Solution:
Let the score for the seventh test be represented below as
[tex]=x[/tex]The mean score t be attained after the sevent tests is
[tex]mean=83[/tex]The scores from the 6 tests are given below as
[tex]88,73,81,80,79,94[/tex]To figure out the seventh score, we will do the calculation below
[tex]\begin{gathered} mean=\frac{additionofthescores}{number\text{ of tests}} \\ 83=\frac{88+73+81+80+79+94+x}{7} \\ 83=\frac{495+x}{7} \\ cross\text{ multpily} \\ 83\times7=495+x \\ 495+x=581 \\ x=581-495 \\ x=86 \end{gathered}[/tex]Hence,
The final asnwer is
[tex]\Rightarrow86[/tex]Use identities to find tan, csc, sec, and cot. Where necessary, rationalize denominators
We are given:
[tex]sin\text{ }\theta=\frac{3}{5},cos\text{ }\theta=\frac{4}{5}[/tex]The tangent is defined as the ratio of the sine and the cosine:
[tex]tan\text{ }\theta=\frac{sin\text{ }\theta}{cos\text{ }\theta}[/tex]Calculating:
[tex]\begin{gathered} tan\text{ }\theta=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{5}\cdot\frac{5}{4} \\ \\ tan\text{ \theta}=\frac{3}{4} \end{gathered}[/tex]The cotangent is the reciprocal of the tangent:
[tex]\begin{gathered} \cot\theta=\frac{1}{\tan\theta} \\ \\ \cot\theta=\frac{1}{\frac{3}{4}}=\frac{4}{3} \end{gathered}[/tex]The secant is the reciprocal of the cosine:
[tex]\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{1}{\frac{4}{5}} \\ \\ \sec\theta=\frac{5}{4} \end{gathered}[/tex]The cosecant is the reciprocal of the sine:
[tex]\begin{gathered} \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{3}{5}} \\ \\ \csc\theta=\frac{5}{3} \end{gathered}[/tex]The radius of a circle is 18 miles. What is the area of a sector bounded by a 72° arc?Give the exact answer in simplest form. ____ square miles. (pi, fraction,)
Area = (π*r^2*α)/360°
α =72°
r = 9 mi
Then
A = (π * 81 * 72°)/360° = 81/5π square meters
Kaitlin sold t-shirts at a festival and made a profit of $71 . She made $4 for each t-shirt she sold. Her total expenses were $25 . How many t-shirts did she sell?
The t-shirts she sell is 24.
What is profit and selling price?
Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.
The selling price is the price that the buyer pays to buy a product or goods. This is a price above cost and includes a profit ratio.
According to Question, Christine sold the t- shirts at $4 each and she earned a profit of $71 and his total expenses were $25
Let the total number of t- shirts sold by Christine be "x"
Profit = Selling price – Expenses
Selling price is given as:
selling price = total number to t-shirt sold ×price of each t shirt
selling price = n ×4
71 = (n×4) -24
71 + 25 = n×4
96/4 = n
n = 24
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The area of a rectangular field is 5082 yd². If the length of the field is 77 yards, what is its width?
Answer:
The width is 66 yardsStep-by-step explanation:
Area of rectangle formula:
A = lw, where l- length, w- widthGivenA = 5082 yd²,l = 77 yd.SolutionFind the width by substituting the given values:
5082 = 77ww = 5082/77w = 66 ydAs a fraction in simplest terms, what would you multiply the first number by to get the second? First number: 62 Second number: 52
We will multiply by 26 / 31 in the first number to get second number for fraction in simplest form.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
In the fraction,
The first number = 62
The second number = 52
Let the number which can be multiply by the fraction = x
Since, The given condition is,
Multiply the first number by to get the second number.
So, We can formulate;
⇒ 62 × x = 52
Solve for x, as;
⇒ 62 × x = 52
⇒ 62x = 52
Divide by 62, we get;
⇒ x = 52 / 62
Multiply and divide by 2;
⇒ x = 26 / 31
Therefore,
We will multiply by the number 26 / 31 in the first number to get second number for fraction in simplest form.
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Please help!
4|x+7| < 8
3
so this is a
You also will not know precisely how many sentences will appear in the random paragraph. But some piano roll artists made a name with pieces that could not possibly be played by an precise individual. Most of his research deal with difficult meters and polyrhythms. Many include distinct voices enjoying the identical line at different tempos, usually in odd ratios. On top of this, most of the traces themselves tend to be highly dissonant and exhausting to actually play. Someday we might come nose to nose with pure house, that could presumably be a nothingness waiting to be filled.
A circle passes through (-2, 6) , (2, 8) , and (5, -1) Using the general form of a circle and the points above, fill in missing numbers to create the system of equations. (-2, 6) creates D + E + 1F = (2, 8) creates D + E + 1F = (5, -1) creates D + E + 1F = Solve the system of equations that you created, and write the equation for the circle by filling in the values for D, E, and F.
The equation of the circle passing through points (-2, 6) , (2, 8) , and (5, -1) is given as follows:
(x - 2)² + (y - 3)² = 25.
Equation of a circleThe equation of a circle with center (x*, y*) and radius r is given according to the following rule:
(x - x*)² + (y - y*)² = r².
The circle passes through point (-2,6), hence the first equation of the system is given as follows:
(-2 - x*) + (6 - y*)² = r².
r² = x*² + 4x* + 4 + y*² - 12y* + 36.
The circle also passes through point (2,8), hence the second equation of the system is given as follows:
(2 - x*) + (8 - y*)² = r².
r² = x*² - 4x* + 4 + y*² - 16y* + 64.
The final point is point (5,-1), meaning that the third equation is:
(5 - x*) + (-1 - y*)² = r².
r² = x*² - 10x* + 25 + y*² + 2y* + 1.
The system of equations to find the coordinates of the center and the radius is given as follows:
x*² + y*² + 4x* - 12y* + 40 - r² = 0.x*² + y*² - 4x* - 16y* + 68 - r² = 0.x*² + y*² - 10x* + 2y* + 26 - r² = 0.The solution to the system is given as follows:
x* = 2, y* = 3, r² = 25.
Hence the equation of the circle is:
(x - 2)² + (y - 3)² = 25.
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hi i need some help. on the “select” part, the options are 1997-2006.
From the given table that represents the population in a small coastal communityfor the period 1997 to 2006, let's answer the following questions.
(a) Average rate of change of the population between 1999 and 2002.
To find the average rate of change, apply the formula below:
[tex]Average=\frac{y2-y1}{x2-x1}[/tex]Where:
x1 = 1999
x2 = 2002
y1 = the population in 1999 = 1,336
y2 = the population in 2002 = 1,483
Thus, we have:
[tex]\begin{gathered} Average=\frac{1483-1336}{2002-1999} \\ \\ Average=\frac{147}{3} \\ \\ Average=49 \end{gathered}[/tex]Therefore, the average rate of change of the population between 1999 and 2002 is
49
(b) What was the average rate of change of the population between 2001 and 2005.
To find the average rate of change, apply the formula:
[tex]Average=\frac{y2-y1}{x2-x1}[/tex]Where:
x1 = 2001
x2 = 2005
y1 = population in 2001 = 1591
y2 = population in 2005 = 801
Thus, we have:
[tex]\begin{gathered} Average=\frac{801-1591}{2005-2001} \\ \\ \text{Average}=\frac{-790}{4} \\ \\ \text{Average}=-197.5 \end{gathered}[/tex]Therefore, the average rate of change in the population between 2001 and 2005 was -197.5
(c) For what period of time was the population increasing.
From the given table, we can see the table was increasing from 1997 to 2001
The population was increasing from 1997 to 2001
(d) For what period was the population decreasing.
From the table, the population was decreasing from 2002 to 2006
The population was decreasing from 2001 to 2006
ANSWER:
• (a) 49
,• (b) -197.5
,• (c) 1997 to 2001
,• (d) 2001 to 2006
For the figure below, give the following
Answer:
Step-by-step explanation:
B
You will have $ in 15 years if you set aside $100 a year at 6%.
The most appropriate choice for simple interest will be given by -
Amount obtained = $28.5
What is simple interest?
Simple interest is the interest earned on a certain principal at a certain rate over a certain period of time.
If principal is p, rate is r%, time is t years
Simple interest = [tex]\frac{p \times r \times t}{100}[/tex]
On adding principal and simple interest, we get amount.
Amount = Principal + Simple interest.
Principal = $15
Rate = 6%
Time = 15 years
Simple interest = [tex]\frac{15 \times 6 \times 15}{100}[/tex]
= $13.5
Amount obtained = $(15 + 13.5)
= $28.5
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Find an
an equation for the perpendicular bisector of the line segment whose
endpoints are (–4,3) and (−8,—3).
Answer:
y = (-2/3)x + 4
Step-by-step explanation:
the number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. (these values are typical of much of the united states.) the national lightning detection network uses automatic sensors to watch for lightning in a sample of 25 randomly chosen square kilometers. what are the mean and standard deviation of the mean number of strikes per square kilometer?
The mean and standard deviation are given as 6 and 0.48 respectively.
According to the question The Population Mean number of strikes per square kilometer (μ) = 6 and the Population standard deviation of strikes per square kilometer (σ) = 2.4. The Sample size is equal to (n) = 16. We know that the sample mean number of strikes per square kilometer (m) = mean Number of strikes per square kilometer in the population. From this observation it is clear that the mean will be equal to
μ = m = 6
So, the Sample mean = 5
Now, the Standard deviation = standard error = σ/√n. Now we get
Standard Error = 2.4 / √25
Standard Error = 2.4 / 5
Standard Error = 0.48
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What is the solution of -8/2y-8 = 5/y+4 - 7y+8/y^2-16?
y = -4
y = -2
y = 4
y = 6
The correct option for the fraction with polynomials is y=6.
Fractions with polynomials.Expressions of more than two algebraic terms that contain different powers of the same variable is a polynomial.
The polynomial fraction is an expression of polynomial divided by another polynomial.
We can solve the fraction to get the value of y as follows;
[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y²-16)]
[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y+4)(y-4)]
[-8/(2y-8)]= [5(y+4)-(7y+8)]/(y+4)(y-4)] (L.C.M) of the fraction
[-8/(2y-8)]= (5y-20-7y-8)/(y+4)(y-4)
[-8/(2y-8)]= (-2y-28)/(y+4)(y-4)
[-8/2(y-4)]= (-2y-28)/(y+4)(y-4)
[-8/2(y-4)]= [-2(y-14)]/(y+4)(y-4)
[-4/(y-4)]= [-2(y-14)]/(y+4)(y-4)
Multiply both sides of the equation by -(y-4)
4= 2(y-14)/(y+4)
Cross multiply
4(y+4)=2(y+14)
Divide through by 2
2(y+4)=y+14
2y+8=y+14
collect like terms
2y-y=14-8
y=6.
Hence, we can state that the value of y for the polynomial with fraction is 6.
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x+3/5 + x-2/5
as a single fraction
Answer:
x+3/5 + x-2/5
simply add variable
x+x +3/5-2/5
2x+3/5-2/5
taking L.C.M
5*2x+3-2/5
10x+1/5
The time in seconds that it takes an object to fall d feet can be found
using the expression ((sqrt(d))/(4)) , Suppose aiden drops a tennis ball from a height of 50 feet at the same time masons drops a similar tennis ball from a height of 20 feet . How much longer will it take Aiden's tennis ball to reach the ground than Mason's tennis ball? Round to the nearest hundredth .
Aiden's tennis ball will reach the ground 0.65 seconds than Mason's tennis ball
How to determine the time difference in reaching the groundThe function of time with respect to distance is given as
(sqrt(d)/(4))
Rewrite the function properly
This is represented as follows
√d/4
It can also be written as
t = 1/4√d
From the question, we have
Aiden = 50 meters
Mason = 20 meters
The time difference is then calculated as
T = t₁ - t₂
So, we have
T = 1/4√d₁ - 1/4√d₂
The equation becomes
T = 1/4√50 - 1/4√20
This gives
T = 1/4(√50 - √20)
Evaluate
T = 0.65
Hence, the time difference is 0.65 seconds
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Please help ASAP starting to fall behind! This equation really confuses me and if someone could help that would be amazing!
Given the function:
f(x) = x² - 4x - 2
Find the following values.
a) f(2)
f(2)=
b) f(4)
f(4)=
c) f(-3)
f(-3)=
I need help with the question below please:A painter must thin some paint for use in a sprayer. If the recommended rate is 1/9 pint of water per gallon of paint, how many total gallons will there be after thinning 36 gallons of paint?
ABCD - FECG B 5 E 6 100° 5 A 60° С 4 120° G w D W = ? 1°
From the figure, draw from D parallel to AB.
Calculate angle D from triangle DWC = 180 - (90+60) = 180 - 150 = 30
Angle D = 30
Angle W = 90 + 30 = 120
Final answer W = 120
y=3/5x+3 graph the line
We want to graph the line:
[tex]y=\frac{3}{5}x+3[/tex]For doing so, we will choose two different x-values, and we will find its correspondent y-values. This gives us two different points, and when we trace the line that passes through those points, we will have the line we wanted.
In this exercise, we will choose x=0, and x=5.
For x = 0
[tex]y=\frac{3}{5}(0)+3=0+3=3[/tex]This gives us the point (0,3).
For x = 5
[tex]y=\frac{3}{5}(5)+3=\frac{15}{5}+3=3+3=6[/tex]This gives us the second point: (5,6).
Now, graphing the points on a cartesian plane, and drawing the line between them, we obtain:
{(2, 1), (-7, -1), (-5, -5), (9, -4), (-3, -3) }
Domain:
Range:
Rewrite one fourteenth times x cubed times y plus three fourteenths times x times y squared using a common factor.
The equation that represents the sentence will be (1/14)xy ·[x² + 3y].
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.
The sentence is given below.
One-fourteenth times x cubed times y plus three-fourteenths times x times y squared.
Convert the sentence into an expression. Then we have
⇒ (1/14)x³y + (3/14)xy²
Simplify the expression, then we have
⇒ (1/14)x³y + (3/14)xy²
⇒ (1/14)xy ·[x² + 3y]
The equation that represents the sentence will be (1/14)xy ·[x² + 3y].
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Pleas help me !!!! Please!!!
The most appropriate choice for domain of a functions will be given by -
What is a domain of a function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
The set of values for which the function is defined is called domain of the function.
Here, from the graph, the set of values of x axis for which the graph is drawn is [tex]-6\leq x \leq 6[/tex].
And values of x - axis represents the domain.
So domain of function is {x ∈ [tex]\mathbb{R}[/tex], [tex]-6 \leq x \leq 6[/tex]}
Third option is correct.
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Look at the table below. Which of the following is the constant rate of change?
Given data:
The first value of x is a=-16.
The first value of y is b=20.
The second value of x is c=-12.
The second value of y is d=15.
The expression for the rate change is,
x=(d-b)/(c-a)
Substitute the given values in thhe above expression.
x=(15-20)/(-12+16)
=-5/4
Thus, he constant rate of change is -5/4.
Which expression is equivalent to 6(−3.1y − 10.8)?
−18.6y − 64.8
−18.6y − 10.8
2.9y − 4.8
2.9y − 10.8
Answer:
The answer for the question is = -18.6y - 64.8
f(x)=6x^2+11 inverse
Answer:
√6(x−11)/6
Step-by-step explanation:
f^−1(x)=√6(x−11)/6
22 Olivia has $700 in her bank account at the beginning of the
summer. She wants to have at least $150 in her account at the
end of the summer. Each week she withdraws $40 for food
and entertainment.
a. Write an inequality for this situation. Let x represent
the number of weeks she withdraws money from her
account.
b. What is the maximum whole number of weeks
that Olivia can withdraw money from her account?
Explain how you know your answer is correct.
a. The amount remaining in the account after x week is 700 - 40x
b. Olivia can withdraw can withdraw money from her account money for approx. 13 weeks.
Let x represent the number of weeks. Then the amount of withdrawal in this time is 40x
So, the amount remaining in the account after x weeks is 700 - 40x
Since he needs 150$ in the account for safety net, we must have
700 – 40x ≥ 150
So,
700 - 150 ≥ 40x
550 ≥ 40x
550/40 ≥ x
x ≤ 13.75
Hence, he can withdraw money for approx. 13 weeks.
What is withdraw?Withdrawal involves removing money from a bank account, savings plan, pension or trust. In some cases, conditions must be met for funds to be withdrawn without penalty, and an early withdrawal penalty usually occurs when a condition of the investment agreement is violated. Withdraw money from account: With this account you can withdraw a maximum of $500 per day. withdraw money/money/savings With the financial crisis, people had to withdraw their savings.
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I dont know how to do this help!
Answer:
4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{48}[/tex] is not in simplest form, however, 48 contains a perfect square as a factor, that is 16 × 3
using the rule of radicals
[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then
[tex]\sqrt{48}[/tex]
= [tex]\sqrt{16(3)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]
= 4[tex]\sqrt{3}[/tex] ← in simplest form
A tree initially measured 18 feet tall. Over the next 3½ years, it grew to a final height of 35½ feet. During those 3½ years, what was the average yearly growth rate of the height of the tree?
Answer:
The average yearly growth o
Explanation:
Given that the tree grew from 18 ft 35 1/2 feet in 3 1/2 years.
The growth within these years is:
35 1/2 - 18
= 35.5 - 18
= 17.5
Now, this averages:
17.5/3.5 (3.5 is the number of years)
= 5
The average is 5 ft per year
Which graph shows y=3⌊x⌋−4? Responses Graph of the function f open argument x close argument equals greatest integer on a coordinate plane. The horizontal x axis ranges from negative 10 to 10. The vertical f of x axis ranges from negative 10 to 10. The graph is a step function with 7 vertical line segments. Each line segment is one unit long, with a closed point on the left side and an open point on the right side. Moving left to right, each line segment is shifted to the right one unit and up one unit, compared to the line segment before it. The endpoints of the first three line segments are as follows. Segment one. Begin ordered pair negative 2 comma negative 10 end ordered pair and begin ordered pair negative 1 comma negative 10. Segment two. Begin ordered pair negative 1 comma negative 7 end ordered pair and begin ordered pair 0 comma negative 7 end ordered pair. Segment three. Begin ordered pair 0 comma negative 4 end ordered and 1 comma negative 4 end ordered pair. The pattern continues with the last line segment at an endpoint. Image with alt text: Graph of the function f open argument x close argument equals greatest integer on a coordinate plane. The horizontal x axis ranges from negative 10 to 10. The vertical f of x axis ranges from negative 10 to 10. The graph is a step function with 7 vertical line segments. Each line segment is one unit long, with a closed point on the left side and an open point on the right side. Moving left to right, each line segment is shifted to the right one unit and up one unit, compared to the line segment before it. The endpoints of the first three line segments are as follows. Segment one. Begin ordered pair negative 2 comma negative 10 end ordered pair and begin ordered pair negative 1 comma negative 10. Segment two. Begin ordered pair negative 1 comma negative 7 end ordered pair and begin ordered pair 0 comma negative 7 end ordered pair. Segment three. Begin ordered pair 0 comma negative 4 end ordered and 1 comma negative 4 end ordered pair.
The graph for the given equation is plotted below.
The given equation is y=3x-4.
What is the 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.
Put x=0, 1, 2, 3, 4,....in the given equation and solve for y
When x=0, y=-4
When x=1, y=-1
When x=2, y=2
When x=3, y=5
Plot the coordinates (0, -4), (1, -1), (2, 2) and (3, 5) on the graph.
Therefore, the graph for the given equation is plotted below.
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5xº35°60°solve for x
In every triangle the addition of all internal angles is always 180 degrees.
So this means we can build this equation
5x + 35 + 60 = 180
now separate x values and numerical values
5x = 180 - 60 - 35
x= (180 - 60 - 35)/ 5 = 85/5 = 17
