16% of what number is 17 ?

The measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.

Complementary angles are a pair of angles whose sum is always equal to 90°.

If A and B are complementary angles, then A + B = 90°.

In the question, we are asked to find the measure of each angle, given that the angles (5x)° and (4x - 18)° are complementary angles.

As we know that these angles are complementary, we can write the equation to solve for x as,

5x + (4x - 18) = 90

or, 5x + 4x - 18 = 90

or, 9x = 90 + 18 = 108

or, x = 108/9 = 12.

Therefore, the value of these angles are:

Therefore, the measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.

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Final answer:

The probability of drawing a red or blue marble from a bag containing 25 marbles (10 black, 13 red, 2 blue) is 3/5. This is calculated by dividing the total number of red and blue marbles (15) by the total number of marbles (25).

Explanation:

The question involves calculating the probability of drawing a red or a blue marble from a bag containing 25 marbles: 10 black, 13 red, and 2 blue. To find the probability of an event happening, we divide the number of ways that event can happen by the total number of outcomes. Here, the total number of marbles is 25.

The total ways to get a red or a blue marble is the sum of red and blue marbles, which is 13 (red) + 2 (blue) = 15. Therefore, the probability of drawing a red or blue marble is 15/25. Simplifying that fraction gives us 3/5.

The correct answer is 3/5. This calculation shows how to approach problems involving the probability of one event or another happening, especially when dealing with specific quantities.

Answer:

Step-by-step explanation:

n=sample size =200

Mean = x bar = 55 hours

Std deviation (Population) = 7 hours

For 99% confidence level

Z critical value = 2.58

Margin of error = ±2.58(std error)

Std error = [tex]\frac{7}{\sqrt{n} } =0.495[/tex]

Hence margin of error = ±0.495(258)=1.28

Confidence interval = (55-1.28, 55+1.28) = (53.72, 56.28)

~(53.73, 56.27)

Hence option A

D is the correct answer.

Step-by-step explanation:

D. Glenda chooses to check 300 monitors.

A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Now, to know about the defects through binomial experiment Glenda must choose a number of computers or trials. So, option D is correct.

The statement that will make this process into a binomial experiment is that,

⇒ Glenda checks the monitors until she has 300 non-defective monitors."

Hence, Option C is correct.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective.

Since, A binomial experiment is defined as a statistical experiment which consists of n repeated trials.

Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Hence, For check several monitors and record if they are defective,

Glenda checks the monitors until she has 300 non-defective monitors."

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Answer:

ΔABP is congruent to ΔBAQ

ΔABP ≡ ΔBAQ

Explanation:

We are given two triangles; ΔABP and ΔABQ

In these two triangles, we have:

AB as a common side

∠ABP = ∠BAQ

AQ = BP

We can conclude that these two triangles are congruent by SAS (side-angle-side) postulate which states that:

"When two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle, then the two triangles are congruent"

Note that when writing congruency statements, the order of the letters is critical as each angle/side in the first triangle must be congruent to its corresponding angle/side in the second triangle.

Based on the above, the congruency statement would be:

ΔABP is congruent to ΔBAQ

Hope this helps :)

Final answer:

To sketch the polynomial graph without plotting points beyond intercepts, identify the x-intercepts from the factors, note the behavior at these points due to the powers, and connect them considering the end behavior akin to y = x^13.

Explanation:

To sketch a possible graph of the given polynomial f(x) = (x + 8)^3(x + 6)^2(x + 2)(x - 1)^3(x - 3)^4(x - 6), we can use its intercepts and the behavior near these intercepts. The intercepts are the x-values for which f(x) = 0. These are at x = -8, x = -6, x = -2, x = 1, x = 3, and x = 6.

Since these factors are raised to different powers, the graph will behave differently at each intercept. Also, since the highest power in the polynomial is 13 (3+2+1+3+4+1), the end behavior of f(x) as x approaches positive or negative infinity will resemble that of y = x^13.

Here's a step-by-step guide for sketching the graph:

Plot the x-intercepts on the x-axis: (-8, 0), (-6, 0), (-2, 0), (1, 0), (3, 0), (6, 0).

For each intercept, note that if the factor has an odd power, the graph crosses the x-axis, and if it has an even power, the graph touches the x-axis and turns back.

At x = -8, since the power is 3 (odd), the graph crosses the axis and behaves similarly to y = x^3, starting from the bottom.

At x = -6 and x = -2, the powers are 2 (even), so the graph will just touch the axis and turn back.

At x = 1, the power is 3 (odd), so the graph will cross the axis with the behavior of y = x^3.

At x = 3, the power is 4 (even), hence the graph touches the axis and turns back.

At x = 6, as the factor is raised to the first power (odd), the graph crosses the x-axis.

Finally, connect these points with smooth curves, keeping in mind the end behavior of the graph will rise on both ends because the degree is 13, an odd number.

Remember that the final graph should show the pattern of rising and falling appropriately between these intercepts based on the powers of each factor.

Next step to isolate the variable is to divide by -3 .

Given,

-3x-9=-27

Firstly,

Add 9 to both side of the equation,

-3x-9+9=-27+9

-3x=-18

Now,

Divide -3 to each side

-3x/-3=-18/-3

x=6

Now,

Check:

-3x-9=-27

Substitute x with 6

-3(6)-9=-27

-18-9=-2

Thus, the next step to isolate the variable is to divide -3 to both side of equation.

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[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]. Option d is correct.

Simplification is defined as the solution making tendency to expressions.

Here,  expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]

Multiply the whole power 3 in the square bracket.
Gives,
⇒[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  

Thus, [tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex].

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Answer: So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 0.64 feet.

Step-by-step explanation:

Since we have given that

Area of Pam 's picture frame which is square in shape = 3 sq. ft.

As we know the formula for "Area of square ":

[tex]Area=Side^2\\\\3=Side^2\\\\\sqrt{3}\ ft=Side[/tex]

So, Perimeter of square frame would be

[tex]Perimeter=4\times side\\\\Perimeter=4\times \sqrt{3}\\\\Perimeter=6.93\ ft[/tex]

Radius of Meg's circular frame = 1 foot

So, Circumference of circular frame would be

[tex]2\pi r\\\\=2\times \dfrac{22}{7}\times 1\\\\=\dfrac{44}{7}\\\\=6.29\ ft[/tex]

So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 6.93-6.29=0.64 feet.

It’s a little surprising that this question didn’t come up earlier.  Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2).  A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.

Answer:

0.75

Step-by-step explanation:

Answer:

Important information like the common difference, 1st term, the # of terms; the last term must be included to find the sum of a series.

Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.

The polar coordinate of any point can be written as:

(r, θ) = (r, θ + 2nπ)                                           --> when positive

 (r, θ) = [ - r, θ + (2n + 1)π ]                           --> when negative

 where n is any integer.

The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).

When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)

where n is any integer.

When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.

Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].

The polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

The coordinates of point p are given as:

p = (5, [tex]\pi[/tex]/3)

A point represented as (r, θ) has the following polar coordinates

(r, θ + 2n[tex]\pi[/tex]) for positive r, and (- r, θ + [2n + 1][tex]\pi[/tex]) for negative r

By comparing (r, θ) and (5, [tex]\pi[/tex]/3), we have:

r = 5

[tex]\theta = \pi/3[/tex]

So, we have:

(r,[tex]\theta[/tex]) = (r, [tex]\theta[/tex] + 2n[tex]\pi[/tex])

The equation becomes

(5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

Also, we have:

(-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

Hence, the polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

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X=k/y

X=2, y=48

2=k/48

K=2*48 = 96

X= 96/24

X=4