Main answer:
a) 18 millions of dollars/year
b) 6 millions of dollars/year
Step-by-step explanation:
a) the average rate of change of annual sales between 2001 and 2002 millions of dollars/year
Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)
= (417 - 399) / (2001 - 2002)
= 18 / 1
= 18 millions of dollars/year
b) the average rate of change of annual sales between 2001 and 2006 millions of dollars/year
Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)
= (369 - 399) / (2006 - 2001)
= 30 / 5
= 6 millions of dollars/year
The average rate of change of annual sales between 2001 and 2002 is 18 millions of dollars/year , between 2001 and 2006 is 6 millions of dollars/year
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a dart board is a regular octagon divided into regions as shown. suppose that a dart thrown at the board is equally likely to land anywhere on the board. what is the probability that the dart lands within the center square?
The probability that the dart lands in centre is = √2-1.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
Let the side of octagon be rexterior angle of octagon = 360/8 = 45So interior angle = 180 -45 = 135So all the triangles will have 45-90-45 combinationsc sides of triangles = r/2√r/2 Calculate the total area of octagon and the area of central squareProbability = area of square /area of octagon = r2/(r2+r2+22√+r2)r2/(r2+r2+22+r2)= 1/(2+22√)take 2 common and multiply and divide byhence,The probability that the dart lands in centre is = √2-1.
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Dad fills the car's gas tank when it is about 1/2 empty. Later, he fills the tank when it is about 3/4 empty. He bought a total of 18 1/2 gallons of gas on those two days. How many gallons does the tank hold?
Dad's car's gas tank holds 14.8 gallons of the gas.
Define the term mixed fraction?A mixed fraction is one generated by integrating a whole number as well as a fraction.
When the car's gas tank is nearly half full, Dad fills it up. Later, when the tank is about 3/4 full, he fills it. Total gas purchased = 18 1/2 gallons of gas.Changed the mixed fraction in decimal.
Total gas purchased = 37/2 = 18.5 gallons of gas.
Let x be the gallons of gas tank contains.
Then,
(1/2)x + (3/4)x = 18.5
Multiply both sides by 4,
2x + 3x = 74
5x = 74
x = 14.8 gallons
Thus, Dad's car's gas tank holds 14.8 gallons of the gas.
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in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal.
a) The Probability density function of given uniform distribution example is
F(x) = 1/3.5 for 8.5 < x< 12
Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where
x ---> minimum value and y---> maximum value
Probability density function is a probability function which defines the density of continuous random variable lying between specified range
values. It is denoted by f( a<X<b)
Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.
We have following informations,
weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.
Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.
this implies a = 8.5 , b = 12
F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12
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#Complete Qestion :
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?
What is the distance between (-5,-6),(-9,-4)
Answer:
The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].
Step-by-step explanation:
Distance Formula :
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Given,
The two points are
[tex](-5,-6),(-9,-4)[/tex]
To calculate the distance between two points, use the distance formula.
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Substitute the actual values of the points into the distance formula.
Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]
[tex]=\sqrt{(81-25)+(16-36)}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
solve the question math
Solve for the roots in simplest form using the quadratic formula:
2x²-28x= -116
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
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Answer:
Step-by-step explanation:
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
What is proportionality?
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
It take Jada 20 minute to walk to chool. It take Andre 80% a long to walk to chool. How long doe it take Andre to walk to chool?
Andre takes 36 minutes to walk to the school.
Given, It take Jada 20 minutes to walks to school.
It takes Andre 80% a long to walk to school.
As, Andre takes 80% more to walk to school
So, the time Andre takes = 20×180/100
the time Andre takes = 2×18
the time Andre takes = 36 minutes
Hence, Andre takes 36 minutes to walk to the school.
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when a certain unfair die is rolled, an even number is times as likely to appear as an odd number. the die is rolled twice. what is the probability that the sum of the numbers rolled is even?
The probability that the sum of the numbers rolled on the dice is even =1/2.
What is referred as probability?A probability is a measure of the magnitude of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages including several from 0% to 100% can be used to describe probabilities.For the given question,
A fair dice is rolled twice.
Six different results are available with a single roll of the dice (1,2,3,4,5,6)
Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².
Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]
Total sample space for sum of even = 18
For the probability that the sum of the numbers rolled is even is -
probability (sum is even) = 18 / 36 = 1/2
Thus, the probability that the sum of the numbers rolled is even is 1/2.
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Solve for x:-
[tex]\sf -10 + x + 4 - 5 = 7x - 5[/tex]
Answer:
x = -1
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ -10 + x + 4 - 5 = 7x - 5
Then the value of x will be,
→ -10 + x + 4 - 5 = 7x - 5
→ -11 + x = 7x - 5
→ 7x - x = -11 + 5
→ 6x = -6
→ x = -6/6
→ [ x = -1 ]
Hence, the value of x is -1.
survey of 397 children given at a local elementary school showed that 175 like chocolate ice cream 225 like pistachio ice cream, and 97 do not like chocolate or pistachio ice cream. how many children like at most one kind of ice cream mentioned in the survey?
297 children like at most one kind of ice cream.
Total number of children = 397
Let C and P be the number of children like chocolate and pistachio ice cream respectively.
n(C) = 175
n(P) = 225
The number of student do not like chocolate or pistachio ice cream is,
n(P' and C') = 97
n(P or C)' = 97, by De Moivre's theorem
n(P or C) = 397-97 = 300
n(P) + n(C) - n(P and C) = 300
175 + 225 - n(P and C) = 300
400 - n(P and C) = 300
n(P and C) = 100
So the required number of children like at most one kind of ice cream = 397-n(P and C) = 397-100 = 297
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A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
The smaller number is 9 and the larger number is 18.
According to the question,
We have the following information:
A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
Now, let's take the larger number to be x and the smaller number to be y.
So, we have the following expressions:
x = 2y ...(1)
x+14 = 4y-4
Putting the values of x from the equation 1:
2y+14 = 4y-4
Adding 4 to both sides of the equation:
2y+14+4 = 4y
2y+18 = 4y
Subtracting 2y from both sides of the equation:
18 = 4y-2y
18 = 2y
Dividing by 2 on both sides:
y = 18/2
y = 9
Now, putting this value in equation 1:
x = 2y
x = 2*9
x = 18
Hence, the smaller number is 9 and the larger number is 18.
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in november's math meet, the little monsters of beast academy solved $\frac{1}{5}$ of the problems. in march's math meet, they solved $\frac 23$ of the problems. (there might be different numbers of problems asked in november and march.) in total, the little monsters solved $13$ of $30$ problems over both math meets. how many problems were asked at march's math meet?
The little monsters solved 15 problems in March's Math meet
Given, that in November's math meet, the little monsters of beast academy solved 1/5 of the problems.
In March's math meet, they solved 2/3 of the problems.
In total, the little monsters solved 13 of 30 problems over both math meets.
Let, the number of problems in November be n,
and the number of problems in March be m
According to the question,
n + m = 30 as, the total problems be 30
Now, (1/5)n + (2/3)m = 13 as, they solved total 13 problems
n + m = 30 ... (1)
n/5 + 2m/3 = 13 ... (2)
On simplifying Eq (2) becomes
3n + 10m = 195 ... (2)
On multiplying Eq (1) by 3, we get
3n + 3m = 90
3n + 10m = 195
On subtracting, we get
- 7m = - 105
m = 105/7
m = 15
So, the problems asked in March's Math meet be 15.
Hence, 15 problems were asked at March's Math meet.
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Which number is greatest? 24/100 0.3 16%
Divide £72 into.
Ratio 4:5
Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.
What is meant by Ratio?A ratio is the number of times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six.Similarly, the lemon to orange ratio is 6:8, and the orange to total fruit ratio is 8:14. A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero.A proportion exists as a equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)Given:
The given ratio is 4:5.
To find: We have to divide 72 in this ratio.
To divide 72 in the 4:5 ratio, we must perform the following steps:
The ratio is 4:5.
We can write the number of the ratio as 4x and 5x by multiplying a constant x.
The total ratio is 4x+5x=9x.
So, 9x is equal to 72.
We can write-
9x=72
x=8.
So, putting the value of x we get-
4×8 and 5×8
So, the numbers are 32 and 40.
Thus 72 divides itself as 32 and 40 in 4:5 ratio.
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The 1st term of a certain sequence is -10, and the 2nd term is 1. Each subsequent term is obtained by adding the 2 immediately preceding terms. What Is the 5th term of this sequence?
In a sequence of first term-10 and the 2nd term is 1. the 5th term of this sequence is -17
How to find the fifth term of the sequenceinformation given in the question
The 1st term of a certain sequence is -10
the 2nd term is 1
Each subsequent term is obtained by adding the 2 immediately preceding terms
the 5th term of this sequence = ?
Each subsequent term is obtained by adding the 2 immediately preceding terms. This statement means is applied as below
Therefore:
third term
3rd term
= first term + 2nd term
= -10 + 1
= -9
4th term
= 3rd term + 2nd term
= -9 + 1
= -8
5th term
= 4th term + 3rd term
= -9 + -8
= -9 - 8
= - 17
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David picked 15 pears. Jenna picked p fewer pears than David. Write an expression that shows how many pears Jenna picked.
Answer:
15-p
Step-by-step explanation:
15-p
Which is the order from least to greatest of the following
4/3, 0.8, 1/5, 30%?
A. 4/3, 0.8, 1/5, 30%
B. 30%, 4/3, 0.8, 1/5
C. 1/5, 4/3, 30%, 0.8
D. 1/5, 30%, 0.8, 4/3
Which is the order from least to greatest of the following
A. 4/3, 0.8, 1/5, 30%
1.33 , 0.8 , 0.2 , 0.3
B. 30%, 4/3, 0.8, 1/5
0.3 , 1.33 , 0.8 , 0.2
C. 1/5, 4/3, 30%, 0.8
0.2 , 1.33 , 0.3 , 0.8
D. 1/5, 30%, 0.8, 4/3
0.2 , 0.3 , 0.8 , 1.33 these are listed smallest to largest
What is the simplest positive form of
-35(mod 6)?
In a recent student government election the ratio of students who voted for the winner to all the students who was 0.70 to the number of students who wrote it was 75 how many votes did the winner get?
The winner received 53 of the 75 votes in the student gov. election according to provided ratio.
What is ratio?
In arithmetic, a magnitude relation shows range times one number contains another.
Main body:
Because the ratio of students who voted for the winner compared to all students who voted is 0.70
we can rewrite this as:
0.70 = 70/100
And, because we know the total number of students who voted is 75 and if we call the number of students who voted for the winner s , we can then write this relationship and solve for s :
[tex]\frac{70}{100} = \frac{s}{75}[/tex]
Multiplying both sides by 75.
75*[tex]\frac{70}{100} = \frac{s}{75}[/tex]*75
s= 75*70/100
s = 5250/100
s = 52.5
s ≈ 53.
Hence ,The winner received 53 of the 75 votes.
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A number is being multiplied by a power of 10. Find the number.
Enter your answers in the boxes.
___________ × 102 = 700
___________ × 103 = 36,000
___________ × 105 = 400,000
Answer:
When you have the base of 10 and an exponential index of “n”, the powers of 10 says that the resulting number will be 1 followed by “n” number of zeros. So for example, 10 to the 7th represents the same thing as 1 followed by 7 zeros. The result is 10,000,000 (10 million). Multiplying whole numbers by a power of ten would mean that you ...
simplify 8^15 ÷8^-3 math is hard for me
Answer:
8^18
Step-by-step explanation:
8^15
8^−3
=
8^15
8−3
= 8^15− (−3)
= 8^18
Round 837 to 1 significant figure
Answer:
800
Step-by-step explanation:
we gotta go with the highest value to round since it’s only one sig fig
In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800.
How do round any digit?To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.
In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep as it is and if it is 5 or greater than 5 then we will round up.
In order to round to 1 significance the remaining digit will mark as zero
As per the given,
837 Here, 1 significant figure is 8.
The ramainging digit = 3 and 7
Put 0 instant of 3 and 7
837 → 800
Hence "In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800".
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7. A bag of marbles contains 3 green, 7 red, 2 white
and 8 black marbles. If a marble is randomly
chosen, what is the probability that the marble will
NOT be green or white?
a. 25%
b. 50%
C. 60%
d. 75%
e. 80%
Answer: 50%
Step-by-step explanation:
Answer:
D. 75%
Step-by-step explanation:
There are 20 marbles, so each 1 has a chance of 5% If you were to choose randomly 75% of the time you will get either red or black and 25% you will get green or white
Suppose m<4 =108 find m<5 and m<7
m ∠5 and m ∠7 is 72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or π (in radians).
How to find angle ?An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.
m ∠4 = 108°
m ∠5 = m ∠1
m ∠1 is in same line of m ∠4
So
m ∠1 = 180 - m ∠4
m ∠1 = 180 - 108
m ∠1 = 72 °
So m ∠5 = 72 °
m ∠7 is opposite to m ∠5 , opposite angles will be equal
Therefor m ∠7 = 72 °
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In Exercises 1-4, graph the equation. Ider
1. y - 2 = 2(x - 2)
passes through T(0, -2), perpendicular to CX with C (0, 3) and X (2, -1)
Answer:
it would be honestly idj
Step-by-step explanation:
im tryin to get point
A triangle has vertices A(−1,2)
, B(2,5)
, and C(3,−4)
. If the image resulting from a rotation has vertices A'(−2,−1)
, B'(−5,2)
, and C'(4,3)
, write the rule that describes the rotation:
Answer: [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
90 degree counter-clockwise rotation around the origin.
===================================================
Explanation:
Focus on A(-1,2) and A'(-2,-1)
The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"
In other words, we've gone from (x,y) to (y,x) to (-y,x)
Representing this with arrows looks like:
[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]
or in short
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
which represents a 90 degree counter-clockwise rotation around the origin.
-----------------------------------
Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]
Sure enough, it works for point B.
Lastly, let's check if it works for point C.
We should go from C(3,-4) to C'(4,3).
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]
All points have been confirmed.
7
Oliver makes a plan to be healthier, starting with exercising more often. He signs up for a karate class, thinking this will be a cool way to get active.After three weeks, Oliver finds himself dreading karate class. He would much rather stay home and play RPG with his friends. Since Oliver has already made the decision, what is the BEST path for him to take?
It a because i told the tese
Find x
80°
x+51
X =
OK
60°
ALGEBRA
For the given triangle and the measures of the given angle the value of x is equal to -11° .
As given in the question,
For the given triangle,
Let us consider the triangle name ABC,
Where, m ∠A = x + 51° ,
m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)
m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)
To get the value of x we have,
Sum of all the interior angles of a triangle is equal to 180°
m ∠A + m ∠B + m ∠C = 180°
⇒ x + 51° + 80° + 60° = 180°
⇒ x + 191° = 180°
⇒ x = 180° - 191°
⇒ x = - 11°
Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .
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