Explanation
We are given the following:
[tex]Jasmine\text{ }can\text{ }run\text{ }4\frac{5}{6}\text{ }miles\text{ }in\text{ }\frac{2}{3}\text{ }of\text{ }an\text{ }hour[/tex]We are required to determine how many miles she can run in 1 hour.
This is achieved thus:
[tex]\begin{gathered} 4\frac{5}{6}miles\Rightarrow\frac{2}{3}hour \\ \therefore1hour\Rightarrow4\frac{5}{6}\div\frac{2}{3} \\ =\frac{29}{6}\div\frac{2}{3} \\ =\frac{29}{6}\times\frac{3}{2} \\ =\frac{29}{2}\times\frac{1}{2} \\ =\frac{29}{4} \\ =7\frac{1}{4} \end{gathered}[/tex]Hence, the answer is:
[tex]7\frac{1}{4}\text{ }miles[/tex]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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simplify completely: 3b2 – 75 / 3b2 – 27b + 60
Answer:
[tex]\frac{(b+5)}{(b-4)}[/tex]
Step-by-step explanation:
[tex]\frac{3b^{2}-75}{3b^{2}-27b + 60}[/tex]
[tex]\frac{3(b^{2}-25)}{3(b^{2}-9b + 20)}[/tex]
Simplify numerator:
where [tex](b^{2} -25) = (b-5)(b+5)[/tex]
[tex]\frac{3(b-5)(b+5)}{3(b^{2}-9b + 20)}[/tex]
Simplify denominator:
looking at [tex]b^{2} - 9b + 20[/tex]
where a = 1
b = -9
and c = 20
We are looking for two numbers that sum to -9 and multiply to 20:
-5 + (-4) = -9
-5 * (-4) = 20
so [tex]b^{2} -9b+20 = (b-5)(b-4)[/tex]
insert into denominator:
[tex]\frac{3(b-5)(b+5)}{3(b-4)(b-5)}[/tex]
remove: 3(b-5) from numerator and denominator:
[tex]\frac{(b+5)}{(b-4)}[/tex]
Suppose a basketball player has made 273 out of 385 free throws. If the player makes the next 3 free throws, I will pay you $27. Otherwise you pay me $16. Step 2 of 2 : If you played this game 891 times how much would you expect to win or lose?
By probability, If you played 891 times, you expect to lose $16.
Total Possible Throws = 385
Number of throws = 273
Let P(T) be the Probability that the player makes the next throw
P(T) = 273 / 385
The probability that the player makes the next three throws is then given by:
= P(T) × P(T) × P(T)
= 273 / 385 × 273 / 385 × 273 / 385
= (273 / 385)²
= 0.35653794139
= 0.357
Let P(T') be the probability the player doesn't make the next two throws
P(T') = 1 - P(T)
P(T') = 1 - 0.357
P(T') = 0.643
The expected gain for the player turns is given by:
(Probability of making both throws) * $27 + (Probability of NOT making both throws) x ( - $16 )
= 0.357 × $27 - 0.643 × $16
= $9.639 - $10.288
= - $0.649
b.
The probability that he makes the next 891 throws.
= P(T)⁸⁹¹
= (273/385)⁸⁹¹
Let P(T') be the probability the player doesn't make the next three throws
P( T' ) = 1 - P( T )
P( T' ) = 1 - 19.449493e-134
P( T' ) = 1
The expected gain or loss for the player turns is given by:
(Probability of making all 626 throws) * $5 + (Probability of NOT making all 626 throws) x (-$10)
= (273/385)⁸⁹¹ × 27 + 1 × - 16
= - $16
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in how many ways can 9 people stand in a line
what is the mathematical expression of “the sum of a number x and three”
Answer: X + 3
Step-by-step explanation:
Sum hints as to an addition statement and it specifies a variable X and the number 3 so the expression would be X + 3.
SUM MEANS ADDITION
HERE IT MEANS THE ADDITION OF x and 3
written as
[tex]x + 3[/tex]
HOPE THIS HELPS
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.
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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11 Evaluate d-fif d = 7 and f = -15.
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?
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]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
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.
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
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 volume of the cone?5 cm21 cmA 70π cm³B 105 cm³C 175 cm³D 525 cm³
The formula to find the volume of a cone is:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \text{ Where} \\ r\text{ is the radius of the base} \\ h\text{ is the height} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} r=5cm \\ h=21cm \end{gathered}[/tex][tex]\begin{gathered} V=\frac{1}{3}\pi r^{2}h \\ V=\frac{1}{3}\pi(5cm)^{2}(21cm) \\ V=\frac{1}{3}\pi(525cm^3) \\ V=\frac{525\pi}{3}cm^3 \\ V=175\pi cm^3 \end{gathered}[/tex]Answer
C 175π
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.
Find the distance between these two points(-5,3) (-2,-3)
Explanations:
Let the first pont be P (-5, 3)
[tex]x_1=-5,y_1=\text{ 3}[/tex]Let the second point be Q (-2, -3)
[tex]x_2=-2,y_2=\text{ -3}[/tex]The distance between two points is given by the equation:
[tex]\begin{gathered} PQ\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Substituting the values of x}_1,y_1,x_2,y_2\text{ into the given equation } \\ PQ\text{ = }\sqrt{(-2-(-5))^2+(-3-3)^2} \\ PQ\text{ = }\sqrt{(-2+5)^2+(-6)^2} \\ PQ\text{ = }\sqrt{(3)^2+(-6)^2} \\ PQ\text{ = }\sqrt{9+36} \\ PQ\text{ = }\sqrt{45} \end{gathered}[/tex]The distance between the two points is √45 units
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
Find the solution(s) to x2 - 16x + 64 = 0.O A. x= -2 and x = 32O B. x = 8 and x= -8O C. x = 8 only7O D. x = 4 and x = 16
Given:
Given the quadratic equationt
[tex]x^2-16x+64=0[/tex]Required: Solution to the quadratic equation
Explanation:
Write the quadratic equation as
[tex]\begin{gathered} (x-8)^2=0 \\ \implies x-8=0 \\ \implies x=8 \end{gathered}[/tex]Option C is correct.
Final Answer: The solution t the squadratic equation is x = 8 only.
A plane flies 452 miles north andthen 767 miles west.What is the angle of theplane's resultant vector?Hint: Draw a vector diagram.[?]
see the figure below to better understand the problem
we have that
tan(x)=452/767
please help asap!a. if the input is -8, what is the output?b. if the output was 21, what was the input?
a) The output is 45
b) The input was -4
Here, we want to use the relationship between the input and the output to answer the questions
While x is our input, f(x) is given as our output
The relationship between the two is given as;
[tex]f(x)\text{ = -6x-3}[/tex]a) Here, we have an input, and we want to get the output
To solve this, we just need to substitute the value of -8 for x in the relation
We have this as follows;
[tex]\begin{gathered} f(-8)\text{ = -6(-8)-3} \\ f(-8)\text{ = 48-3 = 45} \end{gathered}[/tex]b) Here, we have the output, but we want to get the input
What this simply mean is that we are to find the value of x
We simply substitute 21 for f(x)
Thus, we have;
[tex]\begin{gathered} 21\text{ = -6x-3} \\ 21\text{ + 3 = -6x} \\ \\ -6x\text{ = 24} \\ \\ x\text{ = }\frac{24}{-6} \\ \\ x\text{ = -4} \end{gathered}[/tex]The flight of a fireworks rocket is given by the function: h(t)= -16t^2 + 84t+5 Where h(t) is the height in feet and t, the time in seconds. How long will the rocket take to reach its maximum height?Round your answer to 2 decimal places.
Given:
The flight of a fireworks rocket is given by the function:
[tex]h(t)=-16t^2+84t+5[/tex]Required:
How long will the rocket take to reach its maximum height?
Explanation:
We will first find critical points
[tex]\begin{gathered} h^{\prime}(t)=-32t+84 \\ \text{ Now, put }h^{\prime}(t)=0 \\ t=\frac{21}{8} \\ \text{ At }t=\frac{21}{8}\text{ we get stationary points.} \end{gathered}[/tex]To check maximum and minimum value
[tex]\begin{gathered} h^{\prime}^{\prime}(t)=-32(<0) \\ \text{ At }t=\frac{21}{8}\text{ the function is maximum.} \end{gathered}[/tex]Asnwer
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
Simplify the following fraction: \frac{16}{18}
18
16
The simplest form of the fraction 18/16 is 9/4.
Fraction:
A fraction is a number that represents part of a whole.
A fraction is written in the form p/q, where q ≠ 0.
Given,
There has been given a fraction 18/16, that has to be simplified.
The steps to simplifying fractions,
First, we have to find the GCD (or HCF) of numerator and denominator
GCD of 16 and 18 is 2
Now we have to divide both the numerator and denominator by the GCD
16 ÷ 2
18 ÷ 2
Now we get the reduced fraction as, 8/9.
Therefore, 16/18 simplified to lowest terms is 8/9.
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A professor has students keep track of the social interactions for a week the number of social interactions over the week and selling in the following group frequency distribution how many students had at least 60 social interactions for the week?
For at lest 60 social interaction:
So social interaction is:
60 - 64 4
65 - 69 3
70 - 74 0
75 - 79 4
So student of these social interaction is:
[tex]\begin{gathered} =4+3+0+4 \\ =11 \end{gathered}[/tex]So total 11 students had at lest 60 social interaction.
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
Newton's law of cooling is T = AeW! + C, where is the temperature of the object at time t, and is the constant temperature of the surrounding medium. Supposethat the room temperature is 73, and the temperature of a cup of coffee is 174' when it is placed on the table. How long will it take for the coffee to cool to 131" fork = 0.06889192 Round your answer to two decimal places.
Solution
We are given the equation
[tex]T=Ae^{-kt}+C[/tex]Room temperature, C = 73 degrees
Temperature at time t = 0, is T = 174 degrees
[tex]\begin{gathered} T=Ae^{-kt}+C \\ 174=Ae^0+73 \\ 174=A+73 \\ A=174-73 \\ A=101 \end{gathered}[/tex]Therefore, the equation becomes
[tex]T=101e^{-kt}+73[/tex]We want to find t = ?, when T = 131 degrees and k = 0.0688919
[tex]\begin{gathered} T=101e^{-0.0688919t}+73 \\ 131=101e^{-0.0688919t}+73 \\ 131-73=101e^{-0.0688919t} \\ 58=101e^{-0.0688919t} \\ e^{-0.0688919t}=\frac{58}{101} \\ e^{-0.0688919t}=\frac{58}{101} \\ -0.0688919t=ln(\frac{58}{101}) \\ t=-\frac{1}{0.0688919}ln(\frac{58}{101}) \\ t=8.051418328 \\ t=8.05minutes\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]Therefore, the answer is
[tex]8.05minutes[/tex]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]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.
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
