67% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
To calculate probabilities in a binomial experiment, use the binomial probability formula. For exactly five successes, use P(X=k) = C(n,k) * p^k * (1-p)^(n-k). For at least six successes, sum the probabilities of getting exactly six to ten successes. For less than four successes, sum the probabilities of getting zero to three successes.
Explanation:To find the probability of selecting a certain number of U.S. adults with very little confidence in newspapers, we can use the binomial probability formula. For (a) exactly five, we can calculate the probability using the formula P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials (10), k is the desired number of successes (5), p is the probability of success (0.67), and C(n,k) is the number of combinations. Plugging in the values, we find P(X=5) = C(10,5) * (0.67)^5 * (1-0.67)^(10-5).
For (b) at least six, we need to calculate the probability of getting six or more successes. We can find this by summing the probabilities of getting exactly six, seven, eight, nine, and ten successes: P(X>=6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10).
For (c) less than four, we need to calculate the probabilities of getting zero, one, two, or three successes: P(X<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3).
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Rectangle M was dilated to form rectangle M'.
What ratio is the scale factor?
Answer:
The scale factor is the ratio 3/2
Step-by-step explanation:
The picture of the question in the attached image
we know that
A dilation is a non rigid transformation that produce similar figures
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem rectangle M and rectangle M' are similar
so
The scale factor is equal to
[tex]\frac{6}{4}=\frac{3}{2}[/tex]
The scale factor is greater than 1
so
The dilation is an enlargement
one night a theater sold 548 movie tickets. an adult’s costs $6.50 an child’s cost $3.50. in all, $2,881 was takin in. how many of each kind of tickets were sold?
Answer:
321 adult tickets227 child ticketsStep-by-step explanation:
This sort of problem is easily solved by defining a variable to be the quantity of the higher-value contributor. Here, we can let x represent the number of adult tickets. Then total revenue is ...
6.50x +3.50(548-x) = 2881
3x +1918 = 2881 . . . . . . . . . . . . eliminate parentheses, collect terms
3x = 963 . . . . . . . . . . . . . . . . . . subtract 1918
x = 321 . . . . . . . . . . . . . . . . . . . . divide by 3
548-x = 548 -321 = 227 . . . . . .number of child tickets
321 adult tickets and 227 child tickets were sold.
By setting up and solving a system of equations, it was determined that the theater sold 320 adult tickets and 228 child tickets.
Let's denote the number of adult tickets as A and the number of child tickets as C.
The first piece of information given is:
Total tickets sold: A + C = 548
The second piece of information is related to the total revenue:
Total revenue from tickets: 6.50A + 3.50C = 2881
To find the values of A and C, we can use the substitution or elimination method to solve this system of equations. Here, we'll use the elimination method:
Multiply the first equation by 3.50 to align the coefficients of C with the second equation:
Subtract this new equation from the second equation to eliminate C:
Substitute A = 320 into the first equation to solve for C:
Therefore, the theater sold 320 adult tickets and 228 child tickets.
a boat costs $16600 and decreased in value by 14% per year. How much will the boat be worth after 11 years?
The worth of boat after 11 years is $ 3159.3013
Solution:
Given that,
Boat costs $16600 and decreased in value by 14% per year
To find: Worth of boat after 11 years
The formula for decreasing function is given as:
[tex]y = a(1-r)^t[/tex]
Where,
y is the value after "t" years
t is the number of years
a is the initial value
r is decreasing rate in decimal
From given,
a = 16600
t = 11
[tex]r = 14 \% = \frac{14}{100} = 0.14[/tex]
Substituting the values we get,
[tex]y = 16600(1-0.14)^{11}\\\\y = 16600(0.86)^{11}\\\\y = 16600 \times 0.1903\\\\y = 3159.3013[/tex]
Thus the worth of boat after 11 years is $ 3159.3013
Bela started studying how the number of branches on her tree grows over time. Every 2.9 years, the number of
branches increases by an additional 83%, and can be modeled by a function, which depends on the amount
of time, t (in years).
When Bela began the study, her tree had 60 branches.
Write a function that models the number of branches t years since Bela began studying her tree.
Answer:
The required function that models the number of branches t years since Bela began studying her tree is
number of branches = [tex]60(1.83)^{\frac{t}{2.9} }[/tex]
Step-by-step explanation:
Let t be the time in years
Initially Bela's tree had 60 branches.
therefore the function that can be used to model the number of branches after t years will be given by
number of branches( after t years) [tex]= 60\times(1 + \frac{83}{100})^{\frac{t}{2.9} } = 60(1.83)^{\frac{t}{2.9} }[/tex]
The function model is [tex]B(t) = 60 * (1.83)^{\frac{t}{2.9}}[/tex].
