Answer:
C
Step-by-step explanation:
it's well known that the value of sin60 is sqrt 3/2
it's also the same as cos 30
A rectangle made of square tiles measures 10 tiles long and 8 tiles wide.
What is the width of a similar rectangle whose length is 15 tiles?
Answer:
12 tiles
Step-by-step explanation:
Let,
The rectangle with dimensions "10 tiles and 8 tiles" be known as "s".The rectangle with dimension "15 tiles" be known as "l"Since the length of the larger rectangle is similar to the smaller rectangle, we can compare the dimensions of both rectangles by forming a ratio.
[tex]\text{(L of "s")}:\text{(B of "s")}= \text{(L of "l")}: \text{(B of "l")}[/tex]
Let,
⇒ Length of "s" be L₁⇒ Breadth of "s" be B₁⇒ Length of "l" be L₂⇒ Breadth of "l" be B₂[tex]\implies \text{L}_{1} }:\text{B}_{1} = \text{L}_{2} : \text{B}_{2}[/tex]
We are already given:
Length of "s" = L₁ = 10 tilesBreadth of "s" = B₁ = 8 tilesLength of "L" = L₂ = 15 tiles[tex]\implies 10:8 = 15 : \text{B}_{2}[/tex]
To simplify the ratio, multiply the extremes together and take them on one side. Then, multiply the middles together and take them on the other side.
[tex]\implies 10 (\text{B}_{2}) = 15(8)[/tex]
Divide 10 both sides to obtain the width of the larger rectangle.
[tex]\implies \dfrac{10 (\text{B}_{2}) }{10} = \dfrac{15(8)}{10}[/tex]
Simplify the equation as necessary.
[tex]\implies \text{B}_{2} = 12[/tex]
Thus, the width of the larger rectangle is 12 tiles.
how many faraday passes through a resistance in a circuit carrying a current of 1.68 A for 2 days (1F = 965000 (principal quantum number) is 3 A. FB. 2F C. 3F D. 4F
Answer:
b
Step-by-step explanation:
100%
Đ
X
A doctor treated 24, 27, 31, 19, 26, 15, and 19 patients during the past 7 days.
Which is the median number of
patients treated by the doctor?
A 15
B. 19
C. 23
D. 24
E. 31
Answer:
C. 23
Step-by-step explanation:
Add then divide by 7
solve for x [tex]\sqrt7x-2=5[/tex]
Answer:
x=7
Step-by-step explanation:
1, Add 2 to both sides. This gives us [tex]\sqrt{7x} =7[/tex]
2. Square both sides. This gives us [tex]7x=49[/tex]
3. Divide both sides by 7. This gives us [tex]x=7[/tex]
PLEASW HELP
The number of bats in a colony is growing exponentially. After 4 years, there were 2025 bats. After 6
years, there were 18225 bats.
If the colony continues to grow at the same rate, how many bats are expected to be in the colony after
12 years? Do not include units in your answer.
Answer:
there would be around 40,000 colony of bats
There to be about 13,286,025 bats in the colony after 12 years if the growth rate remains constant.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
To solve this problem, we need to use the formula for exponential growth:
N = N₀ (1 + r)ˣ
where:
N is the final number of bats after x years
N₀ is the initial number of bats
r is the annual growth rate (expressed as a decimal)
x is the number of years.
We can use the information given in the problem to find the values of N0, r, and t for the first two time periods:
For the first 4 years:
2025 = N₀(1 + r)⁴
For the next 2 years (6 years in total):
18225 = N₀ (1 + r)⁶
To solve for N₀ and r, we can divide the second equation by the first equation:
18225/2025 = (N₀ (1 + r)⁶) / (N₀(1 + r)⁴)
9 = (1 + r)²
Taking the square root of both sides, we get:
1 + r = 3
r = 2 (since r is expressed as a decimal)
Now that we know r, we can use either of the two original equations to find N₀. Let's use the first equation:
2025 = N₀(1 + 2)⁴
2025 = N₀(81)
N₀ = 25
So the initial number of bats was 25, and the annual growth rate is 200% (or 2 as a decimal).
Now we can use the formula to find the number of bats after 12 years:
N = 25 (1 + 2)¹²
N = 25 (531441)
N = 13,286,025
Therefore, we can expect there to be about 13,286,025 bats in the colony after 12 years if the growth rate remains constant.
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A random sample of banana tree yields has a sample mean of x=67 banana and sample standard deviation of s= 2 bananas. Use the empirical rule to estimate the percentage of banana yields that are less than 61 bananas. Round your answer to the nearest hundredth.
Using empirical rule, 99.85% of the data falls above 61
Data;
Mean = 67standard deviation = 3Empirical RuleUsing empirical rule, it states that 68% of data is within 1 standard deviation from the mean mean± standard deviation 95% of data falls within 2 standard deviations from the mean mean± 2* standard deviation and 99.7% of data falls within 3 standard deviations from the mean mean± 3sd . So we can say that 0.15% of data are below mean minus 3 * standard deviation and 0.15% of data are above mean+3sd. In this case, the mean is 67 , SD = 3.
And if 61 is 3×SD below mean
[tex]Pr(X > 61)=1-Pr(X\leq 61) = 1 - 0.0015 = 0.9985\\1-0.0015=0.9985[/tex]
99.85% of data is above 61
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((BEING TIMED))
A car dealership increased the price of a certain car by 11%. The original price was $33,800.
(a) Fill in the blank to write the new price in terms of the original price.
Write your answer as a decimal. (New price = x Original price)
(b) Use your answer in part (a) to determine the new price.
Answer:
A 37,518
Step-by-step explanation:
this is because you take 11% of 33,800 which is 3,718 and add that back too your orignial value which gives you 37,518. I think that also answers part B for you.
The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {2, 3, 4, 5, 6} and B = {5, 6, 7, 8, 9}, find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) (a) A ∩ B (b) A ∪ B (c) A' (d) B'
Answer:
a) {5, 6}
b) {2, 3, 4, 5, 6, 7, 8, 9}
c) {0, 1, 7, 8, 9}
d) {0, 1, 2, 3, 4}
Step-by-step explanation:
The intersection of sets is the set of elements common to both. The union of sets is the set of all elements that are part of either set. The complement of a set is the set of elements in the universal set that are not in the set of interest.
__
A∩B{2,3,4,5,6} ∩ {5,6,7,8,9} = {5, 6}
__
A ∪ B{2,3,4,5,6} ∪ {5,6,7,8,9} = {2,3,4,5,6,7,8,9}
__
A'U -A = {0,1,2,3,4,5,6,7,8,9} -{2,3,4,5,6} = {0,1,7,8,9}
__
B'U -B = {0,1,2,3,4,5,6,7,8,9} -{5,6,7,8,9} = {0,1,2,3,4}
Find the solution set for the equation
|4x - 9| + 3 = 8
The solution set for the equation |4x - 9| + 3 = 8 are its true values
The solution set is x = 3.5 or x = 1
How to determine the solution set?The equation is given as:
|4x - 9| + 3 = 8
Subtract 3 from both sides
|4x - 9| = 5
Remove the absolute bracket
4x - 9 = 5 or 4x - 9 = -5
Add 9 to both sides
4x = 14 or 4x = 4
Divide both sides by 4
x = 3.5 or x = 1
Hence, the solution set is x = 3.5 or x = 1
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Samantha and Jeanie are each rolling a fair 6-sided die with the numbers 1 through 6. They are trying to see who can roll the most
number of odd numbers. Their rolls are shown in the given tables
Whose name experimental probability is closer to the theoretical probability of rolling an odd number
A.Samantha’s
B. Both Jeanie’s and Samantha’s experimental probability’s are very close to the theoretical probability
C. Jeanie’s
D. It can not be determined because there is not enough information
There are 3 odd numbers on the die so the theoretical probably of getting odd is 3/6 = 1/2
Samantha that rolled the die 4 times and got odd every time so her experimental probability was 4/4 = 1
Jeanie rolled the die 16 times and got 6 odds for an experimental probability of 6/16 = 3/8
3/8 is closer to 1/2
Answer: C. Jeanie’s
please help me Find m
Answer:
60 degrees
Step-by-step explanation:
any closed shape has a sum of 360 degrees, now if you subtract 150 from 360 it gives you 210 minus 90 degrees, it would equal to 120. Now 120 divided by 2 since we still need to find the other two corners we haven't found, that would equal to 60 degrees.
The radius of the circle with a central angle of 138° that intercepts an arc with length 9 miles is miles?
