Answer:
The intersection region shown in the graph attached is the solution of the system of inequalities
Manu has soccer practice at the park at 5:20 P.M. It ends at 6:15 P.M.
How long is Manu's soccer practice?
Answer:
His practice is 55 minutes long
you can look at it this way
from 5:20pm to 6:pm, is only 40 minutes
then from 6:00pm to 6:15pm is only 15 minutes
40 + 15 = 55
the average of students is 15 years if the age of a teacher is included their average becomes 18 years .what is the age of the teacher ?
Answer:
21; the age of the teacher
Step-by-step explanation:
15+x/2=18
Estimate - I estimated in the 20's because it only averaged up a little bit
Started with 23 and kept going until i got to my answer
21
15+21/2
36/2
18
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Find the missing value of x. Show your work.
Answer:
68 degrees
Step-by-step explanation:
Since the angle is a right angle, it is 90 degrees, to figure out the measurement of a section if it, simply subtract the known angle 22, from 90 to get an answer of 68.
Can someone please answer this
the diagram below shows a triangular metal plate with sides 4.5cm,6cm and 7.5cm. it has three small circular holes of radius 4mm.calculate the area of the plate to the nearest square centimeters.
Answer:
d = 4.5 cm
A = 1/4 (p x d²)
= 1/4 (3.14 x d x d)
= 1/4 (3.14 x 4.5 cm x 4.5 cm)
= 15.9 cm2
The area of the plate nearest square centimeters is 12cm².
What is a scalene triangle ?A scalene triangle has three different sides and corresponding to that three different interior angles.
According to the given question we have triangle with sides 4.5cm,6cm and 7.5cm.
We know for a scalene triangle given 3 sides.
area(A) = [tex]\sqrt{s(s-a)(s-b)(s-c)[/tex].
Where S is semi perimeter and a,b,c are the three sides.
= (a+b+c)/2.
= (4.5+6+7.5)/2 cm.
= 18/2 cm.
= 9 cm.
∴ The area of the triangle is
= [tex]\sqrt{9(9-4.5)(9-6)(9-7.5)[/tex]cm².
= [tex]\sqrt{9(4.5)(3)(1.5)}[/tex] cm².
= [tex]\sqrt{182.5}[/tex] cm² this is in between 13 square and 14 square approx 13.5 cm².
Now it has three small circles of radius of 4 mm or 0.4 cm.
We know area of a circle is πr² and area of 3 circles having same radius is 3(πr²) cm².
= 3{π(0.4)²}
= 3{3.14(0.16)} cm².
= 3(0.5024) cm².
= 1.5072 cm².
Now to obtain the area of the scalene triangle with those three holes of 0.4 cm we have subtract the area of the three circles from the triangle which is
= (13.5 - 1.5) cm².
= 12 cm².
learn more about heron's formula here :
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A rectangular storage container with an open top is to have a volume of 14 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 8 dollars per square meter. Find the cost of materials for the cheapest such container.
Answer:
C(min) = 277.95 $
Container dimensions:
x = 2.822 m
y = 1.411 m
h = 3.52 m
Step-by-step explanation:
Let´s call x and y the sides of the rectangular base.
The surface area for a rectangular container is:
S = Area of the base (A₁) + 2 * area of a lateral side x (A₂) + 2 * area lateral y (A₃)
Area of the base is :
A₁ = x*y we assume, according to problem statement that
x = 2*y y = x/2
A₁ = x²/2
Area lateral on side x
A₂ = x*h ( h is the height of the box )
Area lateral on side y
A₃ = y*h ( h is the height of the box )
s = x²/2 + 2*x*h + 2*y*h
Cost = Cost of the base + cost of area lateral on x + cost of area lateral on y
C = 10*x²/2 + 8* 2*x*h + 8*2*y*h
C as function of x is:
The volume of the box is:
V(b) = 14 m³ = (x²/2)*h 28 = x²h h = 28/x²
C(x) = 10*x²/2 + 16*x*28/x² + 16*(x/2)*28/x²
C(x) = 5*x² + 448/x + 224/x
Taking derivatives on both sides of the equation we get:
C´(x) = 10*x - 448/x² - 224/x²
C´(x) = 0 10x - 448/x² - 224/x² = 0 ( 10*x³ - 448 - 224 )/x² = 0
10*x³ - 448 - 224 = 0 10*x³ = 224
x³ =22.4
x = ∛ 22.4
x = 2.822 m
y = x/2 = 1.411 m
h = 28/x² = 28 /7.96
h = 3.52 m
To find out if the container of such dimension is the cheapest container we look to the second derivative of C
C´´(x) = 10 + 224*2*x/x⁴
C´´(x) = 10 + 448/x³ is positive then C has a minimum for x = 2.82
And the cost of the container is:
C = 10*(x²/2) + 16*x*h + 16*y*h
C = 39.82 + 158.75 + 79.38
C = 277.95 $
Nichol walks at a constant pace of 1.2 m/s and takes 15 minutes to get to school.
Sakura walks at 1.4 m/s and takes 20 minutes to get to school.
What is the difference between the distances they walked?
Answer:
The difference between the distances they walked is 600 meters.
Step-by-step explanation:
Let's calculate the distance traveled by Nichol and Sakura with the following equation:
[tex] d = v*t [/tex]
Where:
v: is the speed
t: is the time
The distance traveled by Nichol is:
[tex] d_{n} = 1.2 m/s*15min*\frac{60 s}{1 min} = 1080 m [/tex]
And the distance traveled by Sakura is:
[tex] d_{s} = 1.4 m/s*20 min*\frac{60 s}{1 min} = 1680 m [/tex]
Hence, the difference between the distances they walked is:
[tex] d_{t} = d_{s} - d_{n} = 1680 m - 1080 m = 600 m [/tex]
Sakura traveled 600 meters more than Nichol.
Therefore, the difference between the distances they walked is 600 meters.
I hope it helps you!
What number must you add to complete the square? x^2+26x=11
Answer:
[tex] {x}^{2} + 26x = 11 \\ x = 0.4 \: and \: - 26.4[/tex]
What is the solution to the equation 1/h-5+2/h+5=16/h^2-25
9514 1404 393
Answer:
h = 7
Step-by-step explanation:
Perhaps you want the solution to ...
1/(h -5) +2/(h +5) = 16/(h^2 -25)
Parentheses are required around denominators that have math operations.
Multiply by (h^2-25) and solve the linear equation.
[tex]\displaystyle\frac{1}{h-5}+\frac{2}{h+5}=\frac{16}{h^2-25}\qquad\text{given}\\\\(h+5)+2(h-5)=16\qquad\text{multiply by $h^2-25$}\\\\3h-5=16\qquad\text{simplify}\\\\3h=21\qquad\text{add 5}\\\\\boxed{h=7}\qquad\text{divide by 3}[/tex]
Anne invested $1000 in an account with a 3% annual interest rate. She made no deposits or
withdrawals on the account for 2 years. If interest was compounded annually, which equation
represents the balance in the account after the 2 years?
13. Find the length of X (in the picture)
Answer:
x=2
Step-by-step explanation:
the sides are proportional due the angles being equal
since the hypotonuse is 5 on the bigger one and 2.5 on the small one we can infer there is a ×2 difference
so 4÷2=x
x=2
A company is interested in testing sample sets of 20 Widgets to see how they withstand a heat test. Widgets fail the heat test when they develop cracks in their top paint coating. Suppose historically that 10% of the Widgets develop paint cracks. a. Does this problem represent the application of a Continuous or Discrete Distribution
Answer:
Discrete Distribution.
Step-by-step explanation:
For each widget, there are only two possible outcomes. Either they develop paint cracks, or they do not. The probability of a widget developing paint cracks is independent of any other widgets, which means that the binomial probability distribution, which is a discrete distribution, is used to solve this question. Thus the answer is a Discrete Distribution.
how do I use the following cosine equation to get the Sinusoid Max & Min Times (x values), and Sinusoid Max and Min Values (y values) in order graph a Tidal Wave Chart?
y = 11.412 cos ((5π / 31)(x-3:12)) +174.91
9514 1404 393
Answer:
maximum: (x, y) = (12.4n+3.2, 186.322)minimum: (x, y) = (12.4n+9.4, 163.498)Step-by-step explanation:
You know that cos(α) is a maximum at α=0, 2π, 4π, and all even multiples of π. You know cos(α) is a minimum for α=π, 3π, 5π, and all odd multiples of π.
You can find your value of x at which y will be a maximum by setting the argument of the cosine function equal to zero (and/or 2nπ). If we use α=2nπ, then we have ...
α = (5π/31)(x -3.2) = 2nπ
(x -3.2) = (31/5)(2n) = 12.4n
Tidal maxima will occur at ...
x = 12.4n +3.2 . . . . . for integer values of n
Without bothering to go through the solution for α being odd multiples of π, we can see from this that the period is 12.4 hours. We know the tidal minimum will be half a period later, or 6.2 hours later than this.
Tidal minima will occur at ...
x = 12.4n +9.4 . . . . for integers n
__
Of course, cos(α) has extremes of ±1, so your tidal maximum will be ...
y = 11.412 +174.91 = 186.322
and your tidal minimum will be ...
y = -11.412 +174.91 = 163.498
A 20-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals 150% of the amount of interest due. Each of the last ten payments is X. The lender charges interest at an annual effective rate of 10%. Calculate X.
Answer:
[tex]x = 97[/tex]
Step-by-step explanation:
Given
[tex]t = 20[/tex] --- time (years)
[tex]A =1000[/tex] --- amount
[tex]r = 10\%[/tex] --- rate of interest
Required
The last 10 payments (x)
First, calculate the end of year 1 payment
[tex]y_1(end) = 10\% * 1000 * 150\%[/tex]
[tex]y_1(end) = 150[/tex]
Amount at end of year 1
[tex]A_1=A - y_1(end) - r * A[/tex]
[tex]A_1=1000 - (150 - 10\% * 1000)[/tex]
[tex]A_1 =1000 - (150- 100)[/tex]
[tex]A_1 =950[/tex]
Rewrite as:
[tex]A_1 = 0.95 * 1000^1[/tex]
Next, calculate the end of year 1 payment
[tex]y_2(end) = 10\% * 950 * 150\%[/tex]
[tex]y_2(end) = 142.5[/tex]
Amount at end of year 2
[tex]A_2=A_1 - (y_2(end) - r * A_1)[/tex]
[tex]A_2=950 - (142.5 - 10\%*950)[/tex]
[tex]A_2 = 902.5[/tex]
Rewrite as:
[tex]A_2 = 0.95 * 1000^2[/tex]
We have been able to create a pattern:
[tex]A_1 = 1000 * 0.95^1 = 950[/tex]
[tex]A_2 = 1000 * 0.95^2 = 902.5[/tex]
So, the payment till the end of the 10th year is:
[tex]A_{10} = 1000*0.95^{10}[/tex]
[tex]A_{10} = 598.74[/tex]
To calculate X (the last 10 payments), we make use of the following geometric series:
[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + r)^n[/tex]
[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 10\%)^n[/tex]
[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 0.10)^n[/tex]
[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
The amount to be paid is:
[tex]Amount = A_{10}*(1 + r)^{10}[/tex] --- i.e. amount at the end of the 10th year * rate of 10 years
[tex]Amount = 1000 * 0.95^{10} * (1+r)^{10}[/tex]
So, we have:
[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+r)^{10}[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+10\%)^{10}[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+0.10)^{10}[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1.10)^{10}[/tex]
The geometric sum can be rewritten using the following formula:
[tex]S_n = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]S_n =\frac{a(r^n - 1)}{r -1}[/tex]
In this case:
[tex]a = x[/tex]
[tex]r = 1.10[/tex]
[tex]n =10[/tex]
So, we have:
[tex]\frac{x(r^{10} - 1)}{r -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]\frac{x((1.10)^{10} - 1)}{1.10 -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]\frac{x((1.10)^{10} - 1)}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]x * \frac{1.10^{10} - 1}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
So, the equation becomes:
[tex]x * \frac{1.10^{10} - 1}{0.10} = 1000 * 0.95^{10} * (1.10)^{10}[/tex]
Solve for x
[tex]x = \frac{1000 * 0.95^{10} * 1.10^{10} * 0.10}{1.10^{10} - 1}[/tex]
[tex]x = 97.44[/tex]
Approximate
[tex]x = 97[/tex]
Please I really need help
=======================================================
Explanation:
The triangular face has area of base*height/2 = 8*2/2 = 16/2 = 8 square feet.
Multiply this with the depth of the prism to get 8*12 = 96 cubic feet
----------
For any prism, the volume formula is
V = (area of base)*(depth of prism)
The term "depth" can be replaced with "height" and it's the same idea.
In this problem, we have a triangular prism because the parallel sides are triangles.
explain what it means for a function to be O(1)
Answer:
a function that converges to 0. '' This means that there is some input size past which the function is always between -0.1 and 0.1; there is some input size past which the function is always between -0.01 and 0.01; and so on.
Can you help me with this question
Answer:
Below in bold.
Step-by-step explanation:
We see from the diagram that:
SY = SK + KY
So, substituting the given values:-
36 - x = 13x - 5 + 2x + 9
-x - 13x - 2x = - 5 + 9 - 36
-16x = -32
x = 32/16 = 2.
So SK = 13(2) - 5 = 21.
KY = 2(2) + 9 = 13.
SY = 36 - 2 = 34.
21 + 13 = 34 so this is a check that our calculation is correct.
Solve the following system of equations by graphing.
- 4x + 3y -12
- 2x + 3y -18
Answer:
The solution of the graph is at (-3,-8).
Step-by-step explanation:
The given equations are :
-4x+3y=-12
and
-2x+3y=-18
These are the system of equations in two variables.
The graphs for the equations are :
The solution of the graph is at (-3,-8).
30 points ~ Thirty-eight kids are riding the bus. Half of the kids are girls. How many boys are on the bus?
Answer:
19 boys
Step-by-step explanation:
38 kids on the bus
1/2 are girls, that means 1/2 are boys
1/2 * 38 = 19
There are 19 girls and 19 boys
Pls do this for me I am getting annoyed with this
Answer:
x = 1.7
Step-by-step explanation:
Is triangle XYZ = ABC ? If so, name the postulate that applies. A. Congruent - ASA B. Congruent - SAS C. Might not be congruent D. Congruent - SSS
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST
32 1/3% of animals at an animal shelter are dogs. About what fraction of the animals are dogs
Answer:
about 8/25
Step-by-step explanation:
32.3% = 32/100 = 16/50 = 8/25
rounded percentage down.
put over 100
reduce fraction
1/3(-15 divide 1/2) 1/4 what does it equal
Answer:
-2.5 or - 2 1/2
Step-by-step explanation:
Writing out the expression Mathematically ;
1/3(-15÷1/2)1/4
Using PEMDAS :
Solving the bracket first
(-15 ÷ 1/2) = (-15 * 2/1) = - 30
We have :
1/3(-30)1/4 = - 10 * 1/4 = - 10 / 4 = - 2.5
-2.5 = - 2 1/2
Part A create an equation and solve for X:
Part B find the measure of the unknown angle
Answer:
x = 2 degree and unknown angle = 31 degree
Step-by-step explanation:
149 + 13x + 5 =180 degree (being linear pair)
154 + 13x = 180
13x = 180 - 154
x = 26/13
x = 2 degree
unknown angle = 13x + 5
=13*2 + 5
=26 + 5
=31 degree
The value of the variable x is 2°. Then the value of the unknown angle is 31°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Both angles are supplementary angles. Then the equation is given as,
13x + 5° + 149° = 180°
13x + 154° = 180°
13x = 180° - 154°
13x = 26°
x = 26° / 13
x = 2°
The value of the variable x is 2°. Then the value of the unknown angle is given as,
13x + 5° = 13(2°) + 5°
13x + 5° = 26° + 5
13x + 5° = 31°
The value of the variable x is 2°. Then the value of the unknown angle is 31°.
More about the angled link is given below.
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If a star is 5,699,999,999,999,999 meters from earth, how long does it take light to travel from earth to the star?
Answer
19.013.153,42629466 giây
Step-by-step explanati
van toc ánh sán =299.792.458 m/s
s= v*t
t=s/v
t= 5.699.999.999.999.999/299.792.458= 19.013.153,42629466 giây
FIRST PERSON TO SOLVE THIS IS THE SMARTEST PERSON ON BRAINLY
Answer:
x=161
Step-by-step explanation:
James hits a golf ball 145.7 yards Kayla hit a golf ball 122.95 yards how much farther does James hit a golf ball
every solid shapes sit or stand on me what am I
Answer:
Base
Step-by-step explanation:
Every solid shape has to have a base that they sit/stand on. Because the base is the bottom of the shape and lies on the table. Hence, answering your question.
Hope this helps!
This one was difficult but if your work through it, you will get it.
Keep trying!
I am thinking of a 3-digit number.
When it is divided by 9, the
remainder is 3
When it is divided by 2, the
remainder is 1
When it is divided by 5, the
remainder is 4
What is my number?
Is this problem possible to solve?
Answer:
The answer is 939
Step-by-step explanation:
If you divide 939 by 9 it equals 104 R3.
If you divided 939 by 2 it equals 469 R1
And if you divide 939 by 5 it equals 187 R4
Hope this helps!