Answer:
1/6
Step-by-step explanation:
1/2 (the coin chance) * 2/6 (the dice chance) = 2/12 = 1/6
Answer:
A. 1/6
Step-by-step explanation:
Probability of getting heads: 1/2
Probability of rolling a number >or equal to 5: 2/6
(1/2)(1/3)=1/6
The temperature is 45F. The temperature will decrease by 2F each hour. Let h be the number of hours. When will the temperature be below 2 f
Answer:
23rd hours
Step-by-step explanation:
This is problem based on arithmetic progression in which our first term is 45 , and the common difference is -2
we have to find the n when the nth term is 2.
The formula for nth term of an AP is
[tex]a_{n}=a+(n-1)d[/tex]
replacing the values in the formula
[tex]a_{n}=a+(n-1)d\\2=45+(n-1)(-2)\\2=45-2(n-1)\\-43=-2(n-1)\\21.5 = n-1\\n=22.5\\[/tex]
hence at 22.5 hours it will reach 2F or we can say that after 23 hours the temperature will be below 2F
I suck at geo and need help!!!
Answer: 45°
Step-by-step explanation:
Because AB and CD are parallel, angle x must be congruent with its corresponding angle.
sally has a pet snail that fell into a well the well is 16 feet deep each day the snail climbs up 5 feet but each night it slides back diown 4 feet how many days will it take for sallys snail to get to the top of the well
Answer:
12 days
Step-by-step explanation:
Sally has pet snail that fell into a well.
Depth of the well = 16 feet
Snail climbs up 5 feet but each night it slides back down 4 feet.
So the snail climbs up per day = 5 feet - 4 feet = 1 feet.
Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet
Remaining distance to cover by the snail = 16 - 11 = 5 feet
Number of days to cover remaining 5 feet to reach the top of the well = 1 day
Therefore, snail will take 12 days to reach the top of the well.
Final answer:
The snail climbs up 5 feet and slides back 4 feet each day in a 16-foot deep well. With a net gain of 1 foot per day, the snail will escape on the 16th day after reaching the top without sliding back.
Explanation:
Sally's pet snail finds itself in a classic mathematical problem often associated with algebra and arithmetic sequences. The snail is attempting to escape a 16-foot deep well by climbing up 5 feet during the day and sliding back 4 feet each night. To determine how many days it will take for the snail to get out, we need to calculate the net progress made by the snail each day and then examine how this applies on the final day of the snail's ascent.
Each day, the snail makes a net gain of 1 foot (5 feet up during the day minus 4 feet down at night). After 15 days, the snail would have climbed 15 feet during the day. On the 16th day, the snail climbs up 5 feet and reaches the top of the well, coming out without sliding back down since it already reached the goal during daylight. Therefore, it will take the snail a total of 16 days to escape the well.
Choose the graphs that indicate equations with no solution.
Answer:
It will be any graphs that show a parallel line relationship.
Explanation:
Any graph that shows parallel lines will always be no solution.
Answer:
It have to be a graph that shows functions that doesn't have points in common. The figure show some examples.
What is the following product
For this case we must find the product of the following expression:
[tex]\sqrt [3] {5} * \sqrt {2}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
We rewrite the expression using the lowest common index of 6, then:
[tex]5 ^ {\frac {1} {3}} * 2 ^ {\frac {1} {2}} =[/tex]
We rewrite the terms in an equivalent way:
[tex]5 ^ {\frac {2} {6}} * 2 ^ {\frac {3} {6}} =[/tex]
We rewrite the expression using the property mentioned:
[tex]\sqrt [6] {5 ^ 2} * \sqrt [6] {2 ^ 3} =[/tex]
We combine using the product rule for radicals:
[tex]\sqrt [n] {a} * \sqrt [n] {b} = \sqrt [n] {ab}[/tex]
So:
[tex]\sqrt [6] {5 ^ 2 * 2 ^ 3} =\\\sqrt [6] {25 * 8} =\\\sqrt[6]{200}[/tex]
ANswer:
Option b
12.0 million metric tons of beef produced annually in the U.S. out if 65.1 mikkion metric tons of produced annually worldwide
Approximately 18.42% of the beef production annually worldwide comes from the U.S.
In the U.S., 12.0 million metric tons of beef are produced annually, while worldwide beef production is 65.1 million metric tons.
To find the percentage of beef produced in the U.S. compared to worldwide production, you can divide the U.S. beef production by the worldwide beef production and multiply by 100.
Percentage = ( U.S. beef production / Worldwide beef production ) x 100 = ( 12.0 million / 65.1 million ) x 100 = 18.42%.
Therefore, approximately 18.42% of the beef produced annually in the world is from the U.S.
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Write the equation of a line that passed through the point (-2,1) and has a slope of 4
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad ~\hspace{10em}slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=4[x-(-2)]\implies y-1=4(x+2) \\\\\\ y-1 = 4x+8\implies y=4x+9[/tex]
find the value of c that would complete the square
x² – 16x+c
Answer:
(x−8)2+C−64(x-8)2+C-64
Find the nth term of this quadratic sequence:
4, 7, 12, 19, 28
Answer:
n² + 3
Step-by-step explanation:
It's a quadratic sequence, so it follows the form:
y = ax² + bx + c
We're given five points that satisfy the equation. (1, 4), (2, 7), (3, 12), (4, 19), and (5, 28). Picking any three points, we can form a system of equations.
If we pick (1, 4), (2, 7), and (4, 19):
4 = a(1)² + b(1) + c
7 = a(2)² + b(2) + c
19 = a(4)² + b(4) + c
4 = a + b + c
7 = 4a + 2b + c
19 = 16a + 4b + c
Through substitution, elimination, or trial and error, we can find a = 1, b = 0, and c = 3.
y = x² + 3
So the nth term of the sequence is n² + 3.
Answer:
a(n) = a(n-1) + (2n - 1)
Step-by-step explanation:
Start by analyzing the pattern:
7 is 3 more than 4;
12 is 5 more than 7;
19 is 7 more than 12, and so on.
Each step is an odd number and is 2 greater than the previous step.
a(2) = 7 = 4 + step = 4 + 3 = 7
a(3) = 12 = 7 + step = 7 + 5 = 12
a(4) = 12 + 7 = 19
a(5) = 19 + 9 = 28
and so on.
Looking at a(2), we see that the step is 2+1, or 3;
Looking at a(3), we see that the step is 2(3) - 1, or 5;
Looking at a(4), we see that the step is 2(4) - 1, or 7; and so on.
Looking at a(n), we see that the step is 2n - 1.
Thus, a(n) = a(n-1) + (2n - 1)
Given O below, if WX and YZ are congruent, what is the measure of
Answer:
C
Step-by-step explanation:
Since the angles at the centre subtended by the congruent arcs WX and YZ
Then ∠YOZ = ∠WOX = 103° → C
The measure of the angle YOZ is b°. Option c is correct.
In a circle arc WX and YZ are congruent. Than angle YOZ is to be determine.
Arc is defined as the circular curve or part of circle. Arc = angle * radius.
Here, arc WX = arc YZ
If arc is equal in a circle than angle sub tainted by this arc to center are also equal.
angle YOZ = angle WOX = 103°
Thus, the measure of the angle YOZ is 103°.
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Do you notice clusters or outliners in the data ? Explain your reasoning
Answer:
1,110 is a cluster because it’s a very large number for 52 degrees and 189 is because it’s a very large number for 16 degrees.
Step-by-step explanation: I'm happy to help...
What is the form of the Pythagorean triple generator?
Answer:(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)
Step-by-step explanation:
We can rewrite left side into right side form
(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)
we can expand it
(x^2+y^2)^2=x^4+x^2y^2+x^2y^2+y^4
(x^2+y^2)^2=x^4+y^4+2x^2y^2
we can add and subtract 2x^2y^2
(x^2+y^2)^2=x^4+y^4+2x^2y^2+2x^2y^2-2x^2y^2
(x^2+y^2)^2=x^4-2x^2y^2+y^4+2x^2y^2+2x^2y^2
(x^2+y^2)^2=x^4-2x^2y^2+y^4+4x^2y^2
(x^2+y^2)^2=x^4-2x^2y^2+y^4+(2xy)^2
(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2
The Pythagorean triple generator typically involves an algebraic formula where variables m and n are used to generate the sides of a right triangle such that a^2 + b^2 = c^2, with a common formula being a = m^2 - n^2, b = 2mn, and c = m^2 + n^2 for positive integers m and n.
The form of the Pythagorean triple generator refers to a set of algebraic formulas that produce Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the condition of the Pythagorean theorem (a^2 + b^2 = c^2) for a right triangle.
One well-known formula to generate these triples is given by:
a = m^2 - n^2b = 2mnc = m^2 + n^2where m and n are positive integers with m > n. This formula will produce a Pythagorean triple as long as m and n are coprime and not both odd. It's important to note that not all Pythagorean triples can be generated by this formula, but it is a very common method of finding such triples.
A right triangle has a hypotenuse that measures 42 feet and a length of another side of 31 feet. How long is the third side of the triangle?
Step-by-step explanation:
Use Pythagorean theorem:
c² = a² + b²
Here, c = 42 and a = 31.
42² = 31² + b²
b = √803
b ≈ 28.3
Drag each tile to the correct box.
Ratio Conversion Table
kilometer (km) : meter (m) 1 : 1,000
meter (m) : centimeter (cm) 1 : 100
centimeter (cm) : millimeter (mm) 1 : 10
Using the conversion table, arrange the measures in order from least to greatest.
5,000 cm
5,000 m
50 cm
550 mm
5,000 mm
Answer:
1. 50 cm
2. 550 mm
3. 5000 mm
4. 5000 cm
5. 5000 m
Step-by-step explanation:
We can convert all the measures in same unit to arrange them one by one.
5000 cm:
As there are 10 millimeters in 1 cm,
5000 cm = 5000*10mm
=> 50000 mm
5000 meters:
As there are 100 cms in one meter
5000 m = 5000*100 cm
=> 500000 cm
Now to convert in millimeter
500000*10= 5000000 mm
50 cm:
50*10 = 500 mm
Then there is 550 mm and 5000 mm
So, the order from least to greatest is:
1. 500 mm which is equivalent of 50 cm
2. 550 mm
3. 5000 mm
4. 50000 mm which was equivalent of 5000 cm
5. 5000000 mm which was equivalent of 5000 m ..
Final answer:
To compare the given measurements, we converted each one to millimeters (mm) using a conversion table, then arranged them in ascending order: 50 cm (500 mm), 550 mm, 5,000 mm, 5,000 cm (50,000 mm), and 5,000 m (50,000,000 mm).
Explanation:
To determine which of the given measures is the smallest and which is the largest, we need to convert each measure to the same unit for comparison. Using the ratio conversion table, we will convert all measures to millimeters (mm).
5,000 cm = 5,000 × 10 mm = 50,000 mm5,000 m = 5,000 × 1,000 cm = 5,000,000 cm × 10 mm = 50,000,000 mm50 cm = 50 × 10 mm = 500 mm550 mm is already in millimeters5,000 mm is already in millimetersNow we arrange the measures in order from least to greatest:
50 cm = 500 mm550 mm5,000 mm5,000 cm = 50,000 mm5,000 m = 50,000,000 mmNina graphs the function y = ⌊x⌋ to learn the properties of the parent floor function. What is the value of y when x =5.7?
Answer:
5
Step-by-step explanation:
When you given input of "x" into a floor function y = ⌊x⌋ , it gives as output the "greatest integer less than or equal to x"
For example, if we were to given 1.4 as the input for floor function, it will return the greatest integer that is less than or equal to 1.4, so it would be 1.
So, if we put 5.7 into this function, the floor function would give "5" as the output.
Thus value of y would be 5
Answer:
5
Step-by-step explanation:
Which of these are arithmetic sequences?
Answer:
D
Step-by-step explanation:
The first and last sequence have a common difference in them. The first having d = 4 and the second having d = 7.
The second and third have a common ratio instead and are geometric sequences. The second has r = 2, and the third having r = (-3)
Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour to ski. Black Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same. 10x − 35 = 5x − 40 10x + 35 = 5x + 40 10x + 40 = 5x + 35 10x − 40 = 5x − 35
Answer:
The equation is [tex]10x+35 =5x+40[/tex]
Step-by-step explanation:
Let
x --> the charge per hour to ski
y ---> the total charge for ski
we know that
Bunny Hill Ski Resort
[tex]y=10x+35[/tex]----> equation A
Black Diamond Ski Resort
[tex]y=5x+40[/tex] ----> equation B
equate equation A and equation B
[tex]10x+35=5x+40[/tex]
solve for x
[tex]10x-5x=40-35[/tex]
[tex]5x=5[/tex]
[tex]x=1\ hour[/tex]
Find the value of y
[tex]y=10(1)+35=\$45[/tex]
therefore
At point (1,45) the cost of both ski resort is the same
f(x)=3x+5/x, what is f(a-2)
Replace x with the binomial a - 2.
f(a - 2) = [3(a - 2) + 5]/(a- 2)
f(a - 2) = [3a - 6 + 5]/(a - 2)
f(a - 2) = [3a - 1]/(a - 2)
f(a - 2) = (3a - 1)/(a - 2)
Done.
Factor the following polynomial.
2x^3– 10x^2 – 12x
Enter the GCF of
the polynomial.
The equation [tex]2x^{3} -10x^{2} -12x[/tex] has 2 and x in common. This means you can factor both the 2 and x out of the equation like so...
2x([tex]x^{2} -5x-6[/tex])
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
2x(x - 6)(x + 1)
Step-by-step explanation:
Given
2x³ - 10x² - 12x ← factor out 2x from each term
= 2x(x² - 5x - 6)
To factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)
The factors are - 6 and + 1, since
- 6 × 1 = - 6 and - 6 + 1 = - 5, thus
x² - 5x - 6 = (x - 6)(x + 1) and
2x³ - 10x² - 12x = 2x(x - 6)(x + 1) ← in factored form
What is the slope of the line described by the equation y+1=−3x?
Answer:
-3
Step-by-step explanation:
Answer:
The slope of the line is [tex]m=-3[/tex]
Step-by-step explanation:
For a linear equation of the form
[tex]y = mx + b[/tex]
the slope of the line is the constant m
in this case we have the equation
[tex]y + 1 = -3x[/tex]
Solving for y we have:
[tex]y = -3x -1[/tex]
Then [tex]m = -3[/tex]
The slope of the line is -3
What is the mean absolute deviation for the set of data below?
2,8,10,16
Answer:
5
Step-by-step explanation:
1. Find the Mean
(2+8+10+16)/4=9
2.For each number, subtract the Mean and square the result.
(2-9)^2=49
(8-9)^2=1
(10-9)^2=1
(16-9)^2=49
3. Find the Mean of those squared differences.
(49+1+1+49)/4=25
4.Take the square root of that and this is what you want.
square root of 25 = 5
If the value of the mean is 9. Then the mean absolute deviation will be 4.
What is the mean absolute deviation (MAD)?It is the average distance between each data point and the mean.
The MAD is given as
[tex]\rm MAD = \dfrac{\Sigma _{i = 1}^n|x_i - \mu|}{n}[/tex]
The data set is given below.
2,8,10,16
Then the mean will be
μ = (2 + 8 + 10 + 16) / 4
μ = 36 / 4
μ = 9
Then the mean absolute deviation will be
MAD = (|2 - 9| + |8 - 9| + |10 - 9| + |16 - 9|) / 4
MAD = (7 + 1 + 1 + 7) / 4
MAD = 16 / 4
MAD = 4
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Which graph represents an exponential growth function?
Answer:
The fourth graph shows and exponential growth function.
Step-by-step explanation:
The last graph shows the value increasing by a large amount.
An exponential function can represent growth or decay.
The graph represents an exponential growth function is graph (d)
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where:
b represents the growth or decay rate of the function
When the value of b is greater than 1, then the exponential function represents growth
From the diagrams, only the last graph represent an exponential growth function.
Hence, the graph represents an exponential growth function is graph (d)
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Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.
Let x = the number of games played.
Jorge knows his answer is incorrect because it does not make sense to have a negative number of games. What is Jorge’s error?
A. The variable x should represent the amount of money left.
B. From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
C. The equation should have sums on both sides.
D. From Step 2 to Step 3, Jorge should have subtracted 0.50x from both sides.
Answer:
The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.
Step-by-step explanation:
If Marcel has $8.25 and is only playing $0.25 games, then the equation will be given by: 8.25 - 0.25X.
If Floyd has $9.75 and is only playing $0.75 games, then the equation will be given by: 9.75 - 0.75X.
If we want to find the number of games after which Marcel and Floyd will have the same amount of money remaining, we need to solve the system of equations:
Equation: 8.25 - 0.25X = 9.75 - 0.75X
Step 1: -1.50 - 0.25X = - 0.75X
Step 2: -1.50 = - 0.50X
Step 3: x=3
The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.
Answer: Option B
From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
Step-by-step explanation:
To solve this problem, let's consider the initial equation that Jorge had.
[tex]8.25-0.25x=9.75-0.75x[/tex]
Subtract 9.75 on both sides of equality
[tex]8.25-9.75-0.25x=9.75-9.75-0.75x[/tex]
[tex]-1.50-0.25x=-0.75x[/tex]
Add 0.25x on both sides of equality
[tex]-1.50-0.25x+0.25x=-0.75x+0.25x[/tex]
[tex]-1.50=-0.50x[/tex]
[tex]x=3[/tex]
You can see then that Jorge's error was adding [tex]-0.75x + 0.25x[/tex]
When this sum is correctly done, the result is [tex]-0.50x[/tex]
The answer is the option B.
Central angle measure
Answer:
40°
Step-by-step explanation:
In any circle the following ratios are equal
let x be the measure of the central angle, then
[tex]\frac{arc}{circumference}[/tex] = [tex]\frac{x}{360}[/tex]
circumference = 2πr = 2π × 18 = 36π, so
[tex]\frac{4\pi }{36\pi }[/tex] = [tex]\frac{x}{360}[/tex], that is
[tex]\frac{1}{9}[/tex] = [tex]\frac{x}{360}[/tex] ( cross- multiply )
9x = 360 ( divide both sides by 9 )
x = 40
Hence central angle = 40°
Solve: 5(x + 2) = 3x + 5
A. X=-5/2
B. X=-13/15
C. X=10/11
D. X=5
What is the solution to the following system? 4x+3y-z=-6 6x-y+3z=12 8x+2y+4z=6
A. x = 1, y = –3, z = –1
B. x = 1, y = –3, z = 1
C. x = 1, y = 3, z = 19
D. x = 1, y = 3, z = –2
Answer:
Option B is correct.
Step-by-step explanation:
4x+3y-z= -6 eq(1)
6x-y+3z= 12 eq(2)
8x+2y+4z=6 eq(3)
We need to solve these equations and find the value of x, y and z.
Multiply equation 2 with 3 and then add equation 1 and 2
18x -3y +9z = 36
4x +3y -z = -6
_____________
22x + 8z = 30 eq(3)
Multiply equation 2 with 2 and add with equation 3
12x -2y + 6z = 24
8x +2y +4z = 6
____________
20x + 10 z = 30 eq(4)
Multiply equation 3 with 10 and equation 4 with 8 and then subtract
220x + 80z = 300
160x + 80z = 240
- - -
_________________
60x = 60
x= 60/60
x= 1
Putting value of x in equation 3
22x + 8z = 30
22(1) + 8z = 30
8z = 30 - 22
8z = 8
z = 8/8
z=1
Putting value of x and z in equation 1
4(1)+3y-(1)=-6
4 + 3y -1 = -6
3 + 3y = -6
3y = -6 -3
3y = -9
y = -3
so, Option B x=1, y=3 and z=1 is correct
Answer:
b
Step-by-step explanation:
Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 75% syrup?
Answer:
He needs 3.75 lbs of sugar and 1.25 lbs of water.
Step-by-step explanation:
Let x lbs be the amount of sugar in the syrup. Then 5-x lbs is the amount of water in this syrup.
Note
5 lbs - 100%
x lbs - 75%
Write a proportion:
[tex]\dfrac{5}{x}=\dfrac{100}{75}[/tex]
Cross multiply:
[tex]100x=5\cdot 75\\ \\100x=375\\ \\x=\dfrac{375}{100}=3.75[/tex]
So, he needs 3.75 lbs of sugar and 5 - 3.75 = 1.25 lbs of water.
Answer:
3.75 lbs of sugar and 1.25 lbs of water
Step-by-step explanation:
:)
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 785. Find a linear function which fits this data.
Answer:
y = 4.125x + 496.25
Step-by-step explanation:
Set the data up as points. Then deal with the points.
Givens
(30,620)
(70,785)
y2 = 785
y1 = 620
x2 = 70
x1 = 30
Formula
Slope = (y2 - y1) / (x2 - x1)
Solution
Slope = (785 - 620)/(70 - 30)
Slope = 165 / 40
Slope = 4.125
===================
Now you need the y intercept. Either one of the two given points will give you that.
y = 620
x = 30
m = 4.125
y = mx + b
620 = 4.125*30 + b
620 = 123.75 + b
620 - 123.75 + b
b = 496.25
the linear function that describes the relationship between study hours and exam scores is:
y = 4.125x + 496.25
To find a linear function that fits the data provided, we'll use the points (30, 620) and (70, 785), which represent the number of hours spent studying and the corresponding exam scores. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
First, we calculate the slope (m):
m = (y2 - y1) / (x2 - x1) = (785 - 620) / (70 - 30) = 165 / 40 = 4.125
Next, we use one of the points to solve for b (y-intercept). Let's use the point (30, 620):
620 = 4.125(30) + b
b = 620 - (4.125 × 30) = 620 - 123.75 = 496.25
So the linear function that describes the relationship between study hours and exam scores is:
y = 4.125x + 496.25
Thank you for the help
Answer:
y=3x-7
Step-by-step explanation:
Two points on the line are (3,2) and (4,5) using the slope equation, 5-2/4-3=3/1
y-2=3(x-3)
(2+) y-2=3x-9(+2)
y=3x-7
Find the factored form of
-14a-a^2=0
Answer:
-a (14 +a) =0
Step-by-step explanation:
-14a-a^2=0
Factor out -a
-a (14 +a) =0
Using the zero product property
-a =0 14+a =0
a =0 a = -14