There are a total of 8 possible numbers for each digit and there are 3 digits for the password. Since the problem didn't state that the numbers can't be repeated, then we can apply the following formula:
[tex]C_{n,m}\text{ = }\frac{n!}{m!(n\text{ - m)!}}[/tex]Where "n" is the range of possibilities for each number and "m" is the number of digits we want to arrange them. So applying the data from the problem gives us:
[tex]undefined[/tex]Choose the appropriate pattern and use it to find the product: (p4−q4)(p4+q4).
The expression can be solved by expanding the bracket and multiplying out the terms
[tex](p^4-q^4)(p^4+q^4)[/tex][tex]\begin{gathered} =p^4(p^4+q^4)-q^4(p^4+q^4) \\ =p^8+p^4q^4-p^4q^4-q^8 \\ =p^8-q^8 \end{gathered}[/tex]Therefore, the expression can be simplified as;
[tex]p^8-q^8[/tex]Alternatively, using the theorem of difference of two squares, which is
[tex]a^2-b^2=(a-b)(a+b)[/tex]Hence,
[tex]p^8-q^8=(p^4)^2-(q^4)^2[/tex]
Please help!! College Algebra. Need answer fast!!
One is traveling at a constant pace of 30 mph and is 5 miles south of the intersection. The distance d between the cars changes with time t as [tex]\sqrt{26-320t+1000t ^{2}}[/tex].
Given that,
An intersection is being approached by two cars. One is traveling at a constant pace of 30 mph and is 5 miles south of the intersection. At the same time, the second vehicle is traveling at a constant speed of 10 mph and is located one mile to the east of the intersection.
We have to describe how the distance d between the cars changes with time t.
The distance is d=[tex]\sqrt{(t_{1}) ^{2} +(t_{2}) ^{2}}[/tex]
t₁=1-10t
t₂=5-30t
d=[tex]\sqrt{(1-10t) ^{2} +(5-30t) ^{2}}[/tex]
d=[tex]\sqrt{1-20t+100t^{2}+25-300t+900t ^{2}}[/tex]
d=[tex]\sqrt{26-320t+1000t ^{2}}[/tex]
Therefore, We got the distance d between the cars changes with time t as [tex]\sqrt{26-320t+1000t ^{2}}[/tex].
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Triangle RST has vertices R(1, 2), S(4, -2), and T(2, -5). The triangle is rotated 90° counterclockwise about the origin. Which are the coordinates of the image of vertex T?
Answer:
(5, 2)
Explanation:
If point P with coordinates (x, y) is rotated 90 degrees counterclockwise about the origin, the image will have (-y, x) as coordinates of the image, P'.
So if triangle RST was rotated 90 degrees counterclockwise about the origin, we'll have the below as coordinates of the image of vertex T;
[tex]T(2,-5)\rightarrow T^{\prime}\lbrack(-(-5),2)\rbrack\rightarrow T^{\prime}(5,2)[/tex]A farmers land is separated in sections of size 2 1/7 acres. Suppose there are 4 3/8 such sections. How many acres of land does the farmer own? Write your answer as a mixed number in simplest form.
We were told that the farmer's land is separated in sections of size 2 1/7 acres. Converting 2 1/7 to improper fraction, we multiply 2 by 7 and add 1. The denominator remains 7. it becomes 15/2
There are 4 3/8 such sections. Converting 4 3/8 to improper fraction, it becomes 35/8
Therefore, the number of acres of land that the farmer owns is
15/2 * 35/8 = 525/16
Converting to improper fraction, it becomes
32 13/16 acres
Answer:
32 13/16 acres
Step-by-step explanation:
Classify the triangle as acute, right , or obscure and classify it as equilateral , isosceles , or scalene
Step 1:
What is an isosceles triangle?
What is Isosceles Triangle? A triangle with two sides of equal length is an isosceles triangle.
Step 2: What is an acute angle?
An acute angle is an angle that measures between 90° and 0°.
Step 3:
The figure is an acute isosceles.
Final answer
Acute Isosceles
The perimeter of a rectangular sports court is 122 feet. After a game, a player's coach estimates that the athlete has run a total of 423 feet, which is equivalent to 6 times the court's length plus 9 times its width. What are the dimensions of the sports court?
The dimensions of the sports court is
Width = 19 feet
Length = 42 feet
What is perimeter of rectangle ?A rectangle's perimeter (P) is the sum of the lengths of its four sides. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter: The formula for perimeter is length + length + width + width. P = l + l + w + w.
Given: Perimeter of rectangular sports court = 122 feet
Assume;
Length = l
Width = b
So,
6l + 9b = 423 feet.......Eq1
Perimeter of rectangular sports court = 122 feet
2l + 2b = 122
l + b = 61
l = 61- b
From Eq 1
6l + 9b = 423
6[61 - b] + 9b =423
366 - 6b + 9b = 423
b = 19
Width = 19feet
l + b = 61
l + 19 = 61
l = 42
Length = 42feet
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Solve the equation on the interval 0<=theta<2pi2 sin^2 theta-V3 sin theta = 0
Given the equation
[tex]2\sin ^2\theta-\sqrt{3}\sin \theta=0[/tex]We can rewrite the given equation as:
[tex]2\sin ^{}\theta\sin ^{}\theta-\sqrt{3}\sin \theta=0[/tex]Factoring, we obtain:
[tex]\sin ^{}\theta(2\sin ^{}\theta-\sqrt{3})=0[/tex]Therefore, we can say:
[tex]\begin{gathered} \sin ^{}\theta=0\: \implies\theta=0 \\ \text{Similarly} \\ 2\sin ^{}\theta-\sqrt{3}=0 \\ \implies2\sin ^{}\theta=\sqrt{3} \\ \implies\sin ^{}\theta=\frac{\sqrt{3}}{2} \\ \implies\theta=\sin ^{-1}\frac{\sqrt{3}}{2} \\ \implies\theta=\frac{\pi}{3} \end{gathered}[/tex]Therefore, the solution set in the given interval is:
[tex]\left\lbrace 0,\frac{\pi}{3}\right\rbrace [/tex]2x+y=-11 rewrite in slope intercept form
Answer:
In slope-intercept form:
[tex]y = - 2x - 11[/tex]
A car's rear windshield wiper rotates 130°. the total length of the wiper mechanism is 21 inches and the length of the wiper blade is 14 inches. find the area wiped by the wiper blade. (round your answer to one decimal place.)
We have that the formula for the area of the sector of a circle is:
[tex]A=\frac{\pi\cdot r^2\cdot\alpha}{360}[/tex]In this case, we have to find the area of the sector of a circle with radius r= 21 and then the area in the case of the r=21-14=7, and then find the difference.
Given the information, we have the following:
[tex]\begin{gathered} \alpha=130 \\ r_1=21 \\ r_2=7 \\ \Rightarrow A_1=\frac{(3.1416)(21)^2(130)}{360}=500.3 \\ \Rightarrow A_2=\frac{(3.1416)(7)^2(130)}{360}=55.6_{} \\ \Rightarrow A=A_1-A_2=500.3-55.6=444.7_{} \\ A=444.7 \end{gathered}[/tex]therefore, the area wiped by the wiper blade is 444.7in²Evaluate the expression 4x-2+m when x=3 and m=5
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1300. The law firm assigned a total of 19 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.
The number of associates is 9 and the number of partners is 10.
Given, The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1300.
The law firm assigned a total of 19 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services.
we need to determine the number of associates assigned to the case and the number of partners assigned to the case.
Suppose the number of associates is x and the number of partners be y.
Then the required equations are formed:
x+y=19 ..eq(1)
700x+1300y=19300 ...eq(2)
from eq(1) we get:
y=19-x .. eq(3)
Plug eq(3) into eq(2)
700x+1300(19-x)=19300
700x+24700-1300x=19300
700x-1300x=19300-24700
-600x=-5400
x=9
Thus, y=19-9
y=10
Thus the number of associates are 9 and the number of partners are 10.
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(Score for Question 1: of 10 points)1. Consider the quadratic function.(d) Graph the function on the coordinate plane. Include the axis of symme(b) What is the equation of the axis of symmetry?(c) What are the coordinates of the vertex?(a) What are the x-intercepts and y-intercept?Answer:f(x) = - (x + 4) * (x - 1)
Given:
[tex]f(x)=-(x+4)(x-1)[/tex]Explanation:
a) To draw: The Graph
Let us find the intercepts.
When x = 0, we get
[tex]\begin{gathered} y=-(4)(-1) \\ y=4 \end{gathered}[/tex]Therefore, the y-intercept is (0, 4).
The x-intercepts are,
[tex](-4,0),(1,0)[/tex]Let us find the vertex.
The given function can be written as,
[tex]\begin{gathered} f(x)=-(x+4)(x-1) \\ =-(x^2+3x-4) \\ =-(x^2+3x+(\frac{3}{2})^2-(\frac{3}{2})^2-4) \\ =-[(x+\frac{3}{2})^2-\frac{9}{4}-4] \\ =-[(x+\frac{3}{2})^2-\frac{25}{4}] \\ f(x)=(x+\frac{3}{2})^2+\frac{25}{4} \end{gathered}[/tex]So, the vertex is,
[tex]\begin{gathered} (h,k)=(-\frac{3}{2},\frac{25}{4}) \\ (or) \\ (h,k)=(-1.5,6.25) \end{gathered}[/tex]The graph becomes,
b) The equation of symmetry is,
[tex]x=-\frac{3}{2}[/tex]This line divides the parabola into two equal parts.
c) The coordinates of the vertex is,
[tex](h,k)=(-1.5,6.25)[/tex]d) Intercepts:
The x-intercepts are,
[tex](-4,0),(1,0)[/tex]The y-intercept is (0, 4).
Please helpppppppppp
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Kurt is flying his airplane over a campground. he spots a small fire below at an angle of depression of 32°. If the horizontal d9stance from Kurt's plane to the fire is 3600 feet, find the approximate altitude of his plane.
ANSWER:
A. 2,250 feet
STEP-BY-STEP EXPLANATION:
We can calculate the value of the height thanks to the tangent trigonometric function, which relates the opposite leg (altitude) and the adjacent leg (horizontal), as follows:
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \theta=32\text{\degree} \\ \text{opposite = x} \\ \text{adjacent = 3600} \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \tan 32=\frac{x}{3600} \\ x=3600\cdot\tan 32 \\ x=2249.53\cong2250 \end{gathered}[/tex]The altitude value is 2250 feet
How can each type of sequence be helpful in everyday situations? Provide an example and the corresponding equation for each type.
Answer:
The two types of the sequence include
1) Arithmetic sequence
2) Geometric sequence
An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression.
The Nth term of an arithmetic sequence is given below as
[tex]\begin{gathered} T_n=a+(n-1)d \\ \text{Where,} \\ a=\text{first term} \\ n=Num\text{mber of terms} \\ d=\text{common difference}=T_2-T_1=T_3-T_2 \end{gathered}[/tex]A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
The Nth term of a geometric sequence is given below as
[tex]\begin{gathered} U_n=ar^{n-1} \\ \text{Where,} \\ a=\text{first term} \\ r=\text{common ratio=}\frac{t_2}{t_1}=\frac{t_3}{t_2} \end{gathered}[/tex]Real life illustrations of the types of sequence
Sequences are useful in our daily lives as well as in higher mathematics. For example, the interest portion of monthly payments made to pay off an automobile or home loan, and the list of maximum daily temperatures in one area for a month are sequences.
Example: arithmetic sequence
A boy building a tower with blocks uses 15 for the bottom row. Each row has 2 fewer blocks than the previous row. Suppose that there are 6 rows in the tower. Find a for n = 6
The number of blocks in each row forms an arithmetic sequence with a₁ = 15 and d= −2. The formula to be used is an = a₁ + (n − 1)d.
[tex]\begin{gathered} t_n=a+(n-1)d \\ T_6=15+(6-1)(-2) \\ T_6=15+5(-2) \\ T_6=15-10 \\ T_6=5 \end{gathered}[/tex]Hence,
On the sixth row, he will have 5 blocks left
Example: geometric sequence
A country's population is growing in such a way that each new generation is 1.5 times as large as the previous generation. Suppose there are 100 insects in the first generation. How many will there be in the fifth generation?
Here,the common ratio r=1.5
[tex]U_n=a(1.5)^{n-1}[/tex]I find 4heb diagram.
We are asked to find the volume of the given pyramid.
Recall that the volume of a pyramid is given by
[tex]V=\frac{1}{3}\cdot B\cdot h[/tex]Where B is the area of the base and h is the height of the pyramid.
As you can see from the figure, the base of the pyramid is rectangular
The length is 23 yd and the width is 14 yd of the rectangular base.
So, the area of the rectangular base is
[tex]\begin{gathered} B=l\cdot w \\ B=23\cdot14 \\ B=322\: yd^2 \end{gathered}[/tex]The height of the pyramid is 25 yd
So, the volume of the pyramid is
[tex]\begin{gathered} V=\frac{1}{3}\cdot B\cdot h \\ V=\frac{1}{3}\cdot322\cdot25 \\ V=2683.3\: yd^3 \end{gathered}[/tex]Therefore, the volume of the rectangular pyramid is 2683.3 cubic yards.
The type of pyramid is the rectangular pyramid.
3) Rotate counterclockwise around the origin180°180°Ay41NН.2.4xK44What is the rule? (x,y) - (___)H(__)l'(_,J'(___)K'(__)
We have the next points
H(-4,1)
I(-2,2)
J(-1,-2)
K(-4,-4)
The rule to rotate 180° counterclockwise
[tex](x,y)\rightarrow(-x,-y)[/tex]with rule, we can find the points
H'=(-(-4),-1)=(4,-1)
I'=(-(-2),-2)=(2,-2)
J'=(-(-1),-(-2))=(1,2)
K'=(-(-4),-(-4))=(4,4)
so the answer is
H'=(4,-1)
I'=(2,-2)
J'=(1,2)
K'=(4,4)
we can graph them they are the points in red
what is the value of K in the equation
Simplify the equation to obtain the value of k.
[tex]\begin{gathered} 5k-2k=12 \\ 3k=12 \\ k=\frac{12}{3} \\ =4 \end{gathered}[/tex]So value of k is 4.
On a sheet of paper using the number line below, represent the set of data in a dot plot. Determine the median. 1. Length of summer camps in days: 7, 7, 12, 10, 5, 10, 5, 7, 10, 9, 7, 9, 6, 10, 5, 8, 7, and 8
Graphing the set of data in a dot plot, we have:
Since this set has 18 elements, the median is the average between the 9th and 10th elements using the set in the crescent order.
Looking at the dot plot, the 9th element is 7 and the 10th element is 8, so the median is (7 + 8)/2, that is, the median is 7.5.
Juan is designing an exercise room in his house. How many square feet of rubber flooring will he need to cover the floor? The product is sold in whole square yards. How many square yards should he buy? Explain. 10 ft 3 ft 9 ft 13 ft The total area of the exercise room is 103 ft. This is also the total amount of rubber flooring that Juan must have. (Type a whole number.) The number of square yards equivalent to this total area is 11.4 square yards. (Round to the nearest tenth as needed.) Since rubber flooring is sold in whole sq. yards, Juan must purchase exactly square yards.
The amount of rubber flooring will be the area of the floor.
We can calculate the area as the sum of two rectangles:
Then, the area is:
[tex]A=10\cdot4+9\cdot7=40+63=103ft^2[/tex]We can convert this area into square yards as:
[tex]A=103ft^2\cdot(\frac{1\text{ yd}}{3\text{ ft}})^2=103\cdot\frac{1}{9}\text{ yd}^2\approx11.44\text{ yd}^2[/tex]As we have to purchase a whole number of square yards, we will buy the next integer greater than 11.44, that is 12 sq yd.
Answer:
The floor area is 103 square feet.
This is equivalent to 11.44 square yards.
He has to purchase 12 square yards of rubber floor.
A chemist is using 326 milliliters of a solution of acid and water. If 18.3% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
We have a 326 ml of a solution with 18.3% of acid.
We have to calculate the amount of acid there is.
We can find it as the volume of the solution, 326 ml, times the proportion of acid, 18.3/100 = 0.183:
[tex]326\cdot0.183=59.658\approx59.7[/tex]Answer: there are 59.7 ml of acid.
sketch the graph of the function3.) [tex]y = \sqrt{x} [/tex]I got (0,0) as my answer but I want to see if I got it correct!!
You have to graph the following function
[tex]y=x[/tex]This is a linear function with slope m=1, this means that each time x increases one unit, y also increases one unit.
To sketch this function you have to choose at least two values of x and determine the corresponding value of y.
Then plot the points and draw the line.
I will make a table with 5 points of the line:
Now what's left is to plot all points and link them with a line:
How many presents would Dracula wrap in 8 hours if he wrapped 3 presents every 20 minutes?
First, you can know how many minutes are 8 hours using the rule of three like this
[tex]\begin{gathered} 1\text{ hour}\rightarrow60\text{ minutes} \\ 8\text{ hours }\rightarrow\text{ x minutes} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{8\text{ hours }\ast\text{ 60 minutes}}{1\text{ hour}} \\ x=480\text{ minutes} \end{gathered}[/tex]Now, using the rule of three again, you can find out how many gifts Dracula would wrap in 8 hours if she wrapped 3 gifts every 20 minutes
[tex]\begin{gathered} 20\text{ minutes}\rightarrow3\text{ presents} \\ 480\text{ minutes}\rightarrow x\text{presents} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{480\text{ minutes}\ast3\text{ presents}}{20\text{ minutes}} \\ x=\frac{1440}{20}\text{ presents} \\ x=72\text{ presents} \end{gathered}[/tex]Therefore, Dracula would wrap 72 gifts in 8 hours if he wrapped 3 gifts in 20 minutes
1/2 minute how long does it take for jing to complete 10 questions
ANSWER
A. 300 seconds
EXPLANATION
Half a minute is 30 seconds. If Jing answers 1 question in 30 seconds, then he will answer 10 questions in:
[tex]10\times30=300[/tex]300 seconds.
Answer:
300
Step-by-step explanation:
30 (seconds) x 10 (minutes) = 300 (seconds) hope this helps!
o((>ω< ))o
The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?
O 1-101-181=2 dollars
O -8110) = 80 dollars
O 1-101-8=2 dollars
0 81-101 = 80 dollars
The following describes the total moderate decrease in the wares after 8 weeks is 8 | -10 |= 80 dollars.
What is meant by value?The value refers to the worth of each digit in relation to its position in the number. We compute it by multiplying the digit's place and face values. Place Value + Face Value = Value. As an example: If we look at the number 45. In this case, digit 4 is in the tens column. Values are benchmarks or ideals against which we judge actions, people, things, or situations. Many people support values such as beauty, honesty, justice, peace, and generosity. The actual population value obtained with perfect measuring instruments and without committing any type of error, both in collecting primary data and in performing mathematical operations.
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PLEASE HELP ME I WAS SICK AND I DONT UNDERSTAND.DUE IN 1 HOUR!!!!
Answer:
x=11
Step-by-step explanation:
The inside(interior) angles of a triangle must add up to 180 degrees. A line is 180 degrees, so the angle GFH (the measure of the acute angle at point F) would be 180-(11x+1)
Now we have information on all 3 angles of the triangle; they must sum up to 180, so add all of these equations together
180-(11x+1) = 179-11x
Add this to 3x+19 and 70 gives 268-8x=180
Solving this equation for x we get -8x=180-268
-8x=-88
x=11
Hoped this helped and I hope you feel better!
Answer:
11°
Step-by-step explanation:
Here,
∠FGH=3x+19
∠GHF=70°
∠QFG=11x+1
Now,
11x+1+∠GFH=180[Sum of a straight line is 180°]
∴∠GFH=179-11x
Again,
∠GFH+∠GHF+∠FGH=180[Sum of all angles of a triangle is 180]
179-11x+70+3x+19=180
-11x+3x=180-179-70-19
-8x=-88
∴x=11°
√98-√18
how would I get the answer to this
SURDS
The value of √98-√18 in surds will be 4✓2.
Whet is surds?A surd simply means an expression that include the square root, the cube root or other root symbols.
In this case, the value given is illustrated as:
√98-√18
= ✓(2 × 49) - ✓(2 × 9)
= 7✓2 - 3✓2
= 4✓2
The value is 4✓2.
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Which of the following is an example of a theorem? A. the areas of two congruent figures are equal. B. the area of a square is the square of the length of its side. C. the area of a rectangle is the product of its base and height. D. the area of a rectangle is the sum of all its non-overlapping parts
Theorem is a statement that can be proved or that is proven to be true.
Option A is a theorem because it is proven that the area of two congruent figures are equal.
Option B is a theorem because the area of a square is the square of the length of its side.
[tex]\begin{gathered} A_{square}=l\times l \\ A_{square}=l^2 \end{gathered}[/tex]Option C is a theorem because the area of a rectangle is the product of its base and height.
[tex]\begin{gathered} A_{rec\tan gle}=b\times h \\ A_{rec\tan gle}=bh \end{gathered}[/tex]Thus, A, B and C are CORRECT
Which is the correct simplified version ofthe expression -7(2x - 3)?a. - 14x + 21b. - 14x - 21c. -5x – 10d. -14% - 10
The given expression is - 7(2x - 3)
The first step is to open the bracket by multiplying each term inside the bracket by the term outside. Then we would add or subtract where necessary.
It becomes
- 7 * 2x + - 7 * - 3
Recall, - * - = +
The simplified expression would be
- 14x + 21
The correct option is A
Complete these sentences to describe the rules of dividing signed numbers.
The quotient of two integers with same sign is always
The quotient of two integers with different signs is always
Answer:
1) Positive, 2) NegativeStep-by-step explanation:
The quotient of two integers with same sign is always positive, because:
Positive / positive = positive andNegative / negative = positiveThe quotient of two integers with different signs is always negative, because:
Positive / negative = negative andNegative / positive = negativeAnswer:
1) Positive (+)
2) Negative (-)
Step-by-step explanation:
1) Positive
→ (+) ÷ (+) = (+)
→ (-) ÷ (-) = (+)
Hence, it is proved.
2) Negative
→ (+) ÷ (-) = (-)
→ (-) ÷ (+) = (-)
Hence, it is proved.
