Answer:
C) 5000(0.987783)^t
Step-by-step explanation:
The monthly interest rate is the APR divided by 12, so is 22%/12 ≈ 0.018333.
Each month, the previous balance (B) has interest charges added to it, so the new balance is ...
balance with interest charges = B + (22%)/12×B = 1.018333×B
The minimum payment is 3% of this amount, so the new balance for the next month is ...
balance after payment = (1.018333B)(1 - 0.03) = 0.987783B
Since the balance is multiplied by 0.987783 each month, after t payments, the balance starting with 5000 will be ...
5000×0.987783^t . . . . . . . . . matches choice C
a teacher presented students with four tables which table describes a linear function that has a slope of 2?
Answer:
Table 4
Step-by-step explanation:
Just imagine the data tables are graphs, just presented in a different form.
How do you calculate the slope in a graph? You divide the variation of Y by the variation of X. That's the same thing here. Let's look at each table, and calculate the slope based on the first 2 rows of each table:
Table 1:
S = (1 - -1)/(2-6)= 2/-4 = -2, not the one we want.
Table 2:
S = (8 - 4) / (0 - 2) = 4 / -2 = -2, not the one we want.
Table 3:
S = (4 - 5)/(-4 - -2) = -1 / -2 = 1/2, not the one we want.
Table 4:
S = (0 - 4)/(-2 - 0) = -4 / -2 = 2. Yes! That's the one!
Answer:
Table 4
Step-by-step explanation:
Table 4 has a slope of 2.
(12 - 4)/(4 - 0) = 2
A couple is planning to have 3 children. Assuming that having a boy and having a girl are equally likely, and that the gender of one child has no influence on (or, is independent of) the gender of another, what is the probability that the couple will have exactly 2 girls? The "random experiment" in this case is having 3 children, as odd as that may sound in this context. The next and most important step is to determine what all of the possible outcomes are, and list them (i.e., list the sample space S). In this case, each outcome represents a possible combination of genders of 3 children (note that examples with the same number of boys and girls but a different birth order must be listed separately).
Answer:
44.444%, (B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)
Step-by-step explanation:
We will start with the second part of the question, listing out all of the possible combinations that can occur from this data set. There is a 50/50 chance of having a girl or a boy, and there are three children. For now we'll use B to represent a boy and G for a girl. It goes as follows:
(B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)
I often find it easy to write out a branch diagram to help me visualize this problem and make sure I have all possibilities. (See attached image)
Count the total number of combinations (9). Next, count the number that include exactly 2 girls (4). With this information, we now know that there is a 4 out of 9 chance of having exactly 2 girls and one boy. 4/9 is in simplest form, so all you have to do is find the percentage (44.444%)
Answer:
C or .375
Step-by-step explanation:
1. Drag and drop an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.
2. Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
3. The equation for a circle is x2−8x+y2−2y−8=0 .
What is the equation of the circle in standard form?
Answer:-
Central angle , Ф/2π , A = Ф/2 r²
The ratio is 1/3 , V = 1/3 Bh
The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25
Step-by-step explanation:
* Lets revise the rules of the area of the sector of a circle
- The area of the sector which has a central angle Ф° is
(Ф°/360°) × πr², where 360° is the measure of the circle and r is
the radius of the circle
- The area of the sector which has a central angle Ф radians is
(1/2) r²Ф
* Lets complete the missing in the 1st picture
- The ratio of the sector's area A to the circle's area is equal to the
ratio of the central angle to the measure of a full rotation of the circle
- A full rotation of a circle is 2π. This proportion can written as
A/πr² = Ф/2π
- Multiply both sides by πr² to get A = Ф/2 r² where Ф is the measure
of the central angle and r is the radius of the circle
* Lets revise the rules of the volume of the prism and the volume
of the pyramid, where they have the same base and height
- The volume of the prism = area of the base × its height
- The volume of the pyramid = 1/3 × area of the base × its height
