Answer: 7 years
Step-by-step explanation:
Let the number of years be x. Therefore, their ages in x years will be:
Daughter = x
Mother = 27+x
Father = 30+x
Their mean age will then be:
[x + (27+x) + (30+x)]/3 = 26
(3x + 57) / 3 = 26
Cross multiply
3x + 57 = 26 × 3
3x + 57 = 78
3x = 78 - 57
3x = 21
x = 21/3
x = 7
Therefore, the answer will be 7 years
Check: Daughter = x = 7 years
Mother = 27+x= 27+7 = 34 years
Father = 30+x = 30 + 7 = 37 years
Mean= (7+34+37) / 3 = 78/3 = 26 years
There are 6 students at a club meeting. If they make up 40% of the club, how many total students are in the club?
please answer with mostly numbers and please explain well.
Using basic concept of proportion value and percentage from the total, The answer is there are 15 students in the club.
What do you mean by percentage?A percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, 50% means 50/100 or 0.50. It is commonly used to express rates and proportions. Percentages can be used to express a variety of information, such as discounts, increases, and proportions. For example, if a product is on sale for 20% off, that means the price has been reduced by 20/100 or 0.20 times the original price. If a company's profits have increased by 10%, that means they have gone up by 10/100 or 0.10 times the original amount.
What do you mean by proportion?A proportion is a mathematical relationship between two values that indicates that they are in a specific ratio to each other. Proportions can be expressed in a variety of ways, but one common way is to use the symbol ":" to separate the two values. In statistics, it is common to use proportions to express the relationship between different groups or categories in a population. In physics, proportions can be used to calculate different quantities in systems.
total = x
40% of x =6
40/100 * x =6
x=6*100/40
=15
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What is the surface area
of the square pyramid?
9 in
6 in
Answer:The Surface Area of Pyramid is 105 cm².
Step-by-step explanation:
What is Surface Area of Pyramid?
If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by (½)Pl + B Square units.
Given:
slant height, l= 8 cm
So, the base Perimeter = 4 x 5
= 20 cm
Now, area of the base = 5 cm x 5 cm
= 25 cm²
Then, surface area of a square pyramid
= 1/2 x slant height x base perimeter + area of base
= 1/2 x 8 x 20 + 25
= 80 + 25
= 105 cm²
estimate the product of 5,398 x 47 by rounding to the nearest thousand and ten.
a) 200,000
b)250,000
c)253,706
d)300,000
pls help me
Answer:
b) 250,000
Step-by-step explanation:
You want to estimate the product of 5,398 and 47 by rounding to the nearest thousand and ten.
Rounded valuesRounding 5,398 to the nearest thousand gives 5000.
Rounding 47 to the nearest ten gives 50.
Estimated productThe product of these is the estimate you want:
5000·50 = 250,000
Solve the equation 2^x=1/32•x=
Answer:
2^x=1
x=0
32•x=0
32.0=0
maybe
solve the inequality and explain how
thank you :)
Answer:
the answer is A
[tex]x + 7 > 3[/tex]
need help with this NO BOTS OR LINKS
Answer:
946
Step-by-step explanation:
To find the area, you can split the figure into 2 rectangles. The one on the left has a width of 7 and a height of 28. Multiply 28 * 7 to get the area of the first rectangle, which is 196 in.
The second rectangle has a width of 25 and a length of 30. Multiply 30 by 25 to get the area, which is 750 in.
To find the area of the entire figure, add the areas of both rectangles.
196 + 750 = 946 square inches.
Find the value of x in the following equation:
3.5(5x + 4) = 17.5x + 14
No solution
Infinite solutions
x = 0
x = 1.3
The system of equations .5(5x + 4) = 17.5x + 14 have Infinite solutions.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
Given, A system of equation 3.5(5x + 4) = 17.5x + 14.
17.5x + 14 = 17.5x + 14.
As the LSH and RHS are equal the equation of the two lines is the same and hence they coincide and have an infinite number of solutions.
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Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
The required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
The figure of the triangle is not given the quesiton, An figure is attached after the solution regarding the solution,
From diagram,
Consider the triangle RST and triangle VUT
ST/UT = 2
∠S = ∠U both are of 90°
RS/VU = 2.
So, triangles are similar by the SAS similarity theorem.
Thus, the required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.
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Simplify (2x+5y)(3x-8y)
Answer: = [tex]6x^{2}[/tex] − xy − [tex]40y^{2}[/tex]
Step-by-step explanation:
{Apply\:FOIL\:method}:\quad
\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd
a=2x,\:b=5y,\:c=3x,\:d=-8y
{Apply\:minus-plus\:rules}
+\left(-a\right)=-a
=2\cdot \:3xx-2\cdot \:8xy+5\cdot \:3xy-5\cdot \:8yy
Simplify 2 · 3xx − 2 · 8xy + 5 · 3xy − 5 · 8yy: 6x − xy − 40y
2 2
= [tex]6x^{2}[/tex] − xy − [tex]40y^{2}[/tex]
Hope This Helps!
A window is to be built in the shape of a rectangle surmounted by an isosceles
triangle. The area of the window must be 6m2. Use Lagrange Multipliers to find
the width and height of the rectangle for which the perimeter of the window will be
as small as possible. (Clarications: (1) A rectangle surmounted by a triangle has
the shape of a stick drawing of a house as might be drawn by a child, a rectangle
with a triangle on top. (2) The window's perimeter is made up of three sides of
the rectangle and the two equal length sides of the triangle. Draw a diagram! (3)
This may require some industrial strength algebra!)
The width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).
What is the Lagrange multiplier?
The Lagrange multiplier, λ, measures the increase in the objective function (f(x, y) that is obtained through a marginal relaxation in the constraint (an increase in k). For this reason, the Lagrange multiplier is often termed a shadow price.
To use Lagrange multipliers to solve this problem, we can set up a function to minimize the perimeter of the window, subject to the constraint that the area of the window is fixed at 6 square meters.
Let x be the width of the rectangle, y be the height of the rectangle, and z be the Lagrange multiplier.
The function to minimize is the perimeter of the window, which is P = 2x + 2y + (2 * sqrt(x^2 + y^2))
The constraint is the area of the window, which is A = xy + (x * sqrt(x^2 + y^2))/2 = 6
The Lagrange equation is
L(x,y,z) = P + z(A-6) = 2x + 2y + (2 * sqrt(x^2 + y^2)) + z(xy + (x * sqrt(x^2 + y^2))/2 - 6)
To find the critical points, we will take the partial derivatives of L(x,y,z) with respect to x, y, and z, and set them equal to zero:
∂L/∂x = 2 + zy + zx * (x/sqrt(x^2 + y^2)) = 0
∂L/∂y = 2 + zx + zy * (y/sqrt(x^2 + y^2)) = 0
∂L/∂z = xy + (x * sqrt(x^2 + y^2))/2 - 6 = 0
Solving these equations simultaneously will give us the critical points of the function.
We will get two critical points (x,y) = (3sqrt(2), 2sqrt(2)), (0,2sqrt(2))
We should eliminate the point where x=0 as it does not fulfill the condition of the problem ( the width should be greater than 0)
Hence, the width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).
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Find the first step for solving the system by substitution.... X = 4y - 1
and 9x - 5y = -22
please help me on this
Answer:
80mm
Step-by-step explanation:
According to Pythagorean theorem :
a² + b² = c²
=> a² + (60)² = (100)²
=> a² + 3600 = 10000
=> a² = 10000 - 3600
=> a² = 6400
=> a = √(6400)
=> a = 80
I HOPE THIS ANSWER HELPS ヾ(＾-＾)ノCan someone please help me? :(
Step-by-step explanation:
send the pic clearly i will help surely im sorry
5x + y = 27
- 10x + 7y = -36 what is the x-coordinate
Answer:
For 5x + y = 27; [tex]x=\frac{-1}{5}y+\frac{27}{5}[/tex]
For -10x + 7y = -36; [tex]x=\frac{7}{10}y+\frac{18}{5}[/tex]
Step-by-step explanation:
None because it will be in the screenshots.
Mark me brainliest if you can when someone else answers, if not then it's alright. Have a good day! :D
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
The x-coordinate of the solution can be found by subtracting the second equation from 7 times the first.
7(5x +7) -(-10x +7y) = 7(27) -(-36)
45x = 225 . . . . . simplify
x = 5 . . . . . . . . . . divide by 45
The x-coordinate of the solution is 5.
_____
The y-coordinate is 2.
Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has
A. An area of 12 cubic units, and its sides could measure 12 units and 2 units
B. An area of 24 cubic units, and its sides could measure 2 units, 3 units, and 4 units
O C. A volume of 12 cubic units, and its sides could measure 12 units and 2 units
D. A volume of 24 cubic units, and its sides could measure 2 units, 3 units, and 4 unit
Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has 24 cubic units. So, option D. is correct.
What are cubic units?A cubic unit is a unit of measurement for volume. It represents the amount of space an object occupies in three dimensions: Length, Width and Height. It is often used to measure the volume of three-dimensional shapes such as cubes, square prisms, cylinders, and spheres. Cubic units are most commonly measured in cubic meters or cubic feet, but they can also be expressed in smaller units such as cubic centimeters or cubic inches.
The total volume of the box is 24 cubic units. A side of the box may measure 2 units x 3 units x 4 units = 24 cubic units.
Choice A is incorrect. This is because the area of a shape is a measure of the two-dimensional space it occupies, and the volume of a shape is a measure of the three-dimensional space it occupies.
Choice B is incorrect. This is because the area of a shape is a measurement of the two-dimensional space it occupies, not its volume.
Option C is incorrect because it states that the box has a volume of 12 cubic units, but it is not because the volume he has is 24 cubic units.
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ES = ___ units
Round your answer to the nearest tenth.
Answer:
15
Step-by-step explanation:
What is .0252525252525252525... as a simplified fraction? Will give Brainliest.
Answer:
5/198Hope that helps! :)
-Aphrodite
Step-by-step explanation:
which pair of triangles? multiple choice
Answer:
c
Step-by-step explanation:
/l/b/a×4÷6×0rrrt he 3rjdhdyeeyy3gfwgqrt
solve 2x+4y=4 -2x+y=-4 using substitution 
According to the solving by using substitution method the x and y are x = 6/5 and y = -8/5 respectively.
What is a method of substitution?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.
According to the given information:given equations are 2x+4y = 4 and -2x+ y = -4
Now, simplifying -2x+y = -4
-2x+y = -4
∴ y = -4 + 2x
i.e. y = 2x - 4
By substitution method,
y = 2x - 4 in other given equation 2x+4y = 4,
2x+4y = 4
2x+4(2x - 4) = 4
∴ 2x + 8x - 8 = 4
∴ 10x = 4 + 8
∴10x = 12
∴ x = 12/10
∴ x = 6/5
Now ,
substituting x = 6/5 in y = 2x - 4,
y = 2(6/5) - 4
∴ y = - 8/5
∴ x = 6/5 & y = - 8/5.
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What is the volume, in cubic in, of a rectangular prism with a height of 3in, a width of 10in, and a length of 2in
On solving the provided question, we can say that w = 10 in; l = 2 in; volume of prism = WL = 10 X 2 = 20 in sq
what is prism?The definition of a prism in geometry is a polyhedron with an n-sided polygonal base, a second base that is a shifted copy of the first base, and n additional faces (necessarily all parallelograms), with two Connect the corresponding sides of the base. Translations of the base are all cross sections that are parallel to it. A prism is a two-sided, solid, three-dimensional object. It consists of equal cross-sections, flat sides, and identical bases. A prism has faces that are parallelograms or rectangles without bases. A prism is a homogenous, solid, transparent, refracting object enclosed by two planes that are obliquely angled to one another. Two triangular faces and three parallel rectangular faces make up a typical prism. They are constructed of either glass.
here,
w = 10 in
l = 2 in
volume of prism = WL = 10 X 2 = 20 in sq
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25 students in a class took an algebra test 20 students passed the test what percent passed help
Answer:
80% of the students passed the algebra test
Step-by-step explanation:
So for this question, they want to know the percentage of the people that passed.
20 out of 25 students passed, we could find the percentage using two ways:
-------
1. We can use proportions to figure out the percentage (This can only work if the numbers are factorable by 100 such as 10, 25, 50...)
25 × 4 would equal 100. You must multiply the same number to the top as well.
So 20 × 4 = 80
--------
2. We can divide the two numbers
20 ÷ 25 = 0.8
When changed into a percentage, 0.8 would be 80%
-------
Have a good day :)
In order to summarize qualitative data, a useful tool is a____________.
A) histogram
B) stem-and-leaf diagram
C) scattergram
D) frequency distribution
A (A) histogram is a useful tool for condensing qualitative data.
What is a histogram?An effective tool for summarizing qualitative data is a histogram.
The distribution of numerical data is roughly depicted by a histogram.
Karl Pearson was the person who first coined the phrase.
The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.
The bins are often defined as a series of discrete intervals that don't overlap.
The bins (intervals) must be close together and frequently, though not always, have the same size.
Therefore, a (A) histogram is a useful tool for condensing qualitative data.
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b. The original amount on the gift card was $200. Does Arleen have
enough left on the card to buy a
wheelbarrow for $50? Explain.
Answer:
Yes
Step-by-step explanation:
If there was 200 hundred dollars just subtract 50 dollars if there is still money then yes.
Answer: yes
Step-by-step explanation:
200-50=159
A pole that is 3.2 m tall casts a shadow that is 1.32 m long. At the same , a nearby tower casts a shadow that is 46.75 m long. How tall is the tower? Round your answer to the nearest meter.
Answer:
The tower is 113 meters.
Step-by-step explanation:
We are given a pole and a tower that both create a shadow.
Hence, the figures made are triangles.
If you draw the figure (attached to this response), you can see the two triangles are similar triangles.
⭐What are similar triangles?
two triangles whose corresponding side lengths are proportional and have the same shapeStrategycreate a proportion of the ratios of the corresponding side lengthssolve for the length of the towerCreate a ratio for the corresponding side lengthsThe length of the height of the pole (3.2) corresponds to the length of the height of the tower (x).
The length of the shadow of the pole (1.32) corresponds to the length of the shadow of the tower (46.75).
Therefore, our two ratios are:
[tex]\frac{3.2}{x}[/tex] and [tex]\frac{1.32}{46.75}[/tex]
Create a proportion for the corresponding side lengthsA proportion is when you set two ratios equal to each other:
[tex]\frac{3.2}{x} = \frac{1.32}{46.75}[/tex]
Solve for the length of the tower (x)To solve for x, cross multiply by multiplying the opposite parts of the fraction together.
[tex]\frac{3.2}{x} = \frac{1.32}{46.75}\\46.75(3.2) = 1.32x\\149.6 = 1.32x\\\\113 = x[/tex]
∴ The tower is 113 meters tall!
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Who is restaurant had a higher Q1?
Answer: Sophie's
Step-by-step explanation:
Q1 is the second point.
What is the area of this triangle?
Answer:it’s 21 square units
Step-by-step explanation:do base x height then divide by 2 to get 21
Felix hasa bucket of golf bals, The table shows the number of golf balls of each color in the bucket. Golf Balls in a Bucket Color Pnk White Orange Green Number 11 8 18 (A)e Felix selects a golf ball at random. Based on the Information in the table, which statement is true? A The golf ball is more likely to be green than all other colors combined. B The golf ball is equally likely to be pink, white, orange, or green. C The golf ball is 2 times as likely to be orange as it is to be pink. D The golf ball is 7 times as likely to be green as it is to be white.
The correct statement regarding the probabilities from the table is given as follows:
C The golf ball is 2 times as likely to be orange as it is to be pink.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of balls for this problem is given as follows:
4 + 11 + 8 + 18 = 41.
Hence the probability of selecting each ball is obtained as follows:
Pink: 4/41.White: 11/41.Orange: 8/41.Green: 18/41.Hence statement C is correct, as:
2 x 4/41 = 8/41.
(which is the probability of orange, obtained multiplying the probability of pink by two).
Missing InformationThe number of pink balls is of 4.
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Given the triangle, find the perimeter.
7x-4
3x² + 7x -1
5x²
Answer:
[tex]\text{Perimeter}=8x^2+14x-5[/tex]
Step-by-step explanation:
[tex]\text{Perimeter}=(7x-4)+(3x^2+7x-1)+(5x^2)\\\text{Perimeter}=7x-4+3x^2+7x-1+5x^2\\\text{Perimeter}=5x^2+3x^2+7x+7x-4-1\\\text{Perimeter}=8x^2+14x-5[/tex]
In a single experiment, a die is tossed and a spinner with the letters A, B, and C is spun. Each letter is equally likely.Draw your sample space and then find the probability of getting a 2 or a B.a.The sample space is 9. The probability of getting a B is StartFraction 1 Over 9 EndFraction.b.The sample space is 18. The probability of getting a 2 or a B is StartFraction 18 Over 8 EndFraction
The required probability as calculated from the data given above is found to be as 1 / 9.
Given,
The spinner is having the letters as A, B and C.
The possibility of getting any of these letters when the spinner is rolled is same.
Therefore , the sample space will be as follows ,
6 + 3 = 9
This is due to the fact a die has 6 sides.
Then the probability of getting a B will be , 1/9
Sample space is known as the collection of all values which are used in an experiments. The total number of favorable outcomes are taken from this sample space only.
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What is the first side?
Explanation:
The ASA indicates that the side (S) is between the two angles (A). The order is important. For the bottom triangle, the side between the red angles is segment ST. The upper triangle has the segment UX between the red angles. If we know that ST = UX, then we can use the ASA rule to prove the triangles are congruent.
Side note: ST = UX is the same as UX = ST. Furthermore, ST is the same as TS, and UX is the same as XU. So there are a few ways to fill in that blank.