find measure of angle A

Answer:

[tex]Area =24cm^2[/tex]

Step-by-step explanation:

Given

[tex]L = 8cm[/tex]

[tex]W = 12cm[/tex]

[tex]r = 2[/tex] -- folded twice

Required

The area of the new rectangle

When the length was folder, the new length is:

[tex]l = L/2 = 8cm/2 = 4cm[/tex]

When the width was folder, the new width is:

[tex]w = W/2 = 12cm/2 = 6cm[/tex]

So, the new area is:

[tex]Area =l * w[/tex]

[tex]Area =4cm * 6cm[/tex]

[tex]Area =24cm^2[/tex]

Answer:

108 minutes

Step-by-step explanation:

Lets say that M+A is the time of the movie and the advertisement, so;

M+A = 2

And we know that 10% of that time is advertisement, mathematically that is:

A = 0,1*2

So replacing the second equation in the first one we have;

M + 0,1*2 = 2

M = 2-0,1*2 = 1,8 hours

We can convert hours into minutes multiplying by 60

1,8h*60min/h = 108min

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

Explanation:

The five number summary is the set of these items, in this exact order

So with the five number summary 4.6, 14.3, 19.7, 26.1, 31.2, we see that

Q1 = 14.3 and Q3 = 26.1

Subtracting these two values gets us the IQR (interquartile range)

IQR = Q3 - Q1

IQR = 26.1 - 14.3

IQR = 11.8

Answer:

use test numbers to find where the function is a positive and where it is negative. sketch the function's graph, plotting additional points as guides as negative. choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.

Answer:

PQR+SQR=180°(angles in a triangle)

75°+SQR=180°

SQR=180°-75°

SQR=105°

Answer:

23.5

Step-by-step explanation:

The median is the middle value when the numbers are put in order from smallest to largest

17,19, 20, 21, 22, 25, 29, 30, 32, 35

There are 10 numbers

17,19, 20, 21, 22,      25, 29, 30, 32, 35

The middle is between 22 and 25

(22+25)/2 = 47/2 =23.5

The volume of the water is: [tex]\pi (2)^2(8) - 6 (\frac{4}{3} \pi (1.5)^3)[/tex]

The volume of a cylinder is;

[tex]V = \pi r^2h[/tex]

For the cylinder, we have:

[tex]d = 4[/tex] -- diameter

[tex]h = 8[/tex] --- height of the water in the cylinder

The radius of the cylinder is:

[tex]r =d/2 = 4/2 = 2[/tex]

So, the volume is:

[tex]V = \pi * 2^2 * 8[/tex]

[tex]V = \pi * (2)^2 (8)[/tex]

For the 6 marbles, we have:

[tex]d = 3[/tex] --- the diameter of each

The shape of the marble is a sphere. So, the volume of 1 marble is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

The radius of 1 marble is:

[tex]r = d/2 = 3/2 = 1.5[/tex]

So, the volume of 1 marble is:

[tex]V_1 = \frac{4}{3} * \pi * (1.5)^3[/tex]

Multiply both sides by 6 to get the volume of the 6 marbles

[tex]6 * V_1 = 6 * \frac{4}{3} * \pi * (1.5)^3[/tex]

[tex]6V_1 = 6 * \frac{4}{3} * \pi * (1.5)^3[/tex]

[tex]6V_1 = 6 (\frac{4}{3} \pi (1.5)^3)[/tex]

Recall that the volume of the cylinder is:

[tex]V = \pi * (2)^2 (8)[/tex]

The volume of the water in the marble is the difference between the volume of the cylinder and the volume of the 6 marbles

So, we have:

[tex]Volume = \pi (2)^2(8) - 6 (\frac{4}{3} \pi (1.5)^3)[/tex]

The expression [tex]V = \pi \cdot (2\,in)^{2}\cdot (8\,in) -6\cdot \left[\frac{4\pi}{3}\cdot (1.5\,in)^{3} \right][/tex] can be used to calculate the volume of water in the vase.

As vase is of cylindrical form and the six marbles are spherical, we shall derived an expression from volume formulas respective to Cylinder and Spheres. Firstly, we know that volume of water in the vase is equal to the Volume of the vase minus the volume occupied by the six marbles, that is to say:

[tex]V = V_{v}-6\cdot V_{m}[/tex] (1)

Where:

[tex]V_{v}[/tex] - Volume of the vase, in cubic inches.

[tex]V_{m}[/tex] - Volume of the marble, in cubic inches.

[tex]V[/tex] - Volume of water in the vase, in cubic inches.

Then, we expand (1) by volume formulas for the cylinder and sphere:  

[tex]V = \pi\cdot R^{2}\cdot H - 6\cdot \left(\frac{4\pi}{3} \cdot r^{3} \right)[/tex] (2)

Where:

[tex]R[/tex] - Radius of the vase, in inches.

[tex]H[/tex] - Height of the vase, in inches.

[tex]r[/tex] - Radius of the marble, in inches.

If we know that [tex]R = 2\,in[/tex], [tex]H = 8\,in[/tex], [tex]r = 1.5\,in[/tex], then the following expression can be used to calculate the volume of water in the base:

[tex]V = \pi \cdot (2\,in)^{2}\cdot (8\,in) -6\cdot \left[\frac{4\pi}{3}\cdot (1.5\,in)^{3} \right][/tex]

In a nutshell, the expression [tex]V = \pi \cdot (2\,in)^{2}\cdot (8\,in) -6\cdot \left[\frac{4\pi}{3}\cdot (1.5\,in)^{3} \right][/tex] can be used to calculate the volume of water in the vase.

Part (a)

The standard error (SE) formula is

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

where n is the sample size. We're given SE = 2 and sigma = 34, so,

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\2 = \frac{34}{\sqrt{n}}\\\\2\sqrt{n} = 34\\\\\sqrt{n} = \frac{34}{2}\\\\\sqrt{n} = 17\\\\n = 17^2\\\\n = 289\\\\[/tex]

So we need a sample size of n = 289 to have an SE value of 2.

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

Part (b)

We'll use SE = 1 this time

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\1 = \frac{34}{\sqrt{n}}\\\\1*\sqrt{n} = 34\\\\\sqrt{n} = 34\\\\n = 34^2\\\\n = 1156\\\\[/tex]

Because we require greater precision (i.e. a smaller SE value), the sample size must be larger to account for this. In other words, as SE goes down, then n must go up, and vice versa.

N is the midpoint of MO and NO is 5, so MN would also be 5

MP = MN + NP = 5 + 9 = 14

Answer:

1/2

Step-by-step explanation:

Number of bags = 3

number of bags with $10 bill initially = 2

number of bags with $5 bill initially = 1

assume :

event you pick a $5 bill at first draw = A

event you pick a $5 bill at second draw = B

hence : P ( A n B ) = 1/3 * 1 = 1/3

P( A ) = ( 1/3 * 1 ) + ( 1/3 * 1/2 + 1/3 * 1/2 )  = 2/3

therefore P( that the second drawn bill is $5 )

P( B | A ) = P(A n B ) / P ( A )

              = (1/3) / (2/3) = 1/2

The probability that it, too, is a $ 5 bill is 33.33%.

Since you have 3 bags, and two of them contain a single $ 10 bill, and the third contains a single $ 5 bill, supposing you pick one of these bags uniformly at random and you then add a $ 5 bill to the bag, so it now contains two bills, and the bag is shaken, and you randomly draw a bill from the bag without looking into the bag, supposing it turns out to be a $ 5 bill, if a you draw the remaining bill from the bag, to determine what is the probability that it, too, is a $ 5 bill, the following calculation must be performed:

Therefore, the probability that it, too, is a $ 5 bill is 33.33%.

Learn more in https://brainly.com/question/13243988

Answer:

8x-21

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

(2x-7)(2x+7)

Step-by-step explanation:

7                       4

-----------   + ------------

4x^2 -49    2x+7

Factor  ( notice that it is the difference of squares)

7                       4

-----------   + ------------

(2x)^2 - 7^2    2x+7

7                       4

-----------       + ------------

(2x-7)(2x+7)    2x+7

Get a common denominator

7                       4(2x-7)

-----------       + ------------

(2x-7)(2x+7)    (2x-7)(2x+7)

Combine

7 +4(2x-7)

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

(2x-7)(2x+7)  

7 +8x-28

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

(2x-7)(2x+7)  

8x-21

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

(2x-7)(2x+7)  

Answer:

(8x - 21) / (2x + 7)(2x - 7)

Step-by-step explanation:

7 / (4x^2 - 49)+ 4 / (2x + 7)

= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)

LCM = (2x + 7)(2x - 7)   so we have

(7 + 4(2x - 7) / (2x + 7)(2x - 7)

=   (8x - 21) / (2x + 7)(2x - 7).

Answer:

383

Step-by-step explanation:

Let dryer be d.

(d + 92) + d = 858

2d + 92 = 858

      -92 =  -92

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

    2d = 766

    ----    ------

     2        2

       d = 383

The dryer is $383

Hope this helped.

Answer:

$475

Step-by-step explanation:

The dryer costs x.

Since the washer costs $92 less than the dryer, then the dryer costs x - 92.

Combined, they cost $858.

x + x - 92 = 858

2x - 92 = 858

2x = 950

x = 475

Answer: $475

Answer:

40

Step-by-step explanation:

Based on the Proportional Transversal Theorem, the three parallel lines hat intersects the two transversals, divides the transversal lines proportionally.

Therefore, we would have the following ratio:

28/35 = ?/50

Cross multiply

35*? = 50*28

35*? = 1,400

Divide both sides by 35

? = 1400/35

? = 40

Answer:

Option B, 5/16

Step-by-step explanation:

f(4) = 5•(1/2)⁴

= 5•(1/2⁴)

= 5•(1/16)

= 5/16

Answer:

a.) 1908.30

b.) 96373.15

c.)302491.15

unrounded answers below

Step-by-step explanation:

The amount that is to be loaned out is 380000-110000=270000

The effective montly rate is .07/12=.005833333

a.)

[tex]270000=x(\frac{1-(1+.005833333)^{-(25*12)}}{.005833333})=1908.303833[/tex]

b.)

use what is called the prospective method (the outstanding loan balance at time n is equal to the present value of the remaining payments)

[tex]1908.303833(\frac{1-(1+.005833333)^{-(25*12-20*12)}}{.005833333})=96373.14775[/tex]

c.)

total paid= 1908.303833*12*25=572491.1499

amount of loan: 270000

Total interest paid:

572491.1499-270000=302491.1499

Step-by-step explanation:

d = z - 9

d = 10 - 9  ----> substitute

d = 1

Answer:

Imaginary roots

Step-by-step explanation:

The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].

Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:

[tex]7x^2-5x+1=0[/tex]

Now assign variables:

The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].

What does this tell us about the roots?

Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.

Answer:

1/4

Step-by-step explanation:

There are four probabilities and the probability of her having 1 of the 4 probabilities is 1/4

Answer:

4/7

Step-by-step explanation:

When you multiply by fractions you multiply the numerators and denominators

4/1 x 1/7

Anything that doesnt have anything under it always has a 1 as its denominator

Answer:

0

Step-by-step explanation:

any numbers multiply by zero always equals to zero

Answer:

26 cm

Step-by-step explanation:

P = 2a + 2b

a = side

b = base

Answer:

The area=base×height

=10×4

=40cm^2

perimeter=2(length+breadth)

I think to find the height Dc you use the pythagoras theorem of

Dc^2=de^2+ce^2

=√16+9

=5

therefore the perimeter will be

p=2(5+10)

=20cm

I hope this helps and sorry if it's wrong

Answer:

Step-by-step explanation:

Side=AC=9[tex]\sqrt{2}[/tex]

Side AB= x

Hypotenuse =CB= y

Side AB = 9[tex]\sqrt{2}[/tex]

Hypotenuse CB = 36

Answer:

8/17

Step-by-step explanation:

The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.

The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY

The hypotenuse = XZ

Sin(X) = ZY/XZ

Sin(X) = 1634 = 8 / 17

Answer:

4

Step-by-step explanation:

First, we can take two triangles -- one with 2 as a side and the big one. Literally every side of the triangle with the 2 in it is parallel to its corresponding side the big triangle. Therefore, we can say that the two triangles are similar.

In similar triangles, we can say that the ratios of corresponding sides are the same. Let's say that the bottom side of the big triangle is x, and the question mark is y. Therefore, the hypotenuse of the big triangle is 6+y. Furthermore, the ratio of corresponding sides ((6+y)/y and x/2) are equal, so

(6+y)/y = x/2

Since x is clearly made up of 3 and 2, we can say 3+2=x=5

(6+y)/y = 5/2

multiply both sides by y to remove a denominator

6+y = 5*y/2

multiply both sides by 2 to remove the other denominator

12+2y = 5*y

subtract both sides by 2y to isolate the y and its coefficient

12 = 3y

divide both sides by 3 to isolate the y

y=4

Answer:

The point estimate that should be used in constructing the confidence interval is 0.11.

The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).

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 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.

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.

Midwest:

50% of 1380, so:

[tex]p_M = 0.5[/tex]

[tex]s_M = \sqrt{\frac{0.5*0.5}{1380}} = 0.0135[/tex]

South:

39% of 1300, so:

[tex]p_S = 0.39[/tex]

[tex]s_S = \sqrt{\frac{0.39*0.61}{1300}} = 0.0135[/tex]

Distribution of the difference:

[tex]p = p_M - p_S = 0.5 - 0.39 = 0.11[/tex]

So the point estimate that should be used in constructing the confidence interval is 0.11.

[tex]s = \sqrt{s_M^2+s_S^2} = \sqrt{0.0135^2+0.0135^2} = 0.0191[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

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

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].  

The lower bound of the interval is:

[tex]p - zs = 0.11 - 1.28*0.0191 = 0.0856[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.11 + 1.28*0.0191 = 0.1344[/tex]

The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).

Answer:

Option A i the right option.

First blank is 110-[tex]10\sqrt{61}[/tex] or 10(11-[tex]\sqrt{61}[/tex])

Second blank is 31.898

Let me know if anything didn't make sense.  

Step-by-step explanation:

So a diagonal through a rectangle makes two triangles.  The question wants to know how much walking is saved walking down the diagonal  vs walking along two sides that make the diagonal.  in this case the two non diagonal sides walked are 60 paces and 50 paces.

A diagonal through a rectangle specifically makes a right triangle, so to find the diagonal we can use the pythagorean theorem.  

c^2 = 60^2 + 50^2

c = [tex]\sqrt{60^2 + 50^2}[/tex]

c = [tex]\sqrt{6100} = 10\sqrt{61}[/tex]

if you don't get how to simplify a radical like that let me know.

Anyway, looking at the answers you can see right away the second option says no approximation is necessary.  Well, you need to approximate square root of 61, so we can say the second answer is not right.  So now we need to know what to fill in for option 1.

it wants the distance saved, well we know the distance of the diagonal is [tex]10\sqrt{61}[/tex]  Hopefully you can see the disctance walking the two other sides is just adding them up so 50+60=110.

Now, to find the difference, that is subtraction.  So subtract the smaller number from the larger number.  You do need to remember with a right triangle, the sum of the to non diagonal (hypotenuse) sides are always longer than said hypotenuse.  so that's 110-[tex]10\sqrt{61}[/tex].  That is the exact form.  Or you could use 10(11-[tex]\sqrt{61}[/tex])  They are the same.

Then just plug that into a calculator for a decimal approximation.