The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.
What is distance?Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.
According to question:The Situation column should have two entries: "finding part of a total" and "difference".
The Operation column should have only one entry: "minus".
The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.
To solve for s, we can add 2.3 to both sides of the equation:
s - 2.3 + 2.3 = 6.8 + 2.3
s = 9.1
Therefore, Sam ran 9.1 kilometers.
So, the Situation entries are: "difference" and "finding part of a total".
The Operation entry is: "minus".
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4. Tanya Jackson bought a house and during the first year, was able to rent it for only 7 months at $620 a month. Though the house was vacant for 5 months, Tanya had to pay average expenses of $175 a month for the whole year. She also paid $3,600 in mortgage interest. a. For the first year, what was Tanya's gross income? b. What was her net income or net loss?
A- Tanya's gross income for the first year was $7,940, and b- her net income was $5,840 after subtracting her total expenses.
a. To calculate Tanya's gross income for the first year, we need to multiply the rent per month by the number of months the house was rented:
Gross income from rent = $620/month x 7 months = $4,340
Tanya also paid $175/month in average expenses for the whole year, so her total expenses were:
Total expenses = $175/month x 12 months = $2,100
Adding the mortgage interest paid, Tanya's gross income for the first year was:
Gross income = $4,340 + $3,600 = $7,940
b. To calculate Tanya's net income or net loss, we need to subtract her total expenses from her gross income:
Net income = Gross income - Total expenses
Net income = $7,940 - $2,100
Net income = $5,840
Therefore, Tanya's net income for the first year was $5,840.
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i need help please!!!
Five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).
Finding five points on the functionGiven that
f(x) = 4^x.
To find the inverse of the function f(x) = 4^x,
We need to interchange the positions of x and y and solve for y. So, we have:
x = 4^y
Taking the logarithm base 4 of both sides, we get:
y = log₄(x)
Therefore, the inverse of the function f(x) = 4^x is g(x) = log₄(x)
To find five points on the inverse function g(x), we can choose five x-values and find the corresponding y-values:
If x = 1, then g(x) = log₄(1) = 0, so the point is (1, 0).
If x = 4, then g(x) = log₄(4) = 1, so the point is (4, 1).
If x = 16, then g(x) = log₄(16) = 2, so the point is (16, 2).
If x = 1/4, then g(x) = log₄(1/4) = -1/2, so the point is (1/4, -1/2).
If x = 2, then g(x) = log₄(2) ≈ 0.5, so the point is (2, 0.5).
Therefore, five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).
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17. A babysitter charges a fee for every hour they work. Which statement below could be a
description of the point (1, 8) from this situation?
The point (1, 8) would then represent that the babysitter charges $8 per hour
Which statement could be a description of the point (1, 8)The point (1, 8) in this situation could mean that the babysitter charges $8 for one hour of work.
In general, when working with a fee-per-hour situation, we can use the slope-intercept form of a linear equation, y = mx + b,
Where y represents the total fee, x represents the number of hours worked, m represents the rate (fee per hour), and b represents the initial fee (fee for zero hours worked).If we assume that the initial fee is $0, then the equation for the babysitter's fee would be y = mx, where m is the hourly rate.
The point (1, 8) would then represent that the babysitter charges $8 per hour, since when x = 1 (one hour of work), y = 8 (the fee for one hour).
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Is this quadrilateral a parallelogram?
I believe this quadrilateral is a parallelogram.
What is a parallelogram?There are a few ways to choose within the occasion that a quadrilateral may be a parallelogram: Opposite sides are parallel: Within the occasion that inverse sides of a quadrilateral are parallel, at that point it may be a parallelogram.
Inverse sides are said to be consistent: On the off chance that inverse sides of a quadrilateral are consistent, at that point it may be a parallelogram. From the image attached , you can see the both side red are marked equal hence it is a parallelogram
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Can someone help proving these three distributions？How to get them
The proof of the three distributions as required as shown in the explanation part.
What are the proof of the three distributions?For x² distribution:
Let's start with the sample variance, which is defined as:
s^2 = ∑(y_i - y_bar)² / (n-1)
where;
y_i is the i-th observation in the sample, y_bar is the sample mean, and n is the sample size.We can rewrite this formula as:
s^2 = (∑y_i² - n*y_bar²) / (n-1)
Multiplying both sides by (n-1)/σ², we get:
s^2 / σ² = (∑y_i² - ny_bar²) / (σ²(n-1))
Now, let's define a new variable:
x² = ∑y_i² / σ²
Substituting x² into the above equation, we get:
s^2 / σ² = (x² - n*y_bar²/σ²) / (n-1)
Notice that n*y_bar²/σ² is just the sample mean squared in units of variance. We can rewrite it as:
n*y_bar²/σ² = (y_bar - μ)² / (σ²/n)
where;
μ is the population mean.Substituting this into the above equation, we get:
s^2 / σ² = (x² - (y_bar - μ)² / (σ²/n)) / (n-1)
Now, let's define a new variable:
ss = ∑(y_i - y_bar)² / σ²
Substituting ss into the above equation, we get:
s^2 / σ² = (x² - ss/(n-1)) / n
This is the desired result. We have shown that s²/σ² follows a x² distribution with n-1 degrees of freedom.
For t distribution:
Let's start with the sample mean, which is defined as:
y_bar = ∑y_i / n
We can rewrite this formula as:
y_bar - μ = (∑y_i - n*μ) / n
Now, let's define a new variable:
t = (y_bar - μ) / (s/√n)
where;
s is the sample standard deviation.Substituting y_bar - μ and s into the above equation, we get:
t = (∑y_i - nμ) / (s√n)
This is the desired result. We have shown that t follows a t distribution with n-1 degrees of freedom.
For F distribution:
Let's start with the sample variances, which are defined as:
s₁² = ∑(y_i - y₁)² / (n₁-1)
s₂² = ∑(y_i - y₂)² / (n₂-1)
where;
y₁ and y₂ are the sample means, and n₁ and n₂ are the sample sizes.We can rewrite these formulas as:
s₁² = (ss₁ - n₁*(y₁-μ)²) / (n₁-1)
s₂² = (ss₂ - n₂*(y₂-μ)²) / (n₂-1)
where;
μ is the population mean, and ss₁ and ss₂ are the sum of squares within each sample:ss₁ = ∑(y_i - y₁)²
ss₂ = ∑(y_i - y₂)²
Dividing these equations, we get:
s₁² / s₂² = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))
Now, let's define a new variable:
F = s₁² / s₂
Substituting s₁² / s₂² into the above equation, we get:
F = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))
This is the desired result. We have shown that F follows an F distribution with (n₁-1) and (n₂-1) degrees of freedom.
It's worth noting that the F distribution is only defined for positive values. Therefore, if s₁² / s₂² is less than 1, we need to take the reciprocal of the above equation to ensure that F is positive:
F = (ss₂ / (n₂-1)) / (ss₁ / (n₁-1))
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When rounding to the nearest hundredth, which of the
numbers below will round to 18.96? Select all that apply.
A) 18.974
B) 18.963
C) 18.906
D)18.958
E) 1.896
Answer:
D
Step-by-step explanation:
When a number is 5 or more you round up, but when it's 4 or lower you don't round at all. So, when you round the 8, in answer D, you get 6 making the answer 18.96.
helppp with this EXPONENTS - powers of products
Answer:
Step-by-step explanation:
(3n³ + 2n)² = 9n^6 + 12n^4 + 4n^2
(4k² + 2k³) = 2k²(2 + k)
(3y²-y')' = 6y-y''
(4c+30) = 2(2c+15)
(2b² * b)² = 4b^6
(2gh²)* = 2gh^2
(6w³)² = 36w^6
What is the y-intercept for this line?
-4/3 x + (-1) = y
Answer:
0,-1
Step-by-step explanation:
Hope this helps! =D
Brainliest! =D
Answer:
-1
Remember y=mx+b
m is your slope and b is your y-int
m = -4/3
b = -1
A recipe that uses 1/2 pound of almonds makes 5/6 cup of almond butter.
Which is a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds?
a) less than 1 1/2 cup of almond butter
b) between 1 1/2 and 2 cups of almond butter
c) more than 2 cups of almond butter
Answer: C
Step-by-step explanation:
1/2 pound of almonds = 5/6 cup of almond butter
To find out how much almond butter 1 pound of almonds will make, we need to multiply both sides of the equation by 2:
1 pound of almonds = (2 × 1/2) pounds of almonds = 2 × 5/6 cups of almond butter
Simplifying, we get:
1 pound of almonds = 5/3 cups of almond butter
So, a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds is more than 2 cups of almond butter. Therefore, the answer is (c) more than 2 cups of almond butter.
Answer: b) between 1 1/2 and 2 cups of almond butter
Step-by-step explanation:
We can create a proportion to help us solve this question.
[tex]\displaystyle \frac{\frac{1}{2} lbs\;almonds}{\frac{5}{6}lbs\;butter } =\frac{1lbs\;almonds}{xlbs\;butter}[/tex]
Now we can cross multiply.
[tex]\displaystyle \frac{1}{2} *x=\frac{5}{6} *1[/tex]
[tex]\displaystyle \frac{1}{2}x =\frac{5}{6}[/tex]
Next, we will divide both sides of the equation by one-half.
[tex]\displaystyle x =\frac{5}{6}\div \frac{1}{2}[/tex]
[tex]\displaystyle x =\frac{5}{6}* \frac{2}{1}[/tex]
[tex]\displaystyle x =\frac{10}{6}[/tex]
Lastly, we will find which answer option this falls under by creating an improper fraction. This leads us to answer optoin b, b) between 1 1/2 and 2 cups of almond butter.
[tex]\displaystyle 10-6=4\text{, so } 1\frac{4}{6} =1\frac{2}{3}[/tex]
8 6 points Create an equation that represents the relationship between x and y in the table. HAAA #1 X y 488.8 -1 -2 10 y = 8 Answer -8 0 8 X + 2 6 Answe 4 4
The equation is given as y = -x + 8
What is the purpose of equation?The purpose of an equation is to find the value of the variable that makes the equation true. Equations are used in various fields of mathematics and science to represent relationships between different quantities and to solve problems.
To create an equation that represents the relationship between x and y in the table, we need to first determine the pattern or trend in the data.
From the given data, we can see that as x increases by 2, y decreases by 2. This suggests that there is a linear relationship between x and y.
Using the two points (-2,10) and (0,8), we can find the slope:
m = (y2 - y1) / (x2 - x1) = (8 - 10) / (0 - (-2)) = -1
Now that we have the slope, we can use any point on the line to find the y-intercept. Let's use the point (0,8):
8 = (-1)(0) + b
b = 8
Therefore, the equation that represents the relationship between x and y in the table is:
y = -x + 8
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7
Assignment Active
Describing Exponential Functions
Which statements describe the function f(x) = 3()*? Check all that apply.
Each successive output is the previous output divided by 3.
As the domain values increase, the range values decrease.
The graph of the function is linear, decreasing from left to right.
Each successive output is the previous output multiplied by 3.
The range of the function is all real numbers greater than 0.
The domain of the function is all real numbers greater than 0.
The correct statements regarding the exponential function 3(1/3)^x is given as follows:
Each successive output is the previous output divided by 3.As the domain values increase, the range values decrease.The range of the function is all real numbers greater than 0.How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is given as follows:
f(x) = 3(1/3)^x.
The parameter b is of 1/3 < 1, hence:
Each successive output is the previous output divided by 3.The function is decreasing.The range is all real values greater than 0, as a = 3 is positive and the function has an horizontal asymptote at y = 0.
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A garden is in the shape of a square with a perimeter of 64 feet. The garden is surrounded by two
fences. One fence is around the perimeter of the garden, whereas the second fence is 2 feet from the
first fence on the outside. If the material used to build the two fences is $1.26 per foot, what was the
total cost of the fences?
The perimeter of a square is the sum of its sides and they are all equal, so to obtain the length of each of them we divide the perimeter of the first fence between 4:
[tex]\text{P1}= \dfrac{\text{64 feet}}{\text{4 sides}}[/tex]
[tex]\text{P1}= 16 \ \text{feet}[/tex]
Then, the length of each side of the second fence will increase 2 feet at each end, as shown in the figure. We have then that the perimeter of the second fence is:
[tex]\text{P2 = 20 feet} \times \text{4 sides}[/tex]
[tex]\text{P2 = 80 feet}[/tex]
The sum of the perimeters of both fences is:
[tex]\text{PT = P1 + P2}[/tex]
[tex]\text{PT = 64 feet + 80 feet}[/tex]
[tex]\text{PT = 144 feet}[/tex]
Total cost = $1.26 x 144 feet
Total cost = $181.44
The total cost of the fences was $181.44
Let a =⟨–7, 3⟩ and b =⟨–2, –12⟩, and c = a + b. What is the magnitude and direction angle of c?
Answer: direction angle of c is pi/4.
Step-by-step explanation: We can find c by adding the corresponding components of a and b:
c = a + b = ⟨–7, 3⟩ + ⟨–2, –12⟩ = ⟨–9, –9⟩
To find the magnitude of c, we can use the formula:
|c| = sqrt(c1^2 + c2^2)
where c1 and c2 are the x- and y-components of c, respectively. In this case, we have:
|c| = sqrt((-9)^2 + (-9)^2) = sqrt(162) = 9sqrt(2)
To find the direction angle of c, we can use the formula:
theta = atan(c2 / c1)
where theta is the angle between the positive x-axis and the vector c. In this case, we have:
theta = atan((-9) / (-9)) = atan(1) = pi/4
So the direction angle of c is pi/4.
Therefore, the magnitude of c is 9sqrt(2) and the direction angle of c is pi/4.
At a customer service call center for a large company, the number of calls received per
hour is normally distributed with a mean of 90 calls and a standard deviation of 20
calls. What is the probability that during a given hour of the day there will be between
91 calls and 134 calls, to the nearest thousandth?
Step-by-step explanation:
The number of non square numbers between 12square and 13square are
The circumference of a circle is 20 cm. What is the
area, in square centimeters? Express your answer in terms
of TT.
The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.
What is the circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
[tex]\text{A} = \pi \text{r}^2[/tex]
The circumference of a circle is expressed mathematically as;
[tex]\text{C} = 2\pi \text{r}[/tex]
Given that the area of the circle is 20π cm², we determine the radius of the circle.
[tex]\text{A} = \pi \text{r}^2[/tex]
[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]
[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]
[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]
[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]
[tex]\text{r} = 4.47 \ \text{cm}[/tex]
Now, we determine the circumference of the circle.
[tex]\text{C} = 2\pi \text{r}[/tex]
[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]
[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]
[tex]\text{C} = 8.94\pi[/tex]
Therefore, the circumference of the circle is 8.94π centimeters.
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100 POINTS + BRAINLIEST
A teacher hires a coach for a school trip. The cost is worked out using the
formula C =
m
3 + 40, where C is the cost in pounds and m is the number of
miles the coach travels.
(a) Calculate how much it would cost to hire the coach to travel a distance of
42 miles.
b) If the cost of the hire is £75,how many miles does the coach travel?
Answer:
(a) To calculate how much it would cost to hire the coach to travel a distance of 42 miles, we can substitute m = 42 into the formula and solve for C:
C = (42/3) + 40
C = 14 + 40
C = 54
Therefore, it would cost £54 to hire a coach to travel 42 miles.
(b) To find how many miles the coach travels if the cost of the hire is £75, we can set the formula equal to 75 and solve for m:
75 = (m/3) + 40
35 = m/3
m = 105
Therefore, the coach travels 105 miles if the cost of the hire is £75.
Find the mean of the data set:
87,79,92,71,88,70,91,82,85
Round your answer to the nearest tenth.
Provide your answer below:
The mean of the data set is 82.77
How to calculate the mean of the data set?If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.
The first step is to arrange the data set orderly from smallest to largest;
70, 71,79, 82,88,85,87,91,92
We have nine values in the data set thus the mean is;
70+71+79+82+88+85+87+91+92/9= 745/9= 82.77
Hence the mean of the data set is 82.77
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In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 41) and matching the number on the gold ball (1 through 35). If one ticket is purchased, what is the probability of winning the jackpot?
The probability of winning the jackpot with one ticket is approximately 0.000000003724.
What is the probability?There are a total of C(41, 5) ways to choose five numbers from 41 white balls, and there are 35 possible choices for the gold ball.
Therefore, the total number of ways to win the jackpot is:
C(41, 5) * 35
And the total number of possible outcomes (i.e. all the combinations of 5 white balls and 1 gold ball) is:
C(41, 5) * 35 * C(5, 5)
Since there is only one winning combination, the probability of winning the jackpot is:
1 / (C(41, 5) * 35)
Plugging in the values, we get:
1 / (749,398,832 * 35) = 1 / 26,869,866,120
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Drag each tile to the correct box.
A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Sample A Sample B Sample C
x g(x)
0 60
1 120
2 240
3 480
Sample C starts
with 600 bacteria and
increases at a
rate of 20%.
f(x)=200(3/2)x^
Order the samples by their average growth rate over the interval [1, 3], from least to greatest.
Sample C
Sample A
Sample B
pleaseeee help thank youuu
we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.
How to solve the question?
To determine the average growth rate of each sample over the interval [1, 3], we need to calculate the ratio of the change in bacteria population to the change in time for each sample, and then take the average of these ratios over the given interval.
For Sample A, the change in bacteria population over the interval [1, 3] is 480 - 120 = 360, and the change in time is 3 - 1 = 2. So the average growth rate of Sample A over this interval is 360/2 = 180 bacteria per hour.
For Sample B, the change in bacteria population over the interval [1, 3] is 480 - 240 = 240, and the change in time is 3 - 1 = 2. So the average growth rate of Sample B over this interval is 240/2 = 120 bacteria per hour.
For Sample C, the change in bacteria population over the interval [1, 3] is (1.2600)(1.2*1.2 - 1) = 345.6, and the change in time is 3 - 1 = 2. So the average growth rate of Sample C over this interval is 345.6/2 = 172.8 bacteria per hour.
For Sample A, the growth rate is the highest, followed by Sample C and then Sample B. Therefore, the order of the samples by their average growth rate over the interval [1, 3] from least to greatest is Sample C, Sample A, and Sample B.
It's important to note that the growth rate of Sample C is not constant but increases over time due to the 20% increase in the initial bacteria population. The exponential function f(x) = 200(3/2)in power x represents this growth, and we can see that the growth rate increases as x increases. However, since we are only interested in the average growth rate over the interval [1, 3], we can calculate it using the formula mentioned above.
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Your complete question is :-A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Sample A Sample B Sample C
x g(x)
0 60
1 120
2 240
3 480
Asynchronous activity.
The given information describes a pair of congruent triangles. The corresponding vertices, angles, and sides of the triangles are congruent. The congruent angles are ∠REM ≅ ∠MOC, ∠ERM ≅ ∠MCO, and ∠CMO ≅ EMR. The congruent sides are ER ≅ CO, MO ≅ EM, and CM ≅ RM. The congruent triangles are ΔMER ≅ ΔMOC.
What is the analysis of the two triangles given above?1) the corresponding vertices are
R ~ C and
E ~ 0
2) The corresponding angle are
∠E ~∠O and
∠ R ~ ∠C
3)
The corresponding sides are;
ER ~ CO;
MO ~ EM
CM ~ RM
4) the congruent angles are:
∠REM ≅ ∠MOC
∠ERM ≅ ∠MCO
∠CMO ≅ EMR
5) the congruent sides are:
ER ≅ CO;
MO ≅ EM
CM ≅ RM
6) the congruent triangles are;
ΔMER ≅ ΔMOC
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A baby weighs 4kg when he is born. One week later he weighs 8% less than his birth weight.
a) How much does the baby weigh when he is one week old?
b) The baby gains 200g every two weeks for the next eight weeks. How much does the baby weigh when he is nine weeks old?
Answer:
a)3.68kg
b)900g
Step-by-step explanation:
a) First off we know that he weighs 4kg now and he weighed 8% less the next week. 8% of 4kg=0.32kg. We then have to subtract 0.32 kilograms from the original weight. 4-0.32=3.68
Your answer for A is 3.68 kg
b) If the baby gains 200g every two weeks, assuming it's a constant rate, he should gain 100g every week. 100*9weeks=900g.
Find the margin of error for a survey that has a sample size of 6400.
The margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%.
What is confidence level?Confidence level is a statistical concept that measures the degree of certainty or reliability associated with an estimate, such as the mean, proportion, or regression coefficient, derived from a sample of data.
According to question:The margin of error (ME) for a survey depends on several factors, including the size of the sample, the level of confidence desired, and the population size (if applicable). Assuming a 95% confidence level, a sample size of 6400, and no information about the population size, the formula for calculating the margin of error is:
ME = 1.96 × √[(p × q) / n]
where:
1.96 is the z-score associated with a 95% confidence level
p is the estimated proportion of the population that has the characteristic of interest (this is usually unknown and is typically replaced with 0.5 to get the maximum possible margin of error)
q is 1 - p
n is the sample size
Assuming a conservative estimate of p = 0.5, we have:
ME = 1.96 × √[(0.5 × 0.5) / 6400]
≈ 0.016 or 1.6%
Therefore, the margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%. This means that if the survey were conducted multiple times using the same sample size and methodology, the results would likely differ by no more than 1.6% in either direction (plus or minus) from the true population value.
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How many Cube Cs will fit into Cube A. Enter the max amount.
Answer:
27 cubes
Step-by-step explanation:
The volume of Cube A is 1 cubic centimeter. The volume of one Cube C is 1/27 of a cubic centimeter. So 27 Cube C's will fit into Cube A.
Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!
With this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.
How to solveTo solve this problem, we will need to find the time of flight and the horizontal velocity. We can use the following kinematic equations:
Vertical motion:
Maximum height: h = (v^2 * sin^2(angle)) / (2 * g)
Time of flight: t = 2 * v * sin(angle) / g
Horizontal motion:
Range: R = v * t * cos(angle)
Given:
Initial velocity (v) = 20 m/s
Angle = 45 degrees
Acceleration due to gravity (g) = 9.81 m/s²
Calculations:
Convert angle to radians: 45 degrees = 45 * (π/180) = 0.785 radians
Calculate time of flight: t = 2 * 20 * sin(0.785) / 9.81 = 2.04 seconds
Calculate horizontal range: R = 20 * 2.04 * cos(0.785) = 28.98 meters
So, with this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.
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A ball is thrown with an initial velocity of 20 meters per second at an angle of 45 degrees with respect to the horizontal. How far does the ball travel horizontally (range) before it hits the ground? Assume no air resistance.
Please help me write a summary of the 3 rules on segments
1) When 2 chords intersect inside a circle, and 4 segments are formed
2) When 2 secants intersect outside a circle, and 4 segments are formed
3) When 1 secant and 1 tangent intersect outside a circle, and 3 segments are formed
1. The rule states that the product of the lengths of the two segments of one chord equals the product of the lengths of the two segments of the other chord (i.e., (a1 x a2) = (b1 x b2), where a1 and a2 are segments of chord A, and b1 and b2 are segments of chord B).
2. The rule states that the product of the length of the external segment of one secant and the length of the entire secant equals the product of the length of the external segment of the other secant and the length of the entire secant (i.e., (e1 (e1 + i1)) = (e2 (e2 + i2)), where e1 and e2 are the external segments and i1 and i2 are the internal segments).
3. The rule states that the square of the length of the tangent segment equals the product of the length of the external segment of the secant and the length of the entire secant (i.e., t^2 = e * (e + i), where t is the length of the tangent segment, e is the external segment, and i is the internal segment).
what are the 3 rules on segments all about?The three rules of segments are:
A segment is a part of a line that consists of two endpoints and all the points between them.Two segments are congruent if they have the same length.A segment bisector is a line, segment, or ray that divides a segment into two equal parts, creating two congruent segments.Find more exercises on rules of segments;
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At how many square feet will both companies be at the same amount
If the yard is 2000 feet², both companies will charge the same price.
What is amount?In mathematics, the word "amount" is a broad one that refers to the size or quantity of something, typically given as a numerical value.
It can be used in a number of circumstances where there is a concern with money, measurements, or the quantity of an item.
We must assume both organisations' expenses to be equal and then solve for the yard size to determine the point at which their costs are equal.
Let's assume that x is the yard size at which expenses are equal.
7.5x + 24.5 = 16x + 23.5
When we simplify this equation, we obtain:
0.5x = 1
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Which of the following graphs is decreasing when x > 3?
PLEASE HELP ASAP! EXTRA POINTS!! I BEG HELP ME‼️‼️ (please click the picture and pick one GRAPH) PLEASE
Answer:
A. X
Step-by-step explanation:
You want to know which graph is decreasing for x > 3.
DecreasingA graph is decreasing when it slopes down to the right. The only graph in the group that has any decreasing portion is graph X. The decreasing part of that graph is to the right of x = 3, where x > 3.
Graph X is the one you want.
__
Additional comment
All the other graphs are increasing everywhere, so aren't even worth any consideration.
Many fences in a rectangular area for his dog to play in the backyard. The area measures 35 yards by 45 yards .What is the length of fence that Manny uses a) 1,575 yards b) 160 yards c) 80 yards d) 35 yards
On solving the provided question we can say that Manny would thus require 160 yards of fencing to surround the rectangular plot.
What is perimeter?A boundary is a closed route that embraces, encircles, or delimits a two-dimensional form or length in one dimension. The perimeter of a circle or an ellipse is its outermost section. The perimeter calculation is used in a variety of real-world situations. The perimeter of a form is the radius of its edge. Discover how to calculate the perimeter by adding the lengths of the sides of various shapes. The perimeter of a shape may always be calculated by multiplying the lengths of its sides. The perimeter of a thing is the region that surrounds it. At your house, one example is an enclosed garden. The distance around anything is referred to as its perimeter. A 200-foot fence will be required for a 50-foot-by-50-foot yard.
P = 2(l + w), where l is the length and w is the width, gives the perimeter of a rectangle.
The length in this example is 35 yards, while the breadth is 45 yards. So,
[tex]P = 2(35 + 45)\\= 2(80)\\= 160 yards\\[/tex]
Manny would thus require 160 yards of fencing to surround the rectangular plot.
As a result, option (b) 160 yards is the right answer.
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Use the table, which shows the number of sofas sold at a furniture store over 5 months. The number of sofas sold in June is 597.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248
How does the median change with the new piece of data?
We know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.
What is the median?The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.
It could be referred to as "the middle" value for a data set.
A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.
Arrange in ascending order:
229 234 248 255 263
When, odd terms are there then the middle term is the median:
Median: 248
New Median:
229 234 248 255 263 597
When there are even terms we will add the middle two terms and divide it by 2 as follows:
248+255/2
Median: 251.5
Median change: 251.5 - 248 = 3.5
Therefore, we know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.
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Given the following Confidence Interval for the population mean μ : ( 168.685, 177.315),
find the sample mean used to obtain it
according to the question the sample mean used to obtain the confidence interval was 173.
What is mean?The arithmetic means (in contrast to the geometrical mean) of a dataset is the average of all values split by the total amount of values. The most popular way to measure central tendency is with the "mean," which is widely utilised. This is obtained by dividing the number of values in the dataset by the total number of all the values. Either raw information or information that has been included in frequency tables can be used for calculations. The average of a number is known as the average. Simple math can be used to determine: After summing up all the digits, divide by the number of digits. the sum divided by the number.
given,
The confidence interval's midpoint is determined by the sample mean. Therefore, to find the sample mean, we add the lower and upper bounds of the confidence interval and divide by 2:
Sample mean = (Lower bound + Upper bound)/2
Sample mean = (168.685 + 177.315)/2
Sample mean = 173
Therefore, the sample mean used to obtain the confidence interval was 173.
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