Answer:
jack is 54 and lacey is 13.5. I think
Step-by-step explanation:
Let Jack be J and Lacy be L.
First equation: J=4L
Second equation: (J+9)+(L+9)=63
Solving using substitution:
4L+9+L+9=63
5L+18=63
5L= 45
L = 9
L=9 and J=4L = 4*9 = 36
So Jack is 36 years old and Lacy is 9 years old.
Bodytemperatures ofhealthy koalasarenormally distributed with a mean of 35.6°C and a standard deviation of 1.3°C. a.What is the probability that a health koalahas a body temperature lessthan 35.0°C? (1pt)b.Veterinarians at a nature preserve in Australiathought a population of koalas might be infected with a virus, so they chose a random sample of n=30koalas and measured their body temperatures. If they got a sample mean body temperature less than 35.0°C, do you think that this population of koalas is healthy? Why/why not?Be specific.(4pt)c.List a potential confounding variable for this study and briefly how it might have impactedthe results. (2pt)2.
Answer:
a
[tex]P(X < 35) = 32.3 \%[/tex]
b
[tex]P(\= X < 35) = 0.6 \%[/tex]
Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy
c
A potential confounding variable for this study is the population of the koalas because in the first question the population was not taken into account and the probability was [tex]P(X < 35) = 32.3 \%[/tex] but when the population was taken into account (i.e n = 30) the probability became
[tex]P(\= X < 35) = 0.6 \%[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 35.6^oC[/tex]
The standard deviation is [tex]s = 1.3^oC[/tex]
The sample size is n = 30
Generally the probability that a health koala has a body temperature less than 35.0°C is mathematically represented as
[tex]P(X < 35) = P(\frac{X - \mu }{s} < \frac{35 - 35.6}{1.3} )[/tex]
Here [tex](\frac{X - \mu }{s} = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < 35) = P(Z < -0.46)[/tex]
From the z-table P(Z < -0.46) = 0.323
So
[tex]P(X < 35) = 0.323 [/tex]
Converting to percentage
[tex]P(X < 35) = 0.323 * 100 [/tex]
[tex]P(X < 35) = 32.3 \%[/tex]
considering question b
The sample mean is [tex]\= x = 35[/tex]
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{\= x} = \frac{s}{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x} = \frac{1.3}{\sqrt{30} }[/tex]
=> [tex]\sigma_{\= x} = 0.2373 [/tex]
Generally the probability of the mean body temperature of koalas being less than 35.0°C is mathematically represented as
[tex]P(\= X < 35) = P(\frac{\= X - \mu }{\sigma_{\= x }} < \frac{35 -35.6}{0.2373 } )[/tex]
[tex]P(\= X < 35) = P(Z< -2.53 )[/tex]
From the z-table we have that
[tex]P(Z< -2.53 ) = 0.006[/tex]
So
[tex]P(\= X < 35) = 0.006 /tex]
Converting to percentage
[tex]P(\= X < 35) = 0.006 * 100 [/tex]
[tex]P(\= X < 35) = 0.6 \%[/tex]
Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy
A potential confounding variable for this study is the population of the koalas because in the first question the population was not taken into account and the probability was [tex]P(X < 35) = 32.3 \%[/tex] but when the population was taken into account (i.e n = 30) the probability became
[tex]P(\= X < 35) = 0.6 \%[/tex]
What fraction is 0.16% equivalent to? (16 is repeating)
Answer:
[tex]\frac{16}{10000}[/tex]
Step-by-step explanation:
Answer:
4/25
Step-by-step explanation:
3(x - 2) - 2x + 3 = -12
Sorry I have another question lol
Answer:
Solve for
x by simplifying both sides of the equation, then isolating the variable.
x = − 9
Answer:
x+9
Step-by-step explanation:
Anyone know the question?
Helpp !
Answer:
[tex]-\frac{1}{2}[/tex] is the slope value.
Step-by-step explanation:
By using the definition of slope (Δy/Δx), we can reason that the slope is:
[tex]\frac{-1}{2} = -0.5[/tex]
Given the parent function f(x)=x^2 in red, write the equation for the transformed function g(x) in green.
Answer:
g(x) = 2x² + 1
Step-by-step explanation:
The parabola got thinner, so to show that, you put a 2 before x² to show that the graph was dilated (or thinned) by a factor of 2 (Note: this number can also be negative, so if the dilation factor is negative, it's okay). Since the parabola shifts up by 1, you then add + 1 after x² to show the positive upward shift.
Your full equation would look like this: g(x) = 2x² + 1
Dilation: this just means that every point on the parent function was double (or whatever the factor is) in the transformed function.
A gallon of milk cost 1.99. A half-gallon cost 3.89. Is this proportional or nonproportional?
Answer:
Non Proportional
Step-by-step explanation:
A proportional figure relates to two or more figures that correspond in size or amount to one another. The gallon of milk which costs 1.99 is nonproportional to the half-gallon which costs 3.89.
On the other hand, a nonproportional figure does not correspond to in size or amount to one another.
From the given information;
A gallon of milk cost = 1.99A half-gallon cost 3.89
i.e.
[tex]\mathbf{= \dfrac{1}{2} \times 3.89}[/tex]
= 1.945
Therefore, we can conclude that the gallon of milk which cost 1.99 is nonproportional to the half-gallon which cost 3.89.
Learn more about proportionality here:
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convert a repeating decimal to a fraction
Answer:
Step-by-step explanation:
Convert a Repeating Decimal to a Fraction
Create an equation such that x equals the decimal number.
Count the number of decimal places, y. Create a second equation multiplying both sides of the first equation by 10y.
Subtract the second equation from the first equation.
Solve for x.
Reduce the fraction.
Answer:
2/3 = 0.66 repeated
Step-by-step explanation:
List the next even number after 149
Answer:
150
Step-by-step explanation:
Answer:
152
Step-by-step explanation:
you want to be my friend
Translate the quadrilateral W(-2, 2), X(-3, 3), Y(-6, 5), Z(-6, 3) using the transformation
(x-2, y + 3)
Answer: W (-4, 5) X(-5, 6) Y (-8, 8) Z (-8, 6)
Given that the polynomial f(x) has degree 8, which of the following most accurately describes the number of turning points of f(x)?
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial f(x) that has a degree of 8 will have 7 turning points.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
For any polynomial equation, the number of turning points is always less than or equal to the degree of the polynomial.
Generally, the number of turns is one less than the degree of the polynomial.
Hence, the polynomial f(x) that has a degree of 8 will have 7 turning points.
Learn more about Polynomials:
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Jerome’s parents want to make sure he keeps reading for the summer. So they made deal, for every 7 minutes of reading he earns one minute of game time. How many minutes of video game time will he earn if he reads for 147 minutes?
Answer:
21 minutes of game time.
Step-by-step explanation:
Since its every 7 minutes he reads he gets one minute of game time and reads fir 147 minutes you would divide 147 by 7 to get 21 minutes of game time. hope this helped :)
In quadrilateral ABCD shown below it is known that BC is perpendicular CD, angle A=5x+12, and angle C=7x-36. Given this information, which of the following is the degree measure of angle A?
Answer:
m∠A = 102°
Step-by-step explanation:
In quadrilateral ABCD, BC is perpendicular to CD
m∠BCD = 90°
(7x - 36) = 90°
7x = 90 + 36
7x = 126
x = 18
Since, m∠A = (5x + 12)
Therefore, m∠A = (5×18) + 12
= 90 + 12
= 102°
Measure of angle A = 102°
Use elimination to solve for x and y:
9x - 4y = 11
x + 4y = 19
Select one:
a. (7,3)
b. (4,3)
c. (-1,5)
d. (3,4)
Answer:
multiply second eqyation by 9
Step-by-step explanation:
then subtract with 1 st eqn
Which multiplication equation could represent the area model?
5.03×2.02=10.165 point 0 3 times 2 point 0 2 is equal to 10 point 1 6
3.05×2.02=6.163 point 0 5 times 2 point 0 2 is equal to 6 point 1 6
2.2×5.3=11.662 point 2 times 5 point 3 is equal to 11 point 6 6
2.2×3.5=7.72 point 2 times 3 point 5 is equal to 7 point 7
Answer: y
Step-by-step explanation:
Which expression is equivalent to one over fivem − 20?
one over five(m − 4)
one over five(m − 100)
5(m − 4)
5(m − 100)
Answer:
one over five (m-100)
Step-by-step explanation:
the answer to your question is the 2nd one
Answer:
1 / [ 5(m - 4) ] is equivalent to one over five m -20
Step-by-step explanation:
one over five(m − 4)
5(m − 4)
Factor the denominator:
1 / [ 5m - 20 ] = 1 / [ 5(m - 4) ]
James ran 80 miles, xavier ran 0.75 of the total number that james ran. How many miles did Xavier run?
