(5 points) The probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%. What is the probability that a randomly selected day in April will be rainy or windy?

Answer:

15.757 im not sure but i came up with that one.

Step-by-step explanation:

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Answer:

there are 5 pigs and 5 chickens

Step-by-step explanation:

Im not sure if this is the answer but 5 pigs each pig has 4 legs 5x4=20 and the 5 chickens have 2 legs 2x5+10 10+20+=30

Answer:

43.6 has 3 significant figures.

Answer:   -2

:)

Step-by-step explanation:

Answer:

sin = opposite / hypotenuse

\( \sin(60) = \frac{x}{10} \\ \\ \frac{ \sqrt{3} }{2} = \frac{x}{10} \\ \\ 2x = 10 \sqrt{3} \\ \\ x = \frac{10 \sqrt{3} }{2} \\ \\ x = 5 \sqrt{3} \)

Step-by-step explanation:

for x:

apply the sine rule. so

sinA/a = sinB/b

sin 90/10 = sin 60/ x

(cross multiply)

sin90 x = sin 60 × 10

x= (sin60×10)/sin90

x=8.66

Answer:

Step-by-step explanation:

The balance of an account after a year, when the interest rate is 3% per year and there are no additional withdrawals or deposits, can be represented by the formula:

Balance = Principal + Interest

where Principal is the initial amount of money invested (m) and Interest is the interest earned on that amount for the year.

Interest is calculated as the product of the principal, the interest rate, and the time period. In this case, the interest rate is 3% (or 0.03), and the time period is one year. Therefore the Interest can be represented by the following expression:

Interest = Principal * Interest Rate * Time

Substituting the given values:

Interest = m * 0.03 * 1

So the expression that represents Arianys balance after a year is:

Balance = m + (m*0.03)

= m + 0.03m

= 1.03m

This expression represents her balance after a year, assuming she makes no additional withdrawals or deposits.

Step-by-step explanation:

It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other .   Opposite angles are equal and adjacen angles sum to 180 degrees .

Then remember alternate angles are equal  and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one

Answer:

t= 0.4933

t ≥ t ( 0.025 ,8 ) = 2.306

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0: ud= 0 Ha: ud≠0

The significance level is set at ∝= 0.05

The test statistic under H0 is

t= d`/ sd/√n

which has t distribution with n-1 degrees of freedom

The critical region is t ≥ t ( 0.025 ,8 ) = 2.306

Computations

Student       Scores before      Scores after    Difference           d²

                        reading book                    ( after minus before)

1                          720                   740             20                       400

2                        860                   860              0                           0

3                        850                   840             -10                       100

4                        880                   920             40                       1600

5                        860                   890             30                        900

6                        710                    720              10                         100

7                       850                    840              -10                       100

8                      1200                  1240             40                        1600

9                      950                    970              20                           40

∑                    6930                  8020           140                         4840

d`= ∑d/n= 140/9= 15.566

sd²= 1/8( 4840- 140²/9) = 1/8 (4840 - 2177.778) = 2662.22/8= 332.775

sd= 18.2422

t= 3/ 18.2422/ √9

t= 0.4933

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Answer:

D

Step-by-step explanation:

in order smallest to largest

2, 4, 6, 8, 8, 10, 12

the figure in the middle is 8, therefore the median is 8

hope this helps :)

According to the table, the statement "note sent to parents" is represented by the following inequality:

this can be represented as all integers less than zero. That is all integers to the left of 0.

We can conclude that the correct answer is:

Draw points on the integers to the left of 0.

Answer:

\(4fg^{2}\)

Step-by-step explanation:

1) Remove parentheses.

\(fg^{2} *4\)

2) Regroup terms.

\(4fg^{2}\)

Answer:

The correct answer is...

Step-by-step explanation:

"F^4g^8" Hope this helps!

Answer:

\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)

Step-by-step explanation:

We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

↓ plugging in the given values

\(a^2 + 2^2 = 14^2\)

↓ subtracting 2² from both sides

\(a^2 = 14^2 - 2^2\)

\(a^2 = 196 - 4\)

\(a^2 = 192\)

↓ taking the square root of both sides

\(a = \sqrt{192\)

↓ simplifying the square root

\(a = \sqrt{2^6 \cdot 3\)

\(a = 2^{\, 6 / 2} \cdot \sqrt3\)

\(a = 2^3\sqrt3\)

\(a = 8\sqrt3\)

Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.

\(a = \dfrac{1}{2}x\)

↓ plugging in the a-value we solved for

\(8\sqrt3 = \dfrac{1}2x\)

↓ multiplying both sides by 2

\(\boxed{x = 16\sqrt3}\)

Answer:

Distribute 4 to a and -5.

Step-by-step explanation:

Multiplication goes first.

Find the axis of symmetry and vertex for the parabola y = –x^-8x+8

y = –x^-8x+8

The number line that shows approximately the location of √5 would the number line in option D.

A number line is defined as the expression that can be used to illustrate the position of a given number which show either it is a positive or a negative number with one at the middle.

The given value is thus;

= √5 = 2.236067977 = 2.2

From the chosen number line, the dark dot is just few points after 2.

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Answer:

a. the probability of a type II  error is 0.5319

b. the required sample size to satisfy and the type II error probability  is 59.4441

Step-by-step explanation:

From the information given; we have:

sample size n = 25

Population standard deviation \(\sigma\) = 4

true average lifetime = Sample Mean \(\bar X\) = 62

We can state our null hypothesis and alternative hypothesis as follows:

Null hypothesis:

\(\mathbf{H_o : \mu = 60}\)

Alternative hypothesis

\(\mathbf{H_1 : \mu \neq 60}\)

Where ;

∝ = 0.01

From the standard normal tables at critical value ∝ = 0.01 ; the level of significance is -2.575 lower limit and 2.575 upper limit

The z statistics for the lower limit is:

\(lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}\)

\(-2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}\)

\(-2.575= \dfrac{\bar x - 60 }{0.8}}}\)

\(-2.575*0.8= {\bar x - 60 }{}}}\)

\(-2.06= {\bar x - 60 }{}}}\)

\(\bar x = 60-2.06\)

\(\bar x = 57.94\)

The z statistics for the upper limit is:

\(lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}\)

\(2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}\)

\(2.575= \dfrac{\bar x - 60 }{0.8}}}\)

\(2.575*0.8= {\bar x - 60 }{}}}\)

\(2.06= {\bar x - 60 }{}}}\)

\(\bar x = 60-(-2.06)\)

\(\bar x = 60+2.06\)

\(\bar x = 62.06\)

Thus; the probability of a type II error is determined as follows:

β = P (  \(57.94 < \bar x < 62.06\) )

\(= P ( \dfrac{57.94 -62 }{\dfrac{4}{\sqrt{25}}}<\dfrac{62.06 -62 }{\dfrac{4}{\sqrt{25}}})\)

\(= P ( \dfrac{-4.06 }{0.8}}<\dfrac{2.06 }{0.8})\)

= P ( -5.08 < Z < 0.08 )

= P ( Z < 0.08) - P ( Z < - 5.08)

Using Excel Function: [ (=NORMDIST (0.08)) - (=NORMDIST(-5.08)) ] ; we have:

= 0.531881372 - 0.00000001887

= 0.531881183

≅ 0.5319

b.

What is the required sample size to satisfy and the type II error probability of b(62) = 0.1

Recall that:

The critical value of ∝ = 2.575  ( i. e   \(Z_{1 - \alpha/2 } = 2.575\)  )

Now ;

the critical value of β is :

\(Z _{1- \beta} = 1.28\)

The  required sample size to satisfy and the type II error probability  is therefore determined as :

\(n = [\dfrac{(Z_{1 - \alpha/2} + Z_{1 - \beta} ) \sigma }{\delta}]^2\)

\(n = [\dfrac{(2.575+1.28 ) 4 }{2}]^2\)

\(n = [\dfrac{(3.855 ) 4 }{2}]^2\)

\(n = [\dfrac{(15.42 ) }{2}]^2\)

n = 7.71 ²

n= 59.4441

Thus; the required sample size to satisfy and the type II error probability  is 59.4441

A)

In order to calculate the Type II Error, we proceed with stating the factors:

Hypothesized Mean is given as  =  μ\(_{0} \)        = 60

True Mean  is given as                 =  μa        = 62

Standard Deviation  is given as  = σ           = 4

Sample Size                                   = n           = 25

Standard error of mean                = σx          =σ/\(\sqrt{\\} \)σ               =  0.80

given 0.01 level and two tailed test critical value Zσ             ±  2.58 or approximately 3

Acceptance region is

given as:   = μ - Z∝ * σx ≤ Π ≤ μ+Z∝⇄            =57.9360 ≤x≤   62.0640

Type II Error = probability of not rejecting β    = P(57.94-μa/σx))     <Z< (62.064-μa)/σx))

                                      = P (-5.08   <Z<    0.08)
                                      = 0.5319-0)

                                      = 0.532

B

Hypothesized mean                        = μ₀             =        60

True Mean                                        =μₐ               =       62          

Standard Deviation                          =σ                 =      4

for 0.01 level and two-tailed test critical value Z∝/2              ± 2.58

for 0.01 level of type II error critical value Z\(\beta \)                         = 1.28

Required sample size    = n                                       = (\(Z_{\alpha /2} \) + \(Z_{\beta } \))²σ²/(μ₀-μ₀)²
                                                                                    = 60


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There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.

To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:

Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.

There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.

Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,

So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.

As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.

Number of sets of five marbles that include both the lavender one and exactly one yellow one:

We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.

We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.

To find the number of sets that include both, we can choose any one yellow marble and the lavender one.

There are 2 choices for the yellow marble and 1 choice for the lavender one,

So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.

Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:

Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.

The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,

So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.

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Answer:

Step-by-step explanation:

It’s 20

Answer:

\(\cos(x)=\frac{1}{2}\)

Step-by-step explanation:

\(2\sec(x)+5=9\\\\2\sec(x)=4\\\\\sec(x)=2\\\\\frac{1}{\sec(x)}=\frac{1}{2}\\ \\\cos(x)=\frac{1}{2}\)

Thus, the first option is correct

Answer: cos(x)= 1/2 is correct

Step-by-step explanation: just got the answer right

Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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Answer:

55.82 cm

Step-by-step explanation:

d1= 8.72 cm

a= 15.6 cm

A rhombus= 1/2*d1*d2 = A square

A square= 15.6²= 243.36 cm²

d2= 2A/d1= 2*243.36/8.72 ≈55.82 cm

The two times Tyler selects a shirt from the suitcase are independent events.

The probability that he selects a short-sleeved shirt both times is 9/16.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of shirts = 8

Number of short sleeves = 6

The shirts are replaced after selecting one to select the other shirt.

The two times Tyler selects a shirt from the suitcase are independent events

The probability that he selects a short-sleeved shirt.

= 6 / 8

= 3/4

The probability that he selects a short-sleeved shirt both times.

= 3/4 x 3/4

= 9/16

Thus,

The two times Tyler selects a shirt from the suitcase are independent events.

The probability that he selects a short-sleeved shirt both times is 9/16.

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The complete question is:

Tyler packed 8 shirts for a trip. Six of the shirts are short-sleeved. He randomly selects a shirt from his suitcase, replaces the shirt, and then selects another.

The two times Tyler selects a shirt from the suitcase are __________ events.

The probability that he selects a short-sleeved shirt both times is ________.

options for blank 1: independent, dependent

options for blank 2 :15/28, 9/16, 3/4, 9/14

the number of pancake does it make from 3 1/3 cups of pancake is 30 pancakes.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Here it is given that :

2/3 of a cup of pancake mix makes 6 pancakes

2/3  pancake mix = 6 pancakes

multiply 3/2 both side :

1 pancake mix = 6x3/2 pancakes

1 pancake mix = 9 pancakes

Now to find the number of pancake does it make from 3 1/3 cups of pancake mix multiple 3 1/3 both side That is :

3 1/3  pancake mix = 9 x 10/3 pancakes

3 1/3  pancake mix = 30 pancakes

Therefore, the number of pancake does it make from 3 1/3 cups of pancake is 30 pancakes.

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The maximum budget for equipment and costumes is \(4.85x - $450\).

Let us assume the number of seats available is "x".

Let us represent cost of equipment and costumes with C

The total revenue from ticket sales would be 4.85x.

From 4.85x, the committee wants to have $450 remaining, so we can set up an equation.

The equation will be \(4.85x - 450 = C\)

So, to get maximum budget for equipment and costumes, we need to maximize the cost of equipment and costumes. This occurs when the cost is equal to the left side of the equation above.

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Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

\(y = -x^2 - 4x + 2\)

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

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

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)