a unit vector lies in the xy plane, at an angle of 156 degrees from the x axis, with a positive y component. what is the unit vector? (it helps to draw a diagram.)

The function f(x) evaluated in x = a gives:

f(a) = 3/a + 8

Here we have the function f(x) = 3x^(-1) + 8x^0

Remember that:

x^-1 = 1/x

x^0 = 1

Then we can rewrite our function as:

f(x) = 3/x + 8

Now we can evaluate this in x = a, then we will get:

f(a) = 3/a + 8

That is the correct option.

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Step-by-step explanation:

what shape is this so I can calculate it correctly

The diameter of Mikayla's cereal bowl, is 5.7 in

The distance from one point on a circle through the center to another point on the circle. It is also the longest distance across the circle.

Given that, the rim of Mikayla’s cereal bowl has a circumference of 18 inches. we need to determine the diameter of the cereal bowl,

Since, the rim is circular, therefore,

Circumference of circle = π × diameter

Therefore,

π × diameter = 18

Diameter = 18 / 3.14

Diameter = 5.7

Hence, the diameter of Mikayla's cereal bowl, is 5.7 in

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Answer: 9

Step-by-step explanation:

The temperature at midnight was - 12°C.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The temperature at noon was - 4°C.

Now, At midnight the temperature dropped by 8°C.

So, Dropping by 8°C means - 8°C.

Therefore, The temperature at midnight is - 4°C - 8°C = - 12°C.

Q.Tthe temp at noon was - 4°C by midnight the temp dropped 8c, What was the final temperature at midnight?

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Answer: To simplify the expression 5x +13-5+7x, we need to perform the following steps:

Combine the coefficients of like terms:

-5x + 7x = 2x

5 + 13 = 18

Replace the combined terms:

2x + 18

So, the simplified expression is 2x + 18.

The equation of the curve that passes through points (0,1), (1,8) is y = 1/9 (3x - 1)⁶ + 8/9

multiply dx on both sides, To shift it over. By doing this, we get

dy = 2 (kx - 1)⁵dx

Using integration, Integrate both sides in relation to dy and dx terms next.

dy = 2 (kx - 1)⁵dx

∫ dy = ∫ 2 (kx - 1)⁵dx

y = 2 ∫  (kx - 1)⁵dx

Here, a u-substitution is possible. Suppose u = kx-1, which results in du/dx = k, which becomes du = kdx and rearranges to dx = du/k. Consequently, the subsequent steps can look like, y = 2 ∫  (kx - 1)⁵dx

y = 2 ∫ u⁵ × du/k

y = 2/k ∫ u⁵ × du

y = 2/k ( 1/ 5 +1  u⁵⁺¹ + C )

y = 2/k ( 1/ 6 u⁶+ C )

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

Let's enter (x,y) = (0,1) and use a little algebra to find C. On the right, we'll see an equation in terms of k.

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

1 = 2/k ( 1/ 6 (k × 0 - 1)⁶ + C )

1 = 2/k ( 1/ 6 + C )

k = 2 ( 1/ 6 + C )

k = 1/3 + 2C

3k = 1 + 6C

6C = 3k - 1

C = (3k - 1) / 6

Let's now insert that C value along with (x,y) = (1,8). After that, calculate k to obtain a precise number.

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

8 = 2/k  ( 1/ 6 (k × 1 - 1)⁶ + ( 3k - 1 )/6 )

Find the root of the function using a graphing calculator. The x intercept is 3 and k is the input x. This would get you,  C = (3k - 1) / 6

C = (3 × 3 - 1) / 6

C = 8/6

C = 4/3

Therefore, y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

y = 2/3 ( 1/ 6 (3x - 1)⁶ + 4/3 )

y = 1/9 (3x - 1) ⁶ + 8/9 , hence the final equation.

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Here we fail to reject the null hypothesis.

What is significance level?

"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.

At a 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is:-

not significantly greater than 75%

value = 0.1056 >0.05 (Alpha)..so, we fail to reject the null hypothesis.

Hence we fail to reject the null hypothesis.

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The answer is Z-score. Z-score measures the number of standard deviations that a particular value is away from the mean.

A z-score is a numerical measure used in statistics to measure the number of standard deviations between data point and the mean. It is calculated by the subtracting of the population mean from the individual raw score and then dividing the difference by population standard deviation.

The resulting number is  z-score, which can then also be used to determine the probability of a raw score in the population. Z-Scores are useful for comparing scores on different tests because they allow you to compare scores on different scales.

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Height of a cuboid is three-fourths of its length,breadth is 4 cm and total surface area is 608.

the length of the cuboid is 24 cm and its height is 18 cm.

Let us denote the length of the cuboid as "l" and the height of the cuboid as "h".

Based on the facts provided, we may conclude:

h = (3/4)l

Furthermore, the total surface area is 608, which may be computed as follows:

608 = 2(lb + bh + lh)

Extending the formula and changing the value of h:

608 = 2(lb + bh + l(3/4)l)

2(lb + 4h + (3/4)l^2) = 608

Now that we have the equation, we can solve for l by substituting the values of b (breadth) and h (height):

2(4l + 4h + (3/4)l^2) = 608

8l + 8h + (3/2)l^2 = 304

(3/2)l^2 + 8l + 8h = 304

We can now solve for l using the quadratic formula:

l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 8h))) / (2 * (3/2))

Because h = (3/4)l, we may simplify by substituting this formula for h:

l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 3l))) / (2 * (3/2))

Expanding the square root:

l = (-8 ± √(64 + 12l)) / 3

When we solve for l, we get:

l = 24

Finally, for h, substitute the value of l into the equation:

h = (3/4) * 24 = 18

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The probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

In the given question a parking row has 8 spaces.and four cars are pulled in randomly to park in the parking row.

We have to find the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs.

Number of ways to arrange 4 cars in 8 places = P(8,4)

Number of ways to arrange 4 cars in 8 places = 1680

Number of ways to arrange 4 cars in 2 pairs = N

(Choose 2 pairs of consecutive place from 8 and arrange 4 cars) = 15*4!

= 360

Number of ways to arrange 4 cars in 2 pairs so that there is no space between 2 pairs

= 5*4!

= 120

therefore,

Number of ways no two pairs are consecutive = 360-120

Number of ways no two pairs are consecutive = 240

probability=240/1680

Probability = 1/7

Therefore, the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

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Answer:

Proof below

Step-by-step explanation:

The area of the cross in the flag is equal to A = 5 · x - x².

In this problem we must determine the area of the cross in a flag, this can be seen as a sum of areas of rectangles, whose formula is:

A = w · l

Where:

Now we proceed to determine the area of the cross by following expression:

A = 3 · x + 2 · (1 - 0.5 · x) · x

A = 3 · x + 2 · x - x²

A = 5 · x - x²

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Sample selection is a key part of research design and can determine whether research questions will be answered before the study has even arisen. Good sample selection and actual sample size strengthen a study, protecting valuable time, resources, and money.

In the context of healthcare research, the dirty design could lead to the use of harmful practices, hold in a new treatment, and lost opportunities for high-quality care.

It is risky to take the time to identify the population of interest for the specific research question.

Nursing researchers are normally interested in answering questions about very specific patient populations which can span an incredible array of possibilities applying to international, local, national, and organizational contexts.

Different sampling types are used depending on the aim of the study and whether the research question seeks a confident answer about the population of interest.

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The equation "tan(⍉)• cos(⍉)=sin(⍉)" is true for all values of ⍉.

The equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)" is true for all values of ⍉.

The equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)" is true for all values of ⍉.

To prove the equation "tan(⍉)• cos(⍉)=sin(⍉)", we can use the identity:

tan(⍉) = sin(⍉) / cos(⍉)

Therefore, tan(⍉)• cos(⍉) = (sin(⍉) / cos(⍉)) * cos(⍉) = sin(⍉).

To prove the equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)", we can use the identity:

cos²(⍉) = 1 - sin²(⍉)

So, (1 - cos ⍉) = √(1 - cos²(⍉)) = sin(⍉), and

(1 - cos ⍉)(1 - cos ⍉) = sin²(⍉) = sin (⍉).

To prove the equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)", we can use the identity:

cos²(⍉) = (1 + cos(⍉)) / 2

and

sin²(⍉) = (1 - cos(⍉)) / 2

Therefore, (1 + sin ⍉)(1 - sin ⍉) = (1 + (1 - cos(⍉)) / 2) * (1 - (1 - cos(⍉)) / 2) = (1 + (1 - cos(⍉)) / 2) * (1 + cos(⍉) / 2) = (2 + cos(⍉)) / 2 = cos²(⍉).

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Answer:

  630.72 L

Step-by-step explanation:

You want the number of liters of drinks sold each week if a week's sales are of 72 cartons with 24 bottles each, and each bottle is 365 mL.

The total volume is ...

  (72 cartons) × (24 bottle/carton) × (0.365 L/bottle)

  = 72×24×0.365 L = 630.72 L

The spot sells 630.72 liters of drink each week.

The diameter of the circle is 12.5 inches

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: 157 breaks required to make a circular garden and cover the boundary.

Now each brick is 4 inches long

Thus total length of the circumference of the circular garden we get

157/4=39.25 inches long

Thus the circumference of the circle is given by

2πr=39.25

2r=39.25/3.14

d=12.5 inches

Thus the diameter is 12.5 inches.

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The measure of angle ∠7 will be 58°.

Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.

Given that in the figure line m is parallel to line n. the measure of ∠3 is 58°.

The measure of the angle 7 will be calculated as:-

∠3 = ∠7  ( Corresponding angles)

∠3 = ∠7 = 58°

Therefore, the measure of angle ∠7 will be 58° for the given parallel lines.

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A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. This particular quadrilateral has four sides, two of which are parallel and equal in length, and both of which have equal-sized opposite angles.

A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. This particular quadrilateral has four sides, two of which are parallel and equal in length, and both of which have equal-sized opposite angles. A parallelogram has equal-length opposite sides and diagonals that cut each other in half. It possesses all the characteristics of a parallelogram, including diagonals that are split in half and angles that add up to 360 degrees. Additionally, it is the only quadrilateral in which the angles on either side are equal.

In two dimensions, a parallelogram is a shape with four sides and four angles. It is a particular kind of quadrilateral where the opposing sides are parallel and all sides are the same length. In terms of the intersection of the two sides, it is also symmetrical. A parallelogram has equal opposed angles and diagonals that cut each other in half.A parallelogram's internal angles add up to 360°. The parallelogram is a rectangle if two of its adjacent angles are supplementary. Whenever a parallelogram's angles are all at right angles, it is a square.

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Answer:

The total debits in the trial balance add up to $99,050, while the total credits add up to $88,100. This means that there is a debit balance of $10,950, which suggests that there may be some expenses that have not yet been recorded.

The quadratic function that would match the graph is defined as follows:

f(x) = 4(x² - 6x + 5).

The graph is a parabola, hence the function is a quadratic function.

The x-intercepts of the graph, which are the values of x when the graph crosses the x-axis, are given as follows:

x = 1 and x = 5.

Considering the Factor Theorem, the function is defined as a product of it's linear factors as follows:

f(x) = a(x - 1)(x - 5)

f(x) = a(x² - 6x + 5).

In which a is the leading coefficient.

When x = 0, y = 20, hence the leading coefficient a is obtained as follows:

5a = 20

a = 20/5

a = 4.

Meaning that the function is:

f(x) = 4(x² - 6x + 5).

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The time the golfball takes to reach the ground = 4 seconds

The correct answer is an option (D)

When the golfball reach the ground the the height of a golfball h(t) must be zero.

Consider the function h(t) = -16t² + 32t + 128

Substitute h(t) =  0 in above equation.

-16t² + 32t + 128 = 0

We solve above quadraic equation for t.

using the Quadratic Formula where

a = -16, b = 32, and c = 128

[tex]t=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\t=\frac{-32\pm \sqrt{32^2-4(-16)(128)} }{2(-16)}\\\\t=\frac{-32\pm 96}{-32}[/tex]

t = -64/32    OR    t = 128/32

t = -2       OR     t = 4

t = -2 is not possible.

Thus the time to reach the ground = 4 seconds

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Answer:

Step-by-step explanation:

Perimeter = s+s+s+s = 4s

4(4x+1) = 260

16x + 4 = 260

16x = 256

x = 16

4(16) + 1 = 65

The solution of the system of equations:

-6x + 4y = -28

6x + 7y = 11

is (3.63, 1.55).

Here we want to solve the system of equatios:

-6x + 4y = -28

6x + 7y = 11

Adding the two equations we will get:

(-6x + 4y) + (6x + 7y ) = -28 + 11

11y = -17

y = -17/11 = 1.55

Andthe value of x will be:

6x + 7y = 11

6x + 7*(-17/11) = 11

6x = 11 + 10.8

x = 21.8/6 = 3.63

The solution of the system is (3.63, 1.55).

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Answer:

19.8km (to 3 s.f.)

Step-by-step explanation:

circumference= 39.5km

circumference= 2 × radius

radius= 39.5÷2

= 19.75km

= 19.8km (to 3 s.f.)

There are [tex]5^{7}[/tex] total ways to divide the seven different prizes because each prize is selected from among five students and is awarded to only one.

These total methods also take into account the situations in which one student, two students, three students, or four students do not receive any awards ( not five as it is compulsory to distribute all the prizes ).

We will add the "2 students left out" cases after reducing the "1 student left out" cases, but this will also add the "2 students left out" cases after adding the "3 students left out" cases, so we will reduce them once more before reducing the "4 students left out" cases.

Hence total ways :

student left out”+“2

students left out”−“3

students left out”+“4

students left out”

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The height of the street light can be calculated by using the ratio of the person's height to their shadow length. The street light is 17 feet tall.

The  height of the street light can be calculated by using the ratio of the person's height to their shadow length. In this case, the person is 6 feet tall and their shadow is 8 feet long. This gives us a ratio of 6:8 or 3:4. Since we know the person is standing 29 feet away from the street light, we can use this ratio to calculate the height of the street light. Using the ratio, we can say that for every 4 feet the person is away from the street light, the light is 3 feet tall. So if the person is 29 feet away from the street light, the light must be 3 x 29 ÷ 4 = 21.75 feet tall. However, since the height of the street light must be a whole number, we can round up and say that the street light is 17 feet tall.

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The other rotation that can be used to achieve the transformation is; C: 270° counterclockwise

What is the rotation used?

From the coordinates of XYZ transformed to coordinates of triangle X'Y'Z', we can see that the transformation pattern is;

(x, y) -----> (-y, x)

Now, this pattern of transformation occurs when;

There is a 90° clockwise rotation. However, the other rotation that can be used to achieve this is a 270° counterclockwise rotation

Answer: Triangle XYZ can be rotated 90° counterclockwise using the origin as the center of rotation to create triangle X’Y’Z’. To obtain the original triangle XYZ, we need to rotate the triangle X'Y'Z' by 90° clockwise using the origin as the center of rotation. This means that rotating the triangle X'Y'Z' by 90° clockwise is the same as rotating triangle XYZ by 90° counterclockwise, so the answer is 90° clockwise.

Answer:

yes

Step-by-step explanation:

a ratio is a special form of a fraction, but it is a fraction.

so, all calculation, comparison and transformation rules of fractions apply.

7:4 = 7/4

42:24 = 42/24

and because

7/4 × 6/6 = 42/24

they are both describing the same ratio and form therefore a proportion.

a proportion simply means that two fractions are equal.