In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 19.
The probability of a student scoring less than 19 is.
(Round to four decimal places as needed.)
(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.7 and 27.1.
The probability of a student scoring between 17.7 and 27.1 is.
(Round to four decimal places as needed.)
(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 33.1.
The probability of a student scoring more than 33.1 is
3.1
is.
(Round to four decimal places as needed.)
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
OA. None of the events are unusual because all the probabilities are greater than 0.05.
B. The event in part (c) is unusual because its probability is less than 0.05.
C. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.
D. The event in part (a) is unusual because its probability is less than 0.05.
Help me solve this

Answer: (9, 10800)

Step-by-step explanation:

We will first let x be the number of years and y be the total cost.

In that case, let's plug in the values for each into the equation y=mx+b, where m is the slope and b is the y-intercept.

The y-intercept will be the value we start with before any years pass, so it will be the installation cost. The slope is how fast the total cost will increase. Since the operation costs have to be added on every year, it will be our slope.

With that in mind, let's create both of our equations:

Since y is solved for in the first equation, we can substitute it into the second equation:

[tex]900x + 2700 = 200x + 9000[/tex]

[tex]700x + 2700 = 9000[/tex] [Subtracting 200x from both sides]

[tex]700x = 6300[/tex] [Subtracting 2700 from both sides]

[tex]x = 9[/tex] [Dividing both sides by 700]

We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:

[tex]y = 900(9) + 2700[/tex]

[tex]y = 8100 + 2700[/tex] [Multiplying]

[tex]y = 10800[/tex] [Adding]

Hence, the solution to this linear system is (9, 10800).

Answer:

1/5 :D

Step-by-step explanation:

Lets pick 2 point on the graph :)

We need this to find the slope!

Lets use (-5,1) and (0,2) :)

First we subtract the y coordinates! :)

2 - 1 = 1

Then we subtract the x coordinates!

0 - (-5) = 5

Now we divide!

1/5

Our answer is 1/5!

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

first choice : 1/5

Step-by-step explanation:

need 2 points

one point is (0,2)

another is (5,3)

slope formula is

y2 - y1 / x2 - x1

3 - 2 / 5 - 0

1/5

Answer:

320

Step-by-step explanation:

Is the 3 to 2 part to part?  Out of every 5 people, 3 prefer pizza and 2 do not.  We can us this to set up a proportion.

3/5 = 120/x  The 3 represent the part that like pizza over the whole of 5.  The second ratio is showing the actual number of people that liked pizza over the total number of people.

What would be multiply 3 by to get 120? 40.  So, we will multiply 5 times 40 to get the total number of people.  5 x 40 = 200

The error is that

[tex] {x}^{y} - {x}^{z} \neq {x}^{y - z} [/tex]

Instead, it should be 4⁴ - 4³ = 256 - 64 = 192.

Answer:

no roots.

Step-by-step explanation:

[tex]\left \{ {{2x-y=8} \atop {y=2x-3}} \right. \ = > \ \left \{ {{2x-y=8} \atop {2x-y=3}} \right. \ = > \ no \ solution.[/tex]

The time taken to the closest minutes for the pie to cool to 80∘F is 123 minutes

T(t) = 68e^−0.0174t + 72

80 = 68e^−0.0174t + 72

80 - 72 = 68e^−0.0174t

8 = 68e^−0.0174t

e^−0.0174t = 8/68

e^−0.0174t = 0.11764705882352

ln e (−0.0174t) = ln (0.11764705882352)

1 × −0.0174t = -2.1400661634962708

-0.0174t = -2.1400661634962708

t = -2.1400661634962708 / -0.0174

t = 122.9923

Approximately,

t = 123 minutes

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The surface area of a cone with radius of 4 m and slant height of 5 m is 36π m²

An equation is an expression that shows the relationship between two or more numbers and variables.

The surface area of a cone with radius (r) and slant height (l) is:

S.A = πr(r + l)

Given that r = 4, l = 5, hence:

S.A = π(4)(4 + 5) = 36π m²

The surface area of a cone with radius of 4 m and slant height of 5 m is 36π m²

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Answer:

36π m2

Step-by-step explanation:

The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;

The given angles are;

At James's location; 61°

At Hadley's location; 73°

At Gwen's location; 46°

The distance between James and Hadley = 15 meters

The angle facing the distance between James and Hadley is the angle at Gwen, 46°

The angle facing the distance between Gwen and James is the angle at Hadley, 73°

The angle facing the distance between Gwen and Hadley is the angle at James, 61°

The angle that faces the 15 meter length is the angle at Gwen, which is 46°

By the rule of sines, the distance from Gwen to Hadley is therefore;

[tex] \frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)} [/tex]

Which gives;

[tex] Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24[/tex]

Similarly, we have;

[tex] \frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)} [/tex]

Therefore;

[tex] Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94 [/tex]

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Answer:

Step-by-step explanation:

3 things of triangle are given.

