The value of x can be determined as,
[tex]\begin{gathered} \tan 39^{\circ}=\frac{x}{15} \\ x=15\tan 39^{\circ} \\ x=12.15 \end{gathered}[/tex]Thus, the required value of x is 12.15.
Admission to a baseball game is $4.00 for general admission and $5.50 for reserved seats. The receipts were $5196.50 for 1181 paid admissions. How many of eachticket were sold?
Given:
Admission to a baseball game is $4.00 for general admission and $5.50 for reserved seats.
Let the number of tickets of general admission = x
Let the number of tickets of reserved seats = y
The receipts were $5196.50 ⇒ 4x + 5.5y = 5196.50
The paid admissions 1181 ⇒ x + y = 1181
So, we have the following system of equations:
[tex]\begin{gathered} 4x+5.5y=5196.50\rightarrow(1) \\ x+y=1181\rightarrow(2) \\ \text{from}(2)\colon x=1181-y\rightarrow(3) \end{gathered}[/tex]Substitute with x from (3) into (1) then solve to find y
[tex]\begin{gathered} 4(1181-y)+5.5y=5196.50 \\ 4\cdot1181-4y+5.5y=5196.5 \\ 4724+1.5y=5196.50 \\ 1.5y=5196.50-4724 \\ 1.5y=472.5 \\ y=\frac{472.5}{1.5}=315 \end{gathered}[/tex]Substitute with y into equation 3 to find x:
[tex]x=1181-315=866[/tex]So, the answer will be:
The number of tickets of general admission = 866
The number of tickets of reserved seats = 315
A student was asked to find a 95% confidence interval for widget width using data from a random sample of size n = 17. Which of the following is a correct interpretation of the interval 11.5 < μ < 27.3? Check all that are correct.
The correct interpretation of the 95% confidence interval is that:
We are 95% sure that the true population mean widget width is between 11.5 and 27.3 units.
What is the interpretation of a x% confidence interval?The x% confidence interval means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds of the confidence interval, given by a and b.
The bounds of the confidence interval are given by the estimate of the population parameter plus/minus the margin of error found from the sample size/standard deviation.
In the context of this problem, the bounds of the interval are already given as follows:
11.5 < μ < 27.3
The parameter being estimated is the mean widget width, hence the interpretation is that we are are 95% sure that the true population mean widget width is between 11.5 and 27.3 units.
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Identify the slope and y-intercept of equation y= 3x-10
To answer this question, we need to remember that the slope-intercept form of the line is given by:
[tex]y=mx+b[/tex]Where
• m is the slope of line
,• b is the y-intercept of the line, that is, the point where the line passes through the y-axis. At this point, x = 0.
Since we can see that the given equation is in slope-intercept form:
[tex]y=3x-10[/tex]We can see that the slope of the line is:
[tex]m=3[/tex]And the y-intercept is:
[tex]\begin{gathered} b=-10 \\ (0,-10) \end{gathered}[/tex]In summary, we have that
• The slope of the line is m = 3.
,• The y-intercept of the line is (0, -10)
Classify the equation 6x + 4x - 1 = 2(5x + 4) as having one solution, infinitely many solutions, or no solution. Enter integers or expressions to complete the solution. (Simplify your answers.) Since - 1 = 8, the equation has no solution(s).
Solve;
[tex]\begin{gathered} 6x+4x-1=2(5x+4) \\ \text{Solve the parenthesis,} \\ 10x-1=10x+8 \\ \text{Collect all like terms} \\ 10x-10x=8+1 \\ 0=9 \\ \text{This equation has no solution because 0=9 is not possible} \end{gathered}[/tex]The answer is
No solution
Determine which of the following points is a solution to the inequality 3x + 9y < 18 i (2, 2) ii. (-3,-4) iii. (0.2)
Given the inequality:
[tex]3x+9y<18[/tex]to find which point is a solution to the inequality, there are 2 methods to solve :
by graphing or by substitution by the point in the given inequality
Solving by substitution :
1) point (2 , 2)
so,
[tex]3\cdot2+9\cdot2=24>18[/tex]So, this point is not a solution
2) Point (-3 , -4)
[tex]3\cdot-3+9\cdot-4=-45<18[/tex]This point is a solution
3) Point (0 , 2)
[tex]3\cdot0+9\cdot2=18[/tex]So, this point is not a solution
Another sol
The equation below describes a circle. What are the coordinates of the centerof the circle?(x-4)^2 + (y+12)^2 = 17²O A. (4,12)OB. (-4,-12)O C. (-4,12)OD. (4, -12)21
Solution:
The equation is given below as
[tex](x-4)^2+(y+12)^2=17^2[/tex]Concept:
The general equation of a circle is given below as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where, \\ (h,k)=center \end{gathered}[/tex]Hence,
By comparing coefficients, we will have the center of the circle be
[tex](h,k)\Rightarrow(4,-12)[/tex]Hence,
The final answer is
[tex]\Rightarrow(4,-12)[/tex]OPTION D is the right answer
What is 1875 divided by 41
The value when 1875 is divided by 41 is 45.73.
What is division?
Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division.
Given,
1875 ÷ 41
= 45.73
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Consider the following advertisement.Which of the following calculations represents the cost of 2 dozen iris bulbs?
Answer:
C: (6 x $5)+(6 x $4)+(12 x $3)
Explanation:
The total number of bulbs bought = 2 dozens = 2 x 12 = 24
• The cost per bulb for the first half-dozen = $5
[tex]\text{Cost for the first half-dozen=6 x \$5}[/tex]• The cost per bulb for the next half-dozen = $4
[tex]\text{Cost for the next half-dozen=6 x \$}4[/tex]Out of 24 bulbs, we have calculated the cost for 12.
• The number of bulbs left = 24 - 12 = 12.
,• Each additional bulb is $3 per bulb.
The cost for the last 12 will be:
[tex]12\times\$3[/tex]Therefore, the cost for the 2 dozen iris bulbs will be:
[tex](6\times\$5)+(6\times\$4)+(12\times\$3)[/tex]The correct choice is C.
•
•
The value of a house increased by 6%.
The house then had a value of £265 000
Work out the value of the house before the increase
In a case whereby value of a house increased by 6% and the house then had a value of £265, the value of the house before the increase is £250000.
How can the value of the house before the increase be calculated?To calculate the value of the house before the increase then the formular below can be used in making the calculation:
V = [V₀(1+r)]
where
V = the final price
V₀ = initial price
r = the rate.
V = £265,000
r = 6%,
V₀ = unknown?
Then since we know the variables now, we can substitutes the values into the above equation so that we can simplify the expression as :
we can rearrange the formular by making the unknown the subject of the formula as :
V₀ = [V/(1+r)]
= [265000/(1 + 6%)]
= [265000/(1 + 6/100)[]
= 265000/(106/100)
then the final expression will now be
V₀ = [265000*100/106 ]
= £250000
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Plot points between and beyond the Exitir serves in the vertical asymptote evaluate the function at -5, -2,2,5 and 6 Simplify
Step 1: Write out the definition of the function f:
The function f is given by:
[tex]f(x)=\frac{x^2-9}{x}[/tex]Step 2: Calculate the value of the function f at t=-5:
[tex]\begin{gathered} f(-5)=\frac{(-5)^2-9}{(-5)} \\ \text{Hence,} \\ f(-5)=\frac{25-9}{-5}=-\frac{16}{5} \end{gathered}[/tex]Step 3: Calculate the value of the function f at t=-2:
[tex]\begin{gathered} f(-2)=\frac{(-2)^2-9}{(-2)} \\ \text{Hence,} \\ f(-2)=\frac{4-9}{-2}=\frac{-5}{-2}=\frac{5}{2} \end{gathered}[/tex]Step 4: Calculate the value of the function f at t=2:
[tex]\begin{gathered} f(2)=\frac{(2)^2-9}{(2)} \\ \text{Hence,} \\ f(2)=\frac{4-9}{2}=-\frac{5}{2} \end{gathered}[/tex]Step 5: Calculate the value of the function f at t=5:
[tex]\begin{gathered} f(5)=\frac{(5)^2-9}{(5)} \\ \text{Hence,} \\ f(5)=\frac{25-9}{5}=\frac{16}{5} \end{gathered}[/tex]Step 6: Calculate the value of the function f at t=6:
[tex]\begin{gathered} f(6)=\frac{(6)^2-9}{(6)} \\ \text{Hence,} \\ f(6)=\frac{36-9}{6}=\frac{27}{6}=\frac{9}{2} \end{gathered}[/tex]Hence
Which of the following products is irrational?
Answer:
B, C are irrational
Step-by-step explanation:
Not a ratio
Evaluate the following expression when m = 7. Enter your answer as a simplified fraction in the form a/b. (m/3)^2 = ___
Evaluating m = 7:
[tex](\frac{m}{3})^2=(\frac{7}{3})^2[/tex]Answer:
[tex]\frac{49}{9}[/tex]( 5b. A square has an area of 9 cm². What is its side length?
Answer: 2.25
Step-by-step explanation:
9 divided by 4 = 2.25
4 sides on the shape
2.25 cm on one side!
What makes the value of X that makes l1 l2?
A. 10
Explanation:From the figure provided:
<(4x)⁰ and <(2x+20)⁰ are alternate interior angles
Note that:
Alternate interior angles are equal
4x = 2x + 20
Collect like terms
4x - 2x = 20
2x = 20
x = 20/2
x = 10
find the value of x using the kite below (work required)
Since the diagonals in a kite intersect creating a right angle, the angles 2x° and (10x - 6)° are complementary angles. So we have:
[tex]\begin{gathered} 2x+(10x-6)=90 \\ 12x-6=90 \\ 12x=96 \\ x=\frac{96}{12} \\ x=8 \end{gathered}[/tex]So the value of x is 8.
Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.
Answer:
The expression becomes;
[tex]\frac{3}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x[/tex]Explanation:
Given the trigonometric expression;
[tex]\sin ^4x[/tex]Simplifying and rewriting the expression;
Recall that;
[tex]\begin{gathered} \cos 2x=1-2\sin ^2x \\ \sin ^2x=\frac{1-\cos 2x}{2} \end{gathered}[/tex]So, the expression becomes;
[tex]\begin{gathered} \sin ^4x=(\sin ^2x)(\sin ^2x) \\ =(\frac{1-\cos2x}{2})(\frac{1-\cos2x}{2}) \\ =(\frac{1-2\cos2x+\cos^22x}{4}) \\ =\frac{1}{4}-\frac{2}{4}\cos 2x+\frac{1}{4}\cos ^22x \end{gathered}[/tex]Also;
[tex]\begin{gathered} \cos 4x=2\cos ^22x-1 \\ \cos ^22x=\frac{\cos 4x+1}{2} \end{gathered}[/tex]substituting to the above expression;
[tex]\begin{gathered} =\frac{1}{4}-\frac{2}{4}\cos 2x+\frac{1}{4}(\frac{\cos4x+1}{2}) \\ =\frac{1}{4}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x+\frac{1}{8} \\ =\frac{1}{4}+\frac{1}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x \\ =\frac{3}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x \end{gathered}[/tex]Therefore, the expression becomes;
[tex]\frac{3}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x[/tex]the terminal side θ passes through the point (8,-7) what is the exact value of θ in simplified form?
Given:
the terminal side θ passes through the point (8,-7)
so,
[tex](x,y)=(8,-7)[/tex]The point lying in quarter number 4
so,
[tex]\begin{gathered} \tan \theta=\frac{y}{x}=-\frac{7}{8} \\ \\ \theta=\tan ^{-1}(-\frac{7}{8})=-41.186 \\ \\ \theta=360-41.186=318.814 \end{gathered}[/tex]
Lance had 24 apps on his phone. If the ratio of educational apps to gaming apps is 5:1, how many educational apps are there?
help me with this
6 3/4 ÷ 1 7/8=how do I figure those out?
6The given expression is 6 3/4 ÷ 1 7/8 is :
[tex]6\frac{3}{4}\div1\frac{7}{8}=\text{ }\frac{}{\square}[/tex]Express the mixed frcation in the normal forM :
[tex]\begin{gathered} 6\frac{3}{4}=\frac{6\times4+3}{4} \\ 6\frac{3}{4}=\frac{27}{4} \end{gathered}[/tex]Similarly with the 1 7/8
[tex]\begin{gathered} 1\frac{7}{8}=\frac{1\times8+7}{8} \\ 1\frac{7}{8}=\frac{15}{8} \end{gathered}[/tex]Substitute the value and simplify :
[tex]\begin{gathered} 6\frac{3}{4}\div1\frac{7}{8}=\frac{27}{4}\div\frac{15}{8} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{27}{4}\times\frac{8}{15} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{9}{1}\times\frac{2}{5} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{18}{5} \end{gathered}[/tex]18/5 in the mixed fraction :
18/5 = 3 3/5
Answer : 6 3/4 ÷ 1 7/8 = 18/5 or 3 3/5
The cost C(ar), where a is the number of miles driven, of renting a car for a day is $45 plus $0.25 per mile.
What is the slope of the linear function and its units?
select the correct units
What is the y-intercept and its units?
units
What is the linear function, C(a)? C(x)
C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.
Given,
The cost C(ar), where a is the number of miles driven, of renting a car for a day is $45 + $0.25 per mile.
To find the slope , y - intercept and C(a)
Now, According to the question:
A renting a car for a day is $45 plus $0.25 per mile.
C(x) = 0.25x + 45
This is in the form y = mx + b where m is the slope and b is the y intercept
The slope is .25 dollars per mile and the y intercept is 45 dollars
Hence, C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.
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Unit Rates can also be used to solve problems....hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand
10)
Given:
The cost of 8 ounces of shampoo is $0.89.
The cost of 12 ounces of shampoo is $1.47.
Required:
We need to find a better deal.
Explanation:
Consider the first deal.
The cost of 8 ounces of shampoo is $0.89.
Divide the cost of 0.89 by 8 to find the cost for one ounce.
[tex]The\text{ cost of shampoo for one ounce=}\frac{0.89}{8}[/tex][tex]The\text{ cost of shampoo for one ounce=\$}0.11125[/tex]Consider the second deal.
The cost of 12 ounces of shampoo is $1.47.
Divide the cost of 1.47 by 12 to find the cost for one ounce.
[tex]The\text{ cost of shampoo for one ounce=}\frac{1.47}{12}[/tex][tex]The\text{ cost of shampoo for one ounce=}0.1225[/tex]We know that $0.11125 is less than $0.1225.
The first deal is better than the second deal.
Final answer:
The best deal is,
The cost of 8 ounces of shampoo is $0.89.
7. Use the equation E =2- my for the following questions:2(a) Rearrange the equation so that it's solved for m.Show your work here:Solution:m =
Solution: (a)
Given the equation;
[tex]E=\frac{1}{2}mv^2[/tex]Multiply both sides of the equation by 2;
[tex]\begin{gathered} 2\times E=2(\frac{1}{2})mv^2 \\ 2E=mv^2 \end{gathered}[/tex]Divide both sides by the square of the velocity v;
[tex]\begin{gathered} \frac{2E}{v^2}=\frac{mv^2}{v^2} \\ m=\frac{2E}{v^2} \end{gathered}[/tex]ANSWER:
[tex]m=\frac{2E}{v^2}[/tex](b) Given;
[tex]E=125,000J,v=24ms^{-1}[/tex]We would substitute the value of the energy and the velocity into the formula for mass, we have;
[tex]\begin{gathered} m=\frac{2E}{v^2} \\ m=\frac{2(125000)}{24^2} \\ m=\frac{250000}{576} \\ m=434.03 \end{gathered}[/tex]
Multiply 2 2/3 • 1 5/6 Simplify the answer and write as a mixed number.
Answer:18 and 1/3
Step-by-step explanation:22
3
(15)
6
=
55
3
(Decimal: 18.333333) and then as a mixed number is:
Sandra does her grocery shopping for the week. The total is $212.00 including the sales tax. The bill without tax was $200.00. What is the tax on her groceries?Tax is 6%
You know that:
- The total is $212.00 and the sales tax is included.
- The bill without tax was $200.00.
Let be "x" the tax on her groceries (in dollars).
You need to subtract the bill without tax from the total amount of money Sandra paid for the groceries, in order to find the tax in dollars:
[tex]\begin{gathered} x=212-200 \\ x=12 \end{gathered}[/tex]To check it, you can multiply the total by 6%:
[tex]212\cdot\frac{6}{100}=12[/tex]Hence, the answer is: $12.00 (This is 6% of the total bill)
I need help with this! I don’t know how to do it!!
Answer:
6c+11≤67
Step-by-step explanation:
To write this as an inequality, since it says 6 times a number, write:
6c
Now, since it is increased by 11, write:
6c+11
Finally, since it says at most 67, write
6c+11≤67.
Hope that helps!
Two friends drive off in different directions from the same place. one heads north at 25 miles per hour, while the other heads east at 40 miles per hour. complete an equation for the distance between the friends after t hours.
Answer: [tex]5t\sqrt{89}[/tex] miles
=======================================================
Explanation:
Draw a right triangle. The legs of this triangle represent the directions the two friends travel (one going east, the other going north).
The horizontal leg has side length 40t and the vertical leg has length 25t, where t is the number of hours.
I'm using the idea that distance = rate*time.
We'll use the pythagorean theorem to find the hypotenuse in terms of t.
[tex]a = 40t, \ b = 25t\\\\a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{(40t)^2+(25t)^2}\\\\c = \sqrt{1600t^2+625t^2}\\\\c = \sqrt{2225t^2}\\\\c = \sqrt{25*89t^2}\\\\c = \sqrt{25t^2}*\sqrt{89}\\\\c = 5t\sqrt{89}\\\\[/tex]
At time t hours, the distance between the two friends is exactly [tex]5t\sqrt{89}[/tex] miles.
HELP HELP PLEASE!!!!!!!!!!!!!!!!!!!!
There are 5.65 milliliters of water in a jar. Tess wants only 3.85 milliliters of water in the jar. She calculates that she should remove 1.8 milliliters of water. Which statement shows whether Tess is correct? (1 point)
She is correct. 5.65 + 1.8 = 3.85.
She is correct. 3.85 + 1.8 = 5.65.
She is incorrect. 5.65 + 1.8 = 7.45.
She is incorrect. 3.85 + 1.8 = 4.65.
Answer:
She is incorrect
Step-by-step explanation:
5.65 + 1.8 = 7.45
Answer:
She is correct. 3.85 + 1.8 = 5.65
Step-by-step explanation:
She is correct. 3.85 + 1.8 = 5.65
PLEASE HELP DUE IN 23 and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = 17
Step-by-step explanation:
(6x - 20) and the angle vertically opposite (6x - 4) are same- side interior angles and sum to 180° , that is
6x - 20 + 6x - 4 = 180
12x - 24 = 180 ( add 24 to both sides )
12x = 204 ( divide both sides by 12 )
x = 17
Question 13 of 50
A function is when each domain has only one range.
False
True
Answer:true
Step-by-step explanation:It’s on khan
Answer:
True
Step-by-step explanation:
A function is when each element of the domain has only one corresponding element in the range.
True
How much money will he have , If he leaves the account alone for 6 yrs
$2352.33
Explanation
the account balance is give by the function
[tex]f(x)=425(1.33)^x[/tex]where x represents the time in years
hence, to find how much money Hercules will have after six years, jus replace the x value
so, when x=6
[tex]\begin{gathered} f(x)=425(1.33)^x \\ \text{replace} \\ f(6)=425(1.33)^6 \\ f(6)=425\cdot5.53 \\ f(6)=2352.33 \end{gathered}[/tex]I hope this helps you
