Making 10 chairs would take Marjorie and Blaine 21 hours and 40 minutes.
How long does it take to make 10 chairs?The total time it takes Marjorie and Blaine to perform their respective tasks in building a chair is multiplied by 10 chairs, respectively. This time is known as their speed.
The resulting figures are summed to get the total time.
Data and Calculations:The total time it takes Marjorie to build a chair is 15 hours (1.5 hours x 10)
The total time it takes Baline to sew cushions per chair is 400 minutes (40 x 10) or 6 hours and 40 minutes.
Therefore, the total time to build 10 chairs is 21 hours, 40 minutes (15 hours + 6 hours and 40 minutes).
Thus, making 10 chairs would take Marjorie and Blaine 21 hours and 40 minutes.
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In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of ? Use the distance formula to help you decide: . The graph shows a circle with three points, A is equal to (8, 15), B is equal to (12, 13), and C is equal to (8, 10). C is the center of the circle. A line is joining AC and BC A. 24 units B. 45 units C. 21 units D. 15 units E. 5 units Reset Next
The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.
What is Dilation?Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.
Applying the distance formula, we have:
BC = √[(8−12)² + (10−13)²]
BC = √(−4)² + (−3)²]
BC = √(16+9)
BC = √25
BC = 5 units
Applying the scale factor:
Length of C'B' = 3(5) = 15 units.
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The table gives the scores of 6 students from a class of 25 in a competitive exam. the point estimate of the mean score for the students is
The mean of the scores if 6 students in a competitive exam is 25 marks.
Given scores of 6 students are: 10,30,50,40,20 in a competitive exam.
We have to find out the mean of the mark of 6 students in a competitive exam.
Mean is the sum of all the values in a set of data, such as numbers, measurements, divided by the number of values. It is also known as average.
Mean=∑X/n
∑X=10+30+50+40+20
=150
N=6
Now to calculate the mean we have to divide 150 by number of students which is 6.
Mean=150/6
=25 marks.
Hence the mean of the scores of 6 students is 25 marks.
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Question is incomplete as it should include :
Marks of students =10,30,50,40,20.
A diagonal of a cube measures StartRoot 150 EndRoot cm. The diagonal of a face measures 10 cm.
What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
The side of the edge of the cube is 7. 07cm
How to determine the lengthGiven that a diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.
Let's find the edge of the face
Note that the face of the cube is in the shape of square .
The diagonal of the face is 10 cm.
The formula for diagonal of square = [tex]\sqrt{2a}[/tex]
a is the side of the square face
We have that,
[tex]\sqrt{2a} = 10[/tex]
Make 'a' subject of formula
a = [tex]\frac{10}{\sqrt{2} }[/tex]
Find the surd of the equation, we have
a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]
a = [tex]\frac{10\sqrt{2} }{2}[/tex]
a = [tex]5\sqrt{2}[/tex]
a = [tex]7. 07cm[/tex]
Thus, the side of the edge of the cube is 7. 07cm
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At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
A number line goes from 0 to 25. A line is drawn from 3 to 25. The point at 3 is labeled Start and the point at 25 is labeled End.
Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4.
4.4 meters
7.4 meters
17.6 meters
20.6 meters
The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters
How to calculate the distance?A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.
To find the distance, we will have to determine how much 1:4 represents in the total distance.
Total distance = 25 meters - 3 metes = 22 meters
Thus; 22 * 1/ 5 = 22/5 = 4.4
However, we also know they are three meters behind the start.
Thus, the meter mark at which Ario will be when Miguel starts the race
4.4 + 3 =7.4 meters
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Write and simplify an expression to represent the area. Then determine the area when x = 3
Answer:
5*8 = 40
Step-by-step explanation:
2(3) -1 = 5
3 +5 = 8
area = 5*8 = 40
Answer:
formula-Area=l×b
Step-by-step explanation:
Length (l)=2x-1
Breadth(b)=x+5
We know that,
Area(A)=l×b
=(2x-1)×(x+1)
=(2×3-1)×(3+1)
=5×4
=20cm*2*
look at the pic below and please help.
Answer:
1) Equation's:
y = 500 + 15x y = 350 + 18x2) Number of guest and the charge:
Cost is same for both at 50 meals. The cost is $1250.Part 1
Turn sentences into equation's (Let 'y' be total cost and x per meal) :
(i) charges $500 and $15 per meal
y = 500 + 15x(ii) charges $350 and $18 per meal
y = 350 + 18xPart 2
y = y
500 + 15x = 350 + 18x
18x - 15x = 500 - 350
3x = 150
x = 150/3
x = 50
Charge at guest's 50 meal:
y = 500 + 15(50)
y = $1250
Point : (50, 1250)
help me with the fonction please im stuck U_U
Answer:
It is NOT a function
Step-by-step explanation:
No it is NOT a function.....each value of x can only have one y value....
this has two y values for x = 2 : y = 2 and 4 therefore not a function
Consider the line y=3x-3.
Find the equation of the line that is perpendicular to this line and passes through the point (4, 5)
Find the equation of the line that is parallel to this line and passes through the point (4, 5).
Answer:
Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
Parallel: [tex]y=3x-7[/tex]
Step-by-step explanation:
So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]
P l e a s e h e l p~!!!!!!~!!~~~!
Answer:
A. 100
Step-by-step explanation:
Angle 1 = 40
Angles 1 and 2 are equal. Add the angles 1 and 2 together.
40+40=80
The last step is to subtract 80 from 180.
180-80=100.
∠3=100
Hope this helps!
If not, I am sorry.
Create a list of steps, in order, that will solve the following equation. (x-5)^2=25(x−5) 2 =25left parenthesis, x, minus, 5, right parenthesis, squared, equals, 25 Solution steps:
The value of x in the equation (x - 5)² = 25 is 10.
How to solve an equation?(x - 5)² = 25
Take the square root of both sides
Therefore,
√(x - 5)² = √25
x - 5 = 5
add 5 to both sides
x - 5 + 5 = 5 + 5
x = 10
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A ratio is...
O where two numbers are written as a fraction in lowest terms.
O where two or more values are compared in lowest terms.
O when two numbers are written as a division problem.
O all of these.
Answer:
All of these definitions are correct.
Write a polynomial function with the real
zeros -3, 0, and 3.
[tex]f(x)=x(x-3)(x+3)[/tex]
Kelly has 2 liters of milk in the refrigerator. she used 12 liters of milk in the morning with breakfast. she then used the same quantities of milk at both lunch and dinner, such that she used up all the milk. what quantity of milk did she use at dinner?
Kelly used a volume of [tex]\frac{3}{4}[/tex] liters of milk at dinner.
What is Volume?Each thing in 3-D takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.Given we have, Initial amount of milk is [tex]2[/tex] liters.
The amount of milk used in the morning is [tex]\frac{1}{2}[/tex] Liters.
Now, Milk left = [tex]2[/tex] liters- [tex]\frac{1}{2}[/tex] liter= [tex]\frac{3}{2}[/tex] liters
[tex]\frac{3}{2}[/tex] liters used in half:
[tex]\frac{1}{2} \frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] liters.
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To estimate the number of bass in a lake, a biologist catches and tags 32 bass. several weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged. how many bass are in the lake?
If the biologist catches and tags 32 bass and from sample of 55 he found only 5 tagged then there are 352 bas in the lake.
Given Biologist catches and tags 32 bass, when sample of 55 bass is taken then 5 are found tagged.
Population is basically number of living thing exists in a particular area.
Number of bass which are tagged in lake=32
Sample size=55
Number of bass found tagged=5
means percentage of tagged bas found is 5/32*100=1.6%
We have to calculate number of times 5 is multiplied to get 32 which is 6.4.
Number of bass in the lake=55*6.4
=352 basses.
Hence there are 352 basses in the lake if 5 are found tagged in a sample of 55.
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Write a polynomial function of least degree with integral coefficients that has the given zeros. -1/3, 2/3, -1/4
Step-by-step explanation:
"integral" means here that the factors in the polynomial are integers.
we have 3 zeros.
the least degree of a polynomial with 3 zeros is 3.
and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).
or 4 zeros (at least 4th degree).
it in general n zeros (at least nth degree).
constructing this out of the given zeros is easy.
what happens, when I multiply something by 0 ? the total result will be 0.
and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.
what expression in x turns 0, when x = -1/3 ?
well : x + 1/3 or with integers 3x + 1 (multiplied by 3)
and for x = 2/3 ?
x - 2/3 or with integers 3x - 2
and for x = -1/4 ?
x + 1/4 or with integers 4x + 1
so, our polynomial function (of at least 3rd degree) is then
(3x + 1)(3x - 2)(4x + 1)
basically this could be already the result, depending on what your teacher wants.
for the fully extended form we need to do the multiplications :
(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2
(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =
= 36x³ - 3x² - 11x - 2
the requested polynomial function is
f(x) = 36x³ - 3x² - 11x - 2
According to the rational root theorem, the numbers below are some of the potential roots of f(x) = 10x3 29x2 – 66x 27. select all that are actual roots.
The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.
Given function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].
Function is a relationship between two or more variables expressed in equal to form.
The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.
The polynomial function is given as:
[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]
factorize the above function
[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]
Now put the function f(x) equal to zero.
f(x)=(2x+9)(5x-3)(x-1)
split the function means put all the expressions equal to zero as under:
(2x+9)(5x-3)(x-1)=0
solve each for the value of x
x=-9/2,x=3/5,x=1
Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.
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Answer:
Step-by-step explanation:
helppp!!!
Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
Considering the area of the rectangle, it is found that she will need 17 tiles to cover the floor.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:
A = lw
The dimensions in feet are given as follows:
l = 4 1/2 ft = 4.5 ft.w = 3 3/4 ft = 3.75 ft.Hence the area in square feet is given by:
A = 4.5 x 3.75 = 16.875 ft².
Each tile has 1 square foot, hence, rounding, she will need 17 tiles to cover the floor.
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The price of an emergency light is $375 and it decreased by
2% each year. Find the exponential model representing
this situation.
The price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
Which exponential model represents this situation?
We know that the original price of the light is $375.
This value decreases a 2% each year, so each year we need to multiply the above price by (1 - 2%/100%) = (1 - 0.02) = 0.98
Then, if x represents the number of years, the price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
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find the value of x
A. √30
B. 16
C. 2√2
D. 20
Answer:
A. √30
=================
Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,
or
TW × WU = CW × WVSubstitute the lengths and solve for x:
x*2x = 6*102x² = 60x² = 30x = √30The matching answer choice is A.
Which type of parent function is f(x) = 1/x
Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.
What are rational functions?Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.
The most simple example is given by:
[tex]f(x) = \frac{1}{x}[/tex].
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Answer: Reciprocal
Step-by-step explanation:
Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.
4. A juice bottling company makes a variety pack
with 24 orange juices, 12 apple juices, and 8
grape juices. Describe the ratio of the juices to
one another (orange: apple: grape).
(A) 2:1:1
(B) 3:1:2
(C) 4:2:2
(D) 6:3:2
The ratio of orange juice to apple juice to grape juice is 6: 3 : 2
What is ratio?A ratio says how much of one thing there is compared to another thing.
Therefore, we are comparing the numbers of juice produce by a bottling company.
Hence,
number of orange juice = 24
number of apple juice = 12
number of grape juice = 8
Therefore, the ratio of orange juice to apple juice to grape juice is as follows:
ratio = 24 : 12 : 8
divide through by 4
ratio = 6: 3 : 2
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A company produces candy bags that each hold about 528 cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about 361 candies. When a bag contains only gummy bear candies, then it has about 697 candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies, 7, in the bag and the approximate number of gummy bear candies, g, in the bag? A company produces candy bags that each hold about 528 cubic inches of candy . Each bag is filled with any mixture of lollipop candies and gummy bear candies . When a bag contains only lollipop candies , then it has about 361 candies . When a bag contains only gummy bear candies , then it has about 697 candies . Given any candy bag produced by this company , which of the following equations could relate the approximate number of lollipop candies , 7 , in the bag and the approximate number of gummy bear candies , g , in the bag ?
361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;
1.46•l + 0.76•g = 528How can the correct equation be found?Volume of candy bag = 528 in.³
Number of lollipop candies the bag can hold = 361 candies
Number of gummy bear candies the bag can hold = 697 candies
Therefore;
[tex]1 \: lollipop = \frac{528}{361} = 1.46[/tex]
[tex]1 \: gummy \: bear = \frac{528}{697} = 0.76[/tex]
Which gives the following equation;
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Answer:
l/361 + g/697= 1
Khan Academy Sat Practice
3y > 2x + 12
2x + y ≤ -5
The solution for the inequalities 3y>2x+12, 2x+y<=-5 is the value of x<-27/8 and y<7/4.
Given 3y>2x+12 and 2x+y<=-5.
We are given two inequalities 3y>2x+12 and 2x+y<=-5. Inequality are like equations but in greater than ,less than or in combination with equal to. To solve them we need to first write them properly.
2x-3y<-12
2x+y<=-5
Now assume these are equalities
2x-3y=-12
2x+y=-5
now subtract 2 from 1
2x-3y-2x-y=-12+5
-4y=-7
y=7/4
put the value of y in 2x-3y=-12
2x-3(7/4)=-12
2x-21/4=-12
2x=-12+21/4
2x=(-48+21)/4
2x=-27/4
x=-27/8
Now put the signs between the values
x<-27/8
y<7/4.
Hence the solution of the inequalities 3y > 2x + 12
2x + y ≤ -5 is the value of x<-27/8 and y<7/4.
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Find a cubic polynomial whose zeros are 1/2,1 and -3.
Answer:
2x³+3x²-8x+3
Step-by-step explanation:
So we know x=½,x=1 and x=-3
Then (2x-1)(x-1)(x+3) are the factors
(2x-1)[(x²+3x-x-3)]
(2x-1)[(x²+2x-3)]
2x³+4x²-6x-x²-2x+3
2x³+3x²-8x+3
Given that f(x)=x2−4 and g(x)=x+3 , what are all the values of x for which f(g(x))=0 ?
Answer:
the answer is (x )
math way helps
Step-by-step explanation:
The requried function of function f(g(x)) is given as x² + 6x +5.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given functions,
f(x)=x²−4 and g(x)=x+3
In order to form a function of function we have to function g(x) in function f(x)
Now,
f(g(x)) = f(x)=(g(x))²−4
f(g(x)) = f(x)=(x+3)²−4
f(g(x)) = x² + 6x + 9 -4
f(g(x)) = x² + 6x +5
Thus, the requried function of function f(g(x)) is given as x² + 6x +5.
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In the figure, POG is a diameter of the circle with centre O.
Find x° + y°.
The value of x° + y° is 216°
How to determine the angles
Note that the shape is a regular pentagon
Sum of angle in a pentagon = 540
Angle on each side = 108°
x = 108°
y = 108°
x° + y° = 108 + 108
x° + y° = 216°
Thus, the value of x° + y° is 216°
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D
Distance
ST
Speed
Time
A bus is moving at an average speed of 70 mph on the
motorway.
The journey takes 3 hours 30 minutes.
How far did the bus travel?
miles
The distance would be 231 miles.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
Given information;
Time taken = 3 hours 30 minutes
Speed = 70 mph
We know that,
Distance = speed x time
Distance = 70 x 3.30
Distance = 231 miles
Thus, the distance would be 231 miles.
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Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.
The given geometric series as shown in the question is seen to; Be converging with its' sum as 81
How to identify a converging or diverging series?We are given the geometric series;
27 + 18 + 12 + 8 + ...
Now, we see that;
First term; a₀ = 27
Second Term; a₁ = 2(27/3)
Third term; a₂ = 2²(27/3²)
Fourth term; a₃ = 2³(27/3³)
Thus, the formula is;
2ⁿ(27/3ⁿ)
Applying limits at infinity gives;
2^(∞) * (27/3^(∞)) = 0
Since the terms of the series tend to zero, we can affirm that the series converges.
The sum of an infinite converging series is:
S_n = a/(1 - r)
S_n = 27/(1 - (2/3)
S_n = 81
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f(x) = 4^ x / 8
can you Graph this ?
Answer:
Graph is below
Brainliest, please :)
Find the distance between the two points in simplest radical form.
(−5,−4) and (−2,−6)
Answer: [tex]\sqrt{13}[/tex] units
Work Shown:
[tex](x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (-4-(-6))^2}\\\\d = \sqrt{(-5+2)^2 + (-4+6)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6056\\\\[/tex]
I used the distance formula.
A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).