A bank loaned out $28,500, part of it at the rate of 14% annual interest, and the rest at 4% annual
interest. The total interest earned for both loans was $2,640.00. How much was loaned at each rate?
$
was loaned at 14% and
was loated at 4%.

Answer

i think it is 48.

Step-by-step explanation:

Answer:

By the Central Limit Theorem, the distribution of ¯ x is approximately normal with mean 187 and standard deviation 2.05.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The lengths of adult males' hands are normally distributed with mean 187 mm and standard deviation is 7.1 mm.

This means that [tex]\mu = 187, \sigma = 7.1[/tex]

Suppose that 12 individuals are randomly chosen.

This means that [tex]n = 12, s = \frac{7.1}{\sqrt{12}} = 2.05[/tex]

What is the distribution of ¯ x?

By the Central Limit Theorem, the distribution of ¯ x is approximately normal with mean 187 and standard deviation 2.05.

Answer:

I'm guessing you mean -7 < -12 and if it's true and false, if so the answer would be false because -7 is larger than -12.

Step-by-step explanation:

I'm guessing you mean -7 < -12 and if it's true and false, if so the answer would be false because -7 is larger than -12.

(Tell me the question if this is incorrect. Thanks!!!)

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Answer:

49.2

Step-by-step explanation:

Answer:

ℎℎ ℎ

Step-by-step explanation:

ℎℎℎℎ ℎ ℎ

9514 1404 393

Answer:

  m = 8

  n = 4√3

Step-by-step explanation:

The right triangles in this figure are all similar, so the ratios of hypotenuse to short side are the same.

  (12+4)/m = m/4

  64 = m² . . . . multiply by 4m

  8 = m . . . . . . square root

__

Likewise, the ratio of long side to short side is the same.

  12/n = n/4

  48 = n² . . . . . . multiply by 4n

  4√3 = n . . . . . take the square root

_____

Additional comment

You may have noticed that the ratios of side lengths are ...

  4 : n : m = 4 : 4√3 : 8 = 1 : √3 : 2 . . . . . side lengths of a 30°-60°-90° triangle

This means the unmarked side is 8√3.

__

We supplied all of the missing lengths because we know this problem is likely to be presented in different forms, asking for values other than m.

Answer:

Step-by-step explanation:

Answer:

It's just negative, just enter this sign -

Step-by-step explanation:

The coordinates of the point on the unit circle at an angle -135° are [tex](-\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} )[/tex]

"The coordinates of any point on the circle [tex]x^{2}+ y^{2}= r^{2}[/tex] are [tex](r~cos\theta,r~sin\theta)[/tex]"

sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

For given question,

We need to find the coordinates of the point on the unit circle at an angle -135°

We know, for unit circle radius = 1

So, the coordinates of any point on the unit circle would be [tex](cos\theta, sin\theta)[/tex]

Here, [tex]\theta=-135^{\circ}[/tex]

Now, we find the the value of [tex]sin(-135^{\circ}),~cos(-135^{\circ})[/tex]

[tex]sin(-135^{\circ})\\\\=-sin(135^{\circ})\\\\=-sin(180^{\circ}-45^{\circ})\\\\=-[sin(180^{\circ})cos(45^{\circ})-cos(180^{\circ})sin(45^{\circ})]\\\\=-[0\times \frac{1}{\sqrt{2} }-(-1)\times \frac{1}{\sqrt{2} } ]\\\\=-(0+\frac{1}{\sqrt{2} } )\\\\=-\frac{1}{\sqrt{2} }\\\\=-\frac{1\times \sqrt{2} }{\sqrt{2} \times \sqrt{2} }\\\\=-\frac{\sqrt{2} }{2}[/tex]

and cos(-135°) would be,

[tex]cos(-135^{\circ})\\\\=cos(135^{\circ})\\\\=cos(180^{\circ}-45^{\circ})\\\\=cos(180^{\circ})sin(45^{\circ})+sin(180^{\circ})sin(45^{\circ})\\\\=((-1)\times \frac{1}{\sqrt{2}} )+(0\times \frac{1}{\sqrt{2} }) \\\\=-\frac{1}{\sqrt{2} }+0\\\\ =-\frac{1}{\sqrt{2}}\\\\=-\frac{1\times \sqrt{2} }{\sqrt{2}\times \sqrt{2}}\\\\=-\frac{\sqrt{2} }{2}[/tex]

Therefore, the coordinates of the point on the unit circle at an angle -135° are [tex](-\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} )[/tex]

Learn more about the coordinates of the point on the unit circle here:

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Answer:

373.8

Step-by-step explanation:

Answer:

90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

First group: Sample of 163, 13% has a second episode.

This means that:

[tex]p_1 = 0.13, s_1 = \sqrt{\frac{0.13*0.87}{163}} = 0.026[/tex]

Second group: Sample of 160, 14% has a second episode

This means that:

[tex]p_2 = 0.14, s_2 = \sqrt{\frac{0.14*0.86}{160}} = 0.027[/tex]

Distribution of the difference:

[tex]p = p_1 - p_2 = 0.13 - 0.14 = -0.01[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.026^2+0.027^2} = 0.0375[/tex]

Confidence interval:

The confidence interval is:

[tex]p \pm zs[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

Lower bound:

[tex]p - 1.645s = -0.01 - 1.645*0.0375 = -0.0717[/tex]

Upper bound:

[tex]p + 1.645s = -0.01 + 1.645*0.0375 = 0.0517[/tex]

90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).

Answer:

D. 100

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

There are 2 cards greater than 5 , that is 6 and 7 , then

P( greater than 5 ) = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] = 50%

Step-by-step explanation:

sin(p) = opposite / hypontenuse = 45 / 53

Answer:

A. X-coordinate

Step-by-step explanation:

I calculated it logically

Answer:

I think it's x -coordinate

Answer:

[tex]\displaystyle \sec(\theta)=\frac{9\sqrt{17}}{17}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \sin(\theta)=\frac{8}{9}\text{ and } \tan(\theta)>0[/tex]

And we want to find sec(θ).

First, note that both sine and tangent are positive. The only quadrant in which this can occur is QI. Hence, all trig ratios will be positive.

Also, recall that sine is the ratio of the opposite side to the hypotenuse. Using this information and the Pythagorean Theorem, we can determine the adjacent side:

[tex]a=\sqrt{9^2-8^2}=\sqrt{17}[/tex]

So, with respect to θ, the adjacent side is √(17), the opposite side is 8, and the hypotenuse is 9.

Secant is the ratio of the hypotenuse to the adjacent. Hence:

[tex]\displaystyle \sec(\theta)=\frac{9}{\sqrt{17}}=\frac{9\sqrt{17}}{17}[/tex]

Again, since θ is in QI, all trig ratios are positive.

Answer:

2

Step-by-step explanation:

4(3+2) = 6(2)+4(2)

4(5) = 12 + 8

20=20

Answer:

2

Step-by-step explanation:

4(3+2)=20

6(2)+4(2)

12+8=20

so 2 is the answer i hope this answer helps you and solve the question if you don't know please use calculaotor  this question you need to use substitution so substitute values from the set as x and try putting in to both equation to see both equation has same answer and matches  

Answer:

-1

Step-by-step explanation:

first put the equation in slop int form:

y= x-6

to find the slope of a line that is perpendicular take the negative reciprical of the slope

so the answer is

-x

Answer:

am i suppoesd to do number 7 as well?

Step-by-step explanation:

Two wires

tether a balloon to the ground, as shown. How

high is the balloon above the ground? (Must Use Right

Triangle Trigonometry)

look at picture

The height of the balloon above the ground is 554 ft.

From the attached image, the third angle in triangle 1 would be;

180 - (90 + 85) = 5°

The supplementary angle in triangle 2 to 85° in triangle 1 is;

180 - 85 = 95°(because supplementary angles add up to 180)

The third angle of triangle 2 is; 180 - (95 + 75) = 10°

100/sin10 = z/sin 75

z = 100(sin 75)/(sin 10)

h/z = sin 85

h = z sin 85

h = [100(sin 75)/(sin 10)] × sin 85

h ≈ 554 ft

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Answer: 99.06cm

Step-by-step explanation:

Note that 1 inch = 2.54cm

Therefore, we'll convert the sides of the frame in inches to cm. This will be:

8 1/2 inch = 8.5 × 2.54cm = 21.59cm

11inches = 11 × 2.54cm = 27.94cm

Therefore, the perimeter of a rectangle will be:

= 2(length + width)

= 2(27.94 + 21.59)

= 2(49.53)

= 99.06cm

Answer:

Step-by-step explanation:

Synthetic division is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.

What  you can do with synthetic division you can do   with regular long division .But not the opposite

Answer:

3rd option. [tex]g(x)=x^{2} +2[/tex]

Answer: no possible triangles

Step-by-step explanation:

Answer:

3.1

Step-by-step explanation:

In order to solve for this expected value, you need to do:

(0*0.3)+(1*0.15)+(2*.27)+(3*20)+(4*.13)+(5*.10)+(6*.07)+(7*0.3)+(8*0.2)

Meaning that it is:

0+.15+.54+.6+.52+.5+.42+.21+.16

Which equals to: 3.1

Also: Feel free to correct my answer by any means, I feel like I got some parts wrong.

Answer:

The answer is, 3.1

Step-by-step explanation:

A probability distribution is a statistical function that describes all of the potential values and probabilities for a random variable within a particular range.

To find this predicted value, you must do the following:[tex](0*0.3)+(1*0.15)+(2*.27)+(3*20)+(4*.13)+(5*.10)+(6*.07)+(7*0.3)+(8*0.2)[/tex]

That is to say, it is:

[tex]0+.15+.54+.6+.52+.5+.42+.21+.16[/tex]

3.1 is the value of the random variable.

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