Use the given probability value to determine whether the sample results could easily occur by​ chance, then form a conclusion. A study of the effect of seatbelt use in​ head-on passenger car collisions found that drivers using a seatbelt had a​ 64.1% survival​ rate, while drivers not using a seatbelt had a​ 41.5% survival rate. If seatbelts have no effect on survival​ rate, there is less than a 0.0001 chance of getting these results. What do you​ conclude?

Answer:

[tex](a)-\dfrac{11\sqrt{5}}{25} \\(b) -\dfrac{2\sqrt{5}}{25} \\(c)\dfrac{11}{2}[/tex]

Step-by-step explanation:

[tex]\tan \alpha =\dfrac12, \pi < \alpha< \dfrac{3 \pi}{2}[/tex]

Therefore:

[tex]\alpha$ is in Quadrant III[/tex]

Opposite = -1

Adjacent =-2

Using Pythagoras Theorem

[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\=(-1)^2+(-2)^2=5\\Hypotenuse=\sqrt{5}[/tex]

Therefore:

[tex]\sin \alpha =-\dfrac{1}{\sqrt{5}}\\\cos \alpha =-\dfrac{2}{\sqrt{5}}[/tex]

Similarly

[tex]\cos \beta =\dfrac35, \dfrac{3 \pi}{2}<\beta<2\pi\\\beta $ is in Quadrant IV (x is negative, y is positive), therefore:\\Adjacent=$-3\\$Hypotenuse=5\\Opposite=4 (Using Pythagoras Theorem)[/tex]

[tex]\sin \beta =\dfrac{4}{5}\\\tan \beta =-\dfrac{4}{3}[/tex]

(a)

[tex]\cos(\alpha + \beta)=\cos\alpha\cos\beta-\sin \alpha\sin \beta\\[/tex]

[tex]=-\dfrac{2}{\sqrt{5}}\cdot \dfrac{3}{5}-(-\dfrac{1}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{2\sqrt{5}}{5}\cdot \dfrac{3}{5}+\dfrac{\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{2\sqrt{5}}{25}[/tex]

(b)

[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta[/tex]

[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta\\=-\dfrac{1}{\sqrt{5}}\cdot\dfrac35+(-\dfrac{2}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{\sqrt{5}}{5}\cdot\dfrac35-\dfrac{2\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{11\sqrt{5}}{25}[/tex]

(c)

[tex]\tan(\alpha + \beta)=\dfrac{\sin(\alpha + \beta)}{\sin(\alpha + \beta)}=-\dfrac{11\sqrt{5}}{25} \div -\dfrac{2\sqrt{5}}{25} =\dfrac{11}{2}[/tex]

Answer:

-7/2

Step-by-step explanation:

To find the y coordinate of the midpoint and the y coordinates together and divide by 2

(2+-9)/2

-7/2

Answer:

2 goes in green box

Step-by-step explanation:

(9,2) (-7,-9)

(x1, y1) (x2,y2)

Midpoint is (x1+x2)/2 , (y1+y2)/2

(9-7)/2= 1

(2-9)/2 = -7/2

Answer:

a = 30

b = 6/7

Step-by-step explanation:

The number of yeast cells after t hours is modeled by the following equation:

[tex]f(t) = a(1 + be^{-0.7t})[/tex]

In which a is the initial number of cells.

At time t = 0 the population is 30 cells

This means that [tex]a = 30[/tex]

So

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

And increasing at a rate of 18 cells/hour.

This means that f'(0) = 18.

We use this to find b.

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

So

[tex]f(t) = 30 + 30be^{-0.7t}[/tex]

Then, it's derivative is:

[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]

We have that:

f'(0) = 18

So

[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]

Then

[tex]-21b = 18[/tex]

[tex]21b = -18[/tex]

[tex]b = -\frac{18}{21}[/tex]

[tex]b = \frac{6}{7}[/tex]

Answer:

Number = 34

Step-by-step explanation:

We are looking for our mystery "number". I will call this number N.

We can find out what our equation looks like based on what the question tells us.

"three times a number" is 3N

"added to 2" is + 2

Which so far is 3N + 2

"divided by the number plus 5" is ÷ [tex]{N+5}[/tex]

Combined with the first two parts to give us (3N + 2) ÷ (N + 5)

"the result is eight third" So the above equation is equal to 8/3

Combining all these comments together to get the following equation

(3N + 2) ÷ (N + 5) = 8/3

Rearrange by multiplying both sides of the = by (N+5)

3N + 2 ÷ (N + 5) × (N + 5) = 8/3 × (N + 5)

Simplify

3N + 2 = 8/3 × (N + 5)

3N + 2 = 8N/3 + 40/3

Bring the N numbers to one side and the non N numbers to the other side, by subtracting 2 from both sides of the =

3N + 2 - 2 = 8N/3 + 40/3 - 2

Simplify

3N = 8N/3 + 34/3

and then subtracting 8N/3 from both sides

3N - 8N/3 = 8N/3 - 8N/3 + 34/3

Simplify

1N/3 = 34/3

Simplify for our final answer by multiplying both sides of the = by 3

1N/3 x 3 = 34/3 x 3

N = 34

Many of these steps can be skipped when solving for yourself but I wanted to be thorough

The graph of the compound inequality can be seen at the end.

Here we have two inequalities that depend on p, these are:

4p + 1 > -15

6p + 3 < 45

First, we need to isolate p on both inequalities.

4p + 1 > -15

4p > -15 - 1

p > -16/4

p > - 4

6p + 3 < 45

6p < 45 - 3 = 42

p < 42/6 = 7

So we have the compound inequality:

p > -4

p < 7

or:

-4 < p < 7

Then this represents the set (-4, 7) where the values -4 and 7 are not included, so we should graph them with open circles.

The graph of the inequality is something like the one below.

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Answer:

The 1st graph

Step-by-step explanation:

The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.

Answer:

D.

Step-by-step explanation:

Deus ex machina is the plot device of using something very improbable to resolve a situation.

Answer:

A personality test may be given to assess individual behavior patterns. A personality test may be given to assess individual behavior patterns. This answer has been confirmed as correct and helpful.

Step-by-step explanation:

hopes this helps

Answer:

Interests, values, skill set and basic personality

Step-by-step explanation:

Personality tests are mostly used as an assessment tool be HR managers and employers during the interview process. They can provide a potential employer with information about your interests, values, skill set and even basic personality, which can be very useful to help an employer make a decision about whether you are the best fit for a position.

I hope this helped. I am sorry if you get this wrong.

Answer: 15 dogs

Step-by-step explanation:

75 / 5 = 15

Answer:

15 dogs

Step-by-step explanation:

Let the number of dogs be x

number of cats be y

5 times the number of cats = number of dogs

y = x*5

Since y = 75

75 = 5x

Bring 5 to the other side n divide

x= 75/5

= 15

Answer:

45,000 codes

Step-by-step explanation:

Given:

Code of 5 digits

Condition

Required

Calculate the number of codes available

Digits = {0,1,2....9}

n(Digits) = 10

Let the format of the code be represented as follows;

ABCDE

From the conditions given

A can't be 1;

This means that A can be any of 0,2,3,4....9

This implies that A can be any of the above 9 digits

n(A) = 9

There's no condition attached to BCD;

This means that B can be any of 10 digits

This means that C can be any of 10 digits

This means that D can be any of 10 digits

n(B) = n(C) = n(D) = 10

Lastly, E must be an even number;

This means that E can be any of 0,2,4,6,8

This implies that E can be any of the above 5 digits

n(E) = 5

So,

Number of available codes = n(A) * n(B) * n(C) * n(D) * n(E)

Number of available codes = 9 * 10 * 10 * 10 *5

Number of available codes = 45,000

Hence, there are 45,000 available codes

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].

Answer:

1/12

Step-by-step explanation:

Start with a number, for example 100.

Now divide 100 by several numbers which are greater and greater:

100/1 = 100

100/2 = 50

100/4 = 25

100/10 = 10

100/100 = 1

As you divide the same number, 100, by a greater number, the result becomes smaller.

As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.

Numbers in order from greatest to smallest:

1/12, 1/18, 1/32, 1/48

Answer: The greatest number is 1/12

Answer:

In the case of a Type I error, the null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.

They will start to pay for the software when in fact it does not improve Algebra 1 skills.

Step-by-step explanation:

A Type I error happens when a true null hypothesis is rejected.

The probability of a Type I error is equal to the significance level, as it is the probabilty of getting an sample result with low probability but only due to chance, as the null hypothesis is in fact true.

In this scenario, the null hypothesis would represent the claim that the new technology does not make significant improvement.

In the case of a Type I error, this null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.

They will start to pay for the software when in fact it does not improve Algebra 1 skills.

Answer:

[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.6)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X >1)[/tex]

And for this case we can use the complement rule and we got:

[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Answer:

  $106.67

Step-by-step explanation:

Using the example, for 3 hours work, Alex would be paid ...

  (2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80

At the same rate of pay, for 4 hours work, the pay would be ...

  pay/(4 hr) = $80/(3 hr)

  pay = $80(4/3) ≈ $106.67

Alex's pay for 4 hours of work is $106.67.

Answer: the answer is c (the third answer ) ‼️

Step-by-step explanation:

The data in the given residual plot shows that model C has the best fit.

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

Given:

The residual plot of the values in the graph,

The points in the first graph are very far from the x-axis and y-axis so, it is not the best fit,

The points in the second graph are very far from the x-axis and y-axis, and they are symmetric to the y-axis but not the best fit.

Most of the points are close to the x-axis, so it is the best fit,

Thus, the third graph is the best line of fit.

To know more about the line of fits:

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Answer:

(a)650 ways

(b)650 ways

(c)676 ways

Step-by-step explanation:

There are 26 red and 26 black cards.

If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.

(a)Both cards are red

If both cards are red:

The first red card can be dealt in 26 ways.

The second red card can be dealt in 25 ways.

Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways

(b)Both cards are black

If both cards are black:

The first black card can be dealt in 26 ways.

The second black card can be dealt in 25 ways.

Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways

(c)One card is black and the other is red.

The red card can be dealt in 26 ways.

The black card can be dealt in 26 ways.

Therefore: Both cards can be dealt in: 26 X 26 = 676 ways

Answer:

The correct answer is:

r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.

This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).

Answer:

$9.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

by definition the absolute value is always positive

so |4x-9| >= 0

so the equation |4x-9| > -12 is always true

so all real numbers are solution of this equation

hope this helps

Answer:

17.5

Step-by-step explanation:

Remember PEMDAS

step 1 : divide 7 by 2

7 ÷ 2 = 3.5

step 2 : rewrite the equation

19 + 3.5 - 5

step 3  : add 19 + 3.5

19 + 3.5 = 22.5

step 4 : subtract 22.5 - 5

22.5 - 5 = 17.5

Answer:

csc 270° is the answer.

Answer:

[tex]\boxed{\sf \ \ \ x = -8 \ or \ x = -4 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]4x^2+48x+128=0\\<=> 4(x^2+12x+32)=0\\<=> x^2+12x+32=0\\<=> (x+6)^2 - 36 + 32= 0\\\\<=> (x+6)^2-4=0\\<=> (x+6+2)(x+6-2)=0\\<=> (x+8)(x+4) = 0\\<=> x = -8 \ or \ x = -4[/tex]

vouch, i confirm that -8, -4 are the answers

Answer:

40.5 ft

162 ft

16 in

7.2 in

13.9 ft

Step-by-step explanation:

1) V=√32d

d= ?

V=36 ⇒ 36²= 32d  ⇒ d= 1296/32=40.5 feet

2) S= 5.5√d

S= 70 mph, d=?

70²= 5.5²d ⇒ d= 4900/ 30.25≈ 162 feet

3) d= 0.25√h

d= 1 mile, h=?

1²= 0.25²h ⇒ h= 1/0.0625= 16 in

4) a= 4, b= 6, c=?

c²= a²+b² ⇒ c= √a²+b²= √4²+6² = √52≈ 7.2 in

5) c= 16 foot, b= 8 feet, a=?

c²= a²+b² ⇒ a= √c² - b²= √16²-8²= √256- 64= √192≈13.9 feet

Answer:

[tex] \frac{4 {x }^{2} - 17x - 9 }{ {x}^{3} - 7 {x}^{2} + 7x + 15 } [/tex]

Step-by-step explanation:

In the picture.

I hope I am correct

I hope it helps :)

Answer:

2 is the coefficient

Step-by-step explanation:

2 is the coefficient bc a coefficient is the number next to a variable (such as x)  and 2 is next to x and is the only one in the equation

Answer:

-2

Step-by-step explanation:

Answer:

[tex]\hat p =\frac{X}{n}[/tex]

And replacing we got:

[tex]\hat p =\frac{132}{146}= 0.904[/tex]

And for this case the standard error assuming normality would be given by:

[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

And replacing we got:

[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]

Step-by-step explanation:

For this problem we know the following notation:

[tex] n= 146 [/tex] represent the sample size selected

[tex] X= 132[/tex] represent the number of airplane travelers who after a flight  would fly that airline again

The estimated proportion for this case would be:

[tex]\hat p =\frac{X}{n}[/tex]

And replacing we got:

[tex]\hat p =\frac{132}{146}= 0.904[/tex]

And for this case the standard error assuming normality would be given by:

[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

And replacing we got:

[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]

Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

Step-by-step explanation:

step 1

Find the dimension of the book's garden

we know that

Book scale: 1 inch = 2 feet

That means

1 inch in the drawing represent 2 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 2

so

Length A of the book’s garden

Width B of the book’s garden

step 2

Find the dimension of Rasheeda’s garden

we know that

Rasheeda's Scale: 2 inch = 3 feet

That means

2 inch inches the drawing represent 3 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2

so

Length A of Rasheeda's garden

Width B of Rasheeda's garden

Verify each statement

A. Length A of the book’s garden is 18 ft.

The statement is false

Because, Length A of the book’s garden is 36 ft (see the explanation)

B. Length A of Rasheeda’s garden is 27 ft.

The statement is true (see the explanation)

C. Length B of the book’s garden is 12 ft

The statement is true (see the explanation)

D. Length B of Rasheeda’s garden is 6 ft.

The statement is false

Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

The statement is true

Because the difference between 36 ft and 27 ft is equal to 9 ft

F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

The statement is false

Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.

taffy927x2 and 22 more users found this answer helpful

Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

(second, third, and fifth choices)

Explanation: I did the quiz and got it right.

Hope this Helps!

Answer:

Y = 1, E = -1, A= 1, R = -1

Step-by-step explanation:

YYYY - EEE + AA - R = 1234

First we would break down the digits in the whole numbers into their place value (thousands, hundreds, tens and units).

YYYY = 1000Y + 100Y +10Y + Y

EEE = 100E + 10E + E

-EEE = -100E - 10E - E

AA = 10A + A

R = R

-R = -R

1234 = 1000+200+30+4

Let's equate each place value for each of the numbers.

Thousands: 1000Y = 1000

Y = 1000/1000 = 1

Hundreds: 100Y - 100E = 200

100(1) - 100E = 200

-100E = 200-100

-100E= 100

E = -1

-EEE = -E(111)

Tens: 10Y - 10E + 10A = 30

10(1) - 10(-1) + 10A = 30

20+ 10A = 30

A = 10/10

A= 1

Units: Y - E + A - R = 4

1 - (-1) + 1 - R = 4

3-R = 4

R = 3-4 = -1

YYYY - EEE + AA - R = 1234

1111 - (-111) + 11 - (-1) = 1111+111+11+1 = 1234

All possible values of the digits Y, E, A, R are Y = 1, E = -1, A= 1, R = -1

Answer:

Y=2

E=9

A=1

R=0

Step-by-step explanation:

Let's check our work.

2,222 - 999 + 11 - 0

1,223 + 11 - 0

1,234 - 0

1,234

Also previous answerer how can digits be negative?

Answer:

None

Step-by-step explanation:

The answers are:

1. g(10) -31

2. x= -17/3

3. f(3)= 2

4.x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = x² – 7

g(x) = -3x - 1

j(x)= 2x-9

h(x) = 1

1. g(10)= -3(10) -1 = -30 - 1= -31

2. g(x) = 16

-3x- 1= 16

-3x = 17

x= -17/3

3. f(3)= (3)² – 7 = 9- 7= 2

4. f(x)= 23

x² – 7=  23

x² = 30

x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

8. S(-1) = 3

The value of function s(a) at a=-1 is 3.

10. g(4) = -1

The value of function g(a) at a=4 is -1.

11. h(2) = 8

The value of function h(a) at a=2 is 8.

12. k(2) = 9​

The value of function k(a) at a= 2 is 9.

Learn more about function here:

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Answer:

24

Step-by-step explanation:

Use the Pythagorean theorem.

Where the sum of the two legs squared is equal to the hypotenuse squared.

10² + x² = 26²

100 + x² = 676

x² = 576

x = √576

x = 24

The value of x is 24.

Answer:

15 is the answer to the question

Answer:

15, which for some reason does not seem to be an option.

Step-by-step explanation:

Product means to multiply to numbers, items etc.

5 times 3, as you should know, is 15.

Hope this helps.