Answer:
10^14
Step-by-step explanation:
Number of bacteria For 10^2 hours = 10^13
Number of bacteria for 1 hour = 10^13/10^2 = 10^11
Number of bacteria for 10^3 hours = 10^11 x 10^3 = 10^ (11+3) = 10^14
A school board has determined that there should be 4 teachers for every 50 students. How many teachers are needed for an enrollment of 2,650 students?
Answer:
212 teachers are needed for an enrollment of 2,650 students.
Step-by-step explanation:
This is a kind of question that can be solved using proportions.
Proportions are used when we are asked about finding one unknown value, knowing the value of others that keep a ratio among all of them, including the unknown value.
In this case, we know that a school board estimated that 4 teachers are needed for every 50 students:
[tex]\\ \frac{4_{teachers} }{50_{students}}=ratio[/tex]
If we divide 4 teachers by 50 students, we obtained a ratio, or a constant relationship that remains between teachers and students, that is, how many teachers are needed for the number of students, or more generally "how many times the first number contains the second" [Wikipedia, 2019].
We can also notice that more students require more teachers (which is a relation of direct proportionality), that is, if we require more students, more teachers are also required in the same ratio or constant already mentioned.
Then, we can make a proportion among these values because they keep the same ratio of teachers to students (but can also be students to teachers).
So, we can pose the following question:
If four (4) teachers are needed for every 50 students, how many teachers are needed to attend 2,650 students? Then,
[tex]\\ \frac{4_{teachers}}{50_{students}} = \frac{X_{teachers}}{2650_{students}} [/tex] = the same ratio or constant.
To know the amount of teachers needed for 2,650 students:
[tex]\\ X_{teachers} = \frac{2650_{students} * 4_{teachers} }{50_{students}}[/tex].
or,
[tex]\\ X_{teachers} = \frac{2650 * 4_{teachers} }{50}[/tex].
[tex]\\ X_{teachers} = 212_{teachers}[/tex].
So, for an enrollment of 2,650 students there should be 212 teachers, according to the ratio (teachers/students) previously determined by the school board.
Please help! Im so dumb ( -̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷄ ω-̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷅ )
Look at both pictures!
I need two answers!
ANSWER:
For the first picture, it is the first answer. This is because of the Exterior Angle Theorem.
For the second picture, use the Exterior Angle Theorem again, but this time, solve for x.
[tex]132 = x + (3x-24)\\132 = 4x - 24\\156=4x\\x=39[/tex]
The m∡B = 39°
Ms. Miller wants to give each of her students 1/4 of a pound of modeling clay. She has 26 students. How many pounds of modeling clay does she need?
A) 6
1
2
B) 8
3
4
C) 13
D) 26 what the answer
Answer:
she give each kid about 6
Step-by-step explanation:
26/.25=104
104/16= 6.5
A company manufactured 1,287 drones last year. The company shipped 2 percent of those drones to Australia. How many drones did the company ship to Australia? Round your answer to the nearest whole drone.
What is the domain of f/g, given f(x)=x+2 and g(x)=x-7?
Answer:
(-∞,7) U (7,∞)
Step-by-step explanation:
f(x)= x+2
g(x) = x-7
[tex]\frac{f(x)}{g(x)} =\frac{x+2}{x-7}[/tex]
Here we have x-7 in the denominator
To find domain we set the denominator =0 and solve for x
x-7=0
Add 7 on both sides
x=7
x=7 makes the denominator 0 that is undefined
So we ignore 7 for x
Hence domain is
(-∞,7) U (7,∞)
Answer:
The correct answer i believe is A.
Which table shows a proportional relationship between x and y?
x 3 9 10 15
y 1 3 4 5
x 4 6 8 10
y 6 8 10 12
x 1 5 8 10
y 15 75 120 150
x 2 3 5 6
y 3 4 7 9
Answer:
the third table listed here
Step-by-step explanation:
A "proportional" relationship has the same y/x ratio for all values of x and y.
... first table: all entries but one have y/x = 1/3. The 3rd entry has y/x = 0.4—not the same.
... second table: 6/4 ≠ 8/6
... third table: all entries reduce to y/x = 15
... fourth table: 3/2 ≠ 4/3
write the first five terms of the geometric sequence with a1=-2 and common ratio r=-5/2
Answer:
option D
Step-by-step explanation:
First term is -2
common ratio = -5/2
To get second term we multiply first term -2 by common ratio -5/2
[tex]-2 * \frac{-5}{2} =\frac{10}{2} = 5[/tex]
To get third term we multiply second term 5 by common ratio -5/2
[tex]5 * \frac{-5}{2} =\frac{-25}{2}[/tex]
To get fourth term we multiply third term -25/2 by common ratio -5/2
[tex]\frac{-25}{2}*\frac{-5}{2} =\frac{125}{4}[/tex]
Option D is correct
The first five terms of the geometric sequence with a first term of -2 and a common ratio of -5/2 are -2, 5, -12.5, 31.25, and -78.125.
To find the terms of a geometric sequence, we start with the first term and multiply each subsequent term by the common ratio. In this case, the first term, a1, is -2 and the common ratio, r, is -5/2.
The first term (a1) is -2
The second term (a2) is -2*(-5/2) = 5
The third term (a3) is 5*(-5/2) = -12.5
The fourth term (a4) is -12.5*(-5/2) = 31.25
The fifth term (a5) is 31.25*(-5/2) = -78.125
Therefore, the first five terms of the sequence are -2, 5, -12.5, 31.25, and -78.125.
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I need help with this question 15 points
Answer:
Third option
Step-by-step explanation:
You are correct, right angle forms a 90°
Hope that helps
Answer:
The third option.
Step-by-step explanation:
The first option is acute becuase the angle is less that 90 degrees.
The second options is obtuse because it is more than 90 degrees.
The third option is a right angles becuase it makes an 90 degree angle.
The fourth option is also obtuse because it is more than 90 degrees.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
The polynomial function y = x^3 -3x^2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
Answer: B
Step-by-step explanation:
x³ - 3x² + 16x - 48 = 0
→ x²(x - 3) + 16(x - 3) = 0
→ (x² + 16) (x - 3) = 0
→ (x² - (-16)) (x - 3) = 0
→ (x - 4i)(x + 4i)(x - 3) = 0
→ x - 4i = 0 x + 4i = 0 x - 3 = 0
→ x = 4i x = -4i x = 3
2 imaginary roots and 1 real root
A shoe store marks up it's merchandise by 8 percent what was the selling price of a pair of shoes whose wholesale price is 24.50
The answer is 26.46. I got it correct on my GoFormative.
The price of shoe store merchandise after markup price will be equal to 26.46.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given data given in the question,
The wholesale price of merchandise = 24.50
Markup percentage on merchandise = 8%
Then, the amount of increment in the price will be,
(24.50 × 8)/100
= 196/100
=1.96
Then, the price of merchandise after markup will be,
= 24.50 + 1.96
= 26.46
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Patty earns a raise of 4precent each year .If her starting salary is 24,812.00 , what will be her salary after one year?
Vanessa earns a base salary of \$400.00$400.00 every week with an additional 5\%5% commission on everything she sells. Vanessa sold \$1650.00$1650.00worth of items last week. What was Vanessa's total pay last week?
Answer:
Total pay = 400+ 1650* 5/100= 482,5 $
Step-by-step explanation:
Carl rode a horse about 15 f ode a horse about 15 feet from the center of the car om the center of the carousel. Allison r ousel. Allison rode a horse about 10 f a horse about 10 feet from the center om the center. How much fur . How much further did Carl' ther did Carl's horse s horse travel in one complete turn of the carousel?
Carl's horse traveled approximately 31.4 feet further than Allison's horse in one complete turn of the carousel. The distances were calculated using the circumference formula for each horse based on their distance from the centre of the carousel.
Explanation:The question involves comparing the distances traveled by horses on a carousel based on their distance from the center of the ride. To find out how much further Carl's horse traveled compared to Allison's, we need to calculate the circumference of the circular paths each horse took during one complete turn of the carousel and then find the difference between these two distances.
To calculate the circumference (C) of a circle, we use the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle, in this case, the distance from the center of the carousel to the horse.
For Carl's horse:
CCarl = 2π(15 feet) ≈ 2π×15 ≈ 94.2 feet
For Allison's horse:
CAllison = 2π(10 feet) ≈ 2π×10 ≈ 62.8 feet
The difference in the distances traveled by the horses in one complete turn is CCarl - CAllison, which is approximately 94.2 feet - 62.8 feet = 31.4 feet. Therefore, Carl's horse travelled about 31.4 feet further than Allison's horse in one complete turn.
