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Solution
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Related Questions
Suppose that you want to buy 6 different books and the order that you buy them does not matter. Then thenumber of ways to choose 6 books from 44 available books is
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We have that the order doesn't matter without repetition, so should use combinations that are represented by the next formula:
[tex]C=\frac{n!}{r!(n-r)!}[/tex]Where n is the total of books and r the numbers of the group, in this case, 6 differents books.
Replace these values:
[tex]\frac{44!}{6!(44-6)!}[/tex][tex]C=\frac{44!}{6!(38)!}=7059052\text{ ways to choose 6 books from 44 available}[/tex]Write the percent as decimal 49%
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Solution;
Given: The given number in percentage is 49 %
Required: Decimal value of given percentage.
Explanation:
Convert percentage into decimal as follows:
[tex]49\text{ \%=}\frac{49}{100}[/tex][tex]49\text{ \%=0.49}[/tex]Therefore, the required answer is 0.49
Final answer: The de
Solve for n: 400(1.16)^n=35,120
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The given equation is:
[tex]400\left(1.16\right)^n=35120[/tex]It is required to solve the equation for the value of n.
Divide both sides of the equation by 400:
[tex]\begin{gathered} \frac{400\left(1.16\right)^n}{400}=\frac{35120}{400} \\ \\ \Rightarrow\left(1.16\right)^n=\frac{439}{5} \end{gathered}[/tex]Take the logarithm of both sides of the equation:
[tex]\begin{gathered} \log(1.16)^n=\log\left(\frac{439}{5}\right) \\ \text{ Apply the power property of logarithms:} \\ \Rightarrow n\log(1.16)=\log\left(\frac{439}{5}\right) \end{gathered}[/tex]Divide both sides by log (1.16):
[tex]\begin{gathered} \frac{n\log(1.16)}{\log(1.16)}=\frac{\log\left(\frac{439}{5}\right)}{\log(1.16)} \\ \Rightarrow n=\frac{\operatorname{\log}(\frac{439}{5})}{\operatorname{\log}(1.16)}\approx30.151 \end{gathered}[/tex]The value of n is about 30.151.
How do you know if a sequence is a geometric sequence. A It has a common difference. B It has a common ratio.
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A geometric sequence in which each next term is found by multiplying the previous term by a constant; therefore, every adjacent pair on entires in a geometric sequence have a common ratio. Hence, if any two consecutive entries in a sequence have a common ratio, it is a geometric series; therefore, choice B is the correct one to choose.
QThe image of point A (3, 4) under translation Tis A' (-1,6). What is the translation rule? worth 50 points guy's can someone please give me an answer really quick please!!!
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Here, we want to find the translation rule
Set m to 0.0 to create a horizontal line. Then set x, to 3.0 and y, to -2.0.
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We have the following:
the equation in the slope form is:
[tex]y=mx+b[/tex]m = 0 and goes through (3, -2)
therefore:
[tex]\begin{gathered} -2=3\cdot0+b \\ b=-2 \end{gathered}[/tex]now,
[tex]\begin{gathered} m=0 \\ \text{point = (3,-2)} \\ y=-2 \end{gathered}[/tex]Pick a situation related to your major that would be modeled by one of the models discussed in class. Describe why this model would be helpful. Models are any application/word problem used for exponential/logarithmic functions. For example, exponential growth or decay are models of exponential functions. Now, choose one that would fit with your career path and describe why it would be helpful.
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To measure sound, we use the measure decibel which in fact is a logartimic funcion of the amplitude of a soud
To measure eartquakes, we use the Richter scale whci is a logaritmic function of the amplitude of the force of an earthquake
To calculate how long a body has been dead, the coroner must know how long the body temperature has not been at 98.6 degrees. Because the rate of the body cooling is proportionate to temperature differences between the body and its surroundings, the answer is found by calculating exponential decay using logarithms.
The graph of a function g is shown below.Find g (0) and find one value of x for which g(x) = 4,
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From the graph provided,
a) For g(0), on the graph,
[tex]g(0)=-2[/tex]b) One value of x for which g(x) = 4 is given below as,
[tex]\begin{gathered} g(x)=4 \\ x=3\text{ where g(x) = 4} \end{gathered}[/tex]Hence, g(0) = -2 and one of the value of x for which g(x) = 4 is 3
fing the length of the missing side
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The area is given as
[tex]x^2-6x+9[/tex]We can either divide the area by the side given and get the other side
OR
We can simply factorize the area and hence determine the two factors that were multiplied together. Note that one factor has already been given (that is x-3).
