The confidence interval would help Lucy determine the probability that a parameter will fall between two values around the mean.
How to determine the normal condition for the confidence interval?The question is incomplete, as the needed parameters to answer the question are missing.
So, I will list the normal conditions for constructing the confidence interval
The condition for constructing the confidence interval include:
The sample must be a random sampleThe variables must be independenceThe samples must be a large sample i.e. 30 or greaterThe sample size should be less than or equal to 10% of the population sizeRead more about confidence interval at:
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Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg were
used in a procedure. Write an equation that can be used to determine how much of
the isotope is left after x number of half-lives.
How much would be left after 70 days?
After x half-lifes, the amount of the isotope is:
A(x*T) = 90mg*e{-x*ln(2)}
And after 70 days, there are 5.628 mg
What is the half-life?
We define the half-life as the time such that the inital amount of a given substance reduces to half of it.
If the half-life is T, the amount of the substance can be written as:
A(t) = a*e^{-λ*t}
Where λ = ln(2)/T.
and a is the initial amount.
In this case, T = 17.5 days, then:
λ = ln(2)/17.5 days = 0.0396 / day
And we also have a = 90mg
Then the exponential equation is:
A(t) = 90mg*e^{-t*0.0396 / day}
After x half-lifes, the amount of the isotope left is:
A(x*T) = 90mg*e^{-x*T*ln(2)/T} = 90mg*e^{-x*ln(2)}
And after 70 days the amount is:
A(70 days) = 90mg*e^{-70 days*0.0396 / day} = 5.628 mg
If you want to learn more about exponential decays, you can read:
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Answer:
Y=90mg(0.5)^5
1.86 after 70 days
Step-by-step explanation:
Solve the system of equations by substitution. X + y = 32 y = 7x The solution of the system is (Simplify your answer. Type an ordered pair.)
if you can can you please write out the steps
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
The given equations are :
[tex]\qquad \sf \dashrightarrow \:x + y = 32[/tex]
and
[tex]\qquad \sf \dashrightarrow \:y = 7x[/tex]
Now, plug in the value of y from equation 2 into equation 1 to find out the value of x ~
[tex]\qquad \sf \dashrightarrow \:x + y = 32[/tex]
[tex]\qquad \sf \dashrightarrow \:x + 7x = 32[/tex]
[tex]\qquad \sf \dashrightarrow \:8x = 32[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 32 \div 8[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 4[/tex]
Now, plug the value of x in equation 2 to find y
[tex]\qquad \sf \dashrightarrow \:y = 7x[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 7 \times 4[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 28[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
solve pls brainliest
Answer:
No, no, no, yes, yes.
Step-by-step explanation:
A integer is a whole number, 1, 2, 3, etc.
Use the multiplier method to increase £56 by 14% you must show your working out
Answer:
Step-by-step explanation:
First, we have to find 14% of 56
14% of 56 is = 56 x 14/100
= 7.84
Now we have to increase the number 56 by 14%, which means we have to add 14% of 56 (7.84) to the given number (56)
56 + (14% of 56)
= 56 + 7.84
= £63.84
thankyou for all the help
Answer:
1. x + y = 180
2. x = 50 y= 130
Step-by-step explanation:
They're parallel.
We can label the unamed angle z.
So z = y
and 50 = x
There's 360 degrees in a circle, so x + y= 180 because it's half 360 and half a circle.
x=50
so 50 + 50 = 100.
360 - 100 = 260
so 260 ÷ 2 = 130
y = 130 because y and z are equal so they're the same number
Step-by-step explanation:
1. x+y=180
hope that helps
The height of a projectile that is thrown upward from ground level with an initial velocity of 98 meters per second can be modeled by the equation h = −4. 9t2 + 98t, where h is the height in meters and t is the elapsed time in seconds. Find the time it takes for the projectile to hit the ground
Using the given function, it is found that the projectile hits the ground after 20 seconds.
When does the projectile hits the ground?It hits the ground when it's height, given by h(t), is equals to zero.
In this problem, the function that models it's height is given by:
h(t) = -4.9t^2 + 98t.
Then:
h(t) = 0
-4.9t^2 + 98t = 0.
-4.9t(t - 20) = 0
t - 20 = 0 -> t = 20.
The projectile hits the ground after 20 seconds.
More can be learned about functions at https://brainly.com/question/25537936
Which property can be used to solve the equation?
5 d = 75
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality
Answer: Division Property of equality
Step-by-step explanation:
5d= 75
1. Isolate the variable and remember, if the number is next to the letter, it means to multiply.
2. Reverse PEMDAS so instead of multiplying, divide instead.
3. 75/ 5 equals 15.
d=15
Answer: d=. 15
Step-by-step explanation:
Here is an expression 3/5 divided by 1/4 Which situation matches this expression?