2 sides + 1 angle

so, possible triangles = 1 ans

The simplified expression of the given equation is  [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]

There are three basic steps for addition or subtraction of two fractions

The given expression :- [tex]\frac{x+6}{x+4} +\frac{x-3}{3}[/tex]

Taking LCM or making the denominators same we get,

= {3(x+6) + (x-3)(x+4)}/3(x+4)

= {3x + 18 + x² +x -12}/3(x+4)

={x² + 4x + 6}/3x + 12

= [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]

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Answer:

i believe its B

Step-by-step explanation:

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of alloy #11 and y represent the amount of alloy #15, hence:

(0.36x) + (y * 0.36) = 1(0.36)   (1)

Also:

0.28x + 0.64y = 1(0.55)    (2)

From both equations:

x = 0.25, y = 0.75

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

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The exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

An exponential function is represented as:

[tex]y = b^x[/tex]

The base is 3.

So, we have:

[tex]y = 3^x[/tex]

It is stretched vertically by 2/3.

So, we have:

[tex]y = \frac23(3)^x[/tex]

When reflected over the y-axis, we have:

[tex]y = \frac23(3)^{-x}[/tex]

An asymptote of y = 2, makes the function becomes

[tex]y = \frac23(3)^{-x} + 2[/tex]

Lastly, it passes through the point (0, 3.5).

So, we have:

[tex]y = \frac23(3)^{-x+h} + 2[/tex]

This gives

[tex]3.5 = \frac23(3)^{-0+h} + 2[/tex]

[tex]3.5 = \frac23(3)^{h} + 2[/tex]

Subtract 2 from both sides

[tex]1.5 = \frac23(3)^{h}[/tex]

Multiply by 3/2

[tex]2.25 = (3)^{h}[/tex]

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in [tex]y = \frac23(3)^{-x+h} + 2[/tex]

[tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

Hence, the exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

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The underlined sentence in the text simply functions as; the conclusion of the text and connects ideas in the text, by making the main claim of the text describing why the information provided matters to readers.

The underlined text in the passage functions as the conclusion to the passage in which case, the information intended to be conveyed is that on the occasion that, regular feeding, good housing, occasional gentle corrections and kindness are in place, there'd be no need for such a cat to steal.

Therefore, the structural element of the paragraph in the underlined sentence, and how it connect ideas in the text is; by making the main claim of the text

describing why the information provided matters to readers.

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Answer:

14 days

Step-by-step explanation:

let assume they both work on Monday (today)

devin works every 7 days,that is devin works every Monday.

jamie has to work for 14 days inorder to work with devin again

The total bill after tax is $38.44.

The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14

Now, determine the total cost after delivery fee has been added : $3 +  $32.14 =  $35.14

Now determine the total cost after tax : (1.094) x $35.14 = $38.44

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The total bill after tax of 9.4% is $38.44.

It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price

total cost of 4 pizzas= $6.79 *4

total cost of 4 pizzas=$27.16

total cost of 2 orders of breadsticks=$2.49*2

total cost of 2 orders of breadsticks=$4.98

total cost of purchase prior to adding delivery cost=$27.16+$4.98

total cost of purchase prior to adding delivery cost=$32.14

total cost of purchase after  delivery cost=$32.14+$3

total cost of purchase after  delivery cost=$35.14

total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)

total cost inclusive of 9.4% sales tax=$35.14*1.094

total cost inclusive of 9.4% sales tax=$38.44

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Answer:

[tex]\dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]

Step-by-step explanation:

From inspection of the given graph, we can see that the center of the ellipse is the origin (0, 0) and the longest diameter of the ellipse is across the x-axis.  

