The confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41 where the lower limit is 97.59 and the upper limit is 102.41
How to determine the confidence interval?We have:
Mean = 100
Sample size = 80
Standard deviation = 11
At 95% confidence interval, the critical z value is:
z = 1.96
The confidence interval is then calculated as:
[tex]CI = \bar x \pm z \frac{\sigma}{\sqrt n}[/tex]
So, we have:
[tex]CI = 100 \pm 1.96 \frac{11}{\sqrt {80}}[/tex]
Evaluate the product
[tex]CI = 100 \pm \frac{21.56}{\sqrt {80}}[/tex]
Divide
[tex]CI = 100 \pm 2.41[/tex]
Split
CI = (100 - 2.41,100 + 2.41)
Evaluate
CI = (97.59,102.41)
Hence, the confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41
Read more about confidence interval at:
https://brainly.com/question/15712887
#SPJ1
Jacob invests a sum of money in a savings account with an interest rate of 9% compounded
continuously. After 6 years, the balance reaches $11,303.34. What was the amount of the initial
investment?
Answer:
6587
Step-by-step explanation:
Formula is
A= P(1+r/n)^nt
A = 11303.34
r = .09
n = 365 compounded daily
t = 6 years
solve for P
jessica has 4/8 of a bottle of roitussun on hand the pharmacist instructs to reduce it by 1/2 how much robitussun does the pharmacist need to prepare the prescription
Answer:
1/4
Step-by-step explanation:
4/8 = 1/2
1/2 x 1/2 = 1/4
17. Your friend is betting on a game in which the probability of winning is 1 in 5. He has lost 5 games in a
row, so he says he will double his bet on the next game. What do you tell your friend?
The only problem is you may also go bankrupt before you're able to double your bet enough times.
If the game's events are independent, similar to flipping a coin, then the probability never changes, it's still a 1 out of 5 chance of winning each time.
The coin has no memory, so it will always have the same probability on each flip.
If the games' events are like that, a losing streak doesn't mean a win is now more likely.
But if the events are not independent, it may make sense to increase the bet.
for example, a bag has 10 coins and 2 are worth 100. You reach in and pull out 5 coins, all worth only a penny each.
What is the probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Your odds of getting one of the 2 $100 coins is now much greater than the original 1 out of 5 chance.
You originally had a 2 out of 10 chance on the first draw. But now it's up to 2 out of the remaining 5 or 40% chance of winning.
There is another reason someone may wish to double their bet. If you doubled your bet each time you lost, you would eventually recoup all your losses. It can work.
The only problem is you may also go bankrupt before you're able to double your bet enough times.
That risk is usually considered too great to double your bets on independent events.
To learn more about the probability visit:
https://brainly.com/question/24756209
#SPJ1
Andres rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase
describes the probability that he will roll a number greater than or equal to 1?
I don't know what the word or phrase is, but with the parameters you've given, 100%
What are the intercepts of graphed function.
Answer:
x-intercept is (-1,0)
y-intercept is (0,-3)
Step-by-step explanation:
An intercept is where the graph crosses the axis.
Here the graph crosses the x-axis (numbered horizontal line that goes left and right) at the point (-1,0)
The graph crosses the y-axis (numbered vertical line that goes up and down) at the point (0,-3). These are what are called intercepts.
in a club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different possibilities are there?
The method for calculating how many arrangements are feasible when only a few items are chosen from a collection of items that are unique is as follows:
[tex]^nC_k=\frac{n!}{k!(n-k)!}[/tex]
Where:
n – the sum of all the elements of a set
k – the number of selected objects (the order of the object may change)
! – factorial
For instance, 3!=1×2×3
So, according to the problem, there are [tex]^7C_3[/tex] possible groups of 3 women out of 7 women. And [tex]^5C_2[/tex] possible groups of 2 men out of 5 men.
Combining we get that there are [tex]^7C_3 ~^5C2[/tex] groups of 3 women and 2 men out of 7 women and 5 men.
Therefore, there are [tex]^7C_3 ~^5C2=\frac{7!}{3!4!}\frac{5!}{2!3!}= 350[/tex] possibilities.
Learn more about combinations here-
brainly.com/question/13387529
#SPJ10
Tim earns 96pounds for 16 hours. Tim earns 'time and a half' for overtime. he works 4 hours of overtime in addition to his normal 16 hours. how much does he earn altogether
find hourly rate:
96 / 16 = 6 pounds per hour
6 x 1.5 = 9 pounds per hour for overtime.
9 x 4 = 36 pounds
96 + 36 = 132 pounds total
Suppose a population parameter is 0.8, and many large samples are taken
from the population. If the sample proportions are normally distributed, with
95% of the sample proportions falling between 0.684 and 0.916, what is the
standard deviation of the sample proportions?
Using the Empirical Rule, it is found that standard deviation of the sample proportions is of 0.058.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.0.684 and 0.916 is within 2 standard deviations of the mean(below and above), hence there are 4 standard deviations between these measures, so:
4s = (0.916 - 0.684)
s = (0.916 - 0.684)/4
s = 0.058.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
#SPJ1
Given the following equation of a circle in general form, find the equation in standard form by completing the square.
4x² + 8x + 4y² + 32y +52 = 0
Provide your answer below:
The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have an equation that represents the circle:
4x² + 8x + 4y² + 32y +52 = 0
Divide by 4 on both the sides:
x² + 2x + y² + 8y + 13 = 0
x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0
x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13
(x + 1)² + (y + 4)² = 4
(x + 1)² + (y + 4)² = 2²
Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
Plot the complex number and find its absolute value 2−i
The absolute value of the complex number is √2. The graph is plotted and attached.
What is the complex number?A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The given complex number as;
2−i
The absolute value is found as;
[tex]\rm R = \sqrt{1^2 +(-1)^2 } \\\\ R = \sqrt 2[/tex]
The graph for the complex number is attached.
Hence the absolute value of the complex number is √2.
To learn more about the complex number, refer to the link;
https://brainly.com/question/10251853
#SPJ1
How to translate a graph of y= absolute value of x to obtain the graph of y= absolute value of x-6
Answer: Translate the graph of y=|x| 6 units to the right.
Determine the distance between two points. (9,-9) and (-6,-7)
A shop advertises a 24% off sale. The coat sold for $258 fins the decrease in price and the sale price
Answer:
339.47
Step-by-step explanation:
100 - 24 = 76
258 = 76 percent
3.39473684211 = 1 percent
339.47 = 100 percent
Answer:
The decrease in price is $61.92
The sale price is $196.08
Step-by-step explanation:
24% × 258 = 61.92
258 decrease 24% =
258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08
Which expressions are equivalent to 9b?
Choose all answers that apply
A. b+2(b+2b)
B. 3b+b
C. 2(2b)
Answer:
A. b+2(b+2b)
b + 2b + 4b = 7b
B. 3b + b = 4b
C. 2(2b) = 4b
None of them are equal to 9b
Answer:
[tex]\fbox {None}[/tex]
Step-by-step explanation:
A
b + 2(b + 2b)b + 2(b) + 2(2b)b + 2b + 4b7bB
3b + b4bC
2(2b)4b1. EL precio a la venta de una impresora de inyección de tinta es de $285.000 incluida una Ganancia del 35%. ¿cuánto le cuesta a la tienda cada impresora?
Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.
¿Cómo encontrar el precio de una impresora sin ganancia?
En el enunciado tenemos el precio de una impresora para el consumidor, el cual comprende el dinero invertido por vendedor más la ganancia esperada. Este indicador observa la siguiente fórmula:
C' = C · (1 + r/100) (1)
Donde:
C - Coste asumido por el vendedor, en unidades monetarias.C' - Coste para el consumidor, en unidades monetarias.r - Tasa de ganancia, en porcentaje.Si sabemos que C' = $ 285.000 y r = 35 %, entonces el coste asumido por el vendedor es:
285.000 = 1,35 · C'
C' ≈ 211.111,11
Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.
Para aprender más sobre ganancias: https://brainly.com/question/8421949
#SPJ1
What is the result of M x H?????
I have asked 4 tutors and none of them know how to answer this.
Answer: m x H = [ -9 36 - 9/2 ]
Step-by-step explanation:
In the following month 10% savings on other costs are expected. What is the total other costs target for next month for the five locations
Answer:
The given question is incomplete. The graphs for the question are attached below.
