Answer:
Yes.
Step-by-step explanation:
I don't really know how to explain this other than use a calculator.
Hope that this helps!
A Canadian study examined the pregnancy weight gain of underweight mothers, women who had been underweight before becoming pregnant. A Normal distribution with mean 36.6 lb and standard deviation 11.9 lb is a reasonable model for the distribution of pregnancy weight gains in this population.
a) Perform the appropriate computation and fill in the blank to complete this sentence in context: In this population, the first quartile of pregnancy weight gains is_____.
b) For underweight mothers, health organizations recommend a pregnancy weight gain between 27.5 lb and 39.5 lb. What is the probability that a randomly selected underweight mother in Canada would have a pregnancy weight gain in the recommended range?
Answer:
The correct answer is:
(a) 44.6 lb
(b) 0.371
Step-by-step explanation:
Given values are:
Mean,
[tex]\mu=36.6[/tex]
Standard deviation,
[tex]\sigma=11.9[/tex]
(a)
The z distance third quartile will be:
⇒ [tex]P(Z<0.674)=0.75[/tex]
[tex]z =0.674[/tex]
By using the z-score formula, we get
⇒ [tex]x=z\times \sigma+ \mu[/tex]
[tex]=0.674\times 11.9+36.6[/tex]
[tex]=44.62[/tex]
(b)
⇒ [tex]P(27.5<x<39.5) = P[{\frac{(27.5-36.6)}{11.9} <\frac{(x-\mu)}{\sigma} <\frac{(39.5-36.6)}{11.9} }][/tex]
[tex]=P(-0.76<z<0.24)[/tex]
[tex]=P(z<0.24)-P(z<-0.76)[/tex]
By using the z table, we get
[tex]=0.5948-0.2236[/tex]
[tex]=0.371[/tex]
Let W be part of the solid sphere of radius 4, centered at the origin, that lies above the plane z = 2. Set up an integral in cylindrical coordinates to find the volume of the region. Do NOT actually integrate.
Answer:
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Step-by-step explanation:
Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.
So, r = √(R² - z²)
r = √(4² - z²)
r = √(16 - z²)
Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4
Our volume integral in cylindrical coordinates is thus
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Answer:
[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]
General Formulas and Concepts:
Multivariable Calculus
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
Solid sphere w/ radius 4 centered at (0, 0, 0) → x² + y² + z² = 4²
Plane z = 2
Step 2: Find Volume Pt. 1
Find bounds of z.
[Sphere] Substitute in plane z:∴ 0 ≤ r ≤ 2√3
Step 2: Find Volume Pt. 2
[Sphere] Substitute in plane z:∴ 0 ≤ θ ≤ 2π
Step 3: Find Volume Pt. 3
[Sphere] Substitute in cylindrical conversions:∴ 2 ≤ z ≤ √(16 - r²)
Step 4: Find Volume Pt. 4
Substitute in variables [Volume Formula - Cylindrical Coordinates]:∴ the volume of the region is found with the integral above.
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Learn more about multivariable calculus: https://brainly.com/question/17203772
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Topic: Multivariable Calculus
Unit: Triple Integral Applications
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 423 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled or overfilled
guys please help me :(((((((((( crying
Answer:
18
Step-by-step explanation:
2/6
4/12
6/18
Answer:
x = 18
Step-by-step explanation:
We can write ratios
2 2+4
---- = -----
6 x
Using cross products
2x = 6(2+4)
2x = 6(6)
2x = 36
Divide by 2
2x/2 = 36/2
x = 18
Find the missing terms.
3, _____, _____, 21 (arithmetic)
Answer:
Hello There!!
Step-by-step explanation:
The answer is 3,9,15,21.
hope this helps,have a great day!!
~Pinky~
Answer:
the common difference is 6. So, the missing two terms are 9 and 15 using
3 + (n-1)(6)
Given that f(x) = x + 4 and g(x) = x + 7, find (g – f)(x). Question 2 options: (g – f)(x) = 3 (g – f)(x) = – 3 (g – f)(x) = – 4 (g – f)(x) = 4
Answer:
A. 3Step-by-step explanation:
Given
f(x) = x + 4 and g(x) = x + 7Find (g - f)(x):
(g – f)(x) = g(x) - f(x) = x + 7 - x - 4 = 3Correct choice is A
Write the expression in exponential form nd then evaluate 2.1x2.1
Answer:
exponential form = 2.1^2
evaluation = 4.41
Step-by-step explanation:
it is times-ing 2.1 two times, therefore its 2.1^2
2.1 times 2.1 = 4.41
[tex]2 + y = 1[/tex]
Answer: y= -1
Step-by-step explanation:
2+y=1
y=1-2
y=-1
The cost C of manning household is partly constant and partly varies as the number of people, the cost is 70,000 and for 10 people, the cost is 90,000 find the expression for C in terms of n ii. The weekly cost for 12 people
Answer:
4.196.754
Step-by-step explanation:
god bless stay safe po
Help please…………….6/11/21
9514 1404 393
Answer:
8
Step-by-step explanation:
The notation n=1 .. 8 means that n takes on all integer values from 1 to 8. Each value of n gives one term that is added to the series.
The number of terms is 8.
The red line below is parallel to which of the following?
Answer:
option A
Step-by-step explanation:
X- axis
A . the x-axis
Step-by-step explanation:
The lines never meet
Using ƒ = {(1, 0), (2, 3), (3, 6)}, give the range.
Jose bought a plant. The height, h, of the plant is 2 feet. He noticed that every month, m,
the plant grows by 0.5 feet. What equation represents the height of the tree?
Answer:
the answer is h=0.5m+2 I think
From the observation deck of a skyscraper, Christian measures a 51^{\circ}
∘
angle of depression to a ship in the harbor below. If the observation deck is 1129 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Answer:
1394 feets
Step-by-step explanation:
The solution triangle is attached below :
The horizontal distabce from the base is denoted as d :
Using trigonometry, we can obtain d, thus ;
Tan θ = opposite / Adjacent
Tan 51 = d / 1129
d = tan 51 * 1129
d = 1394.1988 feets
d = 1394 feets
6
Find the slope of the line that passes through
(-4, 7) and (-6,-4)
b) -2/11
a) 2/11
d) -11/2
c) 11/2
Answer:
c) 11/2
Step-by-step explanation:
(-4, 7) and (-6, -4)
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-4 - 7) / (-6 - (-4))
Simplify the parentheses.
= (-11) / (-6 + 4)
= (-11) / (-2)
Simplify the fraction.
-11/-2
= 11/2
This is your slope.
Hope this helps!
Is this quadratic? If so what form is it?
Answer:
Yes. Factored form.
Step-by-step explanation:
Answer:
yes, and it's in intercept form
Step-by-step explanation:
Hi there!
We are given the function f(x)=-2(x-4)(x+3)
A quadratic function is a function that has a degree of 2 (the highest exponent in the function is to the 2nd power)
There are 3 forms to write a quadratic function:
standard form, which is f(x)=ax²+bx+c, where a, b, and c are free coefficients (numbers)
vertex form, which is f(x)=a(x-h)²+k, where a is a free coefficient and (h,k) is the vertex
intercept form, which is f(x)=a(x-[tex]x_{1}[/tex])(x-[tex]x_{2}[/tex]), where a is a free coefficient and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are the x intercepts
You may notice that f(x)=-2(x-4)(x+3) is actually in intercept form; a is -2 and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are 4 and -3 respectively (remember: the formula for intercept form has -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex], but the x intercepts are [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Therefore, the x intercepts should be the opposites of -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex]).
If the formula is in intercept form, it should be quadratic.
However, if you want to be sure it's quadratic, you can expand the function.
f(x)=-2(x-4)(x+3)
first, multiply the binomials together using FOIL
(x-4)(x+3)
x²-x-12
now multiply x²-x-12 by -2
-2(x²-x-12)
do the distributive property
-2x²+2x+24
It's a quadratic function! The value of the highest exponent is 2 :)
Hope this helps!
What is the Greatest Common Factor of:
15x7y5+5x5y4−20x6y
Answer:
5x⁵yStep-by-step explanation:
15x⁷y⁵ + 5x⁵y⁴ - 20x⁶y = 5x⁵y*3x²y⁴ + 5x⁵y*y³ - 5x⁵y*4x = 5x⁵y(3x²y⁴ + y³ - 4x)Necesito ayuda con este ejercicio hay que determinar el valor de la a: [tex]a^{20} : a^{2x} = a^{12}[/tex]
Answer:
x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
Step-by-step explanation:
Solve for x:
a^(20 - 2 x) = a^12
Take reciprocals of both sides:
a^(2 x - 20) = 1/a^12
Take the logarithm base a of both sides:
2 x - 20 = log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Add 20 to both sides:
2 x = 20 + log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Divide both sides by 2:
Answer: x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
when does two plus two equal five
y-4=7(x-6)y−4=7(x−6)
Answer:
I believe the question was written twice on accident
y=7x-38
Step-by-step explanation:
y-4=7(x-6)
y-4=7x-42
y=7x-38
I am majorly stuck lol
The area of a rectangle is given by the expression 8x3 + 26x2 + 31x + 15. If the width of the rectangle is 2x + 3, what is the expression that represents the length of the rectangle?
