The grand total is given by
[tex]n=2+7+5+5=19[/tex]so, the probability of Caffeinated is
[tex]P(Caffeinated)=\frac{5}{19}+\frac{5}{19}=\frac{10}{19}[/tex]the probability of mint is
[tex]P(\min t)=\frac{2}{19}+\frac{5}{19}=\frac{7}{19}[/tex]and the probability of the intersection is
[tex]P(Caffeinated\cap\min t)=\frac{5}{19}[/tex]Then, the probabilty of the union is given by
[tex]undefined[/tex]The surface area of a cube is 42 in2. What is the volume of the cube?
Answer:
7√7 in or 18.52 in=======================
Let the side of the cube be a.
Then its surface area is:
S = 6a²Find the side of the cube:
42 = 6a²a² = 7a = √7Find the volume of the cube:
V = a³ = (√7)³ = 7√7 ≈ 18.52 inThe formula used to convert degrees Celsius to degrees Fahrenheit is
F = C +32.
Convert 77°F to degrees Celsius. Solve the formula for C, and then use it to
convert the temperature.
Which is the correct formula and conversion?
77°F is equivalent to 45°C as per the given equation.
The correct formula for conversion is,°F = (°C × 9/5) + 32, and 77°F is equivalent to 25°C
This is a problem with the temperature conversion. We can solve this problem by following a few steps.
F = C +32 as per the question and the temperature is given as 77°. We have to convert this temperature to degrees Celsius. We can write C as (F-32).
Hence the formula for C can be written as C = F - 32
Now we can find convert the temperature,
C = F - 32
Or, C = 77 - 32 [ subtracting 32 from both sides ]
Or, C = 45
Here we can conclude that 77°F is equivalent to 45°C as per the question.
The correct formula for conversion is,
°F = (°C × 9/5) + 32
Or, 77 = (C × 9/5) + 32
Or, (C × 9/5) = 77 - 32 [ subtracting 32 from both sides ]
Or, (C × 9/5) = 45 [ multiplying both side with 5/9 ]
Or, C = (45×5) / 9 = 25
According to the correct conversion equation, 77°F is equivalent to 25°C
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if Joey drives 222 3/4 miles 3 3/8 hours . if he drives at a constant rate how far will he drive in one hour ?
Start by making the mixed numbers into fractions using that:
[tex]A\frac{b}{c}=\frac{(A\cdot c)+b}{c}[/tex]According to this:
[tex]222\frac{3}{4}=\frac{(222\cdot4)+3}{4}=\frac{888+3}{4}=\frac{891}{4}[/tex][tex]3\frac{3}{8}=\frac{(8\cdot3)+3}{8}=\frac{24+3}{8}=\frac{27}{8}[/tex]To find the rate we divide the distance over the time
[tex]\frac{\frac{891}{4}}{\frac{27}{8}}=\frac{891\cdot8}{27\cdot4}=\frac{7128}{108}=\frac{66mi}{h}[/tex]The rate idicates that joey drives 66 miles in one hour.
Challenge: The price of Stock A at 9 A.M. was $14.76. Since then, the price has been increasing at the rate of $0.09 each hour. At noon the price of Stock B was $15.26. It begins to decrease at the rate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
In one hour, the prices of the two stocks will be the same.
The price of stock A at 9 a.m. was $14.76.The rate of increase in the price of stock A per hour is $0.09.The price of stock B at 12 p.m. was $15.26.The rate of decrease in the price of stock B per hour is $0.14.Let the number of hours after which the prices of the two stocks become the same be "x".We also need to consider that the price of stock A is given at 9 a.m., whereas the price of stock B is given at 12 p.m.14.76 + (3+x)*0.09 = 15.26 - (x)*0.1414.76 + 0.27 + 0.09x = 15.26 - 0.14x0.23x = 0.23x = 1Thus, the number of hours after which the prices of the two stocks become the same is one hour.To learn more about rate, visit :
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The next model of a sports car will cost 13.8% more than the current model. The current model costs $56,000. How much will the price increase in dollars? What will be the price of the next model?
Current model is $56,000
New model is 13.8% more expensive
13.8% of 56,000 = 56000*13.8/100 = 772800/100 = 7728
Nex model price = 56000+7728 = 63728
Answers:
The price increase in dollars is $7,728
The price of the next model is $63,728
Given csc A = 65 and that angle A is in Quadrant I, find the exact value of cot A insimplest radical form using a rational denominator.
The trigonometric expression for relation between csc A and cot A.
[tex]undefined[/tex]Use interval notation to describe all the x-values within or including a distance of the given values. Use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.Distance of 5 units from the number 7AnswerAnswer,AnswerAnswer
The sentence
"Distance of 5 units from the number 7"
The part "From the number 7" indicates that you have to start counting from 7 on. Then the left bound of the interval is number 7.
To determine the right bound of the interval you have to count 5 units starting from 7, so add 5 to 7
[tex]7+5=12[/tex]The right bound of the interval is 12.
So, the values of x within the distance described by the sentence are: (7,12)
LOOK AT THE PICTURE BELOW. Find an approximation for [tex] \sqrt{18} [/tex]
ANSWER:
[tex]\sqrt[]{18}=4.25[/tex]STEP-BY-STEP EXPLANATION:
We have to calculate the square root of 18, to locate it on the graph, like this:
[tex]\sqrt[]{18}=4.2426\cong4.25[/tex]What is the rest of the pattern.
3, 6, 10, 15, _, _, _.
Answer:
3, 6, 10, 15, 21, 28, 36.
Step-by-step explanation:
3 (+3),
6 (+4),
10 (+5),
15 (+6),
21 (+7),
28 (+8),
36
Answer:
If my theory is right the next 3 numbers are 21,28,36
Step-by-step explanation:
Looking at the beginning you see that 3 goes to 6 which is a hop of 3
Then next is 6 to 10 which is a hop of 4
Then next is 10 to 15 which is a hop of 5
So I think it’s going in a chronological number order
So I say the next hops will be 6,7,8
Solve each system of equations by GRAPHING. Clearly identify your solution.4x - y = 33x + y = 4
Answer:
( 1, 1 )
Step-by-step explanation:
Hope this helps :)
A 16-foot ladder leaning against the side of a house reaches 12 feet up the house. What angledoes the ladder make with the ground?
Given:
By the definition of sin
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ }}{\text{hypotenuse}} \\ \theta=\sin ^{-1}(\frac{opposite\text{ }}{\text{hypotenuse}}) \\ \theta=\sin ^{-1}(\frac{12}{16}) \\ \theta=48.59^{\circ} \end{gathered}[/tex]Answer:
[tex]\text{The ladder makes }48.59^{\circ}\text{ with the ground}[/tex]3. Refer to Table 1. Which of the following price floors would be binding in this market?
$1
$2
$3
$4
Explanation:
The term "binding price floor" means "a price that is above equilibrium".
If the floor is at equilibrium or lower, then buyers and sellers will just go for the equilibrium price (as they naturally would have done anyway) and there's no need for the floor. In such cases, the floor is considered non-binding.
As you pointed out in the table, the equilibrium price is $3 where quantity supplied equals quantity demanded. A binding floor price would be $4 since it's above equilibrium.
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A pair of Nike tennis shoes costs $29.10 more than a pair of Reeboks. If Josh buys one of each brand and spends a total of $154.10, what did each brand cost?
Answer:
Nike=RM106.15
Reeboks=RM47.95
Two angles are supplementary. The measure of one angle is x and the measure of the other angle is 4x, find the value of xa. 36b.18c.4d.5
we know that
If two angles are supplementary, then their sum is equal to 180 degrees
so
In this problem
x+4x=180
solve for x
5x=180
x=36
therefore
the answer is the option A
Part 2
Write the equation for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).
Given the figure of the functions f(x) and g(x)
The graph of the function is the shown lines
The equation of f(x):
As shown the line of f(x) passes through the points: (-2, 0) and (0, -1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{0-(-2)}=\frac{-1}{2}[/tex]The y-intercept = -1
so, the equation of f(x) =
[tex]f(x)=-\frac{1}{2}x-1[/tex]The equation of g(x):
As shown the line of g(x) passes through the points: (-2, 0) and (0, 1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-(-2)}=\frac{1}{2}[/tex]The y-intercept = 1
So, the equation of g(x) will be:
[tex]g(x)=\frac{1}{2}x+1[/tex]Identify the reflection that transforms the graph of f(x) to the graph of g(x).
As shown, the functions are symmetric around the x-axis
And as we can see for the same value of x: g(x) = -f(x)
So, the type of transformation is: Reflection over the x-axis
351,528.094 in word form
Three hundred fifty-one thousand five hundred twenty-seven and ninety-four thousandths
Can you find the area of a square using the given side lengths:
Answer
• d) 0.01 m²
,• e) 12.25cm²
Explanation
The area of a square (A) is given by:
[tex]A=s^2[/tex]where s represents the side length.
• d) ,s = 0.1 ,m
Replacing the data we get:
[tex]A=(0.1)^2[/tex]Simplifying:
[tex]A=0.01m^2[/tex]• e) ,s = 3.5cm
Replacing the data we get:
[tex]A=(3.5)^2=12.25cm^2[/tex]Which digit represents 100 times the value of the ones place
Depending upon the position of the digits represent the 100 times the place value of the ones place.
What is place value?
In mathematics, every digit can be defined as a place value in a number. Basically, it is completely depends on the position of the digits in a number. Most of the number has same digits, but their positions are different, which makes the number different.
According to the question, all the digits represents 100 times the place value of the ones place.
Those digits can be defined as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]. But the position of the digit should be at the 100th place.
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In the figure below, circle 1 is a unit circle. Circle 2 has a diameter that is one and half times longer than that of circle 1, and circle 3 has a diameter that is twice as long as that of circle 1. If angle Z is equal to 2 radians, what is the length of the arc between points I and J?
The length of an arc is given by:
[tex]s=r\timesθ[/tex]where r is the radius and θ is the measure of the angle in radians.
To find the radius:
radius in circle 1 = 1 (unit circle)
radius in circle 3 = 2 x 1 = 2.
Hence:
[tex]s=2\times2=4[/tex]ANSWER
the length of the arc between points I and J is 4
if tommy has 34 has apples and she puts them in 3 baskets whats the anwser and with the reminder if it has one
Which is the equation of a circle that is centered at the origin?O (– 1)2 + (y – 1)2 = 4O2? + (y - 1)2 = 2O 2 + y2 = 7Ox+y=8
Standard equation of circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex][tex]\begin{gathered} \text{If centered at the origin:} \\ (h,\text{ k) = (0, 0)} \\ h\text{ = 0, k = 0} \end{gathered}[/tex][tex]\begin{gathered} \text{The equation of circle becomes:} \\ (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}[/tex]comparing the above equation with the options given:
[tex]\begin{gathered} x^2+y^2=7\text{ has the form} \\ x^2+y^2=r^2,wherer^2\text{= }7 \end{gathered}[/tex][tex]x^2+y^2\text{ = 7 (option C)}[/tex]Metric area unit conversion with decimal valuesA rectangular field is 0.35 kilometers long and 0.2 kilometerswide. What is the area of the field in square meters? Do notround your answer.mX 5 ?Conversion facts for length1000 millimeters (mm) = 1 meter (m)100 centimeters (cm) = 1 meter (m)10 decimeters (dm) = 1 meter (m)1 decameter (dam) = 10 meters (m)1 hectometer (hm) = 100 meters (m)1 kilometer (km) = 1000 meters (m) I need help with this math problem.
Given that
The length of the rectangular field is 0.35 km and the width is 0.2 km. And we have to find the area of this field.
Explanation -
The formula for the area of the rectangle is
[tex]Area=length\times breadth[/tex]On substituting the values we have
[tex]\begin{gathered} Area=0.35\times0.2\text{ km}^2 \\ Area=0.07\text{ km}^2 \end{gathered}[/tex]Since the conversions are given as
[tex]\begin{gathered} 1\text{ km = 1000 m}^{\text{ }}=10^3\text{ m} \\ 1\text{ km}^2=10^6\text{ m} \end{gathered}[/tex]So the required answer in sq meters will be
[tex]\begin{gathered} Area=0.07\times10^6\text{ m}^2 \\ Area=7\times10^4\text{ m}^2=70000\text{ m}^2 \end{gathered}[/tex]So the final answer is 70000 sq meters.What is the H.c.f of 16 and 30
The HCF of 16 and 30 is 2.
What is HCF?The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF). The Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF) (GCD).The HCF of two numbers can be determined in a variety of methods. Using the prime factorization technique is one of the easiest techniques to determine the HCF of two or more numbers.SO, the given numbers are 16 and 30
The prime factorization of 16 and 30 are as follows:
16 = 2 × 2 × 2 × 230 = 2 × 3 × 5Multiply all the prime factors that both numbers share in order to determine the HCF:Thus, HCF is = 2.
With the help of prime factorization method we can conclude that the HCF of 16 and 30 is = 2.
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simplify (4z-13)+(9-9z)
Answer:
the answer is -5z-4
Step-by-step explanation:
you just combined the like terms
Expand and simplufy (2x-3)(3x-5)
Answer:
6x² - 19x + 15
Step-by-step explanation:
(2x - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor , that is
2x(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 6x² - 10x - 9x + 15 ← collect like terms
= 6x² - 19x + 15
I need help on B and an explanation. Approximate bearinge angle
The bearing of a given point is the number of degrees in the angle measured in a clockwide direction from the north line.
Since we dont have a complete information about where point P is located with respect to point A and B, we can approximate the bearing point. Let's draw a picture of our problem:
As we can note, the approximate bearing angle is about 260 degres from point P.
Michael wants to buy a comic book and it costs $13.00. He has $6.85. How muchmore money does Michael need to buy the comic book?
To find how much more money Michael needs, you have to subtract his savings from the cost, as follows
$13.00 - $6.85 = $6.15
When are two events considered to be independent? A. when the occurrence of each event is not affected by the occurrence of the other event B. when the occurrence of the second event affects the occurrence of the first event C. when the occurrence of the first event affects the occurrence of the second event D. when the occurrence of each event affects the occurrence of the other
The two events are considered to be independent when the occurrence of each event is not affected by the occurrence of the other event
The event is defined as the outcome or the set of all the outcomes of the random experiment
Independent event is defined as the occurrence of the one event does not depends on the occurrence of another event
So we can say that, two events are independent events when the occurrence of the one event does not depends on the occurrence of the other event.
Hence, The two events are considered to be independent when the occurrence of each event is not affected by the occurrence of the other event
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If a number is added to the number of 5/6 and twice as much is added to the denominator, the result is 3/5, find the number
Answer:
[tex]x=7[/tex]Step-by-step explanation:
We have the number:
[tex]\frac{5}{6}[/tex]If a number is added to the numerator and twice as much is added to the denominator and the result is 3/5, we can create the following equation:
[tex]\frac{5+x}{6+2x}=\frac{3}{5}[/tex]Solve for x, using cross multiplication:
[tex]\begin{gathered} 5(5+x)=3(6+2x) \\ 25+5x=18+6x \\ -x=-7 \\ x=7 \end{gathered}[/tex]PLS HELP !!!!! WILL GIVE BRAINLIEST!!
Answer:
ADB
Step-by-step explanation:
They are the same.