Answer: The radius is 5 units (approximately)
Step-by-step explanation: The area of a sector with central angle X is given as;
Area = (X/360) x pi x r^2
Since the area has been given as 15.71 units, we can input the known values into the formula as follows;
15.71 = (72/360) x 3.14 x r^2
By cross multiplication we now have
(15.71/3.14) = 1/5 x r^2
(15.71/3.14) x 5 = r^2
78.55/3.14 = r^2
25.0159 = r^2
Add the square root sign to both sides of the equation
5.001 = r
The radius is equal to 5 units (approximately)
find the area of the shaded region
Answer:
[tex]x^{2} \\[/tex]+3x
Step-by-step explanation:
2x(2x+1)
x(x+1)
2[tex]x^{2}[/tex]+2x-[tex]x^{2}[/tex]+x
=[tex]x^{2}[/tex]+3x
The base of a triangular prism is an isosceles right triangle with a hypotenuse of 72−−√ centimeters. The height of the prism is 7 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Surface area = lateral area + 2(area of base)
Lateral area = perimeter of base * height.
Because it is a isosceles right triangle, both sides are equal.
[tex]x^{2} +x^{2}[/tex] = 72
2[tex]x^{2}[/tex] = 72. Divide both sides by 2
[tex]x^{2}[/tex] = 36. Square both sides.
x = 6.
So the perimeter of the base = 6 + 6 +[tex]\sqrt{72}[/tex] = 20.485281374239
Lateral area = 20.485281374239 * 7 = 143.397 [tex]cm^{2}[/tex]
Area of base is (1/2)base * height.
(1/2)(6)(6) = 18
Using the surface area formula
surface area = 143.397 + 2(18) = 179.4 [tex]cm^{3}[/tex]
Final answer:
The surface area of the triangular prism can be calculated by finding the areas of the two triangular bases and the three rectangular sides. After calculations, the total surface area of the prism is found to be 2304 square centimeters.
Explanation:
The question asks us to find the surface area of a triangular prism whose base is an isosceles right triangle with a hypotenuse of √72 centimeters and a height of 7 centimeters. We'll use various formulas for geometry, area, and volume to solve this problem.
First, we need to find the legs of the isosceles right triangle which form the base of the prism. Since it is a right triangle, and the legs (a) are equal, we can use Pythagoras' theorem where [tex]a^2 + a^2 = (72)^2[/tex]
Solving this gives us each leg as 36 cm.
The area of the base triangle is then found using 1/2 × base × height, which gives us-
1/2 × 36 × 36 = 648 square centimeters
The prism has two such triangular bases, so their combined area is 2 × 648 = 1296 square centimeters.
For the three rectangular sides, we calculate their areas by using the formula for the area of a rectangle (length × width). Each side has a length of 7 cm (the height of the prism). The widths are equal to the sides of the triangular base: 36 cm, 36 cm, and √(362 + 362) = √2592 = 72 cm. Thus, the total area of these sides is-
2(36 × 7) + (72 × 7) = 504 + 504 = 1008 square centimeters.
The total surface area of the prism is the sum of the areas of the bases and the rectangular sides, which is 1296 + 1008 = 2304 square centimeters.
Ms. Joseph is saving money for a trip to Zearnland over 12 weeks. She starts with 1 dollar. In the second week, she adds 2 dollars. Each week she adds 1 more dollar than she did the week before. For how many weeks will Ms. Joseph be saving money?
Ms. Joseph saves money for 12 weeks, starting with $1 and increasing the amount by $1 each week. By the 12th week, she adds $12. Therefore, she saves money for a total of 12 weeks.
To determine how many weeks Ms. Joseph is saving money, we need to look at the pattern of her savings. Each week, she adds one more dollar than the previous week:
Week 1: $1Week 2: $2Week 3: $3...Week 12: $12We can see that this is an arithmetic sequence where the first term (a) is $1 and the common difference (d) is $1. The nth term of an arithmetic sequence can be found using the formula: aₙ = a + (n-1)d.
For 12 weeks, the amount saved each week would be: a₁₂= 1 + (12-1) ×1 = 12. Ms. Joseph adds $12 in the 12th week. Finally, the total weeks she saves money is 12 weeks.
Can someone word out the equation 3 1\4+7\8 ?ANY RANDOM ANSWER WILL GET REPORTED
Answer:
13/8
Step-by-step explanation:
Answer:
Three and one fourth plus seven eigths
Step-by-step explanation:
Find the area of the parallelogram below.
Image result for area and perimeter of parallelograms
Answer:32 cm2
Step-by-step explanation:Use the formula A=BH, The 7 does not count because it isn't base or height. Use 4 times 8 which will make 32 cm2.
Area of the parallelogram is 32 cm²
Area of the parallelogram:Given that;
Base of parallelograms = 8 cm
Height of parallelograms = 4 cm
Find:
Area of the parallelogram
Computation:
Area of the parallelogram = l × b
Area of the parallelogram = 8 × 4
Area of the parallelogram = 32 cm²
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A recipe for cake needs 2 and 1/4 cups of cake mix. You are making ½ of the recipe. How many cups of flour do you need?
Answer:
x=1 1/8
Step-by-step explanation:
1 cake=2 1/4 cup of cake
1/2 cake=x
1 cake=9/4 cup of cake
1/2 cake= x
Cross multiply
x=9/4×1/2
x=9/8
X=1 1/8
Final answer:
To make ½ of a cake recipe that calls for 2 and ¼ cups of cake mix, you need to divide that amount by 2, resulting in 1 and 1/8 cups of cake mix needed.
Explanation:
To find out how many cups of cake mix you need to make ½ of the recipe, start with the original amount of cake mix required by the recipe, which is 2 and ¼ cups. Since you're making half of the recipe, you'd divide this amount by 2. Perform the division: (2 + ¼) ÷ 2 = 1 and ¹⁸ cups. Thus, you will need 1 and ¹⁸ cups of cake mix for half the recipe.
Here's the step-by-step calculation:
Convert the mixed number to an improper fraction: 2 and ¼ cups = 9/4 cups.
Divide the improper fraction by 2 to make half of the recipe: (9/4) ÷ 2 = 9/4 × 1/2 = 9/8.
Convert the improper fraction back to a mixed number: 9/8 = 1 and 1/8 cups.
So, you need 1 and 1/8 cups of cake mix to make half of the recipe.
what is x+4x+6x= simplify
Answer:
11x
Step-by-step explanation:
Simplify the following polynomial and write the answer in standard form.
(2x² - 4x + 3) + (x² - 4x-4)
A. -8x-1+3x^2
B. 3x^2 - 8x - 1
C. x^2 - 8x - 7
D. -8x - 7+x^2
Answer:
B)
Step-by-step explanation:
I solved it by setting it up as a normal addition problem:
[tex]2x^{2} -4x+3\\+x^{2} -4x-4[/tex]
Simplify:
[tex]3x^{2} -8x-1[/tex]
What is X if Y is 12.8 and Z is 16 in the right triangle below?
Answer:
Im 90% sure its H.
Step-by-step explanation:
Answer:
H) 9.6
Step-by-step explanation:
Use the pythagorean theorem to solve for a right triangle.
Pythagorean Theorem: a^2 + b^2 = c^2
So, 16^2= 12.8^2 + x ------> 256= 163.84 + x^2 (subtract 163.84 from both sides of the equation) -----> x^2= 92.16 (square root) -----> x=9.6
This is my first answer so I hoped it helped! :)
What is 5u+1 when u=3
the vertical asymptote is at x =
Answer:
x=8
Step-by-step explanation:
The vertical asymptote is where the denominator goes to zero
3(x-8) =0
Divide by 3
(x-8) =0
Add 8 to each side
x-8+8=0+8
x=8
The vertical asymptote can be find by solving the 0 of the denominator.
3(x - 8) = 0
3x - 24 = 0
3x - 24 + 24 = 0 + 24
3x = 24
3x/3 = 24/3
x = 8
Besr of Luck!
What is g+1 when g= -9
Answer:
-8
Step-by-step explanation:
plug in -9 as g
(-9) + 1 = -8
Answer:
-8Step-by-step explanation:
If g = -9
Then g + 1 = -9 + 1
-9 + 1 = -8
I hope this helped you!
I'm really stuck on this question and if anyone could help me with it I'd be so grateful
Answer:
150
Step-by-step explanation:
Rate at which volume decrease:
(1 × 2 × 20/100) ÷ 30
= 1/75 m³/min
Total volume:
½ × (1.4 + 0.6) × 2 × 1
= 2 m³
Time = 2 ÷ 1/75
= 150 mins
The Seattle Mariners baseball team wishes to determine the equilibrium price for seats for each of the next two seasons
Answer:
Price Qd1 Qd2 Qs
25 75000 60000 45000
30 60000 55000 45000
35 45000 50000 45000
40 30000 45000 45000
45 15000 40000 45000
[Find the attachment for the graph]
Final answer:
The equilibrium price for the Seattle Mariners baseball team's seats can be found using economic principles of supply and demand, taking into account factors that influence ticket demand, marginal revenue, and costs.
Explanation:
The question involves determining the equilibrium price for Seattle Mariners baseball team seats. This can be addressed using principles from Economics, specifically the supply and demand model. To determine the equilibrium price, one would need to establish the demand curve, which includes factors such as the population and income of the home city, the team's standing, and the number of superstars on the team. As economists such as Ferguson et al. suggest, the marginal cost for sports teams is often assumed to be zero due to the fixed costs of stadium operations. Therefore, the profit-maximizing quantity of seats sold is where marginal revenue is zero. This can be calculated and visualized with a graph showing both demand and marginal revenue curves. Additionally, adjustments such as the addition of new seats or external fees like licensing can affect the equilibrium dynamics, thus changing the equilibrium price and the total revenue.
select all that are true for the graph that represents the function f(x)=5(3)^x
Answer:A. The graph is increasing by a common ratio of 3
C. As x increases, y increases
F. As x decreases, y approaches 0
Step-by-step explanation:
The true statements are:
A. The graph is increasing by a common ratio of 3
C. As x increases, y increases
F. As x decreases, y approaches 0
Information regarding the function:The graph should be rise by ratio of 3. Since x increased so y should also rises. Also, x reduced so y should be 0.Therefore, the option A, C and F is correct. And the other options are incorrect.Find out more information about the graph here: https://brainly.com/question/14375099?referrer=searchResults
13. Jake earns 15% commission on the total amount he sells. If he sells $545 worth of items, how much commission
does Jake earn? A. $21.33 B. $36.33 C. $54.50 D. $81.75
Answer:
Option D - $81.75
Step-by-step explanation:
Given : Jake earns 15% commission on the total amount he sells. If he sells $545 worth of items.
To find : How much commission does Jake earn?
Solution :
Using the commission formula,
[tex]\text{Commission}=\text{Sales}\times \text{Percentage}[/tex]
[tex]\text{Commission}=\$545\times 15\%[/tex]
[tex]\text{Commission}=545\times \frac{15}{100}[/tex]
[tex]\text{Commission}=81.75[/tex]
Therefore, commission does Jake earn is $81.75.
So, option D is correct.
In a video game, the player can choose a character from 4 animal characters and 3 huma
characters. Players can also let the computer randomly select a character for them.
The player will have the computer randomly select his character.
What is the probability it will pick a human character?
Enter your answer as a fraction, in simplest form, in the box.
Will mark brainliest!!
Answer:
3/7
Step-by-step explanation:
3/(3+4)
BRAINLIEST PLZ I ANSWERED FIRST
Answer:
3/7
Step-by-step explanation:
Probability is essentially (# ways specific event can occur) / (# ways any general event can occur).
In this case, the specific event is getting a human avatar. Since there are 3 humans to choose from, the number of ways this specific event can occur is 3 ways. The general event is just choosing any avatar. Since there are a total of 3 + 4 = 7 characters to select from, the number of ways this general event can occur is 7.
Putting it together, we have the probability of choosing a human character as 3/7.
A swimming pool had 2.5 million liters of water in it. Some water evaporated, and then the pool only had 2 million liters of water in it.
What percent of the water evaporated?
25 % of the water had evaporated.
Answer:
20%
Step-by-step explanation:
Since the total amount of water is 2.5 million
And 2 million evaporated,
To determine the amount left,it will be total amount- evaporated
2.5-2=0.5
To determine the% of evaporated water
It will be evaporated/total amount ×100
0.5/2.5 × 100
50/2.5
20%
So the percentage of the evaporated water is 20%
can i please know the answer
Answer:
3840 cubic inches
Step-by-step explanation:
10*24 = 240 in
240*16 = 3840 cubic in
X^2-81
Factor the quadratic completely
Answer:
x ^2 − 9^ 2. hope this helps
Answer:
(x+9)(x-9)
Step-by-step explanation:
whenever its is x^2
you can start off with
(x+_)(x+_)
then your figure out "what times what" is -81 (they have to be the same number!)
Its -9 and 9
and so you plug that in to get
(x+9)(x-9)
Mya's lunchbox is shown. What is the volume of the lunchbox? Round to the nearest tenth if necessary.
There is no picture but the fomula for volume is lengthxwidthxheight for a square or rectangle
If a club consists of 11 members, how many different arrangements of president, vice-president, and secretary are possible?
There are 990 different arrangements of president, vice-president, and secretary
The number of arrangementsThe given parameters are:
Club members, n = 11
Members to arrange, r = 3
The number of arrangements is calculated using the following permutation equation
Ways = nPr
This gives
Ways = 11P3
Evaluate
Ways = 990
Hence, there are 990 different arrangements of president, vice-president, and secretary
Read more about permutation at:
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Final answer:
To find the number of different arrangements of president, vice-president, and secretary in a club of 11 members, we use the concept of permutations. Using the formula for permutations of distinct objects, we calculate P(11,3) = 990. Thus, there are 990 different arrangements possible.
Explanation:
To find the number of different arrangements of president, vice-president, and secretary, we can use the concept of permutations. Since the positions have different roles and can only be assigned to one person each, we use permutations. The number of permutations can be found using the formula for permutations of distinct objects: P(n,r) = n! / (n-r)!.
In this case, we have 11 members and need to assign them to 3 different positions (president, vice-president, and secretary). So, the number of arrangements is P(11,3) = 11! / (11-3)! = 11! / 8! = 11 x 10 x 9 = 990.
Therefore, there are 990 different arrangements of president, vice-president, and secretary possible.
A bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books. A book is randomly selected, not replaced, then another is selected. Find the probability of selecting a biography then a mystery.
Answer:
63/380
Step-by-step explanation:
Initially,
# of Mysteries, M = 9
# of Biographies, B = 7
# of Sci. Fiction, S = 4
Total number of books = 9 + 7 + 4 = 20 books
P (first book selected is biography) = 7/20
After selecting 1 biography book,
# of Mysteries, M = 9
# of Biographies, B = 7 - 1 = 6
# of Sci. Fiction, S = 4
Total number of books remaining = 9 + 6 + 4 = 19 books
P (second book selected is a mystery) = 9/19
Hence (P first book is biography and 2nd book is mystery)
= (7/20 )(9/19)
= 63/380
The probability of selecting a biography then a mystery is 0.14.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, a bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books.
Total number of outcomes = 9+7+4
= 20
The probability of selecting a biography = 7/20
The probability of selecting a mystery = 9/20
Probability of an event = 7/20 × 9/20
= 56/400
= 0.14
Therefore, the probability of selecting a biography then a mystery is 0.14.
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3% percent of the students at Lincoln High School are in orchestra, 5%
are in band and 1% are in both. If a student is selected at random, what is
the probability that the student is in orchestra OR band?
Answer:
The probability of a student to be in the orchestra or the band is 0.07 or 7%.
Step-by-step explanation:
The probability of a student to be in the orchestra or the band is given by the following formula:
p(orchestra or band) = p(orchestra) + p(band) - p(orchestra and band)
p(orchestra or band) = 0.03 + 0.05 - 0.01
p(orchestra or band) = 0.08 - 0.01
p(orchestra or band) = 0.07
The probability of a student to be in the orchestra or the band is 0.07 or 7%.
Final answer:
The probability that a student is in orchestra or band is 7%.
Explanation:
To calculate the probability that a student at Lincoln High School is in either orchestra or band, we will use the formula for the probability of the union of two events, P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A) is the probability of being in orchestra, P(B) is the probability of being in band, and P(A ∩ B) is the probability of being in both orchestra and band.
In this case, we have been given that 3% of students are in orchestra, 5% are in band, and 1% are in both.
Therefore, we have:
P(orchestra) = 0.03 (3%)P(band) = 0.05 (5%)P(both orchestra and band) = 0.01 (1%)Applying the formula:
P(orchestra OR band) = P(orchestra) + P(band) - P(both orchestra and band) = 0.03 + 0.05 - 0.01 = 0.07
Therefore, the probability that a student is in either the orchestra or the band is 7%.
Use the graph of f(x) to explain the relationship between the real zeros of f(x) and its intercept(s). f(x) has one real zero at –2 because the graph of the function has an intercept at (0, –2). f(x) has two real zeros at –4 and –2 because the graph of the function has intercepts at (–4, 0) and (0, –2). f(x) has no real zeros because the graph of the function does not pass through (0, 0). f(x) has one real zero at –4 because the graph of the function has an intercept at (–4, 0).
Answer:
f(x) has one real zero at –4 because the graph of the function has an intercept at (–4, 0).
Step-by-step explanation:
Zeros of a function f(x) are those points where f(x) = 0. Then, zeros coordinates have the form (x1, 0), (x2, 0), et cetera. In the graph, a zero is seen as the interception of f(x) with the x-axis.
Answer:
D on Edge 2020
Step-by-step explanation:
The table represents the function f (x) = 5 x. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled f (x) with entries blank, 0, 5, 10. Which value goes in the empty cell? –51 –5 5 51 Mark this and return
Final answer:
To find the value that goes in the empty cell, we need to multiply each value of x by 5. So, when x = -1, f(x) = 5*(-1) = -5. Therefore, the value that goes in the empty cell is -5.
Explanation:
The table represents the function f(x) = 5x. In the first column, we have the values of x, which are -1, 0, 1, and 2. In the second column, we have the values of f(x), which are blank, 0, 5, and 10. To find the value that goes in the empty cell, we need to multiply each value of x by 5. So, when x = -1, f(x) = 5*(-1) = -5. Therefore, the value that goes in the empty cell is -5.
The sum of two numbers is -36. One number is 106 less than the other. Find the numbers.
Answer:
71 and -35
Step-by-step explanation:
so with this we can set up a system of equations
x+y=36
and
x-y=106
now we can add these equations together to eliminate y
x+y=36 plus
x-y=106 equals
2x=142
divide both sides by 2
x=71
now we can plug that in
71+y=36
subtract 71 from both sides
y=-35
Answer:
-71 and
35
Step-by-step explanation:
Let the numbers be x and y
x + y = -36
x = y - 106
Substitute y - 106 or x in the first equation
We have
x + y = -36
y - 106 + y = -36
y + y - 106 = -36
2y - 106 = -36
Add 106 to both sides to eliminate -106 on the left side
2y - 106 + 106 = -36 + 106
2y = 70
Divide both sides by 2
2y/2 = 70/2
y = 35
Substitute 35 for y in either equation to get x
Using the second equation, we have
x = y - 106
x = 35 - 106
x = -71
The numbers are 35 and -71
Check
x + y = -36
-71 + 35 = -36
-36 = -36
i need help solving 5x= -7x+6
Answer:
x=1/2
Step-by-step explanation:
1.). add 7x to both sides
12x=6
2.) divide by 12 to get x by itself.
x=6/12
3.) simplify the fraction and you get the answer!
x=1/2
Solve the equation using the quadratic formula.
-x^2+27 = 6x
x=-3, X=9
X=-3X=3
x=-9,f=3
x=-9, x=3
The value of x is -9 and 3.Option D.
Step-by-step explanation:
Given,
[tex]-x^{2} +27 = 6x[/tex]
To find the value of x.
We will apply middle term factor formula.
The given equation can be written as,
[tex]x^{2} +6x-27 = 0[/tex]
or, [tex]x^{2}[/tex]+(9-3)x-27 = 0
or, x²+9x-3x-27= 0
or, x(x+9)-3(x+9)=0
or, (x+9)(x-3) = 0
So, x = -9 and x = 3
Hence,
The correct option is Option D.
What is the product? 4,3,-1,-1 x -3,1,-2,2
Answer:
B. [tex]\left[\begin{array}{ccc}-18&10\\5&-3\end{array}\right][/tex]
Step-by-step explanation:
The question is off edg. it is supposed to be [tex]\left[\begin{array}{ccc}4&3\\-1&-1\end{array}\right] * \left[\begin{array}{ccc}-3&1\\-2&2\end{array}\right][/tex] with multiple options. I just used the matrix calculator on edg.