40 POINTS! + BRAINLIEST

What is the measure in radians for the central angle of a circle whose radius is 6 cm and intercept arc length is 5.4 cm?

Make sure to show all calculations.

A. x=-6 or x=2 is the answer

Answer:

The answer is A) 254 m3

Final answer:

Matt's Ice Cream Shoppe can serve 56 sundaes with 7 cups of sprinkles, assuming each sundae uses 1/8 cup of sprinkles.

Explanation:

The question asks: How many sundaes can Matt's Ice Cream Shoppe serve with 7 cups of sprinkles if each sundae is served with 1/8 cup of sprinkles?

To find the answer, we divide the total amount of sprinkles by the amount used per sundae. Here's the calculation:

Therefore, Matt's Ice Cream Shoppe can serve a total of 56 sundaes with their current stock of sprinkles.

Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.

To find out how many sundaes Matt's Ice Cream Shoppe can serve with 7 cups of sprinkles, we need to divide the total amount of sprinkles by the amount of sprinkles used per sundae.

Given:

- Total amount of sprinkles: 7 cups

- Amount of sprinkles per sundae: [tex]\( \frac{1}{8} \)[/tex] cup

Let ( x ) be the number of sundaes that can be served.

We can set up the equation:

[tex]\[ \text{Total amount of sprinkles} = \text{Amount of sprinkles per sundae} \times \text{Number of sundaes} \][/tex]

[tex]\[ 7 = \frac{1}{8} \times x \][/tex]

Now, to solve for ( x ), we can multiply both sides of the equation by 8:

[tex]\[ 7 \times 8 = x \][/tex]

[tex]\[ x = 56 \][/tex]

Therefore, Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.

The toddler crawled a total of 14 feet after converting the initial 2 yards into feet and adding the additional 8 feet crawled.

To determine the total distance the toddler traveled, we first need to convert the units so they are the same. We know that 1 yard is equivalent to 3 feet. If the toddler crawled 2 yards initially, we can calculate this distance in feet as follows:

2 yards * 3 feet/yard = 6 feet

After stopping, the toddler continued to crawl for 8 more feet. To find the total distance traveled, we simply add the two distances together:

6 feet + 8 feet = 14 feet

Therefore, the toddler traveled a total of 14 feet.

Answer:  The required value of f(3) is 81.

Step-by-step explanation:  We are given the following function :

[tex]f(x)=\left(\dfrac{1}{9}\right)9^x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the value of f(3).

Substituting x = 3 in equation (i), we get

[tex]f(3)\\\\\\=\left(\dfrac{1}{9}\right)\times9^3\\\\=9^2\\\\=81.[/tex]

Thus, the required value of f(3) is 81.

Answer:

81

Step-by-step explanation:

APEX

Answer:

36 feet.

Step-by-step explanation:

We have been given that on level ground, a vertical rod 12 feet tall casts a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long.

To find the length of flagpole, we will use proportions as:

[tex]\frac{\text{Actual length of flagpole}}{\text{Shadow of flagpole}}=\frac{\text{Actual length of rod}}{\text{Shadow of rod}}[/tex]

Substitute given values:

[tex]\frac{\text{Actual length of flagpole}}{12\text{ ft}}=\frac{12\text{ ft}}{4\text{ ft}}[/tex]

[tex]\frac{\text{Actual length of flagpole}}{12\text{ ft}}\times 12\text{ ft}=\frac{12\text{ ft}}{4\text{ ft}}\times 12\text{ ft}[/tex]

[tex]\text{Actual length of flagpole}=12\text{ ft}\times 3[/tex]

[tex]\text{Actual length of flagpole}=36\text{ ft}[/tex]

Therefore, the actual length of flagpole is 36 feet.

Final answer:

The perimeter of triangle ABC with the given vertices can be found by calculating the distances between the points. The lengths are 15 units for AB, 9 units for BC, and 12 units for AC, and their sum is 36 units. The correct option is D.

Explanation:

To determine the perimeter of triangle ABC with the given vertices A(-2,9), B(7,-3), C(-2,-3), we first need to calculate the lengths of the sides of the triangle using the distance formula, which is d = √((x₂ - x₁)² + (y₂ - y₁)²).

The perimeter is the sum of the lengths of the sides, so P = AB + BC + AC = 15 + 9 + 12 = 36 units.

The correct answer is 36 units which corresponds to option D.

The total surface area = 910.6 square centimeters. Option B

The surface area of a cylinder with a conical top can be found by calculating the sum of the areas of the circular base, the curved surface of the cylinder, and the lateral surface of the cone.

From the image, we can find that the radius of the cylinder is 5 cm and the height of the cylinder is 13 cm. We are not given the slant height of the cone.

Let's denote the slant height of the cone as sl.

Here's how to find the surface area of each part:

Curved surface area of the cylinder:

2πrh = 2π(5 cm)(20 cm)

= 628.31 cm²

Lateral surface area of the cone

A=πrl+πr2

=  π*5*13+π*5²

= 282 square centimeters

Therefore, the total surface area of the cylinder with a conical top is equal to:

Total surface area = Area of circular base + Curved surface area of cylinder + Lateral surface area of cone

Total surface area  = 282 + 628.31 cm²

Total surface area = 910.6 square centimeters

The answer is 1909.82 (rounded to the cent).

I just took this test.

Answer: The interval would be [71,107]

Step-by-step explanation:

Since we ave given that

Scores received in 3 exams are 99%, 80%, and 70%.

To receive a grade of B in the class, he must have an average exam score between 80% and 89% for all 4 exams for all 4 exams.

So, Minimum marks he needs for all 4 exams is given by

[tex]80\times 4=320[/tex]

Maximum marks he needs for all 4 exams is given by

[tex]89\times 4=356[/tex]

And his total marks in 3 exams is

[tex]99+80+70\\\\=249[/tex]

Minimum marks he needs in final exam is given by

[tex]320-249\\\\=71[/tex]

Maximum marks he needs in final exam is given by

[tex]356-249\\\\=107[/tex]

Hence, the interval would be [71,107]

Answer:

Step-by-step explanation:

first 150 then 60

The question is asking for the correct degree of rotations to simulate the passing of a soup bowl at a circular table. Without specific arrangement details, it's challenging to give a definitive answer, but if people are equidistant, option B 'First 180° and then 72°' would be the closest match.

The question asks which two rotations about the center of a circular table would describe the passing of a soup bowl from Caesar to Jada and then to Haifa. Given that the rotation is counterclockwise, we must determine the correct degree of rotations that match the sequence of passing the soup. We can visualize the table as a circle and consider that a full rotation around a circle is 360°.

Depending on the actual arrangement of the people around the table, the combined angles of rotation to pass the soup from Caesar to Jada to Haifa should add up to less than 360°, as they would not have gone a full circle. If we were to look at the options provided:

The only way to determine the correct answer is to know the specific arrangement of people around the table, which the question does not provide. Without this information, we cannot definitively choose the correct rotations. However, in general terms, if each person is equidistant from the others in a regular polygon arrangement, we can then divide 360° by the number of people to find the angle corresponding to one pass. Assuming five people at the table, each angle would be 72°. In this case, the closest matching option provided would be First 180° and then 72°.