Answer:
Ok, we have a total of 26 letters, and we want to select 5 of them.
Of the 26 letters, 21 are consonants and 5 are vowels.
Suppose that we want to have the consonant in the first selection, so the probability of picking a consonant is equal to the quotient between the number of consonants and the total number of letters.
p = 21/26
now a letter has been selected, so in the set, we have 25 letters left.
In the next 4 selections, we must select vowels.
In the second selection the probability is:
p = 5/25
in the third, the prob is:
p = 4/24 (we already selected one vowel before, so now we only have 4 vowels)
The fourth selection:
p = 3/23
and the last selection:
p = 2/22
The total probability is equal to the product of all the individual proabilities, so we have:
P = (2/22)*(3/23)*(4/24)*(5/25)*(21/26)
Now, remember that we said that the consonant must be in the first place, but it can be in any of the five places, so if we add the permutations of the consonant letter we have:
P = 5*(2/22)*(3/23)*(4/24)*(5/25)*(21/26) = 0.0018
please Help will mark brainliest !!1!Use the linear combination method to solve the system of equations. Explain each step of your solution. 2x -3y = 13 x+2=- 4
Answer:
work is shown and pictured
Find the value of x.
Explanation:
For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.
x+125 = 180
x+125-125 = 180-125 ... subtract 125 from both sides
x = 55
Joylin’s work to solve a math problem is shown below. Problem: Manny walked StartFraction 5 Over 16 EndFraction of the distance to the library in One-third of an hour. If he walks at a constant rate, what is the total amount of time he will spend walking to the library? Step 1: StartFraction 5 Over 16 EndFraction divided by one-third = h Step 2: StartFraction 16 Over 5 EndFraction times StartFraction 3 Over 1 EndFraction = h Step 3: StartFraction 48 Over 5 EndFraction = h Answer: 9 and three-fifths = h What was Joylin’s first error? She switched the divisor and the dividend when creating an equation to model the problem in step 1. She replaced both the divisor and the dividend with their reciprocals when changing division to multiplication in step 2. She multiplied the two numerators and the two denominators to generate her product in step 3. She reduced the improper fraction incorrectly when getting her final answer.
Answer: She replaced both the divisor and the dividend with their reciprocals when changing division to multiplication in step 2
Step-by-step explanation:
Answer:
She replaced both the divisor and the dividend with their reciprocals when changing division to multiplication in step 2.
Step-by-step explanation:
Bart bought a digital camera with a list price of $219 from an online store offering a 6 percent discount. He needs to pay $7.50 for shipping. What was Bart's total cost? A. $205.86 B. $211.50 C. $213.36
Answer:
Barts total cost is (c)213.36
Step-by-step explanation:
First, you subtract 6% from $219
=204.92
add shipping,
+7.50
=213.36
Hope this helps <3
Answer:
C. $213.36
Step-by-step explanation:
The original price is $219 and the discount is 6% which is equal to $13.14
$219 - $13.14 + $7.50 (shipping cost) = $213.36
Find the surface area of the attached figure and round your answer to the nearest tenth, if necessary.
Answer:
[tex] S.A = 246.6 in^2 [/tex]
Step-by-step explanation:
The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.
Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]
Where,
B.A = Base Area of the pyramid = 9*9 = 81 in²
P = perimeter of the base = 4(9) = 36 in
L = slant height of pyramid = 9.2 in
Plug in the values into the given formula to find the surface area
[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]
[tex] = 81 + 18*9.2 [/tex]
[tex] = 81 + 165.6 [/tex]
[tex] S.A = 246.6 in^2 [/tex]
A manufacturing process that produces electron tubes is known to have a 10% defective rate. Suppose a random sample of 15 tubes is selected from the manufacturing process. a) Find the probability that no more than two defectives are found?
Answer:
Probability of obtaining no more than two defective tubes = 0.816
Step-by-step explanation:
The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).
Where n is number of samples;
r is maximum number of defective tubes, r ≤ 2;
p is probability of defective tubes = 10% or 0.1
q is probability of non-defective tubes, q = 1 - p
Further explanations and calculations are given in the attachment below:
aryn needs enough mulch to cover a rectangle flower bed measuring 2 1/4 yd by 3 1/2yd each bag cover 3 square yds and cost $4 how many bags does she need and how much money she need
Answer:
cars are dum
Step-by-step explanation:
3 + 5x, for x = 10
A. 350
B. 120
C. 53
D. 75
Answer:C
Step-by-step explanation:
Pemdas
3+5(10)
5*10=50
3+50=53
find the zeros of the function. enter the solutions from least to greatest f(x)=(x+3)^2-4
Answer:
x= -5, -1
Step-by-step explanation:
To find the zeroes of a function,
First expand the terms to get the form [tex]ax^{2} + bx +c[/tex] where 'a, b, and c' are constants
[tex]f(x)= (x+3)^{2} -4[/tex]
[tex]f(x)= x^{2}+6x+9-4[/tex]
[tex]f(x)= x^{2} +6x +5[/tex]
Now, factor the equation
This can be done using the quadratic formula or other methods
One simple method is to find the two values that would get:
A sum that's equal to the 'b' value and,A product that's equal to the 'c' valueA good way to verify is to expand the terms and make sure the function looks the same
In this case, the equation can broken into
f(x)= (x+1)*(x+5)
Now, look at each term individually and set each of them to equal 0
x+1 =0
x+5=0
Solve for x in each case
x= -1
x= -5
Now, ordering them from least to greatest would be: x= -5, -1
Sixty percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months
Answer:
The probability is [tex]P(X \ge 20 ) = 0.3707[/tex]
Step-by-step explanation:
From the the question we are told that
The population proportion is p = 0.60
The sample size is n = 31
The mean is evaluated as
[tex]\mu = n * p[/tex]
substituting values
[tex]\mu = 31 *0.60[/tex]
[tex]\mu = 18.6[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{n * p * (1- p )}[/tex]
substituting values
[tex]\sigma = \sqrt{31 * 0.6 * (1- 0.6 )}[/tex]
[tex]\sigma = 2.73[/tex]
The the probability that at least 20 of them have looked at their score in the past six months is mathematically represented as
[tex]P(X \ge 20) = 1- P(X < 20)[/tex]
applying normal approximation we have that
[tex]P(X \ge 20) = 1- P(X < (20-0.5))[/tex]
Standardizing
[tex]1 - P(X < 20) = 1 - P(\frac{X - \mu }{\sigma} < \frac{19.5 - \mu }{\sigma } )[/tex]
[tex]1 - P(X < 20) = 1 - P(Z < \frac{19.5 - 18.6 }{2.73 } )[/tex]
[tex]1 - P(X < 20) = 1 - P(Z < 0.33)[/tex]
Form the standardized normal distribution table we have that
[tex]P(Z < 0.0512)[/tex] = 0.6293
=> [tex]P(X \ge 20 ) = 1- 0.6293[/tex]
=> [tex]P(X \ge 20 ) = 0.3707[/tex]
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2
HELP number 12 pls i do nor have long more
Answer:
Dian has $250 originally.
Step-by-step explanation:
Let the total money Dian has originally = $S
Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,
Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]
Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]
= [tex]\frac{\text{5S-2S}}{5}[/tex]
= [tex]\frac{3S}{5}[/tex]
Since Dian has $150 left then the equation will be,
[tex]\frac{3S}{5}=150[/tex]
S = [tex]\frac{150\times 5}{3}[/tex]
S = $250
Therefore, Dian has $250 originally.
4. (a) Two years ago a woman was 7 times as old as her daughter, but in 3 years time
she would be only 4
times as old as the girl. How old are they now?
Answer:
woman is 37, girl is 7
Step-by-step explanation:
7(x-2) = y-2
4(x+3) = y+3
7x - 14 = y - 2
7x - 12 = y
4x + 9 = y
3x - 21 = 0
x = 7
y = 37
What is the value of the expression iºxi1 x 2 x 3 xi4?
a) 1
b) -1
c) i
d) -i
Answer:
Option b.
Step-by-step explanation:
Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].
Let as consider the given expression is
[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]
We know that,
[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]
Using these values, we get
[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]
[tex]=i^2[/tex]
[tex]=-1[/tex]
The value of given expression is -1.
Therefore, the correct option is b.
please I need help with this question!
