Mahelet's age is found to be 14 years by solving the simultaneous equations using the given data.
What exactly is a simultaneous equation?A collection of two or more equations, each having two or more variables, whose values can concurrently fulfil one, more, or all of the equations in the collection, with the number of variables being equal to or fewer than the collection's equations.
Given: Mahelet is four times older than Mr. Jones, who is three years older than Mahelet. The total of their ages is 73.
Let, x = Mahelet's age
y = Mr. Jones's age
We know that,
y = 4x +3
x + y = 73
Solving these equations simultaneously we get,
y = 4(73-y) +3
y = 292 - 4y + 3
5y = 295
y = 59
x = 73 - y = 73 - 59 = 14
Therefore, Mahelet's age is found to be 14 years by solving the simultaneous equations.
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Determine g(x + a) - g(x) for the following function.g(x) = 3x^2 - 5x
Answer:
3a² + 6ax + 5a
Explanation:
Given the following function
g(x) = 3x² - 5x
Determine g(x+a)
g(x+a) = 3(x+a)² - 5(x+a)
Expand the result
g(x+a) = 3(x² + 2ax + a²) - (5x - 5a)
g(x+a) = 3x² + 6ax + 3a² - 5x + 5a
Determine g(x + a) - g(x)
g(x + a) - g(x) = 3x² + 6ax + 3a² - 5x + 5a - (3x² - 5x)
g(x + a) - g(x) = 3x² + 6ax + 3a² - 5x + 5a - 3x² + 5x
Collect the like terms
g(x + a) - g(x) = 3x² - 3x² - 5x + 5x + 6ax + 3a² + + 5a
g(x + a) - g(x) = 6ax + 3a² + 5a
g(x + a) - g(x) = 3a² + 6ax + 5a
Hence the required result for the function g(x + a) - g(x) is 3a² + 6ax + 5a
Sara needs to purchase one notebook and packs of pencils (p) for school. A notebook costs $12.99 and packs of pencils cost $1.19 each. Which equation shows the relationship between the total cost, C, of a notebook and p packs of pencils?
The total cost of all the items mentioned can be expressed as
12.99 + 1.19 P = C
Given : Sara needs to purchase one notebook
Also it is given that pack of pencils is represented by P
Since a notebook costs = $ 12.99
And pack of pencils cost = $ 1.19
Thus the total cost can simply be represented by adding all the above mentioned items
this means it can be written as
12.99 + 1.19 P = C where C represents the total cost { given }
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[tex]\frac{(438)^{3} \sqrt{0.056} }{(388)^{4} }[/tex]
The simplification of the given expression is 0.3404
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
WE have given the expression as;
[tex]\frac{(438)^{3} \sqrt{0.056} }{(388)^{4} }[/tex]
Now solving;
[tex]\dfrac{(438)^{3} \sqrt{0.056} }{(388)^{4} }\\\\\\\dfrac{84027784 \times 0.23}{58411072 }\\[/tex]
= 0.3404
Therefore, the simplification of the given expression is 0.3404
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Which graph shows the ordered triple (2, 3, 3) plotted correctly?
Answer:
the answer is D
Step-by-step explanation:
Which of the following isn’t a solution to cos 2x + cos x=0 on the interval [0,2pi)
Given:
There are given the equation:
[tex]cos2x+cosx=0[/tex]Explanation:
According to the question:
We need to find the value where the given equation is satisfied.
So,
From the equation:
Put the 0 for x for the option first.
[tex]\begin{gathered} cos2x+cosx=0 \\ cos2(0)+cos(0)=0 \\ 1+1=0 \\ 2\ne0 \end{gathered}[/tex]Then,
For the second option:
[tex]\begin{gathered} cos2x+cosx=0 \\ cos2(\frac{\pi}{3})+cos\frac{\pi}{3}\ne0 \end{gathered}[/tex]For option third:
[tex]\begin{gathered} cos2x+cosx=0 \\ cos2(\pi)+cos(\pi)=0 \\ -1+2cos^2(\pi)+cos(\pi)=0 \\ -1+2(-1)^2-1=0 \\ -1+2-1=0 \\ 0=0 \end{gathered}[/tex]Final answer:
Hence, the correct option C.
Which order pair can be plotted together with these four points, so that the resulting graph still represents a function.
The ordered pair that can be plotted together with these four points is
(0, 3).
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The following coordinates are from the graph.
(3, -1), (2, 3), ), (-4, 2), and (-2, -3)
We know that,
A function can have many-to-one but not one-to-many.
So,
We can not have (-2, 0), (-2, 3). and (3, 0) because we already have (-2, 3) and (3, -1).
This is an indication of a one-to-many function that is not possible.
(0, 3) is possible.
Thus,
The ordered pair that can be plotted together with these four points is
(0, 3).
Option C is the correct answer.
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1. What is the equation of the line in standard form? A302-10
Question: What is the equation of the line in standard form?
The standard form for a line is :
y = mx + b
where m is the slope and b is the intercept with y axis.
First, we are going to find the slope, choosing any two points on the line. For example (X1, Y1) = (-4,0) and (X2, Y2) = (0,3). Then, by definition the slope is:
[tex]m\text{ = }\frac{Y2\text{ - Y1}}{X2\text{ - X1}}\text{ = }\frac{3-0}{0-(-4)}\text{ = }\frac{3}{0+\text{ 4}}\text{ = }\frac{3}{4}[/tex]so, our new line equation would be:
[tex]y\text{ = mx + b = }\frac{3}{4}x\text{ + b}[/tex]that is:
[tex]y\text{ = }\frac{3}{4}x\text{ + b}[/tex]Now, we are going to find the y-intercept. This is also accomplished by picking two points on the line and solving for b. For example (X2, Y2) = (0,3). So, for above equation we have:
[tex]3\text{ = }\frac{3}{4}(0)\text{ + b}[/tex]then
[tex]3\text{ = 0 + b = b}[/tex]Then, we have b = 3.
Now, replacing the values of the slope and the intercept previously found, we obtain the equation of the line :
[tex]y\text{ = mx + b = }\frac{3}{4}x\text{ + }3[/tex]that is
[tex]y\text{ = }\frac{3}{4}x\text{ + }3[/tex]a semi-trailer is being packed with boxes that are 1 and 1/2 feet on each Edge the cargo space of the trailer is 28 ft long eight and a half feet wide and 9 and 1 over 6 feet high what is the maximum number of boxes that will fit inside the trailer
The maximum number of boxes that will fit inside the trailer according to the available volume is 540.
A semi-trailer is being packed with boxes. The side length of each box is 1.5 feet. The cargo space of the trailer is 28 feet in length, 8.5 feet wide and 9.167 feet high. Let the number of boxes that can fit according to the length, width, and height of the trailer be x, y, and z. The values of x, y, and z are the greatest whole numbers less than or equal to the ratio of the length, width, and height of the trailer to the length, width, and height of the box, respectively. The first inequality is x ≤ 28/1.5 ≤ 18.67, so the value of x is 18. The second inequality is y ≤ 8.5/1.5 ≤ 5.67, so the value of y is 5. The third inequality is z ≤ 9.167/1.5 ≤ 6.11, so the value of z is 6. The total number of boxes is the product of the three variables.
P = x*y*z = 18*5*6 = 540
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Bryce wants to renovate his kitchen. The construction estimate is $28,400. He can finance through his local bank or directly through the construction company. The bank (loan A) offers a maximum 6-year loan at 8% annual interest, resulting in monthly payments of $497.94.The construction company (loan B) offers a maximum 10-year loan at 5.5% annual interest, resulting in monthly payments of $308.21.Which loan requires Bryce to pay less, and by how much?First, calculate the total payback for each loan.
ANSWER:
Loan A requires Bryce to pay less by $1,133.52
EXPLANATION:
For bank A, we're given;
Length of loan in years(t) = 6 years
Annual interest rate(r) = 8% = 8/100 = 0.08
Loan payment(PMT) = $497.94
Number of compounds per year(n) = 12
We can go ahead and determine the loan amount using the below formula as seen below;
[tex]\begin{gathered} Loan\text{ }amount,P_0=\frac{PMT(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}} \\ \\ =\frac{497.94(1-(1+\frac{0.08}{12})^{-12*6}}{\frac{0.08}{12}} \\ \\ =\text{ \$}28399.77 \end{gathered}[/tex]So we can see that Bryce will pay back;
[tex]\begin{gathered} Bank\text{ }A\text{ }Loan\text{ }Payback=497.94(12*6) \\ \\ =497.94\left(72\right) \\ \\ =\text{\$}35,851.68 \end{gathered}[/tex]For bank B, we're given;
Length of loan in years(t) = 10 years
Annual interest rate(r) = 5.5% = 5.5/100 = 0.055
Loan payment(PMT) = $308.21
Number of compounds per year(n) = 12
We can go ahead and determine the loan amount using the below formula as seen below;
[tex]\begin{gathered} Loan\text{ }amount,P_0=\frac{PMT(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}} \\ \\ =\frac{308.21(1-(1+\frac{0.055}{12})^{-12*10}}{\frac{0.055}{12}} \\ \\ =\text{ \$}28399.57 \end{gathered}[/tex]So we can see that Bryce will pay back;
[tex]\begin{gathered} Bank\text{ B }Loan\text{ }Payback=308.21(12*10) \\ \\ =308.21\left(120\right) \\ \\ =\text{\$}36985.20 \end{gathered}[/tex]We can see that Bryce will pay back $35,851.68 for Loan A and $36,985.20 for Loan B, so Loan A requires Bryce to pay less and by $1,133.52
1) When full, a tank contains 1620 gallons of water. Currently, the tank has 648 gallons of water in it. What percent of the full tank is this?
Answer:
The tank is currently 40% (40 percent) full.
Step-by-step explanation:
We can find this by dividing the current fullness (648 gal) by the full tank (1620 gal).
648 / 1620 = 0.4
0.4 = 40%
How do we know to divide 648 by 1620 and not the other way around?
We know this because that we want to know what percent of the full tank is currently full. It's something that you just need to get used to, once you do enough of these types of problems, I'm sure you'll get the hang of it!
Hope I could help you! If I did, it would mean a lot of you could give braniest or even just a thanks :) If I didn't quite answer your question, please let me know and I'll try my best to assist you!
50% of the tickets sold an amusement park or a discount tickets at the park sold 94 tickets to know how many discount tickets did it sell
we have that
50%=50/100=0.50
Multiply the total tickets sold by the factor of 0.50
so
94*0.50=47 tickets
the answer is 47 ticketsOrder the numbers 7/4 , 1 .6, 1 5/8 , 1. 62 from least to greatest.
Answer:
1.6, 1.62, 1 5/8, 7/4
Step-by-step explanation:
First, let's turn the fractions into decimals:
For 7/4 you simply divide 7 by 4. Which equals 1.75.
Next for 1 5/8 we divide 5 by 8, which equals 0.625. + the 1 in 1 5/8. So we have 1.625.
Now, we arrange the decimals:
1.6, 1.62, 1.625, 1.75
But this is NOT the answer. We have to replace the decimals that WERE fractions back to the original, then order them from there:
1.6, 1.62, 1 5/8, 7/4.
This IS the answer.
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Answer:
the answer to this question is in the screenshot. pls mark this answer as the brainliest
Step-by-step explanation:
(c) The annual membership fee in 2013 is $198 for each adult and $75 for each child. (i) Calculate the total amount the 560 members pay in 2013.
The total amount the 560 members pay in 2013 will be $96,120.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The yearly enrollment expense in 2013 is $198 for every grown-up and $75 for every kid.
Adult = 440 members
Children = 120 members
Then the total amount the 560 members pay in 2013 will be given as,
Total amount = 440 x 198 + 120 x 75
Simplify the expression, then we have
Total amount = 440 x $198 + 120 x $75
Total amount = $87,120 + $9,000
Total amount = $96,120
The total amount the 560 members pay in 2013 will be $96,120.
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The complete question is given below.
The annual membership fee in 2013 is $198 for each adult and $75 for each child.
Adult = 440 members
Children = 120 members
Calculate the total amount the 560 members pay in 2013.
In a class of 30 students, 3 of the 16 boys are left-handed and 2 of the girls are left-handed. One student is chosen at random . Which of the following represents a conditional probability ?
The conditional probability is represented in option A : the probability that the student is left-handed, given that the student is a boy.
The total number of students in the class is 30. The number of boys in the class is 16. The number of boys who are left-handed is 3. The number of left-handed girls is 2. One student is chosen randomly. We need to find a situation that represents a conditional probability. The conditional probability occurs when the probability of one event depends on the occurrence of another event. So, the situation suitable for this to happen is to find the probability that the student is left-handed, given that the student is a boy.
The complete question is :
In a class of 30 students, 3 of the 16 boys are left-handed, and 2 of the 14 girls are left-handed. One student is chosen at random. Which of the following represents a conditional probability?
A. The probability that the student is left-handed, given that the student is a boy
B. The probability that the student is a girl and left-handed
C. The probability that the student is right-handed
D. The probability that the student is not a boy
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write write in equal inequalities to represent each situation Molly went shopping in her bank account got below 7.50
what does pie mean in math
Answer: The symbol used by mathematicians to represent the ratio of a circle's
Step-by-step explanation: circumference to its diameter is the lowercase Greek letter π, sometimes spelled out as pi. In English, π is pronounced as "pie"
The volume of a box is 0.001 cubic Units. If the box is a cube, what is the length of one of its edges?
Answer:
0.1 units
Step-by-step explanation:
The volume formula of a cube is V = s^3
0.001 = s^3
s = 0.1
Brandon has a jar of quarters and dimes with a total value of $6.05. The number of quarters is 7 less than twice the number of dimes. How many quarters and how many dimesdoes Brandon have?Number of quarters -Number of dimes -
SOLUTION:
In this problem.
Let number of dimes = x, then number of quarters = 2x - 7.
The monetary values of quarters and dimes are;
[tex]\begin{gathered} 0.1x+0.25(2x-7)=6.05 \\ 0.1x+0.5x-1.75=6.05 \\ 0.6x=7.8 \\ x=13 \end{gathered}[/tex]Thus, 2( 13) - 7 = 19.
Therefore, there are 13 dimes and 19 quarters.
The height of a triangle is 5 less than double its base, which is 13/2. Find the triangle´s area.
Answer:
The answer you are looking for would be 11 7/2.
Step-by-step explanation:
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What is 4 1/4 - 2 1/2
Answer:
=1 and 3 over 41
=1.75
Step-by-step explanation:
Complete the table. Write each exponent as a simplified fraction or integer.
6 to the power of - 1
6 to the power of - 2
6 to the power of - 3
6 to the power of - 4
Answer + Explanation:
Since you just flip the fraction if you have a negative power, you get
1.) 6 to the power of -1 = 1/6
2.) 6 to the power of -2 = 1/36
3.) 6 to the power of -3 = 1/216
4.) 6 to the power of -4 = 1/1296
Use the graph to determine the point of intersection (4,5)(1,3)(5,4)(3,1)
The intersection point is (4,5) because that's the point where the two lines meet
Brandon buys a two-quart bottle of juice for $8.32. What is the unit rate of the cost of the juice per fluid ounce? 1 gallon = 1 gallon= 4 quarts 4 quarts 1 quart = 1 quart= 2 pints 2 pints 1 pint = 1 pint= 2 cups 2 cups 1 cup = 1 cup= 8 fluid ounces 8 fluid ounces Before you try that problem, answer the question below. How many fluid ounces of juice did Brandon buy? 64 64 What is the cost of juice in dollars per fluid ounce?
The cost of the juice in dollars per fluid ounce s $0.13..
What is the cost of the juice?The first step is to convert quart to ounces.
1 quart = 32 ounces
The quantity of juice bought in fluid ounces : quantity in quart x unit of conversion= 32 x 2 = 64 fluid ounces
The next step is to divide the cost of the bottle of juice by the converted capacity of the juice bottle. Division is the mathematical process of grouping a number into equal parts using another number.
The cost of the juice in dollars per fluid ounce = cost of the bottle / capacity of the bottle in fluid ounces
= $8.32 / 64 = $0.13
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The random variable x has a normal distribution with standard deviation. It is known that the probability that x exceeds is. 90. Find the mean of the probability distribution.
The random variable x has a normal distribution with standard deviation. It is known that the probability that x exceeds is. 90. Therefore, mean of the probability distribution is 133.09.
We are given that the random variable x has a normal distribution with standard deviation 21,i.e;
X ~ N( u, σ=21)
The Z probability is given by;
Z = X- u/σ ~ (0,1)
Also, it is known that the probability that x exceeds 160 is 0.90 ,i.e;
P(X > 160) = 0.90
P( X-u/σ > 160-u /21 ) = 0.90
From the z% table we find that at value of x = -1.2816, the value of
P(X > 160) is 90%
which means; 160-u /21 = -1.2816
160 - = 21*(-1.2816)
= 160 - 26.914 = 133.09
Therefore, mean of the probability distribution is 133.09.
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Between which rational numbers does 30−−√ fall?
Rational number which does the square root of 30 fall is between 5 and 5.5.
Define rational number.A rational number is any number that can be expressed as a ratio (or fraction) of two integers. p/q where q is not equal to 0 is the form of a rational number, which is a sort of real number in mathematics. A rational number is any fraction with a non-zero denominator. 1/2, 1/5, 3/4, and other like numbers are a few examples of rational numbers.
