The comparison of the mean and median of the data set of the dot plot in the first part and the variability and outlier of the dataset in the box and whiskers plot in the second part are;
First part;
1. The median is greater than the mean.
2. Both the mean and median will increase
Second part;
1. School 1 has greater variability
2. The maximum value of school 1 is not an outlier
3. The new athlete needs to spend 21 hours or more
How can the dot and box and whiskers plots be analyzed?First part;
1. The value in the dot plot are;
10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 19
The number of data points = 36
The mean = The sum of the above data divided by 36
Using an online calculator of data sets, we have;
The mean = 15.194The median = 15.5Therefore;
The median is greater than the mean.2. The addition of 60 to the dataset will increase the number of data points from 36 to 37, thereby changing the median, which is the middle value to the 19th number, which is 16, while the mean value will also increase to 16.405, therefore;
The mean and median will both increaseSecond part;
1. A measure of variability of a box plot is the range, which is the difference between the largest and smallest values.
The range of school 1 is; 16 - 1 = 15
The range of school 2 is; 14 - 1 = 13
Therefore;
School 1 has greater variability.2. The maximum value of school 1 is 16
The inter quartile range of school 1 is; IQR = 10 - 4 = 6
An outlier = Q3 + 1.5 × IQR
The third quartile, Q3, for school 1 = 10Which gives;
An outlier ≥ 10 + 1.5 × 6 = 19
The maximum value for school 1 = 16 < 19, is not an outlier.3. Q3 for school 2 = 12
IQR for school 2 = 12 - 6 = 6
Which gives;
Outlier for school 2 ≥ 12 + 1.5 × 6 = 21
To be considered an upper end outlier in school 2, the student needs to spend 21 hours or more in the weight room.Learn more about dot and box and whiskers plots here:
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Using radicals, write an equivalent expression for the expression 2^1/3
\(~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ 2^{\frac{1}{3}}\implies \sqrt[3]{2^1}\implies \sqrt[3]{2}\)
If lindley requests an extension to file her individual tax return in a timely manner, the latest she could pay her tax due without penalty is::_________
If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
What is an individual tax return?A person or married couple must submit an official form known as an individual tax return to a federal, state, or local taxing authority in order to record any taxable income they received within a certain time period, typically the previous year.
This document is used to determine how much tax was paid in excess of what was required during that time period.
In this case, if Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is:
April 15th.
October 15th.
August 15th.
November 15th.
None of the choices are correct.
Two of the angles of a triangle are 65° What is the measure of the third angle? O 65 O 130° O Cat they O 50
Answer: The answer is 50°
Step-by-step explanation: 65 + 65=130 180-130=50
enter the number that belongs in the green box 34° 5 118°
The length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
First, we find the angle opposite the side length 5 as follows;
180 - (34 + 118) = 28 {sum of interior angles of a triangle}
Using the sine rule;
5/sin28° = ?/sin34°
? = (5 × sin34°)/sin28° {cross multiplication}
? = 5.9556
Therefore, the length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.
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Consider the random walk with drift model
xt = δ + xt-1 + wt for t = 1,2,3,… with x0 = 0 and wt is white noise with mean zero and variance σw2.
a. Show the model can be written as xt = δt + ∑1twk (Hint: Use induction.)
v. Find the mean function and autocovariance function of xt.
c. Determine if xt is stationary.
a. To show that the model can be written as xt = δt + ∑1twk, we can use induction.
For t = 1:
x1 = δ + x0 + w1
= δ + 0 + w1
= δ + w1
So the base case holds.
Assume that the model holds for t = k, i.e., xk = δk + ∑1k wk.
For t = k+1:
xk+1 = δ + xk + wk+1
= δ + (δk + ∑1k wk) + wk+1
= δk+1 + ∑1k+1 wk
Therefore, by induction, the model can be written as xt = δt + ∑1twk.
v. To find the mean function of xt, we can take the expected value of both sides of the model equation:
E[xt] = E[δt + ∑1twk]
= E[δt] + E[∑1twk]
= δt + ∑1tE[wk]
= δt
So, the mean function of xt is given by μt = δt.
To find the autocovariance function of xt, we need to calculate Cov(xt, xs) for s ≠ t.
For s < t:
Cov(xt, xs) = Cov(δt + ∑1twk, δs + ∑1swk)
= Cov(δt, δs) + Cov(δt, ∑1swk) + Cov(∑1twk, δs) + Cov(∑1twk, ∑1swk)
= 0 + 0 + 0 + Cov(∑1twk, ∑1swk)
= Cov(∑1twk, ∑1swk)
= Cov(wt + ∑1t-1wk, ws + ∑1s-1wk)
= Cov(wt, ws) + Cov(wt, ∑1s-1wk) + Cov(∑1t-1wk, ws) + Cov(∑1t-1wk, ∑1s-1wk)
= 0 + 0 + 0 + Cov(∑1t-1wk, ∑1s-1wk)
Since wt and wk are white noise with mean zero and variance σw^2, their covariance is zero unless t = s. Therefore, we have:
Cov(xt, xs) = 0 for s < t
For s > t, the covariance remains zero as well, since we can use the same logic as above.
For s = t, we have:
Cov(xt, xs) = Cov(δt + ∑1twk, δt + ∑1twk)
= Cov(δt, δt) + Cov(δt, ∑1twk) + Cov(∑1twk, δt) + Cov(∑1twk, ∑1twk)
= Var(δt) + Cov(∑1twk, ∑1twk)
= Var(δt) + Var(∑1twk) + 2Cov(∑1twk, ∑1twk)
= Var(δt) + Var(∑1twk) + 2∑1t-1Cov(wk, wk)
= Var(δt) + Var(∑1twk) + 2∑1t-1σw^2
Since δ is a constant and wk is a white noise process, Var(∑1twk) = ∑1tVar(wk) = tσw^2.
Therefore, we have:
Cov(xt, xs) = Var(δt) + tσw^2 + 2∑1t-1σw^2
= Var(δt) + tσw^2 + 2σw^2(t-1)
= Var(δt) + 3tσw^2 - 2σw^2
Finally, we can conclude that the mean function of xt is μt = δt, and the autocovariance function of xt is Cov(xt, xs) = Var(δt) + 3tσw^2 - 2σw^2.
c. To determine if xt is stationary, we need to check if the mean function and autocovariance function are independent of time (t).
In this case, the mean function is μt = δt, which is dependent on time. Therefore, xt is not stationary.
Similarly, the autocovariance function Cov(xt, xs) = Var(δt) + 3tσw^2 - 2σw^2 depends on both t and s, so xt is not stationary.
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2x - 1 = 3x + 8
i ended up getting -7 but i know it’s wrong i just don’t know what i did wrong
Answer:
2x-1=3×+8
Step-by-step explanation:
2×-3x=8+1
-x=9
x=-9
mark runs 5 miles in 40 minutes. if he continues at the same rate can he run 14 miles in 120 minutes
Help me with this Question Please.
Answer:
\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)
Heeeeeloepepepelelelelelelelelelloeoepeoepwp
Answer:
C) E = 118°; T = 118°
-----------------------------------
The given figure is a kite since it has two pairs of congruent sides as marked.
Its one pair of opposite angles are congruent. That is:
∠E ≅ ∠TSum of all interior angles of a quadrilateral is 360°:
m∠W + m∠E + m∠S + m∠T = 36029 + x + 95 + x = 3602x + 124 = 3602x = 360 - 1242x = 236x = 118Both the missing angles are 118°.
Salmon and Federico are choosing a number between 1 & 100, picking a color from ROY G BIV, and picking a letter out of "INDIANA". Either one will go first. State the probability of each situation as a percentage, fraction and decimal.
1. Salmon chooses a composite number, A cool color( G BIV) and an A.
2.Federico chooses a prime number, A color starting with a vowel, and a constanant.
3.Either chooses a number divisible by 7 or 8, any color, and a vowel.
4. Either chooses a number divisible by 5 or 4, blue or green, and L or N
To determine the probabilities, we need to consider the number of favorable outcomes for each situation divided by the total number of possible outcomes.
1.Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)
2. Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7%
3. Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)
4.Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)
1. Salmon chooses a composite number, a cool color (G, B, I, or V), and an A:
a) Composite numbers between 1 and 100: There are 57 composite numbers in this range.
b) Cool colors (G, B, I, or V): There are 4 cool colors.
c) The letter A: There is 1 A in "INDIANA."
Total favorable outcomes: 57 (composite numbers) * 4 (cool colors) * 1 (A) = 228
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 1 (possible letter) = 700
Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)
2. Federico chooses a prime number, a color starting with a vowel (E or I), and a consonant:
a) Prime numbers between 1 and 100: There are 25 prime numbers in this range.
b) Colors starting with a vowel (E or I): There are 2 colors starting with a vowel.
c) Consonants in "INDIANA": There are 4 consonants.
Total favorable outcomes: 25 (prime numbers) * 2 (vowel colors) * 4 (consonants) = 200
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 5 (possible letters) = 3500
Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7% (rounded to one decimal place)
3. Either chooses a number divisible by 7 or 8, any color, and a vowel:
a) Numbers divisible by 7 or 8: There are 24 numbers divisible by 7 or 8 in the range of 1 to 100.
b) Any color: There are 7 possible colors.
c) Vowels in "INDIANA": There are 3 vowels.
Total favorable outcomes: 24 (divisible numbers) * 7 (possible colors) * 3 (vowels) = 504
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 3 (possible letters) = 2100
Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)
4. Either chooses a number divisible by 5 or 4, blue or green, and L or N:
a) Numbers divisible by 5 or 4: There are 45 numbers divisible by 5 or 4 in the range of 1 to 100.
b) Blue or green colors: There are 2 possible colors (blue or green).
c) L or N in "INDIANA": There are 2 letters (L or N).
Total favorable outcomes: 45 (divisible numbers) * 2 (possible colors) * 2 (letters) = 180
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 2 (possible letters) = 1400
Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)
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A package of gum that contains 15 pieces advertises 135 calories per package. Which unit rate can be used to describe this package of gum?
9 calories per piece
9 calories per package
9 pieces per calorie
9 pieces per package
Answer:
9 calories per piece
Step-by-step explanation:
9*15=135
Answer:
Step-by-step explanation:
9 cals per piece
In ABC, BAC=96•8°,AC= 12•4cm and BC=15•6cm. Find
i) ABC,
ii) BCA,
iii) the length of AB,
In the triangle ABC, i) ABC = 52.12° ii) BCA = 31.08° and iii) AB = 8.11cm.
Based on the provided information, ∠ BAC = 96.8°; AC = 12.4cm, and BC = 15.6cm
i) According to the law of sine,
Sin ∠A/a = Sin ∠B/b = Sin ∠C/c where a is the length opposite to ∠A, and so forth.
Hence, based on the information, ∠ABC = ∠B
Sin ∠B/AC = Sin ∠A/BC
Sin ∠B/12.4 = Sin 96.8/15.5
Sin ∠B = (Sin 96.8/15.5)*12.4
∠B = Sin^-1((Sin 96.8/15.5)*12.4)
∠B = 52.12°
ii) As the sum of interior angles of a triangle is 180°. ∠As BCA = ∠C
∠A + ∠B + ∠C = 180
96.8 + 52.12 + ∠C = 180
∠C = 31.08
iii) According to the law of cosine,
c^2 = a^2 + b^2 – 2ab cos C where C is the angle opposite to c.
BC^2 = AB^2 + AC^2 – 2(AB)(AC)cos98.6
15.6^2 = AB^2 + 12.4^2 – 2(AB)(12.4)cos98.6
Solving for AB,
AB = 8.11cm
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Question 9:6 + 3 + 7 Marks Let O = (0,0), and a = (2,-1) be points in R2. SetG = Bd? (0,1) = {v = (x, y) € R2: d2(0,v) < 1} H = Bd: (a, 1) = {v = (x,y) € R2: d1(a, v) <1}(a) Describe G and H in terms of (x, y)-curves alone, and where applicable without making use of any absolute value symbol. (b) Give the set S of all possible values of y if v = (13,y) € H. (c) Sketch G and H in separate Cartesian coordinates systems (x,y), indicating only O, a and all possible x-intercepts and y-intercepts.
G and H in terms of x and y is given by H = \(B^d\)(a, 1) and G = \(B^{d_2}(0, 1)\) , the set S of all possible values of y is x+y≥0 the Cartesian coordinates systems is S = [-7/5, -3/5].
Choosing a point O of the line (the origin), a unit of length, and an orientation for the line are all steps in choosing a Cartesian coordinate system for a one-dimensional space, or for a straight line. The line "is oriented" (or "points") from the negative half towards the positive half when an orientation determines which of the two half-lines given by O is the positive half and which is the negative half. Then, depending on which half-line contains P, the distance between each point P on the line and O can be specified.
a) O = (0, 0) a = (2, -1)∈R²
G = \(B^{d_2}(0, 1)\)
D = \(\sqrt{x^2+y^2}\) < 1
So this is a circle until center at (0, 0) and no point on
\(x^2+y^2\) and every point inside it
H = \(B^d\)(a, 1) = {v=(x,y)∈R²: d(a, v)≤1}
b) x-2 + y=1 ≤ 1
x-y ≤4
For, x-2≤0, y+1≥0 we get,
2-x+y+1≤1 y-x ≤-2
For, x-2≤0, y+1≤0, 2-x-y-1≤1
x+y≥0
c) Therefore,
d(a, (13/5, y) ≤ 1
(13/5 -2) + (y +1) ≤ 1
S = [-7/5, -3/5].
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Hi I am Morgen and I need help on this question.
SOLUTION;
Sold for 5/6 of the original price.
The original price was $90.
The sale price of the baseball glove is;
\(\begin{gathered} \frac{5}{6}\text{ X}\frac{\text{\$90}}{1} \\ \\ \text{ \$75} \end{gathered}\)The sale price of the baseball glove is $75.
The question is find the area of the shaded segment. I just need a brief explanation with the answer
SOLUTION
The formula for area of segment is given to be
\(A=\frac{\theta}{360}\pi r^2-\frac{1}{2}r^2\sin \theta\)From the image
\(\theta=120^{\circ},r=4\)substituting these values gives
\(A=\frac{120}{360}\times\pi(4)^2-\frac{1}{2}(4)^2\sin 120\)Solve for A
\(\begin{gathered} A=\frac{1}{3}\times\pi\times16^{}-\frac{1}{2}\times16\times^{}0.8660 \\ A=16.76-6.93 \\ A=9.83 \end{gathered}\)Therefore, the area of the shaded segment is 9.83 square meters
Consider the following key-value pairs:
(1, a), (4, b), (2, c), (17, d), (12, e), (9, e), (19, f), (4, g), (8, c), (12, f)
Use separate chaining to adde key-value to table. Assume table size is 10. Assume its buckets are using a linked list where new elements are appended to the end. (Hint: Chaining probing)
A) Show your hash table after inserting the above key-value pairs in the order given using the hash function h(x) = (x + 3) % 3.
B) How many collisions occurred
A) The resulting hash table with separate chaining is as follows:
[0: (12, e) -> (9, e) -> (12, f)]
[1: (1, a) -> (4, b) -> (17, d) -> (4, g)]
[2: (2, c) -> (19, f) -> (8, c)]
B) The number of collisions that occurred is 4.
A) To construct the hash table using separate chaining with a table size of 10 and the hash function h(x) = (x + 3) % 3, we will insert the key-value pairs in the given order and handle collisions by appending new elements to the end of the linked list in each bucket.
1. (1, a):
- Hash value: h(1) = (1 + 3) % 3 = 1
- Insert (1, a) into bucket 1: [1: (1, a)]
2. (4, b):
- Hash value: h(4) = (4 + 3) % 3 = 1
- Collision occurs in bucket 1
- Append (4, b) to the linked list in bucket 1: [1: (1, a) -> (4, b)]
3. (2, c):
- Hash value: h(2) = (2 + 3) % 3 = 2
- Insert (2, c) into bucket 2: [1: (1, a) -> (4, b)], [2: (2, c)]
4. (17, d):
- Hash value: h(17) = (17 + 3) % 3 = 1
- Collision occurs in bucket 1
- Append (17, d) to the linked list in bucket 1: [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c)]
5. (12, e):
- Hash value: h(12) = (12 + 3) % 3 = 0
- Insert (12, e) into bucket 0: [0: (12, e)], [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c)]
6. (9, e):
- Hash value: h(9) = (9 + 3) % 3 = 0
- Collision occurs in bucket 0
- Append (9, e) to the linked list in bucket 0: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c)]
7. (19, f):
- Hash value: h(19) = (19 + 3) % 3 = 2
- Insert (19, f) into bucket 2: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c) -> (19, f)]
8. (4, g):
- Hash value: h(4) = (4 + 3) % 3 = 1
- Collision occurs in bucket 1
- Append (4, g) to the linked list in bucket 1: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d) -> (4, g)], [2: (2, c) -> (19, f)]
9. (8, c):
- Hash value: h(8) = (8 + 3) % 3 = 2
- Collision occurs in bucket 2
- Append (8, c) to the linked list in bucket 2: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d) -> (4, g)], [2: (2, c) -> (19, f) -> (8, c)]
10. (12, f):
- Hash value: h(12) = (12 + 3) % 3 = 0
- Collision occurs in bucket 0
- Append (12, f) to the linked list in bucket 0: [0: (12, e) -> (9, e) -> (12, f)], [1: (1, a) -> (4, b) -> (17, d) -> (4, g)], [2: (2, c) -> (19, f) -> (8, c)]
The resulting hash table with separate chaining is as follows:
[0: (12, e) -> (9, e) -> (12, f)]
[1: (1, a) -> (4, b) -> (17, d) -> (4, g)]
[2: (2, c) -> (19, f) -> (8, c)]
B) The number of collisions that occurred is 4.
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Find T,N, and κ for the plane curve r(t)=(5t+1)i+(5−t5)j T(t)=()i+()j (Type exact answers, using radicals as needed.) N(t)=(i)i+(j) (Type exact answers, using radicals as needed.) κ(t)= (Type an exact answer, using radicals as needed).
The unit tangent vector T(t), normal vector N(t), and curvature κ(t) for the given plane curve are T(t) = (5/√(1+t^2))i + (-1/√(1+t^2))j, N(t) = (-1/√(1+t^2))i + (-5/√(1+t^2))j, and κ(t) = 5/√(1+t^2).
To find the unit tangent vector T(t), we differentiate the position vector r(t) = (5t+1)i + (5-t^5)j with respect to t, and divide the result by its magnitude to obtain the unit vector.
To find the normal vector N(t), we differentiate the unit tangent vector T(t) with respect to t, and again divide the result by its magnitude to obtain the unit vector.
To find the curvature κ(t), we use the formula κ(t) = |dT/dt|, which is the magnitude of the derivative of the unit tangent vector with respect to t.
Performing the necessary calculations, we obtain T(t) = (5/√(1+t^2))i + (-1/√(1+t^2))j, N(t) = (-1/√(1+t^2))i + (-5/√(1+t^2))j, and κ(t) = 5/√(1+t^2).
Therefore, the unit tangent vector T(t) is (5/√(1+t^2))i + (-1/√(1+t^2))j, the normal vector N(t) is (-1/√(1+t^2))i + (-5/√(1+t^2))j, and the curvature κ(t) is 5/√(1+t^2).
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That's what I need help with and I need the steps to it, please. Its the fraction one.
Answer:
27
Step-by-step explanation:
27/3 = 9, 27/9 = 3. so
9-3= 3+3
6=6
what is (f-2) for f(x)=-1/2x+5
Answer:
6
f(x)=-.5(-2) + 5
select all the expressions that equal.. *see picture for problem*
Answer:
Step-by-step explanation:
oknjbgfkdfrgn jnfbfl
which graph best represents this system of equations and its solution . 8x-4y=-16 3x+15y=-6
Answer:
B
Step-by-step explanation:
The required graph that represents the system of the equation and their solution is shown. Option D is correct.
Given that,
To determine the graph which shows the system of equation 8x-4y=-16 3x+15y=-6 and their solution,
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The given system of equations is 8x-4y=-16 3x+15y=-6,
The solution of the above equation is given when applying methods like substitution, elimination and sublimation is (-2,0).
Plotting the graph of the system of equations it comes out to be as shown.
Thus, the required graph that represents the system of the equation and their solution is shown. Option D is correct.
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The daily production of soda s for a manufacturing company is modeled by the function s= -p^2 +75p-1200, where pis the
amount of workers present at work. If the break-even point for soda manufacturing is where's=0, what is the least number of
workers the company must have present each day in order to break even?
A. 24 workers
B. 11 workers
C. 32 workers
D. 51 workers
Answer:
A
Step-by-step explanation:
Put '0' in for 's' and solve :
0 = -p^2 + 75 p + 1200
Use Quadratic Formula with a = -1 b=75 c = -1200
to find p = ~ 24 OR 52 THE LEAST NUMBER WOULD BE 24
4×5+-8÷(7×9) what is the answer?
Answer:
19.87301587
Step-by-step explanation:
Answer:
Step-by-step explanation:
Ok, so you would use PEMDAS, which is the correct order in which you would need to solve an equation. The idea is that the operations that come first would have to be solved first.
If you don't know it, PEMDAS is:
Parentheses
Exponents
Multiplication/division
Addition/subtraction
In this case, you would need to solve the parentheses. (7x9) is 63.
It would be rewritten as 4x5-8/63
There are no exponents, so you can skip the next operation.
Then you would do multiplication next, which would be 4x5 = 20
The equation would be rewritten as 20-8/63
-0.126984127 is -8/63
Lastly, 19.8730159 is the result of 20-0.126984127
Hope this helps!
please smart people help me with math (it's asked to: Division into square trinomial multipliers (if possible))
Answer:
M. (4x-1) (x+4)
K. (3x-1)(2x-1)
L.(2x-7)(x+5)
N.3x^2-4x+39
O.(3x-1)(3x+4)
Sorry if it's wrong but that's what I got
Gemma has 24 balls out of 24 balls 12 are yellow for pink and the rest are red what is the ratio of the number of red balls to the number of balls that are either yellow or pink
Answer:
12:12
Step-by-step explanation: 24-12 = 12 red balls therefore the ratio would be 12:12.
2. Tell whether each function is linear. If so, graph
the function.
2y = -4x
The function 2y = -4x is linear and the graph is given below.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.
Here the given function is 2y = -4x.
The function is linear since the exponent of the two variables x and y are 1.
This can be written as,
y = -4x / 2
y = -2x
This is a proportional function with slope -2.
Graph will be a decreasing function.
The points on the graph includes (-2, 4), (-1, 2), (0, 0), (1, -2) and (2, -4).
Hence the graph of the function is given below.
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In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance?
Answer: Yes, because the results are unlikely to occur by chance.
Step-by-step explanation: apparently, the weight loss program has a statistical significance, because the results are likely to also occur by chance. because it occurrs by chance, this applits to a happening which has occurred without an intent, volition, or plan. an event or encounter that occurs by chance usually implies an occurrence of some importance.
What is the length of DE?
A A
12
DXE
A. 6
B. 8
C. 5
D. 7
Answer:
A
Step-by-step explanation:
these two triangles are similar
therefore corresping sides are proportionate
12/8=9/x
12x=72
x=72/12=6
Answer:
the answer is 6
Step-by-step explanation:
i hope this is helpful
prove the identity. sinh(2x) = 2 sinh(x) cosh(x)
To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.
We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.
Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).
Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.
By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.
This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.
Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.
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Ravin gets paid $1000 every two weeks and follows the same spending and saving plan unless
an emergency arises. The first thing Ravin does when he gets paid is immediately put $350 in
his savings account. Next, using online bill pay through his bank, Ravin spends about $400 on
bills such as his cell phone, electricity, and rent. Ravin withdraws $150 in cash for daily
expenses, and leaves the remaining amount ($100) in his checking account. Based upon
information about Ravin's spending and saving habits, which statement is TRUE?
the
Ravin's annual household income is approximately $55,000.
Ravin's income is used exclusively as a medium of exchange for goods and services
Ravin operates on a "cash only" basis, which is a very smart personal finance
decision.
Ravin allocates $350 every two weeks as a store of value in his savings account
Based on the given information about Ravin's spending and saving habits, the true statement is "Ravin allocates $350 every two weeks as a store of value in his savings account.
Ravin gets paid $1000 every two weeks.
Every payday, the first thing he does is he immediately puts $350 in his savings account.
Using online bill pay through his bank, Ravin spends about $400 on bills such as his cell phone, electricity, and rent.
Ravin withdraws $150 in cash for daily expenses, and leaves the remaining amount ($100) in his checking account.
From the given information, we can see that Ravin saves $350 every two weeks in his savings account.
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