335 children should be in the park, if the ratio of children to adults at an amusement park is typically 5 to 3 and 201 adults are in the park.
What is ratio?A ratio is the comparison of two similar quantities or the proportion of one similar quantity to another. With the same meaning, ratios can be expressed in three different ways using words or symbols. In other words, ratios can be expressed by sandwiching a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
The ratio of ninth-graders to tenth-graders can take on any of the three forms listed below, using the previous example of comparing the two groups of students in Ms. Jones' class:
10 /20
10 to 20
10 : 20
Given ratio of children to adults is 5:3
5 + 3 = 8
5/8 are children and 3/8 are adults
Let the total no. of people be x
3/8 = 201/x
x = 201 × 8/3
= 536
Now. no. of children is
5/8 × 536
= 335
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For the given piecewise function evaluate for the specific value of X
x = 4
4 > 3 , so , we use:
f(x)= x + 1
Replacing:
f(4) = 4 + 1 = 5
Answer:
f(4)= 5
Integrate the following using substitution method or integrate by part ( that suitable the given equation)
Given:
an integral is given as
[tex]\int\frac{y^2+1}{\sqrt{b+y+\frac{1}{3}y^3}}dy[/tex]Find:
we have to evaluate the given integral.
Explanation:
Let us substitute
[tex]\begin{gathered} b+y+\frac{1}{3}y^3=u \\ (1+y^2)dy=du \end{gathered}[/tex]Therefore, given integral becomes
[tex]\int\frac{1}{\sqrt{u}}du=\int u^{-\frac{1}{2}}du=\frac{u^{\frac{1}{2}}}{\frac{1}{2}}+c=2\sqrt{u}+c[/tex]Now, by back substitution, we have
[tex]\int\frac{y^2+1}{\sqrt{b+y+\frac{1}{3}y^3}}dy=2\sqrt{b+y+\frac{1}{3}y^3}+c[/tex]Therefore, the value of the given integral is
[tex]\int\frac{y^2+1}{\sqrt{b+y+\frac{1}{3}y^3}}dy=2\sqrt{b+y+\frac{1}{3}y^3}+c[/tex]10 candidates are running for president and vice presidentpositions. What is the probability that a particular candidatedoes not win a position?Select one:1/5, 1/20, 1/10, 4/5
The answer is:
[tex]\frac{4}{5}[/tex]Explanation:
To calculate the probability of an event A occurring, we use the formula:
[tex]P(A)=\frac{favorable\text{ }outcomes}{total\text{ }outcome}[/tex]And, if P(A) is the probability of A occurring, the probability of A not occurring is:
[tex]P(\neg A)=1-P(A)[/tex]In this case, for a particular candidate to win a position, the total outcome is 10 people, and the favorable outcome is 2, for the 2 positions to be elected.
Then:
[tex]P(A)=\frac{2}{10}[/tex][tex]P(A)=\frac{1}{5}[/tex]This is the probability of winning a position. The probability of not winning is:
[tex]\begin{gathered} P(\neg A)=1-\frac{1}{5} \\ p(\neg A)=\frac{4}{5} \end{gathered}[/tex]if the vertical line test touches the graph more than once, then the graph is a function.
False
True
The statement is false, the correct one would be:
"if the vertical line test touches the graph more than once, then the graph is not a function."
Is the statement true or false?
A function is a relation that maps inputs x into outputs y, such that each input x can be mapped into only one output.
Remember that the inputs are in the horizontal axis, now, if we draw a vertical line and that line touches the graph twice, this will mean that one input will have two outputs, and thus, that would not be a function.
Then the statement is false
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A substance has a mass of 53 grams. Its volume is 12 ml3. What is thedensity? Round to the nearest Tenth. (1 number after decimal) & be sure toinclude the correct label.Your answerThe density of sulfur is 2.1g/cm3. If you have a volume of 6 cm3, what is the poinmass? Round to the nearest Tenth.
1) Gathering the data
mass = 53 g
V = 12 ml
The density is given using the following formula:
[tex]\begin{gathered} d=\frac{m}{V} \\ d\text{ =}\frac{53}{12\text{ }} \\ d=4.42\text{ g/ml} \end{gathered}[/tex]O FRACTIONSWriting unit fractions with a common denominator to add or...11Let's find312First, write the subtraction so the fractions have denominator 12.Then subtract.113121212?
