Solve for x in the equation x 2 - 4 x - 9 = 29.

Answer:

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622

The margin of error is:

M = T*s = 2.2622*0.3 = 0.68

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF

The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

Answer:

Step-by-step explanation:

Answer:

B) (0,2)

Step-by-step explanation:

2 ≥ 2(0)-1

2 ≥ 0-1

2 ≥ -1

Answer:

expected profit = $-1.48

Step-by-step explanation:

The required expected value can be solved below.

The total number of ticket they will sell = 500 tickets.

So,

expected profit = expected return - expected cost

1 grand price of 2000 = 1/500 × 2000 = 4

4 second price of $400 = 4/500 × 400 = 3.2

16 third price of $10 = 16/500 × 10 = 0.32

expected return = 4 + 3.2 + 0.32 = $7.52

expected cost = $9

expected profit = expected return - expected cost

expected profit = 7.52 - 9

expected profit = $-1.48

Answer:

a = 13

b = 0

Step-by-step explanation:

Conjugate of -3 + 2i is -3 - 2i

(-3 + 2i) (-3 - 2i)

We need to expand:

9 + 6i + -6i + -4i^2

-4i^2 =(-4)(-1) = 4

9 + 4 = 13

a = 13

b = 0

Answer:

89 degrees

Step-by-step explanation:

The angle 1 is the same as angle 3.

Angle 2 is the same as angle 4.

The sum of these four angles is 360 degrees.

We have that:

Angle 2 = Angle 4 = 7x - 14

Angle 3 = Angle 1 = 5x + 14

Finding x:

Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360

2*(5x + 14) + 2*(7x - 14) = 360

10x + 28 + 14x - 28 = 360

24x = 360

x = 15

Angle 1:

5x + 14 = 5*15 + 14 = 89 degrees

Answer:

I think it is B

Step-by-step explanation:

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

Answer:

The trip will take 36 minutes.

Step-by-step explanation:

This question can be solved using a rule of three.

The boat maintains a constant speed of 15 knots (nautical miles per hour). How many minutes it will take to return to its home port 9 nautical miles away?

So in 60 minutes, 15 nautical miles. How many minutes for 9 nautical miles?

60 minutes - 15 nautical miles

x minutes - 9 nautical miles

[tex]15x = 60*9[/tex]

[tex]x = \frac{60*9}{15}[/tex]

[tex]x = 36[/tex]

The trip will take 36 minutes.

Answer:

The event of picking a number from 1 to 3 consists of:

Pick number 1

Pick number 2

Pick number 3

The event of choosing red or white card consists of:

Choose a red card

Choose a white card

=> The sample space for picking a number from 1 to 3 and choosing red or white card:

Pick number 1 and choose a red card

Pick number 1 and choose a white card

Pick number 2 and choose a red card

Pick number 2 and choose a white card

Pick number 3 and choose a red card

Pick number 3 and choose a white card

Hope this helps!

:)

Answer:

AC = 198

Step-by-step explanation:

Since all these points are collinear, we know that the addition of AB plus BC should give the same as AC. We can then set an equation that addresses this identity:

AB + BC = AC

5x +8 +6x - 1 = 12x - 11

Now re-arranging like terms in order to combine them:

8 - 1 + 11 = 12x - 5x - 6x

19 - 1  = 12x - 11x

18 = x

Now that we know the value of 'x", we can determine the value of AC:

AC = 12x - 11

AC = 12 (18) - 11

AC = 216 - 18

AC = 198

Answer:

4

Step-by-step explanation:

A=P0(1+rt).

We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:

A=P0(1+rt)⟹t=A−P0P0r,

and substituting the known quantities gives

r=$3,500−$2,800$2,800×0.075=3.33,

which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.

The answer to your problem is: X=17

Answer:

17

Step-by-step explanation:

x + 10 + 9x=14x-58

x + 9x + 10 =14x-58

10x + 10 =14x-58

By grouping like terms by moving 14x to the left and 10 to the right of the equation; we have:

10x - 14x =-58-10

-4x=-68

x=-68/-4=17{ dividing both sides by -4}

Answer:

2044

Step-by-step explanation:

just follow the story

a person uses a

hanger (2)

to pop a

ball  (0)

then flies

two kites (44)

Answer:

1). 2044

Step-by-step explanation:

The story includes: a hanger, a ball, and two kites (in that order)

From the information given, a hanger is 2, a ball is 0, and a kite is 4.

So it would be 2044.

Answer:

Jaleel is correct because 2 (x + 2) = 2x - 4

Step-by-step explanation:

To solve 2 (x - 2) + 2:

2 (x - 2) + 2

Distribute

2x - 4 + 2

Combine like terms

2x - 2

Lisa did not distribute correctly :)

Answer:

D

Step-by-step explanation:

Answer:

Plot the y-intercept at (0, 2). Plot your second point at (-1, -1).

Step-by-step explanation:

I attached an image of what the finished graph should look like when you press done. *rotate the image so the grey is on the bottom*

Answer:

difference in area = 16 ft²

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Step-by-step explanation:

Jacks rectangular patio

width = a

length = 2a - 1

area = lw

where

l = length

w = width

area = 120 ft²

a(2a - 1)

2a² - a - 120 = 0

(a - 8) (2a + 15)

a = 8 or -15/2

Ron's rectangular patio

width = a

length = a + 5

area = lw

area = 104 ft²

a (a + 5) = 104

a² + 5a -104 = 0

(a + 8)  (a - 13)

a = -8 or 13

How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,

120 - 104 = 16 ft²

The value 8 or 13 can be used for a since the width a have to be the same.

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Answer:

[tex]A = \dfrac{40}{P}[/tex]

Step-by-step explanation:

Pressure [tex]p(in lbs/in^2)[/tex]  varies inversely with the area [tex]A(in$ in^2)[/tex] of the sole of the shoe.

This is written as:

[tex]P \propto \frac{1}{A}\\ $Introducing the constant of variation$\\P = \dfrac{k}{A}[/tex]

When:

[tex]When: A= 40 in^2, P =4 lbs/in^2\\$Substituting into the equation\\P = \dfrac{k}{A}\\4 = \dfrac{k}{40}\\$Cross multiply\\k=4*40\\k=160\\Therefore, the equation that connect these variables is given as:\\P = \dfrac{40}{A}\\$In terms of P\\AP=40\\\\A = \dfrac{40}{P}[/tex]

Answer:

y = 3x +1 (1)

2y = 6x +2  (2)

We can devide equation (2) by 2 and we got:

[tex] y =3x +1[/tex]   (3)

And since equations (1) and (3) are equal we can do this:

[tex] 3x +1 = 3x+1[/tex]

And that implies:

[tex] 0=0[/tex]

And for this case we will have infinite solutions for the sytem given since we have two lines equal

Step-by-step explanation:

For this case we have the following system of equations given:

y = 3x +1 (1)

2y = 6x +2  (2)

We can devide equation (2) by 2 and we got:

[tex] y =3x +1[/tex]   (3)

And since equations (1) and (3) are equal we can do this:

[tex] 3x +1 = 3x+1[/tex]

And that implies:

[tex] 0=0[/tex]

And for this case we will have infinite solutions for the sytem given since we have two lines equal

Answer:

x=2           x =8

Step-by-step explanation:

(x-2)(x-8)=0

Using the zero product property

x-2 = 0    x-8 = 0

x=2           x =8

Answer:x = 2 and x = 8

Step-by-step explanation:

( 2 - 2)( 8 - 8)

(0)(0)

=0

Answer:

1,085

Step-by-step explanation:

The calculation of  number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-

[tex]= N\times (2 \times documentaries\ and\ 1\ horror \ movies)+N\times (3\ documentaries)[/tex]

[tex]=(6C_1)\times (15C_2)+(6C_0)\times (15C_3)[/tex]

= 630 + 455

= 1,085

Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.

Answer:

She will make 125 dollars

Step-by-step explanation:

First figure out how many hours are in between 8 AM and 6PM

Second multiply that number by the salary she makes per hour. In this case its 12.50*10

Lastly Get the answer and add a dollar sign :D

Answer:

A. Observational study

Step-by-step explanation:

In research, an observational study is a type of study in which the researcher observes a phenomenon and tries to establish some relationship between the different variables he/she is observing. In other words, the researcher only observes and doesn't give a treatment.

On the other hand, when we have a experiment, we usually have 2 different groups (one that will receive a treatment and one who won't) and the researcher compares the differences between these two groups because of the treatment. In other words, the researcher does something other than just observing.

In this example, the research is going to determine if there is a relation between hearing loss and exposure to mumps. In this example the researcher is only going to observe how people who have been exposed to mumps are regarding hearing loss (we can say this since it will be unethical for example for the researcher to create an experiment in which he/she exposes a group to mumps). Therefore, he is going to observe how the past exposure to mumps could be related with the hearing loss.

Thus, this is an observational study.

Answer:

21 and 10.5 respectively

Step-by-step explanation:

Remember circumference of a circle is given as;

C= 2×π×r; r is raduis

r = C / 2×π

=65.98/(2×3.142)= 10.50

D= 2× r = 2× 10.50= 21.0( D represent diameter)

Note π = 3.142 a known constant

Answer:

False.

The null hypothesis failed to be rejected.

At a significance level of 5%, there is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the entering class has a mean SAT score that is significantly lower than 1520.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1520\\\\H_a:\mu< 1520[/tex]

The significance level is 0.05.

The sample has a size n=20.

The sample mean is M=1501.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=53.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{53}{\sqrt{20}}=11.851[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1501-1520}{11.851}=\dfrac{-19}{11.851}=-1.6[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=20-1=19[/tex]

This test is a left-tailed test, with 19 degrees of freedom and t=-1.6, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.6)=0.063[/tex]

As the P-value (0.063) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.

1 × 18/100 = 12/100(g+11), is the equation. The answer is 12/100 gallons

Answer:2

Step-by-step explanation: 9+1+2=12

12\3=4

ANSWER : 2

Answer:

give $20 to each person

Step-by-step explanation:

Answer:

I think l

Step-by-step explanation:

first add 96 and4 then 2 I think