Answer/Step-by-step explanation:
1. <ABC and <BCD are alternate interior angles. Alternate interior angles are equal, therefore, since m<ABC = 38°, then m<BCD = 38°
2. m<ECF = m<BCD (corresponding angles)
m<ECF = 38° (substitution)
3. m<DCF + m<ECF = 180° (linear pair)
m<DCF + 38° = 180° (substitution)
m<DCF = 180° - 38° (Subtraction property of equality)
m<DCF = 142°
The measure of the following angles are as follows;
∠BCD = 38°
∠ECF = 38°
∠DCF = 142°
Angles form when a transversal cut parallel linesWhen a transversal line cut across parallel lines, the angles form include corresponding angles, alternate angles etc.
Therefore,
∠BCD = 38 degrees(alternate angles)
∠ECF = 38 degrees(corresponding angles)
∠DCF = 180 - 38 = 142 degrees(angles on a straight line)
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what is the probability of having a 5-card hand that is a flush or royal flush (all 5 cards are the same suit but different values)?
The probability of having a 5-card hand that is a flush or royal flush is 0.00196
What is Probability?Probability: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
Flush, straight flush, and royal flush probabilities are calculated as follows: 5148/2598960≅0.00198
A flush's likelihood (while eliminating straight and royal flushes) is 5108/2598960, ≅0.00196.
Finding the fraction with the number of ways to have a flush as the numerator and the number of possible five-card hands as the denominator will allow us to determine the likelihood.
Combinations will be used to find each of these numbers (we don't care about the draw order; only about what shows up in our hand). Combinations' general formula is Cn,k=n!/(k)!(n-k)! with k=picks and n=population
Let's first determine the denominator by selecting 5 cards at random from a deck of 52 cards: C52,5=52!/(5)!(525)!
=52!/(5!)(47!)
Let's assess it!
52×51×50^10×49×48^2×47!/5×4×3×2×47!=52×51×10×49×2=2,598,960
Let's now determine the numerator.
In order to examine each hand with five cards of the same suit, we will compute all hands that feature a flush (including straight flushes, royal flushes, and flushes) (with a suit having 13 cards in total). We can say that we understand this by:
C13,5
Remember that there are 4 suites in which this might occur, but we only want 1, so multiply by C4,1. Putting it all together, we obtain:
C4,1×C13,5=4!/(1!)(4−1)!×13!/(5!)(13−5)!=4!13!/3!5!8!
Let's assess this.
4!×13×12×11×10×9^3×8!/3×2×5×4!×8!=13×12×11×3=5148
(Remember that we just calculated all hands, including straight flushes and royal flushes, that have a flush component to them!
The probability of getting a hand with a flush is:
5148/2598960≅.00198
We may exclude straight and royal flush possibilities from the 5148 flush hands by excluding those hands (which are hands with 5 consecutive value cards in the same suit, such as 3, 4, 5, 6, and 7 of hearts). Since there are four suits and 10 potential ways to get a straight (A-5, 2-6, 3-7,..., 10-A), we can subtract 4 from 5148 to get 5108 hands, which gives us the result 5108/2598960=0.00196.
The probability of having a 5-card hand that is a flush or royal flush is 0.00196
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Drag numbers to make an expression
that has a value of 10.
5 2 1 1
(_ - _) + (_ x _)= 10
What is The domain for the given function?
Will give crown will post more
Answer:
2, 7, 27, 42
Step-by-step explanation:
y = 5*1 -3 =2
y = 5*2 -3 =7
y = 5*6 -3 = 27
y = 5*9 -3 = 42
Answer:
See below
Step-by-step explanation:
\(y = 5x - 3 \\ \\ \begin{vmatrix}x &\: \: \: y \\ \\ 1&\: \: \: \boxed{\red {\bold 2} } \\ \\ 2&\: \: \: \boxed{\purple {\bold 7} }\\ \\ 6&\: \: \: \boxed{ \orange {\bold {27} } } \\ \\ 9&\: \: \: \boxed{\pink{\bold {42} } } \end{vmatrix}\)
Mark has to pay a state tax of 10% and a federal tax of
25% on the amount he receives from selling his house.
What steps would he have to take to find all the taxes he
will pay on the house he just sold for $250,000?
Answer:Mark needs to calculate the amount of state tax by multiplying 250,000 by 0.10, and the amount of federal tax by multiplying 250,000 by 0.25. He then can add the two tax amounts.
Step-by-step explanation:
Sample response
Simplify -3√72
A
-18√6
B
-6√6
C
-18√2
D
6√2
Answer:
C. -18√2
Step-by-step explanation:
Given the functions f(x) = 3x - 5 and h(x) = -x² + 3x - 2, evaluate the expression: f(7/3)-h(-3)=
Answer: f(7/3)-h(-3)=22
Step-by-step explanation:
\(\displaystyle\\f(x)=3x-5\ \ \ \ h(x)=-x^2+3x-2\\\\f(\frac{7}{3})= 3*\frac{7}{3} -5\\\\f(\frac{7}{3})=7-5\\\\f(\frac{7}{3})=2\\\\h(-3)=-(-3)^2+3*(-3)-2\\\\h(-3)=-9-9-2\\\\h(-3)=-20\\\\f(\frac{7}{3})-h(-3)=2-(-20)\\\\ f(\frac{7}{3})-h(-3)=2+20\\\\f(\frac{7}{3})-h(-3)=22\)
I’ll be very grateful for anyone’s help I added a photo of the question
Answer:
c
Step-by-step explanation:
Answer: C.
Step-by-step explanation: The ratio of made free throws to missed free throws is 64:48, which simplified is 4:3. Colons, fractions, and "to" are all ways to signify a ratio, thus, the answer is C.
A flower pot in the shape of a truncated cone with a height of 8 in. was formed by slicing off the tip of a cone along a plane parallel to the base.The original cone had a height of 12 in. and a volume of 810 in3. What is the volume of the tip that was sliced off?
A)30 in3B)60 in3C)90 in3EliminateD)180 in3
the correct answer is B
hope I helped
pls help ASAP I dont understand at all
Which equation can be used to find the measure of angle LJK?
O sin(x) = 10/15
O sin(x) = 15/10
O cos(x) = 10/15
O cos(x)= 15/10
Answer:
cos(x)=10/15
Step-by-step explanation:
As cosine is Base/Hypotenues
cos(x)=JL/JK
= 10/15
MARK ME AS BRAINLISTThe equation used to find the measure of angle LJK is option C. cos(x) = 10/15.
What are Trigonometric Functions?Trigonometric functions are the functions which are represented as the ratio of the sides of a right angled triangle.
The three main trigonometric functions are sine, cosine and tangent function.
Sine function of an angle is the ratio of the opposite side to the hypotenuse of the triangle.
Cosine function of an angle is the ratio of the adjacent side to the hypotenuse of the triangle.
Here,
Hypotenuse of the triangle = KJ = 15 inches
LJ = 10 inches is the adjacent side with respect to the angle x.
We can use cosine function here.
cos (x) = LJ / KJ = 10/15
Hence the equation used is cos(x) = 10/15.
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hey i can someone pls pls asap
Answer:
y=50x
Step-by-step explanation:
The dots rise up by 50 and go right by one. rise/run=slope
There is no y-intercept because the line intersects at the origin, (0,0)
So, the answer is y=50x.
(1 point) find all values of k for which the function y=sin(kt) satisfies the differential equation y″ 20y=0. separate your answers by commas.
the only values of k for which y = sin(kt) satisfies the differential equation y″ - 20y = 0 are k = nπ/t for any integer n.
We are given the differential equation y″ - 20y = 0, and we need to find all values of k for which y = sin(kt) satisfies this equation.
First, we find the second derivative of y with respect to t:
y′ = k cos(kt)
y″ = -k^2 sin(kt)
Now we substitute these expressions for y, y′, and y″ into the differential equation:
y″ - 20y = (-k^2 sin(kt)) - 20(sin(kt)) = 0
Factorizing out sin(kt), we get:
sin(kt)(-k^2 - 20) = 0
This equation is satisfied when either sin(kt) = 0 or (-k^2 - 20) = 0.
When sin(kt) = 0, we have k = nπ/t for any integer n.
When (-k^2 - 20) = 0, we have k^2 = -20, which has no real solutions.
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An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying. Lisa studies 4 hr for a particular test and gets a score of 72. At this rate, how many hours would she have had to study to get a score of 96?
Answer:
12 hours.
Step-by-step explanation:
Please help me with this problem I will give brainpower to the first person that answers this correctly with an explaination
Hi!
To solve this, we can set up an equation. If L, the length, is 3 less than 2 times W, the width, it would look like this. L = 2w - 3
Now, the perimeter equation is L + L + w + w = 48, so we plug in the L's and get this:
2w - 3 + 2w - 3 + w + w = 48
Now solve, add like terms:
6w - 6 = 48
add 6 to both sides
6w = 54
divide both sides by 6
w = 9
The width is 9, and the length is two times this minus 3, so 2(9) - 3 = 18 - 3 = 15
Therefore your width is 9 and your length is 15
Hope this helps! :D
Bob's car uses 6 L of gasoline per 100 km. How many litres of gas
will he use for a 400 km trip?
The height of a balloon, h, varies directly as the square root of its surface area, A.
When the balloon's surface area is 81 its height is 12
What is its height when its surface area is 144?
The height of the balloon is 21.33
According the the question the relation between height and surface area of balloon is
H=pA
where ,
H is height
p is proportionality constant
A is surface area
Surface area = 81
Height = 12
By Replacing the given values we get,
12=p x 81
p=12/81
Using it in given conditions,
H=(12/81)x144
H=21.33
So the height of the balloon in the given condition is 21.33
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If \( C \$ 1=£ 0.6219 \) and \( £ 1= \) US\$1.2157, how many Canadian dollars would you receive for US\$3,000? Round to the nearest cent
Based on the given exchange rates, if £1 is equal to US$1.2157 and C$1 is equal to £0.6219, we can calculate how many Canadian dollars you would receive for US$3,000. The answer is calculated to the nearest cent.
To calculate the amount of Canadian dollars you would receive for US$3,000, we need to consider the exchange rates between US dollars (USD), British pounds (GBP), and Canadian dollars (CAD).First, we convert US$3,000 to British pounds. Since £1 is equal to US$1.2157, we can divide US$3,000 by the exchange rate to find the equivalent amount in British pounds:
US$3,000 / US$1.2157 = £2,465.48
Next, we convert the amount in British pounds to Canadian dollars. Since C$1 is equal to £0.6219, we can multiply the amount in British pounds by the exchange rate to find the equivalent amount in Canadian dollars:
£2,465.48 * £0.6219 = C$1,532.89.Therefore, you would receive approximately C$1,532.89 for US$3,000, rounded to the nearest cent.
It's important to note that exchange rates fluctuate and may vary depending on the source or institution where the currency exchange is conducted. The rates provided in this answer are based on the given information and are subject to change. It's always recommended to check the current exchange rates before making any currency conversions or transactions.
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Suppose you have a right triangle with side lengths 26, 24, and 10. Which lengths
represent the legs and which length represents the hypotenuse of the triangle?
Use the Pythagorean Theorem to explain how you know.
Answer:
hypotenuse —>26
Legs —> 10 and 24
Step-by-step explanation:
Generally ,the hypotenuse is the longest side .
So in our triangle the hypotenuse is of length 26.
Consequently, the legs are of lengths 24 and 10.
Also ,we can verify that this is right triangle using the Pythagorean theorem:
26^2 = 676
24^2+10^2 = 676
Then
26² = 24²+10².
hi pls help me out with this
what is the range of the possible values of r2? 0 to 1 any positive numerical value -1 to 1 0 to 100
The range of the possible values of r^2 is 0 to 1. It represents the proportion of the dependent variable’s variance that can be explained by the independent variable(s).
The coefficient of determination, often denoted as r^2, measures the proportion of the dependent variable’s variance that can be explained by the independent variable(s) in a statistical model. The value of r^2 ranges from 0 to 1.
A value of 0 for r^2 indicates that the independent variable(s) does not explain any of the variance in the dependent variable. On the other hand, a value of 1 implies that the independent variable(s) fully explain the observed variance in the dependent variable.
Therefore, the range of the possible values of r^2 is 0 to 1. Any positive numerical value within this range indicates a degree of explanatory power, while values outside this range are not meaningful in the context of r^2. It serves as a useful tool for assessing the strength of a statistical relationship and the predictive ability of a model.
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2x^2-9x+9?
I have to simplify
Step-by-step explanation:
Assuming you meant to factor (comment and ill update if you didnt)
we can use the AC method
multiple the A term(2) by the c term(9)
and then factor by grouping \(2x^2+9x+9\\2x^2+9x+18 (We\ use\ 18\ to\ get\ more\ factors,\ then\ we\ set\ it\ back\ to\ 9)\\2x^2+6x+3x+9\\\\2x(x+3)3(x+3)\)\((2x+3)(x+3)\)
In a survey of 60 cars, 25 use diesl, 20 use liquid hydrogen and 22 use electricity. (b) find the number of cars which use diesel but not electricity. (c) find n(d (eul)
Number of cars uses diesel but not electricity = 3/60
What is probability?
The possibility of occurrence a particular event is called probability. It is expressed as the ratio of favorable outcome of an event to the total possible outcome.
What is the probability of the cars use diesel but not electricity?
Total number of cars = 60
number of cars uses diesel = 25
number of cars uses liquid hydrogen = 20
number of cars uses electricity = 22
probability of cars which use diesel = 25/60
probability of cars which uses electricity = 22/60
now, the number of possible cars which uses diesel but not electricity
is 25/60 -22/60 = 3/60
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I'm having trouble solving the system of linear equations. This is the system: 5x + 6y = 50 x - 6y = -26 Can you please help me? Don't give the answer, but can you just explain?
Answer:
y = 5 ; x = 4
Step-by-step explanation:
Given :
5x + 6y = 50 - - - (1)
x - 6y = -26 - - - (2)
From (2)
x = - 26 + 6y
Put - 26 + 6y for x in (1)
5(-26 + 6y) + 6y = 50
-130 + 30y + 6y = 50
-130 + 36y = 50
-130 - 50 = - 36y
-180 = - 36y
y = 180 / 36
y = 5
Put y =5 in x = - 26 + 6y
x = - 26 + 6(5)
x = - 26 + 30
x = 4
y = 5 ; x = 4
A bubble tube of a level has a sensitiveness of 20 ′′
per 2 mm division. Find the error in the reading on the staff held at a distance of 100 m from the level when the bubble is deflected by two divisions from the centre.
The error in the reading on the staff held at a distance of 100 m is approximately 83.91 meters.
To find the error in the reading on the staff, we need to convert the deflection of the bubble into an angular error. The sensitiveness of the bubble tube is given as 20" per 2 mm division, which means that each 2 mm division corresponds to a deflection of 20".
Given that the bubble is deflected by two divisions from the center, the total deflection is 2 divisions * 20" per division = 40".
Next, we need to calculate the angular error. We can use the small angle approximation, which states that for small angles, the tangent of the angle is approximately equal to the angle itself in radians.
Therefore, the angular error can be approximated as 40" * (π/180) radians. Now, to calculate the linear error at a distance of 100 m, we need to consider the relationship between angular error, linear error, and the distance from the level.
This relationship can be expressed as follows:
Linear Error = Distance * Tangent(Angular Error)
In this case, the distance is 100 m, and the angular error is 40" * (π/180) radians. Substituting these values into the equation, we can calculate the linear error:
Linear Error = 100 m * tan(40" * (π/180))
Using a calculator, we find that tan(40" * (π/180)) ≈ 0.8391.
Therefore, the linear error in the reading on the staff held at a distance of 100 m from the level when the bubble is deflected by two divisions from the center is approximately:
Linear Error = 100 m * 0.8391 ≈ 83.91 m.
Hence, the error in the reading on the staff is approximately 83.91 meters.
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Describe the difference between null vs alternative hypothesis
Statistical hypothesis testing employs the null and alternate hypotheses.
The alternative hypothesis of a test expresses the prediction of an effect or relationship based on your study, while the null hypothesis of the test does not yet predict an effect or an association between the variables.
A statement that there is no relationship between two variables is called a null hypothesis. Another hypothesis is that the two variables are statistically correlated.
Alternative unilateral (directional) or the bilateral (non-directional) hypotheses are also possible. Simple, complex, true, and false are the four main categories of null hypotheses. If the p-value is greater than the statistical significance level, null hypothesis is preferred.
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ketch a graph of a function that satisfies each of the following conditions lim f(x) = -1 f(-5) = 4 24-5 lim f(x) = 6 2-4 lim f(x) = 7 41159 f (4) does not exist Q2) Evaluate the limit by dividing out the common factors t(t-5)-24 12- 8t lim Q3) Find the limit lim √1+3x³ using limit properties (rules). Note the Limit Property you use at each step
To sketch a graph of a function that satisfies the given conditions, we can start by determining the behavior around the specified points and limits. For the first condition, the function approaches -1 as x approaches some value. For the second condition, the function has a specific value of 4 at x = -5. For the third condition, the function approaches 6 as x approaches 2 from the left. For the fourth condition, the function approaches 7 as x approaches 4 from the right, but the function value at x = 4 does not exist.
To satisfy the first condition, we can choose a function that approaches -1 as x approaches some value, such as a horizontal line y = -1.
To satisfy the second condition, we can place a point on the graph at (-5, 4) to indicate that the function has a value of 4 at x = -5.
For the third condition, the function approaches 6 as x approaches 2 from the left. We can draw a vertical asymptote at x = 2, with the function approaching 6 as x gets closer to 2 from the left side.
For the fourth condition, the function approaches 7 as x approaches 4 from the right, but the function value at x = 4 does not exist. We can draw an open circle at (4, 7) to indicate that the function has no defined value at x = 4.
To evaluate the limit in Q2, we can divide out the common factors by factoring the quadratic expression t(t-5)-24 = (t-8)(t+3). By canceling out the common factor of (t-8), we can simplify the expression and find the limit.
For Q3, we need to find the limit of √(1+3x³) as x approaches a certain value. To do this, we can use the limit properties and note that the square root function is continuous, so we can evaluate the square root of the limit of the expression inside the square root. By substituting the value of x into the expression inside the square root, we can simplify and find the limit.
By following these steps and considering the given conditions and limit properties, we can sketch a graph that satisfies the conditions and evaluate the limits.
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Misha surveyed students in her school about what writing tool they use. She found that 75 use pens; 30 of the pen users are boys. She also found that 28 boys and 32 girls use pencils. A 4-column table with 3 rows. Column 1 has entries boys, girls, total. Column 2 is labeled pens with entries 30, a, 75. Column 3 is labeled pencils with entries 28, 32, b. Column 4 is labeled total with entries c, d, e. Determine what each letter should be to complete this two-way table. A = b = c = d = e =.
The value of a,b,c,d, and e is 45, 60, 58, 77, and 135 respectively, required to complete the two-way table.
A two-way table shows the connections between two sets of category data visually. Labels are positioned at the top and left sides of the table, which has rows and columns.
The sums for each row are displayed to the right, while the sums for each column are displayed at the bottom.
We must create a two-way table based on the issue to ascertain the worth of each letter.
| Pens | Pencils | Total |
| Boys | 30 | 28 | c |
| Girls | a | 32 | d |
| Total | 75 | b | e |
This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.
Add the entries in the table to get the total and subtract if the total is given and one value is missing.
a= 75-30 = 45
b = 28+32= 60
c= 30+28 = 58
d= 45+32= 77
e= 75+60 = 135
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| Pens | Pencils | Total |
| Boys | 30 | 28 | c |
| Girls | a | 32 | d |
| Total | 75 | b | e |
This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.
Add the entries in the table to get the total and subtract if the total is given and one value is missing.
a= 75-30 = 45
b = 28+32= 60
c= 30+28 = 58
d= 45+32= 77
e= 75+60 = 135
select all of the partial products of 5 x 1,234
[] 20
[] 150
[] 1,000
[] 10,000
FIND THE VOLUME OF EACH FIGURE THANK UUU
Answer:
32
Step-by-step explanation: