Write 1 2/3 as an improper fraction, and multiply the improper fraction by 1/2

By cross multiplication, the state of Oregon has 4 golf courses per 100,000 people.

According to statement of this question, the state of Oregon has 190 golf couses for a population of 4,301,089, the amount of golf courses for a population of 100,000 by cross multiplication:

x = 190 × (100,000 / 4,301,089)

x = 4,417

x = 4 ↓

By means of cross multiplication, there are 4 golf courses per 100,000 people in the state of Oregon.

To learn more on cross multiplication: https://brainly.com/question/15209325

#SPJ1

We will get that the angle theta is:

θ = β/2

Remember that the sum of the interior angles of any triangle must be equal to 180°.

Now, looking at the triangle in the left, we can see that the top angle is equal to:

180 - 2α

The right angle is equal to:

180 - 2β

And the left angle is α

Then we can write:

α + (180 - 2α) + (180 - 2β) = 180

-α - 2β = -180

α = 180 - 2β

Now we can go to the other triangle, where theta is, and write:

α + β + 2θ = 180

Replacing what we found above, we get:

180 - 2β + β + 2θ = 180

-β + 2θ = 0

θ = β/2

That is the best simplification we can get with the given diagram.

Learn more about interior angles at:

https://brainly.com/question/24966296

#SPJ1

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

Read more about confidence interval at

https://brainly.com/question/15712887

#SPJ1

Answer:

a

Step-by-step explanation:

this is because it is right

Answer:

5s^2 - 4s - 12

Step-by-step explanation:

Answer:

5s^2+4-12

Step-by-step explanation:

Answer:

-8x^2+2x+5

Step-by-step explanation:

Distributive Property

The instantaneous acceleration at any time t is given by 10t. The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point.

To use the limit definition of a derivative to calculate instantaneous acceleration, we need to find the derivative of the velocity function with respect to time. The derivative of velocity gives us acceleration.

The limit definition of a derivative is given by:

f'(x) = lim (h→0) [f(x+h) - f(x)] / h

To calculate instantaneous acceleration, we substitute the velocity function, v(t), into the limit definition. Let's say v(t) = 5t^2.

Using the limit definition, we have:

a(t) = lim (h→0) [v(t+h) - v(t)] / h

Substituting v(t) = 5t^2, we get:

a(t) = lim (h→0) [5(t+h)^2 - 5t^2] / h

Expanding and simplifying:

a(t) = lim (h→0) [10th + 5h^2] / h

Now, we can cancel out the h term:

a(t) = lim (h→0) 10t + 5h

Taking the limit as h approaches 0, we get:

a(t) = 10t

Therefore, the instantaneous acceleration at any time t is given by 10t.

The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point. By taking the limit as the change in input approaches zero, we are able to approximate the exact rate of change at that point. This concept is fundamental to calculus and is used in various applications such as physics, engineering, and economics.

Learn more about acceleration

https://brainly.com/question/2303856

#SPJ11

The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.

Given that a card is randomly chosen from 8 cards shown in figure.

We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.

Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Number of cards=8

Number of repeated cards=0

Number of cards showing Q and R =1 each.

Probability of getting Q or R is P(X=Q)+P(X=R)

= 1/8+1/8

=2/8

=1/4

=0.25

Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.

Learn more about probability at https://brainly.com/question/24756209

#SPJ1

The equation of sphere is (x + 4)² + (y - 2)² + (z - 6)² = 49 and the intersection is a circle of radius √33 on yz - plane.

A sphere, like a ball, is defined as a perfectly spherical geometrical entity in three dimensions.

the general equation of a sphere is (x – a)² + (y – b)² + (z – c)² = r² where (a, b, c) is the centre of the sphere and r is the radius of the sphere.

Given, the centre of the sphere C(−4, 2, 6) and radius of sphere 7 units

Equation of sphere: (x - (-4))² + (y - 2)² + (z - 6)² = 7²

                                   (x + 4)² + (y - 2)² + (z - 6)² = 49

It is given that the sphere is intersecting with yz - plane which means x = 0

so, (0 + 4)² + (y - 2)² + (z - 6)² = 49

                     (y - 2)² + (z - 6)² = 33

The intersection is a circle of radius √33 on yz - plane.

To learn more about equation of sphere here:

brainly.com/question/20629418

#SPJ4

The code 1814151418 decodes to RADE using a simple substitution cipher, where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which is the code that maps each letter to a number

The code provided indicates that each number corresponds to a letter in the alphabet. Since 1 is A, 2 is B, and so on, the code 1814151418 would decode as RADE. This is an example of a simple substitution cipher, a type of encryption where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which in this case is the code that maps each letter to a number. Knowing this, it is a simple task to decode any message that has been encrypted with this code.

The code 1814151418 decodes to RADE using a simple substitution cipher, where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which is the code that maps each letter to a number

Learn more about number here

https://brainly.com/question/10547079

#SPJ4

The error in finding the measure of one exterior angle of a regular polygon lies in using the formula 360°/n, where n is the number of sides of the polygon.

The formula 360°/n is used to find the measure of each exterior angle of a regular polygon. It is based on the idea that the sum of all exterior angles of any polygon is always 360 degrees. However, this formula assumes that the polygon has internal angles of 180°, which is true only for regular polygons.

The error occurs when this formula is applied to a non-regular polygon, as non-regular polygons have varying internal angles. Using the formula 360°/n for a non-regular polygon will give incorrect results because the internal angles are not all equal.

For regular polygons, each exterior angle is indeed 360°/n, and the sum of all exterior angles will be 360 degrees. However, for non-regular polygons, this formula cannot be used, and the measures of exterior angles must be calculated differently based on their internal angles and sides.

To know more about regular polygon, refer here:

https://brainly.com/question/29722724#

#SPJ11

The error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

Given that,

There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

Here, at each vertex there are two angles.

So, there must be 5 vertices and 5 sides.

Then, the measure of one exterior angle = 360°/5

= 72°

Therefore, the error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

Learn more about the sum of exterior angles of polygon here:

https://brainly.com/question/1983075.

#SPJ4

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

Describe and correct the error in finding the measure of one exterior angle of a regular polygon. There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

Answer:

the answer is B

Step-by-step explanation:

Step-by-step explanation:

let the equation be y = mx + b.

m = (6 - 2)/(12 - (-4)) = 1/4

sub (12, 6):

6 = 1/4(12) + b

b = 3

therefore, equation of the line is y = 1/4x + 3, aka option 4

Topic: coordinate geometry

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

y = 0.25x + 3

Step-by-step explanation:

solve for slope:

(6-2)/(12+4) = 1/4

solve for b:

6 = 12(1/4) + b

6 = 3 + b

b = 3

equation can also be y = 1/4x + 3

From the equation \(\frac{tan^2(x)}{sec(x)-1}=sec(x)+1\\ \\\), it is possible to find the trigonometric identities: tan²(x)=sec²(x)-1.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

As previously presented the trigonometric ratios are derived by the sides of a right triangle. The main trigonometric ratios are: sinβ, cosβ and tg β. From these ratios, you can calculate other trigonometric ratios such as sec β, csc β and cotg β.

For solving this question, you need to know one of the trigonometric identities: tan²(x)=sec²(x)-1

The question gives: \(\frac{tan^2(x)}{sec(x)-1}=sec(x)+1\\ \\\), then you should multiply the numerator of each side by the denominator of the other side, the result will be: tan²(x)=sec²(x)-1. Exactly, the trigonometric identities tan²(x)=sec²(x)-1.

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

The vertical distance through which the car rises is 16.7 m

"It is a triangle whose one of the angle is 90°."

In right triangle, for angle 'x',

sin(x) = (opposite side of angle x)/hypotenuse

For given example,

Consider the following figure for given situation.

A car travels 120 m along AC.

ΔABC is right triangle with hypotenuse AC.

∠C = 8°

Consider sine of angle C,

\(\Rightarrow sin(C)=\frac{AB}{AC}\\\\\Rightarrow sin(8^{\circ})=\frac{AB}{120}\\\\ \Rightarrow 0.1392=\frac{AB}{120}\\\\ \Rightarrow AB = 0.1392\times 120\\\\\Rightarrow AB = 16.70~ m\)

Therefore, the vertical distance through which the car rises is 16.7 m

Learn more the sine angle here:

https://brainly.com/question/14553765

#SPJ2

A. The magnitude of vector C is  4.676.

B. The direction of vector C, expressed in degrees below the negative x-axis, is 153.82 degrees.

C. The magnitude of vector D is 4.676.

D. The direction of vector D, expressed in degrees above the negative x-axis, is 26.18 degrees.

To calculate the magnitude and direction of vector C = A + B, and vector D = A - B, use the following formulas:

Magnitude:

C= √(Cx² + Cy²)

D = √(Dx² + Dy²)

Direction:

θ = tan²(-1)(Cy / Cx)

θ = tan²(-1)(Dy / Dx)

Given the components of vectors A and B:

A = -4.20i² - 2.05j²

B = -1.76i²- 4.98j²

Let's calculate each part:

(a) Magnitude of C = |C|:

Cx = -4.20

Cy = -2.05

C= √((-4.20)² + (-2.05)²)

= √(17.64 + 4.2025)

= √21.8425

≈ 4.676

(b) Direction of C = θ:

θ = tan²(-1)(-2.05 / -4.20)

≈ 26.18 degrees

Since the question asks for the direction below the negative x-axis, we can subtract this angle from 180 degrees to get:

θ = 180 - 26.18

≈ 153.82 degrees

(c) Magnitude of D = |D|:

Dx = -4.20

Dy = -2.05

|D| = √((-4.20)² + (-2.05)^2)

= √(17.64 + 4.2025)

= √21.8425

≈ 4.676

(d) Direction of D = θ:

θ = tan²(-1)(-2.05 / -4.20)

≈ 26.18 degrees

Since the question asks for the direction above the negative x-axis to make any adjustments.

To know more about vector here

https://brainly.com/question/24256726

#SPJ4

The probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

The probability of dying:

P(dying) = 1/150

P(living) = 1 - P(dying) = 1 - 1/150 = 140/150

There are 120 women.

P(x≥3) = 1 - [P(x=0) +P(x=1) + P(x=2)]

\(\rm P(x\geq 3)=1-[(120 \ choose \ 0)(1/150)^0)((149/150)^{120})+\)  

                  \(\rm (120 \ choose \ 1) ((1/150)^1) ((149/150)^{119}) +\)

                  \(\rm (120 \ choose \ 2)((1/150)^2)((149/150)^{118})]\)

P(x≥3) = 0.047

Thus, the probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

Answer: 6

Step-by-step explanation:

What is the question please?

Answer:

2√7/7.

Step-by-step explanation:

Multiply top and bottom of the fraction by √7:

(2 * √7) / (√7 * √7).

= 2√7/7.

Answer:

Absolute minimum / vertex = (5/6,-133/12)

Step-by-step explanation:

Since a is positive, then the absolute maximum is ∞. The absolute minimum would be the vertex of the parabola, meaning x=-b/2a=-(-5)/2(3)=5/6, and y=3(5/6)^2-5(5/6)-9 = -133/12. Therefore, your absolute minimum / vertex is (5/6,-133/12)

Answer:

just d

Step-by-step explanation:

Hope this helps!❆

Answer:

26

Step-by-step explanation:

SORRY IF IM WRONG

We are given the following information:

The value of ''x'' is not an integer.

This, therefore, means that there is no true solution to the question

The volume of the triangular prism as described is; 15 cubic foot.

A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism is; = (1/3) ×9 × 5

Volume = 15 cubic foot

Therefore, volume of the triangular prism as described is; 15 cubic foot.

Read more on triangular pyramid:

https://brainly.com/question/12807315

#SPJ1

In 100 million years, the seafloor spreading zone will create 10 million square kilometers of new surface area.


The seafloor spreading zone creates 1 centimeter of new crust over its entire 1000 kilometers length every year. To calculate the surface area created, we need to multiply the length of the zone by the amount of new crust created each year.

First, we convert the length from kilometers to centimeters: 1000 kilometers = 100,000,000 centimeters.
Then, we multiply the length by the amount of new crust created each year: 100,000,000 cm * 1 cm = 100,000,000 square centimeters.

Finally, we convert square centimeters to square kilometers: 100,000,000 cm^2 = 10,000 km^2. Therefore, in 100 million years, the seafloor spreading zone will create 10,000 square kilometers of new surface area.

To know more about Seafloor visit.

https://brainly.com/question/12659717

#SPJ11

Angles 6 and 8 are adjacent, they are Linear pair οf angles.

Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.

Angles 1 and 4 are not adjacent, they are vertically opposite.

Angles 5 and 8 are not adjacent, they are vertically opposite.

Angles 6 and 8 are adjacent, they are Linear pair οf angles

Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.

Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles

To know more about  linear pair here

https://brainly.com/question/26355390

#SPJ1

Answer:

4.2

Step-by-step explanation:

I'm not 100% sure, but I did the math and ended up with 4.2! I hope this helps!

If 8x ≤ g(x) ≤ 4x4 − 4x2 + 8 for all x,  x will be evaluated as lim x→1 g(x), 1 is 8.

To evaluate the limit of g(x) as x approaches 1, we must first examine the given inequality. It states that if 8x is less than or equal to g(x), and g(x) is less than or equal to 4x4 - 4x2 + 8, then this is true for all x.

Calculating the limit of g(x) as x approaches 1, we start by substituting x = 1 into the given inequality. This gives us 8(1) ≤ g(1) ≤ 4(1)4 - 4(1)2 + 8. Simplifying, this gives us 8 ≤ g(1) ≤ 8, so g(1) must be equal to 8.

Therefore, the limit of g(x) as x approaches 1 is 8.

To learn more about evaluate, click here:

https://brainly.com/question/28404595

#SPJ4

a. The number of bricks required for the top step is 795.

b. The total number of bricks required for all the steps is 2250.

(a) To find the number of bricks required for the top step, we need to use the information that each successive step requires two less bricks than the prior step.

So, we can start by finding the total number of bricks required for all the steps and then subtracting the number of bricks required for the bottom 29 steps.

The total number of bricks required for all the steps can be found using the formula for the sum of an arithmetic sequence:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40.

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

So, the total number of bricks required for all the steps is 2250.

To find the number of bricks required for the top step, we subtract the number of bricks required for the bottom 29 steps from the total number of bricks required for all the steps:

number of bricks required for top step = total number of bricks - number of bricks for bottom 29 steps

= 2250 - [100 + 98 + 96 + ... + 6 + 4 + 2]

= 2250 - 1455

= 795

Therefore, the number of bricks required for the top step is 795.

(b) To find the total number of bricks required to build the staircase, we simply add up the number of bricks required for each step. We can use the formula for the sum of an arithmetic series again to simplify the calculation:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

Therefore, the total number of bricks required to build the staircase is 2250.

For similar question on bricks.

https://brainly.com/question/30679395

#SPJ11