It is to be noted that Saturn is 1.29 *x 10⁹ km further from the sun than Venus.
What is the computation justifying the above results?Recall that we are given:
approximate distance from the sun for a few different planets.
Hence, to detect how much farther (in km) from the sun Saturn is than Venus we initiate a series of subtractions.
Recall that
Planet approximate distance from the sun ( km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
The distance of Saturn form the sun and Venus is given as
= Distance of Saturn from Sun - Distance of Venus from Sun
= 1.4 x 10⁹ - 1.1 * 10⁸ [Multiply 1.4 x 10 and we've got]
= 14 x 10⁸ - 1.1 * 10⁸
= (14 - 1.1) * 10⁸ [ Collect like terms and consolidate]
= 12.9 x 10⁸ [Revert back to the power of 9 and we have]
= 1.29 x 10⁹ km
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Full Question:
The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus? Express your answer in scientific notation.
Planet Approximate distance from the Sun (in km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
It is found that Saturn is 1.29 x 10⁹ km further from the sun than Venus.
How do scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
We have been given that the approximate distance from the sun for a few different planets.
Hence, to determine the farthest distance (in km) from the sun Saturn is than Venus, we get;
Planet the approximate distance from the sun ( km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
The distance between Saturn from the sun and Venus can be calculated as;
= Distance of Saturn from Sun - Distance of Venus from Sun
= 1.4 x 10⁹ - 1.1 x 10⁸
= 14 x 10⁸ - 1.1 x 10⁸
= (14 - 1.1) x 10⁸
= 12.9 x 10⁸
= 1.29 x 10⁹ km
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Emma has 3/4 credits. It requires 1/4 of a credit to play a video game for one minute. How long can Emma play the video game with her credits? Use standard algorithm to show your work.
Emma can play video games for 3 minutes using the available credits
Credit available with Emma = 3/4 credits
Credits required to play a video game for one minute = 1/4
Credits: In an electronic gaming setting, a value earned through the exchange of cash or currency equivalents is referred to as "gameplay credits." It can also be obtained through gaming as a prize. You can exchange gameplay credits for money or money equivalents.
Time Emma can play video games with the credits:
Credit available with Emma/Credits required to play video game for one minute
= (3/4)/(1/4)
= 3/4*4
= 3
So, she can play for 3 minutes
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A group of friends wants to go to the amusement park. They have no more than $155 to spend on parking and admission. Parking is $18, and tickets cost $24 per person, including tax. What is the maximum number of people who can go to the amusement park?
Answer:
5
Step-by-step explanation:
155-18=137
137/24=5.70833333
5 people are able to join max
In March, Isaiah and Freddie had the same amount of money in their savings accounts. In April, Isaiah deposited $210 into his account. Freddie increased the money in his account by 15%. When they compared their balances, they found that they were still equal.
x + 210 = 1.15x where x is the amount in their accounts in March....subtract x from both sides 210 = .15x divide both sides by .15 x = $ 1400 Hope you get an A+ :))
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number less than 7.The probability of rolling a number less than 7 is
Probability is the quantitative measure of the likelihood of the occurrence of an event.
It is mathematically expressed as:
[tex]P=\frac{number\text{ of selected outcome}}{number\text{ of total outcome}}[/tex]We can decide to call the set of numbers below 7 "A".
A = {1, 2, 3, 4, 5, 6}
|A| = 6
We call the universal set, the set containing all the numbers rollable "U"
|U| = 12
Our probability is therefore:
[tex]undefined[/tex]axline computers manufactures personal computers at two plants, one in texas and the other in hawaii. the texas plant has 45 employees; the hawaii plant has 15. a random sample of 10 employees is to be asked to fill out a benefits questionnaire. (round your answers to four decimal places.) (a) what is the probability that none of the employees in the sample work at the plant in hawaii?
The probability that none of the employees in the sample work at the plant in hawai is 0.0112
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
PH= 20/60 = 1/3
P(T) = 2/3
It is hypergeometric distribution
P(X=k)={\frac {{\binom {K}{k}}{\binom {N-K}{n-k}}}{\binom {N}{n}}},
where
N = 60
K = 20 for Hawai; 40 for Texas
n = 10
P(X=0) = 0.0112
Hence The probability that none of the employees in the sample work at the plant in hawai is 0.0112
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Given the midpoint (M) and either endpoint of AB. find
the other endpoint.
A(-1, 2) and M(3,6)
a B is (7, 10)
b Bis (9, 12)
c B is (10, 10)
d B is (13, 10)
The other endpoint is (7,10).
Assuming that your midpoint M = (x, y) and endpoint A = (x1, y1) are both present: Coordinates of the double midpoints are 2x, 2y. To find the x-coordinate of the missing endpoint, subtract the known endpoint's x-coordinate from the first value: x₂ = 2x - x₁.
The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint.
An alternate solution would be to substitute (-1, 2) for (x1,y1) and (3,6) for (x2,y2) into the midpoint formula:
(x - 1)/2 = 3
x -1 = 6
x =7
(y + 2)/2 = 6
y + 2 = 12
y =10
Solving each equation for (x2,y2) yields the solution (7,10).
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Alan is ordering uniforms for his flag football team. Each uniform costs $14. All orders over $150 receive a 15% discount.
If Alan buys 12 uniforms, what will be the cost?
Answer:
$142.80
Step-by-step explanation:
smarts
Name the property illustrated.
(7 + 8) + 9 = 7 + (8 + 9)
Answer:
24=24 ( associative property )
26. Given: mABD = mFDB; m/1 = m/4
Prove: BC || ED
How would I solve this proof in a two column proof?
Following is the proof of BC||ED using alternate interior angles.
What is the property of alternate interior angles?According to the alternate angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent.
We are given the ∠ABD = ∠FDB
and
∠1 = ∠4
using the above-given conditions we need to prove that line BC is parallel to line BD (i.e. BC || BD)
∠ABD = ∠FDB...................................(i)
∠ABD= ∠1 +∠2
and
∠FDB= ∠3+∠4
now subsituting these values of ∠ABD and ∠FDB in equation(i)
we get,
∠1 +∠2=∠3+∠4
we are also given that ∠1 = ∠4, substituting that,
∠1 +∠2=∠3+∠1
= ∠2=∠3+∠1-∠1
= ∠2=∠3
through the given fig we know,
∠2=∠CBD
and
∠3=∠EDB
i.e.
∠CBD=∠EDB
∠CBD and ∠EDB make alternate interior angles of the lines BC and ED,
and since both the alternate interior angles are equal(∠CBD and ∠EDB) both the lines are parallel (||).
therefore we have BC||ED, hence proved.
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A farmer planted 978 seeds each day for 30 days. How many seeds did the farmer plant in total? 29,140 seeds 29,240 seeds 29,340 seeds 29,440 seeds
Answer:
29,340
Step-by-step explanation:
978 x 30 =29,340
8x-5x+21 = 36-6y
Write the equation so that y is a function of x.
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex].
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Given Data
Function
8x-5x+21 = 36-6y
6y = 36 - 21 - 8x +5x
6y = -3x + 15
y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
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mathhhh helppp pleasee
not to intrude but is that big ideas math?
Omar gave out a survey to some students in his school about their favorite color. 650 of those surveyed said their favorite color was blue. If 65% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
The total number of students surveyed by Omar in his school is 1000.
Here, we are given that Omar conducted a survey of some students in his school about their favorite color.
650 of those surveyed said their favorite color was blue.
Further, 65 percent of the students surveyed said their favorite color was blue.
Let the total number of students surveyed be x
Then, according to the given information,
65% of x is 650
Thus, we can form the following equation-
65/ 100 × x = 650
0.65x = 650
x = 650/ 0.65
x = 65000/ 65
x = 1000
Thus, the total number of students surveyed by Omar in his school is 1000.
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a photocopy of a polygon was reduced to 30% of it's original size. Then, the copy was reduced again to 30% of it's size. What is the ratio of the corresponding sides of the second photo copy of the original? (round to four decimal places as needed)
Let's call a to the length of a side on the original polygon.
Let's call b to the length of the corresponding side to side a in the first photocopy. The length of b is: 0.3a (30% of a).
Similarly, c the length of the corresponding side in the second photocopy is: 0.3b = 0.3x0.3a = 0.09a
Then, the ratio of the corresponding sides of the second photocopy of the original to the sides of the original is 0.09:1
A paper company is designing a new, pyramid-shaped paperweight. Its development team has decided
that to make the width of the paperweight 4 inches less than the length and the height of the
paperweight 3 inches less than the length. The paperweight must have a volume of 12 cubic inches.
What are the dimensions of the paperweight?
The width is
inches, the length is
inches, and the height is
inches
Answer:
4x+3=12
Step-by-step explanation:
At the school 460 of the students walk to school.
1The number of students who take public transit is 20% of the number of students who walk. How many students take public transit?
2The number of students who bike to school is 5% of the number of students who walk. How many students bike to school
3The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
Answer:
92 public transit
23 bike
Step-by-step explanation:
460 / 5 = 92
460 / 20 = 23
Solve it , I need help
y < 2
can't be y <= 2 or y<=1 because the dot is open meaning the point is not included.
the range is talking about the y value, the point is at y = 2. The graph is also negative; therefore, range will be anything less than y = 2
Ples hlep me i need hlep w my hw cuz i cant figure it out and my friend is not here bc they gone and not hear anyways help me ples tysm
The distance traveled by the tip of the minute hand in 45 minutes is approximately 256.77 mm, while the distance traveled by the tip of the hour hand in 1 hour is approximately 267 mm.
A) The hour needle completes a complete rotation of 12 hr, in 45 min = 0.75 hours, it will be 0.75 ÷ 12 of a complete rotation.
Given that the hour arrow's tip touches the rim of a clock, the radius of the clock is equal to the distance of the pointer.
The circumference of a circle is:
C=2 × π × radius
The span crossed by the hand in 12 hours is:
2 × 36=76π mm
The space traversed in 45 min is:
0.75 ÷ 12 × 72π=4.5π mm
in 45min, the min hand will make 45 ÷ 60=3 ÷ 4. If the min hand is 150% of the hour hand, then its length is 150 ÷ 100 × 36 = 54 mm.
As a result, the point of the minute will go around the complete circumference of a circle with a radius of 54 mm, implying that for a full circle, we will have:
2 × π × 54mm = 108π mm.
As a result, the minute hand's tip will have moved 45 minutes in 45 minutes, 108 × 3 ÷ 4 × π = 81π mm.
B) The clock's hour hand measures 30 mm.
As a result, the radius of the minute hand is,
1.5 × 30 = 45mm
And the minute hand moves after one hour 2π × ( r )²:
2 × 3.14 × 45 × 45 = 90π mm
And the minute hand moves,
π ÷ 6 × 30 = 5π mm
As a result, the minute hand moves,
90π - 5π = 85π mm
= 267 mm
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The answers help im confused
Answer:
P' (3, 1)
Q' (5, 1)
R' (5, 4)
S' (3, 4)
T' (3, 3)
U' (1, 3)
V' (1, 2)
W' (3, 2)
Step-by-step explanation:
What does it mean when a point is translated horizontally to the right by 6 units? That means its x coordinate is increased by 6 units, the y-coordinate is unchanged
(If it was translated 6 units to the left, it's x coordinate would decrease by 6 units)
So if we had a point say (1, 1) then its new x-coordinate will be (1+6, 1) or (7,1) The y-coordinate stays unchanged if the translation is horizontal
When a point is translated vertically by 6 units, its x-coordinate is unchanged but the new y coordinate is increased by 6 units (-6 units if the translation is vertically down)
So with a point (1, 1), an up translation will result in a new point (1, 7)
If both translations are applied both x and y coordinates will change to
(7, 7)
To figure out the new coordinates denoted by P'Q'R'S'T' of each of the points PQRST of the given figure:
Add 6 to the x-coordinate of each point and at the same time add 6 to the y-coordinate of that point
If you look at the graph, the original points and translated points for 6 units to right and 6 units up are
P(-3, -5) which translates to P'(-3 + 6, -5 + 6) or P'(3, 1)
The other new points are calculated the same way by adding 6 to both x and y coordinates
Q(-1, -5) ==> Q'(5, 1)
R(-1, -2) ==> R'(5, 4)
S(-3, -2) ==> S'(3, 4)
T(-3, -3) ==> T'(3, 3)
U(-5, -3) ==> U'(1, 3)
V( -5, -4) ==> V'(1, 2)
W(-3, -4) ==> W'(3, 2)
The attached graph shows the translated figure with the translated points. Essentially the original figure has been shifted 6 units to the right and 6 units up
w=0.75f.
What does 0.75 tell us in this situation?
Answer:
it should be in the ratio of 3:4
Step-by-step explanation:
100w= 75f
w/f = 75/100
= 3/4
= 3:4
PLEASE HELPP!!!!!
I WILL GIVE BRAINLIEST!!!
No. 1, 2 and 7 are to be answered.
The price of Stock A at 9 A.M. was $12.17. Since then, the price has been increasing at the rate of $0.06 each hour. At noon the price of Stock B was $12.67. It begins to decrease at the rate of $0.08 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
If at noon the price of Stock B was $12.67. It begins to decrease at the rate of $0.08 each hour. If the two rates continue, the number of hours that the prices of the two stocks be the same is 3.57 hours.
Determining the stock number of hoursLet the hours when they equalize be h
Hence,
12.17 + .06h =12.67 - .08h
Combine like terms
.06h + .08h=12.67 - 12.17
.14h=.5
Divide both sides by .14h
h = .5/ .14
h = 3.57 hours
Therefore we can conclude at the number of hours is 3.57 hours .
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Determine the solutions of the equation:
|1/3x + 9| - 3 = 21
Step-by-step explanation:
21+3=24
1/3x+9=24
24-9=13
1/3x=13
13×1=13
3x=13
13/3=4.33
x=4.33
What is the constant of proportionality in the equation y=3xy=3xy, equals, 3, x?
constant of proportionality ==equals
The constant proportionality is 3
What is Proportionality Constant ?
The proportionality constant is the ratio between two variables that varies directly . For directly proportional variables, their ratio is always a constant and this constant is the proportionality constant.
Now, We have the equation is:
y = 3xy
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k = y/x or y = kx
To get the constant of proportionality,
we will derive both sides of the equation by x.
y/x = 3x/x
y/x = 3
Hence, The constant proportionality is 3
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Work out the area of this semicircle.
Take to be 3.142 and write down all of the digits given by your calculator.
18 cm
Answer:
A = 127.251 cm²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( where r is the radius )
the area (A) of a semicircle is then
A = [tex]\frac{1}{2}[/tex] πr²
given diameter = 18 then r = 18 ÷ 2 = 9 cm , so
A = 0.5 × 3.142 × 9² = 0.5 × 3.142 × 81 = 127.251 cm²
Solve the equation 6p = 2(5 - 2p).
Answer:
p=1
Step-by-step explanation:
6p=2(5-2p)
6p=10-4p
Add 4p on both sides
10p=10
Divide 10 on both sides
p=1
Hello!
Let's solve:
[tex]6p=2(5-2p)\\\\\text{Multiply 2 into the function in the parentheses}6p=10-4p\\\\\text{Add '4p to both sides}\\6p+4p=10-4p+4p\\10p=10\\\\\text{Divide both sides by 10}\\\frac{10p}{10} =\frac{10}{10} \\p=1[/tex]
Hope that helps!
What is the value of x?
Answer:
x=27
Step-by-step explanation:
Answer the 3 question in the photo ( will mark brainliest if correct )
4) The reason for the second step is division property of equality.
5) The reason for the second step is Multiplication property of equality.
6) The reason for the third step is because of substitution property of equality.
How to Interpret Algebraic Properties of Equalities?
4) We are given that;
4x = -24
x = -6
Thus, the reason for the second step is division property of equality because both sides were divided by 4.
5) We are given;
(3x + 5)/2 = 7
Multiply both sides by 2 to get;
3x + 5 = 14
The reason is due to Multiplication property of equality.
6) We are given;
x = 4
y = 3x + 7
y = 3(4) + 7
The reason is because of substitution property of equality.
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which best describes why you might want to rewrite a literal equation?
To solve for a different indicated variable.
To solve for the variable x.
To solve for a different number.
To solve for the variable y.
Sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
What are literal equations?A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v = Dt) and the area of a circle (A = r₂).So, as in the description, it is given that A literal equation is one that is mostly made up of letters.
Therefore, sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
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The correct question is given below:
Which best describes why you might want to rewrite a literal equation?
(A) To solve for a different indicated variable.
(B) To solve for the variable x.
(C) To solve for a different number.
(D) To solve for the variable y.
A race car driver
travels 34 ft in the first second of a race.
If the driver travels 3.5 additional feet each
subsequent second, how many feet did the
driver travel in 52 s?
The number of distance in feet the driver travel in 52 seconds is 216 feet.
How to find the distance in feet the driver can travel in a particular time?The race car driver travels 34 feet in the first second of a race.
The driver travels 3.5 additional feet each subsequent second.
The number of feet the driver travel in 52 seconds can be solved as follows:
Therefore,
the distance travel = 34 + 3.5x
where
x = number of time in seconds the driver travelsTherefore,
the distance travel = 34 + 3.5(52)
the distance travel = 34 + 182
the distance travel = 216 feet
Therefore, if the driver travels 34 feet in the first seconds of the race and travels an additional 3.5 feet each subsequent second, the number of distance in feet the driver will travel in 52 seconds is 216 feet.
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