The distance John can ride his bike in 12 minutes is approximately 1.6 miles.
To find out the distance John can ride his bike in 12 minutes, we can use the information given about his rate of riding.
We are told that John can ride his bike 4 miles in 30 minutes. This implies that his rate of riding is 4 miles per 30 minutes.
To calculate the distance John can ride in 12 minutes, we need to determine the proportion of time he is riding compared to the given rate.
We can set up a proportion to solve for the unknown distance:
(4 miles) / (30 minutes) = (x miles) / (12 minutes)
Cross-multiplying, we get:
30 minutes * x miles = 4 miles * 12 minutes
30x = 48
Now, we can solve for x by dividing both sides of the equation by 30:
x = 48 / 30
Simplifying the fraction, we have:
x = 8/5
So, John can ride his bike approximately 1.6 miles in 12 minutes, at his current rate.
Therefore, the distance John can ride his bike in 12 minutes is approximately 1.6 miles.
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PLS HELP WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Identify x.
Answer:
The answer is, x= 145
Step-by-step explanation:
Since line BD passes through the center E of the circle, then the angle must be a right angle or a 90 degree angle.
Hence angle DAB must be 90 degrees
or,
[tex]angle \ DAB = 0.3(2x+10) = 90\\90/0.3 = 2x+10\\300 = 2x+10\\300-10=2x\\290=2x\\\\x=145[/tex]
Hence the answer is, x= 145
Consider the following pair of points.
(8,−8)
and (−5,−1)
Step 2 of 2 : Determine the midpoint of the line segment joining the pair of points.
The midpoint of the line segment joining the pair of points (8, -8) and (-5, -1) is (1.5, -4.5).
To find the midpoint, we need to take the average of the x-coordinates and the average of the y-coordinates of the two given points.
For the x-coordinate: (8 + (-5))/2 = 3/2 = 1.5
For the y-coordinate: (-8 + (-1))/2 = -9/2 = -4.5
Thus, the midpoint of the line segment is (1.5, -4.5).
In more detail, the midpoint formula is derived by averaging the x-coordinates and y-coordinates separately. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint (xm, ym) is given by:
xm = (x1 + x2)/2
ym = (y1 + y2)/2
In this case, the x-coordinates are 8 and -5, and their average is (8 + (-5))/2 = 1.5. The y-coordinates are -8 and -1, and their average is (-8 + (-1))/2 = -9/2 = -4.5.
Therefore, the midpoint of the line segment joining the two given points is (1.5, -4.5).
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Find the 15th term of the geometric sequence 8,32,128
Answer:
2147483648
Step-by-step explanation:
Write the geometric sequence as an explicit formula
[tex]8,\,32,\,128\rightarrow8(4)^0,8(4)^1,8(4)^2\rightarrow a_n=a_1r^{n-1}\rightarrow a_n=8(4)^{n-1}[/tex]
Find the n=15th term
[tex]a_{15}=8(4)^{15-1}=8(4)^{14}=8(268435456)=2147483648[/tex]
In a group of 105 students, 70 students passed Mathematics, 60 students passed History and 45 students passed Geography; 30 students passed Mathematics and History, 35 students passed History and Geography, 25 passed Mathematics and Geography and 15 passed all three subjects. Draw a Venn Diagram to illustrate this information. Find the number of students who
a) Passed at least one subjects
b) Passed exactly two subjects
c) Passed Geography and failed Mathematics
d) Passed all three subjects e) Failed Mathematics given that they passed History
answer pls
a) Passed at least one subject: 100 students
b) Passed exactly two subjects: 90 students
c) Passed Geography and failed Mathematics: 20 students
d) Passed all three subjects: 15 students
e) Failed Mathematics given that they passed History: 30 students.
To solve this problem, let's draw a Venn diagram to visualize the information given:
In the Venn diagram above, the circles represent the three subjects: Mathematics (M), History (H), and Geography (G). The numbers outside the circles represent the students who did not pass that particular subject, and the numbers inside the circles represent the students who passed the subject. The numbers in the overlapping regions represent the students who passed multiple subjects.
Now, let's answer the questions:
a) Passed at least one subject:
To find the number of students who passed at least one subject, we add the number of students in each circle (M, H, and G), subtract the students who passed two subjects (since they are counted twice), and add the students who passed all three subjects.
Total = M + H + G - (M ∩ H) - (M ∩ G) - (H ∩ G) + (M ∩ H ∩ G)
Total = 70 + 60 + 45 - 30 - 25 - 35 + 15
Total = 100
Therefore, 100 students passed at least one subject.
b) Passed exactly two subjects:
To find the number of students who passed exactly two subjects, we sum the students in the overlapping regions (M ∩ H, M ∩ G, and H ∩ G).
Total = (M ∩ H) + (M ∩ G) + (H ∩ G)
Total = 30 + 25 + 35
Total = 90
Therefore, 90 students passed exactly two subjects.
c) Passed Geography and failed Mathematics:
To find the number of students who passed Geography and failed Mathematics, we subtract the number of students in the intersection of M and G from the number of students who passed Geography.
Total = G - (M ∩ G)
Total = 45 - 25
Total = 20
Therefore, 20 students passed Geography and failed Mathematics.
d) Passed all three subjects:
To find the number of students who passed all three subjects, we look at the overlapping region (M ∩ H ∩ G).
Total = (M ∩ H ∩ G)
Total = 15
Therefore, 15 students passed all three subjects.
e) Failed Mathematics given that they passed History:
To find the number of students who failed Mathematics given that they passed History, we subtract the number of students in the intersection of M and H from the number of students who passed History.
Total = H - (M ∩ H)
Total = 60 - 30
Total = 30
Therefore, 30 students failed Mathematics given that they passed History.
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What function has the same range as f(x) = -2 x - 3 + 8
Answer:
Any equation that has the power of x at 1
Step-by-step explanation:
Since the function f(x) = -2x -3 +8 has an infinite range, so any other equation that only contains x^1 would work
de un grupo de 75 alumnos se sabe que 20 estudian mate y física determina la probabilidad que al escoger un alumno estudie a) estudie solo mate b) estudie mate o fisica c) que no estudié ninguna de las dos d) que estudie mate y fisica
A) The probability that a randomly selected student studies only mathematics would be 20/75.
B) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.
C) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.
D) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.
To determine the requested probabilities, we will use the information provided about the group of 75 students.
a) Study only mate:
We know that there are 20 students studying mathematics and physics, so the number of students studying only mathematics would be the total number of students studying mathematics (20) minus the number of students studying both subjects. Since no information is provided on the number of students studying both subjects, we will assume that none of the students study both subjects. Therefore, the number of students studying only mathematics would be 20 - 0 = 20.
The probability that a randomly selected student studies only mathematics would be 20/75.
b) Study math or physics:
To determine this probability, we need to add the number of students who study mathematics and the number of students who study physics, and then subtract the number of students who study both subjects (we again assume that none of the students study both subjects).
Number of students studying mathematics = 20
Number of students studying physics = X (not given)
Number of students studying both subjects = 0 (assumed)
Therefore, the number of students studying mathematics or physics would be 20 + X - 0 = 20 + X.
The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.
c) That he does not study either:
The number of students not studying either subject would be the complement of the number of students studying mathematics or physics. So it would be 75 - (20 + X).
The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.
d) To study math and physics:
Since no information is provided on the number of students studying both subjects, we cannot determine the exact probability that a student will study mathematics and physics.
In summary:
a) The probability that a randomly selected student studies only mathematics would be 20/75.
b) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.
c) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.
d) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.
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Let V=W+W* be a vector space, being the direct product of the (finite dimensional) vector space W and its dual space W*. Now, let us define a bilinearform B: VxV -> R by
<(a,p), (b,q)> := q(a) + p(b).
Now let us suppose we have both e_1, …, e_n Basis of W and e*_1,….,e*_n Basis of W*.