Therefore, we can use the general equation of a horizontal ellipse with its center at (0, 0):

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

where:

From inspection of the ellipse:

Therefore, a = 7 and b = 6

Substitute the found values of a and b into the formula:

[tex]\implies \dfrac{x^2}{7^2}+\dfrac{y^2}{6^2}=1[/tex]

[tex]\implies \dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given figure shows a Horizontal Ellipse with its centre at origin, and as we observe the figure, we can conclude that :

Length of major axis is :

[tex]\qquad \sf  \dashrightarrow \: 2a = 14[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 7[/tex]

and that of minor axis :

[tex]\qquad \sf  \dashrightarrow \: 2b = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = 6[/tex]

Equation of Ellipse will be ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ {x}^{2} }{ {a}^{2} } + \dfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

[ plug in the values ]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ {x}^{2} }{ {7}^{2} } + \dfrac{ {y}^{2} }{ {6}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{ {x}^{2} }{ {49}^{} } + \dfrac{ {y}^{2} }{ {36}^{} } = 1[/tex]

The critical values are 0.622, 0.707, 0.789 and 0.834

The sample size is given as:

n = 8

Calculate the degrees of freedom using

df = n - 2

So, we have:

df = 8 - 2

df = 6

Using the table of values of critical values, we have:

Critical values = 0.622, 0.707, 0.789 and 0.834

By comparing the critical values and the linear correlation coefficient, we can conclude that there is no significant linear correlation.

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The value of y at x =15 is 9.

Two variables are said to be in Direct Variation when increasing one variable the other also increases.

The direct variation is represented by

y ∝ x

y = kx

where k is the proportionality constant

the value of y =12 , x = 20

12 = k * 20

12/20 = k

k = 0.6

The equation becomes

y = 0.6 x

The value of y at x = 15 is

y = 0.6 * 15

y =9

Therefore, the value of y at x =15 is 9.

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Answer:

Step-by-step explanation:

d = 13.416408

For:

(X1, Y1) = (-4, -5)

(X2, Y2) = (8, 1)

Answer:

L = 9.49 units

Step-by-step explanation:

From the 1st point to the 2nd, x changes by 12; from the 1st to the 2nd, y changes (increases) by 6.  These results (12 and 6) represent the leg length of a right triangle whose diagonal length we wish to calculate using the Pythagorean Theorem:

12^2 = 144 and 6^2 = 36.

Combining these results in the length of the diagonal:

L = √(144 + 36) = √180 = 13.42 units using the Pythagorean Theorem

Rounding off, we get L = 9.49 units

Using the z-distribution, the critical value for a confidence level of 90% is of Z = 1.65.

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.65.

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The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433

The function is given as:

y = 123(1.065)^x

Where x represents years from 1998 to 2013

2003 is 5 years from 1998.

This means that

x = 5

Substitute the known values in the above equation

y = 123(1.065)^5

Evaluate the exponent

y = 123 * 1.37008666342

Evaluate the product

y = 168.520659601

Approximate

y = 169

Hence, the estimate of the number of students studying abroad in 2003 is 169

2018 is 20 years from 1998.

This means that

x = 20

Substitute the known values in the above equation

y = 123(1.065)^20

Evaluate the exponent

y = 123 * 3.52364506352

Evaluate the product

y = 433.408342813

Approximate

y = 433

Hence, the estimate of the number of students studying abroad in 2018 is 433

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The hydroxonium ion concentration of the fruit juice whose pH as given in the task content is; 5.6 can be evaluated as; [H3O+] = 2.51 × 10^-6.

Since the given pH of the fruit juice is 5.6, the hydroxonium ion concentration of the fruit juice can be evaluated by means of the formula as follows;

pH=-log[H3O+].

5.6 = -log[H3O+].

-5.6 = log[H3O+].

[H3O+] = antilogarithm (-5.6)

[H3O+] = 2.51 × 10^-6.

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The equation of the given Absolute Value Function is; y = |-2x + 4|

We can see that the given graph is a Linear graph but since it is V-shaped, we can say that it is a graph of an absolute value function.

Now, from the graph we see that;

At x = 0, y = 4

At x = 1, y = 2

At x = 2, y = 0

At x = 3, y = -2

At x = 4, y = 0

At x = 5, y = 2

We can see that the y-intercept is at y = 4.

Slope between two consecutive points is;

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

Equation is; y = -2x + 4

Now, this is an absolute value function and as such we will write it as;

y = |-2x + 4|

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The graph of the absolute value function can be seen below.

Here we have the absolute value function:

[tex]f(x) = |x^2 - x -2|[/tex]

Notice that the argument of the absolute value function is a quadratic equation, then the graph of the function f(x) will be the graph of the quadratic equation, but such that the part below the horizontal axis is reflected.

Then the graph of the function is the one you can see below:

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Answer:

a = 43 degrees

b = 137 degrees

Step-by-step explanation:

according to the alternate interior angle theorem, angle a equals angle theta, so angle a = 43 degrees

angle b is the supplement of angle a, so angle b = 180-angle a, or 137