People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.
what is eating disorder ?Recurrent episodes of binge eating are the hallmark of a specific type of eating disorder called binge eating disorder. Food addiction and compulsive overeating are both symptoms of this eating disorder. Uncontrollable and quick eating without feeling hungry, as well as negative emotions, depressive symptoms, and guilt over the eating, are prominent symptoms of this illness.
given
People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.
Pica is a kind of pagophagia. It entails consuming ice, snow, or ice water excessively.
Individuals who have pica are not forced to consume ice due to a physical condition like anaemia.
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find the smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0,a]. f(x)= −2x3+8x2−6x+7
The smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0, a] is 2.
The intermediate value theorem states that if a function f is continuous on the closed interval [a, b] and if y is a value between f(a) and f(b), then there exists a point c in the interval [a, b] such that f(c) = y.
In this case, we want to find the smallest integer a such that f(x) has a zero on the interval [0, a]. Since f(0) = 7 and f(x) = -2x^3 + 8x^2 - 6x + 7, we need to find the smallest a such that f(a) < 0.
We can start by finding the values of x where f(x) changes sign. To do this, we can set f(x) equal to 0 and solve for x:
-2x^3 + 8x^2 - 6x + 7 = 0
This is a cubic equation and can be solved using various methods such as factoring, substitution, or the use of a numerical method. However, since we are looking for the smallest integer a, we can use an estimation method such as the Newton-Raphson method to approximate the smallest positive root of the equation.
A common initial guess for the smallest positive root of a cubic equation is x = 1. Using this as the initial guess, we can iterate using the following formula:
x_{n+1} = x_n - f(x_n)/f'(x_n)
where f'(x) is the derivative of f(x) and x_n is the nth estimate of the root.
After several iterations, the estimate for the smallest positive root of the equation can be found to be approximately 1.56. Therefore, the smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0, a] is 2.
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Tanya is training a turtle for a turtle race. For every 5/6of an hour that the turtle is crawling, he can travel 3/20 of a mile. At what rate is the turtle crawling in miles per hour?
Answer:
The rate at which the turtle is crawling can be found by dividing the distance traveled in miles by the time in hours.
So, the turtle can travel 3/20 of a mile in 5/6 of an hour, which means that the turtle is crawling at a rate of (3/20) / (5/6) miles per hour.
To simplify, we need to convert both the numerator and denominator to a common unit. If we multiply the numerator and denominator by 6, we get:
(3/20) * 6 / (5/6) * 6 = 3 / 5 miles per hour.
Therefore, the turtle is crawling at a rate of 3/5 miles per hour.
Carbon-141414 is an element which loses \dfrac{1}{10}
10
1
start fraction, 1, divided by, 10, end fraction of its mass every 871871871 years. The mass of a sample of carbon-141414 can be modeled by a function, MMM, which depends on its age, ttt (in years).
We measure that the initial mass of a sample of carbon-141414 is 960960960 grams.
Write a function that models the mass of the carbon-141414 sample remaining ttt years since the initial measurement.
The function that models the mass of the carbon-14 sample remaining {t} years since the initial measurement is → M{t} = 960 - 0.012t.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Carbon-14 is an element which loses (1/10) of its mass every 871 years. The initial mass of a sample of Carbon-14 is 960 grams. The mass of a sample of carbon-14 can be modeled by a function {M} which depends on its age {t} (in years).
(1/10) x 96 = 96/10 = 9.6 grams.
Carbon - 14 looses 9.6 grams in 871 years.
In 1 year, Carbon - 14 will loose (9.6/871) = 0.012 gram.
We can write the function {M} as -
M{t} = 960 - 0.012t
Therefore, the function that models the mass of the carbon-14 sample remaining {t} years since the initial measurement is → M{t} = 960 - 0.012t.
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Write each rate as a unit rate. 64 ounces in 8 cups.
Answer:
8 ounces per cup or 8/1
Step-by-step explanation:
64 ounces/8 cups = 8
convert from rectangular to spherical coordinates. (use symbolic notation and fractions where needed. give your answer as a point's coordinates in the form (*,*,*).)(5, π/8, 0) ->
The spherical coordinates of the given rectangular coordinates are (10, 0, 60).
The cartesian coordinate or rectangular coordinates describes the location of a point in space using an ordered triple where each coordinate represents a distance. The spherical coordinate system describes the location of a point in space using an ordered triple where coordinate describes one distance and two angles. In the spherical coordinate system, a point is represented by the ordered triple (ρ, θ, φ).
The equations which are used to convert from rectangular coordinates to spherical coordinates are:
ρ^2=x^2+y^2+z^2
tan〖θ= y/x〗
φ=arccos〖z/√(x^2+y^2+z^2 )〗
The given rectangular coordinates are (5√3, 0, 5). Hence,
ρ^2=〖(5√3)〗^2+0^2+5^2 ≈ 100
ρ ≈ √100 ≈ 10
tan〖θ= 0/(5√3)=0〗
θ= tan^(-1)0=0
φ=arccos〖5/√(〖(5√3)〗^2+0^2+5^2 )〗= arccos 5/10=arccos0.5 ≈ 60
Note: The question is incomplete. The complete question probably is: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*). (5√3, 0, 5)
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Determine when the function is positive, negative, increasing, or decreasing: y = 7(5)ˣ
PLEASE HELPPP !!
The function will be positive and increasing for all values of x.
What is Exponential Function?The formula for an exponential function is f (x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given the function,
y = 7(5)ˣ
when x = 0, y = 7
x = -1, y = 1.4
x = 1, y = 35
an exponential function is,
y = abˣ
when a > 0 and b > 0 the function is an exponential growth function, for all values of x.
Hence the function will be positive and increasing.
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The function y = 7(5)ˣ is positive and increasing,
What is Exponential Function?Exponential function, in mathematics, a relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
Given:
y = 7(5)ˣ
As, Exponential functions have the general form: y = aˣ, where a>0
and a is called the base of the exponential function and x is any real number.
If the base a> 1 and has positive exponent(i.e. x>0) then the exponential function is increasing.
If the base 0 < a< 1 and has negative power then the function is decreasing.
Thus, the function y = 7(5)ˣ is increasing.
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Answer D is cut off but if you come to a different conclusion you can always use process of elimination
The total monthly payments is $2169.49
What is mortgage payment?You should understand that a mortgage is a home loan that is secured by the property the borrower finances with the loan funds.
The mortgage payment is
A = (210,000·0.95)(0.045/12)/(1 -(1 +0.045/12)^(-12·15)) ≈ 1526.16
The monthly set-aside for taxes is
3.5%*200,000/12 = 583.33
The monthly set-aside for insurance is
720/12 = 60
So the total of P&I + taxes + insurance will be
In conclusion, the monthly payment is given by :
$1526.16 +583.33 +60.00 = $2169.49
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Dilations produce similar shapes. The size of the figure changes, but the shape does not change. Notation for a
dilation with a scale factor of n is Dn(x, y) (nx, ny).
After dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.
Does a dilation produce a congruent figure?When two figures are congruent, it means they have the same shape and size, whereby, all pairs of corresponding angles and sides of both figures are congruent or equal in measure.
The image attached below shows a dilated figure.
Dilation is a transformation that enlarges a figure or reduces the figure.
After dilation, the new figure maintains the same shape of the original figure.
However, after dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.
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Simplify. (5 × 10^6) ÷ (1 × 10^3) Give the answer in scientific notation.
Answer:
5 x 10^9
Step-by-step explanation:
= ( 5x1) X (10^(6+3) ) = 5 x 10^9
Select the correct answer. Which expression is equivalent to the given polynomial expression? Select the correct answer.
Which expression is equivalent to the given polynomial expression?
The expression is equivalent to the given polynomial expression is
-7[tex]m^4[/tex]n + 18mn - 8m².
How do you find a polynomial expression?In particular, an expression must not contain any square roots of variables, any fractional or negative powers on the variables, and any variables in any fractions' denominators in order to qualify as a polynomial term.
What are the 4 types of polynomials?These are trinomials, binomials, and monomials. A polynomial can be categorised into 4 categories based on its degree. The four are the cubic polynomial, linear polynomial, and polynomial of zero.
From all the options the equivalent polynomial expression as
-7[tex]m^4[/tex]n + 18mn - 8m²
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The Question attached here is incomplete, the complete question is
Which expression is equivalent to the given polynomial expression?
(9mn – 19m4n)19m4n) - (8m2 + 12m4n + 9mn)
A.-7mtn + 8m2
B.-7m4n + 18mn - 8m2
C.-31m 4n – 8m2
D.-31m 4n + 18mn
8m2
find the measure of the angles. please show process!
Answer:
1st question:
10°, 80°, 90°
2nd question:
76°, 52°, 52°
Step-by-step explanation:
For both of these questions we will use the idea that the three angles of a triangle add up to 180°.
In the triangle on the left, two angles are marked and the third is a right angle. The tiny square marking on the third angle means it is a right angle, so it is 90°.
We can write an equation.
x + 8x + 90° = 180°
combine like terms
9x + 90 = 180
subtract 90
9x = 90
divide by 9
x = 10
So the angles are x, 8x and 90°
Since x = 10
the 3 angles are 10°, 80° and 90°
For the second question, two sides are marked to show they are congruent (same, equal) that means the two angles on the base (base angles) are congruent (the same)
One angle is 3x+1 and both the other two angles are 2x+2. Write an equation.
3x+1 + 2x+2 + 2x+2 = 180°
combine like terms
7x + 5 = 180
subtract 5
7x = 175
divide by 7
x = 25
Calculate the angle measures using x = 25
3x+1 = 3(25)+1 = 76°
2x+2 = 2(25)+2 = 52°
The 3 angles of the triangle are 76°, 52° and 52°
Can someone please help me!!!!! -0987
Answer:
I can if you post the question...
Step-by-step explanation:
Both circles have the same center. The circumference of the inner circle is 31.4 miles. What is the area of the shaded region?
The radius of the inner and outer circles is 5 miles and 10 miles. Then the area of the shaded region will be 235.5 square miles.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
Both circles have the same center. The circumference of the inner circle is 31.4 miles. Then the radius of the inner circle is given as,
2πr = C
2 x 3.14 x r = 31.4
r = 5 miles
Then the ratio of the outer circle to the inner circle is 2. Then the radius of the outer circle is given as,
R/r = 2
R / 5 = 2
R = 10 miles
The area of the shaded region is given as,
A = πR² - πr²
A = 3.14 x 10² - 3.14 x 5²
A = 3.14 x (100 - 25)
A = 3.14 x 75
A = 235.50 square miles
The area is 235.50 square miles.
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IT IS NOT 18/42!!1 There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting at least 1 red?
The probability of getting at least 1 red is 6/7
What is the probability of getting at least 1 red?Probability is the likelihood of a desired event happening.
Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.
The probability that the first is blue and the second is blue
p(First blue, Second blue) = 3/7 × 2/6 = 1/7
Thus, the probability of getting at least 1 red, is the complement of getting both blue
That is, P(At least 1 red) = P'(both blue) = 1 - P(Both blue) = 1 - 1/7 = 6/7
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List each zero of f according to its multiplicity in the categories below.
The zeros of f(x) are:
zeros x = 9 and x = 7 → multiplicity 1. zero x = -13 → multiplicity 2. zero x = -5 → multiplicity 3.Which are the zeros and multiplicities?Here we have the polynomial:
f(x) = 6*(x - 9)*(x - 7)*(x + 13)^2*(x + 5)^3
In each factor of the form:
(x - k)^n
the zero is x = k
and the multiplicity is n.
Then:
The zeros x = 9 and x = 7 have multiplicity 1.
The zero x = .13 has multiplicity 2.
The zero x = -5 has multiplicity 3.
These are the zeros of the polynomial.
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PLEASE SOLVE THIS~!! 15 points!!!!!!
The value of a in the triangle is 17 degrees
What is Equilateral triangle?An equilateral triangle is that type of triangle whose all sides and all angles are equal. Recall theat the sum of angles of a triangle is 10 degrees.
This implies that
4a-8 +4a-8 +4a-8 = 180
12a -24 = 180
12a = 180+24
12a = 204
Making a the subject of the relation,
12a/12 = 204/12
Therefore the value of a= 17⁰
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the number of a certain type of bacteria, Y, present in a culture is determined by the equation Y=200(4)^x where X is the number of days the culture has been growing. find the number of bacteria present after 6 days.
A) 2.5X 10^17
B) 4296
C) 2X 10^6
D) 819200
E) 8X 10^6
actually give you 20 points if you can solve this correctly and give you brainless and under 20 minutes
Answer:
Factor 3x+3
3x+3
=3(x+1)
Answer:
P=2[9x-3]
Step-by-step explanation:
perimeter of rectangle =2(L+W)=2L+2W
where P=perimeter of rectangle
L=length of rectangle =3x+3
W=width of rectangle =6x-6
P=2[(3x+3)+(6x-6)]
P=2[3x+3+6x-6]
P=2[9x-3]
Reduce each fractionAnd write a conditional statement 8a+4b/2ab+b^2-2ad-bd
The simplification of the fractions gives 4 / (b - d).
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Given expression is [tex]\frac{8a + 4b}{2ab+b^2-2ad-bd}[/tex].
We have to simplify each of the numerator and denominator in the expression [tex]\frac{8a + 4b}{2ab+b^2-2ad-bd}[/tex].
Take the common factor in each of the expressions in numerator and denominator.
8a + 4b = 4(2a + b)
2ab + b² - 2ad - bd = 2ab - 2ad + b² - bd
= 2a(b - d) + b(b - d)
= (b - d) (2a + b)
[tex]\frac{8a + 4b}{2ab+b^2-2ad-bd}[/tex] = [tex]\frac{4(2a+b)}{(b-d)(2a+b)}[/tex]
= [tex]\frac{4}{b-d}[/tex]
Hence the simplified expression is 4 / (b - d).
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Can anyone please help me with this? thank you!!
Answer: Yes, it is congruent.
Rt is same length as Tu
angle rst is equal to angle tvu
therefore the angle where they both meet would have to be the same aswell, so it is congruent
Step-by-step explanation:
Answe is attached in the above image.
find the savings plan balance after 9 months with an APR of 9% and monthly payments of 250
The balance after 9 months with an APR of 9% and monthly payments of 250 is, $267.38
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
The savings plan balance after 9 months with an APR of 9% and monthly payments of 250.
Now, Let the balance after 9 months with an APR of 9% and monthly payments of 250 is, x
Hence, We can formulate;
⇒ x = 250 (1 + 0.09/12)⁹
⇒ x = 250 × 1.0075⁹
⇒ x = 250 × 1.0695
⇒ x = $267.375
⇒ x = $267.38
Thus, The balance after 9 months with an APR of 9% and monthly payments of 250 is, $267.38
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For ODE y”+5y’+4y=2e^(-2x) what is its particular intergral
We have the differential equation, [tex]y''+5y'+4y=2e^{-2x}[/tex]. The question asks to find the particular solution to the DE.
To find the particular solution look at the right-hand-side and make a “guess” of what the solution could be.
Since we have [tex]2e^{-2x}[/tex] we can guess that the particular solution could be in the form [tex]Ae^{-2x}[/tex], where [tex]A[/tex] is some unknown constant.
Now finding the value of the unknown constant, [tex]A[/tex]. Lets say [tex]g(x)=Ae^{-2x}[/tex], find [tex]g'(x)[/tex] and [tex]g''(x)[/tex].
[tex]g(x)=Ae^{-2x}[/tex]
=> [tex]g'(x)=-2Ae^{-2x}[/tex]
=> [tex]g''(x)=4Ae^{-2x}[/tex]
Now plug [tex]g(x)[/tex], [tex]g'(x)\\[/tex], and [tex]g''(x)[/tex] into the given differential equation.
=> [tex]y''+5y'+4y=2e^{-2x}[/tex]
=> [tex](4Ae^{-2x})+5(-2Ae^{-2x})+4(Ae^{-2x})=2e^{-2x}[/tex]
=> [tex]4Ae^{-2x}-10Ae^{-2x}+4Ae^{-2x}=2e^{-2x}[/tex]
=> [tex]8Ae^{-2x}-10Ae^{-2x}=2e^{-2x}[/tex]
=> [tex]-2Ae^{-2x}=2e^{-2x}[/tex]
Compare the coefficients,
=>[tex]-2A=2[/tex]
=>[tex]A=-1[/tex]
So we can say our "guess" to the particular solution of the given differential equation is, [tex]y_{p} =-e^{-2x}[/tex].
write each rate as a unit rate.
3 inches of rain in 6 hours
Answer: 0.5 inches of rain per hour or 0.5/1
Step-by-step explanation:
divide 3/6 gets you 0.5
Evelyn works in a greenhouse and planted 22 flowers in pots. 8 of the flowers were daisies.
If she wants the ratio of daisies to flowers to stay the same how many daisies would she need to plant if she fills 66 pots?
Answer: 24 Daisies
Step-by-step explanation:
14 flowers are normal and the other 8 are daisies, there are currently 22 flowers.
To fill 66 plots, she'd need to plant 3 times as many flowers as there are now, so there'd be 14*3 non daisies and 8*3 daisies. 8*3 = 24.
Answer:
24
Step-by-step explanation:
[tex]\frac{daisies}{total flowers}[/tex] = [tex]\frac{daisies}{total flowers\\}[/tex]
[tex]\frac{8}{22}[/tex] = [tex]\frac{d}{66}[/tex]
22 x 3 = 66
8 x 3 = 24
Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a. What is the exact volume, in cubic inches, of water flowing out of the pipe every second? Leave your answer in terms of π.
To find the volume of water flowing out of the pipe every second, we first need to find the cross-sectional area of the pipe. The formula for the area of a circle is π * r^2, where r is the radius. So, the radius of the pipe is 8/2 = 4 inches.
The cross-sectional area of the pipe is π * 4^2 = 16π square inches.
Now, since the water is flowing at a rate of 2 feet per second, and 1 foot is equal to 12 inches, the flow rate in inches per second is 2 * 12 = 24 cubic inches per second.
So, the exact volume of water flowing out of the pipe every second is the cross-sectional area of the pipe times the flow rate:
16π * 24 = 384π cubic inches per second.
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3. ABCD is
a. Congruent
b. Similar
c. Neither
to A'B'C'D'.
Answer:
a. Congruent
Step-by-step explanation:
ABCD has the same dimensions of A'B'C'D', so that means that it is congruent, even though it's in a different place on the graph.
Solve for x
A: 4
B: 3
C: 7
D: 10
Answer:
A: 4
Step-by-step explanation:
15 divided by 20 = 0.75
4 + 2 = 6
14 - 6 = 8
So, the smaller triangle base will be 6 and the bigger triangle base will be 8
6 divided by 8 = 0.75
So, A:4 is the correct answer.
Which investment results in the greatest total amount?
Investment A: $4,000 invested for 5 years compounded semiannually at 6%.
Investment B: $5,000 invested for 3 years compounded quarterly at 2.7%.
Find the total amount of investment A.
$ (Round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
The formula to calculate the future value of an investment with compound interest is:
FV = PV * (1 + (r/n))^(n*t)
Where:
PV is the present value (the initial investment)
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years
For Investment A:
PV = $4,000
r = 6% = 0.06
n = 2 (semiannual compounding)
t = 5 years
FV = $4,000 * (1 + (0.06/2))^(2*5) = $4,000 * (1.03)^10
FV = $4,000 * 1.664131669 = $6,656.53
So, the total amount of Investment A is $6,656.53 (rounded to the nearest cent).
How many gallons of paint are required to paint one side of a block wall of the following dimensions: 6'x172'? The paint being used will cover 200ft2 per gallon. 2. Compute the gallons of sealer required to seal a floor 120' x250'. The sealer being used will cover 175 ft2 per gallon. 3. If a concrete column is 20" in diameter and 18'-3" in height, how many cubic yards of concrete would be needed to fill the form? Round off to the next largest cubic yard. 4. What is the circumfrence of a circle with a diameter of 12'-5"?
The Values for rectangle type wall and circle will be gallons of paint that are required to paint one side of a block wall =5.16 gallon, the gallons of sealer required to seal a floor=4.22 gallon and circumference of circle≈39 feet.
What exactly is a rectangle?
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
For example, if one side of a rectangle is 20 cm long, the opposing side is similarly 20 cm long.
A rectangle has two diagonals that intersect. Both diagonals are the same length
P = 2 (Length + Width) is the perimeter.
Rectangle Area=Length*Breadth
Now,
1. Given Length of wall=172 feet and breadth =6 feet then area=172*6=1032
square feet and The paint being used will cover 200 square ft per gallon.
so, gallons of paint that are required to paint one side of a block wall
=1032/200=5.16 gallon
2. Length=250 feet, breadth=120 feet then perimeter=2*370=740 feet
paint used to seal 175 feet floor=1 gallon
then the gallons of sealer required to seal a floor 120' x250'=740/175=4.22 gallon
3. Incomplete question.
4.diameter=12feet 5inch=149 inch
circumference of circle=π*diameter=3.14*149≈39 feet
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(a) Find a vector function, r(t), that represents the curve of intersection of the two surfaces.The cylinderx^2 + y^2 = 25and the surfacez = xyr(t)=??
A possible vector function that represents the curve of intersection of the two surfaces is r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))
The cylinder x^2 + y^2 = 25 represents the set of points in 3D space where the distance from the origin to the point (x, y, z) is equal to 5. The surface z = xy represents the set of points in 3D space where the height of the point (x, y, z) is equal to its x-y coordinate.
The curve of intersection of the two surfaces is given by the set of points in 3D space that are simultaneously on the cylinder and on the surface z = xy. This means that for any point on the curve of intersection, the distance from the origin to the point must be equal to 5, and the height of the point must be equal to its x-y coordinate.
We can find a vector function that represents the curve of intersection by parameterising the points on the curve in terms of a scalar parameter t. For example, a possible parameterization of the curve of intersection is:
r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))
where t is a scalar parameter that ranges over all values between 0 and 2π. The values of x, y, and z are given by 5 cos(t), 5 sin(t), and 5 cos(t) sin(t), respectively, and represent a point on the curve of intersection for each value of t.
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