The exponential growth function to find the monthly growth rate is:
[tex]P(t) = 350~ (1 + 0.02493)^t[/tex]
We have,
To write an exponential growth function to find the monthly growth rate, use the following formula:
[tex]P(t) = P_0 (1 + r)^t[/tex]
Where:
P(t) is the population at time t
P₀ is the initial population (350 in this case)
r is the growth rate per time period (monthly rate in this case)
t is the time in the corresponding time period
To find the monthly growth rate.
[tex]= (1 + r)^{1/12} - 1[/tex]
= [tex](1 + 0.03)^{1/12} - 1[/tex]
= 0.02493
= 2.493 %
Therefore,
The exponential growth function to find the monthly growth rate is:
[tex]P(t) = 350~ (1 + 0.02493)^t[/tex]
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Determine if the scenario involves mutually exclusive events.
32. A cooler contains 12 bottles of sports drinks: 4 lemon-lime flavored, 3 orange-flavored, and 5 fruit-punch flavored. You grab a bottle. It is a lemon-lime or an orange.
33. Find the 5 number summary (Min, Q1, Median, Q3, Max) for the following data and draw a box and whisker graph.
18, 24, 28, 28, 36, 44, 50, 67
Answer:
32) 7/12 ≈ 58.3%
33) Min = 18
Q1 = 26
Median = 32
Q3 = 47
Max = 67
Step-by-step explanation:
Question 32To determine the probability of grabbing a lemon-lime or an orange-flavored bottle from the cooler, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
In the given scenario, there are 4 lemon-lime flavored bottles and 3 orange-flavored bottles in the cooler, plus 5 fruit-punch flavored bottles. Therefore:
Number of favorable outcomes = 4 + 3 = 7Total number of bottles = 4 + 3 + 5 = 12The probability of grabbing a lemon-lime or an orange-flavored bottle is:
[tex]\begin{aligned}\sf Probability &= \sf \dfrac{Favorable\;outcomes}{Total\; outcomes}\\\\&=\dfrac{7}{12}\\\\& \approx 58.3\%\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 33The five-number summary is a statistical summary of a dataset that includes the minimum and maximum values, the median (middle value), and the first and third quartiles. It provides a concise overview of the distribution and central tendency of the data.
First, sort the given data in ascending order (this has already been done for us):
18, 24, 28, 28, 36, 44, 50, 67Minimum valueThe minimum value is the smallest value in the data set.
[tex]\boxed{\sf Minimum \; value = 18}[/tex]
MedianThe median is the middle value of the sorted data.
In this case, we have 8 data points, so the median is the average of the two middle values:
[tex]\boxed{\sf Median\;(Q_2)=\dfrac{28+36}{2}=32}[/tex]
First Quartile (Q₁)The first quartile is the median of the lower half of the data.
In this case, we have 4 data points in the lower half (18, 24, 28, 28), so the median is the average of the two middle values:
[tex]\boxed{\sf First \;Quartile\;(Q_1)=\dfrac{24+28}{2}=26}[/tex]
Third Quartile (Q₁)The third quartile is the median of the upper half of the data.
In this case, we have 4 data points in the upper half (36, 44, 50, 67), so the median is the average of the two middle values:
[tex]\boxed{\sf Third\;Quartile\;(Q_3)=\dfrac{44+50}{2}=47}[/tex]
Maximum valueThe maximum value is the largest value in the data set.
[tex]\boxed{\sf Maximum\; value = 67}[/tex]
Therefore, the five-number summary for the given data set is:
Min = 18Q₁ = 26Median = 32Q₃ = 47Max = 67To construct the box and whisker graph (attached):
Draw a box from the lower quartile (26) to the upper quartile (47).Add the median (32) as a vertical line through the box.The whiskers are horizontal lines from each quartile to the minimum (18) and maximum values (67).The events are mutually exclusive because a bottle cannot be both lemon-lime and orange-flavored simultaneously , the scenario involves mutually exclusive events.
The five-number summary is as follows:
Minimum: 18
Q1: 26
Median: 36
Q3: 47
Maximum: 67
The scenario states that there are 12 bottles of sports drinks in a cooler: 4 lemon-lime flavored, 3 orange-flavored, and 5 fruit-punch flavored. You grab a bottle, and it is either lemon-lime or orange flavored. To determine if this scenario involves mutually exclusive events, we need to assess whether the two events (grabbing a lemon-lime flavored bottle and grabbing an orange-flavored bottle) can occur at the same time or not.
In this case, the events are mutually exclusive because a bottle cannot be both lemon-lime and orange-flavored simultaneously. Therefore, the scenario involves mutually exclusive events.
To find the five-number summary (minimum, first quartile, median, third quartile, and maximum) for the given data and draw a box and whisker plot, we need to arrange the data in ascending order first:
18, 24, 28, 28, 36, 44, 50, 67
Arranging the data in ascending order: 18, 24, 28, 28, 36, 44, 50, 67
The minimum value is 18.
The first quartile (Q1) is the median of the lower half of the data: (24 + 28) / 2 = 26.
The median is the middle value of the data set: 36.
The third quartile (Q3) is the median of the upper half of the data: (44 + 50) / 2 = 47.
The maximum value is 67.
The five-number summary is as follows:
Minimum: 18
Q1: 26
Median: 36
Q3: 47
Maximum: 67
To draw a box and whisker plot, you can use the five-number summary to create a visual representation of the data distribution. However, since I can't draw graphs here, you can create a box and whisker plot yourself. Draw a number line and place a box that spans from Q1 to Q3, with a line inside representing the median. Add "whiskers" extending from the box to the minimum and maximum values.
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The calibration of a scale is to be checked by weighing a 13 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with Sigma = 0.200 kg. Let µ denote the true average weight reading on the scale.
Required:
a. What hypotheses should be tested?
b. With the sample mean itself as the test statistic, what is the P-value?
Solution :
a).
Given : Number of times, n = 25
Sigma, σ = 0.200 kg
Weight, μ = 13 kg
Therefore the hypothesis should be tested are :
[tex]$H_0 : \mu = 13 $[/tex]
[tex]$H_a : \mu \neq 13$[/tex]
b). When the value of [tex]$\overline x = 12.84$[/tex]
Test statics :
[tex]$Z=\frac{(\overline x - \mu)}{\frac{\sigma}{\sqrt n}} $[/tex]
[tex]$Z=\frac{(14.82-13)}{\frac{0.2}{\sqrt {25}}} $[/tex]
[tex]$=\frac{1.82}{0.04}$[/tex]
= 45.5
P-value = 2 x P(Z > 45.5)
= 2 x 1 -P (Z < 45.5) = 0
Reject the null hypothesis if P value < α = 0.01 level of significance.
So reject the null hypothesis.
Therefore, we conclude that the true mean measured weight differs from 13 kg.
Someone actually help me w this ☝
Answer
Sorry If this is not correct, but I believe you keep the X varriable the same and multiply the Y varriable by 4. This means it will move to the right on the grid.
New coordinates: G(3,4) T(1,4) B(3, 20)
Huh?! Its me DaBaby less gooo i need your help with this question. Yeah Yeah!
Answer:
[tex]4\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{48} \\\\4\sqrt{3}[/tex]
Answer:
the second option is correct
Step-by-step explanation:
Write a jingle to advertise
favorite dessert to the tune of
"Twinkle, Twinkle Little Star."
What is so special about this
dessert? How can you describe it
in a memorable, catchy way?
Y’all someone help no link ,will be reported
My Jingle:
Ice cream cake - oh, ice cream cake...
How I love the way you taste...
You melt in my mouth with every bite...
Dreams of you keep me up at night...
Ice cream cake - oh, ice cream cake...
How I love the way you taste.
I hope you like it!
8. How tall is a stack of 26 coins each 0.03 m thick?
Answer:
0.78
Step-by-step explanation:
0.03*26=0.78 simple math lol
(-6, -7) and (3,-4)
Pleaseee helppppppp
Answer:
y = x/3 - 5
Step-by-step explanation:
Answer:
y = (1/3)x - 5 .
Step-by-step explanation:
(-6 , -7) ; (3 ,-4)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]=\frac{-4-[-7]}{3-[-6]}\\\\= \frac{-4 + 7}{3+6}\\\\= \frac{3}{9}\\\\=\frac{1}{3}[/tex]
m = 1/3 ; (3,-4)
y - y1 = m(x - x1)
[tex]y - [-4]=\frac{1}{3}(x-3)\\\\y + 4 = \frac{1}{3}x-3*\frac{1}{3}\\\\y + 4 = \frac{1}{3}x-1\\\\y =\frac{1}{3}x-1-4\\\\y = \frac{1}{3}x - 5[/tex]
Please help ASAP please help
Answer:
64
Step-by-step explanation:
8x4 is 32 multiplied by 2 is 64
V=LxWxH
(length x Width x Height)
I am not good at math, will give brainliest
Answer:
the answer is a
Step-by-step explanation:
Zachary's rectangle measures 4 1 /4 units by 4 1 /4 units. What is its area?
Answer:
169/12 square units.
Step-by-step explanation:
What is the volume of a cylinder with base radius 2 and height 5?
Either enter an exact answer in terms of 3.14 for pi
Answer:
V ≈ 62.83
Step-by-step explanation:
Cylinder Formulas in terms of r and h
Calculate the volume of a cylinder:
V = πr2h
Calculate the lateral surface area of a cylinder (just the curved outside):
L = 2πrh
Calculate the top and bottom surface area of a cylinder (2 circles):
T = B = πr2
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
Solution
V=πr 2h = π · 22 · 5 ≈ 62.83185
Therefore, the volume of the cylinder in the nearest tenths is V ≈ 62.83
Hey I need help .. again we’re doing log lines
Answer:
Step-by-step explanation:
¡4 = -1
O True
False
Answer:
Apparently that's false because 4 does not equal -1, 4 is totally 10 times greater than -1
Hopefully that helps
Step-by-step explanation:
What type of triangle is this if lengths of its sides are 37m, 24m, and 5m *
Answer:
weird triangle
Step-by-step explanation:
Answer:
Scalene triangle
Step-by-step explanation:
Scalene triangle: If the length of all the sides of triangle have different measurements then it is scalene triangle
A cone has the same radius and height as a cylinder which has greater volume the cone or the cylinder
Answer:
The cylinder has the great volume
Step-by-step explanation:
The volume of a cone = (h/3)πr²
The volume of a cylinder = hπr²
The only difference is that h is divided by 3 for the volume of a cone, making the total volume of a cone smaller than the volume of a cylinder with the same radius and height.
Can someone help me with this?
9514 1404 393
Answer:
π/4, 7π/4
Step-by-step explanation:
Adding √2 and dividing by 2 makes the equation ...
cos(θ) = (√2)/2
The first-quadrant solution is ...
θ = arccos((√2)/2) = π/4
The angle in the 4th quadrant with the same reference angle will have the same cosine value.
θ = 2π -π/4 = 7π/4
The two solutions are θ = π/4, 7π/4.
convert 2x + y = -1 to slope intercept form
Answer:
y=-2x-1
Step-by-step explanation:
Your goal from Standard form to slope intercept form is to have the x on the right side of the equal sign. All you have to do is subtract 2x from both sides and you end up with y= -2x-1
What is y if x=6 eqaution=y=4x+5
Find the area of the regular octagon with radius of 14
feet.
Answer:
uhm- ok ok ok level hard o my gosh
the equation p=52+0.04w models relation between the amount of water bill payment p in dollars and the number of units of water w in slope of equation
The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.
Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.
This means that the slope represents the incremental cost of each additional unit of water.
In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.
This indicates a constant rate of increase in the water bill for each additional unit of water used.
It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.
Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.
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The probable question may be:
What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?
A rectangular billboard for a high school is 10 feet high and 20 feet long. In a scale model of the school, the billboard is 3.5 inches long.
How many inches tall is the scale model?
Answer:
I think 1.75
Step-by-step explanation:
the long side is two times the amount of the tall side so take the smaller long side and divide by two.
Suppose that 55% of people own dogs. If you pick two people at random, what is the probability that they both own a dog?
Answer:
The probability to one person to be a dog owner is p=0.56 (because 56% of people own dogs) and the probability that one person is not dog owner is q=1-p=1-0.56=0.44.
Step-by-step explanation:
Choosing two people at random, there are such possibilities:
1. both are dog owners;
2. first owns a dog, second not;
3. first hasn't dog, second owns a dog;
4. both haven't dogs.
Answer: if you pick two people at random the probability that they both own a dog is 0.3136.
Hope this helps! :))
The Probability that they both own a dog is 0.3025.
Here,
55% of people own dogs.
If pick two people at random,
Then we have to find the probability that they both own a dog.
What is Probability?
Probability is defined as the likelihood of something occurring or the chance of something happening.
Now,
55% of people own dogs.
Hence, the probability that they both own a dog = 55% * 55%
= 0.55 * 0.55
= 0.3025
So, The probability that they both own a dog is 0.3025.
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Where do I put the parentheses in 15-3x4+9=12
Answer:
That depends on which operations you want to do first. The order of operations affect to outcome of the equation.
In this case:
15 - (3 x 4) + 9 = 12
Answer:
It varies but this is one example
15 - (3 x 4) + 9 = 12
plz mark as brainliest
Witch is larger? 1/3 or 3/9
Answer:
they are equal
Step-by-step explanation:
1/3 to a decimal is 0.333
3/9 is 0.333
so they are the same the person above me is wrong
What is the area of this figure? I give brainliest :)
Answer:
[tex] 217 \: {mi}^{2} [/tex]
Step-by-step explanation:
Area of the figure
[tex]= 13*7 + 21 * 6 \\ = 91 +12 6 \\ = 217 \: {mi}^{2} [/tex]
Please help me if you can!
"Jonas prepared himself to walk to the stage when the applause ended and the Chief Elder picked up the next folder and looked down to the group to call forward the next new Twelve. He was calm now that his turn had come. He took a deep breath and smoothed his hair with his hand." - The Giver *
1st person
2nd person
3rd person objective
3rd person limited
3rd person omniscient
Answer:
3rd limited
Step-by-step explanation:
Valentina buys a chandelier priced at $713. If the sales tax is 4%, how
much tax will
Valentina pay?
Answer:
$741.52 TRUSTTT
Step-by-step explanation:
Answer:
x + (tax percent out of 100)*x, which is 748.65.
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answer:
Step-by-step explanation:
Answer:
the size of the matrix 2x3
Step-by-step explanation:
just remember that rows are horizontal and columns are vertical hope this helps you out
An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
Answer
16/43
Step-by-step explanation:
17 Male + 27 female = 44 students
now n= 2 so first student was male so one male student was taken out of the equation so 16 male left. now left male students by remaining students so now total left students = 43
so, prob = remaining males/remaining students=16/43