a week before the election, based on a random sample of 1200 voters, the support rate for candidate a is 53%. can we assert, with 95% confidence, that candidate a is winning the election (in other words, his support rate is higher than 50%)?

Solution

Step 1

To convert seconds to hours, divide the seconds by 3600.

Step 2

1 million seconds = 1000000 seconds

We have 128 teams.

In each round, half of the teams remain, so if T is the number of teams and n is the number of rounds, we have:

and we start with n=0 so T(0)=128.

Then, we can use this recursive expression to find T after four rounds (n=4), but it is better if we derive an explicit formula for T in function of n (and not in function of the past terms of the sequence):

With the last expression we can calculate T for any value of n. Then, for n=4, we have:

NOTE: in this case, its better to express the factor 0.5 as a fraction instead of a decimal.

Answer: after 4 rounds there will be 8 teams left.

Answer:

V= 615 cm³

Step-by-step explanation:

the volume (V) of a rectangular box is calculated as

V = Ah ( A is the area of the base and h the height ) , then

V = 205 × 3 = 615 cm³

Answer:

Step-by-step explanation: In order to find the volume of box, we need to know the formula

The formula is

volume= LxBxH where L=length, B= breadth and H= height

SO, area= L x B

we can say,

Volume= area x height= 205 x 3=  615 cm^3

Hence, the volume of the box= 615 cm^3

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we have

f(x)=|x-3|

the vertex of the function is the point (3,0)

the function has a minimum

the vertex is the minimum

so the answer is

The integer n = 53 will make the inequality 4(n - 5) < 3(n + 11) false

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

In this expression, we can solve and find what makes it's true and take the odd one out.

4(n - 5) < 3(n + 11)

4n - 20 < 3n + 33

n < 53

From the options given, the value of n that will make the inequality true is less than 53 and that makes the integer 53 to be false.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

9/16 + 1/16 * (2/3)^(-1)

Step 02:

we must apply the algebraic rules to find the solution

The answer is:

21 / 32

By applying the exterior angle theorem, the measure of the exterior angle to angle ZK in triangle JKL is equal to 157°

In Mathematics, the exterior angle theorem can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.

In order to determine the value of ∠G in triangle JKL (ΔJKL), we would have to apply exterior angle theorem. Mathematically, the exterior angle theorem can be used to model the angles in triangle JKL (ΔJKL) and this is given by:

m<G = m<ZJ + m<L

Substituting the given parameters into the formula above, we have;

m<ZK = 67° + 90°.

m<ZK = 157°.

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Okay, here we have this:

Considering that the intervals are closed, we have the following integers in this interval: -1,0,1.

Answer:

55

Step-by-step explanation:

11 x 5 = total combinations

11 x 5 = 55

The parallel line of y=-1/2x-2 is y=-1/2x

Slope-intercept form y=mx+b of linear equations the slope-m and the y-intercept -b of a line,

here y=-1/2x-2 slope of the linear equation is m=-1/2,

whereas the y-intercept is b=-2,

Parallel lines are those lines that are equidistant from each other, the condition for representing two lines is parallel their slopes should be equal or the same.

here slope of the line is -1/2, and the fundamental equation of a line in slope intercept form is y=mx+b, taking the assumption the parallel line is passing through the origin hence the y-intercept of the parallel line is 0, b=0.

therefore, the parallel line of y=-1/2x-2 is y=-1/2x

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given data

STEP 2: Write the formula for calculating z-scores

By substitution,

Hence, the z score is approximately 0.44 to 2 decimal places

The domain of the given function is the set of all real numbers that is represented as x ∈ (-∝,∝ ) and range of the function is [-15,∝).

The set of values that can be plugged into a function is known as its domain.  The range of a function is the collection of all potential values that can result from the dependent variable, or the collection of all possible values after substituting the domain.

Domain of a polynomial function is the set of all real numbers which is given by x ∈ (-∝,∝ ).

Since the given function y = 0.5(x^2 - 10x - 5) is a polynomial function, it's domain is x ∈ (-∝,∝ ).

To obtain the range of the function, plot the graph of the parabola which is shown in the figure.

The vertex of the parabola is at (5,15). Value of y does not go below 15. Therefore the set of all possible values that the function takes is given by [-15,∝).

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Answer: B

Step-by-step explanation: The question says estimate, meaning you'll have to round the numbers. 194 gets rounded up to 200, while 11 gets rounded down to 10.

200 / 10 = 20, thus the answer is B

Answer:

Only D and B

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

sorry no Step-by-step explanation

You can make one and a half smoothies from one oz of acai juice

Given that:

smoothie recipe uses 2/3 oz of acai juice to make one smoothie and

Acai juice comes in a 5-oz container

In order to know how many smoothies can be made from one container, you divide the volume of the Acai juice container by the volume needed to make one smoothie. Thus the equation is:

No. of smoothies = volume of container/volume needed for one smoothie

The number of smoothies that can be made from one oz of acai is:

No. of smoothie = 1/(2/3) =  1 1/2 smoothies

Therefore, the number that can be made from one oz is one and half smoothies

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Answer: 59.5 ft

Step-by-step explanation:

When the ladder lay on the wall it makes a triangle. And for this equation, we have to use the sin to find the length.

Sin = opposite / hypotenuse

Sin 62 = 27 / h

27 / 0.4539

h= 59.48

h=59.5 feet

Answer:

30.6

Step-by-step explanation:

I AM HIM

The solution of the inequality:

-8 > b

And the graph can be seen below.

Here we start with the inequality:

-0.8*b + 2.3 > 8.7

To solve this we need to isolate the variable b.

Let's do that in the right side:

-8.7 + 2.3 > 0.8*b

-6.4 > 0.8*b

-6.4/0.8 > b

-8 > b

So b is smaller than -8. then the correct graph is:

"number line with an open circle plotted at negative eight and arrow pointing left"

.

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The slope of the line that contains the (-3, -4) and (-6, 2) is -2.

The slope of a line is the change in the dependent variable with respect to the change in the independent variables.

The slope is refer to as rise over run.

Therefore, the slope of the line that contains the points (-3, -4) and (-6, 2) can be found as follows:

slope = y₂ - y₁ / x₂ - x₁

where

x₁ = - 3

x₂ = - 6

y₁ = - 4

y₂ = 2

Therefore,

slope = m = 2 + 4 / -6 + 3

slope = 6/ -3

Therefore,

slope = - 2

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The center of dilation is outside figure A

In this question, rectangle A is dilated to rectangle B.

We know that, the center of a dilation is nothing but a fixed point about which all points are expanded or contracted.

We can observe that B = 1/2 * A

This means, the scaling factor is k = 1/2

Let's determine the center of dilation:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

O(x, y) - Center of dilation.

k - Scale factor

P(x, y) - Original point

P'(x, y) - Resulting point

(3, 1) = O(x, y) + 1/2 [(6, 2) - O(x, y)]

(3, 1) = O(x, y) - 1/2 O(x, y) + (3, 1)

1/2O(x, y) = (0, 0)

so, the center of dilation is the origin (0, 0)

So, in this case the center of dilation is outside figure A.

Therefore, the center of dilation is outside figure A

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The slope intercept form of the required line is x -2y = 12

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

The given line is

[tex]x - 2y = 16\\2y = x - 16\\y = \frac{1}{2}x - \frac{16}{2}\\[/tex]

Slope of the line = [tex]\frac{1}{2}[/tex]

Slope of the line parallel to this line = [tex]\frac{1}{2}[/tex]

The line passes through (2, -5).

Equation of the required line-

[tex]y - (-5)= \frac{1}{2}(x - 2)\\2y + 10 = x - 2\\ x - 2y = 10 + 2\\x-2y = 12[/tex]

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Answer:

I'm pretty sure it's 13.5.

Step-by-step explanation:

Boom first let's do 108 ÷ 8

After that you should get 13.5.

13 and a half gallons per hour.

The cost per ton of x = 300 is 318.18

To solve this, we need to reaplce x in the function:

And then we get the anser

This question is about rotations of polygons.

To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.

To know the exact angle rotation to map the polygon onto itself, we just have to divide 360° by the number of sides.

Answer:

This question is about rotations of polygons.

To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.

To know the exact angle rotation to map the polygon onto itself, we have to divide 360° by the number of sides.

Therefore, the right answer is the third choice.

Step-by-step explanation:

First of all it's important to note that all parallelograms, rhombuses and squares are quadrilateral and they meet the following properties:

- Rhombus: quadrilateral whose four sides have the same length.

- Parallelogram: quadrilateral that has two pairs of parallel sides.

- Square: quadrilateral whose four sides and internal angles have the same length/measure.

With these definitions in mind we can solve the True or False table in the picture.

The first statement is false not every quadrilateral is a rhombus. For example rectangles that are not squares are not rhombuses since their four sides aren't all equal.

The second is true, as we saw before parallelograms are quadrilaterals. The same reason applies to the third statement, squares are qudrilaterals.

Now let's see the last statement. A rhombus with four right angles is a quadrilateral that has four equal sides (because it's a rhombus) and four equal angles (all measuring 90°). These are the conditions required for a quadrilateral to be considered a square so this last statement is true.

Then the answers are:

F

Answer:

B

Step-by-step explanation:

2 x values must be the same to not be a function, therefore b must be the answer.

The measure of the hypotenuse n is 5√3

Hypotenuse

Hypotenuse refers the longest side of a right-angled triangle, the side opposite the right angle. And the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

Given,

Here we have the triangle with some measures on it.

Here we need to find the value of n.

While we looking into the diagram, we have identified that, n is the hypotenuse of the triangle,

So, the value of n is the root of the product of the two hypotenuse segments it touches:

=> n = √(5·15)

=> n = √75

It can be simplified as,

=> n = √(3 x 25)

=> n = 5√3

Therefore, the value of n is  5√3.

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The equation of the line which is parallel to the other equation is;

[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].

What is the Relation between two Parallel Lines?

To determine whether two lines are parallel or not, apply the parallel line's formula. When we have the slope of two lines that we want to compare, the parallel line formula can be used. The separation between the parallel lines remains constant. Parallel lines are those that never cross each other. Since the two lines are equal in this situation and the angle is 180 degrees, they will never intersect.

In the given equation, we have:

The equation of the line is y = -5/7x-10.

and, Line k, which is parallel to the line of the equation :

[tex]y = \frac{-5x}{7} -10.[/tex]

[tex]y + \frac{5x}{7} +10. =0[/tex]

So, the equation of the line which is parallel to the line of the equation is:

[tex]y + \frac{5x}{7} +k. =0[/tex]

and since the two lines are parallels

So, the slope of equation 1 and the slope of equation two will be the same;

Also, It is given that the line includes the point  (-9, 5).

So,

[tex]5 + \frac{5 \times -9}{7} +k. =0[/tex]

⇒[tex]k = -\frac{5 \times -9}{7} -5[/tex]

⇒[tex]k = \frac{10}{7}[/tex]

So, The equation of the line which is parallel to the other equation is;

[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].

Hence,

The equation of the line which is parallel to the other equation is;

[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex]..

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Step 1

State a law of indices that can be used to simplify the problem

Step 2

Apply this to the question and get the solution

Hence option B