The diagonal of the square is the same as the diameter of the circle.
So, the diameter of the circle is 36.
Circumference formula:
C = 2πr
To find the radius, we just need to divide the diameter by two:
36 / 2 = 18
Now, solve using the given values.
C = 2π(18)
C = 36π
Therefore, the answer is D.
Best of Luck!
The sand used for sanding icy roads in the winter is stored in a conical-shaped structure with a radius of 10 m and a height of 16 m. Calculate the maximum amount of sand which can be stored in this structure.
Answer:
1,675.516
Step-by-step explanation:
The formula for a cone is V = pi r^2 h/3.
Plugging in the values of the radius and height, V = pi 10^2 16/3
Solving, you get:
V = pi 100 5.3333333
V = 1,675.516
In a study with four groups and 10 participants in each group, the sum of squares for the between-groups source of variation is 60. What is the value for the mean square between groups in this study
Answer:
20
Step-by-step explanation:
Given that:
The study group n = 4
number of participants = 10
the sum of squares for the between-groups source of variation is 60
The objective is to determine the mean square between groups in this study
The mean square between groups in this study compares the means of the group with the sum of squares for the between-groups source (i.e the grand mean)
For this analysis;
the degree of freedom = n-1
the degree of freedom = 4 - 1
the degree of freedom = 3
Thus; the mean square between groups = [tex]\dfrac{60}{3}[/tex]
the mean square between groups = 20
The tee for the sixth hole on a golf course is 305 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
Correct answer is option D. 96.4 yd.
Step-by-step explanation:
Please refer to the attached figure for labeling of the given diagram.
ABC is a triangle with the following labeling:
A is the hole, B is the Tee and C is the point where the ball is.
Sides are labeled as:
[tex]a =255\ yd\\c = 305\ yd\\\angle B =17^\circ[/tex]
To find:
Side [tex]b = ?[/tex]
Solution:
Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.
We can use cosine formula here to find the value of the unknown side.
[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]
Putting all the values:
[tex]cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd[/tex]
So, the distance between the Ball and hole is 96.42 yd
Correct answer is option D. 96.4 yd.
Answer:
D.) 96.4 yd
Step-by-step explanation:
I got it correct on founders edtell
Find the 20th term from the last term of the AP:3,8,13,..., 253.
Answer:
158
Step-by-step explanation:
The sequence is 3, 8, 13, ..., 253.
Going backwards, it's 253, 248, 243, ..., 3.
First term is 253, common difference is -5.
The nth term is:
a = 253 − 5(n − 1)
The 20th term is:
a = 253 − 5(20 − 1)
a = 158
Jane’s mobile phone plan charges $0.05 per minute at daytime rates before 8 p.m. and $0.03 per minute at nighttime rates after 8 p.m. A conference call costs 1.5 times the normal rate. Calculate the cost of a conference call lasting from 7 p.m. to 8:30 p.m.
Answer
5.85
Step-by-step explanation:
$0.05 x 1.5 = 0,075 x 1 hour (60) = 4,5
$0.03 x 1.5 = 0,045 x half an hour (30) = 1,35
So 4.5 + 1.35 = 5.85
Answer:
Step-by-step explanation:
Cost of the conference call before 8 pm =0.15 * 0.05 = $ 0.075
Cost of the conference call after 8 pm = 0.15 * 0.03 = $ 0. 045
Cost of the conference call from 7pm to 8pm that last 60 minutes= 0.075 * 60
= $ 4.50
Cost of the conference call 8pm to 8:30pm =0.045 * 30 = $ 1.35
Cost of the conference call 7 pm to 8:30 pm = 4.50 + 1.35 = $ 5.85
Can I get some help?? Ty
================================================
Explanation:
Subtract straight down. The x terms subtract to 5x-2x = 3x. The y terms subtract to 3y-3y = 0y = 0, so the y terms go away and are eliminated. The terms on the right hand side subtract to 31-25 = 6.
After all that subtraction, we end up with the equation 3x = 6 which solves to x = 2 after dividing both sides by 3.
Use x = 2 to find the value of y
5x+3y = 31
5(2)+3y = 31
10+3y = 31
3y = 31-10
3y = 21
y = 21/3
y = 7
or
2x+3y = 25
2(2)+3y = 25
4+3y = 25
3y = 25-4
3y = 21
y = 21/3
y = 7
Using either equation has x = 2 lead to y = 7.
Therefore, the solution is (x,y) = (2,7)
If you were to graph the two original equations, then they would intersect at (2,7).
solve systems by substitution method x + y = 20 3x + 4y = 72
Answer:
x = 8; y = 12.
Step-by-step explanation:
x + y = 20
x = -y + 20
3x + 4y = 72
3(-y + 20) + 4y = 72
-3y + 60 + 4y = 72
y = 12
x + 12 = 20
x = 8
Check your work!
3(8) + 4(12) = 72
24 + 48 = 72
72 = 72
Hope this helps!
Answer:
X=-12 and Y= 32
Step-by-step explanation:
x+y=20 -> 1
3x+4y=72 -> 2
Form 1,
[x+y=20]×4
4x+4y=60 ->3
Form 2,
3x+4y=72
4y= 72 -3x ->4
Sub (4) into (3)
4x+72-3x= 60
x = -12
Sub X=-12 into (1)
-12+y=20
y= 32
Hope this helps.
Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB? Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A B C. It is also slightly higher than triangle A B C. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C. Triangles A B C and X Y Z are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C. Triangles A B C and X Y Z are congruent. Triangle A B C is rotated to the right to form triangles X Y Z. Triangle X Y Z is also higher and to the right of triangle A B C.
Answer:
B. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.
Step-by-step explanation:
Translation and reflection are examples of methods of rigid transformation. Translation ensure that each point on a given figure is moved the same distance with respect to the reference plane. Reflection involves the flipping of a given figure across a given line.
From the question, both reflection and transformation would map the triangles into one another. Since the reference line contains AB, then the two triangles are congruent and would share a common side.
Thus, the triangle pairs that can be mapped into each other is that of option B.
Based on the information given, the triangle pairs that can be mapped to each other using both a translation and a reflection across the line containing AB will be A. Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A.
Triangles.The triangle pair that can be mapped to each other using both translation and reflection across line containing AB is the first triangle pair.
The first figure consists of ΔXYZ and ΔABC that are a reflection of each other across the line AB and a translation.
Learn more about triangles on:
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A cylinder has radius r and height h. A. How many times greater is the surface area of a cylinder when both dimensions are multiplied by a factor of 2? 3? 5? 10? B. Describe the pattern in part (a).
Answer: A. Factor 2 => 4x greater
Factor 3 => 9x greater
Factor 5 => 25x greater
Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:
A = 2.π.r.h
A cylinder of radius r and height h has area:
[tex]A_{1}[/tex] = 2πrh
If multiply both dimensions by a factor of 2:
[tex]A_{2}[/tex] = 2.π.2r.2h
[tex]A_{2}[/tex] = 8πrh
Comparing [tex]A_{1}[/tex] to [tex]A_{2}[/tex] :
[tex]\frac{A_{2}}{A_{1}}[/tex] = [tex]\frac{8.\pi.rh}{2.\pi.rh}[/tex] = 4
Doubling radius and height creates a surface area of a cylinder 4 times greater.
By factor 3:
[tex]A_{3} = 2.\pi.3r.3h[/tex]
[tex]A_{3} = 18.\pi.r.h[/tex]
Comparing areas:
[tex]\frac{A_{3}}{A_{1}}[/tex] = [tex]\frac{18.\pi.r.h}{2.\pi.r.h}[/tex] = 9
Multiplying by 3, gives an area 9 times bigger.
By factor 5:
[tex]A_{5} = 2.\pi.5r.5h[/tex]
[tex]A_{5} = 50.\pi.r.h[/tex]
Comparing:
[tex]\frac{A_{5}}{A_{1}}[/tex] = [tex]\frac{50.\pi.r.h}{2.\pi.r.h}[/tex] = 25
The new area is 25 times greater.
B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.
What is the slope of the line through the points (4,2) and (-16,-6)
Answer:
2 / 5.
Step-by-step explanation:
The slope is the rise over the run.
In this case, the rise is 2 - (-6) = 2 + 6 = 8.
The run is 4 - (-16) = 4 + 16 = 20.
So, the slope is 8 / 20 = 4 / 10 = 2 / 5.
Hope this helps!
Answer:
the slope of the line that goes through (4,2) and (-16,-6) is 2/5
m= 2/5
Step-by-step explanation:
in order to find the slope we use the ∆y/∆x which is really the change in y over the change in x.
so all you have to do is find your y's and X's.
your y's are -6 and 2
your X's are -16 and 4
now in order to find the change in y and x you subtract your y's and x'x
the formula for this is:
∆y/∆x = y1-y2/x1-x2= (m aka the slope)
y1 is -6
and y2 is 2
-6 - 2 = -8
now do the X's
X1 is -16
and X2 is 4
-16 - 4 = -20
put that in fraction form and it's -8/-20
simplify that you get 2/5
Clase de estadistica la moda es una medida de tendencia central que: ¿por que? a) tiene muchos datos b) tiene la mayor frecuencia c) tiene poca frecuencia d) al ordenar los datos de menor a mayor es el dato que se ubica en el centro
Answer:
b) tiene la mayor frecuencia
Step-by-step explanation:
Las medidas de tendencia central se refieren a un centro alrededor del cual se encuentran todos los datos y estas medidas son: la media, la moda y la mediana. La media es el valor promedio de un grupo de datos, la moda es el dato que se repite más veces y la mediana es el valor que se encuentra en el centro cuando los datos se ubican de menor a mayor. De acuerdo a esto, la respuesta es que la moda es una medida de tendencia central que tiene la mayor frecuencia.
Los otras opciones no son correctas porque el tamaño del conjunto de datos no depende de las medidas de tendencia central, esto depende de cada situación y pueden ser muchos o pocos datos. Además la opción "al ordenar los datos de menor a mayor es el dato que se ubica en el centro" se refiere a la mediana.
a parabola had a vertex of (-5,0) and passes through the point (-3,1)
Answer:
Step-by-step explanation:
let the parabola be y=a(x+5)²+0
or y=a(x+5)²
∵ it passes through (-3,1)
1=a(-3+5)²
4a=1
a=1/4
so parabola is y=1/4(x+5)²
Problem Water boils at 212^\circ212 ∘ 212, degrees Fahrenheit. Write an inequality that is true only for temperatures (t)(t)left parenthesis, t, right parenthesis that are higher than the boiling point of water.
Answer:
t > 212
Step-by-step explanation:
Given
Boiling point = 212°F
Required
Inequality that shows temperature greater than the boiling point
From the question, temperature is represented with t.
The inequality "greater than" is represented with >
So, temperature greater than the boiling point implies that t > 212
Answer: t > 212
Step-by-step explanation:
The question says "Write an inequality that is true only for temperatures that are higher than the boiling point of water."
This means t has to be higher than 212 since it says only for temperatures that are higher than the boiling point.
But since we have to write an inequality the answer would be: t > 212.
I know I did this very late and you probably don't need it but i was bored
Solve.
5x– 2y = 27
-3x +2y=-17
Enter your answer, in the form (x,y), in the boxes.
Answer:
x=5,y=-1
Step-by-step explanation:
5x– 2y = 27
-3x +2y=-17
Add the two equations together to eliminate y
5x– 2y = 27
-3x +2y=-17
----------------------
2x = 10
Divide by 2
2x/2 = 10/2
x = 5
Now find y
-3x +2y = -17
-3(5)+2y = -17
-15+2y =-17
Add 15 to each side
-15+15 +2y = -17+15
2y = -2
Divide by 2
2y/2 = -2/2
y =-1
Determine the equation for the line of best fit to represent the data.
Answer:
Y= -1/5x + 1
Step-by-step explanation:
Just type it on a graphing calculator an click graph
pleaseeeeeeeeee helllllllpppppp pleaseeeeee hellpppp
Answer:
a. u = 19b. t = 6c. a = 2Step-by-step explanation:
a. Given,
v = 34 , a = 5 , t = 3
[tex]v = u + at[/tex]
plugging the values:
[tex]34 = u + 5 \times 3[/tex]
Calculate the product
[tex]34 = u + 15[/tex]
Move 'u' to L.H.S and change its sign
[tex] - u + 34 = 15[/tex]
Move constant to RHS and change its sign
[tex] - u = 15 - 34[/tex]
Calculate
[tex] - u = - 19[/tex]
The difference sign (-) will be cancelled in both sides:
[tex]u = 19[/tex]
b. Given,
v = 50 , u = 20 , a = 5
[tex]v = u + at[/tex]
plugging the values
[tex]50 = 20 + 5 \times t[/tex]
[tex]50 = 20 + 5t[/tex]
Move 5t to L.H.S and change its sign.
Similarly, Move 50 to R.H.S and change its sign
[tex] - 5t = 20 - 50[/tex]
Calculate
[tex] - 5t = - 30[/tex]
The difference sign (-) will be cancelled in both sides
[tex]5t = 30[/tex]
Divide both sides of the equation by 5
[tex] \frac{5t}{5} = \frac{30}{5} [/tex]
Calculate
[tex]t = 6[/tex]
c. Given,
v = 22 , u = 8 , t = 7
[tex]v = u + at[/tex]
plugging the values
[tex]22 = 8 + a \times 7[/tex]
[tex]22 = 8 + 7a[/tex]
Move 7a to LHS and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - 7a = 8 - 22[/tex]
Calculate
[tex] - 7a = - 14[/tex]
The difference sign (-) will be cancelled in both sides
[tex]7a = 14[/tex]
Divide both sides of the equation by 7
[tex] \frac{7a}{7} = \frac{14}{7} [/tex]
Calculate
[tex]a = 2[/tex]
Hope this helps...
Good luck on your assignment..
Darnell is making improvements to his 3: 13 feet by 12 feet bedroom. Which deal would he best for him?
Paying $7.25 per sq feet
Paying $6.75 per sq feet plus a $100 installation fee
Answer:
paying $7.25 per sq feet
Step-by-step explanation:
So we can start off by solving the area:
12*13=156
so the total area is 156 feet sq
the first deal:
156/7.25= about $21.52
the second deal:
156/6.75= about $23.11, however with the installation fee, it will cost even more.
Please help Asap!!!Math question
Answer:
first one
Step-by-step explanation:
HELP ASAP MONEY & WAGES!
Answer: $26.70 per hour
Step-by-step explanation:
Regular hours consists of 8 hrs
Overtime hours is 12 - 8 = 4 hours
Regular pay at "x" per hour = 5(8)(x) = 40x
Overtime pay at "2x" per hour = 5(4)(2x) = 40x
Total pay = 80x
Total Pay = $2136 = 80x
[tex]\dfrac{\$2136}{80}=x[/tex]
$26.70 = x
What is the domain of the function graphed below
Answer:
-∞ < x< -∞
Step-by-step explanation:
The domain is the values that x takes
The values that x can take is all real values of x
-∞ < x< -∞
Find the value.
9x+6 when x=-2/3
Answer:
0Step-by-step explanation:
Given,
[tex] - \frac{2}{3} [/tex]
Now, let's find the value of 9x + 6
[tex]9x + 6[/tex]
plug the value of X
[tex] = 9 \times (- \frac{2}{3} ) + 6[/tex]
Multiplying a positive and negative equals a negative
[tex]( + ) \times ( - ) = ( - )[/tex]
[tex] = - 9 \times \frac{2}{3} + 6[/tex]
Reduce the number with Greatest Common Factor 3
[tex] = - 3 \times 2 + 6[/tex]
Multiply the numbers
[tex] = - 6 + 6[/tex]
The sum of two opposites equals 0
[tex] = 0[/tex]
Hope this helps..
best regards!!
Jeff's sister drives 14 miles to her collage his brother only drives 5/7/10 miles to his collage how much farther does Jeff's sister drive than his brother
Answer:
8.3miles
Step-by-step explanation:
Here Jeff's sister drives 14 miles
his brother only drives 57/10 miles then the question is only asking the difference between their distance of driving to school knowing fully well that Jeff's sister drive farther than his brother, then we find the difference between their drives which is done bow
14miles -57/10 miles
= 83/10
= 8.3miles
Therefore, Jeff's sister drive 8.3miles farther than his brother
PLEASE ANSWER ASPAA The x-intercept of the equation 2y – x = -6 is: 3. -3. 6. None of these choices are correct.
Answer:
x = 6
Step-by-step explanation:
The x-intercept of the equation is where the graph crosses the x-axis when y = 0. So, we simply plug in 0 for y:
2(0) - x = -6
0 - x = -6
-x = -6
x = 6
Alternatively, you can graph the equation into a graphing calc and analyze where the graph crosses the x-axis.
You measure the sides of a pool and find that it is 20 yards wide and 50 yards long. Approximately, how far would it be diagonally between corners of the pool?
A. 54 yards
B. 58 yards
C. 62 yards
D. 66 yards
Answer:
[tex]\boxed{d = 54 yards}[/tex]
Step-by-step explanation:
Formula for diagonal is as follows:
[tex]d = \sqrt{l^2+w^2}[/tex]
Where d is diagonal, l is length (50 yards) and w is width (20 yards)
[tex]d = \sqrt{(50)^2+(20)^2}[/tex]
[tex]d = \sqrt{2500+400}[/tex]
[tex]d = \sqrt{2900}[/tex]
d = 53.85 yards
d ≈ 54 yards
Answer:
[tex]\boxed{\mathrm{54 \: yards}}[/tex]
Step-by-step explanation:
The shape of the pool is a rectangle.
The diagonal of a rectangle can be found through a formula by using Pythagorean theorem.
[tex]d^2=l^2 +w^2[/tex]
[tex]d=diagonal\\l=length\\w=width[/tex]
The length is given 50 yards, and width is given 20 yards. Find the diagonal.
[tex]d^2 =50^2 +20^2[/tex]
[tex]d^2 =2500+400[/tex]
[tex]d^2 =2900[/tex]
[tex]d=\sqrt{2900}[/tex]
[tex]d \approx 53.851648[/tex]
[tex]d \approx 54[/tex]
A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 5 hours more than the 10-horsepower pump to empty the pool when working by itself. How long will it take to empty the pool using just the 10-horsepower pump?
Answer: 10 hours
Step-by-step explanation:
The 10hp pump takes x hours to empty the pool which means it gets [tex]\dfrac{1}{x}[/tex] of the job done in one hour.
The 6hp pump takes x+5 hours to empty the pool which means it gets [tex]\dfrac{1}{x+5}[/tex] of the job done in one hour.
Together, they can get [tex]\dfrac{1}{x}+\dfrac{1}{x+5}[/tex] of the job done in one hour.
It is given that together they get the job done in 6 hours which means they get [tex]\dfrac{1}{6}[/tex] of the job done in one hour.
10 hp pump + 6 hp pump = Together
[tex]\dfrac{1}{x}\quad +\quad \dfrac{1}{x+5}\quad =\quad \dfrac{1}{6}[/tex]
Multiply by 6x(x+5) to eliminate the denominator:
[tex]\dfrac{1}{x}(6x)(x+5) +\dfrac{1}{x+5}(6x)(x+5) = \dfrac{1}{6}(6x)(x+5)[/tex]
Simplify and solve for x:
6(x + 5) + 6x = x(x + 5)
6x + 30 + 6x = x² + 5x
12x + 30 = x² + 5x
0 = x² - 7x - 30
0 = (x - 10)(x + 3)
0 = x - 10 0 = x + 3
10 = x -3 = x
Since the number of hours cannot be negative, disregard x = -3.
So, the only valid answer is x = 10.
why the system of si unit is developed
Step-by-step explanation:
Hi, there!!!!
The main purpose of developing si unit is to have standard unit of measurements and to bring uniformity in whole world in terms of measurements.
I hope it helps you...
convert this number to scientific notation 1260000
Answer:
1.26 * 10 ^6
Step-by-step explanation:
1260000
Scientific notation is of the form a* 10 ^b
where a is a number between 1 and less than 10
Move the decimal 6 places to the left
1.26 ( dropping the extra zeros)
b = +6 since we moved the decimal 6 places)
1.26 * 10 ^6
The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].
We have,
1260000
Write the zeroes in powers of 10.
Write a number between 1 to 10 along with the power of 10.
Now,
126 x 10000
This can be written as,
126 x [tex]10^4[/tex]
Now,
126 can be written as 126/100 x 100.
i.e
1.26 x 100 or 1.26 x 10²
Now,
1.26 x 10² x [tex]10^4[/tex]
1.26 x [tex]10^{2 + 4}[/tex]
1.26 x [tex]10^6[/tex]
Thus,
The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].
Learn more about scientific notation here:
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helpppppp plsssssss!!!!!!! in the picture below
Answer:
266.67 feet^2.
Step-by-step explanation:
The scale is 1:40.
That means that if the scale has a width of 4 inches, the room will have a width of 4 * 40 = 160 inches. 160 / 12 = 80 / 6 = 40 / 3 feet.
The length in the model is 6 inches, so the room has a length of 6 * 40 = 240 inches. 240 / 12 = 120 / 6 = 60 / 3 = 20 feet.
The area will then be (40 / 3) * 20 = 800 / 3 = 266.67 feet^2.
Hope this helps!
The cylinder shown has a volume of 150 cubic inches and its height is equal to its radius. The cylinder and the sphere shown have the same radius. What is the volume of the sphere?
Answer:
V = 200
Step-by-step explanation:
Cylinder
V = pi r^2 h
150 = pi r^2 h
We know that h = r
150 = pi r^2 r
150 = pi r^3
Divide each side by pi
150 /pi = r^3
Take the cube root of each side
( 150 / pi ) ^ 1/3 = r
3.627831679 = r
Rounding to 3.63
Now find the volume of the sphere
V = 4/3 pi r^3
Replacing r^3 with 150 /pi
V = 4/3 * pi ( 150/pi)
V = 4*150 /3
V = 200
Which of the following is a point-slope equation for a line with the point
(-2, 4) and a slope of 3?
O A. y-2-3(x-4)
B. y-4-3(x-2)
O C. y +2 = 3(x-4)
O D. y - 4 - 3(x+2)
Hi there! :)
Answer:
Choice D. (y - 4) = 3(x + 2)
Step-by-step explanation:
An equation in point-slope form is:
(y - y1) = m(x - x1)
Where:
y1 = y-coordinate of a point
m = slope
x1 = x-coordinate of a point
In this instance, the point given is (-2, 4) with a slope of 3. Therefore, the equation in point-slope form would be Choice D. (y - 4) = 3(x + 2)
Answer:
Step-by-step explanation:
answer is C
Because formula of equation of slop is
Y-y1=m(x-x1)