Answer:
The temperature that separates the bottom 12% from the top 88% is 97.5°F.
Step-by-step explanation:
We are given that human body temperatures are normally distributed with a mean of 98.2°F and a standard deviation of 0.62°F.
Let X = human body temperatures
So, X ~ Normal([tex]\mu= 98.2,\sigma^{2} = 0.62^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean human body temperature = 98.2°F
[tex]\sigma[/tex] = stnadard deviation = 0.62°F
Now, we have to find the temperature that separates the bottom 12% from the top 88%, that means;
P(X < x) = 0.12 {where x is the required temperature}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
P(Z < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
Now, the critical value of x that represents the bottom 12% of the area in the z table is given as -1.1835, that is;
[tex]\frac{x-98.2}{0.62} = -1.1835[/tex]
[tex]{x-98.2}= -1.1835\times 0.62[/tex]
[tex]x = 98.2 -0.734[/tex] = 97.5°F
Hence, the temperature that separates the bottom 12% from the top 88% is 97.5°F.
pls help me hepl me
Answer:
b at most 199
Step-by-step explanation:so the total was 121 and there is a flat fee of 21.50 so you subtract that out and gat 99.5 since its .5 per mile its going to be divided giving 199 and that is the most she could have driven.
Newton's second law says force (f) is equal to mass (m) times acceration (a). A scientist wants to calculate the force of an object where the acceleration of gravity (g) is 9.8 m/s2. Use the function to calculate the force for an object with a mass (m) of 0.29 kilograms. 9.51 Newtons 2.8 Newtons 34 Newtons 0.029 Newtons
Answer:
Force = mass×acceleration
F=ma
m=0.29kg
a=9.8m/s²
F=0.29kg×9.8m/s²
F= 2.84N=2.8N
Answer:Answer:
Force = mass×acceleration
F=ma
m=0.29kg
a=9.8m/s²
F=0.29kg×9.8m/s²
F= 2.84N=2.8N
Step-by-step explanation:
Find the radius of convergence and interval of convergence of the series. (Enter your answer as an improper fraction.) sum_(n = 1)^infinity (7^n (x + 4)^n)/sqrt(n)
Answer:
L=/x/<1 =x ∈ (-1,1)
Step-by-step explanation:
To find the radius of convergence and interval of convergence of the series ∑(n = 1 to ∞) [7^n (x + 4)^n / √n], we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, the series converges.
Let's apply the ratio test to our series:
|[(7^(n+1) (x + 4)^(n+1)) / √(n+1)] / [(7^n (x + 4)^n) / √n]|
Simplifying and rearranging, we get:|7(x + 4) / √(n+1)|
Taking the limit as n approaches infinity:
lim(n→∞) |7(x + 4) / √(n+1)| = |7(x + 4)|
For the series to converge, |7(x + 4)| must be less than 1. Therefore, we have:
|7(x + 4)| < 1
Solving for x, we get:
-1 < 7(x + 4) < 1
Dividing each inequality by 7, we have:
-1/7 < x + 4 < 1/7
Subtracting 4 from each inequality, we get:
-29/7 < x < -27/7
Thus, the interval of convergence is (-29/7, -27/7), and the radius of convergence is the half-length of the interval, which is 1/7.
Therefore, the series converges for x values within the interval (-29/7, -27/7), and the radius of convergence is 1/7.
To learn more about “convergence” refer to the https://brainly.com/question/17019250
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how do i round 17.875 to the nearest tenth
Answer:
17.9
Step-by-step explanation:
The tenth place is the digit 8. After the tenth place is 7, which is higher or equal to 5. Therefore, we must add +1 to the tenth place followed by zeros.
The function f(x) = -x2 + 40x - 336 models the daily profit, in dollars, a shop makes for selling donut
combos, where x is the number of combos sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? Show
the work that leads to the answer. (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? Show
the work that leads to the answer. (5 points)
(10 points)
Answer:
This question should be worth atleast 20 points
Step-by-step explanation:
a. For the vertex, input the funtion into the calculator, and see where the turning piont is, that is the vertex.
b. Solve using this vormula.
x= (-b ±[tex]\sqrt{b^2 - 4ac}[/tex])/2a
you will get two asnwrs, both are correct.
Write the value of y(1) if y is the solution of e^t dy/dt+e^ty=t, y(0)=1, round your answer to four digits after the decimal sign
Answer:
[tex]y(1) = 0.5518[/tex]
Step-by-step explanation:
Given the differential equation [tex]e^{t} \frac{dy}{dt} +e^{t}y = t[/tex]
From the equation;
[tex]e^{t} (\frac{dy}{dt} +y) = t\\\frac{dy}{dt} +y = \frac{t}{e^{t}} \\[/tex]
The resulting equation is a first order differential equation in the form
dy/dt + p(t)y = q(t)
The solution to the DE will be in the form yI = [tex]\int\limits q(t)*I\, dt[/tex] where I is the integrating factor expressed as [tex]I = e^{\int\limits p(t) \, dt }[/tex]
From the DE above p(t ) = 1 and q(t) = [tex]\frac{t}{e^{t} }[/tex]
[tex]I = e^{\int\limits1 \, dt }\\I = e^{t }\\[/tex]
The solution to the DE will become
[tex]y e^{t } = \int\limits e^{t } *\frac{t}{e^{t } } \, dt\\y e^{t } = \int\limits{t} \, dt \\y e^{t } = \frac{t^{2} }{2} + C[/tex]
If y(0) = 1 then;
[tex]1 e^{0 } = \frac{0^{2} }{2} + C\\1 = C[/tex]
[tex]y e^{t } = \frac{t^{2} }{2} + 1\\y(t) = \frac{1}{e^{t } } (\frac{t^{2} }{2} + 1)[/tex]
The value of y(1) will be expressed as;
[tex]y(1) = \frac{1}{e^{1} } (\frac{1^{2} }{2} + 1)\\y(1) = \frac{1}{2e}+\frac{1}{e}\\ y(1) = \frac{3}{2e}[/tex]
[tex]y(1) = \frac{3}{5.4366} \\y(1) = 0.5518[/tex]
pls help help me pls
Answer:
b
Step-by-step explanation:15 x 5 = 75 and 20 x 4 = 80 making 155 and 15 x 3 = 45 and 20 x 2 = 40 making 85
Four different digits from 1 to 9 are required to open a safe.
1. The sum of the digits is 20.
2. The first digit is greater than the third.
3. The second and fourth digits differ by at least 5.
4. Exactly two digits are squares.
5. The first and fourth digits add up to a prime number.
6. The fourth digit is the lowest.
Can you find the four-digit combination?
Answer: 5942
Step-by-step explanation:
Clue 4 states exactly two of the digits = 1, 4, or 9
Clue 1 leaves us with the following combinations:
1, 9, 2, 8
1, 9, 3, 7 eliminate by clue 5
4, 9, 2, 5
1, 4, 7, 8
Clue 5 directs us to the following order for 1,9,2,8
2 __ __ 1 --> 2981 or 2891 eliminate by clue 2
9 __ __ 8 --> 9128 or 9218 eliminate by clue 6
9 __ __ 2 --> 9182 or 9812 eliminate by clue 6
Clue 5 directs us to the following order for 4,9,2,5
5 __ __ 2 --> 5492 or 5942 eliminate 5492 by clue 2
9 __ __ 2 --> 9452 or 9542 eliminate by clue 3
Clue 5 directs us to the following order for 1,4,7,8
4 __ __ 1 --> 4781 or 4871 eliminate by clue 2
The only combination not eliminated is 5-9-4-2, which satisfies all six clues.
1) 5 + 9 + 4 + 2 = 20
2) 5 > 4
3) 9 - 2 > 5
4) 4 & 9 but not 1 are included
5) 5 + 2 = 7, which is a prime number
6) 2 < 5, 9, 4
Choose the equation of the horizontal line that passes through the point (−5, 9). y = −5 y = 9 x = −5 x = 9
Answer:
y = 9
Step-by-step explanation:
Since we are trying to find a horizontal line, our line would have to be y = [a number]. That takes our x = -5 and x = 9 out as answer choices. We are left with y = -5 and y = 9. y = 9 is correct because the horizontal line is the y-values, and since in (-5, 9), our y-value is 9, our line is y = 9.
Gelb Company currently manufactures 54,000 units per year of a key component for its manufacturing process. Variable costs are $5.15 per unit, fixed costs related to making this component are $73,000 per year, and allocated fixed costs are $80,500 per year. The allocated fixed costs are unavoidable whether the company makes or buys this component. The company is considering buying this component from a supplier for $3.90 per unit.
Calculate the total incremental cost of making 54,000 units.
Answer:
$351,100
Step-by-step explanation:
The total incremental cost of making 54,000 units = Variable Cost Per Unit (54,000 unit) + Fixed Manufacturing Costs
Fixed Manufacturing Costs = $73,000
Variable costs are $5.15 per unit
Variable Cost Per Unit = $5.15 * 54,000 unit = $278,100
Hence, the total incremental cost of making 54,000 units = $278,100 + $73,000 = $351,100
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.
a. Develop hypotheses that can be used to test whether the population proportion of those
who will use the coupons is sufficient to go national.
b. The file Eagle contains the sample data. Develop a point estimate of the population
proportion.
c. Use αα= .05 to conduct your hypothesis test. Should Eagle go national with the
promotion?
Answer:
a) Alternative hypothesis: the use of the coupons is isgnificantly higher than 10%.
Null hypothesis: the use of the coupons is not significantly higher than 10%.
The null and alternative hypothesis can be written as:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
b) Point estimate p=0.13
c) At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
Eagle should not go national with the promotion as there is no evidence it has been succesful.
Step-by-step explanation:
The question is incomplete.
The sample data shows that x=13 out of n=100 use the coupons.
This is a hypothesis test for a proportion.
The claim is that the proportion of coupons use is significantly higher than 10%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
The significance level is 0.05.
The sample has a size n=100.
The point estimate for the population proportion is the sample proportion and has a value of p=0.13.
[tex]p=X/n=13/100=0.13[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.0009}=0.03[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.13-0.1-0.5/100}{0.03}=\dfrac{0.025}{0.03}=0.833[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>0.833)=0.202[/tex]
As the P-value (0.202) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
I don't remember how to do this. plz help
Answer:
TRUE
Step-by-step explanation:
In a triangle having sides a, b and c units,
For a right triangle following condition should be fulfilled,
(Largest side)² = (Leg 1)² + (Leg 2)² [Pythagoras theorem]
If the sides of a triangle are 4, 12 and [tex]\sqrt{160}[/tex]
[tex](\sqrt{160})^{2}[/tex] = 4² + 12²
160 = 16 + 144
160 = 160
True.
Therefore, the given statement is TRUE.
When 21 volts are applied the arlent is a amperes. What is the current when 47 volts are applied round to decimal
Answer:
Since it is directly related, then the current is one third of the voltage.
57 / 3 = 19 amperes
Step-by-step explanation:
The school band is going to a competition. Five members play the flute. There are three times as many members who play the trumpet. There are eight fewer trombone players than trumpeters, and eleven more drummers than trombone players. There are twice as many members that play the clarinet as members that play the flute. There are four fewer tuba players than there are trombone player, but three more members play the French horn than play the trombone. The band director, his assistant and six parent volunteers are also going. How many seats are needed on the bus?
Answer:
76
Step-by-step explanation:
Flute players- 5
Trumpet player- 3 times flute players -15
Trombone players- 8 fewer than trumpet-7
Drummers- 11 more than trombone-18
Clarinet- 2 times flute- 10
Tuba-4 fewer than trombone-3
French horn- 3 more than trombone- 10
Band director- 1
Assistant-1
Volunteers- 6
5+15+7+18+10+3+10+1+1+6=76
how many US dollars is 12,986.64 Swiss francs
Answer:13,732.07 usd
Step-by-step explanation: Just search it up "12,986.64 Swiss francs to usd"
A homeowner puts a passcode-enabled lock on her front door. To choose a passcode, she must choose a number, a letter from a list of 5 letters, and then another number.
Number Letter Number
0 A 0
1 E 1
2 I 2
3 O 3
4 U 4
5 5
6 6
7 7
8 8
9 9
How many possible passcodes can she make?
Answer:
500
Step-by-step explanation:
I assume each number is from 0 to 9. Also there are 5 letters.
10 * 5 * 10 = 500
evaluate -x+4 when x = -2
Answer:
6
Step-by-step explanation:
=> -x+4
Given that x = -2
=> -(-2)+4
=> 2+4
=> 6
Answer:
6
Step-by-step explanation:
You just have to input -2 into the statement and then solve
= -(-2) + 4
= 2+ 4
= 6
You are planning to evaluate the mean of a single continuous variable from a study with a sample of n =10 using the t statistic. What are the degrees of freedom for the sample?
a. 11
b. 9
c. 10
d. 8
Answer:
[tex] t=\frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]
And for this case the degrees of freedom are given by:
[tex] df= n-1 = 10-1=9[/tex]
And the best option would be:
b. 9
Step-by-step explanation:
For this case our parameter of interest is the true mean [tex]\mu[/tex] and we have a sampel size of n =10.
We are going to use a t test and then the t statistic given by:
[tex] t=\frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]
And for this case the degrees of freedom are given by:
[tex] df= n-1 = 10-1=9[/tex]
And the best option would be:
b. 9
11. What are the vertices of the ellipse whose equation is (x2)/9 + (y2)/4 = 1? please show the work
Answer: I think that this is the answer
standard form of equation for ellipse with vertical major axis (a^2 under y^2):
(x-h)^2/b^2+(y-k)^2/a^2=1,a>b, (h,k) being the (x,y) coordinates of the center.
For given equation: x^2/9+y^2/36=1
center: (0,0)
a^2=36
a=√36=6
length of vertical major axis=2a=12
Vertices are end points of major axis=(0,0�a)=(0,0�6)=(0,-6) and (0,6)
Vertices are at (0,-6) and (0,6)
Step-by-step explanation:
Answer:
Explanation: General formula for vertical ellipse Given: x24+y29=1 ... Use the equation provided above, and "plug it" in.
What is the simplified fractional equivalent of the terminating decimal 0.48
Answer:
12/25
Step-by-step explanation:
Which absolute value function, when graphed, will be
wider than the graph of the parent function, f(x) = |x|?
f(x) = |x| + 3
f(x) = |x-6|
f(x) = 1/3 |x|
f(x) = 9|x|
Answer: f(x) = (1/3)*IxI
Step-by-step explanation:
Ok, this is a problem of transformations.
First, if we have f(x), then:
f(x - a) is a translation of a units in the x-axis
f(x) + a is a translation of a units in the y-axis.
a*f(x) is a dilation/contraction.
if a is greater than 1, then the graph will be steeper (less wide)
if a is smaller than 1, then the graph will be wider.
Looking at the options, the correct option is:
f(x) = (1/3)*IxI
where we can see that a = (1/3)
Answer:
C
Step-by-step explanation:
if p(A)=0.30,p(B)=0.40and p(AB) =0.20,then p(A/B) is
Answer:
p(A|B) = 2/3Step-by-step explanation:
Given p(A)=0.30,p(B)=0.40and p(A∩B) =0.20,then p(A/B) is expressed as shown:
p(A|B) = p(A∩B)/p(A)
p(A|B) means B is independent and A depends on B.
In your problem P(A)=0.65, P(A∩B) =0.1
Substituting the given values,
p(A|B) = 0.2/0.30
p(A|B) = 2/10 * 10/3
p(A|B) = 2/3
Find the value of x to the nearest tenth
Answer:
X = 5.3Step-by-step explanation:
To do: Find the value of X
Concept : Angle bisector formula
Now,
[tex] \frac{a}{b} = \frac{c}{d} [/tex]
[tex] \frac{6}{9} = \frac{x}{8} [/tex]
[tex]x \times 9 = 6 \times 8[/tex]
( cross multiplication)
[tex]9x = 48[/tex]
Divide both sides by 9
[tex] \frac{9x}{9} = \frac{48}{9} [/tex]
Calculate
[tex]x = 5.3[/tex]
Hope this helps..
Good luck on your assignment...
Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. The lengths of W C and C Y are congruent. Which best explains if quadrilateral WXYZ can be a parallelogram? WXYZ is a parallelogram because diagonal XZ is bisected. WXYZ is not necessarily a parallelogram because it is unknown if CZ = CY. WXYZ is a parallelogram because ZC + CX = ZX. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Answer: The answer is D
Step-by-step explanation:
Edge 2021
The true statement is (d) WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
What are quadrilaterals?Quadrilaterals are shapes with four sides
What are parallelograms?Parallelograms are quadrilaterals that have equal and parallel opposite sides
The quadrilateral is given as:
WXYZ
Also, we have:
WC = CY
The given parameters are not enough to determine if the quadrilateral is a parallelogram or not
Hence, the true statement is (d) WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Read more about quadrilaterals and parallelograms at:
https://brainly.com/question/1190071
The left and right page numbers of an open book are two consecutive integers whose sum is 389. Find these page numbers
Step-by-step explanation:
Maybe the page numbers can be 143 and 246
143 + 246 = 389
Answer:
194 and 195
Step-by-step explanation:
x = 1st page
x + 1 = 2nd page
x + x + 1 = 389
2x + 1 = 389
2x = 388
x = 194
x + 1 = 195
Which of the following p values will lead us to reject the null hypothesis if the level of significance equals .05?
a. 0.100
b. 0.051
c. 0.150
d. 0.015
Answer:
So then our significance level is [tex]\alpha=0.05[/tex] and we need to remember these two conditions:
1) If the p value [tex]p_v <\alpha[/tex] we have enough evidence to reject the null hypothesis at the significance level given
2) If the p value [tex]p_v \geq \alpha[/tex] we have enough evidence to FAIL reject the null hypothesis at the significance level given
And baed on the options we see that the only possibility would be:
d. 0.015
Step-by-step explanation:
We want to know for which value we would REJECT the null hypothesis.
So then our significance level is [tex]\alpha=0.05[/tex] and we need to remember these two conditions:
1) If the p value [tex]p_v <\alpha[/tex] we have enough evidence to reject the null hypothesis at the significance level given
2) If the p value [tex]p_v \geq \alpha[/tex] we have enough evidence to FAIL reject the null hypothesis at the significance level given
And baed on the options we see that the only possibility would be:
d. 0.015
I NEED HELP PLEASE THANKS!
Jenny is sitting on a sled on the side of a hill inclined at 15°. What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds? (Show work)
Answer:
23.29 lbs
Step-by-step explanation:
The force on Jenny due to gravity can be resolved into components perpendicular to the hillside and down the slope. The down-slope force is ...
(90 lbs)sin(15°) ≈ 23.29 lbs
In order to keep Jenny in position, that force must be balanced by an up-slope force of the same magnitude.
Not sure how I would solve this
Answer:
7/6
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
Using the given points
m = (-2 - -9)/(2 -8)
= (-2+9) / (-6)
= 7/6
Solve each equation (images provided).
Answer:
+-2
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
When you solve the equation you should get two parallel lines with x-intercepts at (-2,0) & (2,0)
There is a set of 100 obserations with a mean of 46 and a standard deviation of 0. What is the value of smallest obserstion in a set?
Answer:
Solution = 46
Step-by-step explanation:
I believe you meant standard deviation. Standard deviation is defined as the variation of the data set, or the differences between the values in this set. In order for the standard deviation to be 0, all values should be the same.
Now if the mean is 46, the smallest possible number of each value in the data set should be 46 as well. This is considering the mean is the average of the values, and hence any number of values in the data set being 46 will always have a mean of 46. Let me give you a demonstration -
[tex]Ex. [ 46, 46, 46 ], and, [46, 46, 46, 46, 46]\\Average = 46 + 46 + 46 / 3 = 46,\\Average = 46 + 46 + 46 + 46 + 46 / 5 = 46[/tex]
As you can see, the average is 46 in each case. This proves that a data set consisting of n number of values in it, each value being 46, or any constant value for that matter, always has a mean similar to the value inside the set, in this case 46. And, that the value of the smallest standard deviation is 46.