Answer:
Volume of the sphere(V) is given by:
[tex]V = \frac{4}{3} \pi r^3[/tex] ....[1]
where,
r is the radius of the sphere.
As per the statement:
The diameter of a sphere is 4 centimeters.
Formula for the diameter(d) is given by:
[tex]d = 2r[/tex]
⇒[tex]4 = 2r[/tex]
Divide both sides by 2 we have;
2 = r
or
r = 2 cm
Substitute in [1] and use 3.14 for pi. we have;
[tex]V = \frac{4}{3} \cdot 3.14 \cdot 2^3 = \frac{4}{3} \cdot 3.14 \cdot 8[/tex]
Simplify:
V = 33.4933333 cubic cm
therefore, the volume of the sphere to the nearest tenths is, [tex]33.5 cm^3[/tex]
A cylindrical water tank has a diameter of 6 meters and a height of 9 meters. What is the maximum volume of water the tank can hold? (to nearest whole number) A) 254 m3 B) 509 m3 C) 1018 m3 D) 2290 m3
Answer:
The answer is A) 254 m3
What is the graph of the equation 4x – 5y = 15?
Given the lease terms below, find the total lease cost, assuming that the deposit is nonrefundable.
Terms:
Length of lease: 36 months
MSRP of the car: $21,400
Purchase value of the car after lease: $17,100
Down payment: $1500
Monthly payment: $272
Security deposit: $350
Acquisition fee: $700
The total lease cost is the sum of the down payment, nonrefundable security deposit, acquisition fee, and the total payments over the lease term which amounts to $12,342.
Explanation:The total lease cost can be calculated by adding all fees, the nonrefundable deposit, monthly payments, and any other additional costs. We start by adding the down payment, security deposit, and acquisition fee:
Down payment: $1500Security deposit (nonrefundable): $350Acquisition fee: $700The monthly payment over the term of the lease is calculated by multiplying the monthly payment amount by the number of months in the lease term:
Monthly payment: $272Length of lease: 36 monthsMultiplying the monthly payment by the lease term gives us the total amount paid over the course of the lease:
272 * 36 = $9792Adding all the costs together gives us the total lease cost:
Total lease cost = Down payment + Security deposit + Acquisition fee + Total monthly paymentsTotal lease cost = $1500 + $350 + $700 + $9792Total lease cost = $12342Note that this calculation assumes that the security deposit is nonrefundable, which is often the case in a car lease. It's also important to note that additional costs may apply, such as excess mileage fees or wear and tear.
please help algebra 2!!
Anna took a job that paid $200 the first week. She was guaranteed a raise of 5% each week.
How much money will she make in all over 8 weeks?
Round the answer to the nearest cent.
The answer is 1909.82 (rounded to the cent).
I just took this test.
Matt's Ice Cream Shoppe has 7 cups of sprinkles to use on sundaes for the rest of the day. If each sundae is served with
1/8
cup of sprinkles, how many sundaes can they serve?
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:
Total amount of sprinkles = 7 cups.Amount of sprinkles per sundae = 1/8 cup.Number of sundaes that can be served = Total amount of sprinkles ÷ Amount of sprinkles per sundae = 7 cups ÷ 1/8 cup = 56 sundaes.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.
Find the average rate of change of
f(x) = -2x² - x from x=1 to x=6
Simplify your answer as much as possible
The waiter places a bowl in front of Caesar. In a counterclockwise direction, he passes the soup to jada who then passes it to Haifa. Which two rotations about the center of the table describes passing the soup?
A) First 200° and then 80°
B) First 180° and then 72°
C) First 150° and then 60°
D) First 100° and then 40°
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.
Explanation: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:
First 200° and then 80° adds up to 280°,First 180° and then 72° adds up to 252°,First 150° and then 60° adds up to 210°,First 100° and then 40° adds up to 140°.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°.
When a number is subtracted from x the result is 6. What is that number
HELP PLEASE CAN SOMEONE TAKE A LOOK?
1. The investment you make into a start=up company is also known as ____ (1point)
A. Venture Capital
B. first-time investment
C. entrepreneurial capital
D. beginning capital
The triangle and the rectangle have the same perimeter.
Which represents the solution set of 5(x+5)<85
Solve the following system of equations
x + y =-5
-3x - y =7
A gift box is 12 inches long, 8 inches wide and 2 inches high. how much wrapping paper needed to wrap the box?
A.) 272 inches
B.) 192 inches
C.) 384 inches
D.) 184 inches
Solve for x. Simplify completely.
x^2+4x+4=8
A. x=-6 or x=2 is the answer
The area of a rectangle is 28^2 , and the length of the rectangle is 1ft more than double the width. find the dimensions of the rectangle.
I don't know: Person 1, person 2, and person 3 made $660, if the ratio is 3:4:5, how much did person 1 person 2, and person 3 get?
At a sporting event the price for 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of lemonade is $12. how much does it cost for 1 cheeseburger and 2 cups of lemonade
A toddler crawled 2 yards, stopped, then continued to crawl 8 more feet. How many feet did he travel in total?
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.
What does it mean to say that a polynomial equation is solvable by radicals?
A student received a 75% on an exam. If there were 20 questions on the exam, which ratio would show the number of questions answered correctly to the total number of questions? A. 20:5 B. 5:20 C. 15:20 D. 20:15
If f(x) = (1/9)(9^x) what is f(3)
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
Please I need help with this.
Austin rented a truck for one day. there was a base fee of $15.99 , and there was an additional charge of 82 cents for each mile driven. austin had to pay $123.41 when he returned the truck. for how many miles did he drive the truck?
Please help, I’m so confused :/
You are studying for your final exam on the semester. Up to this point, you received 3 exam scores of 99%, 80%, And 70%. To receive a grade of B in the class, you must have an average exam score between 80% and 89% for all 4 exams including the final. Find the widest range of scores that you can get on the final exam in order to receive a grade of B for the class. Use interval notation
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]
What is the perimeter of triangle ABC with the vertices A(-2,9), B(7,-3),C(-2,-3) in the coordinate plan
A)21 units
B) 15 units
C)34 units
D)36 units
PLZZZZZZZZZZ HELPPPPPPP MEDALS AND FAN
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).
Length of AB: √((7 - (-2))² + ((-3) - 9)²) = √(81 + 144) = √225 = 15 unitsLength of BC: √((-2 - 7)² + ((-3) - (-3))²) = √(81 + 0) = √81 = 9 unitsLength of AC: √((-2 - (-2))² + (9 - (-3))²) = √(0 + 144) = √144 = 12 unitsThe 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.
Using the properties of equality, fill the blanks with the correct value to show the solution for y.
3(y-2)=18
3y-___=18
3y=___
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. how many feet tall is the flagpole?
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.
How can i find one side of a triangle with another side and an angle?