Answer:
33.75
Step-by-step explanation:
Step 1- Find the decimal form of 35%
Step 2- When you find that multiply that by 25
Step 3- When you find the answer to step 2 add that to 25
That is your answer
Final answer:
The price that Fred will pay the groomer the next time when his dog has a haircut is $33.75.
Explanation:
The question asks us to calculate the new price Fred will pay for his dog's haircut after the groomer increases the price by 35%. To find the new price, we'll use the formula for calculating percentage increase, which is: New Price = Original Price + (Original Price * Percentage Increase).
First, convert the percentage increase to a decimal by dividing it by 100, so 35% becomes 0.35. Then, multiply the original price of $25 by 0.35 to find the amount of the increase, which is $8.75.Finally, add the increase to the original price to find the new price, which is $25 + $8.75 = $33.75. So, Fred will pay $33.75 the next time his dog has a haircut.
Find the values of m and b that make the following function differentiable.
f(x) = {x^2, x less than or equal to 2
mx+b, x>2}
thank you so much!!
Both x² and mx + b are differentiable functions of x (they are both polynomials), so if f(x) is also differentiable, we need to pay special attention at x = 2 where the two pieces of f meet.
Continuity means that the limit
[tex]\displaystyle \lim_{x\to2} f(x)[/tex]
must exist.
From the left side, we have x < 2 and f(x) = x², so
[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} x^2 = 4[/tex]
From the right, we have x > 2 and f(x) = mx + b, so
[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (mx+b) = 4m+b[/tex]
It follows that 4m + b = 4.
Differentiability means that the limit
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2}[/tex]
must exist.
From the left side, we again have x < 2 and f(x) = x². Then
[tex]\displaystyle \lim_{x\to2^-}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{x^2-4}{x-2} = \lim_{x\to2} (x+2) = 4[/tex]
From the right side side, we have x > 2 so f(x) = mx + b. Then
[tex]\displaystyle \lim_{x\to2^+}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{(mx+b)-(2m+b)}{x-2} = \lim_{x\to2} \frac{mx-2m}{x-2} = \lim_{x\to2}m = m[/tex]
The one-sided limits must be equal, so m = 4, and from the other constraint it follows that 16 + b = 4, or b = -12.
The sum of the digits of a two-digit number is 13. The units digit is one more than twice the tens digit. Find the number, and...
The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals to the sum of the other two. Find the number.
Answer:
1)49
2)231
Step-by-step explanation:
1)
4+9=13
4*2=8
8+1=9
2)
2+3+1=6
2+1=3
1*2=2
Answer:
#1. 49 #2. 231
Step-by-step explanation:
#1. 4 x 2 + 1 =
8 + 1 =
9
add 40 + 9 = 49
#2. x + 2x + (x + 2x) = 6
6x = 6
x = 1
2x = 2
x + 2x = 3
(2 x 100) + (3 x 10) + 1 or 231.
Can I get Brainliest☺☺☺☺
"How are we ever going to build this bridge?" asks Omkar looking out across the raging river. "Let's start by finding the distance to the big rock on the other side." Melissa replies. Moving 100100100 meters along the river, Melissa looks back and measures the angle between Omkar and the big rock: 33^\circ33 ? 33, degree. Melissa then instructs Omkar to measure the angle between Melissa and the big rock. From his vantage point, Omkar sees an angle of 98^\circ98 ? 98, degree between Melissa and the big rock. What is the distance across the river from Omkar to the big rock? Do not round during your calculations. Round your final answer to the nearest meter.
Answer:
The distance across the river from Omkar to the big rock is 131343149 meters
Step-by-step explanation:
* Lets study the information in the problem
- Let Omkar position is point A
- Let Melissa position is point B
- Let big rock position is C on the other side of the river
* Now we have triangle ABC
- The distance between Omkar and Melissa is 100100100 meters
along the river
- The angle between Omkar and the big rock is angle BAC
∴ m∠BAC = 33°
- The angle between Melissa and the big rock is angle ABC
∴ m∠ABC = 98°
- The big rock is at angle C
* Now we can find the distance between Omkar and the big rock
by finding the length of side AC in the triangle
- By using the sine rule
∵ sin A/BC = sin B/AC = sin C/AB
∵ AB = 100100100 meters
∵ m∠ABC = 98°
- Lets find m∠C
∵ In any triangle the sum of the measures of the interior angles is 180°
∴ m∠A + m∠B + m∠C = 180°
∵ m∠A = 33° , m∠B = 98°
∴ 33° + 98° + m∠C = 180° ⇒ add
∴ 131° + m∠C = 180° ⇒ subtract 131 from both sides
∴ m∠C = 49°
- Now lets use the sine rule
∵ sin ABC/AC = sin C/AB
∴ sin 98/AC = sin 49/100100100 ⇒ by using cross multiplication
∴ AC = (sin 98 × 100100100) ÷ sin 49 = 131343148.8
∴ AC ≅ 131343149 meters
* The distance across the river from Omkar to the big rock is
131343149 meters
Answer:
The distance across the river from Omkar to the big rock is 72 meters.
Step-by-step explanation:
Using the given information draw as triangle as shown below.
According to angle sum property, the sum of interior angles of a triangle is 180°.
In triangle ABC,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]98^{\circ}+33^{\circ}+\angle C=180^{\circ}[/tex]
[tex]131^{\circ}+\angle C=180^{\circ}[/tex]
[tex]\angle C=180^{\circ}-131^{\circ}=49^{\circ}[/tex]
The measure of angle C is 49°.
Sine formula:
[tex]\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}[/tex]
Using sine formula in triangle ABC, we get
[tex]\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]
[tex]\frac{AC}{\sin 33^{\circ}}=\frac{100}{\sin 49^{\circ}}[/tex]
[tex]AC=\frac{100}{\sin 49^{\circ}}\times \sin 33^{\circ}[/tex]
[tex]AC=\frac{100}{0.7547}\cdot0.544639[/tex]
[tex]AC=72.166[/tex]
[tex]AC\approx 72[/tex]
Therefore the distance across the river from Omkar to the big rock is 72 meters.
A parallelogram has vertices (5, 0), (3, -3), (-4, -3), and (-2, 0). What is the approximate perimeter of the parallelogram?
Check the picture below.
so the top and bottom segments are simply 7 units, we can read that off the grid. Let's find the length of the other two segments, "c".
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ c=\sqrt{2^2+3^2}\implies c=\sqrt{13} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of the parallelogram}}{7+7+\sqrt{13}+\sqrt{13}}\qquad \approx \qquad 21.21[/tex]
Answer:
C: 30 units
Step-by-step explanation:
on edge 2021! hope this helps!!~ d=(´▽｀)=b
2 Points
A football coach is trying to decide: When a team is ahead late in the game,
which strategy is better?
• Play the "regular" defense.
• Play a "prevent" defense that guards against long gains but makes short
gains easier.
The coach reviews the outcomes of 100 games.
Win
Loss
8
Total
50
42
Regular defense
Prevent defense
35
15
50
Total
77
23
100
Compare the probability of winning when playing regular defense with the
probability of winning when playing prevent defense. Draw a conclusion
based on your results.
PREVIOUS
Answer:0.76
0.58
Conclusion you are More likely to win by playing regular defense
Step-by-step explanation:
Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Taking the strategy of "regular" defense,
P(winning) = 42
P(losing) = 8
Total regular defense games = 50
Taking the strategy of "prevent" defense,
P(winning) = 35
P(losing) = 15
Total regular prevent games = 50
Total games = 100
Probability of winning when playing regular defense = 42 / 50 = 0.84
Probability of winning when playing prevent defense = 35 / 50 = 0.7
Hence, Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.
Learn more about Probability here :
https://brainly.com/question/11234923
#SPJ7
Solve the equation identify extraneous solutions
Answer:
Step-by-step explanation:
The goal to solving any equation is to have x = {something}. That means we need to get the x out from underneath that radical. It's a square root, so we can "undo" it by squaring. Square both sides because this is an equation. Squaring both sides gives you
[tex]x^2=-3x+40[/tex]
Get everything on one side of the equals sign and set the quadratic equal to 0:
[tex]x^2+3x-40=0[/tex]
Throw this into the quadratic formula to get that the solutions are x = 5 and -8. We need to see if only one works, both work, or neither work in the original equation.
Does [tex]5=\sqrt{-3(5)+40}[/tex]?
[tex]5=\sqrt{-15+40}[/tex] and
[tex]5=\sqrt{25}[/tex]
and 5 = 5. So 5 works. Let's try -8 now:
[tex]-8=\sqrt{-3(-8)+40}[/tex] and
[tex]-8=\sqrt{24+40}[/tex] so
[tex]-8=\sqrt{64}[/tex]
-8 = 8? No it doesn't. So only 5 works. Your choice is the third one down.
Please help me out please!!!!!!!!!
Answer:
Do Addition
Step-by-step explanation:
x=76+78
x= 154
Answer:
x = 77°
Step-by-step explanation:
The measure of x is half the sum of the measures of the arcs intercepted by the angle and it's vertical angle, that is
x = 0.5 × (78 + 76)° = 0.5 ×154° = 77°
Over the summer, for every 14 Okra seeds Dana planted, 9 plants grew. If he planted 182 seeds how many grew into plants
Answer:
117
Step-by-step explanation:
182/14=13
13x9=117
Triangle XYZ is translated 4 units up and 3 units left to yield ?X'Y'Z'. What is the distance between any two corresponding points on ?XYZ and ?X'Y'Z?
Answer:
5 units
Step-by-step explanation:
Let's take point X and X' (it will be the same regardless of the point).
The distance is 3 units to the right then 4 units up.
A direct line will be diagonal and can be found using the pythagorean theorem (refer to visual).
(D: a > 0) 3² + 4² = a² --> 9 + 16 = a² --> a² = 25 --> a = 5
So the distance is 5 units.
When a figure is translated, or moved without rotation or change in size, the distances between corresponding points on the original and new figure remain the same. Therefore, the distance between any two corresponding points on Triangle XYZ and Triangle X'Y'Z' is the same as it was prior to the translation.
Explanation:
In this case, the triangle XYZ is being translated, which means that it is being shifted in the plane. The student has moved the triangle 4 units up and 3 units left. This operation does not alter the size, shape or orientation of the triangle, just its position. Therefore, the distance between any two points on the triangle remains the same before and after the translation. To clarify, if the distance between point X and Y initially is 'd', after the triangle has been translated to yield triangle X'Y'Z', the distance between X' and Y' remains 'd'. This is an important characteristics of translation, a core concept in geometry.
Learn more about translation here:https://brainly.com/question/38241586
#SPJ3
What is the value of coefficient c in this quadratic equation?
5x2 + 6x + 7 = 2(x + 2)
A.
7
B.
4
C.
3
D.
-3
E.
3/5
Answer:
C 3
Step-by-step explanation:
5x^2 + 6x + 7 = 2(x + 2)
Distribute the 2
5x^2 + 6x + 7 = 2x + 4
Subtract 2x from each side
5x^2+6x-2x +7 = 2x-2x+4
5x^2 + 4x + 7 = 4
Subtract 4 from each side
5x^2 +4x+7-4 = 4-4
5x^2 +4x+3 = 0
This is in the form ax^2 + bx +c where c is 3
Answer:
C. 3Step-by-step explanation:
[tex]ax^2+bx+c=0\\\\5x^2+6x+7=2(x+2)\qquad\text{use the distributive property}\\\\5x^2+6x+7=2x+4\qquad\text{subtract}\ 2x\ \text{and 4 from both sides}\\\\5x^2+4x+\boxed{3}=0[/tex]
the time in minutes for each of Sam's phone calls this week are shown in the list
Answer:
Where's the list?
Help, please. Time sensitive.
What are the solutions to the system of equations?
{y=x2−3x−y=1
Solve the system by graphing.
a. (0, −3) and (0, −1)
b. (1, −2) and (−2, 1)
c. (2, 1) and (−1, −2)
d. (1, 2) and (−2, −1)
Answer:
c. (2, 1) and (−1, −2)
Step-by-step explanation:
Assuming you intended y=x²-3 and x-y=1, you can graph the parabola and the straight line (rewrite x-y=1 as y = x-1).
You can then see the intersections at x=-1, y=-2 and x=2, y=1.
plz help!!!
Select the correct answer.
What is the inverse of the function f(x)=x+1/x?
A.)F^-1(x)=x/x+1
B.)F^-1(x)=1/x-1
C.)F^-1(x)=x-1/x+1
D.)F^-1(x)=x/x-1
we know that f(1)=2 so f^-1(2)=1
so B is correct!
Answer: The correct option is
(B) [tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]
Step-by-step explanation: We are given to select the correct expression that is the inverse of the following function :
[tex]f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let y denotes f(x). Then,
[tex]y=f(x)~~~~~~\Rightarrow x=f^{-1}(y).[/tex]
Substituting this value in equation (i), we get
[tex]f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{f^{-1}(y)+1}{f^{-1}(y)}\\\\\\\Rightarrow yf^{-1}(y)=f^{-1}(y)+1\\\\\Rightarrow yf^{-1}(y)-f^{-1}(y)=1\\\\\Rightarrow (y-1)f^{-1}(y)=1\\\\\Rightarrow f^{-1}(y)=\dfrac{1}{y-1}\\\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}.[/tex]
Thus, the required inverse of the given function is
[tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]
Option (B) is CORRECT.
98 POINTS! QUESTION + ANSWERS IN PHOTO! Use squared identities to simplify the following equation....
2sin^2xcos^2x
Using trig functions we know:
sin^2(x) = 1- cos(2x)/2
cos^2(x) = 1 + cos(2x) /2
Now we have:
2sin^2xcos^2x = 2 * 1- cos(2x)/2 * 1 + cos(2x) /2
Simplify to: (1- cos(2x) * 1+cos(2x))/2
Difference of squares is (a-b) (a+b) = a^2 -b^2
(1- cos(2x) * 1+cos(2x))/2 = 1^2 -cos^2(x)/2 *1^2 +cos^2(x) /2
Multiply to get 1-cos(4x) /4
The answer is D.
Pam drove her car 288 miles using a total of 12 gallons. How many gallons would it take for her to drive a total of 156 miles? Gallons
Answer:
6.5 Gallons
Step-by-step explanation:
288 miles / 12 gallons = 24 mpg
156 miles / 24 mpg = 6.5 gallons
Brainliest + Points! Mathematicians needed
In 2008, Adam Lopez set a world record by singing the highest note ever recorded, a C8. That is four octaves above middle C and not on a normal piano keyboard. What is the frequency to the nearest hertz of this musical note if its period is 0.00024?
A.
1,873 hertz
B.
2,631 hertz
C.
3,845 hertz
D.
4,167 hertz
Answer: D. 4167 Hertz
Step-by-step explanation:
We know that the formula to calculate frequency by using time period is given by :-
[tex]\nu= \dfrac{1}{T}[/tex], where T is the time period.
We are given that the time period of a musical note :
[tex]T=0.00024\text{ seconds}[/tex]
Then , the frequency of the musical note is given by :-
[tex]\nu= \dfrac{1}{0.00024}=4166.66666667\approx4167\text{ Hertz}[/tex]
Hence, the frequency of the musical note = 4167 Hertz
Koen is training for a track meet. Last month, he ran for four and a half hours. He averaged a speed of six miles per hour. How many miles did Koen run?
Hopefully I read the question right, if not I'm sorry
Koen ran for 4 and a half hours, which is also 4.5 hours
Since he averaged a speed of 6 mph, I multiply the number of hours by speed each hour, which is 4.5*6
4.5*6=27
Koen ran 27 miles.
Answer:
38 miles
Step-by-step explanation:
study island
Solve the system algebraically. Check your work. 4x + 5y = 12 7x + 5y = 6 Make sure there are NO SPACES in your answer. Be sure to include a comma between the x and y values.
ANSWER
(-2,4)
EXPLANATION
The given equations are:
4x + 5y = 12
7x + 5y = 6
Subtract the first equation from the second equation.
7x-4x+5y-5y=6-12
3x=-6
Divide both sides by 3 to obtain:
x=-2
Put x=-2 into the first equation to get:
4(-2)+5y=12
-8+5y=12
5y=12+8
5y=20
y=20/5
y=4
Checking
4(-2)+5(4)=12
-8+20=12
12=12
Also
7(-2)+5(4)=6
-14+20=6
6=6
Answer:
The solution is (-2,4)
Step-by-step explanation:
* Lets revise how to solve the system of equations algebraically
- If the system of equation is ax+by=c and dx+ey=f, then we can use
the elimination method to solve
- The steps of the elimination method
# Change the coefficient of one variable in one of the two equation
to have the same coefficient with opposite sign of this variable in the
second equation (a = -d)
# Add the two equations to eliminate this variable (by+ey=c+f)
# Solve to find the second variable (y=(c+f)/(b+e))
# Substitute the the value of the second variable in any equation to
find the first variable
* Now lets solve the problem
∵ 4x+5y=12 ⇒ (1)
∵ 7x+5y=6 ⇒ (2)
- The variable y has the same coefficient in the two equations, then
eliminate it by multiply one of the equation by -1 to make
opposite sign
- Multiply equation (2) by -1
∴-7x-5y=-6 ⇒ (3)
- Add (1) and (3)
∴ -3x=6 ⇒ divide both sides by -3
∴ x=-2
- Substitute the value of x in (1) or (2)
∴ 4(-2)+5y=12
∴ -8+5y=12 ⇒ add 8 to both sides
∴ 5y=20 ⇒ divide each side by 5
∴ y = 4
- The solution of the system is the point which has the values of x and y
∴ The solution is (-2,4)
Which of the following points is a solution to the system of linear inequalities?
{y≤2x-5
y>-3x
A.
(1, 1)
B.
(–2, 2)
C.
(5, 3)
D.
(–4, 4)
Answer:
C. (5, 3)
Step-by-step explanation:
this point is within the answer area... look below at the graph of both linear inequalities
For this case we have the following system of inequations:
[tex]y\leq2x-5\\y> -3x[/tex]
We must replace each of the points and verify that the inequalities are met:
Point A: (1,1)
[tex]1 \leq2 (1) -5\\1 \leq2-5\\1 \leq-3[/tex]
It is not fulfilled!
Point B: (-2,2)
[tex]2 \leq2 (-2) -5\\2 \leq-4-5\\2 \leq-9[/tex]
It is not fulfilled!
Point C: (5,3)
[tex]3 \leq2 (5) -5\\3 \leq10-5\\3 \leq5[/tex]
Is fulfilled!
[tex]3> -3 (5)\\3> -15[/tex]
Is fulfilled!
Point D: (-4,4)
[tex]4 \leq2 (-4) -5\\4 \leq -8-5\\4 \leq -13[/tex]
It is not fulfilled!
Thus, the point that is the solution of inequalities is:
(5,3)
ANswer:
(5,3)
State the trigonometric ratios for the triangle below:
Answer:
Step-by-step explanation:
alright, lets get started.
Side 5 is opposite.
Side 12 is adjacent.
Side 13 is hypotenuse.
Using SOH CAH TOA,
sin Θ = [tex]\frac{opposite}{hypotenuse}[/tex]
sin Θ = [tex]\frac{5}{13}[/tex]
cos Θ=[tex]\frac{adjacent}{hypotenuse}[/tex]
cos Θ=[tex]\frac{12}{13}[/tex]
tan Θ=[tex]\frac{opposite}{adjacent}[/tex]
tan Θ=[tex]\frac{5}{12}[/tex] : Answer
Hope it will help :)
The Earth completely rotates on its axis once every 24 hours.
A) How long does it take for it to rotate 310 degrees?
B) How long does it take to rotate 5 radians?
C) The diameter of the Earth is approximately 7920 miles. How far will a point on the equator rotate in 2 hours?
Show all work. Give answers to the nearest hundredth. Include the units in your response.
Answer:
A)
62/3 = 20.67 hours
B)
60.00 hours
C)
2074.29 miles
Step-by-step explanation:
If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.
A)
In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;
(24/360) = (x/310)
solving for x;
x = (24/360) * 310 = 62/3 = 20.67 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;
(24/2π radians) = (x/5π radians)
Solving for x;
x = (24/2π radians)*5π radians = 60 hours
C)
If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;
circumference = 2*π*R = π*D
= 7920π miles
Therefore, the speed of the earth is approximately;
(7920π miles)/(24 hours) = 330π miles/hr
The distance covered by a point in 2 hours will thus be;
330π * 2 = 660π miles = 2074.29 miles
If f(x) and its inverse function, f^-1(x), are both plotted on the same coordinate plane, where is their point of intersection?
Answer:
Step-by-step explanation:
Their point of intersection, assuming there is one, will be somewhere on the line y = x. This line, y = x, is the line of symmetry between a function and its inverse. So if the two do in fact intersect, it will be at some point on that line
Help! Find the value of x to the nearest hundredth
Question 9:
cos x = 10/36
Take the inverse on both sides.
arccos(cos x) = arccos(10/36)
x = 73.8723797868
x = 73.87
Question 10:
tan 89 = x
57.2899616308 = x
57.29
Alicia is sewing a rectangle bedspread that measures 72 inches by 60 inches. The bedspread is red with a gold circle 18 inches in diameter in the center. To the nearest square inch, what is the area of the bedspread that is red?
Answer:
[tex]4,066\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of the bedspread that is red is equal to the area of rectangle minus the area of the circle
step 1
Find the area of rectangle
The area is equal to
[tex]A=72*60=4,320\ in^{2}[/tex]
step 2
Find the area of the circle
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=18/2=9\ in[/tex] ----> the radius is half the diameter
assume
[tex]\pi=3.14[/tex]
substitute
[tex]A=(3.14)(9)^{2}[/tex]
[tex]A=254.34\ in^{2}[/tex]
step 3
Find the area of the bedspread that is red
Find the difference of the areas
[tex]4,320\ in^{2}-254.34\ in^{2}=4,066\ in^{2}[/tex]
Solve for x. Round your answer to 2 decimal places.
Answer:
x = 29.91
Step-by-step explanation:
Cos (53) = 18/x
x = 18 / Cos(53)
x = 18/ 0.6018
x = 29.91
For this case we have that by definition of trigonometric relations of a rectangular triangle, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:
[tex]cos (53) = \frac {18} {x}[/tex]
Clearing x:
[tex]x = \frac {18} {cos (53)}\\x = \frac {18} {0.60181502}\\x = 29,9095226969[/tex]
Rounding:
[tex]x = 29.91[/tex]
Answer:
29.91
How do you solve for the quotient of (x^-1) - 1 ÷ x - 1?
[tex]\bf x^{-1}-1\div x-1\implies \implies \cfrac{1}{x}-1\div x-1\implies \cfrac{\frac{1}{x}-1}{~~x-1~~}\implies \cfrac{~~\frac{1-x}{x}~~}{\frac{x-1}{1}} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^{-1}[/tex]
Cherry is paid $72.00 for working six hours in a library. If the amount paid is proportional to the number of hours worked, what is the constant of proportionality?
Answer:
She's being paid six hours per hour
Step-by-step explanation:
She's being paid six hours per hour
72/6 = 6
A clothing store spends $11 for each pair of shorts it produces and has fixed costs of $450. If the store makes 40 pairs of shorts, how much should the store charge for each pair of shorts in order to break even?
Answer:
Step-by-step explanation:
the answer is $22.95
In order to break even store need to charge $22.25 per pair of shorts.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given,
Fixed cost = $450
Cost of each pair = $11
Number of pairs = 40
So,
The total cost of manufacturing
450 + 11(40) = $890
Now,
Let's say the store charges x per short
Total income = 40x
Now,
At break-even point
The total cost of manufacturing = Total income
890 = 40x
x = $22.25
Hence, In order to break even store need to charge $22.25 per pair of shorts.
For more about the equation,
https://brainly.com/question/10413253
#SPJ2
PLEASE HELP ME! PLEASE!!
Which scale factors produce an expansion under a dilation of he original image?
Choose all answers that are correct.
a)-0.75
b)-2
c)0.75
d)2
Which scale factors produce a contraction under a dilation of he original image?
Choose all answers that are correct.
a)-1.8
b)-0.8
c)1.8
d)0.8
Answer:
1. 0.75
2. -0.8
mark me brainlyest
First when looking at dialations, ignore the negative signs. They do not affect the expansion or contraction.
An expansion is any number greater than 1 and a contraction is any number less than 1.
Expansion: b) -2 and d) 2
Contraction: b) - 0.8 and d) 0.8
If he randomly chooses two students, one at a time, what is the probability that they are both girls?
Answer:
B) 15/91
Step-by-step explanation:
Probability of a girl as first choice is ...
number of girls / total number of students = 6/14 = 3/7
Probability of a girl as second choice (given a girl as first choice) is ...
number of girls / remaining number of students = 5/13
Then the probability of the two events is the product of their individual probabilities:
(3/7)·(5/13) = 15/91 . . . . . matches choice B