find the equation perpendicular to y=-2x+10 through (10, 7)

The probability of choosing a car or a truck is P(Car) + P(Truck).

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Unconstrained population growth equation solved by separation of variables. P = Ce^(Kt). Corrected function found using initial and 5 hour population data. After 10 hours, population is 16,333,333.33.

What is integral ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

(a) Solution by separation of variables:

P' = KP

dp/dt = KP => dP/P = K dt

∫(dP/P) = ∫K dt => ln|P| = Kt + C, where C is the integration constant.

P = Ce^(Kt)

(b) Initial population is 3M and after 5 hours the population is 7M.

Using the formula from (a), we have:

Ce^(K5) = 7M => Ce^(K5) = 7*10^6

3M = Ce^(K0) => 310^6 = C

Therefore, the exact function describing the population growth is:

P = 3*10^6 * e^(Kt)

(c) After 10 hours, the population will be:

P = 310^6 * e^(K10)

(d) The population after 10 hours should be exactly 49/3.

Checking with the formula from (c), we have:

P = 310^6 * e^(K10) = 49/3 * 10^6 = 49,000,000 / 3 = 16,333,333.33

Unconstrained population growth equation solved by separation of variables. P = Ce^(Kt). Corrected function found using initial and 5 hour population data. After 10 hours, population is 16,333,333.33.

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Answer:

yes 2 is only even prime number because it was divide by only 1 and 2

Answer:

yes

Step-by-step explanation:

Yes....every other even number is divisible by two which means they cannot be prime.  Primes are divisible only by 1 and the number itself.

The height of cylinder is 38.772 inches.

Consider r and h as the radius and height of the cylinder, respectively.

Given: Radius of the cylinder (r) = 3 inches

            Surface area of the cylinder = 787 square inches

   Now we have to calculate the height of the cylinder.

As we know the surface area of cylinder

The Surface area of cylinder= Curved Surface + Area of Circular Bases

               787                          =    2πrh + 2πr²

               787                           =    2πr(r+h)

              787                            =    2×3.14×3 (3+h)                 {π=3.14}

              787                             =     18.84 (3+h)

              787÷18.84                   =   (3+h)

              41.772                         =   (3+h)

              41.772-3                      = h

               38.772                        =h

               Height of cylinder= 38.772 inches

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(π/180) x (180) x (7) = (π) x (7) = 21π cm.

The length of the semicircular arc of a circle can be found using the formula:

arc length = (π/180) x (arc degree measure) x (circle's diameter)

If the diameter of the circle is 7cm, then the length of the semicircular arc would be:

(π/180) x (180) x (7) = (π) x (7) = 21π cm.

Answer:11cm

Step-by-step explanation:

Diameter of the circle= 7cm

so, radius of the circle= 7/2= 3.5 cm

for getting length of the semicircular arc= sircumference of circle / 2

circumference of the circle = 2pi r

lenght of the semicircular arc= 2pi r/2

                                             =pi r

                                              = {22/7}*

                                              =11cm

Volume of solid is 343 cubic yards.

Volume is defined as the amount of space occupied by an object within the boundaries in the three dimensional space.

A base of a solid whose height is 7 yards is shown.

Let us consider the solid as cube.

Volume of cube = [tex]a^{3}[/tex] cubic units.

Here side, a =7 yards.

Volume ,V= [tex]7^{3}[/tex] = 343 cubic yards.

Hence, Volume of solid is 343 cubic yards.

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Answer:

Just giving my first answer.I don't know the answer.If I knew I'd tell you

Answer: this will help you

Step-by-step explanation:

A biologist wants to create an SRS to study the effect of a medication on the respiration rate of his subjects.

Answer: B. It is both a random sample and an SRS.

An algorithm to find all nodes less than some value in a binary heap is binary_heap (int, int)

The term called algorithm is defined as  a set of instructions for solving a problem or accomplishing a task.

Here we have know that the binary heap is a full binary tree that means all of its node full with 2 children except last one it may have one child or even empty Also in min heap, all node has value less than its children values in a max heap all node has a value greater than then it can be written as,

void binary_heap(Node *node, int x)

{

   if (node->value >= o(x))

   {

       return 0;

   }

   printf("%d\n", node->value);

   if (node->left != NULL)

       binary_heap(node->left, x);

   if (node->right != NULL)

      binary_heap(node->right, x);

}

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Based on the information we can infer that 25 km is equivalent to 7.5 cm on the map.

To find the relationship between centimeters and kilometers on the map we must take into account the following information:

3cm = 10km

According to the above, we must make a rule of three to find the equivalence of kilometers. Below is the procedure:

According to the above, 7.5 centimeters would represent the 25 kilometers distance on the map.

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The linear inequality in two variables is  3x + 6y ≤ 9 . Option B

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another

Inequalities are math expressions or statements that use the inequalities "less than or equal to", "greater than or equal to", "less than", "greater than", and "not equal to".

Linear expressions are math statements or expressions whose expressions of a degree 1 (Highest exponent).

Variables are mathematical symbol or term that represents the unknown values.

In the problem, the question asks for a linear inequality in two variables. As you can see, all of the choices are linear expressions. The only option that uses one of the inequality symbols and has two unknown variables is the third option. So, it's the option B.

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Answer:

reason 1: Given

reason 2: Property of Cross Multiplication

reason 3: Vertical Angles are Congruent.

reason 4: SAS

Answer:  the answer is $442.80

Answer:

442.80

Step-by-step explanation:

You would first multiply 15 by 36 to get a product of 540. Then you would subtract $540 by $37.80 and $59.40 to get a difference of 442.80

15x36 =540
540 - 37.80 - 59.40 = $442.80

Answer:

The width of the base is 120ft. The length of the base is 60ft less than three times the width [1][2], so the length of the base is 180ft. Therefore, the dimensions of the base are 120ft x 180ft.

The answer will be option C (3.90 cm).

To find the diameter, we need to determine the exact length reading on the main scale and then add the Vernier scale reading. We know that 10 divisions of the Vernier scale coincide with 9 divisions of the main scale.

If the zero of the Vernier scale lies slightly to the left of 3.2 cm on the main scale, then we can assume that it lies between the 3rd and 4th division of the main scale. Since the 4th division of the Vernier scale coincides with a main scale division, we can determine that the length reading on the main scale is 3.3 cm.

Next, we need to determine the Vernier scale reading. Since the 4th division of the Vernier scale coincides with a main scale division, the reading on the Vernier scale is 0.1 cm. Adding the main scale reading (3.3 cm) and the Vernier scale reading (0.1 cm), we get a total length reading of 3.4 cm.

Since the cylinder is tightly placed between the jaws of the callipers, we can assume that this length reading is equal to the diameter of the cylinder. Therefore, the diameter of the cylinder is 3.4 cm. The answer is closest to option C (3.90 cm).

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the probability of success (0.25 in this case), and the number of successes (12 in this case). The command will then calculate the cumulative probability of 12 or fewer employees being late for work.

A company has 20 employees, and each employee has a 25% chance of being late for work. What is the probability that 12 or fewer employees will be late for work?

The calculator command Binomialcdf(20, 0.25, 12) would be used to find the solution.

Binomialcdf is a calculator command used to calculate the cumulative probability of a binomial distribution. The command takes three parameters: the number of trials (20 in this case), the probability of success (0.25 in this case), and the number of successes (12 in this case). The command will then calculate the cumulative probability of 12 or fewer employees being late for work.

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The number of blocks needed to make the 9th figure in the pattern is 24.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Dionne builds a pattern that is represented by the equation b = 2f + 6, where f is the figure number of the pattern and b is the number of blocks in each figure.

For the first figure, number of blocks = (2 × 1) + 6 = 8

For the 2nd figure, number of blocks = (2 × 2) + 6 = 10

This will go on.

For the 9th figure, number of blocks =  (2 × 9) + 6 = 24

Hence there will be 24 blocks in the 9th figure.

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Alright, so they want you to find the probability of landing on 4 or 2.

There are 8 numbers total so that will be our denominator x/8

There are two outcomes we are finding the probability, that gives us 2/8

We must simplify the fraction into its lowest form.

2/8=1/4

Your answer would be 1/4

The solution to the given recurrence relation is (c): ak = (3^k + 1) + 2^k + 1

The solution of the given recurrence relation can be found by substitution. We can substitute the given formula for ak into the equation for a_(k+1) and see if the two are equal. If they are equal, then we have the solution.

Starting with the equation for ak:

a_k = 2a_(k-1) + 3^k

Substituting the formula for ak-1:

a_k = 2(2a_(k-2) + 3^{k-1}) + 3^k

Expanding the right side:

a_k = 4 a_(k-2) + 2 * 3^{k-1} + 3^k

Continuing this process, we can see that the solution is:

a_k = 2^(k) a₀ + (2^{k-1} + 2^{k-2} + ... + 2^1) * 3^{k-1} + 3^k

Since the series 2^k-1 + 2^{k-1} + ... + 2^1 = 2^k - 1, we have:

a_k = 2^(k) a₀ + (2^k - 1) * 3^{k-1} + 3^k

Substituting the initial value a₀ = 5:

a_k = 2^(k) * 5 + (2^k - 1) * 3^{k-1} + 3^k

Simplifying:

a_k = 2^{k} (5 + 3^{k -1}) - 3^{k-1}(1 + 3)

a_k =  2^{k} (5 + 3^{k -1}) - 4* 3^{k-1}

a_k = 5* 2^{k} + 3^{k -1}( 2^{k}  - 4)

So, the solution to the given recurrence relation is (c):

ak = (3^k + 1) + 2^k + 1

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The equation of the line perpendicular to the line 2x + 5y + 5 = 0 is 5x - 2y + 1 = 0.

As per the given data the given equation is 2x + 5y + 5 = 0

Here we have to determine the equation of the line perpendicular to the line 2x + 5y + 5 = 0

Firstly write the equation in y = mx + c format.

2x + 5y + 5 = 0

5y = -2x - 5

y = [tex]$\frac{-2}{5}[/tex]x - 1

[tex]m_{1}=\frac{-2}{5}[/tex]

Condition for two perpendicular lines.

[tex]m_{1} \times m_{2}[/tex] = -1

[tex]$\frac{-2}{5} m_{2} = -1[/tex]

[tex]$m_{2} = \frac{5}{2}[/tex]

Now substitute the slope value in the equation y = mx + c

We get:

y = [tex]$(\frac{5}{2} )[/tex]x + c

2y = 5x + 2c

2y - 5x = 2c

Since the line passes through (-1, -2)

Hence:

2(-2) - 5(-1) = 2c

-4 + 5 = 2c

2c = 1

c = [tex]$\frac{1}{2}[/tex]

Now substitute the value of c in 2y - 5x = 2c

2y - 5x = 2[tex]$(\frac{1}{2} )[/tex]

2y - 5x = 1

(0r)

5x - 2y + 1 = 0

Therefore the equation is 5x - 2y + 1 = 0.

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The area of R is ln(4) - ln(√2) and the value of k is √2.

a) To find the area of the region R, we need to find its definite integral with respect to x. Using substitution, we can write the integral as follows:

Let u = [tex]x^{2}[/tex] + 2, du/dx = 2x, dx = du/2x

Area of R = ∫[0,√6] x/([tex]x^{2}[/tex] + 2) dx = ∫[2,8] (1/2) du/u = (1/2) ln(u) evaluated from 2 to 8 = (1/2) ln(8) - (1/2) ln(2) = ln(4) - ln(√2)

b) The line x = k divides the region R into two regions of equal area if the definite integral of R with respect to x from 0 to k is equal to the definite integral of R with respect to x from k to √6.

Letting k = x in the definite integral, we have:

∫[0,k] x/( [tex]x^{2}[/tex]  + 2) dx = ∫[k,√6] x/( [tex]x^{2}[/tex]  + 2) dx

(1/2) ln([tex]k^{2}[/tex] + 2) - (1/2) ln(2) = (1/2) ln(6 - [tex]k^{2}[/tex] ) - (1/2) ln(2)

Solving for k, we get:

ln( [tex]k^{2}[/tex]  + 2) = ln(6 - [tex]k^{2}[/tex] )

[tex]k^{2}[/tex] + 2 = 6 - [tex]k^{2}[/tex]

2 [tex]k^{2}[/tex]  = 4

k = ±√2

Since k must be in the first quadrant, k = √2.

So, the line x = √2 divides the region R into two regions of equal area.

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The arc length covered by the central angle equal to 72° is 12.56°

Arc length is the distance between two points along a section of a curve.

Given that, a circle with radius 10 units and a central angle equals 72°, we need to find the arc length covered by the central angle = 72°

We know that,

Arc length = 2π × radius × (θ / 360°), where θ is the central angle

Arc length = 2 × 3.14 × 10 × 72°/360°

= 12.56°

Hence, the arc length covered by the central angle equal 72° is 12.56°

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Answer:

(x-4)2=16

Step-by-step explanation:

Answer/Step-by-step explanation:

All numbers that are divisible by 9 are also divisible by 3.

Since 3 goes into 9, if 9 is a factor, 3 is also a factor.

Example:

81 is divisible by 9.

So, 81 is also divisible by 3.



Another example:

1,273,050 is divisible by 9.

So 1,273,050 is also divisible by 3.

But the other way around is not necessarily true. If 3 goes into a number, 9 may or may not go into the number.

That is, if a number is divisible by 3, you cannot necessarily know that it is divisible by 9.

Example (seems like it works):

18 is divisible by 3. 18 is also divisible by 9.

But it doesn't work every single time so it cannot be a rule.

Example(sometimes it doesn't work):

24 is divisible by 3.

24 is not divisible by 9.

z=122/17

Step-by-step explanation:

1) Distribuez: 278=34z+34

2) Soustrayez 34 des deux côtés: 244=34z

3) diviser les deux par 34 puis simplifier: le résultat est z= 122/17

Answer:

0.6 divided by 78 is 0.00769230769

or if you meant

78 divided by 0.6 it is 360

Step-by-step explanation:

The maximum number of major ideas that can be included in a specific purpose statement depends on several factors, but it is generally recommended that the statement include one to three major ideas. This helps the speaker to focus their ideas and organize their content in a way that effectively communicates their message to the audience

A specific purpose statement is a statement that defines the main objective or goal of a speech or presentation. It serves as a guide for the speaker, helping them to focus their ideas and organize their content in a way that effectively communicates their message to the audience.

The number of major ideas that can be included in a specific purpose statement depends on several factors, including the length of the speech or presentation, the complexity of the topic, and the speaker's ability to effectively communicate their message.

In general, it is recommended that a specific purpose statement include only one to three major ideas. This allows the speaker to focus their attention on a limited number of key points and ensures that the audience is not overwhelmed with too much information. Additionally, having a limited number of major ideas makes it easier for the speaker to organize their content and for the audience to understand and retain the information.

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A specific purpose statement should include one or two major ideas that are focused and directly relevant to the topic at hand.

Including too many ideas can make the statement confusing and difficult for the audience to understand, so it's important to be selective about which ideas to include.

The goal is to create a specific purpose statement that is clear, concise, and easy for the audience to understand, while effectively conveying the key ideas of the communication.

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The required triangles that are similar by angle-angle similarity are,

(1)    ΔCDE ≅ ΔGFE    (2)  ΔLQP ≅ ΔLMN     (3)  ΔSTE ≅ ΔCWH

(4) Triangles are not similar.   (5)  Triangles are not similar.

(6) ΔPXQ ≅ ΔZXY

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,

(1)

Consider ΔCDE and ΔGFE

∠C = ∠G   [alternate interior angle of parallel lines]

∠CED = ∠GEF   [opposite angles]

There, for ΔCDE ≅ ΔGFE bu AA postulate.

Similarly,

(2)  ΔLQP ≅ ΔLMN

(3)  ΔSTE ≅ ΔCWH

(4) Triangles are not similar.

(5)  Triangles are not similar.

(6) ΔPXQ ≅ ΔZXY

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