Which ordered pair is a solution of the equation?
7x – 2y = -5

The smallest possible angle that the path of the plane could make with the ground is 9.3 degrees to 1 decimal place.

To find the smallest possible angle that the path of the plane could make with the ground, we need to use trigonometry.

Let's assume that

We know that the height reached by the plane is 8 km, which means that:

tan θ = 8 / d

We also know that the distance traveled by the plane should be in the range 44 km to 49 km. This means that:

44 ≤ d ≤ 49

To find the smallest possible angle θ, we need to find the largest possible value of d that satisfies the above inequality.

tan θ = 8 / 49

θ = arc tan (8 / 49)

θ = 9.2726

θ ≈ 9.3°

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A false statement could be that

"the maximum height attained by the diver was 20 feet

Using the z-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

\(H_0: p \leq 0.5\)

\(H_1: p > 0.5\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

For this problem, the parameters are:

\(n = 48, \overline{p} = \frac{37}{48} = 0.7708, p = 0.5\)

The value of the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.7708 - 0.5}{\sqrt{\frac{0.5(0.5)}{48}}}\)

\(z = 3.75\)

Considering a right-tailed test, as we are testing if the proportion is greater than a value, with a significance level of 0.05, the critical value for the z-distribution is \(z^{\ast} = 1.645\).

Since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

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Answer:

The expression simplified is a^2

Step-by-step explanation:

Here, we are interested in writing the product as a single value.

We have; a^5 • a^-3

This is same as a^5 * a^-3

We proceed here using the first law of indices;

It would result to a^5 * a^-3 = a^(5-3) = a^2

Answer:

Step-by-step explanation:

The formula to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

The formula presented derived from the formula for the circumference of a circle, which is C = 2πr. By rearranging the equation and isolating the radius (r) on one side, we get r = C/(2π).

So, if the circumference (C) of a circle is 18 centimeters, you can use the formula r = C/(2π) to find the radius (r). Plugging in the given value for the circumference (C), we get:

r = 18/(2π)

Simplifying the equation gives:

r = 9/π

Therefore, the radius (r) of the circle is 9/π centimeters.

In conclusion, the formula you can use to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

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Answer:

V = 6 ft^3

Step-by-step explanation:

V = length * width * height

V = 1* 2* 3

V = 6 ft^3

Answer:

6 ft³

Step-by-step explanation:

V = lwh

V = 1 × 2 × 3

V = 6 ft³

This indicates that the cutoff value for the amount of minutes before contacting the consumer is 674 minutes, rounded to the closest minute.

Quartiles are three numbers that divide sorted data into four equal portions with an equal amount of observations each. A quantile is a sort of quantile. The first quartile is sometimes known as the lower quartile or Q1. Second quartile: Also known as the median or Q2. Third quartile: Also known as the higher quartile or Q3.

Here,

To find the upper fence, we need to calculate the following statistics:

Q1 (first quartile), Q2 (median), and Q3 (third quartile) of the data

Interquartile range (IQR), which is the difference between Q3 and Q1

Upper fence, which is Q3 + 1.5 * IQR

First, we need to order the data in ascending order:

339, 350, 358, 388, 430, 458, 458, 463, 480, 489, 501, 536

Next, we can find the quartiles:

Q1 = 388

Q2 = 458

Q3 = 501

IQR = Q3 - Q1 = 501 - 388 = 113

Finally, we can calculate the upper fence:

Upper fence = Q3 + 1.5 * IQR = 501 + 1.5 * 113 = 674

This means that the cutoff point for the number of minutes at which the customer should be contacted is 674 minutes, rounded to the nearest minute.

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The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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The differentials of the given functions are:

dy/dt = (1/2)√(3t) sec^2(√(3t)) dt

dy/dv = -v/2 + v

To find the differential of the function y = tan(sqrt(3t)), we can use the chain rule. Let u = sqrt(3t). Applying the chain rule, we have dy/dt = dy/du * du/dt.

First, we find dy/du by taking the derivative of tan(u), which is sec^2(u). Then, we find du/dt by taking the derivative of sqrt(3t), which is (1/2)√(3t). Multiplying these two derivatives together, we get dy/dt = (1/2)√(3t) sec^2(√(3t)) dt.

To find the differential of the function y = 4 - v^2/4 + v^2, we need to take the derivative with respect to v. The first term, 4, does not depend on v, so its derivative is 0.

For the second term, -(v^2/4), we use the power rule for differentiation. The derivative of v^2 is 2v, and dividing by 4 gives -(v/2).

For the third term, v^2, the derivative is 2v.

Combining these derivatives, we get dy/dv = -v/2 + v.

The differentials of the given functions have been calculated as dy/dt = (1/2)√(3t) sec^2(√(3t)) dt and dy/dv = -v/2 + v. These differentials represent the rate of change of the functions with respect to the respective variables.

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The differential of y = tan(sqrt(3t)) is dy/dt = (1/2)(3t)^(-1/2)(3)(sec^2(sqrt(3t))). The differential of y = 4 - v^2/4 + v^2 is dy/dv = 3v/2.

To find the differential of each function, we will differentiate them with respect to the independent variable.

Let's use the chain rule to differentiate this function.

Therefore, the differential of y = tan(sqrt(3t)) is dy/dt = (1/2)(3t)^(-1/2)(3)(sec^2(sqrt(3t))).

Let's differentiate this function using the power rule and the sum/difference rule for derivatives.

Therefore, the differential of y = 4 - v^2/4 + v^2 is dy/dv = 0 - v/2 + 2v = 3v/2.

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The x-coordinate of vertex of parabola is,

Determine the vertex of parabola.

Substitute 5 for x in the function to obtain the y-coordinate of vertex.

So vertex of parabola is (5,1).

Determine the roots of the function.

Thus function intrsects the x axis at (2.764,0) and (7.236,0).

The function intersect the y-axis at (0,-4).

Plot the function on graph.

1. The probability of selecting exactly one tank with high-viscosity material is 0.

2. The probability of selecting at least one tank with high-viscosity material is 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.

1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.

2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.

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Given the data X₁ = 1, X2 = 4, X3 = 5, X4 = 8, X5 = 10, evaluate Z(X, +5). 1=2Z(X, +5) refers to the standard score of the score X, if it is taken as the new mean of the distribution.

In other words, Z(X, +5) represents how many standard deviations X is from the new mean, which is 5. To evaluate Z(X, +5), we first need to calculate the mean and standard deviation of the data set:Mean = (1+4+5+8+10)/5 = 28/5 = 5.6Standard deviation.

To calculate the standard deviation, we use the formula: σ = √[Σ(X-μ)²/N]where Σ means "the sum of," X is the data point, μ is the mean, and N is the sample size. Plugging in the values: σ = √[(1-5.6)² + (4-5.6)² + (5-5.6)² + (8-5.6)² + (10-5.6)² / 5] = √[79.84/5] = √15.968 = 3.994 .

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Answer:

what are the answer choices. List them out and do the process of elimination and we could go from there ig

Step-by-step explanation:

The equation for the nth term of the arithmetic sequence is  -6n + 14 and the found 50 is -286.

An arithmetic sequence is a series of numbers that are ordered and share a common difference between each succeeding term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6.

Arithmetic is the branch of mathematics that studies numbers by performing various operations on them. A sequence is a numerically ordered list. The three dots indicate that the pattern should be continued. The difference is six.

a + d(n - 1)

a = 8 (first term)

d = -6 (common difference)

8 - 6(n - 1)

= 8 - 6n + 6

= -6n + 14

Find a 50:

-6(50) + 14

= -300 + 14

= -286

Therefore, the equation for the nth term of the arithmetic sequence is  -6n + 14.

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To find the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days, we use the simple interest formula as follows:

Simple Interest = (P × R × T)/100Where:P = Principal or amount borrowedR = Rate of interest per annumT = Time in years or fraction of a year110 days ÷ 360 days = 0.3056 (time as a fraction of a year)The rate of interest, 10(1/3)% is equal to 10 + (1/3) percent = 10.33% per annum in decimal form = 0.1033Substituting the values we have into the formula,Simple Interest = (P × R × T)/100= (3,290 × 0.1033 × 0.3056)/100= $100.68 (rounded to the nearest cent)

Therefore, the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68.

A credit union loan is a type of personal loan that can be used for a variety of purposes. One of the most common reasons people take out credit union loans is to purchase big-ticket items like a new computer system. When you take out a loan, you must pay back the amount borrowed plus the interest charged by the lender. The interest rate is usually expressed as a percentage of the amount borrowed and is charged for a specific period of time known as the loan term. Simple interest is a method of calculating interest that is charged only on the principal amount borrowed.

It does not take into account the interest that has already been paid. Simple interest is calculated by multiplying the principal amount borrowed by the interest rate and the length of the loan term. The answer is more than 100 words.The interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68. Therefore, he would pay $3,290 + $100.68 = $3,390.68 in total to the credit union over the loan term. It is important to note that when rounding dollar amounts to the nearest cent, amounts that end in .50 or higher are rounded up to the next highest cent, while amounts that end in .49 or lower are rounded down to the next lowest cent. In this case, $100.6847 would be rounded up to $100.68. In conclusion, the interest charged on a loan can significantly increase the total amount that must be repaid, making it important for borrowers to understand how interest is calculated and the terms of their loan.

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As the spacing between joists increases, the maximum span for any board size will B. decrease only. This is because the wider the spacing between joists, the more weight and pressure will be placed on the boards that are spanning the gap between them.

This means that the boards will need to be stronger in order to support the weight without bending or breaking.
If the boards are not strong enough, they may sag or bow under the weight, which can create safety hazards or damage to the structure. Therefore, it is important to use the appropriate board size and spacing between joists for any given application in order to ensure structural integrity and safety.
In summary, increasing the spacing between joists will result in a decrease in the maximum span for any board size, as the boards will need to be stronger in order to support the weight and pressure. It is important to choose the right board size and joist spacing to maintain the structural integrity and safety of the building or structure.

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The probability that A selects the red ball is 3/6 = 1/2.

Given that an urn contains 3 red and 7 black balls. Players A and B alternate withdrawing balls from the urn consecutively until a red ball is selected. We need to find the probability that A selects the red ball.Let us assume that A draws first and B draws next. The probability that A selects the red ball is given as follows:Probability of A selecting the red ball = (number of favorable outcomes) / (total number of outcomes)Number of favorable outcomes = 3Total number of outcomes = 3 + 7 = 10

The probability that A selects the red ball is given as:P(A selects the red ball) = (number of favorable outcomes) / (total number of outcomes)P(A selects the red ball) = 3/10Now, let B draw first and A draws next. In this case, A can select the red ball only if B fails to select the red ball. Hence, the probability that A selects the red ball is given as:P(A selects the red ball) = (probability that B does not select the red ball and A selects the red ball)P(A selects the red ball) = (7/10) * (3/6)P(A selects the red ball) = (7/10) * (1/2)P(A selects the red ball) = (7/20)Therefore, the probability that A selects the red ball is 3/10 when A draws first and 7/20 when B draws first. Since players A and B alternate withdrawing balls, the probability that A selects the red ball is the weighted average of these two probabilities.P(A selects the red ball) = (1/2) * (3/10) + (1/2) * (7/20)P(A selects the red ball) = (3/20) + (7/40)P(A selects the red ball) = (9 + 7) / 40P(A selects the red ball) = 16 / 40P(A selects the red ball) = 4 / 10P(A selects the red ball) = 2 / 5.That the probability that A selects the red ball is 2/5.

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Answer:

12 or 1/12

Step-by-step explanation:

Looking at this equation it tells us that the spinner has  12  spaces that are labeled 1-12. And its asking to use the numbers to find the probability of the multiples of both 3 and 4.

So list them out:

3: 0, 3, 6, 9, 12, 15, 18 and so on

4: 0, 4, 8, 12,  20, 24 and so on

So as you can see 12 is a multiple of both numbers. So that is your answer. Hope this helped :)

Answer:

On a coordinate plane, a straight line crosses the y-axis at (0, 0)

Step-by-step explanation:

Required

Which represents a proportion

For a graph to represent a proportion, the line of the graph must pass through the origin (i.e. it must pass through (0,0))

From the list of options, only option (a) passes through (0,0).

Other options (b - d) pass through points other than the origin.

Hence, (a) is correct

Answer:

a + 7

Step-by-step explanation:

x^2 + 2x - 8. on [5,a]

(f(a)-f(5))/( a - 5 )

(( a^2 + 2a - 8 ) - 27 ) / a - 5

( a^2 + 2a - 35 ) / a - 5

(a - 5)(a + 7) / a - 5

a + 7

The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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Answer:

Sunrise Sharks

Step-by-step explanation:

I added all of the numbers then divided them by 5 since there are 5 swim times provided. Have a nice day!

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Answer:

D. 490

Step-by-step explanation:

If you multiply all you get 490 D

Answer:

255.00

Step-by-step explanation:

425.00 x .60 = 255

Answer:

Step-by-step explanation:

-x+3 > 5  0r 4x > -8

-x > 2 or x > -8/4

x< -2 or x > -2

The product of vectors a and b is approximately 5.292.

To find the product of two vectors a and b, we need to use the dot product formula which is a · b = |a| |b| cosθ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
In this case, we are given that |a| = 2 and |b| = 7, and the angle between a and b is 2/3. We can use this information to find cosθ as follows:
cosθ = cos(2/3) ≈ 0.378
Now, we can substitute the values into the formula:
a · b = |a| |b| cosθ
a · b = 2 * 7 * 0.378
a · b ≈ 5.292
Therefore, the product of vectors a and b is approximately 5.292.

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Answer:

x = 8

Step-by-step explanation:

Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Secant:  a straight line that intersects a circle at two points

Tangent: a straight line that touches a circle at only one point

Given:

⇒ x² = 16 · 4

⇒ x² = 64

⇒ x² = √(64)

⇒ x = ±8

As distance is positive, x = 8

Answer:

463×10³

463×1000

=0.463