The volume of the pyramid as shown in the diagram is 363.67 cm³.
What is volume?
Volume is the space occupied by a solid shape.
To calculate the volume of the Pyramid, we use the formula below.
Formula:
V = L²h/3.........................equation 1Where:
V = Volume of the pyramidL = Length of the square baseh = Height of the pyramidFrom the diagram,
Given:
b = 10 cmh = √(12²-25)h = √199h = 10.91 cmSubstitute these values into equation 1
V = 10.91×10²/3V = 363.67 cm³Hence the volume of the pyramid is 363.67 cm³.
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3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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Please help (easy economics question)!!!
The dollar value of total revenue at each price is $\(0\), $\(10\), $\(12\), $\(12\), $\(10\), and $\(6\). Total revenue will be the greatest at a price of $\(4\), with \(3\) units sold.
To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:
Price: $\(6\)
Quantity: \(0\)
Total Revenue: $\(6 \times 0\) = $\(0\)
Price: $\(5\)
Quantity: \(2\)
Total Revenue: $\(5 \times 2\) = $\(10\)
Price: $\(4\)
Quantity: \(3\)
Total Revenue: $\(4 \times 3\) = $\(12\)
Price: $\(3\)
Quantity: \(4\)
Total Revenue: $\(3 \times 4\) = $\(12\)
Price: $\(2\)
Quantity: \(5\)
Total Revenue: $\(2 \times 5\) = $\(10\)
Price: $\(1\)
Quantity: \(6\)
Total Revenue: $\(1 \times 6\) = $\(6\)
To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $\(3\), and the corresponding quantity sold is \(4\) units.
Therefore, at a price of $\(3\), the total revenue will be the greatest, with \(4\) units sold.
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Help me with this please
Answer:
Your answer will be B. A town's population grows at a rate of 7.2% every year.
Step-by-step explanation:
Pls give me brainliest thx
four cities lie along a straight highway in this order city a, city, city c, city d. The distance from city a to city b is 5 times the distance from city b to city c. The distance from city a to city d is 2 times the distance from city a to city d. the distance between city d and city c is 10 miles. What are the distances between the cities?
Dividing the segments and finding the lengths, it is found that the distance between the two cities is of 130 miles.
--------------------------------
We want to find the distance between cities a and d.Due to the cities along the highway, the distance is given by:\(ad = ab + bc + cd\)
--------------------------------
The distance from city a to city b is 5 times the distance from city b to city c, and thus:\(ab = 5bc\)
In terms of x, \(bc = x, ab = 5x\)
--------------------------------
The distance from city b to city c is 2 times the distance from city c to city d, and thus:\(bc = 2cd\)
In terms of x, \(cd = \frac{x}{2}\)
--------------------------------
The distance between city d and city c is 10 miles, thus:\(\frac{x}{2} = 10\)
\(x = 20\)
--------------------------------
The other distances are:\(bc = x = 20\)
\(ab = 5x = 5(20) = 100\)
--------------------------------
The distance between cities a and d is:\(ad = ab + bc + cd = 100 + 20 + 10 = 130\)
The distance between the two cities is of 130 miles.
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Write a multiplication equation to show an equivalent fraction of 15 using fifteenths.
Explain how the two fractions are equivalent.
A multiplication equation to show an equivalent fraction of 15 using fifteenths would gives 10/75
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We have to write an equivalent fraction of 15 using fifteenths.
2/15
So let multiply by 5 .
2 / 15 x 5/ 5 = 10/75
Thus, 10/75 is equivalent expression.
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QUICK! 40 points. Consider this cone with the diameter measure of 17 inches.
A cone with diameter 17 inches and slant height of 22 inches.
What is the surface area of the cone?
SA = Pir2 + Pirl
A. 204Pi in.2
B. 259.25Pi in.2
C. 446.25Pi in.2
D. 663Pi in.2
259.25π in² is the surface area of the cone
The surface area of a cone can be calculated using the formula SA = πr² + πrl
where r is the radius and l is the slant height.
Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.
The slant height (l) is given as 22 inches.
Substituting these values into the formula:
Surface Area = π(8.5)² + π(8.5)(22)
= 72.25π + 187π
= 259.25π
Therefore, the surface area of the cone is 259.25π in²
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A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 61 national seniors reported using them. Conduct a hypothesis test at the 5% level.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Null hypothesis is rejected and it was concluded that proportion of the use of drugs in local seniors is more compare to national seniors.
As given in the question,
Total number of local seniors be n₁ = 100
Total number of national seniors be n₂ = 100
Let us consider proportion of local seniors be p₁
Number of local seniors using drugs = 65
Null hypothesis : p₁ = p₂
Alternative hypothesis : p₁> p₂
p₁ = 0.65
1 - p₁ = 0.35
And proportion of national seniors be p₂
Number of national seniors using drugs = 61
p₂ = 0.61
1 - p₂ = 0.39
Standard error = √ [p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂]
= √0.65( 0.35)/100 + 0.61(0.39)/100
= √0.002275 + 0.002379
= 0.0682
Z =( p₁ - p₂ ) / √ [p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂]
= 0.65 - 0.61 / 0.0682
= 0.04/ 0.0682
=0.5865
p-value = 0.2788 > 0.05
Null hypothesis rejected at the 5% level.
Therefore, from the given proportion of the distribution it is concluded that local seniors uses drugs in higher rate than the national seniors as null hypothesis rejected .
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The triangle ABC is an isosceles triangle. What are each of the congruent base angles if the vertex angle measures 40 degrees?
Therefore the solution to the given problem is the each of the congruent base angles is 70°
What is angle?In Euclidean geometry, an angle is the figure generated by two rays, called the sides of the angle, sharing a common termination, called the vertex of the angle. Angles created by two rays are in the plane where the rays are located. The intersection of two planes also forms angles. We refer to these as dihedral angles.
Here,
As the triangle is an isosceles triangle therefore it will have 2 same angles
thus,
Sum of the 3 angles of a triangle=180°
Vertex angle =40°
Sum of two congruent angles=180°–40°=140°
Measure of each base angle=70°
Therefore the each of the congruent base angles is 70°
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Mathematics question
Answer:
8
Step-by-step explanation:
MP=16
NP = 14
So that means N is farther to O by 2 units
So: 10-2 = 8
Micheal earns $87 for 15 hours of part time work. How long must he work to earn $135
Answer:
23.28 hours
Step-by-step explanation:
He earns 5.8 per hour of part-time work. You can find this by doing 87/15
Because we now know that he earns 5.8 per hour we can just do 135/5.8 (23.28) < this is rounding to the nearest hundreth
A person places $48800 in an investment account earning an annual rate of 3.1%,
compounded continuously. Using the formula V = Pert, where Vis the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 13 years.
When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.
What is compounding?Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.
We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:
Using the formula V = \(Pe^rt\)
Principal (P) = $48,800.00
Annual Rate (R) = 3.1%
Compound (n) = Compounding Continuously
Time (t in years) = 13 years
Result:
V = $73,019.78
V = P + I where
P (principal) = $48,800.00
I (interest) = $24,219.78
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.1/100
r = 0.031 rate per year,
Solving the equation for V:
V = \(Pe^rt\)
V = \(48,800.00(2.71828)^(0.031)(13)\)
V = $73,019.78
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determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). show how you arrived at each answer. use equivalence-style proofs.
From the given formulas, formula A is a tautology or always true. Formula B is a contradiction or never true. And, formula C is contingency or sometimes true.
Using the truth table, a given expression is said to be in tautology when all the values are true. The given expression is said to be a contradiction when all the values are false or never true. And the given expression is said to be contingency when the values are either true or false.
In the given formulas, formula A (p→q)∨(q→r) is a tautology. This is because the values in all rows are true (T).
In the given formulas, formula B (¬(¬(p∧q)→(p→¬q))) is a contradiction. This is because the values in all rows are false (F).
In the given formulas, formula C ((¬p∨q)→q) is a contingency. This is because some values are true and some are false.
The complete question is -
Determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). Show how you arrived at each answer. Use equivalence-style proofs.
A. (p→q)∨(q→r)
B. ¬(¬(p∧q)→(p→¬q))
C. ((¬p∨q)→q)
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Find the area of the rhombus with diagonals a = 4 and b = 5.
A) 20
B) 10
C) 30
D) 40
don't guess. I'll give you brainly.
Answer:
Hey buddy, here is your answer. Hope it helps u
Step-by-step explanation:
The answer is b-10. The area of rhombus is 1/2*d1*d2. So 1/2*4*5=10. D stands for diameter.
Answer:10
Step-by-step explanation:
16.What is the equation of the vertical asymptote for the function f(x) = x-1,x+4(A) x=1(B) x=-1(C) x=4(D) x=-417.
The vertical asymptotes is when the denominator is 0
Hence we have
\(\begin{gathered} x+4=0 \\ x=-4 \end{gathered}\)X=-4 is the vertical asymptote
The right option is D
A dairy farmer wants to mix a 80% protein supplement and a standard 55% protein ration to make 1400 pounds of a high-grade 60% protein ration. How many pounds of each should he use?
If the dairy farmer wants to mix a 80% protein. The amount of pounds of each that he should use is 80% 280 pounds and 55% 1120 pounds.
How to find the number of pounds?Protein I 80% = x pounds
Protein II 55% = 1400 - x pounds
Mixture 60% = 1400
Hence,
80% x + 55% ( 1400 - x ) = 60% × 1400
80 x + 55 ( 1400 - x ) = 84000
80 x + 77000 - 55 x = 84000
Combine like terms
80 x - 55 x = 84000 - -77000
25 x = 7000
Divide both side by 25x
x= 7000/25
x =280 pounds ( Protein I)
Protein II
1400 - x pounds
1400 -280
= 1120 pounds
Therefore the farmer should use 280 pounds and 1120 pounds.
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The triangle above has the following measures.
a=8m
b=8 squared 3m
Use the 30-60-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
The value of m∠Q as shown in the right-angled triangle is 54.718°.
The Formula used is:
m∠Q = cos⁻¹(s/r)........................ (1)
Where:
a = 8 m
b = 8√3 m
Now, Substitute these values into equation 1
m∠Q = cos⁻¹(8/8√3)
m∠Q = cos⁻¹(1/√3)
m∠Q = 54.718.
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The following two way table describes students after school activities find the probability that a randomly selected student is in sports
Answer:
0.65
Step-by-step explanation:
There’s 65 students total in sports, so you divide that by 100 to get your answer
Answer:
0.65Step-by-step explanation:
sophomore + junior + senior = total number of students that play sports
20 + 20 + 25 = 65
65 ÷ 100 = 0.65
0.65 rounded to the nearest hundred would still be 0.65
There are 26 boys and 20 girls in a class.
The boys and the girls have some counters.
The mean number of counters that the boys have is 28.
The mean number of counters that the girls have is 19.
Work out the mean number of counters the 46 children have.
Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.
What is the mean?The mean refers to the average value.
The average is the quotient of the total value divided by the number of items in the data set.
The number of boys in the class = 26
The number of girls in the class = 20
The total number of boys and girls in the class = 46
The mean number of counters that the boys have = 28
The total number of counters that the boys have = 728 (28 x 26)
The mean number of counters that the girls have =19
The total number of counters that the girls have = 380 (19 x 20)
The total number of counters that the class has = 1,108 (728 + 380)
The average or mean number of counters in the class = 24 (1,108 ÷ 46)
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use the multiplier method to increase £88 by 14
Answer:
£88*1.14
Step-by-step explanation:
If you want to increase 88 by 14% that means you get 114% of 88.
This is very easy all you have to do is 88*1.14 and you get the answer.
What scenario depicts two independent events
Step-by-step explanation:
A t
eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.
Answer:
A.The school play opens tonight and it is raining.
B.Neva is hungry and she buys a snack from the concession stand.
C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.
D.Luka paints during school and he stains his shirt.
multiply 3 3/4 how to solve please tell
Step-by-step explanation:
\(3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{9} \\ \)
Exit Ticket: At many county and state fairs, you must purchase
tickets if you wish to go on the rides. Different rides require
different numbers of tickets. The Ferris wheel, for example,
might require three tickets, while the bumper cars might require
two. Before you buy any tickets, it might be helpful to know
which rides you plan to ride, and how many tickets you will need.
Write about it! Each ride requires 3 tickets. If a ticket costs
$1.50, write an equation to find the total cost of y of x rides.
How much will it cost to ride 10 rides?
An equation to find the total cost of y of x rides is y = 3x.
The cost to ride 10 rides is equal to $15.
How to determine the total cost of y of x rides?In order to write an equation that model this situation, we would assign variables to the number of tickets and the total cost respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of tickets.Let the variable y represent the total cost.Next, we would translate the word problem into an algebraic equation based on the fact that each ride requires 3 tickets and a ticket costs $1.50 as follows;
y = 3x
For the cost of 10 rides, we have:
y = 10x
When x = 1.50, the total cost is given by:
y = 10(1.50)
y = $15.
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During the summer isabelle sells corn at her familys produce stand every morning she starts with 250 ears of corn on saterday isabelle sells 150 of the 250 ears of corn she wants to know what percent of the corn she sold
Answer:
60%
Step-by-step explanation:
To find the percent of the corn she sold, divide the amount by the total, then multiply that by 100.
(150 / 250) x 100
0.6 x 100
= 60
So, Isabelle sold 60% of the corn
which mixed number is equivalent to the improper fraction of 41/10
Answer:
4 1/10 when u have a inproper fraction like that every 10 is one whole number
A new concert venue just opened in downtown Houston and they are in the process
of deciding how many tickets they can sell for each show. The venue has three levels,
two general admission that only have standing room, and one level with 150 seats.
The venue thinks each person will occupy 2.25 ft.
.
• The first level of standing room is a square with one side measuring 75ft.
The second level, also standing room, is a rectangle measuring 100' by 50' ft.
. The third level has 150 seats.
How many tickets can they sell for the first level?
Answer:
2500
Step-by-step explanation:
Dimensions of first level
Length = Breadth = 75 ft (since it is a square)
It is assumed that a person will occupy \(2.25\ \text{ft}^2\)
Area of first level
\(75\times 75=5625\ \text{ft}^2\)
When the area of the level is divided by the area of one person then we will get the number of people that can occupy the room or the number of tickets that can be sold.
\(\dfrac{5625}{2.25}=2500\)
The number of tickets that can be sold for the first level is 2500.
a cube has a volume of seven units. what is the edge length of a cube?
Given:
The volume of the cube = seven units.
Let a be the edge length of the cube.
Consider the formula for the volume of the cube.
\(V=a^3\)Substitute V=7 in the formula, we get
\(7=a^3\)Taking cubic root on both sides, we get
\(\sqrt[3]{7}=a\)\(T\text{he edge length of the given cube is }\sqrt[3]{7}\text{ units.}\)or
\(T\text{he edge length of the given cube is }1.91\text{ units.}\)Slopes of parallel/Purpendicular lines - What is the slope of a line parallel to the line whose equation is x + 2y = -14
Explanation:
First we solve for y.
x + 2y = -14
2y = -14 - x
2y = -x - 14
y = (-x - 14)/2
y = -x/2 - 14/2
y = (-1/2)x - 7
The equation is in slope intercept form y = mx+b
m = -1/2 = slopeb = -7 = y interceptParallel lines have equal slopes, but different y intercepts. This means the slope of any line parallel to this given one will have a slope of -1/2
For example, y = (-1/2)x + 10 is parallel to y = (-1/2)x - 7, since both have the same slope of -1/2 but different y intercepts.
--Marking Brainliest whoever answers this first, thank you.
Question is below.
Answer:
(-4,3)
Step-by-step explanation:
Functions are points where there are no more than 1 y value for every x. points (-4,-3) and (-4,3) are points that make it not. function.
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Tim is taking the path shown to bike to Greg's house. Tim travels an average speed of 15 mi/hr.
Determine how much time it will take Tim to get to Greg's house. (You may use decimals here)
Answer:
Road:
Distance to Greg's house = 3.2 + 1.7 =
4.9 miles
Time to get to Greg's house =
(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)
Shortcut:
Distance to Greg's house:
\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)
Time to get to Greg's house:
(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)
The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)
New Hope School started with only 94 students. Now the school has grown to 750% of the original size. How many students are in school now?
94
x7.5
--------
705 students
Answer:
Use maths papa
Step-by-step explanation: