Answer:
3²
Step-by-step explanation:
We have to use BPEMDAS Order of Operations:
B - Brackets
P - Parenthesis
E - Exponents
M - Multiply
D - Divide
A - Addition
S - Subtraction
We use this order left to right. Since we have parenthesis, we look at that first. Inside, we have division and exponents. Since exponents come first, we have to evaluate 3² first.
Answer:
square the 3
Step-by-step explanation:
In the order of operations, you must do the exponent inside the parentheses first, so the first step is:
4(27 ÷ 3²) =
= 4(27 ÷ 9)
Answer: square the 3
What else would need to be congruent to show that ABC = XYZ by SAS?
To show that triangle ABC is congruent to triangle XYZ by side-angle-side congruency theorem, BC must be equal to YZ (BC ≅ YZ).
What are congruent triangles?Two triangles are said to be similar if they have the same shape and the corresponding sides are congruent to each other. Also, corresponding angles are congruent.
To show that triangle ABC is congruent to triangle XYZ by side-angle-side congruency theorem, BC must be equal to YZ (BC ≅ YZ).
Find out more on similar triangles at: https://brainly.com/question/2644832
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With steps... Thanks..
Answer:
[tex]\boxed{-25x-y}[/tex]
[tex]\boxed{-p^2q +5pq^2}[/tex]
Step-by-step explanation:
[tex](-15x+6y)-(10x+7y)[/tex]
Distribute negative sign.
[tex]-15x+6y-10x-7x[/tex]
Combine like terms.
[tex]\boxed{-25x-y}[/tex]
[tex]2pq(p+q)- (3pq(p-q))[/tex]
Expand brackets.
[tex]2p^2 q+2pq^2 -(3p^2q-3pq^2)[/tex]
Distribute negative sign.
[tex]-3p^2q+3pq^2+2p^2q+2pq^2[/tex]
Combine like terms.
[tex]\boxed{-p^2q +5pq^2}[/tex]
Answer:
a. -25x - yb. pq ( - p + 5q )Step-by-step explanation:
a.
[tex] - 15x + 6y - (10x + 7y)[/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] - 15x + 6y - 10x - 7y[/tex]
Collect like terms
[tex] - 15x - 10x + 6y - 7y[/tex]
[tex] - 25x - y[/tex]
b.
[tex]2pq(p + q) - 3pq(p - q)[/tex]
Factor out pq from the expression
[tex]pq(2(p + q) - 3(p - q))[/tex]
Distribute 2 through the parentheses
[tex]pq \: (2p + 2q - 3(p - q)[/tex]
Distribute -3 through the parentheses
[tex]pq \: (2p + 2q - 3p + 3q)[/tex]
Collect like terms
[tex]pq( - p + 5q)[/tex]
Hope this helps...
Best regards!!
Find the equation of the line.
Answer:
y = -2x + 5
Step-by-step explanation:
You use the equation y = mx + b, where m is the slope and b is the y-intercept. We see that the line hits the y-axis at 5, so that will be your b. To find the slope, use [tex]\frac{rise}{run}[/tex]. You have to go down 4 and right 2, so your slope will be [tex]-\frac{4}{2}[/tex] which simplifies to -2. Hope this helps!
Answer: y=2/-5x+5
Step-by-step explanation:
1. 2² X 5⁵ 2⁴ 2. (6⁵)² 6⁷ 3.(2x7)⁵ 7⁴ toloong
Answer:
1. 2⁶
2. 6⁷
3. 14⁵
Step-by-step explanation:
We assume and apply the laws of logarithms and indices in the problems above.
1. Product Rule Law: which states that
loga (MN) = loga M + loga N
Where 2² X 5⁵ = 2²+⁵ = 2⁷
2. The Power rule: in which (6⁵)² = 6⁵+² = 6⁷
3. (2x7)⁵ = (14)⁵ or 5 log 14
plz help me if you can
Answer:
Hey there!
These triangles can be proved congruent by the HL Theorem.
Hope this helps :)
Hey Mate!!
Your answer will be HL Theorem.
Because, Since the triangles overlap, their hypotenuses are the same side and therefore congruent by the reflexive property. This means the triangles are congruent by a hypotenuse, leg and right angle. This is known as HL.
☆ Good Luck ☆
♡ Comments down ♡
By ◇~Itsbrazts ◇~
12)
Solve the problem.
12) A commercial building contractor is trying to decide which of two
projects to commit her company to.
Project A: a profil of $50,000 with a probability of 0.6, a profit of $90,000
with a probability of 0.3, and a profit of $10,000 with a probability of 0.1.
Project B: a profit of $100,000 with a probability of 0.1, a profit of $64,000
with a probability of 0.7, and a loss of $20,000 with a probability of 0.2.
Find answer lines 1 & 2)the expected profit for each & (answer line 3
which project should be selected.
Answer:
Project A : $58,000
Project B: $52800
Project A should be selected as it has a higher expected profit value than project B
Step-by-step explanation:
Given the following:
PROJECT A:
Profit : ---------50000--90,000--10,000
Probability: ----0.6-------0.3--------0.1
PROJECT B:
Loss of 20,000 = -20,000 in profit terms
Profit : -----100,000--64,000--(-20,000)
Probability: ----0.1-------0.7--------0.2
Expected profit:
Profit value * probability of profit
Expected profit on project A:
[(50000*0.6)+(90000*0.3)+(10000*0.1)
30000 + 27000 + 1000 = $58000
Expected profit on project B:
[(100000*0.1)+(64000*0.7)+(-20000*0.2)
10000 + 44800 - 4000 = $50800
Project A should be selected as it has a higher expected profit value than project B
find the coordinates of the point first whose abscissa is -5 and ordinate is 4
Answer:
The coordinate of the point is (-5, 4)
Step-by-step explanation:
In a regular two dimensional graph, the abscissa is the horizontal or x - axis while the y-axis which is the vertical axis is referred to as the ordinate
Abscissa and ordinate are used in mathematics to indicate the coordinate of a point in a two dimensional coordinate system, where the abscissa and ordinate are placed in between a parenthesis, with the abscissa being on the left and the ordinate on the right separated by a comma.
Use special right triangles to solve for the exact value of x. 4 16 9
Answer:
16
Step-by-step explanation:
I took the test and that's the answer.
Answer:
16
Step-by-step explanation:
CHECK THE ATTACHMENT FOR THE FIQURE OF THE QUESTION;
✓The given figure is a special right triangle and it's a 30° 60° 90° angle.
The length of its side have the ratio of
1: √3: 2 i.e adjacent, opposite, Hypotenuse
✓ it has an Hypotenuse which is double in value to the adjacent.
✓ the adjacent ( shortest sides) = 8 unit,
Then the Hypotenuse= ( 2×8)= 16 units
I need helpppppppppppppppppp
Answer:
A:
9×1=9
9×2=18
9×3=27
9×4=36
9×5=45
9×6=54
9×7=63
9×8=72
9×9=81
9×10=90
B:
It goes down by 1 after multiplying a bigger number.
C:
It goes up by 1 after multiplying a bigger number.
Step-by-step explanation:
hope this helps you and have a great day
There are 4 pieces of paper, numbered 10 to 13, in a hat. After another numbered piece of paper is added, the probability of picking a number between 10 and 13 inclusive is 4/5. Which of the following numbers could
Answer: The fifth piece of paper could have any number 9 and less or 14 and greater.
Step-by-step explanation: The list of choices is not given in the question, but it makes sense that the new number would not be a duplicate of any of the numbers 10, 11, 12, 13. Otherwise that would change the probability to 5/5.
So any other number could be a possibility.
Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C. I, II, and III D. I, only
Answer:
Correct answer:
A. I and II
Step-by-step explanation:
First of all, let us have a look at the steps of finding inverse of a function.
1. Replace y with x and x with y.
2. Solve for y.
3. Replace y with [tex]f^{-1}(x)[/tex]
Given that:
[tex]I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3[/tex]
Now, let us find inverse of each option one by one.
I. y = x, a(x) = x
Replacing y with and x with y:
x = y
x = [tex]a^{-1}(x)[/tex] = [tex]a(x)[/tex] Hence, I is true.
II. [tex]y =\dfrac{1}{x}[/tex]
Replacing y with and x with y:
[tex]x =\dfrac{1}{y}[/tex]
[tex]x=\dfrac{1}{a^{-1}(x)}[/tex]
[tex]\Rightarrow a^{-1}(x) = \dfrac{1}{x}[/tex]
[tex]a^{-1}(x)[/tex] = [tex]a(x)[/tex] Hence, II is true.
III. [tex]y =x^{2}[/tex]
Replacing y with and x with y:
[tex]x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)[/tex]
Hence, III is not true.
IV. [tex]y =x^{3}[/tex]
Replacing y with and x with y:
[tex]x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)[/tex]
Hence, IV is not true.
Correct answer:
A. I and II
Jillian has three different bracelets (X, Y, and Z) to give to her friends as gifts in any order she prefers. If bracelet Y is chosen first, in how many ways can Jillian give out the bracelets?
Answer:
B. 2
Step-by-step explanation:
ed2020
If Y bracelet is chosen first then there will be only two ways to give out the bracelets.
What are permutation and combination?
When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.
The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.
Given that Jillian has three bracelets
X, Y, and Z
Said that Y has chosen first
The remaining bracelets are X and Z
Number of ways
[Y] X, Z [Y] Z, XIt means there are only two ways to give out bracelets.
Hence "If Y bracelet is chosen first then there will be only two ways to give out the bracelets".
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HELP ASAP. Please select the best answer from the choices provided.
Answer:
a.
Explanation:
In the chart, the average temperature of each month at the beginning of the year gradually rises until August, where it begins to decrease. This trend is displayed in graph a. Additionally, each month on the x-axis is shown correctly because the months should only span numbers 1-12.
Answer: the answer is A
Step-by-step explanation: hope this helps :D can u plz give a brainliest
first correct answer gets best marks
Answer:
the answer would be x is less than 6.
Step-by-step explanation:
the reason why it would not be x is less than or equal to 6 is that the circle is not filled in.
Answer:
B
Step-by-step explanation:
x≤6
We can see from the graph that it starts from 6 and goes to 5, 4, 3, 2.
Hope this helps ;) ❤❤❤
How do the functions compare over the interval The exponential grows at approximately half the rate of the quadratic. The exponential grows at approximately the same rate as the quadratic. The exponential grows at approximately twice the rate of the quadratic. The exponential grows at approximately four times the rate of the quadratic. Mark this and return
Answer:
Correct Option: B
Step-by-step explanation:
Linear functions are the type of functions that are applied to model occurrences that rise or fall at a constant proportion. These sorts of functions are polynomial functions with a maximum exponent of one on the variable. The graphs of these kind of functions are in the form of a line.
Exponential functions are the type of functions that have the variable in exponent form. The growth rate or decline rate is either slow than quick or quick than slow.
Quadratic functions are of the form f (x) = ax² + bx + c. The graph of this function is in the form of a parabola. The graph first increases, hit a maximum, then decreases or decreases, hit a minimum, then increases.
From the provided graphs it can be seen that, the exponential function grows at approximately the same rate over the interval 0 ≤ x ≤ 1 as the quadratic function.
Answer:
bbb
Step-by-step explanation:
what is the measures of ∠x
Answer:
x = 64
Step-by-step explanation:
∠ HIA and ∠ LJK are corresponding angles and congruent, thus
∠ HIA = 60°
The sum of the 3 angles in Δ HIA = 180° , thus
x = 180 - (60 + 56) = 180 - 116 = 64
6. A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 students to turn in tests was 78. Using the .05 significance level, was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
Answer: Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
Step-by-step explanation:
Given that;
U = 75
X = 78
standard deviation α = 10
sample size n = 20
population is normally distributed
PROBLEM is to test
H₀ : U = 75
H₁ : U ≠ 75
TEST STATISTIC
since we know the standard deviation
Z = (X - U) / ( α /√n)
Z = ( 78 - 75 ) / ( 10 / √20)
Z = 1.3416 ≈ 1.342
Now suppose we need to test at ∝ = 0.05 level of significance,
Then Rejection region for the two tailed test is Zc = 1.96
∴ Reject H₀ if Z > Zc
and we know that Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.
At the null hypothesis, we test if the mean is of 75, that is:
[tex]H_0: \mu = 75[/tex]
At the alternative hypothesis, we test if the mean is different of 75, that is:
[tex]H_1: \mu \neq 75[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
X is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation.n is the size of the sample.For this problem, we have that:
[tex]X = 78, \mu = 75, \sigma = 10, n = 20[/tex]
The value of the test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}[/tex]
[tex]z = 1.34[/tex]
Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.
Looking at the z-table, z = -1.34 has a p-value of 0.0901.
2(0.0901) = 0.1802
The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.
A similar problem is given at https://brainly.com/question/15535901
Find the length of AB , given A(5,-2) and B(-3,-4)
Answer:
sqrt(68) is the length.
Step-by-step explanation:
For this you will use the distance formula, sqrt((x2-x1)^2+(y2-y1)^2)
So for this it is sqrt((5+3)^2+(-2+4)^2)
sqrt(64+4)
sqrt(68)
8.246
Which of the following describes the zeroes of the graph of f(x) = –x^5 + 9x^4 – 18x^3?
Answer:
second option
Step-by-step explanation:
Given
f(x) = - [tex]x^{5}[/tex] + 9[tex]x^{4}[/tex] - 18x³
To find the zeros let f(x) = 0, that is
- [tex]x^{5}[/tex] + 9[tex]x^{4}[/tex] - 18x³ = 0 ( multiply through by - 1 )
[tex]x^{5}[/tex] - 9[tex]x^{4}[/tex] + 18x³ = 0 ← factor out x³ from each term
x³ (x² - 9x + 18) = 0 ← in standard form
x³(x - 3)(x - 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x³ = 0 ⇒ x = 0 with multiplicity 3
x - 3 = 0 ⇒ x = 3 with multiplicity 1
x - 6 = 0 ⇒ x = 6 with multiplicity 1
Answer: It is B
Step-by-step explanation: Checked on a online calculator.
A 13-foot ladder is leaning against a tree. The bottom of the ladder is 5 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
Answer:
12 feet
Step-by-step explanation:
It's a classic 5-12-13 triangle or you can used the Pythagorean Theorem:
[tex]13^{2} -5^{2}=x^{2} \\169-25=x^{2} \\144=x^{2} \\12=x[/tex]
Answer:
The tree is 12 about feet high.
Step-by-step explanation:
The way to find the answer is with Pythagorean Theorem.
The ladder is 13 feet and is the hypotenuse or c.
13^2
The 5 feet away from the tree is one of the two legs or a
5^2
We are trying to find the second leg, b.
b^2
Now you write the formula:
c^2=a^2+b^2
Then insert the numbers:
13^2=5^2+b^2
The isolate the variable:
Subtract 5^2 on each side
13^2 - 5^2=b^2
Now flip the expression so the variable is on the left side:
b^2=13^2 - 5^2
Simplify:
b^2=169 - 25
Simplify:
b^2= 144
Square root both sides to get the variable alone:
srt b^2 is b
srt 144 is 12
b=12
Don't forget units!
The tree is 12 feet high
Find the fraction half way between 1/7 and 1/5
Answer:
6/35
Step-by-step explanation:
add ¹/7+¹/5 =12/35
divide 12/35 by 2
=6/35
A rectangular playground has an area of 180 square yards. The length of the playground is 3 yards longer than the width. Find the length of the playground.
A)15 yards
B)18 yards
C)12 yards
D)13 yards
Answer: The length is 15 yards so the answer is A.
Step-by-step explanation:
If the length is 3 more than the width the we will represent it by the equation L = w+3 where w is the width and to find the area of a rectangle, we need to multiply the length by the width. so the length is w+3 and the width is w so
w(w+3) = 180 solve for the w
w^2 + 3w = 180 subtract 180 from both sides
w^2 + 3w -180 = 0 find two numbers that their product is -180 and add to 3.
the number 12 and -15 works out because -12*15= -180 and -15+ 12 =3
We will now have a new quadratic equation as
w^2 - 12w + 15w - 180 = 0 factor by grouping
w(w-12) 15(w-12)= 0 factor out w-12
(w-12)(w+15) = 0 set them both equal zero.
w -12 = 0 or w+15= 0
w = 12 or w = -15
Since we know that -15 can't represent a distance, then 12 is the width .
So if we are to find the length and it gives us the information that the length is 3 yards more that the width then we will add 3 to the width to equal the length.
L= 12 +3
L = 15
The length of the rectangular playground is 15 yards. The correct answer would be an option (A).
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Since the length is 3 more than the width
So, we will represent it by the equation L = W+3 ...(i)
A rectangular playground has an area of 180 square yards
So, L × W = 180
Substitute the value of equation (i), and we get
W(W+3) = 180
W² + 3W = 180
W² + 3W -180 = 0 ...(i)
Solving the above quadratic equation, we get the values of W :
W = 12 and W = -15
Take positive value because dimensions can't be negative.
Substitute the value of W = 12 in equation (i), and we get
L = 12 + 3 = 15
Therefore, the length of the playground is 15 yards.
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can anyone help me solve this function?
f-g means to subtract g from f:
(4^x - 8) - (5x+6)
Remove the parenthesis and change the equations sings for g:
4^x-8 -5x -6
Combine like terms:
4^x - 5x - 14
The answer is A.
Nolan plots the y-intercept of a line at (0, 3) on the y-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan’s line? y = 2x + 1 y = 2x + 3 y = 3x + 2 y = 3x + 5
Answer:
The answer is
y = 2x + 3Step-by-step explanation:
Equation of a line is y = mx + c
Where m is the slope
c is the y intercept
From the question the y intercept is 3
and the slope is 2
Substituting the values into the above equation
We have
y = 2x + 3Hope this helps you
The equation of a line that passes through [tex](0,3)[/tex] and a slope [tex]2[/tex] is [tex]y=2x+3[/tex].
The equation of a line that passes through a point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is:
[tex](y-y_1)=m(x-x_1)[/tex]
Here, the point is [tex](0,3)[/tex] and the [tex]slope[/tex] is [tex]2[/tex].
So, [tex]x_1=0, y_1=3[/tex] and [tex]m=2[/tex].
So, the equation of the line is
[tex](y-y_1)=m(x-x_1)[/tex]
[tex](y-3)=2(x-0)[/tex]
[tex]y-3=2x-0[/tex]
[tex]y=2x+3[/tex]
So, option B is correct.
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Maya is interning at a law firm over the summer and is paid by the hour. If her hourly wage is $52, which equation represents the proportional relationship between the wages she earns (w) and the number of hours (h)?
Answer: w= 52h
Step-by-step explanation:
Given: Maya is interning at a law firm over the summer and is paid by the hour.
Her hourly pay = $52
i.e. She is paid $52 per hour.
Let the wages she earns is denoted by 'w' and the number of hours is denoted by 'h'.
Now, (Total wages earned) = (hourly pay) x (Number of hours)
w = (52) (h)
⇒ w= 52h
Hence, the equation represents the proportional relationship between the wages she earns (w) and the number of hours (h): w= 52h
Answer:52h
Step-by-step explanation: tried got it right
3. Consider the sequence,-8, -5, -2, 1, ...
a) Determine the explicit formula for the general term, 1,, of this sequence in simplified
form. (2 marks)
b) Use this formula to determine the value of t20. (1 mark)
c) Algebraically determine which term has a value of 40. (1 mark)
Answer:
a) [tex]a_n=3\,n-11[/tex]
b) [tex]a_{20}=49[/tex]
c) term number 17 is the one that gives a value of 40
Step-by-step explanation:
a)
The sequence seems to be arithmetic, and with common difference d = 3.
Notice that when you add 3 units to the first term (-80, you get :
-8 + 3 = -5
and then -5 + 3 = -2 which is the third term.
Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:
[tex]a_n=a_1+(n-1)\,d[/tex]
That in our case would give:
[tex]a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11[/tex]
b)
Therefore, the term number 20 can be calculated from it:
[tex]a_{20}=3\,(20)-11=60-11=49[/tex]
c) in order to find which term renders 20, we use the general form we found in step a):
[tex]a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17[/tex]
so term number 17 is the one that renders a value of 40
solve for e.
0.75(8 + e) = 2 - 1.25e
Answer:
e = -2
Step-by-step explanation:
Well to solve for e in the following equation,
.75(8 + e) = 2 - 1.25e
We need to distribute and use the communicative property to find e.
6 + .75e = 2 - 1.25e
-2 to both sides
4 + .75e = -1.25e
-.75 to both sides
4 = -2e
-2 to both sides
e = -2
Thus,
e is -2.
Hope this helps :)
Which is the simplified form of the expression ((2sqrt-2)(3sqrt4))sqrt-3 * ((2sqrt-3)(3sqrt2))sqrt2
Answer:
[tex]\boxed{-432\sqrt{2} i}[/tex]
Step-by-step explanation:
[tex]( 2 \sqrt{-2} )( 3 \sqrt{4} ) \sqrt{-3} \times ( 2 \sqrt{-3} )( 3 \sqrt{2} ) \sqrt{2}[/tex]
[tex]2 \times \sqrt{-2} \times 3 \times \sqrt{4} \times \sqrt{-3} \times 2 \times \sqrt{-3} \times 3 \times \sqrt{2} \times \sqrt{2}[/tex]
[tex]2 \times \sqrt{-2} \times 3 \times 2 \times \sqrt{-3} \times 2 \times \sqrt{-3} \times 3 \times 2[/tex]
[tex]2 \times \sqrt{-2} \times 3 \times 2 \times -3 \times 2 \times 3 \times 2[/tex]
[tex]-432\sqrt{2}\sqrt{-1}[/tex]
[tex]-432\sqrt{2} i[/tex]
Answer: it’s d!
Step-by-step explanation:
In a fiftness class, there was a warm up of 14 press-ups. Anyone unable to do 14 or more recives a punishment. Jessica can do 10 press-ups without ever failing, however, the chances of her successfully doing each subsequent press-up halves. Whats the probality of her receiving a punishment? A. 1 in 8 B. 1 in 1024 C. 15 in 16 D. 1023 in 1024
Answer:
The correct option is;
C. 15 in 16
Step-by-step explanation:
The given information are;
The number of press-ups required = 14 press-ups
The number of press-ups Jessica is sure to do = 10 press-ups
The chance of Jessica doing subsequent press-ups after 10 halves each time
The consequence of not completing the 14 press-ups = Punishment
The probability that Jessica does goes on to do 11 press-ups = 1/2
The probability that Jessica does goes on to do 12 press-ups = 1/2×1/2
The probability that Jessica does goes on to do 13 press-ups = 1/2×1/2×1/2
The probability that Jessica does goes on to do (completes) 14 press-ups = 1/2×1/2×1/2×1/2 = 1/16
Therefore;
Since the probability that Jessica does not receive a punishment because she completed the 14 push-ups is 1/16, we have;
The probability that Jessica does not complete the 14 press-ups and receives a punishment = 1 - 1/16 = 15/16 which is 15 times out of 16 or 15 in 16.
Choose the Δ that seems to be congruent to the given one. [D - top left] [C - top right] [E - center] [A - bottom left] [B - bottom right] ΔBEC ≅ Δ AEB AED ABD (You guys are probably not gonna get to this in time so I'm putting this out there for the future of you that are gonna need it :) )
Answer:
Δ BEC ≅ Δ AED
Step-by-step explanation:
Consider triangles BCA and ADB. Each of them share a common side, AB. Respectively each we should be able to tell that AD is congruent to BC, and DB is congruent to CA, so by SSS the triangles should be congruent.
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So another possibility is triangles BEC, and AED. As you can see, by the Vertical Angles Theorem m∠BEC = m∠ADE, resulting in the congruency of an angle, rather a side. As mentioned before AD is congruent to BC, and perhaps another side is congruent to another in the same triangle. It should be then, by SSA that the triangles are congruent - but that is not an option. SSA does is one of the exceptions, a rule that is not permitted to make the triangles congruent. Therefore, it is highly unlikely that triangles BEC and AED are congruent, but that is what our solution, comparative to the rest.
Δ BEC ≅ Δ AED .... this is our solution