If a team of minors drill a hole 50.4 m into a rock formation and drill at a steady rate of 2.8 m/min. how long does it take to drill the hole

Answer:

The 90% confidence interval for the difference in the mean common final exam scores between students in the two types of sections is about (-5.3, 0.3).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

35 students from large sections. The mean and sample standard deviation of grades on the common final exam for the students from large sections were 72.8 and 7.4;

This means that:

[tex]\mu_L = 72.8, s_L = \frac{7.4}{\sqrt{35}} = 1.25[/tex]

35 students from small sections. For the students from small sections, the mean and standard deviation were 75.3 and 6.8.

This means that:

[tex]\mu_S = 75.3, s_S = \frac{6.8}{\sqrt{35}} = 1.15[/tex]

Distribution of the difference in the mean common final exam scores between students in the two types of sections:

Has mean and standard error given by:

[tex]\mu = \mu_L - \mu_S = 72.8 - 75.3 = -2.5[/tex]

[tex]s = \sqrt{s_L^2+s_S^2} = \sqrt{1.25^2 + 1.15^2} = 1.7[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs = 1.645*1.7 = 2.8[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -2.5 - 2.8 = -5.3

The upper end of the interval is the sample mean added to M. So it is -2.5 + 2.8 = 0.3

The 90% confidence interval for the difference in the mean common final exam scores between students in the two types of sections is about (-5.3, 0.3).

Answer:

Step-by-step explanation:

Exponential function representing final amount with compound interest compounded continuously,

[tex]A=Pe^{rt}[/tex]

Here, A = Final amount

P = principal amount

r = Rate of interest

t = Duration of investment

For P = $9600

r = 6%

A = 2 × 9600 = $19200

By substituting these values in the formula,

[tex]19200=9600(e)^{0.06\times t}[/tex]

[tex]2=e^{0.06t}[/tex]

[tex]ln(2)=ln(e^{0.06t})[/tex]

ln(2) = 0.06t

t = [tex]\frac{0.693147}{0.06}[/tex]

t = 11.55245

t ≈ 11.5525 years

Any amount will get doubled (with the same rate of interest and duration of investment) in the same time.

Therefore, $960000 will get doubled in 11.5525 years.

Answer:

128

Step-by-step explanation:

PLEASE RECHECK IF POSSIBLE I GOT 128 AS CIRCLE IS 360 and DIAMETER IS 180 ALSO 90 IS MARKED JUST RECHECH LET SOMEONE ELSE ALSO ANSWER.ALL THE BEST

2. 1/3

3.

a) 40

b)30 or 40

c) 110

Answer:

2. [tex]\frac{1}{3} = 33%[/tex]

3. A. [tex]\frac{1}{4} = 25[/tex]

   B. [tex]\frac{1}{2} = 50[/tex]

   C. [tex]\frac{4}{5} = 80[/tex]

Step-by-step explanation:

Hope this helps

9514 1404 393

Answer:

Step-by-step explanation:

When you multiply a fraction by a whole number, the denominator in the product is the same as the denominator of the fraction. The numerator in the product is the product of the whole number and the numerator of the fraction.

__

That's the rule. It is derived from the fact that multiplication indicates repeated addition.

  [tex]\dfrac{2}{7}\times3=\dfrac{2}{7}+\dfrac{2}{7}+\dfrac{2}{7}=\dfrac{2+2+2}{7}=\dfrac{2\times3}{7}\qquad\text{for example}[/tex]

Answer:

the value is 20 out of 100

Step-by-step explanation:

Answer:

The answer is 46

Step-by-step explanation:

Since there is a diagonal, you can't assume that it is the width because if it was the width, it would say so. Since 17 was the measure of the diagonal, I did pythagorean theorem: 15^2 + x^2 =  17^2 --> 225 + x^2 = 289 --> x^2 = 64 --> x = 8. So now we have figured out the width of the rectangle and it's 8. Now we can add: 8 + 8 + 15 + 15 = 46. That is why the answer is 46.

The perimeter of the rectangle  46 feet.

The correct option is (A).

Perimeter is the distance around the edge of a shape.

Learn how to find the perimeter by adding up the side lengths of various shapes.

Given : length= 15 feet and diagonal= 17 feet

Since there is a diagonal.

So, using Pythagorean theorem:

H² = P²+B²

15²+ x² =  17²

or, 225 + x² = 289

or, x² = 64

x = ± 8 feet.

Thus, width = 8 feet

Perimeter of rectangle= 2*(l+b)

= 2*(15+8)

= 2*23

=46 feet

Learn more about perimeter here:

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Answer:

6 apples will weigh about 1,533 grams

Step-by-step explanation:

Set up an equation:

2

Variable x = weight of 6 apples

2/511 = 6/x

Cross multiply

2 × x = 511 × 6

2x = 3066

Divide both sides by 2

x = 1533

Check your work

2/511 = 6/1533

2 × 1533 = 511 × 6

3066 = 3066

Correct

Answer: Herba has a greater balance and Nour has more debt.

Step-by-step explanation: Herba's account balance is a positive number and is clearly greater than Nour's account balance; therefore, Herba has a much greater balance. On the other hand, Nour's account balance is a negative number and is clearly less than Herba's; therefore, Hour is in more debt since he has to pay back the money that he borrowed.

→ When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed).

→ If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located.

Answer:

(a,b) ⇒ (-a,-b)

Step-by-step explanation:

When you reflect over the x-axis, the y-value changes sign.

When you reflect over the y-axis, the x-value changes sign.

So if you reflect across both, both values change sign. That is, if you reflect the point (a,b) across both axes, you will get (-a,-b)

(I've also attached a table that's handy for other reflections if you're curious)

Answer:

2ft

Step-by-step explanation:

because perimeter of a rectangle formula is p=2(l+w)

Answer:

361

Step-by-step explanation:

Answer:

Distance between A and B = 10.4 unit (Approx.)

Step-by-step explanation:

Given:

Coordinate of A = (-5 , 2)

Coordinate of B = (5 , 5)

Find:

Distance between A and B

Computation:

Using distance formula

Distance between two point = √(x1 - x2)² - (y1 - y2)²

Distance between A and B = √(-5 - 5)² - (2 - 5)²

Distance between A and B = √(-10)² - (-3)²

Distance between A and B = √100 + 9

Distance between A and B = √109

Distance between A and B = 10.4403

Distance between A and B = 10.4 unit (Approx.)

Answer:

10.4

Step-by-step explanation:

took the k12 test (:

Answer:

16 cubic units

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

a. [tex]5 \frac{21}{40} [/tex]

b. [tex] \frac{1}{42} [/tex]

Step-by-step explanation:

[tex]a. \: 12 \frac{2}{5} - 6 \frac{7}{8} [/tex]

[tex] \frac{62}{5} - \frac{55}{8} [/tex]

[tex] \frac{62}{8} \times \frac{8}{8} - \frac{55}{8} \times \frac{5}{5} [/tex]

[tex] \frac{62 \times 8 - 55 \times 5}{40} [/tex]

[tex] \frac{221}{40} [/tex]

[tex]5 \frac{21}{40} [/tex]

[tex]b. \: \frac{3}{14} - \frac{4}{21} [/tex]

[tex] \frac{3}{14} \times \frac{3}{3} - \frac{4}{21} \times \frac{2}{2} [/tex]

[tex] \frac{3 \times 3}{42} - \frac{4 \times 2}{42} [/tex]

[tex] \frac{1}{42} [/tex]

Hope it is helpful....

Answer:

616 in²

Step-by-step explanation:

14 × 14 × 22/7

=> 616

Answer:

616 inches squared

Step-by-step explanation:

14 × 14 × 22/7

=> 616

Answer:

27) x = 2^(y) – 5.

Asymptote: x = -5.

D: x > -5; (-5, infinity).

R: -infinity < f(x) < infinity; ARN;

(-infinity, infinity).

x → -infinity, f(x) → -infinity.

x → +infinity, f(x) → +infinity.

________________________

28) x = 2^-(y–3).

Asymptote: x = 0.

D: x > 0; (0, infinity).

R: -infinity < f(x) < infinity; ARN;

(-infinity, infinity).

x → -infinity, f(x) → +infinity.

x → +infinity, f(x) → -infinity.

________________________

29) x = 4^(y–2) + 1.

Asymptote: x = 1.

D: x > 1; (1, infinity).

R: -infinity < f(x) < infinity; ARN;

(-infinity, infinity).

x → -infinity, f(x) → -infinity.

x → +infinity, f(x) → +infinity.

________________________

Answer:

(0, 4) (-4, 3) (-4, 4)

Step-by-step explanation:

Translation rules:

Units UP - Add to the y-coordinate.

Units DOWN - Subtract from the y-coordinate.

Units RIGHT - Add to the x-coordinate.

Units LEFT - Subtract from the x-coordinate.

--------------------------------------------------------------------------------------------------------------

In this case, the word problem is asking for the points after a translation of 3 units up.

(x, y+3)

(0,1) → (0,4)

(4,0) → (4,3)

(4,1) → (4,4)

--------------------------------------------------------------------------------------------------------------Now it's time to reflect the new points over the y-axis.

When reflecting over the y-axis, the y-coordinate remains the same, but the x-coordinate becomes the opposite value. (-x, y)

(0,4) → (0,4)

(4,3) → (-4,3)

(4,4) → (-4,4)

Answer:

106.2

Step-by-step explanation:

First, Multiply 6 and 2.3

6x2.3= 13.8

Once you found your product, add 13.8 and 3.9

13.8+3.9= 17.7

Answer:

The number is 0.0625

Answer:

Step-by-step explanation:

1) ?

I can't see what that one given angle is ..  but it's that  mystery angle subtracted from 180 give the angle   BOA   then you know that's an isosceles triangle again that the BOA is part of... so then just subtract BOA from 180 to find the two other angle of that triangle... they are the small so just divide your answer of  180-BOA /2 is the angle of each.. then since you know those to smaller angles subtract one from 90  to find the angle BAX

2) ( as we would read normally)

You're making this really tough on me.. I can just barely read the equations

I think it's  1+6x  and 7x-3  .  b/c they are the same length sides you can set those equal

1+6x = 7x -3

4+6x = 7x

4 = x

that worked out well :

for the tangent..   it's   Tan(Ф)= Opp/ Adj

but I don't know which side they want to solve for.. I think you may have left off some of the instructions????  :/

ohh I think they really mean.. what's the length of the tangent lines .. that was confusing to me.. :/ just plug in 4 into x for either eq.

1+6(4) = 25

or

7(4)-3=25

tangent is 25

3)

x-2 = 2x-10

x+8 = 2x

8 = x

again they made it work out easy :)

Then plug 8 into either equation to find the length of the tangent lines

8-2=10

tangent is 10

4) = 2)   ??? they are the same question  maybe  you meant to put something else?

Answer:

The answer is (C) BFD

Step by step

We can see that angles DFE and AFB have a common vertex F but they do not have a common side, so the angles are not adjacent. The other options are also incorrect so the answer is C.

0/25 is 0. 5/10 is 0.5 3/4 is 0.75 2/3 is 0.66666

Answer:

n = 0.5

Step-by-step explanation:

Answer: 67.7ft²

Step-by-step explanation:

Note that a heptagon has 7 sides.

The area of a heptagon is given as:

= 1/2 × nsr

where,

n = number of sides = 7

s = length of side = 4.3ft

r = apothem= 4.5ft

Area of the heptagon = ½nsr

= ½ × 7 × 4.3 × 4.5

= 135.45/2

= 67.7ft²

Therefore, the area of the heptagon is 67.7ft²

Answer:

=

5

Step-by-step explanation:

Answer:

X = 5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Equation

2x + 3x + 8 + 7x - 2 = 90        

Solution

Combine like terms on the left

12x + 6 = 90                    Subtract 6 on both sides

12x = 90 - 6

12x = 84                         Divide by 12

x = 84/12

x = 7

Answer:

x = 23

Step-by-step explanation:

A triangle contains 180°. So, simply create the equation m∠A + m∠B + m∠C = 180° and solve for x.

2x + 3x + 1 + 3x - 5 = 180

8x - 4 = 180

8x = 184

x = 23

The value of x in triangle ABC, where m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘ is 23.

According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.

In triangle ABC,

As, the sum of all the angles of triangle is equal to the 180 degree. Thus,

[tex]m\angle A+m\angle B +m\angle C=180^o\\(2x)+(3x+1)+(3x-5)=180\\2x+3x+3x=180+5-1\\8x=184\\x=\dfrac{184}{8}\\x=23^o[/tex]

Thus, the value of x in triangle ABC, where m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘ is 23.

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Answer:

∠A = 42°

Step-by-step explanation:

sin ∠A = 12/18 = 0.6667

∠A = 41.81°

Answer:

42 degrees

Step-by-step explanation: