Answer:
6/17
Step-by-step explanation:
To find the probability that Roy picks a chocolate flavor at random, we need to use the basic probability formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
In this scenario:
- The favorable outcomes are the number of chocolate flavors.
- The total number of possible outcomes is the total number of flavors.
According to the given situation, there are a total of 16 flavors of ice cream, and out of these, 6 flavors contain chocolate.
Using the probability formula:
\[ \text{Probability of picking a chocolate flavor} = \frac{6}{16} \]
To simplify the fraction, we can divide both the numerator and the denominator by the greatest common divisor, which in this case is 2:
\[ \frac{6 \div 2}{16 \div 2} = \frac{3}{8} \]
Now, to express this as a decimal, we divide 3 by 8:
\[ 3 \div 8 = 0.375 \]
Therefore, the probability that Roy picks a chocolate flavor at random is 0.375. If you're looking at multiple-choice answers, you would choose the option that best fits this answer.
the angle turns through 1/5 of the circle what is the measure of the angle
Answe 72
Step-by-step explanation:
360 divided by 5 is 72
A circle is a curve sketched out by a point moving in a plane. The measure of the angle is 72°.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Let the angle that turns through 1/5 of the circle be x.
We know that the measure of the centre of a circle is 360°, while it is given that the angle turns through 1/5 of the circle. Therefore, the angle will turn 1/5 of 360°.
[tex]x = \dfrac15 \times 360^o = 72^o[/tex]
Thus, the measure of the angle is 72°.
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Two linear equations are represented by using the tables below.
The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line.
What is the solution to the system of equations?
A. (-2, -8)
B. (-1, -5)
C. (0, -2)
D. (2, 4)
Answer:
It's B.
Step-by-step explanation:
Have a good day.
What are the x and y-intercepts of the line described by the equation?
-6x + 3y = 18.9
Answer:
x-intercept - x = 1/2y - 3.15
y-intercept - y = 2x + 6.3
Step-by-step explanation:
For x,
-6x + 3y = 18.9
-6x = -3y + 18.9
x = -3y/-6 + 18.9/-6
x = 1/2y - 3.15
For y,
-6x + 3y = 18.9
3y = 6x + 18.9
y = 6x/3 + 18.9/3
y = 2x + 6.3
please help on this 7th grade question
Which choice has a value that is closest to the value of the following expression? 17/12 - 49/40
A. 1/4
B. 1/5
C. 1/6
D. 1/7
Option B
The choice has a value that is closest to the value of the following expression 17/12 - 49/40 is [tex]\frac{1}{5}[/tex]
Solution:
Given that we have to find the value that is closest to the value of following expression
[tex]\frac{17}{12} - \frac{49}{40}[/tex]
Let us take L.C.M of denominators and solve the sum
L.C.M of 12 and 40
List all prime factors for each number
prime factorization of 12 = 2 x 2 x 3
prime factorization of 40 = 2 x 2 x 2 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 x 5 = 120
Thus the given expression becomes:
[tex]\rightarrow \frac{17 \times 10}{12 \times 10} - \frac{49 \times 3}{40 \times 3}\\\\\rightarrow \frac{170}{120} - \frac{147}{120}\\\\\rightarrow \frac{170-147}{120}\\\\\rightarrow \frac{23}{120} = 0.1916 \approx 0.2[/tex]
[tex]0.2 = \frac{1}{5}[/tex]
Thus correct answer is option B
Answer:
B
Step-by-step explanation:
M is the midpoint line cd, where C is (-1,-1) and M is (3,5). Find the coordinates of D
Answer:
The coordinates of point D are (7,11)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
In this problem we have
[tex]M=(3,5)\\C(x1,y1)=(-1,-1)\\D(x2,y2)=?[/tex]
substitute the given values
[tex](3,5)=(\frac{-1+x2}{2},\frac{-1+y2}{2})[/tex]
Solve for x2
[tex]\frac{-1+x2}{2}=3[/tex] ---> [tex]-1+x2=6[/tex] --->[tex]x2=6+1=7[/tex]
Solve for y2
[tex]\frac{-1+y2}{2}=5[/tex] ---> [tex]-1+y2=10[/tex] ---> [tex]y2=10+1=11[/tex]
therefore
The coordinates of point D are (7,11)
Andrew wrote the number 186,425 on the board. In which is the value of the digit 6 exactly 10 times the value of the digit 6 in the number Andrew wrote? A. 681,452. B. 462,017. C. 246,412. D. 125,655
Final answer:
The number where the value of the digit 6 is 10 times the value in the number 186,425 is 462,017, as the 6 is in the ten thousands place, giving it a value of 60,000. The correct answer is option B.
Explanation:
The student is tasked with finding the place value of 6 that is 10 times the value of the 6 in the number 186,425. In 186,425, the 6 is in the thousands place, so its value is 6,000 (6 x 103). Therefore, to find the number where the value of 6 is ten times 6,000, we need a 6 that is worth 60,000. The 6 must be in the ten thousands place to have this value.
Let's inspect the options:
A. 681,452 - Here, the 6 is in the hundred thousands place, so the value of 6 is actually 600,000, which is not 10 times 6,000.
B. 462,017 - The 6 is in the ten thousands place. Here, the value of 6 is 60,000, which is 10 times the value of 6 in the number 186,425.
C. 246,412 - The 6 is in the thousands place again, so the value is 6,000, not 10 times more.
D. 125,655 - The 6 here does not multiply its value since it's in the tens place.
Therefore, the correct answer is option B, where the value of the digit 6 is exactly 10 times the value of the digit 6 in the number Andrew wrote.
The admission fee at a small fair is $1.50 for children, and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults entered?
Answer: 700 adults and 1500 children
Step-by-step explanation:
Let the number of adults be x and the number of children be y , then
x + y = 2200 ........................... equation 1
4x + 1.5y = 5050 ............................ equation 2
solving the system of linear equation by substitution method , from equation 1 make x the subject of the formula , that is
x = 2200 - y ....................... equation 3
substitute x = 2200 - y into equation 2 , that is
4 ( 2200 - y ) + 1.5y = 5050
8800 - 4y + 1.5y = 5050
8800 - 2.5y = 5050
2.5y = 8800 - 5050
2.5y = 3750
y = 3750/2.5
y = 1500
substitute y = 1500 into equation 3 , we have
x = 2200 - y
x = 2200 - 1500
x = 700
Therefore , 700 adults and 1500 children entered
a fast food restaurant had 5 boxes of chicken nuggets for $33.95. A competing restaurant had 4 boxes of chicken fingers for $26.96. which food has a higher unit price.
Answer:
The food at the fast food restaurant of chicken nuggets is having higher unit price.
Step-by-step explanation:
Given:
A fast food restaurant had 5 boxes of chicken nuggets for $33.95.
A competing restaurant had 4 boxes of chicken fingers for $26.96.
Now, to get the food which has a higher unit price.
So, to get the unit price we use unitary method:
In, a fast food restaurant:
5 boxes of chicken nuggets cost for = $33.95.
Thus, 1 box of chicken nuggets cost for = [tex]\$33.95\div 5 = \$6.79.[/tex]
In a competing restaurant:
4 boxes of chicken fingers cost for = $26.96.
Thus, 1 box of chicken fingers cost for = [tex]\$26.96 \div 4 = \$6.74.[/tex]
Now, as comparing the prices of both restaurant the price of chicken nugget in fast food restaurant is $6.79 per box which is higher than the price of chicken fingers cost of $6.74 per box in competition restaurant.
Therefore, the food at the fast food restaurant of chicken nuggets is having higher unit price.
At the beginning of the period, the Cutting Department budgeted direct labor of $46,300 and supervisor salaries of $37,200 for 4,630 hours of production. The department actually completed 5,000 hours of production.
Answer:
$87200
Step-by-step explanation:
Here is the complete question:
At the beginning of the period, the Cutting Department budgeted direct labor of $46,300 and supervisor salaries of $37,200 for 4,630 hours of production. The department actually completed 5,000 hours of production.
Determine the budget of the department assuming that it uses flexible budgeting?
Given: Budget for direct labour= $46300
Supervisor salaries= $37200
Expected production hours= 4630 hours
Completed production hours= 5000 hours
Now, we know that company budget include both fixed and variable cost.
∴ Direct labour cost is a variable cost and Supervisor salaries are fixed cost.
Using flexible budgeting for determining the budget of department, we will pro rate the direct labour cost on the basis of production hours.
Direct labour= [tex]Budget\times \frac{completed\ production\ hours}{expected\ production\ hours}[/tex]
Direct labour= [tex]46300\times \frac{5000}{4630}[/tex]
∴ Direct labour= $50000
we know the department budget = Fixed cost+variable cost
∴ Department budget= [tex]\$ 37200+\$ 50000 = \$ 87200[/tex]
∴ The department budget is $87200.
which equation is equivalent to log^x36=2?
The equation which is equivalent to [tex]\log _{x} 36=2[/tex] is [tex]x^{2}=36[/tex] or x = 6 ([tex]\log _{6} 36=2[/tex]).
Step-by-step explanation:
Given Equation:
[tex]\log _{x} 36=2[/tex]
As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:
[tex]b^{y}=a[/tex]
Then, the base b logarithm of x is equal to y
[tex]\log _{b}(x)=y[/tex]
Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,
[tex]b^{y}=a[/tex]
[tex]x^{2}=36[/tex]
When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as [tex]\log _{6} 36=2[/tex]
Answer:D
Step-by-step explanation:
i got it right
I NEED HELP ASAP!!!
The figure below is a square pyramid where the height of the pyramid is 2 centimeters and the volume is 24 cubic
centimeters. If the volume of a pyramid Bh, then what is the length of the base?
h = 2 cm
V = 24 cm
2 centimeters
4 centimeters
8 centimeters
6 centimeters
We are Given:
Height of the Pyramid(h) = 2 cm
Volume of the Pyramid = 24 cm³
Base of the Pyramid:
We know that the Volume of a square-based Pyramid:
Volume = a²*(h/3)
24 = a² * (2/3) [Replacing the variables]
24 * 3/2 = a² [Multiplying both sides by 3/2]
a² = 36
a = 6 [taking the square root of both sides]
Hence, the length of base of the Pyramid is 6 cm
Final answer:
The length of the base of the square pyramid is 6 centimeters, which is found by solving the equation V = (1/3) * B * h for the area of the base B and then finding the square root of B to get the length of the side.
Explanation:
To determine the length of the base of the square pyramid, we can use the formula for the volume of a pyramid, which is V = (1/3) * B * h, where V is the volume, B is the area of the base, and h is the height of the pyramid. For a square pyramid, the base is a square, so the area of the base B can be expressed as s2, where s is the length of the side of the square.
We are given that the volume V of the pyramid is 24 cm³ and the height h is 2 cm. Using the formula, we can solve for s:
V = (1/3) * s2 * h
24 cm³ = (1/3) * s^2 * 2 cm
24 cm³ = (2/3) * s^2
s^2 = (24 * 3) / 2
s^2 = 36
s =[tex]\sqrt{36}[/tex]
s = 6 cm
Therefore, the length of the base of the square pyramid is 6 centimeters.
Question 4
What is the distance between the points (-6, 7) and
(-1, 1)? Round to the nearest whole unit.
about 13 units
about 7 units
about 61 units
about 8 units
Answer:
[tex]\displaystyle about\:8\:units[/tex]
Step-by-step explanation:
Use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[6 - 1]^2 + [-7 + 1]^2} = \sqrt{5^2 + [-6]^2} = \sqrt{25 + 36} = \sqrt{61} ≈ 7,810249676 ≈ 8[/tex]
Since we are talking about distance, we ONLY want the NON-NEGATIVE root.
I am joyous to assist you anytime.
can anybody please help me??
Answer:
(x, y) = (6, 1) is the solution
Step-by-step explanation:
Each of the equations is written in "slope-intercept" form:
y = mx + b . . . . . . . . where m is the slope and b is the y-intercept
First equation
The y-intercept is +7 and the slope is -1. That means the line goes down 1 unit for each unit it goes to the right. It will go through the points (0, 7) and (7, 0).
Second equation
The y-intercept is -2 and the slope is 1/2. That means the line goes up 1 unit for each 2 units it goes to the right. It will go through the points (0, -2) and (4, 0).
The lines will intersect at the point (6, 1), which is the solution found by graphing.
Alinehasaslopeof1andpassesthroughthepoint
(9, 0) . What
isitsequationin
slope -intercept
form?
Answer: y = x - 9
Step-by-step explanation:
The equation of line slope - point form is given as :
y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex]
From the question
m = 1
[tex]x_{1}[/tex] = 9
[tex]y_{1}[/tex] = 0
Substituting into the formula , we have
y - 0 = 1 (x - 9)
y = x - 9
Therefore , the equation of the line in slope - intercept form is given as
y = x - 9
The equation of the line in slope-intercept form is y = x - 9.
Explanation:The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. Given that the slope of the line is 1 and it passes through the point (9, 0), we can substitute the values into the equation.
Let's substitute the slope m = 1 and the x-coordinate of the point x = 9:
y = 1(9) + b
Since the point (9, 0) lies on the line, we can substitute the y-coordinate y = 0:
0 = 9 + b
Solving for b, we subtract 9 from both sides:
b = -9
Therefore, the equation of the line in slope-intercept form is y = x - 9.
What is the area of a sector with a central angle of 108 degrees and a diameter of 21.2 cm?
Use 3.14 for it and round your final answer to the nearest hundredth.
Answer:
[tex]105.84\ cm^2[/tex]
Step-by-step explanation:
step 1
Find the area of the circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=21.2/2=10.6\ cm[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (10.6)^{2}[/tex]
[tex]A=112.36\pi\ cm^2[/tex]
step 2
Find the area of a sector
Remember that
The area of the circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of a sector with a central angle of 108 degrees
[tex]\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2[/tex]
assume
[tex]\pi=3.14[/tex]
substitute
[tex]33.708(3.14)=105.84\ cm^2[/tex]
At the beginning of the year,
Shelby could run 2 miles. Now
she can run 3.5 miles. What is
the percent increase in the
distance she can run?
Answer:
75%
Step-by-step explanation:
2 x 1.75 = 3.5
The required percentage increase in the distance she can run is 75%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Shelby could run 2 miles.
she can run 3.5 miles.
percentage increase = 3.5 - 2 / 2 × 100%
percentage increase = 75%
Thus, the required percentage increase in the distance she can run is 75%.
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Pls solve the simultaneous equation in the attachment.
