the lengths of human pregnancies (gestation) can be modeled by a bell-shaped distribution with mean 266 days and standard deviation 16 days. a certain pregnancy had a z-score of -2.5 (negative 2.5). how many days did this pregnancy last?

The length of the two sides of the given right triangle is 5√2

A triangle with an angle right angle is called a right triangle.

Given that, a right triangle, with an acute angle of 45° and the length of hypotenuse is 10 units,

We need to find the length of two sides u and v,

The sum of a triangle is 180°, and if one angle is 90° and the other is 45° therefore, the third is also 45°

Now, we know that, sides opposite to equal angles are equal,

Therefore, v = u,

Now, using the Pythagoras theorem,

10² = v²+u²

v² + v² = 100

2v² = 100

v² = 50

v = 5√2

u = 5√2

Hence, the length of the two sides of the given right triangle is 5√2

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The cost per student for the app is $3, and can be found by dividing the total cost of $96 by the number of students, 32, which equals $3 per student.

Let x be the cost of the almonds Sophia bought and y be the cost of the app per student. Then, we have the subsequent two equations:

x + $5 = $15

32y = $96

To find the cost of the app per student, we can solve for y in the second equation:

y = $96 / 32 = $3

So the app costs $3 per student.

To find the cost of the app per student, we need to find the total cost of the app and then divide it by the number of students. Mr. Boone spent $96 on the app for 32 students, so the cost per student would be $96 / 32 = $3. This means that each student paid $3 for the app.

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well, since we know that one root is 5, that is a factor of it is (x-5), so hmmm by the remainder theorem we also know that if we plug "5" as our argument in our f(x), that is, if we do f(5), it must result to 0. so f(5) = 0, if that's so then

[tex]2x^2+bx-10=f(x)\implies 2(5)^2+b(5)-10=f(5) \\\\\\ 2(5)^2+b(5)-10=0\implies 50+5b-10=0\implies 5b=-40 \\\\\\ b=\cfrac{-40}{5}\implies \boxed{b=-8} \\\\[-0.35em] ~\dotfill\\\\ 2x^2-8x-10=0\implies 2(x^2-4x-5)=0\implies 2\stackrel{ {\Large \begin{array}{llll} x=-1 \end{array}} }{(x+1)}(x-5)=0[/tex]

The volume of the silo of cylinder shape containing grain is 8625.24 cubic units.

The volume of the cylindrical shaped grain silo will be calculated by the formula -

Volume = πr²h, where r represents radius and h represents height of the cylinder.

Now, as we know radius is half of the diameter. So, radius = 17/2

Performing division on Right Hand Side of the equation

Radius of the cylinder = 8.5

Keep the values in formula to find the value of volume of silo

Volume = π × 8.5² × 38

Taking square and performing multiplication on Right Hand Side of the equation

Volume = 8625.24 cubic units

Hence, the volume is 8625.24 cubic units.

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Answer:

4

Step-by-step explanation:

First:

(-2 1/2)*(-1 3/5) = 2.5*1.6

Second:

2.5*1.6=5/2*8/5

Third:

5/2*8/5=

4

The length of the candle that has been burning for the total of 240 minutes would be = 9 inches.

The rate at which a candle burns = 2 in/ 2 hours

That is,

2 in = 2 hour; 2 inches = 120 minutes

X in = 240 minutes

Make X the subject of formula;

X = 2×240/120

X= 480/120

X = 4+5

X = 9 inches

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The size of width of each lumber piece will be 3.875 inches.

Logic is the arrangement of all those concepts, whereas algebra is the study of abstract concepts.

Making something a little less complicated while both making it easier to attain or understand is the concept of clarity.

Mrs. Harris intends to divide the breadth of a piece of timber that is 11 ⁵/₈ inches broad into three equal pieces.

Convert the mixed fraction number to a decimal number. Then we have

11 ⁵/₈ = 11 + ⁵/₈

11 ⁵/₈ = 11.625 inches

The width of each lumber piece is given as,

⇒ 11.625 / 3

⇒ 3.875 inches

The size of width of each lumber piece will be 3.875 inches.

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The given statement is transitive property.

Transitive property is also called transitive property of equality when we have two equal values and either of this value is equal to third value.

DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]

This is a transitive property.

Here we have three values, initially first two values are equal and second & third values are equal.

Which gives any one of the value of first and second equals third value.

This is the transitive property.

Hence, the given statement is transitive property.

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Answer:

I got 20 when calculating this

The solution of x in the rhombus is 3

From the question, we have the following parameters that can be used in our computation:

The rhombus

Also, we have

LN = 14

AN = x + 4

Using the above as a guide, we have the following equation:

LN = 2 * AN

Substitute the known values in the above equation, so, we have the following representation

2 * (x + 4) = 14

Evaluate the expression

x + 4 = 7

Subtract 4 from both sides

so, we have the following representation

x = 3

Hence, the solution is 3

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Answer:

75

Step-by-step explanation:

trust me bro

Option d) [tex]y= 30.5(0.7)^x[/tex] is the function that best models the number of game systems sold in millions x years since 2015.

In mathematics, a function is a rule that associates each element in one set (called the domain) with a unique element in another set (called the range). The rule specifies how the input values (the elements of the domain) are transformed into output values (the elements of the range).

A function can be represented using various notations, such as f(x), where f is the name of the function and x is the input value, or y = f(x), where y is the output value and x is the input value. The function can be defined explicitly, as in[tex]f(x) = x^2,[/tex] or implicitly, as in the equation of a circle, [tex]x^2 + y^2 = r^2[/tex], where y is a function of x.

To determine which function best models the number of game systems sold, we need to observe the trend in the data.

We can see that the number of game systems sold is decreasing as time goes on, which means the function should be decreasing as well.

Option a) [tex]y=21.35(0.7)^x[/tex] is an exponential function with a base less than 1, which means it would also be decreasing. However, it starts with a higher initial value than the data suggests.

Option b) [tex]y= 30.5(21.35)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function does not match the trend in the data.

Option c) [tex]y= 30.5(1.3)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function also does not match the trend in the data.

Option d) [tex]y= 30.5(0.7)^x[/tex]is an exponential function with a base less than 1, which means it would be decreasing. Additionally, this function passes through all three data points, and it has a starting value that matches the first data point. Therefore, option d) is the function that best models the number of game systems sold in millions x years since 2015.

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A bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. The chance of spelling "chance" is approximately 0.0108 or about 1.08%.

First, we need to count the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n" from the 15 tiles in the bag. To do this, we use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of items and r is the number of items we want to choose. For example, to choose two "c"s from three, we can calculate:

C(3, 2) = 3! / (2! * (3 - 2)!) = 3

We can use this formula to calculate the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n":

C(3, 2) * C(3, 2) * C(3, 1) * C(3, 1) = 54

Therefore, there are 54 ways to choose the required letters out of the 15 tiles in the bag.

Next, we need to count the total number of ways to choose 6 tiles from the 15 in the bag. We can again use the combination formula:

C(15, 6) = 15! / (6! * (15 - 6)!) = 5005

Therefore, there are 5005 ways to choose any 6 tiles from the bag.

Finally, we can calculate the probability of spelling "chance" by dividing the number of ways to choose the required letters by the total number of ways to choose 6 tiles:

54 / 5005 ≈ 0.0108 or about 1.08%

So the probability of spelling "chance" when picking six tiles one at a time from the bag is approximately 0.0108 or about 1.08%.

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The Linear Equation for the line with slope as -1/3 and the point (-9,-1) is y = (-1/3)x - 4   .

We use the point slope form of a linear equation to write the equation of a line with its slope and a point on the line.

The point-slope form is ⇒ y - y₁ = m(x - x₁)  ;

Where m is = slope of line, and (x₁, y₁) is a point on line.

The Slope (m) of line  is  = -1/3 and point on line (x₁, y₁) is = (-9, -1),

Now , we substitute  these values ;

we get ;

⇒ y - (-1) = (-1/3)(x - (-9)) ;

⇒ y + 1 = (-1/3)(x + 9)  ;

Simplifying further ,

we get ;

⇒ y + 1 = (-1/3)x - 9/3  ;

Subtracting 1 from both sides, we get:

⇒ y = (-1/3)x - 4

Therefore, the equation of the line is y = (-1/3)x - 4  .

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         a = amount given to the 1st share, ratio of 5.

a + 122 = amount given to the 2nd share, ratio of 7.

        T = total amount

so the total amount is really "T", and we'll be splitting that into a 7 : 5 ratio, that is, we'll be dividing "T" by (7 + 5) and distribute accordingly.

[tex]\stackrel{\textit{total split by 7 + 5}}{\cfrac{T}{7+5}\implies \cfrac{T}{12}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{we know the 1st share is}}{a= 5\cdot \cfrac{T}{12}}\implies a=\cfrac{5T}{12} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know the 2nd share is}}{a+122= 7\cdot \cfrac{T}{12}}\implies a+122=\cfrac{7T}{12}\implies \stackrel{\textit{substituting from above}}{\left( \cfrac{5T}{12} \right)+122=\cfrac{7T}{12}} \\\\\\ 122=\cfrac{7T}{12}-\cfrac{5T}{12}\implies 122=\cfrac{2T}{12}\implies 122=\cfrac{T}{6}\implies \boxed{732=T}[/tex]

We will prove that if we remove the root of a k-th order binomial tree, it results in k binomial trees of smaller orders.

Base case: If k = 1, the binomial tree consists of a single node. Removing the root node leaves an empty tree, which can be considered as a collection of 0 binomial trees of smaller orders.

Induction hypothesis: Assume that the statement is true for a k-th order binomial tree.

Induction step: We need to prove that the statement is true for a (k+1)-th order binomial tree, which is formed by joining two k-th order binomial trees.

Remove the root node of the (k+1)-th order binomial tree. This results in two trees, each of which is a k-th order binomial tree.

By the induction hypothesis, removing the root node of each of the two k-th order binomial trees results in k binomial trees of smaller orders.

Thus, removing the root node of the (k+1)-th order binomial tree results in a total of 2k binomial trees of smaller orders, which completes the proof.

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Answer: Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

Step-by-step explanation:

To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:

-x² + 5 = -2x + 2

Expanding the right-hand side:

-x² + 5 = -2x + 2

-x² + 2x + 3 = 0

Solving for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 2, and c = 3

x = (-2 ± √(2² - 4(1)(3))) / 2(1)

x = (-2 ± √(4 - 12)) / 2

x = (-2 ± √(-8)) / 2

Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

Answer: x =1, y = -1

Step-by-step explanation:

-10x+4y=-14

7x+5y=2

Let's eliminate y.

5(-10x+4y= -14)

4(7x + 5y=2)

[ I multiplied the first equation by the coefficient of y in the second equation and did the same in the second equation].

=> -50x+20y =-70

     28x+20y = 8

Notice how the coefficients of y are the same. We can subtract the 2 equations to eliminate y.

Thus,

-78x = -78 ( y has been eliminated)

∴ x=-78/-78 =1.

Put the value of x in any equation to find y.

7x + 5y =2

=> 7(1) + 5y =2

7+5y=2

5y = 2-7

5y = -5

y = -1.

Hope this helps :)

Answer: Look below :)

Step-by-step explanation:

I graphed the inequality below:

from that we can see:

a. Points on the line are combinations of US/Mexico minutes he can do where all of his prepaid money will be used, For example, he could do 50 USA minutes and 80 Mexico minutes, and there would be no money left to spend

b. Points above the line are combinations of US/Mexico minutes that will cost him more than the prepaid $50.

c. Points below the line are combinations of US/Mexico minutes that will leave him with money left over from his $50.

I hope this makes sense! ask questions if you have any :)

Answer:

Step-by-step explanation:

Answer:

199 cm²

Step-by-step explanation:

in the picture

It would be expected to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

The expected value, also known as the mathematical expectation, is a key concept in probability theory and statistics.

Here,
Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.

To find the expected number of correct predictions over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),

39% * 38 = 14.82

So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

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The average speed of Paul Revere's horse, assuming he rode straight to Lexington without stopping, would have been approximately 25.4 miles per hour.

To find the average speed of Paul Revere's horse, we can use the formula:

average speed = total distance / total time

In this case, the total distance is 11 miles, and the total time is 26 minutes, or 0.4333 hours (since there are 60 minutes in an hour).

So, the average speed of Paul Revere's horse would be:

average speed = 11 miles / 0.4333 hours

average speed ≈ 25.4 miles per hour

Therefore, the average speed of Paul Revere's horse, to the nearest tenth of a mile per hour, would have been 25.4 miles per hour.

Using the formula for average speed, we can calculate that Paul Revere's horse would have had to travel at an average speed of approximately 25.4 miles per hour to cover the 11-mile distance in 26 minutes. This assumes that he rode straight through without stopping.

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The complete question is:

On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

The probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.

Simply put, probability is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. Statistics is the study of events that follow a probability distribution.

a) We need to find p(x<68.15)

Standardize x to z, we have, z = (68.15-μ)/σ

=(68.15-57)/8.1

=1.38

Reading from standard normal tables,

p(z<1.38) =0.9162.

Therefore, the probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162.

b) We need to find p(x>54.4)

Standardize x to z, we have, z = (54.4-μ)/σ

=(54.4-57)/8.1

=-0.32

Reading from standard normal tables,

p(z>-0.32) = 0.6255

Therefore, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.

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The value of x is given as follows:

x = 155º.

For the triangle at the left, considering that the sum of the measures of the internal angles of a triangle is of 180º, the angle measures are given as follows:

For the triangle at the right, considering the ray formed at the top, the measures are given as follows:

An angle is supplementary with it's external angle, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:

x = 180 - 25

x = 155º.

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The equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number" is 3 – (n – 1) = 1/2(3n – 4)

Let the number be n.

Gven: "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"

So,

The expression "three minus the difference of a number and one" represent the equation is;  

3 – (n – 1)

Also,

The expression "one-half of the difference of three times the same number and four" represent the equation  is;

1/2(3n – 4)

Hence,

Complete expression represents the equation is

3 – (n – 1) = 1/2(3n – 4)

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(1 – n) – 3 = (4 – 3n)

3 – (1 – n) = (4 – 3n)

(n – 1) – 3 = (3n – 4)

3 – (n – 1) = (3n – 4)