Approximately 68.26% of the measurements fall between 46 and 74 in this distribution.
To find the proportion of measurements between 46 and 74 in a normal distribution with a mean (μ) of 60 and a standard deviation (σ) of 14, we can use the standard normal distribution (z-score) and the cumulative distribution function (CDF).
First, we need to convert the interval endpoints to z-scores using the formula:
z = (x - μ) / σ
Where x is the value in the interval, μ is the mean, and σ is the standard deviation.
For x = 46:
z₁ = (46 - 60) / 14
z₁ = -1
For x = 74:
z₂ = (74 - 60) / 14
z₂ = 1
Using the Excel functions:
=NORM.S.DIST(-1) and =NORM.S.DIST(1)
The probabilities are 0.1587 and 0.8413 respectively.
Now, we want the proportion of measurements between z₁ and z₂, which is:
Proportion = 0.8413 - 0.1587
≈ 0.6826
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Answer:
The measure of ∠SVT is 79°
Step-by-step explanation:
In the given figure
∵ US ∩ RT at V
∴ ∠SVT and ∠UVR are vertically opposite angles
∵ The vertically opposite angles are equal in measures
∴ m∠SVT = m∠UVR
∵ m∠SVT = (5y + 9)°
∵ m∠UVR = (8y - 33)°
→ Equate them
∴ 8y - 33 = 5y + 9
→ Add 33 to both sides
∴ 8y - 33 + 33 = 5y + 9 + 33
∴ 8y = 5y + 42
→ Subtract 5y from both sides
∴ 8y - 5y = 5y - 5y + 42
∴ 3y = 42
→ Divide both sides by 3
∵ =
∴ y = 14
→ Substitute the value of y in the measure of ∠SVT
∵ m∠SVT = 5(14) + 9
∴ m∠SVT = 70 + 9
∴ m∠SVT = 79°
∴ The measure of ∠SVT is 79°
Answer:
Steps given below and graph is attached.
Step-by-step explanation:
First Step:
Find out by substituting
Second Step:
Find out by substituting
Third Step:
Draw a line passing through .
Graph is attached.
Answer:
14^3 = 2,744. Common factors are 1,2,4,7,8,14,28,49,56...
13^4 = 2,197. Common factors are 1, 13, 169, and 2197.
Answer:
V= 22-2t
Step-by-step explanation:
I guess the alphabet should be v instead of y. So I am working using v
The rate at which water is draining from the tank is 2gallons/hour. This is the rate of water removal from the tank. So after an hour, 2 × 1= 2 gallons would have drained. After 5 hours, 2×5 =10 gallons would have drained
Therefore to obtain the amount of water in gallons that have been removed from the tank, you will multiply the rate by the time in hours after which the draining started.
Amount (gallons) =2×t
The amount of water remaining in the tank will be obtained by subtracting the amount of water drained after some hour (2×t) from the initial amount of water in the tank (22)
Therefore, the amount of water present in the tank (v)= 22-2t or 2(11-t) gallons
The formula to express volume of the water v in terms of time t is v = 22 - 2t, where 22 is the initial volume and 2t represents the rate at which the water is draining.
This problem is a mathematical representation of a real-world scenario using a linear equation. The volume of water v in the tank can be represented in terms of time t through the equation v = 22 - 2t. This equation illustrates the initial volume of water in the tank (22 gallons) and accounts for the constant rate at which the water is draining (2 gallons per hour).
When time t = 0 (meaning no time has passed since the water started draining), the volume of water v = 22 (the initial volume). As time increases, the volume gradually decreases at a rate of 2 gallons per hour, represented by the term -2t.
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9514 1404 393
Answer:
225 mL
Step-by-step explanation:
The amount Mariana drank was ...
(4.5 mL/s)×(17 s) = 76.5 mL
The original quantity is that amount added to the amount remaining:
original amount = amount drunk + amount remaining
= 76.5 mL +148.5 mL
original amount = 225 mL
; >-2Find
at x=16
Please show solving
The inverse function theorem says
We have
defined on , for which we get
and
The derivative of is
So we end up with