Find the area of the circle shown below if the diameter is 24 inches. Use 3.14 for π. Use the formula π x r^2
A)1,808.64 inches
B) None of these answers
C)37.68 inches
D)452.16 inches
E)150.72 inches
==============================================================
Explanation:
The diameter is 24 inches, so the radius is half that at r = d/2 = 24/2 = 12 inches.
We'll use this along with the approximation pi = 3.14 to get the area
A = pi*r^2
A = 3.14*12^2
A = 452.16 square inches
Your teacher should have used "square inches" instead of "inches" as the unit.
We can abbreviate the "square inches" into "sq in" or "in^2".
This value is approximate since pi = 3.14 is approximate. Use more decimal digits of pi to find a more accurate value.
The exact area is 144pi
Answer:
D. 452.16 sq inches
Step-by-step explanation:
d = 24 ==> r = 24/2= 12 inches
the area = π×r²
= 3.14 × 12²
= 3.14 × 144
= 452.16 sq inches
Can someone please help me? I'm stuck.
Answer:
Sure i can help you
Step-by-step explanation:
Answer:
Sure! What’s the question?
Step-by-step explanation:
What is the solution to flog4(x+8) - 427
Answer:
4270
Step-by-step explanation:
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9 t 2 + 229 t + 346 . Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
How high above sea-level does the rocket get at its peak?
Answer:
[tex] \displaystyle 1)48.2 \: \: \text{sec}[/tex]
[tex] \rm \displaystyle 2)3021.6 \: m[/tex]
Step-by-step explanation:
Question-1:so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,
to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:
[tex] \displaystyle - 4.9 {t}^{2} + 229t + 346 = 0[/tex]
to solve the equation can consider the quadratic formula given by
[tex] \displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a} [/tex]
so let our a,b and c be -4.9,229 and 346 Thus substitute:
[tex] \rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]
remove parentheses:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]
simplify square:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)} [/tex]
simplify multiplication:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8} [/tex]
simplify Substraction:
[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8} [/tex]
by simplifying we acquire:
[tex] \displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5[/tex]
since time can't be negative
[tex] \displaystyle t = 48.2 [/tex]
hence,
at 48.2 seconds splashdown occurs
Question-2:to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered
[tex] \displaystyle x _{ \text{max}} = \frac{ - b}{2a} [/tex]
let a and b be -4.9 and 229 respectively thus substitute:
[tex] \displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)} [/tex]
simplify which yields:
[tex] \displaystyle t _{ \text{max}} = 23.4[/tex]
now plug in the maximum t to the function:
[tex] \rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346 [/tex]
simplify:
[tex] \rm \displaystyle h(23.4) = 3021.6[/tex]
hence,
about 3021.6 meters high above sea-level the rocket gets at its peak?
Translate the sentence into an equation.
Two more than the quotient of a number and 5 is equal to 4.
Use the variable Y for the unknown number.
Answer:
Step-by-step explanation:
y/5 That's your quotient
y/5 + 2 That's the quotient with 2 added on.
y/5 + 2 = 4 And that's your answer.
Always break the statements into the smallest possible steps that you can. Notice that I broke it down to 3 parts that are not quite equal in length.
Solve for x in the equation x squared + 2 x + 1 = 17.
Step-by-step explanation:
quadratic formula
-b+-√b^2
2a
-2+-√2^2-4×1×-16
2×1
-2+-√68
2
either
x= 3.125
or
x= -5.125
Factor completely
9 – 25x^2
Pls help i will mark the brainliest!
Answer:
more
Step-by-step explanation:
The answer is (5x+3)(-5x+3)
solve the literal equation for C. -3x+2c=-3
Step-by-step explanation:
I'm sorry I can't answer that but I know something so you can answer that. search Chrome quickmath all your problems, equations and more can be solved
Answer:
c = 3/2x + −3/2
Step-by-step explanation:
Let's solve for c
-3x+2c=-3
Step 1: Add 3x to both sides.
2c −3x + 3x = −3 + 3x
2c = 3x −3
Step 2: Divide both sides by 2.
2c = 3x−3
2 2
c = 3/2x + −3/2
Answer:
c = 3/2x + −3/2
Let g(x) be the indicated transformation of f(x). Write the rule for g(x) f(x)=3x + 1: translation 2 units right
Answer:
3x +3
Step-by-step explanation:
3x + 1 + 2units(on the x axis)= 3x +3
