To avoid the problem of not having access to tables of the F distribution with values given for the lower tail when a two-tailed test is required, let the smaller sample variance be _____.

The equation of the parabola in vertex form is y = (1/4)x² - 6.

To write the equation of the parabola in vertex form, we use the formula:

y = a(x-h)² + k

Where (h,k) is the vertex and "a" is a constant that determines the shape of the parabola.

Given that;

The vertex is (0,-6)

Hence:

h = 0 and k = -6.

We can substitute these values into the formula to get:

y = a(x-h)² + k

y = a(x - 0)² - 6

y = ax² - 6

Now we need to find the value of "a". We are also given that the parabola passes through the point (-6,3).

x = -6 and y = 3

We can substitute this point into the equation to get:

y = a(x - h)² + k

3 = a( - 6)² - 6

3 = 36a - 6

9 = 36a

a = 1/4

Now we know the value of "a", we can substitute it back into the equation we derived earlier:

y = ax² - 6

y = (1/4)x² - 6

Therefore, the equation in vertex form is y = y = (1/4)x² - 6.

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The situation that describes potential observer bias is when Dr. Jones knows which patients are receiving the placebo and which are receiving the drug.

In this scenario, Dr. Jones's knowledge of the treatment assignments introduces the potential for bias. Their awareness of the patients' treatment groups can influence their evaluation of the patients' responses to the new therapeutic drug, potentially leading to biased interpretations or assessments. Observer bias can arise when the observer's prior knowledge or expectations consciously or unconsciously influence their observations or judgments. To mitigate this bias, it is important to conduct blinded or double-blinded studies where the researchers or observers are unaware of the treatment assignments.

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Answer:

It's 76 degrees

Step-by-step explanation:

Thanks for branliest

Answer:

76

Step-by-step explanation:

the interior angles of a triangle always add up to 180 degrees, so all we have to do is add the 2 angle values that we know, so 48 + 56=104, then we subtract that from 180 to get 76. Hope this helps!

Weight limit of an elevator = 1800 pounds

Average weight of each person who comes in the elevator = 160 pounds

Quantity of items with them = 3 pounds

Let the number of people who can ride the elevator at one time be x.

Which means :

\( =\tt 160x + 3 = 1800\)

\( = \tt160x = 1800 - 3\)

\( = \tt160x = 1797\)

\( =\tt x = \frac{1797}{160} \)

\( =\tt x = 11\)

Thus, number of people who can enter the elevator is 11.

▪︎Therefore, the correct option is (b) 11.

Answer:

1162.5 words

Step-by-step explanation:

6m = 155 words

45m = \(\frac{45}{6}\) × 155 words

        = 1162.5 words

Answer:

Step-by-step explanation:

If:

155 words =  6 minutes :

Then:

1  minute  = 155/6  = 25.8   words

45 minutes is:

45 × 25.8 = 1,162.5

The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 8.94 feet.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In this case, the fence, building, and ladder form a right triangle, where the fence and building are the legs, and the ladder is the hypotenuse.

We know that the fence is 8 feet tall and the building is 4 feet away from the fence, so the height of the right triangle (the distance from the ground to the top of the building) is also 8 feet.

To find the length of the ladder, we need to use the Pythagorean theorem:

ladder^2 = fence^2 + height^2
ladder^2 = 8^2 + 4^2
ladder^2 = 64 + 16
ladder^2 = 80
ladder ≈ 8.94 feet

Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 8.94 feet.

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The mean is ≈ 8.793. The variance is approximately 9.641. The standard deviation is approximately 2.964

Given frequency table:

Value: 2 3 6 9 12

Frequency: 3 6 9 7 4

a) Mean:

\(\[\text{{Mean}} = \frac{{\text{{Sum of (Value * Frequency)}}}}{{\text{{Total number of observations}}}}\]\[\text{{Mean}} = \frac{{(2 \times 3) + (3 \times 6) + (6 \times 9) + (9 \times 7) + (12 \times 4)}}{{3 + 6 + 9 + 7 + 4}}\]\[\text{{Mean}} = \frac{{189}}{{29}}\]\)

≈ 8.793

b) Variance:\(\[\text{{Variance}} = \frac{{(3 \times (2 - \text{{Mean}})^2) + (6 \times (3 - \text{{Mean}})^2) + (9 \times (6 - \text{{Mean}})^2) + (7 \times (9 - \text{{Mean}})^2) + (4 \times (12 - \text{{Mean}})^2)}}{{29}}\]\)

 ≈ 8.793

c) Standard Deviation:

\(\[\text{{Standard Deviation}} = \sqrt{{\text{{Variance}}}}\]\)

Therefore, the standard deviation is approximately \(\sqrt{8.793} \approx 2.964\)

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Answer:

8.25 cm and 12.5 cm

Step-by-step explanation:

Given a line parallel to a side of the triangle and it intersects the other two sides, then it divides those sides proportionally, that is

(i)

\(\frac{AD}{DB}\) = \(\frac{AE}{EC}\) , substitute values

\(\frac{2.5}{3}\) = \(\frac{3.75}{EC}\) ( cross- multiply )

2.5 EC = 11.25 ( divide both sides by 2.5 )

EC = 4.5 cm

Then

AC = AE + EC = 3.75 + 4.5 = 8.25 cm

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

(ii)

Similarly

\(\frac{AD}{DB}\) = \(\frac{AE}{EC}\) , substitute values

\(\frac{3.6}{10-3.6}\) = \(\frac{4.5}{EC}\) , that is

\(\frac{3.6}{6.4}\) = \(\frac{4.5}{EC}\) ( cross- multiply )

3.6 EC = 28.8 ( divide both sides by 3.6 )

EC = 8 cm

and

AC = AE + EC = 4.5 + 8 = 12.5 cm

Answer:

17000 drops in the bottle

Answer:

Step-by-step explanation:

Common difference is the difference between two consecutive terms:

Or you can use the slope of the line as common difference, which is 8.

Step-by-step explanation:

\(we \: want \: to \: find \: commen \: differe \: nce \\ so \: put \: n= 1 \: and \: n = 2 \\ then \: calculate \: its \: difference \\ then \\ f(n) = 8n + 2 \\ f(1) = 8 \times 1 + 2 = 8 + 2 = 10 \\ f(2) = 8 \times 2 + 2 = 16 + 2 = 18 \\ f(2) - f(1) = 18 - 10 = 8 \\ 8is \: the \: commen \: difference \\ thank \: you\)

Answer:

A bagel costs $1.55, so that would be 155 cents

Step-by-step explanation:

Given Info:

x = cost of a piece of toast

y = cost of a bagel

z = cost of a muffin

2x + y = 3.15

y + z  = 3.30

x + 2y + 3z = 9.15

Calculations:

2x + y - (y + z ) = 3.15 - 3.30

2x - z = -0.15

-z = -0.15-2x

z = 0.15+2x

y = 3.15 - 2x

x + 2y + 3z = 9.15

x + 2(3.15 - 2x) + 3(0.15 + 2x) = 9.15

x + 6.3 -4x + 0.45 + 6x = 9.15

3x + 6.75 = 9.15

3x = 2.4

x = 0.80 cents per piece of toast

2x + y = 3.15

2(0.80) + y = 3.15

1.60 + y = 3.15

y = 1.55

So a bagel costs $1.55

One bagel costs 155 cents.

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

This question is solved using a system of equations.

I am going to say that:

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

Two pieces of toast and a bagel costs $3.15.

This means that \(2x + y = 3.15\)

Since we want to find the cost of a bagel, we write x as a function of y, so:

\(2x = 3.15 - y\)

\(x = -0.5y + 1.575\)

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

A bagel and a muffin costs $3.30.

This means that:

\(y + z = 3.3\)

Since we want y:

\(z = 3.3 - y\)

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

Piece of toast, two bagels and three muffins cost $9.15.

This means that:

\(x + 2y + 3z = 9.15\)

We have x and z as functions of y, so:

\(-0.5y + 1.575 + 2y + 3(3.3 - y) = 9.15\)

\(-0.5y + 1.575 + 2y + 9.9 - 3y = 9.15\)

\(-1.5y + 11.475 = 9.15\)

\(1.5y = 2.325\)

\(y = \frac{2.325}{1.5}\)

\(y = 1.55\)

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

In cents, one bagel costs 100*1.55 = 155.

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Answer:

False

Step-by-step explanation:

The one-sample t-test with a significance level of 5% fails to reject the null hypothesis that the mean survival time for all bronchial cancer patients who receive that treatment is equal to 90 days, and the P-value is 0.0974.

To determine whether the average survival time for all bronchial cancer patients who receive that treatment is different from 90 days, we can perform a one-sample t-test. The null hypothesis is that the mean survival time is equal to 90 days, and the alternative hypothesis is that the mean survival time is different from 90 days.

We can use the following formula to calculate the t-statistic:

\($t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$\)

Substituting the given values, we get:

t = (111.3 - 90) / (62.9 / √12) = 1.83

Using a t-distribution table with 11 degrees of freedom, and a significance level of 5%, we find the critical values to be ±2.201.

Since the calculated t-value of 1.83 falls within the range of -2.201 to +2.201, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that the average survival time for all bronchial cancer patients who receive that treatment is different from 90 days.

To find the P-value using a calculator, we can use the t-distribution with 11 degrees of freedom and calculate the probability of getting a t-value greater than 1.83 or less than -1.83 (since it is a two-tailed test). The P-value turns out to be 0.0974. Rounded to the nearest 4th decimal digit, the P-value is 0.0974.

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Complete question:

Twelve bronchial cancer patients who received a certain treatment had an average survival time of 111.3 days with a standard deviation of 62.9 days. Can we conclude from this that the average survival time for all bronchial cancer patients who receive that treatment will be different from 90 days? We will use a 5% significance level. Do the T-test on your calculator and enter the P-value below. Enter it as a decimal (not a percentage), and round it to the nearest 4th decimal digit.

The value of f(-5) = -130

A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.

A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:

Ax3 + bx2 + cx +d = 0

For the given question the cubic equation will be:

2x3 + bx2 + cx - 5 = 0

Given

Leading coefficient (a) = 2

Constant (T) = -5

f(1) = 0

f(2) = 9

Therefore the equation formed will be:

2x3 + bx2 + cx - 5 = 0

Now f(1) = 0

2(1)3 + b(1)2 + c(1) - 5 = 0

2 + b + c -5 = 0

b + c = 3  

b = 3-c -----(1)

On solving f(2) = 3

2(2)3 + b(2)2 + c(2) - 5 =3

16 + 4b + 2c – 5 =3

4b +2c = 3 – 11

4b + 2c = -8  ----(2)

Now substitute the b value in equation (2)

4(3-c) + 2c = -8  

12 – 4c +2c = -8

-2c = -20

C =10

Now substitute the c value in equation (1)

b= 3 – c

b = 3 -10

b = -7

Now substitute the b and c values in the cubic equation

2x3 - 7x2 + 10x - 5 = 0

Now calculate f(-5)

2(-5)3 - 7(-5)2 + 10(-5) - 5

= -250 + 175 – 50 -5

= -130

Therefore the value of f(-5) = -130

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Step 1:

First count the number of stickers on a page

There are 12 stickers in a page

Step 2

There are 30 pages,

Hence, the number of stickers in 30 pages = 30 x 12 = 360

Final answer

Dana has 360 stickers in all

Dimension of photograph is 35cm and 22cm.

And external dimension of photo frame is 45cm and 30cm

So, the area of the border surrounding the photograph=Area of photo frame−Area of photo.

So, The area of the border surrounding the photograph \(=45\times30-35\times22\)

\(=1350-770=580cm^2\)

A prime number is a number which has exactly two factors its self and on not prime.  

The orange divisor above are the prime factors of the number 663 if we put all of it together we have the factors 3*13*17=663. it can also be written in exponential form as 3^1 * 13^1 * 17^1.

Answer:

3 x 13 x 17

Step-by-step explanation:

Answer:

72.5 ft²

Step-by-step explanation:

There are 3 areas:

First: The top triangle

Area1 =

\( \frac{1}{2} \times 2 \times5 = 5\)

Second Area: The middle rectangle

Area2=

\(5 \times (6 + 5) =5 \times 11 = 55\)

Third Area: bottom triangle

Area3:

\( \frac{1}{2} \times 5 \times 5 = 12.5\)

Area1 + Area2 + Area3 =

\(5 + 55 + 12.5 = 72.5 \: {ft}^{2} \)

Answer:

y=-3x-1

Step-by-step explanation:

Use point-slope form:

(y-2)=-3(x+1)

y-2=-3x-3

y=-3x-1

If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

The energy an item has as a result of motion is known as kinetic energy in mechanics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its propulsion until its speed changes.

The kinetic energy is given as,

KE = (mv²)/2

Where m is the mass and v is the velocity.

Shawn and his bike have a total mass of 48.1 kg. Shawn rides his bike 1.5 km in 12.5 min at a constant velocity.

The velocity is given as,

v = 1.5/12.5

v = 0.12 km/min

v = 0.12 x 1000 / 60

v = 2 m/s

Then the kinetic energy of Shawn will be given as,

KE = (48.1 x 2²) / 2

KE = 48.1 x 2

KE = 96.2 J

If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.

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The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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Answer:

4√7

Step-by-step explanation:

hyp1(9)/alt(x)=hyp2(7)/alt(x)

By cross multiplication, x^2 = 63

thus, alt = √63

Then, with Pythagorean theorem, (√63) ^ 2 + 7 ^ 2 = z ^ 2

Thus, 63 + 49 = z ^ 2

Thus, 112 = z ^ 2

Thus, z = √112

Thus, z = 4 √7

Answer:

Y=18

Step-by-step explanation:

Answer:

Y=18

Step-by-step explanation:

The expected frequency, E i, can be calculated using the formula E i = n x p i.

In this case, n = 110 and p i = 0.6. To find E i, we simply multiply these values together: E i = 110 x 0.6 = 66.

Therefore, the expected frequency for the given values of n and p i is 66.


To find the expected frequency (E i), you can use the formula: E i = n * p i


1. In this case, n = 110 and p i = 0.6.
2. Plug these values into the formula: E i = 110 * 0.6
3. Perform the multiplication: E i = 66


The expected frequency (E i) for the given values of n and p i is 66.

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Each phrase can be epressed as an algebraic expression as:

n/8

4p,

b+14

90x

-16

24-k

3(w)

1+q

13/z

45+c

w-8

An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). A good example of an algebraic expression is 3x2 2xy + c.

A variable expression can be described using its terms and operations on the terms as an algebraic expression. For instance, "3 more than x" can be used to describe x + 3.

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Answer:

x^2+5x

Step-by-step explanation:

Answer:

432

Step-by-step explanation:

Hope this helps!

The best estimate for the weight of a cantaloupe is 2 kilograms (B).

A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.

Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.

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Complete Question:

Choose the best estimate for the weight of a cantaloupe. Responses

A 2 decigrams

B 2 kilograms

C 2 grams

D 2 milligrams

sketch of the line 4x + 3y = 11, slope (-4/3),  y-intercept of the line y = 11/3

Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:

3y = -4x + 11

y = (-4/3)x + 11/3

Step 2: Identify the slope and y-intercept:

From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.

Step 3: Plot the y-intercept:

On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.

Step 4: Use the slope to find additional points:

Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.

Step 5: Connect the points:

Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.

The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.

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