Formula for the area of a circle:
A = πr² [A = area r = radius]
The radius is [tex]\frac{1}{2}[/tex] (half) the diameter. Since the diameter = 10cm, the radius = 5cm.
You know:
r = 5cm Substitute/plug this into the equation
A = πr²
A = π(5)²
A = 25π -> A = 25(3.14)
A = 78.5cm²
The area of the circle when the diameter is 10 cm should be [tex]78.5\ cm^2[/tex].
Calculation of the area of the circle:Since the diameter is 10 cm
We know that
The diameter should be
[tex]= \pi r^2\\\\= 3.14\times 5^2\\\\= 25\times 3.14\\[/tex]
= [tex]78.5\ cm^2[/tex]
Hence, The area of the circle when the diameter is 10 cm should be [tex]78.5\ cm^2[/tex].
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. Hernandez bought 18 pens for her class. Highlighters cost $3 each, and gel pens cost $2.50 each. She spent a total of $50. Use a system of equations to find the number of highlighters and gel pens Mrs. Hernandez bought. Enter your answers in the boxes.
Bonita has $2.95 in dimes and quarters in her pocket. If she has five more dimes than quarters, how many of each coin does she have?
Bonita have 12 dimes and 7 quarters in her pocket.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
Bonita have with dimes and quarters in pocket = $2.95
Bonita have 5 more dimes than quarters.
Now,
Let number of dimes = x
Let number of quarters = y
Since, Bonita have 5 more dimes than quarters.
x = y + 5
Here,
Bonita have with dimes and quarters in pocket = $2.95
So, we can formulate;
0.1x + 0.25y = =$2.95
Substitute the value of x in above equation, we get;
0.1 (y + 5) + 0.25y = $2.95
0.1y + 0.5 + 0.25y = $2.95
0.35y + 0.5 = $2.95
Subtract 0.5 we get;
0.35y + 0.5 - 0.5 = $2.95 - 0.5
0.35y = 2.45
Divide by 0.35 we get;
y = 7
And, x = y + 5 = 7 + 5 = 12
Thus, Bonita have 12 dimes and 7 quarters in her pocket.
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Which equation represents a line that passes through (-9, -3) and has a slope of -6?
y-9=-5(x – 3)
y+9= -6(x + 3)
y-3--5(x – 9)
y+3=-6[X + 9)
Answer:
y +3 = -6(x +9)
Step-by-step explanation:
The point-slope form of the equation of a line is ...
y -k = m(x -h)
for a line with slope m through point (h, k).
You want the line with slope -6 through point (-9, -3), so its equation is ...
y -(-3) = -6(x -(-9))
y +3 = -6(x +9) . . . . . matches the last choice
Find the trapezoid.The trapoized has an area of
Answer: what trapezoid?
Three men are climbing Mt. Meru, which is located in India. Mt. Meru is 6.6 kilometers tall. When the men are 150 meters from the peak of the mountain, the extreme weather forces them to stop climbing and return to the bottom. How high had the men climbed before stopping and going back down the mountain?
Answer:
.15 kilometers or 150 meters
Step-by-step explanation:
A circle has a radius of 2 units. Find the radian measure of a central angle that intercepts an arc length of 5.8 units. Round the radians measure to the nearest tenth.
Answer:
2.9 radians.
Step-by-step explanation:
Please kindly check the attached file for explanation.
The radian measure of a central angle intercepting an arc length of 5.8 units in a circle with a radius of 2 units is 2.9 radians when rounded to the nearest tenth.
The question deals with finding the radian measure of a central angle in a circle with a given radius and arc length. The formula for this calculation is theta = arc length / radius. Given that the circle's radius (r) is 2 units and the arc length (l) is 5.8 units, we substitute these values into the formula to find the radian measure of the central angle.
theta = l / r = 5.8 units / 2 units
This gives us theta = 2.9 radians. However, we need to round this to the nearest tenth, resulting in theta = 2.9 radians as the final answer.
Error Analysis- Charles claimed the function
f(x) = (3) represents exponential decay.
Explain the error Charles made.
Answer:
Answer is below
Step-by-step explanation:
Charles is wrong because 3 doesn't represent exponential decay. This is because 3 is greater than 1, so it represents exponential growth. If the number was less than 1, then it would represent exponential decay.
If this answer is correct, please make me Brainliest!
The correct answer is Charles should represent as Exponential growth instead of exponential decay
What are exponential growth and exponential decay?Exponential growth : In a function [tex]f (x) =b^{x}[/tex] where b is always greater than 1 is known as exponential growthExponential Decay :In a function [tex]f (x) =b^{x}[/tex] where b is always less than 1 is known as exponential DecayHere f(x) = 3 where 3 is greater than 1
so, It is exponential growth instead of exponential decay
Hence , Charles made an error of exponential decay instead of exponential growth.
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Square ABCD has a side length of 4 inches. The square is dilated by a scale factor of 4 to form square A'B'C'D'. What is the side length of square A'B'C'D' ? Type a number for your answer.
We have been given that square ABCD has a side length of 4 inches. The square is dilated by a scale factor of 4 to form square A'B'C'D'. We are asked to find the side length of square A'B'C'D'.
We know that when scale factor is greater than 1, then the resulting figure would be an enlargement.
To find the side length of new square after dilation, we will multiply the original side by scale factor.
[tex]\text{New side length}=\text{Original side}\times \text{Scale factor}[/tex]
[tex]\text{New side length}=\text{4 inches}\times 4[/tex]
[tex]\text{New side length}=16\text{ inches}[/tex]
Therefore, the side length of square A'B'C'D' would be 16 inches.
An object is launched from a platform.
Its height (in meters), xxx seconds after the launch, is modeled by:
h(x)=-5(x-4)^2+180h(x)=−5(x−4)
2
+180h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, minus, 4, right parenthesis, squared, plus, 180
How many seconds after being launched will the object hit the ground?
Answer:
10
Step-by-step explanation:
Ground level is where h = 0, so solve the equation ...
h(x) = 0
-5(x -4)^2 +180 = 0 . . . . substitute for h(x)
(x -4)^2 = 36 . . . . . . . . . . divide by -5, add 36
x -4 = 6 . . . . . . . . . . . . . . positive square root*
x = 10 . . . . . . add 4
The object will hit the ground 10 seconds after launch.
_____
* The negative square root also gives an answer that satisfies the equation, but is not in the practical domain. That answer would be x = -2. The equation is only useful for time at and after the launch time: x ≥ 0.
The object modeled by the quadratic equation h(x)=-5(x-4)²+180 will hit the ground 10 seconds after being launched.
The equation given is a quadratic equation which models the height of an object after being launched from a platform. To find out when the object will hit the ground, we need to determine when the height h(x) is equal to zero. The equation can be written as h(x) = -5(x - 4)² + 180.
To find the time when the object hits the ground, we set the height equal to zero and solve for x:
0 = -5(x - 4)² + 180
Solving the quadratic equation, we divide both sides by -5:
(x - 4)² = 36
Taking the square root of both sides gives two solutions: x - 4 = [tex]\pm6[/tex]. The positive root gives us the time after launch when the object hits the ground:
x - 4 = 6
x = 10
Therefore, the object will hit the ground 10 seconds after being launched.
Tayiln buys 5 ounces of tea leaves for $2.35. At this rate how much money does she need to buy 12 ounces of tea leaves?
Answer:
5.64
Step-by-step explanation:
set up a ratio problem
5 ounces/2.35 = 12 ounces/x
5x = 28.2
x = 5.64
Answer:
5.64
Step-by-step explanation:
5x2.4=12
SO,
2.35x2.4=5.64
Hillel is juggling flaming torches to raise money for charity. His initial appearance raises \$500$500dollar sign, 500, and he raises \$15$15dollar sign, 15 for each minute of juggling performance. The amount RRR of money Hillel raises is a function of t, the length of his performance in minutes. Write the function's formula.
Answer:
$R = $500 + $15(t)
Step-by-step explanation:
in this question, we are told to give a mathematical expression that would model the amount of money that is made by Hillel.
from the question, we were made to understand that the amount of money he makes is a front of his time t. that is noted.
and also, he has a base cost of $500.
now, let’s write an equation;
R = $500 + 15(t)
where t represents the length of the performance as suggested by women
Juan and Lizzy are in the final week of their training for a marathon. Juan's goal is to run one mile on the first day of the week and double the amount he runs each day for the next six days. Lizzy's goal is to run 10 miles on the first day of the week and increase the amount she runs by 3 miles each day for the next six days. 1: Juan's marathon training schedule is an example of a(n) : arithmetic or geometric 2: Lizzy's marathon training schedule is an example of a(n) : arithmetic or geometric 3: Who will be better prepared for the marathon: Juan or Lizzy
Answer:
1. Juan's marathon training schedule is an example of a geometric sequence
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
3. Lizzy will be better prepared for the marathon
Step-by-step explanation:
In the arithmetic sequence there is a common difference between each two consecutive terms
In the geometric sequence there is a common ratio between each two consecutive terms
Juan's Schedule
∵ Juan's will run one mile on the first day of the week
∴ [tex]a_{1}[/tex] = 1
∵ He will double the amount he runs each day for the next
6 days
- That means he multiplies each day by 2 to find how many miles
he will run next day
∴ [tex]a_{2}[/tex] = 1 × 2 = 2 miles
∴ [tex]a_{3}[/tex] = 2 × 2 = 4 miles
∴ [tex]a_{4}[/tex] = 4 × 2 = 8 miles
∴ [tex]a_{5}[/tex] = 8 × 2 = 16 miles
∴ [tex]a_{6}[/tex] = 16 × 2 = 32 miles
∴ [tex]a_{7}[/tex] = 32 × 2 = 64 miles
That means there is a common ratio 2 between each two consecutive days
1. Juan's marathon training schedule is an example of a geometric sequence
Lizzy's Schedule
∵ Lizzy's will run 10 miles on the first day of the week
∴ [tex]a_{1}[/tex] = 10
∵ She will increase the amount she runs by 3 miles each day for
the next six days
- That means she adds each day by 3 to find how many miles
she will run next day
∴ [tex]a_{2}[/tex] = 10 + 3 = 13 miles
∴ [tex]a_{3}[/tex] = 13 + 3 = 16 miles
∴ [tex]a_{4}[/tex] = 16 + 3 = 19 miles
∴ [tex]a_{5}[/tex] = 19 + 3 = 22 miles
∴ [tex]a_{6}[/tex] = 22 + 3 = 25 miles
∴ [tex]a_{7}[/tex] = 25 × 3 = 28 miles
That means there is a common difference 3 between each two consecutive days
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
The rule of the sum of nth term in the geometric sequence is [tex]S_{n}=\frac{a_{1}(1-r^{n})}{1-r}[/tex]
∵ [tex]a_{1}[/tex] = 1 , r = 2 and n = 7
∴ [tex]S_{7}=\frac{1(1-2^{7})}{1-2}[/tex]
∴ [tex]S_{7}[/tex] = 127
∴ Juan will run 127 miles in the final week
The rule of the sum of nth term in the arithmetic sequence is [tex]S_{n}=\frac{n}{2}[a_{1}+a_{n}][/tex]
∵ n = 7, [tex]a_{1}[/tex] = 10 and [tex]a_{7}[/tex] = 28
∴ [tex]S_{7}=\frac{7}{2}(10+28)[/tex]
∴ [tex]S_{7}[/tex] = 133
∴ Lizzy will run 133 miles in the final week
∵ 133 miles > 127 miles
∴ Lizzy will run more miles than Juan
3. Lizzy will be better prepared for the marathon
Please help me out please 10 point
Answer:
Its A.
Step-by-step explanation:
A square sheet of paper measures 25 centimeters on each side. What is the length of the diagonal of this paper?
