Answer:
The domain of the function H(t), is [-5, 30].
The range of the function H(t), is [(10% + average), (average - 20%)]
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable.
For this question, the function is H(t), with the temperature, t, serving as the independent variables and H(t) the evidently dependent variable.
The domain of a function refers to all the possible independent variable values that will give corresponding real dependent variable values.
For this question, Alice's model has the probability for the occurrence of heart disease (in percents relative to the global average) at an area, H(t) varying with the temperature of that area in degree Celsius.
At a temperature of -5°C (the lowest temperature in the model), the probability is 10% above the average.
Then, the probability decreases with increase in temperature, taking a value 20% lower than the average when the temperature is at its highest of 30°C in the model.
So, temperature ranges from -5°C to 30°C and the probability for the occurrence of heart disease ranges from 10% above the average to 20% below the average.
The domain of the function H(t), from the definition given above would therefore be [-5, 30]
And the range of the function H(t), is [(10% + average), (average - 20%)]
Hope this Helps!!!
The Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex]
Given that:
The lowest temperature included in the model is -5° C
The highest temperature included in the model is 30° C
The domain of H includes the values of the temperature. Since the temperature can be non integer too, sometimes rational too, thus we use Real Number type for the domain of H(t).
The domain of H(t) will be given by the following interval on real number line:
[tex]\begin{aligned} Domain(H(t)) = [-5, 30]\\\end{aligned}[/tex]
or [tex]-5 \leq t \leq 30[/tex].
Hence, the Real Number type is more appropriate fro the domain of H(t).
The domain of H(t) is given as [tex]-5 \leq t \leq 30[/tex].
Learn more here:
https://brainly.com/question/9463453
A rectangular field has an area of 1,764 m(squared). The width of the field is 13 m more than the length. What is the perimeter of the field?
Answer:
170m
Step-by-step explanation:
The answer to the above question is letter d which is 170 m. To get the 170 m, kindly check the below solution:
x^2 + 13x = 1764 so x = -49 and 36, we take 36 as its the positive value. And the other side is 49. Now use 2(l+b) to find perimeter. You get (36+49)*2 = 170
Anyone Can help me? Thanks
Answer:
9.8
Step-by-step explanation:
updated
9^2=x^2+4^2
9*9=x*x+4*4
81=x*x-16
+16. +16
97=x*x
√97=√x*x
√97=x
So the answer is √97, but the question wants it rounded so it's actually 9.8
THIS QUESTION IS KILLING ME
Calculate the volume of the object by using the triple integral.
The volume of the solid (call it S) in Cartesian coordinates is
[tex]\displaystyle\iiint_S\mathrm dV=\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{(x^2+y^2)^2-1}^{4-4(x^2+y^2)}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
but I suspect converting to cylindrical coordinates would make the integral much more tractable.
Take
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]
Then
[tex]4-4(x^2+y^2)=4-4r^2=4(1-r^2)[/tex]
[tex](x^2+y^2)^2-1=(r^2)^2-1=r^4-1[/tex]
and the integral becomes
[tex]\displaystyle\iiint_S\mathrm dV=\int_0^{2\pi}\int_0^1\int_{r^4-1}^{4(1-r^2)}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\pi\int_0^1r(4(1-r^2)-(r^4-1))\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^1r(5-4r^2-r^4)\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^15r-4r^3-r^5\,\mathrm dr[/tex]
[tex]=2\pi\left(\dfrac52-1-\dfrac16\right)=\boxed{\dfrac{8\pi}3}[/tex]
The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs at minimum number of swimmers to sign up in order to be cost effective. Last year's data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15. Suppose the instructor wants to conduct a hypothesis test. The alternative hypothesis for this hypothesis test is: "the population mean is less than 15". The sample size is 8, LaTeX: \sigmaσ is known, and alpha =.05, the critical value of z is _______. Group of answer choices
Answer:
The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:
[tex] z_{\alpha/2}= -1.64[/tex]
Step-by-step explanation:
[tex]n=8[/tex] the same size given
[te]\sigma[/tex] the population deviation is known
For this case we want to test if the population mean is less than 15 and that represent the alternative hypothesis and the complement would be the null hypothesis. So then the system of hypothesis are:
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:
[tex] z_{\alpha/2}= -1.64[/tex]
What is the area of a triangle with a =25, b =13, and c =17?
a. 99.1 units 2
c. 98.7 units 2
b. 100.5 units 2
d. 102.3 units 2
Answer:
d. 102.3 units ^2
Step-by-step explanation:
An insurance policy pays a total medical benefit consisting of two parts for each claim. Let X represent the part of the benefit that is paid to the surgeon, and let Y represent the part that is paid to the hospital. The variance of X is 5000, the variance of Y is 10,000, and the variance of the total benefit, X + Y, is 17,000. Due to increasing medical costs, the company that issues the policy decides to increase X by a flat amount of 100 per claim and to increase Y by 10% per claim. Calculate the variance of the total benefit after these revisions have been made
Answer:
= 19300
Step-by-step explanation:
Each claim consists of two parts = X + Y
where
X = the benefit that is paid to the surgeon and
Y = benefit that is paid to the hospital
V(X) = 5000, V(Y) = 10000 and V(X+Y) = 17000
So V(X+Y) = V(X) + V(Y) + 2cov(X,Y)
17000 = 5000 + 10000 +2 cov(X,Y)
17000 -15000 = 2cov(X,Y)
2000 = 2cov(X,Y)
cov(X,Y) = 1000
Now X is increased by flat Rs. 100 per claim and Y by 10% per claim
total benefit = X+100+Y+0.1Y = X+100 + 1.1Y
V(total benefit) = V(X) + 1.1²V(Y) +2(1.1)cov(X,Y) [ V(aX+bY)
= a²V(X) +b²V(Y) +2abcov(X,Y) and V(X+c) = V(X)]
= 5000 + (1.21*10000) + (2.2*1000)
= 5000 + 12100 + 2200
= 19300
Solve for x
A)9
B)33
C)45
D)62
Answer:
A) 9
Step-by-step explanation:
R=7x+17
S=4x-6
Q=180-110=70
4x-6+7x+17+70=18011x+81=19011x=180-8111x=99x=99/11x=95+7.(9-4)
5+7=11
11×5=55
Answer: itz 605
Step-by-step explanation:
Which of the following sequence of transformations takes point J(9, 1) to J'(-3, 7)?
Answer:
Translate point J 12 units down and 6 units right.
I don’t know this one
Answer:
C
Step-by-step explanation:
2/3x - 5>3
Add 5 to each side
2/3x - 5+5>3+5
2/3x > 8
Multiply each side by 3/2
3/2 *2/3x > 8*3/2
x > 12
There is an open circle at 12 and the lines goes to the right
Damian reads 21 pages in 1 hour. How many pages can he read in 3 hours? StartFraction 21 pages Over 1 hour EndFraction = StartFraction question mark pages Over 3 hours EndFraction To go from 1 hour to 3 hours, you _______ . Damian can read _________ pages in 3 hours.
Answer: (Multiply by 3)
63 pages in 3 hours
Step-by-step explanation:
Answer:
To go from 1 hour to 3 hours, you
✔ multiply by 3
.
Damian can read
✔ 63
pages in 3 hours.
Step-by-step explanation:
1. If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest?
Answer:
Age difference between oldest the youngest = 48 years
Step-by-step explanation:
Given: Ratio of ages of Kissi and Esinam is 3:5, ratios of ages of Esinam and Lariba is 3:5 and sum of the ages of all 3 is 147 years
To find: age difference between oldest the youngest
Solution:
Let age of Lariba be x years
As ratios of ages of Esinam and Lariba is 3:5,
Age of Esinam = [tex]\frac{3}{5}x[/tex] years
As ratio of ages of Kissi and Esinam is 3:5,
Age of Kissi = [tex](\frac{3}{5}) (\frac{3}{5}x)=\frac{9}{25}x[/tex] years
Sum of the ages of all 3 = 147 years
[tex]x+\frac{3}{5}x+\frac{9}{25}x=147\\ \frac{25x+15x+9x}{25}=147\\ x=\frac{147(25)}{49}=75[/tex]
Age of Lariba = x = 75 years
Age of Esinam = [tex]\frac{3}{5}(75)=45\,\,years[/tex]
Age of Kissi = [tex]\frac{9}{25}(75)=27\,\,years[/tex]
So,
Age difference between oldest the youngest = 75 - 27 = 48 years
e
65. the perpendicular
bisector of the
segment with
endpoints (-5/2,-2)
and (3, 5)
HELP PLEASE! Picture included!
Answer:
44x +56y = 95
Step-by-step explanation:
To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.
The midpoint is the average of the coordinate values:
((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)
The differences of the coordinates are ...
(3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)
Then the perpendicular bisector equation can be written ...
Δx(x -h) +Δy(y -k) = 0
5.5(x -0.25) +7(y -1.5) = 0
5.5x -1.375 +7y -10.5 = 0
Multiplying by 8 and subtracting the constant, we get ...
44x +56y = 95 . . . . equation of the perpendicular bisector
A and b are similar shapes. B is an enlargement of a with scale factor 1.5 Work out the value of x, h and w
Answer:
x = 54°
h = 7.5cm
w= 6cm
Step-by-step explanation:
Find attached the diagrams as found at Maths made easy.
Similar shapes have same shapes but different sizes.
When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.
B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A
To determine the value of x, h and w, let's look at the relationship of A and B.
h = 1.5 × 5cm
h = 7.5cm
9cm = 1.5 × w
w = 9cm/1.5
w= 6cm
Since the angles do not change when a shape is enlarged, the value of x = 54°
x = 54°
luke is 5 years younger than 3 times sydenys age, s in this situation what does 3s represent
3s represents three times Sydney's age. Sydney's age is symbolized with an S.
The students in Mrs. Willow's reading class are all reading the same novel independently. Four students create a graph of their reading rates, in words per minute, as shown below. Which student reads the fastest? A. Mason B. RIley C. Sarah D. Charlie
Answer:
Mason reads the fastest
Answer:
c
Step-by-step explanation:
try to see how much every person reads every one or two minutes.
Charlie: 350 in two min
Mason :400 in two min
Sarah: 450 in two min (the middle of 300-600 is 450)
so between the three Sarah wins.
now Reilly is a bit more difficult but you can see that she read 4000 in 20 min. so if we divide it by 10 we can see she reads 400 in 2 min. and therefore Sarah os the winner.
What is the result of converting 81 inches to feet ? Remember, there are 12 inches in a foot.
A) 69 feet
B) 8.1 feet
C) 7.25 feet
D) 6.75 feet
Answer:
6.75 ft
Step-by-step explanation:
81 inches
We know there are 12 inches in 1 ft
81 inches * 1 ft/ 12 inches = 81/12 ft =6.75 ft
Solve the problem. When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)
Answer:
73 mph
Step-by-step explanation:
The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).
We have that the model would be:
y = 43.81 - 0.395 * x
We need to solve for x, if y = 15
Replacing:
15 = 43.81 - 0.395 * x
Solving for x we have:
0.395 * x = 43.81 - 15
0.395 * x = 28.81
x = 28.81 / 0.395
x = 72.9
We are asked to round to the nearest number therefore x = 73.
The car will average 15 miles per gallon at the speed of 73 miles per hour.
I need help solving this
Answer:
The answer is the first one on the bottom left.
Step-by-step explanation:
The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rate of change of the volume when r = 9 inches. in.3/min (b) Find the rate of change of the volume when r = 37 inches. in.3/min
Answer:
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
Step-by-step explanation:
given data
radius r of a sphere is increasing at a rate = 3 inches per minute
[tex]\frac{dr}{dt}[/tex] = 3
solution
we know volume of sphere is V = [tex]\frac{4}{3} \pi r^3[/tex]
so [tex]\frac{dV}{dt} = \frac{4}{3} \pi r^2 \frac{dr}{dt}[/tex]
and when r = 9
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (9)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
and
when r = 37 inches
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (37)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
what is the answer to -9x = -27
Answer:
x = 3
Step-by-step explanation:
9x = 27
Divide both sides by 9,
x = 27/9 which on factorization of the numerator is written as
x = 9 x 3/9 = 3
Calculation 2: Exponent Or Index Method
9x = 27
Since 9 = 3² and 27 = 3³, the given equation takes the form
3² x = 3³
This gives
x = 3³ ÷ 3² = 3³¯² [using the formula a^m ÷ a^n = a^(m-n)]
= 3¹ = 3 (since the first power of a number is the number itself)
9 x 1 = 9
9 x 2 = 16
9 x 3 = 279 x 4 = 36
We stop here because we have already got the answer 27, the right-side of the equality, when 9 is multiplied by 3 . So,
x = 3
hope this helped!
Please Answer the following with explanation and formula with neat typing
Answer: A
Step-by-step explanation:
You want to make them both have common denominators. What number does the denominators both go into? Thats easy, its 60.
Multiply 7/12 by 5/5 to get 35/60
Now multiply 4/15 by 4/4 to get 16/60
You need to add a negative number to 35/60 in order to get 16/60
Do 16-35 to get -19/60
(07.01 MC)Of the following sets, which numbers in {0, 1, 2, 3, 4} make the inequality 7x + 3 < 17 true? {0} {0, 1} {0, 1, 2} {2, 3, 4}
Answer:
{0, 1}
Step-by-step explanation:
Solving for 'x' in the inequality:
[tex]7x+3<17\\7x+3-3<17-3 \leftarrow \text{Subtraction Property of Equality}\\7x<14\\7x/7<14/7 \leftarrow \text{Division Property of Equality}\\\boxed{x<2}[/tex]
X's value has to be less than two to make the inequality true. So, {0, 1} should be the correct answer.
