Which measurements of triangle BAC are correct

Answer:

m = 2/3, you were correct

Step-by-step explanation:

plot the point on a graph

calculate the rise by going up alongside the y axis

the rise is 2

calcualte the run it takes to get to the second point

the run is 3

m = rise/run = 2/3

m = 2/3

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Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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Answer:

I'm sorry if you can't read it. I hope I could still help.

Step-by-step explanation:

An approximate 95% confidence interval for the difference in the mean tooth damage is  (6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)

For sweetened samples

The value of n = 10

The mean of the samples = 6.14

The standard deviation of the sample = 5.0

For unsweetened samples

The value of n = 15

The mean of  the sample = 5.20

The standard deviation of the sample = 15.0

We have to assume that necessary conditions for inference are met

The confidence interval = 95%

The equation will be

(6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)

Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)

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Answer:

f(2)= -4 f(3)= 1

Step-by-step explanation:

The rate of decrease of volume of the sphere when its diameter is 6 cm is -96π cubic cm/min.

Given that the snowball is a sphere, we can use the formula for the volume of a sphere.

The formula for the volume of a sphere is

V = 4/3 πr³

We need to find out the rate of decrease of volume when the diameter is 6 cm.

To find the rate of decrease of volume, we need to differentiate the above formula. Differentiating the above formula w.r.t. time, we get

dV/dt = 4/3 π(3r²)(dr/dt)

Where r is the radius of the sphere and dr/dt is the rate of change of the radius.

Let d be the diameter of the sphere. Then we can write,r = d/2

Also, given that dr/dt = -2cm/min

Substituting the values in the equation for the rate of decrease of volume,

dV/dt = 4/3 π(3(d/2)²)(-2) = -8π/3 d²

As the diameter of the sphere is 6 cm, d = 6 cm.Substituting the value in the equation above, we get

dV/dt = -8π/3 (6)² = -96π cubic cm/min

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Answer:

42 centimeters for the length and 12 centimeters for the width.

Step-by-step explanation:

Let's assume that the length of the rectangle is 7x and the width is 2x, where x is a common factor.

The perimeter of a rectangle is given by the formula: P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.\(\hrulefill\)

Given that the perimeter of the rectangle is 108 centimeters, we can write the equation as:

108 = 2(7x + 2x).

Simplifying the equation:

108 = 2(9x).

54 = 9x.

x = 6.

Now, we can find the dimensions of the rectangle:

Length = 7x = 7 * 6 = 42 centimeters.

Width = 2x = 2 * 6 = 12 centimeters.

Therefore, the dimensions of the rectangle are 42 centimeters for the length and 12 centimeters for the width.

Answer:

20 to 3 or 20 : 3

Step-by-step explanation:

White : Black

= 80 : 12

= 80/12

= 20:3

The exact growth rate (r) for the exponential model or the slope (m) and y-intercept (b) for the linear model. More data points or additional information about the population growth pattern would be needed to construct a precise model for P(t).

To find a model for P(t), representing the U.S. population in 1960, we need to determine the growth or decay rate over time. Without additional information or assumptions about the population growth, we cannot provide an exact model. However, we can explore two common models: exponential growth and linear growth.

1. Exponential Growth Model:

If we assume that the U.S. population experienced exponential growth, we can use the formula P(t) = P₀ * e^(rt), where P₀ represents the initial population, r is the growth rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).

Using the given information that the U.S. population in 1960 was 181 million, we can write the equation as follows:

181,000,000 = P₀ * e^(r * 1960)

2. Linear Growth Model:

Alternatively, if we assume that the U.S. population grew linearly, we can use the formula P(t) = mt + b, where m is the slope (rate of change) and b is the y-intercept.

Using the given information, we can form an equation as follows:

181,000,000 = m * 1960 + b

Without further information or data points, we cannot determine the exact growth rate (r) for the exponential model or the slope (m) and y-intercept (b) for the linear model. More data points or additional information about the population growth pattern would be needed to construct a precise model for P(t).

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Answer:270,000

Step-by-step explanation:

i think

Answer: are you sure your equation is correct?

Step-by-step explanation:

Answer:

-5z - 10

Step-by-step explanation:

Subtract 9z from 4z.

Tarzan walked a total of 21 meters distance, including 10 metres up the staircase, 11 metres back to the tower's base, and 0 metres down the slide.

Let's label the extent of the slide x.

Tarzan climbs a 10-meter tower and then rides a straight water slide of length x, according to the issue statement. He travels 11 metres back to the tower's base after landing in the splash pool. This implies that his total travel distance is

10 meters (climbing the tower) + x meters (riding the slide) + 11 meters (walking back to the tower base) = 21 + x meters

We can set up the following equation because the total distance he travels is equivalent to the length of the slide plus the distance he walks back to the base of the tower.

21 + x = length of the slide

Solving for x, we get

x = length of the slide - 21

We get by putting this expression for x into the formula we derived previously.

10 + (length of the slide - 21) + 11 = length of the slide

When we simplify this solution, we get

length of the slide - 30 + 30 = 20 + 10 + length of the slide

Simplifying further, we get

length of the slide = 30 meters

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Matthew has 168 nickels and 200 dimes in his collection.

Let x be the number of nickels and y be the number of dimes in Matthew's collection. From the problem, we can set up a system of linear equations,

Equation 1: x + y = 368 (total number of coins in the collection)

Equation 2: 0.05x + 0.1y = 28.40 (total value of the coins in dollars)

To solve the system, we can use any method of our choice, such as substitution or elimination. Here's an example of using the elimination method:

Multiply Equation 1 by 0.05:

0.05x + 0.05y = 18.4

Subtract this equation from Equation 2:

0.1y - 0.05y = 28.4 - 18.4

0.05y = 10

y = 200

Substitute y = 200 into Equation 1:

x + 200 = 368

x = 168

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Answer:

A. 15 outcomes, B.2, c.5, d.7

-hope that helps just let me know if not

Step-by-step explanation:

The answer is C

Answer:

mean = 10

Step-by-step explanation:

The mean is calculated as

mean = \(\frac{sum}{count}\)

         = \(\frac{6+7+10+12+12+13}{6}\)

        = \(\frac{60}{6}\)

       = 10

tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)

• rewrite tan = sin/cos

… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))

• expand the functions of 2A using the double angle identities

… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))

• factor out sin(A) cos(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))

• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))

• rearrange terms in the product

… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)

… = 4 sin(A) cos(A) / (2 - 1/cos²(A))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(A) cos(A) / (2 - sec²(A))

• divide through again by cos²(A)

… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(A) / (2 sec²(A) - sec⁴(A))

• factor out sec²(A) in the denominator

… = 4 tan(A) / (sec²(A) (2 - sec²(A)))

• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)

… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))

• simplify

… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))

• condense the denominator as the difference of squares

… = 4 tan(A) / (1 - tan⁴(A))

(Note that some of these steps are optional or can be done simultaneously)

Answer:7.5 in2

Step-by-step explanation:A=6a2=6·2.52=37.5in²

The slope of the line that passes through the given points is m = 2.5.

Using the slope formula:

Therefore, the slope of the line that passes through the given points is m = 2.5.

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Answer:

-0.9

Step-by-step explanation:

-5.4 + 1.8 = 4x - 1.8 + 1.8

-3.6 = 4x

-3.6/4 = 4x/4

-0.9 = x

The answers of all the parts are solved below:

1. Significant digits:

12.03: 4 significant digits

58.2: 3 significant digits

0.002: 1 significant digit

0.0030: 4 significant digits

0.00050004: 7 significant digits

2: 1 significant digit

2. Conversions:

0.05 km to mm: 0.05 km = 0.05 x 10^6 mm = 50,000 mm

0.15 hm to cm: 0.15 hm = 0.15 x 100 cm = 15 cm

280 dm to dam: 280 dm = 280 x 10 dam = 2,800 dam

500,000 mm to km: 500,000 mm = 500,000/10^6 km = 0.5 km

85 m to hm: 85 m = 85/100 hm = 0.85 hm

3. Significant digits in calculation:

(a) 25.3456 +888.010 + 53.11 + 7-10: 925.456, 4 significant digits

(b) (45.805 * 2.00) / 5.0 + 0.1: 13.52, 4 significant digits

4. Scientific notation with significant digits:

(a) 70,000,000 * 9.8540 * 2.00 * 10^8 = 1.38 x 10^18, 2 significant digits

(b) 8.888 * 10^14 * 4.00 * 10^-6 - 3.0 * 10^7 = 3.555 x 10^7, 4 significant digits

Trigonometry:

Given triangle ABC with angle B = 56, angle C = 35 and side A = 10. To find side B.

Using the law of cosines, B = sqrt(A^2 + C^2 - 2 * A * C * cos(B)) = sqrt(10^2 + 56^2 - 2 * 10 * 56 * cos(56)) = 115, 3 significant digits.

Thus, All the answers are solved above.

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Willard should interpret the 95% prediction interval for percent potassium when nitrogen is 18 ppm as a range of values within which the true value of percent potassium is likely to fall with a 95% probability.

Specifically, the prediction interval (0.87%, 1.02%) suggests that if Willard were to measure the percent potassium in a large number of soil samples with a nitrogen level of 18 ppm and calculate the prediction interval for each sample, then 95% of the prediction intervals would contain the true value of percent potassium.

The lower and upper limits of the prediction interval correspond to the lower and upper bounds of the plausible range for percent potassium, given the observed nitrogen level. In this case, the interval (0.87%, 1.02%) indicates that Willard can be 95% confident that the true value of percent potassium for a soil sample with nitrogen level 18 ppm falls between 0.87% and 1.02%. However, it is important to note that the prediction interval is based on statistical assumptions and may not capture all sources of uncertainty or variability in the data. Therefore, it is important to interpret the prediction interval with caution and in the context of the specific statistical model and assumptions used to derive it.

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Answer:

weight of a water=0.5

spherical ball is filled With water=0.95.

so dear for

22\7*0.5*0.95=1.49

Answer:

Step-by-step explanation:

1) Find the table

To find the numbers on the table, just substitute the number for x

If x = 0

y=-4x+3

y=-4(0) + 3

y= 0 + 3

y= 3

If x = 1

y=-4x+3

y=-4(1)+3

y= -4 + 3

y= -1

You can see a pattern, each x makes it go down by 4.

So the following will be...

if x = 2 -> -5

if x = 3 -> -9

2) Now fill in the table with the points

(0, 3) (Taken from the table, the x and y)

(1, -1)

(2, -5)

(3, -9)

3) Afterward draw a line through it. You will get your graph.

Answer:

C

Step-by-step explanation:

MAD measures precision (meaning how close the data points are to each other)

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Answer:

Four

Step-by-step explanation:

Let's expand and see how many nonzero terms:

⇒ (x+4)(2x²+3x+9)-3(x³-2x²+7x)=

⇒ 2x³ + 3x² + 9x + 8x² + 12 + 36 - 3x³ + 6 x² - 21 x=

⇒ - x³ + 17x² - 12x + 12

As we see the expression has four nonzero terms

The point slope form of line is y+4 = -4( x+3)

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

Given:

m=4

We know the general form is

y - b = -4(x - a)

So, from the graph attached below

b= -4, a= -3

So, y-(-4)= -4(x-(-3))

y+4 = -4( x+3)

Hence,  point slope form of line is y+4 = -4( x+3).

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Answer:

A + B would be less than A - B

Step-by-step explanation:

Answer:

2π r = Circumference formula

2π r = 18

r = 18/2π

r= 2.86cm

Hope this helps :)!

I'd appreciate if you'd mark me brainliest because ive been stuck on the same rank for wayyy too long :(

Goodluck! :)

Answer:

2.87 is the approximate radius

Step-by-step explanation:

The circumference is given by

C = 2 * pi *r

18 = 2 pi r

Divide each side by 2pi

18/2pi = 2 pir/ 2pi

9/pi = r

Letting pi be approximated by 3.14

9/3.14 = r

2.866242038

2.87 is the approximate radius