Look at the graph of this system of equations y=-3+1 and y=x. At which approximate points are the two equations equal?
у
4
/y=x
5
3
-2
21
1
2
3
4
5
y=-2+1
-3
-5

The rate at which the diameter decreases when the diameter is 10 cm is -0.00798 cm/min.

To find the rate at which the diameter decreases, we can use the relationship between the surface area and the diameter of a sphere.

The surface area of a sphere is given by the formula:

A = \(4\pi r^2\), where A is the surface area and r is the radius (which is half the diameter).

Differentiating both sides of the equation with respect to time t, we get:

dA/dt = 8πr(dr/dt).

We are given that the surface area decreases at a rate of \(1 cm^2/min\), so dA/dt = \(-1 cm^2/min\). We want to find dr/dt when the diameter is 10 cm, which means the radius is r = 10/2 = 5 cm.

Substituting these values into the equation, we have:

-1 = 8π(5)(dr/dt).

Simplifying, we get:

-1 = 40π(dr/dt).

Now, solving for dr/dt:

dr/dt = -1 / (40π).

Using a calculator, this evaluates to approximately -0.00798 cm/min.

Therefore, when the diameter is 10 cm, the rate at which the diameter decreases is approximately -0.00798 cm/min. Note that the negative sign indicates the decrease in diameter.

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Answer:

((1+2)*3+4)*5

Step-by-step explanation:

1+2×3+4×5=65

-----------------------

Answer:  approximately 188.07 feet

======================================================

Explanation:

Refer to the diagram below. Note that the 62 degree angle is from the fact that 90-28 = 62.

With the reference angle 62 degrees in mind, we have an unknown opposite side x feet and a known adjacent side 100 feet.

Use the tangent trig ratio to tie the two sides together, and then solve for x.

tan(angle) = opposite/adjacent

tan(62) = x/100

100*tan(62) = x

x = 100*tan(62)

x = 188.072646534633 approximately

x = 188.07 feet approximately

Your calculator needs to be in degree mode. One way to check is to compute something like tan(45) and the result should be 1.

Exponential growth is a mathematical transformation that grows indefinitely using an exponential function.

Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function

The simplest representation of exponential growth and decay is the formula \(ab^{x}\), where 'a' is the initial quantity, 'b' is the growth factor which is similar to the common ratio of the geometric progression, and 'x' in the time steps for multiplying the growth factor.

Mathematically, for exponential growth, the value of b is greater than 1 (b > 1), and for exponential decay, the value of b is lesser than 1 (b < 1).

In other words, if value of y increase exponentially with increase in value of x, it is exponential growth. Whereas, if value of y decrease exponentially with increase in value of x, it is exponential decay.

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The samples which provides the significance evidence are,

a. Sample A shows that samples have significance evidence.

b. The samples which shows no evidence are samples B, C, and D.

To determine which sample result provides the most significant evidence for the claim,

Perform a hypothesis test using the one-sample proportion test.

The null hypothesis (H₀) is that the proportion of US citizens who can name the capital city of Canada is 0.75 or less (p ≤ 0.75),

while the alternative hypothesis (H₁) is that the proportion is greater than 0.75 (p > 0.75).

Calculate the test statistic z-score and corresponding p-value for each sample result using the formula,

z = (p - p₀) / √(p₀(1 - p₀) / n)

where p is the sample proportion,

p₀ is the hypothesized proportion under the null hypothesis,

and n is the sample size.

Let's calculate the z-scores and p-values for each sample result,

Sample A,

38 successes out of 40

p = 38/40

  = 0.95

z = (0.95 - 0.75) / √(0.75(1 - 0.75) / 40)

  ≈ 3.16

p-value ≈ P(Z > 3.16)

             ≈ 0.0008

Sample B,

31 successes out of 40

p = 31/40

  = 0.775

z = (0.775 - 0.75) / √(0.75(1 - 0.75) / 40)

  ≈ 0.79

p-value ≈ P(Z > 0.79)

             ≈ 0.2146

Sample C,

34 successes out of 40

p = 34/40

  = 0.85

z = (0.85 - 0.75) / √(0.75(1 - 0.75) / 40)

  ≈ 1.58

p-value ≈ P(Z > 1.58)

             ≈ 0.0571

Sample D,

27 successes out of 40

p = 27/40

   = 0.675

z = (0.675 - 0.75) / √(0.75(1 - 0.75) / 40)

  ≈ -1.58

p-value ≈ P(Z < -1.58)

             ≈ 0.0571

a. The sample result that provides the most significant evidence for the claim is Sample A.

It has the highest z-score (3.16) and the lowest p-value (0.0008).

This indicates that the observed proportion of US citizens who can name the capital city of Canada is significantly greater than 0.75.

b. Samples B, C, and D all have p-values above the conventional significance level of 0.05.

These sample results do not provide sufficient evidence to reject null hypothesis and support claim that proportion > 0.75.

Therefore , the possible samples showing the following results,

a. sample A provides the the significance evidence.

b. Samples B, C, and D do not provide sufficient evidence.

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Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

The subtended arc along the circle is 79/360 of the circle's circumference. Therefore, the subtended arc is approximately 0.2194 times as long as 1/360 of the circle's circumference.


To find the length of the subtended arc along the circle, we need to know what fraction of the circle's circumference it represents.

The angle measures 79 degrees, which is a little over 1/5 of a full circle (which measures 360 degrees). Therefore, the subtended arc represents a little over 1/5 of the circle's circumference. More precisely, it represents 79/360 of the circle's circumference.

To find out how many times as long the subtended arc is as 1/360 of the circle's circumference, we can divide the length of the subtended arc by the length of 1/360 of the circle's circumference. This gives us:

(79/360) / (1/360) = 79

So the subtended arc is 79 times as long as 1/360 of the circle's circumference. Alternatively, we can express this as a decimal by dividing the subtended arc by 1/360:

(79/360) ÷ (1/360) = 0.2194

So the subtended arc is approximately 0.2194 times as long as 1/360 of the circle's circumference.

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Answer:

45%

Step-by-step explanation:

i believe it to be true

The 95% confidence interval for the population mean is approximately [20.03, 20.97].

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level.

To calculate the 95% confidence interval for the population mean based on a sample of size 36 with a known variance of 2.1 and a sample mean of 20.5, we can use the formula for a confidence interval for a population mean:

CI = \(\bar X\) ± z * (σ / √n),

where:

CI is the confidence interval,

\(\bar X\) is the sample mean,

z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence),

σ is the population standard deviation,

n is the sample size.

Since we have the population variance (2.1), we can calculate the population standard deviation as σ = √2.1 ≈ 1.45.

Now, let's calculate the confidence interval:

CI = 20.5 ± z * (1.45 / √36).

The z-score corresponding to a 95% confidence level is approximately 1.96 (you can look this up in a standard normal distribution table or use a statistical software).

Substituting the values:

CI = 20.5 ± 1.96 * (1.45 / √36).

Calculating the values within the confidence interval:

CI = 20.5 ± 1.96 * 0.2417.

CI = 20.5 ± 0.4741.

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower bound = 20.5 - 0.4741 ≈ 20.03.

Upper bound = 20.5 + 0.4741 ≈ 20.97.

Therefore, the 95% confidence interval for the population mean is approximately [20.03, 20.97].

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It will cost $1200 to cover both sides of the green roof with plants at a cost of $0.75 per square foot.

To calculate the cost of covering both sides of the green roof, we first need to find the area of the roof. We can use the formula for the area of a rectangle:

area = length x width

Since the roof is 40 feet long, we need to find the width to calculate the area. We can estimate the width from the picture, but it's not given explicitly. So, we can make a reasonable assumption that the width is the same as the length of the shorter side of the roof, which appears to be about 20 feet.

Using this assumption, we can calculate the area of one side of the roof:

area = length x width = 40 ft x 20 ft = 800 sq ft

Since there are two sides to the roof, the total area is twice this amount:

total area = 2 x 800 sq ft = 1600 sq ft

To find the total cost of covering both sides of the roof, we can multiply the area by the cost per square foot of plants:

total cost = area x cost per sq ft

= 1600 sq ft x $0.75/sq ft

= $1200

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Answer: <C = 63°

Step-by-step explanation:

The interior angles in all triangles always equal 180°

47 + 70= 117

180 - 117 = 63°

<C = 63°

hope this helps :)

Answer:

B. 10

Step-by-step explanation:

To find the answer we would plug each given number into x to see if it makes the equation true

A. 2(5) = 20

    10 \(\neq\) 20

B. 2(10) = 20

    20 = 20

C. 2(20) = 20

    40 \(\neq\)20

As you can see, the only answer that makes the equation 2x=20 true, is answer B

Answer:

82cm

Step-by-step explanation:

26+26+15+15=82

Answer:

8

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The poset (n, |) has a unique minimal element 1, but no maximal elements. The poset (n, |) is the set of natural numbers n with the relation "divides" denoted by |. In other words, a | b if and only if a divides b evenly with no remainder.

To determine if there are any minimal elements in this poset, we need to find the smallest element in the set that is related to all other elements. In this case, 1 is the smallest natural number and it is related to all other natural numbers since 1 | n for all n in the set. Therefore, 1 is a minimal element in this poset.

To determine if there are any maximal elements in this poset, we need to find the largest element in the set that is related to all other elements. However, there is no such element in this poset since for any natural number n, there is always another natural number greater than n that is related to it. For example, 2 | 4 and 4 | 8, so 8 is related to both 2 and 4 but it is greater than both of them. Therefore, there are no maximal elements in this poset.

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One way to increase the probability of identifying the optimal decision when using a simulation is to increase the number of iterations or trials in the simulation.

Simulation is a powerful tool for modeling and analyzing complex systems or processes where there are many variables and uncertainties involved. However, the accuracy and reliability of the simulation results depend on the number of iterations or trials used in the simulation. The more trials or iterations are performed, the more accurate the simulation results are likely to be, and the higher the probability of identifying the optimal decision.

Therefore, to increase the probability of identifying the optimal decision in a simulation, one should increase the number of trials or iterations in the simulation. This means running the simulation multiple times with different input values or scenarios and recording the results for each run. By analyzing the results of multiple simulation runs, one can identify patterns, trends, and optimal decisions that are robust and reliable across different scenarios and conditions.

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The function f(m, n) = 3n - 4m is not injective because different pairs of inputs (m, n) can yield the same output value. For example, f(0, 1) = f(2, 3) = -4. Therefore, the function is not one-to-one.

The function f(m, n) = 3n - 4m is surjective because for every integer z, there exist inputs (m, n) such that f(m, n) = z. To verify this, we can rewrite the function as 3n - 4m = z and solve for (m, n) in terms of z. Rearranging the equation, we have 3n = 4m + z. Since m and n can take any integer values, we can choose m = z and n = 0, which satisfies the equation. Thus, for any integer z, there exists a pair of inputs (m, n) that maps to z. Therefore, the function is onto or surjective.

In summary, the function f(m, n) = 3n - 4m is not injective but it is surjective

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Answer:

9.3

Step-by-step explanation:

Answer: 9.3

Step-by-step

1lb = 16 oz

20 x 16 = 320

320 oz + 8 oz = 328

1 oz = 0.283495

328 + 0.283495 = 9.298636

Round 9.298636 = 9.3

Answer:

Table 1:

2 miles = 3520 yards

3 miles = 5280 yards

Table 2:

2 yards = 6 feet

3 yards = 9 feet

Table 3:

2 feet = 24 inches

3 feet = 36 inches

Table 4:

2 yards = 72 inches

Question 5: 4 yards, 130 inches, 10 feet

Question 6: The width of a penny

Step-by-step explanation:

Table 1: Multiply 1760 by 2 (3520), and 3 (5280).
Table 2: Multiply 3 by 2 (6), and 3 (9).
Table 3: Multiply 12 by 2 (24), and 3 (36).
Table 4: Multiply 36 by 2 (72).

Question 5: Convert all measurements to inches (the smallest value).
130 (given)
4 yards = 144 inches
10 feet = 120 inches

In greatest to least, we get 144, 130, 120.

Question 6: The length of a dollar is much wider than 1 inch, and so is a pencil. The width of a penny makes the most sense.

hope this helps!

Answer:

a) In a coordinate plane, the horizontal axis is the x-axis, and the vertical axis is the y-axis.

So, a point (x, y) is at:

A horizontal distance of x units from the origin.

A vertical distance of y units from the origin.

So the point (3, -7) is at:

3 units at the right from the origin

7 units downwards (because is a -7) from the origin.

The graph of the point can be seen below:

Now we want to find a reflection across the x-axis.

b) For a general point (x, y), a reflection across the x-axis gives:

(x, -y)

So, if our point P is:

P (5, 1)

The reflection across the x-axis just changes the sign of the y-value, which gives:

(5, -1)

Then the correct option is point C:

(5, -1)

Answer:

its C on exgenity

Step-by-step explanation:

The given number of different colored gumballs in the gumball machine are as follows:7 red, 8 orange, 9 purple, 7 white, and 5 yellow gumballs.

Therefore, the total number of gumballs = 7 + 8 + 9 + 7 + 5 = 36.Using the formula for combinations, the total number of ways to get 3 gumballs at once is given by:36C3 = (36 × 35 × 34)/(3 × 2 × 1) = 7140a) Find the probability of getting 1 purple, 1 white, and 1 red gumballs There are 9 purple, 7 white, and 7 red gumballs in the machine. The number of ways to choose one purple, one white, and one red gumball is:9C1 × 7C1 × 7C1 = 9 × 7 × 7 = 441.

The probability of choosing one purple, one white, and one red gumball is:441/7140 = 0.0618 (approx)Therefore, the probability of getting 1 purple, 1 white, and 1 red gumballs is 0.0618.b) Find the probability of getting 1 orange and 2 yellow gumballsThere are 8 orange and 5 yellow gumballs in the machine. The number of ways to choose one orange and two yellow gumballs is:8C1 × 5C2 = 8 × (5 × 4)/(2 × 1) = 80The probability of choosing one orange and two yellow gumballs is:80/7140 = 0.0112 (approx)Therefore, the probability of getting 1 orange and 2 yellow gumballs is 0.0112.

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Answer: ask the teacher to break it down for u

Step-by-step explanation:

that simpile

y=6x-26, Although I didn't really get what were you looking for

Answer:

$2.70

Step-by-step explanation:

Cost price = $6

Mark up percentage = 45%

Mark up amount = 45% × $6

                          = 0.45 × $6

                          = $2.70

Selling price = Mark up + cost price

                    = $2.70 + $6

                    = $8.70

Jermaine sells the shirts for $8.70 and makes a profit of $2.70.

Step-by-step explanation:

\( \frac{2}{9} + \frac{1}{3} \\ by \: taking \: out \: the \: lcm \: of \: 9 \: and \: 3 \: \\ we \: get \: 9\: as \: lcm \\ now \\ \frac{2 \times 1 + 1 \times 3}{9} \\ \frac{2 + 3}{9} \\ \frac{5}{9} \)

Answer:

it will be 37.8 cm tall

H0: The distribution of lunch preferences is 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza.

Ha: The distribution of lunch preferences is not 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place.

In hypothesis testing, we have a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis represents the claim or assumption we want to test, while the alternative hypothesis represents the opposite or alternative claim.

In this case, the null hypothesis (H0) states that the distribution of lunch preferences is 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place. The alternative hypothesis (Ha) states that the distribution of lunch preferences is not 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place.

To test these hypotheses, a random sample of 150 students is selected, and their lunch preferences are recorded. The goal is to determine if the observed distribution of lunch preferences in the sample provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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The expression as a radical is the response to the question based on the given expression \(s^{\frac{6}{5} }\).

A symbol for the root of a number or phrase is known as a radical (or root). The square root, which is represented by the sign, is the most typical radical. For instance, since 3 *3 = 9, the square root of 9 is indicated as 9 and equivalent to 3.

A radical expression consists of a radical sign and the radicand, which is an expression or number, underneath it. The non-negative number that,when multiplied by itself, yields the value of the radicand is the value of a radical expression.

In several branches of mathematics, including algebra, calculus, and geometry, radicals are used. They are particularly helpful for simplifying expressions with roots and solving equations.

The fifth root of s raised to the power of 6 is represented by the expression "\(s^{\frac{6}{5} }\)," which is:

\(\sqrt[3]{s^{6} } =s^{\frac{6}{5} }\)

Therefore, the expression as a radical is \(s^{\frac{6}{5} }\).

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why is 20/2 bigger than 25/15​?

because 20/10 = 2

and 25/15 = 5/3 or 1.66

2 is bigger than 1.66