The total mass of 5 x 10³ microorganisms is 1.2 x [tex]10^{-2}[/tex].
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Mass of an organism = 2.4 x [tex]10^{-6}[/tex] grams
The total mass of 5 x 10³ microorganism.
= 5 x 10³ x 2.4 x [tex]10^{-6}[/tex]
= 12.0 x [tex]10^{3 - 6}[/tex]
= 12 x [tex]10^{-3}[/tex]
= 1.2 x [tex]10^{-2}[/tex]
Thus,
The total mass is 1.2 x [tex]10^{-2}[/tex]
Learn more about expressions here:p
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Armando took his dog, Tasha, to the vet. Tasha was placed on the scale and weighed 45.72 pounds. The veterinarian told Armando that Tasha’s breed should weigh no more than Thirty-six and one-half pounds. Armando calculated about how much weight Tasha should lose to be under the breed’s maximum weight. 45.72 rounds to 45 rounds to 37 45 – 37 = 8 pounds Which statements are true about Armando’s calculations? Check all that apply. Armando should have added 37 to 45. Armando should have rounded 45.72 to 45.5. Armando should not have rounded Thirty-six and one-half to 37. Armando should have calculated that the difference between 45 and 37 is 7. Armando’s last step should have shown 45.5 Minus thirty-six and one-half = 9.
Answer: 17 pounds
Step-by-step explanation:
A 25 foot ladder is placed against a building at a point 21 feet from the ground find the distance from the base of the building to the base of the ladder
Answer:
The distance from the base of the building to the base of the ladder is 13.56 feet.
Step-by-step explanation:
This can be solved using Pythagorus theorem.
If the length of the ladder is taken as the hypotenuse and the distance from the building as the base of the triangle then the altitude can be found out by using
c²= a²+b²
Where c is the hypotenuse and b is the base and a is the altitude
Putting the values
25²= a²+ 21²
a²= 25²-21²
a²= 625-441
a²= 184
a= √184= 13.56 feet
The distance from the base of the building to the base of the ladder is 13.56 feet
PLEASEEEEE HELPPPPPPPP
Answer:
142.5
Step-by-step explanation:
It is 142.5 because when finding area you have to do base x height our base here is 15 and are height is 9.5 so now that we know are base and height we just multiply! so 15 × 9.5 = 142.5 Hope this helps!
3.
In which situation below would you want to use the Explicit Formula instead of the Recursive Formula
a.Find the 4th term when the first term is 7 and the common difference is -2.
b.Find the 7th term when the first term is -1 and the common difference is 10.
c.Find the 7th term when the first term is -1 and the common difference is 10.
d.Find the 11th term when the first term is -3 and the common difference is 4.
Answer:
b
Step-by-step explanation:
An explicit formula for a sequence allows you to find the value of any term in the sequence. ... A recursive formula for a sequence allows you to find the value of the nth term in the sequence if you know the value of the (n-1)th term in the sequence.
The explicit formula will be best used in finding the 7th term when the first term is -1 and the common difference is 10, the correct option is B.
What is a Recursive formula?A recursive formula is used to determine the nth term when (n-1) th term is given in the series.
The Explicit formula is when any term of the sequence has to be determined on the basis of the first term and the common difference.
The recursive formula just requires one operation, while the explicit formula requires multiple operations,
The recursive formula is limited to determining the consecutive terms while the explicit formula can be used to determine any term of the sequence.
The explicit formula will be best used in finding the 7th term when the first term is -1 and the common difference is 10.
To know more about Recursive Formula
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The right triangle on the right is a scaled copy of the right triangle on the left.
Identify the scale factor. Express your answer as a whole number or fraction
in simplest form.
15/4
5
Pleaseeee help
Answer:
1.25
Step-by-step explanation:
15 ÷ 4 = 3.75
3.75 ÷ 3 = 1.25
5 ÷ 4 = 1.25
The triangle is scaled by 1.25
Consider a triangle ABC like the one below. Suppose that a = 47, b = 59, and A = 37" (The figure is not drawn to scale.) Solve the triangle,
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or",
Answer:
B = 49.1°
C = 93.9°
c = 77.9
Step-by-step explanation:
Given:
a = 47, b = 59, and A = 37°
Required:
B, C, and c
Solution:
✔️To find B, apply the law of sines:
[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]
Plug in the values
[tex] \frac{sin(37)}{47} = \frac{sin(B)}{59} [/tex]
Cross multiply
[tex] 47*sin(B) = sin(37)*59 [/tex]
Divide both sides by 47
[tex] \frac{47*sin(B)}{47} = \frac{sin(37)*59}{47} [/tex]
[tex] sin(B) = 0.7555 [/tex]
[tex] B = sin^{-1}(0.7555) [/tex]
[tex] B = sin^{-1}(0.7555) [/tex]
B = 49.0690779° ≈ 49.1° (nearest tenth)
✔️C = 180° - (A + B) (sum of triangle)
C = 180° - (37° + 49.1°)
C = 93.9°
✔️To find c, apply the law of sines:
[tex] \frac{sin(B)}{b} = \frac{sin(C)}{c} [/tex]
Plug in the values
[tex] \frac{sin(49.1)}{59} = \frac{sin(93.9)}{c} [/tex]
Cross multiply
[tex] c*sin(49.1) = sin(93.9)*59 [/tex]
Divide both sides by sin(49.1)
[tex] c = \frac{sin(93.9)*59}{sin(49.1)} [/tex]
c = 77.8766982
c ≈ 77.9 (nearest tenth)
The perimeter of a square is 28 cm.
a) Write an equation you can solve to find
the side length of the square.
b) Solve the equation.
