The smallest approximate sample size required for Victoria to estimate the mean weight of apples with a 95% confidence level and a margin of error of no more than 5 grams is 35 apples.
Victoria wants to estimate the mean weight of apples in her orchard with a 95% confidence interval and a margin of error of no more than 5 grams, using an estimated standard deviation of 15 grams. To determine the smallest sample size (n) required, the following formula which incorporates the z-score for the desired confidence level, the standard deviation, and the desired margin of error can be used:
n = (z * σ / E)^2,
where z is the z-score corresponding to a 95% confidence level (which is 1.96), σ (sigma) is the estimated standard deviation (15 grams), and E is the desired margin of error (5 grams).
Plugging the values in gives us: n = (1.96 * 15 / 5)^2 = (1.96 * 3)^2
= 5.88^2 = 34.5744.
Since we cannot have a fraction of an apple, we round up to the nearest whole number. Therefore, the smallest approximate sample size required is 35 apples.
Victoria needs a sample size of at least 35 apples.
Victoria wants to estimate the mean weight of apples in her orchard with a 95% confidence interval and a margin of error no more than 5 grams. We are given the standard deviation of 15 grams.
To find the smallest approximate sample size n, we can use the formula for margin of error (E) in a confidence interval:
E = Z * (σ/√n)
Here, Z is the Z-score for a 95% confidence level, which is 1.96, σ (sigma) is the population standard deviation (15 grams), and n is the sample size.
Rearrange the formula to solve for n:
n = (Z * σ / E)²
Substitute the given values:
Z = 1.96σ = 15 gramsE = 5 gramsCalculate:
n = (1.96 * 15 / 5)²
n = (1.96 * 3)²
n = (5.88)²
n ≈ 34.57
Since the sample size must be a whole number, we round up to the nearest whole number, which is 35. Therefore, Victoria needs a sample size of at least 35 apples to achieve her desired margin of error.
can someone please help answer this problem ASAP!!!:)
Answer:
c
Step-by-step explanation:
i am a really good guesser and i think it is c
how to write 700.06 in
word form
Step-by-step explanation:
seven hundred and six hundredtsorseven hundred point zero sixThe word form of the number 700.06 will be;
'' Seven hundred point zero six.
What is Place value?
The value represented by a digit in a number on the basis of its position in the number is called a Place value.
Given that;
The number is,
⇒ 700.06
Now,
The word form of the number 700.06 will be;
'' Seven hundred point zero six.
Thus, The word form of the number 700.06 will be;
'' Seven hundred point zero six.
Learn more about the place value visit:
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Solve the inequality
−4>x÷3
Answer:
the answer is -12>x or x< -12
Step-by-step explanation:
multiply both sides by 3
Answer:
[tex]\quad x<-12[/tex]
(Please vote me Brainliest if this helped!)
Step-by-step explanation:
[tex]-4>\frac{x}{3}[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]\frac{x}{3}<-4[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}3[/tex]
[tex]\frac{3x}{3}<3\left(-4\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x<-12[/tex]
Compute the distance between (7,-4,9) and (x,y,z).
a. (7 + x)2 + (-4 + y)2 + (9 + 2)2
b. (7 - x)2 + (-4 - y)2 + (9 - 2)2
C.
d.
7- x) + (-4-y) + (9 -23
(7+ x)2 + (-4+ y)2 + (9+ 2)2
Option b:
[tex]\boxed{ d=\sqrt{(7-x)^2+(-4-y)^2+(9-z)^2}}[/tex]
Explanation:Let two points be:
[tex]P_{1}(x_{1},y_{1},z_{1}) \\ \\ P_{2}(x_{2},y_{2},z_{2})[/tex]
The distance formula is defined as:
[tex]d=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2+(z_{1}-z_{2})^2}[/tex]
Therefore, if we define:
[tex]P_{1}(7,-4,9) \ and \ P_{2}(x,y,z) \\ \\ \\ Then: \\ \\ d=\sqrt{(7-x)^2+(-4-y)^2+(9-z)^2}[/tex]
Finally, correct option is b
Answer:
The Answer is correct, he just has the wrong letter.
Step-by-step explanation:
The correct answer is C
Find the range of the function. f(x) =10-x^2
Answer: ( - ∞ , 10 ] , { y| y ≤ 10 }
Step-by-step explanation: You have to find the domain by finding where the function is defined. The range is the set of the values that correspond with the domain.
The range of the function f(x) = 10 - x^2 is all real numbers less than or equal to 10.
To find the range of the function f(x) = 10 - x^2, we need to consider the maximum and minimum values that f(x) can take. The parabola opens downwards since the coefficient of x^2 is negative, which means it has a maximum value and no minimum value. The vertex of this parabola occurs at x = 0, which gives us the maximum value of f(0) = 10. Therefore, the range of f(x) is all real numbers less than or equal to 10, which can be expressed as f(x) ≤ 10 or in interval notation, \\[10, -∞).
a square garden plot has an area of 24 ft2. a. find the length of each side in simplest radical form. b. calculate the length of each side to the nearest tenth of a foot.
The area of a square is equal to the side squared.
[tex]s^{2} = A[/tex]
We can plug in 24 for A and then take the square root of each side to
find s.
[tex]s^{2} = 24[/tex]
[tex]s = \sqrt{24}[/tex]
We can simplify √24.
The prime factorization of 24 is 2 x 2 x 2 x 3.
Since we have 2 x 2 inside the radical we can simplify to have 2
outside the racial.
[tex]\sqrt{24} = \sqrt{4*6} = 2 \sqrt{6}[/tex]
We can then use a calculator to find an approximate decimal value
2√6.
(You could technically calculate it by hend using the Babylonian
method, I don't think youre expectited to do that, though)
[tex]2\sqrt{6} = 4.9 ft[/tex]
reference the right triangle shown below to write the quantity as a fraction in lowest terms
tan P
Answer:
A right angled triangle is a triangle where one of the internal angles is 90°.
Consider the general right angle triangle, in figure 1 below, with angle β and sides labeled as shown below
Right-Angle-Triangle
The sides are labeled with respect to the angle β, so that the nearest side is called the adjacent side, the side that is directly opposite is called the opposite side while the longest side is called the hypotenuse.
Therefore, given any angle in a triangle, it should be easy to identify the adjacent, the opposite side and the hypotenuse.
Example
Reference to the figure below.
Example1
1. Identify the right angle triangles in the above diagram.
Solution: A right angled triangle is a triangle where one of the internal angles is 90°. Such triangles are ABC, ABN, DAC and DNC.
2. Identify the adjacent sides to angles θ, α, β and µ.
Solution:
Angle θ is in triangle DAC. The angle is nearer to line AC hence, it is the adjacent line.
Angle α is in triangle ABN. The angle is nearer to line AB hence, it is the adjacent line.
Angle β is in triangle DNC. The angle is nearer to line DC hence, it is the adjacent line.
Angle µ is in triangle ABC. The angle is nearer to line AB hence, it is the adjacent line.
3. Identify the opposite sides to angles θ, α, β and µ.
Solution:
Angle θ is in triangle DAC. The angle is opposite to line DC hence, it is the opposite line.
Angle α is in triangle ABN. The angle is opposite to line AN hence, it is the opposite line.
Angle β is in triangle DNC. The angle is opposite to line CN hence, it is the opposite line.
Angle µ is in triangle ABC. The angle is opposite to line AC hence, it is the opposite line.
4. Identify hypotenuse with respect to angles θ, α, β and µ.
Solution:
Angle θ is in triangle DAC. The longest side in that angle triangle is AD hence, it is the hypotenuse.
Angle α is in triangle ABN. The longest side in that angle triangle is NB hence, it is the hypotenuse.
Angle β is in triangle DNC. The longest side in that angle triangle is DN hence, it is the hypotenuse.
Angle µ is in triangle ABC. The longest side in that angle triangle is CB hence, it is the hypotenuse.
We will cover the following. Feel free to skip any section as you prefer.
Step-by-step explanation:
Find the perimeter of the colored part of the figure. The figure is composed of small squares with side-length 1 unit and curves that are an arc of a circle(half circle). Use 3.14 for pi.
Answer:
16.56 in
Step-by-step explanation:
4 sides of the squares are exposed
The radius of each semicircle is 1 since they are against 2 squares.
2pi*r=circumfrence
2pi*1=6.28
6.28/2=3.14 because it's a semicircle
3.14*4=12.56 because there are 4 equal semicircles
12.56+4=16.56
A toy boat is bobbing in the water.
Its distance D(t) (in m) from the floor of the lake as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a×sin(b×t) + d.
At t=0, when the boat is exactly in the middle of its oscillation, it is 1 m above the water's floor. The boat reaches its maximum height of 1.2 m after pi/4 seconds.
Find D(t).
Answer:
[tex]D(t) = 1\,m + (0.2\,m)\cdot \sin \left[\right(2\,\frac{rad}{s} \left)\cdot t\right][/tex]
Step-by-step explanation:
The sinusoidal expression has the following form:
[tex]D(t) = D+A\cdot \sin (B\cdot t)[/tex]
Where:
[tex]D[/tex] - Initial distance from the floor of the lake, in meters.
[tex]A[/tex] - Amplitude of oscillation, in meters.
[tex]B[/tex] - Angular frequency, in radians.
Now, each coefficient is derived as follows:
Initial distance from the floor of the lake
[tex]D = 1\,m[/tex]
Amplitude of oscillation
[tex]A = 1.2\,m - 1\,m[/tex]
[tex]A = 0.2\,m[/tex]
Angular frequency
From the statement it is known that boat reaches its maximum height in a quarter of its oscillation. Then, the angular frequency is:
[tex]B = \frac{\frac{1}{2}\pi \,rad}{\frac{1}{4}\pi \,s}[/tex]
[tex]B = 2\,\frac{rad}{s}[/tex]
The expression is:
[tex]D(t) = 1\,m + (0.2\,m)\cdot \sin \left[\right(2\,\frac{rad}{s} \left)\cdot t\right][/tex]
Answer:
0.2sin(2t)+1
Step-by-step explanation:
This is a simplified version of the answer above me.
Which of the following is a reason why Northern Europe’s literacy rate is so high?
A. high taxes
B. Strong government support
C. All of the above
D. Free schooling
A function that decreases proportionally to it's current value. The smaller the function gets, the faster it decreases
Answer:
decay function
Step-by-step explanation:
took the usa test prep
A regular heptagon has a side length of 13.9 and an apothem of 14.4. Find the area of the regular heptagon. Round your answer to the nearest WHOLE NUMBER. ?
Answer: 701
Step-by-step explanation:
A heptagon has 7 sides, therfore a regular heptagon will have 7 equal sides
n = 7 (number of sides)
s = 13.9 (length of each sides of the heptagon)
r = 14.4 (The apothem)
The area of the regular heptagon can be calculated by:
Area = ½ n × s × r
Area = ½ × 7 × 13.9 × 14.4
Area = 700.56 square units
To the nearest whole number, will be:
Area = 701 square units
How do you write the equation of a circle with the center (6,2) and radius r=8?
Answer:
(x-6)^2 + (y-2)^2 = 64
Step-by-step explanation:
We can write the equation of circle as
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r is the radius
(x-6)^2 + (y-2)^2 = 8^2
(x-6)^2 + (y-2)^2 = 64
Circle equation: (x - h)² + (y - k)² = r²
The center is (h, k) and the radius is r.
(x - 6)² + (y - 2)² = 8²
(x - 6)² + (y - 2)² = 64
Best of Luck!
Pablo put $1,260 into a savings account that earns 3% simple interest per year. He does not make any deposits or withdrawals. How much money will be in Pablo's account after 2 years?
Answer:
$1,335.60
Step-by-step explanation:
6% of $1,260 is $75.60. $1,260 + $75.60 = $1,335.60
Hope this helps!!
Sing Lu jogs around a park near her house 3 times a week. The distance around the park is 0.8 mile. How many laps around the park are necessary to run 6 miles?
Answer:
6/0.8 = 7.5
She'll have to jog around the park 7 and a half times.
Christy bought 8 muffins. She chose 2 apple, 2 banana, and 4 blueberry. She and her family ate the apple
and banana muffins for breakfast.
What fraction of the muffins did they eat?
They ate
of the muffins.
/8
Enter an equivalent fraction.
An equivalent fraction is. /2
Answer:
4/8
Step-by-step explanation:
bc the ate 4 muffins of a total of 8
Answer:4:8
Step-by-step explanation:
What is the value of the expression 9 + StartFraction n Over 3 EndFraction minus 6 when n = 12?
1
5
7
12
Answer:
The correct answer for the question is 7
2x + 4x - 5= 37
Help me please it’s multi step equation
Add 2x and 4x together you'll get 6x then add 5 to 37 and get 42 then divide 42 by 6x and 7=x
Answer:
x=7
Step-by-step explanation:
2x + 4x - 5= 37
Combine like terms
6x-5 =37
Add 5 to each side
6x-5+5 = 37+5
6x = 42
Divide each side by 6
6x/6 = 42/6
x =7
A basketball team scored 366 points in S games. Another
in 8 games. Each team played one additional game, maki
scored per game the same for both teams. The equation
number of points scored by each team in the additional
366 +
585 * *
The value of x in the expression given is 72.
From the equation given, we can calculate the value of x thus :
(366+x)/6 = (585+x)/9cross multiply
9(366 + x) = 6(585 + x)
3294 + 9x = 3510 + 6x
9x - 6x = 3510 - 3294
3x = 216
x = 216/3
x = 72
Hence, the value of x is 72
Complete Question:
A basketball team scored 366 points in 5 games. Another basketball team scored 585 points in 8. What is the value of x? A 65 B 73 C 61 D 72 games. Each team played one additional game, making the average number of points scored per game the same for both teams. The equation below can be used to find x, the number of points scores by each team in the additional game. (366+x)/6 = (585+x)/9 .
How many total outcomes are in the sample space of rolling two numbered cubes numbered 1-6
For each cube there are 6 outcomes, so there are 6*6 = 36 outcomes for two dice. Visually you can have a table that is 6 rows and 6 columns leading to 36 cells overall.
A person accidentally dropped a quarter, a dime, and a penny. All three coins landed on heads. What was the probability of this happening?
The probability of a quarter, a dime, and a penny all landing on heads is found by multiplying the individual probabilities for each coin, resulting in a 12.5% likelihood.
Explanation:The question asks about the probability of a quarter, a dime, and a penny all landing on heads when accidentally dropped. To determine this, we assume each coin has a 50-50 chance of landing on heads or tails, i.e., the probability of heads is 0.5 for each coin toss. Since each coin is independent of the others, we apply the product rule of probability for independent events.
Therefore, the probability of all three coins landing on heads is:
Probability(Quarter on heads) × Probability(Dime on heads) × Probability(Penny on heads) = 0.5 × 0.5 × 0.5 = 0.125 or 12.5%.
This represents an application of the product rule, as each coin toss is an independent event and the final probability is the product of the individual probabilities.
Q4. The dimensions of a rectangular sheet of metal are 9.96m by 5.08 m. Find
a. the perimeter of the metal, correct to 1 significant figure
b. the area of the metal, correct to the nearest 0.1 m2
Answer:
a) 30m
b) 50.6m²
Step-by-step explanation:
Perimeter = 2(length + width)
= 2(9.96 + 5.08)
= 30.08 m
Area = length × width
9.96 × 5.08
50.5968 m²
x^2+ 6x - 4 = 3x + 6
Answer:
x=2
x=-5
Step-by-step explanation:
You need to get everything on one side to have a quadratic equation:
x^2+6x-4 -(3x+6) = x^2+3x-10
All factors of 10 are 1*10 and 2*5.
5-2 = 3 and 5*-2 = -10
Factoring x^2+3x-10 gives us (x-2)(x+5)
x=2
x=-5
Answer:
x=-5 x=2
Step-by-step explanation:
x^2+ 6x - 4 = 3x + 6
Subtract 3x from each side
x^2+ 6x-3x - 4 = 3x-3x + 6
x^2+ 3x - 4 = 6
Subtract 6 from each side
x^2+ 3x - 4-6 = 6 - 6
x^2 +3x -10 =0
Factor
What 2 numbers multiply to -10 and add to 3
5*-2 =-10
5+-2 = 3
(x+5) (x-2) =0
Using the zero product property
x+5 =0 x-2 =0
x=-5 x=2
A Ferris wheel has a diameter of 60 feet. Determine the distance around the Ferris wheel
Answer:
Step-by-step explanation:
2*pi*r
here r=D/2=60/2=30
so
s=2*3.14*30=188.4
If 6,000 people voted in the election. How many were from 18 to 29 years old?
The answer would be 600 because 10% of 6,000 is equal to 600
what’s the size of the missing angle
Answer:
23 so the First one or A.
Step-by-step explanation:
ALL triangles angles should add up to 180 so 22+135=157
So... 180-157=23 which equals the third angle measure
You are buying balloons for a party. A small balloon costs $2. A large balloon costs $4. Write an algebraic expression for the cost of x small balloons and y large balloons. Then find the total cost for 10 small balloons and 5 large balloons.
An algebraic expression for the cost of x small balloons and y large balloons is
what.
The total cost for 10 small balloons and 5 large balloons is $
what.
Will mark your answer brainliest if you get it right
Please Answerrrrrrrrrr!
Answer:
2x + 4y
$40
Step-by-step explanation:
Equation for x small balloons and y large balloons
2x + 4y
Total cost of 10 small balloons and 5 large balloons
x = 10, y = 5
2(10) + 4(5)
= 20 + 20
= $40
Do anybody know at all
Answer:
prob b or c
Step-by-step explanation:
I need help with this is khan academy
Answer:
Step-by-step explanation:
It's 500 so yeah there you go
Answer:
y-intercept=32
Step-by-step explanation:
You can find the y-intercept using the slope-intercept form:
[tex]y=mx+b[/tex]
M is the slope and b is the y-intercept. To find the y-intercept, first find the slope. Take two of the points from the table (x,y) and use the slope formula:
[tex](64,12)(48,17)\\\\\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis:
[tex](64(x_{1}),12(y_{1}))\\(48(x_{2}),17(y_{2}))[/tex]
[tex]\frac{17-12}{48-64}= \frac{5}{-16}=-\frac{5}{16}[/tex]
Now that we have the slope, insert into the equation:
[tex]y=-\frac{5}{16} x+b[/tex]
Take a point from the table and insert into the x and y values:
[tex](64_{x},12_{y})\\\\12=-\frac{5}{16}(64)+b[/tex]
Solve for b. Simplify parentheses:
[tex]-\frac{5}{16}*\frac{64}{1}=-\frac{320}{16}=-20[/tex]
[tex]12=-20+b[/tex]
Add 20 to both sides to isolate b:
[tex]20+12=-20+20+b\\32=b\\b=32[/tex]
If b equals 32, then the y-intercept is 32.**
Finito.
**The y-intercept is where x is equal to 0 (0,32)
The population of the town Star City in 2008 was estimated to be 45,000 people with an annual rate of increase of about 2.3%. What is the growth factor of Star City?
Final answer:
The growth factor of Star City is calculated by converting the rate of increase to a decimal and adding it to 1, resulting in a growth factor of 1.023.
Explanation:
The growth factor of Star City with an annual rate of increase of about 2.3% can be calculated as follows:
Identify the percentage of growth as a decimal by dividing the percentage by 100, which would be 2.3/100 = 0.023.
Add this decimal to 1 to find the growth factor: 1 + 0.023 = 1.023.
Therefore, the growth factor of Star City is 1.023.