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The sum of the infinite geometric sequence 16, 8, 4, 2 is 32

The sum can be represented as follows:

s∞ = a / 1  - r

where

r = common ratio

a = first term

Therefore,

r = 8 / 16 = 1 / 2

a = 16

hence,

s = 16 / 1 - 1 / 2

s = 16 / 1 / 2

s = 16 × 2 / 1

s = 32

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Answer:

No sollution

Step-by-step explanation:

It simple

Answer:

20% of players are left-handed

Step-by-step explanation:

First, find how much each player is worth percent-wise

100 / 80 = 1.25

Then find out how much percent of players that makes up

1.25 x 16 = 20

The answer is 20% of players are left-handed, to check it you could do

80 * 0.2 = 16

(80 = total players, 0.2 = 20%, 16 = total left handed players)

Using the normal distribution, it is found that 84 people would be expected to have BP > 160.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

Researching the problem on the internet, the mean and the standard deviation for the BPs are given, respectively, by:

[tex]\mu = 122, \sigma = 22[/tex].

The proportion of adults with BP > 160 is given by one subtracted by the p-value of Z when X = 160, hence:

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

[tex]Z = \frac{160 - 122}{22}[/tex]

Z = 1.73

Z = 1.73 has a p-value of 0.9582.

1 - 0.9582 = 0.0418.

Out of 2000 people:

0.0418 x 2000 = 83.6.

Rounding to the nearest integer, 84 people would be expected to have BP > 160.

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Answer: X-ints = (-1,0) and Y-ints = (1,0)

Step-by-step explanation:

This is quite simple. The way to solve this problem is by visualization, if you have learned how coordinates are created, this is how you would do it.

In a 2D plane, you have an X and Y axis and coordinates are created in the form of (X,Y).

by simply looking at the graph, I can see how the line crosses the positive 1 in the Y-axis, and -1 in the X-axis.

Part A) asks to find the X-intercept(s) which as stated above, it croses -1 on the X-axis and 0 on the Y-axis. Therefore the intercept is:

(-1,0)

part B) asks the same but for the Y-intercepts. We look at the graph and see the line crosses positive 1 in the Y-axis, and 0 in the X-axis. So:

(0,1)

done :)

Answer: (6,-12)

Step-by-step explanation:

For dilations centered at the origin, we can multiply each of the coordinates by the scale factor. This means that [tex]C'=(2 \times 3, -4 \times 3)=\boxed{(6, -12)}[/tex]

Answer:

Assuming you meant 2x^2-7x+6=0,

the answer is x=2, x=1.5

Use the quadratic formula. (-b (+ or  -) sqrt(b^2 - 4ac) )/ (2a)

Answer:

(4:-4)

Step-by-step explanation:

the graphs y- axis starts at 4 and ends at -4

Answer:

50.6

Step-by-step explanation:

Answer: 5(x + 1)(x + 4)

Step-by-step explanation Tell me if it is wrong

Answer: A, C

Step-by-step explanation:

Diagonals of a parallelogram bisect each other, so [tex]4x-7=2x+1 \longrightarrow x=4[/tex]. So [tex]ED=4(4)-7=\boxed{9}[/tex].

Opposite sides of a parallelogram are congruent, so [tex]8y-3=3y+7 \longrightarrow y=2[/tex], so [tex]AD=8(2)-3=\boxed{13}[/tex]

The coordinate is (-1/2, √3/2) and the missing values will be 2 and 3 if the angle is 120 degree.

A polar coordinate system is a two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane.

We have an angle of 120 degree

θ = 120 degree

r = 1 unit

As we know, the coordinate in the polar form from the rectangular form is:

x = rcosθ = cos120 = -1/2

y = rsinθ = sin120 = √3/2

Thus, the coordinate is (-1/2, √3/2) and the missing values will be 2 and 3 if the angle is 120 degree.

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Answer:

Option C . 6 cm , 8 cm and 10 cm

Step-by-step explanation:

Question : Which three side lengths best describe the triangle in the diagram?

As we can clearly see measurement of the scale [ refer to attachment ]

In Triangle ABC

Therefore option C is Correct.

Answer:

[tex]5y=-4[/tex]

Sure hope this helps you  :D

Answer:

Here is the answer:

Step-by-step explanation:

An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent. A kite is a quadrilateral with exactly two pairs of adjacent congruent sides.

Answer:

Midsegment theorem for Traoezoids

Step-by-step explanation:

I hope it helps you

Answer:

7x²a(x + a)

Step-by-step explanation:

7x³a = 7 * x * x * x * a

7x²a² = 7 *x * x * a *a

Common factor = 7x²a

So we have to take the common factor from the two terms

7x³a + 7x²a² = 7x²a ( x + a)

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The amount that will be in the account after 10 years is $651.56.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.

[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]

The principal amount is $400 which is invested for a period of 10 years at an interest rate of 5% annually. Therefore, the amount in the account after 10 years will be,

[tex]A = P(1+ \dfrac{r}{n})^{nt}\\\\A = \$400 (1+ \dfrac{0.05}{1})^{1 \times 10})\\\\A=\$651.56[/tex]

Hence, the amount that will be in the account after 10 years is $651.56.

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Answer:

Hope the picture will help you........

The equation of the median-median line for given data will be y = 3x + 10. Then the correct option is A.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The data set in the table is given below.

X           Y

2           6

4          22

6          30

8          24

10         40

12         46

14         52

16         72

18         60

20        64

For the above after dividing the above data into 3 parts of the set (3,4,3)

Then the equation of the median-median line for given data will be

y = 3x + 10

Then the correct option is A.

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Answer:

In the figure,

AC is the diameter of circle with centre O

∠DAC=37

o

AD || BC

∠ACB=∠DAC (Alternate angles)

Hence,

x=37

o

In Δ ABC,

∠B=90

o

 (angle in semicircle)

By angle sum property of triangle, we get,

∠x+∠y+∠B=180

o

37

o

+∠y+90

o

=180

o

∠y=180

o

−127

o

We get,

∠y=53

o

Step-by-step explanation:

The length and width of the rectangle will be √68 and √17. Then the perimeter of the rectangle will be 2 (√17 + √68).

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The graph is shown below.

Then the perimeter of the rectangle will be

P = 2 (length + width)

The length of the rectangle will be

L² = 2² + 8²

L² = 4 + 64

L² = 68

L = √68

The width of the rectangle will be

W² = 1² + 4²

W² = 1 + 16

W² = 17

W = √17

Then the perimeter will be

P = 2 (√17 + √68)

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Sequence: 24 + 12 + 6 + 3 +...

Explanation:

This is infinite geometric series converges.

[tex]\sf S \infty \ =a_1 \ x \ \dfrac{1}{1-r}[/tex]

Identify the following

Solve:

[tex]\rightarrow \sf S \infty \ =24\ x \ \dfrac{1}{1-\frac{1}{2} }[/tex]

[tex]\rightarrow \sf S \infty \ =48[/tex]

This is series has a sum of 48.

The value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

Arithmetic mean is the mean or average which is equal to the ratio of sum of all the group numbers to the total numbers.  

The two arithmetic means between 3 and 24 are has to be inserted.

3, A₂, A₃, 24

All the four numbers are in arithmetic progression. The nth terms of AM can be found using the following formula:

t(n)=a(n-1)d

Here, d is the common difference a is the first terms and n is the total term.  The first term, a=3 and t₄=24. Thus, the common difference is;

[tex]t(n)=a(n-1)d\\t(4)=3(4-1)d\\24=3(3)d\\24=9d\\d=\dfrac{24}{9}[/tex]

The second and 3rd term are:

[tex]A₂=3+\dfrac{24}{9}=\dfrac{51}{9}\\ A₃=\dfrac{51}{9}+\dfrac{24}{9}=\dfrac{75}{9}[/tex]

Thus, the value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

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(22 + 26) / 8 = x

(/ this means division)

Answer:

If is not one to one is not inverse (no inverse)

Step-by-step explanation:

Answer:

[tex]CI\approx\{0.0076,0.0924\}[/tex]

Step-by-step explanation:

The formula for a z-confidence interval for a difference of proportions is [tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z^*\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}[/tex]:

Let [tex]\hat{p}_1=0.65[/tex] to represent the sample proportion of [tex]n_1=1000[/tex] women who are in favor of stricter gun control laws and let [tex]\hat{p}_2=0.60[/tex] to represent the sample proportion of [tex]n_2=1000[/tex] men who are in favor of stricter gun control laws.

A 95% confidence level corresponds to a critical value of [tex]z^*=1.96[/tex], so now we perform the necessary calculations assuming conditions are met:

[tex]\displaystyle CI=(0.65-0.60)\pm 1.96\sqrt{\frac{0.65(1-0.65)}{1000}+\frac{0.60(1-0.60)}{1000}}\approx\{0.0076,0.0924\}[/tex]

Hence, we are 95% confident that the true difference in the proportion of women and men who favor stricter gun control laws is between 0.0076 and 0.0924

Since the interval does not contain "0" and only contain values greater than "0", it is more likely that the proportion of women who were in favor of stricter gun control laws is higher than the proportion of men who were in favor of stricter gun control laws.