ama is four times as old as akua in ten years time, ama will be twice as old as akua find their ages
Answer:
Akua now -- x
Ama now -- 4x
Akua in 10 years ---- x+10
Ama in 10 years ---- 4x+10
4x+10 = 2(x+10)
solve for x
let Ama's age be X and Akua's age be Y
X=4Y.......
X+10=(Y+10)2......
4Y+10=2Y+20
4Y-2Y=20-10
2Y=10 divide both side by 2
2Y/2=10/2
Y=5
X=4x5
X=20
therefore Ama =20years and Akua=5years
hope it helps..
9 m
Not drawn to scale
Find the volume of the triangular prism.
6 m
6m
Answer:
162 m³Step-by-step explanation:
Volume of the prism is the product of the area of the base and the height of prism.
First, we need to find the area of its triangular base:
A = bh/2 = 9*6/2 = 27 m²Now we can find the volume:
V = 27*6 = 162 m³Area of base
1/2BH1/2(9)(6)9(3)27m²Volume
Area of base×Height27(6)162m³How do I write a comment on the data following the completion of the scatterplot
Rearrange the formula to highlight time
Step-by-step explanation:
[tex]s = 2\pi(r)(r + h)[/tex]
[tex] \frac{s}{2\pi(r)} = r + h[/tex]
[tex] \frac{s}{2\pi(r) } - r = h[/tex]
can someone please help me(20 points will give brainliest!!!)
Answer:
Step-by-step explanation:
F starts at 200 and ends at 900
V starts at 0 and ends at 100
points(0,200) and (100,900)
200-900/0-100
= -700/-100
=7 which means every 7 it goes you another 100
this is all I got hope it helps
Need help!!!!!!! Please help me out
Answer:
10 degrees
Step-by-step explanation:
8x = 2x + 60
6x = 60
x = 10
Pls help!
using the numbers 1-9 fill in the boxes so that it meets the criteria. use each number only once per red box and once per blue box
To fill in the values we have the following
a. log6⁰, log 2 . 1, log 8/3
b. log 1 .4 , 1 , log 4. 6
c. log 9/2, log 3. 5 , log 5⁷
How to find the logarithm of a numberTo do this, you have to decide on that particular number that you want to find the logarithm on. Next you have to find the base of that number.
The logarithm of the number is the power that it would have to be raised for us to obtain a different number. You have to note that the logarithm of the number is the exponent that a base would have to be raised up to in order to get a particular number.
Log6⁰ for instance would give us the solution of 1 as the answer. While telling us that we have that the exponent is 0 while the base is 6.
One good property of logarithm is that log m/n = log m - log n also when we have log mn, it is the same as log m * log n
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Two students compared the scores on their math tests. Their results on 9 tests are shown in the box plots below.
Which statements are true?
Ben has the smaller range of test scores.
The lower quartile and upper quartile of Nadia’s data are both higher than the lower quartile and upper quartile of Ben’s data.
The median of Nadia’s data is equal to the median of Ben’s data.
Nadia had the highest score on a test.
Ben’s lowest score was equal to Nadia’s lowest score.
The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.
Nadia had the highest score on a test.
Which statements are true regarding the scores on the tests?According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.
Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.
Additionally, the highest score by Nadia is 100 while that for Ben is; 99.
Hence, Nadia had the highest score on a test.
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Find the volume of the parallelepiped determined by the vertices (0, 1, 0), (1, 1, 1), (0, 2, 0), (3, 1, 2)
The volume of the parallelopiped is 1 cubic units.
In this question,
A parallelepiped is a three-dimensional shape with six faces, that are all in the shape of a parallelogram. It has 6 faces, 8 vertices, and 12 edges. The volume of a parallelepiped is the space occupied by the shape in a three-dimensional plane.
Let the parallelepiped be PQRS.
The vertices of parallelepiped are P(0, 1, 0), Q(1, 1, 1), R(0, 2, 0), S(3, 1, 2).
The volume of parallelopiped can be found by using following steps.
PQ = Q - P = (1,0,1)
PR = R - P = (0,1,0)
PS = S - P = (3,0,2)
Now, the volume of parallelopiped is
[tex]v=\left\begin{vmatrix}1&0&1\\0&1&0\\3&0&2\end{vmatrix}[/tex]
The determinant the matrix is
⇒ 1(2-0) - 0(0-0) + 1(0-3)
⇒ 1(2) - 0 + (-3)
⇒ 2 - 3
⇒ -1
Hence we can conclude that the volume of the parallelopiped is 1 cubic units.
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30 POINTS FOR THIS QUESTION
Answer:
Perimeter is 4a - 10
Area is a^2 - 5a
Step-by-step explanation:
Two sides of the rectangle are "a" and two sides of the rectangle are "a-5" add all four sides and you get a+a+a-5+a-5 Combine the like terms and you get 4a - 10.
The area is when you multiple the two sides together
A = lw
A - a(a-5) = a^2 - 5a
A cell phone company wants to determine the average amount of data that their smart phone customers use each month. which group would best represent a sample of the population?
The group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
What is a Representative Sample of a Population?A sample that best represents a population under study is a sample that is a subset of the entire population, that is, research subjects that are drawn as samples should reflect the general characteristics of the entire population without leaving out any part of the population. Also, a good sample should enable a researcher make generalization.
A sample that is a subset of a population and reflects the characteristics of the general population would not be biased.
Given the situation above, the population of the study are smart phone customers that use dat in the cell phone company. So, a sample that would better represent this general population would be customers that currently have a smart phone plan, since the average amount of data they use is what the cell pone company wants to ascertain.
Therefore, the group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
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1/3 +1/6 in fraction form
[tex]\Large\texttt{Answer}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
Do you remember that we cannot add fractions when they have unlike denominators? We can onyl add fractions as long as they have the same denominator!
So here's the big idea: fractions must have the same denominator.
If we multiply the first fraction by 2, then both fractions will have the same denominator. *
* Why 2??
- Because:
We need to find the least common multiple of 3 and 6, which is 6. Next, what should 3 be multiplied by to result in 6? That's right, 2.
Also, we can only multiply the denominator by 2 as long as we multiply the numerator by 2!
So that's why we multiply the whole fraction by 2
[tex]\bf{\cfrac{1\times2}{3\times2}+\cfrac{1}{6}}[/tex]
Watch what happens
[tex]\bf{\cfrac{2}{6}+\cfrac{1}{6}}[/tex]
Add the numerators
[tex]\bf{\cfrac{2+1}{6}}[/tex]
[tex]\bf{\cfrac{3}{6}}[/tex]
Simplifying the fractions
[tex]\bf{\cfrac{3\div3}{6\div3}}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
Hope that helped
Answer: 1 / 2
Step-by-step explanation:
Given information
[tex]\frac{1}{3} ~+~\frac{1}{6}[/tex]
Convert the denominator (3, 6) into the same common denominator
Least Common Multiple (LCM) of 3 and 6 = 6
[tex]=\frac{1~*~2}{3~*~2} ~+~\frac{1}{6}[/tex]
[tex]=\frac{2}{6} ~+~\frac{1}{6}[/tex]
Combine two fractions
[tex]=\frac{2~+~1}{6}[/tex]
[tex]=\frac{3}{6}[/tex]
Simplify the fraction by dividing 3 on both numerator and denominator
[tex]=\frac{3~/~3}{6~/~3}[/tex]
[tex]=\Large\boxed{\frac{1}{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. Length of Time (in minutes) Number 1 up to 4 4 4 up to 7 8 7 up to 10 14 10 up to 13 9 13 up to 16 5 16 up to 19 2 What is the mean (in minutes)
The mean in minutes of the length of time given= 9.1
Calculation of mean when frequency table is givenThe formula used for the determination of mean when a frequency table is given is
= total/n
Where total = frequency×midpoint
n = 42
To calculate the total, the mid point of each length of time is determined as follows;
1+4/2 = 2.5 × 4 = 10
4+7/2= 5.5 × 8 = 44
7+10/2 = 8.5 × 14= 119
10+13/2 = 11.5× 9 = 103.5
13+16/2= 14.5×5 = 72.5
16+19/2= 17.5× 2= 35
Total= 10+44+119+103.5+72.5+35 = 384
Therefore mean = 384/42= 9.1
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what’s the inverse function of f
f(x)=x+2/7
Answer: A
Step-by-step explanation:
Let f(y)=x.
[tex]x=\frac{y+2}{7}\\\\7x=y+2\\\\y=7x-2\\\\f^{-1}(x)=7x-2[/tex]
Julia is casting a play with 4 main roles. Six students
have tried out. How many different combinations of 4
students can Julia cast from the 6 students?
Using the combination formula, it is found that Julia can take 15 combinations.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For this problem, 4 students are taken from a set of 6, hence the number of combinations is given as follows:
[tex]C_{6,4} = \frac{6!}{4!2!} = 15[/tex]
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what is coefficient of x in 5x-3y
Answer:
Hey there!
Step-by-step explanation:
This is ur answer...
The coefficient of 5x-3y is 5.Hope it helps!
Brainliest pls!
Have a good day!^^
❄ Hi there,
the coefficient of a variable is a number multiplied by that variable; it can be any real number.
∴,
[tex]\hfill\stackrel{\textbf{coefficient of x}}{5}[/tex]
[tex]\hfill\stackrel{\textbf{coefficient of y}} {-3}[/tex]
That's it.
❄ [tex]\small\pmb{Frozen \ melody}[/tex]
The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the
biggest volume possible. The volume of the cylinder is:
The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].
What is the diagonal of the cube?The diagonal that runs through the middle of a cube is it's main diagonal; the diagonal that runs along one of its faces is not. Any cube's major diagonal can be calculated by multiplying one side's length by the square root of three.Cos-1(2/3) is the angle formed between a cube's diagonal and the diagonal of one of its faces.Body of the diagonal=24cm.
Assume the length of the side= a.
[tex]a^{2} +(a^{2} +a^{2} )=24^{2}[/tex]
[tex]a=\sqrt[8]{3} cm[/tex]
The area of the cylinder base=[tex]\pi R^{2}[/tex]
=[tex]\pi (\frac{1}{2} \sqrt[8]{3} )^{2}[/tex]
=[tex]48cm^{2}[/tex]
The high of the cylinder is[tex]\sqrt[8]{3}cm[/tex]
The volume of the cylinder:
=s*h
=[tex]48\pi *\sqrt[8]{3}[/tex]
=[tex]384\pi \sqrt{3} cm^{3}[/tex]
The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].
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The biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].
What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is [tex]x[/tex], the diameter and the height of the cylinder are also [tex]x[/tex]If the side length of a cube is [tex]x[/tex] unit, then its diagonal will be [tex]x\sqrt{3}[/tex] unit.The formula for the volume of a cylinder is [tex]V=\pi r^2h[/tex], where [tex]r[/tex] is the radius and [tex]h[/tex] is the height of the cylinder. If [tex]d[/tex] is the diameter, then [tex]r=\frac{d}{2}[/tex].Now, given that the diagonal of the cube is [tex]24[/tex] cm. So, if the side length of the cube is [tex]x[/tex] cm, then we must have
[tex]x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}[/tex]
Thus, the side length of the cube is [tex]8\sqrt{3}[/tex] cm.
So, the height of the cylinder with maximum volume will be [tex]h=8\sqrt{3}[/tex] cm and the diameter will be [tex]d=8\sqrt{3}[/tex]cm i.e. the radius will be [tex]r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}[/tex] cm.
So, using the above formula for the volume of a cylinder, we get
[tex]V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3[/tex].
Therefore, the biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].
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Flannery used 303030 lilies and 787878 roses to create six identical flower arrangements. write an equation to describe the relationship between lll, the number of lilies, and rrr, the number of roses.
An equation to describe the relationship between l and r is, as l = r so
5l + 13r = 108.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.To find the equation which represents the relationship between l, the number of lilies, and r, the number of roses:
Let l denote the number of lilies and r denote the number of roses.Flannery employed 30 lilies and 78 roses to create six similar flower arrangements, according to the statement.Total flower count = 30 + 78 = 1086 flower arrangements are required that is l = r = 6.Number of Lilies in one arrangement = 30/6 = 5Number of Roses in one arrangement = 78/6 = 13Then, 5l + 13r = 108.Therefore, an equation to describe the relationship between l and r is, as l = r so 5l + 13r = 108.
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The correct question is given below:
Flannery used 30 lilies and 78 roses to create six identical flower arrangements. Write an equation to describe the relationship between l, the number of lilies, and r, the number of roses.
Answer:
Step-by-step explanation:
r=13/5L
A 3 metre long piece of ribbon is cut into
two pieces in the ratio 3:2.
How long is the shorter piece?
Step-by-step explanation:
3 meters = 300 cm
anyway, the ratio tells us that the whole ribbon can be seen as the combination of 3 + 2 = 5 equally long parts.
one such part is then
3 m / 5 = 0.6 m or 60 cm
the shorter piece is 2 of these parts long :
2 × 0.6 = 1.2 m or 120 cm
crunchee corporation increases the size of its granola packages from 16 ounces to 20 ounces.what is the percent of increase in the size of crunchee's granola packages
The percentage of increase in the size is 25%
According to the statement
We have to given that the
Size of the granola packages from 16 ounces to 20 ounces.
And we have to find the percentage of the size of the crunchee's granola packages.
So, For this purpose,
The formula to calculate the percentage of increase in the size is :
Percentage to increase the size = present size - past size / present size.
Now substitute the values in the given formula is
Percentage to increase the size = (20 - 16 / 16)*100
After solving it
Percentage to increase the size = (4/16) *100
Percentage to increase the size = 25%
So, The percentage of increase in the size is 25%
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What is the solution to the compound inequality in interval notation?
4(x+1)>−4 or 2x−4≤−10
(−∞, −3] or (2, ∞)
(−3, −2]
(−∞, −2) or [3, ∞)
(−∞, −3] or (−2, ∞)
Answer:
Step-by-step explanation:
Because of the word "or", this is a disjunction, or a union of all the solutions to the inequality as they present on a number line.
For the first inequality:
4(x + 1) > -4 we distribute through the parenthesis to get
4x + 4 > -4 and subtract 4 from both sides to get
4x > -8 and then divide both sides by 4 to get
x > -2. That will be graphed on a number line with an open hole over the -2 and the arrow will go to the right where the numbers are bigger than -2. This arrow continues into positive infinity.
For the other inequality:
2x - 4 ≤ -10 we add 4 to both sides to get
2x ≤ -6 and then divide by 2 to get
x ≤ -3. That is a closed hole over -3 and the arrow goes to negative infinity (to the left). Since one arrow goes off to the right forever, and the other arrow goes off to the left forever, and the arrows do not intersect at any point, the interval notation answer is
(-∞, -3] or (-2, ∞). The parenthesis mean that the number following it is not included (you can't include infinity, either negative or positive, because it's not actually a number) and the brackets mean that the number following it IS included. The hole is closed over the -3 so -3 is included in the solution, where the hole over the -2 is open and is not included.
The following lines are ______
4x + 2y = 10 y = -2x + 15
Answer:
Parallel
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + 2y = 10 ( subtract 4x from both sides )
2y = - 4x + 10 ( divide through by 2 )
y = - 2x + 5 ← in slope- intercept form
with slope m = - 2
and
y = - 2x + 15 ← is in slope- intercept form
with slope m = - 2
• parallel lines have equal slopes
then the 2 lines are parallel
Answer:
Parallel
Step-by-step explanation:
They have the same slope, but different y intercepts.
4x + 2y = 10 Subtract 4x from both sides
2y = -4x +10 Now divide both sides by 2
y = -2x + 5 Compare to y = -2x + 15. Both equations have the same slope or steepness, but they do not cross the y axis at the same place. The first equation given crosses the y axis at 5 and the second equation crosses the y axis at 15
Describe the error using mathematical vocabulary:
(3,-2) 2
++
(3, 2)
-3-2
1 2 3
(-3,-2)-2 (-3,2)
-3+
-1
The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the number of years with a company and y represents an employee’s salary in dollars.
Based on the data given, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is C. There's a weak negative correlation between the variables.
How to illustrate the information?From the information given, it can be seen that the value of y is increasing with the increase in the value of x.
This implies that the correlation is positive. Also, the change in the values of y with x are scattered a lot.
Therefore, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is that there's a weak negative correlation between the variables
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5. During the season, the Rangers played 25 games. They won 14 of the games.
What fraction and percent of the games did they lose? Show your work in the
space below. Remember to check your solution.
to find the fraction of losses, we need to divide the total amount of losses by the total amount of games played.
if we know that the Rangers won 14 games but they played 25, we can write an equation to find the amount of games lost.
14 + n = 25, where n equals the amount of losses.
now we isolate by moving the 14 to the other side. to do this, we must subtract 14 from both sides, leaving us with n = 11. now we know they lost 11 games.
to find the fraction of lost games, all we need to do is divide 11 by 25 without completing the division. that leaves us with 11/25.
the Rangers lost 11/25 games during the season
hope this helped!!
one endpoint of a line segment is (1,2) and the midpoint of the midpoint of the segment is (-1,4) what is the other end point ?
What is the numerical value of mswithin when sswithin= 70, the sample size = 17 and the number of groups = 3? group of answer choices mswithin = 70
The numeric value of ms within is = 19.
What is a numeric value?A real number, regardless of its sign, has a numerical value. A definite quantity is a defined amount measurement.To find the numeric value of ms within:
Given: Swithin = 70, sample size = 17 and number of groups = 3.
So, 17 × 3 = 51
70 - 51 = 19
Therefore, the numeric value of ms within is = 19.
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A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called?
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.
We know that,
A dummy variable is a binary variable that takes a value of 0 or 1.
In regression analysis, a dummy variable is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.
The number of dummy variables we must create is equal to k - 1, where k is the number of different values that the categorical variable can take on.
It is an artificial variable created to represent an attribute with two or more distinct categories/levels.
These are being used in order to sort out data into mutually exclusive groups.
It is used typically in time series analysis, response modelling, bio-medical studies, economic forecasting and credit scoring.
Therefore, a variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.
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The area of a park is 2,976 feet squared. If the length of the park is 62 ft, what is the width of the park?
If necessary, round to the nearest whole number.
width =
ft=
Answer:
Area of park = 2976 ft²
Length of park = 62 ft
Width of park = ?
Area of park = length ×width
2976 = 62 × width
width = 2976/62
=48 ft
Please give me a correct answer and the step by step explanation.
keeping in mind that the points are A(-8 , 6) and C(2 , 5), so
[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{2}{5}\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-8)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AC}}}{\left( 10 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left( \stackrel{x_1}{-8}~~+~~\frac{2}{5}(10)~~,~~\stackrel{y_1}{6}~~+~~\frac{2}{5}(-1) \right)\implies \left(-8+4~~,~~6-\frac{2}{5} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill B\left(-4~~,~~5\frac{3}{5} \right)~\hfill[/tex]