When you take the given information and form a z-score in a hypothesis test for the mean, what is the special name of that result?

Answer:

Step-by-step explanation:

To solve the quadratic equation x^2 = x + 3 using the quadratic formula, we first need to write the equation in standard form:

x^2 - x - 3 = 0

Then, we can identify the coefficients a, b, and c as follows:

a = 1, b = -1, c = -3

Now, we can plug these values into the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-1) ± √((-1)^2 - 4(1)(-3))) / 2(1)

Simplifying:

x = (1 ± √(1 + 12)) / 2

x = (1 ± √13) / 2

Therefore, the solutions for the quadratic equation x^2 = x + 3 using the quadratic formula are:

x = (1 + √13) / 2 or x = (1 - √13) / 2

Answer:

Even though negative numbers get smaller as they get further from 0, their absolute value gets bigger, the sum of two negative numbers is a negative number, the product of two negative numbers is a positive number, etc.

Step-by-step explanation:

Answer:

The answer to your problem is, D. $13,564.80

Step-by-step explanation:

We know it took her 4 years to pay this amount. Let's solve for the total amount she paid including the interest.

12,560 x 0.02 = 251.2 per year

251.2 x 4 = 1004.8 dollars for 4 years.

1004.8 + 12,560 = 13,564.8 dollars.

Thus the answer to your problem is, D. $13,564.80

The manager can see the eight applicants in 40,320 different ways.

The number of ways the manager can see the eight applicants, one after another, equals the number of permutations of eight objects taken at a time. The given problem depends on a number of arrangements we can make for the applicants to give interviews one by one, which can be calculated as follows:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

In 40320 ways the applicants are able to give the interview. Therefore, the manager can see the eight applicants in 40,320 different ways.

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Answer:

Step-by-step explanation:

Answer: The speed of the larger pulley is 242 rpm.

Step-by-step explanation: We can use the fact that for a belt and pulley system, the linear velocity of the belt is constant. This means that the product of the radius and the angular velocity of each pulley must be the same.

Answer:

Step-by-step explanation:

[tex]\frac{2}{3}[/tex](y + 57) = 178

distribute [tex]\frac{2}{3}[/tex] into the parentheses

[tex]\frac{2}{3}[/tex]y + 38 = 178

      -38    -38

[tex]\frac{2}{3}[/tex]y = 140

multiply both sides by the reciprocal of [tex]\frac{2}{3}[/tex] which is [tex]\frac{3}{2}[/tex]

( [tex]\frac{3}{2}[/tex] ) [tex]\frac{2}{3}[/tex]y = 140(     [tex]\frac{3}{2}[/tex] )

[tex]\frac{2}{3}[/tex] is cancelled out with only y remaining on the left side

y = 210

The only factors of the given expression are: 8, xy, 4x³

A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on. Now we can also use what's called prime factorization for numbers which actually consist of using factor trees.

The expression that needs to be factored is given as;

2^(5) × x⁴ × y

This can also be written as;

32 × x⁴ × y

Now, looking at the options, it is clear that the only factors are;

8, xy, 4x³

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Step-by-step explanation:

Total yards =    11+11    +   31+31 = 84 yards

84 yd * $9/yd =  $ 756 total

To find the interval(s) over which the function 8-(x-3)^2 is increasing, we need to find the critical points of the function and test the sign of the derivative on either side of these points.

The derivative of the function 8-(x-3)^2 is -2(x-3).

Setting the derivative equal to zero to find the critical points:

-2(x-3) = 0

x = 3

Testing the sign of the derivative on either side of x = 3:

-2(x-3) is negative for x < 3, meaning the function is decreasing on the interval (-infinity, 3).

-2(x-3) is positive for x > 3, meaning the function is increasing on the interval (3, infinity).

Therefore, the interval over which the function 8-(x-3)^2 is increasing is (3, infinity).

The valid conclusion is  A.  We can be 90% ... the mean amount ... is between $217 and $677.

The confidence interval used by the student researcher refers to the probability that the university's population parameter (average amount that students spent on sporting events last year) will fall between $217 and $677 for 90% of the time.

A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence. Confidence, in statistics, is another way to describe probability.

Thus, the interval measurement gives the researcher some degree of certainty that the calculated sample mean falls within the population mean most of the time.

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The complete question is:-

marketing student is estimating the average amount of money that students at a large university spent on sporting events last year. He asks a random sample of 50 students at one of the university football games how much they spent on sporting events last year. Using this data he computes a 90% confidence interval, which turns out to be ($217, $677). Which one of the following conclusions is valid? We can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677. 90% of the sample said they spent between $217 and $677 at sporting events last year. No conclusion can be drawn.

The number of desserts, which can be ordered having 1 flavor of "frozen-yogurt" and 1 "topping" are 48.

In order to find the number of desserts that can be ordered with 1 flavor of frozen yogurt and 1 topping, we use the "multiplication-principle" of counting, which states that if there are "n" ways to selecta a thing and "m" ways to select another thing, then there are "n × m" ways to select both things together.

In this case, there are 8 flavors of frozen-yogurt to choose from and 6 kinds of toppings.

So, using the multiplication principle of counting, we get:

Number of desserts = number of flavors × number of toppings

= 8 × 6

= 48

Therefore, there are 48 different desserts that can be ordered with 1 flavor of frozen yogurt and 1 topping.

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Answer:

X is 55°

Step-by-step explanation:

we need to find 2 angles for this

First the whole D angle

Which is

A+C+D=180

75+20+D = 180

180 - 95 = D

85 is D

Second the BDC angle

2 lines equal = 2 angles equal

BD = CD

So angle CBD would 75

75+75+bdc=180

180-150=BDC

30= angle BDC

For x now

Subtract the second angle BDC from angle D

85-30=55

So the X angle would 55°

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The radius of the given shape when P, perimeter, of the shape is 50 cm is 14 cm

From the question we are to determine the value of r when P is 50 cm.

P is the perimeter of the shape shown in the figure.

The figure is a quadrant.

The perimeter of the quadrant is given by

P = r + r + 1/2(πr)

Therefore,

P = 2r + 1/2(πr)

Now,

To determine the value of r when P is 50, we will substitute the value of P into the above equation

P = 2r + 1/2(πr)

Substitute P = 50

50 = 2r + 1/2(πr)

Solve for r

50 = 2r + 1/2(πr)

Multiply through by 2

100 = 4r + πr

100 = r(4 + π)

Take π = 3.14

100 = r(4 + 3.14)

100 = 7.14r

Divide both sides by 7.14

100/7.14 = r

r = 14.0056

r ≈ 14 cm

Hence, the value of r is 14 cm

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At the end of 3 years with a weekly compounded interest rate of 6.5%, R1,250 will be worth R1,551.00.

To calculate the future value of R1,250 at the end of 3 years with a weekly compounded interest rate of 6.5%, we can use the following formula:

FV = [tex]P(1 + r/n)^{(nt)[/tex]

Where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have:

P = R1,250

r = 6.5% or 0.065 (decimal form)

n = 52 (since interest is compounded weekly)

t = 3 years

So, plugging in these values into the formula, we get:

FV = 1250(1 + 0.065/52)¹⁵⁶

FV = 1250(1.005)¹⁵⁶

FV = 1250(1.2408)

FV = R1,551.00 (rounded to the nearest cent)

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answer: 0 divided by 2 is 0. the exact value of sin is sin(0) is 0

The survey mode that is not mentioned in the text is "puter-administered." The correct option is b: puter-administered.

The following is not a survey mode mentioned in the text: a.person-administered. b: puter-administered. c.self-administered. d.mixed-mode.

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The maximum height reached from the ground is 242.75 m

Here, we have,

The horizontal speed of a projectile is regular, and there's a vertical acceleration because of gravity; its cost is 9.8 m/s/s, down, The vertical speed of a projectile changes via nine.8 m/s every second, The horizontal motion of a projectile is impartial to its vertical movement.

we know that,

Projectile motion is a form of motion experienced with the aid of an object or particle that is projected in a gravitational field, such as from Earth's floor, and movements alongside a curved route below the action of gravity best.

Projectile motion is the movement of an object thrown (projected) into the air. After the initial force that launches the item, it most effectively reports the pressure of gravity. The object is known as a projectile, and its route is called its trajectory.

Calculation:-

vertical velocity = 70 cos 35° = 57.34 m/s.

height = 64 m tall

time = ?

S = ut +1/2 at²

75 =  57.34t + 1/2×9.8 t²

4.9t² + 57.34t - 75 = 0

t = 1.50035 Sec

V² = U² - 2aS

0 =  U² - 2aS

U² = 2aS

S = U² /2a

  =  (57.34)²/2× 9.8

  = 167.75

Total height = 75 + 167.75

                    = 242.75 m

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complete question:

A man fired a bullet from the top of a tree whick is 64m tall. The bullet is fired with а velocity of 70ms-1 and angle of 35° to the horizontal line from the eye view of the man. If Sitting position the man is 0.8m Tall. Find the maximum height reached from the ground.

​

Answer:

The correct answer is 5 and 8. A right triangle has two sides whose lengths are the square root of two consecutive integers and one side whose length is the difference between those two integers. In this case, the two consecutive integers are 34 and 35. This means that the side lengths of the right triangle would be √34 and √35, or 5 and 8.

The rectangular form of given polar equation r⁶=cos θ is x⁴ + y²x² = x³ + y³.

To convert the polar equation r⁶=cos θ to rectangular form, we need to use the relationships between polar and rectangular coordinates. Recall that:

r² = x² + y² (the Pythagorean theorem for polar coordinates)

cos θ = x/r

sin θ = y/r

Using these equations, we can rewrite the given polar equation as:

(r²)³ = (cos θ)³

(x² + y²)³ = (x/r)³

Simplifying this equation by multiplying both sides by r³, we get:

x³ + y³ = x²r³

Now, using the fact that r² = x² + y², we can substitute x² + y² for r² in the above equation, which gives:

x³ + y³ = x²(x² + y²)

Expanding the right-hand side of the equation and simplifying, we get:

x⁴ + y²x² = x³ + y³

This is the rectangular form of the given polar equation. Therefore, the rectangular form of r⁶=cos θ is x⁴ + y²x² = x³ + y³.

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Answer:

3/250

Step-by-step explanation:

21/35 divided by 50 = 21/1750

Simplify this into 3/250

The least expensive C.A.R.S. that can be built to those specifications has dimensions of approximately 4.3088 m x 2.1544 m x 1.7321 m and will cost about $265.47 to build.

Let's start by looking at the dimensions of the base. We know that the length of the base is twice its width. Let's represent the width of the base as "x." This means that the length of the base is "2x." The area of the base is simply the product of the length and the width, which is 2x * x = 2x².

Next, let's look at the dimensions of the sides. The height of the box is going to be represented by "h." The length of each side is going to be equal to the length of the base, which we already know is 2x. The width of each side is going to be equal to the width of the base, which is just x. So the area of each side is simply 2hx.

Now we can use the formula for the volume of a rectangular prism to find the value of "h" in terms of "x." The volume of the box is given as 10 m^3, so:

V = lwh = (2x)(x)(h) = 10

Simplifying this equation, we get:

2x²h = 10

Solving for "h," we get:

h = 5/x²

Now that we have an expression for "h" in terms of "x," we can use it to find the total surface area of the box, which is the sum of the area of the base and the area of the four sides. We can then use this expression to find the minimum cost for a given volume of the box.

The total surface area of the box is given by:

A = 2x² + 4(2hx)

Substituting the expression we found for "h" into this equation, we get:

A = 2x² + 4(2x)(5/x²)

Simplifying this equation, we get:

A = 2x² + 40/x

Now we can take the derivative of this expression with respect to "x" and set it equal to zero to find the value of "x" that will minimize the cost of the box. Differentiating and setting equal to zero, we get:

dA/dx = 4x - 40/x² = 0

Solving for "x," we get:

x^3 = 10

Taking the cube root of both sides, we get:

x ≈ 2.1544

Now we can use this value of "x" to find the dimensions of the least expensive C.A.R.S. that can be built to those specifications. The length of the base is twice the width, so:

Length = 2x ≈ 4.3088

Width = x ≈ 2.1544

Height = 5/x² ≈ 1.7321

So the dimensions of the least expensive C.A.R.S. that can be built to those specifications are approximately: Length = 4.3088 m Width = 2.1544 m Height = 1.7321 m

These dimensions will allow us to build a C.A.R.S. with a volume of 10 m^3, while using the least amount of material possible, which means that the cost will be minimized. We can verify this by calculating the total surface area of the box and the cost of the materials needed.

The total surface area of the box can be calculated by substituting the values we found for "x" and "h" into the expression we derived earlier:

A = 2(2.1544)² + 4(2)(5)/(2.1544)² ≈ 28.2742 m²

Now we can calculate the cost of the materials needed to build the box:

Cost = (Area of base)(Cost per square meter for base) + (Area of sides)(Cost per square meter for sides)

Cost = (2.1544²)(10) + (28.2742 - 2(2.1544²))(6) ≈ $265.47

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A dilation with a scale factor of 1 will create an image and a pre-image that are similar figures

Given data ,

Let the figure be represented as A

Now , let the transformed image be represented as A'

Now , A dilation with a scale factor other than 1 would create an image and a pre-image that are similar figures, so the answer is either A or C.

Since a dilation with a scale factor of 1 would produce congruent figures, the correct answer is C, a dilation with a scale factor of 2.

Hence , the solution is a dilation with scale factor of 1

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The length of the arc that has a central angle measure of 45 degrees and a circle radius of 12 cm is calculated as: 9.42 cm.

The length of an arc can be calculated by using the formula below:

length of arc = ∅/360 * 2πr, where:

∅ = central angle measure

r = the radius of the circle.

The central angle measure (∅) = 45°

Radius (r) = 12 cm

Plug in the values:

length of arc = 45/360 * 2 * 3.14 * 12

length of arc = 9.42 cm

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The ratio of syrup to sparkling water for jug B itself is 10:29.

Jug A holds 150ml of syrup as well as 450ml of sparkling water. Jug B, on the other hand, possesses 350ml of syrup and 1050ml of sparkling water. When Paddy combines both jugs, he ultimately creates a total of 2 litres, which is equivalent to 2000ml of lemonade altogether. Let us denote the amount of syrup present in this mixed formula as ‘z’ and the corresponding quantity of sparkling water as 3z. Taking into account the ratio of syrup to sparkling water in the blend being 11:29, we can express this through an equation as follows:

z/3z = 11/29

29z = 33z

z = (33/29)z

We may consider two different approaches for calculating the entirety of syrup in the mixed lemonade. Initially, The overall amounts of syrup can be calculated simply by adding the measurements of jugs A and B, resulting in the total sum of 500ml. Concomitantly, we may express the same glyph as a fraction of the total quantity of lemonade—we can deduce that z = (11/40) x 2000ml, which translates to 550ml. Subsequently, when aligning these equations together they ultimately equal out to 500ml = 500ml. This confirms that our calculations are indeed correct.

Now, one might find the amount of sparkling water in the blended concoction by first determining 3z, then cross-multiplying this figure with the initial solution to yield 1450ml. Ultimately, the total figures assigned to syrup and sparkling water are approximately 500ml and 1450ml, respectively. Furthermore, we can illustrate the ratio of each ingredient as 500:1450 or more succinctly, 100:290 (dividing both sides by 5). Thus, the ratio of syrup to sparkling water for jug B itself is 10:29.

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Answer:  Does, 8, 3

Step-by-step explanation:

It does have a max  because it is in vertex form already there is a - in front of parenthesis so it is facing down.

the vertex is (3, 8)

to answer question

does

8

3

The value of z at 99.2% confidence is 2.41 in the proportion of population.

To find the value of z at a specific confidence level, we need to use a standard normal distribution table or a calculator that can perform normal distribution calculations.

The z-value corresponding to a 99.2% confidence level can be found by looking up the area of 0.996 (which is 1 - 0.008, where 0.008 is half of the 0.016 area corresponding to the tail probability beyond the z-value) in the standard normal distribution table or using a calculator in the interval. Using a standard normal distribution table, we can find that the z-value corresponding to an area of 0.996 is approximately 2.41. Therefore, the answer is 2.41.

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The probability that the first card is a king and the second card is a king, given that the sampling is done without replacement, is 1/221 or approximately 0.45%.

When two cards are randomly selected from a standard 52 card deck without replacement, there are 52 possible choices for the first card and 51 possible choices for the second card. The probability of selecting a king on the first draw is 4/52, or 1/13, since there are four kings in the deck.

If a king is drawn on the first draw, there will be 51 cards remaining in the deck, including three kings. So, the probability of drawing a king on the second draw, given that a king was drawn on the first draw, is 3/51.

To find the probability of both events occurring, we multiply the probabilities:

P(First card is a king and second card is a king) = P(First card is a king) x P(Second card is a king given that the first card was a king)

P(First card is a king and second card is a king) = (4/52) x (3/51) = 1/221

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The future value of the investment of $3000 for 13 years  compounded annually at 6. 5%  is equal to $6,802.46.

Initial amount 'Principal'  P = $3,000

The annual interest rate as a decimal 'r' = 6.5%

                                                                  = 0.065

The time in years 't ' = 13 years

The future value of the investment, use the formula for compound interest,

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

where,

A = the future value

n = the number of times the interest is compounded per year

= 1 compounded annually

Substitute the values in the formula we get,

A = $3,000(1 + 0.065/1)¹³

  = $3,000(1.065)¹³

  =  $3,000 × 2.2675

  = $6,802.46

Therefore, the future value of the investment is $6,802.46.

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