How many Mondays would there be in 171 school days?
There are 5 days to a school week: Monday, Tuesday, Wednesday, Thursday and Friday.
Divide number of school days by 5 to find the number of weeks:
171 / 5 = 34.2 weeks.
The weeks start with Monday, so there would be 35 Mondays. ( 34 full weeks and the partial week would begin with a Monday)
Divide 171 by 7 (as there are 7 days in each week), obtaining 24.4. There's one Monday in every 7 days, so in 168 days there'd be exactly 24 Mondays, and in 171 days there'd still be exactly 24 Mondays, with 3 days left over.
On a map of Chicago, 1cm represents 100m. Select all statements that express the same scale. A. 5cm on the map represents 50m in Chicago. B. 1mm on the map represents 10m in Chicago. C. 1km in Chicago is represented by 10cm on the map. D. 100cm in Chicago is represented by 1m on the map.
Answers: The statement that express the same scale are Options B and C.
Solution:
A. 5 cm on the map represents 50 m in Chicago?
Rule of three:
1 cm represents 100 m
5 cm represents x
x=(5 cm).(100 m) / (1 cm)
x=500 m
5 cm on the map represents 500 m in Chicago.
The statement A doesn't express the same scale.
B. 1 mm on the map represents 10 m in Chicago?
1 mm = 0.1 cm
Rule of three:
1 cm represents 100 m
0.1 cm represents x
x=(0.1 cm).(100 m) / (1 cm)
x=10 m
1 mm = 0.1 cm on the map represents 10 m in Chicago.
The statement B expresses the same scale.
C. 1 km in Chicago is represented by 10 cm on the map?
1 km = 1,000 m
Rule of three:
1 cm represents 100 m
x represents 1,000 m
x=(1 cm).(1,000 m) / (100 m)
x=10 cm
1 km = 1,000 m in Chicago is represented by 10 cm on the map.
The statement C expresses the same scale.
D. 100 cm in Chicago is represented by 1 m on the map?
100 cm = 1 m
Rule of three:
1 cm represents 100 m
x represents 1 m
x=(1 cm).(1 m) / (100 m)
x=0.01 cm
100 cm = 1 m in Chicago is represented by 0.01 cm on the map.
The statement D doesn't express the same scale.
Answer:
a,b,c d is incorrect but a,b,c is right
Step-by-step explanation:
just took the test
50 POINTS!
What is the reason for each step in the solution of the equation?
3(x+2)=4x+1
Drag and drop the reasons into the boxes to correctly complete the table.
Convert the following repeating decimal to a fraction.
0.37 repeating
[tex]x=0.\overline{37}\\\\100x=37.\overline{37}\\\\100x-x=37.\overline{37}-0.\overline{37}\\\\99x=37\\\\x=\dfrac{37}{99}[/tex]
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B.
Part (a)
The variable y is the dependent variable and the variable x is the independent variable.
Part (b)
The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:
[tex]0.75\times 18=13.5[/tex] dollars
Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.
Therefore, the price of the fair admission is: $33.50-$13.50=$20
If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be written as:
[tex]y=0.75x+20[/tex]......Equation 1
Part (c)
The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.
Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.
Mr. Spencer has 7 1/5 L of juice. Do you wanna support equal amounts of juice into three punch bowls. How many liters of juice should he poured to each bowl
Into each bowl, he will pour
... (1/3)×(7 1/5) = (1/3)×(6 6/5) = 2 2/5 . . . liters of juice
_____
Here, we have elected to rewrite 7 1/5 as 6 6/5 so each part of the number (whole number, fraction) will be divisible by 3.
You may have been taught to convert 7 1/5 to an improper fraction before doing the multiplication. That method looks like ...
... (1/3)×(36/5) = 12/5 = 2 2/5 . . . . same result
Find the measures of the angles of a triangle whose angles have a measure of x, 1/2x, and 1/6x. Also, what kind of triangle is it?
the sum of the angles in a triangle = 180°, thus
x + [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{6}[/tex] x = 180
multiply through by 6
6x + 3x + x = 1080
10x = 1080 ( divide both sides by 10 )
x = 108
the angles are 108°, 54° and 18°
Since all the angles are different and the largest is 108°
The triangle is an obtuse scalene triangle
The measures of the angles of the triangle are approximately 108 degrees, 54 degrees, and 18 degrees. This type of triangle is a scalene triangle, as all of its angles are different.
Explanation:To find the measures of the angles of a triangle whose angles are x, 1/2x, and 1/6x, we will use the fact that the sum of the angles in a triangle is always 180 degrees. The equation representing this is:
x + 1/2x + 1/6x = 180
Combine like terms:
1.6667x = 180
Then solve for x:
x ≈ 108 degrees
Now plug x into the original angle measures to get:
Angle 1 = 108 degrees
Angle 2 = 1/2x = 54 degrees
Angle 3 = 1/6x = 18 degrees
Lastly, in terms of the type of triangle, this is a scalene triangle because all of its angles are different.
Learn more about Triangle Angle Measurement here:https://brainly.com/question/27681289
#SPJ2
one type of insect is 0.0052 meter long. what is the length in scientific notation.
Here, we need to write the length of the insect in scientific notation.
The given length of the insect is 0.0052 meter
Now, to write 0.0052 meter in scientific notation we need to follow this:
Scientific notation always start with non-zero digit followed by a decimal point.
Since in our number the decimal is needed to be moved three places to the right to get the first non-zero digit.
The exponent of the 10 is [tex]-3[/tex].
[tex]10^{-3}=\frac{1}{1000} =0.001[/tex]
Therefore, our number 0.0052 can be written as:
[tex]5.2 \times 10^{-3}[/tex]
Hence, the require scientific notation is [tex]5.2 \times 10^{-3}[/tex].
Help with this question please!
∠1 and ∠2 are alternate exterior angles where transversal BE crosses parallel lines AC and DF, therefore they are equal. ∠2 and ∠3 are opposite angles of a parallelogram, therefore they are equal.
... ∠1 = ∠2
... 3x -5 = 2x +15 . . . . substitute the given values
... x = 20 . . . . . . . . . . . add 5-2x
The measures of angles 1, 2, and 3 are 2·20+15 = 55 . . . degrees.
Use the continuous change function A(t) = Pe^rt to answer the question.
You invest $10,500 in an account that grows 3.75% each year. What will be your investment amount after 9 years?
A.
$14,715.12
B.
$14781.48
C.
$15,049.96
A
note that r = 3.75% = 0.0375
A(9) = 10500 × [tex]e^{0.0375(9)}[/tex] = 10500 × [tex]e^{0.3375}[/tex] = 14, 715.12
We are given formula for continuous change function A(t) = Pe^rt.
We need to find the value of $10,500 investment amount grows 3.75% each year after 9 years.
Plugging values of P=10500
r= 3.75% = 0.0375 and
t=9 in given formula.
We get
[tex]A(9) = 10500e^{0.0375\times 9}[/tex]
Let us simplify it now.
[tex]e^{0.0375\times 9}=e^{0.3375}=1.40144[/tex]
[tex]=10500\times \:1.40144\dots[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:10500\times \:1.40144\dots =14715.11589\dots[/tex]
Rounding it to the nearest cents.
=14715.12.
Therefore, $14715.12 will be investment amount $10,500 after 9 years.It takes 18 electricians 35 days to wire a new housing subdivision. How many days would 28 electricians require to do the same job?
Assuming one electrician-day is the same as another, the total job is ...
... (18 electricians)×(35 days) = 630 electrician·days
When that work is split among 28 electricians, it can be expected to take ...
... (630 electrician·days)/(28 electricians) = 22.5 days
Compute the following volume and surface area. A rectangular pyramid has a base measuring 4 in. on each side and an altitude of 6 in. What is its volume? cubic inches
32 inches³
the volume V of a pyramid = [tex]\frac{1}{3}[/tex] × area of base × height
area of base = 4² = 16 and h = 6
V = [tex]\frac{1}{3}[/tex] × 16 × 6 = 32
PLEASE HELP ASAP NEED TO GET GRADE UP AND I NEED ANSWERS!!!!
What is the value of f(-4)?
f:x>3-x ( Thats an arrow not a greater then sign)
A.) 3
B.) 7
C.) -4
D.) -1
what is the range of the function shown in the graph? ( The vertex is at (0,-1) and it is arcing down)
A.) {yly ≤0}
B.) {yly ≤-1}
C.) {yly ≥ -1}
D.) {yly ≥ 0}
Answer:
1. B) 7
2. B) {y|y ≤ -1}
Step-by-step explanation:
1. Put -4 where x is in the function definition and do the arithmetic.
... 3 - (-4) = 3 +4 = 7
2. If the maximum function value is -1 and the values extend to -∞ from there, then the range is (-∞, -1]. In your notation, that is ...
... {y | y ≤ -1}
B and B
f(x) → 3 - x
to evaluate f(- 4 ) substitute x = - 4 into f(x)
f(- 4 ) = 3 - (- 4 ) = 3 + 4 = 7 → B
the range of a function are the values of y for the function
this function ( probably quadratic ) has a vertex at (0, - 1), that is the y-value is - 1
Since the function opens down then the values of y are tending to negative infinity
so the range of values for y are less than or equal to - 1 to negative infinity
{y | y ≤ - 1 } → B
What angle, to the nearest degree, does the wooden plank form with the ground?
29°
Consider the right triangle between the plank and the ground
the angle can be found using tangent ratio
tanx° = [tex]\frac{opposite}{adjacent}[/tex]
where adjacent = 18 and opposite = 10
tanx° = [tex]\frac{10}{18}[/tex]
x = [tex]tan^{-1}[/tex]([tex]\frac{10}{18}[/tex]) = 29.0546 ≈ 29°
Answer:
29 degrees to nearest degree.
Step-by-step explanation:
This is the angle whose tangent is 10/18 or 5/9.
this = 29 degrees
Help me with this pls!
The third angle of the triangle will be the supplement of the sum of the given angles. In order for the triangle to be isosceles, two of the three angles must have the same value.
a) 180 -40 -75 = 65 . . . not isosceles
b) 180 -30 -100 = 50 . . . not isosceles
c) 180 -35 -70 = 75 . . . not isosceles
d) 180 -50 -80 = 50 . . . matches one of the other angles. This triangle is isosceles.
The appropriate choice is ...
... 50 and 80
What’s the answer to this? Help ASAP!
the area of a rectangular wall of a barn is 117 square feet. its length is 4 feet longer than the width. find the length and width of the wall of the barn?
Area is the product of length and width. If you assume the dimensions are integers, you are looking for factors of 117 that differ by 4.
117 = 1×117 = 3×39 = 9×13
These last two factors differ by 4, so we know the dimensions of the barn are ...
... 9 ft wide by 13 ft long
PLZZZ HELP WITH 2 PROBLEMS
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. y= 1/3 x− 2/3
Given the graph of a line y=−x.Write an equation of a line which is perpendicular and goes through the point (8,2).
Answer:
1. (0, -2/3), (2, 0)
2. y = x-6
Step-by-step explanation:
1. Since the equation is in slope-intercept form, you know the y-intercept is -2/3. The x-coordinate there is 0, so the ordered pair is (0, -2/3).
Substituting y=0 into the equation gives the value of the x-intercept.
... 0 = 1/3x -2/3
... 0 = x - 2 . . . . . multiply by 3
... 2 = x . . . . . . . . add 2
The x-intercept is (2, 0).
2. The given line has slope -1, so the perpendicular line has a slope that is the negative reciprocal of that: -1/-1 = 1. Then the point-slope equation of the line can be written ...
... y = 1(x -8) +2
... y = x - 6 . . . . simplify
(1)
to find the intercepts
• let x = 0, in the equation for y-intercept
• let y = 0, in the equation for x-intercept
x = 0 : y = - [tex]\frac{2}{3}[/tex] → (0, - [tex]\frac{2}{3}[/tex]) ← y-intercept
y = 0 : [tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] = 0 ( multiply by 3 )
x - 2 = 0 → x = 2 → (2, 0 ) ← x- intercept
(2)
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - x is in this form with slope m = - 1
the slope of a perpendicular line = - [tex]\frac{1}{m}[/tex] = 1
the partial equation of the perpendicular line is
y = x + c
to find c substitute (8, 2 ) into the partial equation
2 = 8 + c → c = 2 - 8 = - 6
y = x - 6 ← equation of perpendicular line
Write an equation of the line passing through each of the following pairs of points. c (4, 0), (−2, 8)
Moving from -2 to 4 is a gain of 6 in the x-direction and a drop of 8 in the y-direction. Thus, the slope of this line is m = -8/6, or m = -4/3.
Then, using the point-slope formula, y - 0 = (-4/3)(x-4), or y = (-4/3)x + 16/3
y=-1 1/3x+5 1/3
I hope this helps
help me with this equations please
We know:
The product of two negative numbers is positive.
Therefore
(-12)(12)(-6.3)(-0.2)(-15.9) = (-12)(-6.3) (-0.2)(-15.9)(12) > 0 ANSWER
(12)(-6.3)(-0.2)(-15.9) < 0
(-12)(12)(-6.3)(-0.2)(-15.9)(0) = 0
(12)(12)(6.3)(0.2)(-15.9) < 0
On a recent test, Shawna was given the following problem:
Shawna's work is shown below:
1. a2+72=252
2. a2+14=50
3. a2=36
4. a=6 m
In which step did Shawna make an error?
