a geometric sequence, g(n) starts 20, 60, .... define g for the nth term

To test the theory proposed by the researcher using the given information, we need to set up a hypothesis test. Let's define the null and alternative hypotheses:

Next, we need to determine the test statistic and the critical value based on the significance level (α) of 0.05.

The test statistic in this case is the z-score.

To perform the hypothesis test, we need the following information:

- Number of students: n = 124

- Number of students selecting a three-grill display: x = 85

Now, let's calculate the test statistic (z-score) using the formula:

x = (x - np) / sqrt(np(1 - p))

Where:

- p is the hypothesized proportion (under the null hypothesis), which is consistent with the theory proposed by the researcher. We do not have the specific value of p in the question, so we assume p to be 0.5 for testing purposes since we have no prior information.

- np is the expected number of students selecting a three-grill display under the null hypothesis, which is np = n * p.

- sqrt(np(1 - p)) is the standard deviation of the proportion.

Let's calculate the z-score:

p = 0.5

np = 124 * 0.5 = 62

sqrt(np(1 - p)) = sqrt(62 * 0.5 * 0.5) = sqrt(15.5) ≈ 3.937

x = 85

z = (x - np) / sqrt(np(1 - p))

z = (85 - 62) / 3.937

z ≈ 5.84

Now, we compare the calculated z-score to the critical value at the significance level of α = 0.05. Since it is a two-tailed test, we need to find the critical z-values that cut off 2.5% from the upper and lower tails of the standard normal distribution.

The critical z-value for α/2 = 0.05/2 = 0.025 is approximately 1.96.

Since the calculated z-score of 5.84 is larger than the critical z-value of 1.96, we can reject the null hypothesis.

Therefore, based on the given information and using a significance level of α = 0.05, we can conclude that the theory proposed by the researcher is not supported.

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It takes 22.5 min to complete 1 mile

From the question, we have the following parameters that can be used in our computation:

Rate = 1/15mi in 1.5 min

using the above as a guide, we have the following:

Rate = 1/15mi per 1.5 min

Take the inverse

So, we have

Inverse rate = 1.5 min per 1/15mi

Evaluate the quotient

So, we have

Inverse rate = 22.5 min per mile

Hence, it takes 22.5 min to complete 1 mile

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Answer:

X=18

Step-by-step explanation:

4.5 x 2=9  9x2 =18

Or 18/4.5-2=2

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Here we go ~

\(\qquad \sf  \dashrightarrow \: 4(1 - 5x) + 2 \leqslant 166\)

\(\qquad \sf  \dashrightarrow \: 4 - 20x + 2 \leqslant 166\)

\(\qquad \sf  \dashrightarrow \: - 20x + 6\leqslant 166\)

\(\qquad \sf  \dashrightarrow \: - 20x \leqslant 166 - 6\)

\(\qquad \sf  \dashrightarrow \: - 20x \leqslant 160\)

\(\qquad \sf  \dashrightarrow \: - x \leqslant 160 \div 20\)

\(\qquad \sf  \dashrightarrow \: - x \leqslant 8\)

\(\qquad \sf  \dashrightarrow \: x \geqslant 8\)

[ Inequality changes as we multiply -1 on both sides ]

the ratio 1 is to 2 is equivalent to 3: 6

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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The volume of the solid generated when the right triangle below is rotated about side is 564.2.

The volume will be calculated by using the formula:

= 1/3πr²h

where, r = 7

h = 11

Therefore, the volume will be:

= 1/3πr²h

= 1/3 × 3.14 × 7² × 11

= 564.2

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Answer: multiply both sides by 2

Answer:

3. would be one above the negative 5

4. 3 up from positive 4

5. would be on the negative 2

write the letters on those points respectively.

The exact value of the expression is -1.

The expression involves tan 25° and tan 110°. The expression you provided is:

tan 25° + tan 110° / (1 - tan 25° tan 110°)

First, we need to recognize that tan (180° - x) = -tan x. Since 110° = 180° - 70°, we have:

tan 110° = -tan 70°

Now, we can rewrite the expression as:

tan 25° - tan 70° / (1 + tan 25° tan 70°)

Next, we can apply the tangent addition formula, which is:

tan (a - b) = (tan a - tan b) / (1 + tan a tan b)

Comparing this formula with our expression, we see that a = 25° and b = 70°. So, the expression simplifies to:

tan (25° - 70°) = tan (-45°)

Since tan (-x) = -tan x, we have:

tan (-45°) = -tan 45°

Lastly, we know that tan 45° = 1, so:

-tan 45° = -1

Therefore, the exact value of the expression is -1.

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Answer:

J. -13-18

Step-by-step explanation:

J will give the value -31

The number 4.5x10⁻⁶ can be expressed in standard notation as decimal 0.0000045.

In scientific notation, numbers are expressed as a decimal number between 1 and 10 multiplied by a power of 10. In this case, 4.5 is the decimal number and 10⁻⁶ represents the power of 10.

To convert this to standard notation, we move the decimal point six places to the left to match the negative exponent of 10⁻⁶. This gives us:

0.0000045

In standard notation, this number is written as 0.0000045, where the zeros after the decimal point indicate the value of the number in the place of each digit. The last non-zero digit in this case is 5, which is in the sixth decimal place.

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The complete question:

What is 4.5x10⁻⁶ in standard notation?

Answer:

4 times greater

Step-by-step explanation:

see attached picture

This is a scalene obtuse triangle

An obtuse triangle is a triangle with an angle greater than 90 degrees,  A scalene triangle is a triangle that has three different side lengths.  You can find the side lengths(2,3,sqrt6) by plotting the triangle and using Pythagorean theorem.  It is also visually clear that the triangle is obtuse if it is plotted.

Hope it helps <3

Answer:

41

Step-by-step explanation:

360-(104+104+111)=41

Answer: Nova Scotia

Step-by-step explanation:

British Columbia people per police officer:

= Population number / no. Of policemen

= 3,282,000/6,149

= 534 people per policeman

Nova Scotia

= 900,000 / 1,542

= 584 people per policeman

Answer: \(38.7^{\circ}\)

Step-by-step explanation:

Use a calculator.

To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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Answer:

201.06 square feet.

Step-by-step explanation:

=> The diameter of a circle is equal twice its radius. So we divide the diameter by 2 to get its radius.

=> The area of any given circle is π times the square of the radius. The radius of this circle is equal to 8 feet.

=> Area of the circle = π × r² = 3.1415 × 8 feet = 201.056 square feet

Answer:

The radius is just under 4 cm.

Step-by-step explanation:

The central angle for the entire circle is 360 degrees.

The fraction (89/360)(total circle area) = 12.36m^2.

Solving for the total circle area, we get (360/89)(12.36m^2) = 50 cm^2.

Area of a circle (in general) is A = πr²

Here we know A and π and must find r² and then r:

                                        A

A = πr² becomes r² = ----------

                                        π

Here, r² = 50 cm^2 / 3.14 = 15.92 cm^2

and r = square root of r² = 3.99, or approximately 4 cm

Weight, w of Mark's sister is 34 pounds

What is given in the question?

Mark's weight = 74 lb.

Mark's sister's weight = w lb.

Since Mark and his sister together weigh 6 lb. more than thrice the weight of Mark's sister alone.

We can write: 74 + w = 6 + 3w

According to the given question:

To solve this equation for w, first add -w to both sides of the equation.

74 + w - w = 6 + 3w - w

74 = 6 + 2w

Now add -6 to both sides and simplify:

74 - 6 = 6 + 2w -6  

68 = 2w

Therefore, w= (68/2) = 34 lb

Let's verify the answer

Marks weight = 74 lb.

Marks's sister's weight = 34 lb

Sum of Mark and his sister's weight = 108

Three time Mark's sister's weight

= 3*34 = 102

Also 108 = 102+6 which is the statement of the problem.

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Barton should use a luggage scale to get the most accurate and appropriate measurement of his packed suitcase before he leaves to catch a flight. A luggage scale is a compact and portable device that is designed specifically to weigh luggage. Using a luggage scale is easy and convenient as it allows travelers to weigh their bags accurately, ensuring that they are within the airline's weight limit. To use a luggage scale, Barton should follow these simple steps:

Step 1: Attach the luggage strap Barton should attach the luggage strap to the handle of his suitcase.The strap should be attached in such a way that it can support the weight of the suitcase without slipping or coming off.

Step 2: Turn on the luggage scale Barton should turn on the luggage scale and wait for it to calibrate. This usually takes a few seconds. Once the scale is calibrated, it will display a zero reading.

Step 3: Lift the suitcase Barton should lift the suitcase by the luggage strap until it is off the ground. The luggage scale will display the weight of the suitcase on its digital display. This reading is the weight of the suitcase including all the contents inside.

Step 4: Check the weight If the weight of the suitcase is less than 50 pounds, Barton can go ahead and catch his flight without worrying about any extra charges. If the weight of the suitcase is more than 50 pounds, Barton will have to remove some items from the suitcase or pay the extra fee charged by the airline.

Therefore, using a luggage scale is the most accurate and appropriate method for travelers like Barton to measure their suitcase weight before boarding their flight.

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Answer:

use a standard digital bathroom scale.

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-7-41)(8-6)

-48*2

-96

This is what I got. I don't see anything in the equation that has "i" in it.

If it is supposed to be (-7-4i)(8-6) foil the problem.

-56+42-32i+24i  combine like terms

the answer is -14-8i

Answer:

In this equation R would equal 88 because it satisfies the equation.

Step-by-step explanation:

You must solve for R by isolating the variable(which is R). To move the 1/8, multiply both sides by 8. You would do this because 8 is the reciprocal of 1/8. With R on it's own, to keep both sides equal multiply 11*8. That equals 88, which satisfies the equation, which is why 88 is the solution.

Hope this helps :)

The given calculation, -3+1-7- (-4)+10, can be rewritten as (1+4) so that it only involves addition and the result is 5.

According to the question,

We have the following expression:

-3+1-7- (-4)+10

Now, we have to remove all the negative signs from this expression.

So, we will first solve this expression to the step where we have only addition.

Now, we know that the multiplication of two negative integers is always positive.

-3+1-7+4+10

Adding the numbers with the negative sign:

-10+10+1+4

1+4

5

Hence, -3+1-7- (-4)+10 can be rewritten as (1+4) so that it only involves addition and the result is 5.

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13 19  27  33  36  44  52

The median is 33

The zeros of f(x) = x^4 - 49 are ±√7.  

To find all zeros of f(x) = x^4 - 49, let us proceed by factoring the equation into the product of its factors as shown below:

x^4 - 49 = 0⇒ (x^2)^2 - 7^2 = 0⇒ (x^2 - 7)(x^2 + 7) = 0

By applying the zero product rule, we get:x^2 - 7 = 0 or x^2 + 7 = 0

Taking the square root of both sides in the first equation gives:x^2 = 7

Taking the square root of both sides in the second equation gives: x^2 = -7, which has no real solution.

Therefore, x^2 = 7 has two solutions given by:x = ±√7

Hence, the zeros of f(x) = x^4 - 49 are ±√7.  

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Answer:

the answer to the question is 12cm

\(\\ \bull\tt\dashrightarrow 5x-5=74\)

\(\\ \bull\tt\dashrightarrow 5x=74+5\)

\(\\ \bull\tt\dashrightarrow 5x=79\)

\(\\ \bull\tt\dashrightarrow x=\dfrac{79}{5}\)

\(\\ \bull\tt\dashrightarrow x\approx 16\)

Answer:

• These is an isosceles triangle, meaning base angles are equal.

• let the upper angle of the first triangle be y;

\({ \tt{y + 74 \degree + 74 \degree = 180 \degree}} \\ \\ { \tt{y + 148 \degree = 180 \degree}} \\ \\ { \tt{y = 32 \degree}}\)

• Therefore:

\({ \tt{m \angle 2 + y = 90 \degree}} \\ \\ { \tt{(5x - 5) + 32 = 90}} \\ \\ { \tt{5x + 27 = 90 }} \\ \\ { \tt{5x = 63}} \\ \\ { \tt{x = \frac{63}{5} }} \\ \\ { \boxed{ \tt{ \: \: x = 12.6 \: \: }}}\)

The terms in the given equations represent various physical quantities and processes related to the zonal and meridional motion of a fluid.

The term "rho1*∂y/∂p" represents the horizontal pressure gradient force in the meridional direction. It describes the change in pressure with respect to meridional distance and influences the fluid motion. The pressure gradient force acts perpendicular to the isobars (lines of constant pressure) and drives the fluid from regions of high pressure to low pressure.

The term "rho1" represents the density of the fluid, which determines its mass per unit volume. The density influences the magnitude of the pressure gradient force and is typically assumed to be constant in these equations.

The term "∂y/∂p" represents the derivative of meridional distance with respect to pressure. It quantifies the spatial variation of the meridional coordinate as pressure changes. A larger ∂y/∂p indicates a steeper meridional gradient and can result in stronger pressure gradient forces.

The combined term "rho1*∂y/∂p" captures the effect of the pressure gradient force in the meridional direction, driving fluid motion across lines of constant pressure.

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