The sum of two numbers is 24. One is 6 less than twice the other. Find the two numbers.

(apply polya's problem solving method)​

Answer:

The second box plot represents the data

Step-by-step explanation:

A box and whisker plot gives you the five-number summary of the data, which includes:

the minimum (lowest value of the data)

the maximum (highest value of the data)

Q1 (25% of the data lies below this point)

Q3 (75% of the data lies below this point), and

the median (the middle of the data).

The two ticks at the far left and far right of the box-and-whisker plot are the minimum and maximum respectively.  From the data, we see that the minimum is 5 and the maximum is 10.

Although both plots have a minimum value of 5, only the second plot has the accurate maximum at 10.

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

Answer:

The answer is D

Step-by-step explanation:

103 is exactly the same as 103

Answer:

D

Step-by-step explanation:

103 is the same number as 103 so it is equal. Sorry if its wrong.

The indicated measures:

m∠ABC =  138° and m∠BCD = 52°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠DAE = 16° and m∠EDC = 64°.

The diagonals of the kite intersect at 90°.

(1).

In ΔAED,

the sum of all the angles of the triangle is 180°.

m∠DAE + m∠ADE + m∠AED = 180°

m∠ADE = 180 - 90 - 16

m∠ADE = 74°

According to the angle addition postulate,

m∠ADE + m∠EDC = m∠ADE

m∠ADE = (74 + 64)°

m∠ADE = 138°

From the property of kites,

m∠ADE = 138° =  m∠ABC.

(2).  m∠EBC =  m∠EDC,

m∠EBC = 64°

In ΔBCD,

the sum of all the angles of the triangle is 180°.

m∠DBC + m∠BCD + m∠CDB = 180°

m∠BCD = 180 - 64 - 64

m∠BCD = 52°

Therefore,  138° =  m∠ABC and m∠BCD = 52°.

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The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer:

y = -3/4x + 3

Step-by-step explanation:

lmk if you want an explanation

Each of the given pairs shape A is congruent to shape B.

We need check from the given pair, shape A is congruent to shape B or not.

Congruent shapes are shapes that are exactly the same. The corresponding sides are the same and the corresponding angles are the same. To do this we need to check all the angles and all the sides of the shapes. If two shapes are congruent they will fit exactly on top of one another.

From both pairs shape A is congruent to shape B.

Shape A is congruent to Shape B because if you were to rotate one of the two and flip it the would like up and match.

Therefore, each of the given pairs shape A is congruent to shape B.

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Answer:  450 cm

Step-by-step explanation:

10 x 9 = 90 x 5 = 450

Answer:

  B.  b(a) = a/6 -9

Step-by-step explanation:

Solve the given equation for b.

  a = 12(b +9)/2

  a = 6(b +9) . . . . simplify

  a/6 = b +9 . . . . divide by 6

  a/6 -9 = b . . . . subtract 9

Then the inverse relation is ...

  b(a) = a/6 -9 . . . . . . . matches choice B

Answer:

To create the equation, we'd write the following: Initial value - Amount initial value has decreased by = Remaining value. 15 (his starting number of sheep) - 3 (the number of sheep he sold) = 12 (the number of sheep he has left). Another example: John gets paid 20 to clean his neighbor's car.

For more in formation visit: Describe Situation Using Integers - MathVine.com

Answer:

He would make $234.00.

Step-by-step explanation:

Divide $169 by 13 hours, this will tell you how much money he earns every hour. $169 divided by 13 = $13. Now, you know that Adbul makes $13 per hour. Then, multiply $13 by 18 hours of work. $13 x 18 = $234.00.

That is your answer!

Answer: y = -7x - 8

Step-by-step explanation: the slope formula is y = mx + b, so just replace the variables.

Answer:

$97

Step-by-step explanation:

just add 72 and 25 dude

Answer:

$97

Step-by-step explanation:

3.083 when rounded up to 2 decimal places is equal to 3.08.

Center of the sphere would be (-4.5, 1, -6)  and radius be 6.086.

Write the equation of the sphere?

A sphere's general equation is (x - a)2 + (y - b)2 + (z - c) 2 = r2, where (a, b, c) represents the sphere's center, r represents the radius, and x, y, and z are the coordinates of points on the sphere's surface.

To complete the square, we need to add and subtract the square of half of the x coefficient and y coefficient, and the square of half of the z coefficient.

The equation will be : \((x + 9/2)^2 + (y - 1)^2 + (z + 6)^2 = (9/2)^2 + 1^2 + 6^2\)

So the standard form of the equation of the sphere is,    

          \((x + 4.5)^2 + (y - 1)^2 + (z + 6)^2 = 37\)

The center of the sphere is (x, y, z) = (-4.5, 1, -6) and the radius is √37 ≈ 6.086

Therefore, Center of the sphere would be (-4.5, 1, -6) and radius be 6.086.

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Answer:

D

Step-by-step explanation:

...................

The solutions to the quadratic equation x² + 10x - 13 = 17 are x = -5 + √55 and x = -5 - √55. The correct answer is option D.

The quadratic equation is given as:

x²+10x-13 =17

Move the constant term to the right side of the equation:

x² + 10x - 13 - 17 = 0

x² + 10x - 30 = 0

Take half of the coefficient of the x-term (10) and square it: (10/2)² = 25.

Add the squared value to both sides of the equation:

x² + 10x + 25 - 30 = 25

(x + 5)² - 30 = 25

Simplify the equation:

(x + 5)² = 25 + 30

(x + 5)² = 55

Take the square root of both sides of the equation:

√((x + 5)²) = ±√55

x + 5 = ±√55

Solve for x by subtracting 5 from both sides:

x = -5 ± √55

Therefore, the solutions to the equation x² + 10x - 13 = 17 are:

x = -5 + √55 and x = -5 - √55.

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Answer:

its 7,320 its the same

Step-by-step explanation:

The expanded form of 7,320 will be 7000 + 300 + 20.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the number 7,320

The expanded form of 7,320 contains thousand whole, hundred whole, and tens whole.

So,

The expanded form of 7320 = 7000 + 300 + 20.

Hence "7000 + 300 + 20 will be expanded form of the given number".

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Answer:

Answer: 10 inches

Explanation: You are given one side of the aquarium which is 18 inches. The top and the bottom of the aquarium is 18 inches because that’s what the diagram gives us. So you can multiply 18 x 2=36. Now, to find the missing side length, subtract the perimeter (56 inches) by 36 and you get 20 inches. However, that’s not your final answer because you have to divide 20/2=10 inches. 10 inches is the missing side length for the left and right side lengths

The missing length of the lid of her aquarium in the pricure is 18 inches.

The shape of the lid of her aquarium is a rectangle. A rectangle is a quadrilateral with four sides.

The perimeter of the rectangle = 2(length + width)

56 = 2(18 + l)

56/2 = 18 + l

28 = 18 + l

l = 28 - 18 = 10 inches

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each sunflower is $2.25. please mark brainliest and have a great day.

Answer:

13.5 %

Step-by-step explanation:

For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)

To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean

= 95-68 = 27 %

Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5

The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

Given that, average age managers = 52 years standard deviation = 2.5 years.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Considering the equation Z =  (X−μ)/σ

Where, X is the lower or higher value, as the case may be μ  is the average σ  is standard deviation

Now, z1= (54.5 - 52)/2.5

= 1

z2= (57 - 52)/2.5

= 2

Now, z2-z1= 2-1

= 1

P(54.5>Z<57)= 0.8413

Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

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Answer:

The label “Sum” is located at 0

The label “p” is located between 0 and -1 (-2/3)

The label “2/3” is located between 0 and 1

Answer:

Step-by-step explanation:

0

,

8

Answer:

  (d)  y = 3x² +2x -6

Step-by-step explanation:

The equation of a parabola through thee points can be found different ways. One is to use a quadratic regression tool. Another is to write and solve linear equations in the coefficients. (3 equations in 3 unknowns).

__

Here, we can eliminate answer choices that don't work to arrive at the correct answer choice.

The point (0, -6) is the y-intercept of the function. That means the value of the constant term in the quadratic is -6. (Eliminates A and C.)

The y-values of the other two points are both greater than -6, indicating the parabola opens upward. That means the leading coefficient is positive. (Eliminates B.)

The only reasonable choice is D:

  y = 3x² +2x -6

__

Additional comment

You get the same answer if you use a regression tool.

Answer:

\(y = 3\, x^{2} + 2\, x - 6\).

Step-by-step explanation:

In general, the equation of a parabola is in the form \(y = a\, x^{2} + b\, x + c\) for some constants \(a\), \(b\), and \(c\), where \(a \ne 0\).

Let \(y = a\, x^{2} + b\, x + c\!\) denote the equation of this parabola for some constants \(a\), \(b\), and \(c\) where \(a \ne 0\). A point \((x_{0},\, y_{0})\) is on this parabola if and only if the equation of this parabola holds after substituting in \(x = x_{0}\) and \(y = y_{0}\):

\(y_{0} = a\, {x_{0}}^{2} + b\, x_{0} + c\).

Thus, each of the three distinct points on this parabola would give a equation about \(a\), \(b\), and \(c\):

Simplify the equations:

\(\left\lbrace\begin{aligned}& 9\, a - 3\, b + c = 15 \\ & c = 6 \\ & 4\, a + 2\, b + c = 10\end{aligned}\right.\).

Solve this linear system of three equations and three unknowns for \(a\), \(b\), and \(c\):

\(\left\lbrace \begin{aligned} & a = 3 \\ & b = 2 \\ & c = (-6) \end{aligned}\right.\).

Therefore, the equation of this parabola would be:

\(y = 3\, x^{2} + 2\, x - 6\).

Answer:

Step-by-step explanation:

hello

Answer:

B. Graph B

(Symbolab Graphing Calculator is really helpful to do this kind of stuff ^^)

The function f(x) = \(6 \times0.4^x\) is graph B.

Option B is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of y = 6 x (0.4)^x is an exponential function.

The base of the function is 0.4, which means that as x increases, the value of y decreases.

However, the coefficient in front of the exponential term is 6, which means that the function starts off with a relatively high value of y when x is close to 0.

As x increases, the exponential term (0.4)^x decreases quickly, causing the overall value of the function to decrease rapidly.

However, the coefficient of 6 helps to slow down the rate of decrease, so the function doesn't drop off as quickly as it would without that coefficient.

Thus,

The function f(x) = \(6 \times0.4^x\) is graph B.

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To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

Quantity of  cranberry juice = 95  ml  

Quantity of  orange   juice = 95  ml

Step-by-step explanation:

Step 1

Given ,

We have  80% cranberry juice and  4% of  orange juice.

We have to find how much each should be mixed to make 190 ml of a  60% cranberry-orange juice blend.

Step 2

Let's assume

Quantity of  cranberry juice =x ml  

Quantity of  orange   juice =y  ml  

Then,

x + y = 190

and

x×80100 +y×4100 = 190×60100  

⇒ 0.8x+0.4y = 114    

⇒ 2x+y = 285  

⇒ y = 285−2x  

Step 3

Substituting   y = 285−2x  in  x + y = 190  

⇒ x+285−2x = 190  

⇒ −x = 190−285  

⇒ −x = −95  

⇒ x = 95  ml  

Substituting x = 95   in  x + y = 190

⇒ 95 + y = 190  

⇒ y = 190−95  

⇒ y = 95 ml  

So,

Quantity of  cranberry juice =95  ml  

Quantity of  orange   juice = 95  ml  

Answer:

1/6 = 1.6 would be t e answer