Marsha deposited $5500 into savings with 5% interest rate
1st year, Marsha will earn : [tex]0.05 \times 5500 = 275[/tex]
2nd year, Marsha will earn: [tex]0.05 \times 5775 = 288.75[/tex]
3rd year, Marsha will earn: [tex]0.05 \times 6063.75 = 303.19[/tex]
4th year, Marsha will earn: [tex]0.05 \times 6366.94 = 318.35[/tex]
How many inches are in 5 1/4 feet?
Answer: 63 inches
Step-by-step explanation:
Answer:
63 inches
Hope this helps :)
[tex]\left \{ {{y=x^2+x-1} \atop {y + 2 x = 3}} \right.[/tex]
Solve the following system of equations algebraically or by graphing, and give the answer as points. Which method did you pick and why?
How could you check your answer afterwards?
Solving the system of equations using the algebraic method gives x = 1 or x = -4
How to solve the system of equations algebraically?Given: y = x²+x-1 and y+2x=3
In order to solve the system of equations algebraically
First, rewrite y+2x=3 to make y the subject:
y = 3-2x
Then, equate the two y of the equations and solve for x:
x²+x-1 = 3-2x
x²+x-1-3+2x = 0
x²+3x-4 = 0 (factorize)
x²+4x-1x-4 = 0
(x-1)(x+4) = 0
x-1 = 0 or x+4 = 0
x = 1 or x = -4
Therefore, the solution of the system of equations is x = 1 or x = -4
I pick the algebraic method because it is easier, faster and more accurate
I can check my answer by substituting the values of x into the equation
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Answer:
(-4, 11) and (1, 1)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x^2+x-1\\y+2x=3\end{cases}[/tex]
The solutions to the given system of equations are the points of intersection of the two graphs.
To solve the given system of equations algebraically, first rearrange the second equation to make y the subject:
[tex]\implies y=3-2x[/tex]
Substitute the found expression for y into the first equation:
[tex]3-2x=x^2+x-1[/tex]
Rearrange to a quadratic equation and factor:
[tex]x^2+3x-4=0[/tex]
[tex]x^2+4x-x-4=0[/tex]
[tex]x(x+4)-1(x+4)=0[/tex]
[tex](x+4)(x-1)=0[/tex]
Apply the zero-product property to solve for x:
[tex](x+4)=0\implies x=-4[/tex]
[tex](x-1)=0\implies x=1[/tex]
To find the y-values of the solutions, substitute the found x-values into the rearranged second equation:
[tex]x=-4 \implies y=3-2(-4)=11[/tex]
[tex]x=1\implies y=3-2(1)=1[/tex]
Therefore, the solutions to the given system of equations are:
(-4, 11) and (1, 1)Find the values of x and y that satisfy the equation.
22 + 1/5yi = 2x - 2
Answer:
[tex]x=12, y=0[/tex]
Step-by-step explanation:
[tex]22+\frac{1}{5}yi=2x-2 \\ \\ (24-2x)+\frac{1}{5}yi[/tex]=0[/tex]
Setting the real and imaginary parts of the left hand side equal to 0,
[tex]24-2x=0 \implies x=12 \\ \\ \frac{1}{5}y=0 \implies y=0[/tex]
consider the matrix
what is the value of |C|
If the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12
The given matrix is
C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]
The matrix is defined as the set of numbers that arranged in rows and columns to form a rectangular array. The numbers in the matrix are called the elements of the matrix.
Here we have to find the determinant of the matrix C
The determinant of the matrix is defined as the scalar value calculated for a given square matrix.
The determinant of C is represented by |C|
Then,
C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]
|C| = -6×4 - 6×-2
= -24 -(-12)
= -24 + 12
= -12
Hence, if the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12
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Ms. Patel purchased some pliers, wrenches, and chisel sets for her shop. She bought twice as many pliers that cost $17. 50 each as wrenches that cost $21. 50 each. She bought 3 fewer chisel sets than pliers. How many of each tool did Ms. Patel buy if she paid a total of $141 and each chisel set costs $28?
NEED ASAP!
This comes to $141, indicating that Ms. Patel spent that money on four sets of pliers, two wrench sets, and a chisel set.
Define the meaning of the term ratios?A ratio is the relationship and comparison involving two numbers belonging to the same unit in order to determine how much larger one number is than the other.The given condition states that;
For her shop, Ms. Patel bought some sets of chisels, wrenches, and pliers. She purchased twice as many wrenches, which were $21.50 each, as she did pliers, which were $17.50 each. She purchased 3 fewer sets of chisels than pliers.Make a ratio first.
This ratio might be expressed as 4:2:1 (in pliers, wrenches, and chisels).
Then, multiply every one of these sums by their respective prices before adding them all up.
Pliers : 4 times 17.50 equals $70
Wrenches : $2 x $21.5 = $43
Chisels : 1 x 28 equals $28
Thus,
Sum = $70 + $43 + $28
Sum = $141
This amounts to $141, proving that she purchased a chisel set, two wrench sets, and four pairs of pliers.
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represent the following expressions as a power of the number a (a≠0) (a^-1xa^-2)^-3
The solution of the exponential expression will be a⁹.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.
Given exponential expression is (a⁻¹ x a⁻²)⁻³. The expression will be solved as below,
E = (a⁻¹ x a⁻²)⁻³
The base is the same and the variables are in multiplication with powers then the powers will be added,
E = (a⁻³)⁻³
E = a⁹
Therefore, the solution of the exponential expression will be a⁹.
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PLEASEE HELP ME !! Find the volume of each shape and then compare do not reduce your fractions.
Answer:
1.) 150/512 in.
2.) 64/125 in.
Step-by-step explanation:
1.) V = l x w x h That's the formula to find the volume of a rectangle
V = 6/8 x 5/8 x 5/8 in. Plug in the numbers
V = 150/512 in. Multiply
V = 75/256 in. Simplify
Since you're asked to not reduce don't write this answer. I only put it to show that it can be simplified.
2.) V = l^3 This is the formula to find the volume of a cube
V = (4/5)^3 in. Plug in the numbers
V = 64/125 in. Miltuply
a grocery store has an average sales of $7,100 per day. the store introduced several advertising campaigns in order to increase sales. to determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. it was found that the average was $7,275 per day. from past information, it is known that the standard deviation of the population is $1,500. we know that the test statistic is 1.1667. find the p-value.
The P value of the question in the given condition is less than 0.05 hence it reject the null hypothesis.
What is null hypothesis?According to the null hypothesis, an independent variable and a dependent variable have no association with one another. The results might be the result of an experimental or sampling error if the hypothesis indicates a link between the two factors. There is a relationship in the measured phenomena, but, if the null hypothesis is incorrect.
First we find the value of small z
z = (x - μ) / (α / [tex]\sqrt{100}[/tex])
z = (7275 - 7100) / (1500/[tex]\sqrt{100}[/tex])
z = (175) / 150
z = 1.1667
As we have verified the test statistic value and it matched.
Then,
P value approach
Hence P value must be equal to 0.0013
As p value is less than 0.05 , Reject the null hypothesis.
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Can yall help me on this?
x-intercept is (-250, 0) and y-intercept is (0, 100)
What is x-intercept and y-intercept
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.
First, find x-intercept
For x-intercept it means y = 0
observe the graph and see the blue line cuts the x-axis when y = 0
We see, x = -250
so, the x-intercept is = (-250, 0)
Now, same thing do to find y-intercept
For y-intercept it means x = 0
observe the graph and see the blue line cuts the y-axis when x = 0
We see, y = 100
so, the y-intercept is = (0, 100)
Therefore, x-intercept is (-250, 0) and y-intercept is (0, 100).
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What is the least common multiple of 8, 29, and 22?
Answer:
1
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
x +
y
The equation in standard form is x - y = 9
How to determine the equation in standard form?From the question, we have the following parameters that can be used in our computation:
Points = (8, –1) and (2, –5)
Point-slope form is y + 1 = (x – 8).
Recall that the point-slope form is y + 1 = (x – 8).
So, we have
y + 1 = (x – 8)
Open the brackets
y + 1 = x – 8
Subtract 1 from both sides
y = x - 9
Rewrite as
-x + y = -9
Multiply through by -1
x - y = 9
Hence, the equation is x - y = 9
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Write an expression to represent:
8 less than the product of 2 and x.
Answer:
(2x)-8 is the correct answer
Step-by-step explanation:
Hope this helps
One gallon of paint usually covers about 350 square feet. How many square feet will 2.5 gallons cover? Show your work, including labeling your answer with the appropriate units of measure.
someone please help!!!
Answer:
875 square feet.
Step-by-step explanation:
Multiply 350 square feet by 2.5 gallons.
PLEASE FIND X ALGEBRA 1
Answer:
x = 135
Step-by-step explanation:
You need to find the supplementary angle of x.
Find the angle to the left of 100°. Recognize that the vertical angle theorem can be used. It equals 35°Now, you can use the triangle sum theorem to find the needed supplementary angle. 100+35+z=180, where z is the supplementary angle. z = 45.To find x, use the supplementary angle theorem. (The angles "lie" on a straight line, so they add up to 180°, or a straight line.)
45+x = 180
x = 135
Describe the relationship as parallel intersecting or skew AB or BC
Based on the image attached, the relationship are:
a). AB and BC - Both the segments are said to be perpendicular and they are intersecting at the point B.
b). AE and BF - Both segments are said to be parallel
c). EF and ED - Both are skew
d). Plane ABC and plane ABF - Both of the planes do intersect at point AB
e). Plane AED and plane BFC - Both of the given planes are known to be parallel
How do you know if lines are parallel intersecting or skew?if the ratio equality is accurate, parallel. If the lines are not parallel or if you can solve them as a system of simultaneous equations, the lines will intersect. If two crossing lines have a zero dot product, they are perpendicular.
If the lines are not parallel or intersecting, they are said to skew. Lines that are parallel never cross.
Therefore,
if lines are in the same plane, do not intersect, and are parallelif lines only meet at one point, then they are intersecting.If lines are on two distinct planes and don't intersect, they skew.Learn more about parallel intersection from
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Find the slope of a line crossing through the following points: (4, -3) and (10,-7). (Answer in a simplified fraction if necessary... Example: 4/5)
A jewel case contains 7 white gems, 5 green gems, and 3 blue gems. Gems are selected at random. Explain why
the events picking a green gem and then another green gem without replacement are dependent. Then, identify
the probability.
A.) P(green) is the same when it is known that a green gem has been picked already.
P(green and green) = 4/45
B.) Pgreen) is different when it is known that a green gem has been picked already.
P(green and green) = 2/21
C.) P(green) is different when it is known that a green gem has been picked already.
P(green and green) = 5/42
D.) Pgreen) is the same when it is known that a green gem has been picked already.
P(green and green) = 1/9
The second probability is affected by the first probability. So, we can say that this is a dependent probability.
Probability of choosing the first gem green = 1/3Probability of choosing the second gem green = 2/7Given,
Number of white gems = 7
Number of green gems = 5
Number of blue gems = 3
Total number of gems = 7 + 5 + 3 = 15
We have to find the probability when picking a green gem and then another green with out replacement are dependent.
Here,
Probability of choosing the first gem green = Number of green gems / total number of gems
Probability = 5/15 = 1/3
Now,
Number of green gems = 4
Total number of gems = 14
Probability of choosing the second gem green = Number of green gems / Total number of gems
Probability = 4/14 = 2/7
Here,
The second probability is affected by the first probability. So, we can say that this is a dependent probability.
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8. If a population doubles every 5 years, how many years will it take for the population to increase by 10 times
its original amount?
First: If the population gets multiplied by 2 every 5 years, what does it get multiplied by each year? Use this
to help you answer the question.
After ≈16.61 years the population will increased by times it's original amount.
What do you mean by population?
A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.
Given: If a population doubles every 5 years.
Assume, 'A' is the starting population, and 't' is the passing time in years.
Given the fact that a population doubles every five years, our population is growing exponentially, as per the question.
Here, the equation can be written as follows: [tex]A(t) = A(2)^{\frac{t}{5} }[/tex] (1)
We now need to determine when the population will have multiplied by 10 by that time.
Let's substitute [tex]A(t) = 10A[/tex] in the above equation.
[tex]10A = A(2)^{\frac{t}{5} }[/tex]
[tex]10 = (2)^{\frac{t}{5} }[/tex]
Taking the natural log of both sides we get:
[tex]ln10 = \frac{t}{5} \times ln2[/tex] {[tex]ln(a)^n= nln(a)[/tex]}
2.3025 x 5 = t x 0.6931
[tex]t = \frac{2.3025}{0.6931}\\t = 16.6096[/tex]
Therefore, After ≈16.61 years the population will increased by times it's original amount.
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Which comic section is formed in the image
Answer:hyper bola
Step-by-step explanation:
All you have to do is look up all the answers on images and then pick the one that looks the most similar
At a math convention, nine out of eleven people are bored by cable news. If there 122 at the convention who are not bored by cable news, then how many people at the convention are bored by cable news?
A total of 549 of people at the convention are bored by the cable news
How to determine the number of people at the convention that are bored?From the question, we have the following parameters that can be used in our computation:
Not bored = 122
Bored = 9/11 of the people
This means that
Not bored = 1 - Bored
So, we have
Not bored = 1 - 9/11
Evaluate
Not bored = 2/11
Recall that Not bored = 122
So, we have
2/11 * x = 122
Where x = the number of people
This gives
x = 122 * 11/2
Evaluate
x = 671
Recall that
Bored = 9/11 of the people
So, we have
Bored = 9/11 * 671
Evaluate
Bored = 549
Hence, the number of people at the convention that are bored is 549
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When parallel lines are cut by a transversal, then
Answer:
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
Please help!!
Solve this system of equations by graphing. First graph the equations, and then type the solution.
x+2y=2
y=–x+4
(you'll need to graph this).
By graphing, the solution of the system of equations is: (6, -2).
How to Solve a System of Equations by Graphing?To solve the system of equations by graphing, plot each of the line of the equations, then find the coordinates of the point where both lines intersect. Where they intersect is the solution to the systems of equations.
Given the following equations:
x + 2y = 2
y = -x + 4
x + 2y = 2 can be rewritten as y = -1/2x + 1. The graph for x + 2y = 2 will intercept the y-axis at 1 and also has a slope of -1/2. (It is the red line in the image below).
The graph of y = -x + 4 will also have a slope of -1 and intercept the y-axis at 4. (It is the blue line in the image below).
The graph of the equations are shown below, and they intersect at (6, -2), which is the solution to the system of equations.
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Divide.
8 3/4÷(−3 1/2)
Enter your answer as a mixed number, in simplified form, in the box.
what is the future amount of 12,000 invested for 5 years at 14% compounded monthly?
Answer:
$24,067.32
Step-by-step explanation:
If you look up a compound interest calculator and put in the data correctly you should get $24,067.32
10. Coach deposits $4250 in the bank and gets 2.3% simple interest. He keeps the money in the
bank for 42 months without any deposits or withdrawals. How much money will he have in the
bank after 42 months? Round to the nearest cent.
With the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.
What exactly are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.We can recall the PEMDAS steps in the following order: Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction (from left to right).So, we know that coach gets 2.3% simple interest monthly.
Now, calculate the total amount after 42 months as follows:
4250/100 × 2.3 = $97.75Then, on monthly basis, the coach gets $97.75 as interest.
Then, for 42 months:
97.75 × 42 = $4,105.5Hence, the total amount after 42 months:
4250 + 4,105.5 = $8,355.5Rounding off: $8,356Therefore, with the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.
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Correct question:
Coach deposits $4250 in the bank and gets 2.3% simple interest monthly. He keeps the money in the bank for 42 months without any deposits or withdrawals. How much money will he have in the bank after 42 months? Round to the nearest cent.
I need help like asap !!!
only numbers and decimal points
Answer:
b = 8 ft
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (10)² = b² + (6)²
→ 100 = b² + 36
→ b² = 100 - 36
→ b = √64
→ [ b = 8 ft ]
Hence, value of b is 8 ft.
Find the measurement of V.
Answer:
60°
Step-by-step explanation:
As we can conclude from the equal measured side lengths, this is an equilateral triangle so all angles have equal measurement.
Since the sum of interior angles in a triangle is equal to 180 to find the measure of angle V we need to divide 180 by 3:
180 ÷ 3 = 60
Solve this equation:
11x^2=-8
Answer:
See below
Step-by-step explanation:
11x^2 = - 8
x^2 = - 8/11
x = + - i sqrt (8/11) or - .727 i or .727 i
Ben bowled 151 and 183 in his first two games. What must he bowl in his third game to have an average of at least 1702
Answer:
1368
Step-by-step explanation:
let 3rd game be x
151+183+x=1702
334+x=1702
x=1702-334
x=1368
Factor completely, than place the factors in the proper location on the grid
Y^2x -y^x-20
Answer: Cannot be factored
Step-by-step explanation:
= Factor Y^2x -y^x-20
= Cannot be factored