To factorize the polynomial;
[tex]\begin{gathered} x^2-6x+9 \\ =(x-3)(x-3) \end{gathered}[/tex]This means the other side is also (x - 3)
henry has one bag of groceries that weighs 9 pounds he has another bag of groceries that weighs 62 ounces how many ounces of grocery bags weigh altogether
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You can first use a rule of three to convert 9 pounds of groceries to ounces:
[tex]\begin{gathered} 1\text{ pound}\rightarrow16\text{ ounces} \\ 9\text{ pounds}\rightarrow x\text{ ounces} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{9\text{ pounds}\cdot16\text{ ounces}}{1\text{ pound}} \\ x=\frac{9\cdot16\text{ ounces}}{1} \\ x=\frac{9\cdot16}{1}\text{ ounces} \\ x=9\cdot16\text{ ounces} \\ x=144\text{ ounces} \end{gathered}[/tex]Now, add up all the groceries Henry has:
[tex]\begin{gathered} \text{Total weight of groceries}=9\text{ pounds }+62\text{ ounces} \\ \text{Total weight of groceries}=144\text{ ounces }+62\text{ ounces } \\ \text{Total weight of groceries}=206\text{ ounces } \end{gathered}[/tex]Therefore, in total the bags of groceries of Henry weight 206 ounces.
What is the determinant of H= 0 2 3-1 3 56 3 -2
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1) Since this is a Matrix 3x3 we can make use of the Sarrus Rule to find the determinant of this Matrix:
[tex]\begin{bmatrix}0 & 2 & 3 \\ -1 & 3 & 5 \\ 6 & 3 & -2 \\ \end{bmatrix}[/tex]2) We can do that by copying two columns to the right of the Matrix, and multiplying the entries, this way:
Now, let's add algebraically each diagonal and subtract from the other like this:
[tex]\begin{gathered} \det (H)=\lbrack60-9+0\rbrack-\lbrack54+4+0\rbrack \\ \det H)=51-58 \\ \det (H)=-7 \end{gathered}[/tex]f(x) = -3x² + 6x + 1
find f(6)
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Step-by-step explanation:
this is a college question ? and you don't know how to do this ?
come on, remember ! I don't know how you ever made it into college, if you don't understand this.
with f(6) we say x = 6, and now we simply have to put 6 into all the places of x and calculate.
f(6) = -3×6² + 6×6 + 1 = -3×36 + 36 + 1 = -2×36 + 1 =
= -72 + 1 = -71
Write the point-slope form of the equation of the line through the points (-1, -1) and (2, 4)
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The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.
The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.
The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.
Slope m = (y2-y1) / (x2-x1)
Let,
(x1, y1) = (-1, -1)
(x2, y2) = (2, 4)
Slope (m) = ((4) - (-1)) / ((2) - (-1))
= 5/3
y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))
=> y+1 = 5/3(x + 1)
=>y = 5/3(x+1)-1
Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.
To know more about point-slope form:
https://brainly.com/question/24907633
You are to show how to correctly graph y = -x - 5
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Answer and Explanation:
The slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = the slope of the line
b = the y-intercept of the line
So given the equation;
[tex]y=-x-5[/tex]Comparing the two equations, we can deduce the following;
* m = -1
This means that the line will have a negative slope
* b = -5
This means that the line will cut the y-axis at -5.
We can now choose values for x and determine the corresponding values of y and then proceed to plot the graph.
When x = 1;
[tex]\begin{gathered} y=-1-5 \\ y=-6 \end{gathered}[/tex]When x = 0,
[tex]\begin{gathered} y=-0-5 \\ y=-5 \end{gathered}[/tex]When x = -2,
[tex]\begin{gathered} y=-(-2)-5 \\ y=2-5 \\ y=-3 \end{gathered}[/tex]When x = -4,
[tex]\begin{gathered} y=-(-4)-5 \\ y=4-5 \\ y=-1 \end{gathered}[/tex]When x = -6;
[tex]\begin{gathered} y=-(-6)-5 \\ y=6-5 \\ y=1 \end{gathered}[/tex]With the above values and information, we can then go ahead and plot our graph as shown below;
Each of these is a pair of equivalent ratios for each pair explain why they are equivalent ratios or draw a diagram that shows why they are equivalent ratios 2:7 and 10,000:35,000
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Given this pair of equivalent ratios:
[tex]\begin{gathered} 2:7 \\ \\ 10,000:35,0000 \end{gathered}[/tex]It is important to remember that equivalent ratios represent the same value, but they have different forms.
Equivalent ratios can be obtained by multiplying both parts of a ratio by a common number.
In this case, you can identify that:
[tex]2\cdot5,000=10,000[/tex][tex]7\cdot5,000=35,000[/tex]Therefore, both parts of the original ratio can be multiplied by 5,000 in order to get the other ratio.
Hence, the answer is: They are equivalent ratios because they have the same value when they are simplified, and the second ratio can be obtained by multiplying both parts of the first ratio by 5,000.
Jose Is cooking a roast. The table below gives the temperature (1) of the roast (In degrees Celsius), at a few timest (In minutes) after he removed it from theoven.Timet Temperature R (1)(minutes)(c)010305070226.6205.6157.6119.661.6(a) Find the average rate of change for the temperaturefrom 0 minutes to 10 minutes.0 °C per minute(b) Find the average rate of change for the temperaturefrom 30 minutes to 50 minutes.[ °C per minute
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(a). From the given table,
R(0)=226.6
R(10)=205.6
The average rate of change for the temperature from 0 minutes to 10 minutes is
[tex]\begin{gathered} A=\frac{R(10)-R(0)}{10-0} \\ =\frac{205.6-226.6}{10} \\ =-2.1 \end{gathered}[/tex](a) The average rate of change for the temperature from 0 minutes to 10 minutes is -2.1 (in degree centrigrade)
Minus sign implies that the temperature is deacreasing with increasing time
(b). Again,
R(30)=157.6
R(50)=119.6
The average rate of change for the temperature from 30 minutes to 50 minutes is
[tex]\begin{gathered} A=\frac{R(50)-R(30)}{50-30} \\ =\frac{119.6-157.6}{20} \\ =-1.9 \end{gathered}[/tex](b) The average rate of change for the temperature from 30 minutes to 50 minutes is -1.9 (in degree centrigrade)
Minus sign implies that the temperature is deacreasing with increasing time
1/ (gg^2 e^5)^2 Write your answer with only positive exponents
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ANSWER
[tex]\frac{1}{g^6e^{10}}[/tex]EXPLANATION
In the denominator, we have the product of g and g². The product of two powers with the same base is the base raised to the sum of the exponents,
[tex]\frac{1}{(gg^2e^5)^2}=\frac{1}{(g^{2+1}e^5)^2}=\frac{1}{(g^3e^5)^2}[/tex]Now, we also have the power of a product. The exponents can be distributed into the multiplication,
[tex]\frac{1}{(g^3e^5)^2}=\frac{1}{(g^3)^2(e^5)^2}[/tex]And finally, for both g and e, we have the power of a power. The result is the base raised to the product of the exponents,
[tex]\frac{1}{(g^3)^2(e^5)^2}=\frac{1}{g^{3\cdot2}e^{5\cdot2}^{}}=\frac{1}{g^6e^{10}}[/tex]Hence, the simplified expression is,
[tex]\frac{1}{g^6e^{10}}[/tex]Maria invested her savings in two investment funds. The amount she invested in Fund A was $7000 less than the amount she invested in Fund B. Fund Areturned a 7% profit and Fund B returned a 3% profit. How much did she invest in Fund B, if the total profit from the two funds together was $1610?
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It is given that,
The amount she invested in Fund A was $7000 less than the amount she invested in Fund B.
So, A=B-7000
And it is given that, Fund A returned a 7% profit and Fund B returned a 3% profit.
The total profit from the two funds together was $1610.
It can be written as,
7% of A +3% of B=1610
Substitute A=B-7000, we get
7% of (B-7000) +3% of B=1610
On solving we get,
[tex]\begin{gathered} \frac{7}{100}(B-7000)+\frac{3}{100}B=1610 \\ \frac{7}{100}B-490+\frac{3}{100}B=1610 \\ \frac{10}{100}B-490=1610 \\ \frac{1}{10}B=1610+490 \\ \frac{1}{10}B=2100 \\ B=21000 \end{gathered}[/tex]Hence, the investment in fund B is $21,000.
need help- don’t mind the writing in pencil I forgot to erase it
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We will deteremine the length of segment TV as follows:
[tex]A=\frac{WU\cdot TV}{2}\Rightarrow200=\frac{16\cdot TV}{2}[/tex][tex]\Rightarrow400=16\cdot TV\Rightarrow TV=25[/tex]So, the lenght of segment TV is 25 centimeters.
a cylinder has a volume of 105 and a radius of eight what is the height of the cylinder give an exact answer or approximation to three decimals
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We are asked to determine the height of a cylinder given its radius and its volume. To do that we will use the formula for the volume of a cylinder:
[tex]V=\pi r^2h[/tex]now, we solve for the height, we get:
[tex]\frac{V}{\pi r^2}=h[/tex]Now, we plug in the values:
[tex]\frac{105}{\pi(8)^2}=h[/tex]Solving the operations:
[tex]0.522=h[/tex]Therefore, the height is 0.522.
if sin = -3/5 and cos >0 what is exact value of cot?5/3-4/33/4-4/5
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Explanation
Given the following information:
[tex]\begin{gathered} Sin=\frac{-3}{5} \\ Cos>0 \end{gathered}[/tex]This implies that the value of sin is negative while that of cos is positive.
This occurs in the fourth quadrant. This also means that the value of tan is negative.
We know that sin uses the value of the opposite and the hypotenuse.
We need to determine the value of the adjacent.
[tex]\begin{gathered} Adjacent=\sqrt{Hyp^2-Opp^2} \\ where \\ Hyp=5 \\ Opp=3 \end{gathered}[/tex][tex]\begin{gathered} Adjacent=\sqrt{5^2-3^2}=\sqrt{25-9}=\sqrt{16} \\ Adj=4 \end{gathered}[/tex]We know that cot is the reciprocal of tan. The value of tan is given as:
[tex]\begin{gathered} Tan=\frac{Opp}{Adj}=\frac{3}{4} \\ But\text{ tan is negative in the fourth quadrant. } \\ \therefore Tan=\frac{-3}{4} \end{gathered}[/tex]We can now determine the value of cot to be:
[tex]Cot=\frac{-4}{3}(reciprocal\text{ of tan\rparen}[/tex]Hence, the answer is the second option i.e. -4/3.
what is the slope of the line described by 5x+7y=19
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Answer:
-5/7
Explanation:
Given the equation 5x+7y = 19
The standard form of an equation is y = mx+c
m is the slope
c is the intercept of a line
Make y the subject of the formula from the given equation
5x+7y = 19
7y = -5x + 19
Divide through by 7
7y/7 = -5x/7 + 19/7
y = -5/7 x + 19/7
Comparing with general formula;
mx = -5/7 x
m = -5/7
Hence the slope of the line is -5/7
Arectangular field has an area of 646 square feet. The width of the field is 19 feetWite a number in the box to show the missing measurement What is the length of the field?
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The area of a rectangle is
[tex]A=19\cdot x=76[/tex]x is the number missing in the box
[tex]x=\frac{76}{19}=4[/tex]the length of the field is 30+4 =34 feet
what are the points that are on the graph of the line 2x + 4y = 20
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Answer:
The points are 10 on the x-axis, and 5 on the y-axis
Explanation:
Given the line:
2x + 4y = 20
The values that satisfy this equation are x = 10, y = 5
The points are 10 on the x-axis, and 5 on the y-axis
Look at the graph of the line below:
The line intersects the x-axis at point 10, and the y-axis at point 5
complete the Pattern 444 4440 44,400 there are three empty lines I need to finish the pattern
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Given:
d. 444 4,440 44,400
e. 9.5 950 9500
The pattern for d as you can see all numbers have 444 but they keep adding extra 0's to each number.
So the next number should have another extra 0 after 44400.
The pattern for all parts a to e seem to be multiplying each number by 10 or dividing by 10 that is why for d. 444 has no 0's but then if you multiply by 10 you get 4440.
If you do 4440*10 you get 44400.
Answer:
The same pattern applies to e.
For the first blank divide 9.5 by 10 so then 9.5 ÷ 10 = 0.95
For the 2nd blank. Multiply by 10 to 95,000 so you get 950,000. Notice how 950,000 has an extra 0.
3rd blank should be 9500000
The triangle is a 45°-45°-90° triangle.x√2 = 66²36X =(√2)²x = 18Did not multiply the numerator by the radicalShould have squared the denominator only.No ErrorShould have squared the numerator onlyJUN1O6V2=82
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Answer:
Did not multiply the numerator by the radical
Explanation:
The hypotenuse of a 45-45-90 triangle is equal to the leg times √2.
In this case, the leg is x and the hypotenuse is 6, so we have the following equation
hypotenuse = leg √2
6 = x √2
To solve for x, we get
[tex]\begin{gathered} x\sqrt{2}=6 \\ \\ x=\frac{6}{\sqrt{2}} \end{gathered}[/tex]Then, we need to multiply the numerator and denominator by √2, so
[tex]x=\frac{6}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{6\sqrt{2}}{(\sqrt{2})^2}[/tex]Therefore, the solution is equal to
[tex]x=\frac{6\sqrt{2}}{2}=3\sqrt{2}[/tex]Therefore, the error in the process was that they did not multiply the numerator by the radical
Telephone numbers are in the form NYZ-ABC-XXXX. the following restrictions were placed; N can only be numbers: 2-9; Y can only be numbers 0-7 and A&C cannot be 2. how many phone numbers are there?
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Answer
The answer = 5,184,000,000
There are 5,184,000,000 possible phone numbers.
Explanation
The question told us that telephone numbers are in the form NYZ-ABC-XXXX, then proceeds to give us the restrictions on some of the positions available.
- N can only be numbers: 2-9;
- Y can only be numbers 0-7
- and A&C cannot be 2
We are then told to calculate the number of phone numbers possible.
This question is a special type of permutation and combination.
To solve it, it will be a multiplication of the possible numbers that can take up each position.
N, can only be numbers 2 to 9. Number of possible digits = 8
Y, can only be numbers 0 to 7. Number of possible digits = 8
Z, no restriction, can have numbers 0 to 9. Number of possible digits = 10
A, number cannot be 2. Number of possible digits = 9
B, no restriction, can have numbers 0 to 9. Number of possible digits = 10
C, number cannot be 2. Number of possible digits = 9
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
Total number of possible phone numbers
= 8 × 8 × 10 × 9 × 10 × 9 × 10 × 10 × 10 × 10
= 5,184,000,000
Hope this Helps!!!
At a charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 5 over 18. Find the odds in favor of receiving a gift.
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Odds in favor of receiving a gift = 5/13
Explanation:The probability of receiving a gift, P(R) = 5/18
Probability of not receiving a gift, P(nR) = 1 - 5/18 = 13/18
The odds in favor of receiving a gift is calculated below:
[tex]Odds(R)=\frac{P(R)}{P(nR)}[/tex]Therefore:
[tex]\begin{gathered} Odds(R)=\frac{5}{18}\div\frac{13}{18} \\ \\ Odds(R)=\frac{5}{18}\times\frac{18}{13} \\ \\ Odds(R)=\frac{5}{13} \end{gathered}[/tex]Odds in favor of receiving a gift = 5/13
Points L,M and N are collinear.M is between L and N. You are given LM=13 and LN=20.Find the length of MN
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ANSWER
MN = 7
EXPLANATION
Let's draw a diagram first:
Since all the points are collinear we can use the segment addition postulate:
[tex]LM+MN=LN[/tex]Replacing with the values we know:
[tex]13+MN=20[/tex]And solving for MN:
[tex]MN=20-13=7[/tex]We have that the length of segment MN is 7.
a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
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a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
the equation is equal to
Multiply the number of tanks by 24
so
24c
the answer is 24cPart 2
1/13 is the reciprocal of 13
because
(13)(1/13)=1
a number multiplied by its reciprocal is equal to 1