ANSWER ASAP CORRECT ANSWER GETS BRAIN THINGY!!!
Given the spinner below, the
probability of landing on an
A is . Predict how many times you would land on an A if you spun the spinner 24 times
A. 8
B. 9
C. 10
D. 12
Answer:
B. 9
Step-by-step explanation:
The probability of landing on A is 3/8. Now, multiply the fraction by the number of times it will be spun.
3/8 × 24 = 9
Hope this helps!
Answer:
9 times
Step-by-step explanation:
Probability for landing on A is 3/8. So, for every 8 times you spin, you predict that you will land on A 3 times (3 times out of 8 spins).
So you either
A.) multiply the probability by the total spins:
(3/8) * (24) = 9 times you land on A
or
B.) divide the 24 spins by 8, to get 3 different repeats of the probability.
So 3 * 3 = 9 times.
what percentage of 4 m is 20 cm
Answer: 5%
Step-by-step explanation:
1 m = 100 cm
20 cm/100 = 0.2m
0.2/4 = 0.05
0.05 x 100 = 5%
Answer:
5%
Step-by-step explanation:
Need help with 20y + 60 = 100
Answer:
2
Step-by-step explanation:
puting right terms together to find value of y
Answer:y = 2
Step-by-step explanation:
IF we are solving for y...
20y + 60 = 100
Subtract 60 from both sides to get y by itself...
20y = 40
divide by 20 to get y...
y = 2
A helicopter is sighted at the same time by two ground observers who are 5 miles apart, both ahead of the helicopter and in its direction of travel. They report angles of elevation of 19.5° and 31.2° to the helicopter. Find the distance from the helicopter to the further observer, to the nearest tenth of a mile.
Answer:
The distance from the helicopter to the further observer is:
d = 12.77 miles
Step-by-step explanation:
The observer with 19.5° of elevation will be denoted by 1
The observer with 31.2° of elevation will be denoted by 2.
Here we have two right triangles. Both of them have the same opposite sides, so will be useful to use the tangent function.
For the second observer:
[tex]tan(31.2)=\frac{h}{x}[/tex] (1)
Where:
h is the opposite sidex is the adjacent side (distance from the observer 2 to the point where the angle of elevation is 90° )For the first observer:
[tex]tan(19.5)=\frac{h}{5+x}[/tex] (2)
Where:
h is the opposite side5+x is the adjacent side (distance from the observer 1 to the 90° elevation point, 5 miles is the distance between observes )Let's find x from equations (1) and (2). Both of them have the variable "h" so we can equal these equations.
[tex]xtan(31.2)=(5+x)tan(19.5)[/tex]
[tex]x(tan(31.2)-tan(19.5))=5tan(19.5)[/tex]
[tex]x=\frac{5tan(19.5)}{tan(31.2)-tan(19.5)}[/tex]
[tex]x=7.04\: miles[/tex]
Now, if we use the right triangle with 19.5° of elevation, the hypotenuse will be the distance from the helicopter and the further observer (let's call d).
Let's use the cosine function to find d.
[tex]cos(19.5^{\cric})=\frac{5+x}{d}[/tex]
[tex]d=\frac{5+7.04}{cos(19.5^{\cric})}[/tex]
[tex]d=12.77\: miles[/tex]
I hope it helps you!
please answer quickk
Answer:
t + 25 = 26
t = 26 - 25
t = 1
I hope it's helps you
Y=x2= is that a function?
Simplify the expression and choose the appropriate result.
3 (2+39)
Answer:
setup below, you'll have to do the final calculation
Step-by-step explanation:
first perform the operation in parenthesis
2+39= 41
then do the multiplication 3 x 41
in general do calculations in this order
1. Parenthesis
2. Multiplication
3. Division
4. Addition
5. Subtraction
working from left to right
The function ggg models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area. Which of these statements are true? Choose all answers that apply: Choose all answers that apply: (Choice A) A More rainfall relates to more mosquitoes as long as rainfall is less than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice B) B More rainfall relates to more mosquitoes as long as rainfall is more than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice C) C When there is no rainfall, there are about 111 million mosquitoes. (Choice D) D When there is no rainfall, there are about 222 million mosquitoes.
Answer:
(Choice A) A More rainfall relates to more mosquitoes, as long as rainfall is less than 2 cm²
Step-by-step explanation:
The given function for the number of mosquitoes, (by analysis of the options) is, g(x) = 4·x - x²
Where;
x = The amount of rainfall
g(x) = The number of mosquitoes in millions
The given function can be expressed as follows;
g(x) = 4·x - x² + 0
The maximum point is given by g'(x) = d(4·x - x²)/dx = 4 - 2·x = 0
At the maximum (turning point), we have;
4 - 2·x = 0
4 = 2·x
x = 4/2 = 2
The level of rainfall that gives the maximum number of mosquitoes is, x = 2 cm²
The number of mosquitoes increases from zero rainfall up to the maximum number of 4 million mosquitoes at 2 cm² rainfall and then decreases to zero as the rainfall increases further more than 2 cm², as shown in the attached graph of the function g(x) that models the number of mosquitoes created with MS Excel
Therefore, the true statement is (Choice A) more rainfall relates to more mosquitoes, as long as (the level of) rainfall is less than (the maximum) 2 cm².
The ratio of two sums of money is 5:7 if the smaller amount is $250, what is the largest amount?
Answer:
$350
Step-by-step explanation:
[tex]\frac{250}{y} :\frac{5}{7}[/tex]
y · 5 = 250 · 7
5y = 1750
5y ÷ 5 = 1750 ÷ 5
y = 350
Answer:
$350
Step-by-step explanation:
5 is to 250 as 7 is to 'x'
5/250 = 7/x
cross-multiply:
5x = 1750
x = 350
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16 % are pennies and 30 % are dimes. There are 2 more nickels than pennies. How much money does the bag contain?
I invest $1,000 at 5% interest that compounds annually. How much will I have in 5 years?
Answer:
$250....................
Subtract 6 2/5 - 1 1/4. Simplify the answer and write as a mixed number.
Answer:5 3/20
Step-by-step explanation:
6 8/20 0- 1 5/20= 5 3/20
Need help!!!!!!!!!!!!!!!!!!!!
Answer:
Take a look at the picture below
Have a good day :)
pls and thanks Solve the equation 4(c-3) = 8 what is the value of c
Answer: C=5
Hope this helps!
Find the area of the figure
Answer:
A = 76.912Step-by-step explanation:
Area of triangle with angle of 30°:
[tex]A_1=\frac12\cdot 5^2\cdot\sin(30^o)=\dfrac{25}4=6.25[/tex]
Area of triangle with angle of 50°:
[tex]A_2=\frac12\cdot 5^2\cdot\sin(50^o)=\dfrac{25}2\cdot0.766=9.575[/tex]
Area of the rest of the figure:
[tex]A_3=\dfrac{(360-30-50)^o}{360^o}\cdot\pi\cdot5^2=\dfrac79\cdot\pi\cdot25 =61.087[/tex]
Therefore:
[tex]A=A_1+A_2+A_3=6.25+9.575+61.087=76.912[/tex]
Jello someone help is this correct answer
No links or files
Correct answer please
Answer:
c is the right answer
Step-by-step explanation:
Please help me!! How do I do this?
Answer:
I think 12 * 12/ 60 = ?
12*12= 144
144/ 60= ?
Answer:
360°
Step-by-step explanation:
I think
1/2 base ×height
1/2×60×12
30×12
=360
: A box contains 512 grams of cereal. One serving of cereal is 56 grams. How many servings of cereal does the box contain? A. 9 1/4 B. 9 1/8 C. 9 8/56 D. 9 8/512
Answer:
C. 9 8/56
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Box contain = 512 grams
One serving = 56 gram
So, we can calculate the number of serving by using following formula,
Number of serving = Box contain ÷ One serving
By putting the value, we get
Number of serving = 512 ÷ 56
= 9.14 or 9 8/56
JOeseph uses a sports drink mix. The mix is 25% orange juice and 65% cranberry juice and 10% Sprite. His bottle holds 8 cups of drink. How much cranberry juice does she need to fill the bottle?
Answer:
Cranberry juice needed to fill the bottle = 5.2 cups
Step-by-step explanation:
sports drink mix:
Orange juice = 25%
Cranberry juice = 65%
Sprite = 10%
His bottle holds 8 cups of drink.
How much cranberry juice does she need to fill the bottle?
Cranberry juice needed to fill the bottle = 65% of 8 cups
= 65/100 × 8
= 0.65 × 8
= 5.2 cups
Cranberry juice needed to fill the bottle = 5.2 cups
Orange juice needed to fill the bottle = 25% of 8 cups
= 25/100 × 8
= 0.25 × 8
= 2 cups
Orange juice needed to fill the bottle = 2 cups
Sprite needed to fill the bottle = 10% of 8 cups
= 10/100 × 8
= 0.1 × 8
= 0.8 cups
Sprite needed to fill the bottle = 0.8 cups
David can run at a consistent rate of 8.2 miles per hour. If he has 3 and a half hours to
run, how far will he run if he runs at that rate?
Answer:
David can run 28.7 miles in 3.5 hours.
Step-by-step explanation:
8.2mph × 3.5hours = 28.7miles
good luck, i hope this helps :)
8 km
b
17 km
What is the length of the missing leg?
Can 12:18 be simplified
Answer:
Yes, 12:18 is simplified to 2:3
Step-by-step explanation:
Answer:2/3 is the simplest form of 12/18.
Step-by-step explanation:
yes, 12/18 can simplified
Can anyone asnswer any of these questions?? I don't get this topic
Answer:
one
Step-by-step explanation:
one