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
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what is the number whose 10% is 12?
Answer:
120
Step-by-step explanation:
10%=12
20%=12x2
100%=12x10
=120
Answer:
Let the number be x.
Compute 10% of x and equate it to 12 to compute the value of x as follows:
[tex]x[/tex] x [tex]\frac{10}{100} = 12[/tex]
[tex]x[/tex] = 12 x [tex]\frac{100}{10}[/tex]
[tex]x[/tex] = 120
Thus, the number is 120.
Please helpppp!!!!!!!!!!
The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:
f(x) = (x + 1)² + 2
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the function is:
f(x) = x² + 2x + 3
Completing the squares, we find the equation in vertex form, as follows:
f(x) = (x + 1)² + 2
As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.
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On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
A restaurant uses 80 pounds of potatoes per week. The restaurant owner buys the potatoes in 10-pound bags from a local farmer. How many bags will the owner need to buy this week?
Answer:
1. santina drove 14 more miles than carole
2. the owner will need to buy 8 bags this week
Step-by-step explanation:
1. 203-189= 14
2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds
1. 14
2. 8
3. 48
4. 318
5. 23
6. 4
7. a) 10 b) 60 c) 8 d) 107
8. $1,532
9. 1
10. $15.50
11. .95
Step-by-step explanation:
What is the average of the following numbers?
2, 5, 8, 1
Answer:
average of the no. = sum of all no. / no. of terms
= 2 + 5 + 8 + 1 / 4
= 16/4
= 4
4 is the answer
Write an expression that contains atleast two terms and is in simplest form
Answer: x-1
Step-by-step explanation:
perform the following operation.
-49 - +65 =
Answer:
Step-by-step explanation:-49 - + 65= ?, 65-49 = 16 , so we take 65-49 as normal which is = 16 but it's -16,cuz we were given negative45
Suppose that x and y vary inversely. Write a function that models each inverse
variation.
x = -13 when y = 100
EE ⁹⁹ 흐흐흐≡
Q√ C
Since the product of variables in inverse proportion is constant, the equation is [tex]\boxed{xy=-1300}[/tex]
Find the sum of the first six terms in the sequence {1, 5, 9, 13, …}
Answer:
66
Step-by-step explanation:
The sequence you provided seems to be arithmetic as it increases as 4 each term. Assuming 1 is the first term the equation would be [tex]a_{n}=1 + 4(n-1)[/tex]. You could just take the first 6 terms and add them together since you already have 4 values calculated and you could calculate the other 2 by adding 4. This would give you
(1 + 5 + 9 + 13 + 17 + 21) = 66
But there's an easier way to do it. You could use the formula [tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]. You can calculate [tex]S_6[/tex] by plugging in those values. You would need to calculate [tex]a_6[/tex] before hand, but you can calculate that using the formula I defined above. Which in general is [tex]a_n = a_1 + d(n-1)[/tex] where d is like the slope, or how much it changes each term. So if you calculate [tex]a_6[/tex] you'll get [tex]1+4(6-1) = 1+4(5) = 21[/tex]. Now plug this into the series formula above and you get [tex]S_6 = \frac{6(1+21)}{2}=\frac{6(22)}{2}=\frac{132}{2}=66[/tex] which is exactly what you get if you add the first 6 terms as shown above when you do it manually.
[tex]\text{First let's find two more terms, because we have only six. We can do that by}\\\text{adding 4:: 13+4=17; 17+4=21}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now we just add the terms: 1+5+9+13+17+21}[/tex]
[tex]\rule{300}{1.7}\\\text{66}[/tex]
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 8% each week. The following function represents the weekly weed growth: f(x) = 86(1.08)x. Rewrite the function to show how quickly the weeds grow each day.f(x) = 86(1.08)7x; grows approximately at a rate of 5.6% daily
f(x) = 86(1.087)x; grows approximately at a rate of 0.56% daily
f(x) = 86(1.01)x; grows approximately at a rate of 0.1% daily
Feedback for this selection: Don't forget to multiply the power by 7.
f(x) = 86(1.01)7x; grows approximately at a rate of 1% daily
please explain how you got the answer!
The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
The following function represents the weekly weed growth:
f(x) = 86(1.08)x.
we'll represent the growth function by day g(x). If x is to represent days, then x/7 represents weeks.
We can write,
g(x) = f(x/7) = 86·1.08^(x/7)
g(x) = 86·(1.08^(1/7))^x
g(x) = 86·1.011055^x
The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.
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In pqr the measure of r=90 qp=65 rq=33 and pr=56 what ratio represents the sine of q
We can use sine ratio in given right angled triangle.
The sine of ∠Q is represented by ratio 48/73.
Given data:
∠R=90°,
QP = 73,
PR = 48,
RQ = 55
We know that;
The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.
Since, against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.
Thus, we have:
sin Q = PR/PQ
= 48/73
Thus, the sine of ∠Q is represented by ratio,
48/73.
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(10^4)^4 as an expression (simplified)
[tex](10^4)^4[/tex]
[tex]10^8[/tex]
Therefore in simplified form [tex](10^4)^4[/tex] is [tex]10^8[/tex]
Need help with the following question
what is -36 degrees converted
to radians
Answer:
Answer: 0.628 radian
Step-by-step explanation:
how to convert from degrees to radians?
Answer:To convert the value of the angle in degree, to its equivalent radians, we need to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.
Answer:
See below
Step-by-step explanation:
- 36 * PI / 180 = -pi/5 radians = - .6283 R
Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( 20 , 6 ) b. If an American is randomly chosen, find the probability that this American will receive no more than 24 Christmas cards this year. 0.7486 c. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year. d. 66% of all Americans receive at most how many Christmas cards? (Please enter a whole number)
The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
Probabilitya. Distribution
X ~ N (20 , 6)
b. P(x ≤24)
= P[(x - μ ) / σ (24 - 20) / 6]
= P(z ≤0.67)
= 0.74857
=0.7486
Hence:
Probability = 0.7486
c. P(21 < x < 26)
= P[(21 - 26)/ 6) < (x - μ ) / σ < (24 - 20) / 6) ]
= P(-0.83 < z < 0.67)
= P(z < 0.67) - P(z < -0.)
= 0.74857- 0.2033
= 0.54527
Hence:
Probability =0.54527
d. Using standard normal table ,
P(Z < z) = 66%
P(Z < 0.50) = 0.66
z = 0.50
Using z-score formula,
x = z× σ + μ
x = 0.50 × 6 + 20 = 23
23 Christmas cards
Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
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Jeff and Kirk can build a 75-ft retaining wall together in 4 hours. Because Jeff has more experience, he could build the wall by himself 1 hour quicker than Kirk. How long would it take Kirk (to the nearest minute) to build the wall by himself?
Answer:
8 hours 32 minutes
Step-by-step explanation:
Working together, the construction rates add. We can use the given relation to write an equation for the total time when the pair work together.
__
setupLet k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...
1/k +1/(k -1) = 1/4
__
solutionMultiplying by 4k(k-1), we have ...
4(k-1) +4k = k(k -1)
k² -9k = -4 . . . . . . . . subtract 8k and simplify
k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square
k -4.5 = √16.25 . . . . . . . . . take the square root
k = 4.5 +√16.25 ≈ 8.531129 . . . hours
The fractional hour is ...
0.531129 × 60 min ≈ 31.9 min ≈ 32 min
It would take Kirk about 8 hours 32 minutes to build the wall by himself.
_____
Additional comment
For most "working together" problems the rates of completing work need to be expressed in jobs per unit time. Usually, the rates are given in terms of time per job, as they are here. That is why reciprocals get involved.
It will take Kirk about 8 hours 32 minutes to build the wall by himself.
What is Quadratic Polynomial?Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.
Here, Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...
1/k +1/(k -1) = 1/4
Multiplying by 4k(k-1), we have ...
4(k-1) +4k = k(k -1)
k² -9k = -4 . . . . . . . . subtract 8k and simplify
k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square
k -4.5 = √16.25 . . . . . . . . . take the square root
k = 4.5 +√16.25 ≈ 8.531129 . . . hours
The fractional hour is ...
0.531129 × 60 min ≈ 31.9 min ≈ 32 min
Thus, It will take Kirk about 8 hours 32 minutes to build the wall by himself.
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Find the volume of a cone that has a diameter of 7 and a height of 8.
98/3 Pi
448/3 Pi
131 Pi
24 Pi
Lesson Posttes
Which of the following composition of transformations would create an image that is congruent to its original
image?
A translation 2 units to the left followed by dilation by 1/2.
The correct option is (B).
What is congruency?It states that that two triangles are said to be congruent if they are copies of each other and when superposed, they cover each other exactly.
The complete question is:
Which of the following composition of transformations would create an
image that is not congruent to its original image?
A rotation of 45° followed by a reflection across the x-axis
A translation 2 units to the left followed by dilation by 1/2
A reflection across the y-axis followed by a rotation of 60°
A rotation of 135º followed by a translation of 4 units to the right.
After a translation of 2 units to the left followed by dilation by 1/2 the image will not be congruent to its original image.
All other options are reflection and rotation, which not fit into the situation.
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find the perimeter.
D. 9.5 cm
To find the perimeter you need to add all the sides.
2.1 + 2.1 + 1 + 3.3 + 1 = 9.5
Prepare the journal entry to record each of the following four separate insurances of stock a. corporation issue 4000 share of 5$ par value common stock for 35000 cash
The preparation of the journal entry to record the accounting transaction can be seen in the table below.
How do you prepare a journal entry to record an account?Initially, when preparing a journal, you have to read the transaction carefully and comprehend it. Discover which accounts need to be credited and debited before entering a journal entry.
From the given information:
The common stock par value = no of shares × par value of shares
The common stock par value = 4000 shares × $5/ share
The common stock par value = $20000
However, the amount paid in capital excess of the par value for the common stock is:
= $35000 - $20000
= $15000
Therefore, the Journal entry can be computed as follows:
Date Account Title Post Ref Debit ($) Credit ($)
Cash 35,000
Paid-in capital in excess of par
value, common stock 20,000
(To record the insurance of common stock)
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Eugene and Shanice each improved their yards by planting sod and geraniums. They bought their supplies from the
same store. Eugene spent $36 on 9 ft² of sod (s) and 2 geraniums (g). Shanice spent $63 on 9 ft² of sod and 5
geraniums. What is the solution to the system of equations? What is the cost of one ft² of sod and the cost of one
geranium?
The cost of one ft² of sod is $2 and the cost of one geranium is $9.
What are the linear equations that represent the question?9s + 2g = 36 equation 1
9s + 5g = 63 equation 2
What is the cost of one feet of sod and geranium?
Subtract equation 1 from equation 2:
3g = 27
g = 27 / 3
g = $9
Substitute for g in equation 1
9s + (2 x 9) = 36
9s + 18 = 36
9s = 36 - 18
9s = 18
s = 18 / 9
s = $2
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Factor out the GCF from the polynomial.
r(2²-24) + (2²-24)
Answer: -20
Step-by-step explanation: i hope its right
solve for a
(log(a-6)^2 =log10
Answer:
It is 98. Just look down for the explanation↓:
Step-by-step explanation:
Log 10 (x + 2) = 2
So, the Inverse log is:
10^2 = x + 2
100 = x + 2
98 = x
1
..S
4 in.
Find h.
10 in.
h = √[?] in.
Answer:
√96
Step-by-step explanation:
halve the diameter to set up the pythagorean theorem
2²+b²=10²
4+b²=100
-4 on each side
b²=96
square root each side
b=√96
it could the be further simplified to 4√6
Point T is at (–16.8, 31.7) and point M is at (1.2, 12.5). Point M is the midpoint of the line segment whose endpoints are S and T. What are the coordinates of endpoint S? (–34.8, 50.9) (–7.8, 22.1) (19.2, –6.7) (20.4, –5.5)
Answer:
option c (19.2, -6.7) is correct
Step-by-step explanation:
Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.
if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is
given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]
according to question :
given : end point T(-16.8, 31.7) and mid point M(1.2, 12.5)
let coordinates of another end point S (a, b)
therefore, using mid point formula
1.2 = (-16.8 + a)/2
2.4= (-16.8 + a)
19.2 = a
and,
12.5 = (31.7 + b)/2
25 = 31.7 + b
-6.7 = b
so the option c (19.2, -6.7) is the correct answer
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Please help! Solve the equation on the interval [0,2pi)
Answer:
[tex]\frac{5pi}{6}[/tex]
Step-by-step explanation:
Answer:
[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]
Therefore, the value of x in the interval [0, 2π) is:
[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]
Value of x or y so that the line through the points has the given slope:
(X,9) and (9,-3), slope is -6/7
Sorry if it’s not worded great.
If we want the slope to be -6/7, then the value of x must be -5.
How to find the value of x?Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:
[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]
Where on the second line we multiplied and divided the right fraction by 2.
Comparing the fractions, we see that we must have:
9 -x = 14
9 - 14 = x
-5 = x
So the value of x must be -5.
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Brainliest to who answers :>
Answer:
L is not valid.
Step-by-step explanation:
For any triangle, the sum of the two legs must be greater than the hypotenuse. Otherwise the two legs would not be long enough to touch.
Answer:
L
Step-by-step explanation:
to add to the previous basically correct answer :
for a triangle the sum of any 2 sides must be greater than the third side (not just legs and Hypotenuse).
for all other options any combination of sum of 2 sides being bigger than the third side works.
but for L
2 + 5 = 7, which is smaller than the third side (8). so, this cannot be a triangle.
How do you classify the following polynomial?
-4x³ + 2x² - 5x+3x²
Answer:
-4 x³+2x²-5x+3x²
combine like terms
-4x³ +5x²-5x
common factors
-1(4x³-5x²+5x)
find one factors
Ans: -x (4x²-5x+5)
which matrix equation has the soul ut ion X
Step-by-step explanation:
option 2 is correct
here the question ask for value of X
to find it we multiple the matrix X with the given matrix in question and equate the answer.
Piece Wise function Math...help!
The Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.
What is a function?A function is a type of relation, or rule, that maps one input to a specific single output.
Given
Base salary = $2500 per month
Commision = 3% on Sales over 48000
Determine the function s(x) for sales over $48000
Let's Represent the total sales in a month with s.
So, the function s(x) is:
s(x) = Base Amount + Commission x Sales over $48000
s(x) = 2500 + 3% (s - 48000)
s(x) = 2500 + 0.03(s - 48000)
s(x) = 2500 + 0.03s - 1440
s(x) = 0.03s - 1060
Hence, the Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.
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