Answer:
60 miles
Step-by-step explanation:
01:37:35
What is the difference between the largest prime number less than 50 and the smallest composite number greater than 10
Answer:
35
Step-by-step explanation:
47-12=35
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answer:
2.333333333
Step-by-step explanation:
divide 3 into 7 and it's is repeating
Answer:
Step-by-step explanation:
The ticket prices at a movie theater are shown in the table. A family purchased tickets for 2 adults and 3 children, and the family purchases 3 boxes of popcorn of the same size. The family spent a total of $40.25 how much did each box of of popcorn cost
Answer:
$2.25
Step-by-step explanation:
The first thing you do is multiply the prices of tickets by how many they bought.
$8.50 x 2= $17
$5.50 x 3= $16.50
You then add these two numbers together and subtract that from $40.25.
$17+$16.50=$33.50
$40.25-$33.50=$6.75
You then divide $6.75 by 3 to find the answer
$6.75/3=$2.25
wat is the answer to [x l 2 < x < 2]
Answer: the empty set
Step-by-step explanation:
There are no real numbers x such that x>2 and x<2, simultaneously.
Answer:
x= -0.7667
Step-by-step explanation:
please look at the picture below
Answer:
A
Step-by-step explanation:
domain is the input and range is the output
8^x = 2
What is X
Thank you :))))
Answer:
1/3
Step-by-step explanation:
A manufacturing company produces 355 units per day currently. The company's goal is to increase the number of units manufactured per day by 35 each year. If the company meets the goal how many units will it be producing per day 4 years from now?
Write a ratio for the following situation: For every 5 female teachers, there are 2 male teachers
Answer:
the answer would be 5:2
x - 2y = 10
3x - 5y = 4
Answer:
y = -26
x = -42
Step-by-step explanation:
3x - 5y = 4
x - 2y = 10
x - 2y = 10
x = 2y + 10
3x - 5y = 4
3(2y + 10) - 5y = 4
6y + 30 - 5y = 4
y + 30 = 4
y = -26
x - 2y = 10
x - 2(-26) = 10
x + 52 = 10
x = -42
Check:
x - 2y = 10
(-42) - 2(-26) = 10
-42 + 52 = 10
10 = 10
Xavier exercises by riding his bike. During his first week of training, he rides a total of 15 miles. Each week he increases the number of miles biked by 0.4 miles. How many total weeks will it take Xavier to first bike more than 500 miles total? 8 15 19 26
Answer:
I believe the answer is D) 26.
Step-by-step explanation:
Xavier will need 26 weeks to first bike more than 500 miles.
Arithmetic ProgressionAn arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the successive terms is the same.
Sum of n terms of an arithmetic progressionThe distance biked by Xavier during his first week of training is 15 miles.
The increase in the distance biked each week is 0.4 miles.
And we have to find the number of weeks required to first bike more than 500 miles total.
The given situation represents an arithmetic progression (AP) in which,
First term, a = 15
The common difference, d = 0.4
And the sum of n terms, Sn = 500
The formula to find the sum of n terms of an AP is,
[tex]\text{S}_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
How to check which option is correct?We will check which option is correct by putting them in the above equation.
For n = 8, we have
[tex]\text{S}_n = \dfrac{8}{2}[2\times15+(8-1)0.4][/tex]
Sn = 4[30+2.8]
Sn = 131.2
Which is not more than 500, so option (A) is incorrect.
For n = 15, we have
[tex]\text{S}_n = \dfrac{15}{2}[2\times15+(15-1)0.4][/tex]
Sn = 7.5[30+5.6]
Sn = 267
Which is not more than 500, so option (B) is incorrect.
For n = 19, we have
[tex]\text{S}_n = \dfrac{19}{2}[2\times15+(19-1)0.4][/tex]
Sn = 9.5[30+7.2]
Sn = 353.4
Which is not more than 500, so option (C) is incorrect.
For n = 26, we have
[tex]\text{S}_n = \dfrac{26}{2}[2\times15+(26-1)0.4][/tex]
Sn = 13[30+10]
Sn = 520
Which is more than 500, so option (D) is the correct answer.
Hence, Xavier would bike more than 500 miles in 26 weeks.
Learn more about arithmetic progression here - https://brainly.com/question/27029595
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I’LL GIVE BRAINLY IF UR CORRECT!!!!!! Plus 25 points
what is the best estimate of the sum of the fractions? 31/4 + 17/3 + 8/18
13.86 would be about how much that is
Answer:it’s 13
Step-by-step explanation:
³√3²×5²×2³√3×5 help me plz
Answer:
750
3000 6^√3= 3602.8109
Step-by-step explanation:
i cant tell for the middle part if its
2. ³√3 or 2³. √3
so the first answer is for the first one and the second is for the second one
What is the length of segment LM?
thank you :)
Answer:
length of segment LM is 23.
answerrr pleaseeeeeeeeeeeee