You are conducting a left-tailed test of a claim about a population mean when sigma is unknown with a sample size of 7.

If
α
=
.005
, find the critical value, to two decimal places.

Answer:

18

Step-by-step explanation:

12 / 4 = 3

4.5 / 1.5 = 3

6.75 / 2.25 = 3

in conc we can see that 3 is most obviously the "scale factor" (id/k what else to call it)

6 x 3 = 18

Answer:

D) $18

Step-by-step explanation:

12 / 4 = 3

4.50 / 1.5 = 3

6.75 / 2.25 = 3

6 x 3 = $18

Answer:

I'm really sorry if i am wrong but i think Gold chip is most likely to be pulled from the bag.

Step-by-step explanation:

Let's convert each fraction given to the decimal form:

(Purple) \(\frac{1}{5}\) = 0.2

(Gold) \(\frac{6}{10}\) = 0.6

(White) \(\frac{1}{10}\) = 0.1

(Red) \(\frac{2}{20}\) = 0.2

=> since Gold chips' value is the most, the answer would be Gold Chip.

Hope this helps!

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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_____________________

\(\huge\blue{\mid{\fbox{\tt{Answer}}\mid}}\)

\(\huge\blue{\mid{\fbox{\tt{Explanation}}\mid}}\)

Multiplication - Multiplication, otherwise known as the inverse of division repeats a certain number's value into what it has been multiplied by. Ex. \(4\cdot4=16\)

Fraction - A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.

Algebra - Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all mathematics

Reciprocal - In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by \(\frac{1}x\) or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction \(\frac{a}b\) is \(\frac{b}a\). For the multiplicative inverse of a real number, divide 1 by the number.

_____________________

Answer:

y = 6

x = -3

Explanation

-7x - 6y +-15

x - 2y=-15

-7x - 6y =-15

7x - 14y = -105

-20y = -120

y=6

x-2 x 6 = -15

x=-3

Answer:1/4 + 1/4 = 1/2 = 0.5

Using the binomial distribution, it is found that:

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

For this problem, the parameters are given as follows:

n = 8, p = 0.09.

Hence the mean and the standard deviation are, respectively:

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The objective function that can be used to maximize the profit is Profit = 15a + 8b

Let a is the number of units of product A and b is the number of units of product B.

Profit = 15a + 8b

This function represents the total profit earned by producing a units of product A and b units of product B

Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.

To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

The top box in the middle, should be 15.

The bottom box on the left should be 1.5

Yep thts prettyyyy much it

Answer:

E

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{a}{sin64}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a = \(\frac{9.3sin64}{sin31}\) ≈ 16.23 ( to 2 decimal places )

then to find b , using

\(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

\(\frac{b}{sin85}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b = \(\frac{9.3sin85}{sin31}\) ≈ 17.99 ( to 2 decimal places )

Answer:

a) Proved below

b) AD = 13.9 cm

Step-by-step explanation:

a) Finding the length of AC by Pythagorean Theorem

c² = a² + b²

c² = 12² + 5²

c² = 144 + 25

c² = 169

Taking sqrt on both sides so

AC = 13 cm

Hence proved that AC = 13 cm

b) Calculating AD by Pythagorean Theorem

c² = a² + b²

c² = 13² + 5²

c² = 169 + 25

c² = 194

Taking sqrt on both sides

AD = 13.9 cm

Answer:a) Proved belowb) AD = 13.9 cmStep-by-step explanation:a) Finding the length of AC by Pythagorean Theoremc² = a² + b²c² = 12² + 5²c² = 144 + 25c² = 169Taking sqrt on both sides soAC = 13 cmHence proved that AC = 13 cmb) Calculating AD by Pythagorean Theoremc² = a² + b²c² = 13² + 5²c² = 169 + 25c² = 194Taking sqrt on both sides

AD = 13.9 cm

I HOPE THIS HELPED YOU!

Answer:

The answer is C

Step-by-step explanation:

Edgy 2021 Unit Test

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

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"200" (and any subsequent words) was ignored because we limit queries to 32 words

Kate is reading 40 pages per hour.

The whole book takes 12.5 hour to complete.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

From the data we have (5, 200) and (5,0)

then slope= (200-0) / 5

                = 40

So, Kate is reading 40 pages per hour.

Now, to read the whole book i.e., 500 pages it takes

= 500/40

= 12.5 hours

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Answer:

29.3 degrees

Step-by-step explanation:

90 - 60.7 = 29.3 degrees

Answer:

Step-by-step explanation:

70000

The number of times more high school football players were there is 500.

Given that, in 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States.

Here, the number of times more high school football players were there

= 1×10⁶/2×10³

= 1×10³/2

= 1000/2

= 500

Therefore, the number of times more high school football players were there is 500.

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"Your question is incomplete, probably the complete question/missing part is:"

In 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States. About how many times more high school football players were there?​

He would have saved $87,221.02  after 1 year

He would have saved $268,335.90   after 3  years

What is an ordinary annuity?

An ordinary annuity means a fixed amount invested at specific intervals, in this case, $7,185.51 is invested monthly, which means that its future value can be computed using the future value formula of an ordinary annuity as shown below:

FV=PMT*(1+r)^N-1/r

FV=future value of an ordinary annuity

PMT=monthly payment invested every month

r=monthly interest rate=annual interest/12

N=number of months that monthly payments were

FV after 1 year:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in 1 year=12

FV=$7,185.51*(1+0.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*(1.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*0.02528845698324970/0.00208333333333333

FV=$87,221.02

FV after 3  years:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in  3 years=36

FV=$7,185.51*(1+0.00208333333333333)^36-1/0.00208333333333333

FV=$268,335.90

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They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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The rate of change of the function h(x) = 2x on the interval 2 ≤ x ≤ 4 is 6.

Using proportions, it is found that you are standing 31.8 ft from the lamp post.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, when the measures have a degree of proportionality among them, using operations such as multiplication or division.

For this problem, the procedure is relatively simple, as we just find the proportional relationship between the the heights and shadows, and apply a rule of three to find the desired measure.

For this problem, we have that the heights and shadows are related as follows:

Hence the following proportional equation is built:

5.5/10 = 12/(d - 10)

0.55 = 12/(d - 10).

Applying cross multiplication, we can solve for d as follows:

0.55d - 5.5 = 12

0.55d = 17.5.

d = 17.5/0.55

d = 31.8.

You are standing 31.8 ft from the lamp post.

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Answer:

16.1 cm (nearest tenth)

Step-by-step explanation:

Pythagoras’ Theorem

\(a^2+b^2=c^2\)

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for c:

\(\implies 16^2+2^2=c^2\)

\(\implies 256+4=c^2\)

\(\implies c^2=260\)

\(\implies c=\sqrt{260}\)

\(\implies c=2\sqrt{65}\)

\(\implies c=16.1 \sf \: cm\:(nearest\:tenth)\)

16.1 is rounded to the nearest tenth

Answer:

A

Step-by-step explanation:

the answer is A

(f+g)(x)= f(x)+g(x)

Answer:

  x = 6

Step-by-step explanation:

Compare the given formula to the equations shown in the attachment. First of all, you see that all of the numbers are scaled by a factor of 4. Removing that gives ...

  \(r=\dfrac{6.6}{1+1.1\cos{\theta}}=\dfrac{1.1\cdot6}{1+1.1\cos{\theta}}\)

This matches the formula for the hyperbola with e=1.1 and d=6, for a directrix of x = 6.

The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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