If ST≅SV and m∠SUT=w+10° and m

Answer:

at 95% confidence interval,  the mean amount of sleep per night is ( 7.87, 8.05 ).

Option b) (7.87, 8.05) is the correct answer.

Step-by-step explanation:

Given the data in the question;

sample size n = 1140

sample mean x" = 7.96

standard deviation σ = 1.6

At 95% confidence interval,

significance level ∝ = 1 - 95% = 1 - 0.95 = 0.05

∝/2 = 0.05 / 2 = 0.025

Z-Critical [tex]Z_{\alpha /2[/tex] = [tex]Z_{0.025[/tex] = 1.96

Top get the Margin of error E;

E = [tex]Z_{\alpha /2[/tex] × ( σ /√n )

we substitute

E = 1.96 × ( 1.6 /√1140 )

E = 0.09

So, At 95% confidence interval of the population mean is;

⇒ x" ± E

⇒ x" - E or x" + E

we substitute

⇒ 7.96 - 0.09, 7.96 + 0.09

⇒ 7.87, 8.05

Therefore, at 95% confidence interval,  the mean amount of sleep per night is ( 7.87, 8.05 ).

Option b) (7.87, 8.05) is the correct answer.

Answer:

Smallest Number = 35

Other Number  = 42

Step-by-step explanation:

Let the smaller number be x.

Let the other number be y.

Given:

x : y = 5 : 6

That is,

          [tex]\frac{x}{y} = \frac{5}{6}[/tex]

             [tex]=> 5y = 6x\\\\=>x = \frac{5y}{6}[/tex]

Next: Let the smaller number be reduced by 5, x - 5

        Let the other number be increased by 3, y + 3

Given : (x - 5) : (y + 3) = 2 : 3

That is,

        [tex]\frac{x-5}{y+3} = \frac{2}{3}\\[/tex]

[tex](x-5) \times 3 = (y+3)\times 2\\\\substitute \ x = \frac{5y}{6}\\\\3(\frac{5y}{6} -5) = 2y + 6\\\\\frac{5y}{2} - 15 = 2y + 6\\\\\frac{5y}{2} - 2y = 6 + 15\\\\\frac{5y-4y}{2} = 21\\\\y = 21 \times 2 = 42\\\\Substitute \ y \ in \ x = \frac{5y}{6} \\\\x = \frac{5 \times 42}{6} = 35[/tex]

Answer:

xy

Step-by-step explanation:

xy³ and x³y

GCF is xy

Answer:

I think it's xy

Step-by-step explanation:

just find the prime factors of each term

Answer:

282.74

Step-by-step explanation:

Answer:

$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.

Step-by-step explanation:

95% confidence interval: $72 to $198.

This means that we are 95% sure that the true mean spending is between $72 and $198.

From this confidence interval the assistant concluded that people spend an average of $200 a month on entertainment. Is this a reasonable conclusion and why?

$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.

Answer:

You need variability

Step-by-step explanation:

Variability measures the degree to which the scores are spread out or clustered together in a distribution.

Hope this helps:)

Answer:

77.14 minutes.

Step-by-step explanation:

Jack's time = 3 hours

Jill's time = 2.25 hours = 2 1/4 = 9/4 hours

Combined time = x

Rates :

Jack = 1/3 ; jill = 1 / 2.25 = 1 / 9/4 = 4 /9

Combined rate = 1/x

Setting up the equation :

1/3 + 4/9 = 1/x

Lcm of 3 and 9 = 9

(3 + 4) / 9 = 1/x

7/9 = 1/x

Cross multiply :

7x = 9

x = 9/7 hours

x = (9/7)* 60

x = 77.14 minutes

Combined time = 77.14 minutes.

Answer:

Step-by-step explanation:

½X+7

Answer:

 64degrees

Step-by-step explanation:

Give the following

Height of tree H = 36feet

length of the shadow L = 40feeet

Requires

Angle of eleation

Using the SOH CAH TOA identity

Sin theta = opposite/hypotenuse

Sin theta = H/L

Sin theta = 36/40

SIn theta = 0.9

theta  = arcsin0.9

theta = 64.16

Hence the required angle is  64degrees

Answer:

A. 339.12 cu. in.

Step-by-step explanation:

I calculated it logically

Answer:

All of them except a trapezoid

Step-by-step explanation:

The playground has two pairs of sides that are congruent to each other (70 = 70, 50 = 50), but a trapezoid only has ONE pair of sides that are congruent to each other; the other two are not the same. Therefore, this playground can be any shape besides a trapezoid.

Answer:

It's true because 5-3/2 is grater than 1/3

Answer:

8/9 (simplified)

Step-by-step explanation:

Total marbles = 18

Total of marbles not white = 16

Numerator = 16 / Denominator = 18

= 16/18

= 8/9 (simplified)

Total number of marble=18

probability of getting white marble = 2/18 =1/9

Now,

probability of not getting white marble = 1 - 1/9 = 8 / 9

y=-x

J(-4,3)

K(3,-4)

L(1,1)

Answer:

[tex]\text{a) }1,080^{\circ}, \\\text{b) }360^{\circ}, \\\text{c) }135^{\circ}, \\\text{d) }45^{\circ}[/tex]

Step-by-step explanation:

a) The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, substitute in [tex]n=8[/tex]:

[tex](6-2)180=\boxed{1,080^{\circ}}[/tex]

b) The sum of the exterior angles for any polygon is equal to [tex]360^{\circ}[/tex].

c) By definition, all regular shapes have equal angles and sides. Since we've found the total sum of the interior angles of an octagon in part a, each interior angle of a regular octagon must be [tex]\frac{1080}{8}=\boxed{135^{\circ}}[/tex]

d) Similar to part c, all regular shapes must have equal angles and sides. From part b, we know the sum of the exterior angles of a octagon is [tex]360^{\circ}[/tex], thus we have [tex]\frac{360}{8}=\boxed{45^{\circ}}[/tex]

Answer:

160000m³

Step-by-step explanation:

Volume of a rectangular prism= A x h

V= l x b x h

V= 80x 50 x 40

V= 160000m³

Answer:

Step-by-step explanation:

slope=y2-y1/x2-x1

here x1=2 , y1=-4 , x2=-6 , y2=1

=1-(-4)/2-(-6)

=1+4/2+6

=5/8

-5/8  fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

the slope formula for the line containing (2, -4) and (-6, 1) we calculate by plugging the values to the slope formula.

m=1-(-4)/-6-2

m=1+4/-8

m=-5/8

Hence, -5/8  fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ2

Step-by-step explanation:

you could count the squares around the shape or you could do it by points

For example point M is (2,3)

L is (6,3)

We want to find the length of this side so we subtract the x values

6 - 2 = 4 units

that gives use the length of that leg and since a rectangle is symmetrical, you can just measure 2 sides

Answer:

[tex]0.156[/tex]

Step-by-step explanation:

[tex]15.6 \div 100[/tex]

[tex]0.156[/tex]

Answer:

with what?

Step-by-step explanation:

Answer:

a) 4,913

b) 10

Step-by-step explanation:

a) [2(3 + 4) + 3]³

= [2(7) + 3]³

= (14 + 3)³

= 17³

= 4913

b) 5 + (3² - 2²)

= 5 + (9 - 4)

= 5 + 5

= 10

Answer: 1560 = 30(52) + b

Step-by-step explanation:

Based on the information given in the question, the straight line passes through two points which are (40, 1200) and (52, 1560). Then, the equation if the straight line will be:

y - 1560 = (1200 - 1560)/(40 - 52) (x - 52)

y - 1560 = (-360)/(-12) (x - 52)

y - 1560 = 30(x - 52)

Lets put the value of x to be 0.

y - 1560 = 30(x - 52)

y - 1560 = 30(0 - 52)

y - 1560 = -30(52)

Therefore, 1560 = 30(52) + b

Answer:

It's the hexagon and pentagon.

Answer:

A. 140 feet

Step-by-step explanation:

I calculated it logically

Answer:

skateworld

Step-by-step explanation:

26x3+50=128 aka skate worlds price

26x5=130 aka roller land price

Antionio should use skateworld and he would save 2$

Answer: SkateWorld. He saves $2

Step-by-step explanation:

SkateWorld:

21 *3 =63

5*3=15

63+15=78

78+50= 128

Roller Land:

21*5= 105

5*5=25

105+25=130

130-128= 2

0°

In each figure below find m∠1 and m∠2, if a||b. Show your work with statements.

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Have a nice and great day!

#PilipinasAngBayanKo

0°

Sana Maka help ako tnx

Answer:

A. 2468 sq. ft.

Step-by-step explanation:

I calculated it logically