is [tex]1.2345 \: repeating \: \times \sqrt{4} [/tex]irrational or rational?

Answers

Answer 1

If we can write this expression as a fraction, then this will be rational. Otherwise, irrational.

First, let's write the repeating decimal as fraction. Excluding the 1 point to the left of the decimal.

We have:

0.234523452345...

We can write it as:

[tex]\frac{2345}{9999}[/tex]

Tagging along the "1", we have:

[tex]1\frac{2345}{9999}[/tex]

Then, we have square root of 4, which is "2".

If we multiply the fraction shown above by 2, we will definitely have a fraction.

That will be a rational number.


Related Questions

A Gallup poll conducted in November of 2011 asked the following question, "What would you
say is the most urgent health problem facing this country at the present time?" The choices
were access, cost, obesity, cancer, government interference, or the flu. The responses were
access (27%), cost (20%), obesity (14%), cancer (13%), government interference (3%), or the
flu (less than 0.5%).

The following is an excerpt from the Survey Methods section. "Results for this Gallup poll are based on telephone interviews conducted Nov. 3-6, 2011, with a random sample of 1,012
adults ages 18 and older, living in all 50 U.S. states and the District of Columbia. For results
based on a total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±4 percentage points."

Based on this poll, we are 95% confident that between_____% and ______% of U.S. adults feel that access to health care is the most urgent health-related problem.

(Enter numbers only. Do not include the %, e.g. enter 50 not 50%)

Answers

Based on this poll, we are 95% confident that between 23% (lower limit) and 31% (upper limit) of U.S. adults feel that access to health care is the most urgent health-related problem.

How do we determine the lower and upper limits for the confidence level?

The lower limit is the lowest percentage of poll participants who choose access to health care as the most urgent health-related problem.

The upper limit is to the highest percentage of poll participants who choose access to health care as the most urgent health-related problem.

Using the lower and upper limits, the Gallup poll can confidently estimate the range of the poll participants who pin-pointed access to health care as the most urgent.

Mean responses who choose access = 27%

Margin of error = ±4

Lower Limit = µ - margin of error

= 27% - 4%

=23%

Upper Limit = µ + margin of error

= 27% + 4%

=31%

Thus, at a 95% confidence level, the Gallup poll can claim that 27% ±4% of poll participants rated access to health care as the most urgent issue.

Learn more about the lower and upper limits of confidence intervals at brainly.com/question/17102070

#SPJ1

John purchased 4
apples for $1.25
each and 1 orange
for 2.49 How
much does he
spend in all?

Answers

4 x 1.25= 5
5+2.49= 7.49
Answer John spent 7.49$

Answer:

$7.49

Step-by-step explanation:

$1.25 x 4 = $5

1 x $2.49 = $2.49

5 + 2.49 = $7.49

Jill works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Jill to surprise them with the flavor. The teas are categorized by flavor and caffeine level. Mint Fruity Caffeine-free 2 7 Caffeinated 5 5 What is the probability that a randomly selected tea is caffeinated or mint? Simplify any fractions.

Answers

The grand total is given by

[tex]n=2+7+5+5=19[/tex]

so, the probability of Caffeinated is

[tex]P(Caffeinated)=\frac{5}{19}+\frac{5}{19}=\frac{10}{19}[/tex]

the probability of mint is

[tex]P(\min t)=\frac{2}{19}+\frac{5}{19}=\frac{7}{19}[/tex]

and the probability of the intersection is

[tex]P(Caffeinated\cap\min t)=\frac{5}{19}[/tex]

Then, the probabilty of the union is given by

[tex]undefined[/tex]

4. Find the value of p if 2P=2^2 p-7

Answers

Answer:

P = 7

Step-by-step explanation:

[tex]{ \tt{ {2}^{p} = {2}^{2p - 7} }} \\ [/tex]

- From the law of indices; If an index has same base, then the powers are equal.

[tex]{ \boxed{ \rm{ \blue{ ({x}^{a} = {x}^{b}) \rightarrow{ \red{a = b}} }}}}[/tex]

[tex]{ \tt{p = 2p - 7}} \\ { \tt{p -2 p = - 7}} \\ { \tt{p = 7}}[/tex]

OR:

Applying logarithms can also be borrowed;

[tex]{ \tt{ log( {2}^{p} ) = log( {2}^{2p - 7} ) }} \\ \\ { \tt{p log(2) = (2p - 7) log(2) }} \\ \\ { \tt{ \frac{p log(2) }{ log(2) } = \frac{(2p - 7) log(2) }{ log(2) } }} \\ \\ { \tt{p = 2p - 7}} \\ \\ { \tt{p - 2p = - 7}} \\ \\ { \tt{p = 7}}[/tex]

3. Consider the following system of equations.Line 1: 2x - y = -3Line 2: -6x - 2y = -6Part A:Is (0,3) a solution to Line 1? Explain your answer.Part B:Is coordinate (0, -3) is a solution to Line 2? Explain your answer.Part C:What are the slopes of Linel and Line 2?Part D:What are the y-intercepts of Line 1 and Line 2?

Answers

[tex]\begin{gathered} 2x-y=-3 \\ -6x-2y=-6 \end{gathered}[/tex]

Part A

replace (0,3) on (x,y)

[tex]\begin{gathered} 2(0)-(3)=-3 \\ 0-3=-3 \\ -3=-3 \end{gathered}[/tex]

the equivalence is correct so (0,3) is a solution of the first equation

Part B.

replace (0,-3) on (x,y)

[tex]\begin{gathered} -6(0)-2(-3)=-6 \\ 0-(-6)=-6 \\ 6=-6 \end{gathered}[/tex]

the equivalence is incorrect so (0,-3) isnt a solution of the second equation

Part C

To find the slope we need to solve each expresion and take the coefficient of x

first equation

[tex]\begin{gathered} 2x-y=-3 \\ y=2x+3 \end{gathered}[/tex]

the slope is 2

second equation

[tex]\begin{gathered} -6x-2y=-6 \\ 2y=-6x+6 \\ y=-3x+3 \end{gathered}[/tex]

the slope is -3

Part D

the y-intercept is the constant without variable on each equation

first equation

[tex]y=2x+3[/tex]

the y-intercept is 3

second equation

[tex]y=-3x+3[/tex]

the y-intercep is 3 too

The Graph

we need two points of the line and join by a right infinite line

first equation

the points (0,3) and (-3/2,0) belong to the line 1

second equation

the points (0,3) and (1,0) belong to the line 2

Solution of the system

we can note the two lines trought the point (3,0) so this is the solution and we can check matching the equations and solving x

[tex]\begin{gathered} 2x+3=-3x+3 \\ 2x+3x=3-3 \\ 5x=0 \\ x=0 \end{gathered}[/tex]

and replace x=0 on any equation to solve y I will use the first equation

[tex]\begin{gathered} y=2x+3 \\ y=2(0)+3 \\ y=3 \end{gathered}[/tex]

so the solution point is (0,3)

solve step through stepx + 2y = 83x - 2y = 0

Answers

Add both the equations

[tex]\begin{gathered} x+2y=8 \\ 3x-2y=0 \\ \text{Add left hand side terms together and right hand side terms together.} \\ x+2y+3x-2y=8+0 \\ 4x=8 \\ x=\frac{8}{4}=2 \end{gathered}[/tex]

Substitute 2 for x in x+2y =8 to find y

[tex]\begin{gathered} 2+2y=8 \\ 2y=8-2 \\ 2y=6 \\ y=\frac{6}{2}=3 \end{gathered}[/tex]

The solutions to the equations are x=2 and y=3.

Please show and explain this please

Answers

Answer:

b

Step-by-step explanation:

The root at [tex]x=1[/tex] has a multiplicity of 1, and corresponds to a factor of [tex](x-1)[/tex].

The root at [tex]x=-2[/tex] has a multiplicity of 1, and corresponds to a factor of [tex](x+2)[/tex].

The root at [tex]x=3[/tex] has a multiplicity of 2, and corresponds to a factor of [tex](x-3)^2[/tex].

Hello, I need help with this practice problem, thank you!

Answers

In order to find the distance between the given points, use the following formula:

[tex]d=\sqrt[]{(x_2-x_1_{}^{})^2+(y_2-y_1)^2}[/tex]

where (x1,y1) and (x2,y2) are the coordinates of the points.

In this case, you have:

(x1,y1) = K(1,-1)

(x2,y2) = F(6,-9)

Replace the previous values of the parameters into the formula for d and simplify:

[tex]\begin{gathered} d=\sqrt[]{(6-1)^2+(-9-(-1))^2} \\ d=\sqrt[]{(5)^2+(-9+1)^2} \\ d=\sqrt[]{25+(-8)^2}=\sqrt[]{25+64} \\ d=\sqrt[]{89} \end{gathered}[/tex]

Hence, the distance between K and F points is √89.

The prime factorization of $756$ is
\[756 = 2^2 \cdot 3^3 \cdot 7^1.\]Joelle multiplies $756$ by a positive integer so that the product is a perfect square. What is the smallest positive integer Joelle could have multiplied $756$ by?

Answers

The smallest positive integer Joelle could have multiplied 756 by

15876

This is further explained below.

What is a perfect square?

Generally, A perfect square number is a number in mathematics that, when its square root is calculated, yields a natural number.

To solve this problem we can do:

[tex]\sqrt{756}[/tex]

By properties of roots

[tex]\begin{aligned}&\sqrt{756}=\sqrt{6\cdot126} \\&=\sqrt{6 * 6 * 21} \\\\ =\sqrt{6^2 * 21} \\&=6 \sqrt{21}\end{aligned}[/tex]

So, so that the multiplication of 756 by an integer becomes a perfect square, you have to multiply it by 21 to make $21^2$ and thus "eliminate" the root.

756 * 21=15876

In conclusion,  You can verify that 15876is a perfect square since root (15876)=132 and 132 is a natural number

Read more about perfect square

https://brainly.com/question/385286

#SPJ1

Answer choicesReflection:1. reflect in the x-axis2. No reflectionStretch/Compress:1. No stretch nor compression2. Vertical Stretch of 2Horizontal Translation:1. Shift 6 units left2. Shift 5 units left3. Shift 6 units right4. Shift 5 units rightVertical Translation:1. Shift 5 units up2. Shift 6 units down3. Shift 6 units up4. Shift 5 units down

Answers

First, the parent function is translated 5 units to the left, then it is reflected over the x-axis, and finally, it is translated 6 units down.

Answer:

Reflection: reflect in the x-axis.

Stretch: No stretch nor compression.

Horizontal Translation: Shift 5 units left.

Vertical Translation: Shift 6 units down.

Answer the following Formula:[tex]5 \times 5 \times 6 \times 8 - 6 \times 9 \times 524 \times 8 \times 6 + 9 - 725 \times 6[/tex]

Answers

we have the expression

[tex]5\times5\times6\times8-6\times9\times524\times8\times6+9-725\times6[/tex]

we know that

Applying PEMDAS

P ----> Parentheses first

E -----> Exponents (Powers and Square Roots, etc.)

MD ----> Multiplication and Division (left-to-right)

AS ----> Addition and Subtraction (left-to-right)

solve Multiplication First

5x5x6x8=1,200

9x524x8x6=226,368

725x6=4,350

substitute

1,200-6x226,368+9-4,350

solve

6x226,368=1,358,208

1,200-1,358,208+9-4,350

Solve the addition and subtraction

1,200-1,358,208+9-4,350=-1,361,349

answer is-1,361,349
Your answer would be -1,361,349! You can get that easier by doing it is order! You get the same thing!

Solve the inequality for x and identify the graph of its solution. 4[x+ 2] < 8

Answers

Answer:

x < 0

Step-by-step explanation:

4(x + 2) < 8

4x + 8 < 8

4x < 0

x < 0

◀━━━━━|──>

                      0

Janet is getting balloons for her grandmother's birthday party. She wants each balloon string to be 12 feet long. At the party store, string is sold by the yard. If Janet wants to get 84 balloons, how many yards of string will she need?

Answers

Using conversion factors we can conclude that Janet needs 336 yards of string.

What do we mean by conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an equal value. For instance, 12 inches equals one foot when converting between inches and feet.

So, yards of string are needed:

1 balloon string will be 12 feet longSo, 84 balloons will have:12 × 84 = 1,008 feet strings

We know that:

1 feet = 0.3333 yardsThen, 1008 feet = 336 yards

Therefore, using conversion factors we can conclude that Janet needs 336 yards of string.

Know more about conversion factors here:

https://brainly.com/question/97386

#SPJ3

Let f(a) = x^2 + 5.a) Find the y-value when x = 0.The y-value, output value is ___b) Find the y-intercept, when x = 0.The y-intercept is ___c) Find the x-values, when y = 46.The x-values are ____

Answers

To solve a, we need to replace x = 0 in the formula of the function:

[tex]\begin{cases}f(x)=x^2+5 \\ x=0\end{cases}\Rightarrow f(0)=0^2+5=5[/tex]

The y value when x = 0 is 5.

b is asking the same as a but in a different way. The y-intercept of a function is when x = 0, we just calculated that. The point of y-intercept is (0, 5)

