Answer:
(a) Explained below.
(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).
Step-by-step explanation:
The information provided is:
n (Men who finished the marathon) = 25,221
n (Women who finished the marathon) = 12,883
Compute the proportion of men and women who finished the marathon as follows:
[tex]\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988[/tex]
The combined proportion is:
[tex]\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989[/tex]
(a)
The hypothesis is:
H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.
Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.
Compute the test statistic as follows:
[tex]Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78[/tex]
Compute the p-value as follows:
[tex]p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075[/tex]
The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.
Thus, concluding that the rate of those who finish is the same for men and women.
(b)
Compute the 99% confidence interval for the difference between proportions as follows:
The critical value of z for 99% confidence level is 2.58.
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
[tex]=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\[/tex]
Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).
The Historic Triangle in Virginia connects Jamestown, Williamsburg, and Yorktown. The interior angle at Williamsburg is 120°. The interior angle at Jamestown is twice the measure of the interior angle at Yorktown. Find the measures of the interior angles at Jamestown and Yorktown.
Answer: Interior angles at Jamestown and Yorktown are 40° and 20°, respectively
Step-by-step explanation: Jamestown, Williamsburg and Yorktown form a triangle. The sum of the interior angles of a triangle is 180°.
Suppose interior angle at Yorktown is x. As Jamestown is twice the measure at Yorktown, it means this interior angle is 2x.
Then, the measures will be:
2x + x + 120 = 180
3x = 60
x = 20
Angle at Yorktown is 20°.
So, angle at Jamestown is
2x = 2.20 = 40°
The measures of the interior angles at Jamestown and Yorktown are 40° and 20°, respectively.
Five less than 3 times a number is 25. What is the number?
Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
[tex]3x - 5 = 25[/tex]
[tex]3x = 30[/tex]
[tex]x = 10[/tex]
Answer:
10?
Step-by-step explanation:
I think this is the right answer
I hoped this helped :)
solve -1 < x + 1 ≤ 6
Answer:
-2<x≤5
Step-by-step :
-1<x+1≤6 So fisrt what every we do to one side we must do to the other. In this case it's a bit different since we are dealing with inequalities.
-1<x+1≤6 I would start off by isolating x in the middle.
-1<x+1≤6 I subtracted 1 from all three sides.
-1 -1 -1
Now your equation should look like this:
-2<x≤5 Now there is really nothing much we can do here since we were just trying to get x by its self.
Answer : -2<x≤5
Which line on the graph below has an undefined slope?
○ P
○ Q
○ R
○ S
Answer:
R
Step-by-step explanation:
Answer:
R
Step-by-step explanation:
Last year, Ivy's pant measured 12 inches. This year, her plant is 75% taller.
How many inches did her plant grow?
Answer:
The plant grew 9 more inches since last year.
Step-by-step explanation:
75% of 12 is 9 and the initial plant growth was 12 inches.
So, the plant grew 9 more inches since last year.
The plant is now 21 inches.
Answer:
9
Step-by-step explanation:
Divide 12 by 4 to get 25% = 3
25% x 3 = 75%
3 x 3 = 9
Apparently, I'm putting in a phrase that hurts Brainly's feelings. So I'm gonna put in a picture instead : )
Answer:
11
Step-by-step explanation:
Because you put the four into the equation like this: f(x)= 2(4)+3
And 2 times 4 equals 8
And 8 plus 3 equals 11
Have a great day!
PLEASE HELP ME ASAP!!!!!!
Answer:
b
Step-by-step explanation:
I’ll name brainliest✨
Answer: -5 1/2 or -5.5
Step-by-step explanation: Negative five and a half. Its technically -5 2/4 but simplify 2/4 its 1/2
Answer:
Point B is located at -5.5
Step-by-step explanation:
Point B is located at the mid point between -6 and -5 on the scale. So, the answer would be 5 and 1/2 or -5.5
I hope this helped to answer your question.
what is the quotient of 4 divided by 1/8
Answer:
32
Step by step explanation
Zola and her friends are going bowling. The bowling alley charges each person a $14 fee to rent shoes, plus $4.50 per game. Which equation represents the cost, y, for each friend to go bowling in terms of the number of games played, x?
Answer:
X+14=y
Step-by-step explanation:
find the surface area of this cylinder using pie.
3. The triangles are similar. Find the value of x.
Answer:
yeah
Step-by-step explanation:
Answer: Is it 3?
Step-by-step explanation:
Emma earns $2 less than three times as much as Rachel. Nick earns twice as much as Emma. Together they earn $594 per week. How much does each person earn per week?
Answer:
290$
Step-by-step explanation:
Answer:
Mei earn $2 less than three times as much as Olivia. Shane earns twice as much as mei. Together they earn $594 per week. How much does each person earn per week?
***
Step-by-step explanation:
let x=amt Olivia earns
3x-2=amt Mei earns ($2 less than three times as much as Olivia).
2(3x-2)=amt Shane earns (twice as much as mei)
..
x+3x-2+2(3x-2)=594
x+3x-2+6x-4=594
10x=600
x=60
3x-2=178
2(3x-2)=356
amt Olivia earns=$60
amt Mei earns=$178
amt Shane earns=$356
Mary bought these art supplies: 4 paint brushes at $1.29 each, 6 dowel rods at $1.49 each, a jar of paste at $1.25, and 2 canvases at $6.00 each. How much change did she get from $40?
A. $8.25
B. $9.35
C. $10.45
D. $12.65
I'll give brainliest!
Answer: The answer is D.
Step-by-step explanation:
Multiply the art supplies with their assigned prices, then combine like terms.
Complete the following sentence.
If x is to 9 as 8 is to 12, then x is equal to
.
Answer:
Srry im late
Step-by-step explanation:
what i miss
Which function is equivalent to g (k) = -k'+ 6k-9?
a g(k) = -(k- 3)
g(k) = (-k+ 3)(k+ 3)
© g(k) =-(k+3)
O
g(k) = (-k- 3)(–k+ 3)
Answer:
I believe it’s g(k)=(-k- 3)(-k+3)
Step-by-step explanation:
The equivalent function is g(k) = -(k - 3)².
The correct option is A.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
We can start by completing the square of the quadratic function g(k) = -k² + 6k - 9:
g(k) = -(k² - 6k + 9 ) = -(k - 3)²
Option A can be simplified as:
g(k) = -(k - 3)²
Compared with the completed square form of g(k), we can see that option A is equivalent to g(k).
Therefore, the answer is A. g(k) = -(k - 3)²
To learn more about the quadratic function;
https://brainly.com/question/11485644
#SPJ5
The complete question:
Which function is equivalent to g (k) = -k²+ 6k-9?
A. g(k) = -(k- 3)²
B. g(k) = (-k+ 3)(k+ 3)
C. g(k) = -(k+3)²
D. g(k) = (-k- 3)(–k+ 3)
I need help with this
Answer: 0.6 grams
Step-by-step explanation: divide grams by cm and its 0.6
Help plzzzzzzzzzzzzzz
Answer:
∠E
Step-by-step explanation:
∠E is between PE and EN
35
How do you write as a percentage?
50
Answer:
0.7 is a decimal and 70/100 or 70% is the percentage for 35/50.
Step-by-step explanation:
Hope this helps!
(Need help ASAP)
How many solutions does the equation have:
3x - 5 = -5 + 3x
Answer:
Infinitely many
Step-by-step explanation:
Add 5 to both sides and subtract 3x on both sides. that results in 0=0. if the numbers are the same, than its infinitely many.
Answer:
0=0
Step-by-step explanation:
3x-5=-5+3x
0=0
Enter an equation to describe the linear relationship.
The temperature, y, of a pot of water is 45 °F. The temperature increases by 25 °F per minute,x , when being heated.
The equation is y=
Jen and Kamlee are walking to school. After 20 minutes, Jen has walked 45 mile. After 25 minutes, Kamlee has walked 56 mile. Find their speeds in miles per hour. Enter the correct answers in the boxes.
Answer:
Jen's speed = 135 miles per hour (Approx)
Kamlee's speed = 134 miles per hour (Approx)
Step-by-step explanation:
Given:
Jen walk = 45 miles
Jen's time = 20 min = 20/60 = 0.333 hour
Kamlee walk = 56 miles
Kamlee's time = 25 min = 25/60 = 0.416667 hour
Find:
Speed
Computation:
Jen's speed = 45 / 0.333
Jen's speed = 135 miles per hour (Approx)
Kamlee's speed = 56 / 0.416667
Kamlee's speed = 134 miles per hour (Approx)
Which expressions are equivalent to 5x?
(Didn’t expect the test to be this hard ;C)
A: 5x + 0
B: x (0) + 4x
C: x + (0 + 4x)
D: 4x + (1) x
E: 5x multiplied by 0
F: 5x (1)
Answer:
A, E, F
Step-by-step explanation:
Your welcome
Answer:
its a,d,c,e, and f
Step-by-step explanation:
Jennifer had 3 \frac{3}{4}
4
3
lbs of tomatoes. She used \frac{1}{3}
3
1
OF that amount to make a salad. How many pounds OF tomatoes did she use? (LEAVE ANSWER AS A MIXED NUMBER)
Answer:
She used 1/4 of a pounds for salad
Step-by-step explanation:
Here, we want to calculate the amount of pounds of tomatoes used to make salad
From the question, she has 3/4 pounds and used 1/3 of what she has to make salad
What she used will be;
3/4 * 1/3 = 1/4
A mom mixes 9 ounces of juice with 3 ounces of water. What present of the drank is juice?
Answer:
6 ounces of juice
Step-by-step explanation:
Answer:
12 ounces
Step-by-step explanation:
A mom mixes 9 ounces of juice with 3 ounces of water. This means that the total ounces of drink= 9+3 = 12 ounces. The percent of the drink which is juice is: Ratio of the quantity of juice to the total quantity of drink and multiplying this obtained quantity by 100.
PLS HELP WILL GIVE BRAINLIEST
What are 3 different methods for solving systems of equations and when would you use each one? (10 pts)
How do you graph the solution set to a system of linear inequalities in two variables? (10 pts)
How do you determine if a system of linear equations has one solution, no solutions or infinitely many solutions? (10 pts)
Step-by-step explanation:
graphing.
substitution method.
elimination method.
We will use as an example the following system of inequalities:
3x +2y ≥ 5x -4
y < (1/2)x +3
For each inequality, do the following:
1. If it is not this way already, arrange the inequality so that each variable appears on only one side of the inequality. Putting the inequality into any of the standard forms will do this. It will be helpful later if you arrange the inequality so that at least one variable has a positive coefficient. (You may have to multiply by -1 (and change the sense of the inequality) to do this.)
Our example inequalities are now ...
-2x +2y ≥ -4 . . . . . or divide by 2 to get . . . . -x +y ≥ -2
y < (1/2)x +3
2. Notice the inequality symbol, and whether it includes the "or equal to" case.
the first inequality is ≥, so includes "or equal to"
the second inequality is <, so does not include "or equal to"
3. Replace the inequality symbol with an equal sign and graph the resulting equation. If the "or equal to" case is included, the line is graphed as a solid line. If it is not, then the line is graphed as a dashed line.
the first equation (-x +y = -2) is graphed with a solid line
the second equation (y = (1/2)x +3) is graphed with a dashed line
4. It is not necessary, but is less confusing, to choose a variable in the inequality (after step 1) that has a positive coefficient. Notice whether this variable is "less than" or "greater than" the stuff on the other side of the inequality.
y ≥ . . . . for the first inequality
y < . . . or . . . x > . . . . for the second inequality
If it is less than, shade the portion of the graph below (for y <) or to the left (for x <) of the line you graphed in step 3.
the second inequality has y < , so the graph will be shaded below the dashed line. It also has x > , so will be shaded to the right of the dashed line. (These are the same shading.)
If it is greater than, shade the portion of the graph above (for y >) or to the right (for x >) of the line you graphed in step 3.
the first inequality has y ≥ , so the graph will be shaded above the solid line.
5. The solution set is where the shaded areas overlap. Any point on a dashed line is not in the solution set.
_____
The graph for the example inequalities is attached. The first one is graphed and shaded in red; the second one is graphed and shaded in blue.
A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.
Three methods of solving inequalities are the graphing method, substitution method, and elimination method.
What is inequality in math?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
We will use as an example the following system of inequalities:
3x +2y ≥ 5x -4
y < (1/2)x +3
For each inequality, do the following:
If it isn't already set up this way, organize the inequality so that each variable only appears on one side. This can be accomplished by putting inequality into any of the accepted formats. If you set up the inequality so that at least one variable has a positive coefficient, it will be useful later. To accomplish this, you might need to multiply by -1 (and alter the inequality's sense).
Our example inequalities are now ...
-2x +2y ≥ -4 . . . . . or divide by 2 to get . . . . -x +y ≥ -2
y < (1/2)x +3
Take note of the inequality sign and whether the "or equal to" instance is present.
The first inequality is, so "or equal to" is included. The second inequality is, so "or equal to" is not included.
Create a graph of the equation that results from replacing the inequality symbol with the equal sign. The line is graphed as a solid line if the "or equal to" scenario is present. If not, a dashed line is used to represent the line on the graph.
Graphing the first equation (-x + y = -2) using a solid line
Graphing the second equation (y = (1/2)x + 3) uses a dashed line.
Choosing a variable in the inequality that has a positive coefficient after step one is not required, but it is less ambiguous. If there is an inequality, pay attention to whether this variable is "less than" or "greater than" the items on the other side.
For the initial inequality, y
In the case of the second inequality, y or x >
Shade the area of the graph below (for y) or to the left (for x) of the line you graphed in step 3 if it is smaller than.
The graph will be darkened below the dashed line since the second inequality has the value y. It will be tinted to the right of the dashed line because it also has x >. The shading here is the same.
Shade the area of the graph above (for y >) or to the right (for x >) of the line you graphed in step 3 if it is bigger than.
The graph will be shaded above the solid line because the first inequality has y.
The overlap of the colored areas is the solution set. The solution set does not include any points on a dashed line.
When the lines are parallel, a system cannot have a solution. If you get a false statement after solving the system (a number that is equal to a different number), there are no solutions.
Learn more about inequalities here:
https://brainly.com/question/12679763
#SPJ2
Which equation describes the line that passes through (-3,1) and is parallel to the line described by y =4x+1
28. How much plain yogurt will you need to make 2 1/2 dozen cookies? Show your work.
Answer:
[tex]\frac{5}{6}[/tex] cups
Step-by-step explanation:
Normally, when working with mixed numbers, I would prefer to turn them into improper fractions first before evaluating.
1 [tex]\frac{1}{2}[/tex] cookies --- [tex]\frac{1}{2}[/tex] cup plain yogurt
[tex]\frac{3}{2}[/tex] cookies --- [tex]\frac{1}{2}[/tex] cup plain yogurt
2[tex]\frac{1}{2}[/tex] cookies --- ? cup plain yogurt
[tex]\frac{5}{2}[/tex] cookies --- [tex]\frac{5}{3}[/tex] × [tex]\frac{1}{2}[/tex] cup plain yogurt = [tex]\frac{5}{6}[/tex] cups plain yogurt
HELP THIS IS TIMED
i need answers asap
Answer:
7
Step-by-step explanation:
I am 100% sure
[tex]\sf{\bold{\green{\underline{\underline{Given}}}}} [/tex]
⠀⠀⠀⠀
AD = 24cmDB = 25 cm______________________[tex]\sf{\bold{\green{\underline{\underline{To\:Find}}}}} [/tex]
⠀⠀⠀⠀
AB = d = ?? ______________________[tex]\sf{\bold{\green{\underline{\underline{Solution}}}}} [/tex]
⠀⠀⠀⠀
Using Pythagoras theorem ;
⠀⠀⠀⠀
[tex]\sf{\red{\boxed{\bold{( hypotenuse )^2 = ( base )^2 + ( height )^2 }}}}[/tex]
⠀⠀
First , lets understand the concept ;
⠀⠀
What is Pythagoras theorem ??
⠀⠀⠀⠀
In Pythagoras theorem the square of hypotenuse is equal to the square of base in the square of corresponding height when one angle is 90° .⠀⠀⠀⠀
What is hypotenuse ?
⠀⠀⠀⠀
The side in the front of right angle is known as hypotenuse .⠀⠀⠀⠀
In the given Δ ;
⠀⠀⠀⠀
Hypotenuse = DB = 25 cm
⠀⠀
Acc. to the formulae ;
⠀⠀⠀⠀
➠ 25² = 24² + d²
⠀⠀⠀⠀
➠ d² = 25 ² - 24 ²
⠀
➠ d² = 625 - 576
⠀⠀⠀⠀
➠ d² = 49
⠀
➠ d = √49
⠀⠀⠀⠀
➠d = 7cm
⠀⠀⠀⠀
______________________[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}} [/tex]
⠀⠀⠀⠀
Value of d is 7cmNeed help, please would be helpful
Answer:
90
Step-by-step explanation: