Answer:
8/17
Step-by-step explanation:
You want the ratio of 32 mm to 6.8 cm, compared in mm.
RatioThe ratio of interest is ...
(32 mm)/(6.8 cm) = (32 mm)/(68 mm) = (4·8)/(4·17) . . . . . mm cancels
= 8/17
The ratio of ball diameters is 8/17.
8. The percentage of the moon's surface that is visible to someone on the Earth varies due to
the time since the previous full moon. The moon passes through a full cycle in 28 days. The
maximum percentage of the moon's surface that is visible from Earth is 50%. Find a function
for the percentage, P, of the surface that is visible as a function of the number of days, t,
since the previous full moon.
A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
What is a functiοn?In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.
Here, we have
Given:
Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C
After 14 days, the percentage οf the mοοn is zerο
A = (max-min)/2 = 50/2 = 25
The periοd = 28 days
P = Acοs(BT = t) + c
B = 2π/periοd = 2π/28 = π/14
c = min + A = 0 + 25 = 25
We get,
P = 25cοs(π/14t) + 25,
Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.
Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
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What is the value of the expression below?
6 + 5(9 ÷ 3)2
Answer:
36
Step-by-step explanation:
Divide 9 and 3
6 + 5 x 3 x 2
6+30
= 36
Can some one help with this problem
Step-by-step explanation:
Area of the trapezoid = height x average of bases
area = 4 x (8+13)/2) = 42 in^2
Area of triangle = 1/2 base * height = 1/2 (13-8) * 4 = 10 in^2
Help me with this parallelogram please :)
Parallel sides of parallelogram are equal in length
\(\\ \sf\longmapsto AD=BC\)
\(\\ \sf\longmapsto 6x+14=9x-4\)
\(\\ \sf\longmapsto 9x-6x=14+4\)
\(\\ \sf\longmapsto 3x=18\)
\(\\ \sf\longmapsto x=6\)
AD=6x+14=6(6)+14=36+14=50
Option D
The opposite sides of parallelogram are equal in length, so we can infer that :
BC = ADnow, let's solve for value of x :
\(9x - 4 = 6x + 14\)\(9x - 6x = 14 + 4\)\(3x = 18\)\(x = 18 \div 3\)\(x = 6\)we have to find the measure of AD,
\(6x + 14\)Plugging the value of x as 6 :
\((6 \times 6) + 14\)\( 36 + 14\)\(50\)The Correct option is D. 50
Please solve for a: b = 2 - (1/a)
\(b = 2 - \dfrac 1a\\\\\implies ab = 2a -1\\\\\implies 2a -ab = 1\\\\\implies a(2-b) =1\\\\\implies a = \dfrac 1{2-b}\)
A drawer contains 10 blue pens, 12 black pens, and 3 red pens. Without looking, Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answer: 4.8%
Step-by-step explanation: the total amount of pens in the drawer is (10+12+3) = 25
the amount of red pens in the drawer is 3
the probability of picking out a red pen from the drawer = 3/25
the amount of blue pens in the drawer is 10
the probability of picking out a red pen from the drawer = 10/25
the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%
Anju's office uses paper cups shaped like cones to serve water. Each cup has a maximum diameter of 8 cm and a height of 10 cm. Anju fills the cup to of its height to prevent spills.
What is the approximate volume of water in Anju's cup?
Answer:
V = 167.55
Step-by-step explanation:
V = pir^2 h/3
V = pi(4)^2 (10/3)
The approximate volume of water in Anuj's cup is 42 cubic cm.
What is volume?Volume is a measure of capacity that an object holds.
Formula for finding the volume of cone
volume of cone = \(\frac{1}{3} \pi r^{2} h\)
where,
r is the radius of cone
h is the height of cone
π = 3.14
According to the given question
paper cups are of the shape of cone.
and,
diameter = 8cm
⇒ radius = \(\frac{8}{2}\) = 4cm
the approximate volume of water in cup = \(\frac{1}{3} \pi r^{2} h\)
=\(\frac{1}{3}\)×\(2^{2}\)×π×10
=\(\frac{1}{3}\)×4×3.14×10
= 41.86 = 42 cubic cm.
Hence, the approximate volume of water in Anuj's cup is 42 cubic cm.
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The drama club at Del Rosa Middle School is having a production.
Tickets cost $3 for students and $5 for adults. A total of 500 tickets
were sold, bringing in $1860. How many of each kind of ticket was
sold?
Answer:
320 Student Tickets
180 Adult Tickets
Step-by-step explanation:
You can solve this problem by using system of equations. First, we need to figure out our equations.
Equation 1: x as students and y as adults
\(x+y=500\)
We get this equation because the total tickets sold was 500. The x represents the students sold to students, and the y represents the tickets sold to adults.
Equation 2:
\(3x+5y=1850\)
We get this equation based on the prices. Each student ticket costs $3, and each adult ticket costs $5. The total amount earned was $1850.
Now that we have out equations, we can use system of equations to find our students and adults.
\(x+y=500\)
\(3x+5y=1860\)
Typically elimination is the easiest strategy because you are able to cross out variables.
\(3(x+y=500)\)
\(3x+5y=1860\)
Becomes:
\(3x+3y=1500\)
\(3x+5y=1860\)
We see that both equations now have 3x. We can cancel out 3x.
\(-2y=-360\)
\(y=180\)
Now that we know y=180, we can plug it back into one of our equations to find x.
\(x+180=500\)
\(x=320\)
320 student tickets and 180 adult tickets were sold.
identify the slope and write the equation of the line in slope intercept form that goes through the point (-5,-1) and is perpendicular to 5x - y = 1
The slope of this line is equal to -1/5.
An equation of the line in slope-intercept form that goes through the point (-5,-4) and is perpendicular to 5x - y = 1 is y = -x/5 - 2.
How to determine an equation of this line?Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the information provided, we have the following:
5x - y = 1. Therefore, the slope, m is equal to 5.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
5 × m₂ = -1
m₂ = -1/5
At point (-5, -1), an equation of this line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
y - (-1) = -1/5(x - (-5))
y + 1 = -x/5 - 1
y = -x/5 - 1 - 1
y = -x/5 - 2
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he entire graph of the function is shown in the figure below.
Write the domain and range of using interval notation.
Someone please help me. I really nee help. this question is due tonight before 8 and im stuck.
The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].
The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).
In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.
So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.
In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].
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Graph the line y=-4x-3
A machine that is programmed to package 1.20 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively.Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the cereal boxes. Use the .05 level of significance.
Answer:
As the calculated value of z= 2 lies in the critical region z ≥ z∝/2= ± 1.96 the null hypothesis is rejected that the machine is working improperly and it is either underfilling or overfilling the cereal boxes
Step-by-step explanation:
Here n= 36
Sample mean = x`= 1.22
Required Standard mean = u= 1.20
Sample Standard deviation = s= 0.06
Level of Significance.= ∝ = 0.05
The hypothesis are formulated as
H0: u1=u2 the machine is working properly
against the claim
Ha: u1≠u2
i.e the the machine is not filling properly
For two tailed test the critical value is z ≥ z∝/2= ± 1.96
The test statistic
Z= x`-u/s/√n
z= 1.22-1.20/0.06/√36
z= 2
As the calculated value of z= 2 lies in the critical region z ≥ z∝/2= ± 1.96 the null hypothesis is rejected that the machine is working improperly and it is either underfilling or overfilling the cereal boxes
What are the coordinates of the point on the directed line segment from (-10, -3)
to (2, -3) that partitions the segment into a ratio of 5 to 3?
Answer:
(-2.5,-3)
Step-by-step explanation:
Initial points, \((x_1,y_1)=(-10,-3)\)
Final points, \((x_2,y_2)=(2,-3)\)
The ratio in which the points divides is 5:3. KLet (x,y) be the coordinates of the point that is directed on the line segment from (-10, -3) to (2, -3).
Using section formula,
\(x=\dfrac{m_1x_2+m_2x_1}{m_1+m_2}, y=\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\\\\x=\dfrac{5\times 2+3\times (-10)}{5+3}, \dfrac{5(-3)+3(-3)}{5+3}\\\\x=-2.5, y=-3\)
So, the coordinates of the point is (-2.5,-3).
Ximena pays a flat cost of $44.50 per month and $4 per gigabyte. She wants to keep her bill at $50.10 per month. How many gigabytes of data can she use while staying within her budget?
Answer:
Ximena can use 1 gigabytes of data
Step-by-step explanation:
The first thing you want to do is subtract
51.10 - 44.50 = 5.6
5.6 is the amount of money she will have to spend on data
With each gigabyte costing 4 dollars and only 5 dollars to spend
she can only use one gigabyte
what is the twelfth term in the sequence 13,26,39, ...?
Answer:
166
Step-by-step explanation:
Brainliest and a thanks??
Term 1: 13
Term 2: 26
Term 3: 39
Term 4: 52
Term 5: 65
Term 6: 78
term 7 : 91
Term 8: 104
Term 9: 117
Term 10: 130
Term 11: 143
Term 12: 156
OR 13*12=156
Add 13 every time until you add it 12 times you will get 156. Or you can mulitply 13*12 you will get 156. Multiply is much easier though!!
Hope this helps!
Answer=156
Have a great day!
- Hailey!
(nothing is copied or pasted!!!)
How many 2 1/3 m lengths of rope can be cut from a rope of length 21 m?
Find the sector are. Round your answer to the nearest tenth.
A. 254.5 m2
B. 93.5 m2
C. 848.2 m2
D. 14.1 m2
im almost sure its a ............
Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 14, 11, 15, 19, 12, 10 Send data to calculator Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth. movies X Ś
The mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).
To find the mean number of movies the students saw, you need to calculate the average of the given data. Here are the reported numbers of movies seen by the 6 students: 14, 11, 15, 19, 12, 10.
To calculate the mean, you sum up all the reported numbers and divide by the total number of students. In this case, the total number of students is 6.
So, let's calculate the mean:
(14 + 11 + 15 + 19 + 12 + 10) / 6 = 81 / 6 = 13.5
Therefore, the mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).
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29.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
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Amadi is three times as old as Chima. The sum of their ages is 24
Answer:
Amadi: 20 years old
Chima : 4 years old
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a)
The bases for the row space and null space of A, we put A into reduced row echelon form and solve for the null space. The dot product of basis vectors shows they are orthogonal.
To find the bases for the row space and null space of A, we perform row operations on A until it is in reduced row echelon form:
[ 1 -1 3 | 5 ] [ 1 -1 3 | 5 ]
[ 2 1 -5 | -9 ] -> [ 0 3 -11 | -19]
[-1 -1 2 | 2 ] [ 0 0 0 | 0 ]
[ 1 1 -1 | -1 ] [ 0 0 0 | 0 ]
The reduced row echelon form of A tells us that there are two pivot columns, corresponding to the first and second columns of A. The third and fourth columns are free variables. Therefore, a basis for the row space of A is given by the first two rows of the reduced row echelon form of A:
[ 1 -1 3 | 5 ]
[ 0 3 -11 | -19]
To find a basis for the null space of A, we solve the system Ax = 0. Since the third and fourth columns of A are free variables, we can express the solution in terms of those variables. Setting s = column 3 and t = column 4, we have:
x1 - x2 + 3x3 + 5x4 = 0
2x1 + x2 - 5x3 - 9x4 = 0
-x1 - x2 + 2x3 + 2x4 = 0
x1 + x2 - x3 - x4 = 0
Solving for x1, x2, x3, and x4 in terms of s and t, we get:
x1 = -3s - 5t
x2 = s + 2t
x3 = s
x4 = t
Therefore, a basis for the null space of A is given by the vectors:
[-3 1 1 0]
[ 5 2 0 1]
To verify that every vector in the row space of A is orthogonal to every vector in the null space of A, we compute the dot product of each basis vector for the row space with each basis vector for the null space:
[ 1 -1 3 | 5 ] dot [-3 1 1 0] = 0
[ 1 -1 3 | 5 ] dot [ 5 2 0 1] = 0
[ 0 3 -11 | -19] dot [-3 1 1 0] = 0
[ 0 3 -11 | -19] dot [ 5 2 0 1] = 0
Since all dot products are equal to zero, we have verified that every vector in the row space of A is orthogonal to every vector in the null space of A.
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_____The given question is incomplete, the complete question is given below:
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a). a = [ 1 -1 3 5 2 1 0 1 -2 -1 -1 1]
Is 0.3682 a non-repeating decimal?
Answer:
its a non-repeating decimal
Step-by-step explanation:
repeating decimals continue you on for a while, if decimals have a line over top of the last ending number that means it kept repeating so they cut it short, this one however doesn't have that symbol.
Identify an equation in point-slope form for the line parallel to y = 3/4 x - 4 that passes through (–1, 7).
Let's take this problem step-by-step:
If a line is parallel to each other:
⇒ their slope must be equal
Thus the line parallel to: \(y=\frac{3}{4}x-4\)
⇒ that line's slope: 3/4
The point-slope form is: \((y-y_1)=m(x-x_1)\)
m: the value of the slope of that line(x₁,y₁): point on that lineLet's put that line into the point-slope form:
\((y-7)=\frac{3}{4}(x+1)\) <== Answer
Hope that helps!
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Answer:
\(y - 7 = \frac{3}{4} (x+1)\)
Step-by-step explanation:
We are given the equation y = 3/4x-4, and we want to write an equation of a line that is parallel to y=3/4x-4, and that also passes through (-1, 7), in point-slope form.
Point-slope form is written as \(y-y_1=m(x-x_1)\), where \(m\) is the slope, and \((x_1, y_1)\) is a point
If two lines are parallel to each other, it means they have the same slope.
The line y = 3/4x-4 is written in the form slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.
As 3/4 is in the place of where m is, 3/4 is the slope of this line.
It is also the slope of our new line.
So we can substitute 3/4 as m in \(y-y_1=m(x-x_1)\).
\(y-y_1=\frac{3}{4} (x-x_1)\)
Now, we need to replace the values of \(x_1\) and \(y_1\) with a point.
Since we are given (-1, 7), and that it passes through the line, it means that we can use its values in the equation.
Note that we have subtraction in this equation, so when we use a negative number, we still write the subtraction sign in front of the minus sign the negative number has. Just because the number is already negative doesn't mean we ignore the minus sign the formula gives.
\(y-7=\frac{3}{4} (x--1)\)
We can simplify this equation, as --1 is the same as +1.
\(y-7=\frac{3}{4} (x+1)\)
unction g is a transformation of the parent tangent function such that
. Which graph represents function g?
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.
B.
The trigonometric functions intercept the x-axis at minus 4.2, minus 1.1, 2, and 5 units also pass parallel to the g of the x-axis.
C.
The trigonometric functions intercept the x-axis at minus 3.5, minus 0.2, and 3 units also pass parallel to the g of the x-axis.
D.
The trigonometric functions intercept the x-axis at minus 5, minus 2, 1, and 4.2 units also pass parallel to the g of the x-axis.
Answer:
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.
1. Set A represents rational numbers. Set B represents integers. Which diagram shows
the numbers placed in the correct
sets?
Set A
Set A
1.5
1
10
3
3.1
С
Set B
Set B
-12
Set A
Set A
7.1
10
2
win
mi
B
D
Set B
Set B
-3.4
-6.8
Answer: Choice C) Upper right corner (aka northeast corner)
====================================================
Explanation:
Rational numbers are ones where we can write as a fraction of two integers. Any rational number is in the form a/b where a,b are integers and b is nonzero.
Terminating decimals can be written as a rational number. Something like 3.1 is equivalent to 31/10.
Of the four answer choices, only choice C is correct.
Choice A has the value '3' as a rational number, but it doesn't have it in the set of integers as well. So that's why choice A is incorrect.
Choice B has -3.4 in the set of integers, which is not correct. Integers do not have any decimal portion. The same applies to choice D also. We can rule choices B and D out.
rearrange the formula to make x the subject 4(x-3)/a=y
Answer:
x=3+ay/4a
Step-by-step explanation:
4(x-3)/a=y
a*4(x-3)/a=a*y
4a(x-3)=ay
4a(x-3)/4a=ay/4a
x-3=ay/4a
x-3+3=3+ay/4a
x=3+ay/4a
you want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. you assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. using the following random digits to execute as many simulations as possible, what is your estimate of the probability? 19226 95034 05756 07118
The probability of getting exactly one head and one tail in two tosses of a fair coin is 0.6
We are asked to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin and it is given that the digits 0, 1, 2, 3, 4 are assigned to heads and 5, 6, 7, 8, 9 are assigned to tails.
By Making a pair of two digits the outcomes on basis of random digits are HT, HH, TT, TH, HH, HT, TT, TH, TH, HT.
Hence, the probability of head and tail = Total pairs with one head and one tail/Total number of pairs
= 6/10
= 0.6
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how many integers between 2023 and 5757 have 12, 20, and 28 as factors
Answer:
9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.
Step-by-step explanation:
An integer that has 12, 20, and 28 as factors must be divisible by the least common multiple (LCM) of these numbers. The LCM of 12, 20, and 28 is 420. So we need to find the number of integers between 2023 and 5757 that are divisible by 420.
The first integer greater than or equal to 2023 that is divisible by 420 is 5 * 420 = 2100. The last integer less than or equal to 5757 that is divisible by 420 is 13 * 420 = 5460. So the integers between 2023 and 5757 that are divisible by 420 are 2100, 2520, ..., 5460. This is an arithmetic sequence with a common difference of 420.
The number of terms in this sequence can be found using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms. Substituting the values for this sequence, we get:
5460 = 2100 + (n - 1)420 3360 = (n - 1)420 n - 1 = 8 n = 9
So there are 9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.
With a choking victim, the rescuer will provide abdominal thrusts which should be performed
by:
A. None apply
B. Pressing in the person's chest with hard and fast compressions,
C. Making quick inward and upward thrusts to the abdominal cavity with your fist.
D. Lying the person on their back and pushing up into their stomach and rib cage.
3 * (4-2) +6
Simplify
Answer:
It would be 12 hope this helps!
DJ FL eui EU ghi ti Rio ri gj fyi tui
3x2+6
6+6=12
that all