Answer:
y = 2x-6
Step-by-step explanation:
2x-y=6
Solve for y
Subtract 2x from each side
2x-y-2x = -2x+6
-y = -2x+6
Multiply both sides by -1
y = 2x-6
Slope intercept form is y = mx +b where m is the slope and b is the y intercept
In a survey of adults aged 57 through 85 years, it was found that 86.6% of them used at least one prescription medication. Complete parts (a) through (c) below.
a. How many of the 3149 subjects used at least one prescription medication?
(Round to the nearest integer as needed.)
b. Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.
(Round to one decimal place as needed.)
Answer:
a) 272 used at least one prescription medication.
b) The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).
Step-by-step explanation:
Question a:
86.6% out of 3149, so:
0.866*3149 = 2727.
272 used at least one prescription medication.
Question b:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 3149, \pi = 0.866[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 - 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.856[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 + 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.876[/tex]
For the percentage:
0.856*100% = 85.6%
0.876*100% = 87.6%.
The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).
The number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is: [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%
How to construct confidence interval for population proportion based on the sample proportion?Suppose that we have:
n = sample size[tex]\hat{p}[/tex] = sample proportion[tex]\alpha[/tex] = level of significance = 1 - confidence interval = 100 - confidence interval in percentageThen, we get:
[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
where [tex]Z_{\alpha/2}[/tex] is the critical value of Z at specified level of significance and is obtainable from its critical value table(available online or in some books)
For this case, we have:
n = 3149confidence interval is of 90%[tex]\alpha[/tex] = level of significance = 100 - 90% = 10% = 0..10[tex]\hat{p}[/tex] = sample proportion = ratio of 86.6% of n to n (at the least)Part (a):
The number of subjects used at least one prescription medication is:
[tex]\dfrac{3149}{100} \times 86.6 \approx 2727[/tex]
Thus, the sample proportion we get is:
[tex]\hat{p} = \dfrac{2727}{3149} \approx 0.8659[/tex]
For level of significance 0.10, we get: [tex]Z_{\alpha/2} = 1.645[/tex]
Thus, the confidence interval needed is:
[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\CI \approx 0.8659\pm 1.645 \times \sqrt{\dfrac{0.8659(1-0.8659)}{3149}}\\\\\\CI \approx 0.8659 \pm 0.0099[/tex]
Thus, CI is [0.8659 - 0.0099, 0.8659 + 0.0099] = [0.8560, 0.8758]
Thus, the number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is: [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%
Learn more about population proportion here:
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1. To determine the height of a tree, a botanist
makes the following diagram. What is the
height of the tree?
70°
20 ft
Answer:
54.94954839
Step-by-step explanation:
tan(70) = x/20
tan(70) times 20 = x
a mountain railway AB is of length 864m and rises at an angle of 120° to the horizontal.
A train is 856m above sea level when it is at A.
calculate the height above sea level of the train when it reaches B.
Answer:
The height above sea level at B is approximately 1,604.25 m
Step-by-step explanation:
The given length of the mountain railway, AB = 864 m
The angle at which the railway rises to the horizontal, θ = 120°
The elevation of the train above sea level at A, h₁ = 856 m
The height above sea level of the train when it reaches B, h₂, is found as follows;
Change in height across the railway, Δh = AB × sin(θ)
∴ Δh = 864 m × sin(120°) ≈ 748.25 m
Δh = h₂ - h₁
h₂ = Δh + h₁
∴ h₂ ≈ 856 m + 748.25 m = 1,604.25 m
The height above sea level of the train when it reaches B ≈ 1,604.25 m
What the additional information fill in the blanks
Answer:
QXV=WXV
Step-by-step explanation:
Find the integer solution of the equation
a)5x+25=-3xy+8y^2
b)2y^2+x+y+1=x^2+2y^2+xy
Answer:
the answer is as follows:
Step-by-step explanation:
a)
The equation has the following integer solutions:
5*x+25=-3*xy+8*y^2
Number of solutions found: 3
x1=-31; y1=-10
x2=-7; y2=-2
x3=-5; y3=-0
b)
The equation has the following integer solutions:
2*y^2+x+y+1=x^2+2*y^2+xy
Number of solutions found: 2
x1=0; y1=-1
x2=2; y2=-1
Do not forget to give appriciation.
What is tanA?
Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 17, adjacent A C is 8, opposite B C is 15.
a.
StartFraction 15 Over 17 EndFraction
c.
StartFraction 8 Over 15 EndFraction
b.
StartFraction 8 Over 17 EndFraction
d.
StartFraction 15 Over 8 EndFraction
Answer:
D. [tex] \frac{15}{8} [/tex]
Step-by-step explanation:
Recall: SOH CAH TOA
Thus,
Tan A = Opposite/Adjacent
Reference angle (θ) = A
Length of side Opposite to <A = 15
Length of Adjacent side = 8
Plug in the known values
[tex] Tan(A) = \frac{15}{8} [/tex]
Decide whether the relation is a function or not.
{(-3, 5), (-2, 5), (0, 5), (1, 5), (2, 5)}
Answer:
[see below]
Step-by-step explanation:
A functions input is assigned to exactly one output. This means that the inputs must not repeat.
{(-3, 5), (-2, 5), (0, 5), (1, 5), (2, 5)}
Since no inputs repeat, the relation given is a function.
Hope this helps.
Answer:
Yes, it's a function.
Step-by-step explanation:
X or input no repeated.
What’s the answers ?
hope this helps! feel free to clarify if unsure
Here’s Question three
Answer:
BD = 3 units
Step-by-step explanation:
Since, AD is an angle bisector of ∠BAC,
m∠BAD = m∠CAD = 20°
CD = 3 units
In ΔACD and ΔABD,
m∠BAD = m∠CAD = 20° (Given)
AD ≅ AD [Reflexive property]
Therefore, by H-A property of congruence both the triangles will be congruent.
And by CPCTC,
CD ≅ BD = 3 units
What is the measure of ∠
A. 60°
B. 6°
C. 42°
D. 49°
can someone help me explain this please
In case of linear function the graph will be a straight line as the change is constant in every interval. But in case of non-linear function, instead of straight line the graph will generate curve line as the change is not constant in every interval.
Will give Brainliest Please help me!
Derrick and jimmy start working on the same day. Derrick earns $30 every day. Jimmy earns $1 everyday on the first day. Every day thereafter, Jimmy earns $1 on the 1st day. Everyday thereafter, Jimmy earns $1 moe than he did h previous day. How many days will it take derrick and jimmy to have earned the same amount of money
Answer:
me and you have the same questions
Please I need help who want to earn 13 points ..
Answer:
Triangle ISK
Step-by-step explanation:
Answer:
Triangle ISK
Step-by-step explanation:
if the angles and sides of one triangle are equal to the corresponding sides and angles of the other triangle, they are congruent.
∠Q = ∠I
∠R = ∠S
∠S = ∠K
HELPPP MEEEE OUTTTTTT ITS URGENTTTTT!!!!
Answer:
(x-12)^2+(y-2)^2=4
Step-by-step explanation:
I need help I don’t understand this
Answer:
[tex]\frac{13}{5}=2\frac{3}{5}[/tex]
Step-by-step explanation:
Given fraction is [tex]\frac{13}{5}[/tex].
To convert this fraction into a mixed number, divide the numerator 13 by the denominator 5.
5) 13 (2
10
3
Here, quotient = 2
Remainder = 3
Divisor = 5
Therefore, given fraction can be written as,
[tex]2\frac{3}{5}[/tex]
Lawrence sells 40% of the apples on his cart, and are left with 420 apples. How many apples had Lawrence started with?
Answer:
700 apples
Step-by-step explanation:
Let
x = Total number of apples in the cart
Percentage of apples sold = 40%
Number of apples sold = Percentage of apples sold * Total number of apples in the cart
= 40% * x
= 0.4 * x
= 0.4x
Number of apples left in the cart = 420
Total number of apples in the cart = Number of apples sold + Number of apples left in the cart
x = 0.4x + 420
x - 0.4x = 420
0.6x = 420
x = 420/0.6
x = 700
x = Total number of apples in the cart = 700
Lawrence started with 700 apples
i am thinking of a number.l take away 5. the result is 14 . what number did i think
Step-by-step explanation:
First sentence
Let the number be X
second sentence
X-5
Third sentence
X-5=14
X=19
The number is 19
Hi there!
»»————- ★ ————-««
I believe your answer is:
19
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\text{"I am thinking of a number. l take away 5. The result is 14."}\\\\\text{5 taken away from 'said number' would be 14.}\\\\\boxed{n-5=14}\\\\\\\boxed{\text{Solving for 'n'...}} \\\\\rightarrow n - 5 + 5 = 14 + 5\\\\\rightarrow \boxed{n = 19}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Identify the slope and y-intercept of the line with the given equation. Use the slope and y-intercept to graph the equation.
1. y= -2x+3
2. y= -4-x+1
3. y= -2
4. 3x+y= -1
5. 2x-3y=0
6. 5x-2y=-4
Answer:
1. -2, 3
2. 4, -1
3. 0, -2
4. -3, -1
5. 2/3, 0
6. 5/2, 4
Step-by-step explanation:
1) 18,27 – 9,756 =
2) 6 – 2,407 =
3) 18 – 5,432 =
4) 10 – 7,602 =
5) 13,013 – 12,5 =
6) 972,5 – 247,451 =
7) 83,12 – 90,2 + 12,3 =
8) 46,75 – 60,13 + 32,50 =
9) 254,0187 – 29,34682 =
10)1.015,568 – 123,712 =
no entiendo me ayudan
Answer:
1) -7929
2) -2401
3)-5414
4) -7592
5) 12888
6)-237726
7) 7287
8)-4588
9)-394495
10) 891856
3. What is the length of MA to the nearest tenth?
a) 0.1 cm
b) 3.5 cm
c) 17.0 cm
d) 7.7 cm
7.7cm
the rest is vastly (a and d) off or just enough off (can't be less then 5.2, because that's already the shortest side), to solve this by looking at it
Evaluate this expression when a=9
Answer:
63
Step-by-step explanation:
a=9
7a
7(9)
63
When Adam got a new locker at the gym, he had to choose a password. For this locker, a password consists of
4 non-repeated letters from A - Z. How many different passwords are there to choose from?
Given:
Adam's locker has a password that consists of 4 non-repeated letters from A - Z.
To find:
The number of different passwords.
Solution:
Total number of letters from A - Z is 26.
So, the number of selecting a letter for first place is 26.
The passwords consists non-repeated letters. So, the remaining numbers is [tex]26-1=25[/tex].
The number of selecting a letter for second place is 25.
Similarly,
The number of selecting a letter for third place is 24.
The number of selecting a letter for fourth place is 23.
The total number of possible different passwords is:
[tex]26\times 25\times 24\times 23=358800[/tex]
Therefore, the total number of different passwords is 358800.
Please help :)
Given AB intersects DE at point C.
Prove:
What is the missing reason in step 5?
•linear pair postulate
•given
•definition of complementary angles
•congruent complements theorem
The missing statement is linear pair postulate of intersecting lines
What are the angles formed by 2 intersecting lines?Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.
Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.
When lines intersect, two angle relationships are formed:
Opposite angles are congruent
Adjacent angles are supplementary
Given data ,
Let the lines be represented as l and m
where AB intersects DE at point C
Now , from the figure ,
∠BCA + ∠ECA = 180° ( angles on the straight line = 180° )
Therefore , ∠BCA + ∠ECA = supplementary and the postulate is linear pair
Hence , ∠BCA is supplementary to ∠ECA
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A) Determina el largo y el ancho de tres rectángulos de distintas formas que tienen el área de 24cm2.
Answer:
Para un rectángulo de largo L y ancho W, el área se define como:
A = L*W
Ahora sabemos que nuestro rectángulo tiene un área de 24cm^2
Entonces queremos encontrar 3 pares de valores L y W tal que:
L*W = 24cm
Esto es bastante trivial, podemos simplemente definir una de las dos variables, y así encontrar el valor de la otra.
Por ejemplo, si definimos L = 1cm
tenemos:
(1cm)*W = 24cm^2
W = (24cm^2)/(1cm) = 24cm
Entonces un posible rectángulo tiene un largo de 1cm y un ancho de 24cm
Si tomamos L = 3cm tenemos:
(3cm)*W = 24cm^2
W = (24cm^2)/(3cm) = 8cm
Un rectángulo con 8cm de ancho y 3cm de largo es otra opción.
Si tomamos L = 4cm tenemos:
(4cm)*W = 24cm^2
W = (24cm^2)/(4cm) = 6cm
Un rectángulo con 6cm de ancho y 4cm de largo también es un posible rectángulo.
Así, los 3 rectangulos que se piden pueden ser:
1) largo 1 cm, ancho 24cm
2) largo 3cm, ancho 8cm
3) largo 4cm, ancho 6cm
Aubrey is making dumplings. If she uses \tfrac{4}{5} 5 4 cup of dough for each dumpling, how many cups of dough does Aubrey need to make 12 dumplings? Express your answer in simplest form.
Answer:
Number of cups of dough needed = 15 cups
Step-by-step explanation:
Cup of dough needed for each dumpling = 4/5 cup of dough
Total dumplings = 12
how many cups of dough does Aubrey need to make 12 dumplings?
Number of cups of dough needed = Total dumplings / Cup of dough needed for each dumpling
= 12 ÷ 4/5
= 12 × 5/4
= 60/4
= 15
Number of cups of dough needed = 15 cups
There are 5 more girls than boys in a class. The girls are 60 percent
a. How many pupils are in the class?
Answer:
25.
Step-by-step explanation:
Let the number of pupils be x, then:
there are 0.6x girls and 0.4x boys.
From the given information:
0.6x - 0.4x = 5
0.2x = 5
x = 5/0.2
= 50/2
= 25.
Log5 =0,699 find log 0,5
Answer:
-0.301
Step-by-step explanation:
Correct Question :-
If log 2 = 0.301 , find log 0.5
Solution :-
We are here given that the value of log 5 is 0.699 . Here the base of log is 10 .
[tex]\rm\implies log_{10}2= 0.301 [/tex]
And we are supposed to find out the value of log 0.5 . We can write it as ,
[tex]\rm\implies log_{10}(0.5) = log _{10}\bigg( \dfrac{5}{10}\bigg)[/tex]
Simplify ,
[tex]\rm\implies log _{10}\bigg( \dfrac{1}{2}\bigg)[/tex]
This can be written as ,
[tex]\rm\implies log_{10} ( 2^{-1})[/tex]
Use property of log ,
[tex]\rm\implies -1 \times log_{10}2 [/tex]
Put the value of log 2 ,
[tex]\rm\implies -1 \times 0.301 =\boxed{\blue{-0.301}} [/tex]
Hence the value of log (0.5) is -0.301 .
*Note -
Here here there was no use of log 5 in the calculation .
HELPPPPP ME OUUTTTTTTT!!!!
Answer:
20 degrees
Step-by-step explanation:
we can consider 33 to be the radius of a circle.
31 would then be the cos of the angle in that circle.
the regular cos function is defined for the standard circle with radius 1. so, that would be multiplied by 33 for this circle here.
31 = cos(?) × 33
cos(?) = 31/33 = 0.9393...
? = 20.05 ≈ 20 degrees
Consider the function given by the graph. What are
these values?
f(-2) =
f(0) =
f(4) =
Answer:
the values of it is the first one. meaning: f(-2)
Answer:
Step-by-step explanation:
2
3
-1
Instructions Solve for x ?
Answer:
[tex]2x = \frac{1}{2} \times 20 = 10 \\ = > x = 5[/tex]