Answer:
Part a) The solution is the ordered pair (6,10)
Part b) The solutions are the ordered pairs (7,3) and (15,1.4)
Step-by-step explanation:
Part a) we have
[tex]\frac{x}{2}-\frac{y}{5}=1[/tex] ----> equation A
[tex]y-\frac{x}{3}=8[/tex] ----> equation B
Multiply equation A by 10 both sides to remove the fractions
[tex]5x-2y=10[/tex] ----> equation C
isolate the variable y in equation B
[tex]y=\frac{x}{3}+8[/tex] ----> equation D
we have the system of equations
[tex]5x-2y=10[/tex] ----> equation C
[tex]y=\frac{x}{3}+8[/tex] ----> equation D
Solve the system by substitution
substitute equation D in equation C
[tex]5x-2(\frac{x}{3}+8)=10[/tex]
solve for x
[tex]5x-\frac{2x}{3}-16=10[/tex]
Multiply by 3 both sides
[tex]15x-2x-48=30[/tex]
[tex]15x-2x=48+30[/tex]
Combine like terms
[tex]13x=78[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=\frac{x}{3}+8[/tex]
[tex]y=\frac{6}{3}+8[/tex]
[tex]y=10[/tex]
The solution is the ordered pair (6,10)
Part b) we have
[tex]xy=21[/tex] ---> equation A
[tex]x+5y=22[/tex] ----> equation B
isolate the variable x in the equation B
[tex]x=22-5y[/tex] ----> equation C
substitute equation C in equation A
[tex](22-5y)y=21[/tex]
solve for y
[tex]22y-5y^2=21[/tex]
[tex]5y^2-22y+21=0[/tex]
Solve the quadratic equation by graphing
The solutions are y=1.4, y=3
see the attached figure
Find the values of x
For y=1.4
[tex]x=22-5(1.4)=15[/tex]
For y=3
[tex]x=22-5(3)=7[/tex]
therefore
The solutions are the ordered pairs (7,3) and (15,1.4)
PLEASE HELP!! Will mark brainliest!!
Answer: 12 small candles and 16 large candles.
Step-by-step explanation:
Notice that an small candle costs $4 and a large candle costs $6.
Let be "s" the number of small candles you sold and "l" the number of large candles you sold.
Set up a System of equations:
[tex]\left \{ {{4s+6l=144} \atop {s+l=28}} \right.[/tex]
Use the Elimination Method to solve it:
- Multiply the second equation by -4.
- Add the equations.
- Solve for "l".
Then:
[tex]\left \{ {{4s+6l=144} \atop {-4s-4l=-112}} \right.\\.......................\\2l=32\\\\l=16[/tex]
- Substitute the value of "l" into the second equation and solve for "s":
[tex]s+16=28\\\\s=12[/tex]
which is the graph of the cube root function f(x)=3 square root x
The student is probably asking about the cube root function multiplied by 3, which is an increasing function and is defined for all real numbers, including negative values.
Explanation:The phrase 'f(x)=3 square root x' seems to be a typo. Assuming this refers to the cube root function, such as 'f(x) = 3 √x,' then this function represents the cube root of 'x' multiplied by 3. To graph this function, start by plotting points, taking the cube root of various values of 'x' and scaling these by 3.
The graph will pass through the origin and rise less steeply than a linear function; it will be an increasing function for all 'x' as the cube root of a real number is always real. This also means that the function will be defined for all real numbers, including negatives, as cubing can produce both positive and negative results.
problem solving involving rational equation
1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
2.The sum of a number and 6 times its reciprocal is -5. Find the number.
3. The reciprocal of the product of two consecutive intergers is 1/72.
4. The reciprocal of the product of two consecutive integers is 1/42
Answer:
Step-by-step explanation:
1) 1/5 + 1/7 = 1*7/5*7 + 1*5/7*5
=7/35 + 5/35 = 7+5/35 = 12/35
2) Let the number be x
x +6*1/x = -5
x + 6/x = -5
(x² + 6 ) / x = -5
x² + 6 = -5x
x² +5x + 6 = 0
x² + 3x +2x + 2*3 = 0
x(x+3) + 2(x+3)= 0
(x+3)(x+2) = 0
x + 3 = 0 or x +2 = 0
x = -3 or x = -2
the number is (-3) or (-2)
GEOMETRY! PLEASE HELP!!!
Answer:
Option C is correct.
Step-by-step explanation:
See the diagram attached.
Given that YZ bisects MO, hence, MZ = ZO ........ (1)
If we want to prove that point N is equidistant from points M and O, then we have to prove that Δ MNZ ≅ Δ ONZ, so that we can prove that MN = ON.
Now, to prove Δ MNZ ≅ Δ ONZ, we must have another condition that MO ⊥ YZ or, NZ ⊥ MO.
So, we have (i) MZ = OZ {from equation (1)}
(ii) ∠ NZM = ∠ NZO = 90° {Since, NZ ⊥ MO} and
(iii) NZ is the common side
Hence, by SAS criteria it is proved that Δ MNZ ≅ Δ ONZ and hence, proved that MN = ON.
Therefore, option C is correct. (Answer)
the original price for a motorcycle was $11,000. The sale price this week is $9799. What is the percent decrease to the nearest percent?
Answer:
11%
Step-by-step explanation:
To fine the percentage decrease, we use the formula change/original x 100. In this case, the change is $11000-$9799=$1201 while the original is $11000. So 1201/11000 x 100 = 10.9% ≈ 11%
25 POINTS!
Which answer is an equation in point-slope form for the given point and slope?
point: (−3,5) ; slope: 4
y−5=4(x−3)
y+5=4(x+3)
y+5=4(x−3)
y−5=4(x+3)
Answer:
y-5=4(x+3)
Step-by-step explanation:
y-y1=m(x-x1)
y-5=4(x-(-3))
y-5=4(x+3)
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g - f)(3)?
Final answer:
To find (g - f)(3) with given functions f(x) and g(x), subtract f(x) from g(x) to get the new function, then evaluate this function at x = 3. The result is 23.
Explanation:
The student is asking to find the result of the operation (g - f)(3) where f(x) = 4 - x2 and g(x) = 6x. (g - f)(x) means we subtract the function f from the function g, and then evaluate the resulting function at x = 3.
To solve this:
First, find the function g(x) - f(x):g(x) is 6x, and f(x) is 4 - x2, so g(x) - f(x) is 6x - (4 - x2) = 6x - 4 + x2.Next, evaluate this new function at x = 3: (6*3) - 4 + (32) = 18 - 4 + 9 = 23.So (g - f)(3) is 23.
Solve the following triangle. Given A=51 degrees b=40 c=45
Answer:
[tex]a=36.87\ units[/tex]
[tex]B=57.47^o[/tex]
[tex]C=71.53^o[/tex]
Step-by-step explanation:
step 1
Find the length side a
Applying the law of cosines
[tex]a^2=b^2+c^2-2(b)(c)cos(A)[/tex]
substitute the given values
[tex]a^2=40^2+45^2-2(40)(45)cos(51^o)[/tex]
[tex]a^2=1,359.4466[/tex]
[tex]a=36.87\ units[/tex]
step 2
Find the measure of angle B
Applying the law of sines
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex]
substitute the given values
[tex]\frac{36.87}{sin(51^o)} =\frac{40}{sin(B)}[/tex]
[tex]sin(B)=\frac{sin(51^o)}{36.87}{40}[/tex]
[tex]B=sin^{-1}(\frac{sin(51^o)}{36.87}{40})=57.47^o[/tex]
step 3
Find the measure of angle C
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]A+B+C=180^o[/tex]
substitute the given values
[tex]51^o+57.47^o+C=180^o[/tex]
[tex]108.47^o+C=180^o[/tex]
[tex]C=180^o-108.47^o=71.53^o[/tex]
There are 2.54 centimeters in every inch. If a bug moves at a rate of 3.5 inches per second, then Which of the following is closest to its speed in meters per second?
The bug's speed is approximately 5.33 meters per minute, which is closest to option (2).
To find the bug's speed in meters per minute, we need to convert its speed from inches per second to meters per minute.
First, let's convert the bug's speed from inches per second to inches per minute:
[tex]\[3.5 \text{ inches per second} \times 60 \text{ seconds per minute} = 210 \text{ inches per minute}\][/tex]
Now, let's convert inches to meters:
[tex]\[210 \text{ inches} \times \frac{2.54 \text{ centimeters}}{1 \text{ inch}} \times \frac{1 \text{ meter}}{100 \text{ centimeters}} = 5.33 \text{ meters per minute}\][/tex]
So, the bug's speed is closest to option (2) 5.33.
Complete Question:
There are 2.54 centimeters in every inch. If a bug moves at a rate of 3.5 inches per second, then which of the following is closest to its speed in meters per minute?
(1) 3.86
(3) 6.25
(2) 5.33
(4) 7.19
A scale model of a house is 1 foot long the actual house is 36 feet long in the model the door is 2 inches high how many feet high is the actual door
Final answer:
To find the actual height of the door based on a scale model, the scale factor between the model and the actual house (1:36) is used, leading to the conclusion that the real door is 6 feet high.
Explanation:
The question involves scale and measurement to find the actual height of the door of a real house based on its scale model. The scale model of the house is 1 foot long, and the actual house is 36 feet long. The door in the model is 2 inches high. To find the actual height of the door, we use the scale factor between the model and the real house.
First, we identify the scale factor: Since the model house is 1 foot long and the actual house is 36 feet long, the scale factor is 1:36. Next, we convert the height of the door from inches to feet in the model scale (since 1 foot = 12 inches, 2 inches = 1/6 feet). Using the scale factor, the height of the actual door is calculated as follows:
Height in the model (in feet) x Scale factor = Height of the actual door
1/6 feet x 36 = 6 feet
Therefore, the actual height of the door is 6 feet.
The height of the actual door is 6 feet, calculated using the scale factor of 1:36 from the 2-inch model door height.
Explanation:To find the height of the actual door from the scale model measurements, we first need to determine the scale factor between the model and the real house. The scale model is 1 foot long, and the actual house is 36 feet long, which means that the scale factor is 1:36. This implies that every inch on the model would represent 36 inches (or 3 feet) on the actual house. Since the door on the model is 2 inches high, we can calculate the height of the actual door by multiplying the model door height (2 inches) by the scale factor.
So, height of actual door = 2 inches * 36 inches/inch = 72 inches.
To convert 72 inches to feet, we divide by 12, since there are 12 inches in a foot.
Therefore, height of actual door in feet = 72 inches / 12 inches/foot = 6 feet.
The actual door is 6 feet high.
how do you know a mixed number in a decimal
Ahsley had a summer lemonade stand where she sold small cups of lemonade for $1.25 And large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, How many cups of each type did she sell.
Ashley sold 98 small cups and 57 large cups of lemonade.
Step-by-step explanation:
Given,
Price of small cup of lemonade = $1.25
Price of large cup of lemonade = $2.50
Total cups sold = 155
Total worth of cups = $265
Let,
x represent the number of small cups sold
y represent the number of large cups sold
According to given statement;
x+y=155 Eqn 1
1.25x+2.50y=265 Eqn 2
Multiplying Eqn 1 by 1.25
[tex]1.25(x+y=155)\\1.25x+1.25y=193.75\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](1.25x+2.50y)-(1.25x+1.25y)=265-193.75\\1.25x+2.50y-1.25x-1.25y=71.25\\1.25y=71.25[/tex]
Dividing both sides by 1.25
[tex]\frac{1.25y}{1.25}=\frac{71.25}{1.25}\\y=57[/tex]
Putting y=57 in Eqn 1
[tex]x+57=155\\x=155-57\\x=98[/tex]
Ashley sold 98 small cups and 57 large cups of lemonade.
Keywords: linear equation, elimination method
Learn more about elimination method at:
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The histogram represents a data distribution with uniform class widths 1.
Which of the following is the mean of the data distribution?
2
3
4
5
6
7
8
9
10
A. 4.1
B. 4.5
C. 4.7
D. 4.9
Answer:
b
Step-by-step explanation: