Using the z-distribution, as we have the standard deviation for the population, it is found that the 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.90[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
Researching on the internet, the other parameters are given by:
[tex]\overline{x} = 6.16, \sigma = 1.3, n = 14[/tex]
Hence:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 6.16 - 1.645\frac{1.3}{\sqrt{14}} = 5.59[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 6.16 + 1.645\frac{1.3}{\sqrt{14}} = 6.73[/tex]
The 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).
More can be learned about the z-distribution at https://brainly.com/question/25890103
The magnitude of vector λ a is 5. Find the possible values of λ, if a=(5,12). Brainliest for correct answer. Look at photo.
Step-by-step explanation:
this is the answer for you
8) Evaluate this expression.
7.4 - (-3.7)
A) -3.7
B) 8.4
C) 11.1
D) 13.21
Answer:
C) 11.1
Step-by-step explanation:
7.4 -(-3.7)
- and - make +
7.4 + 3.7 = 11.1
Need help with this geometric question ASAP, Thank you
Help please in picture below
Answer:
vertex is a point where two sides meet
fx=x^2-2x+8
I need some help with this math problem if you can give me the process
Answer:
x³/3 - x² + C
Step-by-step explanation:
∫ x² - 2x + 8 dx
= x³/3 - x² + C
when finding the derivative, you need to take the power plus 1 then divide by the power x^(2+1)/(2+1) = x³/3
the same goes for 2x and the 2/2 is 1 so you would get x²
since you are finding the derivative for x and 8 is a constant it equals zero.
when integrating you always need to add C at the end and C stands for a constant. The only time you do not add C is when the integral goes from one constant to the next.
Example: [tex]\int\limits^1_0 {x^2 - 3x +9} \, dx[/tex] like this...
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
URGENT I NEED IT NOW PLEASE HELP ME!!!!
Brian buys a lawn ornament priced at $78. Shipping and handing are an additional 5% of the price. How much shipping and handing will Brain pay?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 78}}{\left( \cfrac{5}{100} \right)78}\implies 3.9[/tex]
Rosa invests $1100 in one account and $1300 in an account paying 3 % higher interest. At the end of one year she had earned $255 in interest. At what rates did she invest?
$1100 invested at __%
$1300 invested at __%
Answer:
$1100 at 9%$1300 at 12%Step-by-step explanation:
The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.
Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...
1100x +1300(x+0.03) = 255
2400x +39 = 255 . . . simplify
2400x = 216 . . . . . . subtract 39
x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x
Rosa invested $1100 at 9%, and $1300 at 12%.
Please Help I have tried and can not get the correct answer
Find the x- and y-intercepts of the graph of the function f(x) = -4|x+1| +8
Enter your answers as points, (a,b)
Enter the x-intercepts in order of increasing x-value. if there are no x-intercepts, enter NA in both answer areas
x-intercepts: __________
__________
y-intercepts ___________
Answer:
(-3, 0) and (1, 0)
(0, 4)
Step-by-step explanation:
x-intercept is the point where y = 0.
y-intercept is the point where x = 0.
or points ...
f(x) = y = -4×|x + 1| + 8
let's start with the y-intercept (x = 0)
y = -4×1 + 8 = -4 + 8 = 4
the y-intercept point (only 1 point) is (0, 4).
for x = 0 the absolute value function contains 0+1. and that is always +1.
the x-intercept(s) :
0 = -4×|x + 1| + 8 (dividing by -4)
0 = |x + 1| - 2
|x + 1| = 2
because of the absolute value we have 2 possibilities :
+(x + 1) = 2
x + 1 = 2
x = 1
and
-(x + 1) = 2
-x - 1 = 2
-x = 3
x = -3
so the points of x-intercept are (-3, 0) and (1, 0)
the formula P=F/A,where P=pressure,F=force,andA=area,is used to caculate pressure.solve this formula for F
[tex]P= \dfrac FA \implies F = PA[/tex]
Find the area for all of them. Pleaseee help me I don’t understand.
Answer:
Step-by-step explanation:
top = 120sq m
middle = 17sq cm
bottom = 102 sq feet
Solve the following inequalities if it is known that function f is increasing on its domain f(4x-3)≥f(2-x^2), Df=(-8,4)
Solve the following inequalities if it is known that function f is decreasing on its domain f(5-x^2)≥f(3x-5), Df=(-∞,4)
The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions
The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
How to solve the inequalities?Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)
The function increases at (-8,4).
So, we have:
4x - 3 ≥ 2 - x^2
Rewrite as:
x^2 + 4x - 2 - 3 ≥ 0
Evaluate the like terms
x^2 + 4x - 5 ≥ 0
Expand
x^2 + 5x - x - 5 ≥ 0
Factorize the expression
x(x + 5) - 1(x + 5) ≥ 0
Factor out x + 5
(x - 1)(x + 5) ≥ 0
Solve for x
x ≥ 1 or x ≥ -5
Rewrite as:
-5 ≤ x ≤ 1
Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)
The function decreases at (-∞,4).
So, we have:
5 - x^2 ≥ 3x - 5
Rewrite as:
x^2 + 3x - 5 - 5 ≤ 0
Evaluate the like terms
x^2 + 3x - 10 ≤ 0
Expand
x^2 + 5x - 2x - 10 ≤ 0
Factorize the expression
x(x + 5) - 2(x + 5) ≤ 0
Factor out x + 5
(x - 2)(x + 5) ≤ 0
Solve for x
x ≤ 2 or x ≤ -5
Rewrite as:
-5 ≤ x ≤ 2
Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
Read more about inequalities at:
https://brainly.com/question/11234618
Can someone help me with this please
Answer:
6.46 seconds
Step-by-step explanation:
[tex] - 16 {t}^{2} + 65t + 248 = 0[/tex]
[tex]t = 6.46[/tex]
Write this ratio as a fraction in simplest form without any units six weeks to 18 days
Answer:
7/3
Step-by-step explanation:
To write the ratio with no units. we need to have both parts of the ratio in the same units. That way the units cancel.
__
6 weeks : 18 days = (6×7) days : (6×3) days = 7 : 3
The ratio as a fraction is ...
(6 weeks)/(18 days) = 7/3
[tex] \rm \int_{0}^{ \pi } \cos( \cot(x) - \tan(x)) \: dx \\ [/tex]
Replace x with π/2 - x to get the equivalent integral
[tex]\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]
but the integrand is even, so this is really just
[tex]\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]
Substitute x = 1/2 arccot(u/2), which transforms the integral to
[tex]\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du[/tex]
There are lots of ways to compute this. What I did was to consider the complex contour integral
[tex]\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz[/tex]
where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be
[tex]\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}[/tex]
which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit
[tex]\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}[/tex]
and it follows that
[tex]\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}[/tex]
It has been found that 50.3% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 171 owned some type of stock. At what level of significance in a two- tailed test would you conclude that this was a significant difference
Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.
What are the hypothesis test?At the null hypothesis, we test if the proportion is of 50.3%, hence:
[tex]H_0: p = 0.503[/tex]
We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:
[tex]H_1: p \neq 0.503[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In this problem, the parameters are:
[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]
[tex]z = 2.32[/tex]
What is the p-value?Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.
More can be learned about the z-distribution at https://brainly.com/question/26454209
how many 5 seater taxis do you need for78 people
Step-by-step explanation:
Answer: 78 /5 = 15.6 = 16 taxis. Step-by-step explanation: I HOPE THIS WILL HELP YOU AND MARK IT AS BRAINLIEST ANSWER PLEASE.
Donte is making brownies. For one batch, the recipe requires 1 5/6 cups of chocolate chips, and 1/6 cup of sugar. What is the combined amount, in cups, of chocolate chips and sugar that is used in one batch of brownies?
Answer:
2
Step-by-step explanation:
1 ⅚ + ⅙ = 1 6/6, also known as, 2
Adding and subtracting I need it right now the answer
Answer:
Just give me the questions and ill do it
Step-by-step explanation:
a right triangle with a long leg (x+7) and a short leg with (x) and the hypothenuse is 13
Answer:
Area is 30cm^2 if thats what your asking
Step-by-step explanation:
Answer:
X = 5
Step-by-step explanation:
You need to use the Pythagorean theory to solve this question.
[tex] {13}^{2} = {x}^{2} + {(x + 7)}^{2} [/tex]
[tex]169 = {x}^{2} + ( {x}^{2} + 14x + 49)[/tex]
[tex]169 = 2 {x}^{2} + 14x + 49[/tex]
[tex]0 = 2 {x}^{2} + 14x + 49 - 169[/tex]
[tex]0 = 2 {x}^{2} + 14x - 120[/tex]
Now simply the equation by dividing everything by 2.
[tex]0 = {x}^{2} + 7x - 60[/tex]
[tex]0 = (x - 5)(x + 12)[/tex]
Now, you can find the possible solutions by setting each bracket to 0.
[tex]0 = x - 5[/tex]
[tex]5 = x[/tex]
OR
[tex]0 = x + 12[/tex]
[tex] - 12 = x[/tex]
However, a measurement on a triangle cannot be negative. Therefore, we can ignore -12 and say that the answer is x = 5.
Without dividing,
how can you tell if the quotient for
5,873 = 8 is greater than 700? Explain
whether the quotient is less than 800.
Answer:
The quotient is between 700 and 800Step-by-step explanation:
Prove by multiplication
700*8 = 5600 < 5873Similarly
800*8 = 6400 > 5873So the expression is 5873/8
Now
We can prove the given statement to multiplication
Multiply with 8
700×85600And
800×86400Yes
We see 5873 lies between 5600 and 6400 hence the quotient is greater than 700 but less than 800
A cuple travels 420 miles to dr0p their dughter off at summer camp. The trip back has a short cut and is only 360 miles. And the gas mileage is 50% better
due to a lighter load. Write an expression for the total gas used and simplify.
The expression for the simplified total gas used is 1.43x.
How to write the expression of the total gaslet the gas used on the way to camp "x"
Then the gas used on the way back can be calculated as follows:
360 / 420 × 0.5 × x
To calculate the total fuel used, We need to add this to the 'x' used on the way.
Therefore,
total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x
learn more on expression here: https://brainly.com/question/1462980
Which function grows at the fastest rate for increasing values of x?
g(x) = 10x + 15
f(x) = 2•3^x
h(x) = 5x^2 + x + 10
Answer:
The answer is g(x) = 10x + 15
Step-by-step explanation:
Given;g(x) = 10x + 15 f(x) = 2•3ˣ 5x² + x + 10To Find;function grows at the fastest rate for increasing values of x.Here, If we assume the value of x is 1 we get,
g(x) = 10x + 15
g(1) = 10(1) + 15
g(1) = 10 + 15
g(1) = 35
Here, We get the answer 35.
Now,
f(x) = 2•3ˣ
f(1) = 2•3¹
f(1) = 2•3
f(1) = 6
Here, We get the answer 6.
Now,
h(1) = 5x² + x + 10
h(1) = 5(1)² + 1 + 10
h(1) = + 5 + 1 + 10
h(1) = + 16
Thus, The answer is g(x) = 10x + 15.
-TheUnknownScientist 72
How do I solve for y?
Answer:
Step-by-step explanation:
The angle containing y and 63 are vertically opposite. They are equal.
y + 23 = 63 Subtract 23 from both sides
y +23-23 = 63 - 23
Answer y = 40
when a square's side is two units long,its perimiter is eight units
Answer:
Yes
Step-by-step explanation:
Because it has 4 sides and 4 x 2 = 8
HELP 50pts!!!
Ivanna drove 225 miles using 10 gallons of gas. At this rate , how many gallons of gas would she need to drive 441 miles ?
____ gallons
19.6 gallons
Explanation:
225 miles → 10 gallons1 miles → (10/225) gallons441 miles → [ (10/225)*441 ] gallons441 miles → 19.6 gallonsLeslie’s puppy has 4 toys. Her cat has 36 toys.How many times more toys does the cat have than the puppy?
A.6
B.7
C8
D.9
The statement "7 is 21 less than 28" is interpreted 7 = 21 - 28.
it's interpreted as 28 - 21 = 7
Solve the system using elimination.
2x – 2y = –8
x + 2y = –1
(–3, 1)
(–14, 1)
(0, 4)
(1, 5)
Answer:
(- 3, 1 )
Step-by-step explanation:
2x - 2y = - 8 → (1)
x + 2y = - 1 → (2)
adding the 2 equations term by term will eliminate y
3x + 0 = - 9
3x = - 9 ( divide both sides by 3 )
x = - 3
substitute x = - 3 into either of the 2 equations and solve for y
substituting into (2)
- 3 + 2y = - 1 ( add 3 to both sides )
2y = 2 ( divide both sides by 2 )
y = 1
solution is (- 3, 1 )
Answer:
(–3, 1)
Step-by-step explanation:
Step 1: Solve for x
2x – 2y = –8 -----------(1)
x + 2y = –1. -------------(2)
Add equation 1 to 2⇒2x + x| -2y + 2y |= -8 -1
⇒3x = -9
Divide both side by the coefficient of x⇒3x/3 = -9/3
⇒x = -3
Step 2; Solve for y
Substitute into equation 2x + 2y = –1
(-3) + 2y = -1
Add 3 from both sides-3 + 2y + 3 = -1 + 3
2y = 2
divide both side by two2y/2 = 2/2
y = 1
So, ( x,y) ⇒(-3,1)
Solve the equation X=
Step-by-step explanation:
I think the answer is x=70