if distance between points p(3,a) and q(3,1 is 4 units find the value of a ​

The exact value of the sine of angle R is equal to 1 / 2.

In this problem we find the representation of a right triangle, where two side lengths are known and the exact value of a trigonometric function must be found. First, determine the length of side PR:

PR = 72 cm - PQ

PR = 72 cm - 24 cm

PR = 48 cm

Second, determine the length of side PQ by Pythagorean theorem:

RQ = √[PR² - PQ²]

RQ = √[(48 cm)² - (24 cm)²]

RQ = 24√3 cm

Third, determine the exact value of a trigonometric function of angle R by definition of sine:

sin R = PQ / PR

sin R = (24 cm) / (48 cm)

sin R = 1 / 2

Fourth, determine the exact value of a trigonometric function of angle R by definition of cosine:

cos R = RQ / PR

cos R = (24√3 cm) / (48 cm)

cos R = √3 / 2

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A number line that models the expression 1/8 - (-3/4) is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Next, we would evaluate and add the given numbers together as follows:

Number = 1/8 - (-3/4)

Number = 1/8 + 3/4

Number = 7/8

In conclusion, you would start at 1/8 on the number line and move 3/4 places to the right.

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In a relay race each friend run a distance of 0.52 miles.

The distance of the race divided by the runners' times will give you their average velocities.

We are given that

Total distance covered in a race = 3.12 miles

Total number of persons = 6

Each person runs equal parts of the race.

We have to find the miles run by each person.

To find the distance covered by each person we will divide the total distance by total number of persons who took part in a race.

Each person runs = Total distance/ Total number of persons

Each person runs= 3.12 / 6 miles

Each person runs = 0.52 miles

Hence, each person runs 0.52 miles.

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The data does not take into account population increases over the two years. It is possible that there were more people in 2002, so the number of cases could have gone up without there being an actual increase in the rate of infection.

It could also be the case that better reporting and the more accurate diagnosis were responsible for the increase in numbers. The two-year period could also be too short to draw any meaningful conclusions. Diseases can have long-term cycles of increase and decrease, so it is possible that the increase in numbers was just part of a longer-term cycle that had already been in progress.

To accurately assess the situation, it would be necessary to look at longer-term data and take into account changes in population size.

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According to the parallelogram, the slope of the segment QR is 3/2

In math the term called parallelogram is a closed quadrilateral with parallel and congruent opposite sides is referred to as a parallelogram and the opposite pairs of sides have the same slope and the sum of two adjacent angles is 180 degrees.

Here we have know that values of P is located at (-1, 6) and S is located at (-7,-3). Then the slope of QR is calculated by using the the slope formula for a line segment passing through two points,

It can be calculated as,

=> m = (-3 - 6) / (-7 - (-1)

When we simplify this one then we get,

=> m = -9/-6

=>  m = 3/2

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A measure computed from the entire population is called a parameter. Option D is the correct answer.

A parameter is a numerical characteristic of the population, and it is usually estimated from a sample of the population. Parameters are usually unknown and are estimated using a variety of mathematical methods.

Examples of parameters include the population means, median, and standard deviation. Parameters can also be used to describe the characteristics of a population, such as the percentage of people who are a certain color, race, or gender.

Parameters are usually reported in summary form, such as the mean or median of a population. In contrast, a statistic is a measure computed from a sample and is not representative of the entire population. Statistics are used to make estimates and predictions about a population and are usually reported in the form of a confidence interval.

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If the town has a population of 20000 and grows at 5% every year , then the time required for the population to reach 41600 is 15 years .

To find out how long it will take for the town's population to reach 41600, we can use the formula :

⇒ A = P(1 + r)ⁿ

Where:

A = final population of town , P = initial population o town

r = percent increase (as a decimal)

let n = number of years for population to reach 41600 .

We know the final population is 41600, the initial population is 20000, the percent increase is 5% = 0.05  and we have to solve for n.

Substituting the values ,

we get ;

⇒ 41600 = 20000(1 + 0.05)ⁿ  ;

⇒ 41600 = 20000(1.05)ⁿ  ;

⇒ 41600/20000 = (1.05)ⁿ  ;

taking "log" on both sides ,

we get ;

⇒ log(41600/20000) = n × log(1.05)  ;

⇒ n = log(41600/20000)/log(1.05)  ;

⇒ n = 15.0105 ≈ 15

Therefore ,  it will take approximately 15 years for the town's population to reach 41600, to the nearest tenth of a year.

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The meaning of the rate of change in the context of this problem is 4/7.

P-8 / p(14)

8p / p(14) =4/7

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Answer:

The square root of 50 can be simplified to the radical form of 5*sqrt(2)

Step-by-step explanation:

To simplify the square root of 50, we factor the number 50, which is 50 = 510 = 552. The square root of any number that is a perfect square, such as 55, is equal to the number inside the square root, which is 5 in this case. The square root of any number that is not a perfect square, such as 2, remains under the radical sign.

Therefore, the simplified radical form of the square root of 50 is √50 = 5√2.

The square root of 50 in simplest radical form is 5√2.

To find the square root of 50 in simplest radical form, we need to determine if there are any perfect square factors in 50 that can be taken outside the square root symbol.

The prime factorization of 50 is 2 × 5².

We can see that 5² is a perfect square factor of 50.

Therefore, we can rewrite the square root of 50 as the square root of (2 × 5²).

Using the property of square roots, we can split the square root of a product into the product of the square roots of each factor:

√(2 × 5²) = √2 × √(5²)

The square root of 5² simplifies to 5, so we have:

√(2 × 5²) = √2 × 5

Therefore, the square root of 50 in simplest radical form is 5√2.

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Answer: (-5, -2)

Step-by-step explanation:

         We will substitute the first equation into the second and then solve for x. Then we will substitute x into the equation and solve for y.

Given:

    5x + 3y = -31

Substitue:

    5x + 3(x + 3) = -31

Distribute:

    5x + 3x + 9 = -31

Combine like terms:

    8x + 9 = -31

Subtract 9 from both sides of the equation:

    8x = -40

Divide both sides by 8:

    x = -5

Given:

    y = x + 3

Substitute x into the equation and solve for y.

    y = (-5) + 3

Combine like terms:

    y = -2

We can also graph it. The point of intersection is the solution, see below.

Answer:

5650

Step-by-step explanation:

3 (1/8)% =3.125% but compound daily = 3.125% /365 = 0.00856%

so everyday the money grows at 1.00856%, so compound 365 times, it'll become 1.00856%^365 =3.1742% annually equivalent.

so now you can compare the 2 - apples to apples.

so 3.1742%^15years * 59000 = $94,279.80

2.75%^15years * 59000 = $ $88,629.74

diff is 5650$

The increase in earnings brought on by producing one extra unit is known as the marginal profit. The proper domain for functions is the integers (0, 1, 2, ...).

By dividing marginal revenue by marginal cost, one can compute marginal profit. Because it can help determine whether to raise or lower the level of output, marginal profit analysis is useful.

Any quantity of output below the one at which marginal profit equals zero has a positive marginal profit, meaning that profit can be increased by producing more of that quantity. Conversely, any quantity of output above the one at which marginal profit equals zero has a negative marginal profit, meaning that profit can be increased by producing less of that quantity.

A company that manufactures and sells shirts. Daily profit of...

A company that manufactures and sells shirts. The daily profit the company makes depends on the number of shirts sold. The profit in dollars if a company sells x shirts can be found using the function f(x)=7x-40. Locates and interprets given function values ​​to determine the appropriate domain for the function.

f(-10) = -110, which means that if the company sells -10 shirts, it will make a profit of -$110. This interpretation makes no sense in the context of the problem.

f(10) = 26.5, so if the company sells 9.5 of his shirts, he makes a profit of $26.5. This interpretation makes no sense in the context of the problem

f(9.5) = 26.5, so if the company sells 9.5 shirts, it makes a profit of $26.5. This interpretation makes no sense in the context of the problem.

Therefore, based on the above observations, it is clear that the proper domain for functions is the integers (0, 1, 2, ...).

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The amount of commission that Joan earns this month on sales will be $480.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Joan earns an 8% commission on her sales this month Joan had $6000 in sales.

Let 'x' be the commission. Then the equation is given as,

x / $6,000 = 0.08

x = 0.08 · $6,000

x = $480

The amount of commission that Joan earns this month on sales will be $480.

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Answer: 10. 3

Step-by-step explanation: 4x3=12, ad 3x3 is 9 so all the sides of the triangle are multiplied by 3

Answer:

68888jours 9999999888

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = - 3x + 2.5

The value of the equation at x = 1 will be given as,

y = - 3 × (1) + 2.5

y = - 3 + 2.5

y = - 0.5

The value of the equation at x = - 1.5 will be given as,

y = - 3 × (-1.5) + 2.5

y = 4.5 + 2.5

y = 7

The value of the equation at x = 8.5 will be given as,

y = - 3 × (8.5) + 2.5

y = - 22.5+ 2.5

y = - 20

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

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Complete question:

The length of the hypotenuse is 43.37 .

Now, According to the question:

Pythagorean triples are [tex]a^2+b^2 = c^2[/tex] where a, b and c are the three positive integers. These triples are represented as (a, b, c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle. The most known and smallest triplets are (3,4,5).

Now, Solving the problem:

There are two sides :

a = 9

b = 40

and, to find the length of the hypotenuse.

According to the Pythagoras formula:

[tex]a^2+b^2 = c^2[/tex]

Plug the values in above formula:

[tex]9^2+40^2=c^2[/tex]

81 + 1600 = [tex]c^2[/tex]

[tex]c^2[/tex] = 1681

c = [tex]\sqrt{1681}[/tex]

c = 43.37

Hence, The length of the hypotenuse is 43.37 .

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A graph of the solution to this inequality a > -3 is shown on the number line attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given inequality a > -3 as shown on the number line (graph) attached below.

In conclusion, the circle on the number line (graph) is open because of the greater than (>) symbol and it increases to the right of the number line.

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Complete Question:

Find the solution to this inequality a > –3.

The function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1 because the limit of h(t) as t approaches 1 is equal to h(1).

First, we need to show that the limit of h(t) as t approaches 1 is equal to h(1).

Since h(t) = (2t-3t^2)/(1+t^3), we can rewrite the limit of h(t) as t approaches 1 as:

lim t->1 (2t-3t^2)/(1+t^3) = lim t->1 (2-3t)/(1+t^3)

We can now use the properties of limits to evaluate the limit.

Substituting t=1 into the expression for the limit, we have:

lim t->1 (2-3t)/(1+t^3) = (2-3(1))/(1+(1)^3) = -1/(2)

Now, we can use the definition of continuity to show that h(t) is continuous at a=1.

Since the limit of h(t) as t approaches 1 is equal to h(1), then h(t) is continuous at a=1.

Thus, we have successfully shown that the function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1.

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The required distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.

This problem is related to the chapter fractions. The relation between the distances travelled by both the people is given, so that we can calculate the actual distance travelled by the second person.

Karis ran 3 2/3 miles on Monday.

It is said that Benita ran half of the distance ran by Karis.

So, the distance ran by Benita would be,

⇒ 3 2/3 × 1/2

⇒ 11/3 × 1/2

⇒ 11/6 miles

Thus, the distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.

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Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.

As per the data given in the above question are as bellow,

A material has a half-life when it takes a particular length of time for half of it to disappear or change.

11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.

We thus split the 3 mg sample in half three times.

3 ÷ 2 = 1.5

1.5 ÷ 2 = 0.75

0.75 ÷ 2 = 0.375

After 11.46 days, there will only be 0.375mg of radon-222 left.

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If in the energy category, Khalil scored low on the intuitive function in which he must he have scored high on the function, which involves looking for the facts, focusing on specifics, taking realistic. This is an example of : A. observant

To be observant can be defined as the way in which a person tend to watch others  or when a person observe the event happening around him/her .

This scenario is an example of observant based on the fact that this person  watch the event happening in  Khalil life and this was done by carefully observing Khali and things that happen around Khali.

Therefore the correct option is A.

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Janet's total tax allowances for the year are $27,200.

The first step is to convert the monthly gross salary to the annual gross salary by multiplying it by 12.

The insurance allowance is computed by applying the rate to the annual gross salary.

The personal and insurance allowances are added to determine the total tax allowances.

Generally, tax allowances reduce the taxpayer's taxable income.

Gross salary per month = $24,000

Annual gross salary = $288,000 ($24,000 x 12)

Personal allowances per year = $20,000

National insurance = 2¹/₂%

= $7,200 ($288,000 x 2¹/₂%)

Total allowances for the year = $27,200 ($20,000 + $7,200)

Thus, Janet is entitled to a total tax allowance of $27,200 for the year.

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60% of the pieces of candy in the bowl are chocolate.

(15/25)*100 = 60%

If the lamp is 3.6 m above the ground, the length of her shadow is 1.2 m.

In algebra proportionality is equality between two ratios. In the mathematical expression a/b = c/d, a and b are in the same proportion as c and d.

Height of the girl = 0.9 m.

Height of the lamp = 3.6 m.

Distance between the lamp and the girl = 4.8 m.

Let the length of her shadow = x m.

From proportionality relation:

3.6 : 4.8 = 0.9 : x

3.6/4.8 = 0.9/x

3.6x = 4.8 × 0.9

x  = (4.8 × 0.9) ÷ 3.6

x = 1.2

Hence, the length of her shadow is 1.2 m.

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The volume of One cone held 1.1017.36 inches3 of water when it was full.

A cone's volume is determined using the following formula:

V = 1/3πr²h

R is the radius, and H is the height.

the aforementioned conditions

A cone's volume is determined using the following ,

V = 1/3πr²h

R is the radius, and H is the height.

the aforementioned conditions

r = 12/2 = 6in

h =27in

Discover the volume V = 1/3(3.14)(6)2*27

V = 1.1017.36

In light of this, one cone held 1.1017.36 inches of water.

One cone held 1.1017.36 inches of water.

The complete question is,

Construction cones were soaked with water while a project was underway due to a strong downpour. A cone has a 12 inch diameter and a 27 inch height.

How much water was used to fill each cone?

Put a decimal in the box for your response. Pi is equal to 3.14; in3

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Answer:

I think the answer is C

-3,-2

The domain and range for the function for the maximum height of the rockets Kate fires is; h = 70·t - 16·t² are;

Domain; 0 ≤ t ≤ 4.375

Range; 0 ≤ h ≤ 39.06

A function is a rule that defines the relationship between input variables and output variables, such that the each value from the set of input variables are assigned to exactly on variable from the set of output variables.

The possible specified function in the question is; h = 70·t - 16·t², and the possible required details is the domain and range that best represent the situation.

The domain of the above function is the set of possible input (t) values, which is found by the time it takes the rocket to land after flight as follows;

At ground level, h = 0, therefore;

h = 70·t - 16·t² = 0

(70 - 16·t)·t = 0

A possible solution is therefore, t = 0

The other solution is found as follows;

(70 - 16·t) = 0

70 = 16·t

16·t = 70

t = 70/16 = 4.375

The other solution or time at which the rocket is at ground level is t = 4.375

The range is the set of possible h values, which is obtained as follows;

The maximum point of the quadratic function, f(x) = a·x² + b·x + c, is the point, x = -b/2·a. Therefore, comparison between the function, f(x) = a·x² + b·x + c, and h = 70·t - 16·t², we get;

a = -16

b = 70

c = 0

The maximum height reached, therefore is obtained at the point, at which; t = -70/(2 × (-16)) = 2.1875

The maximum height, [tex]h_{max}[/tex], is therefore;

[tex]h_{max}[/tex] = 70 × 2.1875 - 16 × 2.1875² =  76.5625

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The quotient of 6y^4 + 10y³ - 8y² by 2y is given as follows:

6y³ + 10y² - 4y.

The dividend is given as follows:

6y^4 + 10y³ - 8y²

The common factors are given as follows:

Hence the dividend can be simplified as follows:

2y²(6y² + 10y - 4).

Simplifying by 2y, the result of the quotient is given as follows:

y(6y² + 10y - 4) = 6y³ + 10y² - 4y.

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The expression can be simplified as follows:

2(x - y)/[y(x + y)]

The condition for the expression is given as follows:

x ≠ y, y ≠ 0.

The expression for this problem is defined as follows:

[(x - y)²]/(2xy + 6y) x (4x + 12)/(x² - y²)

The factors of the expression can be simplified as follows:

The terms that can be simplified are given as follows:

Hence the product is given as follows:

(x - y)/(x + y) x 2/y

2(x - y)/[y(x + y)]

As the expression is a fraction, the denominator cannot be zero, hence the conditions are given as follows:

x ≠ y, y ≠ 0.

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