Determine whether (3,2) is a solution of y = 3x +2.​

Answer:

-0.5f - 4.52 = -25.52 + 1f

-1.5f = 21

f = 14

Answer:

14

Step-by-step explanation:

-4.52 + 25.52 = f + 0.5f

21 = 1.5f

f = 14

Answer:

x-intercept = 2

y-intercept = 6

Step-by-step explanation:

x-intercept:  6x = 12;  x = 2

y-intercept:  2y = 12;  y = 6

Answer:

x = 652.7

Step-by-step explanation:

x = (tan 40° x 500) + (tan 25° x 500) = 419.55 + 233.15 = 652.7

The value of d after addition or subtraction is 7.5

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.

Given that : the equation is 5.5 = −2+d

5.5 = −2+d

5.5 + 2 = d

7.5 = d

The value of d after addition or subtraction is 7.5

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To find the equation of the tangent line to the curve y = tan²(2x) at x = π/4, we need to determine the slope of the tangent line at that point and then use the point-slope form of a line to write the equation.

First, let's find the derivative of y with respect to x. Using the chain rule, we have:

dy/dx = 2tan(2x) sec²(2x).

Now, let's substitute x = π/4 into the derivative:

dy/dx = 2tan(2(π/4)) * sec²(2(π/4))

      = 2tan(π/2) * sec²(π/2)

      = 2(∞) * 1

      = ∞.

The derivative at x = π/4 is undefined, indicating that the tangent line at that point is vertical. Therefore, the equation of the tangent line is x = π/4. Note that the equation y = 2/tan(2x) (sec²(2x) + 1/2) is not the equation of the tangent line, but rather the equation of the curve itself. The tangent line, in this case, is vertical.

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Answer:

16 pounds

Step-by-step explanation:

Given that:

Soap box derby rules :

Racer ≤ 250 pounds

Weight of math club car = 266 pounds

Amount of weight to be removed = a:

266 - a ≤ 250

266 - 250 ≤ a

a ≥ 16 pounds

The slope-intercept representation of a linear function is given by the rule shown as follows:

y = mx + b

The coefficients of the function, along with their meaning, are listed as follows:

Given two points, only one line will pass through them.

Using a calculator, the lines are given as follows:

Then the x-coordinate of the point in which the lines intersect is obtained as follows:

4x - 1 = -1.25x + 10.5

5.25x = 11.5

x = 2.19.

The y-coordinate can be found in any of the equations, hence:

y = 4(2.19) - 1 = 7.76.

Another point on the line y = 4x - 1 has a x-coordinate of 3 and an y-coordinate obtained as follows:

y = 4(3) - 1 = 12 - 1 = 11.

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The length of the surface in scientific form is

\(3 \times {10}^{ - 2}\)

Given that :

Width = 0.0002 m

Width = 0.0002 mArea = 0.000006 m²

Length = l

Recall :

Area of rectangle = Length × width

Length = width / Area of rectangle

Length = 0.000006 / 0.0002

Length = 0.03 m

In scientific form ; 0.03 = 3 × 0.01 = 3 × 10^-2

=

\(3 \times {10}^{ - 2} \)

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Answer:

69

Step-by-step explanation:

3.3x21=69.3

Answer: 0 bottles of Brand X and 10 bottles of Brand Y

(please let me know if I read the question wrong and I will do my best to fix it)

Step-by-step explanation:

This problem can be solved using linear programming. Let x be the number of Brand X bottles and y be the number of Brand Y bottles. The objective is to minimize the cost, given by:

Cost = 25x + 15y

Subject to the following constraints, which represent the minimum nutrient requirements:

3x + 9y ≥ 30 (Nutrient A)

3x + 2y ≥ 16 (Nutrient B)

7x + 2y ≥ 24 (Nutrient C)

x ≥ 0, y ≥ 0 (Non-negativity constraint)

We can solve this system of inequalities graphically by finding the feasible region and the corner points.

Nutrient A constraint (3x + 9y ≥ 30):

Divide the inequality by 3:

x + 3y ≥ 10

Nutrient B constraint (3x + 2y ≥ 16):

Divide the inequality by 2:

1.5x + y ≥ 8

y ≥ 8 - 1.5x

Nutrient C constraint (7x + 2y ≥ 24):

Divide the inequality by 2:

3.5x + y ≥ 12

y ≥ 12 - 3.5x

Now we will graph the inequalities on the xy-plane:

y ≥ 10 - x/3

y ≥ 8 - 1.5x

y ≥ 12 - 3.5x

The feasible region is the area where all three inequalities are satisfied. It's a triangular region with corner points A(0,10), B(4,4), and C(8/3, 2).

Now we need to find the cost at each corner point:

Cost A (0, 10) = 25(0) + 15(10) = $150

Cost B (4, 4) = 25(4) + 15(4) = $160

Cost C (8/3, 2) = 25(8/3) + 15(2) ≈ $153.33

The minimum cost is $150, which occurs when 0 bottles of Brand X and 10 bottles of Brand Y are used. So, the public aquarium should add 0 bottles of Brand X and 10 bottles of Brand Y to satisfy the needs of the reef tank at the minimum possible cost.

Therefore , the solution of the given problem of fraction comes out to be  1/729.

Any arrangement of components of the same size can be put together to represent the whole. Quantity is described as "a portion" in a certain measure in Standard English. 8, 3/4. Fractions are included in wholes. The ratio, which would in arithmetic is a pair of numbers, has these as its divisor. These are just a few examples of how to divide basic fractions into whole numbers. The remainder is a difficult fraction even though the quantity itself involves a fraction.

Here,

Jayne may have calculated StartFraction 1 Over 729 EndFraction, which is the cube of the reciprocal of 9:

=> (1/9)³

=>  1/(999)

=>  1/729

Therefore , the solution of the given problem of fraction comes out to be  1/729.

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Step-by-step explanation:

x= 0 y= 5

y=mx+b

5=b

x= -3 y= -4

-4= -3m +5

-3m = -9

m= 3

y= 3x +5

The system of linear inequalities graphed is the option;

x < -3, y ≤ -x - 1

An inequality is the comparison between expressions that are not equal

The points on the graph are; (-1, 0), and (0, -1)

The slope, m, of the line on the graph is therefore;

m = (0 - (-1))/(-1 - 0) = -1

The equation is therefore;

y - 0 = -1 × (x - (-1)) = -x - 1

y = -x - 1

The shaded region of the graph is the region below the line, y = -x - 1

The type of the line of the graph is a solid line, which gives the inequality;

y ≤ -x - 1

The equation of the dashed line is x = -3

The shaded region is to the left of the line x = -3, which indicates that the inequality is; x < -3

The correct options that represent the graphed linear inequality is; x < -3, y ≤ -x - 1

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Answer:

Your answers are:

A, B and C

Step-by-step explanation:

So 12 over 3 is equal to 4 which is a Whole number. meaning Not a fraction, an Integer is a whole number (not a fractional number) that can be positive, negative, or zero. Rational numbers would include this example as well

Hope this helped have a wonderful day/night/afternoon

The domain of the function f(x, y) = 1 / √(x² + y² - 24) in the xy plane is the region inside a circle, excluding the circle itself.

The correct answer is "The region in the xy plane inside a circle, excluding the circle."

The function f(x, y) = 1 / √(x² + y² - 24) represents a three-dimensional surface in the xyz space. When considering its domain in the xy plane, the function is defined for all points inside the circle centered at the origin with a radius of √24. This is because the square root term must have a non-negative value for the function to be defined.

However, the function is not defined at any point on the circle itself where the denominator becomes zero.

Therefore, the domain of the function in the xy plane is the region inside the circle, excluding the circle itself. This can be visualized as a filled disk in the xy plane. In other words, any point within the disk, but not on its boundary, is in the domain of the function.

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The range of ƒ can be expressed in interval notation as:

ƒ(x, y, z) = CV(17² - 37) + (-∞, 3), where (-∞, 3) represents the open interval of values that satisfy z² + 3y² < 3.

To find the range of the function ƒ(x, y, z) = 2x + CV(17² - 37) - ƒ(z, y) - ln(3 - z² - 3y²), we need to determine the set of all possible values that ƒ can take.

For the first term, 2x + CV(17² - 37), the range of x does not affect the outcome. The term CV(17² - 37) will be a constant value.

For the second term, -ƒ(z, y) - ln(3 - z² - 3y²), we need to consider the range of z and y.

Since the natural logarithm function is only defined for positive values, we have the restriction 3 - z² - 3y² > 0. Simplifying this inequality, we get z² + 3y² < 3.

Combining these results, the range of the function ƒ is determined by the constant term CV(17² - 37) and the restriction z² + 3y² < 3.

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Answer:

-1/2f I think

Step-by-step explanation:

distribute the -1/2

use differentiation rules

calculate all together

then simplify

Hope this helps

Answer: 6 candies

Step-by-step explanation:

So if the teacher buys 12 packs of 8 candies she will have 96 candies in total giving each of the 30 students 3 candies. That leaves her with 6 candies to enjoy by herself.

Answer:

The arteries

Step-by-step explanation:

Answer:

Question 1: Artery

Question 2: Cardiovascular Activity

Step-by-step explanation:

Answer:

23.6 and 106.4

Step-by-step explanation:

The height of the triangle as calculated from the data given above is found out to be as √60 meters.

The given question can be solved by the implication of Pythagorean theorem as the figure is in the form of a triangle.

Let the, base of the triangle be , 2 meters

the hypotenuse be , 8 meter.

Therefore the height of the pole will be ,

AB² = AC²  - BC²

      = 64 - 4

      = 60

Then , we can say that AB = √60

Therefore, the height of the pole is found to be as √60 meters.

Pythagoras theorem states that the sum of two side of a triangle is equal to the hypotenuse of that triangle , AB² = AC²  - BC² .

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The estimated value of the explanatory variable is not statistically significant at the 5%-level if a. the t-statistic is greater than 2.5.

The t-test is a hypothesis testing technique used to decide whether the estimated coefficient of a linear regression model is statistically significant or not. The t-value is used to measure the size of the difference between the estimated coefficient and the hypothesized value. When the t-value exceeds a critical value, such as 2.5, the estimated value of the explanatory variable is not significant at the 5%-level. It implies that the null hypothesis, which assumes that the explanatory variable's coefficient is zero, cannot be rejected.

The p-value is a measure of the probability of obtaining a more extreme value of the test statistic than the observed value if the null hypothesis is true. A small p-value implies that the null hypothesis should be rejected. When the p-value is less than 0.05, it means that the estimated value of the explanatory variable is significant at the 5%-level.

The confidence interval is a range of values that is expected to include the true value of the population parameter with a specified level of confidence. A 95% confidence interval means that the true value of the population parameter lies within the range 95% of the time. The 95% confidence interval does not contain zero implies that the estimated value of the explanatory variable is statistically significant at the 5%-level since it suggests that the population parameter is different from zero at the 5%-level. Conversely, if the 95% confidence interval contains zero, the estimated value of the explanatory variable is not statistically significant at the 5%-level since it means that the population parameter is not different from zero at the 5%-level. Therefore, it is essential to examine the t-statistic, p-value, and confidence interval while conducting hypothesis testing to make an informed decision.

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The area of the playground of dimensions 18 and 240is 432 \(m^{2}\).

Given  If the dimensions of the playground in the layout are given by 180 cm x 240 cm.

The area of rectangle is length *breadth.

The given playground is in the shape of rectangle because there are two sides given and both the sides are different. In a rectangle length of opposite side found to be equal and each side form an angle of 90 degree.

Area=length*breadth

=180*240

=43200 \(cm^{2}\)

We have to convert in meters so we have to divide by 100.

Area=43200 \(cm^{2}\)

=43200/100

=432 \(m^{2}\)

Hence the area of playground having dimensions 180 cm and 240 cm is 432\(m^{2}\).

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Answer:

\(\dfrac{1}{2}\) day

Step-by-step explanation:

Given that:

Owen who is an alien has only 4/5 of his socks clean.

and he wears 2/5 socks a day.

Out of his total 4/5 clean socks.

It will take him (4/5 ÷ 2/5) days to wash all his socks

i.e

the numbers of days since he washed all his socked is:

= \(\dfrac{4}{5} \div \dfrac{2}{5}\)

= \(\dfrac{4}{5} \times \dfrac{5}{2}\)

= \(\dfrac{1}{2}\)

The probability that exactly one tank in the sample contains high-viscosity material is P(A)=0.461.

We will use two concepts in solving this problem.

The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

a) The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )!    ⇒  C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!  

( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2    ⇒  C ( 24,4) =  10626

TE = 10626

Splitting the group of tanks in two 6 with h-v  and 24-6 (18) without h-v

we get that the total number of favorable events is the product of:

FE = 6* C ( 18, 3)  = 6 * 18! / 3!*15!  =  18*17*16*15!/15!

FE =  4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0.4607

b) P(B) will be the probability of at least 1 tank containing h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

The total number of favorable events for the occurrence of P is C (18,4)

FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

FE = 18*17*16*15/4*3*2

FE = 3060

Then P = 3060/10626

P = 0.2879

And the probability we are looking for is

P(B) = 1 - 0.2879

P(B) = 0.7120

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No, just like the average (mean) it is a mathematical quantity that is determined by its mathematical definition and the everyday meaning of “expected” is only a descriptive hint toward what it represents.

What does the expected value of a random variable mean?

Is the expected value always equal to the mean?

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Answer:

6 cm

Step-by-step explanation:

Given that:

A line that contains the points R, S and T.

Distance between R and S = \(2x\)

Distance between S and T = \(3x\)

To find:

The distance between S and T = ?

Solution:

The given situation and dimensions can be represented in the form of a diagram as shown in the attached diagram.

As per given statement and in the diagram, we can deduce that the sum of distance between R and S, S and T is equal to distance between R and T.

i.e. RS + ST = RT

\(2x + 3x = 10\\\Rightarrow 5x=10\\\Rightarrow x = 2\)

ST = 3\(x\) = 3 \(\times\) 2 = 6 cm

Therefore, the answer is:

Distance between S and T is 6 cm.

If the space between R and S is 2x, the space between S and T is 3x, and RT is 10 centimeters long, then ST is 6 centimeters

Point S lies between points R and T on Line segment RT

RT   =  RS   +  ST

The space between R and S is 2x

That is, RS  =  2x

The space between S and T is 3x

That is, ST  =  3x

RT is 10 centimeters long

RT  =  10cm

Substitute RT = 10, ST = 3x and RS = 2x into the equation RT = RS + ST

10  =  2x  +  3x

10   =  5x

x  =  10/5

x   =  2

If x = 2, then

ST  =  3x

ST = 3(2)

ST =  6 centimeters

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Answer:

Use the graph of the exponential growth function

f(x) = a(2x) to determine which statement is true.

f(0) = 2 when a = One-half.

f(0) = 3 when a = 3.

f(1) = 9 when a = 9.Step-by-step explanation:

\(3x + 20 = (5 \times 1095) - 14 \\ 3x + 20 = 5475 - 14 \\ 3x = 5461 - 20 \\ 3x = 5441 \\ x = \frac{5441}{3} \)