Answer:
The sales tax on a 320 dollars purchase is of $29.6.
Step-by-step explanation:
State sales tax y is directly proportional to retail price x.
This means that:
[tex]y = cx[/tex]
In which c is the constant of proportionality.
An item that sells for 156 dollars has a sales tax of 14.42 dollars.
This means that [tex]x = 156, y = 14.42[/tex]. We use this to find c. So
[tex]y = cx[/tex]
[tex]14.42 = 156c[/tex]
[tex]c = \frac{14.42}{156}[/tex]
[tex]c = 0.0924[/tex]
Then
[tex]y = 0.0924x[/tex]
What is the sales tax on a 320 dollars purchase?
y when [tex]x = 320[/tex]. So
[tex]y = 0.0924(320) = 29.6[/tex]
The sales tax on a 320 dollars purchase is of $29.6.
the focus of a parabola is (-5,-1) and the directrix is y= -3.
what is an equation of the parabola? (one of the answered above)
Answer:
Step-by-step explanation:
-2
One root of a third degree polynomial function f(x) is -5 + 2i. Which statement describes the number and nature of all
roots for this function?
f(x) has two real roots and one imaginary root.
f(x) has two imaginary roots and one real root.
f(x) has three imaginary roots.
f(x) has three real roots.
Answer:
f(x) has two imaginary roots and one real root.
Step-by-step explanation:
Complex roots:
I a complex number [tex]a + bi[/tex] is a root of a polynomial, it's conjugate [tex]a - bi[/tex] is also a root.
One root of a third degree polynomial function f(x) is -5 + 2i.
This means that -5 - 2i is another root of the polynomial, and thus, 2 of the roots are complex.
Third degree, so it has three roots, which means that the third root is real(not possible to have a complex root without it's conjugate), and thus, the correct answer is:
f(x) has two imaginary roots and one real root.
Answer:
B!
Step-by-step explanation:
just did it
Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 13 years. What is the probability of failure in the first 5 years
Answer:
The right answer is "0.3193".
Step-by-step explanation:
According to the question,
Mean,
[tex]\frac{1}{\lambda} = 13[/tex]
[tex]\lambda = \frac{1}{13}[/tex]
As we know,
The cumulative distributive function will be:
⇒ [tex]1-e^{-\lambda x}[/tex]
hence,
In the first 5 years, the probability of failure will be:
⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]
[tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]
[tex]=1-e^(-\frac{5}{13})[/tex]
[tex]=1-0.6807[/tex]
[tex]=0.3193[/tex]
Which value of n makes the equation true?
-1/2n=-8
Answer:
16?
Step-by-step explanation:
I'm not sure. I hope so.
A license plate consists of a letter, followed by three numbers, followed by another
letter. Due to possible confusion, the letters I and O are not used. Repetition is not
allowed.
How many different license plates are possible?
This is one single number that's slightly smaller than 400 thousand.
======================================================
Explanation:
There are 26 letters in the english alphabet. We don't use letters i or o, so we have 26-2 = 24 choices for that first slot.
Then we have 10 choices for the second slot because there are 10 single digits 0 (zero) through 9.
After making the selection for the second slot, we have 10-1 = 9 choices left for the third slot. The fourth slot has 10-2 = 8 digits to pick from. The subtraction occurs because we cannot reuse the digits.
Finally, the last slot will be a letter. We have 24-1 = 23 letters left to pick from.
Overall, we have 24*10*9*8*23 = 397,440 different license plates possible.
--------------------
Extra info (optional section)
You may be wondering "why do we multiply those values?". Well consider a simple example of having only 2 slots instead of 5.
Let's say the first slot is a letter A to Z, excluding letters i and o. The second slot will be the digit from 0 through 9.
If you make a table with 24 rows and 10 columns, then you'll have 24*10 = 240 cells overall. Notice the multiplication here. The 24 rows represent each letter, and the 10 columns are the digit numeric digits.
Each inner cell is a different two character license plate. For example A5 is one such plate. This idea can be extended to have 5 characters.
Find the area of the irregular figure. Round to the nearest hundredth.
Answer:
[tex]67.5\text{ [square units]}[/tex]
Step-by-step explanation:
The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.
Formulas:
Area of rectangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=bh[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]By definition, the base and height must intersect at a 90 degree angle.
The rectangle has a base of 10 and a height of 5. Therefore, its area is [tex]A=10\cdot 5=50[/tex].
The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 2\cdot 5=5[/tex].
Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 5\cdot 5=12.5[/tex].
Thus, the area of the total irregular figure is:
[tex]50+5+12.5=\boxed{67.5\text{ [square units]}}[/tex]
Suppose 49% of the doctors in America are dentists. If a random sample of size 689 is selected, what is the probability that the proportion of doctors who are dentists will be less than 47%
Answer:
[tex]P(<47\%)=0.1468[/tex]
Step-by-step explanation:
From the question we are told that:
Percentage of Dentist Doctors P(D)=49\%
Sample size n=689
Generally the equation for probability that the proportion of doctors who are dentists will be less than [tex]P(<47\%)[/tex] is mathematically given by
[tex]P(<47\%)=Z>(\frac{\=x-P(D)}{\sqrt{\frac{P(D)*1-P(D)}{n}}})[/tex]
[tex]P(<47\%)=Z>(\frac{0.47-0.49}{\sqrt{\frac{0.49*0.51}{689}}})[/tex]
[tex]P(<47\%)=Z>(1.05)[/tex]
Therefore from table
[tex]P(<47\%)=0.1468[/tex]
Please help it’s a test and I can’t get logged out
Answer:
the anwer is B ( i mean second option)
And you can try it
you will find ;
[tex]y = \frac{x}{3} - 1[/tex]
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
work out the area of this shape
Answer:
1000
Step-by-step explanation:
Add. Please show work too.
Answer:
-36m^3-21n^3+85mn^2+36m^2n
Step-by-step explanation:
That's what the calculator says:).
Answer pllllllleeeaaaaasssss
(3.1) … … …
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2x-y}{x-2y}[/tex]
Multiply the right side by x/x :
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2-\dfrac yx}{1-\dfrac{2y}x}[/tex]
Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :
[tex]x\dfrac{\mathrm dv}{\mathrm dx} + v = \dfrac{2-v}{1-2v}[/tex]
This DE is now separable. With some simplification, you get
[tex]x\dfrac{\mathrm dv}{\mathrm dx} = \dfrac{2-2v+2v^2}{1-2v}[/tex]
[tex]\dfrac{1-2v}{2-2v+2v^2}\,\mathrm dv = \dfrac{\mathrm dx}x[/tex]
Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives
[tex]-\dfrac12\ln\left|2v^2-2v+2\right| = \ln|x| + C[/tex]
Solve for v, then for y (or leave the solution in implicit form):
[tex]\ln\left|2v^2-2v+2\right| = -2\ln|x| + C[/tex]
[tex]\ln(2) + \ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]
[tex]\ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]
[tex]v^2-v+1 = e^{\ln\left(1/x^2\right)+C}[/tex]
[tex]v^2-v+1 = \dfrac C{x^2}[/tex]
[tex]\boxed{\left(\dfrac yx\right)^2 - \dfrac yx+1 = \dfrac C{x^2}}[/tex]
(3.2) … … …
[tex]y' + \dfrac yx = \dfrac{y^{-3/4}}{x^4}[/tex]
It may help to recognize this as a Bernoulli equation. Multiply both sides by [tex]y^{\frac34}[/tex] :
[tex]y^{3/4}y' + \dfrac{y^{7/4}}x = \dfrac1{x^4}[/tex]
Substitute [tex]z(x)=y(x)^{\frac74}[/tex], so that [tex]z' = \frac74 y^{3/4}y'[/tex]. Then you get a linear equation in z, which I write here in standard form:
[tex]\dfrac47 z' + \dfrac zx = \dfrac1{x^4} \implies z' + \dfrac7{4x}z=\dfrac7{4x^4}[/tex]
Multiply both sides by an integrating factor, [tex]x^{\frac74}[/tex], which gives
[tex]x^{7/4}z'+\dfrac74 x^{3/4}z = \dfrac74 x^{-9/4}[/tex]
and lets us condense the left side into the derivative of a product,
[tex]\left(x^{7/4}z\right)' = \dfrac74 x^{-9/4}[/tex]
Integrate both sides:
[tex]x^{7/4}z=\dfrac74\left(-\dfrac45\right) x^{-5/4}+C[/tex]
[tex]z=-\dfrac75 x^{-3} + Cx^{-7/4}[/tex]
Solve in terms of y :
[tex]y^{4/7}=-\dfrac7{5x^3} + \dfrac C{x^{7/4}}[/tex]
[tex]\boxed{y=\left(\dfrac C{x^{7/4}} - \dfrac7{5x^3}\right)^{7/4}}[/tex]
(3.3) … … …
[tex](\cos(x) - 2xy)\,\mathrm dx + \left(e^y-x^2\right)\,\mathrm dy = 0[/tex]
This DE is exact, since
[tex]\dfrac{\partial(-2xy)}{\partial y} = -2x[/tex]
[tex]\dfrac{\partial\left(e^y-x^2\right)}{\partial x} = -2x[/tex]
are the same. Then the general solution is a function f(x, y) = C, such that
[tex]\dfrac{\partial f}{\partial x}=\cos(x)-2xy[/tex]
[tex]\dfrac{\partial f}{\partial y} = e^y-x^2[/tex]
Integrating both sides of the first equation with respect to x gives
[tex]f(x,y) = \sin(x) - x^2y + g(y)[/tex]
Differentiating this result with respect to y then gives
[tex]-x^2 + \dfrac{\mathrm dg}{\mathrm dy} = e^y - x^2[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy} = e^y \implies g(y) = e^y + C[/tex]
Then the general solution is
[tex]\sin(x) - x^2y + e^y = C[/tex]
Given that y (1) = 4, we find
[tex]C = \sin(1) - 4 + e^4[/tex]
so that the particular solution is
[tex]\boxed{\sin(x) - x^2y + e^y = \sin(1) - 4 + e^4}[/tex]
One-ninth of all sales at a local Subway are for cash. If cash sales for the week were $690, what were
Subway's total sales?
Select one:
O a. $22,600
O b. $2,611
O c. $6,210
O d. $2,610
e. None of these
Answer:
c. $6,210Step-by-step explanation:
Total sales = x
x*1/9 = 690x = 690*9x = 6210Correct choice is C
Let Y1 and Y2 denote the proportions of time (out of one workday) during which employees I and II, respectively, perform their assigned tasks. The joint relative frequency behavior of Y1 and Y2 is modeled by the density function.
f (y 1,y2)=y 1+y 2 o<=y 1<=1, 0<=y2<=1(0 elsewhere)
a. Find P (Y1< 1/2,y2>1/4)
b. Find P(Y 1+Y2<=1)
Are Y1 and Y2 independent?
(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,
{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}
Integrate the joint density over this region:
[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]
(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,
{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}
Integrate to get the probability:
[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]
Y₁ and Y₂ are not independent because
P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)
To see this, compute the marginal densities of Y₁ and Y₂.
[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]
[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]
[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]
but this clearly does not match the joint density.
What is the slope of (-4,1) and (-1,3)
Answer:
slope is 2÷3 of giving line points
NEED ANSWER QUICK
Timmy and Tommy are two boys whose ages add up to 23. Timmy is 5
years older than Tommy. How old are they?
Answer:
Tommy's age is 9 years old.
Timmy's age is 14 years old.
Step-by-step explanation:
Take Tommy's age to be x and Timmy's age to be x+5
x+x+5=23
2x+5=23
2x=23-5=18
x=18÷2=9
x+5=9+5=14
What does point b represent on the graph ?
Answer:
Step-by-step B represents the $14 John earned in the 2 hours he worked.
explanation:
Help me or ill fail plz
Answer:
1,108 in²
Step-by-step explanation:
SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)
+ (2×20×11)
= 240+320+108+440
= 1,108 in²
Please help meeee pleaseeee
Explanation:
Refer to the diagram below. There are n = 9 sides
S = 180(n-2)
S = 180(9-2)
S = 180(7)
S = 1260
This nonagon (9 sided polygon) has its interior angles add up to 1260 degrees.
Find m angle QSRIf m angle TSQ=15x , m angle TSR=173^ , and m angle QSR=10x-2
[tex]{\color{red}{\huge{\underbrace{\overbrace{\mathfrak{\:\:\:\:\:\:\:꧁"Answer"꧂\:\:\: }}}}}}[/tex]
[tex]\small\color{blak}{{\underline{\bold{ Find \:a X } } } }[/tex]
[tex]\small\color{black}{{\underline{\bold{173°=15z+10x-2 } } } } \\ = 173 = 25x - 2 \\ = - 25x = - 2 - 173 \\ = - 25x - 175 \\ = \small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: x=7\:\:\:\: }}}}[/tex]
[tex]\small\color{blak}{{\underline{\bold{ Find\:a\:m<QSR } } } }[/tex]
[tex]\small\color{blak}{{\underline{\bold{ 10(7)-2 } } } }\\=70-2\\=\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: m<QSR=68°\:\:\:\: }}}}[/tex]
[tex]\Large\color{red}{{\underline{\mathfrak {{꧁"Carry\:on\: learning"꧂ }}}}}[/tex]
The measure of angle QSR is 68 degrees.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression.
According to the given question.
m ∠TSQ = 15x
m ∠TSR = 173 degrees
m ∠QSR = 10x -2
Since,
m ∠TSR = m ∠TSQ + ∠QSR
Substitute the value of m ∠TSR, m ∠TSQ and m ∠QSR in the above expression.
⇒ [tex]173 = 15x + 10x - 2[/tex]
⇒ [tex]173 = 25x - 2[/tex]
⇒ [tex]175 = 25x[/tex]
⇒ [tex]x = \frac{175}{25}[/tex]
⇒ [tex]x = 7[/tex]
Again, for finding the value of angle QSR substitute the value of x in 10x - 2.
Therefore,
m ∠QSR = 10(7) - 2
⇒ m ∠QSR = 70 - 2
⇒ m ∠QSR = 68 degrees
Hence, the measure of angle QSR is 68 degrees.
Fid out more information about substitution here:
brainly.com/question/27810586
#SPJ3
Which equation represents a line which is parallel to the line y = -7x - 8?
7x + y = -3
x+ 7y = 7
y - 7x = 6
x- -7y = -28
Answer:
7x+y=-3
Step-by-step explanation:
if m is the slope of a line, then the slope of its parallel line will have the same slope m,
in the given equation, y=-7x-8, the slope is -7
among the options, 1st option has a slope of -7, since,
7x+y=-3
or, y=-7x-3
Answered by GAUTHMATH
FREE
Circle O has a circumference of approximately 250 ft.
What is the approximate length of the diameter, d?
O 40 ft
O 80 ft
O 125 ft
O 250 ft
Save and Exit
Next
Submit
Mark this and return
Answer:
Step-by-step explanation:
circumference = πd ≅ 250 ft
d ≅ 250/π ≅80 ft
Tammy makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answer:
P=8(h)
Step-by-step explanation:
P is her total pay. You find that by multiplying what she makes an hour (8) by the total number of hours she has worked (h).
Answer:
p=8h
Step-by-step explanation:
Pay equals $8 per the number of hours
The graphs below have the same shape the equation of the bluegrass is f(x)=x^3 what is the equation of the red graph
Answer:
g(x) = x^3 - 2
Step-by-step explanation:
As you can see on the graph, the line has been translated down 2 units.
If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2
g(x) = x^3 - 2
Hope this helps!!
Find the distance between the points ( 4, 7) and (-1,2
Answer:
7.07 (3 significant figures)
Step-by-step explanation:
the distance between the two points on the x axis is 5 and the distance between the two point son the y axis is 5. thus by using pythagerous theorem you are able to get the hypotenuse which is the distance between the two points which in this case is 7.07 when rounded to 3 significant figures. not sure if im correct but i hope it helps
Which graph shows the solution to the system of linear inequalities?
y>2/3x+3
y ≤ -1/3x+2
Answer:
Graph 2 which has both solid and dashed line
Step-by-step explanation:
Given the linear inequalities :
y>2/3x+3 - - - (1)
y ≤ -1/3x+2 - - - (2)
One quick observation that can be made from the two graphs is the type of line used to plot the two linear inequalities;
Inequalities that uses either the < or > sign are plotted using a dashed line while inequalities with makes use of ≤ or ≥ are plotted using the solid line. Therefore we can conclude that the graph which uses both the solid line and the dashed line to represent the linear inequality conditions is the correct choice.
The data on the box plot describes the weight of several students in sixth grade. Which of the following statements are true about the data set? Select all that apply.
One-fourth of the students weigh between 90 and 101 pounds.
One-half of the students weigh between 75 and 90 pounds.
The median weight of the sixth graders is 85 pounds.
One-fourth of the students weigh less than 75 pounds.
One-fourth of the students weigh more than 75 pounds.
The total range of weight is 40 pounds.
Answer:
Step-by-step explanation:
B
I'm not sure how to do this so I'm just asking for help.
Answer:
C
Step-by-step explanation:
In ∆DEG, we are given that all the three angles are congruent.
This means that all the three angles have equal measure. Thus,
<D = <E = <F
An equilateral triangle has equal angle measure. ∆DEF is an equilateral triangle.
Since the sum of a triangle is 180°, therefore, each angle in ∆DEF = 60°
m<D = 60°
What is the measure of e?
Answer:
[tex] \theta = 4~radians [/tex]
Step-by-step explanation:
[tex] s = \theta r [/tex]
[tex] 20~cm = \theta \times 5~cm [/tex]
[tex] \theta = 4~radians [/tex]
Find the volume of the figure. Express answers in terms of t, then round to the nearest whole number
Please help :)
Answer:
729π ft³
Step-by-step explanation:
Applying,
Volume of a cone
V = πr²h/3.............. Equation 1
Where r = radius of the base, h = height, π = pie
From the question,
Given: r = 9 ft, h = 27 ft
Substitite these values into equation 1
V = π(9²)(27)/3
V = 729π ft³
Hence the volume of the figure in terms of π is 729π ft³
help me guys, I really need your help
Answer:
The answer should be like this;
a) A-B
b) BUC
c) C-A
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
