There are 36 possible outcomes from rolling a die twice (or two dice once) and these result in sums from 2 to 12.
Possible ways to make a sum of 2: 1
Possible ways to make a sum of 3: 2
Possible ways to make a sum of 4: 3
Possible ways to make a sum of 5: 4
Possible ways to make a sum of 6: 5
Possible ways to make a sum of 7: 6
Possible ways to make a sum of 8: 5
Possible ways to make a sum of 9: 4
Possible ways to make a sum of 10: 3
Possible ways to make a sum of 11: 2
Possible ways to make a sum of 12: 1
This means there are 21 ways to make a sum greater than 6.
21/36 ≈ 58.33%
There are 24 ways to make sums that are not divisible by 3 and not divisible by 6. (Note that if a number isn't divisible by 3, it's also not divisible by 6, so that's a weird thing to include.)
24/36 ≈ 66.67%
1. Fill in the missing Statement/Reason for the following proof:
Given: LN bisects ZMLO and LM = LO
Prove: ALMN = ALON
M
STATEMENT
1.
2.
3.
4. LN = LN
5.
ALMN a ALON
REASON
N
1.
2.
3. def of Angle Bisector
4.
5.
| I
The completed proof that demonstrates that: ΔLMN ≅ ΔLON is:
LN Bisects ∠MLO; and LM ≅ LO [Given]∠MNL ≈ ∠ONL = 90° [Definition of Angle Bisector]LN ≅ LN [Definition of Reflexive Property]; ThusΔLMN ≅ ΔLON [AAS Postulate]What is the Angle-Angle-Side Postulate (AAS)?The Angle-Angle-Side Postulate (AAS) is a rule used in geometry to prove that two triangles are congruent. It states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the two triangles are congruent.
The reflexive property of equality in algebra asserts that a number is always equal to itself. Equality has a reflexive attribute. If x positive integer, then x = x.
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Which of the following relations is a function?
Answer:
b
Step-by-step explanation:
make sure the y axis doesnt repeat
In the diagram below, point O is the center of the circle.
C
A
(2x+5)°
0
B
Use the given information in the diagram to determine the value of x.
The value of x for the angle C in the triangle ABC is equal to 42.5
What is a triangle formed by a circle diameterA triangle formed by the diameter of a circle is a right triangle, with one side being the diameter of the circle and the other two sides being radii of the circle. Since the diameter of a circle bisects the circle into two equal halves, it also bisects the right angle formed by the radii into two equal angles of 45 degrees each.
The angle C is equal to 90° and we shall solve for the value of x as follows:
2x + 5 = 90°
2x = 90° - 5 {subtract 5 from both sides}
2x = 85°
x = 85°/2 {divide through by 2}
x = 42.5
Therefore, the value of x for the angle C in the triangle ABC is equal to 42.5
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Solve for v.
k = mv²
2
Ov=±m√2km
Ov=±2k√m
V = + √2km
±
v
m
0₂₁v = ±
√km
4
The equation for v is ±√k/m
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is k=mv²
k equal to m times of v square.
Where k is a formula of kinetic energy.
We need to solve for v
To do this we have to isolate the variable v
To isolate the variable v we have to Divide both sides by m
v²=k/m
v square equal to k by m.
Square root on both sides.
v=±√k/m
v equal to plus or minus square root of k by m.
Hence, the equation for v is ±√k/m
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Identify the number types that describe .
O A. Rational, integer
OB. Real, rational
O C. Real, integer
OD. Real, irrational
The type of number types that are being described are A. Rational, integer.
What is a Rational Number?A rational number in mathematics is one that can be stated as the quotient or fraction of two integers, p and q, with p being the numerator and q being the denominator, respectively.
Therefore, whole numbers are the numbers 0, 1, 2, 3, 4 and so on and negative numbers are not considered whole numbers.
natural numbers are called the counting numbers that are the numbers 1, 2, 3, 4, and so on. they are positive numbers and zero is not considered a natural number as you can see.
integers are all the whole numbers and their opposite (negative) but negative numbers are NOT whole or natural numbers. fractions and decimals are not integers.
irrational numbers are an infinite number of digits to the right of the decimal point, without repeating.
Thus, option A is the answer
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Classify the real number. (Choose all that apply). –9 A.) Rational B.) Whole C.) Irrational D.) Natural E.) Integer
If you toss 10 fair coins, in how many ways can you obtain at least one head and one tail?
Answer:1/2 head and 1/2 tails
Step-by-step explanation: no.of experiments for heads = 5
total no of experiments=10
probability=5/10=1/2
no.of experiments for = 5
total no of experiments=10
probability=5/10=1/2
Select the correct answer.
A right triangle C B A with lengths of sides as follows: C B is the wall of length equals 12 feet; A C is the ladder of length equals 13 feet. Right angle is at B.
According to the diagram, a 13-foot ladder leans against a 12-foot wall. The distance from the base of the ladder to the base of the wall is 5 feet. Based on this information, which trigonometric ratio has the value
?
A.
tan C
B.
cos C
C.
tan A
D.
sin A
Reset Next
Trigonometric Ratios: Mastery Test
©
Answer:
Option A
Step-by-step explanation:
A = opposite/hypotenuse = 12/5
I don't really have anymore explanation I could give you because that just what I could think of!
Answer: I think D. Sin A…..
Step-by-step explanation: hope this helps:)
Complete the sentence below.
325 is a hundred times bigger than
Answer:
325 is a hundred times bigger than 32500
Step-by-step explanation:
if it is ten times bigger, add one 0 at the end
if it is one hundred times bigger, add two 0 at the end
The velocity v, in meters per second, of a certain type of wave is given by v(h) = 3√h, where h is the depth, in
meters, of the water through which the wave moves. What is the rate of change, in meters per second per meter, of
the velocity of the wave with respect to the depth of the water, when the depth is 2 meters?
Answer:
The rate of change of the velocity of the wave with respect to the depth of the water is 3/2 meters per second per meter when the depth is 2 meters. This can be found by taking the derivative of v(h) with respect to h, which is 3/2√h. When h is 2, the rate of change is 3/2√2, which is equal to 3/2 meters per second per meter.
0
A
B
A"
C'
B'
2. What is the relationship among AC, A'C', and A"C"?
B"
Relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides
What is Graph?a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
To widen or enlarge an opening or hollow structure beyond its usual size in simple way changes the the size.
The scale factors is the factor in which each linear measure of the figure is multiplied.
AC is a smaller triangle which is dilated to get A'C' and this A'C' is dilated to get A''C''.
the relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides with a scale factor.
Hence, relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides
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Write the numeral in its expanded form.
34
x 10
) + (4 x 10
)
Answer:
380
Step-by-step explanation:
(34 * 10) + (4 x 10) =
= 10 * (34 + 4) =
= 10 * 38 =
= 380
Find the Nth term sequence
Answer:
[tex]a_{n}[/tex] = 6n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
7 - 1 = 13 - 7 = 19 - 13 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 6 , then
[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5
A plane traveled 4160 miles with the wind in 6.5 hours and 3900 miles against the wind in the same amount of time.
Find the speed of the plane in still air and the speed of the wind.
...
Answer:s
Step-by-step explanation:
Find the area of the trapezoid.
14 mm
15 mm
36 mm
1. 270 mm²
2. 375 mm²
3. 750 mm²
5. 3780 mm²
Answer: no one cares
Step-by-step explanation:
because it's to hard[tex]\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \left \{ {{y=2} \atop {x=2}} \right. x_{123} \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \left \{ {{y=2} \atop {x=2}} \right. \sqrt{x} \sqrt{x} \sqrt{x} \alpha \pi x^{2} x^{2} x^{2} \\ \\ \neq \pi \pi 5069967.94389438.494898 that's the answer[/tex]Can anybody help me with question 20 please?
Answer:
N?A
Step-by-step explanation:
You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 99% confidence level
and a margin of error of 3%. A pilot survey reveals that 8 of the 48 sampled hold two or more jobs. (Use t Distribution Table & z
Distribution Table.)
How many in the workforce should be interviewed to meet your requirements? (Round z-score to 2 decimal places. Round up your
answer to the next whole number.)
Number of persons to be interviewed
Number of persons to be interviewed = 599.
What is number?Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
To calculate the required sample size for the survey, the formula for a confidence interval for a proportion can be used:
n = (Z-score)²×p×(1-p)/margin of error²
Where:
Z-score = 1.96 (this is the z-score for the 99% confidence level from the z-distribution table)
p = 0.167 (this is the proportion of the sample that hold two or more jobs, 8/48)
margin of error = 0.03 (this is the margin of error you have specified)
Therefore, the required sample size is:
n = (1.96)²×0.167×(1-0.167)/(0.03)²
n = 598.8
To meet your requirements, you should interview 599 persons (rounding up the answer to the next whole number).
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What are the coordinates of (-5,6) after a dilation of 2 centered at the origin
Answer:
(-10, 12).
Step-by-step explanation:
A dilation with a scale factor of 2 centered at the origin expands distances from the origin by a factor of 2. If a point in the plane is represented by the coordinates (x, y), then the point obtained by a dilation centered at the origin with scale factor k is represented by (kx, ky).
So, if the original point is (-5, 6), then after the dilation of 2 centered at the origin, the new point is represented by (2 * -5, 2 * 6) = (-10, 12).
So the coordinates of (-5, 6) after a dilation of 2 centered at the origin are (-10, 12).
Find the number of subsets of {1, 2, 3, 4, 5, 6, 7 that are subsets of neithe{1, 2, 3, 4, 5}nor{4, 5, 6, 7, 8}.
If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9
Let the sets be
A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
B = {1, 2, 3, 4, 5}
C = {4, 5, 6, 7, 8, 9}
Then
B ∩ C = {4, 5}
Subsets of B ∩ C = {4}, {5}, {4,5}, {}
If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}
No. of elements in A = 9
No. of subsets of A = [tex]2^9[/tex]
No. of elements in B = 5
No. of subsets of B = [tex]2^5[/tex]
No. of elements in C = 6
No. of subsets of C = [tex]2^6[/tex]
If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C
But the null set will be subtracted twice
Also as the subsets of B ∩ C excluding null set will be subtracted twice
Therefore, total number of subsets of A not the subsets of B or C
[tex]k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414[/tex]
The sum of the digits of k=9
The complete question is-
If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.
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Without solving, determine the character of the solutions of the equation in the complex number system.
3x^2 + 7×=3.
(Simplify your answer.)
Answer:
Step-by-step explanation:
To determine the character of the solutions of the equation in the complex number system, we need to analyze the nature of the coefficients of the equation, specifically the discriminant, which is obtained by the equation: b^2 - 4ac, where a, b and c are the coefficients of the equation.
In this case, the equation is
3x^2 + 7x - 3 = 0
So, the coefficients are a = 3, b = 7, and c = -3.
We can now calculate the discriminant as follows:
b^2 - 4ac = 7^2 - 4 * 3 * -3 = 49 + 36 = 85
Since the discriminant is positive, we know that the equation has two distinct real solutions. The exact solutions can be obtained using the quadratic formula, but that's not required to determine the character of the solutions.
Therefore, the equation has two real solutions.
Please I just need help so badly asap Please
Answer:
- It is a parallelogram
Step-by-step explanation:
- The interior angle sum of a quadrilateral is 360°
Considering the four angles;
[tex]{ \tt{m \angle A + m \angle B + m \angle C + m \angle D = 360 \degree}} \\ \\ { \tt{(x + 12) + \{2(x + 3) \} + ( \frac{3}{2} x - 15) + ( \frac{7}{3} x - 12) = 360}} \\ \\ { \tt{(x + 2x + \frac{3}{2}x + \frac{7}{3}x) + (12 + 6 - 15 - 12) = 360 }} \\ \\ { \tt{ \frac{41}{6} x - 9 = 360}} \\ \\ { \tt{ \frac{41}{6}x = 369 }} \\ \\ { \tt{41x = 2214}} \\ \\ { \tt{x = 54}}[/tex]
- Therefore, substitute in x and find the angles.
[tex] { \tt{m \angle A = (x + 12) = (54 + 12) = 66 \degree}} \\ \\ { \tt{m \angle B = 2(x + 3) = 2(54 + 3) = 114 \degree}} \\ \\ { \tt{m \angle C = ( \frac{3}{2}x - 15) = \{( \frac{3}{2} \times 54) - 15 \} = 66 \degree }} \\ \\ { \tt{m \angle D = ( \frac{7}{3}x - 12) = \{( \frac{7}{3} \times 54) - 12 \} = 114 \degree }}[/tex]
Which two sets of values make the inequality 3(n – 2) ≤ 2n – 3 true?
A. {−2, −1, 3}
B. {−2, −1, 4}
C. {−1, 0, 3}
D. {−1, 1, 4}
E. {1, 0, 5}
why is this graph not a function?
The graph is not a function because it fails the vertical line test
How to determine why it is a not functionFrom the question, we have the following parameters that can be used in our computation:
The graph (added as an attachment)
The given graph when represented as an equation, is a circle equation
As a general rule, we have
Circle equations are not functions and they do not represent a function on a graph
This is so because they do not pass the vertical line test
Hence, the graph is not a function
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A boat has a top speed of 26 knots and a displacement of approximately 93,000 tons. Express the top speed in miles per hour and the displacement in metric tons
The boat's displacement is approximately 84,016.8 metric tons.
How to convert from knots to miles?To convert the boat's top speed from knots to miles per hour, we can use the conversion factor of 1.15078 miles per hour per knot:
26 knots × 1.15078 miles per hour per knot = 29.86 miles per hour (rounded to two decimal places)
Therefore, the boat's top speed is approximately 29.86 miles per hour.
