Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.
What is Scientific notation ?
Scientific notation is the way to express the large value in short form. The number in scientific notation have two parts. The digits (decimal point will place after first digit) × 10 ( the power which put the decimal point where it should be).
Here it is given that The distance between the earth and the sun is approximately 93 million miles and 1 million miles equals 1,00,000 miles.
Now, writing 93 millions Scientific notation by writing 1,00,000 in power of 10 and 93 as 9.3 x 10 :
93 million miles = 9.3 x 10 x 1,00,000
= 9.3 x 10^7
Therefore, Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.
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The distance between the Earth and the Sun (93 million miles) in scientific notation is [tex]9.3 *10^7 miles[/tex].
To write the distance between the Earth and the Sun (93 million miles) in scientific notation, follow these steps:
First, write 93 million as a standard numeral: 93,000,000.
Next, identify how many places to move the decimal point to get a number between 1 and 10. For 93,000,000, the decimal point moves 7 places to the left.
After moving the decimal point in 93,000,000.00 by 7 places, you get 9.3, which is between 1 and 10. This is known as mantissa.
Mantissa = 9.3
Write the number as a coefficient multiplied by 10 raised to the number of places the decimal was moved. This is called the exponent term. Exponent term = [tex]10^7[/tex].
Scientific notation of a number = Mantissa*Exponent term
So, 93,000,000 = [tex]9.3 *10^7[/tex].
Therefore, the distance between the Earth and the Sun in proper scientific notation is [tex]9.3 *10^7 miles[/tex].
At the middle school graduation dance, the DJ played 12 slow dances, which was equal to the quotient of the number of fast dances and two.
quotient means divide
so 12 = x/2
x = 12*2 = 24
x =24 fast songs
The sum of two numbers is 33. Twice the first number minus the second number equals 18. Find both numbers.
The both numbers are = 17 and 16
Solving for the unknown numbersThe sum of two numbers = 33
Let the two numbers be X and y.
therefore X + y = 33 ----> equation 1
Twice the first number minus the second number= 18.
That is,
2x - y = 18 -----> equation 2
From equation 1 make X the subject of formula;
X = 33 – y
substitute X into equation 2,
2(33 – y) - y = 18
66 – 2y – y = 18
66 – 3y = 18
66 – 18 = 3y
48 = 3y
y = 48/3
y = 16
Substitute y = 16 into equation 1
Therefore, X +16 = 33
X = 33 –16
X = 17
Therefore, he both numbers are = 17 and 16
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In 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg
Answer: it’s 1:1
Step-by-step explanation:
The cells of a certain culture of bacteria double every 6 minutes. If the culture contains 100 cells in the beginning, then the total number of cells P in this culture after t minutes is given by the exponential equation P = 100(2)t/6. Identify the number of minutes it will take for the number of cells to exceed 50,000.
A) 53 min
B) 49 min
C) 48 min
D) 54 min
Since the growth is exponential, therefore I believe the correct form of the equation is:
P = 100 (2)^(t / 6)
Where t / 6 is the exponent of 2
So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:
P = 100 (2)^(t / 6)
50000 = 100 (2)^(t / 6)
500 = 2^(t / 6)
log 500 = (t / 6) log 2
t / 6 = log 500 / log 2
t = 6 * 8.96578
t = 53.8 mins = 54 mins
Answer:
D. 54 min
Which is heavier 9 5/8 pounds or 9 3/4 pounds
Which algebraic expression represents “the difference of 54 and a number”?
For this case, the first thing we should do is define a variable.
We have then:
x: unknown number
Then, we write the algebraic expression that models the following problem:
the difference of 54 and a number.
We have then:
[tex]54-x[/tex]
Answer:
An algebraic expression that represents "the difference of 54 and a number" is:
[tex]54-x[/tex]
Answer:
A
Step-by-step explanation:
Rectangular prisms A and B are similar.
The edge of prism B is 3 times that of prism A. How many times the volume of prism A is the volume of prism B?
Find the area of a sector that has a central angle of 40 and a radius of 2 cm. Round your answer to the nearest 100th. Use 3.14=
From 75 campsites to 120 campsites
subtract 75 from 120
120-75 =45 more campsites
Driving on the North West Express-way, Debbie averaged 62 miles per hour for 3 & one fourth hours. How far did she drive?
1/4 = 0.25
s0 3 1/4 = 3.25
62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form
I have 3 questions here , one of them I just need my answer checked on and the other two I really need help with. Thank you!!
If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?
Answer:
If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?
Step-by-step explanation:
If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.
If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.
True or false the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle
Answer:
True
Step-by-step explanation:
Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.
Then
EB=EC;FC=FA;GA=GB.Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then
m∠OBE=m∠OCE=90°;m∠OCF=m∠OAF=90°;m∠OBG=m∠OAG=90°.You get three pairs of congruent triangles:
ΔOBE≅ΔOCE;ΔOCF≅ΔOAF;ΔOBG≅ΔOAG.This gives you that
[tex]OB=OC=OA.[/tex]
Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.