Answer:
I took the quiz and the answer is B
Step-by-step explanation:
in four lines determine how to find a perimeter and area of garden with specific dimensions
Answer:
[tex]Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
Step-by-step explanation:
Let assume the l1 is the length of the garden and b1 is the breadth of garden then
[tex]Perimeter\ of\ the\ Garden\ = 2 ( L ength + Breadth )\\Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
Now,
[tex]Area\ of\ Garden\ = Length * Breadth[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
Given the following data, find the weight that represents the 53rd percentile.
Weights of Newborn Babies9.4 7.5 5.4 7.5 7.1
6.0 8.1 5.7 7.1 6.6
9.4 5.8 8.7 5.7 9.3
Answer:
Step-by-step explanation:
Rearranging the weights in ascending order, it becomes
5.4, 5.7, 5.7, 5.8, 6.0, 6.6, 7.1, 7.1, 7.5, 7.5, 8.1, 8.7, 9.3, 9.4, 9.4
The formula for determining the percentile is expressed as
n = (P/100)N
Where
n represents the value of the given percentile
P represents the given percentile
N represents the number of items(weights)
From the information given, the number of items, n is 15
P = 53
Therefore,
n = (53/100) × 15
n = 7.95
n = 8
Therefore, the weight that represents the 53rd percentile is the 8th value. It becomes 7.1
53rd percentile is 7.1
The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosome). Approximately 79% of American men and 0.4% of American women are red-green color-blind.1 Let CBM and CBW denote the events that a man or a woman is color-blind, respectively.
(a) If an Americal male is selected at random, what is the probability that he is red-green color-blind? P(CBM) =
(b) If an American female is selected at random, what is the probability that she is NOT red-green color-blind? P (not CBW) =
(c) If one man and one woman are selected at random, what is the probability that neither are red-green color-blind? P=(neither is color-blind) =
(d) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind? P=(at least one is color-blind)
Answer:
(a) P(CBM) = 0.07
(b) P(not CBW) = 0.996
(c ) P(neither is color-blind) = 0.926
(d) P=(at least one is color-blind) = 0.074
Step-by-step explanation:
The correct data is that Approximately 7% of American men and 0.4% of American women are red-green color-blind.
(a) Probability that he is red-green color-blind:
[tex]P(CBM) = 0.07[/tex]
(b) Probability that she is NOT red-green color-blind:
[tex]P(not\ CBW) =1- P(CBW)\\P(not\ CBW) = 1 -0.004\\P(not\ CBW) =0.996[/tex]
(c) Probability that neither are red-green color-blind
[tex]P(neither) = P(not\ CBW)*P(not\ CBM) \\P(neither) = 0.996 *(1-0.07)\\P(neither)=0.926[/tex]
(d) Probability that at least one of them is red-green color-blind
[tex]P(at\ least\ one) = 1- P(neither) \\P(at\ least\ one) = 1-0.926\\P(at\ least\ one) = 0.074[/tex]
0.2x + (-0.9) + 1.7 = 9.6
0.2x + 0.8 = 9.6
X=
WHAT DOES x =
Answer:
x =44
Step-by-step explanation:
0.2x + (-0.9) + 1.7 = 9.6
Combine like terms
.2x +.8 = 9.6
Subtract .8 from each side
.2x +.8 -.8 = 9.6 -.8
.2x = 8.8
Divide each side by .2
.2x/.2 = 8.8/.2
x =44
Which of the following is not approximately equivalent to one of the metric units: 1 meter, 1 kilogram, or 1 liter
Answer:
A meter is not part of the metric system. It's part of the U.S. customary system.
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 1.15−1.15 and draw a sketch of the region.
Answer:
Step-by-step explanation:
Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 0
σ = 1
the probability that a given score is less than negative 1.15 is expressed as
P(x < - 1.15)
z = (- 1.15 - 0)/1 = - 1.15
Looking at the normal distribution table, the probability corresponding to the z score is 0.13
P(x < - 1.15) = 0.13
The sketch of the region is shown in the attached photo
The histogram represents the daily low and high temperatures in a city during March. Which comparison of the distributions is true?
A)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is nearly symmetric.
B)The distribution of low temperatures is skewed right, and the distribution of high temperatures is nearly symmetric.
C)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is skewed right.
D)The distribution of low temperatures is skewed right, and the distribution of high temperatures is skewed right.
Answer:
ITS C
Step-by-step explanation:
The other answer is wrong, I just tried it.
Answer:
It's C on EDG
Step-by-step explanation:
