Does the formula represent a linear or nonlinear function? Explain

Answer:

a) 4ABC such that LA is obtuse

c) AABC such that C is acute

Step-by-step explanation:

An angle is obtuse if it measures more than 90 degrees and acute if it measures less than 90 degrees. In statement a), the angle LA is obtuse, which means it measures more than 90 degrees. In statement c), the angle C is acute, which means it measures less than 90 degrees. These two statements contradict each other because they cannot both be true at the same time.

Answer:

Cells

Step-by-step explanation:

HTH!

y≤−5x−10 and y>x+2 The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.

To graphically solve this system of linear inequalities, we can start by graphing each inequality on the same coordinate system:

First, let's graph the inequality y ≤ -5x - 10. We can start by graphing the line y = -5x - 10, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,-10), and draw a straight line passing through them.

Next, we need to determine which side of the line satisfies the inequality y ≤ -5x - 10. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y ≤ -5x - 10 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:

0 ≤ -5(0) - 10

0 ≤ -10

This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.

Now, let's graph the inequality y > x + 2. We can start by graphing the line y = x + 2, which is the boundary line of the inequality. We can plot two points on this line, say (-2,0) and (0,2), and draw a straight line passing through them.

Next, we need to determine which side of the line satisfies the inequality y > x + 2. We can choose any point on one side of the line, say (0,0), and test it in the inequality. If y > x + 2 is true for (0,0), then that side of the line satisfies the inequality. Otherwise, the other side satisfies the inequality. Testing (0,0), we have:

0 > 0 + 2

This is false, so the side of the line containing the origin does not satisfy the inequality. The other side of the line does.

Now, we can shade the region that satisfies both inequalities. The shaded region is the region that is below the line y = -5x - 10 (including the line itself) and above the line y = x + 2 (excluding the line itself).

The shaded region is shown below:

Graph of y≤−5x−10 and y>x+2

The shaded region satisfies both inequalities and represents the solution to the system of linear inequalities.

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Answer:

a) 0.426 = 42.6% probability that a customer waits less than a second for credit card approval.

b) 0.189 = 18.9% probability that a customer waits more than 3 seconds.

c) The minimum approval time for the slowest 5% of transactions is 5.39 seconds.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

The probability of finding a value higher than x is:

\(P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)

An online retailer has determined that the average time for credit card transactions to be electronically approved is 1.8 seconds.

This means that \(m = 1.8, \mu = \frac{1}{1.8} = 0.5555\)

(a) Use an exponential density function to find the probability that a customer waits less than a second for credit card approval.

This is \(P(X \leq 1)\).

\(P(X \leq 1) = 1 - e^{-0.5555*1} = 0.426\)

0.426 = 42.6% probability that a customer waits less than a second for credit card approval.

(b) Find the probability that a customer waits more than 3 seconds.

This is P(X > 3).

\(P(X > x) = 1 - P(X \leq 3) = 1 - (1 - e^{-0.5555*3}) = 0.189\)

0.189 = 18.9% probability that a customer waits more than 3 seconds.

(c) What is the minimum approval time for the slowest 5% of transactions

This is x for which \(P(X \leq x) = 0.95\)

So

\(P(X \leq x) = 1 - e^{-\mu x}\)

\(0.95 = 1 - e^{-0.5555x}\)

\(e^{-0.5555x} = 0.05\)

\(\ln{e^{-0.5555x}} = \ln{0.05}\)

\(-0.5555x = \ln{0.05}\)

\(x = -\frac{\ln{0.05}}{0.5555}\)

\(x = 5.39\)

The minimum approval time for the slowest 5% of transactions is 5.39 seconds.

Answer:

100% increase

Step-by-step explanation:

0.1 to 0.2

0.1 = 100% (original number)

0.2 - 0.1 = 0.1

0.1 = 100%

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

Step-by-step explanation:

Hello!

Given the variables

X₁: Weight of a safety helmet for racers

X₂: Price of a safety helmet for racers

Note, there is n= 17 observed values for each variable so for all calculations I'll use this number and disregard the 18 mentioned in the text.

a) Scatterplot in attachment.

b) If you look at the diagram it seems that there is a negative linear regression between the price and the weight of the helmets, meaning, the higher the helmet weights, the less it costs.

c) The estimated regression equation is ^Yi= a + bXi

n= 17; ∑Y= 6466; ∑Y²= 3063392; ∑X= 1008; ∑X²= 60294; ∑XY= 367536

Y[bar]= 380.35; X[bar]= 59.29

\(b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{367536-\frac{1008*6466}{17} }{60294-\frac{(1008)^2}{17} } = -30.18\)

\(a= Y[bar]- bX[bar]= 380.35-(-30.18)*59.29= 2169.77\)

The estimated regression equation for the price of the helmets as a function of their weight is:

^Yi= 2169.77 -30.18Xi

I hope it helps!

Answer:

\(12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}\)

Step-by-step explanation:

Answer:

59.5

Step-by-step explanation:

He is asking for angle A

cosA = adjacent/hypotenuse

= 33/65

we'll do shift cos(33/65) = 59.48 to bring A

Answer:

n + 11

Step-by-step explanation:

or you can express it as x = n + 11

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x = − 5Y/4 − 15/2

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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Answer:

(0,-2)

Step-by-step explanation:

Answer:

Solutions below.

Step-by-step explanation:

This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.

To find the x-intercept, we know that y = 0.

Therefore we can substitute y = 0 into the line equation:

\(0 = - \frac{1}{4} x + 2 \\ - \frac{1}{4} x = - 2 \\ x = - 2 \div - \frac{1}{4} \\ = 2 \times 4 \\ = 8\)

Therefore the point of the x-intercept is (8,0).

Likewise to find the y-intercept, we know x = 0.

Therefore we can substitute x = 0 into the line equation:

\(y = - \frac{1}{4} (0) + 2 \\ = 0 + 2 \\ = 2\)

Therefore the point of the y-intercept is (0,2).

Answer:

x-intercept:  (8, 0)

y-intercept:  (0, 2)

Step-by-step explanation:

Given equation:

\(y=-\dfrac{1}{4}x+2\)

The graph intersects the y-axis when x = 0.  

To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:

\(\begin{aligned}x=0 \implies y&=-\dfrac{1}{4}(0)+2\\y&=0+2\\y&=2\end{aligned}\)

Therefore, the coordinates of the point of intersection with the y-axis are:

The graph intersects the x-axis when y = 0.  

To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:

\(\begin{aligned}y=0\implies \-\dfrac{1}{4}x+2&=0\\-\dfrac{1}{4}x&=-2\\x&=8\end{aligned}\)

Therefore, the coordinates of the point of intersection with the x-axis are:

Answer:

The Area of the Sign is 120 square inches.

You mulitply the perimeter by 4.

Also this might be wrong so you might want to double check it lol

Answer:

Step-by-step explanation:

12

Answer:

1/27

Step-by-step explanation:

We can substitute x=0 into the function to get:

The number of bags of sand that has to be used would be 92

diameter = 30 yards

width of path = 5 yards

diameter with path

30 + 2 * 5

= 40 Yd

area of path = area of garden with path - ara of garden

= 3.14 * 40² / 4 - 3.14 * 30² / 4

= 1256 - 706.5

= 549.5

area covered by bag = 549.5 / 6

= 91.58

= 92 bags

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De acuerdo con la información presentada se puede inferir que la relación entre los números y letras es 1b, 2d, 3a, y 4c (opción a)

Los números enteros son todos los números que pertenezcan a la categoría de los números naturales. Adicionalmente, se incluyen sus opuestos negativos incluyendo el número cero (0).

De acuerdo con lo anterior, debemos asociar los números con la forma correcta de escribirlos. Primero debemos tener en cuenta el número que está antes de la coma.

Por ejemplo el primer número solo puede relacionarse con las opciones B y D, debido a que estos comienzan con el 3.

Posteriormente, nos fijamos en el número que está después de la coma que en el caso del primer número sería cuatro mil ciento cinco millonésimos. Entonces el número 1, se asociaría con la letra b.

Entonces la opción 2 se debe relacionar con la opción restante que dice tres, antes de la coma, es decir, la opción d.

En cuanto a las opciones que comienzan con el 32, antes de la coma realizamos el mismo procedimiento de fijarnos en el número que está después de la coma. En el caso del número 3. tiene el número cuatrocientos un mil cinco millonésimas después de la coma, entonces sería la opción A.

Por último, la única opción que queda sería la opción C que se relaciona con el número 4.

Nota: Esta pregunta está incompleta debido a que hay información faltante. Aquí está la información faltante:

1) 3,04105

2) 3,4105

3) 32,401005

4) 32,040105

A) Treinta y dos enteros con cuatrocientos un mil cinco millonésimos.

B) Tres enteros con cuatro mil ciento cinco millonésimos.

C) Treinta y dos enteros con cuarenta mil ciento cinco millonésimos-

D) Tres enteros con cuatro mil ciento cinco diezmilésimos.

Opciones de respuesta:

A. 1b, 2d, 3a, 4c

B. 1a, 2d, 3b, 4c

C. 1a, 2c, 3b, 4d

D. 1b, 2a, 3d, 4c

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The length οf the guide wire frοm the grοund tο the palm tree οf the given trigοnοmetric functiοn  is apprοximately 7.8 feet(οptiοn b)

In mathematics , trigοnοmetric functiοns which is alsο called circular functiοns οr angle functiοns are thοse which are real functiοns that relate the angle οf a right triangle tο the ratiοs οf twο side lengths.

We here use the trigοnοmetric functiοn cοs tο sοlve the prοblem.

cοs angle =(adjacent side)/hypοtenuse

cοs 40° = 6/x

length(x)= 6/cοs40°

length= 6/0.766044

length= 7.8

Hence, the length is apprοximately 7.8 feet.

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Roland's percent error is approximately 3.889%.

This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.

The positive sign indicates that Roland's measured value is slightly lower than the actual value.

To calculate Roland's percent error, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100

Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:

Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100

Simplifying the expression within the absolute value:

Percent Error = (|-0.007| / 0.180) \(\times\) 100

Since the absolute value of -0.007 is 0.007, we have:

Percent Error = (0.007 / 0.180) \(\times\) 100

Calculating the division:

Percent Error = 0.03889 \(\times\) 100

Percent Error = 3.889%.

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The graph that represents the function f(x) = -2sin(x) +37 is graph D

The graph of the function f(x) = -2sin(x) +37 is a sinusoidal wave with an amplitude of 2 and a vertical shift of 37. The negative sign in front of the sine function indicates that the wave is inverted or reflected about the x-axis.

In this graph, the maximum value of the function is 39 (when x = 0) and the minimum value is 35 (when x = π).

In conclusion, the graph that represents the function f(x) = -2sin(x) +37 is graph D

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Answer:

Step-by-step explanation:

Calculate the total hours used: We add up the hours used each year to find the total hours used:

2,800 + 1,400 + 1,500 + 2,500 + 2,300 + 2,000 = 12,500

Calculate the total depreciation: We subtract the residual value from the cost to find the total depreciation:

$219,000 - $19,500 = $199,500

Calculate the annual depreciation expense: We divide the total depreciation by the number of years to find the annual depreciation expense:

$199,500 / 6 = $33,250

Calculate the depreciation expense per hour: We divide the annual depreciation expense by the estimated total hours to find the depreciation expense per hour:

$33,250 / 12,500 = $2.66

So the depreciation expense per hour is $2.66.

Calculate the depreciation expense for each year: We multiply the hours used each year by the depreciation expense per hour to find the depreciation expense for each year:

Year 1: 2,800 * $2.66 = $7,448

Year 2: 1,400 * $2.66 = $3,724

Year 3: 1,500 * $2.66 = $3,990

Year 4: 2,500 * $2.66 = $6,650

Year 5: 2,300 * $2.66 = $6,118

Year 6: 2,000 * $2.66 = $5,320

So the depreciation expense for each year is:

Year 1: $7,448

Year 2: $3,724

Year 3: $3,990

Year 4: $6,650

Year 5: $6,118

Year 6: $5,320

Answer:  you would need to cross the bridge 5 times

Step-by-step explanation:

costing a total of $42.50 for each option.

hope this helps

Answer: anita's age= 7 yrs

basilio age = 2.5 yrs

Step-by-step explanation:

Let age of anita and basilio be x

since anita is 4 1/2 years older than basilio

thereforce basilio age=x - 4.5

ATQ,

=>3x + 6(x-4.5) = 36

=>3x + 6x - 27=36

=>9x = 63

=>x=7

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

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Answer:

Wait, the vector from despicable me or the math vector?

Step-by-step explanation:

If its the math vector than here: The correct answer is a vector

Answer:

p=2

Step-by-step explanation:

4p+2≤10

    -2   -2

4p≤8

divide by 4

p≤2

Answer:

p ≤ 2

Step-by-step explanation:

Answer:

12.4m

Step-by-step explanation:

In order to solve this equation, we can use the length of a carriage as our unknown value (using the engine is a bit more difficult). The questions says that the whole train: 4 carriages and an engine = 86.8m

If we represent carriage length as 'x', we can write the following equation:

4x (length of 4 carriages) + (2/3)x (length of engine as it is 2/3 of a carriage) = 86.8m

4x+(2/3)x = 86.8

From here we can combine into one fraction:

\(4x+\frac{2}{3} x=\frac{14}{3}x\)

So now our equation looks like this:

\(\frac{14x}{3}=86.8\)

Now all we need to do is multiply both sides by 3 and then divide both sides by 14 to isolate and solve x:

\(\frac{14x}{3}*3=86.8*3\\ 14x=260.4\\\frac{14x}{14}=260.4/14\\ x=18.6\\\)

Now that we know the carriage length, we can use it to find the engine length:

Engine length = 2/3 Carriage length

\(E=\frac{2}{3}x\\ E=\frac{2}{3} (18.6)\\E = 12.4m\)

Hope this helped!

Length of a carriage = x

Length of four carriages = 86.8 m

Length of each carriage =

\(86.8 \div 4 \: m \\ = \: 21.7 \: m\)

Length of one carriage = 21.7 m

Length of the engine =

\( = \frac{2}{3} x\)

\( = \frac{2}{3} \times 21.7\)

\( = 43.4 \: m\)

\(43.4 \div 3 \: m \\ = 14.4666666667 \: m\)

∴ The length of the engine is 14.4666666667 m .