Answer: 58 %
Step-by-step explanation:
Let M represents the event of taking medicine, M' represents the event of not taking medicine and C represents the event of clearing skin,
Thus, according to the question,
n(M) = 55,
n(M') = 45,
n(M∩C) = 30,
n(M'∩C)= 22,
⇒ n(C) = n(M∩C) + n(M'∩C) = 30 + 22 = 52
Let S shows the total number of people,
⇒ n(S) = 100
Hence, the probability of cleared skin,
[tex]P(C)=\frac{n(C)}{n(S)}=\frac{52}{100}=0.52[/tex]
And, the probability of cleared skin of that people who took the medicines,
[tex]P(M\cap C)=\frac{n(M\cap C)}{n(S)}=\frac{30}{100}=0.3[/tex]
Thus, the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin,
[tex]P(\frac{M}{C})=\frac{P(M\cap C)}{n(C)}=\frac{0.3}{0.52}=0.57692307692\approx 0.58 = 58\%[/tex]
Answer: 0.58
Step-by-step explanation:
Let A = Event that the patients received the acne medication.
B = Event that the patients did not receive the acne medication.
C = Patient reported reported clearer skin.
Now,
[tex]P(A)=\dfrac{55}{100}=0.55\ \ ,P(B)=\dfrac{45}{100}=0.45[/tex]
[tex]P(C|A)=\dfrac{30}{55}\ \ , P(C|B)=\dfrac{22}{45}[/tex]
Using Bayes theorem, The probability that a patient chosen at random from this study took the medication, given that they reported clearer skin:
[tex]P(A|C)=\dfrac{P(A)\cdot P(C|A)}{P(A)\cdot P(C|A)+P(B)\cdot P(C|B)}\\\\=\dfrac{0.55\cdot\dfrac{30}{55}}{0.55\cdot\dfrac{30}{55}+0.45\cdot\dfrac{22}{45}}=0.576923076923\approx0.58[/tex]
Hence, the required probability : 0.58
Joaquin recorded a temperature of 62°F this morning for science class. The temperature increased 6 1/2°F in the afternoon before decreasing 8.7°F in the evening. What was the evening temperature?
Answer: [tex]59.8^{\circ} F[/tex]
Step-by-step explanation:
Given : Joaquin recorded a temperature of 62°F this morning for science class.
The temperature increased [tex]6\dfrac{1}{2}^{\circ}F[/tex] in the afternoon before decreasing 8.7°F in the evening.
We can write [tex]6\dfrac{1}{2}[/tex] as [tex]6+\dfrac{1}{2}=6+0.5=6.5[/tex] .
Now According to the question , the temperature at evening will be :-
[tex]62^{\circ}F+6\dfrac{1}{2}^{\circ}F-8.7^{\circ}F\\\\=62^{\circ}F+6.5^{\circ}F-8.7^{\circ}F\\\\=(62+6.5-8.7)^{\circ}\ F=59.8^{\circ}\ F[/tex]
Hence, the evening temperature was [tex]59.8^{\circ} F[/tex] .
The length of a rectangle is five times its width. The perimeter of the rectangle is at most 96 cm. Which inequality models the relationship between the width and the perimeter of the rectangle?
2w+2⋅(5w)>96
2w+2⋅(5w)<96
2w+2⋅(5w)≤96
2w+2⋅(5w)≥96
Let
L--------> the length of the rectangle
W-------> the width of the rectangle
we know that
the perimeter of the rectangle is equal to
[tex]P=2L+2W[/tex]
[tex]P\leq 96\ cm[/tex]
so
[tex](2L+2W)\leq 96[/tex] ---------> equation [tex]1[/tex]
[tex]L=5W[/tex] ---------> equation [tex]2[/tex]
Substitute equation [tex]2[/tex] in equation [tex]1[/tex]
[tex]2*(5W)+2W\leq 96[/tex]
therefore
the answer is the option
2w+2⋅(5w)≤96
Answer:
2w+2⋅(5w)≤96
Step-by-step explanation:
6. What property is being shown? 5 3 ∙ 1 = 5 3
The volume of each cube is given. Estimate the side length of the cube to the nearest integer. Use the formula V=s(cubed). The volume of the cube is 520cm cubed
What happened to the owl who swallowed a watch It's a math riddle can you answer it?
Answer:Explained below
Step-by-step explanation:
"Owl no longer needs to watch as he already has one"
Michael drove 210 miles in 3 1/2 hours. Jordan drove 330 miles in 6 hours. Which is an accurate comparison of the rates at which the two people drove?
Michael = 210 / 3.5 = 60 miles per hour
Jordan = 330/ 6 =55 miles per hour
Michael drove 5 miles per hour faster than Jordan
Answer:
M 5
Step-by-step explanation:
For your summer babysitting jobs you have 10 weeks to work before your family vacation and before you return to school in the fall. You are planning on earning and saving at least $1500 for your future car. Mrs. Harris is paying you $8.00 an hour to babysit during the day and Mrs. Sanchez is paying you $6.00 per hour to babysit her child in the evening.
• Let x = the number of hours you babysit for Mrs. Harris
• Let y = the number of hours you babysit for Mrs. Sanchez
1. Write an inequality describing the number of hours you want to work each week to reach your summer goal of at least $1500. Remember you have 10 weeks to work. How much do you want to average per week?
The inequality that represents the given situation is (8x + 4y [tex]\geq[/tex] 1500) and this can be determined by using the given data.
Given :
You have 10 weeks to work before your family vacation and before you return to school in the fall. For your future car you are planning on earning and saving at least $1500.$8 per hour is paid by Mrs. Harris.$6 per hour is paid by Mrs. Sanchez.The following steps can be used in order to determine the inequality that describes the number of hours you want to work each week to reach your summer goal of at least $1500:
Step 1 - Let the number of hours you babysit for Mrs. Harris be 'x' and the number of hours you babysit for Mrs. Sanchez be 'y'.
Step 2 - So, the inequality that represents the given situation is given below:
8x + 4y [tex]\geq[/tex] 1500
Now, the average per week can be determined by dividing 1500 by 10. So, you have to make $150 per week.
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650mL = how many ounces ?
A student wants to find the density of an egg as part of an experiment. If the weight of the egg is 57 g, and its volume is 48.25 mL, which measurement could be the most precise value of the density of the egg, in g/mL?
The most precise value of the density of the egg will be 1.18 g / mL.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Weight of the egg = 57 g
Volume = 48.25 mL
Now,
Since, Weight of the egg = 57 g
Volume = 48.25 mL
We know that;
⇒ Density = Mass / Volume
Substitute all the values, we get;
⇒ Density = 57 g / 48.25 mL
= 1.18 g / mL
Thus, The density of the egg = 1.18 g/mL
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what is the square root of 92 of the thenth place
Consider the following formula
ax - bx + y = z
which of the following represents the formula that could be used to find x?
A.) x= z-y/a-b
B.) x=a-b/z-y
C.) x= z-y/b-a
D.) x=y-z/b-a
Answer:
The right answer is C I took the assessment
The solution is:
x = (z - y)/(a - b), represents the formula that could be used to find x, from the expression ax - bx + y = z.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
the expression is:
ax - bx + y = z
now, we have to : Solve for x
Subtract y on both sides:
ax - bx = z - y
Factor GCF:
x(a - b) = z - y
Isolate x:
x = (z - y)/(a - b)
Hence, The solution is:
x = (z - y)/(a - b), represents the formula that could be used to find x, from the expression ax - bx + y = z.
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You and your friend buy 2 fruit smoothies and leave a tip. You split the total and your half comes to 3.60. What percent tip did you and your friend leave if the fruit smoothies each cost $3 each
Scientists find the same type of index fossil in two different locations on Earth. What can they conclude from this discovery?
Answer:
The index fossils are the same geological age.
Step-by-step explanation:
This could happen due to the split of the Earth millions of years ago. The Continental drift theory states that the Earth's continents have moved over geologic time relative to each other. Then, animals who were together at some time were separated by the continents drift.
Whats 95 closer to 64 or 125
To find out if 95 is closer to 64 or 125, we compare the absolute differences. 95 is 31 units away from 64 and 30 units away from 125. Therefore, 95 is closer to 125.
To determine whether 95 is closer to 64 or 125, we need to calculate the absolute differences between 95 and each of the two numbers:
Difference between 95 and 64: |95 - 64| = 31Difference between 95 and 125: |125 - 95| = 30Since 30 is smaller than 31, 95 is closer to 125 by 1 unit.
(1.21 × 10^5) - 9500
To prepare for the upcoming competition season, an Olympic skier trains 5 days per week. The average number of miles the skier will ski in 1 day is 25.7. How many miles does the Olympic skier ski in 1 week?
The results of a car race are shown. Determine who drove the fastest. Explain. Cutwright: 35 laps, 84 minutes. Evans: 42 laps, 96.6 minutes. Loza: 38 laps, 102.6 minutes.
the cost of a $12.95 pizza was shared evenly by 5 friends. How much did each person buy?
ANSWER NOW PLSSSSSSSSSSSSSSSSSSSSSSSSS
The high temperature on Saturday was 6 F. The low temperature was -3 F. What was the difference between the high and low temperatures for the day?
It's the last Q in pic
how can we rewrite and/ or simplify expressions in exponential form?
A car factory is able to produce a 120 cars per day. A new technology innovation improves the production by 10%. How many cars can the factory now produce in 5 days?
The number of cars produced in 5 days is 660.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Number of cars produced per day = 120
Increased in production = 10%
Now,
We can make an equation for the number of production of cars in x days.
y = (110% of 120)x
y = 132x
Now,
The number of cars produced in 5 days.
= 132 x 5
= 660
Thus,
The number of cars produced in 5 days is 660.
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The terms in sequence A increase by 3. The terms in sequence B increase by 8. In which sequence do the terms form a steeper line when graphed as points on a coordinate plane? Justify your reasoning.
the table shows the amount of rainfall in maryville during each week in april what was the total amount if rain in that month of april
The total amount of rainfall in Maryville for the month of April, when expressed as a mixed fraction, is 5 and 1/24 inches. Therefore the correct option is H.
Step 1: Convert mixed numbers to improper fractions
For Week 1, we have 2 2/3 inches, which is a mixed number. We convert it to an improper fraction. Since 2 is equal to 6/3, adding 2/3 gives us 8/3 inches.
Step 2: Sum up the rainfall for all weeks
Now we add the rainfall for each week:
- Week 1: 8/3 inches
- Week 2: 1/8 inches
- Week 3: 1 3/4 inches, which is the same as 7/4 inches when converted to an improper fraction.
- Week 4: 1/2 inches
Step 3: Calculate the total rainfall
The total rainfall for April is the sum of all these amounts.
Let's perform this calculation.
The total amount of rainfall in Maryville for the month of April, when summed up and expressed as an improper fraction, is \( \frac{121}{24} \) inches.
This total is reached by adding the rainfall for each week:
- Week 1's rainfall is [tex]\( \frac{8}{3} \)[/tex] inches.
- Week 2's rainfall is [tex]\( \frac{1}{8} \)[/tex] inches.
- Week 3's rainfall is [tex]\( \frac{7}{4} \)[/tex] inches.
- Week 4's rainfall is [tex]\( \frac{1}{2} \)[/tex] inches.
Adding all these fractions together gives us the total rainfall for the month.
The total amount of rainfall in Maryville for the month of April, when expressed as a mixed fraction, is 5 and [tex]\( \frac{1}{24} \)[/tex] inches.
Solve the inequality. -3/4x+1<10
To make hummingbird nectar you must use 4 cups of water and 1 cup of sugar. What is the ratio of water to sugar?
What are some ways to describe the relationship between sets of numbers?
So like real numbers, Rational numbers, Integers, Whole Numbers, and Irrational numbers.
3x+1/5 y= 7 solve for x
If the area of a park is exactly between 2.4 and 2.5 acres what is the area of the park?
Answer:
The area of the park is 2.45 acres
Step-by-step explanation:
In order to get a number exactly between other two numbers, you have to add them and then divide that result by two. In a mathematical expression: (a + b)/2, where a and b are those two numbers. In this case, the exactly between 2.4 and 2.5 acres is (2.4 + 2.5)/2 = 2.45 acres.
Alim buys 2 t-shirts for $9.50 each, a 3-pack of socks for $7.95, and a pair of shoes for $7.95 and a pair of shoes for $49.95. The sales tax is 6%. to the nearest cent, what is the total cost of Alim's purchases? Helpp
Number 39 I'm so stuck help plz