Your credit card has a balance of $3300 and an annual interest rate of 14%. You decided to pay off the balance over two years. If there are no further purchases charged to the card, you must pay $158.40 each month, and you will pay a total interest of $501.60. Assume you decided to pay off the balance over one year rather than two. How much more must you pay each month and how much less will you pay in total interest?

Answer:

0.6826 = 68.26% probability that you have values in this interval.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

X~N(8, 1.5)

This means that [tex]\mu = 8, \sigma = 1.5[/tex]

What is the probability that you have values between (6.5, 9.5)?

This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So

X = 9.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{9.5 - 8}{1.5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

X = 6.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{6.5 - 8}{1.5}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability that you have values in this interval.

Answer:

Step-by-step explanation:

ΔABC has the vertices as A(1, 1), B(4, 1) and C(4, 5).

Rule for the transformation has been given as,

f(x, y) → (x - 5, -y - 2)

By this rule vertices of the transformed image will be,

A(1, 1) → A'(1 - 5, -1 - 2)

         → A'(-4, -3)

B(4, 1) → B'(4 - 5, -1 - 2)

          → B'(-1, -3)

C(4, 5) → C'(4 - 5, -5 - 2)

           → C'(-1, -7)

Answer:

Q2) 29 degree       as unrounded to nearest degree is 28.95 degree

Q3) 69 degree       as unrounded to nearest degree is 68.56 degree

Step-by-step explanation:

QU 2)

When they speak of plane we see ABCD and also see ABC

So we need the length of AB and BC to find the diagonal CA

AB^2 + BC^2 = CA^2

16.4^2 + 9.1^2 = sqrt 351.77

CA^2 = sqrt 351.77 = 18.8 cm

We know CG = 10.4cm

We identify the hypotenuse for ACG triangle

We do trig tan x = opp/adj for CGA angle

Tan x = tan-1 10.4/18.8 = 28.95099521 degree

Tan x = tan-1 18.8/10.4 = 61.04900479 degree

so we know one is much smaller than the other

We also know ACG angle is 90 degree and that angle from ABCD that meets line AG is the smaller angle.

Answer therefore must be 28.95 degree = or 29 degree

QU 3)

we are basically looking for angle where VB meets BC line or AVB meets ABC we have the slant length, so step 1 is find the height by first dividing square base by 2 then finding the height.

= 7.6/2 = 3.8 cm

Then Pythagoras

BV^2  -  1/2 BC =  height

10.4^2  - 3.8^2 = height

Height = sq rt 93.72 =9.68090905 = 9.7cm

Which means  V to midpoint VC = V to midpoint  AB

They are the same and the midpoints are 90 degree angles.

To find the required angle for VB + BCmidpoint or we wont be able to determine the right angle hypotenuse.

We do the same as last question determine the hypotenuse and where the angle sought is is where we use the trig function = adj/hyp

Because if it was the midpoint angle then it would be opp/adj like the question 1  so this time its cos of x.

cos x = adj/hyp = cos-1 (3.8/ 10.4) = 68.5687455

Answer is 68.56 degree

The reason we show the height is so we can check by doing opp/hyp

= sin of x = sin-1 (9.68090905/3.8) = 23.11171135

and 90 -23.11171135 = 66.8882887

= 67 degree

So we go with the first one and assume 9.68 was already simplified to 9.7cm

= sin-1 (3.8/9.7) = 23 degree  90-23 = 67 degree

but when rounded to 10.4cm for slant we get the same

= sin-1 (3.8/10.4)

So we realise here trig functions -1  doesn't work on the same 90 degree angle for both lines that meet such 90 degree angle.

We try the sin-1 (10.4/ 9.68090905) = 68.5687455 = 69 degree

and that where the lines join away from the 90 degree angle we can always find true answer, and see it is a match with the first cos trig function we did.

This proves that cos line 1/line2  = sin line 1/line 2 are the same when the larger number is numerator for sin representing the hypotenuse slant for sin as shown and when the larger of the sides is numerator for cos di

and smallest side acts as denominator for both trig functions.

Answer:

cylinder:

curved sa = 2πrh

=> rectangle, breath = h, width = perimeter of circle =  2πr

total sa = 2πrh+2πr^2

=> curved sa + area of 2 circles

cone:

curved sa = πrl

=> treated as a triangle, base = circumference of circle, height = slant height

total sa = πr^2+πrl

=> curved sa + area of base (circle)

Use Bayes Theorem to compute that probability. I will denote bath as [tex]B[/tex] and nap as [tex]N[/tex], the probability will be denoted as [tex]P(B)[/tex] or [tex]P(N)[/tex].

By Bayes Theorem

[tex]P(B\mid N)=\frac{P(N\mid B)\cdot P(B)}{P(N)}[/tex]

Which reads,

"What is the probability of [tex]B[/tex] given [tex]N[/tex]".

We know that [tex]P(N\mid B)[/tex] is 1 because we already took a bath. So the formula simplifies to,

[tex]P(B\mid N)=\frac{P(B)}{P(N)}[/tex]

Now insert the data,

[tex]P(B\mid N)=\frac{1/5}{4/5}=\boxed{\frac{1}{4}}[/tex]

So the probability that you will take a bath is [tex]0.25[/tex] after you have taken a nap.

Hope this helps. :)

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is translated a units right and b units up, the new point is at A'(x + a, y + b).

If a point A(x, y) is reflected across the line y = -x, the new point is at A'(-y, -x).

If a point A(x, y) is rotated counterclockwise by 270 degrees, the new point is at A'(y, -x).

Let us assume that triangle ABC has vertices at A(-6, -1), B(-3, -3) and C(-1, -2).

If it is moved 5 units to the right and 2 units up, the new point is at A'(-1, 1), B'(1, -1) and C'(3, 0). If it is reflected across the line y = -x, the vertices are at A"(-1, 1), B"(1, -1) and C"(0, -3). If it is then rotated counterclockwise about the origin by 270°, the new point is at A'"(-1, -1), B"'(1, 1), C"'(3, 0)

Answer:

Domain: input values, independent variables

Range: output vales, dependent variables

Step-by-step explanation:

Think of it like a graph: the domain are the x-values and the range is the y-values. if you're doing a problem with time, the time will go on the x-axis and cannot be influenced by the y-values, but the y-vales are depending on what the x-values are (independent/dependent). for the input/output, usually when solving equations on a graph, you plug in the x-value and find the y-value. you're INPUTTING the x-value to receive the OUPUT.

Domain = set of allowed inputs

The input x is the independent variable as it can do whatever it wants without relying on y.

-------------------------

Range = set of possible outputs

The output is the dependent variable. It depends on what the input x is. Often, we make y the output dependent variable.

-------------------------

For example, with y = 2x+5, we can plug in anything we want for x (it doesn't need to look to y for guidance or anything). Once we pick something for x, it will directly determine what y is.

Let's say we picked x = 10. That would mean y = 2x+5 = 2*10+5 = 25. The input x = 10 in the domain leads to y = 25 in the range. We see that the output y = 25 depends entirely on the independent input x = 10.

9514 1404 393

Answer:

  (0, 2), (2/5, 0)

Step-by-step explanation:

In this slope-intercept form, the y-intercept is the constant in the equation: 2. That is the point of intersection on the y-axis is (0, 2).

__

When y=0, the value of x is the x-intercept.

  0 = -5x +2

  5x = 2 . . . . . . add 5x

  x = 2/5 . . . . . divide by 5

The point of intersection of the graph with the x-axis is (2/5, 0).

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Each point moves to the same distance on the other side of the mirror line. The slope of the mirror line is 1, so the points move along a line perpendicular to that, one with a slope of -1. You can make sure the distances are the same by counting the grid squares.

Answer:

y = 3x + 5

Step-by-step explanation:

just by going through the options and plugging in values from the chart, you can guess and check

y = 3x + 5 is the only answer that works

5 = 0 + 5

11 = 6 + 5

23 = 18 + 5

etc.

hope this helps!

AS IN THE PICTURE...........

Answer:

[tex]Given:[/tex] Δ ABC ≈ ΔDEF

[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²

⇒ 34/A(ΔDEF)=9²/(13.5)²

⇒34/A(ΔDEF)=81/182.25

⇒A(ΔDEF)=34×182.25/81

⇒Area of ΔDEF=76.5 cm²

----------------------------------

Hope it helps...

Have a great day!!!

Answer:

42

Step-by-step explanation:

2,​4,6,10,​16,26,​___

The pattern is adding the previous two numbers to get the next number

2+4 = 6

4+6 = 10

6+10 = 16

10+16 = 26

16+26 =42

Answer:

FALSE

Step-by-step explanation:

First, define y and x.

In statistics, we have what we call variables. Variables are items or symbols that can take on various values. We have dependent variables - whose values are derived from other variables in an equation - and independent variables - whose values are given and are used to determine the values of dependent variables.

Usually, y represents the dependent variable while x represents the independent variable. So the simplest form of regression equation is

y = f (x)

Said as "y is a function of x"

A logistic regression equation can be used to calculate y when x values are given.

Here, the independent variable function (the X function) is a logistic function and it is used to find a binary dependent variable (a Y value, out of two possible values).

In logistic regression equations, the value of Y is not numerical like 1, 0.2, 3/4, and so on. It is categorical, e.g.

Black/White, Gain/Lose, Pass/Fail, Eat/Drink, etc.

Answer:

Hence the probability that the mean weight of the sample of 55 cows would differ from the population mean by less than 12 lbs is 0.66545.

Step-by-step explanation:

Answer:9oooooooooooooooooooooooooooooooooooo

Step-by-step explanation:

Answer:

54, 55, 56, 57, 58

Step-by-step explanation:

Answer:

56 problems

Step-by-step explanation:

Set up an equation.

[tex]\frac{3}{5}x<35<\frac{13}{20}x[/tex]

Why do we do this? We are told that she solved MORE than 60%, or [tex]\frac{3}{5}[/tex], and LESS than 65%, or [tex]\frac{13}{20}[/tex]. Therefore, if we set the TOTAL number of problems to x, we have an equation we can solve.

[tex]\frac{3}{5}x<35<\frac{13}{20}x\\[/tex]

Multiply all parts of the inequality by 20 to get rid of the denominators.

[tex]20*\frac{3}{5}x<20*35<20*\frac{13}{20}x\\ \\12x<700<13x[/tex]

Now we can solve TWO individual inequalities to isolate the x variable.

[tex]12x<700\\x<\frac{700}{12}\\x < 175/3\\x<58[/tex]

We can approximate 175/3 to about 58 (rounding down). We will sometimes round down when we have to deal with whole numbers.

The second inequality is as follows.

[tex]13x>700\\x>700/13\\x>53[/tex]

Therefore, we can combine the two inequalities.

[tex]53<x<58[/tex]

There were in between 53 and 58 questions. Since the number of questions must be a whole number, there can be 54, 55, 56, 57, OR 58. Why does 58 also work? When you plug 58 back into the original equation, you get that it STILL works. This is due to the fact that inaccuracies in computations allow you to round UP.

However, the last thing to keep in mind is that there are four sections with an equal number of questions. Meaning, the final answer has to be a multiple of four. The only multiple of 4 is 56; therefore, the final answer is 56.

Answer:

if you mean 15k as is 15 thousand then the answer would be 15,010

Answer:

[tex]x = 0[/tex]

Step-by-step explanation:

[tex]3 |3x + 4| - 7 = 5[/tex]

[tex]3 |3x + 4 | = 12[/tex]

[tex] |3x + 4| = 4[/tex]

[tex]3x + 4 = 4[/tex]

[tex]3x = 0[/tex]

[tex]x = 0[/tex]

Answer:

Step-by-step explanation:

Integration (4t√t+a)dt

[tex]\int \left ( 4 t\sqrt t +a \right )dt\\\\=\int\left ( 4 t^{(\frac{3}{2})} +a\right ) dt\\\\= 4\times 2\times \frac{t^{\frac{5}{2}}}{5} + a t\\\\= 8 \frac{t^{\frac{5}{2}}}{5} + a t[/tex]

cto cto cto cto cto cto cto cto cto cto

Answer:

2

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

SOH CAH TOA is a mnemonic intended to remind you of the relevant trig relations.

  Sin = Opposite/Hypotenuse   ⇒   opposite = 15×sin(19°) ≈ 4.88 units

  Cos = Adjacent/Hypotenuse   ⇒   adjacent = 15×cos(19°) ≈ 14.18 units

Answer:

For plato users the correct option is D.

Step-by-step explanation:

D. 4.9 units, 14.2 units

===========================================================

Explanation:

Since we have an odd number of values, this tells us that the median is part of the data set. It's the middle most item after we sort the values.

Recall that the mode is the most frequent item. Since the mode and median are the same, this must mean x can only be equal to one of the following

4, 9, 7 or 8

We can only pick one of those values.

----------------------

If x = 4, then the set {4,9,7,8,x} updates to {4,9,7,8,4} which sorts to {4,4,7,8,9}

The middle most item is in slot 3, which would be 7. So the median is 7.

The median 7 does not match with the mode 4.

So we cross x = 4 off the list.

-----------------------

If x = 7, then we have {4,7,7,8,9}

The mode is 7 and the median is 7. So far, so good.

Now let's compute the mean. Add up the values and divide by 5 because there are 5 items.

(4+7+7+8+9)/5 = 35/5 = 7

We've shown that the set {4,7,7,8,9} has mean 7.

Overall, that set has the same mean, median and mode. So the answer is confirmed.

I'll let you check the cases when x = 8 and x = 9.

Answer:

Đối tượng kế toán là sự hình thành và biến động của tài sản mà kế toán phải phản ánh và giám đốc trong quá trình hoạt động của đơn vị được thể hiện ở hai mặt là Tài sản và Nguồn vốn. Tài sản của đơn vị; Sự vận động của tài sản.

Answer:

22

Step-by-step explanation:

The sum of the angles in a triangle are 180

Let the third angle be x

82+76+x = 180

158 +x = 180

x = 180-158

x =22

Now keep the,

Third unknown angle as y.

The formula we use,

→ Sum of all angles of triangle = 180°

Let's solve for y,

→ y + 82 + 76 = 180°

→ y + 158 = 180°

→ y = 180 - 158

→ [y = 22°]

Thus, option (B) is the answer.

Answer:

-55 +11p

Step-by-step explanation:

-11(5-p)

Distribute

-11*5 -11*(-p)

-55 +11p