A scientist conducted an experiment to determine whether an organic cleaner is as effective as a non-organic cleaner in killing germs that cause colds and the flu. To conduct the experiment, the scientist randomly selected 50 doorknobs in a hospital. He cleaned 25 of the door knobs with the organic cleaner, and he cleaned the remaining 25 door knobs with the non-organic cleaner. After cleaning and testing all of the doorknobs, the scientist reported that the organic cleaner killed 90% of germs that cause colds and the flu on the doorknobs, while the non-organic cleaner killed 95% of germs that cause colds and the flu on the doorknobs. What can be concluded from the scientist's report?
Therefore, an organic cleaner is not as effective as a non-organic cleaner in killing germs that cause colds and the flu.
Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 81 mm, 7 mm, 6 mm B. 81 mm, 7 mm, 72 mm C. 81 mm, 7 mm, 88 mm D. 81 mm, 7 mm, 77 mm
The correct option is B. 81 mm, 7 mm, 72 mm could be the lengths of the sides of a triangle.
To determine if a set of numbers could be the lengths of the sides of a triangle, the Triangle Inequality Theorem must be satisfied. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this theorem to each set of numbers:
A. 81 mm, 7 mm, 6 mm
- The sum of the two smallest sides is 81 + 6 = 87 mm, which is greater than the third side, 7 mm. However, the sum of the two smallest sides, 7 + 6 = 13 mm, is not greater than the largest side, 81 mm. Therefore, these lengths cannot form a triangle.
B. 81 mm, 7 mm, 72 mm
- The sum of the two smallest sides is 7 + 72 = 79 mm, which is greater than the third side, 81 mm. This set satisfies the Triangle Inequality Theorem.
C. 81 mm, 7 mm, 88 mm
- The sum of the two smallest sides is 81 + 7 = 88 mm, which is equal to the third side, 88 mm. According to the Triangle Inequality Theorem, the sum must be strictly greater than the third side, so these lengths cannot form a triangle.
D. 81 mm, 7 mm, 77 mm
- The sum of the two smallest sides is 7 + 77 = 84 mm, which is greater than the third side, 81 mm. However, the sum of the two smallest sides, 81 + 7 = 88 mm, is not greater than the third side, 77 mm. Therefore, these lengths cannot form a triangle.
Based on the Triangle Inequality Theorem, the only set of lengths that can form a triangle is option B: 81 mm, 7 mm, 72 mm.
Alfonso went to famous Sam’s appliance store
Use the Babylonian method to estimate √80 to the nearest hundredth.
A child’s piggy bank contains quarters and dollar coins. There are 6 times as many quarters as dollar coins. If there are 140 coins the piggy bank, what is the total amount of money it contains?
A recipe for dessert calls for 2/4 cup of powdered sugar and 1/6 cup of brown sugar . What is the total amount of sugar needed for the recipe
Kevin had 6 nickles and 4 dimes in his pocket. If he took out one count and then a second coin without replacing the first coin-
what is the probability that both coins were nickels?
what is the probability that both coins were dimes?
what is the probability that the first coin was a nickel and the second a dime?
In this detailed answer, the probabilities of drawing two coins from Kevin's pocket - with 6 nickels and 4 dimes - are explained. The probabilities of both coins being nickels and dimes are 0 due to the lack of replacement, while the probability of one nickel and one dime is 4/15.
To calculate the probabilities of drawing coins from Kevin's pocket, where he has 6 nickels and 4 dimes:
Probability both coins are nickels: Since each draw affects the remaining number of nickels and dimes, the probability is 0.
Probability both coins are dimes: Similarly, as the draws are not independent, the probability here is also 0.
Probability of one nickel and one dime: Since Kevin has 6 nickels and 4 dimes, the probability of drawing a nickel first is 6/10 (6 nickels out of 10 coins) and drawing a dime second is 4/9 (4 dimes remaining out of 9 coins), which equals 24/90 or 4/15.
What is the surface area of the ramp in square feet and if each square foot of wood on the ramp is sold for three dollars how much would the ramp sell for
write and solve an inequality for this situation. To honor 50 years of business, All Strikes Bowling is having an anniversary special. Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes, how many games can he bowl?
To honor 50 years of business, All Strikes Bowling is having an anniversary special. The game he can bowl is 25.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
To honor 50 years of business, All Strikes Bowling is having an anniversary special.
Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes.
Charlie can bowl 25 games.
= 20 - 1.25
= 18.75
So, he can bowl game
= 18.75/ 0.75
= 25 games
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A rectangular bathtub is 5 1/2 feet Long, 1 1/2 feet wide, and 3 feet high. Daniel fills the tub to a depth of 2 feet. What is the volume of the water in the tub?
What’s $54.00 for 3 tickets in unit rate
Factor completely 2x3 + 10x2 + 4x + 20.
2(x3 + 5x2 + 2x + 10)
2[(x + 5)(x2 + 2)]
(2x + 10)(x2 + 2)
(x + 5)(2x2 + 4)
Answer:
Step-by-step explanation:
Alright, lets get started.
The given expression is :
[tex]2x^3+10x^2+4x+20[/tex]
taking 2 common factor
[tex]2(x^3+5x^2+2x+10)[/tex]
[tex]2(x^3+2x+5x^2+10)[/tex]
[tex]2[(x+5)(x^2+2)][/tex]
So, the correct answer is option B : answer
Hope it will help :)
which equation models the population (in millions), p, of austinberg t years after january 1, 2000
Khalil is wrapping a cylindrical candle for a gift. The candle is 10 inches tall and has a diameter of 1.5 inches. How many square inches of wrapping paper will Khalil need to cover the candle? Use 3.14 for pi.
Final answer:
To cover a cylindrical candle with a height of 10 inches and diameter of 1.5 inches, Khalil would need at least 50.635 square inches of wrapping paper, calculated by adding the lateral surface area and the areas of the top and bottom circles.
Explanation:
Khalil needs to calculate the amount of wrapping paper to cover a cylindrical candle. To find the surface area needed to wrap around the sides of the candle, we'll use the formula for the lateral surface area of a cylinder, which is Area (A) = 2πrL, where 'r' is the radius and 'L' is the height of the cylinder. Given that the candle is 10 inches tall and has a diameter of 1.5 inches, we calculate as follows:
The radius (r) is half of the diameter, so r = ½ × 1.5 inches = 0.75 inches.The height (L) of the candle is 10 inches.Using π as 3.14, the area A is A = 2×π× r× L = 2× 3.14 × 0.75 inches × 10 inches = 47.1 square inches.To calculate the area needed to cover the top and bottom of the candle, we use the formula for the area of a circle, which is Area (A) = πr². The candle has two circular ends.
The area for one end A = π × 0.75² inches = 3.14 × (0.5625) inches² = 1.7675 square inches.Since there are two ends, the total area for both is 2 × 1.7675 square inches = 3.535 square inches.Adding the side area and the areas of the ends, the total wrapping paper needed is 47.1 square inches + 3.535 square inches = 50.635 square inches. Khalil should therefore use at least 50.635 square inches of wrapping paper to fully cover the cylindrical candle.
write an equation that represents each mixed number as a sum of whole numbers and unit fractions 4 1/4
The equation that represents each mixed number as a sum of whole numbers and unit fractions of [tex]4\frac{1}{4}[/tex] is [tex]4\frac{1}{4}[/tex] = 4 + 1/4.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
We have the mixed fraction,
[tex]4\frac{1}{4}[/tex].
Converting the mixed fraction to an improper fraction,
[tex]4\frac{1}{4}[/tex] = 17/4
We need to write it as a sum of whole numbers and unit fractions:
So, it becomes,
[tex]4\frac{1}{4}[/tex] = 4 + 1/4
[tex]4\frac{1}{4}[/tex] = (16 + 1)/4
[tex]4\frac{1}{4}[/tex] = 17/4
Therefore, [tex]4\frac{1}{4}[/tex] = 4 + 1/4 is the required equation.
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if a ship sailed due south from iceland to antarctica, it would sail through an angle of rotation of about 140 degrees around Earth's center. Find this measure in radians. Then, using 3960 miles for Earth's radius, find how far the ship would travel
the ship would travel approximately 9685.82 miles from Iceland to Antarctica.
To convert the angle from degrees to radians, we use the conversion factor[tex]\( \pi \)[/tex]radians = 180 degrees.
[tex]\[ \text{Angle in radians} = \frac{\text{Angle in degrees} \times \pi}{180} \][/tex]
In this case, the angle in degrees is 140 degrees:
[tex]\[ \text{Angle in radians} = \frac{140 \times \pi}{180} \]\[ \text{Angle in radians} = \frac{140}{180} \times \pi \]\[ \text{Angle in radians} = \frac{7}{9} \pi \][/tex]
Next, we'll find how far the ship would travel using Earth's radius. The distance traveled on a circle is given by the formula:
[tex]\[ \text{Distance} = \text{radius} \times \text{angle in radians} \][/tex]
Given Earth's radius as 3960 miles and the angle in radians as [tex]\( \frac{7}{9} \pi \)[/tex], we can calculate the distance:
[tex]\[ \text{Distance} = 3960 \times \frac{7}{9} \pi \]\[ \text{Distance} = 3080 \pi \]\[ \text{Distance} \approx 9685.82 \text{ miles} \][/tex]
So, the ship would travel approximately 9685.82 miles from Iceland to Antarctica.
What is 0.(24) ̅ (the 24 is repeating) expressed as a fraction in simplest form?
What is 0.24 ̅ (the 4 is repeating) expressed as a fraction in simplest form?
What is 0.24 expressed as a fraction in simplest form?
PLEASE SHOW YOUR WORK
If a PENNY has a circumference of 59.69 millimeters, what is the radius?
The radius of the penny is 9.54 millimeters.
What is circumference?The circumference means the length of the literal line that surrounds and forms a circle.
What is the formula for the circumference of circle?The formula for the circumference of the circle is given by
[tex]circumference = 2\pi r[/tex]
Where,
r is the radius
and π = 3.14
What is radius?A radius is a straight line from the center of a circle to the circumference of a circle.
According to the given question.
We have a penny whose circumference is 59.69 millimeters.
Let r be the radius of the penny and 2πr be the circumference of the penny.
Since we know that, the shape of the penny is circular.
Therefore,
The radius, r of the penny is given by
[tex]2\pi r= 59.69[/tex]
[tex]\implies r = \frac{59.69}{2\pi }[/tex]
[tex]\implies r = \frac{59.69}{2(3.14)}[/tex]
[tex]\implies r = \frac{59.69}{6.28}[/tex]
[tex]\implies r = 9.54\ millimeters[/tex]
Hence, the radius of the penny is 9.54 millimeters.
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toothbrushes are $4.00 each. there is a 10% discount but also 6% sales tax. What is the new price?
A bag contains 5 red marbles, 7 white marbles, and 6 blue marbles. Find P(red or blue).
Answer:
P(red or blue) = 5/18 + 6/18 = 11/18
At what position does the ball have its maximum potential energy
A) a
B) d
C) f
D) g
A hamster wheel has a diameter of 8.5 in. How many inches does the hamster run in one revolution? Use 3.14 to approximate for π .
As hamster wheel is circular so for revolution we will find the circumference.
Diameter of the Hamster wheel = 8.5 in
One revolution of the wheel = circumference of the wheel
Circumference = π × d
π = 3.14 and d = 8.5
So, Circumference = 3.14 × 8.5
Circumference = 26.69 in
So in one revolution the hamster wheel travels a distance of 26.69 in
If Mrs garcia maintains a constant speed, consistent with the results above, how many words can she type in 49 minutes
Need help with finding the volume of this cone for #35
Find the unknown. = (764 × 2) + 12
The function f(x) = 68(1.3)x represents the possible squirrel population in a park x years from now. Each year, the expected number of squirrels is ____ the number the year before. A. 3 times B. 1.3 times C. 3 more than D. 0.3 times
Seed corn was $5 per bag, whereas dog food cost only $3 per bag. Wewoka bought 50 bags and spent $190. How many bags of dog food did she buy?
Answer:
30 bags
Step-by-step explanation:
Nc + Nd = 50
5Nc + 3Nd = 190
Multiply by -5 becomes:
-5Nc - 5Nd = -250
5Nc + 3Nd = 190
Equals:
-2Nd= -60
simplify:
-2Nd/-2 and -60/-2 = Nd= 30 bags
help me pls with the answers pls, identify each pair of angles as complementary,supplementary, or neither
Kristin’s three-year old sister is trying to arrange pink and red Starbursts in rows. She has 360 pink Starbursts and 150 red Starbursts. She wants to arrange them in rows so that there are either only pink or only red Starbursts in each row, and so that each row has the same number of Starburts. What is the least number of rows she can make?
The least number of rows she can make is when she puts N marbles in each row, such that N is the greatest common factor between 150 and 360.
To find the greatest common factor between 150 and 360 we can write them as the product of prime numbers.
150 = 15*10 = (3*5)*(2*5)
360 = 36*10 = (6*6)*(2*5) = (2*3*2*3)*(2*5)
greatest common factor between 150 and 360 is the product of these 3 factors:
GCF = 2*3*5 = 30
this means that we need to make rows with 30 marbles each.
150/30 = 5 rows of red marbles
360/30 = 12 rows of pink marbles.
A total of 5 + 12 = 17 rows.
Latoya drives 8 miles to work in 13 minutes what is her average rate