The length of diameter of the base of the cone will be 112 cm.
What is meant by an equation?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Equations are mathematical expressions with two algebras flanking the equal (=) sign on either side. This relationship is illustrated by the left and right expressions being equal to one another. Left-hand side equals right-hand side is a basic, straightforward equation.
By using Pythagoras's theorem,
106² = 90² + r²
simplifying the above equation, we get
r² = 106² - 90²
r = √3136
radius = 56 cm.
Then, the diameter will be,
Diameter = 2 × radius
substitute the values in the above equation,
D = 2(56)
D = 112 cm.
Therefore, the correct answer is option b. 112 cm.
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I need help!!! It’s factor out the quadratic
\(20f^3 -24f^2 -35f+42\\\\=4f^2(5f-6) -7(5f-6)\\\\= (5f-6)(4f^2-7)\)
\(\sf \longmapsto \: 20f {}^{3} −24f^2+42−35f\)
\(\sf \longmapsto20f^3−24f^2−35f+42\)
\(\sf \longmapsto \: (5f−6)(4f^2−7)\)
There are no like terms.So we can't simplify it.\( \sf \: (5f−6) \times (4f^2−7)\)
Identify the amount, base, and percent in the problem:
4.8 is what percent of 12?
A. The amount is 12, the base is 4.8, and the percent is unknown.
B. The amount is 4.8, the base is 12, and the percent is unknown.
C. The amount is unknown, the base is 4.8, and the percent is 12 %
D. The amount is unknown, the base is 12, and the percent is 4.8%
The amount is 4.8, base is 12 and the precent of the given condition is unknown.
Define base:
In mathematics, the term "base" refers to a fixed number or symbol used as a point of reference for counting, measuring or representing a quantity.
In the decimal system, for example, the base is 10, because there are 10 possible digits (0-9) that can be used to represent a number. In binary system, the base is 2, because there are only 2 possible digits (0 or 1) that can be used to represent a number.
What about precent?
In mathematics, percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred," so a number expressed as a percent represents a fraction of 100.
To convert a number to a percent, we multiply it by 100. For example, if we want to express the number 0.25 as a percent, we can multiply it by 100 to get:
⇒ 0.25 x 100 = 25%
According to the given information:
Percent: The precent is the number with the % symbol
Base: The base is the whole amount which in this case is 12.
Amount: The amount based on the precent is 4.8
So, from overall condition we have that option 'a' is correct.
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Which pair of angles are corresponding angles?
PLEASE HELP ME THIS IS DUE TMR
Answer:
the answer is 3 and 7
Step-by-step explanation:
Angles formed when a transversal line cuts across two straight lines are known as corresponding angles. Corresponding angles are located in the same relative position, an intersection of transversal and two or more straight lines.
Use the tree diagram to complete each statement.
The probability of no promotion, given that a salesperson hit the quota: A is
.
The probability of a promotion, given that a salesperson missed the quota: B is
.
The probability of no promotion, given that a salesperson missed the quota: C is
.
The probability that a salesperson hit the quota and got promoted: D is
.
The probability that a salesperson hit the quota, given that the salesperson was promoted is 0.88. Therefore, option D is the correct answer
From the tree diagram, there are two ways to obtain the promotion:
0.41 of 0.68 (hit the quota).
0.14 of 0.32 (did not hit the quota).
So, the probability of getting a promotion is:
P(A) = 0.41 × 0.68 + 0.14 × 0.32 = 0.3236.
The probability of both getting a promotion and hitting the quota is:
P(A and B) = 0.41 × 0.68 = 0.2788.
So, the conditional probability is:
P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.88 (approximately).
Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Salespeople at a certain company must meet a quota each month. On average, they hit the quota 68% of the time. If a salesperson hits the quota, the probability of being promoted in the next six months is 0.41. If a person doesn’t hit the quota, the probability of being promoted is 0.14.
Use the tree diagram to determine the probability that a salesperson hit the quota, given that the salesperson was promoted.
A. 0.28
B. 0.32
C. 0.41
D. 0.88
a. 5x + 3x b. 9s - 3s + 4s
Answer:
Step-by-step explanation:
A) 5x+3x
5x+3x
= 8x
B) 9s-3s+4s
9s-3s+4s
6s+4s
=10s
Determine when the function is positive, negative, increasing, or decreasing: y = -9ˣ
Help (ಥ‿ಥ)
Factor the perfect square trinomial 25x2 - 60x + 36.
A. (5x – 4)(5x-9)
B. (5x-6)2
C. (5x - 3)2
D. (5x - 12)(5x - 3).
Answer: B
Step-by-step explanation:
In how many ways can a quality-control engineer select a sample of3 transistors for testing frm a batch of 100 transistors?
