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3 years ago

Number 12 please answer and show steps

Mathematics

1 answer:

stellarik [79]3 years ago

3 0

The answer is 2. 4. 6. 8. 4. 8. 12. 16. 3. 6. 9. 12. 2. 4. 6. 8

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Can anyone help me with this problem

Soloha48 [4]

Answer:

126 Inches are in 3.5 yards

8 0

3 years ago

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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist

frosja888 [35]

Answer:

a) 0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

b) 0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

c) 0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday

d) 0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

Step-by-step explanation:

We solve this question using the normal approximation to the binomial distribution.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

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

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

Sample of 723, 3.7% will live past their 90th birthday.

This means that $n = 723, p = 0.037$ .

So for the approximation, we will have:

$\mu = E(X) = np = 723*0.037 = 26.751$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{723*0.037*0.963} = 5.08$

(a) 15 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 15 - 0.5) = P(X \geq 14.5)$ , which is 1 subtracted by the pvalue of Z when X = 14.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{14.5 - 26.751}{5.08}$

$Z = -2.41$

$Z = -2.41$ has a pvalue of 0.0080

1 - 0.0080 = 0.9920

0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 30 - 0.5) = P(X \geq 29.5)$ , which is 1 subtracted by the pvalue of Z when X = 29.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{29.5 - 26.751}{5.08}$

$Z = 0.54$

$Z = 0.54$ has a pvalue of 0.7054

1 - 0.7054 = 0.2946

0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

This is, using continuity correction, $P(25 - 0.5 \leq X \leq 35 + 0.5) = P(X 24.5 \leq X \leq 35.5)$ , which is the pvalue of Z when X = 35.5 subtracted by the pvalue of Z when X = 24.5. So

X = 35.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{35.5 - 26.751}{5.08}$

$Z = 1.72$

$Z = 1.72$ has a pvalue of 0.9573

X = 24.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{24.5 - 26.751}{5.08}$

$Z = -0.44$

$Z = -0.44$ has a pvalue of 0.3300

0.9573 - 0.3300 = 0.6273

0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday.

(d) more than 40 will live beyond their 90th birthday

This is, using continuity correction, P(X > 40+0.5) = P(X > 40.5), which is 1 subtracted by the pvalue of Z when X = 40.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40.5 - 26.751}{5.08}$

$Z = 2.71$

$Z = 2.71$ has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

6 0

3 years ago

What is equal to 4 5/6 + 5 1/4?

kherson [118]

Make it so that the fractions have common denominators. 12 is a common denominator we can use.

5/6= 10/12 1/4= 3/12

Multiply both numbers by 2. Multiply both by 3.

Now, add.

4 10/12+ 5 3/12= 9 13/12

Simplify.

10 1/12.

I hope this helps!
~cupcake

4 0

3 years ago

Unit 7: Polygons and Quadrilaterals Homework 6: Kites Need Help Stat PLEASE HELP!!!!! 20 POINTS

balu736 [363]

1) The measures of angles H and F are 121°, respectively.

2) The measures of angles U and V are 65° and 139°, respectively.

3) The missing angles are $m \angle 1 = 72^{\circ}$ , $m\angle 2 = 72^{\circ}$ , $m\angle 3 = 47^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m\angle 5 = 18^{\circ}$ , $m\angle 6 = 47^{\circ}$ and $m\angle 7 = 43^{\circ}$ .

4) The missing angles are $m \angle 1 = 55^{\circ}$ , $m\angle 2 = 35^{\circ}$ , $m\angle 3 = 35^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m \angle 5 = 55^{\circ}$ , $m \angle 6 = 67^{\circ}$ , $m\angle 7 = 67^{\circ}$ , $m\angle 8 = 23^{\circ}$ and $m \angle 9 = 23^{\circ}$ , respectively.

5) The measure of side $QT$ is $\sqrt{105}$ .

6) The measure of side $DF$ is $4\sqrt{26}$ .

7) The measure of side $NP$ is $3\sqrt{65}$ .

8) The value of $x$ is 17.

9) The value of $x$ is 6.

10) The measure of angle EDC is 107°.

11) The measure of angle RST is 122°.

<h3>How find missing angles and sides in rhombuses</h3>

1) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles H and F are 121°, respectively. $\blacksquare$

2) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles U and V are 65° and 139°, respectively. $\blacksquare$

3) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are $m \angle 1 = 72^{\circ}$ , $m\angle 2 = 72^{\circ}$ , $m\angle 3 = 47^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m\angle 5 = 18^{\circ}$ , $m\angle 6 = 47^{\circ}$ and $m\angle 7 = 43^{\circ}$ , respectively. $\blacksquare$

4) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are $m \angle 1 = 55^{\circ}$ , $m\angle 2 = 35^{\circ}$ , $m\angle 3 = 35^{\circ}$ , $m\angle 4 = 90^{\circ}$ , $m \angle 5 = 55^{\circ}$ , $m \angle 6 = 67^{\circ}$ , $m\angle 7 = 67^{\circ}$ , $m\angle 8 = 23^{\circ}$ and $m \angle 9 = 23^{\circ}$ , respectively. $\blacksquare$

5) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$QT = \sqrt{PQ^{2}-PT^{2}}$

$QT = \sqrt{13^{2}-8^{2}}$

$QT = \sqrt{105}$

The measure of side $QT$ is $\sqrt{105}$ . $\blacksquare$

6) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$DF = 2\cdot DH$ , $DH = \sqrt{DE^{2}-EH^{2}}$

$DF = 2\cdot \sqrt{DE^{2}-EH^{2}}$

$DF = 2\sqrt{15^{2}-11^{2}}$

$DF = 4\sqrt{26}$

The measure of side $DF$ is $4\sqrt{26}$ . $\blacksquare$

7) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$NK = 7\cdot x - 1$ , $NM = 10\cdot x - 13$ , $KM = 24$ , $NK = NM$ , $KP = \frac{KM}{2}$

$NP = \sqrt{NK^{2}-KP^{2}}$

$NP = \sqrt{[7\cdot (4)-1]^{2}-12^{2}}$

$NP = 3\sqrt{65}$

The measure of side $NP$ is $3\sqrt{65}$ . $\blacksquare$

8) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of $x$ is 17. $\blacksquare$

9) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of $x$ is 6. $\blacksquare$

10) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, we have the following expressions:

$m\angle EDC = 180^{\circ}-90^{\circ}-[2\cdot (2)+13]$

$m\angle EDC = 107^{\circ}$

The measure of angle EDC is 107°. $\blacksquare$

11) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, the angle RST is:

$m\angle RST = 2\cdot (3\cdot 12 +25)$

$m \angle RST = 122^{\circ}$

The measure of angle RST is 122°. $\blacksquare$

To learn more on quadrilaterals, we kindly invite to check this verified question: brainly.com/question/25240753

8 0

3 years ago

Need help plz due on Monday I believe

ra1l [238]

Answer:

1(a) = 10

1(b) = 9

1(c) = 12

2(a) = 8

2(b) = 10

2(c) = 1

Step-by-step explanation:

1(a) = 22 - 2.6

= 22 - 12 = 10

1(b) = 6 - 1/4 . 16 + 21 / 3

= 6 - 16/4 + 7

= 6 - 4 + 7

= 9

1(c) = (8-5). (5-3)^2

= 3*2^2

= 3*4

= 12

2(a) = 4(x-2)/(x-1) when x = 0

= 4(0-2)/ (0-1)

= 4*-2/-1

= -8 / -1

= 8

2(b) = (-3x^2 + 4) / 4 when x = -2

= (6^2 + 4) / 4

= (36 + 4) / 4

= 40 / 4 = 10

2(c) = [-2x/4 + 4*(x-1)] / x^2 - 1 when x = 2

= (-1 + 4 * 1) / 4 - 1

= 3 / 3

= 1

6 0

3 years ago

Read 2 more answers