Answers
Determine the base of right triangle by using pythagoras theorem.
[tex]\begin{gathered} b=\sqrt[]{(15.7)^2-(8.5)^2} \\ =\sqrt[]{174.24} \\ =13.2 \end{gathered}[/tex]Determine the area of base of figure.
[tex]\begin{gathered} A=\frac{1}{2}\cdot13.2\cdot8.5 \\ =56.1 \end{gathered}[/tex]Determine the volume of the figure.
[tex]\begin{gathered} V=A\cdot6.2 \\ =56.1\cdot6.2 \\ =347.82 \end{gathered}[/tex]So volume of the figure is 347.82 yards square.
Related Questions
A surveyor wants to find the height of a tower used to transmit cellular phone calls. he stands 120 ft away from the tower and measure the angle of evolution to be 40° . how tall is the Tower?
Answers
EXPLANATION
Let's represent the situation on a graph:
Let's call x to the height of the tower.
The height of the tower is given by the following trigonometric relationship:
[tex]\text{tangent 40}=\frac{opposite\text{ cathetus}}{\text{adjacent cathetus}}[/tex]Replacing terms:
[tex]\text{tangent 40 = }\frac{x}{120}[/tex]Multiplying 120 to both sides:
[tex]120\cdot tangent\text{ 40 = x}[/tex]Solving the argument:
[tex]120\cdot0.72=\text{ x}[/tex]Multiplying numbers:
[tex]120\cdot0.72=86.4\text{ ft}[/tex]The tower is 86.4 ft tall
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
Answers
100+3=103
The answer is＄103
Is it ten people
For the given piecewise function evaluate for the specific value of X
Answers
x = 4
4 > 3 , so , we use:
f(x)= x + 1
Replacing:
f(4) = 4 + 1 = 5
Answer:
f(4)= 5
Which triangles are similar?17Triangle A12)151037g8Triangle BTriangle cA. Triangles A, B, and CB. Triangles A and CC. Triangles B and CD. Triangles A and B
Answers
The answer is C. triangles B and C are similar.
Similar triangles only differs between them by the size. All angles must be the same and all sides must be multiplied by the same factor of scale to transform from one triangle from another.
the only 2 triangles that share the same angle values are B and C. thus, the answer is option C
Integrate the following using substitution method or integrate by part ( that suitable the given equation)
Answers
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?
Answers
The volume of a prism = Base area x Height
Base area = 43
Height = 11
Volume = 43 x 11
Volume = 473
thanks for the help!!!
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
cos x [tex]cos^{-1}[/tex] = 1
The value of [tex]cos(cos^{-1} \frac{5}{13} + cos^{-1}\frac{7}{25})[/tex] is 166/195.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]cos(cos^{-1} \frac{5}{13} + cos^{-1}\frac{7}{25})[/tex]
We will distribute cos with the expression.
[ cos x [tex]cos^{-1}[/tex] = 1 ]
So,
= cos x [tex]cos^{-1}[/tex] (5/13) + cos x [tex]cos^{-1}[/tex] (7/15)
= 5/13 + 7/15
= (75 + 91) / 195
= 166/195
Thus,
The value of [tex]cos(cos^{-1} \frac{5}{13} + cos^{-1}\frac{7}{25})[/tex] is 166/195.
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HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answers
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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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?
Answers
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 hoursA coin is flipped 2,500 times. It lands on heads 1,223 times and tails 1,277 times. A die was rolled 60 times. It landed on one—11 times, two—9 times, four—12 times, five—12 times, and six—8 times. What is the empirical probability of flipping heads on the coin AND rolling a four on the die?
Answers
The empirical probability of flipping heads on the coin AND rolling a four on the die is 0.623.
What is probability?
When we do not really know how something will turn forth, we can talk about the probability of one outcome or the likelihood of several.
Given that,
the coin is flipped = 2,500 times.
heads =1,223 times and tails= 1,277 times.
and
A die was rolled = 60 times
one—11 times, two—9 times, four—12 times, five—12 times, and six—8 times.
The empirical probability of flipping heads on the coin AND rolling a four on the die = (1223/2500) + (8/60)
=0.623
The empirical probability of flipping heads on the coin AND rolling a four on the die is 0.623.
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find the x and the y intercept there should be 2 ordered pairs for the each solution
Answers
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)
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
Answers
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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Part C
Compare and contrast the relative frequency for the whole table in part B with the two-way frequency table given in the
activity introduction. What trends or generalizations can you identify from the data in the tables?
Answers
A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample
What is a frequency table?A frequency table shows the values of a set together with how frequently they occur. The frequency of a certain data value in your dataset is how frequently it appears. You can learn which data values are typical and uncommon by using these tables.This refers to the representation of the frequency of an event in the form of a table.Therefore, when a two-way frequency table is employed, it illustrates the potential relationship between several sets of data visually.Please be aware that the answer to your query was given as a general overview because you did not supply the frequency table that was required or the patterns and generalizations that needed to be found.To learn more about frequency table refer to:
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Y=3/4x-5, C(12,-2) find perpendicular line
Answers
Why is perpendicular
Given the figure is a square, find x, y, and z.
Answers
Answer:
x=9
z=58 deg
y=37
Step-by-step explanation:
8x+50=12x+14
-8x from both sides
50=4x+14
-14 from both sides
36=4x
*1/4 to both sides
9=x
Because it is a square all the angles = 90
z+32=90
-32 from both sides
z=58
8*9+50=122
all sides are equal
y+85=122
-85 from both sides
y=37
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.
Answers
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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11 Type the correct answer in each box. x + 3x + 5+ 2= __ x + __4s-2s + 10= __ s + 10n + n + 7 + n + 4= __ n + __
Answers
SOLUTION
(1) We want to add
[tex]\begin{gathered} x+3x+5+2 \\ x\text{ means 1}x \\ \text{adding we have } \\ 4x+7 \end{gathered}[/tex]Hence, the answer is 4x + 7
(2)
[tex]\begin{gathered} 4s-2s+10 \\ =2s+10 \end{gathered}[/tex]Hence, the answer is 2s + 10
(3)
[tex]\begin{gathered} n+n+7+n+4 \\ we\text{ place the n's together and the numbers together, we have } \\ n+n+n+7+4 \\ \text{This also means } \\ 1n+1n+1n+7+4 \\ =3n+11 \end{gathered}[/tex]Hence, the answer is 3n + 11
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?
Answers
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
order from least to greatest 2/4, 25%, 0.2
Answers
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.
Answers
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.
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,
Answers
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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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?
Answers
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]What is the measure of ZCOBWhat is the measure of ZCAB?
Answers
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
What is the solution to the equation below? 3* 3 O A. X= 12 OB. X= 18 C. X= 6 O D. x=9
Answers
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]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)
Answers
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]I’m stuck on my mat please help me I did it but I just want to recheck my answer
Answers
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.
show algebraically that 0.681 can be written as 15/22
Answers
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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14. Mason has 2 quarters, and he needs 50 cents more to pay the turnpike toll. There are 5 dimes, 6 quarters, and 10 nickels in his glove compartment. If he reaches in and selects two coins at random without replacing the first one, find the probability of choosing two quarters. 99
Answers
we have in total of coins are
5+6+10=21
For the first coin, we have the probability of 6/21
Then we only left 5 quarters and 20 coins in total, the next probability will be 5/20
the total probability is
[tex]\frac{6}{21}\cdot\frac{5}{20}=\frac{30}{420}=\frac{1}{14}[/tex]the answer is 1/14
Michael launched a new website to share news and photos of his town. The equation below estimates the number of followers, y, in x weeks after his launch. y = 82(1.045)^x Complete each of the 2 activities for this Task. Activity 1 of 2 What is the rate of growth for the number of followers each week? A 45% B. 1,045% C. 4.5% D. 82% Activity 2 of 2 How many followers should Michael expect in the 4th week? Round to the nearest whole number. Show your work please!
Answers
Consider the given expression,
[tex]y=82(1.045)^x[/tex]The first derivative gives the rate of growth for the number of followers.
Solve for the first derivative as,
[tex]\begin{gathered} \frac{dy}{dx}=82\times\frac{d \square}{dx}(1.045)^x \\ \frac{dy}{dx}=82\times(1.045)^x\ln (1.045) \\ \frac{dy}{dx}=y\times0.045 \\ \frac{dy}{dx}=4.5\text{ percent of y} \end{gathered}[/tex]Thus, the rate of growth of followers is approximately 4.5% each week.
Therefore, option C is the correct choice.
The number of followers corresponding to the 4th week is calculated as,
[tex]y=82\times(1.045)^4=82\times1.1925=97.7865\approx98[/tex]Thus, Michael should expect approximately 98 followers in 4th week.
Select the TABLE tab. What do all the points on this line have in common?
Answers
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.
