Rico saved $30 to buy office supplies. He needed a binder that cost $9.99 , including tax,and three pens that cost $1.99 each,including tax. How much money will Rico have left after he buys the pens and the binder?
A typist charges $0.90 a page and averages 45 pages per work day. If she works 3 days a week, how much does she earn in a week?
Final answer:
The typist earns $121.50 per week by multiplying the charge per page ($0.90) with the daily page average (45 pages) and the number of days worked per week (3 days).
Explanation:
The question asks us to calculate the weekly earnings of a typist who charges $0.90 per page and averages 45 pages per day, working 3 days a week. To find the total weekly earnings, we can multiply the number of pages typed per day by the charge per page, and then multiply that result by the number of days worked in a week.
Multiply the number of pages (45) by the charge per page ($0.90): 45 pages × $0.90 = $40.50 per day.
Multiply the daily earnings by the number of days worked in a week (3): $40.50 × 3 days = $121.50 per week.
Therefore, the typist earns $121.50 per week.
Q1 :Let f(x)=2x^2−8
The quadratic function g(x) is f(x) translated 2 units down
What is the equation for g(x)
Q2 Let f(x)=[tex] \frac{3}{4} [/tex]x2−1.
The function g(x) is a vertical stretch of f(x) by a factor of 8.
What is the equation of g(x)?
Q3 The graph of the function g(x) is a transformation of the parent function f(x)=x2 .
Which equation describes the function g?
(refer to picture attached)
A. g(x)=x2+2
B. g(x)=(x−2)2
C. g(x)=(x+2)2
D. g(x)=x2−2
What is the equation of the line that passes through the points (0, -4) and (2, 8)?
A. y = 6x - 4
B. y = 6x + 4
C. y = 4x + 6
D. y = -4x + 6
What is the radius of convergence of the maclaurin series (2x)/(1+x^2)?
The radius of convergence of the maclaurin series is 1 unit.
It is given that maclaurin series [tex]\rm \frac{2x}{(1+x^2)}[/tex]
It is required to find the radius of the convergence of the maclaurin series.
What is maclaurin series?It is defined as the expansion of a function that provide the approximation of the given function at any point of function.
We have:
[tex]\rm \frac{2x}{(1+x^2)}[/tex]
To find the radius of convergence of the maclaurin series, we must find the roots of denominator hence:
[tex]\rm 1+x^2= 0\\\\\rm x^2 = -1\\\\[/tex]
From the complex number: the roots are imaginary:
[tex]\rm x_1 = i\\x_2 = -i[/tex]
i is the iota
and the distance from the origin (0,0) is 1.
Thus, the radius of convergence of the maclaurin series is 1 unit.
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Express answer in exact form.
Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)
Answer:
A = { 9/2 π - 9 } in^2
Step-by-step explanation:
I just did this
Hope this helps !
To find the area of the segment, subtract the area of the triangle from the area of the sector.
Explanation:To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we need to find the area of the sector formed by the circle and subtract the area of the triangle formed by the diagonal of the square.
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Park rangers notice a negative correlation between the number of available campsites in a park and the amount of litter on the park's trails. Which variable is most likely the lurking variable that explains the correlation? Question 3 options: age of trees in the park number of eagles spotted in the park number of visitors to the park density of trees in the park
We have been given that a park rangers notice a negative correlation between the number of available campsites in a park and the amount of litter on the park's trails.
We need to figure out the lurking variable that describes the given correlation.
Out of the given options, the most appropriate variable that describes that negative correlation between number of available campsites in the part and the amount of litter on the park's trails is number of visitors to the park.
The reason, why number of visitors to the park is the lurking variable for the given negative correlation, is that more the number of visitors, more the litter they produce and consequently, lesser the number of available campsites.
Complete the equation of the line through (-8,8) and (1,-10). Use exact numbers.
The equation of the line through (-8,8) and (1,-10) is y = -2x - 8
Using the slope intercept form equation.
y = mx + b
where
m = slope
b = y-intercept
Therefore,
(-8,8) (1,-10)
m = -10 - 8 / 1 + 8 = - 18 / 9 = -2
Therefore,
let's find b as follows:
(1, -10)
y = -2x + b
-10 = -2(1) + b
b = -10 + 2
b= -8
Therefore,
y = -2x - 8
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The resonance frequency f in an electronic circuit containing inductance L and capacitance C in series is given by f=1/2π√LC. Determine the inductance L in an electric circuit if the resonance frequency is 6.2 and the capacitance is 0.0001. Round your answer to the nearest tenth.
10270.1
6.6
256.8
0
Which of the following gives all of the coefficients of the algebraic expression -2x^2 +17-15x+7xy
The coefficients of the algebraic expression -2x² + 17 -15x + 7xy are -2, 17, -15 and 7
How to determine the coefficient of the expression
From the question, we have the following parameters that can be used in our computation:
-2x² + 17 -15x + 7xy
Consider an expression represented as
Ax
Where A is a constant and x is the variable
The coefficient of the expression is A
Using the above as a guide, we have the following:
The coefficients of the algebraic expression are -2, 17, -15 and 7
Question
Which of the following gives all of the coefficients of the algebraic expression -2x^2 +17-15x+7xy
a. 2, 17, 15 and 7
b. -2, 17, -15 and 7
c. -2, -17, -15 and 7
d. -2, -17, 15 and 7
For the function f(x) = x2, what effect will multiplying f(x) by 1/2 have on the graph?
PLEASE ANSWER + BRAINLIEST!!!
What is the value of 3x^2 - 5xy + 5y^2 for x = -6 and y = 2?
A. -68
B. -4
C. 188
D. 208
Daniela is a stain glass artist; she created the window below for her living room. What is
the area of the window she created?
The square root of 53 lies between which two numbers?
What is the trigonometric ratio for sin C?
Anyone know this geometry question? Will give brainiest
If you add the lengths of the focal radii of an ellipse, what other value will you produce?
2a
2b
2c
The eccentricity
Equation of an ellipse
→having center (0,0) , vertex ([tex](\pm a ,0)[/tex] and covertex [tex](\pm b ,0)[/tex] and focus [tex](\pm c ,0)[/tex] is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}=1[/tex]
As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c = [tex]F_{1}[/tex]
Distance from (-a,0) to (c,0) is = a + c = [tex]F_{2}[/tex]
[tex]F_{1} + F_{2} =[/tex] a -c + a +c
= a + a
= 2 a →(Option A )
The Candle Emporium is pouring cylindrical candles. Each candle has a radius of 5 inches and a height of 18 inches. Which formula represents the correct way to find the volume of a candle?
a. Volume= 5x18
b. Volume= pi (5) (18)
c. Volume= pi (18)squared (5)
d. Volume= pi (5)squared (18)
Answer:
Option D is correct.
Step-by-step explanation:
We are given,
Height of the candles, h = 18 inches
Radius of the candles, r = 5 inches
Candles are in shape of cylinder.
We have to find correct representation of volume of candle.
Volume of cylinder = [tex]\pi r^2h[/tex]
Volume of candle = ]tex]\pi (5)^2\times18[/tex]
Therefore, Option D is correct.
Write the function associated with the graph below
Since the value of the function is decreasing exponentially as x decreases ,
The function is of the form [tex] y=ae^{bx}+c,b>0 [/tex].
Since the curve passes through (0,6),
[tex] 6=ae^{0}+c,6=a+c [/tex],
Since the curve passes through (-1,0),
[tex] 0=ae^{-b}+c [/tex].
Since [tex] y=-3 [/tex] is a horizontal asymptote,
[tex] -3=ae^{-\infty}+c,c=-3 [/tex]
From the above 3 equations,
[tex] c=-3,a=9,9e^{-b}=3,e^b=3,b=\ln 3 [/tex].
Therefore, the required function is
[tex] y=9e^{\ln 3 x}-3\\
y=9*3^{ x}-3 [/tex].
It can be verified that the curve [tex] y=9*3^{ x}-3 [/tex] passes through [tex] (-2,-2) [/tex].
A. (-3,-5)
B.( -2,-2)
C. (4,9)
D.(13,5)
A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.
Which system of inequalities is represented by the graph
Determine whether the given coordinates are the vertices of a triangle. Explain.
L(–24, –19), M(–22 ,20), N(–5, –7)
A:
yes:
LM + MN > LN,
LM + LN > MN,
LN + MN > LM
B:
no:
LM + MN = LN
C:
no:
LM + MN < LN
D:
yes:
LM + MN < LN,
LM + LN < MN,
LN + MN < LM
Final answer:
After computing the distances between the points L, M, and N using the distance formula and comparing them, it is clear that the sum of the lengths of any two sides is greater than the length of the third side, satisfying the conditions of a triangle.
Explanation:
To determine whether the given coordinates are the vertices of a triangle, we can check if the sum of the lengths of any two sides is greater than the length of the third side, which is a principle derived from the triangular inequality theorem. First, we calculate the distances between the points L(–24, –19), M(–22, 20), and N(–5, –7) using the distance formula: √((x2-x1)² + (y2-y1)²).
For LM: √((-22 + 24)² + (20 + 19)²) = √(4 + 1521) = √(1525)
For MN: √((-5 + 22)² + (-7 - 20)²) = √(289 + 729) = √(1018)
For LN: √((-5 + 24)² + (-7 + 19)²) = √(361 + 144) = √(505)
Now we compare the lengths:
LM + MN > LN
LM + LN > MN
LN + MN > LM
Since all three conditions are satisfied, the points L, M, and N form a triangle.
Which expressions are equivalent to the one below? Check all that apply.
21^x/7x
A. 3^x-7
B. 3
C. 3^x
D. (21-7)^x
E. 7^x * 3^x/ 7^x
F. (21/7)^x
After simplifying the original expression, the equivalent expressions to [tex]21^x/7x[/tex] are C. [tex]3^x[/tex] and F. [tex](21/7)^x.[/tex]
Explanation:The original expression in the question is [tex]21^x/7x[/tex]. To find equivalent expressions, we first simplify the original expression. The expression [tex]21^x[/tex]is the same as [tex](7*3)^x,[/tex] which, by property of exponents, can be written as [tex]7^x * 3^x.[/tex]Then, given the expression is divided by 7x, the x in the denominator cancels out with the x from [tex]7^x.[/tex] Hence, the simplified form will be [tex]3^x.[/tex] Now, we compare it with the given options.
Option C is directly equal to the simplified form. While options A,D, E, and B are not equivalent to the original expression. Considering option F, 21/7 simplifies to 3 and so, [tex](21/7)^x[/tex] can be rewritten as [tex]3^x[/tex] which is equal to the simplified form. Therefore, the equivalent expressions are C. [tex]3^x[/tex]and F. [tex](21/7)^x.[/tex]
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The equivalent expressions to [tex]21^x/7x[/tex] are 3^x and [tex]7^x * 3^x/ 7^x[/tex], and[tex](21/7)^x,[/tex]which can all be simplified to result in 3^x.
Explanation:The expressions equivalent to 21^x/7x are checked by determining if they simplify down to the same value as the original expression. Taking the original expression 21^x/7x, it's clear that 21 can be rewritten as 7*p, so 21^x/7x simplifies to [tex](7*3)^x/7x = 7^x*3^x/7x = 3^x[/tex] (because [tex]7^x/7^x = 1).[/tex]
From the given options, Option C: 3^x, and Option E: [tex]7^x * 3^x/ 7^x[/tex]satisfy this criterion, as they also simplify to 3^x. Option F: (21/7)^x also simplifies as explained earlier to 3^x. So, options C, E, and F are equivalent to the original expression.
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Find the amount in a continuously compiunded account for the following condition. Principal, $4000; Annual interest rate, 5.1%; time, 2 years
Using the given principal of $4000, an annual interest of 5.1%, and a time period of 2 years, the amount in a continuously compounded account will be approximately $4483.48 using the formula A = P*e^(rt).
Explanation:In this question, we are asked to find the amount in a continuously compounded account. The formula to calculate this is A = P*e^(rt), where A is the amount, P is the principal, r is the rate, t is the time, and e is the base of the natural logarithm, approximately equal to 2.71828.
In this case, P = $4000, r = 0.051 (5.1% expressed as a decimal), and t = 2.
Substituting these values into the formula, we get: A = 4000 * e^(0.051*2). Using a calculator, we can find this to be approximately $4483.48.
So, after 2 years with an annual interest rate of 5.1%, compounded continuously, the account will contain about $4483.48.
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What is the solution to the linear equation ? 2/5+p=4/5+3/5p
Answer:
p=1
Step-by-step explanation:
2/5+p=4/5+3/5p
[tex]\frac{2}{5} +p= \frac{4}{5} +\frac{3}{5} p[/tex]
p or p/1 are same
LCD is 5, multiply 5 with each term. the equation becomes
[tex]\frac{2}{5} \cdot 5+p \cdot 5= \frac{4}{5} \cdot 5 +\frac{3}{5}p \cdot 5[/tex]
[tex]2+5p = 4 +3p[/tex]
Subtract 3p from both sides
[tex]2+2p = 4[/tex]
Subtract 2 on both sides
[tex]2p= 2[/tex]
Divide by 2 on both sides
p= 1
So the value of p =1 for the given equation
20 points!
Looking at circle O, ∠BOC is a(n)
Please contact your teacher immediately if you do not see the image.
Question options:
minor angle
central angle
inscribed angle
major angle
solve for z (attachment)
22 POINTS, NEED URGENT HELP
Write the equation of each circle:
1. R with center R(-1, 8) and radius 5
2. K with center K(4,0) and that passes through (2,0)
how do you convert cos(x) into sin(x) and tan(x) ?