To model the growth of branches on Bela's tree over time, we can use an exponential growth function. Given that the number of branches increases by 83% every 2.9 years, and the initial number of branches is 60, the function can be derived as follows:
The growth factor after each period of 2.9 years can be expressed as 1 + 0.83 = 1.83. If we let t represent the time in years, we need to determine how many 2.9-year periods have passed. This is given by [tex]\frac{t}{2.9}[/tex].
Thus, the function modeling the number of branches, B(t), after t years is:
[tex]B(t) = 60 * (1.83)^{\frac{t}{2.9}}[/tex]
This function accounts for the exponential growth of the number of branches on Bela's tree over time.
Triangle XYZ undergoes a single
transformation to form the image,
triangle X'Y'Z'. The image is congruent
to the original figure. Which of the
following best describes the possible
transformation that took place?
O A. a reflection only
O B. a rotation only
OC. a translation only
O D. a reflection, rotation, or a
translation
Answer:
D
Step-by-step explanation:
When something is forgoing a transformation that stays congruent, if it is rotating, it is simply turning a given amount of degrees: if it is translating, it is simply move up/down or right/left on the x and y axis; and finally, if it reflects, it is simply being inverted across either the x or y axis. None of these transformations result in changing the shape and/or size of the triangle.
Final answer:
The possible transformation that could have taken place is either a reflection, a rotation, or a translation, as they all preserve the congruency of the original triangle. Option D is correct.
Explanation:
If triangle XYZ is transformed to form triangle X'Y'Z' and the image is congruent to the original triangle, then the transformation could be a reflection, a rotation, or a translation. Congruent transformations are those that preserve the size and shape of a figure. Since the original triangle is congruent to its image after the transformation, we can conclude that the transformation is one that preserves congruency. Reflections across a line, rotations about a point, and translations (which slide a figure) all preserve the size and shape of the figure, and hence the triangles would remain congruent after any of these transformations.
Please help me... Has to be in my 1pm today and I have no idea... out of my league but I need to pass to get into the course I want
Answer:
AB = -4i -7j
CD = -5i + 4j
Step-by-step explanation:
i.) vector AB = -4i -7j
where i is the unit vector in the x direction and j is the unit vector in the y direction.
vector AB is 7 units down and 4 units west
ii)vector CD = -5i + 4j
vector CD is 5 units west and 4 units up
Determine the slope of a line that is perpendicular to the line y = -2x + 7
Select one:
O A. Slope = -1/2
O B. Slope = 2
O C. Slope = 1/2
O D. Slope = -7
Answer:
C)
Step-by-step explanation:
Perpendicular means negative reciprocal of the current slope.
And the negative reciprocal of -2 is 1/2.
What are multiples of nine
Step-by-step explanation:
We have,
Nine
To find, the multiples of nine = ?
The multiples of nine are:
1 × 9, 2 × 9, 3 × 9, 4 × 9, 5 × 9, 6 × 9, 7 × 9, .......
= 9, 18, 27, 36, 45, 54, 63, .....
∴ The multiples of nine are 9, 18, 27, 36, 45, 54, 63, .....
Thus, the multiples of nine are 9, 18, 27, 36, 45, 54, 63, ..... .
What are the x-intercepts of the graph of the equation y = x² + 4x - 5 ?
5 and 1
-5 and 1
-5 and 0
5 and -1
Answer:
The x-intercepts of the graph of the equation y = x² + 4x - 5 is -5 and 1
Step-by-step explanation:
Given:
y = x² + 4x-5
To Find:
x-intercepts
Solution:
Finding the value of the x by using quadratic formula
x = [tex]\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
On substituting the values ,
x = [tex]\frac{-4 \pm \sqrt{(4)^2 -(4(1)(-5))}}{2(1)}[/tex]
x = [tex]\frac{-4 \pm \sqrt{16 -(-20)}}{2}[/tex]
x = [tex]\frac{-4 \pm \sqrt{36}}{2}[/tex]
x = [tex]\frac{-4 \pm6 }{2}[/tex]
[tex]x = \frac{-4-6}{2}[/tex] [tex]x = \frac{-4+6}{2}[/tex]
[tex]x = \frac{-10}{2}[/tex] [tex]x = \frac{2}{2}[/tex]
x = -5 x = 1
The cost of a rental car at a certain company is a $50 fee plus $0.40 for each mile driven up to 100 miles. For every
mile over 100 miles it is $0.50 per mile. What would the total cost be for renting the car and driving it 120 miles?
A. $40
B. $50
C. $90
D. $100
E. $110
Answer:
D
Step-by-step explanation:
50 + .40(100) = 90
.50(20) = 10
90 + 10= 100
Answer:
D: 100
So the first multiply 0.4 times 100 which you would get 40 now add the 50 dollar fee to 40 which you would get 90 dollars. Now for the 20 miles remaining multiply 0.5 times 20 which you would get 10. Now add everything together 90+10 which would equal 100.
How many unique ways are there to arrange the letters in the word THAT?
Answer:
12
Step-by-step explanation:
its 12
because its 12
Answer: 12
Step-by-step explanation:
Solve the system of linear equations by graphing.
y = 2x
2x + y = - 4
In graph form
Answer:
2x + 2x = 4
4x = 4
x = 1
y = 2(1)
y = 2
(1,2)
Ilana drew a marble at random from a bag containing 4 blue, 3 red, 2 yellow, and 5 green marbles. What is the probability that she picked a marble that is not red?
20 points for best answer
Answer:
[tex]\frac{11}{14}[/tex]
Step-by-step explanation:
Total number of marbles = 4+3+2+5=14
number of not red marbles = 4+2+5=11
then
the probability that she picked a marble that is not red = 11/14
2 Points
A radio wave has a wavelength of 357 m. What is this wavelength in scientific
notation?
Step-by-step explanation:
[tex]357 \: m = 3.57 \times {10}^{2} \: m[/tex]
The wavelength of the radio wave in scientific notation is 3.57 x 10^2 m.
Explanation:The wavelength of a radio wave is given as 357 m. Since this is already a simple number, converting it to scientific notation would be 3.57 x 102 m. Here, '3.57' is the significant part of the number (the significand) and '2' is the power to which 10 is raised (the exponent). In scientific notation, we aim to express numbers between 1 (inclusive) and 10 (exclusive).
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
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Mr. Walker needs to purchase another pair of Crocs. He got an email coupon for 20% off an de free shipping at Shoebye.com. The pair he regularly $49.00 at Shoebuy. He also sees the same shoes on sale at Crocs.com for $35.00 plus $4.30 shipping and handling. Which is the better buy? Show your work to prove your answer.
Answer: Shoebuy.com
Step-by-step explanation:
20% of $49.00 is $9.8. When you subtract $9.80 from $49, you end up with $39.2. Now to look at Crocs.com, in order to get the total, add the price of the shoes, $35 and the shipping cost, $4.30, you'll end up with $39.30. Because Shoebuy is $.10 less than Crocs.com, it is the better choice.
After calculating the total costs, purchasing the Crocs from Shoebye.com with the 20% discount and free shipping comes out to be cheaper by $0.10 than buying them on sale at Crocs.com with added shipping and handling.
Explanation:Mr. Walker is trying to determine the better buy for a new pair of Crocs. The comparison involves a 20% discount and free shipping at Shoebye.com versus sale price with additional shipping and handling at Crocs.com.
Calculation at Shoebye.com:
Original price: $49.00
Discount (20% of $49): $9.80
Discounted price: $49 - $9.80 = $39.20
Shipping: $0 (free)
Total cost at Shoebye.com: $39.20
Calculation at Crocs.com:
Sale price: $35.00
Shipping and handling: $4.30Total cost at Crocs.com: $35.00 + $4.30 = $39.30
Comparing both totals, Shoebye.com's offer of $39.20 is slightly better than Crocs.com's offer of $39.30. Thus, purchasing from Shoebye.com would save Mr. Walker $0.10.
PLEASE HELP!
Suppose the radius of a circle is 8 What is its circumference?
Answer:
The circumference of the given circle is 50.24
Step-by-step explanation:
C = 2piR
C = 2pi8
C = 16(3.14)
C = 50.24
Answer:
50
Step-by-step explanation:
Find the value of x in the isoceles triangle shown below.
PLEASE HELPPPPP
Answer:
The measure of 'x' is 6 units.
Step-by-step explanation:
Given:
An isosceles triangle.
The two equal arms length = [tex]\sqrt{13}[/tex]
Measure of the altitude = [tex]2[/tex]
Note:The altitude to the base of an isosceles triangle bisects the base.
The altitude also forms 90 degree at the base.
So, the base length can also be seen as 'x' which we can also be written as [tex]x=\frac{x}{2} +\frac{x}{2}[/tex]
And [tex]\frac{x}{2}[/tex] is a part of the right angled triangle.
Where hypotenuse = [tex]\sqrt{13}[/tex]
Perpendicular length =[tex]2[/tex]
Base length = [tex]\frac{x}{2}[/tex]
Now,
From Pythagoras formula we know that:
[tex](hypotenuse)^2 =(perpendicular)^2+ (base)^2[/tex]
Plugging the values:
⇒ [tex](hypotenuse)^2 - (perpendicular)^2 = (base)^2[/tex]
⇒ [tex]\sqrt{ (hypotenuse)^2 - (perpendicular)^2} = (base)[/tex]
⇒ [tex]\sqrt{(\sqrt{13})^2-(2)^2} =\frac{x}{2}[/tex]
⇒ [tex]\sqrt{13-4}=\frac{x}{2}[/tex]
⇒ [tex]\sqrt{9} =\frac{x}{2}[/tex]
⇒ [tex]3=\frac{x}{2}[/tex]
⇒ [tex]3\times 2=x[/tex]
⇒ [tex]6 = x[/tex]
So the value of base 'x' = 6 units.
Option D is the rigth choice.
The sides 5, 6, and 12 form a triangle. True or False
To form a triangle The sum of any two length must be greater the the third side.
5+ 6 =11, which is less than 12 so it can’t form a triangle
The sides 5, 6, and 12 form a triangle is false. C will always be the biggest number because it is the hypotenuse, and the others numbers can either be A or B.
[tex]12=\sqrt{5^2+6^2} \\\\12=\sqrt{25+36}\\\\12=\sqrt{61}\\\\12\neq 7.81024967591[/tex]
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)
- Cutiepatutie ☺❀❤
May had 66 books. She gave 3 books to 11 friends. Then, she got 51 more. How many books does May have now?
Answer:
81
Step-by-step explanation:
Answer:
84
Step-by-step explanation:
So 3 and 11 make 33 and subtract that from 66. That gives you 33. Add 51 and you get 84.
Simplify: (m – 3n)2
m2 – 9n2
m2 + 9n2
m2 – 3mn + 9n2
m2 – 6mn + 9n2
(m - 3m)^2
(m - 3n)(m - 3n)
Use the FOIL method.
First m^2
Outer -3mn
Inner -3mn
Last 9n^2
Equation form:
m^2 - 3mn - 3mn + 9n^2
Simplify terms to get...
m^2 - 6mn + 9n^2
The answer is answer D, m^2 - 6mn + 9n^2.
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Write 4,570,000 in scientific notation
Answer:
4.57 x 10(little 6 lol )
Step-by-step explanation:
4.57 x 10^6
(use the caret symbol [^] to type or write)
4.57E+6
(Scientific E-notation)
4570000
(Real Number)
ans
Directions: Type your answer in the box without the dollar sign.
Brian purchased 4 items that were $1.00 each. The sales tax rate is 5.5%. How
much was Brian's total bill including sales tax?
The correct answer is $4.22.
Is states that Brian purchased 4 items that were $1.00.
That means he has spent a total of $4.00.
5.5% of $4.00 is 0.22.
Add that together and it gives you the sum/answer of $4.22.
What is the domain of the function y = StartRoot x EndRoot + 4
Answer:
third option !!!! 0 less-than-or-equal-to x less-than infinity
Step-by-step explanation:
The domain of the function y = √x + 4 is all real numbers x such that x ≥ 0, because the square root of a negative number is not a real number in the set of real numbers.
Explanation:The given function is y= x +4. The square root function x is defined only for non-negative values of x. This is because the square root of a negative number is not a real number in the real number system.
Therefore, for the given function to be defined, the expression inside the square root (x) must be greater than or equal to zero. Mathematically, this condition is expressed as:x≥0
This inequality ensures that the square root is always defined for any real number x in the domain of the function.
So, the domain of the function y= x +4 is all real numbers x such that x≥0. In interval notation, this can be expressed as [0,∞).
Find the 59th term of the arithmetic sequence 29,37,45
Answer:
[tex]T_{59}= 493[/tex]
Step-by-step explanation:
Given:
Arithmetic sequence
29, 37, 45............
n = 59
We need to find the 59 term of the arithmetic sequence.
Solution:
Using formula for nth term of arithmetic sequence.
[tex]T_{n}= a + (n-1)d[/tex] -------------(1)
Where:
a = first term of the sequence.
d = Common difference.
first find the the common difference of .
[tex]d = a_{2}-a_{1}[/tex]
[tex]d=37-29[/tex]
d = 8
Substitute a = 29, d = 8 and n = 59 in equation 1.
[tex]T_{59}= 29 + (59-1)8[/tex]
[tex]T_{59}= 29 + 58\times 8[/tex]
[tex]T_{59}= 29 + 464[/tex]
[tex]T_{59}= 493[/tex]
Therefore, 59th term of the arithmetic sequence [tex]T_{59}= 493[/tex]
Answer:
the 59th term of the arithmetic sequence is T=493
Step-by-step explanation:
Here is prove
How many times does seven go into 52
49 remainder of 3
Step-by-step explanation:
52 divided by 7 is 49 R 3
Answer:
7.42857142857
Step-by-step explanation:
divide 7 into 52 and you will get 7.42857142857
David bought 3 dvds and 4 books for $40 at a yard sale. Anna bought 1 dvd and 6 books for $18. How much did each dvd and book cost?
Answer: d=$12, b=$1
d represents DVDs
b represets books
Step-by-step explanation:
Whenever you have 2 examples of 2 different things (such as books and dvds), make a systems of equations.
Step 1: Write a system of equations
3d+4b= 40
d+6b= 18
Step 2: Eliminate any letter. I'll just choose d.
To elimiate d, you have to make them both equal to the biggest d variable. In other words, make both d terms equal to 3d. To do this, miultiply the 2nd equation by 3, and keep the 1st one the same.
3d+4b=40
3d+18b= 54
Now, elimiate d, by doing 3d-3d= 0. Now use subtraction to solve for b since we used this to get 3 and 3 to 0.
4b-18b=40-54
-14b= -14
b= -14÷-14
b= 1
Each book costs 1 dollar.
Step 3: Plug in b=1 to find how much each dvd costs (plug into any equation)
3d+4b=40
3d+4(1)=40
3d+4=40
3d=40-4
3d=36
d=36÷3
d=12
Each dvd is $12
Step 4: Checks--plug d=12 and b=1 into any equation
3d+4b=40
3(12)+4(1)=40
36+4=40
40=40
It's correct ✅
Also i know this was answered really late but id appreciate if i could get brainliest as i worked pretty hard for this :) Hope i could help the best i could :D
Find the length of the missing side of the triangle below
PLEASE HELPP!!
To find the length of the missing side, you can use the Pythagorean Theorem, which you can only use for right triangles.
Pythagorean Theorem: a² + b² = c²
[ c is the hypotenuse or the longest side of the triangle, and a and b are the other sides, I think it doesn't matter which side ]
Plug in what you know:
b = 8
c = 14
a² + b² = c²
a² + (8)² = (14)²
a² + 64 = 196 Subtract 64 on both sides
a² = 132 Square root both sides to get "a" by itself
[tex]\sqrt{a^2} =\sqrt{132}[/tex]
a = [tex]\sqrt{132}[/tex] inches
If you need to simplify more, you need to find two numbers that multiply to = 132 where one of them can be square rooted, to do so you can list the greatest common factors of 132
132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The only number that can be square rooted is 4, so you can do:
[tex]a=\sqrt{4*33}[/tex]
[tex]a=\sqrt{4} *\sqrt{33}[/tex]
[tex]a=2\sqrt{33}[/tex]
Given that point P partitions AB into a ratio of 3:2, and A is found at (-4, -3) and P is found at (3, 6), find the coordinates for B.
Answer:
The coordinates of B are (7.67,12)
Step-by-step explanation:
Let the coordinates of B are (h,k).
Now, point P(3,6) partitions AB into a ratio of 3 : 2 and A is found at (-4,-3).
We have to find B(h,k).
Now, from the formula of coordinate geometry we have,
[tex]3 = \frac{2(- 4) + 3h}{3 + 2}[/tex]
⇒ 3h - 8 = 15
⇒ 3h = 23
⇒ h = 7.67
And, [tex]6 = \frac{2(- 3) + 3k}{2 + 3}[/tex]
⇒ 3k - 6 = 30
⇒ 3k = 36
⇒ k = 12
Therefore, the coordinates of B are (7.67,12) (Answer)
HELP WILL GIVE BRAINLIEST
a) Rewrite 0.00000296 in scientific notation. Explain.
b) Write7.35x10^-5 in standard form. Explain.
Step-by-step explanation:
[tex](a) \: 0.00000296 = 2.96 \times {10}^{ - 6} \\ \\ (b) \: 7.35 \times {10}^{ - 5} \\ \\ = 7.35 \times \frac{1}{{10}^{ 5} } \\ \\ = \frac{7.35}{{100000} } \\ \\ = 0.0000735 \\ [/tex]