- From them the ratio of the volume of the pyramid to the volume
of the prism is 1/3
- The formula of the volume of the prism is V = Bh, where B is the
area of the base and h is the height, the formula of the volume
of the pyramid is V = 1/3 Bh
* Lets revise the standard form of the equation of a circle with
center (h , k) and radius r
- The equation is: (x - h)² + (y - k)² = r²
∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0
∵ x² - 8x + y² - 2y - 8 = 0
- Lets equate the two equation
∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0
∵ -2h = -8 ⇒ ÷ -2
∴ h = 4
∵ -2k = -2 ⇒ ÷ -2
∴ k = 1
∵ h² + k² - r² = -8
∴ (4)² + (1)² - r² = -8
∴ 16 + 1 - r² = -8
∴ 17 - r² = -8 ⇒ subtract 17 from both sides
∴ -r² = -15 × -1
∴ r² = 25
* Substitute the values of h , k , r in the equation of the standard
form of the circle
∴ (x - 4)² + (k - 1)² = 25
* The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25
Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise.The circulation line integral of F=<(2xy^2),(4x^3)+y> where C is the boundary of {(x,y): 0<=y<=sinx, 0<=x<=pi}
The line integral you need to compute is
[tex]\displaystyle\int_C\langle2xy^2,4x^3+y\rangle\cdot\mathrm d\vec r[/tex]
By Green's theorem, this is equivalent to the double integral,
[tex]\displaystyle\iint_D\left(\frac{\partial(4x^3+y)}{\partial x}-\frac{\partial(2xy^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_D(12x^2-4xy)\,\mathrm dx\,\mathrm dy[/tex]
where [tex]D[/tex] is the region with boundary [tex]C[/tex]. This integral is equal to
[tex]\displaystyle\int_0^\pi\int_0^{\sin x}(12x^2-4xy)\,\mathrm dy\,\mathrm dx=\int_0^\pi(12x^2\sin x-2x\sin^2x)\,\mathrm dx=\boxed{\frac{23\pi^2}2-48}[/tex]
write a function to model the situation.
a digital image is reduced or enlarged by dragging the corner. the height to width ratio is always maintained as that the width is 1.25 times the height. write a function to model the area of the image as a function of its height.
please help and thank you !!
Answer:
a(h) = 1.25h²
Step-by-step explanation:
The formula for the area of a rectangle is ...
A = HW . . . . . where H represents the height and W represents the width
If the image has a height of h, then the width is 1.25 times that, or 1.25h. Putting these values into the formula, we have ...
A = h·(1.25h)
A = 1.25h²
In function form, we can write a(h), area as a function of height, as ...
a(h) = 1.25h²
Half of a number, x, increase by 7 is greater than -11 and less than-3. What are the possible solutions?
Answer:
What i got was -1 .
Step-by-step explanation:
Which is the answer ?
Answer:
(a) y = ±(√x)/2
Step-by-step explanation:
You want to find y such that ...
x = f(y)
x = 4y^2 . . . . . . . put in the expression for f(y)
x/4 = y^2 . . . . . . .divide by 4
±√(x/4) = y . . . . . take the square root
y = ±(√y)/2 . . . . . simplify
Which function can be used to find the number of cells of bacteria in the population at time t
Answer:
db / dt = kb
this becomes b(t) = Ce^(kt)
C = 100, the initial population
P(1) = 420 = 100 e^(1k)
4.2 = e^k
ln 4.2 = k
a) thus, b(t) = 100 e^(t ln 4.2)
b) b(3) = 100 e^(3 ln 4.2)
c) growth constant will still be ln 4.2 (constant percentage of populatioin)
d) 10000 = 100 e^(t ln 4.2)
100 = e^(t ln 4.2)
ln 100 = t ln 4.2
t = ln 100 / ln 4.2
Step-by-step explanation:
the kerns pen company makes ballpoint pens. the fixed cost of operation for one month averages $53500. the cost of producing one pen is $.75 and the pens are sold for $1.05 each. how many pens must be sold in order for the oay to break even?
Answer:
178,334 pens
Step-by-step explanation:
The company makes $0.30 above the variable cost on each pen, so must sell $53,500/$0.30 ≈ 178,334 pens to cover the cost of operation.
_____
Sale of 178,333 pens will result in a total cost of $0.10, so doesn't quite make the company break even. Sale of 178,334 pens will result in profit of $0.20.
1 joule/sec=1
Watt
Horsepower
Newton
Meter
The answer is watt. :D
Look at the picture below
ANSWER
Option A
EXPLANATION
The graph of g(x) has equation:
[tex]g(x) = \sqrt[3]{ x + 2 } - 4[/tex]
The parent function is
[tex]f(x) = \sqrt[3]{x} [/tex]
To obtain the graph of g(x), we must shift f(x) 2 units to the left and 4 units down.
The graph of this function is shown in the attachment.
The correct choice is option A.
Please see attached below and please explain how to solve.
Answer:
The 6% simple interest account earns more interest in 2 years.
Step-by-step explanation:
You can compare the multipliers in the interest formulas.
For simple interest, the amount in the account (A) starting with principal P and earning at rate r for t years will be ...
A = P(1 +rt)
For the values given, r=.06 and t=2, the multiplier is ...
1 +rt = 1 +.06·2 = 1.12
__
For interest compounded annually, the amount will be ...
A = P(1 +r)^t
For the given values, the multiplier is ...
(1+r)^t = (1.04)^2 = 1.0816
__
Since 1.12 > 1.0816, the account earning simple interest will earn more interest.
If 15% of the customer's total is $22.05, then the customer's total is _______."
let's say is "x", so "x" is then 100% of the whole bill.
we know 15% is 22.05, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 22.05&15\\ x&100 \end{array}\implies \cfrac{22.05}{x}=\cfrac{15}{100}\implies 2205=15x \\\\\\ \cfrac{2205}{15}=x\implies 147=x[/tex]
Answer:
$147
Step-by-step explanation:
15% over 100 is .15
So you get .15x= 22.05
Get x by itself by dividing .15 by .15
whatever you do to one side you have to do to the other so divide 22.05 by .15 and you get $147
Please help, I need an explanation because I'm confused on how to do this.
Answer:
15°
Step-by-step explanation:
If CB is a diameter, the arc BKAC is a semicircle and has a degree measure of 180. If the measure of angle BCK is 20 and it is an inscribed angle, then the measure of the arc it intercepts is twice that. So arc BK measures 40 degrees. That means that arc KA has a measure that is found by subtracting arc AC and arc BK from 180. 180 - 40 - 110 = 30. If that arc is 30 and the angle that intercepts it is inscribed, then the angle measure is half the measure of the arc. So the angle is 15°
determine standard from of the equation for the circle with center (h,k)=(-1/50,1/3),r=1/2
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-\frac{1}{50}}{ h},\stackrel{\frac{1}{3}}{ k})\qquad \qquad radius=\stackrel{\frac{1}{2}}{ r} \\\\\\ \left[ x-\left( -\frac{1}{50} \right) \right]^2+\left[ y-\frac{1}{3} \right]^2=\left( \frac{1}{2} \right)^2\implies \left( x+\frac{1}{50} \right)^2+\left( y-\frac{1}{3} \right)^2=\frac{1^2}{2^2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( x+\frac{1}{50} \right)^2+\left( y-\frac{1}{3} \right)^2=\frac{1}{4}~\hfill[/tex]
please help and explain the answer!
Answer:
462 cm^2
Step-by-step explanation:
The centerline of the cloth area has a radius of (28 cm + 14 cm)/2 = 21 cm, so its length will be 1/4 of the circumference of a circle of that radius:
cloth centerline length = (1/4)·2πr = (π/2)·21 cm = (22/7)/2 · 21 cm = 33 cm
The width of the cloth portion is ...
28 cm - 14 cm = 14 cm
so the area of the cloth portion will be the product of centerline length and width:
(33 cm)(14 cm) = 462 cm^2
Write an equation of a parabolawith a vertex (-5,2) and a directrix y = -1.
Answer:
[tex]y=\frac{1}{12}(x+5)^2+2[/tex]
Step-by-step explanation:
We start with the standard form of a parabola which is
[tex](x-h)^2=4p(y-k)[/tex]
We know h and k from the vertex, we just need to solve for p and then simplify the equation. P, by definition, is the distance between the directrix and the vertex. That is 3 units. So p = 3. Fitting that into our equation along with h and k gives us:
[tex](x+5)^2=4(3)(y-2)[/tex]
Divide both sides by 12, then add the 2 to both sides and we have our parabola!
A regular polygon could not have an interior angle measure of _____.
A.
45º
B.
90º
C.
150º
D.
160º
Answer:
A. 45°
Step-by-step explanation:
The smallest interior angle measure of any regular polygon is that of an equilateral triangle: 60°.
___
The corresponding exterior angle measure for interior angle x will be its supplement: 180° -x. This value must be a divisor of 360° 360° is not evenly divisible by 180°-45°=135°.
If the terminal side of an angle In standard position passes through the point (20, -21), then which of the following functions will be positive?
A. Cosecant
B. Secant
C. Tangent
Answer:
B
Hope This Helps! Have A Nice Day!!
Answer:
b
Step-by-step explanation:
The sum of two numbers is 842. The difference is 314. Find the numbers.
Let's call the two numbers x and y.
We know that x+y = 842 and that x-y = 314
Now that we have two equations, we can solve using substitution by solving for one variable in one of the equations, and plugging that in for the same variable in the other equation.
Lets solve for x in the second equation to get:
x = 314 + y
Now plug in 314+y for x in the first equation:
(314 + y) + y = 842
Combine like terms:
314 + 2y = 842
Now solve for y:
2y = 842-314
2y = 528
y = 264
Finally, plug 264 in for y to solve for x:
x + 264 = 842
x = 842-264
x = 578
The two numbers are 578 and 264.
Question 5(Multiple Choice Worth 7 points)
Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 3 as x approaches 3 from the left.
∞ ; x = -3
-∞ ; x = -3
-∞ ; x = 3
1 ; no vertical asymptotes
Answer:
-∞ ; x = 3
Step-by-step explanation:
The graph tends toward -∞ as x approaches 3 from the left. Thus there is a vertical asymptote at x=3, the value of x that makes the denominator zero.
Someone explain to me how I do this law of sines problem
Answer:
44.1 cm
Step-by-step explanation:
In order to find the length of side "a", you need to know the measure of angle A. That is found by making use of the fact that the sum of angles in a triangle is 180°.
102° + 28° + A = 180°
A = 180° -130° = 50°
Now, you can fill in the given information in the given equation and solve for "a":
sin(A)/a = sin(B)/b
sin(50°)/a = sin(28°)/(27 cm)
Multiplying by a(27 cm) gives ...
sin(50°)(27 cm) = a·sin(28°)
Dividing by the coefficient of "a", we get ...
a = (27 cm)sin(50°)/sin(28°) ≈ 44.0563 cm
Rounded to the nearest tenth, this is ...
a ≈ 44.1 cm
_____
Since we're looking for a side length (not an angle), I prefer to write the Law of Sines formula "upside down" from that shown:
a/sin(A) = b/sin(B) = c/sin(C)
Then it is one step to get to ...
a = b·sin(A)/sin(B) . . . . . . multiply by sin(A)
A can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company’s clients needs a cylindrical can that has the same volume but is 15 cm tall. What must the new radius be to meet the client’s need? Round to the nearest tenth of a centimeter.
2.7 cm
4.9 cm
7.3 cm
24.0 cm
Answer:
4.9 cm
Step-by-step explanation:
The original can has a volume of ...
V = πr²h = π(6 cm)²(10 cm) = 360π cm³
The new can will have the same volume, but a different height:
360π cm³ = πr²(15 cm)
24 cm² = r² . . . . . divide by 15π cm
r = √24 cm ≈ 4.9 cm . . . . . take the square root
The new radius must be about 4.9 cm.
Answer:
the anwser is 4.9
Step-by-step explanation:
Find the area. The figure is not drawn to scale.
Area of parallelogram(A) = base×hight
=4.7×3.3=15.51 sq. cm
Answer:
[tex]Area=15.51cm^2[/tex]
Step-by-step explanation:
The given figure is a parallelogram.
The area of a parallelogram is calculated using the formula:
[tex]Area=b\times h[/tex]
The base of the 4.7 cm.
The height is 3.3 cm.
We substitute the given values into the formula to obtain;
[tex]Area=4.7\times 3.3[/tex]
We multiply out to obtain;
[tex]Area=15.51cm^2[/tex]
Find the volume of the cylinder in terms of pi. The diagrams are not drawn to scale.
H: 15 m
R: 1.7 m
NEED HELP ASAP!!!!!!!!!!!!!!
Answer:
[tex]V=43.35\pi[/tex] [tex]m^3[/tex]
Step-by-step explanation:
The equation for the volume of a cylinder is [tex]V=\pi r^2h[/tex]
As we know what h and r are, we can plug them into the equation to get
[tex]V=\pi (1.7)^2(15)[/tex]
This then simplifies to
[tex]V=43.35\pi[/tex] [tex]m^3[/tex]
The volume of the cylinder in terms of pi is 43.35π cm³
Calculating the volume of a cylinderFrom the question, we are to determine the volume of the cylinder
The volume of a cylinder can be calculated by using the formula,
V = πr²h
Where V is the volume of the cylinder
r is the radius
and h is the height
From the given information,
h = 15m
r = 1.7 m
Putting the parameters into the formula, we get
V = π × 1.7² × 15
V = π × 2.89 × 15
V = 43.35π m³
Hence, the volume of the cylinder is 43.35π cm³.
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Pencils are on sale for $0.99 per dozen. Ms. Klein buys 8 pencils for each of her 96 students. How much will she spend on pencils?
Answer:
$63.36
Step-by-step explanation:
First we need to determine how many pencils are needed
8 pencils times 96 students
8*96 =768 pencils
A dozen is 12 pencils
Divide the number of pencils needed by 12 to determine how many dozen pencils are needed
768/12 =64
We need 64 dozen pencils
They cost .99 per dozen
64*.99 =63.36
It will cost $63.36 for the pencils
{35 POINTS} A factory produces t-shirts. The production cost, C(x), for x t-shirts can be modeled by a quadratic function.
Each of the following functions is a different form of the quadratic model for the situation given above. Which form would be the most helpful if attempting to determine the number of t-shirts that would minimize cost?
A.
C(x) = 0.02(x2 - 720x + 144,600)
B.
C(x) = 0.02(x - 360)2 + 300
C.
C(x) = 0.02x2 - 14.4x + 2,892
D.
C(x) = 0.02x(x - 720) + 2,892
Answer:
B. C(x) = 0.02(x - 360)2 + 300
Step-by-step explanation:
The minimum of a quadratic function is found at its vertex. The vertex form of the equation lets you read the coordinates of the vertex directly, so that is the form most helpful for finding minimum cost.
___
Perhaps the next most helpful form is that of option D, sometimes called "intercept form." The vertex is located halfway between the intercepts, so will be halfway between 0 and 720. Of course, the vertex location at 360 is read directly from the vertex form of option B.
Answer:
A
Step-by-step explanation:
Please use " ^ " to denote exponentiation: x^2 (not x2).
To determine the number of t-shirts that would minimize cost, we'd want to have a quadratic function graph that opens up, and to determine the vertex (which point would also be the minimum cost).
Equation A is the one we want. Why? because we can ignore the coefficient 0.02 in determining the minimum cost. We see immediately that the coefficient of the x^2 term is a = 1 and that of the x term is b = -720.
Recall that the axis of symmetry passes through the vertex / minimum, and has equation
720
x = -b / (2a). With a = 1 and b = -720, x = - --------- = 360
2
Again, A is the correct answer. The miminim cost occurs at x = 360 (shirts).
Martin ordered a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-
inch diameter. What is the approximate difference in area of the two pizzas?
Answer:
113 inches^2
Step-by-step explanation:
Select the statement that correctly describes the solution to this system of equations.
5x + 10y = 5
4x + 8y = 5
There is no solution
There is exactly one solution at (5,5)
There are infinitely many solutions
There is exactly one solution at (1,0)
Answer:
No solution
If you multiply the 1st by 4 and the second by -5
The result is
20x +40y= 20
-20x-40y= -20
When you add both equations the result is 0=0
Step-by-step explanation:
There is no solution for 5x + 10y = 5; 4x + 8y = 5 as they are parallel lines.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
The given pair of equation is :
5x + 10y = 5
4x + 8y = 5
[tex]a_1[/tex] =5, [tex]b_1[/tex]=10, [tex]c_1[/tex]=5
[tex]a_2[/tex]= 4, [tex]b_2[/tex]= 8, [tex]c_2[/tex]= 5
Now, checking the different condition on two pair of equations
So, we have the satisfied condition as
[tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]
= [tex]\frac{5}{4} =\frac{10}{8}\neq \frac{5}{5}[/tex]
which is condition for parallel.
Thus, There is no solution
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Hospital floors are usually covered by bare tiles. Carpets would cut down on noise but might be more likely to harbor germs. To study this possibility, investigators randomly assigned 8 of 16 available hospital rooms to have carpet installed. The others were left bare. Later, air from each room was pumped over a dish of agar (a gelatinous substance obtained from various kinds of red seaweed and used in biological culture media). The dish was incubated for a fixed period, and the number of bacteria colonies were counted. The response variable in this experiment is
Answer:
Given the details of the study carried
out on Hospitals to study the possibility that carpers might be more likely to harbor
germs, in which air from rooms with carpet and those without carpet was pumped over a
dish of agar, and the number of bacteria colonies were counted after incubating
the dish for a fixed period of time. The response in this study is number of bacteria colonies in a dish.