The given format of the sum is
[tex]a(b+c)[/tex]The sum is,
24+16
The greatest common factor of 24 and 16 is 8, since,
[tex]\begin{gathered} 24=12\times2=3\times2\times2\times2 \\ 16=8\times2=4\times2\times2=2\times2\times2\times2 \end{gathered}[/tex]Therefore we can write, 24+16 as,
[tex]24+16\rightarrow8\times3+8\times2=8(3+2)[/tex]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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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.
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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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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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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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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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
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
What is the solution to the equation below? 3* 3 O A. X= 12 OB. X= 18 C. X= 6 O D. x=9
Here, we want to solve the given equation
What we have to do here is to square both sides of the equation
We have this as follows;
[tex]\begin{gathered} \frac{\sqrt[]{3x}}{\sqrt[]{x-6}\text{ }}\text{ = 3} \\ \text{Squaring both sides will remove the roots on the left and we have;} \\ \frac{3x}{x-6}\text{ = }3^2 \\ \\ 3x\text{ = 9(x-6)} \\ 3x\text{ = }9x-54 \\ 9x-3x\text{ = 54} \\ 6x\text{ = 54} \\ \text{ x= }\frac{54}{6} \\ x\text{ = 9} \end{gathered}[/tex]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
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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find the x and the y intercept there should be 2 ordered pairs for the each solution
We have the line in standard form:
[tex]4x+5y=-20[/tex]We have to find the 2 intercepts.
The y-intercept correspond to the value of the line when x=0, so we can find the value of y that correspond to x=0 replacing x in the equation and solving for y:
[tex]\begin{gathered} 4x+5y=-20 \\ 4(0)+5y=-20 \\ 5y=-20 \\ y=-\frac{20}{5} \\ y=-4 \end{gathered}[/tex]Then, the ordered pair for the y-intercept is (0,-4).
In the case of the x-intercept the concept is equivalent but the coordinate that has a value of 0 is y. So we will replace y with 0 in the equation and solve for x:
[tex]\begin{gathered} 4x+5(0)=-20 \\ 4x=-20 \\ x=-\frac{20}{4} \\ x=-5 \end{gathered}[/tex]Then, the ordered pair for the x-intercept is (-5,0).
We can graph the line and its intercepts as:
Answer:
X-intercept: (-5, 0)
Y-intercept: (0,-4)
order from least to greatest 2/4, 25%, 0.2
To compare the three numbers we can pass to decimal form all of them:
[tex]\begin{gathered} \frac{2}{4}=\frac{1}{2}=0.5 \\ \text{25\%}=\frac{25}{100}=\frac{25}{4\cdot25}=\frac{1}{4}=0.25 \\ So,\text{ the order from }least\text{ to greatest is:} \\ 0.2,\text{ 25\%, }\frac{2}{4} \end{gathered}[/tex]A satellite is in orbit 600 km above Earth's surface. Earth's radius is about 6370 km. Using the Pythagorean Theorem, the distance (x) from the satellite to Earth's horizon is ______ km.What is the km? round the answer to the nearest whole number.
Answer:
2829.13 km.
Explanation:
If the radius of the Earth is 6370 km, the distance of the segment CD is also 6370 km.
Then, the sides of the rigth triangle are:
CB = 6370 km
AC = AD + DC
AC = 600 km + 6370 km
AC = 6970 km
AB = x
So, using the Pythagorean theorem we can calculate the value of x as follows:
[tex]\begin{gathered} AB=\sqrt[]{(AC)^2-(CB)^2} \\ x=\sqrt[\square]{6970^2-6370^2} \end{gathered}[/tex]Because AC is the hypotenuse and CB is on the legs of the triangle.
Therefore, solving for x, we get:
[tex]x=2829.13\text{ km}[/tex]Then, the answer is:
The distance (x) from the satellite to Earth's horizon is 2829.13 km.
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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Tony is registered for MAT-003, which meets from 8:00 AM – 9:15 AM, Monday – Thursday. How many total minutes does his class meet Monday – ThursdayTony is registered for MAT-003, which meets from 8:00 AM – 9:15 AM, Monday – Thursday How many hours does Tony’s class meet Monday – Thursday?
From 8:00AM to 9:15Am there are 1 hour (60 minutes) and 15 minutes.
Then, in a day the total minutes of class are 75. Multiply it by the number of days Monday-Thursday (4 days) to find the to tal minutes;
[tex]75\min \cdot4=300\min [/tex]Turn it into hours:
[tex]\begin{gathered} 1h=60\min \\ \\ 300\min \cdot\frac{1h}{60\min }=5h \end{gathered}[/tex]Then, Tony's class meet Monday-Thursday a total of 5 hoursPeople 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]You select a family with three children. If M represents a male child and F a female child, the set of equally likely outcomes for the children's genders is shown below. Find the probability of selecting a family with at least three male children.
{MMM, MMF, MFM, MFF,
The probability to select a family with atleast three male children is only 1/8.
What is Probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
First, you have the sample of the children.
We know that the family with 3 children, can have the sample space as given {MMM,MMF,MFM,FMM,FFM,FMF, FFF}
MMM: 3 Males
MMF: 2 males, 1 female
MFF: 1 male, 2 females
MFM: 2 males, 1 female (different order)
FMM: 1 female, 2 males
FFM: 2 females, 1 male
FMF: 2 females, 1 male
FFF: 3 females
If we count all of these possibilities, we have 8 possible cases of family with the childrens.
In only one of them, we have atleast three males , which is the first one
Therefore, the probability to select a family with atleast three male children is only 1/8.
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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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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.
The water park charges a $10 entry fee per person and a $3 parking fee per family vehicle. What is the total cost in tepeople ride in the same vehicle? what is the dependent variable
Vectors and Complex numbers Part AYou drive 30 miles due east in a half hour. Then, you turn left and drive 30 miles north in 1 hour. What are your average speed andvelocity, and what are the rectangular and polar coordinates of your position?Part BYou have already travelled 30 miles east and then 30 miles north. To get back to the start, you travel 30 miles west in 1 hour and then 30 minutes south in a half hour. What are your average speed and average velocity for the whole rally?
Part A.
30 miles east in half hour next
turn left and drive 30 miles north in 1 hour
The average speed is given by
the total distance divided by the total amount of time.
In this case,
[tex]\begin{gathered} \text{average velocity=}\frac{30+30}{1.5+1} \\ \text{average velocity=}\frac{60}{2.5} \\ \text{average velocity=}24\text{ }\frac{miles}{hour} \end{gathered}[/tex]Now, the position in rectangular coordinates is (30,30)
In polar coordinates, we must find the angle theta and the lenght r.
This can be given as
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \end{gathered}[/tex]In our case x=30 and y=30, hence
[tex]\begin{gathered} r=\sqrt[]{30^2+30^2} \\ r=\sqrt[]{2\cdot30^2} \\ r=30\sqrt[]{2} \end{gathered}[/tex]On the other hand, angle theta is given by,
[tex]\theta=tan^{-1}\frac{y}{x}[/tex]hence,
[tex]\begin{gathered} \theta=tan^{-1}\frac{30}{30} \\ \theta=tan^{-1}1 \\ hence, \\ \theta=45\text{ degr}ees \end{gathered}[/tex]Therefore, in polar coordinates, point (30,30) is given by
[tex](r,\theta)=(30\sqrt[]{2},45)[/tex]Part B
Until now, we drove 30 miles east, next 30 miles north. Now, we must drive 30 miles west and 30 miles south.
Hence, we will drive 30+30+30+30=4*30=120 miles. Therefore, the average velocity is
[tex]\begin{gathered} \text{average velocity=}\frac{120}{1.5+1+1.5+1.5} \\ \text{average velocity=}\frac{120}{5.5} \\ \text{average velocity=}21.81\text{ }\frac{miles}{hour} \end{gathered}[/tex]Part A. Velocity.
Velocity is a vector. In this case, we must add to vectors:
vector V1 is given by
[tex]\begin{gathered} v_1=(\frac{30}{1.5},0) \\ \text{which is equal to } \\ v_1=(20,0) \end{gathered}[/tex]Vector V2 is given by
[tex]\begin{gathered} v_2=(0,\frac{30}{1}) \\ v_2=(0,30) \end{gathered}[/tex]then, resultant vector velocity is
[tex]\begin{gathered} v=v_1+v_2 \\ v=(20,0)+(0,30) \\ v=(20,30) \end{gathered}[/tex]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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Y=3/4x-5, C(12,-2) find perpendicular line
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
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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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
- 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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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]The prism below has a base that is a regular pentagon whose perimeter is 25 feet and whose area is 43 squarefeet. The height of the prism is 11 feet. Which of the following is the volume of the prism?
The volume of a prism = Base area x Height
Base area = 43
Height = 11
Volume = 43 x 11
Volume = 473
