Solve the equation. Express radicals in simplest form.
-4k2 - 13 = -77

Answer:

≈ 11.78 in

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{\frac{\pi }{4} }{2\pi }[/tex] ( cancel 2π on numerator/ denominator )

     = 15 × [tex]\frac{\pi }{4}[/tex]

     = [tex]\frac{15\pi }{4}[/tex]

     ≈ 11.78 in ( to 2 dec. places )

Using the t-distribution, it is found that since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

At the null hypothesis, it is tested if the average box of cereal does not contain more than 368 grams, that is:

[tex]H_0: \mu \leq 368[/tex]

At the alternative hypothesis, it is tested if it contains, that is:

[tex]H_1: \mu > 368[/tex]

We have the standard deviation for the sample, hence, the t-distribution is used to solve this question.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

In this problem, the values of the parameters are: [tex]\overline{x} = 372.5, \mu = 368, s = 15, n = 25[/tex].

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{372.5 - 368}{\frac{15}{\sqrt{25}}}[/tex]

[tex]t = 1.5[/tex]

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, with 25 -1 = 24 df, is of [tex]t^{\ast} = 1.71[/tex].

Since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630

Answer:

Merry Christmas too!!

Step-by-step explanation:

Stay safe lovelots

#LEARN WITH BRAINLY

Answer:

  71.6°

Step-by-step explanation:

The angle can be found from the dot product of PQ and PR.

  PQ·PR = |PQ|×|PR|×cos(α)

where α is the angle between the two segments.

  cos(α) = (Q -P)·(R -P)/(|Q -P|×|R -P|)

  = ((0, 1, 0) -(1, 0, 0))·((0, 0, 2) -(1, 0, 0))/(|Q -P|×|R -P|)

  = (-1, 1, 0)·(-1, 0, 2)/(√(((-1)² +1²)((-1²) +2²)) = (1+0+0)/√10

  α = arccos(1/√10) ≈ 71.6°

The angle at P is about 71.6°.

_____

Additional comment

The side lengths of the triangle are √2, √5, √5. As we have seen, the angle at P is bounded by the sides of length √2 and √5. The law of cosines can also be used to arrive at the angle between these sides.

Answer:

129, because you split the shape into two find the area of them separately and then add them up

Answer:

C

Step-by-step explanation

It makes the most sense

Answer:

check online for more information

Answer:

5 weeks

Step-by-step explanation:

John deposits $5 per week and has $10, so his equation is 5x + 10.

Jasmine's equation is 3x + 20.

Make them equal to each other and solve for x:

5x + 10 = 3x + 20

Subtract 10 from each side

5x = 3x + 10

Subtract 3x from each side

2x = 10

Divide each side by 2

x = 5

Answer:

5 weeks

Step-by-step explanation:

John:$10,$15,$20,$25,$30,$35

Jasmine:$20,$23,$26,$29,$32,$35

5 weeks

Step-by-step explanation:

x = pounds birdseed

y = pounds sunflower seeds

x + y = 30

0.57x + 0.87y = 30×0.81

with this last trick (to calculate the full cost of the whole 30 pounds based on the targeted individual price per pound) we bring both constraints into the play.

from the first equation we get

x = 30 - y

and we use that in the second equation :

0.57×(30-y) + 0.87y = 30×0.81 = $24.30

17.1 - 0.57y + 0.87y = 24.3

0.3y = 7.2

y = 24

x = 30 - y = 30 - 24 = 6

she uses 6 pounds of birdseed and 24 pounds of sunflower seeds.

Answer:

What supplies?

Step-by-step explanation:

Answer:

r <= 12.6

Step-by-step explanation:

Let's calculate the rate at which he descends:

r = (46.7 - 15.2)/212 = 0.15 feet/minute

Answer:

1. given

2. inscribed circle theorem

3. substitution

4. definition of congruent angles

Answer:

no solutions exist

Step-by-step explanation:

We can solve this by using system of equations and using substitution.

2(8-3y)+6y=2      Substitute x=8-3y into the first equation.

16-6y+6y=2         Distribute.

16=2                     Simplify.

16 does not equal 2, so there are no solutions.

Answer:

using the pithagerum therom

a² + b² = c²

this formula is to find the side of your triangle with 2 sides already known

the answer is A) 17.7

Answer:

300

Step-by-step explanation:

[(-4 2/7) x (-18)] x (-3 8/9) x (-1)

= [-30/7 x -18] x -35/9 x -1

= 540/7 x -35/9 x -1

= -300 x -1

= 300

Answer:

check if the question I used is right or not

Answer:

rthrthrt

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Step-by-step explanation:

The Pythagorean theorem is:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the hypotenuse.

The two wires in the sketch are the hypotenuse so we just use the formula

let the wires=x

So:

[tex] {x}^{2} = {12}^{2} + {6}^{2} [/tex]

[tex] {x}^{2} = 144 + 36[/tex]

[tex] {x}^{2} = 180[/tex]

[tex]x = \sqrt{180} [/tex]

[tex]x = 13.42[/tex] feet

For the 20ft from doc. Set up triangle, with dr/dt on the hypotenuse = 2. 6 on the y, 20 on the x. Use x^2+ y^2= r^2. Differentiate and solve for dx/dt. 2x(dx/dt) + 2y(dy/dt)=2r(dr/dt); Since y value does not change, your y vector is equal to 0. Giving us 2x(dx/dt)=2r(dr/dt) ; dx/dt=(2r(dr/dt))/2x

Do the same thing for 10ft

No it is not surprising because as the angle between the dock and the boat decreases, more force is being used to pull up on the boat, not pull it inwards. Thus, the boats horizontal velocity will slow down as it beats the dock.

Answer:

(f-g)(x) is given by -x^2+4x+6

Step-by-step explanation:

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve ~

you can further simplify to get ~

Answer:

400

Step-by-step explanation:

10 movies * 5 drinks * 8 candy = 400 ways different ways to choose

Answer:

400

Step-by-step explanation:

Answer:

The answers can be seen in the photo

It will take 29 years to reach $725 to $2000 compounded twice in a month.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded twice each month is,

A = P(1 +(r/24)/100)²⁴ⁿ.

Given, A = 2000, P = 725, r = 3.5.

∴ 2000 = 725(1 + (3.5/24)/100)²⁴ⁿ.

(1 + (3.5/24)/100)²⁴ⁿ = 2.76.

(1.00146)²⁴ⁿ = 2.76.

24n = [tex]log_{1.00146}2.76[/tex].

24n = 695.87.

n = 29 years.

learn more about compound interest here :

https://brainly.com/question/14295570

#SPJ2

Answer:

5.12

Step-by-step explanation:

1 lb               .79 lbs

------------ =  -----------

6.49             x dollars

Using cross products

1x = 6.49 * .79

x =5.12 dollars

Step-by-step explanation:

100% - 25% off = 75%

Here, 75% of the initial price X, is the sale price of jeans during the season which is $60.

75/100 × X = $60

75X/100 =$60

( cross multiply)

75X=100×60

75X= 6000

X=6000÷75

X= $80