The area of a sector of a circle is given by the equation , 3.142S/360 where r is the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write?
Answer:
C.
Step-by-step explanation:
What’s 3 1/3 times 4 3/4
select the location on the number line to plot the points 8/3 and 11/3
Answer:
8/3 is between 2 and 3 above 2.5
11.3 is between 3 and 4 above 3.5
Step-by-step explanation:
8/3 converts to the decimal 2.666666... which means its located on the number line between 2 and 3 above 2.5.
11/3 converts to 3.6666.... which means its located on the number line between 3 and 4 above 3.5.
Draw a horizontal number line. Mark the point 8/3 at approximately 2.67 and the point 11/3 at approximately 3.67 to visually represent these values.
To plot the points 8/3 and 11/3 on a number line.
Draw a Horizontal Number Line
Start by drawing a horizontal line on a piece of paper or a whiteboard. This line will serve as your number line.
Make sure it's long enough to accommodate the range of values working with.
Mark the Point for 8/3 (approximately 2.67)
To plot the point 8/3 on the number line, need to find its approximate location.
To do this, you can divide 8 by 3 to calculate its decimal value:
8 ÷ 3 ≈ 2.67 (rounded to two decimal places).
Now, locate the point approximately at 2.67 on the number line, and make a small mark or dot to represent this point.
Mark the Point for 11/3 (approximately 3.67)
To plot the point 11/3 on the number line, calculate its approximate location in a similar way:
11 ÷ 3 ≈ 3.67 (rounded to two decimal places).
Locate the point approximately at 3.67 on the number line and make a small mark or dot to represent this point.
Label the Points (Optional)
label these points to indicate what they represent.
label the point at 2.67 as "8/3" and the point at 3.67 as "11/3" to provide context for the values you've plotted.
Therefore, the plotting of the points 8/3 and 11/3 on the number line is on the right side of zero between 2 and 4.
Learn more about number line here
brainly.com/question/32029748
#SPJ3
A teacher made a pair of foam dice to use in math games. Each cube measured 10 in. On a side. How many square inches of fabric were needed to cover the two cubes?
Final answer:
A teacher will require 1200 square inches of fabric to cover the surface area of two foam cubes, with each side measuring 10 inches.
Explanation:
The question involves finding the total surface area of two foam cubes to determine how much fabric a teacher needs to cover both cubes. To solve this, we must calculate the surface area of one cube and then multiply by two because there are two identical cubes. Each face of a cube measures 10 inches on a side.
The area of one face is given by:
Area of one face = side × side = 10 in × 10 in = 100 square inches
Since a cube has 6 faces, the total surface area of one cube would be:
Total surface area of one cube = 6 × Area of one face = 6 × 100 square inches = 600 square inches
Therefore, for two cubes, we need:
Total surface area for two cubes = 2 × 600 square inches = 1200 square inches
The teacher will require 1200 square inches of fabric to cover the two cubes.
The formula for finding the present value of an item that depreciates yearly is v = c - crt. In this formula, v is the present value, c is the original cost, r is the rate of depreciation per year, and t is the number of years that have passed. After 7 years, what is the value of a car originally costing $27,000 that depreciated at a rate of 0.1 per year
Final answer:
To calculate the present value of a car after 7 years, using the formula v = c - crt with the given values, the present value is $8,100.
Explanation:
The question involves finding the present value of a depreciating asset, in this case, a car. Using the provided formula v = c - crt where v is the present value, c is the original cost, r is the rate of depreciation per year, and t is the number of years, we can calculate the value of a car after a certain time period.
Given that the original cost c is $27,000, the rate of depreciation r is 0.1 (or 10%), and the time t is 7 years, we can substitute these values into the formula to find the present value of the car after 7 years. The calculation is as follows: v = $27,000 - ($27,000 × 0.1 × 7). Simplifying, we get: v = $27,000 - ($27,000 × 0.7) = $27,000 - $18,900 = $8,100.
Suppose heights of 20-year-old men are approximately normally distributed with a mean of 71 in. and a population standard deviation of 5 in. a random sample of twenty 20-year-old men is selected and measured. find the probability that the sample mean x lies between 68 and 74 inches.
Factor
25m^100 − 121n^16
1. (5m^50 - 11n^8)^2
2. (5m^10 - 11n^4) (5m^10 + 11n^4)
3. (5m^50 - 11n^8) (5m^50 + 11n^8)
4. (5m^10 - 11n^4)^2
The correct answer is C) (5m^50 - 11n^8) (5m^50 + 11n^8)
We can tell this because of the rule regarding factoring the difference of two perfect squares. When we have two squares being multiplied, we can use the following rule.
a^2 - b^2 = (a - b)(a + b)
In this case, or first term is 25m^100. So we can solve that by setting it equal to a^2.
a^2 = 25m^100 -----> take the square root of both sides
a = 5m^50
Then we can do the same for the b term.
b^2 = 121n^16 ----->take the square root of both sides
b = 11n^8
Now we can use both in the equation already given
(a - b)(a + b)
(5m^50 - 11n^16)(5m^50 + 11n^16)
solve 5x<-10
help plz
Emily dropped a coin from rest, and the distance traveled by the coin is given by the formula below, where s is the distance the coin has fallen, g is a constant representing Earth's gravity, and t is the duration of time over which the coin falls. Emily measured the distance in feet, the time in seconds, and now wants to calculate the value of g. What must be the units of g?
To match the units of distance in feet and time in seconds, the units of the gravitational constant g must be feet per second squared (ft/s^2). On Earth, g is roughly 32.17 ft/s² in U.S. Customary units.
When Emily drops a coin from rest, the distance traveled by the coin (s) can be used to calculate the acceleration due to gravity (g) when the time (t) the coin took to fall is known. The formula provided suggests that distance is equal to 0.5 times gravity acceleration times the square of time (s = 0.5 * g * t²).
Given that Emily measured the distance in feet and the time in seconds, the units for g must be compatible with these measurements. Since distance is in feet and time is squared in seconds, the unit for g must be feet per second squared (ft/s²) to ensure that all units cancel out correctly, leaving us with the unit of distance in feet. On Earth's surface, the value of g using U.S. Customary units is approximately 32.17 ft/s².
Which conversion requires division? Use the metric table to help answer the question.
Answer:
Decigrams to Decagrams/Dekagrams
Step-by-step explanation:
1 decigram is equal to 0.01 Deca/Dekagrams
Decigrams have less value than Decagrams.
Therefore,
You divide 1 decigram by 100 to get 0.01 decagrams.
Which is the correct input-output table for the function ?f(x)=3/x+4 HELP what are the table answers
Answer:
The correct tabe is here,
let take f(x)=y
then if
x=1,f(x)=7
x=2,f(x)=11/2
x=3,f(x)=5
x=4,f(x)=19/4
and so on so so far
Annie is planning a business meeting for her company. She has a budget of $1325 for renting a meeting room at a local hotel and providing lunch. She expects 26 people to attend the meeting. The cost of renting the meeting room is $270. Which inequality shows how to find the amount, x, Annie can spend lunch for each person? A. 26x + 270 ≥ 1,325 B. 26x + 270 ≤ 1,325 C. 270x + 26 ≥ 1,325 D.270x + 26 ≤ 1,325
Answer: B. [tex]26x+270\leq1,325[/tex]
Step-by-step explanation:
Let 'x' denote the amount of money Annie can spend lunch for each person.
Given: The cost of renting the meeting room = $270
The number of people attend the meeting = 26
Then, the expression for total amount spent on lunch will be :-
[tex]\text{Total amount on lunch}=26x[/tex]
The expression for total spent by Annie will be:-
[tex]26x+270[/tex]
Since, the budget for renting a meeting room at a local hotel and providing lunch= $1325
Thus, the inequality shows how to find the amount, x, Annie can spend lunch for each person will be :-
[tex]26x+270\leq1,325[/tex]
Lucy has been given a list of 5
bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?
Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with a mean equal to 100 and a standard deviation equal to 15. explain your reasoning. (a) p(90≤sample mean≤110) for a random sample of size n = 10 (b) p(90≤sample mean≤110) for a random sample of size n = 20
To decide which random sample has a higher probability, we need to consider the sample size. As the sample size increases, the sample mean tends to approach the population mean more closely. We can use the properties of the normal distribution and the formula for the standard error of the mean to calculate the probabilities for each random sample size.
Explanation:To decide which has a higher probability, we need to consider the sample size of each random sample. In general, as the sample size increases, the sample mean tends to approach the population mean more closely.
Given that each sample is from a population that is normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution to calculate the probabilities.
(a) For a random sample of size n = 10, the probability of the sample mean being between 90 and 110 can be calculated using the formula for the standard error of the mean:
Standard error of the mean = standard deviation / sqrt(sample size)
Using this formula, the standard error of the mean for n = 10 is 15 / sqrt(10) = 4.74.
Since the sample mean follows a normal distribution, we can use the properties of the normal distribution to find the probability:
p(90 ≤ sample mean ≤ 110) = p((90 - 100) / 4.74 ≤ (sample mean - 100) / 4.74 ≤ (110 - 100) / 4.74)
We can look up the probabilities for the z-scores using a standard normal distribution table or a calculator to find the probability for the given range.
(b) For a random sample of size n = 20, we can follow the same steps as above to calculate the probability of the sample mean being between 90 and 110.
The standard error of the mean for n = 20 is 15 / sqrt(20) = 3.35.
p(90 ≤ sample mean ≤ 110) = p((90 - 100) / 3.35 ≤ (sample mean - 100) / 3.35 ≤ (110 - 100) / 3.35)
We can again use a standard normal distribution table or a calculator to find the probability for the given range.
What is 1/x divided by 1/y equal to ?
Final answer:
To calculate 1/x divided by 1/y, you multiply 1/x by the reciprocal of 1/y, which is y, resulting in y/x.
Explanation:
The question asks us to find the value of 1/x divided by 1/y. This is a division problem involving fractions and can be solved using the rules of division for fractions.
To divide one fraction by another, we multiply the first fraction by the reciprocal of the second. In this case, the reciprocal of 1/y is y/1 which simplifies to y. Therefore, the division 1/x ÷ 1/y becomes 1/x × y.
When we multiply these together, we get:
So, the answer is y/x.
Ship A receives a distress signal from the east, and ship B receives a distress signal from the same vessel from the northwest. At what location is the vessel in distress located? Describe how you arrived at your conclusion using complete sentences. You must show all work in order to receive credit.
See the attached figure.
E direction is a line which is parallel to x-axis. (blue line).
NW direction lies on a line that is at an angle of 135 degrees to the positive direction of the x axis. (red lines).
Intersection between red line and blue line will give the coordinates of the vessel in distress location which is point C (3,2)
If a sequence us defined recursively by f(0)= 3 and f (n+1)= -f (n) +5 for n>_ 0 then f (2) is equal to?
Rocky's car moves to G then it moves to B.His ride is 360 degrees
Answer:
150
Step-by-step explanation:
30+30+30+30+30=150
Also 5*30=150
Write the equation of the parabola in vertex form.
vertex (0,4), point (1,-3)
f(x)=
The equation of the parabola in vertex form is f(x) = -7x^2 + 4
Explanation:To write the equation of a parabola in vertex form, we use the formula f(x) = a(x - h)^2 + k where (h, k) represents the vertex. In this case, the vertex is (0,4) so our equation becomes f(x) = a(x - 0)^2 + 4 which simplifies to f(x) = ax^2 + 4. To find the value of a, we substitute the coordinates of the point (1,-3) into the equation and solve for a. Plugging in these values, we get -3 = a(1)^2 + 4, which simplifies to -3 = a + 4. Solving for a, we find that a = -7. Therefore, the equation of the parabola in vertex form is f(x) = -7x^2 + 4.
Learn more about Parabola Equation here:https://brainly.com/question/32658868
#SPJ11
15a^2 + 14a -8 use A.C method
PLEASE HELP ME WITH THIS!!! Also make sure I can understand it it is also preferable to post a picture but either one will do thank you. (NEVER MIND I GOT IT IF YOU NEED IT JUST TELL ME)
I have 11 hundreds 13 tens 2 ones and 15 tenths what number am I
can someone please tell me the answer to theses 2 questions
Write 24 as a product of its prime factors.
Answer:
Prime factors of 24 is 2× 3×2×2
Step-by-step explanation:
Given : Number 24.
To find: Write 24 as a product of its prime factors.
Solution : We have given that number 24
Prime number : numbers which are divisible by 1 or itself only
Example = 2, 3, 5, 7,....etc
So we will find the factor of 24 by prime factorization
24 is divisible by 1
24 ÷ 3 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Hence we can write 24 as 2× 3×2×2
Therefore, Prime factors of 24 is 2× 3×2×2
Sam's Discount Store offers a 2% discount for paying cash. How much would Joan pay if she pays cash for a set of skillets priced at $38.95?
a. 38.17
b.34.82
c.3695
Answer:
$ 38.17
Step-by-step explanation:
the length of rectangular garden is 5 feet longer than the width. If the are of the garden is 50 square feet, find the length and the width of the garden
Final answer:
To solve for the length and width of the garden, we set up a quadratic equation based on the given area and the relation between length and width. Upon solving the quadratic equation, we find the width to be 5 feet and the length to be 10 feet.
Explanation:
The problem states that the length of a rectangular garden is 5 feet longer than its width and that the area of the garden is 50 square feet.
To find the length and width, let's define the width as w feet. Therefore, the length will be w + 5 feet. The area of a rectangle is found by multiplying the length and width, so we have the equation:
w × (w + 5) = 50
Expanding this we get:
w^2 + 5w - 50 = 0
Now we need to solve this quadratic equation for w. Factoring the quadratic, we find that (w + 10)(w - 5) = 0, which gives us two possible solutions for w: -10 and 5.
Since a width can't be negative, we discard -10 and take w = 5 feet. So, the width of the garden is 5 feet and the length is 5 + 5 = 10 feet.
What is the equation of the line?
y = 0 . . . . is the equation of the line.
_____
The line shows y to have the same value for every value of x. Thus the value of y is a constant, and there is no dependence on x at all. This is true for any horizontal line. Here, the constant value is zero, so the equation is ...
... y = 0
What percent decrease occurs when a stock goes from 6.50 per share to 4.25 per share?
The diameter of small nerf balls manufactured at a factory in china is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. suppose a random sample of 20 balls is selected. find the interval that contains 95.44 percent of the sample means.
Answer:
The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 5.2, \sigma = 0.08, n = 20, s = \frac{0.08}{\sqrt{20}} = 0.0179[/tex]
Find the interval that contains 95.44 percent of the sample means.
0.5 - (0.9544/2) = 0.0228
Pvalue of 0.0228 when Z = -2.
0.5 + (0.9544/2) = 0.9772
Pvalue of 0.9772 when Z = 2.
So the interval is from X when Z = -2 to X when Z = 2
Z = 2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2 = \frac{X - 5.2}{0.0179}[/tex]
[tex]X - 5.2 = 2*0.0179[/tex]
[tex]X = 5.2358[/tex]
Z = -2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 5.2}{0.0179}[/tex]
[tex]X - 5.2 = -2*0.0179[/tex]
[tex]X = 5.1642[/tex]
The interval that contains 95.44 percent of the sample means is between 5.1642 inches and 5.2358 inches
wendy weighs 8lb less than jean if jeans weight is p lb then what is an appropriate expression fir wendys weight
Answer:
p-8
Step-by-step explanation: