Which of the following graphs best represents a function that has a minimum value and x-intercepts of 3 and -1?

To determine the intervals on which the function [tex]f(x) = x^4 - 4x^3 + 3[/tex] is concave up or concave down, we need to find the second derivative of the function and analyze its sign.

First, let's find the first derivative of f(x):

[tex]f'(x) = 4x^3 - 12x^2[/tex]

Next, let's find the second derivative of f(x) by taking the derivative of f'(x):

[tex]f''(x) = 12x^2 - 24x[/tex]

To determine the intervals of concavity, we need to find where f''(x) is positive (concave up) or negative (concave down). We can do this by analyzing the sign of f''(x).

Now, let's find the values of x for which f''(x) = 0, as these will give us potential inflection points:

[tex]12x^2 - 24x = 0[/tex]

12x(x - 2) = 0

x = 0 or x = 2

The potential inflection points are x = 0 and x = 2.

To analyze the concavity of the function, we'll use test points within the intervals between the potential inflection points and beyond.

For x < 0, let's choose x = -1 as a test point:

[tex]f''(-1) = 12(-1)^2 - 24(-1) = 12 + 24 = 36[/tex]

Since f''(-1) = 36 > 0, the function is concave up for x < 0.

For 0 < x < 2, let's choose x = 1 as a test point:

[tex]f''(1) = 12(1)^2 - 24(1) = 12 - 24 = -12[/tex]

Since f''(1) = -12 < 0, the function is concave down for 0 < x < 2.

For x > 2, let's choose x = 3 as a test point:

[tex]f''(3) = 12(3)^2 - 24(3) = 108 - 72 = 36[/tex]

Since f''(3) = 36 > 0, the function is concave up for x > 2.

In summary:

The function is concave up for x < 0 and x > 2.

The function is concave down for 0 < x < 2.

The inflection points are x = 0 and x = 2.

I hope this clarifies the concavity and inflection points of the given function. Let me know if you have any further questions!

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Bob is exerting a force of 200 N on a 30 kg filing cabinet, but it remains stationary due to the static friction between the cabinet and the floor. The coefficient of static friction is given as 0.80.

The static frictional force acts between two surfaces in contact when there is no relative motion between them. The magnitude of static friction can be determined using the equation F_static = μ_static * N, where μ_static is the coefficient of static friction and N is the normal force.

In this scenario, Bob is applying a force of 200 N to the filing cabinet. In order to overcome the static friction and set the cabinet in motion, the applied force must be greater than or equal to the maximum static frictional force. The maximum static frictional force can be calculated by multiplying the coefficient of static friction with the normal force.

Since the cabinet is stationary, the applied force of 200 N is not sufficient to overcome the maximum static frictional force. The maximum static frictional force can be determined as F_static = μ_static * N = 0.80 * (30 kg * 9.8 m/s^2) = 235.2 N.

As the applied force of 200 N is less than the maximum static frictional force of 235.2 N, the filing cabinet remains stationary. Bob would need to apply a force greater than 235.2 N to overcome the static friction and set the cabinet in motion.

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Answer:

12 - m = 20

Explanation: Less than can also be a subtraction symbol so 12 less than a number, which the number is unknown in this case would be replaced with m then equals to 20. 12 - m =20

Answer:

280 and 8

Step-by-step explanation:

the LCM is the lowest common multiple

the lowest multiple that can Divide 40 and 56 without a remainder = 280

the Hcf Is the highest common factor of 40 and 56

the highest number that can Divide both =8

The probability of obtaining exactly 3 heads is 5/16.

We can find the probability of obtaining exactly 3 heads by considering the different ways in which this can happen.

First, suppose we toss the two normal coins and the biased coin with the two heads.

There is a probability of getting heads on each toss of the biased coin: 1/2

A  probability of getting heads on each toss of the normal coins: 1/2

Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/2) = 1/8

Now suppose we toss the two normal coins and the biased coin with the two heads, but we choose to use the biased coin twice. In this case, we need to get two heads in a row with the biased coin, and then a head with one of the normal coins.

The probability of getting two heads in a row with the biased coin is: 1/2, and the probability of getting a head with one of the normal coins is: 1/2. Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/2) = 1/8

Finally, suppose we use the biased coin and one of the normal coins twice each. In this case, we need to get two heads in a row with the biased coin, and then two tails in a row with the normal coin. The probability of getting two heads in a row with the biased coin is: 1/2,

and the probability of getting two tails in a row with the normal coin is :

(1/2) * (1/2) = 1/4.

Therefore, the probability of getting exactly 3 heads in this case is:

(1/2) * (1/2) * (1/4) = 1/16

Adding up the probabilities from each case, we get:

1/8 + 1/8 + 1/16 = 5/16

Therefore, the probability of obtaining exactly 3 heads is 5/16.

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In a two-way between subjects ANOVA, a significant main effect for B means that option A - the mean for B1 is not equal to the mean for B2.

In a two-way ANOVA, we are examining the effects of two independent variables (factors) on a dependent variable. One of the factors is referred to as factor A, and the other as factor B. A main effect for B indicates that there is a significant difference between the means of the levels of factor B. Therefore, if we observe a significant main effect for B, it implies that the mean for B1 (one level of factor B) is not equal to the mean for B2 (another level of factor B). This suggests that the variable represented by factor B has a significant influence on the dependent variable, and there is a difference in the outcome between the two levels of factor B.

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Answer:

The answer is A, C, and D

The graph should be 7 units for x and 2 units for y.

Step-by-step explanation:

Full Question: Graph y = 2/7x

Look at attachment:

Hope this helps! :)

The graph of the linear function y = (2/7)x will be given below.

The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of line is given as

y = mx + c

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

The function is given below.

y = (2/7)x

Compare the function with standard equation of the line,

Then the slope of the function is 2/7 and the y-intercept is zero, that means the line is passing through origin.

Then the graph of the linear function y = (2/7)x will be given below.

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1. The given word is "MILLIMICRON". The word has 11 letters in total and consists of 2 M's, 2 I's, 2 L's, 1 C, 1 R, 1 O, and 1 N. So, we can use the formula for finding permutations of n objects of which p are of the same kind, q are of another kind, r are of the third kind, and so on. The formula is `n!/(p!q!r!...)`. Here, we have p = 2, q = 2, r = 2, and so on. So, the number of distinguishable ways that the letters of the word "MILLIMICRON" can be arranged in order is: `11!/(2!2!2!) = 4989600` 2. We are given that the distinguishable orderings of the letters of "MILLIMICRON" begin with "M" and end with "N". We have fixed two letters at the beginning and end.

Now, we have 9 letters left which can be rearranged in the remaining 9 spots. So, the number of distinguishable orderings of the letters of "MILLIMICRON" that begin with "M" and end with "N" is: `9!/(2!2!1!) = 22680`3. We are given that the distinguishable orderings of the letters of "MILLIMICRON" must contain the letters "CR" next to each other in order and also the letters "ON" next to each other in order. We can group "CR" and "ON" together as a single letter. So, we have 9 letters: {M, I, L, L, I, M, C, RON, O}. We need to find all the distinguishable orderings of these letters. Let's consider the group "RON" as a single letter. Now, we have 8 letters: {M, I, L, L, I, M, C, RON}. These 8 letters can be arranged in 8! ways. Within the group "RON", we can arrange the letters "R", "O", and "N" in 3! ways. So, the total number of distinguishable orderings of the letters of "MILLIMICRON" that contain the letters "CR" next to each other in order and also the letters "ON" next to each other in order is: `8!×3! = 20,160`.

Hence, the answers are: 1. 4,989,6002. 22,6803. 20,160

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The power series solutions for the Hermite equation of 2 are zero for the first four terms of the given equation.

Equation = y''-2xy'+4y=0

The solutions can be expressed as power series using the Hermite equation of degree 2 can be calculated as:

y = ∑(n=0 to ∞) [tex]a_n x^{n}[/tex]

where [tex]a_n[/tex] is the coefficient of the nth term and x is the variable.

Differentiating y with regard to x,

y = ∑(n=0 to ∞) [tex]a_n x^{n-1}[/tex]

Double integrating the y with respect to x:

y'' = ∑(n=0 to ∞) [tex]a_nn(n-1)x^{n-2}[/tex]

Substituting the above equation in the Hermite equation

∑(n=0 to ∞) [tex]a_nn(n-1)x^{n-2}[/tex] - 2x∑(n=0 to ∞) [tex]a_n x^{n-1}[/tex] + 4∑(n=0 to ∞) [tex]a_n x^{n}[/tex] = 0

∑(n=0 to ∞)[tex][a_n(n(n-1) - 2n + 4)] x^{n}[/tex] = 0

Taking the coefficients of each term as zero:

[tex]a_n[/tex](n(n-1) - 2n + 4) = 0

The first four non-zero terms:

If n = 0,

[tex]a_o[/tex](0(0-1) - 2(0) + 4) = 0

[tex]a_o[/tex](4) = 0

[tex]a_o[/tex] = 0

If n = 1,

[tex]a_1[/tex](1(1-1) - 2(1) + 4) = 0

[tex]a_1[/tex](2) = 0

[tex]a_1[/tex] = 0

If n= 2,

[tex]a_2[/tex](2(2-1) - 2(2) + 4) = 0

[tex]a_2[/tex](2) = 0

[tex]a_2[/tex]= 0

If n = 3,

[tex]a_3[/tex] (3(3-1) - 2(3) + 4) = 0

[tex]a_3[/tex] (2) = 0

[tex]a_3[/tex]  = 0

Therefore we can conclude that the power series solutions for the Hermite equation of 2 are zero.

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Answer:

Step-by-step explanation:

Answer:

12 cm of coastline

Step-by-step explanation:

Multiply the years (factor) by the receding amount, 3cm, (constant) BAM answer.

Answer:

If Then proof has been explained below!

Step-by-step explanation:

1.) If segment XY ║ ZW, then the 154° angle ≅ ∠2 (vertical angles)

2.) If segment XY ║ ZW, then ∠2 is complementary to ∠4

3.) If ∠2 is complementary to ∠4, then ∠4 = 28°

I hope this helps! If you have any questions, feel free to add it into the comments and please rate my answer and consider marking as brainliest!

Answer: Solution in photo

The probability of making a gain that exceeds one standard deviation from the mean for stock XYZ on any given day is approximately 31.73%.

The probability of making a gain that amounts to more than one standard deviation from the mean on any given day for the stock XYZ can be found using the properties of the normal distribution.

To calculate this probability, we need to find the area under the normal distribution curve beyond one standard deviation from the mean in the positive direction. In this case, the mean (μ) is 20 basis points and the standard deviation (σ) is 40 basis points.

Using the standard normal distribution, we can convert the value one standard deviation above the mean (μ + σ) to a z-score by subtracting the mean and dividing by the standard deviation.

Z = (X - μ) / σ

Z = (μ + σ - μ) / σ

Z = σ / σ

Z = 1

Once we have the z-score, we can look up the corresponding probability using a standard normal distribution table or a statistical calculator.

The area under the normal curve beyond one standard deviation from the mean in the positive direction corresponds to approximately 0.1587 or 15.87%.

Therefore, the probability of making a gain that amounts to more than one standard deviation from the mean on any given day for stock XYZ is approximately 0.1587 or 15.87%.

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Answer:

i would say B but i dont know

Step-by-step explanation:

The mean is 1, variance is 0.9, and standard deviation is 0.948, rounded to three decimal places. Given data: Of all the registered automobiles in Colorado, 10% fail the state emissions test.

Ten automobiles are selected at random to undergo an emissions test.a. Find the probability:

1) That exactly three of them fail the test.

For the number of success (x) and number of trials (n),

the probability mass function (PMF) for binomial distribution is given by: [tex]P(X = x) = C(n, x) * p^{(x)} * q^{(n-x)},[/tex]

where [tex]C(n, x) = (n!)/((n-x)! * x!) ,[/tex]

p and q are the probabilities of success and failure, respectively. Here, the probability of success is the probability of an automobile to fail the test, p = 0.10 and the probability of failure is q = 1 - p = 0.90.

Now, X is the number of automobiles that fail the test.

Thus, n = 10, x = 3, p = 0.10, and q = 0.90.

Using the above formula:

[tex]P(X = 3) = C(10, 3) * (0.10)^{(3)} * (0.90)^{(10-3)}\\= 0.057[/tex]

The required probability is 0.057, rounded to three decimal places.

1) That fewer than three of them fail the test.

The required probability is P(X < 3).P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) Using the above formula:

[tex]P(X = 0) = C(10, 0) * (0.10)^{(0)} * (0.90)^{(10)}[/tex]

= 0.3487P(X = 1)

= [tex]C(10, 1) * (0.10)^{(1) }* (0.90)^{(9)}[/tex]

= 0.3874P(X = 2) = [tex]C(10, 2) * (0.10)^{(2)} * (0.90)^{(8)}[/tex]

 = 0.1937

Now, P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.3487 + 0.3874 + 0.1937

 = 0.9298

The required probability is 0.9298, rounded to three decimal places.

1) That at least eight of them fail the test.

The required probability is

P(X ≥ 8).P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) Using the above formula:

[tex]P (X = 8) = C(10, 8) * (0.10)^{(8)} * (0.90)^{(2) }[/tex]

= 0.0000049

[tex]P(X = 9) = C(10, 9) * (0.10)^{(9)} * (0.90)^{(1) }[/tex]

= 0.0000001

[tex]P(X = 10) = C(10, 10) * (0.10)^{(10)} * (0.90)^{(0)}[/tex]

= 0.0000000001

Now,

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

= 0.0000049 + 0.0000001 + 0.0000000001 = 0.000005

The required probability is 0.000005,

rounded to three decimal places.

b. Find the mean, variance, and standard deviation of the number of automobiles fail the test.

The mean (μ) for binomial distribution is given by: μ = n * p,

where n is the number of trials and p is the probability of success.

The variance ([tex]= 1 \sigma ^ 2 = n * p * q = 10 * 0.10 * 0.90 ^2[/tex]) for binomial distribution is given by: [tex]\sigma ^2 = n * p * q[/tex]

The standard deviation (σ) for binomial distribution is given by:

σ = √(n * p * q)

Here, n = 10 and p = 0.10.

Thus, q = 0.90.

Using the above formulas:

μ = n * p = 10 * 0.10

[tex]= 1\sigma ^2 = n * p * q = 10 * 0.10 * 0.90[/tex]

= 0.9σ = √(n * p * q)

= √(10 * 0.10 * 0.90)

= 0.948

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The inverse of matrix A is given by;

A^-1 = |5/139   -189/139 29/139 |

         |-10/139 129/139 -27/139 |
         |-5/139   19/139 -3/139  |

The given matrix is A =

| -5  -10  21 |
| -2   -5   9 |
|  1    2  -4 |

To find the inverse of a matrix, first find the determinant of that matrix. The determinant of matrix A is given as;

|A| = -5(-5(-4) - 2(9)) - (-10)(-2(-4) - 1(21)) + (21)(-2(2) - 1(-5))

|A| = -5(10) + 100 - 21(9)

|A| = -50 + 100 - 189

|A| = -139

Thus, the determinant of matrix A is -139. Now, we can use the formula of inverse of a 3x3 matrix;

A^-1 = 1/|A| * |(b22b33 - b23b32)  (b13b32 - b12b33)  (b12b23 - b13b22)|
| (b23b31 - b21b33)  (b11b33 - b13b31)  (b13b21 - b11b23)|
| (b21b32 - b22b31)  (b12b31 - b11b32)  (b11b22 - b12b21)|

where b is the cofactor of each element of matrix A.

The cofactor of element aij is denoted as Aij and given as Aij = (-1)i+j|Mij|.

Thus, the cofactors of matrix A are;

|-5  -10  21|
| -2  -5  9 |
|  1   2 -4 |

M11 = | -5  9 |
         |  2 -4 |

M12 = | -2  9 |
          |  2 -5 |

M13 = | -2 -5 |

M21 = | -10 21 |
         |   2 -9 |

M22 = |  -5 -21 |
           |  -2  5 |

M23 = |  -2 -2 |

M31 = | -10 -5 |
         |  2  9 |

M32 = |  -5 -9 |
          |  2  2 |

M33 = |  -2 -2 |

Now we can find the inverse of matrix A as follows;

A^-1 = 1/-139 * |(5   189  -29)|
                      |(-10 -129  27)|
                      |(-5   19  -3) |

Hence, the inverse of matrix A is given by;

A^-1 = |5/139   -189/139 29/139 |

         |-10/139 129/139 -27/139 |
         |-5/139   19/139 -3/139  |

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Answer:

60 and 90

Step-by-step explanation:

150/15 = 10

6 x 10 = 60

9 x 10 = 90

The required number of toys that can be divided among two groups is 60  and 90.

Given that,
To divide 150 toys amongst two groups of children in a ratio of 6:9​.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Ratio = 6 / 9
Total of ratio = 15
Now,
For 1 group toys = 150 [6 / 15] = 60
For group 2 toys = 150 [9 / 15] = 90

Thus, the required number of toys that can be divided among two groups is 60  and 90.

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Answer:

394.2 ft

Step-by-step explanation:

7.8(9)=70.2

This is the measurement for the two triangular sides

9(12)(3)=324 This is the measurement for the three triangular sides

70.2 +324 = 394.2 APPROX

Given a linear function f: X -> R that is bounded above on a neighborhood V of the origin, we need to prove that there exists a neighborhood W of the origin such that f(x) < y for all x in W.

To prove this statement, we can use the properties of linear functions and the topology of X. Since f is linear, we know that f(0) = 0.

Let's consider the open ball B(0, y) centered at the origin with radius y. Since f is bounded above on V, there exists a constant M > 0 such that f(x) < M for all x in V.

Now, let's define a neighborhood W = V ∩ f^(-1)(B(0, y/M)). W is the intersection of V and the inverse image of the open ball B(0, y/M) under the function f.

By the properties of inverse images, we know that f(x) < y/M for all x in W.

Therefore, we have found a neighborhood W of the origin such that f(x) < y for all x in W, satisfying the condition we needed to prove.

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Only the side lengths 12, 16, and 20 can be used to create a right triangle.(Option-A)

The Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides, must be satisfied for a set of side measurements to create a right triangle.

This theorem allows us to determine which sets of side measurements can create a right triangle. 202 = 400 for the set of measures 12, 16, and 20.

[tex]12^2 + 16^2[/tex] = 144 + 256 = 400

The measurements could result in a right triangle because they meet the Pythagorean theorem.

Measurements 6, 14, and 19 are as follows: 192 = 361 62 + 142 = 36 + 196 = 232 . (Option-A)

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Answer:

12, 16, 20

Step-by-step explanation:

A right triangle is a triangle that has one right angle, which is an angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse. The other two sides are called the legs.

We can use the Pythagorean theorem to determine which set of side measurements. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

So, for each set of side measurements, we can calculate the square of each side and add them together. If the sum is equal to the square of the hypotenuse, then the set of side measurements could be used to form a right triangle.

Set 1: 12, 16, 20

The sum of the squares of the legs is 144 + 256 = 400.

The square of the hypotenuse is also 400.

Therefore, set 1 could be used to form a right triangle.

Set 2: 6, 14, 19

The sum of the squares of the legs is 36 + 196 = 232.

The square of the hypotenuse is 361.

Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 2 could not be used to form a right triangle.

Set 3: 6, 8, 15

The sum of the squares of the legs is 36 + 64 = 100.

The square of the hypotenuse is 225.

Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 3 could not be used to form a right triangle.

Set 4: 4, 5, 6

The sum of the squares of the legs is 16 + 25 = 41.

The square of the hypotenuse is 36.

Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 4 could not be used to form a right triangle.

Therefore, the only set of side measurements that could be used to form a right triangle is set 1.

Step-by-step explanation:

(FE+BC)/2=<FDE

<FDE=<BDC

it is basically the average of x and 70.

(x+70)/2=104

x=138

Hope that helps :)

Answer:

The answer is probly 70 degrees

i might be wrong

i just hope this works

good luck

Answer:  A. 4p + $17.50 = $53.50; p = $9.00

1:  17.50+4p=  Nothing further can be done with this topic. Please check the expression entered or try another topic.

17.5 + 4 p

2:  4p=53.50-17.50=  4p=53.50-17.50

Step-by-step explanation:  9

The total bill: $53.50

17.50 + 4 x = 53.50

4 x = 53.50 - 17.50

4 x = 36

x = 36 : 4

x = $9

Answer: The price of each shrub is $9.

...............................................................................................................................................

Answer:

$9

Step-by-step explanation:

Let   be the price of each shrub.

4 shrubs at    each costs    dollars

Potting soil is $17.50

Hence, total cost is the expression  

We know that total bill is $53.50, so we can equate it to the expression:

This equation can be solved for    to find cost of each shrub.

Solving for    gives us:

So price of each shrub is $9

Answer:

see the explanation below

Step-by-step explanation:

The expression for the cost can be given as

y=mx+c

where x= the distance

           m= the cost to move x distance

            c= the fixed cost

Therefore the total cost to ship the cost will be y

a)

b) If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is evidence that the proportion is greater than 0.132.

c. Two possible explanations for the evidence that Jenna found are given below.

Solution:

a.

Identify the population, Parameter, sample, and statistic.

Population: All pennies in the container

Parameter: p = Proportion of pre-1982 copper pennies in the container

Sample: 50 randomly selected pennies from the container

Statistic: Number of pre-1982 copper pennies in the sample = 11

b.

To determine if Jenna has convincing evidence that more than 13.2% of her pennies are pre-1982 copper pennies, we can perform a hypothesis test.

Let's assume that the null hypothesis is that the proportion of pre-1982 copper pennies in the container is equal to 0.132, while the alternative hypothesis is that the proportion is greater than 0.132.

Then, we can calculate the test statistic and compare it to the critical value.

If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is evidence that the proportion is greater than 0.132.

c. Two possible explanations for the evidence that Jenna found could be:

1. The container has a higher proportion of pre-1982 copper pennies than the national average.

2. Jenna's sample is not representative of the container, and the sample proportion is higher than the population proportion by chance.

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Answer:

75

Step-by-step explanation:

Answer:

the angle that is 75 degrees

Step-by-step explanation:

Because the longest side is always opposite of the largest angle and the smallest side is always opposite of the smallest angle.

Answer:

Step-by-step explanation:

Answer:

<ABC = 17

Step-by-step explanation:

I'm going to make a guess. My guess is that you want the measure of angle B.  I didn't see that the diagram asks that very question.

If you join <ADC, that angle is also 34 degrees. By the property of angles touching the circumference of a circle, the angle touching the circumference is 1/2 the central angle

1/2 34 = 17

Answer:

180 customers made additional purchases

Step-by-step explanation:

In order to find the percent of something like 72% of 250 you need to convert the percentage to a decimal and multiply it to the number.

0.72 * 250 = 180

Answer:

180 customers

Step-by-step explanation:

Since 72% of the customers made additional purchases and there were 250 customers, we need to look for 72% of 250. To do this we convert 72 into a fraction, which makes it 0.72 and we turn the word "of" into a multiplication symbol (as of most commonly means multiplication in math). So, 0.72*250=180. Therefore, 180 customers made additional purchaces.