Step-by-step explanation:
\begin{gathered}x^2 + y^2 + 17 = 138\\x^2 + y^2 = 138 - 17\\x^2 + y^2 = 121\\x^2 + y^2 = 11^2\\Radius = 11\end{gathered}
x
2
+y
2
+17=138
x
2
+y
2
=138−17
x
2
+y
2
=121
x
2
+y
2
=11
2
Radius=11
What are the vertices of A'B'C if ABC is dilated by a scale factor of 1/6?
The coordinates of the vertices A'B'C when ABC is dilated by a scale factor of 1/6 are 1/6(x,y)
How to determine the vertices?The rule of transformation is given as:
Dilation by a scale factor of 1/6
Mathematically, this is represented as:
(x,y) => 1/6(x,y)
This means that the coordinates of the vertices ABC are multiplied by 1/6 to get the coordinates of the vertices A'B'C
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Describe the graph of the function. y = 9x2 + 18x – 6
The graph is a parabola with axis of symmetry at x = –1.
The graph is a parabola with axis of symmetry at x = 6.
The graph is a parabola with axis of symmetry at x = 1.
The graph is a parabola with axis of symmetry at x = 9.
Answer: y = 9x2 + 18x – 6
Step-by-step explanation:Describe the graph of the function. y = 9x2 + 18x – 6
The graph is a parabola with axis of symmetry at x = –1.
The graph is a parabola with axis of symmetry at x = 6.
The graph is a parabola with axis of symmetry at x = 1.
The graph is a parabola with axis of symmetry at x = 9.
1. If1=3
2=3
3=5
4=4
5=4
Then, 6=?
Answer:
Hence, 6 = 3 ans.
Step-by-step explanation:
hope it's help
.
Fill in the blanks to find the difference in the expressions.
-2x+5
8
A
A x2+
С
X
B x +
11
x +4
X +3
x2 + 7x +
D
[tex]\dfrac{-2x+5}{x+4} - \dfrac{8}{x+3}\\ \\= \dfrac{(-2x+5)(x+3)-8(x+4)}{(x+4)(x+3)}\\\\=\dfrac{-2x^2-6x+5x+15 -8x -32}{x^2+3x+4x+12}\\\\=\dfrac{-2x^2-9x-17}{x^2+7x+12}\\\\\\=\dfrac{-2x^2+(-9)x +(-17)}{x^2+7x+12}\\\\\text{Hence, }~ A=-2,~ B=-9, ~C=-17, ~D=12[/tex]
Consider the sequence below:
5, 8, 13, 20, 29 …
What is the 10th term of the sequence?
Its counting by odd numbers
3, 5, 7, 9, 11, 13, 15, 17, 19, 21
5,8,13,20,29,40,53,68,85,104,125
Answer:
40,53,68,85,104,125,148, 173, 200, 229
27. To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a
randomized block design in which the subjects were blocked by age-group (under 40 years and 40 years or
older). Which of the following must be true about the randomized block design of the experiment?
(A) The number of subjects in each block is different.
88 Treatments are randomly assigned to subjects within each block.
(C) The design cannot have a control group because subjects are blocked by age-group.
fo) The experiment uses a matched-pairs design, where subjects from one block are paired with subjects from
the other block.
E) The subjects in one block receive one treatment, and the subjects in the other block receive the other
treatment
In a randomized block design, it is expected treatments are randomly assigned within each block.
What does a randomized block design imply?Subjects are divided into blocks based on a specific features such as age, gender, education, etc.Within each block subjects that receive treatment and does who do not are randomly assigned.The treatment in all blocks is the same. For example, if the purpose is to study the effect of medicine all treatment subjects should receive the same medicine and dose.What is the purpose of this design?The purpose is to minimize the effect of certain factors such as age.
Based on the above, it is expected in this experiment the treatment is randomly assigned to a specific number of subjects within each block.
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Simplify the expression. Write the answer using scientific notation.
a) 2.52 × 10–3
b) 2.52 × 10–2
c) 2.52 × 10–1
d) 4.3 × 10–2
Answer:
b) 2.52 x 10^(-2)
Step-by-step explanation:
0.7 X 3.6 = 2.52
2.52 X 10^(-2)
Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24.
Answer:
NoYesYesYesNoNoStep-by-step explanation:
18+x=24 and 6x+3 fail distributive property, while 3(6+x)=72 is not the same as 3(6+x)=24
Point B (1 -3) is reflected across the x-axis to point D. What are the coordinates of point D?
Answer:
D (1;3).
Step-by-step explanation:
1) the condition 'across the X-axis' means the x-coordinate is not changed, the y-coordinate is changed to positive value. Then
2) the required coordinates of point D are (1; 3).
note, the suggested option is not the only one.
Help picture below problem 15
Answer:
x = 25°
Step-by-step explanation:
→ Remember key fact
Angles in triangle add up to 180°
→ Set up equation
34 + 121 + x = 180
→ Simplify
155 + x = 180
→ Minus 155 from both sides
x = 25°
8
11 Juan is multiplying 68 x 73 using the area model method
One of the partial products is missing.
What number should juan write in the blank space in the model above?
A 420
B 42,000
C 4,200
D 130
Answer:
C 4,200
Step-by-step explanation:
THE FIRST ANSWER I PUT WAS INCORRECT 70 TIMES 60 = 4,200 because 70 has one 0 and 60 has one 0 use that as a strategy so there's two 0,s when you combine it and its at the end of 4,200 so sice 6 times 7 or 7 times 6 = 42 put the two 0,s at the end and add it to 42 then you get 4,200 or 4200 you don't have to put the comma but it helps let you know 4,000 is part of the thousands and lets you know to seperate it from the hundreds so it's better to add the comma if you want to if you don't want to then it's okay but you might get a answer wrong without a comma so the answer is C 4,200!!!!!!!!!!
Alan bought 120 pens at the cost of €2 per pen. He sold 72 of them for €2.50 per pen and the remaining at the price of €2 per pen. Find his percentage profit or loss.
Answer:
His profit was 15%
Step-by-step explanation:
120*2€ = 240€
72*2.5€ = 180€
120-72 = 48
48*2€ = 96€
And now a simple proportion:
240€ = 100%
276€ = x
x = (276*100)/240 %
x = 115%
115%-100% = 15%
His profit was 15%
Use the drop downs to determine which symbols
would complete the inequality for the domain.
5
ch
-4__(a)___*_(b)__4
(a)
X
-5
5
(b)
The domain of the graph in the form of inequality will be -4 ≤ x < 4.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The domain means all the possible values of x and the range means all the possible values of y.
The domain of the graph will be [-4, 4). Then the domain of the graph in the form of inequality will be -4 ≤ x < 4.
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Convert the unit of length. Round the answer to one decimal place if necessary. 170 cm ≈ _____ ft ?
Answer:
5.56 ft
Step-by-step explanation:
30.48 cm per foot
170 cm ÷ 30.48 cm/ft = 5.56 ft
Hope this helps!
what’s the answer????
Answer:
3.6 m/h
Step-by-step explanation:
Distance (d) = 9 Km
Time (t) = 2.5 hour
Speed ( s )
Speed = Distance / Time
s = d / t
s = 9 / 2.5
s = 90 / 25
s = 18 / 5
s = 3.6 Km/h
PLEASE HELP PLEASE PLEASE PLEASE HELP
A calendar use seven boxes of nails to build 10 bird houses he used blank of a box on each birdhouse
Use calculus to find the volume of the following solid S:
The base of S is a circular disk with radius r. Parallel cross-sections perpendicular to the base are squares.
I assume the base of S is the disk centered at the origin, or x² + y² ≤ r². Solving for y gives two solutions corresponding to the upper and lower halves of the circular boundary,
[tex]x^2+y^2 = r^2 \implies y = \pm \sqrt{r^2-x^2}[/tex]
and the vertical distance between them - i.e. the side length of each cross section - is
[tex]\sqrt{r^2-x^2} - \left(-\sqrt{r^2-x^2}\right) = 2\sqrt{r^2-x^2}[/tex]
Then the volume of each square cross section 4 (r² - x²) ∆x, and the volume of S is
[tex]\displaystyle \int_{-r}^r 4(r^2-x^2) \, dx[/tex]
By symmetry, this is the same as
[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx[/tex]
which gives a volume of
[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx = 8 \left(r^3 - \frac{r^3}3\right) = \boxed{\frac{16r^3}3}[/tex]