What is the matrix of this bilinear form?
(I know how these matrices usually look like, but the inner product makes me very confused about the layout of this matrix).
What is the product of (p^3)(2p^2 - 4p)(3p^2 - 1)?
Answer:
Step-by-step explanation:
To find the product of the given expression, we can use the rules of multiplication and apply them to each term within the parentheses:
(p^3)(2p^2 - 4p)(3p^2 - 1)
Expanding the expression, we multiply each term within the parentheses:
= p^3 * 2p^2 * 3p^2 - p^3 * 2p^2 * 1 - p^3 * 4p * 3p^2 + p^3 * 4p * 1
Simplifying further, we combine like terms and perform the multiplication:
= 6p^7 - 2p^5 - 12p^6 + 4p^4
Therefore, the product of (p^3)(2p^2 - 4p)(3p^2 - 1) is 6p^7 - 2p^5 - 12p^6 + 4p^4.
The product of the expressions (p^3)(2p^2 - 4p)(3p^2 - 1) is computed using the distributive property, resulting in 6p^7 - 12p^6 - 2p^5 + 4p^4.
Explanation:To find the product of the given expressions: (p^3)(2p^2 - 4p)(3p^2 - 1), you will need to apply the distributive property, also known as the multiplication across addition and subtraction.
First, distribute p^3 across all terms inside the brackets of the second expression, then do the same with the result across the terms of the third expression.
Steps are as follows:
p^3 * 2p^2 gives 2p^5. p^3 * -4p gives -4p^4. So (p^3)(2p^2 - 4p) gives 2p^5 - 4p^4. Distribute 2p^5 - 4p^4 across all terms inside the brackets of the third expression. 2p^5 * 3p^2 gives 6p^7 and 2p^5 * -1 gives -2p^5. Similarly, -4p^4 * 3p^2 gives -12p^6 and -4p^4 * -1 gives 4p^4.
All together, it results in: 6p^7 - 12p^6 - 2p^5 + 4p^4. That is the product of the initial expressions.
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3,20,110 _1715 This is an mathematics question
The pattern between the numbers 3, 20, 110, and 1715 can be found using a mathematical method. In order to get the following number from each, there is a sequence that must be applied.Let's take a look at the sequence that was used to generate these numbers:
The first number is multiplied by 2 and then increased by 14 to get the second number. For example:
3 x 2 + 14 = 20
Then, the second number is multiplied by 3 and 20, and 110 is added.
20 x 3 + 110 = 170
The third number is multiplied by 4 and then increased by 110.
110 x 4 + 110 = 550
Finally, the fourth number is multiplied by 5 and then increased by 110.
550 x 5 + 110 = 2825
Therefore, using the above formula, the next number in the sequence can be calculated:
1715 x 6 + 110 = 10400
As a result, the sequence of numbers 3, 20, 110, 1715, 10400 can be calculated using the mathematical formula stated above.
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Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 80,000 shares of cumulative preferred 3% stock, $20 par and 410,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $31,000; second year, $73,000; third year, $80,000; fourth year, $120,000. Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00". 1st Year 2nd Year 3rd Year 4th Year Preferred stock (dividends per share) $fill in the blank 1 $fill in the blank 2 $fill in the blank 3 $fill in the blank 4 Common stock (dividends per share)
a square pyramid has a base with a side length of 3 feet and lateral with a height of 6 feet. what is the area of the pyramid. A.9 square feet B. 27 square feet C. 36 square feet D. 45 square feet
Answer:
D. 45 square feet
Step-by-step explanation:
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular lateral faces.
Finding the area of the baseFirst, let's find the area of the base (square).
[tex]\boxed{\begin{minipage}{7 cm}Base area = side length $\times$ side length\\ \\Base area = 3 $\times$ 3 \\ \\Base area = 9 square feet\end{minipage}}[/tex]
Finding the area of the triangular lateral facesNow, let's find the area of the triangular lateral faces.
Finding the area of one triangular lateral faceAs stated in the problem, the slant height of the triangle is 6 feet. We can find the area of one triangular lateral face:
[tex]\text{Triangle area = $\frac{1}{2}$ $\times$ base $\times$ height}\\\\\text{Triangle area = $\frac{1}{2}$ $\times$ 3 $\times$ 6} \\\\\text{Triangle area = 9 square feet}[/tex]
Finding the total lateral areaSince there are four triangular lateral faces, we need to multiply this area by 4:
[tex]\text{Total lateral area = 4 $\times$ 9}\\\\\text{Total lateral area = 36 square feet}[/tex]
Total surface areaFinally, we add the base area and the total lateral area to find the total surface area of the pyramid:
[tex]\text{Total surface area = base area + total lateral area}\\\\\text{Total surface area = 9 + 36}\\\\\text{Total surfacel area = 45 square feet}[/tex]
ConclusionSo, the area of the square pyramid is 45 square feet. Which is option D.
________________________________________________________
Answer:
D. 45 square feet
Step-by-step explanation:
You want the surface area of a square base pyramid with a side length of 3 feet and a slant height of 6 feet.
Area formulasThe area of a triangular face is given by ...
A = 1/2bh . . . . . base b and height h
The area of the square base is given by ...
A = s²
The total surface area of the pyramid is the area of the base plus the areas of the 4 triangular faces:
total area = s² +4(1/2bh) . . . . where b = s
This can be simplified to ...
total area = s(s +2h) . . . . . area of a square pyramid with slant height h
ApplicationFor the pyramid with a square base 3 ft on a side, and a slant height of 6 ft, the total area is ...
total area = (3 ft)(3 ft + 2·6 ft) = (3 ft)(15 ft) = 45 ft²
The area of the pyramid is 45 square feet.
<95141404393>
What's the lateral area of the cylinder?
A. 251 yd.²
B. 314 yd.²
C. 503 yd.²
D. 13 yd.²
Answer:
2π(5)(10) = 100π yd² = about 314 yd²
B is the correct answer.
Determine the surface area and volume
Answer:
Volume : 300
Surface Area : 280
Step-by-step explanation:
Volume : 6*5*10
Surface Area : 50+50+30+30+60+60
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $123,525?
In order to achieve a profit of $123,525, the Vilas County News would require a subscriber base of 6,355,500 individuals.
Let's break down the problem step by step to find the number of subscribers needed to bring a total profit of $123,525.
First, we know that the Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. This means that the current profit from the 3,000 subscribers is $20 x 3,000 = $60,000.
Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. This means that for every additional subscriber, the profit increases by $0.01. Therefore, we need to find how many additional subscribers are required to reach a total profit of $123,525 - $60,000 = $63,525.
To find the number of additional subscribers needed, we divide the additional profit required by the increase in profit per subscriber: $63,525 / $0.01 = 6,352,500.
However, we need to remember that this number represents the total number of additional subscribers needed, not the final total number of subscribers. To find the final total number of subscribers, we add the additional subscribers to the current number of subscribers: 6,352,500 + 3,000 = 6,355,500.
Therefore, to bring a total profit of $123,525, the Vilas County News would need a total of 6,355,500 subscribers.
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Solve for the measure of the indicated arc.
O 127°
165°
164°
157°
52 °
K
53°
L
M
C
Answer:
? = 157°
Step-by-step explanation:
the measure of the secant- secant angle KLM is half the difference of the intercepted arcs , that is
[tex]\frac{1}{2}[/tex] (CJ - KM) = ∠ KLM , that is
[tex]\frac{1}{2}[/tex] (? - 53) = 52° ( multiply both sides by 2 to clear the fraction )
? - 53° = 104° ( add 53° to both sides )
? = 157°
a sector has radius 10 mm and area 40/3 pie mm^2. what is the measure, in degrees, of the central angle of the sector?
The central angle of the sector is 540°.
The area of the sector formula is A = (1/2) r² θ Where, A = Area of sector r = Radius of sectorθ = Central angle of sector Given that the radius of the sector is 10mm and area is 40/3 pie mm²
To find the measure of central angle θ, plug the given values in the formula as shown; A = (1/2) r² θ40/3 pie = (1/2)(10)² θ40/3 pie = (1/2)100 θ40/3 pie = 50θ (multiply by 3/40)θ = (3/40) × 40πθ = 3π.
So, the measure, in degrees, of the central angle of the sector is;θ = (180/π) × 3πθ = 540°Therefore, the central angle of the sector is 540°.
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K
Find the horizontal asymptote, if any, of the graph of the rational function.
20x²
Sử Hồ
g(x)=
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The horizontal asymptote is. (Type an equation.)
OB. There is no horizontal asymptote.
are statistical questions?
Which subjects do the students What is the number of students
in my class like?
in my class?
How many servings of fruit did
I eat each day this month?
What is my height?
What is my favorite color?
What is the highest temperature
of each month this year?
Reset
Next
What is the height of each
student in my class?
What is my mother's favorite
fruit?
How many students from each
school in this city love football?
The statistical questions for this problem are given as follows:
Which subjects do the students like?How many servings of fruit did I eat each day this month?What is the highest temperature of each month this year?What is the height of each student in my class?How many students from each school in this city love football?What is an statistical question?A question is classified as statistical if it can receive answers of data that vary, that is, questions that do not have an exact answer.
When the answer is exact, it must be composed by a set of data, such as the number of students that like football in each school, the number will vary for each school.
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y = 1/3x -1
x-intercept (3,0)
How did they get this answer? Somebody please help
Answer:
Step-by-step explanation:
x-intercept is where the line cuts the x-axis. That is, when y=0.
Substitute y=0 and we get:
[tex]0=\frac{1}{3} x-1[/tex]
[tex]1=\frac{1}{3} x[/tex]
[tex]x=3[/tex]
So x-intercept is the point (3,0).
Can anyone help me solving this question I forgot how to solve it it’s important
The statement that is correct about the dot plots is that:
A) The distribution for Class M is approximately symmetric
How to identify symmetric distribution?A symmetric distribution in dot plots is defined as a distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median.
A symmetric distribution is one that occurs when the values of a variable occur at regular frequencies, and often the mean, median, and mode all occur at the same point. If we draw a line through the middle of the chart, we can see that the two planes mirror each other.
Now, from the given two dot plots of class M and Class N, it is very clear that class M is very close to being symmetric about the data value 3.
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PLEASE I NEED HELP I DONT UNDERSTAND THIS
Answer:
- 15pr
Step-by-step explanation:
- 5p(3r) ← means multiply 3r by - 5p
= - 5p × 3r
= - 5 × 3 × p × r
= - 15 × pr
= - 15pr
1.Lim as x approaches 0 (sin3x)/(2x-Sinx)
2. Lim as x approaches infinity x^-1 lnx
3. Lim x approaches infinity x/ e^x
Using L’Hospals rule for all
1. The limit of (sin3x)/(2x - sinx) as x approaches 0 is -27.
2. The limit of x^(-1)lnx as x approaches infinity is -1.
3. The limit of x/e^x as x approaches infinity is 0.
1. To find the limit of (sin3x)/(2x - sinx) as x approaches 0 using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (sin3x) = 3cos3x
Denominator: d/dx (2x - sinx) = 2 - cosx
Now, we can find the limit of the differentiated function as x approaches 0:
lim x->0 (3cos3x)/(2 - cosx)
Again, differentiating the numerator and denominator:
Numerator: d/dx (3cos3x) = -9sin3x
Denominator: d/dx (2 - cosx) = sinx
Taking the limit as x approaches 0:
lim x->0 (-9sin3x)/(sinx)
Now, substituting x = 0 into the function gives:
(-9sin0)/(sin0) = 0/0
Since we obtained an indeterminate form of 0/0, we can apply L'Hôpital's rule again.
Differentiating the numerator and denominator:
Numerator: d/dx (-9sin3x) = -27cos3x
Denominator: d/dx (sinx) = cosx
Taking the limit as x approaches 0:
lim x->0 (-27cos3x)/(cosx)
Now, substituting x = 0 into the function gives:
(-27cos0)/(cos0) = -27/1 = -27
Therefore, the limit of (sin3x)/(2x - sinx) as x approaches 0 is -27.
2. To find the limit of x^(-1)lnx as x approaches infinity using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (lnx) = 1/x
Denominator: d/dx (x^(-1)) = -x^(-2) = -1/x^2
Now, we can find the limit of the differentiated function as x approaches infinity:
lim x->∞ (1/x)/(-1/x^2)
Simplifying the expression:
lim x->∞ -x/x = -1
Therefore, the limit of x^(-1)lnx as x approaches infinity is -1.
3. To find the limit of x/e^x as x approaches infinity using L'Hôpital's rule, we can differentiate the numerator and denominator separately and take the limit again:
Let's differentiate the numerator and denominator:
Numerator: d/dx (x) = 1
Denominator: d/dx (e^x) = e^x
Now, we can find the limit of the differentiated function as x approaches infinity:
lim x->∞ (1)/(e^x)
Since the exponential function e^x grows much faster than any polynomial function, the denominator goes to infinity much faster than the numerator. Therefore, the limit of (1)/(e^x) as x approaches infinity is 0.
Thus, the limit of x/e^x as x approaches infinity is 0.
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Please awnser asap I will brainlist
The system has exactly one solution. The solution is (13, 8)
How to calculate the solution to the system of equationsFrom the question, we have the following parameters that can be used in our computation:
Country A: -x + 20y = 147
Country B: -x + 10y = 67
Country C: y = 8
So, we have
-x + 20y = 147
-x + 10y = 67
y = 8
Substitute 8 for y in the first and second equations
So, we have
-x + 20 * 8 = 147
-x + 10 * 8 = 67
Evaluate the products
-x + 160 = 147
-x + 80 = 67
So, we have
x = 160 - 147
x = 80 - 67
Evaluate
x = 13
x = 13
Hence, the solution to the system of equations is (13, 8)
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what is 34.6285 rounded to the nearest hundreds
Answer:
34.63
Step-by-step explanation:
The 2 in 34.6285 marks the hundredths place
We can round by seeing what number is to the right of it which is 8.
Since 8 is larger than 5, we round up by 1.
Thus, 34.63 is our answer
The answer is:
34.63
Work/explanation:
Rounding to the nearest hundredth means rounding to 2 decimal places (DP).
So we have 2 decimal places, and the 3rd one matters too because it will determine the value of the 2nd DP.
The third DP is 8. Since it's greater than 5, then the value of the 2nd DP will be rounded up. I will add 1 to it.
Remember that we round up when the digit that we're rounding to is followed by another digit that is greater than or equal to 5.
So we round :
[tex]\bf{34.6285 =\!=\!\!\! > 34.63}[/tex]
Therefore, 34.6286 rounded to the nearest hundredth is 34.63.Tell whether the information in the diagram allows you to conclude that c is on the perpendicular bisector of an
11. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB.
12. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because C is equidistant from AB.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector can be used for bisecting or dividing a line segment exactly into two (2) equal halves, in order to form a right angle with a magnitude of 90° at the point of intersection.
Question 11.
By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB:
AC ≅ BC
CD ≅ CD
AE ⊥ EC
Question 12.
By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector because C is equidistant from line segment AB.
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1 Express 12 + 5i in polar form (i.e in form of \[z=r\cos\theta + i\sin\theta\]
A. [13(\cos 22.6 - i\sin 22.6)\]
B [13(\cos 22.6+i\sin 22.6)\]
C. [13(\cos 23.5 - i\sin 23.5)\]
D. [13(\cos 23.6 - i\sin 23.6
The correct option is A. [13(cos 22.6 - isin 22.6)] in which the modulus is 13 and the argument is 22.6 degrees.
Given the complex number z = 12 + 5i. We have to express this complex number in the polar form which is\[z=r\cos\theta + i\sin\theta\]where r is the modulus and θ is the argument of the complex number.
The modulus of the complex number is given by,|z|=√(12²+5²)=√(144+25)=√169=13
Therefore, the modulus of the complex number is 13.
Now, we need to find the argument of the complex number, which is given byθ=tan⁻¹(b/a)Where a and b are the real and imaginary parts of the complex number z.θ=tan⁻¹(5/12)So, θ=22.6 degrees. (approximate value)
Thus, the complex number z = 12 + 5i can be expressed as\[z=13\cos(22.6^{\circ}) + i\sin(22.6^{\circ})
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87,959 →
round to nearest hundred
pls help help needed rn asap
Step-by-step explanation:
87,959 ==> 88,000 is the nearest hundred
The answer is:
87.96Work/explanation:
When rounding to the nearest hundredth, round to 2 decimal places (DP).
Which means we should round to 5.
5 is followed by 9, which is greater than or equal to 5. So, we drop 9 and add 1 to 5 :
87. 96
Therefore, the answer is 87.96.Given f(x) = √6x and g(x)=
-9
=
Which value is in the domain of fᵒg?
-1
1
x - 6
Click on the correct answer.
6
7
The values in the domain of fᵒg are all real numbers.
Therefore, the correct answer is: x - 6.
To determine the domain of the composite function fᵒg, we need to find the values of x that are valid inputs for the composition.
The composite function fᵒg represents applying the function f to the output of the function g. In this case, g(x) is equal to -9.
So, we substitute -9 into the function f(x) = √6x:
f(g(x)) = f(-9) = √6(-9) = √(-54)
Since the square root of a negative number is not defined in the set of real numbers, the value √(-54) is undefined.
Therefore, -9 is not in the domain of fᵒg.
To find the values in the domain of fᵒg, we need to consider the values of x that make g(x) a valid input for f(x).
Since g(x) is a constant function equal to -9, it does not impose any restrictions on the domain of f(x).
The function f(x) = √6x is defined for all real numbers, as long as the expression inside the square root is non-negative.
So, any value of x would be in the domain of fᵒg.
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Kelly started with 2 pennies in her penny jar. She puts 2 more pennies in her penny jar every day. How many pennies will she have on Day 10
On Day 10, Kelly will have a total of 20 pennies in her penny jar.
To determine how many pennies Kelly will have on Day 10, we need to consider the progression of pennies added to her jar each day.
On Day 1, Kelly starts with 2 pennies. On Day 2, she adds 2 more pennies, resulting in a total of 2 + 2 = 4 pennies. This pattern continues, with 2 more pennies being added each day.
To find the number of pennies on Day 10, we can observe that the number of pennies on any given day can be calculated using the formula:
Number of pennies = Initial number of pennies + (Number of days - 1) * Number of pennies added per day
Using the provided information, we can substitute the values into the formula:
Number of pennies on Day 10 = 2 + (10 - 1) * 2
= 2 + 9 * 2
= 2 + 18
= 20
Therefore, on Day 10, Kelly will have a total of 20 pennies in her penny jar.
To summarize, starting with 2 pennies and adding 2 more pennies each day, Kelly will have a total of 20 pennies in her penny jar on Day 10.
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Pls help I need this answer
The expression is completed as (x-4)(x -7)
How to determine the valueFrom the information given, we have that the polynomial is given as;
x² - 11x + 28
Using the factorization method, we have;
First, find the product of the coefficient of x squared and the constant value
Then, we have;
1(28) = 28
Now, find the pair factors of the product that adds up to -11, we have;
-7x and -4x
Substitute the values, we have;
x² - 7x - 4x + 28
Group in pairs, we get;
x(x-7) - 4(x - 7)
Then, we have the expressions as;
(x-4)(x - 7)
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