(x+1)^2 + 4[/tex]
Solving (a): The vertex;
Assume the general form of a function is
[tex]f(x) = a(x-h)^2+k[/tex]
The vertex is determined by [tex](h,k)[/tex]
By comparison, we have:
[tex]-h = 1[/tex]
Solve for h, we have:
[tex]h = -1[/tex]
[tex]k = 4[/tex]
So, the vertex is:
[tex](h,k) = (-1,4)[/tex]
The domain; x is all real numbers
From the function;
[tex]f(x) = -(x+1)^2 + 4[/tex]
This can be rewritten as:
[tex]f(x) = 4 - (x+1)^2[/tex]
This implies that:
Whatever the value of [tex](x + 1)^2[/tex] is, it will be subtracted from 4 to give y or f(x);
Hence:
y is less than 4
Option B answers the question
The population of New Town is increasing by 6% a year.
If the population was 19613 on January 1st, 2000, what was it on January 1st, 2020?
Give your answer to the nearest 100 people.
Answer:
After population (A) = 62,902 (Approx)
Step-by-step explanation:
Given:
Current population (P) = 19613
Number of years (n) = 2020 - 2000 = 20 year
Rate of growth (r) = 6% = 0.06
Find:
After population (A)
Computation:
[tex]After\ population (A) = Current\ population (P)[1+r]^n \\\\After\ population (A) = 19613[1+0.06]^{20} \\\\After\ population (A) = 19613[1.06]^{20} \\\\After\ population (A) = 62,901.548[/tex]
Lines E, F, and G are parallel lines cut by transversal H as shown below. What is the value of
a+b+c+d?
Answer:
okay now i get it its not easy at first but look at it for a bit and yoll get it
Evaluate each expression for s=4 and t=8
1) (25)^2t
2) 2st^2-5^2
3) 2s^2-t^3/16
Answer:
1. 2.328×[tex]10^{22}[/tex]
2. 487
3. 30.52 OR 0 (see explanation↓)
Step-by-step explanation:
1.[tex](25)^{2t}[/tex]
(sub for t=8)
=[tex]25^{2*8}[/tex]
=[tex]25^{16}[/tex]
=2.328×[tex]10^{22}[/tex]
2.[tex]2st^{2} -5^{2}[/tex]
(sub for s=4 and t=8)
=2×4×[tex]8^{2}[/tex]-[tex]5^{2}[/tex]
=512-25
=487
3.[tex]2s^{2} -t^{3/16}[/tex] (the equation is not clear so I will do [tex]2s^{2} -\frac{t^{3} }{16}[/tex] as well)
FOR [tex]2s^{2} -t^{3/16}[/tex]
(sub s=4 and t=8)
=2×[tex]4^{2}[/tex]-[tex]8^{3/16}[/tex]
=32-1.476826146
=30.52 (to the nearest 2 decimal place)
FOR [tex]2s^{2} -\frac{t^{3} }{16}[/tex]
(sub s=4 and t=8)
=2×[tex]4^{2}[/tex]-[tex]\frac{8^{3} }{16}[/tex]
=32-32
=0
Convert 6 feet to meters.
Conversion table:
1 meter = 3.281 feet
Answer:
6 feet = 1.8288 meters
Step-by-step explanation:
Hope this helps and have a phenominal day!
*HELP*. I need help on this stuff on I-ready... *HELP*
Answer:
First one
Step-by-step explanation:
50 + 30 can be broken up into (10x5)+(10x3). You can simplify that into 10(5+3) because 10 x 5 =50 and 10x 3 = 30. :)
Answer:
10(5+3)
Step-by-step explanation:
If If you multiply 5 and 3 by 10 you'll get 50 + 30
Looking at the picture below, what are two things that you would correct about this student's posture and playing position if you were the teacher.
Please answer ASAP
Answer:
The Student has good posture on the chin rest but The way that there are not standing straight up and how there holding the bow is incorrect
Step-by-step explanation:
Sitting up straight, turn your head enough that your nose lines up with the left foot. Drop your chin and place the violin so that it's also aligned with your left foot. Hold your spine straight and relax into this position; you should be able to keep the violin steady using only your chin.
I'm not 100 percent sure this correct
1. Refer to the equation 3x − 5y = 15. (a) Create a table of values for at least 4 points. Show your work on how you found the values for each coordinate pair, and validated the points were on the line. Work for Point 1 Work for Point 2 Work for Point 3 Work for Point 4
Answer:
We have the equation:
3x - 5y = 15
a) We want to create a table with at least 4 points.
To do this, first, let's write the equation as a function: We must isolate one of the variables. Let's isolate y.
