Hey there! I'm happy to help!
We want to put this 0.002 into scientific notation, where you put it as a one digit number multiplied by 10 raised to a certain power.
If we move the decimal to the right 3 times, we will have 2. We will multiply this 2 by [tex]10^-^3[/tex] to show that it is still equal to 0.002.
So, the mass of the mustard seed is 2×[tex]10^-^3[/tex].
Now, we multiply this mustard seed mass by the number of mustard seeds to find the weight of all of the mustard seeds combined.
(2×[tex]10^-^3[/tex])×(4.3602×[tex]10^4[/tex])
Let's round 4.3602 to the nearest whole number, which is 4. We multiply those two together.
2×4=8
And we multiply the two exponents. When multiplying them, you add the numbers in the exponent. -3 and 4 combined gives us 1, and 10 the first power is just 10.
So, a good estimate for the mass of the mustard seeds is 80 grams, which is the same as (2×[tex]10^-^3[/tex])×(4×[tex]10^4[/tex])=8×[tex]10^1[/tex]
Have a wonderful day! :D
Answer:
Hey There!! The answer to this is B: The mass of a single seed can be written as
There are total of seeds in the jar
Total mass is the multiplication of these both numbers.
Since we want an estimate, we can use 4 instead of 4.3602 in the 2nd number.
The rule to multiply two numbers in scientific notation is:
So using this formula we multiply the 2 numbers and get answer as follows:
Thus, Answer choice B is right.
Hope It Helped!~ ♡
ItsNobody~ ☆
(k) 2 cos 16A + 1 = (2 cos 2A - 1).(2 cos 2A + 1).(2 cos 4A-1).(2cos 8A-1).
I need help to prove this......
Qno. k.
Answer: see proof below
Step-by-step explanation:
Use the following Double Angle identity: cos 2A = 2cos²A - 1
We are going to find one factor at a time:
2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)
↓ ↓ ↓ ↓
factor last factor 2nd factor 1st
Proof LHS → RHS:
Given: 2 cos16A + 1
let α = 8A, then 2·cos2α + 1
Identity: 2(2cos²α - 1) + 1
Distribute: 4cos²α - 2 + 1
Simplify: 4cos²α - 1
Factor: (2cosα - 1)(2cosα + 1)
Substitute: (2cos8A - 1)(2cos8A + 1)
let β = 4A, then 2·cos2β + 1
Identity: 2(2cos²β - 1) + 1
Distribute: 4cos²β - 2 + 1
Simplify: 4cos²β - 1
Factor: (2cosβ - 1)(2cosβ + 1)
Substitute: (2cos4A - 1)(2cos4A + 1)
let Ф = 4A, then 2·cos2Ф + 1
Identity: 2(2cos²Ф - 1) + 1
Distribute: 4cos²Ф - 2 + 1
Simplify: 4cos²Ф - 1
Factor: (2cosФ - 1)(2cosФ + 1)
Substitute: (2cos2A - 1)(2cos2A + 1)
(2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) [tex]\checkmark[/tex]
Answer:Use the following Double Angle identity: cos 2A = 2cos²A - 1
We are going to find one factor at a time:
2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)
Step-by-step explanation:
Please solve the one w the underline please ❤️❤️
Answer:
6 ÷ 6 + 6 x 6
Step-by-step explanation:
Hope this helps :D
How many ways can 4 people sit in a row of 7 chairs?
[tex]7\cdot6\cdot5\cdot4=840[/tex]
A diver dives 17 2/3 yards and then comes back to the surface. Then, she dives 9 3/8 yards deeper than her first dive. What is her depth, in yards, in relation to the surface of the water?
(giving the points this website is allowed to give me)
The total depth covered by the diver is 27(1/24) yards.
What is yard?Yard is a unit to measure length. 1 yard is equal to 36 inches.
1 yard= 3 feet or (0.9144 meter)
What is
Given that,
First time depth reached by diver = 17(2/3) yards
In the second time, the depth reached by the diver is 9(3/8) yards more than the first time,
To find total depth,
Add depth covered by first time and second time,
Total depth = 17(2/3)+9(3/8)
=53/3+75/8
= 27(1/24)
The total depth covered by the diver is 27(1/24) yards.
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a contractor is in charge of hiring people for construction project the number of days it would take to complete a project with ex full time workers can be found using the function f (x) equals 1 26/x.assume once workers are assigned to the project no workers may be added or taken out the project until it is finished find and interpret the given function values and determine an appropriate domain for the function
This is about understanding domain of a function.
The domain of the function is x is a set of positive integers.
We are given the function;f(x) = 126/x
Where;
f(x) is the number of days it would take to complete a project with x number of workers
x is number of workers it will take to complete the project.
We want to find the domain for the given function.Domain is defined as the set of all possible input values for which the function is defined.
Let's try x = 0 workers.
f(x) = 126/0 ; this is undefined and so x cannot be zero.
Let's try x = 1 worker
f(x) = 126/1 = 126 days
Let's try x = 10 workers
f(x) = 126/10 = 12.6 days
Let's try x = 100 workers
f(x) = 126/100 = 1.26 days
We see that every positive integer is a possible value of x that can make the function defined. Since 0 and negative numbers will make the function invalid.
Thus, the domain of the function is x is a set of all positive integers.
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Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle_______ more red bottles than plant A. Plant C would recycle________________ more red bottles than plant D.
Answer:
70
80
Step-by-step explanation:
Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle___70____ more red bottles than plant A. Plant C would recycle_____80___________ more red bottles than plant D.
A = We first multiply 150 x 2.333 (2 1/3) = 350 tbottles 60 x 2.333 = 140
B = Then multiply 350/200 = 200 x 1.75 350 tbottles RED = 120 x 1.75=210
First answer = 210-140 = B recycles 70 more than A
C = We first multiply 175 x 2 = 350 tbottles RED = 110 x 2 = 220
D = We first find LCM of 180 and 350
Then find 18x now equals 1/10 x 35x tbottles RED = 72 / 18 = 4 then 4 x 35 = 140
Second answer = 220-140 = C recycles 80 more than D.
Answer:
Plant B would recycle 60 more red bottles than plant A. Plant C would recycle 38 more red bottles than plant D.
Hope this helps!
Sorry for answering so late!
Select all decimals that are equivalent to (9 x 100) + (2 x 10) + (3x ) + (5 x it).
A. 92.35
B. 920.350
C. 902.35
D. 92.350
D E 920.35
F. 920.035
Answer:
the answer to the question is letter E I believe
Complete the statement. The line x = −2 is _______.
Answer:
see explanation
Step-by-step explanation:
The line x = - 2
Is a vertical line parallel to the y- axis
It passes through all points with an x- coordinate of - 2
write an equation of the line that passes through the given points
(-2,9) and(1,-3)
Answer:
Y = -4x + 1
Step-by-step explanation:
1. We know the equation of a line is y=mx+b.
2. using the slope formula, [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], to find the slope. -12 / 3 = -4, so the slope is -4.
3. we need to find the Y intercept, or the Y coordinate at X=0. if at x=1 the Y is -3, and the slope is -4, then if we go down to x=0 then the Y would be 4 higher. therefore the Y intercept is 1.
4. now we can make the equation; Y = -4x + 1
apples are on sale for $3 and 12 per kilogram is the total cost of the apples proportional to the total yes or no
Answer:
yes the apples are porportinal
Step-by-step explanation:
Answer:
apple is proportional
Step-by-step explanation:
Please help me with this geometry question:((
Answer:
a.ans=(1,3)
b.ans=(1,2,3,4,5,6,7,9,11,12)
c.ans=(1,3,5,7,9,11)
Step-by-step explanation:
Between A and C (1,3) are common.So it is the intersection.
(1,2,3,4,5,6,7,9,11,12) are all the number belongs to set A and set C.So it is called the union of both sets.
C denotes the complement and the number except set b belong to the complement.
Which equation represents an ellipse with foci at (3, 2) and (-9, 2)
that passes through the point (-3, 10)?
Answer:
D, since it horizontal ellipse, a is greater than b
An ellipse has two foci. The correct option is D.
What is the equation of ellipse if its major and minor axis and centre are given?Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Coordinates of its foci would be: (h±c, k) where c² = a² - b²
If its major axis is parallel to the y-axis, then,
coordinates of its foci would be: (h, k±c) where c² = a² - b² and its equation would be:
[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]
Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,
[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]
Hence, the correct option is D.
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3 to the power of 5 equals 243. Explain how to use that fact to quicky evaluate 3 to the power of 6.
Answer:
3^6 = 729
Step-by-step explanation:
3 to the power of 5 equals 243. Explain how to use that fact to quickly evaluate 3 to the power of 6
Symbolically, we have:
3^5 = 243 (given)
Multiplying both sides by 3, we get:
3^6 = 3(243)
If you want to take this further, multiply 3(243): 3^6 = 729
The value of [tex]3^6[/tex] is 729.
Important information:
[tex]3^5=243[/tex]Exponents:We need to find the value of [tex]3^6[/tex].
Using the rules of exponents, we get
[tex]3^6=3^{5+1}[/tex]
[tex]3^6=3^{5}*3^{1}[/tex] [tex][\because a^{m+n}=a^ma^n][/tex]
[tex]3^6=243*3[/tex]
[tex]3^6=729[/tex]
Therefore, the value of [tex]3^6[/tex] is 729.
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Plzz help I’ll mark brainliest
Answer:
6cot 50
Step-by-step explanation:
Tan 50=6/x
x= 6/(tan 50)
x= 6cot 50°
Answer:
? = 6 cot 50
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 50 = 6 /?
? tan 50 = 6
? = 6 / tan 50
We know that 1 / tan 50 = cot 50
? = 6 cot 50
URGENT!!!! PLEASE HELP NOW!!! WHO EVER GIVES THE CORRRECT ANSWER WILL GET BRAINLIEST!!!
Items Sold at a Clothing Store
The bar graph shows the number of each item sold at a clothing store. Which
statement about the graph is true?
Answer:
The correct ans is..... ( which i believe )
3rd option
Hope this helps...
Pls mark my ans as brainliest
If u mark my ans as brainliest u will get 3 extra points
Answer:
3rd option
Step-by-step explanation:
because 2/5 of 40 is equal to 16, and thats the equivelent of the pants sold.
Find the value of x.
X
10
A. 52
B. 10/2
C. 512
D. 5
А
В
URGENT
[tex] \huge{ \bold{ \bigstar \: pythagoras \bigstar}}[/tex]
Pythagoras :
[tex] {10}^{2} = {x}^{2} + {x}^{2} [/tex]
[tex]100 = 2{x}^{2}[/tex]
[tex]100 \div 2 = {x}^{2} [/tex]
[tex]50 = {x}^{2} [/tex]
[tex]x = \sqrt{50} [/tex]
[tex]x = \sqrt{25 \times 2} [/tex]
[tex] \red{x = 5 \sqrt{2} }[/tex]
Answer:
Step-by-step explanation:
Compare this to a similar figure with hypotenuse √2 and leg lengths all 1.
Write and solve an equation of ratios, as follows:
x 10
------ = ------
1 √2
10√2
'then x = -------- = 5√2
2
You are planning to use a tile design in your new room. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 11 cm, what will be the exact area of each hexagonal shape? A. 3,993 cm^2 B. 181.5 root 3 cm^2 C. 132 root 3 cm^2 D. 33 cm^2
Answer:
B. 181.5√3 cm^2
Step-by-step explanation:
The area of a regular hexagon with side length s is given by ...
A = (3√3/2)s²
For side length s = 11 cm, the area is ...
A = (3√3/2)(11 cm)² = 363√3/2 cm²
A = 181.5√3 cm²
A formula to find the period, T, of cyclic phenomena based on the frequency, F is T= 1/F
Solve the formula for F in terms of T
Answer:
F = 1/T
Step-by-step explanation:
In order to solve for F, you would need to isolate F.
(F)T = 1/F (F) --> multiply F on both sides to cancel out the F on the right side
FT/(T) = 1/(T) --> divide T on both sides to cancel out the T on the left, so the F is isolated
F = 1/T
Hope this helps!
Answer:
F = 1/T
Step-by-step explanation:
T= 1/F
USING CROSS MULTIPLICATION TECHNIQE
T(F) = 1
DIVIDE BOTH SIDES BY T
F = 1/(T)
CAN SOMEWON HELP ME PLZ I NEED HELP
Answer:
1.791875241e13
Step-by-step explanation:
5.67811 x 10⁵ = 567811
3.15576 x 10⁷ = 31557600
31557600 x 567811 = 1.791875241e13
Answer:
1.791875241e13
write the slope- intercept form of the equation for the line.
Y=2x-1
Y=1/2x-1
y=-2x-1
y=1/2x+1
Answer:
The answer will be y=2x-1
Step-by-step explanation:
With the graph we are able to use the formula rise/run, which means we count down from the top point, and then over, and then divide.
Going down is 4 points, and over is 2.
4/2 is 2.
This leaves us with two answers. With this information, we look at the direction the graph is going, it is going upwards, making it positive. Which means that your answer is the first one. Plus the line goes through -1.
Thank you, if you need any more help let me know.
On a map the scale showing is 1 inch by 5 mi if a park is 75 square miles what is the area of the park on the map. The parks area is _____ square inches on the map
Answer: 15 square Inches
Step-by-step explanation: I believe you should divide 75 and 5(75mi÷5mi=15in) to get 15in.
Answer: 3 square inches.
If the park is 25 square miles, it could be 5×5 miles. If the scale is 1 inch = 5 miles, that would be 1×1 inch or 1 square inch on the map. Since 75 is 3×25, it will be 3×1 square inches on the map.
Step-by-step explanation: Remember that the scale represents linear measurements. For area, you must square the linear "sides" to get the number of actual square units represented by a square unit on the map.
Please Help me!! An 8 foot high camel is loping away from a streetlight. The camel is loping at 12 feet/second. The streetlight is 20 feet high. How fast is the camel’s shadow growing?
Answer:
Camel's shadow is growing at a rate of 8 ft/sec.
Step-by-step explanation:
Given:
Height of camel = 8 ft
Height of streetlight = 20 ft
Speed of camel = 12 ft / sec
To find:
How fast is the camel's shadow growing = ?
Solution:
First of all, have a look at the image attached for the situation as given in the question statement.
PQ be the streetlight.
AB be the camel.
Camel is loping away from the streetlight.
BT will be the shadow of the camel.
We are given that speed of camel = 12 ft / sec
And we know that Speed is the Rate of change of distance w.r. to time.
i.e. as per the image, we are given:
[tex]\dfrac{dx}{dt} = 12 ft /sec[/tex]
And we have to find the value of:
[tex]\dfrac{ds}{dt} = ?[/tex]
(Because s is the shadow length and we have to find the rate of change of shadow's length w.r.to time.)
Here, let us consider the two similar triangles [tex]\triangle TAB\ and\ \triangle TPQ[/tex]as per the image attached:
Ratio of corresponding sides will be same.
[tex]\dfrac{AB}{PQ}=\dfrac{TB}{TQ}\\\Rightarrow \dfrac{8}{20}=\dfrac{s}{s+x}\\\Rightarrow 8s+8x=20s\\\Rightarrow 12s = 8x\\\Rightarrow s = \dfrac{2}{3}x[/tex]
Now, differentiating w.r.to t:
[tex]\dfrac{ds}{dt}=\dfrac{2}{3}\dfrac{dx}{dt}\\\Rightarrow \dfrac{ds}{dt}=\dfrac{2}{3}\times 12\\\Rightarrow \dfrac{ds}{dt}=\bold{8\ ft/sec}[/tex]
Camel's shadow is growing at a rate of 8 ft/sec.
PLEASE HELP WILL GIVE BRAINLY!!!!!!!
Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options.
A) q= 5/5
B) q= -5/5
C) q= 3/5
D) q= -3/5
E) q= 25/5
Answer:
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Since there is no constant value. This must be a special case.
So,
(q+5[tex]\sqrt{5}[/tex])(q-5[tex]\sqrt{5}[/tex])
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Simplify: 15 7/12 x−9 1/3 x
Perform the following calculation and express the answer in scientific
notation: 1.2 x 10^-2 m x 3.0 x 10^-6 m =
Answer:
Hey there!
1.2 x 10^-2 times 3.0 x 10^-6 = 3.6 x 10^-8 m^2.
Hope this helps :)
Help pls will give brainliest
Answer:
The surface area of the rectangular prism is 292 cm²
If the Federal Resene sets the reserve rate to 20%, what is the resulting money multiplier?
Answer:
5
Step-by-step explanation:
Money multiplier helps to explain how an economic activity boosts the economic output for the country. It shows how saving in terms of deposit increases the net supply of money in any economy.
Money multiplier = 1/reserve ratio
given reserve ratio = 20% = 20/100 = 0.2
thus,
Money multiplier = 1/0.2 = 5
What is the domain of the function shown in the graph below? answer type: interval, all real values except one, all real values except two, all real numbers Interval:
Answer: the domain is negative infinity to positive infinity
Step-by-step explanation:
the graph covers all x values
Order matters in a combination.
True
False
Answer:
False
Step-by-step explanation:
So, in Mathematics we use more precise language: When the order doesn't matter, it is a Combination. When the order does matter it is a Permutation.
Find the total surface area of this square based
pyramid.
10 in
5 in
Answer:
125 in²
Step-by-step explanation:
Each triangular face has a base of 5 in and a height of 10 in. The area of it is given by the formula ...
A = (1/2)bh
A = (1/2)(5 in)(10 in) = 25 in²
The square base has an area given by the formula ...
A = s² . . . . . where s is the side length
A = (5 in)² = 25 in²
The total area is the sum of the areas of the 4 faces and the base:
total area = 4 × (area of 1 face) + (area of base)
total area = 4 × (25 in²) + 25 in²
total area = 125 in²
Answer: The Surface Area is 125 in^
Step-by-step explanation:
Surface area = 4 × (area of 1 face) + (area of base)
total area = 4 × (25 in²) + 25 in²
Surface area = 125 in²