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]What postulate or theorem is used in the picture below?
If we have that in two triangles we have that the corresponding sides and the included angle are congruent, then we can say that both triangles are congruent. This is called the SAS (side-angle-side) postulate.
Then, in summary, the method that proves that both triangles are congruent is SAS (Side-Angle-Side) postulate (second option).
Can you please check number 4 and check parts a, b, and c to make sure it’s right please
if the scale in the drawing is 1 centimeter= 20 meters, then:
a) Playground 3 centimeters.
[tex]\begin{gathered} \frac{1cm}{20m}=\text{ }\frac{3cm}{x}= \\ \text{ x\lparen1cm\rparen=\lparen20m\rparen\lparen3cm\rparen} \\ x=\text{ 60 meters} \end{gathered}[/tex]b) Tennis courts= 5.2cm
[tex]\begin{gathered} \frac{1cm}{20m}=\text{ }\frac{5.2cm}{x} \\ x(1cm)=\text{ \lparen5.2cm\rparen\lparen20m\rparen} \\ x=\text{ 104 meters} \end{gathered}[/tex]c) Walking trail= 21.7 cm
[tex]\begin{gathered} \frac{1cm}{20m}=\frac{21.7cm}{x} \\ \\ x(1cm)=(21.7cm)(20m) \\ x=\text{ 434 meters} \end{gathered}[/tex]If mQR = 80° and mQS = 150°, what is m
we have that
m
by exterior angle
so
substitute given values
m
mUse a 30 - 60 - 90 triangle to find the tangent of 60 Degrees
Let's put more details in the given figure to better understand the solution:
Let's now determine the Tangent of 60 degrees:
[tex]\text{ Tangent (60}^{\circ})\text{ = }\frac{\text{ Opposite}}{\text{ Adjacent}}[/tex][tex]\text{ = }\frac{\text{ }\sqrt[]{3}}{1}[/tex][tex]\text{ Tangent (60}^{\circ})\text{ = }\sqrt[]{3}[/tex]Therefore, the tangent of 60 degrees is √3.
The answer is Option 1 : √3
Manuel used pattern blocks to build the shapes below. The block marked A is a square, B is a trapezoid, C is a rhombus (aparallelogram with equal sides), and D is a triangle. Find the area of each of Manuel's shapes.
Solving for area of first figure
Recall the following formula for area of 2D figures
[tex]\begin{gathered} A_{\text{square}}=s^2 \\ A_{\text{trapezoid}}=\frac{a+b}{2}h \end{gathered}[/tex]The first figure consist of 2 figures with a square of side length of 2.5 cm, and a trapezoid with length 2.5 cm for the upper base, 5 cm for the lower base, and 2 cm for the height.
Calculate the area by getting the sum of the areas of the two figures
[tex]\begin{gathered} \text{Square: }s=2.5\text{ cm} \\ \text{Trapezoid: }a=2.5\text{ cm},b=5\text{ cm},h=2\text{ cm} \\ \\ A=s^2+\frac{a+b}{2}h \\ A=(2.5\text{ cm})^2+\frac{2.5\text{ cm}+5\text{ cm}}{2}\cdot2 \\ A=6.25\text{ cm}^2+\frac{7.5\text{ cm}}{\cancel{2}}\cdot\cancel{2}\text{ cm} \\ A=13.75\text{ cm}^2 \end{gathered}[/tex]The area of the first figure therefore is 13.75 square centimeters.
Solving for the area of the second figure
Recall the following areas for 2D figures
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}bh \\ A_{\text{rhombus}}=bh \end{gathered}[/tex]Using the same procedures as above, we get the following
[tex]\begin{gathered} \text{Triangle: }b=2.5\text{ cm},h=2.2\text{ cm} \\ \text{Rhombus: }b=2.5\text{ cm},h=2\text{ cm} \\ \\ A=\frac{1}{2}(2.5\text{ cm})(2.2\text{ cm})+(2.5\text{ cm})(2\text{ cm}) \\ A=\frac{1}{2}(5.5\text{ cm}^2)+5\text{ cm}^2 \\ A=2.75\text{ cm}^2+5\text{ cm}^2 \\ A=7.75\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the second figure is 7.75 square centimeters.
Quadrilateral A'B'C'D'is the image of quadrilateral of ABCD under a rotation of about the origin (0,0)a. -90b. -30c. 30d. 90
In this problem we have a couterclockwise about the origin
sp
Verify
option D
rotation 90 degrees counterclockwise
(x,y) -----> (-y,x)
so
A(-2,3) ------> A'(-3,-2) ------> is not ok
therefore
answer is option CHow many different combinations of nine different carrots can be chosen from a bag of 20? O 125,970 O 167,960
We have a bag of 20 carrots, all different, and we have to calculate the possible combinations in groups of 9 carrots.
We can calculate this with the formula for combinations (as the order does not matter):
[tex]_{20}C_9=\binom{20}{9}=\frac{20!}{9!(20-9)!}=\frac{20!}{9!11!}=167960[/tex]Answer: there are 167,960 possible combinatios
The accompanying table shows the value of a car over time that was purchased for 13700 dollars, where x is years and y is the value of the car in dollars Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth . Using this equation , determine the value of the car, to the nearest cent , after 12 years ,
ANSWER
[tex]y=13700(0.919)^x[/tex]Value of the car after 12 year: $4971.72
EXPLANATION
The exponential regression equation is
[tex]y=ab^x[/tex]Using the values of the table we can find both a and b. Note that a is the value of y when x = 0, so a = 13700.
For b replace a, and x and y with the next values of the table:
[tex]\begin{gathered} 12590=13700b^1 \\ b=\frac{12590}{13700} \\ b\approx0.919 \end{gathered}[/tex]The equation is
[tex]y=13700(0.919)^x[/tex]To find the value of the car after 12 years, replace x = 12:
[tex]y=13700(0.919)^{12}\approx4971.72[/tex]Find the length of an arc of a circle whose central angle is 212º and radius is 5.3 inches.Round your answer to the nearest tenth.
The formula for the arc length is,
[tex]L=2\pi r\cdot\frac{\theta}{360}[/tex]Substitute the values in the formula to determine the arc length.
[tex]\begin{gathered} L=2\pi\cdot5.3\cdot\frac{212}{360} \\ =19.61 \\ \approx19.6 \end{gathered}[/tex]So answer is 19.6 inches.
There are two types of tickets sold at the Canadian Formula One Grand Prix race. The price of 6 grandstand tickets and 4 general admission tickets is $3200. The price of 8 grandstand tickets and 8 general admission tickets is $4880. What is the price of each type of ticket?
Let:
x = price of the grandstand ticket
y = price of the general admission ticket
The price of 6 grandstand tickets and 4 general admission tickets is $3200, so:
[tex]6x+4y=3200[/tex]The price of 8 grandstand tickets and 8 general admission tickets is $4880, so:
[tex]8x+8y=4880[/tex]Let:
[tex]\begin{gathered} 6x+4y=3200_{\text{ }}(1) \\ 8x+8y=4880_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} 2(1)-(2)\colon_{} \\ 12x-8x+8y-8y=6400-4880 \\ 4x=1520 \\ x=\frac{1520}{4} \\ x=380 \end{gathered}[/tex]replace the value of x into (1):
[tex]\begin{gathered} 6(380)+4y=3200 \\ 2280+4y=3200 \\ 4y=3200-2280 \\ 4y=920 \\ y=\frac{920}{4} \\ y=230 \end{gathered}[/tex]The price of the grandstand ticket is $380 and the price of the general admission ticket is $230
what is the anss? btw this is just a practice assignment.
Anime, this is the solution:
Part A. This exponential is decay because the factor of the exponential is below one, and it decreases every year.
Part B.
5,100 * (0.95)^5 =
5,100 * 0.77378 =
3,946 (rounding to the nearest carbon atom)
The sales tax rate is 10%. If Lindsey buys a fountain priced at $125.40, how much tax will she Inay? $
We have to calculate the sales tax over a purchase of $125.40.
The sales tax rate is 10%, so we can calculate:
[tex]\text{Sales tax}=\frac{10}{100}\cdot125.40=0.1\cdot125.40=12.54[/tex]Answer: the sales tax on this purchase is $12.54,
Hugo is serving fruit sorbet at his party He has 1 gallon of fruit sorbet to serve to 32 friends. If each person receives the same amount, how many cups of fruit sorbet will each person get? A. 1/4 cupB.1/2 cupC. 3/4 cupD. 1 cup
Since 1 gallon is equal to 16 cups, each person will get
[tex]\begin{gathered} \frac{16}{32}\text{ cup} \\ \frac{16}{32}=\frac{1}{2} \\ \\ \text{ each person will get } \\ \frac{1}{2}\text{ cup} \end{gathered}[/tex]r(x)=−x−7 when x=−2,0, and 5
Given,
The expression of the function,
[tex]r(x)=-x-7[/tex]The value of r(x) at x = -2 is,
[tex]r(-2)=-(-2)-7=2-7=-5[/tex]The value of r(x) at x = 0 is,
[tex]r(0)=-(0)-7=0-7=-7[/tex]The value of r(x) at x = 5 is,
[tex]r(5)=-(5)-7=-5-7=-12[/tex]Hence, the value of r(x) is -2, -7 and -12.
Determine if the following side lengths could form a triangle. Prove your answer with an inequality 3,3,7
According to the definition of triangle, the sum of two sides of a triangle must be greater than the third one.
In this case, the sum of 3 and 3 is 6 which is not greater than 7, it means that these length can't form a triangle:
[tex]3+3<7[/tex]That is the inequality that explains why they can form a triangle.
8. An urn contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and
count the number of red marbles in the 4 picks, the probabilities associated with this experiment are
P(0) = 0.24, P(1) = 0.41, P(2)= 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of less than
2 red marbles is:
a. 0.41.
b. 0.65.
c. 0.915.
d 0.991
The probability of less than 2 red marbles is B. 0.65.
What is probability?Probability is the likelihood that an event will occur.
In this case, the urn contains 3 red, 2 blue, and 5 green marbles. Also, the probabilities associated with this experiment are give as:
P(0) = 0.24, P(1) = 0.41, P(2)= 0.265, P(3) = 0.076,
Therefore, the probability of less than 2 red marbles will be:
P(0) + P(1)
= 0.24 + 0.41
= 0.65.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
A swimmer is 1 mile from the closest point on a straight shoreline. She needs to reach her house located 4miles down shore from the closest point. If she swims at 3 mph and runs at 6 mph, how far from her house should she come ashore so as to arrive at her house in the shortest time?
Let's draw a diagram of this problem.
ABC is the shore.
D to A is 1 miles (given).
A to C is 4 miles (given).
If we let AB = x, then BC would be "4 - x".
Now, using pythgorean theorem, let's find BD:
[tex]\begin{gathered} AB^2+AD^2=BD^2 \\ x^2+1^2=BD^2 \\ BD=\sqrt[]{1+x^2} \end{gathered}[/tex]We know
[tex]D=RT[/tex]Where
D is distance
R is rate
T is time
Swimmer needs to go from D to B at 3 miles per hour. Thus, we can say:
[tex]\begin{gathered} D=RT \\ T=\frac{D}{R} \\ T=\frac{\sqrt[]{1+x^2}}{3} \end{gathered}[/tex]Next part, swimmer needs to go from B to C at 6 miles per hour. Thus, we can say:
[tex]\begin{gathered} D=RT \\ T=\frac{D}{R} \\ T=\frac{4-x}{6} \end{gathered}[/tex]So, total time would be:
[tex]T=\frac{\sqrt[]{1+x^2}}{3}+\frac{4-x}{6}[/tex]We want to find the shortest possible time. From calculus we know that to find the shortest possible time, we need to differentiate the function T, set it equal to 0 to find the critical points and then use that point in the function T to find the shortest possible time.
Let's differentiate the function T:
[tex]\begin{gathered} T=\frac{\sqrt[]{1+x^2}}{3}+\frac{4-x}{6} \\ T=\frac{1}{3}(1+x^2)^{\frac{1}{2}}+\frac{4}{6}-\frac{1}{6}x \\ T=\frac{1}{3}(1+x^2)^{\frac{1}{2}}+\frac{2}{3}-\frac{1}{6}x \\ T^{\prime}=(\frac{1}{2})\frac{1}{3}(1+x^2)^{-\frac{1}{2}}\lbrack\frac{d}{dx}(1+x^2)\rbrack-\frac{1}{6} \\ T^{\prime}=\frac{1}{6}(1+x^2)^{-\frac{1}{2}}(2x)-\frac{1}{6} \\ T^{\prime}=\frac{2x}{6(1+x^2)^{\frac{1}{2}}}-\frac{1}{6} \\ T^{\prime}=\frac{x}{3\sqrt[]{1+x^2}}-\frac{1}{6} \end{gathered}[/tex]Now, we find the critical point:
[tex]\begin{gathered} T^{\prime}=\frac{x}{3\sqrt[]{1+x^2}}-\frac{1}{6} \\ T^{\prime}=0 \\ \frac{x}{3\sqrt[]{1+x^2}}-\frac{1}{6}=0 \\ \frac{x}{3\sqrt[]{1+x^2}}=\frac{1}{6} \\ \text{Cross Multiplying:} \\ 6x=3\sqrt[]{1+x^2} \\ \text{Square both sides:} \\ (6x)^2=(3\sqrt[]{1+x^2})^2 \\ 36x^2=9(1+x^2) \\ 36x^2=9+9x^2 \\ 36x^2-9x^2=9 \\ 27x^2=9 \\ x^2=\frac{9}{27} \\ x=\frac{\sqrt[]{9}}{\sqrt[]{27}} \\ x=\frac{3}{3\sqrt[]{3}} \\ x=\frac{1}{\sqrt[]{3}} \end{gathered}[/tex]Plugging this value into the equation of T, we get:
[tex]\begin{gathered} T=\frac{\sqrt[]{1+x^2}}{3}+\frac{4-x}{6} \\ T=\frac{\sqrt[]{1+(\frac{1}{\sqrt[]{3}})^2}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{\sqrt[]{1+\frac{1}{3}}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{\sqrt[]{\frac{4}{3}}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{\frac{2}{\sqrt[]{3}}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{2}{3\sqrt[]{3}}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \end{gathered}[/tex]Now, we can use the calculator to find the approximate value of T to be:
T = 0.9553 hours
This is the optimized time.
Converting to approximate minutes, it will be:
57.32 minutes
Answer:[tex]T=0.9553\text{ hours}[/tex](−2) × 36 × (−5) = ______.
we have 3 terms, two of them are negative
when operating multiplications, minus by plus gives minus and minus byminus gives plus, so the final result will be positive.
[tex]\begin{gathered} (-2)\cdot36\cdot(-5)=\text{?} \\ (-2)\cdot36\cdot(-5)=360 \\ \end{gathered}[/tex]The anwer is 360
Question 7Find the slope of the line that goes through the given points.(-1, 7).(-8, 7)1092
Given:
There are given that the two points;
[tex](-1,7)\text{ and (-8,7)}[/tex]Explanation:
To find the slope of the line from the given point, we need to use the slope formula:
So,
From the formula of the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=-1,y_1=7,x_2=-8,y_2=7_{}[/tex]Then,
Put all the above values into the given formula:;
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7_{}-7_{}}{-8_{}-(-1)_{}} \end{gathered}[/tex]Then,
[tex]\begin{gathered} m=\frac{7_{}-7_{}}{-8_{}+1_{}} \\ m=\frac{0}{-7} \\ m=0 \end{gathered}[/tex]Final answer:
The slope of the given line is 0.
Hence, the correct option is B (0)
What is the best approximation for the area of a semi-circle with a diameter of 11.8 ( Use 3.14 for pie
Answer:
54.7units^2
Explanation:
Area of a semi-circle = \pid^2/8
d is the diameter of the semi circle
Given d = 11.8
Area = 3.14(11.8)^2/8
Area of the semi circle = 3.14(139.24)/8
Area of the semi circle = 437.2136/8
Area of the semi circle = 54.6517units^2
Hence the best approximation is 54.7units^2
is 88∘ more than the smaller angle. Find the measure of the larger angle.
Let
x -----> large angle
y ----> smaller angle
so
Remember that
If two angles are supplementary, then their sum is equal to 180 degrees
so
x+y=180
y=180-x ------> equation A
and
x=y+88
y=x-88 -----> equation B
equate both equations
180-x=x-88
x+x=180+88
2x=268
x=134 degrees
the answer is 134 degreesA company purchased 10,000 pairs of men's slacks for $18.86 per pair and marked them up $22.63. What was the selling price of each pair of slacks? Use the formula S=C+M
Problem:
A company purchased 10,000 pairs of men's slacks for $18.86 per pair and marked them up $22.63. What was the selling price of each pair of slacks? Use the formula S=C+M.
Solution:
Cost = $18.86
Markup = $22.63
Markup = Sell Price - Cost
Sell Price = Cost + Markup
Sell Price = 18.86+ 22.63
Sell Price = $41.49
The selling price of each pair of slacks was $41.49.
Select the appropriate graph for each inequality.1. {x|x<-3}a.<用HHHHH>-10 -1 -8 -7 -6 - 4 -3 -2 -1 01 23 4 5 6 7 8 9 10
Given the inequality x| x< -3
The graph of the inequality will be as following :
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens answers. If there are 90,000 citizens in the community, how many chose hamsters, fish, snakes?
ANSWER :
27000
EXPLANATION :
From the problem, 7% chose hamsters, 15% chose Fish and 8% chose Snakes.
A total of 7 + 15 + 8 = 30%
Multiply this percentage by the population (90,000) to get the number of people who chose these pets.
That will be :
[tex]90000(0.30)=27000[/tex]Please help me im so stressed rnIS (-2, 6) a solution of -3y + 10= 4x?
Given the expression:
[tex]-3y+10=4x[/tex]Let's check if (x,y) = (-2,6) is a solution by substituting each value on the equation:
[tex]\begin{gathered} x=-2 \\ y=6 \\ -3y+10=4x \\ \Rightarrow-3(6)+10=4(-2) \\ \Rightarrow-18+10=-8 \\ \Rightarrow-8=-8 \end{gathered}[/tex]since we got on both sides -8, we can see that (-2,6) is a solution of -3y+10=4x
It is reported that approximately 20 squaremiles of dry land and wetland were convertedto water along the Atlantic coast between 1996and 2011. A small unpopulated island in the AtlanticOcean is 2000 ft wide by 9,380 feet long. Atthis rate, how long before the island issubmerged?
2 months
1) Notice that the sinking rate is 20miles² per 5 years (2011-1996) so:
[tex]\frac{20}{5}=\frac{4m^2}{y}[/tex]So the rate is 4 square miles per year.
2) We need to convert those measures from feet to miles:
[tex]\begin{gathered} 1\text{ mile=5280ft} \\ 2000ft=\frac{2000}{5280}=0.378miles \\ 9380ft=\frac{9380}{5280}=1.7765miles \end{gathered}[/tex]So, now let's find the area multiplying the width by the height:
[tex]\begin{gathered} A=1.7765\cdot0.378 \\ A=0.671517m^2 \end{gathered}[/tex]Now, considering the sinking rate of 4miles²/year we can write the following pair of ratios:
[tex]\begin{gathered} 1year-------4miles^2 \\ x----------0.6715 \\ 4x=0.6715 \\ \frac{4x}{4}=\frac{0.6715}{4} \\ x=0.17 \\ \\ --- \\ 0.17\times12\approx2 \end{gathered}[/tex]Note that we found that approximately 0.17 year is necessary to submerge tat island, converting that to months, we can state that in approximately 2 months
find first four terms of an arithmetic series if last term is 10 times first term and sum to n terms is 121
Answer: 120
Step-by-step explanation:
S = n/2 (a(1) + a(n)), where n is the number of terms (10), a(1) is the first term (3), and a(n) is the last term (21).
By substitution, we have,
S = 10/2 (3 + 21)
S = 120
. A pie company made 57 apple pies and 38 cherry pies each day for 14 days. How many apples pies does the company make in all?
To determine the total number of apples pies done, multiply the number of apple pies done each day by 14:
[tex]57\cdot14=798[/tex]Hence, the company made a total of 798 apple pies.
Find the value of x.
Answer
Option A is correct.
x = 5 units
Explanation
We can draw the triangle and divide it into two similar right angle triangles shown below
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For each of the triangles,
a = 4
b = 3
hyp = x
a² + b² = (hyp)²
4² + 3² = x²
x² = 16 + 9
x² = 25
x = √25
x = 5 units
Hope this Helps!!!
Write a recursive formula for the sequence: 8, 4, 2, 1,...Tn + 1 = Tn × 12Tn + 1 = Tn × (2)Tn + 1 = Tn - 4(n - 1)Tn + 1 = Tn + 4(n - 1)
Given:
The sequence is:
8, 4, 2, 1,...
Required:
Find a recursive formula for the given sequence.
Explanation:
The given sequence is:
8, 4, 2, 1,...
The common ratio of the sequence is:
[tex]\begin{gathered} \frac{4}{8}=\frac{1}{2} \\ \frac{2}{4}=\frac{1}{2} \\ \frac{1}{2} \end{gathered}[/tex]Since the common ratio for the given series is 1/2.
[tex]\begin{gathered} \frac{T_{n+1}}{T_n}=\frac{1}{2} \\ T_{n+1}=\frac{1}{2}T_n \end{gathered}[/tex]Final Answer:
The recursive formula for the given sequence is
[tex]T_{n+1}=\frac{1}{2}T_{n}[/tex]