Answer:
Part A
The most correct option is;
b. y = 128(0.989)x + 72
Part B
Ella can drink the tea after 7:22
Step-by-step explanation:
Here we have the temperature variation with time given in an exponential equation as follows;
Let the temperature at time x (in minutes) = y
Therefore, y = a × mˣ + b
Where:
b = Shift of the curve or the limit value of the decreasing exponential function as x → ∞
When y = 200, x = 0
Therefore. 200 = a × m⁰ + c = a + c
We note that c is the shift of the graph, the value upon which temperature increases = final temperature = 72°F
Hence a = 200 - 72 = 128°F
When y = 197, x = 2 minutes
Therefore, 197 = 128·m² + 72 =
m² = (197 - 72)/128 = 125/128
m = √(125/128) = 0.98821
Hence the exponential equation of cooling is presented in the following equation;
y = 128 × (0.98821)ˣ + 72
Therefore, the most correct option is b. y = 128(0.989)x + 72
Part B
When the temperature is 172°F we have;
172 = 128 × (0.989)ˣ + 72
∴ (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32
log(0.989)ˣ = log(25/32)
x·log(0.989) = log(25/32)
x = log(25/32)/log(0.989) = 22.32 minutes
Hence Ella can drink the tea after 7:22.
Starting at home, Michael traveled uphill to the gift store for 25 minutes and just 10 mph. He then travel back home along the same path downhill at the speed of 30 mph.
What is his average speed for the entire trip from home to the gift store and back?
Answer:it took him 8 minutes on the return trip, for a round-trip time of 32 minutes. his average speed was (8mi/32min) (60min/hr)=15 mph for the whole trip
Step-by-step explanation:
-3(x + 4) = (-x - 1)
Answer:
x=-5.5
Step-by-step explanation:
-3(x+4)=(-x-1)
1. Distribute
-3x+(-12)=-x-1
2. Simplify
-3x-12=-x-1
-2x-12=-1
-2x=11
x=-11/2
x=-5.5
Answer:
-11/2 or 5.5
Step-by-step explanation:
2. Sumara Kato's savings account has a balance of $1663. After 19 years, how much interest
will she have eamed if her rate is 5.5% compounded annually?
Answer:
Step-by-step explanation:
interest = Amount - principal
A = P(1+r)^t
r = 5.5% = 5.5/100 = 0.055
A = 1663(1+ 0.055)^19
A = 1663 (1.055)^19
A = 4,599.270812203411
Let’s say A = 4,599
interest = 4,599-1663 = 2,936
Need help Soon as possible
Answer:
D; D
Step-by-step explanation:
The common difference of the first sequence is 10, so the coefficient is 10. The first term minus the common difference is -8, so that is the constant
The common difference of the second sequence is 3, so the coefficient is 3. The first term minus the common difference is -9, so that is the constant.
you flip a coin 20 times. you land on heads 13 times. what is the percent error?
Answer:
65%
Step-by-step explanation:
You have to do 13 divided by 20 and get 0.65 and then multiply by 100
and get 65
You randomly survey men and women about whether they plan to watch a football game on Sunday afternoon. A total of 40 men plan to watch a football game and a total of 17 women do not plan to watch a football game. A total of 45 women are surveyed. A total of 33 people do not plan to watch a football game. How many people did you survey?
Answer: 101
Step-by-step explanation:
45 women total
17 women will not watch the game
So 33 people did not want to watch the game and 17 are women
33-17 = 16 men who won’t watch the game
So 40 men who will and 16 men who won’t equals 56 men and 45 women
56+45= 101
Frank measured 56 cm. The actual length was 61 cm. Which expression shows his percent error?
Answer: 8.54701% difference
Step-by-step explanation: (61-56)/[(61+56)/2] x 100= 8.55%
In parallelogram WXYZ, what is CY?
Answer:
The correct answer is 11 ft.
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.
Subtract x from each side:
x+4-x=2x-7-x
4=x-7.
Add 7 to both sides:
4+7=x-7+7
11=x
Answer:
11
Step-by-step explanation:
On edge
What is the value of x?
Answer: x = 9, y = 5
Step-by-step explanation:
If all of the sides are equal, it is an equilateral triangle. Equilateral triangles are also equiangular. The angles of a triangle add up to 180 degrees, so each angle must equal 60 degrees.
set the equation equal to 60 to solve for x
7x - 3 = 60
add three to both sides
7x = 63
divide both sides by 7
x = 9
find y by setting the equation equal to 60
11y + 5 = 60
subtract 5 from each side
11y = 55
divide both sides by 11
y = 5
what is m if 9/7m= 1/7
Answer: [tex]m=\frac{1}{9}[/tex]
Step-by-step explanation:
[tex]\frac{9}{7}m=\frac{1}{7}[/tex]
Multiply by the reciprocal to isolate m.
[tex](\frac{7}{9} )\frac{9}{7}m=\frac{1}{7}(\frac{7}{9} )[/tex]
[tex]m=\frac{1}{9}[/tex]
7. What is the value of the expression 3(2 - 7)
Answer:
-15
Step-by-step explanation:
3(2 - 7)
PEMDAS says parentheses first
Subtract
3 (-5)
Multiply
-15
When we plot all the points that satisfy an equation or inequality we __ it.
Everything what’s the answer using the order of operations
Answer:
7*3=21
8-5=3
21+3-24
Step-by-step explanation:
Find the percent of all values in a normal distribution for which z ≤ 1.00, to the nearest tenth of percent.
Answer:
84.1% of all values in a normal distribution have z ≤ 1.00.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
The percent of all values in a normal distribution for which z ≤ 1.00.
This is the pvalue of Z = 1.
Z = 1 has a pvalue of 0.8413.
Converting to percentage, to the nearest tenth.
84.1% of all values in a normal distribution have z ≤ 1.00.
A washer and a dryer cost 1021 combined. The washer costs 71 more than the dryer. What is the cost of the dryer?
Answer:
475
Step-by-step explanation:
1021-71
950/2
If P(A)=35, P(B)=13, and P(A∩B)=18, are A and B independent?
Select the option that provides both the correct answer and the correct reason.
No, because 35(13)≠18.
Yes, because 35(13)=18.
Yes, because 35+13=18.
No, because 35÷13≠18.
No, because 35+13≠18.
Answer:
P(A) x P(B) = 35 x 13 = 455
P(A∩B) = 18
=> P(A) x P(B) ≠ P(A∩B).
=> A and B are not independent.
=> Option A (No, because 35(13)≠18) is correct.
Hope this helps!
:)
A and B are not independent because 35(13)≠18), the correct option is A
What is the independent probability?Independent events and probability can be defined as those occurrences that are not dependent on any specific event.
P(A)=35, P(B)=13, and P(A∩B)=18, are A and B independent.
It is to note here that A and B are the odd number outcome and multiples of 3 respectively. So, P (A ∩ B) = 18
P(D│E) = P (D ∩ E)/ P(B)
P(D│E) = 18/13
Here P(D) = P(D│E) = 18/13, which entails that the occurrence of event E will not be affected by the probability of event D’s occurrence.
Taking A and B as independent events, then P(D│E) = P(D).
Here, A and B are not independent because 35(13)≠18), the correct option is A.
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ2
What is 2/3 ÷ 4/5 = ?
Answer:
5/6
Step-by-step explanation:
2/3 ÷ 4/5 = ⇒ changing division to multiplication by reciprocal of the second fraction2/3 × 5/4 = ⇒ simplify and multiply numerators and denominators5/6 ⇒ here is the answerPlease help please please now I nee help
Answer:
AC =3.76
Step-by-step explanation:
sin theta = opposite / hypotenuse
sin 70 = ? / 4
Multiply each side by 4
4 sin 70 = ?
3.758770783 = ?
Rounding to nearest hundredth
3.76 = ?
AC =3.76
Answer:
3.76 units
Step-by-step explanation:
We want to use trigonometry to solve this - specifically, the trigonometric function sine, which is opposite divided by hypotenuse.
Here, the opposite side is AC, which is what we want to find, while the hypotenuse is AB, which is 4. The angle itself is angle ABC, which is 70 degrees. Now, write:
sin(70) = opposite / hypotenuse = AC / 4
Multiply both sides by 4:
AC = 4 * sin(70) ≈ 3.76 units
4 inches 6 inches and 9 inches
v= in3
Answer:
what are you asking the total or what
A shelf at a grocery store contains 500 packages of corn and flour tortillas. If 22% of the packages are flour tortillas how many packages are corn tortillas
Beth participated in a free throw contest. She took 10 shots, and she made 6 of them.
Beth wants to know how to describe the number of baskets she made.
Answer:
Beth made 60% of her shots.
Step-by-step explanation:
Given:
Total shots take = 10
Total goal = 6
Find:
Best describer this number.
Computation:
Converting goal numbers into percentage:
⇒ Total goal percentage = [Total goal/Total shots take]100
⇒ Total goal percentage = [6/10]100
⇒ Total goal percentage = 60%
Beth made 60% of her shots.
Answer:
6:10 is the ratio
Step-by-step explanation:
as a fraction it would be 6/10
as a decimal it would be 0.60 or 0.6
and she made 60% of her shots
-189=4x-3(-4x+15) help me i need help badly
Answer:
Step-by-step explanation:
−189=4x−3(−4x+15)
−189=16x−45
16x−45=−189
16x−45+45=−189+45
16x=−144
16x /16
= −144 /16
x=−9
Good luck honey !!
Answer:
x=-9
Step-by-step explanation:
-3×-4= 12x -3×15=-45
4x+12x-45=-189
4x+12x=16x
16x-45=-189
16x=-144
x=-9
If X - 14 = 465, what is the value of X?
Answer: The value of x is 479
Step-by-step explanation:
x -14 = 465
+14 +14
x= 479
Answer:
x=479
Step-by-step explanation:
x-14=465 Move constant to the right-hand side and change its sign
x=465+14 add the numbers
x=479
HOPE THIS HELPS :)
Please help!! A box contains 7 yellow, 5 blue, and 4 red balls. Three balls are drawn at random. What is the probability that exactly two balls are yellow?
Answer:
7/16 or (if you are looking for a word) likely
Step-by-step explanation:
Plz help! Question is in the picture :)
Answer:
32.94%
Step-by-step explanation:
Hope this helps
what is k if k-3/4 = 10
Answer:
Move all terms not containing k to the right side of the equation.
Exact Form:
k = 43/4
Decimal Form: k = 10.75
Mixed Number Form:
k = 10 3/4
In construction, floor space must be planned for stair cases. If the vertical distance between the first and second floors it's 3.6 m and a contractor is using the standard step pattern of 28 cm wide for 18 cm high and how many steps are needed to get the first to the second floor and how much linear distance( ie "width" or "base" ) Will be needed for the staircase? What is the length of the railing that would be attached to these stairs
Answer:
665.73 cm or 6.65 m
Step-by-step explanation:
The first thing is to pass the distance in meters to centimeters, knowing that 1 meter equals 100 centimeters:
3.6m * 100cm / 1m = 360cm
Now we calculate the number of steps:
360 cm / 18 cm = 20 steps
Now each step measures 28 cm, therefore:
20 * 28 = 560 cm
To calculate the length of the ladder, we must apply Pythagoras:
c ^ 2 = a ^ 2 + b ^ 2
a = 360; b = 560
replacing:
c ^ 2 = 360 ^ 2 + 560 ^ 2
c ^ 2 = 443200
c = 665.73
665.73 cm in meters would be 6.65 meters.
Emter 2/2/8 as an inpropper fraction
Answer:
The answer is 9/4
Step-by-step explanation:
What is the first step to solving the quadratic equation x2=9over 16
Answer:
divide both sides by 2
Step-by-step explanation:
divide both sides by 2 then simplify and get x = 9 over 32
Answer:
Transposing square to rhs,it becomes root
Step-by-step explanation:
[tex]x^{2} =9/16[/tex]
[tex]x=[/tex][tex]\sqrt{9}/\sqrt{16\\[/tex] (transposing square to rhs,it becomes root)
[tex]x= 3/4[/tex]
Hope it helps...Pls mark as Brainliest!!!
Please help asap! Will give brainliest! Please answer correctly! No guessing. Check all that apply.
Answer:F
Step-by-step explanation:
Answer:
i honestly think that its A, C, D, F.
Step-by-step explanation:
for the A i think that you need to write down the facts so you dont forget and you remember when someone asks you a question.
For C you should gather your resources so you can do the experiment again if your not satisfied with the first result.
For D you should draw a diagram so you can keep track of your information that you used to get the final solution.
For F, you should always make sure that you didn't mess up and that you can redo it to double check.
