The 12 months past and the fruit turned into sonic the hedge hog #PERIODAHHPERIODUHH
4. A park charges $8 for adults and $4 for kids. How many of each type of ticket was sold if a total of 325 tickets were sold for a total of $1812?
Answer:
1300 and 750
Step-by-step explanation:
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1. Name a plane parallel to plane WXT
2. Name two segments parallel to VU.
3. Name two segments parallel to SW.
4. Name two segments skew to XY.
5. Name two segments skew to VZ.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
What are parallel lines ?Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given : The quadrilateral prism
Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
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{2x+7y=-20
{x-3y=16
Solve for systems of equations
By solving the linear equations we get the final values of x = 4 & y = 4.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order term are included.
We have,
2x + 7y = -20 ----------(i)
x - 3y = 16 ----------(ii)
By multiplying equation (ii) with 2 we get,
2x + 7y = -20 ---------(III)
2x - 6y = 32 -----------(IV)
taking subtraction of equations (III) and (IV), we get
y = 4
by putting value of y in equation (ii) we get,
x = 4
Hence by solving the linear equations we get the values of x = 4 & y = 4.
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a new shopping mall is gaining in popularity. every day since it opened, the number of shoppers is 5% more than the number of shoppers the day before. about how many total shoppers would be expected after 10 days, if there were 100 shoppers on the first day?
After 10 days, the expected number of shoppers at the shopping mall is 163.
It is given that the number of shoppers increases daily by 5% from the number of shoppers the previous day.
As we can see that the increase in the number of shoppers is going to change every day, and the above case is compounded daily.
The formula of compound increase is
Amount = Base X (1 + r/n)ⁿˣ
where,
Base = original amount
r = rate of change
n = no. of times the change occurs in the time period
t = time
Here,
Base = 100
r = 5/100
n = 1, since it changes once every day
x = 10
Therefore we get
100 X (1 + 5/100)¹⁰
= 100 X 1.05¹⁰
162.88
Since the number of people cannot be in decimal,
the expected number of people is 163
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There are 10 girls and 20 boys in a class.
The class has a test.
The mean mark for all the class is 70
The mean mark for all the boys is 62
Work out the mean mark for the girls.
Answer:
86
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
given mean mark for class of 30 is 70 , then
[tex]\frac{sum}{30}[/tex] = 70 ( multiply both sides by 30 )
sum = 2100
given the mean mark for 20 boys is 62, then
[tex]\frac{sum}{20}[/tex] = 62 ( multiply both sides by 20 )
sum = 1240
the sum for the 10 girls is then 2100 - 1240 = 860
then mean score for the 10 girls is
mean = [tex]\frac{860}{10}[/tex] = 86
The Question: An employer provides two payment options for employees.
Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.
Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.
My Answer: Option A; 200, 250, 300, 350, 400, 450. Option B; 200, 220, 242, 266.2, 292.82, 322.1
Am I correct?
Answer:
Your first option is correct but your second is wrong
Step-by-step explanation:
In option b-
when an employee receives 10% additional for each of the following weeks:
10% of 200= 10/100 x200= 20
it means he will get $20 in extra in every week
so it will be- 220,240,260
a gardener has 1040 feet of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing. garden bordered by a river what dimensions would guarantee that the garden has the greatest possible area?
The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
Let length be l and width be b of garden .
According to question ,
l + 2b = 1040
Area of garden = l * b
Substituting value of l in formula for area ,
Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]
Taking derivative of Area wrt. b and putting it equal to 0 ,
1040 - 4b = 0
b = 1040 / 4
b = 260 feet
Therefore , l = 1040 - 520 = 520 feet .
Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .
Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
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Absolutely value equations |m-2|-1=4
The value of 'm' in the absolute value equation is 3
What is a linear equation?A linear equation can be described as an equation having the highest power of the variable as 1.
It is also referred to as a one-degree equation.
Example;
x + 1 = 4
What is absolute value?Absolute value of a number can be defined as the value of that number irrespective of its direction to zero on the number line.
The value must take a positive sign.
The symbol used to represent the absolute value of a number is '| '
We have the equation;
|m-2|-1=4
Let's take the absolute value
m + 2 - 1 = 4
Now, collect like terms, we get;
m = 4 - 1
Add or subtract like terms
m = 3
Hence, the value is 3
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A-B =2
A+2= B
What is A and B
The given system of equations has no solution.
The given system of equations are A-B =2 and A+2= B.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here,
A-B =2 --------(I) and A+2= B --------(II)
From equation (II) substitute B=A+2 in the equation (I), we get
A-(A+2)=2
⇒ A-A-2=2
⇒ 0-2=2
Hence, the given system of equations has no solution.
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The slope from problem 7 was 2.
The y-coordinate is 2 when x=0.
What is a slope?The slope or gradient of the line is a mathematical term used to describe the direction and steepness of a line. The ratio of the change in the y coordinate to the change in the x coordinate is known as the slope of a line. Δ y and Δx are the net changes in the y and x coordinates, respectively.
The slope of a line is calculated as the proportion of the rise to the run, or the increasing divide by the run. The coordinate plane, it describes the slope of the line. Finding the slope between two different points and calculating the slope of a line are similar tasks.
The slope-intercept form is y= mx +c
Here, given that slope m=2
Let us consider that the above equation is passing through (2,2)
2=2(2)+c
c=2
y=2x+2
Therefore, when x=0,
y=2(0)+2
y=2
Therefore, the y-coordinate is 2 when x=0
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The weight of four different boxes is shown in pounds. Which list shows the weights in order from least to greatest?
16.4, 16 1/2, 16.625 , 16 3/5
Answer: 16.4, 16 1/2, 16 3/5 16.625,
Step-by-step explanation: 16.4, 16 1/2, 16 3/5 16.625,
16 1/2 = 16.5, 16 3/5 = 16.6
Sutton takes 48 minutes to walk to work. after getting a new job, sutton takes 30.72 minutes to walk to work. what was the percent decrease in the travel time?
The percent decrease in the travel time after getting a new job is 36%.
Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".
First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.
decrease in time = 48 - 30.72
decrease in time = 17.28
Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.
percent decrease = (17.28 / 48) x 100
percent decrease = 36%
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algebra 2 please help!!
Answer:
A
Step-by-step explanation:
Translation of 3 units is a plus 3 away from the x
for g(x)=x to the power of 2 minus x, find g(x) when x=-2
The value of the function g(x) when x = -2 is 6
How to evaluate the function?The definition of the function is given as
g(x)=x to the power of 2 minus x
Rewrite the above function properly
So, we have the following representation
g(x) = x² - x
To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2
This is represented by
Calculate g(x), when x = -2
Substitute -2 for x in the equation g(x) = x² - x
So, we have the following equation
g(-2) = (-2)² - (-2)
Evaluate the exponents
This gives
g(-2) = 4 - (-2)
Evaluate the sum
g(-2) = 6
Hence, the value of the function is 6
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The legs of an isosceles triangle are 0.3 foot less than twice the base. The perimeter of the triangle is 4.9 feet.
What is the length of one of the triangle’s legs?
A. 1.1 feet
B. 1.4 feet
C. 1.9 feet
D. 2.2 feet
The length of the given isosceles triangle legs is 1.9 feet.
What is a Linear equation?A linear equation is a equation that has degree as one.
To find the solution of n unknown quantities n number of equations with n number of variables are required.
Given that,
The perimeter of an isosceles triangle is 4.9 feet.
And, legs of the triangle are 0.3 foot less than twice the base.
Suppose the base of the triangle be x.
Then, its legs are 2x - 0.3.
As per the question the expression for the perimeter of the triangle is,
2x - 0.3 + 2x - 0.3 + x = 4.9
=> 5x - 0.6 = 4.9
=> 5x = 5.5
=> x = 1.1
Thus, the legs can be found by substituting x = 1.1 in 2x - 0.3 as below,
2 × 1.1 - 0.3
= 1.9
Hence, the length of one of the triangle’s legs is 1.9 feet.
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Nora leans a 24-foot ladder against a wall so that it forms an angle of 76^{\circ} ∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
23.29 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.
