The radius of a circle is 4 millimeters. What is the circle's area? Use 3.14 for pi.
(The answer MUST BE ONE OF THE ANSWERS BELOW)

Answer:

24 minutes

Explanation:

Given:

Formula:

time taken = distance/speed

Applying the formula:

time taken = 6/15 = 0.4 hours = 24 minutes

Now

let's name the vertices of the triangle as A B C and D as the image shown above

In triangle ABC

sin 60° = AB/AC

√3/2 = 8√2/ AC

AC = 16√2/√3

In triangle ACD

sin 45° = AC/AD

1/√2 = 16√2/ 3 AD

Then the money borrowed insurance company is $1,000.

Money borrowed from insurance company = $1000

Let the money borrowed by her friend at 8% interest = x

Then the money borrowed by the bank at 9% interest = 2x

Total money borrowed = $10,000

So, the money borrowed from the insurance company = 10,000-(2x+x)

= 10,000-3x

Total interest for the first year = $830

We have the equation,

8%(x) + 9%(2x) +5% (10,000-3x) = 830

8x+18x+50,000-15x = 83,000

11x = 83000-50000

11x = 33,000

x = $3000

Then the money borrowed insurance company = 10,000-3x

Then the money borrowed insurance company is $1,000.

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There will be 354087.24 mosquitoes on the 19th of May.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

.

Using the relation :

y = 180000(1.07)^x

x = Number of days since May 6 ;

y = Number of mosquitoes after x days

x = May 9 May 19  = 10 days

Therefore, a number of mosquitoes inhabiting the city on May 19 will be :

y = 180000(1.07)^10

y = 180000  x  1.96715136

y = 354087.24

y = 354087.24  (nearest whole number).

Therefore there will be 354087.24 mosquitoes on the 19th of May.

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Answer:

a² b² c² equals mc² and that is the answer

Answer:

the value of x is between -4 and 4

Answer:

25

Step-by-step explanation:

find the greatest common factor (GCF) of the 3 quantities using prime factorisation.

125 = 5 × 5 × 5

150 = 2 × 3 × 5 × 5

225 = 3 × 3 × 5 × 5

Next, identify those prime factors that the 3 numbers have in common and multiply them.

the common factors are 5 × 5 = 25

then

125 ÷ 25 = 5

150 ÷ 25 = 6

225 ÷ 25 = 9

the 25 students each get 5 apples, 6 oranges and 9 mangoes

Answer:

[tex] \dfrac{149}{40} [/tex]

[tex] \dfrac{38}{15} [/tex]

Step-by-step explanation:

[tex] (\dfrac{7}{8} + \dfrac{4}{5}) - (\dfrac{9}{20} + \dfrac{-5}{2}) =  [/tex]

[tex] = (\dfrac{7}{8} \times \dfrac{5}{5} + \dfrac{4}{5} \times \dfrac{8}{8}) - (\dfrac{9}{20} + \dfrac{-5}{2} \times \dfrac{10}{10}) [/tex]

[tex] = (\dfrac{35}{40} + \dfrac{32}{40}) - (\dfrac{9}{20} + \dfrac{-50}{20}) [/tex]

[tex] = \dfrac{67}{40} - (-\dfrac{41}{20}) [/tex]

[tex] = \dfrac{67}{40} + \dfrac{41}{20} \times \dfrac{2}{2} [/tex]

[tex] = \dfrac{67}{40} + \dfrac{82}{40} [/tex]

[tex] = \dfrac{149}{40} [/tex]

[tex] (-\dfrac{6}{4} + \dfrac{3}{2}) + (\dfrac{6}{5} + \dfrac{4}{3}) = [/tex]

[tex] = (-\dfrac{3}{2} + \dfrac{3}{2})+ (\dfrac{6}{5} \times \dfrac{3}{3} + \dfrac{4}{3} \times \dfrac{5}{5}) [/tex]

[tex] = 0 + \dfrac{18}{15} + \dfrac{20}{15} [/tex]

[tex] = \dfrac{38}{15} [/tex]

Answer:

143°

Step-by-step explanation:

supplementary angles are angles that combine to form a straight line (and we know that a straight line = 180 degrees)

you can think of an angle as needing another angle to "supplement" it into being a full line.

So, we know that one angle = 37°

And that: one angle + supplementary angle = 180 degrees

                 37° + x  = 180°

                - 37           -37

                     x    = 143

So, the measure of this angle's supplement is 143°

hope this helps!!

Answer:

143 degrees

Step-by-step explanation:

180 - 37 = 143

The trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)

The height of the tree can be found using trigonometric ratios.

Therefore,

tan ∅ = opposite / adjacent

Hence,

for the higher wire

tan 75 = h / 4

4 tan 75 = h

This can be express as follows:

tan 75 = tan(45 + 30)

Hence,

4 × 3.73205080757 = 14.9282032303 ft = 14.9ft

Hence, the trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)

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Answer:

Graphs Attached Below

Step-by-step explanation:

Hello!

Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]

From our Equation:

There are several values that are needed to drawing a parabola:

Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]

The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.

A parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.

To calculate the AOS, we use the formula [tex]AOS = \frac{-b}{2a}[/tex], from the values of the equation.

Calculate

The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.

The vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.

To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.

Calculate

The y-value is -2. The vertex is (2, -2).

The x-intercepts are the points where the graph intersects the x-axis (y = 0).

Solve by Factoring

The roots are (0,0) and (4,0).

Now we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.

Image Attached

The Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.

That means we remove the parts of the line that don't belong in that domain.

Image Attached

Answer:

60°, arms 6

Step-by-step explanation:

let the total arms = n

total generated angles in a regular polygon is = (n-2)×180

now,

(n-2)×180 = 120 n

or, 180n - 360 =120n

or, 60n = 360

or, n = 6

2) [tex]\overline{EK} \cong \overline{KG}, \overline{HK} \cong \overline{KF}[/tex]

3) Opposite sides of a parallelogram are congruent.

4) [tex]\triangle EF \text{ }K \cong \triangle GHK[/tex]

Answer: The domain is [tex]\boxed{(-4, 4)}[/tex] and the range is [tex]\boxed{[-4, 4]}[/tex].

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

It takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc.

It should be noted that a quadrilateral simply means a shape that has four sides and four angles.

In orde to prove that triangles are similar, we only need to prove corresponding angles congruency.

On the other hand, it takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc. This makes them more elaborate.

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Answer:

5

Step-by-step explanation:

2x²y³ + 4y³ = 149 + 3x²

[tex] 2x^2y^3 - 3x^2 = 149 - 4y^3 [/tex]

[tex] x^2(2y^3 - 3) = 149 - 4y^3 [/tex]

[tex] x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} [/tex]

[tex] x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} [/tex]

Try y = 1

[tex]x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}[/tex]

For y = 1, x is imaginary.

Try y = 2

[tex] x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3[/tex]

Since x and y are positive integers, ignore x = -3.

When x = 3, y = 2.

x + y = 3 + 2 = 5

The value of x + y is 5.

Polynomials are expressions which consist of variables, constants, coefficients and exponents.

We have the equation,

2x²y³ + 4y³ = 149 + 3x²

2x²y³ - 3x² = 149 - 4y³

x² (2y³ - 3) = 149 - 4y³

x² = (149 - 4y³) / (2y³ - 3)

x = √[(149 - 4y³) / (2y³ - 3)]

Now, we have to find two positive integers.

We can use trial and error method here.

Trial putting y = 1.

x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]

  = √[145 / (-1)]

  = √(-145)

There is no real root for √(-145). So y = 1 is not applicable.

Trial putting y = 2.

x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]

  = √[117 / 13]

  = √(9)

  = ± 3

But we need positive integers. So we ignore -3.

So x = 3 and y = 2 ⇒ x + y = 5

Hence x + y = 5.

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John invested the money at simple interest for 4.22 years.

We have,

Invested amount = $ 4500

Rate of interest = 5.5 %

Time = t years

Maturity value = $ 5545

So,

Total interest earned =  $ 5545 - $ 4500 = $ 1045

And,

Simple interest = (Principal × Rate × Time ) / 100

So, Using the mentioned formula,

1045 = ( 4500 × 5.5 × t ) /100

1045 = 45 × 5.5 × t

⇒

t = (1045) / (45 × 5.5)

⇒ t = 4.22 years

Therefore, John invested the money at simple interest for 4.22 years.

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The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.

A function is a law that relates a dependent and an independent variable.

The options mentioned below needs to be studied to determine which forms a function.

Option A , C and D doesn't really form a function ,

For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.

height of a building in feet, height of the building in inches

Height of building in feet = (height of building in inches/12)

so this is a function

Therefore Option B is the right answer.

The missing options are

If the relationships below are given in the form (input, output), which pairing always describes a function?

A) (number of doors in a car, number of cup holders in the car)

B) (height of a building in feet, height of the building in inches)

C) (beverage charge on a bill, total meal charge on the bill)

D) (distance from home during a trip, time elapsed during the trip)

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The multiplicity of the function is 1 for each term after factorization.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial function:

[tex]\rm F(x)= 4x^3+19x^2-41x+9[/tex]

After factorization:

[tex]\rm F(x) = \left(4x-1\right)\left(x^2+5x-9\right)=0[/tex]

[tex]\rm F(x) =(4x-1)^1(\:x-\frac{-5+\sqrt{61}}{2})^1(\:x+\frac{-5-\sqrt{61}}{2})^1[/tex]

The multiplicity of the function is 1 for each term.

Thus, the multiplicity of the function is 1 for each term after factorization.

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The correct answer is option A which is the operating profit will be $73000.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

We will consider the following notations and will make the expression for operating profit.

P = profit

S = sales = $900000

F = Fixed cost = $197000

V = 07S = variable cost

So the expression will be given as:-

P = S - F - V

P = S - F - 0.7S

P = 9000000 - 1797000 - ( 0.7 x 9000000)

P = 703000 - 630000

P = $73000

Therefore the correct answer is option A which is the operating profit will be $73000.

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Answer:

B will be the answer...

Step-by-step explanation:

The second equation in system B is only in terms of y, so we need to use elimination to eliminate the x term from the second equation in system A.

To do that, we need to multiply the first equation by 5.

5 (-x − 2y = 7)

-5x − 10y = 35

Add to the second equation.  Notice the x terms cancel out.

(-5x − 10y) + (5x − 6y) = 35 + (-3)

-16y = 32

Combining this new equation with the first equation from system A will get us system B.

-x − 2y = 7

-16y = 32

Answer:

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution to system A.

Step-by-step explanation:

exact answer

Answer:

[tex]f(z) = z^2-3z+2[/tex]

[tex]f(x+1) = x^2-x[/tex]

[tex]f(\sqrt{2}+1) = 2-\sqrt{2}[/tex]

Step-by-step explanation:

[tex]f(x+1) = x^2+2x+1-3x-3+2[/tex]

[tex]f(\sqrt{2}+1) = 2+2\sqrt{2}+1-3\sqrt{2}-3+2[/tex]

Answer:

slope: -1

y-intercept: 6

Step-by-step explanation:

y-intercept is when x is 0 so it's 8 and the slope can be found using the slope formula (y2-y1)/(x2-x1)

(6-8)/(0 - (-2)) = -2/2 = -1

12.5% is the percentage of numbers randomly generated by Taylor's computer that is less than 0.5.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

The percentage of numbers randomly generated by Taylor's computer are less than 0.5 is given by

P(0≤X≤0.5)

=[tex]\int_{0}^{0.5}\frac{1}{4}dx[/tex]

[tex]=\frac{1}{4}x|^{0.5}_{0}[/tex]

[tex]=\frac{1}{4}(0.5-0)[/tex]

[tex]=0.25(0.5)[/tex]

= 0.125

That is 12.5%

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Answer:

A

Step-by-step explanation:

In this case you have to show that 1 + 2 = 180

This way when you show that 2 + 3 = 180, that proves 1 & 3 are congruent.

Answer:

A. 2. ∡1 is supplementary to ∡2 (linear pair theorem)

Step-by-step explanation:

Given the following proof so far, we have:
1. Line a and line b intersect => given

2. ? => ?

3.  ∡3 is supplementary to  ∡2 => linear pair theorem

4.  ∡1 ≅ ∡3 => congruent supplements theorem

Now let's take a look at the reasoning for statement 4, which says that angle 1 and 3 are congruent due to congruent supplements theorem.

In this theorem, if 2 angles are supplementary (add up to 180 degrees) to the same angle, it means those 2 angles are congruent.

Why does this work?
________________________________________________________
Let's say x + y = 180, and z + y = 180

By transitivity (if a = b and b =c, then a=c), x + y is equal to z + y

x + y = z + y

Subtract y from both sides

x = z

________________________________________________________

Statement 3 says  ∡3 is supplementary to  ∡2, and because of congruent supplements theorem being our last reason (where  ∡1 and  ∡3 are congruent), we need to make statement 2 also have ∡1 being supplementary to ∡2, (∡2 is like y in the example above - it's the angle that  ∡1 and  ∡3 are both supplementary to).

This will eliminate choices B (which has  ∡1, but also  ∡4 which isn't necessary), C ( ∡which mentions nothing about  ∡1), and D (which also doesn't mention anything about  ∡1, and which also isn't necessary as we have statement 3 essentially saying the same thing), leaving A as the correct answer.

Answer:

b

Step-by-step explanation:

2 ml/200 mg so divide and you get 1 ml per 100 mg then multiply that my 3 to get 3ml/300 mg therefore the answer is b

Answer:

b. 3 ml

Step-by-step explanation:

300 mg  / 200 mg/ 2 ml   =   300 * 2  / 200 ml = 3 ml

Answer:

Values: 3,4,5

Step-by-step explanation:

I hope this helps:)

Answer: 597

Step-by-step explanation:

The common difference is 5-1=4, so the explicit formula is [tex]a_{n}=1+(n-1)(4)[/tex]

Substituting in n=150,

[tex]a_{150}=1+(150-1)(4)=\boxed{597}[/tex]

Answer: D

Step-by-step explanation:

[tex]\left(\frac{f(x)}{g(x)} \right)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{4x+1}[/tex].

This eliminates A and B.

Also, the domain excludes when the denominator equals 0, which in this case, makes the answer D