QUESTIONS: SOLVE FOR X

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9514 1404 393

Answer:

  30x +25y = 148

Step-by-step explanation:

We can use substitution to find the point of intersection of ...

Using the second equation, we can write an expression for y:

  y = 6 -x

Substituting that into the first equation gives ...

  3x +14 = 2(6 -x)

  3x +14 = 12 -2x . . . . . eliminate parentheses

  5x = -2 . . . . . . . . . . . add 2x-14

  x = -0.4 . . . . . . . . . divide by 5

  y = 6 -(-0.4) = 6.4

__

Now, we want an equation for a line through the point (-0.4, 6.4) that is perpendicular to 5x = 6y+1

The perpendicular line will have the coefficients swapped with one of them negated. The constant will accommodate the given point.

  6x = -5y + c

  6(-0.4) +5(6.4) = c = 29.6

The perpendicular line can be written ...

  6x = -5y +29.6

In standard form, the equation is ...

  30x +25y = 148

Answer:

Diffrent between altitude = 14,021 ft

Step-by-step explanation:

Given:

Heighest altitude = 14,309 ft

Lowest altitude = 288 ft

Find:

Diffrent between altitude

Computation:

Diffrent between altitude = Heighest altitude - Lowest altitude

Diffrent between altitude = 14,309 - 288

Diffrent between altitude = 14,021 ft

Answer:

B. Same-side interior angles

Step-by-step explanation:

Angle w and angle x lie on the same side of the transversal that cut across the two parallel lines, and are also within the two parallel lines. They are therefore regarded as same-side interior angles. Same-side interior angles are supplementary.

The table that represents exponential growth is the second table.. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows.

Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.

In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the X's increase by 1, the Ys increase by a multiple of 4.

One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.

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Answer:

What equation?

Step-by-step explanation:

Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

If a point, (x, y) is translated c units to the left, the new coordinate would be

(x - c, y)

Given that point A with coordinates, (3, 4) is translated 4 units left, the new coordinate would be

(3 - 4, 4)

= (- 1, 4)

If a point, (x, y) is reflected across the x-axis, the sign of the x coordinate remains unchanged while the sign of the y coordinate would change. This gives us (x, - y). Thus, if (- 1, 4) is reflected across the x-axis, the new point would be

(- 1, - 4)

If a point, (x, y) is translated c units down, the new point would be (x, y - c)

Thus, if (- 1, - 4) is translated 2 units down, the new point would be (- 1, - 4 - 2)

= (- 1, - 6)

The final coordinate is

(- 1, - 6)

Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

Answer:

Option d: Your friend is wrong, the statement should be revised as "the probability of obtaining a sample mean of 105 or more extreme from a random sample of n = 40 when the true population mean is assumed to be 100."

Step-by-step explanation:

We are given;

Null hypothesis; H0 : μ = 100

Alternative hypothesis; HA : μ ≠ 100

Sample mean; x = 105

Sample standard deviation; s = 10

Sample size; n = 40

p - value = 0.0016

Looking at the options, the first option is wrong because the sample size is not irrelevant her since it's more than 30.

The second option can't be correct because they just told us he is right without giving explanation.

The third option is wrong because 100 is the true population mean and not 150.

Thus we are left with Option D as the correct answer.

Answer:

x=3

(26x+50degreese) = 134 degreese

Step-by-step explanation:

Answer:

49.98

Step-by-step explanation:

Answer:

D

product of 4 and n is the same as 4× n

and it is equal to 4n

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

0.5

Step-by-step explanation:

Given that: An average concentration of 1 coliform bacteria per 20 cc of the river water.

This implies that in 20 cc of the water, it is certain that 1 coliform bacteria would be found. So that:

pr(1 bacteria in 20 cc of water) = 1

i.e the probability of getting 1 bacteria in 20 cc of water is 1.

The probability of the 10 cc sample of water containing 2 coliform bacteria can be determined as:

pr(2 bacteria in 10 cc of water) = \(\frac{1}{2}\)

                                                   = 0.5

The mean monthly rainfall, Rounded to the nearest thousandth, is 2.520 inches.

To determine the mean monthly rainfall, we need to calculate the average of the rainfall values provided in the table. Here is the table:

| Month | Rainfall (in inches) |

|-------|----------------|

| January   | 2.3                

| February  | 1.7                

| March     | 3.2                

| April     | 2.9                

| May       | 2.5                

To find the mean monthly rainfall, we add up the rainfall values for each month and divide the sum by the total number of months. In this case, we have five months:

Mean Monthly Rainfall = (2.3 + 1.7 + 3.2 + 2.9 + 2.5) / 5

Calculating the sum of the rainfall values:

Mean Monthly Rainfall = 12.6 / 5

Dividing the sum by the number of months:

Mean Monthly Rainfall = 2.52

Rounded the result to the nearest thousandth, the mean monthly rainfall is approximately 2.520 inches.

Therefore, the mean monthly rainfall, rounded to the nearest thousandth, is 2.520 inches.

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Answer:

Discrete random variable.

Step-by-step explanation:

Discrete variable:

Countable numbers(0,1,2,3,...)

Continuous variable:

Can assume decimal values, such as 0.5, 2.5,...

Number of bald eagles:

Number of bald eagles is a countable value, either there a 0, 100, 1000,... so it is a discrete random variable.

Answer:

Discrete random variable.

Step-by-step explanation:

Answer: Its B

Step-by-step explanation:

there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

answer is D. None of the above.

To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:

X2 = (n-1)*(s2/σ2)

where n is the sample size, s2 is the sample variance and σ2 is the population variance.

In this case, n = 16, s2 = 3.25 and σ2 = 4

X2 = (16-1)*(3.25/4) = 12.1875

The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

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Answer:

Part D is correct

Step-by-step explanation:

Answer:

y = -5/4x -4

Step-by-step explanation:

slope(m)= -5/4

x1=-4,y1=1

using the formula for one point form

y-y1=m(x-x1)

y-1= -5/4(x-(-4))

y-1 = -5/4x + -5/4 × +4

y - 1 = -5/4x -5

y=-5/4x -5 + 1

y = -5/4x -4.

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After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.

The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted  measurement regarding the distance around the outside of a two-dimensional shape. In this system  the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m

Answer:

77 boxes each

Step-by-step explanation:

1,000/13

Answer:

Step-by-step explanation:

1000/13= 76.9 .... Each girl needs to sell 77 boxes

Answer:

D

Step-by-step explanation:

0.6x17.5 which is 10.5

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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Check the picture below.

Answer:

 \(\dfrac{x^2+8x+8}{2x+4}\\\\\)

Step-by-step explanation:

Simplify:

        \(\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}\)

Multiply the denominator and the numerator of the first term by 2,

                        \(=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}\)

                       \(\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\\)

Answer:

\(x-3\)

Step-by-step explanation:

The area of the flagpole base is \(x^2-6x+9\ \text{yd}\)

where the factor of the equation is the length of the base.

In order to find the length we need to factorize the equation

\(x^2-6x+9\)

\(=x^2-3x-3x+9\)

\(=x(x-3)-3(x-3)\)

\(=(x-3)(x-3)\)

The length of the base of the flagpole is \((x-3)\ \text{yd}\).

The area of a square base is the product of the side lengths.

The length of the base is x - 3

The area is given as:

\(\mathbf{Area =x^2 - 6x + 9}\)

Expand

\(\mathbf{Area =x^2 - 3x - 3x + 9}\)

Factorize

\(\mathbf{Area =x( x- 3) - 3(x - 3)}\)

Factor out x - 3

\(\mathbf{Area =( x- 3) (x - 3)}\)

Express as squares

\(\mathbf{Area =( x- 3)^2}\)

Rewrite the area as:

\(\mathbf{Length^2 =( x- 3)^2}\)

Take square roots of both sides

\(\mathbf{Length =x- 3}\)

Hence, the length of the base is x - 3

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