Answer:
The club leader needs $73 for pizzas for 9 students.
Step-by-step explanation:
p(x) = 2x +1
r(x) = 4x − 3
r(p(x)) = 4(2x +1) − 3
r(p(x)) = 8x +4 − 3
r(p(x)) = 8x +1
r(p(9)) = 8(9) +4 − 3
r(p(9)) = 72 +1
r(p(9)) = $73
A recipe requires 3.5 teaspoons of sugar to make a tart. which equation shows the number of teaspoons of sugar, y, needed to make x tarts? x = 3.5y y = 3.5x y = 3.5 x x = 3.5 y
x = 3.5y equation shows the number of teaspoons of sugar, y, needed to make x tarts.
What is the linear equation in two variable?
Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called linear equation in two variable.
According to the given question
A recipe require 3.5 teaspoons of sugar to make a tart.
y represents the number of teaspoons of sugar.
x represents the number of tarts.
Now, for x tart 3.5y teaspoons of sugar required.
⇒ x = 3.5y
Hence, the linear equation in two variable that shows the number of teaspoons of sugar y, needed to make x number or tarts is x = 3.5y.
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A teacher gave her class two tests. 50% of the class passed the first
test, but only 25% of the class passed both tests. What percentage of
those who passed the first test also passed the second test? %
25
100
50
12.5
Answer: 50
Step-by-step explanation:
50% of the class passed the first test, so that 25% that passed both test has to be part of the 50% that passed the first test. 25% that passed both is 50% of the 50% that passed the first test. Hopefully that makes sense.
Find the radius of convergence R, then determine the interval of convergence
By the ratio test, the series converges for all [tex]x[/tex], since
[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(k+1)^2 x^{k+4}}{(k+1)!} \cdot \frac{k!}{k^2 x^{k+3}}\right| = |x| \lim_{k\to\infty} \frac{(k+1)^2 k!}{k^2 (k+1)!} = |x| \lim_{k\to\infty} \frac1{k+1} = 0 < 1[/tex]
Then the radius of convergence is R = ∞, and the interval of convergence is the entire real line, -∞ < x < ∞.
The radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.
Find the radius of convergence R and the interval of convergence:Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = β
If β < 1, then the series convergesIf β > 1, then the series divergesIf β = 1, then the series inconclusiveHere aₙ = (n²/n!) xⁿ⁺³ and aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴
Now limit is taken,
[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} /(n+1)!) x^{n+4} }{(n^{2} /n!) x^{n+3} } |[/tex]
= [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} ) n!x^{n+4} }{(n+1)!(n^{2} ) x^{n+3} } |[/tex]
= [tex]\lim_{n \to \infty} | \frac{((1+1/n)^{2} ) x }{(n+1)} |[/tex]
= [tex]\lim_{n \to \infty} | \frac{ x }{(n+1)} |[/tex] = 0 < 1
Since the limit is less than 1 the series is converging.
We get that,
interval of convergence = (-∞, ∞)
radius of convergence R = ∞
Hence the radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series.
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What is the equation in slope-intercept form for the line that passes through the points (-2, -1) and (1, 5)?
Answer:
Step-by-step explanatio
Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x.
What is the value of x?
The value of x from the given diagram is 20
Triangular altitude theoremAccording to theorem, the right triangle altitude theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.
Using the theorem above;
RT^2 = 9 * 16
RT^2 = 144
R = 12 units
Determine the value of x using the Pythagoras theorem;
x² =12² + 16²
x² = 144 + 256
x² = 400
Take the square root of both sides
x = √400
x = 20
Hence the value of x from the given diagram is 20
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Sariah has just begun training for a half-marathon, which is latex: 13.1 13 . 1 miles. since she was on vacation, she started the training program later than the rest of her running club. there are latex: 6 6 weeks of training runs remaining before the race. in her first week of training, sariah ran latex: 3 3 miles. she ran latex: 4.5 4 . 5 miles the second week and latex: 6 6 miles the third week. if she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance? describe how you would solve this problem using polya's four-step problem-solving method. complete each task as part of your response. be sure to number your answers task 1–task 4 so that your instructor can tell which part you are answering. otherwise, you may not receive credit.