To convert the boat's displacement from tons to metric tons, we can use the conversion factor of 0.907185 metric tons per ton:
93,000 tons × 0.907185 metric tons per ton = 84,016.8 metric tons (rounded to one decimal place)
Therefore, the boat's displacement is approximately 84,016.8 metric tons.
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Simplify the given trigonometric expression (sin (30° + x)+sin (30° - x))
The simplified expression is cos(x) of trigonometric expression (sin (30° + x)+sin (30° - x))
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We can simplify this expression using the sum-to-product formula for sine:
sin(a + b) + sin(a - b) = 2 sin(a) cos(b)
Let's use this formula by setting a = 30° and b = x:
sin(30° + x) + sin(30° - x) = 2 sin(30°) cos(x)
We know that sin(30°) = 1/2, so we can substitute:
sin(30° + x) + sin(30° - x) = 2(1/2) cos(x)
sin(30° + x) + sin(30° - x) = cos(x)
Therefore, the simplified expression is cos(x).
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Siri has decided to examine his checking account statements. Last month‘s account balance was $100 this month is 42. What is the percent of decrease in Pere’s account balance
Answer:
58% decrease
Step-by-step explanation:
A child is allowed to pick three candy treats from a bin of 15 different candies. How many ways can the child select 3 treats?
The number of ways for the child to select 3 treats is given as follows:
455 ways.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The order in which the treats are chosen is not relevant, hence the combination formula is used to solve this question.
Three treats are chosen from a set of 15, hence the number of ways is given as follows:
C(15,3) = 15!/(3! x 12!) = 455 ways.
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or problems 2-7, find the slope of the line.
1.
1.
-10
-10
2 PRACTICE
y
y
10
10
3.
y
10
H
5.
-10-
y
10
2
+
10
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The slope of the line in graph 2 is equal to 1.
The slope of the line in graph 3 is equal to 1/2.
The slope of the line in graph 4 is equal to 3/4.
The slope of the line in graph 5 is equal to 3.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (7 - 2)/(7 - 2)
Slope, m = 5/5
Slope, m = 1.
For the line in graph 3 with the given data points, we have:
Slope, m = (3 + 2)/(6 + 4)
Slope, m = 5/10
Slope, m = 1/2.
For the line in graph 4 with the given data points, we have:
Slope, m = (6 - 0)/(8 - 0)
Slope, m = 6/8
Slope, m = 3/4.
For the line in graph 5 with the given data points, we have:
Slope, m = (6 - 0)/(2 - 0)
Slope, m = 6/2
Slope, m = 3.
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PLEASE HELP WITH CHART:
You can fill in the rest of the table as shown below.
How to fill in the rest of the table?The derivative of a function is a concept from calculus that measures the rate of change of a function at a specific point. It provides information about how the value of the function changes as its input changes.
Use the following differentiation rules to fill the table:
d/dx(f(x)·g(x)) = f(x)·g'(x) + f'(x)·g(x) (product rule)
d/dx(f(x)/g(x)) = [ g(x)·f'(x) - f(x)·g'(x) ] / [(g(x))²] (Quotient rule)
d/dx(g(x)/f(x)) = [ f(x)·g'(x) - g(x)·f'(x) ] / [(f(x))²] (Quotient rule)
x f(x) f'(x) g(x) g'(x) d/dx(f(x)·g(x)) d/dx(f(x)/g(x)) d/dx(g(x)/f(x))
0 3 -2 -4 3 17 -1/16 1/9
1 2 -1 1 0 -1 -1 1/4
2 4 2 3 1 10 2/9 -1/8
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HELP ASAP!!! WILL MARK BRAINIEST
The value of the network density is 0.9
How to determine network density?
Since the potential connections (PC) formula is n(n-1)/2 and number of nodes is 5 (i.e. n = 5). We have:
PC = n(n-1)/2
PC = 5(5-1)/2
PC = (5*4)/2
PC = 20/2
PC = 10
Actual connection (AC) = 9
Network Density = AC/PC
Network Density = 9/10
Network Density = 0.9
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What is the frequency of the function given? f(x)=9cos(4πX)+10
Answer:
Step-by-step explanation:
The frequency of a cosine function is related to the number of cycles that the function completes in a unit interval (usually in 2π radians).
The frequency of a cosine function with the form f(x) = A * cos(Bx + C) is given by B/(2π), where A, B, and C are constants.
For the function f(x) = 9cos(4πx) + 10, the frequency is given by 4π / (2π) = 2 cycles per unit interval.
So, the frequency of the function f(x) = 9cos(4πx) + 10 is 2 cycles per unit interval.