Step 1
Given;
[tex]\frac{1}{3}-\frac{1}{12}[/tex]Required; To write the subtraction so that the denominators are all 12. Then subtract.
Step 2
Use equivalent fractions to make the denominator of 1/3 12
[tex]\begin{gathered} \frac{1}{3}=\frac{x}{12} \\ 12=3x \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, we will have;
[tex]\frac{1}{3}-\frac{1}{12}=\frac{4}{12}-\frac{1}{12}[/tex][tex]\frac{4}{12}-\frac{1}{12}=\frac{3}{12}=\frac{1}{4}[/tex]The answer will thus be;
[tex]\frac{1}{3}-\frac{1}{12}=\frac{4}{12}-\frac{1}{12}=\frac{3}{12\text{ }}\text{ which is =}\frac{1}{4}[/tex]Answer = 3/12 or 1/4 when reduced
- Part A: Is x = 6 a solution of the equation 8x+8 = 56? Explain. Part B: Suppose the solution x = 6 increases to x = 9, and the left side of the equation stays the same. How would the right side need to change if the solution is now x = 9?
Answers to both subparts are given below:
(A) Yes, x = 6 is the solution of the equation 8x+8 = 56.(B) We need to add 24 on the right side of the equation when x = 9.What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, (A) x = 6 is the solution of equation 8x+8 = 56:
Substitute x = 6 in equation 8x+8 = 56 as follows:
8x+8 = 568(6)+8 = 5648 + 8 = 5656 = 56Yes, x = 6 is the solution of the equation 8x+8 = 56.
(B) The change on the right side if x = 9:
Substitute x = 9 in equation 8x+8 = 56 as follows:
8x+8 = 568(9) + 8 = 5672 + 8 = 5680 = 56Now,
80 - 56 = 24So, we need to add 24 on the right side of the equation when x = 9.
The answers to both subparts are given below:
(A) Yes, x = 6 is the solution of the equation 8x+8 = 56.(B) We need to add 24 on the right side of the equation when x = 9.Know more about equations here:
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In which of the following categories do the three families spend about the same dollar amount each month (within $25 of each other)? Select all that apply.HousingFoodChildcareTransportationInsuranceOther NeedsTaxes
Answer:
Food
Transportation
Explanation:
To find thh correct category, we need to calculate the amount spend on each category for each family, so taking into account the circle graphs, we get:
Family A (income: $5,400)
Housing: 5400 x 19% = 1026
Food: 5400 x 14% = 756
Childcare: 5400 x 18% = 972
Transportation: 5400 x 11% = 594
Insurance: 5400 x 23% = 1242
Other Needs: 5400 x 9% = 486
Taxes: 5400 x 5% = 270
Saving: 5400 x 1% = 54
Family B (income $4675)
Housing: 4675 x 16% = 748
Food: 4675 x 16% = 748
Childcare: 4675 x 18% = 841.5
Transportation: 4675 x 13% = 607.75
Insurance: 4675 x 28% = 1309
Other Needs: 4675 x 7% = 327.25
Taxes: 4675 x 2% = 93.5
Family C (income: $6675):
Housing: 6675 x 14% = 934.5
Food: 6675 x 11% = 734.25
Childcare: 6675 x 30% = 2002.5
Transportation: 6675 x 9% = 600.75
Insurance: 6675 x 20% = 1335
Other Needs: 6675 x 6% = 400.5
Taxes: 6675 x 10% = 667.5
Now, we need to calculate the differences in each categories:
Housing
A - B = 1026 - 748 = 278 > 25
Food
A - B = 756 - 748 = 8
B - C = 748 - 734.5 = 13.5
A - C = 756 - 734.25 = 21.75
Childcare
A - B = 972 - 841.5 = 130.5 > 25
Transportation
A - B = 594 - 607.75 = -13.75
B - C = 607.75 - 600.75 = 7
A - C = 594 - 600.75 = -6.75
Insurance
A - B = 1242 - 1309 = -67 < -25
Other Needs
A - B = 486 - 327.25 = 158.75 < 25
Taxes
A - B = 270 - 93.5 = 176.5 > 25
Therefore, the answers are:
Food
Transportation
I’m stuck on my mat please help me I did it but I just want to recheck my answer
Solution
Step 1:
Final answer
The line plot has 14 dots plotted on it.
The least value plotted on the line plot is 18.0
The greatest value plotted on the line is 22.0
The height of 19.50 inches occurs the most often.
I need help solving: c= 8a-3b and solve for a
hello
[tex]c=8a-3b[/tex]solve for a
step 1
add 3b to both sides of the equation
reason; we're doing this so that we take -3b to the other side of the equation so the we can have a and it's coefficient on one side of the equation
[tex]\begin{gathered} c=8a-3b \\ c+3b=8a-3b+3b \\ c+3b=8a \end{gathered}[/tex]or we can simply say take -3b to the other side of the equation in order to make it easy to equate a
but note that whenever a variable or real number crosses an equality or inequality sign, the sign changes from either positve (+ve) to negative (-ve) or negative (-ve) to positive (+ve).
in this case, -3b
now we have our equation almost set
step 2
divide both sides by 8 to solve for a
[tex]\begin{gathered} 8a=c+3b \\ \frac{8a}{8}=\frac{c+3b}{8} \\ a=\frac{c+3b}{8} \end{gathered}[/tex]show algebraically that 0.681 can be written as 15/22
The expression 0.681 can be written as 15/22 because 0.681 approximates to 15/22
How to show that the expressions are equivalent?The expressions are given as
0.681 and 15/22
Start by converting 0.681 to fraction
So, we have the following equation
0.681 = 681/1000
Multiply the fraction by 1
So, we have
0.681 = 681/1000 x 1
Rewrite 1 as 22/22
0.681 = 681/1000 x 22/22
Switch the numerator and the denominator
So, we have
0.681 = 681/22 x 22/1000
Simplify
0.681 = 681/22 x 11/500
Multiply 681 by 11
So, we have
0.681 = 7491/22 x 1/500
Divide 7491 by 500
So, we have
0.681 = 14.98/22
Approximate
0.681 = 15/22
Hence, the expressions are equivalent
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Which equation applies the associative property of multiplication?
A 8/9x7/4x(-5/8)=8/9x(-5/8)x7/4
B(-9/4x3/2)x(6/3x5/7)=-9/4x(3/2x6/3)x5/7
C(-1/2x4/7)+(-1/2x2/3)=-1/2x(4/7+2/3)
D-6/5-(5/3-1/4)=(-6/5-5/3)- 1/4
8/9x7/4x(-5/8)=8/9x(-5/8)x7/4 this equation applies the associative property of multiplication .
Option A is correct
What is the multiplication associative property equation?(a b) c = a b (c) is the formula that makes the associative property of multiplication the most intuitive.
What three attributes does multiplication possess?Multiplication's characteristics
The product remains unchanged when the order of the factors is changed since multiplication is commutative.
The product remains unchanged when the factors are reorganized, according to the associative property of multiplication.
Multiplication's identity property states that the result of multiplying 1 by any number equals that number.
What do you mean by "associative property"?What does "associative property" mean? The associative property is a mathematical principle that states that the product of a multiplication problem is unaffected by the arrangement of the factors.
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Farmer Jill needz to ship 9,918 apples if each crate can hold 21 apples how many full crates of apples will jill get how many will be leftover
The most appropriate choice for division will be given by -
Number of crates = 472 and number of apples remaining = 6
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Here,
Total number of apples = 9918
Number of apples in one crate = 21
Total number of apples = 9918 ÷ 21
Quotient of 9918 ÷ 21 = 472 and remainder = 6
Number of crates = 472 and number of apples remaining = 6
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A spherical tank for liquefied petroleum is 8.0 in. In diameter. What is the ratio of the surface area to the volume of tank
The ratio of the surface area to the volume of the tank is 3 : 4
What is volume?The volume of a shape is the amount of space in it
How to determine the ratio?The given parameter is
Diameter, d = 8.0 inches
Calculate the radius of the above diameter
So, we have
r = d/2
Substitute the known values in the above equation
r = 8/2
Evaluate
r = 4
The surface area of a sphere is
A = 4πr²
Where r represents radius
So, we have
A = 4π(4)²
The volume of a sphere is
V = 4/3πr³
Where r represents radius
So, we have
V = 4/3π(4)³
The ratio is represented as
Ratio = A : V
So, we have
Ratio = 4π(4)² : 4/3π(4)³
Divide by 4³π
Ratio = 1 : 4/3
Multiply the ratio by 3
Ratio = 3 : 4
Hence, the ratio is 3 : 4
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Your tractor broke down and was in the shop for 4 days.
Mechanics worked on it for 21.4 hours at $48 per hour. They
replaced $1875.42 worth of parts. You lost $18 per hour by not
having the use of the tractor. You work a 15 hour day. How
much did the labor cost? How much did you lose by not having
the use of your tractor?
The total labor cost for repairing the tractor including the parts replacement is $2902.62 and the loss by not having the use of tractor is $1080.
What is Direct Labor?An individual product, cost center, or work order is assigned to a certain amount of direct labor, which is labor used in production or services. The production team that creates items, such as machine operators, assembly line workers, painters, and so on, is referred to as direct labor when a business generates products.
Total hours of mechanic worked is 21.4Cost for mechanic per hour is $48Cost for replacement of parts = $1875.42Total labor cost = (Total hours of mechanic worked)(Cost for mechanic per hour) = (21.4)(48) = $1027.2Total labor cost including replacement of parts = (Total labor cost)+(Cost for replacement of parts) = $2902.62 Total days the tractor kept in the mechanic shop is 415 hours of work is done with a profit of $18 per hourThe loss by not having the use of tractor= (Total days the tractor kept in the mechanic shop) (hours of work is done in a day) (profit per hour)The loss by not having the use of tractor= (4)(15)(18) = $1080To learn more about Direct labor, refer to:
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ONLY (e) questionThe turning points of the graph are ___Type in ordered pair, round each coordinate to two decimal places
Answer:
[tex]\begin{gathered} (-4.85,-243) \\ (-1.5,136.69) \\ (1.85,-243) \end{gathered}[/tex]Explanation:
Given the function:
[tex]f(x)=3 x\left(x^{2}-9\right)(x+6)[/tex]The graph of f(x) is attached below:
From the graph, the turning points are:
[tex]\begin{gathered} (-4.85,-243) \\ (-1.5,136.69) \\ (1.85,-243) \end{gathered}[/tex]What is the measure of ZCOBWhat is the measure of ZCAB?
In the figure, we have two tangents that intersect with the radii of the circle. This makes angles at C and B right angles (90 degrees).
To find angle at O, we employ the angle at centre is 2ce that subtended at circumference making angle at O = 2 x 65 = 130 degrees.
Now we have Quadilateral ABOC and we know that the total angles in a quadrilateral are 360 degrees.
Therefore angle at A = 360 - (90 + 90 + 130)
Angle A = 360 - 310 = 50 degrees
Therefore, angle CAB = 50 degrees
Wilfred measured the width of his living room to be 18 feet 9 inches. How wide is his living room in feet? Type your answer in decimal format. Leave a space between the number
we get that 9 inches in feet are
[tex]\frac{9}{12}ft=0.75ft[/tex]so in total the wilfred's room is 18.75 feet wide
Select the TABLE tab. What do all the points on this line have in common?
All the points in this line have the same value of y, as the slope is m=0 and y does not change with x.
A={1,2,6} B= {x | x is an odd whole number less than 8}. Find A∪B.
The value of set A union set B is A ∪ B = { 1, 2, 3, 5, 6, 7 }.
Consider the set,
A = { 1, 2, 3 }
And, B = { x | x is an odd whole number less than 8 }
An integer's parity determines whether it is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd.
Therefore, all the numbers less than 8 are:
1, 3, 5, 7
Therefore, the set B will be:
B = { 1, 3, 5, 7 }
In set theory, the set containing every element in a collection is the union of all its sets.
So,
A ∪ B = { 1, 2, 6 } ∪ { 1, 3, 5, 7 }
A ∪ B = { 1, 2, 3, 5, 6, 7 }
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Please Help! Match the correlation coefficient with its relationship
Strong, Positive Correlation
Weak, Negative Correlation
Moderate, Positive Correlation
No Correlation
Weak, Positive Correlation
Strong, Negative Correlation
Moderate, Negative Correlation
The correlation for the given values are estimated.
What is defined as the term Correlation?Correlation coefficients measure the strength of a linear relationship between the variables x and y.
The correlation coefficient can have values ranging from -1.0 to 1.0. In other words, this same values cannot be greater than 1.0 or less than -1.0. A correlation of -1.0 represents a perfect negative correlation, while a correlation of 1.0 represents a perfect positive correlation. A positive relationship exists is if correlation coefficient is higher than zero. If a value is less than zero, the relationship is negative. A zero value indicates that the two variables have no relationship.For the given question, the correlation are -
r = - 0.8; Strong, Negative Correlationr = 0.55; Moderate, Positive Correlationr = - 0.62; Moderate, Negative Correlationr = 0.22; Weak, Positive Correlationr = 0.83; Strong, Positive Correlationr = 0; No Correlationr = -0.26; Weak, Negative CorrelationThus, the correlation for the given values are found.
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Identify the digit with the given place value. 116.625 thousandths
The given number : 116.625
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
The domain can be best described using interval notation. The domain is [-7,8].
The range can be best described using interval notation. The range is [-4,3]
The graph of a function is given. As the graph is a straight line, it is clear that the function is a linear function. Also the function graphed has no breaks or jumps. Hence the function is continuous.
The domain of a function is the x-values for which the function is defined or the function has values.
The values of the function corresponding to the x-values in the domain is called the range. It is also called image and is a subset of the co-domain set.
Now since the graph of the function given is continuous we can better describe the domain and range of the function in the form of intervals.
The x-values for which the function is defined lies form -7 to 8 on the x-axis and hence it is the domain.
The y-values corresponding to the x-values in the domain lies between -4 and 3 on the y-axis and hence it is the range.
That is, The domain is [-7,8] and The range is [-4,3].
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A jogger goes 0.8 mi east and then turns south. If the jogger finishes 1.7 mi fromthe starting point, how far south did the jogger go?
We can use Pythagoras theorem:
[tex]\begin{gathered} H^2=a^2+b^2 \\ \\ \end{gathered}[/tex]Where H=hypotenuse and "a" and "b" are the other sides of the triangule.
In the current problem, we have:
H = 1.7, a = 0.8, b=?
Then:
What is the area of the corn field?
Answer:
23x-3
Step-by-step explanation:
5x+2+8x-11+4x+3+3+2x+4x Got this from adding the area around the field
5x+8x+4x+2x+4x+2-11+3+3 I grouped like-terms
23x+2-11+3+3 I added like-terms
23x-3 Then I got
At a lacrosse tournament, students are charged $7 per ticket and adults are charged $10 per ticket. If 450 people attended the tournament, and a total of $4,200 was collected in ticket fees, how many students attended the tournament?
60
100
200
280
The number of students that attended the tournament is 100.
How many students attended the tournament?The simultaneous equations that would be used to solve this question is:
10a + 7s = 4,200 equation 1
a + s = 450 equation 2
Where:
a = number of adults s = number of studentsThe elimination method would be used to solve the equations.
Multiply equation 2 by 10
10a + 10s = 4500 equation 3
3s = 300
Divide both sides of the equation by 3
s = 300 / 3
s = 100
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Why were the colonists prepared to meet the British at the Battles of Lexington and Concord?
OA. They had organized their own sovereign governments and militias.
OB. They had feared and prepared for British efforts to seize their arms.
C. They knew that war had already been declared by British authorities.
OD. They believed that they could prevent open conflict by showing their resolve.
The British invaded Lexington and Concord with the goal of disarming any potential rebels by taking their guns.Instead, the Revolutionary War's opening conflict was precipitated by their activities.
Why did the battle of Lexington and Concord happen?
The American Revolutionary War began on April 19, 1775, with the Battles of Lexington and Concord (1775-83).Residents of the 13 American colonies and the British government had been at odds for many years, especially in Massachusetts.Hundreds of British soldiers marched from Boston to nearby Concord that evening, April 18, 1775, in attempt to take an arsenal.The Redcoat column was about to be intercepted when Paul Revere and other horsemen raised the alarm.The conflict began with an altercation on the Lexington town green, and soon the British were fleeing under heavy fire.After numerous additional conflicts, the colonists finally achieved official independence in 1783. Battles of Lexington and Concord's lead-upGreat Britain began taking a number of actions in 1764 to increase revenue from its 13 American possessions.The colonists revolted against "taxation without representation" as a result of many of these laws, such as the Sugar Act, Stamp Act, and Townshend Acts.One of the biggest hubs of opposition was Boston, the location of the 1770 Boston Massacre and the 1773 Boston Tea Party.In June 1774, King George III of Britain increased the military presence there and closed the city's harbor until the colonists paid for the tea that had been poured overboard the year before.The British Parliament soon after declared that Massachusetts was in full-fledged rebellion. Paul Revere never yelled the infamous remark that was later ascribed to him ("The British are coming!") as he traveled from town to town on April 18, 1775, at midnight.Considering that large numbers of British soldiers were skulking in the countryside of Massachusetts, the operation was designed to be carried out as covertly as possible.Colonial Americans also thought of themselves as British at that time.A source inside the British high command informed Joseph Warren, a physician and Sons of Liberty member, on April 18 that Redcoat troops would march on Concord that evening.Paul Revere, a silversmith, and William Dawes, a tanner, were sent as two messengers by Warren to inform the populace. In the event that one of them was captured, they took separate paths.To reach Charlestown, where fellow Americans were waiting for a signal regarding the movement of British troops, Revere traveled across the Charles River by boat.The Old North Church steeple in Boston, Massachusetts, was pointed out to the patriots to be seen because it was the highest point in the city.The British were coming by land if there was even a single lantern hanging in the steeple.In the event that there were two, the British arrived by sea.The secret signal was commemorated by American poet Henry Wadsworth Longfellow in his poem "Paul Revere's Ride," where he stated: "If by land, one; if by sea, two; and I on the other shore, ready to ride and give the alarm Through every Middlesex village and farm, For the country men to be up and to arm."Dawes left Boston and made his way along the Boston Neck peninsula as Revere completed his mission in Charlestown.A few miles east of Concord, where revolutionary leaders John Hancock and Samuel Adams had taken refuge, the two came together in Lexington.Revere and Dawes set out again after successfully convincing those two to go.They encountered Samuel Prescott, a third rider, who traveled all the way to Concord by himself.A British patrol arrested Revere, while Dawes escaped.
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HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Since 1.2 is positive whereas all other are negative. So, the order will be:
1.2 > -1.6 > - 1.7 > -1.71
What are Decimals?A decimal numeral is a broad term for a number's notation using the decimal numeral system. Sometimes a decimal separator is used to identify decimals. Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Term "terminating decimals" refers to decimal numerals in this context that have a predetermined number of non-zero digits following the decimal separator. An infinite decimal that, after a certain point, repeats the same digit sequence endlessly is said to be repeating. If and only if it has a finite number of non-zero digits or is a repeating decimal, an infinite decimal can be used to represent a rational number, the product of two integers.Therefore,
-8/5 = -1.6 …............ Number 3
-1.7 …............ Number 2
-30/-25 = 6/5 = 1.2 …............ Number 4
-1.71 .................. Number 1
Since 1.2 is positive whereas all other are negative.
So, the order will be:
1.2 > -1.6 > - 1.7 > -1.71
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People were asked if they have cable TV at home. The people were divided by gender and the results are listed below. Yes No Male 59 72 Female 63 76 a)Find the probability that a person has cable TV at home. b)Find P(Yes | Female) c) Find P(Female | Yes)
ANSWER:
a) 0.45
b) 0.45
c) 0.52
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the total of YES and the total of NO. In the same way the total of male and female.
[tex]\begin{gathered} \text{Yes }=59+63=122 \\ \text{No }=72+76=148 \\ \text{Male }=59+72=131 \\ \text{Female }=63+76=139 \end{gathered}[/tex]a)
The probability if the person has cable TV would be the proportion between the total of YES and the total number of people.
Just like that:
[tex]P\text{ (has cable TV)=}\frac{122}{122+148}=\frac{122}{270}=0.45[/tex]b)
The probability of having cable being female would be the proportion between the YES, are female and the total amount of female.
Just like that:
[tex]P\text{ (Yes | Female) }=\frac{63}{139}=0.45[/tex]c)
The probability of being female having a cable would be the proportion between the YES, are female and the total number of YES.
Just like that:
[tex]P\text{ (Female| Yes) }=\frac{63}{122}=0.52[/tex]If this trapezoid is moved through the translation (x+3, y-2), what will the coordinates of B’ be?
The coordinates of B' in the image of the trapezoid upon translation would be; (-2, 2).
What would be the coordinates of B' after the translation (x+3, y-2) has been done on the trapezoid?It follows from the task content that the coordinates of the point, B' on the trapezoid after the translation (x+3, y-2) has been carried out is to be determined.
On this note, since it follows from the image attached that the coordinates pair of point B, in the trapezoid's pre-image is; (-5, 4).
It simply follows that upon carrying out the transformation; (x+3, y-2) on the trapezoid, the coordinates pair of point B is; (-5+3, 4 -2).
Hence, the required coordinate pair of point B' is; (-2, 2).
Read more on translations;
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