Given,
25 and 36, which are the squares of 5 and 6, respectively, are the perfect squares that are most similar to 30.
Therefore, the square root of 30 will lie between 5 and 6. Additionally, the square root of 30 will be between 5 and 5.5 because it is closer to 25 than it is to 36.
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2v²+8v=-7 i need 5 points to graph range solutions
Given the quadratic equation below
[tex]\begin{gathered} 2v^2+8v=-7 \\ \Rightarrow2v^2+8v+7=0 \\ \therefore y=2v^2+8v+7 \end{gathered}[/tex]Note: y is function defined by v ( independent variable)
To plot the graph of the function above, we will take a range of values for v, i.e
[tex]\begin{gathered} -2\le v\le2 \\ \text{The range}\Rightarrow-2,-1,0,1,2 \end{gathered}[/tex]Given the range of values above, find the corresponding y-values . This can be done by substituting for v in the quadratic equation above
[tex]\begin{gathered} \text{when v=-2} \\ y=2(-2)^2+8(-2)+7=2(4)-16+7=8+7-16=15-16=-1 \end{gathered}[/tex][tex]\begin{gathered} \text{When v=-1} \\ y=2(-1)^2+8(-1)+7=2(1)-8+7=2+7-8=9-8=1 \end{gathered}[/tex][tex]\begin{gathered} \text{When v=0} \\ y=2(0)^2+8(0)+7=0+0+7=7 \end{gathered}[/tex][tex]\begin{gathered} \text{When v=1} \\ y=2(1)^2+8(1)+7=2+8+7=17 \end{gathered}[/tex][tex]\begin{gathered} \text{When v=2} \\ y=2(2)^2+8(2)+7=2(4)+16+7=8+16+7=31 \end{gathered}[/tex]The table of values is shown below
Hence, the graph of the solution is shown below
Using only a compass and straightedge, construct an isosceles triangle with base and legs congruent to the segments shown below.
I will write out the procedure to draw the isosceles triangle;
- Using the straight edge, measure the length of the base and draw a straight line congruent to the base length.
- Measure the length of the legs.
- Using the compass, set the compass to the same length as the length of the legs.
- From each edge of the base line drawn, Use the compass (already set to the length of the legs) to draw an arc each at the top of the base line;
- Then join each edge of the base line to the point at which the two arcs meet.
- Then you'll have an isosceles triangle, with base and legs as shown above.
Taylor received a paycheck of $1575. First, she spent 30% of her paycheck to make a house payment. Next, she spent 3/14 of the remaining amount to make a car payment. What amount was still left over from Taylor's paycheck after these two payments?
$866.25
1) Gathering the data
$1575
she spent 30%
she spent 3/14
2) Let's calculate it, starting with the 30% expense. Writing a factor, we have already the value:
1575 x ( 1 -0.3)
1575 x (0.7)
1102.50
Now let's proceed with the deduction of 3/14, which can be calculated through that:
1102.5 -3/14x (1102.5)
$866.25
3) Hence, Taylor's balance was after those payments of $866.25
help help help help help help help help help help help help help help help help help help helppppooppppppppp
From the given figure
The prism formed from 5 cubes long, 2 cubes wide, and 2 cubes height, then
Its length = 5 cubes
Its width = 2 cubes
Its height = 2 cubes
Since the side of each cube = 1/2 cm, then
Its length = 5 x 1/2 = 5/2 cm
Its width = 2 x 1/2 = 1 cm
Its height = 2 x 1/2 = 1 cm
The volume of the prism = length x width x height, then
[tex]\begin{gathered} V=\frac{5}{2}\times1\times1 \\ V=\frac{5}{2}cm^3 \end{gathered}[/tex]The volume of the prism is 5/2 cubic cm
The answer is A
Jerome is making beef stew for his family. The recipe calls for 3.5 pounds (lbs.) of stew meat. He notices that he has 1.25 pounds (lbs.) in his refrigerator. How much stew meat should buy when he goes to the grocery in order to have enough? a) What operation (add, subtract, multiply or divide) would you use to solve this? b) How did you know?
EXPLANATION
Let's see the facts:
Call for---> 3.5 lbs of stew meat
Refrigerator -------> 1.25 lbs stew meat
He would buy:
Required - Available ----> 3.5 - 1.25 = 2.25 lbs of stew meat
The operation that we apply is subtraction because 3.5lbs (required) is greater than 1.25lbs (available).