A puffin leaves a cliff and flies 38 km due east then 54 km due north to an island.
Work out the bearing from the cliff to the island.
Give your answer to the nearest degree.

Answer:

Width=56 yards

length=224 yards

Step-by-step explanation:

let:

Width=x

length= x*4= 4x

perimeter = 2*x + 2*4x

working

[tex](x \times 2) + (4x \times 2) = 560[/tex]

[tex]2x + 8x = 560[/tex]

[tex]10x = 560[/tex]

[tex] \frac{10x}{10} = \frac{560}{10} [/tex]

[tex]x = 56[/tex]

[tex]4x = 56 \times 4 = 224[/tex]

width =56 yards

length = 224 yards

The missing expense values are given as follows:

The missing expenses are obtained applying the proportions in the context of this problem.

The rent expense of $2,400 is 40% of the total expenses, hence the total expenses are given as follows:

0.4x = 2400

x = 2400/0.4

x = $6000.

The utilities expenses are 5% of that, hence:

0.05 x 6000 = $300.

The labor expenses are 15% of the total, hence:

0.15 x 6000 = $900.

The supplies expenses are 30% of the total, hence:

0.3 x 6000 = $1800.

The advertising expenses are 10% of the total, hence:

0.1 x 6000 = $600.

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The linear function for the cost is:

f(x) = 6.5*x + 2.5

A general linear function is something like:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we know that there is a fixec charge of $2.50 plus $6.50 for each sweatshirt, then if you buy x of these, the cost will be modeled by the linear function below:

f(x) = 6.5*x + 2.5

The slope is the cost of each item and the y-intercept is the fixed cost.

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Answer:

Step-by-step explanation:

You can solve for a, b, and c by using a system of linear equations.

Starting with the first equation:

a + b + c = 90

You can isolate a by subtracting b and c:

a = 90 - b - c

Next, substitute the expression for a into the second equation:

12(90 - b - c) + 10b + 6c = 870

Expanding the equation:

1080 - 12b - 12c + 10b + 6c = 870

Combining like terms:

1070 - 2b + -6c = 870

Adding 2b and 6c to both sides:

1070 = 870 + 2b + 6c

Subtracting 870 from both sides:

200 = 2b + 6c

Dividing both sides by 2:

100 = b + 3c

Finally, subtracting 3c from both sides:

100 - 3c = b

To find c, substitute the expressions for a and b back into the first equation:

a + b + c = 90

90 - b - c + b + c = 90

90 - c = 90

-c = 0

Therefore, c = 0.

To find b, substitute c = 0 into the expression for b:

100 - 3c = b

100 = b

Therefore, b = 100.

Finally, to find a, substitute b = 100 and c = 0 into the expression for a:

a = 90 - b - c

a = 90 - 100 - 0

a = -10

Note that negative values for a, b, and c are possible, but not necessarily meaningful for this specific problem or context.

The solution is:

a = -10

b = 100

c = 0

The piecewise function of the tax expressed below

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

The table of values

To determine the piecewise function, we make use of the following variables:

x = taxable income

f(x) = tax

Using the above and the table of values as guides, we have the following:

f(x) = 0.1x, 0 ≤ x ≤ 9700

f(x) = 970 + 0.12(x - 970), 9701 ≤ x ≤ 39475

f(x) = 4543 + 0.22(x - 39475), 39476 ≤ x ≤ 84200

f(x) = 14382.5 + 0.24(x - 84200), 84201 ≤ x ≤ 160725

f(x) = 32748.5 + 0.32(x - 160725), 160726 ≤ x ≤ 204100

f(x) = 46628.5 + 0.35(x - 204100), 204101 ≤ x ≤ 510300

f(x) = 153798.5 + 0.37(x - 510300), x > 510300

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The translation of the verbal expression "4 less than twice a number" in to an algebraic expression is 2n - 4.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression.

Let the number is n.

The phrase can be expressed as,

2n - 4.

Therefore, the expression is 2n - 4.

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taking a looksie at the picture above, we can see the parabola has zeros/solutions at x = -2 and x = 1, we can also see that it passes through (0 , 2) as well, so

[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a( x +2 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ a ( 0 +2 )( 0 -1 ) = 2\implies -2a=2\implies a=\cfrac{2}{-2}\implies \boxed{a=-1} \\\\[-0.35em] ~\dotfill\\\\ -(x+2)(x-1)=y\implies -(x^2+x-2)=y\implies {\Large \begin{array}{llll} -x^2-x+2=y \end{array}}[/tex]

Check the picture below.

The slope of the graph of the equation: y = 2x + 5

Slope = 2

The y-intercept of the graph of the equation: y = 2x + 5

Y-intercept = 5

The slope of the graph of the equation: y = 5 - 3x

Slope = -3.

The y-intercept of the graph of the equation: y = 5 - 3x

Y-intercept = 5

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

1) y = 2x + 5 Slope = 2 is the slope of the equation's graph.

2.) The equation's graph's y-intercept is written as y = 2x + 5 Y-intercept = 5.

3) y = 5 - 3x Slope = -3 is the slope of the equation's graph.

4) The graph's y-intercept is as follows: y = 5 - 3x Y-intercept = 5.

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The volume of the cylinder will be 138.2 inches³

From the information, the shape has a height 3 in more than 4 times the radius of the cylinder's base.

The volume of a cylinder is equal to V = πr²h

where

r is the radius of the base

h is the height

In the problem, h = 3 + 4r

r = 2 inches

To calculate h, h = 3 + 4 × 2

h = 11 inches

The volume of a cylinder is equal to:

v = πr²h

v = π × 2² × 11

v = 44π inches³

V = 138.2 inches³

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Write a function rule for the volume of the cylinder shown at the right with a height 3 in more than 4 times the radius of the cylinder's base. What is the volume of the cylinder when it has a radius of 2 in?

Answer:

x>-7

Step-by-step explanation:

x-5>-12

x>5-12

x>-7

x > -7.

[tex]x-5 > -12[/tex]

[tex]x-5+5 > -12+5\\ \\x > -7[/tex]

If x >-7 is the correct answer, then substituting x by "-7" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).

Substituting:

[tex](-7)-5 > -12\\ \\-12 > -12[/tex]

That's correct! x > -7 is the correct answer.

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The point slope form of the equation of the line through the given point with the given slope is y - 4 = -2(x + 1).

The equation in slope intercept form is y = -2x + 2.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-1, 4), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -2(x - (-1))

y - 4 = -2(x + 1)

Next, we would rewrite the equation in slope-intercept form as follows;

y - 4 = -2(x + 1)

y = -2x - 2 + 4

y = -2x + 2

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Answer:

1. Women

Store

66-34= 32

Online

13

Total

32+13= 45

2. Men

Total

34+9=43

3. Total

online

13+9=22

total

66+22= 88

Answer:

2560/11

Step-by-step explanation:

�

=

640

11

and

�

=

2560

11

The congruency rule that shows us that ΔBLK ≅ ΔACK by; SAS Congruency Postulate

The image showing the triangles tell us that;

∠BKL ≅ ∠CKA by opposite angles theorem

Likewise we see that BL is parallel to AC and as such;

∠BLK ≅ ∠ACK by alternate angles theorem

Similarly, we will also see that;

∠LBK ≅ ∠CAK by alternate angles theorem

Finally, we see that BL ≅ CA and as such we can conclude that ΔBLK is congruent to ΔACK by SAS Congruence Postulate

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There are 435 members in the House of Representatives.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Let's call the number of members in the Senate "s".

The expression for the number of members in the House of Representatives is "h".

According to the problem, there are 35 more members in the House than four times the number of members in the Senate, so the expression for the number of members in the House is:

h = 4s + 35

If there are 100 members in the Senate, then we can substitute this value into the expression:

h = 4 × 100 + 35

h = 435

So, there are 435 members in the House of Representatives.

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the real limits are; Lower Real Limits = 249.5 and Upper Real Limits = 250.5

Given the data in the question;

1 minute being the smallest unit on the scale

so we say; 1/2 which 0.5 minutes which we will use to calculate pur real limits time;

given that; the first subject sleeps 250 minutes

so

Lower Real Limits will be;

Lower Real Limits will = 250 - 0.5 = 249.5

Also our Upper Real Limits will be;

Upper Real Limits = 250 + 0.5 = 250.5

Therefore; the real limits are;

Lower Real Limits = 249.5

Upper Real Limits = 250.5

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The values of a and b, considering the range of the function, are given as follows:

The range of a function is the set that contains all the output values that can be assumed by the function.

Hence, considering the graph, the range of a function is given by the values of y from the graph.

The minimum and maximum value of the function are given as follows:

Hence the values of a and b are given as follows:

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Based on the provided information, standard error is 0.138, z-score is 2.898, and p value is 0.0013995.

The standard error of a statistic refers to the standard deviation of its sampling distribution or an estimate of that standard deviation. It indicates how different the population mean is likely to be from a sample mean. Standard error of two samples is given by:

SE = √((S1^2)/n1+(S2^2)/n2)

In the given case s1 = 0.5, n1 = 40, s2 = 0.8, and n2 = 50. Hence,

SE = √(〖0.5〗^2/40+〖0.8〗^2/50)=0.138

Z-score for two samples is given by:

z = ((x1-x2)/SE) where x1 and x2 are sample means

In the given case x1= 5.35 and x2 = 4.95. Hence,

z = ((x1-x2)/SE) = (5.35-4,95)/0.138=2.898

The p -value from the table is when p(x >z) = 0.0013995.

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The cubic regression equation is y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69 and the estimated the number of graduates in 2001 is 5565

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

See attachment

Using a graphing calculator, we have the following summary:

The model from the above summary is

y = 27.1349x^3 - 473.4406x^2 + 2829.3314x - 4381.6892

Approximate

y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69

In the year 2001, we have

x = 11

So, we have

y = 27.13 * 11^3 - 473.44 * 11^2 + 2829.33 * 11 - 4381.69

Evaluate

y = 5565

The estimated the number of graduates in 2001 is 5565

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The percent of Dan's average did he score during this game is 11.11%

Dan's score in the high school basketball team during last game= 18 points

Dan's score in the high school basketball team during this season = 20 points

Percent of Dan's score during this game = (20 - 18) / 18 × 100

= 2/18 × 100

= 11.11%

In conclusion, Dan scored an average percentage of 11.11% during this game.

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Based on the given task content; 5/11 is closer to 1/2.

A fraction is a number which has a numerator and a denominator. A numerator refers to the upper or top value while a denominator refers to the lower or bottom value of a fraction.

5/11

= 0.454545454545454

Approximately,

= 0.5

1/2 = 0.5

Hence, 1/2 is closer to 5/11

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The volume of the solid that is generated when the region that is enclosed by the given curves V=253/5π

When the volume of a solid is calculated by using the shell method, the result will be a definite integral that represents the sum of the volumes of infinite thick cylinders.

If the axis of rotation is horizontal, the cylinders are horizontal same. The volume of a horizontal cylinder will be 2πrh dy.

The graph defines the area enclosed by a parabola concave upwards, the y-axis, and the line x = 3 in the first quadrant.

There is the volume of the solid is calculated by using the formula:

[tex]V=2\pi \int\limits^d_c {y[g(y)-h(y)]} \, dy[/tex]

y is the radius of the cylinder

h is the height of the cylinder.

Given information is that:

g(y)=3, h(y)=y¹/², c=0, d=9

Now plug the values in the formula:

[tex]V=2\pi \int\limits^9_0 {y(3-y^\frac{1}{2} )} \, dy\\\\\\V=2\pi \int\limits^9_0 (3y-y^\frac{3}{2} )} \, dy[/tex]

Solving the integral:

[tex]V=2\pi (\frac{3}{2} y^2-\frac{2}{5} y^\frac{3}{5})|_0^9[/tex]

Apply the fundamental theorem of calculus:

[tex]V=2\pi [(\frac{3}{2} (9)^2-\frac{2}{5} (9)^\frac{3}{5})-V=2\pi (\frac{3}{2} (0)^2-\frac{2}{5} (0)^\frac{3}{5})]\\\\V=2\pi (\frac{243}{10} -0)\\\\V=2\pi (\frac{243}{10})\\[/tex]

V=243/5π

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The bearing from point point A to point B is given as follows:

57º.

From the text in this problem, the bearing from point B to point A is given as follows:

237º.

To obtain the inverse bearing, that is, the bearing from point A to point B, we must subtract the bearing from point B to point A given in this problem by 180º, as follows:

237 - 180 = 57º.

Hence the bearing from point point A to point B is of 57º.

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If 84% of products come off the line ready to ship to distributors, then the probability of a product being within specifications is 0.84.

Since we are selecting 12 products randomly from the line each hour, the number of products within specifications (x) follows a binomial distribution with parameters n = 12 and p = 0.84.

Using a binomial cumulative distribution function (CDF), we can calculate the probability that x is less than a certain value. For example, if x is less than 7, the probability of this outcome would be considered unusual and the production line should be repaired.

So, the answer is "fewer than 7".

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Answer:

(5x-2)=3x4

Step-by-step explanation:

add that's in the () first

Answer: .

Step-by-step explanation:

The minimum value of [tex]$\|\mathbf{v}\|$[/tex] is zero.

The minimum value of [tex]$\|\mathbf{v}\|$[/tex] is zero, as it is the distance between the origin and a point on the line. To solve this problem, the formula [tex]$\|\mathbf{v}\| = \sqrt{x^2 + y^2}$[/tex] can be used, where x and y are the coordinates of the point on the line. Since the equation of the line is [tex]$\dbinom{10}{3} \dbinom{-2}{1}t$[/tex], the coordinates of the point on the line can be found by substituting [tex]$t = 0$: $x = 10 \cdot 0 - 2 \cdot 0 = 0$, and $y = 3 \cdot 0 + 1 \cdot 0 = 0$[/tex] . Substituting these values into the formula for [tex]$\|\mathbf{v}\|$ gives $\|\mathbf{v}\| = \sqrt{0^2 + 0^2} = 0$[/tex]. Therefore, the minimum value of [tex]$\|\mathbf{v}\|$[/tex] is zero.

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The point that is a solution if the inequality:

y < (2/3)*x + 2

is (1, 2).

Here we want to find a solution for the inequality below:

y < (2/3)*x + 2

To check if an ordered pair is a solution, then we need to replace the values of the ordered point and check if the inequality is true.

If we try with the first point we will get:

3 < (2/3)*0 + 2

3 < 2

That is false.

The correct option is (1, 2)

2 < (2/3)*1 + 2

2 < 8/3

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(a) The probability that a call is classified as long (L) is [tex]$P[L] = 1 - P[B_3] = 1 - \alpha (1-\alpha)^2 = 0.829$.[/tex]

(b) The probability that a call will be billed for nine minutes or less is

[tex]P[B1] + P[B2] + P[B3] + P[B4] + P[B5] + P[B6] + P[B7] + P[B8] + P[B_9] = \alpha + \alpha(1-\alpha) + \alpha(1-\alpha)^2 + \alpha(1-\alpha)^3 + \alpha(1-\alpha)^4 + \alpha(1-\alpha)^5 + \alpha(1-\alpha)^6 + \alpha(1-\alpha)^7 + \alpha(1-\alpha)^8 = 0.958[/tex]

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is expressed as a number from 0 to 1, with 0 indicating that an event is impossible and 1 indicating that it is certain to occur. Probability is used to calculate the chance of a random event happening or to predict the outcome of a situation. Probability theory is also used to describe the underlying mechanics and dynamics of random phenomena

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Complete question:

For the telephone usage model of Example 1.18, let [tex]$B_m$[/tex] denote the event that a call is billed for $m$ minutes. To generate a phone bill, observe the duration of the call in integer minutes (rounding up). Charge for M minutes [tex]$M=1,2,3, \ldots$[/tex] if the exact duration T is [tex]$M-1 < t \leq M$[/tex]. A more complete probability model shows that for $m=1,2, \ldots$ the probability of each event [tex]$B_m$[/tex] is

[tex]$$P\left[B_m\right]=\alpha(1-\alpha)^{m-1}$$[/tex]

where [tex]$\alpha=1-(0.57)^{1 / 3}=0.171$[/tex]