Finally, to solve c, we need to find the values of x that gives us a value of f(x) = 46:

[tex]f(x)=46\Rightarrow46=x^2+5[/tex]

Then solve:

[tex]\begin{gathered} x^2=46-5 \\ x=\pm\sqrt[]{41} \end{gathered}[/tex]

Remember that we must that plus-minus the value when we take square root. ± √41 is the answer to c.

given the equation 7x + 3 = 7X - _______ , what's would go in the blank to make each of the following true:so the equation is true for no values of xso the equation is true for all values of xso the equation is true for only one value of x

Answers

Let k be the number in the blank, so that:

[tex]7x+3=7x-k[/tex]

Substract 7x from both sides:

[tex]3=-k[/tex]

These two equations are equivalent regardless the value of x. We can change the conclusions that we may obtain by choosing different values for k.

Then, the equation:

[tex]7x+3=7x-0[/tex]

Is true for no values of x.

If we want the equation to be false regardless of the value of x, then set k so that -k is different from 3. For example, set k=0:

[tex]\begin{gathered} 3=-0 \\ \Rightarrow3=0 \end{gathered}[/tex]

Since this is contradictory, then there are no values of x that make the equation true.

If we want the equation to be true for all values of x, then 3=-k must be an identity. Then, let k=-3:

[tex]\begin{gathered} 3=-(-3) \\ \Rightarrow3=3 \end{gathered}[/tex]

Then, the equation:

[tex]7x+3=7x-(-3)[/tex]

Is true for all values of x.

If we want the equation to be true for only one value of x, we have to bring back x into the equation 3=-k. So, we can take k=x. This way, we would have:

[tex]\begin{gathered} 7x+3=7x-x \\ \Rightarrow3=-x \\ \Rightarrow x=-3 \end{gathered}[/tex]

Jessica has a barrel to fill with water. The barrel is 24 inches high with a radius of 12 inches. She is using a cup to fill the the barrel. The cup has a height of 6 inches and diameter of 4 inches. How many full cups will she need in order to fill the barrel?

Answers

SOLUTION.

The barrel and the cub are both cylinders. To find how many cups that will fill the barrel, we find the volumes of both the cup and the barrel and divide that of the barrel by the cup

Volume of a cylinder is given as

[tex]\begin{gathered} \text{Volume = }\pi r^2h,\text{ r is radius and h is height of the cylinder } \\ radius\text{ of the barrel = }12,\text{ height = 24} \\ \text{Volume of barrel = }\pi r^2h \\ \text{Volume of barrel = 3.14}\times12^2\times24 \\ \text{Volume of barrel = }10851.84inch^3 \end{gathered}[/tex]

Volume of the cub becomes

[tex]\begin{gathered} \text{radius of cup = }\frac{4}{2}=2 \\ \text{Volume of barrel = }\pi r^2h \\ \text{Volume of cup = }3.14\times2^2\times6 \\ \text{Volume of cup = }75.36inches^3 \end{gathered}[/tex]

Number of cups become

[tex]\frac{10851.84}{75.36}\text{ = 144 cups }[/tex]

The point (5,4) is rotated 270 degrees clockwise, would the answer be (-4,5)?

Answers

The image of the point (5, 4) after being rotated 270 degrees clockwise around the origin is (- 4, 5).

How to determine the image of a point by rotation around the origin

In this problem we find the case of a point to be rotated by a rigid transformation, represented by a rotation around the origin. The transformation rule is defined by the following expression:

P'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

(x, y) - Coordinates of point P(x, y).θ - Angle of rotation (counterclockwise rotation is represented by positive values).P'(x, y) - Coordinates of the resulting point.

If we know that P(x, y) = (5, 4) and θ = - 270°, then the coordinates of the image are, respectively:

P'(x, y) = (5 · cos (- 270°) - 4 · sin (- 270°), 5 · sin (- 270°) + 4 · cos (- 270°))

P'(x, y) = (- 4, 5)

The image of the point (5, 4) is (- 4, 5).

To learn more on rigid transformations: https://brainly.com/question/1761538

#SPJ1

HELP NOW PLS !!! 100 POINTS
The points (5,8) and (10,2) fall on a particular line. What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

Answers

Answer:

[tex]y-8=-\dfrac{6}{5}(x-5)[/tex]

Step-by-step explanation:

Define the given points:

(x₁, y₁) = (5, 8)(x₂, y₂) = (10, 2)

First find the slope of the line by substituting the given points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-8}{10-5}=-\dfrac{6}{5}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-8=-\dfrac{6}{5}(x-5)[/tex]

Choose if each statement is True or False.

{(2, 2), (3, 2), (4, 2), (6, 2)} is a function:

{(-1, 5), (0, 8), (3, 12), (6, 21)} is a function:

Answers

Answer:

The first one in red is a function. The second one in blue is not a function.

Step-by-step explanation:

Using the vertical line test, if you were to draw a vertical line and move the line from left to right, it should not have two points of intersection (if the vertical line intersects the relation more than one, then the relation is not a function).

What is the GCF of 12 and 24

Answers

Answer:

12

Step-by-step explanation:

The GCF of 12 and 24 is 12. To calculate the most significant common factor of 12 and 24, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; characteristics of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the most significant factor that exactly divides both 12 and 24, i.e., 12.

12
12(1,2,3,4,6,12)
24(1,2,3,4,6,8,12,24)

given the following trig equations find the exact value of the remaining five trig functions.cos0 = 4/9 where sin0 < 0( sin, tan, csc, cot, sec)

Answers

we have that:

[tex]\sin ^2\theta=1-\cos ^2\theta=1-\frac{16}{81}=\frac{65}{81}\rightarrow\sin \theta=-\frac{\sqrt[]{65}}{9}[/tex]

having this we get that

[tex]\tan \theta=\frac{-\sqrt[]{65}}{4},\cot \theta=-\frac{4}{\sqrt[]{65}},\sec \theta=\frac{9}{4},\csc \theta=-\frac{9}{\sqrt[]{65}}[/tex]

I can't figure out how to do (i + j) x (i x j)for vector calc

Answers

In three dimensions, the cross product of two vectors is defined as shown below

[tex]\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}[/tex]

Then, solving the determinant

[tex]\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}[/tex]

In our case,

[tex]\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}[/tex]

Where we used the formula for AxB to calculate ixj.

Finally,

[tex]\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}[/tex]

Thus, (i+j)x(ixj)=i-j

(12-1) (-2-3) slope p l z

Answers

[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 3 - ( - 1)}{ - 2 - 12} \\ m = \frac{ - 3 + 1}{ - 14} \\ m = \frac{ - 2}{ - 14} \\ m = \frac{1}{7} [/tex]

ATTACHED IS THE SOLUTION..I also provided you with the formula used to get the gradient.

what is the diameter of a circle if the circumference is 18 cm

Answers

5.73 cm diameter (rounded)

Please help and round to the nearest minute if needed

Answers

Solution

For this case we have the following angle:

30 1/6 º

and then we need to convert to degrees and minutes so we can do this:

1 º= 60 min

then 1/6º* (60min/ 1º)= 10 min

Then the answer is:

30º 60'

PLEASE HURRY
What is the quotient of (−152) ÷ (−19) ÷ (−4)?

Answers

Answer:

-2

I did the math and it came out -2

The length of a rectangular room is 5 yards more than the width. If the area is 300 yd2, find the length and the width of the room.

Answers

Okay, here we have this:

Considering that the area of a rectangle is:

Area=length*width

Replacing we obtain:

300=(5+x)*x

300=5x+x²

0=5x+x²-300

0=(x-15)(x+20)

This mean that:

x-15=0 or x+20=0

x=15 or x=-20

And considering that the distances are positive we are left with the first solution, x=15; this mean that:

Width=15 yd

Length=(15+5) yd=20 yd.

Finally we obtain that the width is 15 yd and length is 20 yd.

ASAP I NEED HELP WITH THIS PROBLEM AND WILL GET THE BRAINLIEST FOR THE CORRECT ANSWER

Answers

Answer: (x, y) -> (x, -y)

Step-by-step explanation:

1) You can easily find the transformation by substituting one point on the figure.

For this example, I will substitute S and S' points. (4, 1) and (4, -1)

2) Replace the numbers with x and y.


Set the numbers equal. They are already equal so no change.

(4, 1) -> (4, -1)

Replace with X and Y

(x, y) -> (x, -y)

Beginning with the general form of a quadratic equation. ax^2+bx+c=0, solve for x by using the completing the square method, thus deriving the quadratic formula. To earn full credit be sure to show all steps/calculations. You may want to do the work by hand and upload a picture of that written work rather than try to type it out.

Answers

to solve ax^2 + bx + c = 0 using completing the square method

divide all terms by a so as to reduce the coefficient of x^2 to 1

x^2 + bx/a + c/a = 0

subtract the constant term from both sides of the equation

x^2 + bx/a = -c/a

to have a square on the left sie the third term (constant) should be

(b/2a)^2

so add that amount to both side

x^2 + bx/a + (b/2a)^2 = (b/2a)^2 - c/a

rewrite the left side as a square

(x + (b/2a))^2 = (b/2a) - c/a

take the square root of both sides

x + (b/2a) = + square root of (b/2a)^2 - c/a

subtract the constant term on the left side from both sides

[tex]\begin{gathered} x\text{ = }\pm\sqrt[]{(\frac{b}{2a}})^2\text{ - c/a - (b/2a)} \\ x\text{ = -b }\pm\sqrt[]{\frac{b^2\text{ - 4ac}}{2a}} \end{gathered}[/tex]

An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of
280 days and a standard deviation of 13 days. An alleged father was out of the country from 242 to 301 days before the birth
of the child, so the pregnancy would have been less than 242 days or more than 301 days long if he was the father. The birth
was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father?
Calculate the z-scores first, and then use those to calculate the probability. (Round your answer to four decimal places.)
What is the probability that he could be the father? (Round your answer to four decimal places.)

Answers

1. The z scores in the question are - 2.92 and 1.615

2. The probability that he is the father = 0.054905

How to solve for the probability and the z score

The z score for the 242 days

= 242 - 280 / 13

= -2.92

The z score for the 30 days

= 301 - 280 / 13

= 1.615

Next we have to solve for The probability that he is not the father

this is written as

p(242 < x < 301)

p value of -2.92 = 0.00175

p value of 1.615 = 0.946845

Then we would have 0.946845 - 0.00175

= 0.945095

The probability that he is the father is given as 1 - probaility that he is not the father of the child

= 1 - .945095

= 0.054905

The probability that he is the father is 0.054905

What is probability?

This is the term that is used in Statistics and also in the field of mathematics to explain the chances and the likelihood of an event occurring.

Read more on probability here:

brainly.com/question/24756209

#SPJ1

Other Questions
Can someone please help me on this? for each equation complete the table and then graph the equation The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.4w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown.graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8Which of the following statements is true about the graph shown? The graph is incorrect and the line should go through the point (0.4, 1). The equation c = 0.4w is correctly represented by the graph. The x-axis and y-axis are labeled incorrectly. The graph does not show a proportional relationship. Suppose you walk 16 m straight east and then 22 m straight south. At what angle, in degrees South of East, is a line connecting your starting point to your final position? 3x6 = 7x - 8What equations have the same solution set? What is the equation of the line that passes through the point (5, 3) and has anundefined slope? there are 15 pieces in 3 building set. How many pieces are there in 8 building set? The following data are the ACT score of all student in the history class In the group of ordered pairs shown, the x-values are inputs and the y-values are outputs. Select all the statements that are true.(2, 4), (6, 3), (5, 4), (7, 3), (8, 2) A. There is only one input for every output. B. There is only one output for every input. C. There is more than one output for some inputs. D. There is more than one input for some outputs. E. The group of ordered pairs represents a function. during a(n) interview, the interviewer explores what the applicant has actually done in the past. combination strategies, such as combining differentiation and low cost, makes it easier for rivals to imitate because it is harder for the primary firm to provide value. true false can you draw a quadrilateral with 2 pairs of congruent parallel sides and 4 right angles A superelastic collision is one in which1) kinetic energy before the collision equals kinetic energy after the collision.2) kinetic energy after the collision is zero.3) kinetic energy before the collision is less than kinetic energy after the collision.4) kinetic energy before the collision is greater than kinetic energy after the collision Use the given values to write an equation that relates x and y. Wukong and Nice are playing a soccer matchand the probabilities of them scoring are7/8 and 5/6 respectively. What is the probability that atleast one of them will score a goal if they eachplay the ball once? Is the island in Thomas Moores book, Utopia, a dystopia, a utopia, or something else? Explain why and support your answer with information from the text. Three students that share a townhouse find that their electric bill for October is $5.29 less than the September bill. The total of both bills is $155.93, and each bill is split evenly among the roommates how much they each owe in September? Given that F( x) = x + 2, evaluate F(2) What inference does Kennedy make in this part of his speech? Berlin shows that communism is a harmful system that hurts the people living under it. Berlin shows that democracy will never be accepted in the West. The Soviets should come to Berlin to help restore the city. The Soviets should come to Berlin to learn the right way to practice communism.y'all better give me sum so I can get extra points smhnn What do you need to do before you analyze yourcurrent work systems?