Given:
The markdown of a bicycle = $1500
Which is 20% of the original selling price
Let the original selling price = x
so, 20% of x = 1500
so,
[tex]\begin{gathered} \frac{20}{100}\cdot x=1500 \\ \\ x=\frac{1500\cdot100}{20}=7500 \end{gathered}[/tex]so, the answer will be:
a) the original selling price = $7,500
b) the new selling price = 7500 - 1500 = $6,000
The number of hits to a website follows a Poisson process. Hits occur at the rate of1.4 per minute between 7:00 P.M. and 10:00 P.M. Given below are three scenarios for thenumber of hits to the website. Compute the probability of each scenario between 9:30 PM and9:35 P.M. Interpret each result.(a) exactly four(b) fewer than four(c) at least four
Given that:
Rate at which the hits occur between 7 PM and 10 PM = 1.4 per minute
Then:
Number of hits between 9:30 AM and 9:35 AM
[tex]\begin{gathered} =5\cdot(1.4) \\ =7 \end{gathered}[/tex]The probability distribution function of Poisson distribution is
[tex]P(X=x)=\frac{e^{-\lambda}\lambda^x}{x!}[/tex](a) P(x=4)
[tex]\begin{gathered} =\frac{e^{-7}7^4}{4!} \\ =0.0912 \end{gathered}[/tex](b) P(x < 4) = P(x=0)+P(x=1)+P(x=2)+P(x=3)
[tex]\begin{gathered} =\frac{e^{-7}7^0}{0!}+\frac{e^{-7}7^1}{1!}+\frac{e^{-7}7^2}{2!}+\frac{e^{-7}7^3}{3!} \\ =e^{-7}+7e^{-7}+\frac{49e^{-7}}{2}+\frac{343e^{-7}}{6} \\ =0.0818 \end{gathered}[/tex](c) To find
[tex]\begin{gathered} P(x\ge4)=1-P(x<4) \\ =1-0.0818 \\ =0.9182 \end{gathered}[/tex]A plane rises from take-off andflies at an angle of 18with thehorizontal runway. When it hasgained 200 feet, find thedistance that the plane hasflown.
Answer:
647 ft
Explanation:
Given the below figure;
To determine the value c, we have to take the sine of angle 18 degrees as seen below;
[tex]\begin{gathered} \sin18=\frac{opposit\text{e side to angle 18}}{hypotenuse\text{ to angle 18}}=\frac{200}{c} \\ \sin18=\frac{200}{c} \end{gathered}[/tex]Let's cross multiply;
[tex]c*\sin18=200[/tex]Let's divide both sides by sin 18;
[tex]\begin{gathered} \frac{c*\sin18}{\sin18}=\frac{200}{\sin18} \\ c=\frac{200}{\sin18} \\ c=647ft \end{gathered}[/tex]So the distance the plane has flown is 647 ft
Solve using substitution:2x + 3y - 4z = 9 4y – 6z = 16z = 2
ANSWER
x = -2, y = 7, z = 2
EXPLANATION
We are given a system of three equations:
2x + 3y - 4z = 9 ________(1)
4y - 6z = 16 ___________(2)
z = 2 ________________(3)
Since we have been given the value of z, from (3) we have that (2) becomes:
4y - 6(2) = 16
4y - 12 = 16
4y = 12 + 16 = 28
y = 28 / 4
y = 7
Put the values of y and z in (1):
=> 2x + 3(7) - 4(2) = 9
2x + 21 - 8 = 9
2x + 13 = 9
Collect like terms:
2x = 9 - 13 = -4
x = -4 / 2
x = -2
So, x = -2 and y = 7 and z = 2
If lines a and b are parallel, what is the value of x?
============================================================
Explanation:
Let y be the angle just to the left of angle x. Angle x and angle y are adjacent.
Since line a is parallel to line b, this means y = 120 because the 120 degree angle and angle y are alternate interior angles.
Then we can say:
x+y = 180
x+120 = 180
x = 180-120
x = 60
--------------
An alternative method:
Let w be the angle just above angle x
The angle marked "120 degrees" and angle w are corresponding angles. They are congruent if and only if line a is parallel to line b.
This makes w = 120
Solving w+x = 180 leads to x = 60 similar to the previous set of steps.
--------------
Side note:
The 115 degree angle is never used. It was probably put in there as a distraction.
[tex]1 = 0 = \times 013430[/tex]could you help me please
Given the expression:
what does x-4>-8 equal
We need to solve the following inequality:
[tex]x-4>-8[/tex]To do that we have to isolate the variable on the left side. The first step is to add "4" on both sides.
[tex]\begin{gathered} x-4+4>-8+4 \\ x>-4 \end{gathered}[/tex]The value of x must be greater than -4 for this inequality bo be valid.
To graph this result we need to draw a line at the point that x = -4, then we collor the side that is greater than that.
A better drawing can be seen below:
To graph it at the line we need to go to the point that solves the equation, in this case is -4 and if the signal is ">" we collor the right part of the line.
Marla has 578 yards of fabric. She makes a jacket with 334 yards. DoesMarla have enough fabric left to make the same jacket for her friend?
Solution:
Given that Maria has 5 7/8 yards of fabrics, and she makes a jacket with 3 3/4 yards, this implies that the amount of fabric left after making her own jacket is evaluated as
[tex]\begin{gathered} 5\frac{7}{8}-3\frac{3}{4} \\ converting\text{ the mixed fractions into improper fractions, we have} \\ \frac{47}{8}-\frac{15}{4} \\ =\frac{47-30}{8} \\ =\frac{17}{8} \\ converting\text{ the improper fraction to a mixed fraction, we have} \\ =2\frac{1}{8} \end{gathered}[/tex]Since she is to make the same jacket for her friend, she requires another
[tex]3\frac{3}{4}\text{ yards of fabrics}[/tex]But the amount of fabric left after Maria has made her own jacket is
[tex]2\frac{1}{8}\text{ yards}[/tex]Hence, Maria does not have enough fabric left for her friend.
Solve- (-8/5)x - 6 = -54and explain
Giveb data:
The given expression is (-8/5)x-6=-54.
The given expression can be written as,,
[tex]\begin{gathered} (-\frac{8}{5})x-6=-54 \\ -\frac{8}{5}x=-48 \\ x=\frac{5\times48}{8} \\ =30 \end{gathered}[/tex]Thus, the value of x is 30.
About 9% of the population has a particular genetic mutation. 700 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 700. Round your answer to two decimal places.
Given:
n = 700
p = 0.09
q = 1 - p = 0.91
The formula for standard deviation is:
[tex]σ=(npq)^{\frac{1}{2}}[/tex]hence:
[tex]\begin{gathered} σ=(700\times0.09\times0.91)^{1/2} \\ σ=7.57 \end{gathered}[/tex]ANSWER
σ ≈ 7.57
In 2-3 well crafted sentences, explain how to determine if a quadratic trinomial is factorable or not.
The quadratic equation is factorizable if the result of the discriminant gives a perfect square. This is a kind of a perfect square test
How do you know if a quadratic equation is factorizable?We know that a quadratic equation is factorizable by the use of the discriminant. The discriminant is something that could tell us about the character of the quadratic equation.
We know that the discriminant is the square root of b^2 - 4ac. If the result of this operation is a perfect square, then we can know that the equation as we have it in any particular situation is factorizable.
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Find the smallest Distinct positive numbers that provide a counter example to show the statement is false.The sum of any two different odd numbers is divisible by 4.
Answer:
The counter example is:
[tex]2+4=6[/tex]Explanation:
We want to show that the statement "The sum of any two different odd numbers is divisible by 4" is false.
We need to use the smallest positive numbers. T
to complete the square for the equation, x²+6x-2=0, you will have to add ___ to both sides ⚪ 3⚪ 6⚪ 9⚪ 12
Simplify the equation.
[tex]\begin{gathered} x^2+6x-2=0 \\ x^2+2\cdot3\cdot x-2+(3)^2=0+(3)^2 \\ (x+3)^2=9+2 \\ (x+3)^2=11 \end{gathered}[/tex]Thus to complete the square 9 is added to both side of the equation.
Answer: 9
Pls complete fast and be sure of ur answer 
The number of students which are either in algebra or physics are 23 which is the second option.
Given that:-
Total number of students = 30
Number of students both in physics and algebra = 4
Total number of students in Physics = 12
Total number of students in Algebra = 19
We have to find the number of students which are either in algebra or physics.
Number of students in physics but not in algebra = 12 - 4 = 8
Number of students in algebra but not in physics = 19 - 4 = 15
We know that:-
Number of students which are either in algebra or physics = Number of students in physics but not in algebra + Number of students in algebra but not in physics
Hence, we can write,
Number of students which are either in algebra or physics = 8 +15 = 23.
We can also do this question using Venn diagram.
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find the value or measure. Assume all lines that appear to the tangent are tangent. mJH=
From the arc-angle relationship
By comparing both pictures, we have that
[tex]55=\frac{76+mJH}{2}[/tex]now, we must isolate MJH, hence we have
[tex]\begin{gathered} 76+\text{mJH}=2\cdot55 \\ 76+\text{mJH}=110 \end{gathered}[/tex]and we must move 76 to the right hand side as -76, this gives
[tex]\begin{gathered} \text{mJH}=110-76 \\ \end{gathered}[/tex]Finally, mJH is 34.
Consider the following algebraic expression:4x - 6Step 1 of 2: Identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For avariable term, identify the variable and the coefficient of the term.
ANSWER and EXPLANATION
We want to identify the first term of the algebraic expression given:
[tex]4x-6[/tex]The first term of the expression is:
[tex]4x[/tex]The variable in the expression is the algebraic term. The algebraic term is:
[tex]x[/tex]Therefore, the coefficient of the first term is:
[tex]4[/tex]Write a number sentence that results in the sum or difference of zero.
Answer:
5x + 3 = 0
OR
35*35 /35 -35
hope this helps
The radius of a can is (3x^2-10). The height of the can is 2x. What is the surface area of a label that would be glued around the can?
Given:
The radius of a can is (3x^2-10). The height of the can is 2x.
To find:
The surface area of a label that would be glued around the can.
Solution:
It is known that the curved surface area of the cylinder is given by:
[tex]\text{CSA}=2\pi rh[/tex]So, the curved surface area of the given cylinder is:
[tex]\begin{gathered} \text{CSA}=2\pi(3x^2-10)(2x) \\ =2\pi(6x^3-20x) \\ =\pi(12x^3-40x) \end{gathered}[/tex]Thus, the answer is given above.
“Please help me I’ll mark u brainly please don’t do this for the points”
The measure of angle x in each of the triangles is:
1) 20°
2) - 49°
3) 8°
4) 33.33°
5) 10°
6) 3°
7) 1°
8) 2°
9) 6°
1) The measure of the inner angles in the triangle are 100°, 40°, and 2x°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
100° + 40° + 2x = 180°
140° + 2x = 180°
2x = 40°
x = 20°
2) The measure of the inner angles in the triangle are 99°, 37°, and (- x - 5)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
99° + 37° + ( - x - 5 )° = 180°
136° + (- x - 5)° = 180°
( - x - 5 )° = 44°
x = - 49°
3) The measure of the inner angles in the triangle are 60°, 60°, and ( - 12 + 9x)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
60° + 60° - 12 + 9x = 180°
120° - 12° + 9x = 180°
108° + 9x = 180°
9x = 72°
x = 8°
4) The measure of the inner angles in the triangle are 36°, 46°, and ( 2 - 3x)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
36° + 46° - 2° + 3x° = 180°
82° - 2° + 3x° = 180°
80° + 3x° = 180°
3x = 100°
x = 33.33°
5) The measure of the inner angles in the triangle are 71°, 50°, and ( 6x - 1 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
71° + 50° - 1° + 6x° = 180°
121° - 1° + 6x° = 180°
120° + 6x° = 180°
6x = 60°
x = 10°
6) The measure of the inner angles in the triangle are 45°, 90°, and ( 8x + 21 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
45° + 90° + 21° + 8x° = 180°
156° + 8x° = 180°
8x = 24°
x = 3°
7) The measure of the inner angles in the triangle are 85°, 64°, and ( 4x + 27 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
85° + 64° + 27° + 4x° = 180°
176° + 4x° = 180°
4x = 4°
x = 1°
8) The measure of the inner angles in the triangle are 44°, 104°, and ( 7x + 18 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
44° + 104° + 18° + 7x° = 180°
166° + 7x° = 180°
7x = 14°
x = 2°
9) The measure of the inner angles in the triangle are 125°, 25°, and ( - 5x )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
125° + 25° - 5x° = 180°
150° + 5x° = 180°
5x = 30°
x = 6°
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the poster has a border whose width is 2 cm on each side. if the printed material has the length of 6 cm and width of 8 cm, then find the area of the border.
Since the border has a width of 2cm, the length of the printed material and its border
is 2 + 6 + 2 = 10cm
and it's width iis
2 + 8 + 2 = 12cm
Hence the area is 10 x 12
Therefore,
the area of the border = 10x12 - 6x8 = 120 - 48 =72 square centimeters
Jenny wants to build a square deck that is attached to the back of her house.Because the deck will be square, each side of it will be equal in length to the back ofJenny's house. When Jenny's deck is finished, its area will be 324 ft? What is the lengthof the back of Jenny's house?
Jenny's deck is a square deck and has a side length equal to that of the back of Jenny's house. The area of a square of length L is;
[tex]A=L^2[/tex]Thus, we have;
[tex]\begin{gathered} L^2=324ft^2^{} \\ L=\sqrt[]{324} \\ L=18ft \end{gathered}[/tex]Therefore, the length of the back of Jenny's house is 18 feet.
What is the value of x? R x+820 P Q
Since we're working on a circumference, the sum of all the angles must be 360°
This way,
[tex]85+3x+73+x+82=360[/tex]Solving for x :
[tex]\begin{gathered} 85+3x+73+x+82=360 \\ \rightarrow240+4x=360 \\ \rightarrow4x=120 \\ \rightarrow x=\frac{120}{4} \\ \Rightarrow x=30 \end{gathered}[/tex]Between 6pm and 7pm, 5 mystery novels, 3 non-fiction books, 7 picture books, and 2 science fiction novels were returned to the library. What is the experimental probability that the next book returned to the library is a picture book?
Hey anyone mind helping me out? I would appreciate it!
We will use the relation [tex]\frac{QS}{SR}=\frac{PO}{OR}[/tex]
The correct option is option C)
What is similarity in triangle?
We say two triangles are similar if all the corresponding angles of the two triangle are equal and all the corresponding sides are in equal proportions.
We are given the diagram
We first prove that Δ[tex]POR[/tex]≅Δ[tex]QSR[/tex]
∠[tex]PRO[/tex]≡∠[tex]QRS[/tex] (Same angle)
∠[tex]RPO[/tex]≡∠[tex]RQS[/tex] (Corresponding angle)
Hence by AA test of similarity the two triangles are similar
And therefore the corresponding sides of two triangles are in same ratio
Therefore we have,
[tex]\frac{PO}{QS}} =\frac{OR}{SR} =\frac{PR}{QR}[/tex]
[tex]\frac{PO}{QS}} =\frac{OR}{SR}[/tex]
And hence, [tex]\frac{QS}{PO}} =\frac{SR}{OR}[/tex]
[tex]\frac{QS}{SR}} =\frac{PO}{OR}[/tex]
Hence we will select option C)
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Find the monthly interest payment in the situation below.Vic bought a new plasma TV for $2400. He made a down payment of $100 and then financed the balance through the store. Unfortunately, he was unable to make the first monthly payment and now pays 4% interest per month on the balance (while he watches his TV).What is Vic's monthly interest payment? $ enter your response here (Round to the nearest dollar as needed.)
Given:
Vic bought a new plasma TV for $2400.
He made a down payment of $100 and then financed the balance through the store.
The interest per month is 4% on the balance.
To find:
Vic's monthly interest payment.
Explanation:
The cost of a plasma Tv is $2400.
The down payment made is $100.
Balance amount for financing is $2400 - $100 = $2,300.
Since the interest rate is 4% per month
So, the monthly interest payments will be,
[tex]2300\times\frac{4}{100}=92[/tex]The monthly interest payments will be $92.
Final answer:
The monthly interest payments will be $92.
PLEASE SOLVE SOON
Solve for x and explain each step you take as you solve the problem. Verify your answer is correct.
-7 over 6 times x - 6 equals -48
The value of x for the given algebraic expression is 36.
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=9x+1.
The question gives the linear expression in text format. Therefore, you should convert the text in algebraic expression. See some tips:
the word over in math can be represented by division (÷ or / )the word times in math can be represented by product ( x or · )the word equals in math can be represented by equality ( = )Converting the text into algebraic expression, you have:
[tex]\frac{-7}{6}[/tex] * x - 6 = -48
-7x -6*6= -48*6 ( Multiply both sides by 6)
-7x -36 = -288
-7x = -288 +36
-7x = -252
x= -252 / -7
x=36
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Notebook paper is approximately 0.004 in. thick. Using the formula for the width W, determine how wide a square piece of notebook paper would need to be successfully fold it in half 13 times , alternating horizontal and vertical folds.
The question has already provided a formula to determine the width (W). The question also provides the thickness as well as the number of times (n) the paper would be folded. Hence, we have;
[tex]\begin{gathered} W=\pi\times T\times2\frac{3(n-1)}{2} \\ W=3.14\times0.004\times2\times\frac{3(13-1)}{2} \\ W=0.02512\times\frac{3(12)}{2} \\ W=0.02512\times18 \\ W=0.45216\text{ inches} \end{gathered}[/tex]The notebook paper would have to be 0.45216 inches wide
The formula has also been provided that would help in calculating the length of a long rectangular piece of paper. We've been given the thickness of the paper and the number of times it (n) it would be folded. Therefore, we now have;
[tex]\begin{gathered} L=\frac{\pi T}{6}(2^n+4)(2^n-1) \\ L=\frac{3.14\times0.002}{6}(2^{12}+4)(2^{12}-1) \\ L=0.00104667(4096+4)(4096-1) \\ L=0.00104667(4100)(4095) \\ L=17573.066\text{ inches} \end{gathered}[/tex]the area of a rectangle is[tex]2x ^{2} - 7x - 4[/tex]if the area is 45, what is the positive value for x
The given expression is,
[tex]2x^2-7x-4=45[/tex]As the area is equal to 45 and equating the areas.
[tex]\begin{gathered} 2x^2-7x-49=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{ =}\frac{\text{7}\pm\sqrt[]{49+4\times2\times49}}{2\times2} \\ =\frac{7\pm21}{4} \\ =7 \end{gathered}[/tex](taking positive values)
The answer is 7
Is the point (11,37) on the graph of the function f(x) = 4x - 3?
Yes
No
It is impossible to determine
The point (11 , 37 ) does not lies in the given function f(x) = 4x - 3. Since the values x , y does not satisfy the condition .
Explanation:How to check whether the points satisfy the equation :
Choose x and solve the equation for y, or, to find points on the line y = mx + b. Select y and solve for x, to check a system of equations by substitution.Enter your x and y values into the original equations. Your answer is correct if both simplified expressions are true.Given function, f(x) = 4x - 3
also given a point (11 , 37)
to check whether the given point satisfies the given function,
(x , y) = (11,37)
substitute values of x and y in the given function,
y = 4x - 3
37 = 4 x (11) - 3
37 = 44 -3
37 ≠ 41
∴ the given points (11,37 ) does not satisfy the given function
f(x) = 4x-3.
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Which is the graph of the given function? ft=5sin3t
The graph is based on amplitude.
Given the function:
f(t) = 5sin3t
To draw the graph of above function.
The function g(t) = sin t is a periodic function with amplitude [tex]a_{0}[/tex] = 1 and period [tex]t_{0}[/tex] = 2[tex]\pi[/tex]
For our case, the 5 that multiplies g (t) increases the amplitude so that,
a = 5 x 1 = 5 and the 3 that multiplies the variable increases the period being t = 2[tex]\pi[/tex] x 1/3 = 2[tex]\pi[/tex]/3
What is Graph?
Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.
See the graph in the bottom of explanation.
Hence, The graph is based on amplitude.
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Shannon went to the book store. She bought a book for $7.00, a magazine for $4.25 and a bookmark for $1.99. Her purchase was 15% off. She handed the cashier a $20 bill. How much change did she
Show work?
Answer:
8.74$
Step-by-step explanation:
so first what you want to do is that you want to add $7 with 4.25 dollars plus 1.99 dollars the next thing you want to do is take 85% of this number you will get 0.85 times that sum
that sum is 13.24. now because she is getting 15% off of her purchase that means you want to take 85% of that 13.24 number . so you will get 1 1.254 you will need to round this because it is in dollars . so you will get 11.25 as her purchase price . now because she gave a $20 bill you need to subtract that number from 20 and you will get 8.746 which is rounded to 8.74 because it is in dollars that is the answer that is her change