Step 1. She incorrectly applied the Pythagorean theorem.
Step 2. She incorrectly squared the numbers.
Step 3. She incorrectly isolated a2
Step 4. She incorrectly solved for a.
Answer: Step 2. She incorrectly squared the numbers.
Solution:
The correct steps are:
1. a^2+7^2=25^2
2. a^2+49=625
3. a^2=576
4. a=24
In which step did Shawna make an error?
Step 2. She incorrectly squared the numbers.
Since, we are given right angled triangle
so, we use pythagoras theorem to find 'a'
step-1:
Using pythagoras theorem
[tex]a^2+7^2=25^2[/tex]
step-2:
we know that
[tex]7^2=7\times 7 =49[/tex]
[tex]25^2=25\times 25 =625[/tex]
so, we get
[tex]a^2+49=625[/tex]
she made error in second step
step-3:
Subtract both sides by 49
[tex]a^2+49-49=625-49[/tex]
[tex]a^2=576[/tex]
step-4:
Take sqrt both sides
we get
[tex]a=24[/tex]
so,
Answer is:
Step 2. She incorrectly squared the numbers.
(15 Points)
Find the derivative of each of the following (inverse function)
[tex]f(x) = x^2 arctan(x)[/tex]
[tex]f(x) = xarcsin(1-x^2)[/tex]
ANSWER 1
Note that,
[tex]f(u)=tan^{-1}(u)[/tex]
is the same as
[tex]f(u)=arctan(u)[/tex]
We apply the product rule.
[tex]f(x)=x^2tan^{-1}(x)[/tex]
So we keep the second function and differentiate the first,plus we keep the first function and differentiate the second.
[tex]f'(x)=(x^2)'tan^{-1}(x)+x^2(tan^{-1}(x))' [/tex]
Recall that,
If
[tex]f(u)=tan^{-1}(u)[/tex]
Then,
[tex]f'(u)=\frac{1}{1+u^2}} \times u'[/tex]
This implies that,
[tex]f'(x)=2xtan^{-1}(x)+\frac{x^2}{x^2+1} [/tex]
ANSWER 2
We apply the product rule and the chain rules of differentiation here.
[tex]f(x)=xsin^{-1}(1-x^2)[/tex]
[tex]f'(x)=x'sin^{-1}(1-x^2)+x(sin^{-1}(1-x^2))' [/tex]
Recall that,
If
[tex]f(u)=sin^{-1}(u)[/tex]
Then,
[tex]f'(u)=\frac{1}{\sqrt{1-u^2}} \times u'[/tex]
This implies that,
[tex]f'(x)=sin^{-1}(1-x^2)+x \times \frac{1}{\sqrt{1-(1-x^2)^2}}\times (-2x) [/tex]
[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-(1-2x^2+x^4)}} [/tex]
[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-1+2x^2-x^4}}[/tex]
[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{2x^2-x^4}}[/tex]
At the bank, Sheila made 5 deposits, each in the same amount. Her sister Sherri made 4 deposits, each in the same amount. Each of Sherri's deposits was $15 more than each deposit Sheila made. Both sisters deposited the same amount in the end. How much did each sister deposit each time?
- Write an equation. Let x represent the amount of one of Sheila’s deposits.
- Solve the equation. Show your work.
- Check your solution. Show your work.
- State the solution in complete sentences.
The equation would be 4y=5x 4(x+15)=5x x+15=y
let x be the amount that Shelia deposits each time
let y represent the amount that Sherri deposits each time
4(x+15)=5x
4x+60=5x
-4x -4x
60=x
Check:
x+15=y 60+15=y y=75
4(75)=5(60)
300=300
Shelia deposits $60 each time.
DERIVAR :
(2x – 1) / √ x2 + 1
An amusement park offers a yearly membership of $275 that allows for free parking and admission to the park. Members can also use the water park for an additional $5 per day. Nonmembers pay $6 for parking, $15 for admission, and $9 for the waterpark.
Write and solve an equation to find the number of visits it would take for the total cost to be the same for a member and a non-member if they both use the waterpark at each visit.
The yearly membership cost plus the cost per visit was set equal to the non-member cost per visit, and solving the equation gave us the result.
We need to find the number of visits it would take for the total cost of a member and a non-member to be the same if they both use the waterpark at each visit. Let's denote the number of visits as x.
The yearly membership cost is $275, and each visit to the waterpark costs an additional $5 for a member. So, for x visits, the total cost for a member is:
Member cost = $275 + $5x
Non-members pay $6 for parking, $15 for admission to the park, and $9 for the waterpark per visit. Therefore, the total cost for a non-member is:
Non-member cost = ($6 + $15 + $9)x = $30x
Setting both costs equal to find the number of visits where the costs are the same:
$275 + $5x = $30x
Now we solve for x:
$275 = $30x - $5x
$275 = $25x
x = $275/$25
x = 11
Therefore, it would take 11 visits for the total cost to be the same for a member and a non-member if they both use the waterpark at each visit.
PLEEEAAASSSEEE HEEEELLLPPP!!!
For ΔABC, ∠A = 4x - 4, ∠B = 6x - 1, and ∠C = 8x - 13. If ΔABC undergoes a dilation by a scale factor of 2 to create ΔA'B'C' with ∠A' = 51 - x, ∠B' = 4x + 21, and ∠C' = 6x + 9, which confirms that ΔABC∼ΔA'B'C by the AA criterion?
A) ∠A = ∠A' = 44° and ∠B = ∠B' = 71°
B) ∠A = ∠A' = 36° and ∠C = ∠C' = 67°
C) ∠B = ∠B' = 59° and ∠C = ∠C' = 67°
D) ∠B = ∠B' = 65° and ∠C = ∠C' = 75°
The angle in the dilated figure is the same as the original angle in each case, a fact that should be confirmed by the way the answer choices are shown.
∠A = ∠A'
... 4x -4 = 51 -x
... 5x = 55
... x = 11
∠A = 4·11 -4 = 40 . . . . . . doesn't match any offered choice
___
∠B = ∠B'
... 6x -1 = 4x +21
... 2x = 22
... x = 11
... ∠B = 6·11 -1
... ∠B = ∠B' = 65 . . . . . matches selection D)
_____
∠C = ∠C'
... 8x -13 = 6x +9
... 2x = 22
... x = 11
... ∠C = 6·11 +9 = 75
... ∠C = ∠C' = 75 . . . . . matches selection D)
A large balloon holds 3 cubic feet of helium gas. How many balloons can be filled with 2,301 cubic feet of helium gas? A) 747 B) 757 C) 767 D) 777
i think it will be c not really 100 percent sure
Answer:
C 767
Step-by-step explanation:
2031 ÷ 3 = 767
and took test
Helpp!!!Evaluate the piecewise function at the indicated values from the domain:
Answer:
f(-1) = -1 . . . . matches the last selection
Step-by-step explanation:
When evaluating piecewise functions, the first step is to determine the applicable piece. The argument -1 is in the range of the middle definition, (-2, 1). So, the function value is ...
... (-1)³ = -1
Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers
let Leo's speed = x mile/hr
so Ethan speed = (x + 6) miles per hour
Distance = Speed × Time
so distance traveled by Leo in 2 hours = x × 2 = 2x
and distance traveled by Ethan in 1.5 hours = 1.5( x + 6 ) = 1.5x + 9
since they meet on the path , After Ethan has ridden 1.5 hours and Leo has ridden 2 hours , so together the have traveled on complete path that is 65 miles.
⇒ distance traveled by leo in 2 hours + distance traveled by Ethan in 1.5 hours = 65
⇒ 2x + 1.5x + 9 = 65
⇒ 3.5x = 56
⇒ x = 16
Hence Leo's speed = x miles/hr = 16 miles/hour
and Ethan's speed = (x + 6) miles/hr = 16 +6 = 22 mile/hour
Answer:
Leo's Speed = 16
Ethan's Speed = 22
Step-by-step explanation:
Terri wants to make a triangle on her driveway with one side 8ft, one side 17 ft, and one side 8ft. Write an indirect proof to show that Terri’s design is not possible.
The third side of a triangle must always be less than the sum of the other 2 sides
here 8 + 8 = 16 and 17 ( the third side ) 17 > 16
Hence this is not a valid triangle
1.complete the column of proof
given < B=<D, m<b=80
prove <c=100
2.complete the paragraph proof
GIVEN<a a=and <b are complementary and <b and <c are complementary proof <a =<c
The first question probably has a drawing that is not included. Can you please include whatever drawing cam with it?
The Qeustion 2:
starting with writing the complementary angles:
The angles <a and <b being complementary means that
<b = 180 - <a
The angles <b and <c are complementary - that means
<c = 180 - <b
now plug in the first equation for <b to get:
<c = 180 - (180 - <a) = 180-180+<a= <a
so
<c = <a
which was to be proved!