Find the missing length indicated x=

Answer:You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Alvin paddled for 3 hours with a 7 -km/h current to reach a campsite. The return trip against the same current took 10 hours. Find the speed of the boat in still water. Alvin paddled for 3 hours with a 7 -km/h current to reach a campsite.

Step-by-step explanation:

The most reasonable temperature for a snowy day is given as follows:

C. -6°C

Considering that it snows, the temperature is either negative or very low positive, as snow only happens on temperatures close to freezing (like 2º C) or negative.

17ºC and 26ºC are far from cold enough to generate snow, hence the most reasonable temperature for a snowy day is given as follows:

C. -6°C

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The range of the quadratic function f(x) = 2x² + 8x - 5 is: (-∞, -13]

The quadratic function is given as:

f(x) = 2x² + 8x - 5

To determine the range of a quadratic function, we will begin by analyzing the vertex of the parabola.

The vertex of the parabola with equation f(x) = ax²  + bx + c is given by the coordinates (-b/2a, f(-b/2a)).

In the quadratic function f(x) = 2x² + 8x - 5, we have:

a = 2, b = 8, and c = -5.

The x-coordinate of the vertex is -b/2a = -8/(2*2)

= -8/4 = -2.

To find the y-coordinate of the vertex, we substitute x = -2 into the equation:

f(-2) = 2(-2)² + 8(-2) - 5

= 2(4) - 16 - 5

= 8 - 16 - 5

= -13

Therefore, the vertex of the parabola is (-2, -13).

Since the coefficient of the x² term (a = 2) is positive, the parabola opens upwards, indicating that the vertex is the minimum point of the function.

This means that the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -13.

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The slope of the curve  y⁴ = y² - x² is 1 and repeat the process for the second point.

Find the slopes of the curve y⁴ = y² - x² at the given points, we need to differentiate the equation implicitly with respect to x.
Differentiating both sides of the equation with respect to x, we get:
4y³ * (dy/dx) = 2y * (dy/dx) - 2x
Next, we can solve for (dy/dx) by isolating it on one side of the equation:
4y³ * (dy/dx) - 2y * (dy/dx) = -2x
(2y - 4y³) * (dy/dx) = -2x
(dy/dx) = -2x / (2y - 4y³)
Now, substitute the x and y values for each point into the equation to find the slopes at those points.
For example, if one point is (1, 1), we substitute x = 1 and y = 1 into the equation:
(dy/dx) = -2(1) / (2(1) - 4(1)³)
(dy/dx) = -2 / (2 - 4)
(dy/dx) = -2 / -2
(dy/dx) = 1
Repeat the process for the second point, and you will have the slopes of the curve at both points.

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a) The monthly payment of the 20-year mortgage is $394.92 greater than the monthly payment of the 30-year mortgage.

b) The total interest paid over the life of the 20-year loan is $171,307.60 less than the amount of interest paid over the life of the 30-year loan.

The monthly payments and the total interests over the two loan terms can be determined using an online finance calculator.

N (# of periods) = 240 months (20 years x 12)

I/Y (Interest per year) = 6.55%

PV (Present Value) = $349,000

FV (Future Value) = $0

Results:

PMT = $2,612.33

Sum of all periodic payments = $626,960

Total Interest = $277,960

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 6.55%

PV (Present Value) = $349,000

FV (Future Value) = $0

Results:

PMT = $2,217.41

Sum of all periodic payments = $798,267.60

Total Interest = $449,267.60

Comparison of 20-year and 30-year Mortgages:

                                   20 Years      30 Years         Difference

Monthly payments   $2,612.33       $2,217.41        $394.92 ($2,612.33 - $2,217.41)

Total Interest           $277,960    $449,267.60     $171,307.60 ($277,960 - $449,267.60)

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The speed of the plane in still air is 180 mph while that of the wind is 30 mph.

An equation is an expression that shows how numbers and variables are related to each other.

Let a represent the speed of the plane in still air and b represent the speed of the wind.

Against the wind, the plane traveled 175 miles in 1 hour 10 min.

1 hour 10 min = 1 hr + (10/60)hr = 1.167 hr

Hence:

(a - b) = 175/1.167    (1)

Coming back, it spent 50 minutes = (50/60) hr = 0.833 hr

Hence:

a + b = 175 / 0.833   (2)

From both equations:

a = 180, b = 30

The speed of the plane in still air is 180 mph while that of the wind is 30 mph.

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The regression equation for the line is y = 50x - 25. The slope is 50 which means "Amount spent on hair increases by $50 per hour". The predicted cost for 6 hour salon appointment is $275.

The equation of fit is defined generally as :

slope = (75 - 25)/(2 - 1) = 50

Taking a pair of (x, y ) values : (2, 75)

75 = 50(2) + c

75 = 100 + c

c = -25

Hence, the fit equation is :

B.)

The slope interpretation means that the amount spent for every one hour increase is $50

Hence, the slope interpretation

C.)

Cost of 6 hours hair salon

y = 50(6) - 25

y = 300 - 25

y = 275

Hence, the cost would be $275

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Answer:

9557.3 in.³

Step-by-step explanation:

V = (1/3)Bh

V = (1/3)(32 in. × 32 in.)(28 in.)

V = 9557.3 in.³

Answer:

12/5

Step-by-step explanation:

We know that tanθ = opposite/adjacent. Opposite means the side that is opposed to θ. Adjacent is the side between the right angle and θ.

Therefore, tan67° means finding the ratio of the side that is opposed to 67° (which is 12) and the side that is between 90° and 67° (which is 5). Therefore,

[tex]\displaystyle{\tan 67^{\circ} = \dfrac{12}{5}}[/tex]

Answer:

The center of the circle is (5,0) and the radius is 9.

Step-by-step explanation:

The center of the circle is (5,0) and the radius is 9.

The probabilities of rolling each number on a fair die based on the given results are: 1 (12%), 2 (16%), 3 (25%), 4 (18%), 5 (15%), and 6 (24%).

To find the probability of getting each number (1, 2, 3, 4, 5, and 6) when rolling a fair die, we need to calculate the frequency of each number and divide it by the total number of rolls, which in this case is 100.

From the provided results, we can see the following frequencies for each number:

Number 1: 12 occurrences

Number 2: 16 occurrences

Number 3: 25 occurrences

Number 4: 18 occurrences

Number 5: 15 occurrences

Number 6: 24 occurrences

To calculate the probability of each number, we divide the frequency of each number by the total number of rolls (100):

Probability of getting 1: 12/100 = 0.12 or 12%

Probability of getting 2: 16/100 = 0.16 or 16%

Probability of getting 3: 25/100 = 0.25 or 25%

Probability of getting 4: 18/100 = 0.18 or 18%

Probability of getting 5: 15/100 = 0.15 or 15%

Probability of getting 6: 24/100 = 0.24 or 24%

It is important to note that these probabilities are specific to the data provided and may not perfectly represent the true probabilities of rolling each number on a fair die unless the sample is representative of the entire population of possible rolls.

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Answer:

Rounded to the nearest hundred: 3,600

Rounded to the nearest ten: 3,640

Rounded to the nearest thousand: 4,000

Rounded to one significant figure: 4,000

Step-by-step explanation:

Rounding to the nearest---

One: 3,640

Ten: 3,640

Hundred: 3,600

Thousand: 4,000

Hope this helps!

Answer:

4n²(7n-10)(n+2)

Step-by-step explanation:

The first step is to factor out a 4n² or take common from each term:

The next step is to factor 7n² + 4n - 20. We can do this by grouping:

Therefore, the complete factorization is:

The volume of the pyramid with a square base which has an edge length of 2 cm and a measure of an angle BAC is 45° is equal to 4.8 cm³.

In mathematics 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m³, cm³, in³ etc.

A pyramid's edge length is 2 cm.

The bottom is square.

Base area = (2)²

A is the center of the square base B is the apex of the right triangle BCA.

m∠BAC = 45°

m∠ABC = 45°

AC = BC

AC length = 3.6 cm

BC height = 3.6 cm

Volume (pyramid) = (1 ÷ 3) × base area × height

Volume (pyramid) = (1 ÷ 3) × (2)² × 3.6

Volume (pyramid) = 4.8 cm³

Therefore, the dimension of a pyramid with only a square base, a 2 cm edge length, and a BAC angle of 45° is 4.8 cm³.

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Answer: *11* is the correct answer.

Step-by-step explanation:

To find *range*, use the *formula*,

 *Range= Highest value - Lowest value*

From the given data, we can see that, the *highest value* is *13* and *lowest value* is *2*. So, *13-2=11*.



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The correct answer is Amy's Compliance Adherence percentage (CA%) is approximately 66.67%.

To calculate Amy's CA% (Compliance Adherence percentage), we need to determine the number of intervals she actually worked compared to the total number of intervals scheduled.

Total intervals scheduled: 12 intervals

However, there were two incidents that affected her adherence:

Technical Issue: Amy experienced a technical issue during her first interval, resulting in a 15-minute disruption. As Arise Technical Support issued an individual waiver, this interval is not counted as non-adherent.

Interval affected: 1

Waived interval: 1

Missed Intervals: Amy completely missed three intervals in a row due to mistakenly looking at her schedule incorrectly. These intervals count as non-adherent.

Intervals affected: 3

To calculate her CA%:

Total intervals worked = Total intervals scheduled - Waived intervals - Non-adherent intervals

Total intervals worked = 12 - 1 (waived) - 3 (non-adherent)

Total intervals worked = 8

CA% = (Total intervals worked / Total intervals scheduled) * 100

CA% = (8 / 12) * 100

CA% = 66.67%

Therefore, Amy's Compliance Adherence percentage (CA%) is approximately 66.67%.

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Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

Step-by-step explanation:

The properties used in each step of solving the linear equation are as follows:

Step 1: To isolate the variable term on one side of the equation, the property used is subtraction property of equality. Subtracting 5 from both sides of the equation maintains the equality.

Step 2: To solve for x, the property used is division property of equality. Dividing both sides of the equation by 4 gives the value of x.

Step 3: The expression x = 1/2 represents the final solution of the equation. This is not necessarily a specific property, but rather the result of performing the previous operations correctly.

Therefore, the properties used in each step are as follows:

Step 1: Subtraction property of equality.

Step 2: Division property of equality.

Step 3: Representation of the solution.

Answer:

41 3/10

Step-by-step explanation:

solved with wolfram alpha.

The population of New Jersey in 2045 is (b) 10475

from the question, we have the following parameters that can be used in our computation:

The table of values

Using the least squares, we have the following summary

The regression equation is

y = mx + b

Where

m =  SP/SSX = 18640/437.5 = 42.60571

b = MY - bMX = 9326 - (42.61*17.5) = 8580.4

So, we have

y = 42.61x + 8580.4

In 2045, we have

y = 42.61 * 45 + 8580.4

y = 10497.85

Hence, the prediction is (b) 10475

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The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

106.78 g

Step-by-step explanation:

For lead, d = 11.33 g/cm³.

V = πr²h

m = Vd

m = π × (1 cm)² × 3 cm × 11.33 g/cm³

m = 106.78 g

To determine whether the normal curve can be used as an approximation to the binomial probability in this scenario, we need to verify the necessary conditions:

1. The number of trials, n, is sufficiently large.

2. The probability of success, p, is not extremely close to 0 or 1.

Let's check these conditions:

1. The number of trials, n, is 149, which is reasonably large.

2. The probability of success, p, is given as 2%. To check if p is not extremely close to 0 or 1, we can calculate np and n(1 - p) and check if both values are greater than or equal to 5.

np = 149 * 0.02 = 2.98

n(1 - p) = 149 * (1 - 0.02) = 146.02

Since both np and n(1 - p) are greater than or equal to 5, the condition is satisfied.

Therefore, both conditions necessary for using the normal curve as an approximation to the binomial probability are satisfied in this case.

We can approximate the binomial probability of more than 39 houses losing power once a year using the normal distribution.

Answer:

4x - xy + 46

Step-by-step explanation:

sum the first 2 expressions

3x + 2xy - 22 - x + 7xy + 11 ← collect like terms

= (3x - x) + (2xy + 7xy) + (- 22 + 11)

= 2x + 9xy + (- 11)

= 2x + 9xy - 11

now subtract this sum from the third expression

6x + 8xy + 35 - (2x + 9xy - 11) ← distribute parenthesis by - 1 )

= 6x + 8xy + 35 - 2x - 9xy + 11 ← collect like terms

= (6x - 2x) + (8xy - 9xy) + (35 + 11)

= 4x + (- xy) + 46

= 4x - xy + 46

Answer:

17[tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]

simplifying the given radicals

[tex]\sqrt{45}[/tex]

= [tex]\sqrt{9(5)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]

= 3[tex]\sqrt{5}[/tex]

-----------------

[tex]\sqrt{20}[/tex]

= [tex]\sqrt{4(5)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex]

= 2[tex]\sqrt{5}[/tex]

------------------

Then

5[tex]\sqrt{45}[/tex] + 3[tex]\sqrt{20}[/tex] - 4[tex]\sqrt{5}[/tex]

= 5(3[tex]\sqrt{5}[/tex]) + 3(2[tex]\sqrt{5}[/tex]) - 4[tex]\sqrt{5}[/tex]

= 15[tex]\sqrt{5}[/tex] + 6[tex]\sqrt{5}[/tex] - 4[tex]\sqrt{5}[/tex] ← collect like radicals

= 21[tex]\sqrt{5}[/tex] - 4[tex]\sqrt{5}[/tex]

= 17[tex]\sqrt{5}[/tex]

Answer:

S = π(2²) + 2π(2)(6) + π(2²) + π(2)(10)

= (4 + 24 + 4 + 20)π = 52π = 163.36

Letting π = 3.14, S = 52(3.14) = 163.28

The correct answer is C.

Answer:The slope of a line is its vertical change divided by its horizontal change, also known as rise over run. When you have 2 points on a line on a graph the slope is the change in y divided by the change in x. The slope of a line is a measure of how steep it is.

Step-by-step explanation:

The answer is:

undefined

Work/explanation:

We can use the slope formula to find the slope, but we notice something - the x co-ordinates of both points are identical. Whenever this phenomenon occurs, we understand that the line that passes through the points is vertical. That means its run is 0 (remember that Slope : rise/run) so whatever the rise is, we'll just have rise/0, which is an operation that cannot be done. So in this case, the slope's undefined.

Hence, the slope of the line which passes through (3,-2) and (3,4) is undefined.

The correct option is the second one, this function does not have an inverse.

A function y  = f(x) has in inverse only if the function is one-to-one.

That means that each output is linked to only one input.

In this case, we have an absolute value function:

y = |x - 2|

Notuice that if x = -2

y = |- 2 - 2| =4

And if x = 6

y = |6 - 2| = 4

So two inputs give the same outputs, thus, this function is not one-to-one, so it does not pass the horizontal line test, then it does not have an inverse.

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The functions that have a maximum and are transformed to the left and down of the parent function f(x) = x^2 are options O and Q.

To identify functions that have a maximum and are transformed to the left and down of the parent function f(x) = x^2, we need to analyze each of the given functions and determine their characteristics. Let's go through each option:

Option O: p(x) = 14(x + 7)^2 + 1
This function is a transformation of the parent function f(x) = x^2. It has a maximum point because the coefficient in front of the squared term is positive. However, it is transformed to the left by 7 units and down by 1 unit due to the shift in the parentheses. Therefore, option O satisfies the conditions.

Option Q: q(x) = -5(x + 10)^2 - 1
Similar to option O, this function also has a maximum point as the coefficient in front of the squared term is negative. It is transformed to the left by 10 units and down by 1 unit. Thus, option Q satisfies the given conditions.

Option S: s(x) = (x - 1)^2 + 0.5
This function is the parent function f(x) = x^2 with a vertical shift upward by 0.5 units. It does not have a maximum point or any horizontal or vertical transformations to the left or down. Hence, option S does not meet the requirements.

Option G: g(x) = 2x^2 + 10x - 35
This function is the parent function f(x) = x^2 multiplied by a positive constant (2). It does not have any horizontal or vertical transformations to the left or down. Therefore, option G does not satisfy the conditions.

Option T: t(x) = -2^2 - 4x - 3
This function is a linear function, not a quadratic one. Therefore, it does not have a maximum point or any transformations relative to the parent function f(x) = x^2. Thus, option T does not meet the requirements.

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Answer:

The function r is neither even nor odd.

The function s is even.

The function g is even.

The function h is neither even nor odd.