Answer:
161700 ways.
Step-by-step explanation:
The order in which the transistors are chosen is not important. This means that we use the combinations formula to solve this question.
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
In this question:
3 transistors from a set of 100. So
\(C_{100,3} = \frac{100!}{3!(100-3)!} = 161700\)
So 161700 ways.
what is 7:30 + 46 minutes
The answer would be 8:16
bella answered 33 questions on her math test. she earned a 92% on the test. how many questions did she answer correct
Answer: 30.36
Step-by-step explanation:
92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.
Solve the system of equations.
4x - 2y = 8
3x + 4y = 17
A. (2, 0)
B. (7, -1)
C. (3, 2)
D. (4, 4,)
Answer:
The answer is option C
Step-by-step explanation:
The solution is in the image
Answer:
Step-by-step explanation:
8x - 4y = 16
3x + 4y = 17
11x = 33
x = 3
12 - 2y = 8
-2y = -4
y = 2
(3, 2)
answer is C
can anyone help with the vertical angles
Answer:
a
Step-by-step explanation:
do the ones that are congruent and right in front of eachother
\(\angle JLK \ \ \& \ \ \angle MLN\\\\\angle JLM \ \ \& \ \ \angle KLN\)
See the diagram below. I've marked the angles in question using different colors. Angles JLK and MLN are in red. Angles JLM and KLN are in blue.
Vertical angles are opposite one another when we have an X shape like this. Vertical angles are always congruent.
Imagine math Item 994395
Start with the equation 0.2=0 to explain why -4-2 must equal -8.
Drag descriptions and equations to the table to complete the explanation.
In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.
1. Begin with the equation 0.2 = 0.
2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.
This simplifies to 0 = -0.2.
3. Observe that the right side of the equation, -0.2, is a negative number.
4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.
5. Rewrite the equation as 0 = +0.2.
6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.
7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.
8. Simplify the equation to 0 = +0.2.
9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.
10. As a result, the original equation 0.2 = 0 is invalid.
11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.
12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.
To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.
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6th grade math ok thanks
192.78
Hope this helps!
✧◝(⁰▿⁰)◜✧
Answer:
192.78
Step-by-step explanation:
0.34 X 567 = 192.78
Given the triangle ABC at points A = ( 2, 2 ) B = ( 4, 5 ) C = ( 6, 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.
To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:
1. Reflect A over the y-axis to get A': (-2, 2)
2. Reflect A' over the x-axis to get A'': (-2, -2)
Therefore, the new point A'' is (-2, -2).
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the Binomial Theorem to find the binomial expansion of the given expression. Show your work.
\((2x-3y)^5\)
The binomial theorem states that: \((x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k\). So, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).
Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]
Term k = 0: \( {5 \choose 0} (2x)^5 (-3y)^0\) = 32x⁵
Term k = 1: \({5 \choose 1} (2x)^4 (-3y)^1\) = -240x⁴y
Term k = 2: \({5 \choose 2} (2x)^3 (-3y)^2\) = 720x³y²
Term k = 3: \({5 \choose 3} (2x)^2 (-3y)^3\) = -1080x²y³
Term k = 4: \({5 \choose 4} (2x)^1 (-3y)^4\) = 810xy⁴
Term k = 5: \({5 \choose 5} (2x)^0 (-3y)^5\) = -243y⁵
Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:\((2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\)
Therefore, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).
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if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Farid makes a $12,000 investment that yields an average yearly return of 4%. If he makes no additional investments, how much will his investment be worth in 15 years?
Therefore, Farid's investment will be worth $21,611.32 after 15 years.
What justifies our use of the average?Averages are calculated because they are a very useful way to show a lot of facts. Instead of looking through hundreds or thousands of pieces of information, we simply need to glance at one number to summarize the full set of data. Averages are useful for quickly comparing data, but they have limitations like outliers giving an inaccurate average.
To calculate the future value of Farid's investment, we can use the formula for compound interest:
FV = PV * (1 + r)ⁿ
where FV is the future value, PV is the present value (the initial investment), r is the annual interest rate, and n is the number of compounding periods (in this case, the number of years).
Plugging in the given values, we get:
FV = 12,000 * (1 + 0.04)¹⁵
FV = 12,000 * 1.800
FV = 21,611.32
Therefore, Farid's investment will be worth $21,611.32 after 15 years.
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The original price of a dining table set is $400. The set is on sale for 40% off. What is the sale price of the set?
Answer: Your answer will be $240
Step-by-step explanation:
What’s the answer helpppp
Answer:
the answer would be the second one
Answer:
Second choice
Step-by-step explanation:
18=2x9
9=3^2
X^7=(x)x^6)
root 18x^7
=3x^3root 2x
A solid cube of side 8 cm was melted to form a solid circular cone. The base radius of the cone is 4 cm. Calculate, correct to one decimal place, the height of the cone. [Take π = 22/7 ]
A solid cube of side 8 cm was melted to form a solid circular cone.
Side of cube = 8 cm .
Volume of cube = a³where a is side of the cube.
Volume of cube = (8)³
Volume of cube = 8 × 8 × 8 = 512 cm³
The base radius of the cone is 4 cm.
Since the solid cube is melted to form a solid circular cone, but the volume will remains the same.
Volume of cone = Volume of cylinder = 512 cm³
Formula to calculate the volume of cone :
\( \rm Volume (cone) = \dfrac{1}{3} \pi { r}^{2} h\)
Plugging in the values of radius and volume
\(512 = \dfrac{1}{3} \times \dfrac{22}{7} \times {(4)}^{2} \times h \\ \\ 512 = \dfrac{22}{21} \times 16 \times h \\ \\ 512 = \dfrac{352}{21} \times h \\ \\ 512 = 16.76 \times h \\ \\ h = \dfrac{572}{16.76} \\ \\ h \approx 34.1\)
\( \therefore\) The height of the cone is 34.1 cm
Need as much help as I can get before 7 minutes are over
Answer:
think the answer is E but not 100%. been a while. let me know either way
What is the point in the solution set?
The point in the solution set from the graph is (0, 0)
Solving the systems of inequalities graphicallyFrom the question, we have the following parameters that can be used in our computation:
y < -5/2x - 2
y ≥ -1/2x + 2
Next, we plot the graph of the system of the inequalities
The graph is given
From the graph, we have solution to the system to be the shaded region
The point in the solution set from the graph is (0, 0)
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What is the area, measured in square centimeters, of the triangle below? Do
not include units in your answer.
Answer here
Answer:
The area of this triangle is (1/2)(9)(8) = 36.
PLEASE HELP FAST !!!!!
The distribution of pitches thrown in the
80 at-bats in a baseball game is as follows.
Pitches 1 2 3 4 5
Frequency 12 16 32 12 8
Find the relative frequency that the pitcher
will throw exactly 4 pitches in an at-bat.
?
Relative Frequency =
Do NOT simplify your answer.
The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
3/20.
How to calculate a relative frequency?A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of at bats in this problem is given as follows:
80.
In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
12/80 = 3/20.
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An employee makes $10.51 per hour but is getting a 3% increase. What is his new wage per hour to the nearest cent? What percentage of the original wage is his new wage?
The employee's new wage per hour is $10.83. The percentage increase of the original wage to his new wage is 3%.
What is a percentage increase?A percent increase means how much a percentage has gone up over time. To find this number, one would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease. The formula for percent increase equals to "Increase / original number (value) x 100".
Given data:
First, we find 3% of $10.51 to get new wage per hour
= 0.03$ * $10.51
= $0.32
Then, we add this increase to $10.51.
= $10.51 + $0.32
= $10.83
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how many solutions does 10+5x/15=4 have
Answer:
3
Step-by-step explanation:
Standard form
1/3 x +6 = 0
Factorization
1/3 (x + 18) = 0
Solutions
x = -90/5 = 18
What is the simplified form of 7 log3x + 4 log3z – 6 log3y?
The simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).
What is the simplified form of the expressionWe can simplify the expression using the following logarithmic rule:
log a + log b = log ab (product rule)
log a - log b = log(a/b) (quotient rule)
c log a = log a^c (power rule)
Using these rules, we can simplify 7 log3x + 4 log3z - 6 log3y as follows:
7 log3x + 4 log3z - 6 log3y
= log3x^7 + log3z^4 - log3y^6 (using the power rule)
= log3(x^7 z^4 / y^6) (using the quotient rule)
Therefore, the simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).
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95°
60°
29
o
X =
Plzzzz I need this
Answer:
x=95
Step-by-step explanation:
They are vertical angles
what is the perpendicular and parallel lines of y= -2 -4x
y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.
The equation y= -2 -4x in the form of slope intercept form y=mx+b is y=-4x-2.
Where m represents the slope and y intercept is -2.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.
The negative reciprocal of -4 is 1/4.
Therefore, the slope of the perpendicular line is 1/4.
The perpendicular line is y=1/4x-2.
We know that the parallel lines have same slope.
y=-4x+3
Hence, y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.
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