The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?



If x represents the first number, then which of the following equations could be used to solve the problem?

69 = 7x - 8
x = 6x - 8
69 = 6x - 8

The answers to the questions are:

1. x = 4

2.  x = 1.5

3. x = 1.875

4. x = 1

1. 4x + 3 = 19

4x = 19 - 3

4x = 16

divide by 4

x = 4

(4/3)x + 5 = 17

= 1.33x + 5 = 7

Take like terms

1.33x = 7-5

1.33x = 2

divide through by 1.33x to get 2

x = 2/1.33

x = 1.5

4x(6 - 2) - 10 = 20

Multiply and open the bracket

24x - 8x - 10 = 20

Take like terms

16x = 20+10

16x = 30

x = 30/16

= 1.875

4.3x + 0.7 = 5

4.3x = 5 - 0.7

4.3x = 4.3

x = 1

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5 minutes per bracelet.

because 15/3 = 5 mins.

To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:

constant of proportionality =15/3= 5 minutes.

Now, we're going to consider an example of a proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.

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Answer:

Step-by-step explanation:

I would use the law of sins.

13/sin90 = 5/sin s

sin s  = (5 sin 90)/13

sin s = .3846.  

Now put in your calculator sin-1 .3846 and you will get the angle of 22.6 degrees rounded to the tenths place.

Answer:

22.6 = 113/5

Step-by-step explanation:

The sum of the pulses allows us to find that the answer for the sum at a point x is

If the waves travel in the same direction, their sum gives resulting waves that can be maximum or minimum depending on the phase between them, un stationary patterns.

If the directions are coincident directions, they add place to the interference processes, in this case, stationary patterns are formed on a screen.

If the waves travel in the opposite direction the sum of the two waves gives rise to a wave that maximum is the sum of the amplitudes of the two pulses

In the case of a pulse that corresponds to a single wavelength, the result is an instantaneous maximum,  which after the pulse passes, returns to zero.

Consequently, there is no stationary pattern, so there is no interference between the two pulses.

In conclusion with the sum of the pulses, we can find that the answer is No interference pattern is produced as the amplitude does not remain constant.

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The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.

Step 1: Finding the range for the function f(x) = -(x + 1)² - 4

The given function is quadratic in the form of a(x - h)² + k,

So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0

For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4

∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}

Step 2: Finding the range for the function f(x) = -4x + 11

This is a linear function. So, the range is R.

∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}

Step 3: Finding the range for the function f(x) = 2/3x - 8

This is also a linear function. So, the range is R.

∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}

Step 4: Finding the range for the function f(x) = 2^x + 3

This is an exponential function. So, the range is y > k

Here k = 3.

∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}

Step 5: Finding the range for the function f(x) = x² + 7x - 9

This is a quadratic function.

we can write it as,

f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9

     = (x + 7/2)² - 85/4

This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4

Since a > 0, the range of the function is y ≥ -85/4

∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}

Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}

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The map scale to use would be: 1 in. = 5 miles.

The scale of a map relates the actual distance of two places to the distance on paper on a scale drawing. It is a ratio between length on the map and distance in real life.

Given that, 6 inches would equal actual distance of 30 miles, let x be the actual distance on ground. We would have:

6/30 = 1/x

Solve for x

x = (30 × 1)/6

x = 5.

Therefore, the scale of the map is: 1 in = 5 miles.

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Answer: 144 [tex]cm^{2}[/tex]

Step-by-step explanation:

The rectangle's length is twice as long as it's width as the square is folded in half. Let's say that the width's length is x, we get the equation

x + 2x + x + 2x = 36

6x = 36

x = 6 cm

The length of the rectangle is the length of the square which is 2x = 2 * 6 = 12 cm

So the area of the square is 12 * 12 = 144 [tex]cm^{2}[/tex]

Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For the first ticket, since 5 out of 26 letters are vogal, the probability is:

5/26.

For the second ticket, since there is no replacement, the probability is:

4/25.

The probability of both tickets is:

[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]

0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

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Using the monthly payment formula, it is found that her down payment should be of $1,419.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For this problem, the parameters are:

A = 250, r = 0.072, n = 72.

Hence:

r/12 = 0.072/12 = 0.006.

We solve for P to find the total amount of the monthly payments, hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250[/tex]

0.0171452057P = 250

P = 250/0.0171452057

P = $14,581.

The total payment is of $16,000, hence her down payment should be of:

16000 - 14581 = $1,419.

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The widgets should be sold for $22.08 for the company to make the maximum profit.

To maximize a function, y = f(x), we differentiate it with respect to x, to get y' = f'(x). Equate it to zero to get the points on inflections.

Differentiate y' = f'(x) again with respect to x, to get y'' = f''(x), and put in the points of inflections to check whether y'' is greater than or less than zero. If it is greater than zero, then we have a minimum, and if it is less than zero, then we have a maximum.

In the question, we are given a profit function y, with respect to the sale price of each widget x. We are asked to find the sale price that maximizes the profit.

The function given is:

y = -30x² + 1325x - 8569.

Differentiating this with respect to x, we get:

y' = -60x + 1325.

To find the point of inflection, we equate this to zero, to get:

0 = -60x+ 1325,

or, x = 1325/60 = 22.0833

Now, we differentiate, y' = -60x + 1325, with respect to x, to get:

y'' = -60 < 0, thus we have a maximum at x = 22.0833.

Thus, the widgets should be sold for $22.08 for the company to make the maximum profit.

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The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

According to the statement

we have given that the sint=1/8 then we have to find the exact value of

sin(2t) , cos(2t) , and tan(2t).

Here the value of Sint = 18

then sin2t becomes

sin2t = 2*1/8 then

sin2t = 1/4.

And

(Cos2t)^2 = 1 - (Sin2t)^2

(Cos2t)^2 = 1 - 1/16

(Cos2t)^2 = (16 - 1)/16

(Cos2t)^2 = 15/16

(Cos2t) = (15/16)^1/2

then

tan2t = sin2t/cos2t

tan2t = (1/4)/(15)^1/2 / 4

tan2t = 1/(15)^1/2

these are the values of given terms.

So, The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

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The equation of the parallel line is y = -5x - 1

The equation is given as:

5x + y = 4

Make y the subject

y = -5x + 4

The slope of the above equation is

m = -5

Parallel lines have equal slope.

This means that the slope of the new line is 5

The equation is then calculated as:

y = m(x - x1) + y1

So, we have:

y = -5(x + 1) + 4

Expand

y = -5x - 5 + 4

Evaluate

y = -5x - 1

Hence, the equation of the parallel line is y = -5x - 1

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Answer:

Below.

Step-by-step explanation:

12.  That is a semicircle

The central angle is 180 degrees.

Answer:1+1

Step-by-step explanation:

The congruency proof that can be used to show that ∠P≅∠R is as given in the steps below.

From the figure as seen online, we can see that;

The figure shows the same triangles PQS and RQS as in the beginning of the task. Angles SPQ and SRQ are highlighted in red.

Thus, the 2 column proof to show that ∠P≅∠R is;

Statement 1; ∠SPQ≅∠SRQ

Reason 1; Given

Statement 2; SQ bisects ∠PSR

Reason 2; Given

Statement 3; ∠PSQ≅∠QSR

Reason 3; Definition of angle bisector

Statement 4; SQ ≅ SQ

Reason 4; Reflexive Property of Congruence

Statement 5; △PQS≅△RQS

Reason 5; Angle - Angle Side (AAS) Congruency Postulate

Statement 6; PS ≅ SR

Reason 6; CPCTC (Corresponding parts of congruent triangles are congruent)

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Answer:

x intercepts: (1,0), (-3,0)

the roots are 1 and -3

Step-by-step explanation:

Using the Quadratic Formula:

x=−b±sqrt(b2−4ac)/2a

Substitute:

x= -8±sqrt(8^2-4(4)(-12))/2(4)

x=-8±sqrt((64- -192))/8

x=-8±sqrt(256)/8

Solve two equations (±)

x=-8±16/8

x=8/8  and x=-24/8

x=1 and x=-3

Answer:

x = -3

x = 1

Step-by-step explanation:

Hello!

We can solve the quadratic by Factoring the Equation and using the Zero Product Property.

We want to find two numbers that multiply out to -3, but add up to 2. The numbers that work are -1 and 3. We can expand 2x to -x and 3x and factor by grouping.

Set each factor to 0 and solve for x in both.

Therefore, the x-interecpts are -3 and 1.

El número decimal que no es un decimal periódico es dado por:

B. [tex]\frac{11}{400}[/tex].

Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.

La conversión de las fracciones para decimales són:

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(D) 200 DVD players were repaired in the first year.

Given:

The DVD player shipped 960 players last month

There is a record that out of every 24 players, the 5 would be repaired.

So we need to find the number of DVD players that were repaired in these 960 players.

So,

[tex]\frac{960*5}{24} \\=200[/tex]

Therefore, (D) 200 DVD players were repaired in the first year.

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The question you are looking for is here:

A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were repaired during the first year of ownership. How many of the 960 DVD players were repaired in the first year?

A: 40

B: 120

C: 192

D: 200

Evaluating the given expressions and inequalities, we have;

[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]

12) (8•a - 5•b) - 2•(a + b) = 4

[tex] 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]

[tex] 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]

[tex] 16) \: x \geq 11\frac{2}{3} [/tex]

17) k > 9

18) v > 9

20) m ≤ 16

The given expressions are;

[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right)[/tex]

Where x = 4, and y = 6, we have;

[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4[/tex]

Therefore;

[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]

12) (8•a - 5•b) - 2•(a + b)

Where a = 3 and b = 2, we have;

(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4

Therefore;

[tex]13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} [/tex]

Where a = 7, and p = 6, we have;

[tex] \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 [/tex]

Therefore;

[tex] \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]

[tex]14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } [/tex]

Where m = 5, and n = 6, we have;

[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 [/tex]

Therefore;

[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]

[tex]16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} [/tex]

Which gives;

[tex] \frac{7}{6} \times 10 \leq x [/tex]

[tex] \mathbf{ \frac{35}{3} }\leq x [/tex]

[tex] x \geq 11\frac{2}{3} [/tex]

17) 20 < k + 11

Therefore;

k > 20 - 11 = 9

18) 6•v > 54

v > 54 ÷ 6 = 9

Therefore;

[tex]20) \: 8 \geq \mathbf{ \frac{m}{2}} [/tex]

Therefore;

2 × 8 = 16 ≥ m

Which gives;

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Answer:

Domain:[-4,∞)

Range:[0, ∞)

Thus, choice C is the exact answer

The simplification of the polynomial expression will give 3x² - 20x + 8.

The polynomial expression is given as:

(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)

= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7

Then collect like terms

= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19

= 3x² - 20x + 8.

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Answer:

The answer to your question is P=56

Step-by-step explanation:

P=7a=7·8=56

I hope this helps and have a good day!

Answer:

[tex]\frac{9\pi }{4}[/tex] inches

Step-by-step explanation:

I suppose they are asking you for the length of the red part.

18[tex]\pi \\[/tex] * [tex]\frac{45}{360}[/tex] = [tex]\frac{9\pi }{4}[/tex] inches

Answer:

L = 7.07 in

Step-by-step explanation:

L = arc lenght

[tex]L=\frac{\pi (45)(9)}{180} =2.25\pi =7.07in.[/tex]

Hope this helps

The lifetime of the batteries in a package is 14.31 hours which exceeds that value for only 5% of all packages.

Give sample mean of 13 hours and standard deviation of 1 hour and sample size is 9.

We have to apply t test in this because the value of n which is sample size is less than 30.

We have been given the p value of the required mean so we have to find the t value for this with degree of freedom (9-1)=8

t value=2.306.

We know that

t=X bar-μ/s/[tex]\sqrt{n}[/tex]

s/[tex]\sqrt{n}[/tex]=1/[tex]\sqrt{3}[/tex]=0.57

Put all the values in the above formula to calculate required mean.

2.306=X bar-13/0.57

X bar=1.31442+13

=14.31442

after rounding off we get

X bar=14.31

Hence the lifetime of the batteries is 14.31 for which  the percentage exceeds 5%.

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Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

For the given question,

A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.

It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.

Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,

[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]

⇒ [tex]E(X)=\infty[/tex]

Consider the following example,

You throw a coin until it lands tails.

Let n be the number of heads

Then number of heads can be found by, 2ⁿ

Now, the expected value function is

[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]

⇒ [tex]E(X)=\infty[/tex]

Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.

Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

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The probability that a male is selected, then a female is 0.26

The probability that a female is selected, then a male is 0.26

The probability that two males are selected is 0.18

The probability that two females are selected is 0.30.

The probability that no males are selected is 0.30.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26

The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26

The probability that two males are selected = (11/25) x (10/24) = 0.18

The probability that two females are selected = (14/25) x (13 / 24) = 0.30

The probability that no males are selected =  (14/25) x (13 / 24) = 0.30

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Using the hypergeometric distribution, it is found that there is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the parameters are given as follows:

N =A + B = 54, k = 4, n = 4.

The probability of getting exactly two winning numbers with one ticket is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,54,4,4) = \frac{C_{4,2}C_{50,2}}{C_{54,4}} = 0.0232[/tex]

There is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.

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The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.

The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.

Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.

Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

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The projection discussed are the isometric and the orthographic projection.

The isometric projection is how the object look to the eyes when seen from a distance. It should be noted that orthographic projection give the actual measurements of the object.

The isometric drawing is through 100% true measurement of the height, width, and the depth.

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Answer:

OA

Step-by-step explanation:

because it only got a y parameter for each x

Answer:

Option A. (2,4),(3,9),(4,16),(5,25)