Total savings on other costs expected in the following month is 13,950.
Total other costs targeted for next month for the five locations:
Washington Place = 14,850
Lincoln Square = 9,900
Millienium Concourse = 18,000
The old mill = 13,500
CWG Tenton = 0
Step-by-step explanation:
According to the graphs, there are two parts to this question
1. In the following month, 10% savings on other costs are expected.
The graph is attached below for reference
10% savings on other costs are expected in the following month:
=> (4,000 + 2,000 + 5,000 + 2,000 + 2,500) * (1-10%)
=> 15,500 * [tex](1-\frac{10}{100})[/tex]
=> 15,500 * [tex]\frac{90}{100}[/tex]
=> 13,950
Total savings on other costs expected in the following month is 13,950
2. Total other costs target for next month for the five locations are:
Washington Place = 6,000+3,000+3,500+ 4,000 = 16,500 * 0.9 = 14,850
Lincoln Square = 5,000+ 2,000+ 2,000+2,000= 11,000 * 0.9 = 9,900
Millienium Concourse =7,000+3,000+5,000+5,000= 20,000 * 0.9 = => 18,000
The old mill = 6,000+ 5,000+ 4,000=15,000 * 0.9 = 13,500
CWG Tenton = 0 * 0.9 = 0
Total other costs target for next month for the five locations:
Washington Place = 14,850
Lincoin Square = 9,900
Millienium Concourse = 18,000
The old mill = 13,500
CWG Tenton = 0
Read to know more about a similar question: https://brainly.com/question/16379147?referrer=searchResults
#SPJ10
*Will give 30pts*Consider function f. f(x)=2x^2.What is the value of (f•f)(x)?
Answer:
[tex]\textbf {B}[/tex]
Step-by-step explanation:
f(x) = 2x²
f [f(x)]
f [2x²] = 2(2x²)²
f[f(x)] = 2(4x⁴)
f[f(x)] = 8x⁴
Three out of every 20 students in ms. jones’ Math class earned a grade of A. What percent of the students earned a grade of A?
Answer:
15%
Step-by-step explanation:
3/20x100=15
If f(x) = |x| + 9 and g(x) = –6, which describes the range of (f + g)(x)?
(f + g(x)>3 for all values of x
(f + g)(x)<3 for all values of x
(f + g)(x)>6 for all values of x
(f + g)(x)<6 for all values of x
Answer: for all values of x
Step-by-step explanation:
[tex](f+g)(x)=|x|+9-6=|x|+3[/tex]
Since the range of y = |x| is [tex]y \geq 0[/tex], adding 3 to this shifts the graph 3 units up, giving us that [tex](f+g)(x) \geq 3[/tex] for all values of x.
What mistake did he make ?! I need everybody Anwser
Answer:
he subtracted the wrong coordinates to find the horizontal leg
Step-by-step explanation:
It should be 4-(-3) but he labeled 4-(-1)
A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h_The distance he has to walk is
Answer:
0.5km or 500m
Step-by-step explanation:
Given Distance = Speed x Time
In this case, we should use the difference in speed and time of the 2 scenarios.
Difference in Time = 20 mins(late) + 10 mins(early)
= 30 mins or 0.5 hour
Difference in Speed = 4km/h - 3km/h = 1km/h
Distance = 1km/h x 0.5 hr = 0.5km or 500m.
question is in the image below please help
Answer:
p= 80
Step-by-step explanation:
p+8 = 8 x 11
p+8 = 88
p= 88-8
p= 80
In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.
Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3.
To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and
∠DFE is 4 times greater than ∠GFH.
∠FHG is One-fourth the measure of ∠FED.
∠DFE is congruent to ∠GFH.
∠FHG is congruent to ∠EFD.
To prove that △DFE ~ △GFH by SAS similarity theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.The correct answer is option C.
The image of the triangle is attached with the answer below:-
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:
By comparing ΔDEF and ΔGFH
DF = DG + GF
= 12 + 4
DF = 16
Also,
EF = EH + HF
= 9 + 3
EF = 12
Comparing the sides of ΔDEF and ΔGFH, we have;
[tex]\dfrac{DF}{GF}[/tex] = [tex]\dfrac{EF}{HF}[/tex]
[tex]\dfrac{16}{4}=\dfrac{12}{3}[/tex]
4 = 4
Thus, the two triangles have similar sides.
Comparing the included angle <DFE and <GFH, then;
∠DFE is congruent to ∠GFH
Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;
[tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.
Learn more about congruency at
brainly.com/question/14418374
#SPJ1
Answer:
C
Step-by-step explanation:
Edg
Using a rounded version of a conversion ratio allows for a quick estimate of a unit conversion
using mental math or paper and pencil (no calculator or phone). Show an example of a unit cuz
conversion estimation using this strategy.
The conversion ratio that can be illustrated will be converting 2030m to kilometers.
How to illustrate the conversion?The unit conversion that can be illustrated based on the information can be convert 2030m to kilometers.
It should be noted that 1000 meters makes 1 kilometer. Therefore, rounding up 2030m mentally will be 2000m and the conversion to kilometers will be:
= 2000/1000
= 2 km
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
The graphs below have the same shapes. What is the equation for the red graph?
The equation for the red graph will be g(x) = x² + 3.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function f(x) is given below.
f(x) = x²
Then the function g(x) will be given as
g(x) = x² + 3
Then the equation for the red graph will be g(x) = x² + 3.
The missing graph is given below.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
The ratio of the number of laps Andy swam to the number of laps Ben swam
on the first day of a swimming lesson was 5: 6. The ratio of the number of
laps Andy swam to the number of laps Ben swam on the second day of the
swimming lesson was 9: 5. If Ben swam 33 laps on both days, how many laps
did Andy swim on the second day of the swimming lesson?
Answer:
10
Step-by-step explanation:
3(x-5)² +14(x-5)-24
Answer:
3x^{2} -16x-19
Step-by-step explanation:
If we are going to be simplying this problem, then we need to take it step by step.
Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.
Answer:
(3x - 19) • (x + 1)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((3•((x-5)2))+14•(x-5))-24
STEP
2
:
Equation at the end of step 2
(3 • (x - 5)2 + 14 • (x - 5)) - 24
STEP
3
:
Trying to factor by splitting the middle term
Factoring 3x2-16x-19
The first term is, 3x2 its coefficient is 3 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is -19
Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57
Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .
-57 + 1 = -56
-19 + 3 = -16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3
3x2 - 19x + 3x - 19
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-19)
Add up the last 2 terms, pulling out common factors :
1 • (3x-19)
Step-5 : Add up the four terms of step 4 :
(x+1) • (3x-19)
Which is the desired factorization
two sides and an angle are given below. determine whether the given information results in one triangle, two triangles, or no triangle at all. solve any resulting triangle(s). b = 8, c= 7, b = 170°
Answer:
A. single triangle. C = 8.74°, A = 1.26°, a = 1.01
Step-by-step explanation:
When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.
Law of SinesThe law of sines tells us the sides and angles have the relation ...
sin(A)/a = sin(B)/b = sin(C)/c
We can use this first to find angle C:
sin(C) = c/b·sin(B)
C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°
∠C ≈ 8.74°
Remaining measuresNow that we know two angles, we can find the third:
A = 180° -B -C = 180° -170° -8.74° = 1.26°
∠A = 1.26°
Using the law of sines again, we can find the measure of side 'a'.
a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346
The measure of segment 'a' is about 1.01 units.
__
Additional comment
If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.
The volume of a cubical box is
54.872 cm3. The length of the side of
the box is
(b) 3.6 cm
(c) 3.8 cm
(a) 3.4 cm
(d) 3.2 cm
The sides length of the cubical box is 3.8 cm if the volume of a cubical box is 54.872 cm³ option second is correct.
What is a cube?It is defined as three-dimensional geometry that has six square faces and eight vertices.
We have a volume of a cubical box is 54.872 cm³
V = 54.872 cm³
As we know the volume of the cube:
V = side³
54.872 = side³
Taking cube root on both sides:
side = 3.8 cm
Thus, the sides length of the cubical box is 3.8 cm if the volume of a cubical box is 54.872 cm³ option second is correct.
Learn more about the cube here:
brainly.com/question/15420947
#SPJ1