Answer:
35.36 cm
Step-by-step explanation:
The diagonal of a square will be given by
[tex]D=\sqrt {a^{2}+b^{2}}[/tex]
Where a is the length of one side and b is the length of another side. For a square, botj sides are equal hence the diagonal calculations will be as follows
Given that a is 25 then
[tex]D=\sqrt {25^{2}+25^{2}}[/tex]
D=35.3553390593274
Rounding off the nearest two decimal place
D=35.36 cm
The length of the diagonal (c) of the square paper that measures 25 cm on a side can be found using the Pythagorean Theorem (a² + b² = c²). In this case, a = 25cm, b = 25cm, and by solving for c we get c = √(25² + 25²) ≈ 35.36 cm.
Explanation:In order to answer your question about the length of the diagonal of a square, you would need to use the Pythagorean Theorem. The Pythagorean Theorem is a mathematical principle which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as: a² + b² = c².
In a square, all sides are equal, so we can consider the given measurement of 25 cm for both 'a' and 'b'. Hence, a = 25cm and b = 25cm. That would make our equation: 25² + 25² = c². When you calculate it, we get 625 + 625 = c², summing them up you get 1250 = c². To find 'c', you will take the square root of 1250 which equals approximately 35.36 cm. So, the length of the diagonal of the square paper is around 35.36 cm.
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Nancy bought 570 crayons that came in packs of 15 how many packs of crayons did Nancy buy
Answer:
38
Step-by-step explanation:
Answer:
38 packs
Step-by-step explanation:
g(r) = r^2 – 6r – 55
1) What are the zeros of the function?
The zeros of the function [tex]G(r) = r^2 - 6r - 5[/tex]5 are r = 11 and r = -5.
To find the zeros of the function [tex]G(r) = r^2 - 6r - 55[/tex], we set G(r) equal to zero and solve for r:
Now, we can use the quadratic formula to solve for r:
r = [-b ± √[tex](b^2 - 4ac)[/tex]] / 2a
where a, b, and c are the coefficients of the quadratic equation [tex](r^2 - 6r - 55 = 0)[/tex].
In this case, a = 1, b = -6, and c = -55. Let's substitute these values into the formula:
r = [-( -6) ± √[tex]((-6)^2 - 4 * 1 * (-55))[/tex]] / 2 * 1
r = [6 ± √(36 + 220)] / 2
r = [6 ± √256] / 2
Now, let's consider the two possible solutions:
1) r = [6 + √256] / 2
r = [6 + 16] / 2
r = 22 / 2
r = 11
2) r = [6 - √256] / 2
r = [6 - 16] / 2
r = -10 / 2
r = -5
So, the zeros of the function are r = 11 and r = -5.
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Lyle went fishing for 1 hour and 30 minutes until he ran out of bait at 6:40 p.m. At what time did Lyle start fishing? *
Answer:
he started fishing by 5:10pm
Step-by-step explanation:
just subtract 1:30 from 6:40
whats 138 divided by 2 lol
Answer:
69
Step-by-step explanation:
The solution is, 138 divided by 2 is 69.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
138 divided by 2
i.e. 138/2
= 69
Hence, The solution is, 138 divided by 2 is 69.
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what is the solution of the system equations y =-3x +8 y = -5x -2
Answer:
Since both equations are equal to y, we can set them equal to each other.
y =-3x +8
y = -5x -2
-3x +8 = -5x -2
Solve for x.To do this, we need to get x by itself. First, move all the numbers to one side of the equation, and all the variables to the other.
-3x +8 = -5x -2
Add 5x to both sides
-3x+5x +8=-5x+5x -2
2x+8=-2
Subtract 8 from both sides
2x+8-8 = -2-8
2x=-10
Now, all the numbers are on one side, with the variables on the other. x is not by itself, it is being multiplied by 2. To undo this, divide both sides by 2
2x/2= -10/2
x= -5
Now, to find y, substitute -5 in for x in one of the equations.
y = -5x -2
y= -5(-5) -2
y=25-2
y=23
Put the solution into (x,y)
The solution is (-5, 23)
Suppose you are a designer making the traffic sign above. What is the sum of the interior angles of the equilateral triangle? What is the measure of ∠N? What is the measure of ∠M? Explain your reasoning. (2 points)
Answer:
Measure of <N = 60°
(angles in an equilateral triangle are all equall 60°)
the measure of ∠M= 60°
(angles in an equilateral triangle are all equall 60°)
Step-by-step explanation:
Sum of angles in a triangle is equall to 180....
And in equilateral triangle of all sides equall...all angles are equal to 60° because all sides are equal.
So <m= <n=<o=60°
A psychological study found that men who were distance runners lived, on average, five years longer than those who were not distance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years. Which of the following is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners?
Answer:
C 84.2-79.2/SQRoot(10.2^2/50 + of of 6.8^2/30)
Step-by-step explanation:
Final answer:
To determine if there is a significant difference in lifespan between men who are distance runners and those who are not, a two-sample t-test test statistic is calculated as approximately 1.051 using the provided sample means, standard deviations, and sample sizes.
Explanation:
To determine if men who are distance runners live significantly longer, on average, than men who are not distance runners, we would use a two-sample t-test statistic. The test statistic formula for a two-sample t-test is:
t = (x1 - x2) / [tex]\sqrt{(s1^2/n1 + s2^2/n2)[/tex]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes of the two groups.
In this case, the mean age at death for men who are distance runners is 84.2, the standard deviation is 10.2, and the sample size is 50 (n1 = 50). The mean age at death for men who are not distance runners is 79.2, the standard deviation is 6.8, and the sample size is 30 (n2 = 30).
Plugging the values into the formula, we calculate the test statistic as follows:
t = (84.2 - 79.2) / [tex]\sqrt{(10.2^2/50 + 6.8^2/30)[/tex]
t = 2.0 / [tex]\sqrt{((104.04/50) + (46.24/30))[/tex]
t = 2.0 / [tex]\sqrt{(2.0808 + 1.5413)[/tex]
t = 2.0 / √3.6221
t ≈ 2.0 / 1.9032
t ≈ 1.051
This is the test statistic that you would use to determine whether there is a significant difference in lifespan between the two groups.
An aquarium tank can hold 5400 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 90 minutes. The second pipe can fill the tank in 60 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
Answer:
36 minutes when both pipes are working together
Step-by-step explanation:
capacity of tank = 5400 liters
Pipe A flow per mint. = 5400/90 = 60 liters per mint.
Pipe B flow per mint. = 5400/60 = 90 liters per mint.
Flow of A + B per mint. 60 + 90 = 150 liter per mint.
Therefore, 5400 / 150 = 36 minutes to fill the tank
A shop sells packs of black pens, packs of red pens and packs of green pens.
There are:
3 pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pens
On Monday
number of packs sold of black, red and green pens = 7 : 2 : 4
A total of 220 were sold.
Work out the number of green pen sold. Show your working out.
Answer: There are 96 green pens sold.
Step-by-step explanation:
Since we have given that
Number of pens in each pack of black pens = 3
Number of pens in each pack of red pens = 5
Number of pens in each pack of green pens = 6
Ratio of number of packs sold of black, red and green pens = 7: 2: 4
Number of total pens sold = 220
So, ratio of pens in number of packs would be
[tex]7\times 3:2\times 5:4\times 6\\\\=21:10:24[/tex]
So, Number of green pens sold would be
[tex]\dfrac{24}{55}\times 220\\\\=24\times 4\\\\=96\ pens[/tex]
Hence, there are 96 green pens sold.
96 green pens were sold.
Since the number of packs sold of black, red and green pens are in the ratio 7 : 2 : 4
Also, a total 220 pens were sold. Let x represent the total number of packs, hence:
Number of black pens = 7x/13 * 3 = 21x/13
Number of red pens = 2x/13 * 5 = 10x/13
Number of green pens = 4x/13 * 6 = 24x/13
Hence:
21x/13 + 10x/13 + 24x/13 = 220
21x + 10x + 24x = 2860
55x = 2860
x = 52
Number of green pens = 24x/13 = 24(52)/13 = 96
Hence 96 green pens were sold.
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What is the solution to the system of equations below? Negative 4 x + 6 y = negative 18 and y = negative 2 x + 21
If I had to guess that it mean -4x + 6y = -18 and y = -2x+21:
Since we have a y =, we can plug that in.
-4x + 6(-2x + 21) = -18
-4x -12x + 126 = -18
-16x = -18 -126
-16x = -144
-16x/-16 = -144/-16
x = 9
The value of x is equal to 9 and the value of y is equal to 3
Data given;
-4x + 6y = -18y = -2x + 21System of EquationsTo solve the linear equations above, we have to use substitution method.
from equation 1
[tex]-4x + 6y = -18[/tex]
Make x the subject of formula
[tex]-4x + 6y = -18\\x = \frac{9 + 3y}{2}[/tex][tex]-4x + 6y = -18\\-4x = -18 - 6y \\\frac{-4x}{-4} = \frac{-18-6y}{-4}\\ x = \frac{9 + 3y}{2}[/tex]
substitute the value of x into equation 2
[tex]y = -2x + 21\\y = -2(\frac{9+3y}{2})+ 21\\ y = {-9-3y} + 21\\y = -3y + 12\\4y = 12\\4y/4 = 12/4\\y = 3[/tex]
substitute the value of y into either equation 1 or 2
[tex]y = -2x + 21\\3 = -2x + 21\\2x = 21 - 3\\2x = 18\\2x/2 = 18/2\\x = 9[/tex]
From the calculations above, the value of x is 9 and y is 3
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What are two ways to name the marked angle? *
If f(x)=3x+5/x find f(2)
Steps to solve:
f(x) = 3x+5/x; x = 2
~Substitute
f(2) = 3(2)+5/2
~Simplify
f(2) = 6+5/2
~Add
f(2) = 11/2
~Simplify
f(2) = 5.5
Best of Luck!
How to find radius diameter circumference and area
Answer:
To find the radius diameter circumference and area, The area of a circle = π x radius^2, Circumference of a circle = π x diameter, Remember that the diameter = 2 x radius.
Step-by-step explanation:
Write each equation in logarithmic form.
5^3 = 125
Answer:
log5(125)=3 The 5 should be smaller and a little lower.
Step-by-step explanation:
Maria drives at a rate of 60 miles per hour. It takes her 3 hours to get to her aunt's house. How long will it take if she drives at a rate of 50 miles per hour?
Answer:
3.4 miles
Step-by-step explanation:
60 × 3 = 180
she has to drive 180 miles
180 ÷ 50 = 3.4
3.4 miles
In this problem, we need to understand the relationship between rate, time and distance. Here, we establish that Maria's aunt's house is 180 miles away. When Maria drives at a rate of 50 miles per hour, it takes her 3.6 hours to reach her aunt's house.
Explanation:This is a problem of rate, time, and distance, specifically about understanding how changes in rate (or speed) affect time. Here, Maria drives to her aunt's house at a rate of 60 miles per hour, which takes 3 hours. The distance to her aunt's house, then, is 60 miles/hour times 3 hours, or 180 miles. We know that distance = rate times time (D = rt).
Now, when Maria drives at a rate of 50 miles per hour, the time will change. To find the new time, we rearrange the formula to t = D/r. Plugging the values in, t = 180 miles / 50 miles/hour, we get 3.6 hours. So, it would take Maria 3.6 hours to reach her aunt's house if she drives at a rate of 50 miles per hour.
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jsjsjjs jsjsjjs Help
Answer:
84,500
Step-by-step explanation:
8.45*10^4
8.45 * (10*10*10*10)
8.45 * 10000
84500
the decimal place moves to the right for however many zeros you have :)
i hope this helps :)