If each 2 cm on the scale drawing equals 10 feet, what are the actual dimensions of the room? (5 points) Length = 11 feet, width = 9 feet Length = 30 feet, width = 20 feet Length = 8 feet, width = 12 feet Length = 22 feet, width = 20 feet

Answer:

larger number is 6 and smaller number is 1.

Step-by-step explanation:

Let x be larger number and y be the smaller number

x-y=5 (difference of numbers is 5)

3x+2y=20 (3 times larger number+2 times the smaller number is 20)

Multiply x-y=5 by 2

2(x-y)=2*5

2x-2y=10

Solve both equations by elimination/add equations.

3x+2y=20

2x-2y=10

———————-

5x-0=30

x=30/5=6

Substitute x=6 in x-y=6 to get the value of y

6-y=5

y=6-5=1

So, larger number is 6 and smaller number is 1.

You check your answer by substituting the values of x and y in the equations and checking if it is a solution of the equation.

A graph of the line going through the point (-6, 1) with a slope of -2/3 is shown in the image below.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-6, 1) and a slope of -2/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -2/3(x + 6)  

y = -2x/3 - 4 + 1

y = -2x/3 - 3

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Answer:

Line B

Step-by-step explanation:

pass the 2 on the y axis

Answer:

Line B because it hits the Y axis with a Y value of 2.

Brainliest please?

Using the exponential growth formulas, we get the population at 10 years would be 2593.

What is exponential growth?

A process called exponential growth sees a rise in quantity over time. It happens when the derivative of a quantity's instantaneous rate of change with respect to time is equal to the original quantity.

Given Initial population is Pt= 1725.

The doubling time of the population is D=17

Now we need to find the population at time t=10

Using the formula,

\(P_{t}=P_{0} (2)^{\frac{t}{D} } \\P_{t}=1725 (2)^{\frac{10}{17} } \\P_{t}=1725 (2)^{0.588}\\P_{t}=1725 \space\ . \space\ 1.503\\P_{t}=2593\)

Hence the population of the island in 10  years would be 2593.

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It takes 7/5 hours to paint one room.

To find the time it takes to paint one room, we need to determine the reciprocal of the fraction representing the number of rooms painted per hour.

If it takes 3/7 hours to paint 3/5 of a room, then the fraction representing the rate of painting is (3/5) / (3/7). To divide fractions, we multiply by the reciprocal of the second fraction. Therefore:

(3/5) / (3/7) = (3/5) * (7/3) = (3 * 7) / (5 * 3) = 21/15

So, it takes 21/15 hours to paint one room. This can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

21/15 = (21/3) / (15/3) = 7/5

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Option B : The area of the rhombus is 119 square inches. It's important to note that the units of the sides and height are both in inches, so the units of area will be in square inches.

A rhombus is a four-sided polygon with equal sides and opposite angles that are congruent. To calculate the area of a rhombus, we use the formula (base x height) / 2, where the base is the length of one of its sides, and the height is the perpendicular distance between the base and the opposite side.

The area of a rhombus can be calculated by multiplying its base by its height and then dividing by 2.

In this case, the base of the rhombus is given as 17 inches, and the height is given as 14 inches. We simply substitute these values into the formula and simplify:

Area = (base x height) / 2

Area = (17 x 14) / 2

Area = 238 / 2

Area = 119 square inches

Therefore, the area of the rhombus is 119 square inches.

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A rhombus with a base of 17 inches and a height of 14 inches.

What is the area of the rhombus?

A. 62 in2

B. 119 in2

C. 124 in2

D, 238 in2

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Answer:

Given function

#15 Find the inverse of h(x)

Substitute x with y and h(x) with x and solve for y:

The inverse is:

#16 The graph with both lines is attached.

The x- and y-intercepts of both functions have reversed values.

#17 Table of the inverse function  will contain same numbers with swapped domain and range.

Initial look is like this:

The rest of the table is filled in by finding the values:

Answer:

..

Step-by-step explanation:

Answer:

3;8

Step-by-step explanation:

The correct answer is b). Yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. Since the p-value is small we reject the null hypothesis of no relationship.

In statistics, the p-value is used to determine the likelihood that the observed relationship between two variables occurred by chance. If the p-value is small, it means that the relationship is statistically significant and unlikely to have occurred by chance. In this case, the p-value of 0.039 indicates that there is a statistically significant positive relationship between age and body fat percentage.

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Answer:

It looks different. Can you provide some formulae based on it. I may help you out in the comment section!

The diameter of the circle is 48 in.

A circle's sector is a pie-shaped portion made up of the arc and its two radii. At both ends of the arc, when a section of the circle's circumference (also known as an arc) and two of its radii meet, a sector is produced. A sector of a circle resembles a piece of pizza or a pie in shape.

As per the given data:

Central angle of the sector (θ) = 30°

Area of the sector (A) = 150 in²

A = (1/2) × r² × θ {where θ is in radian and r is radius}

Converting 30° to radian.

= 30 × (π/180)

= π/6

150 = (1/2) × r² × π/6

r = √(1800/π)

r = √(576)

r = 24 in

Diameter = 2r

= 2 × 24 in

= 48 in

Hence, the diameter of the circle is 48 in.

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Answer:

7 hours and 50 minutes

7.5 is equal to 7 hours and 50 minutes

Answer:

∠ H = 22.5°, ∠ I = 45° , ∡ J = 112.5°

Step-by-step explanation:

The 3 angles in a triangle sum to 180° , then

x + 2x + 5x = 180 , that is

8x = 180 ( divide both sides by 8 )

x = 22.5

Then

∠ H = x = 22.5°

∠ I = 2x = 2 × 22.5° = 45°

∠ J = 5x = 5 × 22.5° = 112.5°

Answer:

11

Step-by-step explanation:

r=6+5

=11

if my answer helps please mark as brainliest

Answer:

r = 11

Step-by-step explanation:

Add 5 to both sides of the equation:

6 + 5 = r - 5 + 5

Add the numbers

11 = r - 5 + 5

11 = r

Move the variable to the left

r = 11

The mean of the sampling distribution of sample means is equal to the population mean.

In this case, it is 272 days.

a. The standard deviation (or standard error) of the sampling distribution of sample means can be calculated using the formula: σ_sample = σ_population / √n, where σ_sample is the standard error, σ_population is the population standard deviation, and n is the sample size. In this case, σ_sample = 14 days / √24 ≈ 2.86 days.

b. The graph of the sampling distribution of sample means will be a normal distribution with a mean of 272 days and a standard deviation of 2.86 days. The curve will be symmetrical around the mean value and will have a bell shape.

c. If the sample size is increased to 28, the mean of the sampling distribution remains the same (272 days) since it's equal to the population mean. However, the standard error will decrease because the sample size is larger: σ_sample = 14 days / √28 ≈ 2.65 days. The graph of this distribution will still be a normal distribution with a mean of 272 days, but it will be slightly narrower due to the smaller standard error of 2.65 days.

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Answer:

68.4210526

Step-by-step explanation:

Hope this helps :)

Answer:

68.42

Step-by-step explanation:

and you can also derive that 38 percent of 68.42 equals 26.

Answer:can see the line

Step-by-step explanation:

if it is linear it is =Ax+By=C

Answer: the length of BE is 27

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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The image of the point after the rotation is:

(-6, 7)

We have the point (-7, -6) and we want to apply a rotation of 270° counterclockwise.

This is equivalent to a rotation of 90° clockwise, so we will go from the third quadrant to the second quadrant, such that:

Then the image after the rotation is:

(-6, 7)

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The statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The statement is false. An eigenvector is a non-zero vector that, when multiplied by a matrix, produces a scalar multiple of itself. In other words, if v is an eigenvector of a matrix A, then Av = λv, where λ is the corresponding eigenvalue.

The statement suggests that if a is an nn matrix (presumably an n x n matrix), and a scalar α exists such that αv is an eigenvector of a, then v must also be an eigenvector of a. However, this is not necessarily true.

Let's consider a counterexample to demonstrate this. Suppose we have the 2x2 identity matrix I:

I = [[1, 0],

    [0, 1]]

In this case, any non-zero vector v will satisfy the condition αv = v for α = 1. However, not all non-zero vectors v are eigenvectors of I. In fact, the only eigenvectors of I are [1, 0] and [0, 1] with corresponding eigenvalues of 1.

Therefore, the statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

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There are 20 sets of four consecutive positive integers such that the product of the four integers is less than 100,000. The maximum value of the smallest integer in each set is 20.

To determine the number of sets of four consecutive positive integers whose product is less than 100,000, we can set up an equation and solve it.

Let's assume the smallest integer in the set is n. The four consecutive positive integers would be n, n+1, n+2, and n+3.

The product of these four integers is:

n * (n+1) * (n+2) * (n+3)

To count the number of sets, we need to find the maximum value of n that satisfies the condition where the product is less than 100,000.

Setting up the inequality:

n * (n+1) * (n+2) * (n+3) < 100,000

Now we can solve this inequality to find the maximum value of n.

By trial and error or using numerical methods, we find that the largest value of n that satisfies the inequality is n = 20.

Therefore, there are 20 sets of four consecutive positive integers whose product is less than 100,000.

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Answer:

Step-by-step explanation:

50/3=16.66666667

Answer:

la fracción completa es 50/3 o 48 2/3.

Step-by-step explanation:

50 dividido por 3 es una fracción: 50/3 Entonces el número mixto será 48 2/3

¡Hasta luego amigo!

Clark spends $ 12775 on these items which he does not need in a year (if we consider 365 days) where the average spend in a month is $35.

Clark finds that in an average month, he spends $35 on things he really doesn't need and can't afford.

Let us consider the month in consideration here to be of 30- days and ignore any months other number of days.

Thus, calculating the average, say x' , by formula, we get,

x' = (Summation of values of all observations ) / ( Number of observations)

⇒ 35 = Total spend / 30

⇒ Total spend = $ ( 35*30)

⇒ Total spend = $ 1050

Therefore, total spend on a year, that is 12 months (considering all months to be of 30- days ) = $( 1050*12) = $ 12600

But we know a year does not have 360 days. So we calculate the total spend on these 5 days where average month spend is $35 is $175.

Hence the total spend for a year with 365 days is = $( 12600 + 175 ) = $12775

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The challenge requires you to change the equation from f(t)=a(x-h)2 + k to the parabola function f(t)=a(x-h)2 + k.

The centripetal acceleration is therefore given by the equation ac= v2/r = 2gh/r at every point along the frictionless roller coaster, where h is the distance from the highest point and r is the local radius of curvature.

If f(t) = 4t2 -8t + 7 then

= (4t2 - 8t + 4) + 7 - 4

=4 (t2 - 2t + 1) + 3

= 4 (t-1) 2 +3

As a result, options C and D are no longer possible.

recognising the f (t),

The maximum/minimum value is at f'(t) = 0 and f'(t) = 8t - 8.

0 = 8t – 8

t = 1

figuring out whether f"(t) > 0 or if minimum, f"(t) 0 maximum

Since f"(t) = 8 > 0, the minimal

f(1) =4(1)^2 – 8(1) +7= 3

Consequently, the minimal height is 3.

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Answer: t=5 t=8

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

x and 114° are same- side interior angles and are supplementary, then

x = 180 - 114 = 66