Which situation matches this expression?
A: An athlete runs 3/5 kilometers in 4 minutes. At that rate, how many kilometers does the athlete run in 1 minute?
B: A teacher fills an empty white pitcher with 3/5 gallons of water and an empty blue pitcher with 1/4 gallon of water. How many more gallons of water are now in the white pitcher than in the blue pitcher?
C: Mr. Smith has 3/5 pounds of beans. He uses 1/4 pound of beans each week. At the rate, for how many weeks will beans last?
D: A worker cuts pieces of string that are each 3/5 yards in length. How many pieces of string can the worker cut from a piece of string that is 1/4 yard in length?
Answer:
C
Step-by-step explanation:
To find A you have to divide 3/5 by 4 so that would not work.
To find B you have to subtract 1/4 from 3/5 and that doesn't match the problem.
To find C you do divide 3/5 by 1/4 which matches the problem.
And lastly for D you would divide 1/4 by 3/5 which is the opposite of what the question is asking for.
Find the perimeter of the polygon with the vertices H(3, 2), I(5, 2), J(5, 7), K(3, 7).
Answer:
14
Step-by-step explanation:
2x((5-3)+(7-2)) = 14
Carley can mow the lawn in 5 hours. When Carley and her dad work together, they can do it in 2
hours. How long does it take Carley's dad to mow the lawn?
The time it will take Carley's dad to mow the lawn is 3.3 hours.
What is rate?Rate is the ratio between two related quantities in different units. Therefore,
The rate Carley do the lawn = 1 / 5
When they work together they do it the 1 / 2 rate.
Therefore,
let
the hours it takes Carley dad = x hours . Therefore,
1 / 5 + 1 / x = 1 / 2
x + 5/ 5x = 1 / 2
cross multiply
2(x + 5) = 5x
2x + 10 = 5x
10 = 5x - 2x
10 = 3x
x = 10 / 3
x = 3.3 hours
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Hailey paid 40$ for a jacket whose regular price was 50$. What percent of the regular price did hailey pay?
Answer:
Step-by-step explanation:
Hailey paid 80% of the regular price.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have Hailey who paid 40$ for a jacket whose regular price was 50$.
Assume that she paid [x]% of the regular price.
Then, we can write -
40 = x% of 50
40 = (x/100) x 50
x = (4000/50)
x = 80%
Therefore, Hailey paid 80% of the regular price.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer: Statements 3, 4, 5
Step-by-step explanation:
Statement (3) is true because an interior angle and its exterior angle are supplementary.
Statement (4) is true by the exterior angle theorem.
Statement (5) because the sum of the angles of a triangle is 180 degrees.
y = 7x + 20
4x - y = -11
solve by substitution
Answer:
x = - 3, y = - 1
Step-by-step explanation:
y = 7x + 20 -----> equation 1
4x - y = - 11
4x - ( 7x + 20 ) = - 11
4x - 7x - 20 = - 11
- 3x = - 11 + 20
- 3x = 9
x = 9 / - 3
x = - 3
Substitute x = - 3 in equation 1,
y = 7 ( - 3 ) + 20
= - 21 + 20
y = - 1
Hence,
x = - 3
y = - 1
Answer:
x = -3y = -1Explanation:
y = 7x + 20 __ equation 1
4x - y = -11
y = 11 + 4x __ equation 2
using substitution method,
11 + 4x = 7x + 20
4x - 7x = 20 - 11
-3x = 9
x = -3
Find y,
y = 7x + 20
y = 7(-3) + 20
y = -1
PLS HELP ME FRENDS I NEED HELP HELP THIS IS MY LAST CHANCE What is the area of the real object that the scale drawing models?
Answer:
D. 16 square cm
Step-by-step explanation:
To solve this problem, we will have to look at the Scale factor.
1 : 8 = 1 cm (in the scale drawing) = 8cm (in the real object)
Since the area of the scale drawing is 2 cm, the equation will be 2 x 8 = 16.
Therefore, 16 will be the area of the real object.
-kiniwih426
Last month, luke spent $1,300 on his mortgage (home loan payment), $320 for food, $280 on entertainment, $275 for his car payment, $60 on car insurance, and $75 on clothing. what was the difference for the month between his fixed expenses and variable expenses? brainly
The mayor of a city believes a large park in the city is becoming more popular and wants to expand nature programs at the park. A random sample of 30 summer days are selected and the number of park visitors is determined for each of those days. From this sample, the mean number of visitors was X(xbar) = 98.3 with a standard deviation of Sx = 11.2. Calculate a 99% confidence interval for the true mean number of visitors on summer days. Assume the conditions for inference are met.
a. 95.192 to 101.410 visitors
b. 34.123 to 162.480 visitors
c. 92.664 to 103.940 visitors
d. None of these is correct.
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 99% confidence interval for the true mean number of visitors on summer days is given by:
c. 92.664 to 103.940 visitors
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 30 - 1 = 29 df, is t = 2.756.
The other parameters are given as follows:
[tex]\overline{x} = 98.3, s = 11.2, n = 30[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 98.3 - 2.756\frac{11.2}{\sqrt{30}} = 92.664[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 98.3 + 2.756\frac{11.2}{\sqrt{30}} = 103.94[/tex]
Hence option c is correct.
More can be learned about the t-distribution at https://brainly.com/question/16162795
all expressions for 10x-30
Springsville runs a summer program for children at the park. The participants can choose from several activities throughout the day. The choices are shown in the table.
The answer is A. Springsville has several different activities.
Do number 17 please.
Answer:
667.2
Step-by-step explanation:
aP/2 apothem is 13.9, perimeter is 16(6)= 96
multiply apothem and perimeter then divide by 2.
what's the square root of the area of a square with side 13?
Area :-
[tex]\\ \rm\rightarrowtail side^2[/tex]
[tex]\\ \rm\rightarrowtail 13^2[/tex]
[tex]\\ \rm\rightarrowtail 169[/tex]
Square root:-
√169=13What is the value of x in the equation −5 + x = −2?
[tex]-5+x = -2\\\\\implies x = -2 +5 = 3[/tex]
Answer:
x=3
Step-by-step explanation:
−5 + x = −2
Add 5 to each side
−5+5 + x = −2+5
x = 3
State if each is a right triangle?
Answer:
yes
Step-by-step explanation:
because the hypotenus is the longest of all the other sizes
What is the area of triangle ABC?
Answer:
Step-by-step explanation:
pls help!! 15 points!
A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m2. The surface area of the image is 315 m². The height of the pre-image is 5.8 m. What is the height of the image? Enter your answer as a decimal in the box m
When trapezoidal prism undergoes a dilation, the size of the prism changes
The height of the image is 52.2 meters
How to determine the height of the image?The given parameters are:
A1 = 35 m²
A2 = 315 m²
H1 = 5.8 m
To calculate the height of the image, we make use of the following equivalent ratio
A1 : H1 = A2 : H2
So, we have:
35 : 5.8 = 315 : H
Express as fractions
35/5.8 = 315/H
Make H the subject
H = 315 * 5.8/35
Evaluate the product
H = 52.2
Hence, the height of the image is 52.2 meters
Read more about dilation at:
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Answer:
17.4
Step-by-step explanation:
Find the surface area of the prism shown below.
Find the value of X
And tell whether the side lengths form a Pythagorean triple
Answer:
8 and yes
Step-by-step explanation:
c² - b² = a²
100 - 36 = a²
64 = a²
a = 8
the three sides form a sequence, 6, 8, 10, which is the pythagorean triple.
The graph of $y = f(x)$ is symmetric across the line $x = 5$. The graph also passes through the point $(8,-7).$ Find another point that must lie on the graph of $y = f(x).$
Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.
Which other point must lie on the graph?If a function has a line of symmetry at x = x₀, then we know that:
f(x₀ + x) = f(x₀ - x).
So we have symmetry around that line.
Then, if the line of symmetry is at x = 5 and we know that:
f(8) = f(5 + 3) = -7
We also must have:
f(2) = f(5 - 3) = -7
Then the point (2, - 7) must be on the graph.
If you want to learn more about symmetry you can read:
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-4-(3) =
3+(-5) =
4+6=
-5-9=
-4+(-9) =
Step-by-step explanation:
-4-(3)=-7
step two
3+(-5)=-2
step three
4+6=10
step four
-5-9=-14
step five
-4+(-9)=-13
Answer:
a) -4 - ( 3) = - 7
b) 3 + ( -5) = 3 - 5 = -2
c) 4 + 6 = 10
d) -5 -9 = - 14
e) -4 + ( -9) = -4 -9 = - 13...
Fill in the table using this function rule
y=2x+2
Photo ⬇️
Answer:
Step-by-step explanation:
Put the values of x to the equation y = 2x + 2 and calculate the value of y:
x = 2
y = 2 · 2 + 2 = 4 + 2 = 6
x = 5
y = 2 · 5 + 2 = 10 + 2 = 12
x = 6
y = 2 · 6 + 2 = 12 + 2 = 14
x = 8
y = 2 · 8 + 2 = 16 + 2 = 18
Rob goes to a store and buys a camera originally priced at $30. The store is running a discount of 18%. The sales tax rate is 7.4%. What is the final price of the camera?
pls help asap
Answer:
$26.42
Step-by-step explanation:
P = 30 * 0.82 * 1.074 = 26.42