5y = 3x - 15
y = (3/5)*x - 3.
Then we have a linear equation.
Now, we can input different values of x, and see what value takes y in each case, then in this way we can be sure that the points will be on the line.
x = 0.
y = (3/5)*0 - 3
y = -3
Then we have the point (0, -3).
x = 1.
y = (3/5)*1 - 3 = 3/5 - 15/5 = -12/5
y = -12/5
Then we have the point (1, -12/5)
x = 5
y = (3/5)*5 - 3 = 3 - 3 = 0
y = 0
then we have the point (5, 0)
x = 10
y = (3/5)*10 - 3 = 6 - 3 = 3
y = 3
Then we have the point (10, 3).
Now we can create the table
[tex]\left[\begin{array}{ccc}x&y\\0&-3\\1&-12/5\\5&0\\10&3\end{array}\right][/tex]
Below you can see a graph, where the blue dots are our 4 points, and the green line is the line that represents the equation.
In a group of 80 people, 50 can speak Nepali, 45 can speak English and 7 of them do not
speak both languages.
a) Find the number of people who speak both languages.
b) Also illustrate the above information in Venn diagram.
Answer:
Universal set is 80
Number of people that speak Nepali is 50
Number of people that speak English is 45
Number of people that do not speak both is 7
a. Number of people that speak both languages is 22
b. As above
Step-by-step explanation:
a. Let make number of people that speak both languages x
To get x
(50-x) + (45-x) + x + 7 = 80
(50-x) + (45-x) + x = 80 - 7
(50-x) + (45-x) + x = 73
Open bracket
50-x+45-x+x= 73
50+45-2x+x = 73
95 - x = 73
-x = 73 - 95
-x = -22
x = 22
Therefore, number of people that speak both languages is 22
b. To get venn diagram
Number of people that speak Nepali is 50 - 22 = 28
Number of people that speak English is 45 - 22 = 23
Therefore, total = 28+23+22+7 = 80
I need help please
The average of 4,-8,6,14,-3 is
Answer: The average is 2.6
Step-by-step explanation:
The average is the same as the mean so to find the mean of the numbers add them up and divide it by the number of values.
(4) + (-8) + (6) + ( 14) + (-3) = 13
13/5 = 2.6
Multiply 3/5 by 10/21 Express your answer in simplest form
Answer:
2/7
Step-by-step explanation:
Answer:
3/5 * 10/21= 2/7
If f(x) = 2x2 + x-1, then f(-5)
= ?
Answer:
-54
Step-by-step explanation:
(-5)^2 = -25
2(-25)+ -5 +1 =-54
Answer:
f(-5) = -2
Step-by-step explanation:
f(-5) = 2x2 + -5 -1
f(-5) = 4 - 6
f(-5) = -2
Two shooters, Rodney and Philip, practice at a shooting range. They fire 100 rounds each at separate targets. The targets are marked with circles and each bullet hitting a particular circle gets them a particular number of points. 60 rounds are selected at random. The sample mean scores of Rodney and Philip are 8 and 10, respectively. And, their variances are 0.25 and 0.50, respectively The standard error of the difference between their mean scores is ______________ (Round your answer to two decimal places.) The 95% confidence interval for the difference between the mean scores Rodney and Philip is ________ _____________: (Enter a minus sign if your answer is negative. Round your answer to two decimal places.)
Answer:
A) SE = 0.1118
B) 95% Confidence interval is;
-2.22 < μ1 - μ2 < -1.78
Step-by-step explanation:
We are given;
Sample size; n = 60
Sample mean 1; x1 = 8
Sample mean 2; x2 = 10
Variance 1; v1 = 0.25
Variance 2; V2 = 0.5
Now,
Standard deviation is given by the formula ;
σ = √variance
Thus;
σ1 = √0.25
σ1 = 0.5
σ2 = √0.5
σ2 = 0.7071
Formula for standard error of mean is;
SE = σ/√n
Thus;
SE1 = 0.5/√60
SE1 = 0.06455
SE2 = 0.7071/√60
SE2 = 0.0913
The standard error of the difference between their mean scores would be;
SE = √[(SE1)² + (SE2)²]
SE = √(0.06455² + 0.0913²)
SE = 0.1118
Formula for 95% confidence interval is;
(x1 - x2) - ((Z_α/2) × SE) < μ1 - μ2 < (x1 - x2) + ((Z_α/2) × SE)
Where Z_α/2 is the critical value. At confidence interval of 95%, we have a critical value of 1.96 from tables.
Thus, plugging in the relevant values, we have;
(8 - 10) - (1.96 × 0.1118) < μ1 - μ2 < (8 - 10) + (1.96 × 0.1118)
-2.22 < μ1 - μ2 < -1.78
How can a transformed quadratic equation be used real life situation?
Answer:
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.
Step-by-step explanation:
sixteen people wore white socks. The ratio of those who wore white socks to those who wore black socks 1:2. How many people wore black socks?
Answer:
It should be 32.
Step-by-step explanation:
Hewwo! can anyone answer this? giving brainliest to whoever explains! tysm c:
Answer:
4
Step-by-step explanation:
Basically it's dividing the pounds of dog food to the bags of food by 4
t> -5
can someone show step by step how to solve this equation?
Answer: The equation cannot be simplified any further.
Explanation: The variable(t) is greater than any number than negative five.
Plz mark brainliest:)
Nate and his brother are saving money to buy a gaming system. The system they want cost $349. The store is having a sale and the system is 30% off. State sales tax 6%.
Answer:
258.96
Step-by-step explanation:
%30 = 0.3
%6 = 0.06
so..
349 - (349 × 0.3)
349 - 104.7
244.3
then do the tax which is %6 or 0.06
244.3 + (244.3 × 0.06)
244.3 + 14.66
258.96
Good Job! Pls Brailniest! it would mean a lot ;) !
In Mrs. Munson's 9th hour science class there are 15 girls and 9 boys. Which of the
following is the ratios of girls to boys IN SIMPLEST form?
O 5:1
15:9
O 5:3
30:18
Answer:
15-9
Step-by-step explanation:
Answer:
5:3
Step-by-step explanation:
[tex]15 \div 3 = 5[/tex]
[tex]9 \div 3 = 3[/tex]
The density of a certain material is such that it weighs 5 kilograms for every 8.5 fluid
ounces of volume. Express this density in ounces per liter. Round your answer to the
nearest whole number.
Answer:
701 ounces per liter
Step-by-step explanation:
it's from delta math
The required density in ounces per liter is 140 onces per liter.
The density of a certain material is such that it weighs 5 kilograms for every 8.5 fluid ounces of volume.
To determine density in ounces per liter.
Volume is defined as the ratio of the mass of an object to its density.
As given that, t weighs 5 kilograms for every 8.5 fluid ounces of volume.
1 KG = 7.0474 ounces
5kg = 35.247
8.5 fluid of ounces = 0.251 liter
Density is given as,
= mass / volume
= 35.274 / 0.251
= 140 ounces per liter.
Thus, the required density in ounces per liter is s140 ounces per liter.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ2
7(10x+5-9x)=70
I rly need help on this
Answer:
x = 5
Step-by-step explanation:
1. Combine like terms
2. Multiply by 1
3. Distribute
4. Subtract 3
5 from both sides of the equation
5. Simplify
6. Divide both sides of the equation by the same term
7. Simplify
The answer is 118 as well right??
Answer: 118 is the correct degree
Step-by-step explanation:
The ratio of chocolate
chip cookies to total
cookies on a tray is 3:5.
What percent of the tray
is chocolate chip
cookies?
Answer:
The percent is 75%
Step-by-step explanation:
What percent of 60 is 15?
Answer:
15 is 25% of 60.
Step-by-step explanation:
Find the mean of these numbers:
2,57, 38, 42,6
Answer:no
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
add all of those numbers and divide it by the value of how many numbers there are in total.
Express the number 7,980 in scientific notation.
Answer:
7.98x10^3
Step-by-step explanation:
10^3=1000
Answer:7.980 × 10^3
Step-by-step explanation:
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma ran the loop in of an hour. What is Selma’s unit rate in miles per hour for Monday’s run?
In this activity, you will use the common denominator method to calculate a unit rate that involves fractions. Answer the questions that follow to calculate Selma’s unit rate in miles per hour.
part A. According to the question, the unit rate is to be expressed in which units?
Part B. Now, write Selma’s jogging rate as a complex fraction. A complex fraction is one whose numerator, denominator, or both are fractions. Be sure to include units in your answer.
Part C. Find the least common denominator of the two fractions from part B. To do this, list and compare the first five multiples of the denominators. The smallest number that appears in both lists is the least common denominator. Show your work.
Part D. Rewr
Complete question :
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Length of trail = 3/4 of a mile.
Time taken = 1/6 of an hour
A) unit rate will be expressed in:
Length of trail = miles
Time taken. = hour
= miles per hour (mph)
B) Jogging rate :
Length of trail / time taken
3/4 miles ÷ 1/6 hour
3/4 * 6/1
18/4 = 4 2/4 = 4 1/2
Answer:
3/4/3/6 miles per hour