A ratio shows us the number of times a number contains another number. Caitlin is right.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the ages of Mandy and Sandy is 2:5. Therefore, the ratio will be,
M/S = 2/5
M = 2S/5
After 8 years, their ages will be in the ratio 1:2, therefore,
(M+8)/(S+8) = 1/2
2M + 16 = S + 8
2M - S = -16 + 8
Substitute the value of M,
2(2S/5) - S = -8
-0.2S = -8
S = 40
Now, if we substitute the value of S in the first ratio,
M/S = 2/5
M/40 = 2/5
M = 16
Now, if we take the difference in their ages the difference will be 24(40-16).
Since the difference is 24, we can conclude that Caitlin is right.
Hence, Caitlin is right.
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How many solutions exist for each system of equations?
x + 2y = –1
2x + 3y = 0
Answer:
2 solutions x = 3 y = -2.
Step-by-step explanation:
x + 2y = –1
2x + 3y = 0
Multiply first equation by -2:
-2x - 4y = 2 Adding this to second equation:
- y = 2
y = -2.
Plug this into first equation:
x - 4 = -1
x = 3.
Can someone help me with this graph please
There are 5 dessert courses in a restaurant. They will be presented two at a time in an order. How many different arrangements are there?
Answer:
3 I think.
Step-by-step explanation:
5 would be broken up to 2 groups of 2 and 1 group of 1.
In 20 different ways 5 dessert courses can be arranged taken 2 at a time.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, There are 5 dessert courses in a restaurant and they will be presented two at a time in an order.
Here we have to use permutation as order matters.
Now, the permutation of 5 different things taken 2 at a time is,
= [tex]^5P_2[/tex].
= 5!/(5 - 2)!.
= 5!/3!.
= 5 × 4.
= 20 different ways.
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How many real solutions exist for this system of equations? y = x^2 + 4 y = 4x
Answer:
This system of equations has one real solution, (2, 8).
Step-by-step explanation:
Given:
y = x² + 4
y = 4x
1. Substitute the given value of y into y = x² + 4:
⇒ 4x = x² + 4
2. Solve for x (by factoring):
⇒ 4x = x² + 4
⇒ 0 = x² - 4x + 4
⇒ 0 = (x - 2)² [perfect square rule: a² -2ab + b² = (a - b)²]
⇒ 0 = (x - 2)² [take the square root of both sides]
⇒ [tex]\sqrt{0} = \sqrt{(x - 2)^2}[/tex]
⇒ 0 = x - 2 [add 2 to both sides]
⇒ 0 + 2 = x - 2 + 2
⇒ 2 = x
3. Find the value of y by substituting the given value of x into y = 4x:
⇒ y = 4(2)
⇒ y = 8
4. Check your work:
⇒ y = x² + 4 and ⇒ y = 4x
⇒ 8 = 2² + 4 and ⇒ 8 = 4(2)
⇒ 8 = 4 + 4 and ⇒ 8 = 8 ✔
⇒ 8 = 8 ✔
Solution: (x, y) ⇒ (2, 8)
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A(n) _________ is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.
A correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.
What is correlation?A correlation can be defined as the relationship that exists between two variables when one of them is related to the other in some way.
It is also a measure that expresses the extent to which two variables are closely or linearly related which entails that they change together at a constant time.
Hence, correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.
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Donna is making a cookie recipe that calls for 1 ¾ cups of sugar. However, when she goes to take out the measuring cups she can only find the one-half cup measuring cup. How many one-half cups will she need to fill to get the correct amount of sugar for her cookie recipe?
Group of answer choices
3 1/2
7
2 1/4
3
Answer:
D. 3
Step-by-step explanation:
You are building a brick patio. the length of the patio is (x+11) feet.
the total area of the patio can be represented by x^2+14x+33. write an expression for the width of the patio
The expression that represents the width of the patio is (x+3) feet
Calculating areaFrom the question, we are to determine the width of the patio
The area of the patio = Length of the patio × Width of the patio
From the given information,
Length of the patio = (x+11) feet
Area of the patio = x^2+14x+33 = x²+14x+33
Putting the parameters into the formula,
x²+14x+33 = (x+11) × Width of the patio
∴ Width of the patio = (x²+14x+33) / (x+11)
First, we will factor x²+14x+33
x²+14x+33
x²+11x+3x+33
x(x+11) +3(x+11)
(x+3)(x+11)
Thus,
Width of the patio = [(x+3)(x+11)] / (x+11)
∴ Width of the patio = (x+3) feet
Hence, the expression that represents the width of the patio is (x+3) feet
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A "golden rectangle” is a rectangle where the ratio of the longer side to the shorter side is the "golden ratio.” These rectangles are said to be visually pleasing. An example of a "golden rectangle” has a length equal to x units and a width equal to x – 1 units. Its area is 1 square unit. What is the length of this golden rectangle?
The length of the given golden rectangle is; 1.618 units
How to find the length of a golden triangle?We are told that, for the golden rectangle;
Length = x units,
Width = (x - 1) units,
Area = 1 unit².
The area of this rectangle will have the formula;
A = x(x - 1)
Thus;
x(x - 1) = 1
Expanding gives;
x² - x - 1 = 0
Using online quadratic equation calculator, we have;
x = 1.618 or -0.618.
Length has to be positive and so we choose x = 1.618
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Pls show full work thank you so much:)))
Answer x= 30
M angle A = 85
M angle C = 45
Reason - see picture for the math
Calculate the perimeter of this shape.
Help!! Which of the following is equivalent to 3 6
— = —— ?
X X-4
Answer:
3rd Option - 3(x-4) = 6x
Step-by-step explanation:
To remove the fractions we escalate them up to the other side. So to remove the x under 3 we do the following :
[tex]\frac{3}{x} = \frac{6}{x-4}[/tex] -----> [tex]{3}= \frac{6x}{x-4}[/tex] (As you can see the x now goes to the numerator of the right side)
Now to remove x-4 under 6x we do the following :
[tex]{3}= \frac{6x}{x-4}[/tex] ------> [tex]3(x-4)= {6x[/tex]
Therefore giving our answer as the 3rd option.
Hope this helped and have a good day
Grandma baked 969696 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received ccc fewer cookies than she would have received had all of the cookies been evenly divided among the 888 grandchildren.
How many cookies did Cindy receive?
Cindy gets (12-c) amount while others get 12 cookies.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
From the question, we are informed that Grandma baked 96 cookies
And there are 8 grandchildren available
To calculate the number of cookies each of them gets we have,
= 96 /8
= 12 cookies
This means each gets 12 cookies
But Cindy received fewer cookies with less C amount.
Therefore Cindy gets (12-c) amount while others get 12 cookies.
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Given a line with slope = −6and passing through (−5,−9) , which of the following is the correct point-slope equation of the line? y−9=−6(x−5
The equation of the line with Slope = −6 and passing through (-5,−9) is y +9 = -6(x+5)
Equation of a lineThe equation of a line in pint slope form is expressed as:
y - y1 = m(x-x1)
where
m is the slope = -6
(x1, y1) is the point = (-5, -9 )
Substitute into the formula
y - (-9) = -6(x -(-5))
y +9 = -6(x+5)
Hence the equation of the line with Slope = −6 and passing through (-5,−9) is y +9 = -6(x+5)
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what is the domain of the function shown in the table. X {3, 5, 7, 9} Y {-4, -3, 3, 4}
Answer:3,5,7,9
Step-by-step explanation:I’m pretty sure all the inputs are the domains
???? please help lol
Answer:
150π ft²10π ft.Step-by-step explanation:
Area of the sector :
[tex]Area (sector) = \pi r^{2} \times \frac{\theta}{360^{o}}[/tex]
Finding the area given r = 30 ft. and θ = 60° :
⇒ Area = π × (30)² × 60/360
⇒ Area = π × 900/6
⇒ Area = 150π ft²
===========================================================
Length of the arc :
[tex]Length (arc) =2 \pi r} \times \frac{\theta}{360^{o}}[/tex]
Finding the arc length given r = 30 ft. and θ = 60° :
⇒ Arc Length = 2 × π × 30 × 60/360
⇒ Arc Length = 60/6 × π
⇒ Arc Length = 10π ft.
Answer:
1. 150π ft²
2. 10π ft²
Step-by-step explanation:
Hello there!
Here is how we solve the given problem:
Area of the sector of a circle refers to the fractional circle area. Which is given by; (∆°/360°) × πr². Where ∆° is the angle subtended by the arc.the arc length also refers to the length swept by the arc with angle theta (∆°) - subtended. Given byL = ∆°/360° ×2πr
From our problem,
∆ = 60°, r = 30ft
Lets substitute the values
1. A = (∆°/360°) × πr²
= 60°/360° × π × 30²
= 150π ft²
2. L = ∆°/360° × 2πr
= (60/360) × 2 × 30 × π
= 10π ft²
NOTE:
Use the formulas given below to be on a save side;
A = (∆°/360°) × πr² L = ∆°/360° × 2πr.I hope this helps.
Have a nice studies. :)
Translate the english phrase into an algebraic expression: the quotient of m and the sum of n and p.
enter all quotients as fractions.
The English phrase can be written as the fraction:
[tex]\frac{m}{n + p}[/tex]
How to write the algebraic expression?Remember that the quotient between two numbers gives a fraction.
Now, we have the sentence:
"the quotient of m and the sum of n and p."
Then we know that the numerator is m, and the denominator is (n + p) (the sum of n and p).
So the expression will just be the fraction:
[tex]\frac{m}{n + p}[/tex]
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Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1? 3, –6, 12, –24, 48, … f (n 1) = –3 f(n ) f (n 1) = 3 f(n ) f (n 1) = –2 f(n ) f (n 1) = 2 f(n)
The recursive formula will be equal to f(n + 1) = –2 f(n).
The complete question is given below:-
Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48, …
f (n + 1) = –3 f(n )
f (n + 1) = 3 f(n )
f (n + 1) = –2 f(n )
f (n + 1) = 2 f(n)
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The recursive formula for this sequence is calculated as we will put the different values of n to find the values of the function in the series.
n = 1
f(n) = 3
n = 2
f(2) = -2 (3) = -6
n = 3
f(3) = -2 (-6) = 12 and so on
Therefore the recursive formula will be equal to f(n + 1) = –2 f(n).
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use the number line to find each product
- (3)(-3) =
Answer:
it's 9
Step-by-step explanation:
type it in a calculater
he price of a used motorbike is 4975. Danny, a buys the motorbike for 3781. What is the discount percent given?
well, we know the discount is 4975 - 3781 = 1194.
if we take 4975 to be the 100%, what is 1194 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 4975 & 100\\ 1194& x \end{array} \implies \cfrac{4975}{1194}~~=~~\cfrac{100}{x}\implies \cfrac{26}{6}=\cfrac{100}{x} \\\\\\ 26x = 600\implies x=\cfrac{600}{26}\implies x\approx 23.08[/tex]
Answer:
0.76
Step-by-step explanation:
4975 × 0.76 = 3781
the discount percent given is .76%
is this correct ,please check
Choices B, C, and D are correct. Nice work.
Further explanation:
Choice A is ruled out because we aren't multiplying 5 by 6Choice B is correct because 4*5 is the same as 5*4. Similarly, 3(2+6) is the same as 3(6+2). We can add in any order, and multiply in any order. See the commutative property for more details.Choice C is correct for similar reasoning as choice BThe distributive property allows us to go from 3(2+6) to 3*2+3*6, showing that choice D is the same as B and C.You can confirm each answer by using a calculator. The result of simplifying the original expression is 44. You should find that expressions B, C and D also result in 44. Only choice A is the one that doesn't fit in since it results in 56.Here is a diagram of a black circle inside a white square and a diagram of a small grey square inside a white square.
The two white squares are the same size.
AB = 8x.
The sides of the square are tangents to the circle at the points E, F, G and H.
W, X, Y and Z are the midpoints of AB, BC, CD and DA respectively.
Work out the ratio of the area of the black circle to the area of the white square to the area of the grey square. Give your answer in its simplest form.
Hi, I don't understand this. Can someone please explain? It's 50 points.
The ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2
How to determine the ratio of the areas?The side length AB is given as:
AB = 8x
The area of the white square is calculated as
White = (AB)²
This gives
White = (8x)²
Evaluate
White = 64x²
The side length AB represents the diameter of the black circle.
So, the radius is:
r =AB/2
This gives
r = 8x/2 = 4x
The area is then calculated as:
Circle = πr²
This gives
Circle = π(4x)²
Evaluate
Circle = 16πx²
Next, calculate AW and AZ using:
AZ = AW = AB/2
Evaluate
AZ = AW = 8x/2 = 4x
Calculate WZ using the following Pythagoras theorem
WZ² = AW² + AZ²
This gives
WZ² = (4x)² + (4x)²
Evaluate
WZ² = 2(4x)²
Take the square root of both sides
WZ = 4x√2
The area of the gray square is:
Gray = WZ²
This gives
Gray = 2(4x)²
Evaluate
Gray = 32x²
At this point, the areas are:
White = 64x²Circle = 16πx²Gray = 32x²The ratio is then represented as:
Ratio = Circle : White : Gray
This gives
Ratio = 16πx² : 64x² : 32x²
Divide through by 16x²
Ratio = π : 4 : 2
Hence, the ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2
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The volume of a box is 143.4 in3. find the volume of a larger, similarly shaped box that has a scale factor of 3. round your answer to the nearest tenth.
3,871.8 in3
430 in3
1,290.6 in3
47.8 in3
Answer:
1,290.6 in3
nut.
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Create a comparative box plot for the morning and afternoon dogs, and label each with its five-number summary.
Sara's dogs:
Morning:
39, 21, 12, 27, 23, 19, 19, 31, 36, 25
Afternoon:
15, 51, 8, 16, 43, 34, 27, 11, 8, 39
Answer:
see attached
Step-by-step explanation:
Morning:
12, 19, 19, 21, 23, 25, 27, 31, 36, 39
Min value: 12
Lower quartile (Q1): 19
Median (Q2): 24
Upper Quartile (Q3): 31
Max value: 39
Afternoon:
8, 8, 11, 15, 16, 27, 34, 39, 43, 51
Min value: 8
Lower quartile (Q1): 11
Median (Q2): 21.5
Upper Quartile (Q3): 39
Max value: 51
Answer:
7. AM IQR: 12 PM: IQR: 28 8. see below in explanation
Step-by-step explanation:
7. 31-19=12
39-11= 28
You subtract Q1 from Q3 to get the IQR.
8. I believe the morning group of dogs would be easier to walk as one group because the group has a closer range of weights (12-39) compared to the afternoon group of (8-51). Walking a large group of dogs with similar weights would be easier than walking a group of very small and very large dogs at the same time because their pace of walking would be so different.
The area of the garden was 2 2/5yd2. if the lrngth is 1 1/2 yd, find the width
What is the perimeter of WXYZ?
There are two triangles, triange WXZ and triangle YXZ having a common side XZ. The vertex W and vertex Y are on opposite sides of the side XZ. The length of the side WX is 15 and the length of the side XZ is 11. Angle ZWX is congruent to angle WXZ and all the angles of the triangle YXZ are congruent.
Its 48
33+15
Step-by-step explanation:11+11+11+15= Perimeter
33+15 = Perimeter
48 = Perimeter
Write the equation of a line that goes through point (0, −8) and has a slope of 0.
Answer: y = -8
Step-by-step explanation:
Lines that have a slope of Zero means that the line is horizontal and y is always the same. So your equation is y = -8
Answer:
y = - 8
Step-by-step explanation:
A line with a slope of 0 is a horizontal line parallel to the x- axis with equation
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (0, - 8 ) with y- coordinate - 8 , then
y = - 8 ← equation of line
Find the height of the trapezoid.
Answer:
height = 7
Step-by-step explanation:
[tex]2\cdot\frac{42}{8.7 + 3.3} = 7[/tex]
Use the following scenario to answer the question below:
You are deciding between two cars with different engines and want the bigger of the two. One engine displaces 350 cubic inches. The other displaces 5,500 cubic centimeters. How many significant figures do the values in this problem involve?
A. 4
B. 1
C. 3
D. 2
The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.
We need the answer in cubic centimeters. So let's convert 350 cubic inches to cubic centimeters. We will do it unit conversion way (the long way).
We will write cubic inches as three inches side-by-side
350 in^3
What is the ratio of the centimeter?This way, we can multiply this by the ratio of centimeters to inches [2.54 cm = 1 inch], so that the units cancel and we have cubic centimeters (what we desire).
350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in
So, we can cancel the three inches top and bottom thus we have the answer in centimeters cubed. And the value is
350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in.
350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in=5735.47.
So 350 cubic inches is approximately 5735.5 cubic centimeters (rounded to 1 decimal place).
This is larger than a 5500 cubic centimeters engine.
5735.5-5500=235.5cubic centimeters.
The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.
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A triangular brace has an angle measure of 30 degrees, with a side opposite
this angle measuring 8 inches. The base of the triangular brace, which is
adjacent to the given angle measure, is 11 inches in length. Which of the
following statements is correct?
A. There is not a solution for the angle opposite the side measuring
11 inches.
B. The angle opposite the side measuring 11 inches has one solution
of approximately 43 degrees.
C. The angle opposite the side measuring 11 inches has one solution
of approximately 62 degrees.
D. The angle opposite the side measuring 11 inches, has two
solutions of approximately 43 degrees and 137 degrees.
The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,
8/ Sin(30°) = 11/ Sin(θ)
Sin(θ) = [11 × Sin(30°)]/8
Sin(θ) = 0.6875
θ = Sin⁻¹ (0.6875)
θ = 43.4325° ≈ 43°
Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
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Elijah made 14 quarts of punch for a party. How many gallons of punch did he make?
Answer:
3.5 gallons of punch
Step-by-step explanation:
There are 4 quarts in 1 gallon.
Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.
Elijah made 3.5 gallons of punch.