Step-by-step answer:
APY (annual percentage yield) is the amount of interest in percent one would actually earn by investing a sum of money in a year.
It takes into account the interest rate expressed in any particular form, and the compounding period.
In the current market, most interest rates (for example, credit cards) are expressed in APR (Annual percentage rate) which is an underestimate of the actual amount to be paid, by NOT taking into account the compounding period, monthly (instead of annually) most of the time. The shorter compounding period increases the APY.
Here the APR is 4.4%. to take into account the compounding period, we divide the interest rate by 12 to give the monthly rate, 4.4%/12=0.044/12.
This rate will then be compounded 12 times to give the APY, or the future value after 12 months.
Future value = (1+0.044/12)^12 = 1.044898
Therefore the APY is 1.044898 less initial deposit, or
1.044898-1 = 0.044898, or 4.4898%, or 4.49% (rounded to 2 decimal places)
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.
0.1346
0.1285
0.1946
0.1469
Answer:
0.1469
Step-by-step explanation:
Given from the question;
Mean=8.4 hrs=μ
Standard deviation=1.8 hrs=δ
Sample size, n=40
Let x=8.7
z=(x-μ)÷(δ÷√n)
Find z(8.7)
z=(8.7-8.4)÷(1.8÷√40)
z={0.3×√40}÷1.8=1.05409
z=1.0541
Read from the standard normal probabilities table
P(z>1.0541)
=0.1459
Final answer:
Using the Central Limit Theorem and standard error calculation, the probability that the mean rebuild time by 40 mechanics exceeds 8.7 hours is found to be approximately 0.1469.
Explanation:
To find the probability that the mean rebuild time for a 2005 Chevrolet Cavalier transmission by 40 mechanics exceeds 8.7 hours, given that the mean is 8.4 hours and the standard deviation is 1.8 hours, we will use the concept of the sampling distribution of the sample mean. Since the standard deviation of the population is known, we apply the Central Limit Theorem, which states that the distribution of the sample means will be approximately normal if the sample size is large enough (n>30 in this case).
First, calculate the standard error of the mean (SEM) using the formula: SEM = σ/√n, where σ is the standard deviation of the population and n is the sample size. Therefore, SEM = 1.8/√40 = 0.285.
Next, find the z-score that corresponds to a mean rebuild time of 8.7 hours using the formula: z = (X - μ)/SEM, where X is the value of interest (8.7 hours), and μ is the population mean (8.4 hours). Thus, z = (8.7 - 8.4)/0.285 = 1.05.
Finally, look up the z-score in a z-table or use a statistical calculator to find the probability that Z is greater than 1.05, which is approximately 0.1469.
Therefore, the probability that their mean rebuild time exceeds 8.7 hours is 0.1469.
Round 0.249 to the nearest tenth
Answer:
.250
Step-by-step explanation:
4 is in the tenths place, if the number to the right of a number is five or higher you round the number up.
Answer:
Step-by-step explanation:
Math courses just love this kind of question. The only worse question would be something like -0.949 rounded to the nearest 1/10
Your question should round to 0.2.
The one I presented should round to -0.9
the graph shows a system of equations
What is the solution to the system of equations?
A.(-1,3)
B.(1, -3)
C.(1,3)
D.(-1,-3)
Answer:
B. (1, -3)Step-by-step explanation:
The solution of the system of equations is the coordinates of the intersection of the lines.
(1, -3)
Answer:
B.(1, -3)
Wherever the lines intersect is the solution. Hope this helps!
Step-by-step explanation:
Please help this is my last tutorial in this subject.......
Answer: is there anyway U can give me a more zoomed in pic
Step-by-step explanation:
Given that (X+3) is a factor of the expression x^3 + 4x^2 + px + 3 , find the value of p. Hence, solve the equation x^3 + 4x^2 + px + 3=0, expressing the complex number in the form a + bi
Answer:
[tex]p=4[/tex]
[tex]x=\frac{-1}{2} \pm \frac{\sqrt{3}}{2}i[/tex]
Step-by-step explanation:
We are given (x+3) is a factor of [tex]x^3+4x^2+px+3[/tex], which means if were to plug in -3, the result is 0.
Let's write that down:
[tex](-3)^3+4(-3)^2+p(-3)+3=0[/tex]
[tex]-27+36-3p+3=0[/tex]
[tex]9-3p+3=0[/tex]
[tex]9+3-3p=0[/tex]
[tex]12-3p=0[/tex]
[tex]12=3p[/tex]
[tex]p=4[/tex]
So the cubic equation is actually [tex]x^3+4x^2+4x+3=0[/tex] that they wish we solve for [tex]x[/tex].
To find another factor of the given cubic expression on the left, I'm going to use synthetic division with that polynomial and (x+3) where (x+3) is divisor. Since (x+3) is the divisor, -3 will be on the outside like so:
-3 | 1 4 4 3
| -3 -3 -3
---------------------
1 1 1 0
So the other factor of [tex]x^3+4x^2+4x+3[/tex] is [tex](x^2+x+1)[/tex].
We must solve [tex]x^2+x+1=0[/tex].
Compare this to [tex]ax^2+bx+c=0[/tex].
We have [tex]a=1,b=1, \text{ and } c=1[/tex].
The quadratic formula is
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
Plug in the numbers we have for [tex]a,b, \text{ and } c[/tex].
[tex]x=\frac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex].
Simplify inside the square root while also performing the one operation on bottom:
[tex]x=\frac{-1 \pm \sqrt{1-4}}{2}[/tex]
[tex]x=\frac{-1 \pm \sqrt{-3}}{2}[/tex]
Now our answer will include an imaginary part because of that sqrt(negative number).
The imaginary unit is [tex]i=\sqrt{-1}[/tex].
So our final answer is:
[tex]x=\frac{-1}{2} \pm \frac{\sqrt{3}}{2}i[/tex]
Final answer:
To find the value of p, substitute -3 into the polynomial since (X+3) is a factor, thus yielding p=3. With p known, the polynomial becomes [tex]x^3 + 4x^2 + 3x + 3[/tex] = 0, and can now be solved for x.
Explanation:
Finding the Value of p
Given the polynomial [tex]x^3 + 4x^2 + px + 3[/tex] and the fact that (X+3) is a factor, we can use polynomial division or synthetic division to find the value of p. Since (X+3) is a factor, when we substitute -3 for x in the polynomial, the result should be zero.
Substituting -3 into the polynomial yields:
[tex](-3)^3 + 4(-3)^2 + p(-3) + 3[/tex] = 0
-27 + 36 - 3p + 3 = 0
9 - 3p = 0.
Solving for p gives us:
3p = 9
p = 3.
Solving the Equation
Now that we know p, we rewrite the polynomial as [tex]x^3 + 4x^2 + 3x + 3 = 0[/tex] and use the fact that (X+3) is a factor to perform the division. The remainder of the division gives us a quadratic polynomial which we can solve using the quadratic formula or factoring.
Factor by grouping.
a2 + 2ab – 24b2
(a + 6b)(a + 4b)
(a – 6)(a + 4b)
(a + 6b)(a – 4b)
(a – 6b)(a – 4b)
Answer:
(a + 6b)(a - 4b)
Step-by-step explanation:
You want your midst term to result in 2ab, NOT -2ab.
I am joyous to assist you anytime.
What is the solution to the equation -4(2x+3) = 2x+6-(8x+2)?
0
x=-10
0
L
0
|
0
Answer:
x = -8
Step-by-step explanation:
-4(2x+3) = 2x+6-(8x+2)
Distribute
-8x-12= 2x+6-8x-2
Combine like terms
-8x-12 = -6x+4
Add 8x to each side
-8x-12 +8x = -6x+4+8x
-12 = 2x+4
Subtract 4 from each side
-12-4 = 2x+4-4
-16 = 2x
Divide each side by 2
-16/2 = 2x/2
-8 =x
Which shows x^2 + 2x = 3 as a perfect square equation? What are the solution(s)?
a. x^2+2x-3=0; -3 and 1
b. x^2+2x+1=0; -1
c. (x+1)^2=4; -3 and 1
d. (x+1)^2=0; -1
First we can rewrite the equation to,
[tex]x^2+2x-3=0[/tex]
Which factors to,
[tex](x+3)(x-1)=0[/tex]
And this leads towards two solutions,
[tex]x_1\Longleftrightarrow x+3=0\Longrightarrow x_1=-3[/tex]
and,
[tex]x_2\Longleftrightarrow x-1=0\Longrightarrow x_2=1[/tex]
The answer is A.
Hope this helps.
r3t40
Answer:
c
Step-by-step explanation:
Given
x² + 2x = 3
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(1)x + 1 = 3 + 1
(x + 1)² = 4 ( take the square root of both sides )
x + 1 = ± [tex]\sqrt{4}[/tex] = ± 2 ( subtract 1 from both sides )
x = - 1 ± 2, hence
x = - 1 - 2 = - 3 and x = - 1 + 2 = 1
if A= (-1,3) and B=(11,-8) what is the length of ab
Answer:
16.3 units ( to 1 dec. place )
Step-by-step explanation:
Using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = A(- 1, 3) and (x₂, y₂ ) = B(11, - 8)
AB = [tex]\sqrt{(11+1)^2+(-8-3)^2}[/tex]
= [tex]\sqrt{12^2+(-11)^2}[/tex]
= [tex]\sqrt{144+121}[/tex]
= [tex]\sqrt{265}[/tex] ≈ 16.3 ( to 1 dec. place )
The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of the areas?
Answer:
8:7 and 64:49
Step-by-step explanation:
If the widths of two similar rectangles are 16 cm and 14 cm, the ratio of the areas are 8:7 and 64:49.
What is the solution to the system of equations graphed below?
y = --3/2x+2
y = 5x + 28
Answer:
(-4, 8) → x = -4 and y = 8Step-by-step explanation:
We only need two points to plot the graph of each equation.
[tex]y=-\dfrac{3}{2}x+2\\\\for\ x=0\to y=-\dfrac{3}{2}(0)+2=0+2=2\to(0,\ 2)\\\\for\ x=2\to y=-\dfrac{3}{2}(2)+2=-3+2=-1\to(2,\ -1)\\\\y=5x+28\\\\for\ x=-4\to y=5(-4)+28=-20+28=8\to(-4,\ 8)\\\\for\ x=-6\to y=5(-6)+28=-30+28=-2\to(-6,\ -2)[/tex]
Look at the picture.
Read the coordinates of the intersection of the line (solution).
Answer:
(-4,8)
Step-by-step explanation:
Given system of equations,
[tex]y=-\frac{3}{2}x+2-----(1)[/tex]
[tex]y=5x+28------(2)[/tex]
In equation (1), If x = 0, y = 2,
If y = 0,
[tex]-\frac{3}{2}x+2=0\implies -\frac{3}{2}x=-2\implies -3x=-4\implies x=\frac{4}{3}[/tex]
Join the points (0,2) and (4/3,0) in the graph we get the line (1),
In equation (2), if x = 0, y = 28,
If y = 0,
[tex]5x+28=0\implies 5x=-28\implies x=-5.6[/tex]
Join the points (0, 28) and (-5.6,0) in the graph we get the line (2),
Hence, by graph,
The intersection point of line (1) and (2) is (-4,8)
Which is the required solution.
The parent function f(x)=5^x has been virtually compressed by a factor of 1/2, shifted to the left three units and up two units. Chose the correct function to represent the transformation.
Answer:
Option 2 is correct
[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]
Step-by-step explanation:
We can se ethat the given function is an exponential function.
The function is:
5^x
In order to compress the function the original function is multiplied a constant.
As the function is compressed by a factor of 1/2
The function will become:
g(x) = 1/2 * 5^x
Now the function is shifted to left which is a horizontal shift. For horizontal shift of n units, n is added to the power so the function will become:
[tex]g(x) = \frac{1}{2}5^{x+3}[/tex]
Then the function is shifted upwards two units, the vertical shhift is added to the whole function so the function will become:
[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]
Hence, Option 2 is correct ..
How many multiples of three are between 10 and 787 and show work pls
As per the concept of arithmetic sequence, there are 259 multiples of three between 10 and 787
To solve this problem, we need to find the first and last multiples of three within the given range and then count how many integers are there in between
Step 1: Find the first multiple of three greater than or equal to 10.
The first multiple of three greater than or equal to 10 is 12.
Step 2: Find the last multiple of three that is less than or equal to 787.
The largest multiple of three less than or equal to 787 can be calculated as follows:
Divide 787 by 3:
787 ÷ 3 ≈ 262.33
The largest multiple of three less than or equal to 787 is:
262 × 3 = 786
Step 3: Count the multiples of three within the range.
Now that we have found the first and last multiples of three within the range, we need to count the number of multiples of three between them, including the endpoints.
The multiples of three between 12 and 786 are:
12, 15, 18, ..., 783, 786.
Step 4: Calculate the total count of multiples.
To calculate the total count, we can use the formula for finding the number of terms in an arithmetic sequence:
Number of terms = (last term - first term) / common difference + 1.
In this case, the first term is 12, the last term is 786, and the common difference (the difference between consecutive terms) is 3.
Number of terms = (786 - 12) / 3 + 1
Number of terms = 774 / 3 + 1
Number of terms = 258 + 1
Number of terms = 259.
To know more about multiples here
https://brainly.com/question/24327271
#SPJ2
you can calculate the probabilityof a random event, such as the rolling of dice or dealing of cards, by _____
Answer:
Making a fraction.
Step-by-step explanation:
Put the favored outcome as the numerator. Then, put the total number of outcomes as the denominator and boom, you have calculated probability. *Thumbs Up*
Solve the inequality: –3(x + 2) > 4x + 5(x – 7)
Answer:
29/12 > x
Step-by-step explanation:
–3(x + 2) > 4x + 5(x – 7)
Distribute
-3x -6 > 4x +5x-35
Combine like terms
-3x-6 > 9x -35
Add 3x to each side
-3x+3x-6 > 9x+3x -35
-6 > 12x-35
Add 35 to each side
-6+35 > 12x -35+35
29 > 12x
Divide each side by 12
29/12 > 12x/12
29/12 > x
The point (-3,-2) is rotated 180 degrees about the origin. The coordinates of its image are:
Answer:
(3,2)
Explanation:
The rotation of a point 180 degrees about the origin follows the rule:
(x,y) → (-x, -y)That means that both the x-coordinate and the y-coordinate transform into their negative values.
So, - 3 transforms into - (-3) = 3, and - 2 transforms into - (-2) = 2.
The result is (-3, -2) → (3,2).
Situation 1: In Lakeville, Melinda’s television cable bill is a flat rate of $50 per month, plus $1.50 for every movie she rents. After one month of service, her bill is $66.25.
Situation 2: In Oceanside, Kimberly’s television cable bill is a flat rate of $60 dollars per month, plus $1.25 for every movie she rents.
If you were to model these two situations with equations to solve for all the unknowns, what similarities and differences would the equations have? Can you solve for all the unknowns in both situations?
Answer:
situation 1 : flat rate of 50....1.50 per movie.....after 1 month her bill is 66.25
66.25 = 1.50x + 50
situation 2 : flat rate of 60....1.25 for every movie...
y = 1.25x + 60
both situations have a flat rate fee plus a charge for every movie. In situation 1, u can solve for x (the number of movies rented) because u know how much she was charged. However, in situation 2, without more information, u cannot solve this equation...what u would need to solve it would either be the number of movies rented or the total bill showing what she was charged. So basically, in situation 1, u are given more information then in situation 2.....enough information to be able to solve for the variable x...whereas, in situation 2, u are not given enough info to solve for a variable and get a numerical answer
BRAINLIEST PLEASE!!!!!
Answer: Situation 1 involves one independent variable that stands for the number of movies Melinda rented. Situation 1 gives a total for the monthly bill, but situation 2 does not give a total for the monthly bill. Because situation 2 leaves the total value out, it needs an additional variable. Therefore, situation 2 involves two variables—the number of movies Kimberly rented (the independent variable) and the monthly cable bill (the dependent variable). In this situation, we can’t solve for one variable without knowing the other.
Step-by-step explanation: ed.men.tum answer. DO NOT copy and paste!
Given that h=10, b=5, and r=3.8, find the area of the unshaded region. Use 3.14 for π as necessary. All answers are expressed in square units.
A. 70.34
B. 36.93
C. 25
D. 20.34
The area of the circle is found using the formula Area = PI x r^2
The area of a triangle is found using the formula Area = 1/2 x base x height.
Using the given dimensions:
Area of the circle = 3.14 x 3.8^2 = 45.3416 square units.
The area of the triangle is 1/2 x 5 x 10 = 25 square units.
To find the area of the unshaded part, subtract the area of the shaded triangle from the circle:
Area = 45.3416 - 25 = 20.3416
Round to two decimal places = 20.34
The answer is D. 20.34
D. 20.34
In this case, we must calculate first the Areas of the Triangle ([tex]A_{t}[/tex]), in square units, and the Circle ([tex]A_{c}[/tex]), in square units, later we subtract the Area of the former from the Area of the latter to determine the Area of unshaded region ([tex]A_{u}[/tex]), in square units. The Area formulas for each figure are, respectively:
Triangle
[tex]A_{t} = \frac{1}{2}\cdot b\cdot h[/tex] (1)
Circle
[tex]A_{c} = \pi\cdot r^{2}[/tex] (2)
Unshaded Area
[tex]A_{u} = A_{c} - A_{t}[/tex] (3)
Where:
[tex]h[/tex] - Height of the triangle.
[tex]b[/tex] - Base of the triangle.
[tex]r[/tex] - Radius of the circle.
If we know that [tex]h = 10[/tex], [tex]b = 5[/tex] and [tex]r = 3.8[/tex], then the area of the unshaded region is:
[tex]A_{t} = \frac{1}{2}\cdot (5)\cdot (10)[/tex]
[tex]A_{t} = 25[/tex]
[tex]A_{c} = \pi\cdot 3.8^{2}[/tex]
[tex]A_{c} \approx 45.365[/tex]
[tex]A_{u} = 45.365-25[/tex]
[tex]A_{u} = 20.365[/tex]
The correct answer is D.
Please see this question related to Area problems: https://brainly.com/question/16151549
Is X=-2 a solution of inequation
2x+1> X-3? why?
Answer:
-2 >-4
This is true, so it is a solution
Step-by-step explanation:
2x+1> x-3
Subtract x from each side
2x-x+1> x-x-3
x +1 > -3
Subtract 1 from each side
x+1-1 >-3-1
x > -4
x =-2 Substitute this into the inequality
-2 >-4
This is true, so it is a solution
What is the sqaure root of 40?
Answer:
6.32455532034 or just 6
Step-by-step explanation:
Answer:
2√10
Step-by-step explanation:
Find two numbers that multiply to forty, where one of them is a NON-PERFECT square. Those numbers would be 10 and 4. Take the square root of both and you will see that 2 comes from the 4, so that moves to the outside, and √10 stays the way it is because there is no perfect square to factor from this. With that being said, you have your answer.
I am joyous to assist you anytime.
find sec theta if theta is in quadrant 4 and sin theta= -1/5
Answer:
[tex]\frac{5}{2\sqrt{6} }[/tex]
Step-by-step explanation:
Since Θ is in fourth quadrant then cosΘ > 0, as is secΘ
Given
sinΘ = - [tex]\frac{1}{5}[/tex], then
cosΘ = [tex]\sqrt{1-(-1/5)^2}[/tex]
= [tex]\sqrt{1-\frac{1}{25} }[/tex] = [tex]\sqrt{\frac{24}{25} }[/tex] = [tex]\frac{2\sqrt{6} }{5}[/tex]
Hence
secΘ = [tex]\frac{1}{\frac{2\sqrt{6} }{5} }[/tex] = [tex]\frac{5}{2\sqrt{6} }[/tex]
Answer:
[tex]\sec(\theta)=\frac{5\sqrt{6}}{12}[/tex]
The answer is the last one.
Step-by-step explanation:
If we are in quadrant 4, then x (cosine) is positive and y (sine) is negative.
Since cosine is positive, secant is positive because secant is the reciprocal of cosine.
So we already know the answer is not the 1st one or the 3rd one.
I'm going to use a Pythagorean Identity to find cosine value of theta.
[tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex]
Enter in -1/5 for [tex]\sin(\theta)[/tex]:
[tex]\cos^2(\theta)+(\frac{-1}{5})^2=1[/tex]
Simplify a bit:
[tex]\cos^2(\theta)+\frac{1}{25}=1[/tex]
Subtract 1/25 on both sides:
[tex]\cos^2(\theta)=1-\frac{1}{25}[/tex]
Write 1 as 25/25 so you have a common denominator on the right hand side:
[tex]\cos^2(\theta)=\frac{25}{25}-\frac{1}{25}[/tex]
[tex]\cos^2(\theta)=\frac{24}{25}[/tex]
Take the square root of both sides:
[tex]\cos(\theta)=\pm \sqrt{\frac{24}{25}}[/tex]
[tex]\cos(\theta)=\pm \frac{\sqrt{24}}{\sqrt{25}}[/tex]
I will worry about simplifying the square root part when finding secant.
We said that cosine was positive because we were in the fourth quadrant.
[tex]\cos(\theta)=\frac{\sqrt{24}}{\sqrt{25}}[/tex]
Now recall that cosine and secant are reciprocals of each other:
[tex]\sec(\theta)=\frac{\sqrt{25}}{\sqrt{24}}[/tex]
Let's simplify the square part not.
Usually people hate the square root on both and also if you look at your choices none of the choice have square root on bottom.
So we are going to multiply top and bottom by [tex]\sqrt{24}[/tex]. I'm going to also write 5 instead of [tex]\sqrt{25}[/tex].
[tex]\sec(\theta)=\frac{5}{\sqrt{24}} \cdot \frac{\sqrt{24}}{\sqrt{24}}[/tex]
[tex]\sec(\theta)=\frac{5\sqrt{24}}{24}[/tex]
Now let's simplify the square root of 24.
We know 24 is not a perfect square, but 24 does contain a factor that is a perfect square. That factor is 4.
[tex]\sec(\theta)=\frac{5\sqrt{4}\sqrt{6}}{24}[/tex].
[tex]\sec(\theta)=\frac{5(2)\sqrt{6}}{24}[/tex]
[tex]\sec(\theta)=\frac{10\sqrt{6}}{24}[/tex]
Now both 10 and 24 share a common factor of 2 so let's divide top and bottom by 2:
[tex]\sec(\theta)=\frac{5\sqrt{6}}{12}[/tex]
The answer is the last one.
Your company is introducing a fruit drink packaged in an aluminum box with a square
base. Find the surface area of this box as a function of its dimension of its base, S, given
that volume of the box is 36 in. Graph this function and determine the dimensions that
produce a minimum surface area for this aluminum box.
Answer:
See explanation
Step-by-step explanation:
Let x in be the base side length and y in be the height of the box. Since the base is a square, we have
[tex]S=x^2\Rightarrow x=\sqrt{S}[/tex]
The volume of the box is
[tex]V=S\cdot y\\ \\36=Sy\Rightarrow y=\dfrac{36}{S}[/tex]
The surface area of the box is
[tex]SA=2x^2+4xy\\ \\SA(S)=2S+4\cdot \sqrt{S}\cdot \dfrac{36}{S}=2S+\dfrac{144}{\sqrt{S}}[/tex]
The graph of the function SA(S) is shown in attached diagram.
Find the derivative of this function:
[tex]SA'(S)=(2S+144S^{-\frac{1}{2}})'=2-\dfrac{1}{2}\cdot 144\cdot S^{-\frac{1}{2}-1}=2-\dfrac{72}{S\sqrt{S}}[/tex]
Equate this derivative to 0:
[tex]2-\dfrac{72}{S\sqrt{S}}=0\\ \\2S\sqrt{S}=72\\ \\S\sqrt{S}=36\\ \\S^{\frac{3}{2}}=6^2\\ \\S=6^{\frac{4}{3}}[/tex]
So, the dimensions that produce a minimum surface area for this aluminum box are:
[tex]x=\sqrt{6^{\frac{4}{3}}}=6^{\frac{2}{3}} \ in\\ \\y=\dfrac{6^2}{6^{\frac{4}{3}}}=6^{\frac{2}{3}}\ in.[/tex]
Vivian can type 94 words in 4 minutes. At this rate how many words can she type in 12 minutes?
Answer:
The answer is 282
because 94 in 4 mins so you need to use multiple 94 x 3 the answer is 282.
An item is regularly priced at $39. Ashley bought it at a discount of 55% off the regular price.
55% off the regular price means she paid 45% of the regular price. ( 100% - 55% = 45%
Multiply the original price by 45%:
39 x 0.45 = 17.55
She paid $17.55
(If you need to know how much she saved: 39 - 17.55 = $21.45)
Answer:
Ashley bought the item for $17.55
In each family of functions, the _____function is the most basic function in
the family.
Answer:
parent funtion is most basic
Step-by-step explanation:i just took the test
I need help solving
[tex]3D-2E=3\left[\begin{array}{cc}5&5\\-3&7\\1&3\end{array}\right] -2\left[\begin{array}{cc}6&7\\2&-7\\0&5\end{array}\right] \\\\3D-2E=\left[\begin{array}{cc}15&15\\-9&21\\3&9\end{array}\right] -\left[\begin{array}{cc}12&14\\4&-14\\0&10\end{array}\right] \\\\3D-2E=\left[\begin{array}{cc}3&1\\-13&35\\3&-1\end{array}\right][/tex]
The function f(x) 32(1.5) represents the chipmunk population of a forest x years after it was first studied. What was the original population of chipmunks?
A) 32
B) 21
C) 48
D) 72
Answer:
A) 32
Step-by-step explanation:
I will assume the function is
f(x) = 32 (1.5)^x
This is in the form
y =a b^x
in which a is the initial value, b is the growth rate, x is the time
a =32, which is the initial population
b= 1.5, which means 1.5-1 = .5. which means it grows at a 50% increase
x = number of years
which of the following is a factor of x^6 + 1000?
Well,
[tex]x^6+1000=(x^2)^3+10^3[/tex]
From here we use [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex],
[tex](x^2+10)\boxed{(x^4-10x^2+100)}[/tex]
And the found our factor.
Hope this helps.
r3t40
Answer:
Option B
Step-by-step explanation:
40 POINTS
The sides of an isosceles triangle are 5, 5, and 7. Find the measure of the vertex angle to the nearest degree.
Answer:
Answer:
89
°
to the nearest degree.
Explanation:
The base of the triangle 7 can be divided in half by a line of symmetry of the isosceles triangle, which will bisect the vertex angle. This creates two right triangles:
Each with a base of 3.5 and a hypotenuse of 5.
The side opposite the half of the vertex angle is 3.5, the hypotenuse is 5.
The sine function can be used to find the angle.
sin
θ
=
o
p
p
h
y
p
sin
θ
=
3.5
5
=
0.7
Use the inverse sin function or a table of trig functions to find the corresponding angle . (Arcsin)
arcsin
0.7
=
44.4
°
Remember that this is the value of half of the vertex angle so double the value to find the vertex angle.
2
×
44.4
=
88.8
°
rounded off to the nearest whole degree =
89
°
Determine whether the relation represents y as a function of x.
1.) x^2+y^2=9
2.) 2xy=1
Answer:
1 is not a function
2 is a function because you can write it (AS) f(x)=1/(2x).
Step-by-step explanation:
1) x^2+y^2=9 is a circle with center (0,0) and radius 3.
To get this all I did was compare to (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.
A circle is not a function.
You can solve solve for and see that you will get two values for y which is no go for a function.
Let's do that:
[tex]x^2+y^2=9[/tex]
Subtract x^2 on both sides:
[tex]y^2=9-x^2[/tex]
Square root both sides:
[tex]y=\pm \sqrt{9-x^2}[/tex].
2) 2xy=1
Divide both sides by 2x:
y=1/(2x).
This is a function only one y there.