The quotient of 212,960 divided by 1,000 is 212.960, achieved by moving the decimal point to the left by three places, reflecting the three zeros in 1,000.
Explanation:The question asks to find the quotient when 212,960 is divided by 1,000. To find the quotient, you essentially move the decimal point three places to the left. When dividing by powers of 10, each power of 10 represents the number of places you move the decimal to the left. Therefore, 212,960 divided by 1,000 gives us 212.960. This methodology is similar to the examples provided in the reference where dividing by 10, 100, and 1000 shifts the decimal point to the left by one, two, and three places respectively.
Remember that when multiplying or dividing by powers of 10, the decimal point is moved rather than actually performing the multiplication or division action. This is one of the reasons why working with decimals and powers of 10 is simpler compared to other numbers.
Solve the inequality:
4x – 2 < 10
Answer:
The solution for x is (-∞, 3).
Step-by-step explanation:
The provided inequality is: [tex]4x-2<10[/tex]
Solve for x a follows:
[tex]4x-2<10\\\\Add\ 2\ to\ both\ sides\\\\4x-2+2<10+2\\\\4x<12\\\\Divide\ both\ sides\ by\ 4\\\\\frac{4x}{4}<\frac{12}{4}\\\\x<3[/tex]
The range of the values of x is
[tex]x<3\\This\ implies\ that\ x\ belongs\ to\ the\ interval\ (-\infty, 3)[/tex]
Thus, the range of the values of x is (-∞, 3).
equation
slope (m) =
y-intercept =_4
Answer:
x = m+-4
Step-by-step explanation:
We are trying to figure out the slope and the slope equals m, Then we have the y-intercept which that equals -4
h(x) = x^2 - 1
Over which interval does h have a negative average rate of change?
The function h(x) = x^2 - 1 has a negative average rate of change over the interval from x = -∞ to x = 0, which is where the parabola is decreasing toward its vertex at the origin.
Explanation:The student asked over which interval the function h(x) = x^2 - 1 has a negative average rate of change. The average rate of change is negative when the function is decreasing. In the case of h(x) = x^2 - 1, which is a parabola opening upwards, the function decreases as x moves from the left to the right towards the vertex. Therefore, the interval in which the function has a negative average rate of change is from x = -∞ to x = 0, because this is where the function values are falling. To find the average rate of change between two points x1 and x2, we can use the formula: (h(x2) - h(x1)) / (x2 - x1). If x1 is to the left of the y-axis (x1 < 0) and x2 is the y-axis (x2 = 0), we will get a negative result since h(x2) < h(x1) in that interval, showing a negative average rate of change.
The function h(x) = x^2 - 1 has a negative average rate of change over the interval − 3 ≤ x ≤ 1. This interval includes the vertex of the parabola at x = 0, where the function is decreasing, resulting in a negative rate of change.
The function h(x) = x2 - 1 has different average rates of change depending on the interval we are considering. To find an interval where the average rate of change is negative, we need to look at intervals where the function is decreasing. The function h(x) will be decreasing on any interval that includes the value x = 0 since this is where the vertex of the parabola represented by h(x) is located, and it is a parabola opening upwards.
Analyze intervals around x = 0 to find where the function decreases. Looking at Choice C (−3 ≤ x ≤ 1), we can calculate the average rate of change as:
[(h(1) - h(-3)) / (1 - (-3))] = [(12 - 1) - ((-3)2 - 1)] / (4) = [0 - (9 - 1)] / 4 = -8 / 4 = -2Since the average rate of change is negative (-2), Option C is the interval over which h(x) has a negative average rate of change.
the complete Question is given below:
h(x)=x 2 −1h, left parenthesis, x, right parenthesis, equals, x, squared, minus, 1 Over which interval does h hh have a negative average rate of change? Choose 1 answer: Choose 1 answer: (Choice A) A − 3 ≤ x ≤ 5 −3≤x≤5minus, 3, is less than or equal to, x, is less than or equal to, 5 (Choice B) B 1 ≤ x ≤ 4 1≤x≤41, is less than or equal to, x, is less than or equal to, 4 (Choice C) C − 3 ≤ x ≤ 1 −3≤x≤1minus, 3, is less than or equal to, x, is less than or equal to, 1 (Choice D) D − 1 ≤ x ≤ 5 −1≤x≤5minus, 1, is less than or equal to, x, is less than or equal to, 5 Show Calculator
Janice is creating a scrapbook page with vertices (2,1), (7,1), (7,7), and (2,7). What is the area of the page she will be covering if each grid represents 4 square inches?
Answer:
The actual area of the page will be 120 square inches.
Step-by-step explanation:
Janice is creating a page of scrapbook having vertices (2,1), (7,1), (7,7), and (2,7).
If we plot the points on the coordinate plane then we will see that the page is of a rectangular shape with length (7 - 1) = 6 units which is parallel to the y-axis and width (7 - 2) = 5 units which is parallel to the x-axis.
So, the area of the page is (6 × 5) = 30 square units.
Now, given that 1 square unit is equivalent to 4 square inches.
Therefore, the actual area of the page will be (30 × 4) = 120 square inches. (Answer)
A bag contains 5 red marbles, 3 blue marbles, 7 yellow marbles, and 2 green marbles which ratio can be used to compare the yellow marbles to the blue marbles
Answer:
7 : 3
Step-by-step explanation:
Answer:7:3
Step-by-step explanation:
The other colors are just to throw you off,7 yellow to 3 blue is 7:3
What is 4 raised to the power of 2 ÷ 2 raised to the power of 3
Answer:
4³
Step-by-step explanation:
2 / 2 = 1
4 raised to the power of one is 4
4 raised to the power of 3 is 4³
her 6. Karen buys a sweatshirt for $30. The sales
suld be tax in her state is 7%. What is the total
amount Karen will pay for the sweatshirt,
including sales tax?
The total amount that Karen will be for the sweatshirt including tax will be $32.10.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Karen buys a sweatshirt for $30. The sales sold be tax in her state is 7%.
The total amount that Karen will be for the sweatshirt including tax will be calculated as,
Total cost = $30 x (1 + 7%)
Total cost = $30 x (1 + 0.07)
Total cost = $30 x (1.07)
Total cost = $32.10
The total amount that Karen will be for the sweatshirt including tax will be $32.10.
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Ben bowled 133 and 206 in his first two games. What must he bowl in his third game to have an average of at least 170?
Answer:
171
Step-by-step explanation:
(133+206+x)/3 = 170
133+206+x = 510
339 + x = 510
x = 171
(133+206+171)/3 =
The world's population has grown at an average rate
of 1.9 percent per year since 1945. There were
approximately 4 billion people in the world in 1975.
Which of the following functions represents the
world's population P, in billions of people,
1 years since 1975 ? (1 billion = 1,000,000,000)
A) P(t) = 4(1.019)
B) P(t) = 4(1.9)
C) P(t) = 1.194 + 4
D) P(t) = 1.0197 +4
Answer:
[tex]P(t)=4(1.019)^t[/tex]
Step-by-step explanation:
we know that
The equation of a exponential growth function is equal to
[tex]P=a(1+r)^t[/tex]
where
P ---> is the world's population
t ---> is the number of years since 1945
a ---> is the initial population in 1945
r ---> is the percent rate of growth
we have
[tex]r=1.9\%=1.9/100=0.019[/tex]
substitute
[tex]P=a(1+0.019)^t[/tex]
[tex]P=a(1.019)^t[/tex]
Remember that
There were approximately 4 billion people in the world in 1975
That means
Since year 1975 the initial value a=4 billion people
substitute
[tex]P(t)=4(1.019)^t[/tex]
Riley has 3 5/9 gallons of fuel left in his car. He uses 7/16 of the fuel to drive to the bank. Then, he uses 2/5 of the remaining fuel to drive to the comic book store. How many gallons of fuel does Riley have left after driving to the bank and the comic book store?
What have you done?
5. Claire is buying a new bicycle for $295. If the
sales tax is 4.75%, what will she pay in total?
Claire will pay $309.01 for the bike.
Kwame's team will make two triangular pyramids to decorate the entrance to the exhibit. They will be wrapped in the same metallic foil. Each base is an equilateral triangle. If the base has an area of about 3.9 square feet, how much will the team save altogether by covering only the lateral area of the two pyramids? The foil costs $0.24 per square foot. Kwame's team will save $
, altogether by covering only the lateral area of the two pyramids.
Answer:
Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87
Step-by-step explanation:
i.) Let the side of the equilateral triangle base be a
ii.) the area of the base = 3.9 square feet
iii.) the area of equilateral triangle is = [tex]\frac{\sqrt{3} }{4} a^{2}[/tex] = 3.9
iv.) Base area = 3.9 square feet
v.) The area that is not covered is the base.
vi.) The total area that is not covered = 3.9 [tex]\times[/tex] 2 since there are two pyramids
therefore the total area not covered = 7.8 square feet
vii.) therefore Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87
booker owns 85 video games. He has 3 shelves to put the games on. Each shelf can hold 40 video games. How many video games does he have room for?
Answer:
(3 x 40) - 85
120 - 85
35 video games
The sum of two numbers is 21,and their difference is 9
Answer:
The numbers are 15 and 6.
Step-by-step explanation:
We can solve the problem algebraically (using equations). First, write equations that represent the situation.
Choose variables to represent the numbers:
let the numbers be "x" and "y"
Take apart each section of the problem and make an equation.
"The sum of two numbers is 21"
x + y = 21 Sum means the answer when you add numbers
"Their difference is 9"
x - y = 9 Difference means the answer when you subtract numbers
Using the two equations, you can solve using elimination. With this method, you get rid of one of the variables, so you can easily solve for the other one. You can use elimination when one of your variables have the same variable number. Both equations have "1x" and "1y" ("1" is never written).
Add the equations together by adding normally, with each of the terms with the same variable.
. x + y = 21 Add each term
+ x - y = 9 (x + x = 2x) (y + (-y) = 0) (21 + 9 = 30)
. 2x + 0 = 30 "y" variable cancelled out
. 2x = 30
. 2x/2 = 30/2 Divide both sides by "2" to isolate "x"
. x = 15 Answer for one number
To find the other number, substitute 'x' for 15 into one of the equations.
x + y = 21
15 + y = 21 Isolate "y" now
15 - 15 + y = 21 - 15 Subtract 15 from both sides
y = 21 - 15 15-15 cancelled out on the left side. Solve right side.
y = 6 Answer for second number
Therefore the two numbers are 15 and 6.
" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a
height of 6 inches.
If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches wnd let
it melt, will the cone hold all of the ice cream?
Use mathematics to explain and justify your answer.
Answer:
No, the cone will not hold all of the ice cream.
Step-by-step explanation:
Given:
" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a height of 6 inches.
If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches would let it melt.
Now, to explain mathematically will the cone hold all of the ice cream.
Taking the value of π = 3.14.
So, to get the volume of waffle cone we put formula:
Height (h) = 6 inches.
Diameter = [tex]2\frac{5}{8}=\frac{21}{8}\ inches.[/tex]
Thus radius (r) = Diameter ÷ 2 = [tex]\frac{\frac{21}{8}}{2} =\frac{21}{16} \ inches.[/tex]
[tex]Volume=\pi r^2\frac{h}{3}[/tex]
[tex]Volume=3.14\times \frac{21}{16} \times \frac{21}{16} \times \frac{6}{3}[/tex]
[tex]Volume=3.14\times 1.31\times 1.31\times 2[/tex]
[tex]Volume=10.78\ inches^3.[/tex]
The volume of waffle cone = 10.78 inches³.
Now, to get the volume of scoop which is in the shape of sphere we put formula:
Diameter = [tex]2\frac{7}{8} =\frac{23}{8} \ inches.[/tex]
Thus radius (r) = Diameter ÷ 2 [tex]=\frac{\frac{23}{8}}{2} =\frac{23}{16} \ inches.[/tex]
[tex]Volume = \frac{4}{3} \pi r^3[/tex]
[tex]Volume = \frac{4}{3} \times 3.14\times \frac{23}{16} \times \frac{23}{16} \times \frac{23}{16}[/tex]
[tex]Volume=1.33\times 3.14\times 1.44\times 1.44\times 1.44[/tex]
[tex]Volume=12.47\ inches^3.[/tex]
The volume of one scoop of ice cream = 12.47 inches³.
So, as the volume of scoop of ice cream is more than the volume of cone.
Thus, if placing one scoop of ice cream in the cone and let it melt, the cone will not hold all of the ice cream.
Therefore, no the cone will not hold all of the ice cream.
The ice cream scoop will not fit into the cone due to volume differences.
The ice cream scoop will not fit into the cone. To determine this mathematically, we need to compare the volume of the cone to the volume of the ice cream scoop.
The volume of the cone can be calculated using the formula for the volume of a cone: V = 1/3 × π × r² × h.
Similarly, the volume of the sphere (ice cream scoop) can be calculated using the formula for the volume of a sphere: V = 4/3 × π × r³.
By plugging in the given measurements, we can determine that the volume of the ice cream scoop will be greater than the volume of the cone, indicating that the ice cream scoop will not fit into the cone.
Sydney started biking to the bookstore traveling 9 mph, after some time the bike got a flat so Sydney walked the rest of the way, traveling 7 mph. If the total trip to the bookstore took 7 hours and it was 57 miles away, how long did Sydney travel at each speed?
Answer:
By bike= 4 hours
By walk= 3 hours
Step-by-step explanation:
Given: Sydney travel by bike at 9 mph
Sydney travel by walk at 7 mph.
Total trip time= 7 hours
Distance to bookstore= 57 miles.
Lets assume the time spent travelling by bike be "x".
∴ Time spent travelling by walk is [tex](7-x)[/tex]
Now, lets find the distance travelled on bike and by walk.
we know, [tex]Distance= speed\times time[/tex]
∴ Distance by bike= [tex]9\times x= 9x[/tex]
Distance by walk= [tex]7\times (7-x)[/tex]
Using distributive property of multiplication.
∴ Distance by walk= [tex]49-7x[/tex]
Next, forming an equation for total distance travelled to find x.
⇒ [tex]9x+ (49-7x)= 57\ miles[/tex]
Opening parenthesis
⇒ [tex]9x+49-7x= 57[/tex]
⇒[tex]2x+49= 57[/tex]
Subtracting both side by 49
⇒[tex]2x= 8[/tex]
dividing both side by 2
⇒[tex]x= \frac{8}{2}[/tex]
∴[tex]x= 4\ hours[/tex]
Hence, time spent travelling on bike is 4 hours.
Subtituting the value x to find the time spent travelling by walk.
Times spent travelling by walk= [tex]7-4= 3\ hours[/tex]
hence, time spent travelling by walk= 3 hours
At a convention of science teachers, various attendees are asked to name their favorite subject in high school.
a.
teachers at the convention
c.
favorite subject
b.
teachers surveyed
d.
cannot be determined
Please help me i rlly need it
Answer:
im stuck on a similar problem right now
Answer:
8.2
Step-by-step explanation:
Use cosine law:
BC² = 7² + 9² - 2(7)(9)cos(60)
BC² = 67
BC = sqrt (67)
BC = 8.1853
BC = 8.2 (nearest tenth)
what is the answer? plzzz
Answer:
The costs of the ski packages will be the same if you set them equal to each other. The cost will be the same after 5 hours. The cost will be $35 for both packages.
Step-by-step explanation:
5 + 5x = 20 + 2x Set the equations equal
-5 -5 Subtract 5 from both sides
5x = 15 + 2x
-2x -2x Subtract 2x from both sides
3x = 15 Divide both sides by 3
x = 5
4.
Nat had some stamps. He divided them into sets
of six to put in his album. He made 17 sets. How
many stamps did Nat have?
Answer:
102
Step-by-step explanation:
Nat had a total of 102 stamps which he divided into 17 sets. Each set contained six stamps.
To find out how many stamps Nat had, we need to multiply the number of sets by the number of stamps per set. Nat divided his stamps into sets of six. He made 17 sets. To calculate the total number of stamps, we perform the multiplication:
Multiply the number of stamps in each set (6) by the number of sets (17).
6 stamps/set × 17 sets = 102 stamps
Hence, Nat had 102 stamps in total.
Reynaldo Is making a model of a school building. the actual building is 28 feet tall and 128 feet long. if the model is 16 inches long, how tall should the model be?
3.5 inches
Step-by-step explanation:
128 feet : 16 inches
28 feet : x inches
Then,
128 / 16 = 28 / x
8 = 28 / x
x = 28 / 8
Therefore,
x = 3.5 inches
Answer:
B= 3.5 in.
Step-by-step explanation:
parallel to x = 3 and passes through (6, 1)
Answer:
x = 6
Step-by-step explanation:
x = 3 is the equation of a vertical line parallel to the y- axis.
The equation of a parallel line will therefore be a vertical line.
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (6, 1) with x- coordinate 6, thus
x = 6 ← equation of parallel line
Final answer:
The equation of the line that is parallel to x = 3 and passes through (6, 1) is x = 6.
Explanation:
The question relates to finding the equation of a line that is parallel to another line, specifically the line x = 3, and that also passes through a given point, namely (6, 1). Since the line x = 3 is a vertical line, any line parallel to it will also be vertical and have an equation of the form x = k, where 'k' is a constant.
In this case, the line we are looking for must go through the point (6, 1), which means it will have the same x-coordinate as this point. Therefore, the equation of the line is simply x = 6.
-12 + 8a = -a + 6(2a - 2)
Answer:
41/6
Step-by-step explanation:
-12+81=-1+6(2a-2)
first distribute:
-12+81=-1+12a-12
combine like terms:
-12+81= -1+12a-12
69=-13+12a
add -13 with 69:
82=12a
divide 82 and 12:
82/12= 41/6
Answer:
a = 0
Step-by-step explanation:
given
-12 + 8a =-a + 6(2a -2)
Distribute the righ side
-12 + 8a = -a +6x2a -6x2
-12 + 8a = -a +12a - 12
-12 + 8a = 11a -12
Collect like terms
-12 + 12 = 11a - 8a
0 = 3a
Divide both sides by 3
0/3 = 3a/3
0 = a
a = 0
The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons. What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?
Answer:
0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 4000 gallons
Standard Deviation, σ = 125 gallons
Sample size, n = 40
We are given that the distribution of amount of fuel is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Central limit theorem:
As the sample size increases, the distribution of sample mean has a similar popular distribution shape.
P(sample of 40 jumbo jets will be less than 3950 gallons)
P(x < 3950)
[tex]P( x < 3950) = P( z < \displaystyle\frac{3950 - 4000}{125}) = P(z < -0.4)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 3950) = 0.6554 = 65.54\%[/tex]
0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.
The probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.
it is given that
Mean μ= 4000 gallons
Standard deviation σ = 125 gallons
Number of trials x = 3950 gallons
What is the formula for a z-score?Z-score = (x-μ)/σ
Z-score = (3950-4000)/125
Z-score = -0.4
So probbaility P(x<3950) = P(z<-0.4)
From the standard normal table,
P(x<3950) = 0.66
Therefore, the probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.
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A bicycle wheel travels 26π in. for each revolution. What is the radius of the wheel?
Answer:
13
Step-by-step explanation:
Circumference=2πr
2πr=26π
2r=26
r=13
Final answer:
The radius of a bicycle wheel that travels 26π inches per revolution is found using the circumference formula. By solving 26π = 2πr, the radius is determined to be 13 inches.
Explanation:
The question asks to determine the radius of a bicycle wheel that travels 26π inches per revolution. To find the radius, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we know the wheel travels 26π inches for each revolution, this distance is the circumference of the wheel.
Setting up the equation 26π = 2πr, we can solve for the radius r by dividing both sides of the equation by 2π:
26π = 2πrr = (26π) / (2π)r = 26 / 2r = 13 inchesThe radius of the bicycle wheel is 13 inches.
A cup is filled with
100 milliliters of water. Every second, 2
milliliters of water are poured out of the
cup. Which function shows the amount
of water in the cup after t seconds?
Answer:
t=100-2x
Step-by-step explanation:
The amount of water in the cup after t seconds can be represented by the linear function Y = 100 - 2t. This equation is derived from the initial amount of water in the cup and the rate at which water is being poured out.
Explanation:The function that shows the amount of water in the cup after t seconds is a linear function. It can be represented as Y = 100 - 2t. In this equation, Y represents the amount of water left in the cup and t represents time in seconds.
This equation comes from the initial amount of water (100 milliliters) minus the rate of water being poured out of the cup (2 milliliters per second times the number of seconds). For example, after 3 seconds, the amount of water left would be 100 - 2*3 = 94 milliliters.
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Simplify 2(6(3.5+2.1))
Answer:67.2
Step-by-step explanation:
3.5+2.1=5.6
6 times 5.6 is 33.6 then 33.6 times 2 is 67.2
How would you solve 936=78p?
Answer:
p=12
Step-by-step explanation:
936=78p
divide 78 from both sides.
12=p
Answer:
12
Step-by-step explanation:
you have to get the variable by itself. so you would divide by 78. taking 936/78=12
The measure of one acute angle in this right triangle is 45°.
What is the measure of the other acute angle?
Answer:
45°
Step-by-step explanation:
90-45=45°
What is the cube root of 8/125
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Note the [tex]\sqrt[3]{8}[/tex] = 2 and [tex]\sqrt[3]{125}[/tex] = 5
Thus
[tex]\sqrt[3]{\frac{8}{125} }[/tex] = [tex]\frac{\sqrt[3]{8} }{\sqrt[3]{125} }[/tex] = [tex]\frac{2}{5}[/tex]
Answer:
2/5
Step-by-step explanation:
8 = 2^3
125 = 5^3