Jannie's adjusted monthly pocket money can be calculated by multiplying his current pocket money (R150) by the ratio of the increase (6:5). The calculation involves finding the equivalent fraction of the ratio and multiplying it by the current pocket money.
To calculate Jannie's adjusted monthly pocket money, we need to determine the amount of increase based on the given ratio of 6:5. The ratio indicates that for every 6 parts, the pocket money increases by 5 parts.
First, we convert the ratio to an equivalent fraction. The ratio 6:5 can be written as 6/5. This fraction represents the increase in pocket money per month.
Next, we calculate Jannie's adjusted pocket money by multiplying his current pocket money (R150) by the fraction representing the increase. The calculation is as follows:
Adjusted pocket money = Current pocket money × Fraction representing the increase
= R150 × 6/5
= R180
Therefore, Jannie's adjusted monthly pocket money after the increase is R180.
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volume of cylinder 8cm and 12 cm
[tex]v=\pi(8)(12)[/tex]
The volume of the cylinder is 301.593 cubic centimeter.
What is the volume of the given cylinder ?Volume exists as a scalar quantity representing the amount of three-dimensional space enclosed by a sealed surface. For example, the space that a substance or 3D shape inhabits or contains. The volume stands often quantified numerically utilizing the SI-derived unit, the cubic meter.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it has been regarded as a prism with a circle as its base.
The dimensions of the cylinder is given as - 8 cm and 12 cm .
The formula of the volume of the cylinder is given as -
V = π * (8) * (12)
Thus the volume is = 96π ≈ 301.593 cubic centimeter.
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Find and compare the growth rates in the weekly number of specialty items produced at each factory.
Show your work.
0.129 is the change in the growth rate of company.
According to statement
we have to find and compare the growth rate of the company weekly.
we use the growth rate formula is
GROWTH RATE = present - past / present
Substitute the values in this formula
1st week = 220-190 / 220
1st week = 0.136
2nd week = 252-220 / 252
2nd week = 32 / 252
2nd week = 0.126
3rd week = 290-252 / 290
3rd week = 0.131
4th week = 337 - 290 / 337
4th week = 0.139
5th week = 380 - 337 / 380
5th week = 0.113
6th week = 440 - 380 / 440
6th week = 0.136
7th week = 505 - 440 / 505
7th week = 0.128
Now we find the average value of growth rate
Average = 0.136 + 0.126+0.131+0.139+0.113+0.136+0.128 /7
Average = 0.909/7
Average = 0.129
So, 0.129 is the change in the growth rate of company.
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A rectangle is 8 feet longer than it is wide. find the dimensions of the rectangle if its area is 345 sq-feet.
The width of rectangle is 15 feet and the length of rectangle is 23 feet.
According to the statement
Width of rectangle = x
Length of rectangle = x+10
Area of rectangle = 345 sq-feet.
we know that the area of rectangle is
Area of rectangle = L*W
Substitute the values in it then
345 = (x) (x+8)
345= (x)^2 + 8x
(x)^2 + 8x - 345 = 0
By factorisation
(x-15) (x+23) = 0
So, width of rectangle is 15 feet and the length of rectangle is 23 feet.
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Suppose the probability that a Wide Receiver catches a ball thrown to him is 0.9. Let X model the number of catches he has if he is targeted 8 times in a game. What is the mean number of balls you would expect him to catch
Using the binomial distribution, the mean number of balls you would expect him to catch is of 7.2.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are:
n = 8, p = 0.9.
Hence the mean is:
E(X) = np = 8 x 0.9 = 7.2.
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Irene knows her blood type is A, but William does not know his blood type. However, William knows that his mother and father both had blood type B. Irene and William's first child is a boy with type O blood. Based on this information, William's blood type could be
Based on this information, William's blood type could be either B or O.
What is Segregation of alleles?
Allele pairs (several features of the same gene) are segregated during meiosis so that they can be transferred selectively to different gametes.During meiosis, maternal and paternal alleles separate.What is genotype vs phenotype ?
Genotype: An organism's genetic makeup. Phenotype. physical characteristic that arises within an organism as a result of its genotype. Probability law.Genotype - the set of alleles that make up an organism.How does genotype influence phenotype ?
The alleles you have for a specific gene or collection of genes are referred to as your genotype. The physical attribute itself, or phenotype, can be affected by both genotype and environmental variables.Learn more about Genotype
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations have the same solution are 2.3p – 6.5p + 0.01p =– 4 + 10.1 and -4.19p = 6.1
linear equationThis are equations that has a leading degree of 1. GIven the expression as shown below
2.3p – 10.1 = 6.5p – 4 – 0.01p
Collect the like terms
2.3p – 6.5p + 0.01p =– 4 + 10.1
Simplify
-4.19p = 6.1
Hence the equations have the same solution are 2.3p – 6.5p + 0.01p =– 4 + 10.1 and -4.19p = 6.1
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What is another way to name angle 3?
O Angle MVK
O Angle LVM
O Angle LVK
O Angle KVM
Answer:
intimately there are three types of angles a cute angle and angle between zero and 90° right angle and angle 90 degree angle of two angle and angle between 90 and 180 degree
please help! this is the last one i need and i forgot how to do it!
Based on the information, Christian would have $5525.5 of annuity.
How to calculate the annuity?According to given information, the number of coffees per week is 3 then, per month is 3x4 = 12
For each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54
Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133
n = number of payments = 8 x 12 = 96
We can use the formula for finding the future value as below
FV = C x [ ( 1 + r )n-1 ] / ( r )
FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)
= 54 x [ (1.13609 - 1)] / (0.00133)
= 54 x 0.13609 / (0.00133)
= 54 x 102.3233
= 5525.5
Therefore Christian would have $5525.5 of annuity.
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Find two consecutive numbers such that sum of four times the first and triple the second is 157. (Linear Function)
Step-by-step explanation:
Set up a system of equations,
Consective numbers appear before and after so we need two number such that
[tex]x + 1 = y[/tex]
or
[tex]x - y = - 1[/tex]
Likewise, we also know that
[tex]4x + 3y = 157[/tex]
Let multiply the top equation by 3.
We get
[tex]3x - 3y = - 3[/tex]
Then we add the bottom equation to that
[tex]4x + 3y = 157[/tex]
[tex]7x = 154[/tex]
[tex]x = 22[/tex]
Then we plug in x for the original equation,
[tex]22 + 1 = 23[/tex]
So the two numbers are 22,23.
Find the area of the figure
Answer:
36 in.
Step-by-step explanation:
find the area of the rectangle and triangle first
area of rectangle = length x height
aR = (6 + 6) x 5
aR = 12 x 5
aR = 60
area of triangle = base x height x 1/2
aT = (6 + 6) x 4 x 1/2
aT = 12 x 4 x 1/2
aT = 24
now, to find the area of the shaded area subtract the triangle from the rectangle
area = rectangle - triangle
a = 60 - 24
a = 36
A track-and-field coach recorded the length of each student's standing long jump. The data is summarized in the box plot.
Standing Long Jumps
0
+
2
4
+
Feet
6
8
10
Choose all of the statements that can be concluded from this data.
A. The median jump length is 5 feet, which is the average length of a standing long jump for the students represented in the box plot.
B. The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of
their long jump.
C. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 4 feet of the
median.
D. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 2 feet of the
median.
A
Answer:
A because of the average length showed
Which of the following systems of linear inequalities is represented by the
solution graphed below?
O A. y>2 and ys x
O B. y22 and rex
O C. x> 2 and y2 x
O D. x22 and y > x
The solution graphed below represents the y>2 and [tex]y\leq x[/tex] system of linear inequalities.
When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.
Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities.
Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities.
Equivalent inequality refers to linear inequalities with the same solution.
From the given graph, it can be seen that the line parallel to the x-axis represents y>2 and the other inclined line represents [tex]y\leq x[/tex] .
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Lola wins $240
She spends $48 on a dress.
What percentage of the $240 has she spent?
Answer:
Step-by-step explanation:
$240 = 100
$48 = X
100 * 48 = 240X
4800 / 240 = 240X / 240
X = 20
She spent 20% on the dress
Solve for this equation:
x(x+3)(x+3)=0
Answer:
x^3+6x^2+9x
if you are trying to find the original function
if not, and you are trying to find the zeros is
x=-3
x=0
Step-by-step explanation:
multiply x(x+3)
x^2+3x
then multiply that by x+3 and that should give you the answer
Answer:
x = 0 or x = -3 or x = -3
Step-by-step explanation:
set up factors as:
x = 0
x + 3 = 0
x + 3 = 0
the first will remain as x = 0 while the others become x = -3 once subtracted
i hope this helped!
The equation y=ax^2 describes a parabola. If the value of a is positive, which way does the parabola open?
A.Up
B.Right
C.Left
D.Down
A. Up
Step-by-step explanation:Parabolas are graphs that make U-shapes and are formed from quadratic equations.
Vertical Parabolas
There are 2 different types of parabolas: vertical and horizontal.
Vertical parabolas have a vertical axis of symmetry. So, they open up or down.Horizontal parabolas have a horizontal axis of symmetry. So, they open left or right.If the x-value is squared, then the parabola is vertical. So, this graph must open up or down.
Positive A-Value
The a-value is the coefficient before the squared term. In a vertical parabola, the graph opens up if the a-value is positive. On the other hand, the graph opens down when the a-value is negative.
In this case, the graph is a vertical parabola that opens up. This means that the range will have a minimum value but no maximum.
The table represents a function.
X f(x)
-4 -2
-1 5
3 4
5 -8
What is f(5)?
-8
-1
1
8
Answer: -8
Step-by-step explanation:
When x = 5, f(x) = -8.
The value of the function f(5) = -8.
We have,
The concept used to find the value of f(5) is function evaluation.
In this case, we are given a function represented by a table with x and f(x) values.
To evaluate the function at a specific value, such as f(5), we look for the corresponding x-value in the table and determine the corresponding f(x) value.
In this example, we found that when x = 5, f(x) is -8 by looking at the table provided.
To find the value of f(5), we need to look at the table and find the corresponding value of the function when x = 5.
From the given table, when x = 5, f(x) is -8.
Therefore,
The value of the function f(5) = -8.
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Solve the equation. -9×+1==×+17 O x=-8 O x = -2 O x=2 © ) x=8
What is the tax due for a single taxpayer reporting a taxable income of $65,725?
The tax due for the single taxpayer whose income is as described is; $14,459.5.
What is the tax due for the single taxpayer?It follows from the task content that the tax due for a single taxpayer whose taxable income is; $65,725 is to be determined.
Since, the taxable income falls between the range; $40,526 to $86,375, 22% of the income is the tax due and hence, the tax due can be evaluated as follows;
= (22/100) × $65,725
= 14,459.5
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Your family is going on vacation for two nights. You don't want to spend more than $135 on a hotel room for your vacation. Write an inequality to represent how much you can spend each night on your hotel room.
Answer:
Step-by-step explanation:
$135 is less than or equal to 2 nights at the hotel (h)
135</=2h
What is the square root of pi?
Pi is a Greek number that plagues mathematics, physics, and circles to the point where pi-fatigue is actually a thing. Pi is an infinite number, however it will henceforth only be written as 3.14159.
I have two solutions to your problem.
The first, and probably less appealing answer, but most used everywhere, would be to use a calculator.
But if you find yourself without a calculator at the ready, I hope you’re prepared to math quite dubiously.
Finding the square power, inverse of a radical, or whatever is multiplied by itself to equal 3.14159, is the second step. We must start someplace to start our attempt, and that place is 3.14159. Since 1 squared equals 1 and 2 squared equals 4, our result, expressed in decimal form, is larger than 1 but less than 2. After that, we just start divising and multiplying the decimals again until we have calculated the square root of pi.
TL;DR
1.7724531 is the approximate square root of pi.
Answer:
1.77245385091
Step-by-step explanation:
what is the volume of the prism
Answer:
8/15 cm
Step-by-step explanation:
Volume = length x width x height
Volume = 4/5 cm x 1/5 cm x 10/3 cm
Volume = 4/25 cm x 10/3 cm
Volume = 40/75 cm = 8/15 cm
Brainliest, please :)
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
Volume of prism = [tex]l[/tex] · [tex]w[/tex] · [tex]h[/tex]
which means
[tex]\frac{10}{3} *\frac{4}{5} *\frac{1}{5}[/tex]
which is [tex]\frac{8}{15}[/tex] by using cross simplify
Hope this helps ;D
2. 2x+6y=6
-x-3y = -3
Solution(s):
PLEASE HELP SOLVE FOR X AND Y
Answer:
x = 0, y = 1
Step-by-step explanation:
2x + 6y = 6 → (1)
x - 3y = - 3 ( add 3y to both sides )
x = 3y - 3 → (2)
substitute x = 3y - 3 into (1)
2(3y - 3) + 6y = 6 ← distribute parenthesis and simplify left side
6y - 6 + 6y = 6
12y - 6 = 6 ( add 6 to both sides )
12y = 12 ( divide both sides by 12 )
y = 1
substitute y = 1 into (2)
x = 3(1) - 3 = 3 - 3 = 0
solution is x = 0 , y = 1
Using the equation y = 2x - 3, what would the input need to be for an output of 7?
00
O 11
05
08
The length of a rectangle is 5 5/3 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68
(question and answers attached)
The perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The perimeter of any object is the total sum length of its boundary.
The perimeter of a rectangle with length l units and width w units is given as:
Perimeter = 2(l + w) units.
In the question, we are given that the length of a rectangle is 5 3/5 inches and its width is half of its length. We are asked to find the perimeter of the rectangle.
The length of the given rectangle (l) = 5 3/5 inches = 28/5 inches.
The width of the given rectangle (w) = Half of length = 1/2 * 28/5 inches = 14/5 inches.
Thus, the perimeter of the rectangle = 2(l + b) = 2(28/5 + 14/5) inches,
or, the perimeter = 2(42/5) inches,
or, the perimeter = 84/5 inches,
or, the perimeter = 16.8 inches.
Thus, the perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The given question is incorrect. The correct question is:
"The length of a rectangle is 5 3/5 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68"
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Consider an unstructured overlay network in which each node randomly chooses c neighbors. If P and Q are both neighbors of R, what is the probability that they are also neighbors of each other
The probability value become is 2c/(N-1).
According to the statement
we have given that If P and Q are both neighbors of R, and by considering unstructured network in which each node randomly chooses c neighbors.
we have to find that the probability of neighbors that they are also neighbors of each other.
So, For this purpose to find the probability is
Consider a network of N nodes unstructured and let
If each node chooses c neighbors at random,
then the probability that P will become by choose Q, or Q chooses P is roughly 2c/(N-1).
And the probability outcomes value become is 2c/(N-1).
So, The probability value become is 2c/(N-1).
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Which expression is equivalent to -7(y - 2)
The expression equivalent to -7(y - 2) is -7y + 14
Which expression is equivalent to -7(y - 2)?
Given the expression; -7(y - 2)
We expand the expression by multiplying each element inside the parentheses the element out i.e -7
-7(y - 2)
[ -7 × y and -7 × -2 ]
-7y + 14
Therefore, the expression equivalent to -7(y - 2) is -7y + 14.
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WILL MAKE BRAINLIEST!!
Solve for x.
Answer:
8
Step-by-step explanation:
51 + 4x + 7 = 90 - combine like terms
58 + 4x = 90 - subtract 58 from each side
4x = 32 - divide both sides by 4
x = 8
Answer:
x = 8
Step-by-step explanation:
The red square indicates that there is a right triangle. All right triangles have angles equal to 90°. Therefore, we can find the value of "x" by setting the sum of both the interior angles to 90°.
(4x + 7) + 51° = 90° <----- Sum of both angles is 90°
4x + 58 = 90° <----- Combine 58 and 7
4x = 32 <----- Subtract 58 from both sides
x = 8 <----- Divide both sides by 4
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The solution to the inequality is x > 3
The number line that represent the solution set will be:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. The correct option is the second option
Linear InequalitiesFrom the question, we are to determine the number line that represents the solution set for the given inequality
The given inequality is
3(8 – 4x) < 6(x – 5)
First, we will solve the inequality
3(8 – 4x) < 6(x – 5)
Clear the brackets
24 - 12x < 6x - 30
Collect like terms
24 + 30 < 6x + 12x
54 < 18x
Divide both sides by 18
3 < x
∴ x > 3
Hence, the number line that represent the solution set will be:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. The correct option is the second option
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please help thank you! will give brainliest!
A'(-6, -10), B'(-3, -13) and C'(-5, -1) are the vertices of the ΔA'B'C' given that the vertices of the ΔABC are A(-6, -7), B(-3, -10) and C(-5, 2) and translation rule (x, y) → (x, y-3) is applied. This can be obtained by putting coordinate values of vertices in the translation rule and then vertices of ΔA'B'C' are found.
Find the vertices of ΔA'B'C' :Given that,
In ΔABC, the vertices are A(-6, -7), B(-3, -10) and C(-5, 2)
The translation rule that must be applied is ⇒ (x, y) → (x, y-3)
By applying the translation rule to each of the vertices of ΔABC we get,
A(-6, -7) → A'(-6, -7-3) = A'(-6, -10)B(-3, -10) → B'(-3, -10-3) = B'(-3, -13)C(-5, 2) → C'(-5, 2-3) = C'(-5, -1)That is,
(-6, -7) → (-6, -10)(-3, -10) → (-3, -13)(-5, 2) → (-5, -1)These new coordinates are the vertices of ΔA'B'C'.
Hence A'(-6, -10), B'(-3, -13) and C'(-5, -1) are the vertices of the ΔA'B'C'.
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Please give the answer
Answer: See the attached image below for the filled in table.
=========================================================
Explanation:
The domain is the set of all allowed x inputs of a function.
The term "radicand" refers to the stuff under the square root.
We cannot have a negative number under the square root. Therefore, the radicand must be 0 or larger.
The first function must have [tex]4x+6 \ge 0[/tex] which becomes [tex]4x \ge -6[/tex] and leads to [tex]x \ge -\frac{6}{4}[/tex] aka [tex]x \ge -\frac{3}{2}[/tex]
So x = -3/2 is the smallest input allowed. Which is where the interval notation of [tex]\left[-\frac{3}{2}, \infty)[/tex] comes from. It's the interval spanning from -3/2 (inclusive) to infinity. This represents the set of all possible x inputs of the first function.
--------
Follow this same idea for problem 2. The steps would be something like this:
[tex]-20x - 6 \ge 0\\\\-20x \ge 6\\\\x \le \frac{6}{-20}\\\\x \le -\frac{3}{10}\\\\[/tex]
The inequality sign flips because we divided both sides by a negative number. That then leads to the interval notation of [tex](-\infty, -\frac{3}{10}\big][/tex]
The interval spans from negative infinity (exclusive) to -3/10 (inclusive).
--------
Problem 3 would have these steps
[tex]5x-16 \ge 0\\\\5x\ge 16\\\\x\ge \frac{16}{5}\\\\\big[\frac{16}{5}, \infty)\\\\[/tex]
No sign flip happens since we divided both sides by a positive number.
--------
Lastly, here are the steps for problem 4
[tex]20+6x \ge 0\\\\6x \ge -20\\\\x \ge -\frac{20}{6}\\\\x \ge -\frac{10}{3}\\\\\big[-\frac{10}{3}, \infty)[/tex]
Don't forget to use the square bracket to include the endpoints mentioned. We always use curved parenthesis for either infinity because we can't ever reach infinity. In a sense, we "approach" infinity.
Once again, all of this is summarized in the filled out table shown below (attached image). Feel free to ask any questions if they come to mind.