Solve the equation. 2 = \dfrac{f}{8}2= 8

f

​

2, equals, start fraction, f, divided by, 8, end fraction

f =\,f=f, equals

The correct critical value for this hypothesis test is -2.33.

In the given hypothesis test, where the null hypothesis (H₀) states that μ ≥ 64 and the alternative hypothesis (Hₐ) states that μ < 64, we need to find the critical value z for a significance level (α) of 0.01.

Since the alternative hypothesis is one-tailed (μ < 64), we are interested in the left-tail area of the standard normal distribution.

For a significance level of 0.01, the critical value z can be found by looking up the z-value that corresponds to an area of 0.01 in the left tail of the standard normal distribution.

The critical value z for α = 0.01 is approximately -2.33.

Therefore, the correct critical value for this hypothesis test is -2.33.

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Answer:

1.42857143

Step-by-step explanation:

Answer:

             70

Step-by-step explanation:

The total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.20.

To calculate the total cost, we need to determine the cost of each type of binder clip separately and then sum them up.

The cost of medium binder clips is $5 per pound, and Kayla purchased 0.1 pounds. Therefore, the cost of medium binder clips is 0.1 pounds * $5 per pound = $0.50.

The cost of jumbo binder clips is $6 per pound, and Kayla purchased 0.2 pounds. Thus, the cost of jumbo binder clips is 0.2 pounds * $6 per pound = $1.20.

Finally, to find the total cost, we add the individual costs together: $0.50 + $1.20 = $1.70.

Therefore, the total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.70.

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Answer:

  x = -9.7 or +5.7

Step-by-step explanation:

You want the approximate solution to x² +4x = 56.

The solution is found easily by rewriting the equation to the form ...

  x² +4x -56 = 0

The solution(s) will be the x-intercept(s) of the graph of x² +4x -56.

The solutions are -9.7 and +5.7.

We can add 4 to both sides of the equation to complete the square. (This added value is the square of half the x-coefficient.)

  x² +4x +4 = 56 +4

  (x +2)² = 60

  x +2 = ±√60 = ±2√15

  x = -2 ±2√15

  x ≈ -2 ± 7.7 = -9.7, +5.7

The sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

What is sampling distribution ?

An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population.            

                         It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given,

Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325.

Simulation A will consist of 1500 trials with a sample size of 100.

Simulation B will consist of 2000 trials with a sample size of 50.

Center for Simulation A and Simulation B will be roughly equal.  

Overall Sample size of Simulation A will be

  = 1500 * 100  = 150000

Overall Sample size of Simulation B will be

 = 2000 *  50  =  100000

Hence, the sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

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The complete question is -

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

\(\huge\text{Hey there!}\)

\(\huge\textbf{ORIGINAL equation:}\)
\(\mathsf{\dfrac{2}{3}y - 2(\dfrac{4}{3}y + z)}\)

\(\huge\textbf{DISTRIBUTE \boxed{\rm{\bf -2}} within the}\\\\\huge\textbf{parentheses:}\)

\(\mathsf{\dfrac{2}{3}y - 2(\dfrac{4}{3}y + z)}\)

\(\mathsf{= \dfrac{2}{3}y - 2(\dfrac{4}{3}y) - 2(z)}\)

\(\mathsf{= \dfrac{2}{3}y - \dfrac{8}{3}y - 2z}\)

\(\huge\textbf{COMBINE the like terms:}\)

\(\mathsf{= (\dfrac{2}{3}y - \dfrac{8}{3}y) - (2z)}\)

\(\mathsf{= \dfrac{2}{3}y - \dfrac{8}{3}y - 2z}\)

\(\mathsf{-2y - 2z}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{-2y - 2z}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

If the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.

Given that the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.

We are required to find the cost of 1 kg of mushrooms and the cost of 1 kg of turnips.

Cost is basically the expenditure that we do in order to buy or produce a product.

Suppose the cost of 1 kg of mushrooms be x and the cost of 1 kg of turnips be y. The equations will be as under:

2x+2.5y=8.55------1

3x+4y=13.10-------2

Equation1 *3 and Equation2 *2.

6x+7.5y=25.65-----3

6x+8y=26.20-------4

Subtract 4 from 3.

6x+7.5y-6x-8y=25.65-26.20

-0.5y=-0.55

y=1.1

Put the value of y in 1.

2x+2.5*1.1=8.55

2x+2.75=8.55

2x=8.55-2.75

2x=5.80

x=2.9

Hence if the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.

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Question 37:  The following is a solution to the differential equation y = t - 1. d.

Question 38:  The tea temperature be after a very long time is dT/dt = k(S - T); T ≈ 20 degrees after a very long time. a.

To determine the solution to the given differential equation: t²(d²y/dt²) - 6t(dy/dt) + 12 = 0, we can solve the equation by assuming a solution in the form of y = tⁿ, where n is a constant.

By differentiating y with respect to t, we can substitute the derivatives into the differential equation to determine the value of n.

Let's differentiate y = tⁿ with respect to t:

dy/dt = n × tⁿ⁻¹

d²y/dt² = n(n-1) × tⁿ⁻²

Substituting these derivatives into the differential equation:

t²(n(n-1)tⁿ⁻²) - 6t(ntⁿ⁻¹) + 12 = 0

Simplifying the equation:

n(n-1)tⁿ - 6ntⁿ + 12 = 0

n(n-1)tⁿ - 6ntⁿ = -12

Since this equation must hold for all values of t, the coefficients of the tⁿ terms on both sides of the equation must be equal.

We can equate the coefficients:

n(n-1) = 0

n = 0 or n = 1

The general solution to the differential equation is y = c₁ + c₂ × t, where c₁ and c₂ are constants.

According to Newton's law of cooling, the rate of change of the temperature T of an object is proportional to the temperature difference between the object's temperature T and the surroundings' temperature S.

We can write the differential equation as follows:

dT/dt = k(S - T)

dT/dt represents the rate of change of temperature, k is the proportionality constant, and (S - T) represents the temperature difference between the object and the surroundings.

The cup of tea starts at 100 degrees and cools to 50 degrees in 3 minutes, with the room temperature at 20 degrees.

We can assume that the temperature of the tea will tend toward the room temperature as time goes to infinity.

This option correctly represents that as time goes to infinity, the temperature T of the tea will approach the temperature S of the surroundings, which is approximately 20 degrees.

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Answer: 2

Step-by-step explanation:

1) substitute

2) calculate the difference before the absolute value

3) calculate the absolute value

4) convert into whole numbers/reduce

5) subtract the whole numbers

this is what i think might be wrong

Answer:

(-3,-2), (-3,-5), (-4,-5), (-7,-2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

-10.6*0.5=m+11.7

-5.3=m+11.7

-5.3-11.7=m

-17=m

14.2=2(-5.8+t)

14.2=-11.6+2t

14.2+11.6=2t

25.8=2t

25.8/2=t

12.9=t

The answer would look like this:

(2^8 × 5^–5 × 19^0)–2 ×× 228 = (2^–16 × 5^10 × 19^0) × × 2^28 = (2^–16 × 5^10 × 1) × × 2^28 = (2^–16 × 5^10 × 1) × 5^–8 × 2^–12 × 2^28 = (2^–16 × 2^–12 × 2^28) ×(5^10 ×5^–8) = 2^–28 × 2^28× 5^2 = 2^0 × 25 = 25

The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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According to the triangle:- perpendicular (p) = 8√3

hypotenuse (h) = x

\( \sec(60) = \frac{p}{h} \)

\( \frac{8 \sqrt{3} }{x} = \sin(60) \\ \frac{8 \sqrt{3} }{x} = \frac{ \sqrt{3} }{2} \\ 2\times 8 \cancel{ \sqrt{3} } = x \times \cancel{ \sqrt{3} } \\ 2 \times 8 = 16 = x = hypotenuse\)

Your Answer :- hypotenuse = X = 16

Dilation by a scale factor of 5 does not preserve congruence, hence the correct answer is option c.

1. Rotation transformation: A rotation is a transformation in which the object is rotated about a fixed point. The direction of rotation can be clockwise or anticlockwise.

2. Reflection transformation: In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection.

3. Translation transformation: Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

4. Dilation transformation: Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape.

Congruence is preserved by reflection, translation & rotation, as the image & pre-image have the same side lengths & angle measurements. But in case of dilation transformation, the side lengths change, hence this transformation does not preserve congruence.

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The value of the car in 2000 is expected to be $3800, given a starting value of $7700 in 1990 and a decrease of $390 per year for 10 years.

To find the value of the car in each subsequent year, we can subtract $390 from the previous year's value. Let's calculate the value of the car for each year from 1990 to 2000.

Year 1990: $7700

Year 1991: $7700 - $390 = $7310

Year 1992: $7310 - $390 = $6920

Year 1993: $6920 - $390 = $6530

Year 1994: $6530 - $390 = $6140

Year 1995: $6140 - $390 = $5750

Year 1996: $5750 - $390 = $5360

Year 1997: $5360 - $390 = $4970

Year 1998: $4970 - $390 = $4580

Year 1999: $4580 - $390 = $4190

Year 2000: $4190 - $390 = $3800

Therefore, the value of the car is expected to be $3800 in the year 2000.

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Answer:

maybe $825

Step-by-step explanation:

Im not sure but I think Its accurate

Answer:

20 cupcakes

15 cookies

Step-by-step explanation:

20*$1.75=$35

15*$0.75=$14.25

$35+$14.25=$49.25

Answer:

23 cupcakes and 12 cookies

Step-by-step explanation:

we have that

1.5 meters represents 100%

so

Applying proportion

Find out how much percentage represents the difference (1.53-1.50=0.03 m)

100/1.5=x/0.03

solve for x

x=(100/1.5)*0.03

x=2%

therefore

Step-by-step explanation:

(gof)(x) is basically g(f(x))

= 4 × (3x - 1)² + 9

= 4 × (9x² - 6x + 1) + 9

= 36x² - 24x + 4 + 9

= 36x² - 24x + 13

Answer:

x = 103

Step-by-step explanation:

Using the far right intersection, we can figure out that in inner angle is 32 degrees.

32 + 34 = 66 which is the angle of the left side of the middle cross.

x = 37 + 66 = 103

Answer:

Step-by-step explanation:

let price of  one pretzel=x

price of one soda=y

3x+4y=11.25   ...(1)

5x+2y=8.25    ...(2)

multiply by 2

10x+4y=16.50   ...(3)

(3)-(1) gives

7x=5.25

x=0.75

from (1)

3(0.75)+4y=11.25

2.25+4y=11.25

4y=11.25-2.25

4y=9

y=9/4=2.25

cost of one pretzel=$0.75

cost of one soda=$2.25

The outstanding balance on the invoice is $47,000. Ralph Corp. received an invoice dated September 9 for $50,000 with terms of 3/10, n/30.

On September 16, Ralph mailed a partial payment of $3,000, leaving a remaining balance of $47,000.

The terms of 3/10, n/30 mean that the buyer (Ralph Corp.) is entitled to a discount of 3% if the payment is made within 10 days of the invoice date, and the full payment is due within 30 days without any discount.

Since Ralph Corp. made a partial payment of $3,000 on September 16, which is within the 10-day discount period, this amount qualifies for the discount. The discount can be calculated as 3% of $50,000, which equals $1,500. Therefore, the effective payment made by Ralph Corp. is $3,000 - $1,500 = $1,500.

To determine the outstanding balance, we subtract the effective payment from the original invoice amount: $50,000 - $1,500 = $47,000. Thus, the outstanding balance on the invoice is $47,000, indicating the remaining amount that Ralph Corp. needs to pay within the designated 30-day period.

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Area of trapezoid = 675 in², Area of triangle = 54 in² and Total Shaded Area = 621 in²

A trapezοid, alsο knοwn as a trapezium, is a flat clοsed shape having 4 straight sides, with οne pair οf parallel sides.

The parallel sides οf a trapezium are knοwn as the bases, and its nοn-parallel sides are called legs. A trapezium can alsο have parallel legs. The parallel sides can be hοrizοntal, vertical οr slanting.

The perpendicular distance between the parallel sides is called the altitude.

From the figure given:

Area of trapezoid \(\rm = \frac{a + b}{2} \cdot h\)

Area of trapezoid \(\rm = \frac{24 + 51}{2} \cdot 18\)

Area of trapezoid = 675 in²

Area of triangle = 1/2 × base × height

Area of triangle = 1/2 × 9 × 12

Area of triangle = 54 in²

Total Shaded Area = 675 - 54

Total Shaded Area = 621 in²

Thus, Area of trapezoid = 675 in², Area of triangle = 54 in² and Total Shaded Area = 621 in²

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The answer is \(z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$\)

What do you understand by differential equation?

An ordinary derivative or a partial derivative can both be found in a differential equation. The differential equation describes the relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.

Given equation:

\($$\begin{aligned}&e^{-7 z} d z=7 t d t \\&:(-1 / 7) e^{-7 z}=3.5 t^2+C\end{aligned}$$\)

\($C=-1 / 7$\)

\($$(-1 / 7) e^{-7 z}=3.5 t^2-1 / 7$$\)

\($$e^{-7 z}=1-24.5 t^2$$\)

\($$\begin{aligned}-7 z &=\ln \left(1-24.5 t^2\right) \\z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$\)

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hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

Answer:

2(x - 7) = 2x - 14

Step-by-step explanation:

→ Expand out equation

2x - 14 = 2x - 14

→ Minus 2x from both sides

-14 = -14