Answer:
With replacement, 0.037, independent
Without replacement, 0.031, dependent
Step-by-step explanation:
There are 5 vowels (not including y).
The probability the first letter is a vowel is 5/26.
With replacement, the probability the second letter is a vowel is also 5/26.
The total probability is (5/26) (5/26) = 0.037.
Since the first letter is replaced, the probability of the second letter is not affected, so the events are independent.
Without replacement, the probability the second letter is a vowel is 4/25.
The total probability is (5/26) (4/25) = 0.031.
Since the first letter is not replaced, the probability of the second letter is affected, so the events are dependent.
1. Solve the equation using the zero-product property.
-x(5x – 4) = 0
Answer:
x = 0, 4/5
Step-by-step explanation:
The zero-product property states that if the product of a and b is zero, then either a = 0, b = 0, or both terms equal zero
Here our a term is -x and our b term is (5x - 4)Setting each term equal to zero and solving for x we get-x = 0 → x = 05x - 4 = 0 → 5x = 4 → x = 4/5 What is the best category for the system of equations shown:
2x + 6y = 14
- 2x+2y =- 10
1.Consistent / Independent
2.Consistent / Dependent
3.Inconsistent / Independent
4.None of the above.
Answer:
Option (1)
Step-by-step explanation:
System of equations has been given as
2x + 6y = 14
By dividing this equation by 2
x + 3y = 7 --------(1)
Second equation is,
-2x + 2y = -10
-x + y = -5 -------(2)
By adding equation (1) and equation (2)
(x + 3y) + (-x + y) = 7 - 5
2x = 2
x = 1
By putting x = 1 in the equation (1)
1 + 3y = 7
3y = 6
y = 2
So, we get exactly one solution pair (1, 2) where these lines are intersecting.
Therefore, the best category that defines the system of equations is Consistent/Independent
Option (1) will be the answer.
How many ways can the letters be arranged in the word: GLASS
Answer:
120
Step-by-step explanation:
A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70°? I need this asap someone help please
Answer:[tex]8.75\ m^2[/tex]
Step-by-step explanation:
Given
Area of circle is [tex]A=45\ m^2[/tex]
Arc measure [tex]\theta =70^{\circ}[/tex]
and area of sector is given by
[tex]\Rightarrow \frac{\theta }{360^{\circ}}\times \text{Area of circle}[/tex]
[tex]\Rightarrow \frac{70}{360}\times 45[/tex]
[tex]\Rightarrow 0.194\times 45[/tex]
[tex]\Rightarrow 8.75\ m^2[/tex]
So, area of sector is [tex]8.75\ m^2[/tex]
A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical trials, 200,000 children were randomly divided in two groups. The subjects in group 1 (the experimental group) were given the vaccine, while the subjects in group 2 (the control group) were given a placebo. Of the 100,000 children in the experimental group, 21 developed the disease. Of the 100,000 children in the control group, 30 developed the disease.
a) Does it appear to be the case that the vaccine was effective? Use the α = 0.01 level of significance.
Identify the null and alternative hypotheses for this test.
c) Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)
Answer:
1) No, there is not enough evidence to support the claim that the vaccine was effective (P-value=0.104) .
The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
being the subindex 1 for the experimental group and subindex 2 for the control group.
2) Test statistic z=-1.26
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the vaccine was effective.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
The significance level is 0.01.
The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.
[tex]p_1=X_1/n_1=21/100000=0.0002[/tex]
The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.
[tex]p_2=X_2/n_2=30/100000=0.0003[/tex]
The difference between proportions is (p1-p2)=-0.0001.
[tex]p_d=p_1-p_2=0.0002-0.0003=-0.0001[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=P(z<-1.26)=0.104[/tex]
As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the vaccine was effective.
ali's tyre pressure gauge shows a reading witch is 8 % lower than the actual pressure when the gauge shows 33.58
The actual pressure when the gauge shows 33.58 would be 36.5.
Used the concept of the percentage that states,
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.
Given that,
Ali's tire pressure gauge shows a reading which is [tex]8 \%[/tex]lower than the actual pressure.
And, the gauge shows [tex]33.58.[/tex]
Let us assume that,
The actual pressure of Ali's tires = x
Hence, we can formulate the equation,
[tex]x \times (1 - 8\%) = 33.58[/tex]
Solve the equation for x,
[tex]x \times (1 - \dfrac{8}{100} ) = 33.58[/tex]
[tex]x \times (1 - 0.08) = 33.58[/tex]
[tex]x \times 0.92 = 33.58[/tex]
Divide both sides by 0.92;
[tex]x= \dfrac{33.58}{0.92}[/tex]
[tex]x = 36.5[/tex]
Therefore, The actual pressure of Ali's tires = 36.5
To learn more about the percentage visit:
https://brainly.com/question/24877689
#SPJ6
The complete question is,
Ali's tire pressure gauge shows a reading which is 8% lower than the actual pressure.
What is the actual pressure of Ali's tires when the gauge shows 33.58?
Math workshops and final exams: The college tutoring center staff are considering whether the center should increase the number of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy.Which is the response variable?a) Whether the student attended a workshop. b) Number of workshops attended.c) Whether the student passes the course.d) Final exam score.
Answer:
Option D
Step-by-step explanation:
The response variable is also known as the dependent variable. It depends on another factor which is the independent variable to cause change/ response to it.
In this study, they want to test if an increase in the number of Math workshop which is the independent variable will cause a change in the final exam scores which is the dependent variable. The response to this inquiry is thus the final exam score which is also known as the response variable.
What is the equation of the line that is perpendicular to f(x) and passes through the point (4, –6)? a.4x + 3y = –2 b. 3x + 4y = –12 c.4x – 3y = 34 d.3x – 4y = 36
Answer:
8
Step-by-step explanation: because its even
a national survey asked 1261 US adult fast food customers which meal (breakfast, lunch, dinner, snack) they ordered.
Identify the variable
Is the variable quantitative or qualitative?
What is the implied population?
Answer:
Can you answer mine? I willl answer yours
Step-by-step explanation:
Sasha’s daily tips this work week were $43, $32, $65, $88, $50, and $72. Is Sasha correct in thinking that the mean accurately represents how much money she makes in daily tips? Yes, Sasha is correct. The mean amount she makes is $58.33 in a day. Yes, Sasha is correct. The mean amount she makes is $65.33 in a day. No, Sasha is not correct. The median amount she makes is $53.00 in a day. No, Sasha is not correct. The median amount she makes is $60.00 in a day.
Answer: $58.33
Step-by-step explanation:
Yes, Sasha is correct. The mean amount she makes is in a day.
Answer:
a: Yes, Sasha is correct. The mean amount she makes is $58.33 in a day
Step-by-step explanation:
edg2020
Kenney High School's swimming pool is 25 yards long. The pool has 8 lanes, each of which is 3 yards wide. The pool is filled to a depth of 6 feet.
What are the lengths and width in terms of feet?
Answer:
length: 75 ftwidth: 72 ftStep-by-step explanation:
Length: (25 yd)(3 ft/yd) = 75 ft.
Width: (8 lanes)(3 yd/lane)(3 ft/yd) = 72 ft.
The length and width are 75 ft and 72 ft, respectively.
Answer:
length; 75 ft
width; 72 ft
Step-by-step explanation:
A third grade class has 16 girls and 15 boys a fourth grade class has 18 boys and 15 girls when picking for PE captains will make one selection from the fourth grade class and one selection from the third grade class before the other team pics assuming everyone has an equally like lee chance of being selected what is the probability that the first captain will choose two boys on the first pick
Answer:
[tex]\dfrac{90}{341}[/tex]
Step-by-step explanation:
3rd grade:
Number of girls = 16
Number of boys = 15
Total number of students = 31
4th grade:
Number of girls = 15
Number of boys = 18
Total number of students = 33
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability of picking a boy from 3rd grade, [tex]P_{1} = \dfrac{15}{31} ..... (1)[/tex]
Probability of picking a boy from 4th grade, [tex]P_{2} = \dfrac{18}{33} ..... (2)[/tex]
These are two independent events of picking a boy from 3rd grade and 4th grade.
So, probability the captain chooses 2 boys in the first pick can be found by multiplying (1) and (2) above.
[tex]P = P_{1} \times P_{2}\\\Rightarrow \dfrac{15}{31} \times \dfrac{18}{33}\\\Rightarrow \dfrac{90}{341}[/tex]
Answer:
a
Step-by-step explanation:
The original price, p, of a pair of shoes was discounted by 20% and a sales tax of 8% was applied to the sales price. Which expression is equivalent to the new price?
Answer:
0.864p
Step-by-step explanation:
A discount of 20% is (1 - .2) = .8
8% tax is 1.08
.8 * 1.08 = 0.864
That means the new price is 0.864p
LOIHal y LU LIC LOIVCI SC VILHC ISUSLCICS langic TCUICHT
2. What type of angle is ZDBC if it measures exactly 180° and its rays form a straight line?
roofs
onships
8
on to
angles
Properties
DESCRIPTION
Answer:
straight angle
Step-by-step explanation:
A straight angle is one whose measure is 180°. Its formative rays point in opposite directions from the vertex and make a straight line.
which number is located between 1.2 and 1.4
Answer: 1.3
Step-by-step explanation: Ok, let's make a number line...
0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6
From the number line, the only number that fits is 1.3
I hope this helps!
Answer:
1.3
Step-by-step explanation:
Hope this helps have a wonderful day
Two towers face each other separated by a distance = 15 m. As seen from the top of the first tower, the angle of depression of the second tower’s base is 60° and that of the top is 30°. What is the height (in meters) of the second tower?
Answer:
Height of second tower = 17.32m
Step-by-step explanation:
I have attached a diagram depicting the question.
From the diagram, The first tower is depicted by side AEB and the second tower CD.
While d is the distance that separates the two towers and it's given as 15m.
Now, since the angle of depression of the second tower’s base is 60°, then for triangle BAC. Angle C = 60°.
Thus; using trigonometric ratios;
tan 60° = AB/AC.
This gives; AB = d*tan 60°
Similarly, for the triangle BED, BE = d*tan 30°
Since, AE = CD, thus ;
CD = AB − BE
CD = d (tan 60° − tan 30°)
CD = 15(1.7321 − 0.5774)
CD = 15 × 1.1547
CD ≈ 17.32 m.
So, height of second tower = 17.32 m
Find he least common multiple of 16, 21, and 24
Answer:
336 is the answer
Step-by-step explanation:
hope this helps
v=1/6√π S 3/2 find V when s=60m'2 π=3.14
Answer:
137.26 m^3
Step-by-step explanation:
Put the numbers into the formula and do the arithmetic.
v = (1/6)(√3.14)(60 m^2)^(3/2) = 137.26 m^3
what happened to www.brainy.com?
As far as I'm concerned, it still exists
What do you mean becauae nothing happened
Divide 10x^4-14x³-10x²-10 by x³-3x²+x-2
The quotient is
The remainder is
Answer:
The quotient is [tex]10x+16[/tex]
The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]
Step-by-step explanation:
(See my image for my work)
Once the problem is set up, we need to figure out how to make [tex]x^3[/tex] become [tex]10x^4[/tex]. To do this, we must multiply it by [tex]10x[/tex].
This becomes the first number at the top of our work.
Now, we need to create the second row. To do this, we need to multiply all of the terms on the left by [tex]10x[/tex] and then multiply it by a negative.
Once that is done, we need to subtract these two rows.
After we subtract, we are left with [tex]16x^3-20x^2+26x-10[/tex]
Now we can do the same thing. This time, the number that we must multiply by is 16, so that is the next term on top
Next, we multiply the terms on the left by 16 and then subtract them from the previous expression
This leaves us with [tex]34x^2+10x+22[/tex].
As this has a smaller power than the left-hand side, this is our remainder, which we need to divide by the left hand side.
Our quotient is the number that we have found on the top.
This gives us the answer of
The quotient is [tex]10x+16[/tex]
The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]
(Sorry. This process is hard to do in this form, so I had to write it by hand.)
Answer:
the quotient is 10x + 16
the remainder is 28x² + 10x + 22
What is the arc length if the radius is 12 cm?*
A
B
60°
O 12 pi cm
O 3 pi cm
O 4 pi cm
024 pi cm
Answer:
4π cm
Step-by-step explanation:
The length of an arc of a circle with radius r and central angle θ is given by ...
s = rθ
where θ is in radians.
Here, your arc measures 60° = π/3 radians, so the arc length is ...
s = (12 cm)(π/3) = 4π cm
I need help with question C
What is the equation of the blue line ?
Rise over run. Or I believe. Like If I chose (-1,2) and (0,-1) the rise or in this case since the line is going down, if I move down 4 units. I am one unit to the left of (0,-1) so 4/1 so rise/run
The equation of the line is y+2x+1 = 0.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
In the given graph,
Line intersect x-axis at -1/2
And intersect y-axis at -1
The points are (-1/2,0) and (0,-1)
The slope of the line m = -1-0/(0-(-1/2)) = -2
The required equation of the line that passes through the point (-1/2,0) and slope is -2,
y-0 = -2(x-(-1/2))
⇒y=-2x-1
⇒y+2x+1 = 0
The equation of the line is y+2x+1 = 0.
To know more about Equation of line on:
https://brainly.com/question/21511618
#SPJ5
HELP PLEASE
The table shows Amy's, Jenny's, and Meg's sales for the month of February. They get a 5% commission on their sales. Which matrix gives the commission they earned for each type of product?
Answer:
a
Step-by-step explanation:
A percentage is a way to describe a part of a whole. The correct matrix is C.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that the table shows Amy's, Jenny's, and Meg's sales for the month of February. They get a 5% commission on their sales. Therefore, the commission on each product category and for each person can be calculated as shown below.
Commission on book sales for Amy, a₁₁ = 120 × 0.05 = 6
Commission on book sales for Jenny, a₁₂= 250× 0.05 = 12.5
Commission on book sales for Meg, a₁₃ = 215 × 0.05 = 10.75
Commission on Games sales for Amy, a₂₁ = 155 × 0.05 = 7.75
Commission on Games sales for Jenny, a₂₂= 106 × 0.05 = 5.3
Commission on Games sales for Meg, a₂₃ = 175 × 0.05 = 8.75
Commission on Tables sales for Amy, a₃₁ = 350 × 0.05 = 17.5
Commission on Tables sales for Jenny, a₃₂= 400 × 0.05 = 20
Commission on Tables sales for Meg, a₃₃ = 290 × 0.05 = 14.5
Now, the matrix can be made as shown below,
[tex]\left[\begin{array}{ccc}6&12.5&10.75\\7.75&5.3&8.75\\17.5&20&14.5\end{array}\right][/tex]
Hence, the correct matrix is C.
Learn more about Percentages here:
https://brainly.com/question/6972121
#SPJ5
A researcher wanted to test the claim that, "Seat belts are effective in reducing fatalities." A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. If a significance level of 5% is used, which of the following statements gives the correct conclusion?
a. Since p >α we conclude that this data shows that seat belts are effective in reducing fatalities.
b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities U
c. Since p >α we conclude that this data shows that seat belts aren't effective in reducing fatalities.
d. Since p<α, we conclude that this data shes that seat belts aren't effective in reducing fatalities.
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the occupants not wearing seat belts and occupants wearing seat belts. The population proportion of occupants not wearing seat belts and occupants wearing seat belts would be p1 and p2 respectively.
P1 - P2 = difference in the proportion of occupants not wearing seat belts and occupants wearing seat belts.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 > p2
p1 - p2 > 0
it is a right tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples.
For occupants not wearing seat belts,
x1 = 31
n1 = 2823
P1 = 31/2823 = 0.011
For occupants wearing seat belts,
x2 = 16
n2 = 7765
P2 = 16/7765 = 0.0021
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (31 + 16)/(2823 + 7765) = 0.0044
1 - pc = 1 - 0.0044 = 0.9956
z = (P1 - P2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.011 - 0.0021)/√(0.0044)(0.9956)(1/2823 + 1/7765) = - 0.0089/0.00145462023
z = 6.81
From the normal distribution table,
p < 0.00001
0.00001 < 0.05, we would reject the null hypothesis.
Therefore,
b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities
Is -1.27 a rational number
Answer:
Yes.
Step-by-step explanation:
Answer:
si
Step-by-step explanation:
12 is 1/3 of what number
Answer:
The number is 36.
Step-by-step explanation:
Given that 1/3 of a number is 12. So let's make this number into any variable, I will choose x which means that 1/3 of x is equals to 12. Next we have to write an expression :
[tex] \frac{1}{3} \times x = 12[/tex]
In order to solve x, you have to multiply 3 to both sides :
[tex] \frac{1}{3} \times x \times 3 = 12 \times 6[/tex]
[tex]x = 36[/tex]
To find out what number 12 is one-third of, we can set up an equation. Let's assume the unknown number is represented by "x".
According to the given statement, we can write the equation as: 12 = (1/3)x To solve for x, we need to isolate it on one side of the equation.
We can do this by multiplying both sides of the equation by 3, canceling out the fraction: 3 * 12 = (1/3)x * 3 36 = x Therefore, 12 is one-third of 36. In other words, if we take one-third of 36, it will equal 12.
To know more about equation visit:
https://brainly.com/question/33622350
#SPJ2
Which values are solutions to the inequality –3x – 4 < 2?
Answer: x>-2
Step-by-step explanation:
To find the values of the inequality, you treat this like it would be any other equation.
[tex]-3x<6[/tex]
[tex]x>-2[/tex]
__-112=225+125 need help
Answer:
I think it's 462. I'm sry if I'm wrong.
Factor 9x^2+6x+1 completely
Answer:
[tex](3x+1)^2[/tex]
Step-by-step explanation:
[tex]9x^2+6x+1=\\(3x+1)^2[/tex]
You can confirm this by working and expanding backwards:
[tex](3x+1)^2=\\(3x+1)(3x+1)=\\9x^2+3x+3x+1=\\9x^2+6x+1[/tex]
Hope this helps!
The factorized form of 9x² + 6x + 1 is indeed (3x + 1)².
To find the factorized form of the quadratic expression 9x² + 6x + 1 is (3x + 1)², we can expand the factorized form and compare it with the given expression to check if they are equal.
Expanding (3x + 1)² using the square of a binomial formula, we get:
9x² + 6x + 1
= 9x² + 3x + 3x + 1
= 3x (3x + 1) + 1 (3x + 1)
(3x + 1)² = (3x + 1)(3x + 1)
Comparing the expanded form of (3x + 1)² with the given expression 9x² + 6x + 1, we can see that they are equal.
Therefore, we have found that the factorized form of 9x² + 6x + 1 is indeed (3x + 1)².
To learn more about the factorization;
https://brainly.com/question/28187946
#SPJ6