acccording to this diagram what is cos 28

Answer:

c(x) = 40 (x) + $6,900

Step-by-step explanation:

According to the scenario, given data are as follows,

Total cost of 100 bicycles (x1) = $10,900

Total cost of 120 bicycles (x2) = $11,700

Let Number of bicycles = X

Than cost of X bicycles = c(X)

let, fixed cost be F and variables cost be V, than

c(X) = V(X) + F

So, we can calculate variable cost by using following method,

V = c(x2) - c(x1) ÷ ( x2 - x1)

= ( $11,700 - $10,900) ÷ ( 120 - 100)

= $800 ÷ 20

= $40

So, calculate fixed cast by putting value to equation,

$10,900 = ($40 ×100) + F

F = $10,900 - $4,000 = $6,900

So, For x number of bicycles, cost equation will be,

c(x) = 40 (x) + $6,900

We're given the vectors

\(\vec a = 3\vec\imath + \vec\jmath - \vec k = \langle3,1,-1\rangle \\\\ \vec b = -3\,\vec\imath-\vec\jmath + \vec k = \langle-3,-1,1\rangle \\\\ \vec c = \vec\imath + \dfrac13\,\vec\jmath + \dfrac13\,\vec k = \left\langle1,\dfrac13,\dfrac13\right\rangle \\\\ \vec d = \vec\imath + 3\,\vec\jmath + 4\,\vec k = \langle 1,3,4\rangle \\\\ \vec g = \vec\imath + 3\,\vec\jmath - \vec k = \langle1,3,-1\rangle\)

(a) Two vectors are perpendicular if their dot product is zero. For instance, \(\vec a\) and \(\vec b\) are not perpendicular because

\(\vec a\cdot\vec b = \langle3,1,-1\rangle\cdot\langle-3,-1,1\rangle = 3\times(-3)+1\times(-1)+(-1)\times1 = -11\)

You'll find that none of these vectors taken two at a time are perpendicular to each other.

(b) Recall for any two vectors \(\vec x\) and \(\vec y\) that

\(\vec x\cdot\vec y = \|\vec x\| \|\vec y\| \cos(\theta)\)

where \(\theta\) is the angle between \(\vec x\) and \(\vec y\). If these vectors are parallel, then the angle between them is 0 rad or π rad, meaning they point in the same or in opposite directions, respectively.

We have cos(0) = 1 and cos(π) = -1, so

\(\vec x\cdot\vec y = \pm\|\vec x\| \|\vec y\|\)

For instance, we know that

\(\vec a\cdot\vec b = -11\)

and we have

\(\|\vec a\| = \sqrt{3^2 + 1^2 + (-1)^2} = \sqrt{11} \\\\ \|\vec b\| = \sqrt{(-3)^2+(-1)^2+1^2} = \sqrt{11}\)

so \(\vec a\) and \(\vec b\) are indeed parallel and point in opposite directions, since -11 = - √11 × √11.

On the other hand, \(\vec a\) and \(\vec c\) are not parallel, since

\(\vec a\cdot\vec c = \langle3,1,-1\rangle\cdot\left\langle1,\dfrac13,\dfrac13\right\rangle = 3\times1+1\times\dfrac13+(-1)\times\dfrac13 = 3 \\\\ \|\vec a\|\|\vec c\| = \sqrt{3^2+1^2+(-1)^2}\times\sqrt{1^2+\dfrac1{3^2}+\dfrac1{3^2}} = \dfrac{11}3\)

and clearly 3 ≠ ±11/3.

It turns out that (a, b) is the only pair of parallel vectors.

(c) The cosine of an angle measuring between 0 and π/2 rad is positive, so you just need to check the sign of

\(\cos(\theta) = \dfrac{\vec x\cdot\vec y}{\|\vec x\|\|\vec y\|}\)

For instance, we know \(\vec a\) and \(\vec b\) are parallel and have an angle of π rad between them. cos(π) = -1, so this pair doesn't qualify. Meanwhile, the angle between

\(\cos(\theta)=\dfrac3{\frac{11}3}\right) =\dfrac9{11} > 0\)

so \(\vec a\) and \(\vec c\) do qualify.

You'd find that the pairs ((a, c), (a, d), (a, g), (c, d), (c, g), (d, g)).

(d) An angle between π/2 and π has a negative cosine. None of the vectors are perpendicular to each other, so this happens for the remaining pairs, ((a, b), (b, c), (b, d), (b, g)).

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Answer:

R= p + 1

R= 29

D= 5p

D= 140

C= 5p + 6

C= 146

Step-by-step explanation:

Logic...

Answer:

8 X 5 = $40

Step-by-step explanation:

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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Step-by-step explanation:

Flip f(x) about the x-axis by multiplying it by -1

  - f(x)

  the squish it skinnier by multiplying it by 4

g(x) = - 4 f(x)   = -4 x^2

We need to use the place values to compare different numbers.

By only looking at the place value, we can see that the largest number is: 0.1

Let's see how to get the solution.

We can define place value as the place where a digit is with respect to the decimal point.

The digits that are at the far left are the larger ones, for example in:

11

The left one represents 10, while the right one represents 1:

10 + 1 = 11

The same happens when we look at the right of the decimal point, there the digits at the left will be larger than the ones at the right.

0.10 is larger than 0.01

From this, we can see that for the set:

{0.1, 0.02, 0.003, 0.0004, 0.00005}

The largest number will be the one with the leftmost first digit different than zero, which is the first one: 0.1

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Therefore ,When Sebastian needs to buy coffee If he buys from the warehouse, this should cost $240 even by end of the year of annual year.

An entry fee is a yet another charge that must be paid each year when you apply for a particular credit card. Special benefits usually cover these expenditures, that ranged from $95 to $500. These benefits include the possibility of earning air miles, tickets, or cash back.

Here,

Given :

If he continues to buy his coffee from of the nearby shop, this should cost $300 by the conclusion of the year.

If he buys from the warehouse, this should cost $240 even by end of the year.

Therefore ,When Sebastian needs to buy coffee, the best financial advise is to buy it at a warehouse shop since he will save money at the end of every year.

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The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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Answer: f(x)=2-x^2

Step-by-step explanation:

The quadratic equation is

y=ax^2+bx+c

and c is equal to the y-intercept.

in the twi graphs shown both have the same shape but different y-intervepts.

c(the y-intercept) in the first graph is 5 and in the second graph(F) is 2.

On the graphing calculator it says that f(x)=2-x^2 is the correct answer therefore it is correct.

Answer:

B) y = 7x

Step-by-step explanation:

Start with:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Substitute in two points from the graph.

(Let's use (8,56) & (16,112)

\(m=\frac{112-56}{16-8}\)

Combine like terms.

\(m=\frac{56}{8}\)

Simplify.

\(m=7x\)

Answer:

y = 7x

Step-by-step explanation:

We need to find the slope

We have two points (0,0) and (8,56)

m = (y2-y1)/(x2-x1)

   = (56-0)/( 8-0)

  = 56/8

  = 7

The proportional relationship is

y= kx where k is the slope

y = 7x

Correct graph: C

Answer:

0.36

Step-by-step explanation:

Given that:

Mean = 70

Standard deviation = 5.5

score (x) = 72

Formular for obtaining Standardized score (Zscore) :

Zscore = [score (x) - mean] / standard deviation

Hence,

Zscore = (72 - 70) / 5.5

Zscore = 2/ 5.5

= 0.3636363

Zscore = 0.36 ( 2 decimal place)

Answer:

-1.67

Step-by-step explanation:

khan academy

The system of equations has an infinite number of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

3x + 2y = 6 ____(1)

6x + 4y = 12 _____(2)

Applying the substitution method.

3x + 2y = 6

x = (6 - 2y)/3 in (2)

6 (6 - 2y)/3 + 4y = 12

2 (6 - 2y) + 4y = 12

12 - 4y + 4y = 12

12 = 12

This means,

It has an infinite number of solutions.

Thus,

An infinite number of solutions.

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The complete question is:

Graph the system of equations

3x + 2y = 6

6x + 4y = 12

and find the solution to the system.

After setting \(u=\sqrt{1+e^{2x}}\), partially solving for x in terms of u gives

\(u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1\)

Then taking differentials, you get

\(2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du\)

Replacing everything in the original integral then gives

\(\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}\)

Split up the integrand into partial fractions:

\(\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12\)

so that

\(\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C\)

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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The height of the tree by using the trigonometric ratios will be 44.37 feet.

The angle of elevation to a nearby tree from a point on the ground is measured to be 32 º.

Now, we know that, angle of elevation is when you are measuring the angle from the floor or the ground.

So, by using the trigonometric ratios, we will have:

tan 32 º = h / 71

0.6249 = h / 71

h = 0.6249 × 71

h = 44.3679 feet

h ≈ 44.37 feet

Therefore, we get that, the height of the tree by using the trigonometric ratios will be 44.37 feet.

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Answer:the least common denominator is 10 because 5x2 is 10 and then 10x1 is 10 its the least for both of them

Step-by-step explanation:

Answer:

(3,-6)

Step-by-step explanation:

Coordinate for the point R is (3, -6)

A polygon with four sides and four vertices is called a quadrilateral. Quadrilateral literally means "four sides" because "quad" means four and "lateral" implies sides. Quadrilaterals come in a variety of sizes, forms, and angles, but they all have four sides in common.

If all of the matching sides and angles of two quadrilaterals are equal in size, they are said to be congruent.

Given that the quadrilateral PQRS congruent to the quadrilateral JKLM.

Find out the all sides and angles of given quadrilateral JKLM and quadrilateral PQRS,

according to the graph the points are:

for quadrilateral JKLM,

J (-6, 2)

K (-3, 5)

L (-5, 8)

M (-8, 4)

for quadrilateral PQRS,

P (9, -7)

Q (6, -4)

R  ( _, _ )

S (7, -9)

By the formula distance between any two points is:

\(d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}\)    

where, \(x_{1}, x_{2} , y_{1}, y_{2}\) are the points of two sides of line.

using that formula we have to find out the points of R is (3, -6)

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Answer:

To find the first blank number, you can use reverse operations. Something + 7 must equal 3. So, the blank number is 7 subtracted from 3.

3-7=-4

The first blank number is -4. To find the second blank number, add 10 to the first blank number (-4).

-4+10=6

The second blank number is 6.

Hope this helps! :)

After 3 hours both Kathy and Jared will have the same amount of charges.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Kathy:

The amount charged after x hours.

= 18 + 12x _____(1)

Jared:

The amount charged after x hours.

= 36 + 6x _____(2)

From (1) and (2) we can find the number of hours at which both their amount are equal.

18 + 12x = 36 + 6x

Subtract 6x on both sides.

18 + 12x - 6x = 36

18 + 6x = 36

Subtract 18 on both sides.

6x = 36 - 18

6x = 18

Divide both sides by 6.

x = 3

Thus,

After 3 hours both Kathy and Jared will have the same amount of charges.

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Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

Answer: I believe the answer is C. All of the other options dont have anything to do with lee and her construction

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

Spring stiffness is a characteristic that describes the relationship between load and deflection. If k is stiffness, P is load, and x is deflection, P = kx. The smaller the deflection at a constant load, the stiffer the spring, k.

Given that,

If spring A has a spring constant which is 8 times spring B's spring constant,

Let us assume,

A spring is cut into two parts of length La and Lb

Also given that La : Lb

La : Lb = 1 : 8

The total of spring constant is = 1 + 8 = 9

If the length of spring is L , then La

La = \(\frac{L}{9}\)

And length of B , Lb

Lb = \(\frac{8L}{9}\)

We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .

K ∝ 1 / L

If initial spring constant is k then,

kL= KaLa = KbLb

Then,

Ka = \(\frac{K}{\frac{1}{9} }\)

Ka = 9K

And Kb = \(\frac{K}{\frac{8}{9} }\)

Kb = \(\frac{9K}{8}\)

Hence, stiffness of A is given by, 9K

Stiffness of B is given by  \(\frac{9K}{8}\)

Therefore,

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

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Answer:

25cents/ounce

Step-by-step explanation:

Given parameters:

Ounce of cereal box = 16ounces

Cost  = $4

Unknown:

cents per ounce  = ?

Solution:

To solve this problem;

 Convert the dollar bill to cents

       $1  = 100cents

       $4 will give us 4 x 100  = 400cents

Cost in cents per ounce= \(\frac{400}{16}\)   = 25cents/ounce

Answer:

what he said

Step-by-step explanation: