The number of ways a judge can award first, second, and third places in a contest with 10 entries is:
720
Step-by-step explanation:We know that the choosing and arranging of r entries out of a total of n entries is given by the method of permutation and the formula is given by:
[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]
Here we have to chose and arrange 3 people according to their ranks out of a total of 10 entries.
i.e. r=3 and n=10
Hence, the formula is given by:
[tex]{10}_P_3=\dfrac{10!}{(10-3)!}\\\\\\{10}_P_3=\dfrac{10!}{7!}\\\\\\{10}_P_3=\dfrac{10\times 9\times 8\times 7!}{7!}\\\\\\{10}_P_3=10\times 9\times 8\\\\\\{10}_P_3=720[/tex]
Hence, the answer is:
720 ways
Solve each equation (Isolating first)
[tex]3[/tex] · [tex](\frac{1}{8})^{2x} = 12[/tex]
[tex]2[/tex] ·[tex](\sqrt[3]{5})^{4x} = 50[/tex]
[tex]3 \times {( \frac{1}{8} )}^{2x} = 12 \\ \Leftrightarrow {( \frac{1}{8} )}^{2x} = 4 \\ \Leftrightarrow {( {2}^{ - 3}) }^{2x} = {2}^{2} \\ \Leftrightarrow {2}^{ - 6x} = {2}^{2} \\ \Leftrightarrow - 6x = 2 \\ \Leftrightarrow x = - \frac{1}{3} \\ \\ 2 {\sqrt[3]{5}}^{4x} = 50 \\ \Leftrightarrow { \sqrt[3]{5} }^{4x} = 25 \\ \Leftrightarrow {5}^{ \frac{4x}{3} } = {5}^{2} \\ \Leftrightarrow \frac{4x}{3} = 2 \\ \Leftrightarrow 4x = 6 \\ \Leftrightarrow x = \frac{3}{2} [/tex]
Answer to Q1:
x= -1/3
Step-by-step explanation:
We have given the equations.
We have to solve these equations.
The first equation is :
[tex]3.(\frac{1}{8})^{2x}[/tex]
[tex](\frac{1}{8})^{2x}=4[/tex]
[tex](2^{-3x})^{2x}=4[/tex]
[tex]2^{-6x}=4[/tex]
[tex]2^{-6x}=2^{2}[/tex]
As we know that bases are same then exponents are equal.
-6x = 2
x = 2/-6
x=-1/3
Answer to Q2:
x = 3/2
Step-by-step explanation:
The given equation is :
[tex]2.\sqrt[3]{5}^{4x}=50[/tex]
We have to find the value of x.
First,we multiply both sides of equation by 1/2 we get,
[tex]5^{4x/3}=25[/tex]
[tex]5^{4x/3}=5^{2}[/tex]
4x/3=2
4x = 6
x = 3/2
Need help ASAP
What is the area of this triangle
Enter your answer as a decimal in the box
[tex]\boxed{A=43.54cm^2}[/tex]
Step-by-step explanation:To find this area we will use the law of cosine and the Heron's formula. First of all, let't find the unknown side using the law of cosine:
[tex]x^2=12^2+8^2-2(12)(8)cos(65^{\circ}) \\ \\ x^2=144+64-192(0.42) \\ \\ x^2=208-80.64 \\ \\ x^2=127.36 \\ \\ x=\sqrt{127.36} \\ \\ \therefore \boxed{x=11.28cm}[/tex]
Heron's formula (also called hero's formula) is used to find the area of a triangle using the triangle's side lengths and the semiperimeter. A polygon's semiperimeter s is half its perimeter. So the area of a triangle can be found by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] being [tex]a,\:b\:and\:c[/tex] the corresponding sides of the triangle.
So the semiperimeter is:
[tex]s=\frac{12+8+11.28}{2} \\ \\ s=15.64cm[/tex]
So the area is:
[tex]A=\sqrt{15.64(15.64-12)(15.64-8)(15.64-11.28)} \\ \\ \therefore \boxed{A=43.54cm^2}[/tex]
The Homerun Hitter's Academy charges thirty-five dollars per hour for batting lessons, with a registration fee of fifteen dollars per year. Janice's parents paid $155 in the month of August.
Answer:
Step-by-step explanation:
If you are asking how many hours she spent on the batting lessons, we can use an equation to solve this type of problem.
Lets represent the hours she spent batting in august with h.
$35h+15=$155
Since each hour costs 35 dollars, its reasonable that $35 times the number of hours she spent practicing would be the correct way to represent that.
Now, lets solve.
Subtract 15 on both sides.
$35h=$140
Divide both sides by 35 to isolate h.
h=4
She spent four hours on batting lessons that month.
Hope this helps!
The number of hours will be 4 hours.
Let the number of hours used be represented by h.
Based on the question, the equation that will be used in solving the question will be:
15 + (35 × h) = 155
15 + 35h = 155
Collect like terms.
35h = 155 - 15
35h = 140
Divide both side by 35
35h/35 = 140/35.
h = 4.
The number of hours is 4 hours.
Read related link on:
https://brainly.com/question/12432183
A small box of raspberries costs $2. A large box of raspberries costs $6. Use this information to complete the sentence below.
What sentence below
(0.0196N) x (0.016m) =
Answer: [tex]0.0003136\ J[/tex] or [tex]3.136*10^{-4}J[/tex]
Step-by-step explanation:
By definiition, when you multiply 1 Newton (N) by 1 meter (m), the unit obtained is an unit called "Joule", whose symbol is J.
Joule (J) is an unit of energy, work or heat.
Then to solve the exercise, you must multiply 0.0196 N by 0.016 m. Therefore, you obtain that the product is:
[tex](0.0196N)(0.016m)=0.0003136J[/tex] or [tex]3.136*10^{-4}J[/tex]
Answer: 0.000314mn
Step-by-step explanation:
(0.0196N)*(0.016M)
0.000314mn
What describes the number and type of the roots of the equation 4x+7=0
a. 1 imaginary root
b. 1 real root and 1 imaginary root
c. 2 real roots
d. 1 real root
Answer:
D : One Real Root
Step-by-step explanation:
Isolate "4x" by subtracting 7 from both sides.
So we get
4x = -7
Then we divide each side by 4 to get -7/4
x = -7/4 so there is only one real root.
Final answer:
The equation 4x+7=0 is a linear equation with only one real root, which is -1.75. Therefore, the correct option is d. 1 real root.
Explanation:
The given equation 4x+7=0 is a linear equation, not a quadratic equation. To find the roots, we only have one variable raised to the first power, which means this equation will only have one solution. We can solve this by isolating the variable x:
4x = -7
x = -7 / 4
x = -1.75
Therefore, the correct answer is d. 1 real root, as the equation has exactly one real solution and no imaginary roots.
Please help me if you can!
Answer:
y = 7Step-by-step explanation:
We know that the sum of the measures of angles on one side of the parallelogram is 180°.
We have the equation:
(6x - 12) + (132 - x) = 180
6x - 12 + 132 - x = 180 combine like terms
(6x - x) + (-12 + 132) = 180
5x + 120 = 180 subtract 120 from both sides
5x = 60 divide both sides by 5
x = 12
Opposite angles in the parallelogram are congruent.
Therefore:
6y + 18 = 6x - 12
Put the value of x to the equation and solve it for y:
6y + 18 = 6(12) - 12
6y + 18 = 72 - 12
6y + 18 = 60 subtract 18 from both sides
6y = 42 divide both sides by 6
y = 7
Which of the following statements is not true? a) The standard deviation of the sampling distribution of sample mean = σ/√n b) The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean. c) The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. d) The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric for n > 30 or n = 30. e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken. f) None of the above
Answer:
e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.
Step-by-step explanation:
The central limit theorem states that
"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."
This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean. This does not state that the sample mean will always be the same as the population mean.
correct answer is option (c)
The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.
What is Standard deviation?
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.
How Standard deviation is calculated?
Standard deviation is calculated by taking the square root of a value derived from comparing data points to a collective mean of a population. The formula is:
[tex]\begin{aligned} &\text{Standard Deviation} = \sqrt{ \frac{\sum_{i=1}^{n}\left(x_i - \overline{x}\right)^2} {n-1} }\\ &\textbf{where:}\\ &x_i = \text{Value of the } i^{th} \text{ point in the data set}\\ &\overline{x}= \text{The mean value of the data set}\\ &n = \text{The number of data points in the data set} \end{aligned}[/tex]
So, In the given options,
The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken is False, because according Central limit theorem,
regardless of the shape of the population(X): If the sample size is greater than 30. The Sample distribution will be Normal Distribution.
Hence,
The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.
To know more about the Standard deviation refer to the below link:
https://brainly.com/question/475676
#SPJ2
A box contains 48 snack size bags of popcorn the weight of the box when it is empty is 5 ounces the weight of the box with all the bags of popcorn is 35 ounces what is the weight in ounces of each bag of popcorn
each bag weighs 0.625 ounces
The cost of each bag of popcorn will be 0.625 ounces.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
As per the given,
Weight of empty bag = 5 ounce
Weight of full bag = 35 ounce
Weight of popcorns bag = 3 5 - 5 = 30 ounce
Number of bags = 48
Per bag weight = 30/48 = 0.625 ounce
Hence "The cost of each bag of popcorn will be 0.625 ounces".
To learn more about the arithmetic operators,
brainly.com/question/25834626
#SPJ5
Griffin and three friends go golfing. Two of the friends spend $6 each to rent clubs. The total cost for the rented clubs and green fees was $76. Define a variable, and write and solve an equation to find the cost of the green fees for each person.
Answer:
2·6 +4g = 76green fees for each person were $16Step-by-step explanation:
Let g represent the green fee each person pays. Then the cost of the two club rentals and four green fees is ...
2·6 + 4g = 76 . . . . . . the equation for total cost
4g = 64 . . . . . . . . . . . subtract 12
g = 16 . . . . . . . . . . . . divide by 4
The cost of the green fees was $16 per person.
csc x= -√2 for π≤x≤3π/2
Answer:
A
Step-by-step explanation:
We can write this as Sinx by "flipping" the [tex]-\sqrt{2}[/tex].
So we will have: [tex]Sin(x)=-\frac{1}{\sqrt{2} }[/tex]
From basic trigonometry, we know the value of [tex]\frac{1}{\sqrt{2}}[/tex] of sine is of the angle [tex]\frac{\pi}{4}[/tex]
But when is sine negative? Either in 3rd or 4th quadrant. But the answer has to be between 0 and [tex]\frac{3\pi}{2}[/tex], so we disregard 4th quadrant.
To get the angle in 3rd quadrant, we add π to the acute angle of the first quadrant (which is π/4 in our case). Thus we have:
[tex]\frac{\pi}{4}+\pi\\=\frac{\pi +4\pi}{4}\\=\frac{5\pi}{4}[/tex]
A is the right answer.
Please answer this question, will give brainliest!
Answer:
MN = 9.1 cmStep-by-step explanation:
If MN is tangent of a circle then the angle M is a right angle.
We have a dimeter of acircle d = 8 cm.
Therefore the radius CM = 8 cm : 2 = 4cm.
In a right triangle CMN use the Pythagorean theorem:
[tex]CM^2+MN^2=CN^2[/tex]
Substitute CM = 4cm and CN = 9.9 cm:
[tex]4^2+MN^2=9.9^2[/tex]
[tex]16+MN^2=98.01[/tex] subtract 16 from both sides
[tex]MN^2=82.01\to MN=\sqrt{82.1}\\\\MN\approx9.1[/tex]
The area of a rectangle is given by the expression x2 + 5x + 4. If the length of one side is given by x + 2, what is the length of the other side? A. `x + 3` B. `(2)/(x + 2)` C. `x + 3 ? (2)/(x + 2)` D. `x + 3 + (2)/(x + 2)`
Answer:
x + 3 - 2/ (x + 2).
Step-by-step explanation:
The length of the other side = area / length of the known side
= (x^2 + 5x + 4) / (x + 2)
Do the long division:
x + 2 ( x^2 + 5x + 4 ( x + 3 < - quotient
x^2 + 2x
------------
3x + 4
3x + 6
----------
- 2 <--- remainder.
The answer is x + 3 - 2/ (x + 2).
[15] full joint probability distributions consider this full joint probability distribution involving four boolean-valued random variables (a-d): a b c d prob f f f f 0.10 f f f t 0.01 f f t f 0.05 f f t t 0.15 f t f f 0.02 f t f t 0.03 f t t f 0.04 f t t t 0.05 t f f f 0.20 t f f t 0.01 t f t f 0.01 t f t t 0.03 t t f f 0.02 t t f t 0.04 t t t f 0.08 t t t t ? i. compute p(a = true and b = true and c = true and d = true). ii. compute p(a = false | b = true and c = true and d = false). iii. compute p(b = false | a = false and d = true). iv. compute p(b = false). v. compute p(a = false or b = true | c = true or d = true).
HELP PLEASE!!!!!!!!!!!!!!MATH IS HARDDDDDDDDDDDDDD
Answer:
92
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
140 = x+2 + 2x
Combine like terms
140 = 3x +2
Subtract 2 from each side
140-2 = 3x+2-2
138 = 3x
Divide by 3
138/3 = 3x/3
46=x
We want to find angle B
B = 2x
B = 2(46)
B = 92
Sphere A is similar to sphere B. If the radius of sphere A is 3 times the radius of sphere B, then the volume of sphere A is times the volume of sphere B.
Answer:
27 times
Step-by-step explanation:
Given that sphere A is similar to sphere B
Let radius of sphere B be x. Then the radius of
sphere A be 3 times radius of sphere B = 3x
Volume of sphere A = [tex]V_A=\frac{4}{3} \pi (3x)^3\\V_A=36 \pi x^3[/tex]
Volume of sphere B = [tex]V_B = \frac{4}{3} \pi x^3[/tex]
Ratio would be
[tex]\frac{V_A}{V_B} =\frac{36 \pi x^3}{\frac{4}{3}\pi x^3 } \\=27[/tex]
i.e. volume of sphere is 27 times volume of sphere B.
Answer: 27
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
about what point on parabola y=x^2 is 5 units away from the origin along the curve
the distance from the origin is 5, so
sqrt(x²+y²)=5
x²+y²=25
substitue y=x²
y+y²=25
y²+y-25=0
solve using calculator or the formula
to get
y =( -1+sqrt(1+4*25))/2
or y = (-1-sqrt(1+4*25))/2
the second solution is rejected because a square cannot be negative
the value of x is the positive or negative (sqrt... or -sqrt...) or y
which statements are true about these lines? check all that apply. please help!
Answer:
we cant see what the lines look like soooo
Step-by-step explanation:
is f(x)= x+12/5 a function
Answer:
Yes
Step-by-step explanation:
This is a function since it is one to one. The writing is unclear here though since the function could be f(x) = x + (12/5) or f(x) = (x+12)/5. Either way the function passes the vertical line test when graphed. Both functions show a linear function. See the two attached graphs. Both are functions since the vertical line does not cross more than once through the function when drawn.
Petra wants to buy a skateboard. The skateboard deck usually costs $37.50, but it is on sale for 20% off. If the sales tax rate is 5.2%, how much will Petra pay for the skateboard deck in all?
A. $30.00
B. $31.56
C. $31.95
D. $39.45
Answer:31.56
Step-by-step explanation:
take 37.50 and divide it by 100
then multiply that by 80
you should get 30,
30 is 80% of 37.50 which is 20% off of the original price
then you divide 30 by 100 and multiply it by 5.2
this will get you 1.56
add that to 30 and you get 31.56
PLZ HELP ME i need Lesson 11: Linear Functions Unit Test Algebra 1 A, Part 2 Unit 2: Linear Functions i cant fail this class plz help
the first question is,
For the data in the table,does y vary directly with x? If it does , write an equation for the direct variation.
x | y
8 |28
16 |56
20|70
A.)yes;y=5x
B.)yes;x+20
C.)yes;3.5x
D.) no;y does not vary directly with x
PLZ HELP ITS FOR CONNECTIONS ACADEMY!!!!!!!!
Answer:
so ans is C.)yes;3.5x
Step-by-step explanation:
x | y
8 |28
16 |56
20|70
8*3.5=28
16*3.5=56
20*3.5=70
so ans is C.)yes;3.5x
The y varies directly with x and the proportional relation is y = 3.5x option (C) yes;3.5x is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
We have data in the table:
x | y
8 |28
16 |56
20|70
y ∝ x
y = kx
Plug x = 8 y = 28
28 = 8k
k = 3.5
y = 3.5x
Thus, the y varies directly with x and the proportional relation is y = 3.5x option (C) yes;3.5x is correct.
Learn more about the proportional here:
brainly.com/question/14263719
#SPJ2
Determine the values. The value of x is . The measure of is degrees. The measure of is degrees.
Answer:
X= 5
EF= 58 degrees
GH= 55 degrees
Step-by-step explanation:
Answers on edg.
Answer:
14
Step-by-step explanation:
Which geometric object is defined as the set of all points in a plane equidistant from a single point and a single line
Answer:
parabola
Step-by-step explanation:
That would be a parabola. The "single point" is the "focus" of the parabola, and the "given line" is the "directrix."
Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y= -7 sec x
Answer:
Option c. Reflection across the x-axis and vertical stretch by a factor of 7
Step-by-step explanation:
If the graph of the function [tex]y = cf(x)[/tex] represents the transformations made to the graph of [tex]y = f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor a.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor a.
If [tex]c <0[/tex] then the graph is reflected on the x axis.
In this problem we have the function [tex]y = -7secx[/tex] and our paretn function is [tex]y = secx[/tex]
therefore it is true that
[tex]c = -7\\\\|-7|> 1\\\\-7 <0[/tex].
Therefore the graph of [tex]y = secx[/tex] is stretched vertically by a factor of 7 and is reflected on the x-axis
Finally the answer is Option c
Determine all numbers at which the function is continuous.
If the graph of any function is an unbroken curve, then the function is continuous. Let's study the function at the the point [/tex]x=5[/tex]:
At this point the function has the following value:
[tex]f(5)=-\frac{3}{4}[/tex], so the function in fact exists here, but let's find the limit here using:
[tex]f(x)=\frac{x^2-7x+10}{x^2-14x+45}[/tex]
So:
[tex]\underset{x\rightarrow5}{lim}\frac{x^2-7x+10}{x^2-14x+45}[/tex]
By factoring out this function we have:
[tex]\underset{x\rightarrow5}{lim}\frac{(x-2)(x-5)}{(x-5)(x-9)} \\ \\ \therefore \underset{x\rightarrow5}{lim}\frac{(x-2)}{(x-9)} \\ \\ \therefore \frac{(5-2)}{(5-9)}=-\frac{3}{4}[/tex]
Since [tex]\underset{x\rightarrow5}{lim}f(x)=f(5)[/tex] then the function is continuous here.
Let's come back to our function:
[tex]f(x)=\frac{x^2-7x+10}{x^2-14x+45}[/tex]
If we factor out this function we get:
[tex]f(x)=\frac{(x-2)}{(x-9)}[/tex]
Notice that at x = 9 the denominator becomes 0 implying that at this x-value there is a vertical asymptote. The graph of this function is shown below and you can see that at x = 9 the function is not continous
Therefore, the answer is:
b. continous at every point exept [tex]x=9[/tex]
Answer:
B: continuous at every real number except x = 9
Step-by-step explanation: EDGE 2020
What is the slope-intercept form of the function that contains the points (6, 2) and (4, 8)?
Answer:
y = -3x + 20
Step-by-step explanation:
See attached photo for explanation
What are the different measurements for angles and how do we convert between them? Explain with examples of your own.
Angles are usually given in degrees or in radians.
A circle is 360 degrees.
To convert degrees to radians, multiply the known degree by π/180.
Example 45 degrees = 45 x π/180 = 0.7854 radians.
To convert radians to degrees, multiply the known radian by 180/π.
5 radian = 5 x 180/π = 286.48 degrees.
The correlation between the measurements is written below.
What is an Angle ?An angle is a combination of two rays with a common endpoint.
The endpoint is called as the vertex of the angle,the rays are called the sides.
The various units in which angle is measure are Degree, radians and revolutions
A revolution is the measure of an angle formed when the initial side rotates all the way around its vertex until it reaches its initial position
One radian (1 rad) is the measure of the central angle (an angle whose vertex is the center of a circle) that intercepts an arc whose length is equal to the radius of the circle.
A degree is equal to 360 revolutions.
The correlation between the measurements can be written as
[tex]\rm 1 \;radian =(\dfrac{180}{\pi })^o = \dfrac{1}{2\pi } revolution[/tex]
For example 30° = π/6 radian = 1/12 revolutions
To know more about Angle
https://brainly.com/question/13954458
#SPJ2
A line has the equation 3x ? 4y = 1. Choose the equation of a line that is parallel to the given line.
Answer:
Find a line which also has 3/4 as the slope or 3x - 4y in standard form.
Step-by-step explanation:
If the line is 3x - 4y = 1 then the line which is parallel will have the same coefficients of x and y. Parallel lines never cross and to ensure this have the same slope. The slope is a ratio which can be solved for in an equation using the coefficients of x and y. Here the slope is:
3x - 4y = 1
-4y = -3x + 1
y = 3/4x - 1/4.
Find a line which also has 3/4 as the slope or 3x - 4y in standard form.
Answer: y= 3/4x +5
Step-by-step explanation: just did it
Please help me with this :)
Answer:
It is the answer C
Step-by-step explanation:
Sold the equation. Round to the nearest hundredth.
17 · [tex]1.8^{-x+7} = 5[/tex]
Answer:
Final answer is approx x=4.26.
Step-by-step explanation:
Given equation is [tex]1.8^{-x+7} = 5[/tex]
Now we need to solve equation [tex]1.8^{-x+7} = 5[/tex] and round to the nearest hundredth.
[tex]1.8^{-x+7} = 5[/tex]
[tex]\log(1.8^{-x+7}) = \log(5)[/tex]
[tex](-x+7)\log(1.8) = \log(5)[/tex]
[tex](-x+7) = \frac{\log(5)}{\log(1.8)}[/tex]
[tex](-x+7) = \frac{0.698970004336}{0.255272505103}[/tex]
[tex]-x+7 = 2.73813274192[/tex]
[tex]-x = 2.73813274192-7[/tex]
[tex]-x =−4.26186725808[/tex]
[tex]x =4.26186725808[/tex]
Round to the nearest hundredth.
Hence final answer is approx x=4.26.