Sariah has just begun training for a half-marathon, which is latex: 13.1 13 . 1 miles. since she was on vacation, she started the training program later than the rest of her running club. there are latex: 6 6 weeks of training runs remaining before the race. in her first week of training, sariah ran latex: 3 3 miles. she ran latex: 4.5 4 . 5 miles the second week and latex: 6 6 miles the third week. if she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance? describe how you would solve this problem using polya's four-step problem-solving method. complete each task as part of your response. be sure to number your answers task 1–task 4 so that your instructor can tell which part you are answering. otherwise, you may not receive credit. Understand the problem.
Task 1: Read the problem and restate in y0ur own words what the question asks.
2. Formulat3 a plan.
Task 2: Identify the model y0u would use to represent the problem and explain why y0u chose that model.
3. Implement th3 plan.
Task 3: Solve the problem and state y0ur answer.
4. Review th3 results.
Task 4: Explain the problem-solving process and how y0u know y0ur answer is correct.
What is half-marathon?Half of a marathon's distance, or 21.0975 kilometers (13 miles 192.5 yards), is covered during a half marathon. Using nearly the same course with a later start, an earlier finish, or shortcuts, a half marathon event is sometimes held alongside a marathon or a 5K race. If finisher medals are given out, they might not look exactly like the ones given out for the full marathon. Although these measurements are rounded and not officially correct, the half marathon is frequently referred to as a 21K, 21.1K, or 13.1 miles.
The International Association of Athletics Federations recognizes a half marathon world record.
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6x+4y-3z,7x-11y-9z,14x+8y-6z
Step-by-step explanation:
i donot know
sorry about this
Rewrit using factored form solve using zero product property
Answer:
Step-by-step explanation:
a. d^2 - 7d + 6 = 0
(d - 1)(d - 6) = 0
d - 1 = 0, d - 6 = 0 therefore:
d = 1, 6.
b, x^2 + 18x + 81 = 0
(x + 9)(x + 9) = 0
x = -9 multiplicity 2.
c u^2 + 7u - 60 = 0
(u + 12)(u - 5) = 0
u = -12, 5.
If point O represents the origin, PQ = 12 units, and P'Q' = 3 units, find the scale factor. (Note: point O represents the origin, what is the scale factor to dilate a shape on the other side of the origin?)
Answer:
1/4
Step-by-step explanation:
To transform PQR into P'Q'R, dilate the preimage by 1/4, or shrink it by a scale factor of 4 because 3/12 = 1/4
Find the midpoint of UV thanks so much
Answer:
(0, -5/2).
Step-by-step explanation:
The coordinates of the mid point of (x1, y1) and (x2, y2) are
(x 1 + x2)/2 , (y1 + y2)/ 2
So here we have:
(-3 + 3)/ 2, (-4 + -1)/2
= 0/2, -5/2
= (0, -5/2).
I am a 2-dimensional shape with all my sides of equal length.
I have an angle sum of 180 degrees.
What am I?
Answer:
=> Equilateral Triangle
Step-by-step explanation:
Equilateral Triangle is having 2-d shape with all equal sides and the sum of angles of any triangle is 180° .
What is the vertex of the graph of the function f(x)=x^2+8x-2 !?
Answer:
(-4, -18).
Step-by-step explanation:
f(x = x^2 + 8x - 2 Completing the square on x^2 + 8x:-
= (x + 4)^2 - 16 - 2
= (x + 4)^2 - 18
- which is the vertex form of f(x)
The vertex of
(x - h)^2 + k is at (h, k)
So the vertex of f(x) is at (-4, -18)
JUST NEEDDD A BIT OF HELPPP PLSS
Answer:
They are all true except for D
Step-by-step explanation:
What they are asking you to do, is take your rectangle and flip it over the top. QR would stay right where it is and line ST would now be on top and line QR would be the bottom. If you can picture that, you can see that all the statements would be true but D.
Logistic regression analyses require that your single dependent variable is a ratio variable.
a. true
b. false
14. The average age of 4 siblings is 12.5 years. If 3 of the siblings are 12-year-old triplets, how old is the fourth sibling? (A) 11.5 (B) 13 (C) 13.5 (D) 14
Answer:
D) 14
Step-by-step explanation:
12+12+12 is 36 we don't know hold old the fourth sibling is so they are X
to get the average of 12.5 you need to add all the siblings ages then divide it by 4
(36+X)/4=14 so the other sibling is 14
Answer:
B
Step-by-step explanation:
12.5x3=37.5
37.5 +11.5 =49
49÷4 =12.25
If a doctor charges $500 per hour for her services, how much would it cost to hire this doctor for 45 minutes?
It will cost $375 to hire the doctor for 45 minutes
The doctor charges $500 for an hour
60 minutes makes 1 hour
60 minutes= $500
Therefore the amount that will be charged for 45 minutes can be calculated as follows
60 minutes= $500
45 minutes= x
Cross multiply both sides
60x= 500×45
60x= 22500
x= 22500/60
x= 375
Hence it will cost $375 to hire the doctor for 45 minutes
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The function yp(t)=ln(3 2t), t>−32, is a particular solution to the differential equation y′′ 7y=g(t). find g(t)?
This might help a bit, i hope
How many pages are in a book, if the total numbering on all the pages ( from the first to the last) required 720 digits?
Solving a linear equation, we conclude that the book has 276 pages in total.
How many pages has the book?From pages 1 to 9, each page needs one digit, so at this point we have 9 digits.
From page 10 to 99, each one needs 2 digits. Then in these pages we have:
(99 - 9)*2 = 180 digits.
So at this point we have 180 + 9 = 189 pages.
Now, for each page after this point, we will add 3 digits more.
So if there are x pages after this point, the total number of digits will be:;
N = 189 + x*3
Now we need to solve this linear equation for N = 720 digits, then:
720 = 189+ x*3
720 - 189 = x*3
531 = x*3
531/3 = x = 177
So there are 177 pages after page number 99, this means that the book has:
99 + 177 = 276 pages in total.
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Use a comparison test (either normal or limit) to determine whether the following series converges or diverges. Be sure to clearly identify what you are comparing too and if that converges or diverges.
By the comparison test, the series converges.
We have
[tex]\dfrac1{k\sqrt{k+2}} \le \dfrac1{k \sqrt k} = \dfrac1{k^{3/2}}[/tex]
so we can compare to a convergent [tex]p[/tex]-series,
[tex]\displaystyle \sum_{k=1}^\infty \frac1{k\sqrt{k+2}} \le \sum_{k=1}^\infty \frac1{k^{3/2}} < \infty[/tex]
By the comparison test, the series converges.
What are convergence series and diverging series?
If the infinite series converges to a real number it is called converging if not then it is called diverging series.
If the larger series is convergent the smaller series must also be convergent. Likewise, if the smaller series is divergent then the larger series must also be divergent.
For this series to be converging it must follow the following :
⇒ [tex]| \frac{t_{n+1} }{t_{n} } | \leq 1[/tex]
⇒Putting n = 1
[tex]| \frac{t_{2} }{t_{1} } | \leq 1[/tex]
[tex]\t_{2} t_{1}[/tex] [tex]t_{2}[/tex]= 1/4
[tex]t_{1}[/tex]=1/[tex]\sqrt{2}[/tex]
[tex]\frac{t_{2} }{{t_{1} }}[/tex] = 1/2[tex]\sqrt{2[/tex]
⇒ t₂/t₁≤1
⇒ Hence it converges
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Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?
Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.To find the order of matrix:
We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.Dimension is assigned to the provided matrix: 6 × 5This means the given matrix contains six rows and five columns.As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.To prove:
In other words, the inner products of the dimensions should be equal.That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.The dimensions of the matrix are given by, row × column.Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
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35*71+71*65+51*23+23+49
Answer:
35x71+71x65+51x23+23+49=8,345
Step-by-step explanation:
Answer:
8345
Is the correct answer
Step-by-step explanation:
hope it will help you
Amal used the tabular method to show her work dividing –2x3 11x2 – 23x 20 by x2 – 3x 4.
The true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
How to determine the true statement?The complete question is added as an attachment
From the table, we have
Divisor = x^2 - 3x + 4
Quotient = 2x + 5
Dividend = -2x^3 + 11x^2 - 23x + 20
See that the signs of the leading coefficients of the dividend and the divisor are different
This means that the leading coefficient of the quotient must be negative
From the question, we have:
Quotient = 2x + 5
The expression 2x + 5 has a positive leading coefficient
Hence, the true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
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Which of the following equations represents the area of a sector?
1.) A360nxr², where n is the central angle of the sector
2.)A = n², where n is the central angle of the sector
n
3.) A= TT, where n is the central angle of the sector
360°
4.) A =
360
T², where n is the central angle of the sector
From the given options we can say that the only one that represents the area of the sector is; A = n/360 * πr²
What is the Area of the Sector?
In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
θ/360 * πr²
where;
θ is the central angle of the sector
r is radius
Now, looking at the given options we can say that the only one that represents the area of the sector is;
A = n/360 * πr²
where n is the central angle of the sector
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Answer:
A!
Step-by-step explanation:
Simplify the expression:
-2(-1 + 2w) =
Submit please
[tex]-2(-1+2w)[/tex]
distribute
[tex]2-4w[/tex]
put in standard form
[tex]-4w+2[/tex]
The temperature during a day can be modeled by a sinusoid. Answer the following question given that the low temperature of 7 degrees occurs at 5 AM and the high temperature for the day is 45 degrees.
Find the temperature, to the nearest degree, at 9 AM.
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
What is the temperature of a place at a given time?
Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:
T(t) = A · sin (2π · t / T + C) + B (1)
Where:
A - Temperature amplitude, in degrees.B - Middle temperature, in degrees.T - Period, in hours.C - Angular phase, in radians.The temperature amplitude and the middle temperature can be found by the following expressions:
A = (t' - t'') / 2 (2)
B = (t' + t'') / 2 (3)
Where t' and t'' are maximum and minimum temperatures, in degrees.
Then, we proceed to find each constant of the sinusoidal model:
A = (45 - 7) / 2
A = 38 / 2
A = 19
B = (45 + 7) / 2
B = 52 / 2
B = 26
We assume a period of 24 hours (T = 24).
If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:
7 = 19 · sin [(π / 12) · 0 + C] + 26
- 19 = 19 · sin C
sin C = - 1
C = π
T(t) = 19 · sin (π · t / 12 + π) + 26
Then, the temperature at 9 AM is: (t = 4)
T(4) = 19 · sin (π · 4 / 12 + π) + 26
T(4) ≈ 9.545
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
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Find the standard deviation for the set of data. {15,17,23,5,21,19,26,4,14} a. 7.17 b. 7.39 c. 7.1 d. 6.65
The standard deviation exists as the positive square root of the variance.
So, the standard deviation = 6.819.
How to estimate the standard deviation?Given data set: 15, 17, 23, 5, 21, 19, 26, 4, 14
To calculate the mean of the data.
We know that mean exists as the average of the data values and exists estimated as:
Mean [tex]$=\frac{15+17+23+5+21+19+26+4+14}{9}[/tex]
Mean [tex]$=\frac{144}{9}[/tex]
Mean = 16
To estimate the difference of each data point from the mean as:
Deviation:
15 - 16 = -1
17 - 16 = 1
23 - 16 = 7
5 - 16 = -11
21 - 16 = 5
19 - 16 = 3
26 - 16 = 10
4 - 16 = -12
14 - 16 = -2
Now we have to square the above deviations we obtain:
1 , 1, 14, 121, 25, 9, 100, 144, 4
To estimate the variance of the above sets:
variance [tex]$=\frac{1+ 1+14+ 121+25+ 9+ 100+ 144+ 4}{9}[/tex]
Variance [tex]$=\frac{419}{9}[/tex]
Variance = 46.5
The standard deviation exists as the positive square root of the variance.
so, the standard deviation [tex]$\sqrt{46.5} =6.819[/tex] .
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Jamie has 2 dimes, 4 nickels and 8 pennies. in how many different ways can she make 26 cents?
Answer:
(2 dimes + 6 pennies)
(4 nickels + 6 pennies)
(1 dime + 2 nickels + 6 pennies)
( 2 dimes + 1 nickels + 1 penny)
(1 dime + 3 nickels + 1 penny)
5 different ways that Jamie can make 26 cents.
Find the area of the figure with the coordinates, S(-3, 5), A (1, 5), L(2, 1) and T(-6, 1).
Answer: a = 24 units²
Step-by-step explanation:
Let us graph the figure given. This shape appears to be a trapezoid. Now, we can solve for the area. This shape also has a height of 4, which I forgot to show in the picture.
In the formula, h is the height, a is a base, and b is the other base.
[tex]\displaystyle a=\frac{a+b}{2} h[/tex]
[tex]\displaystyle a=\frac{4+8}{2} 4[/tex]
[tex]\displaystyle a=\frac{12}{2} 4[/tex]
[tex]\displaystyle a=(6)4[/tex]
[tex]\displaystyle a=24\; \text{units}^{2}[/tex]
Let f(x, y) = x2 6y2. find the maximum and minimum values of f subject to the given constraint?
The minimum and maximum values are (16/9)√3 and -(16/9)√3.
According to the statement
we have given that the function
First of all, since the constraint's graph is a circle, which is a closed loop, and f is continuous in [tex]R^2[/tex], there must exist a constrained global maximum and minimum value.
Lagrange Multipliers:
f(x,y) = xy^2
g(x,y) = x^2 + y^2
We want ∇f = λ∇g so we get the following system of equations
1. y^2 = 2λx
2. 2xy = 2λy
3. x^2 + y^2 = 4 ← The constraint.
Equation 2 implies that y = 0 or λ = x
We can ignore y = 0, since that will make f(x,y) = 0 and clearly f(x,y) takes on both positive and negative values subject to the constraint.
Plugging in the alternative, λ = x to equation 1 gives y^2 = 2x^2.
Plugging this into the constraint gives 3x^2 = 4 so that x^2 = 4/3 and y^2 = 8/3
Taking square roots gives
x = ±√(4/3) = ±(2/3)√3
y = ±√(8/3) = ±(2/3)√6
At the points < (2/3)√3 , ±(2/3)√6 >, f(x,y) = (16/9)√3 ← Maximum
At the points < -(2/3)√3 , ±(2/3)√6 >, f(x,y) = -(16/9)√3 ← Minimum
So, The minimum and maximum values are (16/9)√3 and -(16/9)√3.
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Mrs. Gurung allowed 10% discount on her fancy items to make 25% profit and sold a lady bag for Rs 5,085 with 13% VAT. Due to the excessive demands of her items, she decreased the discount percent by 2%. By how much was her profit percent increased?
Her profit % was increased by 2.77%
Answer:
Solution Given:
discount =10%
profit =25%
S.P with 13% vat = Rs 5,085
S.P+Vat% of S.P= Rs 5,085
S.P(1+13%)=Rs 5,085
S.P=Rs 5,085/1.13
S.P =Rs 4,500
Again
M.P = S.P+discount% of M.P
M.P- discount% of M.P= Rs 4,500
M.P(1-10%)=Rs 4,500
M.P=Rs 4,500/0.9
M.P = Rs 5,000
Now
C.P= (S.P*100)/(1+profit%)
C.P=(4,500*100)/(100+25%)
C.P= Rs 3,600
Again
profit =S.P- C.P= Rs 4,500-Rs 3,600=Rs 900
Again
Due to the excessive demands of her items, she decreased the discount percent by 2%.
So,
New discount = 10%-2%=8%
New S.P= M.P -discount% of M.P
=M.P(1-discount%)
=Rs 5,000(1-8%)
=Rs 4,600
Again
Profit=S.P- C.P
New profit =Rs 4,600 - Rs 3,600=Rs 1,000
Profit% =profit/C.P*100%= 1000/3600*100=27.77%
Profit % increased =New profit%- profit%
=27.77-25
=2.77%