Option B, maximum 8 marks An isosceles has two sides of equal lengths. Find the lengths of the sides of the isosceles triangle which has a perimeter of 12 cm and a maximum area.

Answer:

The first choice

Step-by-step explanation:

It says that its decreasing so the slope is negative.

It also starts of with 565 so that's the y intercept

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine the probability of home and away wins, we need to know the number of wins for each category. Let's assume that Sasha's team won 8 games at home and 10 games away.

The probability of a home win can be calculated by dividing the number of home wins by the total number of home games:

Probability of Home Win = Number of Home Wins / Total Number of Home Games = 8 / 12 = 2/3 ≈ 0.67

The probability of an away win can be calculated by dividing the number of away wins by the total number of away games:

Probability of Away Win = Number of Away Wins / Total Number of Away Games = 10 / 12 ≈ 0.83

Based on these calculations, the probability of an away win (0.83) is higher than the probability of a home win (0.67). Therefore, Sasha's belief that her team plays better at away games seems to be supported by the data, as they have a higher probability of winning in away games compared to home games.

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Answer:

\(x = 127\)

Step-by-step explanation:

The sum of the interior angles of a hexagon = 720°

\(x + 112 + 133 + 128 + 100 + 120 = 720 \\ \\ x + 593 = 720 \\ x = 720 - 593 \\ x = 127\)

I hope I helped you^_^

The price of a ticket exceeds its expected value by $0.75.

In this raffle scenario, we need to find out by how much the price of a ticket exceeds its expected value.

Step 1: Determine the probability of winning each prize.
- The probability of winning the first prize: 1/1000 (1 winning ticket out of 1000)
- The probability of winning a second prize: 3/1000 (3 winning tickets out of 1000)
- The probability of not winning any prize: 996/1000 (996 losing tickets out of 1000)

Step 2: Calculate the expected value of each outcome.
- Expected value of winning the first prize: (1/1000) * $100 = $0.10
- Expected value of winning a second prize: (3/1000) * $50 = $0.15
- Expected value of not winning any prize: (996/1000) * $0 = $0

Step 3: Add the expected values together.
- Total expected value: $0.10 + $0.15 + $0 = $0.25

Step 4: Determine the difference between the price of a ticket and its expected value.
- Difference: $1.00 (ticket price) - $0.25 (expected value) = $0.75

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To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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Answer:

35/16      2 2/16

Step-by-step explanation:

1 1/4 = 5/4

1 3/4 = 7/4

5 * 7 = 35

4 * 4 = 16

35/16

Answer:

2 3/16

Step-by-step explanation:

First, we have to convert our mixed numbers to improper fractions, so our new equation is:

5/4 x 7/4 = 35/16

35/16 = 2 3/16

If Miles Makes $18.26 per hour, his over time rate if he were to work over 40 hours in a week is: $27.39.

The amount of extra money an employee receives for working over their usual workday is referred to as their overtime rate. Most of the time an employee is paid an overtime rate in addition to their normal hourly wage.

Using this formula to find the overtime rate

Overtime rate = Regular hourly rate × Overtime multiplier

Where:

Regular hourly rate = $18.26

Overtime multiplier = 1.5

Let plug in the formula

Overtime rate = $18.26 × 1.5

Overtime rate = $27.39

Therefore the overtime rate would be $27.39 per hour .

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Answer:

the answer is c

Step-by-step explanation:

add 14 9 times and then whatever that number is double it and remove the negative sign

The area of rectangle B is 560 square inches.

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.

Given that,

Scale factor = 4

Rectangle A has

length = 5 inches

breadth =  7 inches

Area of a rectangle A = length×breadth

                                    = 5×7

                                    = 35 square inches

Scale factor is 4 so length and width of a new rectangle is

length = 5×4 = 20 inches

breadth =  7×4 = 28 inches

Area of a rectangle B = length×breadth

                                    = 20×28

                                    = 560 square inches

Hence, The area of rectangle B is 560 square inches.

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Answer:

64

Step-by-step explanation:

I think it is 8 times 8 I’m probably wrong I don’t do this math.

Answer:

16

Step-by-step explanation:

Alex will run 16 laps in the time it take for Carlos to run 12 laps.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given are the values related to the number of laps run by Alex and Carlos.

The number of laps run by Alex is forming the multiples of 4 or 4x.

Number of laps run by Carlos is forming the multiples of 3 or 3x.

When x = 1,

Alex : 4 × 1 = 4

Carlos : 3 × 1 = 3

When x = 2,

Alex : 4 × 2 = 8

Carlos : 3 × 2 = 6

When x = 3,

Alex : 4 × 3 = 12

Carlos : 3 × 3 = 9

When x = 4,

Alex : 4 × 4 = 16

Carlos : 3 × 4 = 12

Hence Alex ran 16 laps in the same time for which Carlos ran 12 laps.

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The two friends have the shortest distance between them are Carrie and Nayla.

In order to determine the distance of the friends from each other, the value of the angles have to be determined. The given figure is a triangle. Sum of angles in the triangle equal 180 degrees.

The first step is to determine the value of x:

20x + 7) + (5x + 50) + (5x + 3) = 180

Add similar terms togethers

30x + 60 = 180

Combine similar terms

30x = 180 - 60

30x = 120

x = 120 / 30

x = 4

The second step is to determine the value of each angle

Nayla = 20(4) + 7 = 87

Carrie = Second angle = 5(4) + 50 = 70

Maria = Third angle = 180 - (70 + 87) = 23

Nayla and Carrie live closest to each other

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Answer:

last answer

Step-by-step explanation:

Answer: y = -3x -3

Step-by-step explanation:

y = mx + b

3x + y = -3

y = -3x -3

Answer:

slope intercept form: y=mx+c

*m = gradient

*c = y-intercept

3x + y = -3

y = -3x - 3

The length of the arc will be 22 cm.

Length of the radius 'r'= 28 cm

central angle 'a' in degrees = 45

The formula for length of arc is 2πra÷360

The standard value of pie that we take is 22÷7

so after putting all the given values, we get,

2×22/7×28×45 = 22cm.

Radius is any line that we draw from the centre of the circle to its outside edge.

Arc is the part of the circle's circumference.

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Answer:

Angle 1

Step-by-step explanation:

Angle 3 and angle 1 are vertical angles. That means that whatever the measure of angle 3 is, angle 1 is also the same.

The intermediate value theorem tells us that for all values of k between 0 and 6 (inclusive), there exists a c in the interval [0, 1] such that f(c) = k.

To apply the intermediate value theorem, we need to show that f(x) is a continuous function on the interval [0, 1].

Since f(x) is a polynomial, it is continuous everywhere. Therefore, it is also continuous on the interval [0, 1].

Now, let's consider some values of k and see if we can use the intermediate value theorem to find a c in the interval [0, 1] such that f(c) = k.

For any value of k, we have:

f(0) = 0 + 0 = 0

f(1) = 4(1)^2 + 2(1)^2 = 6

So, if k is any value between 0 and 6, then by the intermediate value theorem, there exists a number c in the interval [0, 1] such that f(c) = k.

Conversely, if k is outside the range [0, 6], then the intermediate value theorem does not guarantee the existence of a number c in the interval [0, 1] such that f(c) = k.

Therefore, the intermediate value theorem tells us that for all values of k between 0 and 6 (inclusive), there exists a c in the interval [0, 1] such that f(c) = k.

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Answer:

x=10 degrees.

Step-by-step explanation:

(6x-5)+5x+75=180

180 from the measure of degrees in a triangle*

Solve this equation.

11x+70=180

11x=110

x=10

x=10 degrees.

Answer:

-60

Step-by-step explanation:

Factor the problem out using FOIL.

The end result is: −60\(x^{2}\)−84x+9

The value of coefficent a (the number in front of the x^2) is -60.

In order for a function to be continuous at a point, then,

The limit of f(x) as x approaches the x coordinate of the point from the left and the right equals the value of the function at that point.

What does the term "continuous function" mean?

A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap.

                            This indicates that there aren't any discontinuities, or sharp shifts in value.

What does it mean when a function is continuous or discontinuous?

If one can sketch a function without picking up a pencil, one can say that it is continuous. A function is considered discontinuous if it is not.

                          If there is no break in the graph of the given function at the point, then a function f(x) in calculus is continuous at x = c.

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Answer:

Below in bold.

Step-by-step explanation:

4y + 2 > 2.8

4y > 2.8 - 2

4y > 0.8

y > 0.8/4

y > 0.2.

Given:

Aim:

Explanation:

Take square root on both sides of the given equation.

Final answer:

The solution set is

Answer:

900

Step-by-step explanation:

since 258 is over half of 250, the number will end up 300. 631 falls behind on being half so it'll be only 600. 300+600=900

Hello,

\(34 = p + 19\)

\(34 - 19 = p + 19 - 19\)

\(15 = p\)

\(p = 15\)

Answer:

Its A

Step-by-step explanation:

3.2 + 4.2= 7.4

10^5 x 10^8 = 10^13

Since your final answer is in scientific notation, its 7.4 x 10^13

(a) To find the elasticity of demand E(p), we need to compute the derivative of the demand function D(p) with respect to price p and then multiply by the ratio of price to demand:
E(p) = (dD(p)/dp) * (p / D(p))
First, let's find the derivative of D(p) with respect to p:
D(p) = 6000e^(-0.02p)
dD(p)/dp = -0.02 * 6000e^(-0.02p) = -120e^(-0.02p)

Now, we can compute E(p):
E(p) = (-120e^(-0.02p)) * (p / (6000e^(-0.02p)))
E(p) = -120p / 6000
E(p) = -p / 50

(b) Now, we can determine whether the demand is elastic, inelastic, or unit-elastic at the price p = 30:
E(30) = -30 / 50 = -0.6

Since the absolute value of E(p) is less than 1 (0.6 < 1), the demand is inelastic at the price p = 30. So the correct answer is:
b. -inelastic

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Answer:

Step-by-step explanation:

who cares about SOME boys and girls