The weight of adult males in Boston are normally distributed with mean 69 kilograms and variance 25 kilograms.
I. what percentage of adult male in Boston weigh more than 72 kilograms?
ii. what must an adult male weigh in order to be among the heaviest 10% of the population?
Thank you in advance!
Answer:
lmkjhvjgcfnhjkhbmgnc gfghh
Step-by-step explanation:
Nearsightedness: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) What proportion of children in this sample are nearsighted?
(b) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the Z statistic).
(d) What is the p-value for this hypothesis test?
(e) What is the conclusion of the hypothesis test?
Answer:
a)the proportion of student is 0.1082
b)
H1: p = .08
H2: p not equal to 0.08
H1: p =0 .08
H2: p < .08
H1: p =0 .08
H2: p >0 .08
c)z=1.45
d) the p value is 0.1470
e)null hypothesis cannot be accepted,There is no enough evidence to reject the null hypothesis.
Step-by-step explanation:
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
15 points + brainliest if you can figure this out!
Answer:
(H1, T1)
Step-by-step explanation:
Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).
Answer:
D. (H1, T1)
Step-by-step explanation:
Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is
D. (H1, T1)
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean pulse rate (in beats per minute) of students in a large math class is greater than 71. A simple random sample of the students has a mean pulse rate of 71.7. Choose the correct answer below.
A. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
Answer:
The correct option is (D).
Step-by-step explanation:
In this case, we need to test whether the mean pulse rate (in beats per minute) of students in a large math class is greater than 71.
The hypothesis can be defined as follows:
H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.
Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.
It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.
The sample mean is not very different from the population mean.
So, it cannot be said in confidence that the sample is unusual.
Thus, the correct option is (D).
"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."
given g(x)=3/x^2+2x find g^-1(x)
Answer:
A
Step-by-step explanation:
[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]
Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.
Plz help answer a - d 1. Miguel is playing a game in which a box contains four chips with numbers written on them two of the chips have the number one one chip has the number three and the other chip has the number 5 Miguel must choose to chips if both chips have the same number he wants to dollars if the two chipsy chooses have different numbers he loses $1 (-$1) Look at pictures for the questions
Answer:
Step-by-step explanation:
Hello!
Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"
If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:
S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}
The sample space for the experiment has 7 possible combinations.
a)
Be X: the amount of money Miguel will receive or owe.
If two chips with the same number are chosen he will receive $2
If the chips have different number he will owe $1
Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)
So the probability of him receiving $2 will be 1/7
Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7
xi | $2 | -$1
P(xi) | 1/7 | 6/7
b)
To calculate the expected value or mean you have to use the following formula:
[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57
c)
The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.
d)
To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:
(2*4/7)+(-1*3/7)= $0.71
I hope this helps!
Tree diagram:
Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow. If he draws one of the pieces without looking, what is the probability of drawing the green before the red?
Answer: [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.
We assume that repetition is not allowed
Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex] [By permuattaions]
[tex]=\dfrac{4\times3\times2}{2}=12[/tex]
Favourable outcome = First green then red (only one way)
So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{12}[/tex]
hence, the required probability =[tex]\dfrac{1}{12}[/tex]
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of −3, −1, and 2, and passes through the point (1,10).
Answer:
[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Step-by-step explanation:
Hello,
Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).
[tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]
We know that the point (1,10) is on the graph of this function, so we can say.
[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]
Then the solution is:
[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
How to do this? what is the answer??
Answer:
I think that is the C
Step-by-step explanation:
Answer:
Option B is the correct answer.
Step-by-step explanation:
here, arc RT =162°
as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.
so, its value must be 81°only.
hope it helps..
A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts. The following is the setup for this hypothesis test:
H0:p=0.65
Ha:p<0.65
In this example, the p-value was determined to be 0.277. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Select the correct answer below:
A. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
B. There is NOT sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
C. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 35%.
D. There is NOT sufficient evidence to conclude that the pronortion of people wearing seat belts is less than 35%
Answer:
Option A - There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%
Step-by-step explanation:
The police officers claim is that the proportion of people wearing seat belts is less than 65%.
Now, we are told that the p - value is 0.277.
In hypothesis, for a significance value of 0.05, if the P value is less than 0.05, we reject the null hypothesis and if P value is greater than or equal to 0.05, we fail to reject the null hypothesis.
Now, since the significance level is 5% = 0.05,we can see that the P-value is greater than the significance value of 0.05. Thus, we fail to reject the police claim that the proportion of people wearing seat belts is less than 65%.
So the correct option is A.
Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale. A cylinder with width 4 and height unknown is labeled glass 1, and a cone with height 6 and width 5 is labeled glass 2. 0.2 centimeter 1.7 centimeters 3.9 centimeters 5.6 centimeters
Answer:
1.7
Step-by-step explanation:
1. Find the volume of Glass 2 (volume of a cone = 1/3πr² ·h)
1/3 · 3.14 · 2.5² · 6 = 39.25 cm³
2. Subtract the volume of Glass 2 from the amount of water poured
60 - 39.25 = 20.75 cm³
3. Set up the equation for Glass A using x for the height being solved for (volume of a cylinder = πr² · h)
3.14 · 2² · x = 20.75
12.56x = 20.75
4. Solve for x by dividing both sides by 12.56 (round to the nearest tenth)
x = 1.7
The answer should be 1.7
Find the zeros of the quadratic function: y = 6(7x + 9)(8x – 3)
Answer:
hello :- 9/7 and 3/8
Step-by-step explanation:
y = 6(7x + 9)(8x – 3)
y=0 means : 7x+9=0 or 8x-3=0
7x = -9 or 8x=3
x= - 9/7 or x= 3/8
Answer:
-9/7, 3/8
Step-by-step explanation:
The zeroes can be found in the parenthesis.
You need to set each parenthesis to zero first.
7x+9=0
subtract 9
7x=-9
divide 7
x=-9/7
For 8x-3=0
add the 3
8x=3
divide the 8
x=3/8
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem, and then find the values of the six trigonometric functions for angle B. Rationalize denominators when applicable. b=4, c=7
Answer:
Side a^2 = 49 + 16
Side a^2 = 65
Side a = 8.062
sin (B) = 4 / 8.062
cos (B) = 7 / 8.062
tan (B) = 4 / 7
cot (B) = 7 / 4
sec (B) = 8.062 / 7
csc (B) = 8.062 / 4
Step-by-step explanation:
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 6x + 9 = 11
Answer:
x = 3 ± sqrt(11)
Step-by-step explanation:
x^2 - 6x + 9 = 11
Recognizing that this is a perfect square trinomial
(x-3) ^2 =11
Taking the square root of each side
sqrt((x-3) ^2) = ± sqrt(11)
x-3 =± sqrt(11)
Add 3 to each side
x = 3 ± sqrt(11)
Answer:
[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]
Do not hesitate if you have any question
Hope this helps
The coordinates of the vertices of a rectangle are given by R(- 3, - 4), E(- 3, 4), C (4, 4), and T (4, - 4). A. Use the Pythagorean Theorem to find the exact length of ET. B. How can you use the Distance Formula to find the length of ET? Show that the Distance Formula gives the same answer.
Answer:
see explanation
Step-by-step explanation:
Pythagorean Theorem
7² + 8² = x²
49 + 64 = x²
113 = x²
x = √113 or 10.63
Distance Formula
√(-4 - 4)² + (4 - -3)²
= √8² + 7²
= √113 or 10.63
Lisa, a dentist, believes not enough teenagers floss daily. She would like to test the claim that the proportion of teenagers who floss twice a day is less than 40%. To test this claim, a group of 400 teenagers are randomly selected and its determined that 149 floss twice a day. The following is the setup for this hypothesis test: H0:p=0.40 H0:p<0.40 The p-value for this hypothesis test is 0.131. At the 5% significance level, should the dentist reject or fail to reject the null hypothesis?
Answer:
The dentist should fail to reject the Null hypothesis
Step-by-step explanation:
From the question we are told that
The sample size is n = 400
The sample mean is [tex]\= x = 149[/tex]
The level of significance is 5% = 0.05
The Null hypothesis is [tex]H_o : p = 0.40[/tex]
The Alternative hypothesis is [tex]H_a : p < 0.40[/tex]
The p-value is [tex]p-value = 0.131[/tex]
Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis