True or false: f(x) is a function

Answer:

True student distribution will approach the standard

The maximum value of c=4x+2y subject to the constraints is 14

The objective function is given as:

c = 4x+2y

The constraints are given as:

x≥0 y≥0

2x+2y≤10

3x+y≤9

Rewrite 2x+2y≤10 and 3x+y≤9 as equations

2x+2y = 10

3x+y = 9

Divide 2x+2y = 10  through by 2

x+y = 5

Subtract x+y = 5 from 3x+y = 9

3x - x + y - y = 9 - 5

Evaluate the difference

2x = 4

Divide by 2

x = 2

Substitute x = 2 in x+y = 5

2+y = 5

Solve for y

y = 3

So, we have

(x, y) = (2, 3)

Substitute (x, y) = (2, 3) in c = 4x+2y

c = 4 * 2 + 2 * 3

Evaluate

c = 14

Hence, the maximum value of c=4x+2y subject to the constraints is 14

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The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.

According to the statement

we have given that:

Monthly Rate = $20, Number of customers = 5000

If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.

And we have to find that The type of model that best fits the given situation.

So, according to the linear representation model

Monthly Rate = $20, Number of customers = 5000

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1  = $19, Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1  = $18, Number of customers = 5500 + 500 = 6000

Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.

We have 2 pair of values here,

x = 20, y = 5000

x = 19, y = 5500

Let us write the equation in slope intercept form:

y = mx + c

And Slope of a function is

m = y₂ - y₁ / x₂ - x₁

Then

m = 5500 - 5000 / 19 - 20

m = -500

So, the equation become

y = -500x +c

And find the value of by putting the values.

So, c = 15000

And the equation become

y = -500x + 15000.

According to this linear model is perfect for this situation.

So, The linear representation model is best for this situation.

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The pairs of angles that fit the description are

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

From the question, we are to list the angles that fit the given descriptions

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W;

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

Hence, the pairs of angles that fit the description are

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

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yes it will be a rational number.

square having area 400 sq units will have a length of 20 on each side by increasing the length of each side by 1 we get 21 then the area will be

21 ^ 2=441

Then we will have a rational number.

first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.

let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so

[tex]cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}[/tex]

The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).

A linear function is modeled by:

y = mx + b

In which:

The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:

g(x) = 5 + 2x.

The solution to the system of equations is found as follows:

f(x) = g(x)

2x² + x + 4 = 5 + 2x

2x² - x - 1 = 0

Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:

When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).

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Answer:

D. (1,7)

Step-by-step explanation:

I took the exam

Answer:

23.6

Step-by-step explanation:

→ Identify length not given

Opposite

→ Find a formula without opposite

Cos = Adjacent ÷ Hypotenuse

→ Rearrange

Adjacent = Cos × Hypotenuse

→ Substitute

cos 38 × 30 = 23.6

Answer:

[tex]x = 23.6[/tex]

Step-by-step explanation:

To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.

In this case:

• The side adjacent to the given 38° angle is [tex]x[/tex] (required).

• The hypotenuse is 30 units.

The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:

[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].

Substituting into the formula:

[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]

⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]

⇒ [tex]x = 23.6[/tex]

a) 1. The backpack weight sample mean is 6.375 pounds.

a) 2. The backpack weight sample mean is 6.375 pounds.

a) 3. The backpack weight sample mean is 6.625 pounds.

b) The range of the sample means is between 6.375 and 6.625, which approaches 0.250 pounds, plus or minus.

c) Since the students are using the sample means to estimate the mean backpack weight of their schoolmates, the true statements are A. and D.

The farther the range of the sample means is from O, the less confident they can be in their estimate.

A sample mean is a statistic computed from a sample of data or variables.

The sample mean represents the average value of the sample data.

The range describes the difference between the largest number and the smallest number.

Thus, based on the range of the sample means, the farther it is from 0, the less confident the students can be in their estimate.

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The hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.

The following can be deduced from the information:

x1 = 275

x2 = 170

n1 = 500

n2 = 500

The sample proportion will be:

p1 = 275/500 = 0.55

p2 = 170/500 = 0.34

The pooled proportion will be:

= (275 + 170)/(500 + 500)

= 0.44

The test statistic is 6.681. It should be noted that the test statistics is a number that's calculated by a statistical test. It shows how the observed data are far from the null hypothesis.

The p value in this scenario is extremely small. The p value is a measurement used to validate a hypothesis against the observed data. Therefore, we have to reject the null hypothesis.

In this case, the hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.

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The correct equation that has been shown by the graph is y<-2x+1. Option D

The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.

Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D

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Answer: The correct equation that has been shown by the graph is y<-2x+1. Option D

What is inequality?

The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.

Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D

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Step-by-step explanation:

The equation that represents the function g(x) is g(x) = log₅(x - 3)

The equation of the function f(x) is given as:

f(x) = log₅(x)

From the graph, we can see that the function g(x) is 3 units to the right of the function f(x)

This means that

g(x) = f(x - 3)

The function f(x - 3) is calculated as follows

f(x - 3) = log₅(x - 3)

Substitute f(x - 3) = log₅(x - 3) in g(x) = f(x - 3)

g(x) = log₅(x - 3)

Hence, the equation that represents the function g(x) is g(x) = log₅(x - 3)

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Answer:

Step-by-step explanation:

answer is 1/2

Answer:

23 children and 9 adults

p <= 70/9

Step-by-step explanation:

Let x = # of adults and y = # of children. The number of children is 5 more than twice the number of adults, so x = 2y + 5. The total cost of entrance is $6525, so 225x + 150y = 6525.

x = 2y + 5

225x + 150y = 6525

x - 2y = 5

225x + 150y = 6525

75x - 150y = 375

225x + 150y = 6525

300x = 6900

x = 23

x = 2y + 5

23 = 2y + 5

18 = 2y

y = 9

225p + 3750 <= 5500

225p <= 1750

p <= 70/9

Answer:

1) 9.69

2) 87.36

3) 171.42

4) 18.75

5) 16.29

Step-by-step explanation:

Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5

The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet

The given parameter is

Perimeter, P = 520 feet

Represent the shorter side with x and the longer side with y

One side of the garden is bordered by a river:

So the perimeter is:

P = 2x + y

Substitute P = 520

2x + y = 520

Make y the subject

y = 520 - 2x

The area is

A = xy

Substitute y = 520 - 2x in A = xy

A = x(520 - 2x)

Expand

A = 520x - 2x^2

Differentiate

A' = 520 - 4x

Set to 0

520 - 4x = 0

Rewrite as:

4x= 520

Divide by 4

x= 130

Substitute x= 130 in y = 520 - 2x

y = 520 - 2 *130

Evaluate

y = 260

The area is then calculated as:

A = xy

This gives

A = 130 * 260

Evaluate

A = 33800

Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet

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The view of war doves with respect to the Vietnam War was that: B. as a localized civil war that should not include the United States of America (US).

The Vietnam War is also referred to as Second Indochina War or the Vietnam conflict and it can be defined as a short, costly, protracted and divisive conflict between the communist government of North Vietnam and South Vietnam, which ended on the 30th of April, 1975.

Based on historical information and records, the Vietnam War officially started on the 1st of November, 1955 in the following locations:

In conclusion, we can infer and logically deduce that the view of war doves with respect to the Vietnam War was that it is a a localized civil war and as such should not include the United States of America.

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A one-tailed test's p-value is half that of a two-tailed test.

Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.

Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.

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The trigonometry illustrates that the four angles whose cosine is the same as cos pi/3 will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3

From the information, given cos (x), the value that is similar to cos x will be the sum of the angle and multiple of 360.

Therefore, for the angle cos(∏/3), the angles that are similar to this angle will be expressed as Cos(2∏n + ∏/3) where n is any positive integer.

Then the other four angles will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3. Also, the statement that all angles that have the same cosine will have the same sine is false. The sine of an angle is simply equal to the cosine of the complementary angle.

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Answer:

Step-by-step explanation:

true

Answer:

False because the account isn't full

Answer:

○ [tex]F = \frac{S + 24}{3}[/tex]

Step-by-step explanation:

We know that:

[tex]S = 3F -24[/tex],

where F is the length of the foot of a person, and S is their shoe size.

To solve for the length of a person's foot, we have to rearrange the given equation to make F the subject:

[tex]S = 3F -24[/tex]

⇒ [tex]S + 24 = 3F[/tex]     [adding 24 to both sides]

⇒ [tex]\frac{S + 24}{3} = F[/tex]          [dividing both sides by3]

⇒ [tex]F = \frac{S + 24}{3}[/tex]          [swapping the sides]

Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.

The length of the straight line AB = 80cm

The angle at a point = 360°

Angle AQB= 360 - 210° = 150

But the angle that makes up a triangle= 180°

180-150= 30°

But <QAB = <QBA because triangle AQB is an isosceles triangle.

30/2 = 15°

To calculate the length of the straight line the following is carried out using the sine laws.

a/ sina, = b sinb

a= 8cm, sin a { sin 15)

b= ? , sin B = 150

make b the subject formula;

8/sin15= b/sin 150

b= 8 × sin 150/sin 15

b= 80cm

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The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].

A perfect square exists as a number that can be described as the product of an integer by itself or as the second exponent of an integer.

The perfect square trinomial exists

[tex](a[/tex] ± [tex]b)^2[/tex] = [tex]a ^2[/tex] ± 2ab + [tex]b ^2[/tex]

[tex]$x^2-6x=1[/tex]

[tex]x^2-2*3x=1[/tex]

then [tex]$2ab = 2 * 3*x = 2 * x *3[/tex]

The value of a = x and b = 3

[tex]$b^2=3^2=9[/tex]

[tex]$x^2-6x+9=1+9[/tex]

[tex]$x^2-6x+9=10[/tex]

The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].

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The correct order is 3,1,4,2.

Marshaling of assets:

Therefore, the correct order is 3,1,4,2.

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The correct question is given below:
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is:

(1) $20,000 loan from a partner.

(2) $30,000 of profits from the last year of operations.

(3) $3,000 payable to a supplier.

(4) $100,000 in capital balances of the partners.

The measure of Arc AU of the given Circle Geometry is; 50°

The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”

We can express the above theorem as;

Angle at the center = 2 × Angle at the circumference

From the attached image below  and from the given statement in the question, we are given that; ∠QUA = 111°

Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA

m∠QDA = 2 × 111° = 222°

Which gives;

∠QOA =  = 360° - 222° = 138°

∠QOA = ∠QOU + ∠UOA (by angle addition property)

Thus;

∠QOA = 138° = 88° + ∠UOA

∠UOA = 138° - 88° = 50°

Thus, the measure of Arc AU is;

Arc AU = ∠UOA = 50°

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Answer: b

Step-by-step explanation:

Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

Below in bold.

Step-by-step explanation:

This figure is a trapezoid.

We can find the missing side  length by applying the Pythagoras Theorem to the right triangle on the left of the figure.

The dotted line has length 12 cm and the base of the triangle = 25 - 18 = 7 cm

So x^2  = 12^2 + 7^2     (where x = missing length)

            =  144 + 49

            = 189

x = √189

  =  13.75 to nearest hundredth

So the perimeter

  =    18 + 12 + 25 + 13.75

  =    68.75 cm.

Area of a trapezoid = 1/2 (a + b) * h.

Area =  1/2 *(18 + 25) * 12

        =  258 cm^2.