20 POINTS, PLEASE HELP ASAP!!!!
Applying the distributive property, the expression becomes (3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4). What is the simplified product in standard form?
Solve 2x + 5y = −13
3x − 4y = −8
A quiz has 4 multiple-choice questions with 4 possible answer choices each. for each question, there is only 1 correct answer.a student guesses each answer at random. what is the probability of getting exactly 3 questions correct, to the nearest percent?(3 correct and 1 incorrect)
Answer: (quartered spinner) (4) (1/256)
Write an equation for the translation of the function. y = cos x; translated 6 units up
Answer:
[tex]y=cos(x)+6[/tex].
Step-by-step explanation:
We are asked to write an equation for the translation of the function [tex]y=cos(x)[/tex] to 6 units upwards.
Let us recall transformation rules.
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:
[tex]y=cos(x)+6[/tex]
Therefore, our required equation would be [tex]y=cos(x)+6[/tex].
The sum of two numbers is 54 . the smaller number is 12 less than the larger number. what are the numbers?
if a radius of a circle is perpendicular to a chord, then it _____ that chord.
a. is equal in length to
b. bisects
c. is congruent to
d. parallels
If a radius of a circle is perpendicular to a chord, then it _bisects____ that chord.
What is radius of circle?
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.
What is chord?
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.
According to question, we have to fill in the blank.
The property of the circle is that if a radius of a circle is perpendicular to a chord, then it bisects that chord.
Hence we can conclude that Option(B) is correct.
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Final answer:
A radius of a circle that is perpendicular to a chord bisects the chord, dividing it into two equal segments.(Option b)
Explanation:
If a radius of a circle is perpendicular to a chord, then it bisects that chord. This statement is supported by a theorem in geometry which states that, in a circle, the radius bisecting an angle at the centre is perpendicular to the chord which subtends the angle and also bisects this chord. Therefore, by drawing a radius from the center of a circle to the midpoint of a chord, you create two equal segments, effectively bisecting the chord.
Thus, a perpendicular radius drawn from the center of a circle to a chord's midpoint ensures that the chord is bisected into two equal segments. This geometric principle facilitates chord division and enhances the understanding of circle properties.
Julio checked the temperature of a bag of frozen peas and found it was at −13°C. After he left the bag out of the freezer for an hour, its temperature rose to 8°C. What was the change in temperature in an hour?
a)−21°C
b)21°C
c)5°C
d)−5°C
What is -11-8-13(-10)? And how did you get you're answer
A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the slant height is 5 cm. Find the VOLUME of the tea bag.
The cells of a certain culture of bacteria triple every 2 minutes. If there are 40 cells in the beginning, in how many minutes will there be more than 9500 cells?
A) 4 min
B) 5 min
C) 11 min
D) 10 min
Answer: 10 min
Step-by-step explanation:
Final answer:
The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).
Explanation:
The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:
N = N0 × 3t/2
Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.
We want N to be greater than 9500, so we solve the inequality:
9500 < 40 × 3t/2
Dividing both sides by 40 gives:
237.5 < 3t/2
Next, we find the smallest t for which the inequality holds by applying logarithms and solving:
t > 2 × (log3(237.5))
Calculating the right side, we get:
t > 10.096
So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min
(05.05)What is the rate of change of the linear relationship modeled in the table?
x y
1 2
3 5
5 8
7 11
negative three over two
two over three
one
1 three over two
Answer: three over two
Step-by-step explanation:
We know that the rate of change of a function [tex]y=f(x)[/tex] is given by :-
[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]
From the consecutive values in the table, the change in x = [tex]3-1=2[/tex]
Change in y = [tex]5-2=3[/tex]
Now, the rate of change of the linear relationship modeled in the table will be ;-
[tex]k=\dfrac{3}{\text{2}}[/tex]
Please help me !!!!!!!!
Someone help me please !!!
Answer:
1. 10
2. 12
3. Sqrt 130
4. Sqrt 45
Step-by-step explanation:
To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.
1. a=6, b=8, c=?
[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]
2. a=5, b=?, c=13
[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]
3. a=7, b=9, c=?
[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]
4. a=2, b=?, c=7
[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]
The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(4)=64
Bryce is testing whether school is more enjoyable when students are making high grades. He asked 100 students if they enjoyed school and whether their GPA was above or below 3.0. He found that 33 of the 40 students with a GPA above 3.0 reported that they enjoyed school, and 5 of the 60 students with a GPA below 3.0 reported that they enjoyed school. What is the probability that a student with a GPA below 3.0 does not enjoy school?
85%
92%
65%
75%
Answer:
The answer is 92%.
Step-by-step explanation:
5 of the 60 students reported that they like school. This means that the other 55 don't like school. You then divide 55/60 and you get 92%. So, therefore, your answer is 52%.
Find the area of the larger regular pentagon if the smaller pentagon has an area of 43.01 inches^2. The side length of the small pentagon is 5 and the side length of the large pentagon is 8.