An experiment consists of randomly selecting a marble from a bag, keeping it, and then selecting another marble. The bag contains 4 blue marbles, 3 green marbles, 7 red marbles, and 1 yellow marble. What is the probability of selecting a red marble and then a blue marble? SHOW ALL WORK!
Answer:
2/15
Step-by-step explanation:
How many marbles are in the bag
4blue + 3 green + 7 red + 1 yellow = 15 marbles
On the 1st draw:
red/total = 7/15
Since we keep the marble, there are only 14 marbles left
4blue + 3 green + 6 red + 1 yellow = 14
On the 2nd draw:
blue/total = 4/14 = 2/7
To find the probability of the two draws, we multiply them together
1st draw * 2nd draw
7/15 * 2/7 = 2/15
Simplify. 4x^2-x/16x^2-1
[tex]\dfrac{4x^2-x}{16x^2-1}=\dfrac{x(4x-1)}{(4x)^2-1^2}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x(4x-1)}{(4x-1)(4x+1)}=\dfrac{x}{4x+1}\\\\Answer:\ \boxed{\dfrac{4x^2-x}{16x^2-1}=\dfrac{x}{4x+1}}[/tex]
By simplifying (4x ² - x ) / (16 x² -1) we get :
= x / 4x + 1 .
Explain simplification?Simplifying an expression is the same as solving a math problem. When you simplify an expression, you are attempting to write it in the simplest possible manner. There should be no more adding, subtracting, multiplying, or dividing to do at the end.The basic rules and steps for simplifying any algebraic expression are as follows:
By multiplying factors, you can get rid of any grouping symbol, such as brackets and parentheses.If the terms contain exponents, use the exponent rule to remove grouping.By adding or subtracting like terms, you can combine them.Add the constants together.Given equation, (4x ² - x ) / (16 x² -1)
Factorize 4x² - x ,
= x ( 4x - 1) / 16x² - 1
factorize 16x² -1,
= x (4x - 1) / (4x + 1 ) (4x - 1 )
By cancelling common factor 4x - 1,
= x / 4x + 1
Simplifying (4x ² - x ) / (16 x² -1) = x / 4x + 1 .
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From 19801980 to 20002000, the annual profit of a company was determined by subtracting from \$625{,}000$625,000 the product of \$25{,}000$25,000 and the number of years either before or after 19901990. Which of the following equations below could be used to determine in which year, xx, the profit was \$550{,}000$550,000?
a.550−25∣x−1990∣=625
b.625 - 25 | x - 1990 | = 550625−25∣x−1990∣=550
c.625 +25 | x - 1990 | = 550625+25∣x−1990∣=550
d.625 +25 | x + 1990 | = 550625+25∣x+1990∣=550
Answer: b) 625 - 25 |x - 1990| = 550
Step-by-step explanation:
According to the question,
The annual profit of a company was determined by subtracting from $625,000 the product of $25,000 and the number of years either before or after 1990.
That is, On x year the total profit is,
P(x) = 625,000 - 25,000 |x - 1990|
But again according to the question,
On x years the profit is $ 550,000
Thus, 625,000 - 25,000 |x - 1990| = 550,000
⇒ 625 - 25 |x - 1990| = 550 ( by dividing both sides by 1000)
Therefore, Option b) is correct.
The correct equation for determining the year when the profit was $550,000 is 625 - 25 | x - 1990 | = 550, where x represents the year, option B.
The annual profit of the company can be determined by the equation that subtracts the product of a certain amount ($25,000) and the number of years before or after 1990 from $625,000. If we are given that the profit was $550,000 in year x, we need to find the value of x that satisfies this condition. We will represent the difference in years as the absolute difference from 1990, which accounts for years before and after 1990 equally.
The correct equation based on this would be the one that represents the profit ($550,000) after subtracting the product of $25,000 and the absolute difference in years from $625,000. Thus, the correct equation should subtract from $625,000 (not add to it), and it should involve the absolute value of x - 1990 to denote the number of years before or after 1990.
The equation that fits these criteria is:
625 - 25 | x - 1990 | = 550
Here, when we solve for x, we're trying to find the year in which the profit was $550,000. Therefore, option (b) is the correct choice.
Paul uses 2 and 1/4 cups of raisins to make 4 servings of trail mix. How many cups raisins are in each serving?
Answer:
9/16
Step-by-step explanation:
(2+1/4)/4=(8/4+1/4)/4=(9/4)(1/4)=9/16
Find the coordinates of the midpoint of the segment whose endpoint are H(9,4) and K(7,2)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad K(\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+9}{2}~~,~~\cfrac{2+4}{2} \right)\implies (8,3)[/tex]
find the value of x.
a) 10
b) 5
c) 6
d) 3
Answer:
x=5.
Step-by-step explanation:
set 7x-4=31 and solve.
Answer:
B)
X=5
Step-by-step explanation:
7x-4=31
+4 on both sides
7x=35
divide by 7 on both sides
x= 5
Which of the following functions best describes this graph
Answer: Choice C)
y = (x-2)(x-2)
note: This is the same as y = (x-2)^2
======================================================
The x intercept or root is x = 2, so x-2 is a factor. There is only one root visible, but this is a parabola, so it's technically a double root (it repeats itself). That is why (x-2) shows up twice giving (x-2)(x-2)
If the equation was simply y = x-2, then it would be a linear equation instead of a curved parabola.
Note how plugging in x = 2 leads to the following y value
y = (x-2)(x-2)
y = (2-2)*(2-2)
y = 0*0
y = 0
So (2,0) is the only x intercept.
Saul simplifies the expression 2x3 + 4x3 to 6x6. Use the drop-down menus to complete the statements below to explain why Saul's solution is correct or incorrect.
Answer:
Saul is incorrect. The proper answer should be 6x^3
Step-by-step explanation:
Think of "x^3" as "x". So we have 2x+4x = 6x. Similarly, 2x^3+4x^3 = 6x^3. The exponents of the like terms do not change.
As a more real world example, let's say that we replace "x^3" with "dogs". Saying "2x^3" could mean "2 dogs". Same goes for "4x^3" meaning "4 dogs". So "2x^3+4x^3" turns into "2 dogs + 4 dogs", and you can see that leading to 6 dogs total. The last step is to replace "dogs" with "x^3" to end up with 6x^3. The x^3 stays the same the whole time in much the same way that "dogs" do not change either.
Answer:
saul is incorrect
2x3 + 4x3 is the same as (2 . x^3) + (4 . x^3)
6x6 is the same as 6x . x. x. x. x. x
2x3 + 4x3 simplifies to 6x^3
Step-by-step explanation:
Mr. Ramirez receives 4 sets of books each set has 16 fiction books and 14 nonfiction books he puts 97 books in his lilbarry and donates the rest how many books does he donate
Mr. Ramirez donates 23 books.
Explanation:To find the number of books that Mr. Ramirez donates, we first need to calculate the total number of books he receives. Since each set has 16 fiction books and 14 nonfiction books and he receives 4 sets, the total number of books he receives is 4 sets * (16 fiction books + 14 nonfiction books) = 4 * (16 + 14) = 4 * 30 = 120 books.
Since Mr. Ramirez puts 97 books in his library, he donates the remaining books. To find the number of books he donates, we subtract the number of books he keeps from the total number of books he receives: 120 books - 97 books = 23 books.
Therefore, Mr. Ramirez donates 23 books.
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Mr. Ramirez donates 23 books.
Explanation:To find out how many books Mr. Ramirez donates, we need to first calculate how many books he receives in total.
Each set has 16 fiction books and 14 nonfiction books, so each set contains 16 + 14 = 30 books.
Since Mr. Ramirez receives 4 sets, he receives a total of 4 x 30 = 120 books.
We know that Mr. Ramirez keeps 97 books in his library, so he donates the rest.
To find out how many books he donates, we subtract the number of books kept from the total number of books received:
120 - 97 = 23 books.
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Shelly is trying to improve her running time for a track race she ran the first race in 43.13 seconds her time was 43.1 seconds in the third race of this pattern continues what will Shelly time will be inthe fourth race
Answer:
The time in the fourth race is 43.04 seconds.Step-by-step explanation:
Shelly's first race time is 43.13 seconds.
Shelly's second race times is 43.1 seconds.
Basically, she improved 0.03 seconds, because 43.13 - 43.1 = 0.03.
If she keeps this patterns that means she will improve 0.03 each race.
So, the third race times is 43.1 - 0.03 = 43.07 seconds.
The fourth race time is 43.07 - 0.03 = 43.04 seconds.
Therefore, the time in the fourth race is 43.04 seconds, because she's improving at a constant rate of 0.03 seconds per race.
What is the relationship between the ratios? 48/72 and 6/9 Drag and drop to complete the statement.
a. proportional
b. not proportional
The graph shows calories compared to grams of protein.
What information can you draw from the point (3, 12) on the graph?
A. There are 12 calories in 3 grams of protein.
B. There are 3 calories in 1 gram of protein.
C. There are 3 calories in 12 grams of protein.
D. There is 1 calorie in 4 grams of protein.
Answer:
By the looks of it i would assume 3 grams of protein and 12 calories burned but i am not sure either i am stuck on the same question
Step-by-step explanation:
Amanda put $1500 in her savings account. After five years she had $1833 in the account. What rate of interest did she earned use the formula a equals PE to the power of rt and t is time and
Answer: 4.01% interest rate
This value is approximate. It is rounded to the nearest hundredth of a percent.
============================================
Work Shown:
A = P*e^(r*t)
1833 = 1500*e^(r*5)
1833/1500 = e^(5r)
1.222 = e^(5r)
e^(5r) = 1.222
5r = Ln(1.222)
5r = 0.2004888607494
r = 0.2004888607494/5
r = 0.04009777214989
r = 0.0401
r = 4.01%
Ivan's favorite colors are \blue{\text{blue}}blue and \green{\text{green}}green. He has \blue{\text{1 blue shirt}}1 blue shirt, \green{\text{1 green shirt}}1 green shirt, \blue{\text{1 blue hat}}1 blue hat, \green{\text{1 green belt}}1 green belt, \blue{\text{1 blue pair of pants}}1 blue pair of pants, and \green{\text{1 green pair of pants}}1 green pair of pants. Ivan selects one of these garments at random. Let A be the event that he selects a green garment and B be the event that he chooses a pair of pants. What is P(A\text{ or }B)P(A or B), the probability that the garment Ivan chooses is either green or a pair of pants?
Answer:
P(A or B) = 2/3
Step-by-step explanation:
Blue Garments = 1 blue shirt, 1 blue hat, 1 blue pair of pants
Total blue garments = 3
Green garments= 1 green shirt, 1 green hat, 1 green pair of pants
Total green garments = 3
Total no. of garments = blue garments +green garments = 6
A = event that Ivan selects a green garment
P(A) = Favourable outcomes/Total no. of outcomes
P(A) = 3/6
B = event that Ivan chooses a pair of pants
P(B) = 2/6
We need to find P(A or B) = P(A∪B)
By formula, P(A∪B) = P(A)+P(B)-P(A∩B)
P(A∩B) = Probability that a green pair of pant is chosen = 1/6
P(A∪B) = 3/6+2/6-1/6
= 4/6
=2/3
Answer:
1/2
Step-by-step explanation:
Which input value produces the same output value for the two functions on the graph?
X= -3
X= -1
X= 1
X= 3
Answer:
X=3
Step-by-step explanation:
We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship. This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.
Answer:
The correct option is 4.
Step-by-step explanation:
If the graph of a function represent in coordinate plane, then x-axis represents the domain of the function and y-axis represents the range of the function.
We have to find the input value that produces the same output value for the two functions on the graph.
From the given graph it is clear that the intersection point of both functions is at (3,-1).
At x=3 the output value of f(x) is -1.
At x=3 the output value of g(x) is -1.
It means both functions have same output -1 at x=3.
Therefore the correct option is 4.
What is the area of this parallelogram? 4.9 cm? 12.25 cm? 17.15 cm? 24.01 cm? Parallelogram A B C D is composed of a square and two triangles. The square has a length and height of 3.5 centimeters each. There are two identical triangles. Each triangle has a base of 1.4 centimeters and a height of 3.5 centimeters.
Answer:
(C) 17.15
Step-by-step explanation:
PLEASE NEED HELP ASAP WILL GIVE 50 POINTS
What is the value of x?
Enter your answer in the box.
x =
Answer: x = 3
Those angle markings tell us that all three angles are the same measure (60 degrees). So this is an equilateral triangle with each side congruent to each other.
Pick 2 sides, equate the expressions, solve for x. I'm going to pick AB and AC to work with
AB = AC
6x - 3 = 3x+6
6x-3x = 6+3
3x = 9
x = 3
----------
This works with any pair of sides, such as AC and BC
AC = BC
3x+6 = 5x
6 = 5x-3x
6 = 2x
2x = 6
x = 3
----------
and let's do the last one to be complete (it's optional)
AB = BC
6x-3 = 5x
6x-5x = 3
x = 3
Either way, we get the same result each time.