To find how high up the wall the ladder reaches, use the sine trigonometric ratio:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
where:
θ is the angle.O is the side opposite the angle.H is the hypotenuse (the side opposite the right angle).The angle of elevation is 76°, so θ = 76°.
Let x be the height the ladder reaches up the wall, so O = x.
H is the length of the ladder, so H = 24.
Substitute the given values into the sine ratio and round the answer to the nearest hundredth:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]
[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]
[tex]24 \sin(76^{\circ})= x[/tex]
[tex]x=24 \sin(76^{\circ})[/tex]
[tex]x=23.28709743...[/tex]
[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]
Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.
You deposit $3000 in an account that
earns simple interet at an annual rate of
5%. How long must you leave the money
in the account to earn $500 in interest?
Answer:
3 ¹/₃ years
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = Total interest.P = Principal amount.r = Annual interest rate (in decimal form).t = Time (in years).Given:
I = $500P = $3,000r = 5% = 0.05Substitute the given values into the formula and solve for t:
[tex]\sf \implies 500=3000 \times 0.05 \times t[/tex]
[tex]\sf \implies 500=150t[/tex]
[tex]\sf \implies t=\dfrac{500}{150}[/tex]
[tex]\implies \sf t=3\frac{1}{3}[/tex]
Therefore, the money must be left in the account for 3 ¹/₃ years for the account to earn $500 interest.
the ph measurements of water specimens from various locations along a given river basin are normally distributed with mean 8 and standard deviation 0.3. what is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2? 0.7475 0.2525 0.7525 0.2475
0.7475 is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2
P( A ≥ 8.2) = P( (Z ≥ 8.2 − 8)/0.3)
= P(Z ≥0.66)
= 0.7475
normsdist(0.666666) =0.7475
The standard normal cumulative distribution function is returned. The mean of the distribution is 0 (zero), while the standard deviation is one. Instead of a table of standard normal curve areas, use this function.The concentration of hydronium (H3O+) ions in an aqueous solution is measured by pH. It is measured from 0 to 14 on a negative logarithmic scale.
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Factorise completely:
Answer:
2xy(8x + 5)
Step-by-step explanation:
16x²y + 10xy ← factor out 2xy from each term
= 2xy(8x + 5)
What is the value of blank and 40.01 is close to 1
The number that is the numerator of a fraction with denominator of 40.01 and is equals to a coefficient of one is:
40.01.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:
Fraction = x/y.
The terms are named as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Hence the quotient of the division is the numerator divided by the denominator.
In this problem, interpreting the blank variable as x, the fraction that represents the situation is:
x/40.01 = 1.
Applying cross multiplication, the numeric value of the variable x is obtained as follows:
x = 40.01 x 1
x = 40.01.
Missing InformationThe complete problem asks for which number divided by 40.01 is close to 1.
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Can anyone state the vertex of the graph?
The graph has no vertex and the transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?By definition, the vertex of a function is the maximum or the minimum of the function
From the graph, we can see that the graph only has a turning point; it has no maximum or minimum
So, we can conclude that there is no vertex in the graph
The transformationHere, we have:
We can see that:
The graph is 4 units to the left of the origin and 2 units below the origin
This means that the function has been shifted down and shifted to the left
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During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2
The values are not equivalent to 2.2 include
2.6 - 0.6
1.8 + 2.5
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, 2.6 - 0.6 will be:
= 2.6 - 0.6
= 2.0
Also, 1.8 + 2.5 will be:
= 1.8 + 2.5
= 4.3
Therefore, they're not equivalent to 2.2
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Complete question
During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2
1.2 + 1.0
2.6 - 0.6
0.9 + 1.3
1.8 + 2.5
1. 1/4 of a vegetable garden has broccoli and 2/3 of the garden has peppers. How much of the garden has vegetables growing in it?
2. Jessica and Maria are both making slime with different recipes. Jessica’s recipe calls for 1 1/2 cups of flour and Maria’s recipe calls for 2/3 cups of flour. How many cups of flour will they need in order to make both of their batches of slime?
3. Donnie has a pool and recently discovered a leak. He continues to patch the leak until someone can come out to repair it. After all the water has completely drained out of the pool due to the patch coming off, it takes him two days to fill the pool back up. It takes three days for the pool to drain completely. How long would it take to fill the pool if the patch is off while Donnie is refilling it?
4. I baked a cake for my sibilants. My brother ate 1/8 of the cake and my sister ate 3/4. How much of the cake is left for me?
5. Amanda is making oatmeal cookies with raisins and pecans for her club. The recipe makes seventeen oatmeal cookies. It takes 1/4 of a cup of nuts and 1/2 a cup of radon’s just for seventeen cookies! There are thirty-four members in Amanda’s club. If she makes exactly thirty-four cookies, how many cups of nuts will she need?
6. Felipe has a business where he builds and sells birdhouses. To build 12 birdhouses, he needs 5 1/4 meters of wood. During the holiday season, Felipe was asked to make 4 1/2 times the number of birdhouses he usually makes. How many meters of wood does Felipe need to make that many birdhouses?
7. It is Nadine’s birthday, and she is making walnut brownies for her sleepover. She invited eight of her friends to her party. The recipe that she is using makes twenty-four brownies, but she only wants to make eight. The recipe for twenty-four calls for 4 1/2 cups of walnuts. How many cups of walnuts will she need for eight people?
8. A candy bar is 5 1/3 inches long. If it is divided into pieces that are 1 1/4 inches long, then how many pieces of candy bar will there be?
9. A maple tree can grow in average to be 90 feet tall. Redwood trees can grow to be 2 2/3 times bigger than a maple tree. What is the average height of a Redwood tree?
10. A piece of rope is 24 1/2 feet long. How many 1/4- foot sections can be cut from it?
Broccoli and peppers occupy 11/12 of the gardenAs a result, 11/12 of the garden is filled with vegetables.
How can I determine how much of a garden's growing veggie there is?1,Let's add up those two fractions to determine how much of the entire garden contains broccoli and peppers since we know that 1/4 of the garden has broccoli and 2/3 of the garden contains peppers.
Consequently, 1/ 4 + 2/3 =?
It is necessary for the denominator to match.
Consequently, 1/4 x 3/ 3 = 3 / 12.
2/3 × 4 /4 = 8 / 12
Hence, 3 / 12 + 8 / 12 = 11 / 12
2 ,Amount of flour needed to complete both recipes =2+1/4+1
3, Baked cake 1 /8 +3/4,
6 , Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes
= 54 / 12 x 5¹/₄
= 23 ⁵/₈ meters
7, 24 brownies = 9/2 cups of walnuts
8 brownies =1 1/2 cups of walnuts
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an important issue facing americans is the large number of medical malpractice lawsuits and the expenses that they generate. in a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were later dropped or dismissed (based on data from the physician insurers association of america). construct a 99% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed.
About [0.7479, 0.8091] of medical malpractice cases are abandoned or dismissed, according to the estimate with a 95% confidence level.
A confidence interval is a method for estimating a population parameter, such as the population proportion, at a given level of confidence, using the sample statistic, such as the sample proportion, and the confidence coefficient, such as the critical value.
arbitrary sample size, n = 1228
number of those who were dropped or dismissed, x = 856
The sample percentage of later discarded or dropped, p = 956 / 1228 ≅ 0.7785
Level of confidence = 0.99
Level of significance α = 0.01
The population proportion's 99% confidence interval estimate is calculated as follows:
p ± [tex]z_{a/2}[/tex] * [tex]\sqrt\frac{p (1 - p)}{n}[/tex]
Using the Excel function or the z-distribution table for calculation
[tex]z_{a/2} = z_{0.01/2} = z_{0.005}[/tex]
=NORMSINV(0.05)
[tex]z_{0.01/2}[/tex] ≅ ±2.58
The interval's computation is as follows:
0.7785 ± 2.58 * [tex]\sqrt\frac{0.7785 (1 - 0.7785)}{1228}[/tex]
= 0.7785 ± 2.58 * 0.0118
= = 0.7785 ± 0.0306
(0.7479, 0.8091)
As a result, the estimate of the proportion of medical malpractice claims that are withdrawn or dismissed at a 99 percent confidence interval is roughly [0.7479, 0.8091].
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The ratio of money in Brian's wallet to
Colin's wallet one day was 7:2.
Brian spent £39 that day.
Brian now had £4 less than Colin.
How much did Brian initially have?
Brian has £63 Initially, by using the ratio and proportion method.
What are Ratio and Proportion?
In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.
An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".
In the question, It is given that:
The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.
Let 7x denotes the amount in Brian's wallet and 2x denote the amount in Colin's wallet on that day.
we know that:
Brian spent £39 that day.
Amount left in Brian's wallet = 7x- 39
Brian now had £4 less than Colin.
⇒ 2x -4= 7x- 39
⇒ 7x-2x=4+39
⇒ 5x=35
⇒ x=7 [Divide both sides by 5 ]
So , The initial amount in Brian's wallet = 7(7)= £49
The initial amount in Colin's wallet = 2(7)= £14
The amount they had together = £49+£14 = £63
So, They had £63 altogether initially.
Therefore, Brian has £63 Initially.
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Answer: £14
Step-by-step explanation: Because Hegarty Maths says it is when I got this same Question Wrong :(
In the diagram, ABGH = CDEF.
Find the value of x.
X = ___
The value of x is 25
What is congruent polygons ?
A polygon is said to be congruent if it has the same shape as the polygon it is compared to, as well as the identical side lengths and interior angles. In order to meet the condition, congruent shapes must all have the same kind of shape. Because they are different shapes, a rectangle and a pentagon cannot be congruent.
Two squares or two hexagons can be considered congruent polygons since they both have equal-length sides and angles. However, it's crucial to keep in mind that the length of the sides must also be equal. A square is not congruent if it is larger than another square.
1. Pairs of congruent corresponding parts
∠A = ∠C AB = CD
∠B = ∠D AH = CF
∠H = ∠F HG = FE
∠G = ∠E GB = ED
To find the value of x
4x + 5 = 105
4x = 105 - 5
4x = 100
x = [tex]\frac{100}{4}[/tex]
= 25
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Can anyone answer question 8?
PLEASE HELP!! WILL GIVE BRAINLIEST
The mass of a test sample is 10g, and it has the volume of 2.5cm^3 . What is its density?
A. 10g/cm^3
B. 2.5cm^3/g
C. 4g/cm^3
D. 4cm^3/g
E. 0.25g/cm^3
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
Define density.The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.
Given,
Volume = 2.5 cm³
Mass = 10 g
For density:
Mass ÷ volume
10 ÷ 2.5
4
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
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A gigameter is 1.0×10^6 kilometers. How many square kilometers are in 5 square gigameters?
Write your answer in scientific notation.
The number of kilometers in 5 square gigameters is 5. 0 × 10^18
What is proportion?Proportion can be described as an expression or equation in which two ratios are made equal to each other.
It is also known as the mathematical comparison between two numbers or elements.
From the information given, we have;
1 gigameter = 1.0×10^6 kilometers
But,
5 square gigameters = 5. 1.0×10^6 . 1.0×10^6
Add the powers
5 square gigameters = 5..0×10^12
If 1 gigameter = 1.0×10^6 kilometers
Then 5. 1.0×10^12 gigameter = x
cross multiply
x = 5.0×10^12 × 1.0×10^6
x = 5. 0 × 10^18 kilometers
Hence, the value is 5. 0 × 10^18 kilometers
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Pls answer
Use the complete the method to solve
2y²+2y-5=0
The required solutions to the given quadratic function are below as:
[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
The quadratic function is given in the question:
2y² + 2y - 5 = 0
Compare the given function to the standard quadratic function f(x) = ax² + b x + c.
We get a = 2, b = 2 and c = -5
Using the quadratic formula to solve the above quadratic function
[tex]y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a = 2, b = 2 and c = -5 in the above formula
[tex]y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}[/tex]
[tex]y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}[/tex]
Separate the solutions as:
[tex]y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}[/tex]
[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]
Therefore, the required solutions to the given quadratic function are below as:
[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]
Learn more about quadratic function here:
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