Alice plans to buy a house. She has $2,000 in her savings account.
She plans to contribute $150 to the account each month.
We know that with each month, n, she deposits $150 and so, each month, her savings account balance increases by $150.
This simply means that after n months, her savings account balance would have increased by:
150 * n = 150n
Her initial balance was $2000, therefore, her balance after n months will be the sum of 150n and the amount that was initially there.
That is:
f(n) = 2000 + 150n
This is the function that describes the relationship between the number of months and her balance.
Find the surface area of a cylinder with a height of 7 in and a base diameter of 8 in.
Use the value 3.14 for pi and do not do any rounding.
Be sure to include the correct unit.
The total surface area of the cylinder whose height is 7 units and diameter is 8 units is 226.08 units.
What is surface area?
The surface area of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves or the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated. This definition of surface area, based on infinitesimal calculus methods, uses partial derivatives and double integration.
The formula to calculate the total surface area of a cylinder is:
[tex]S = 2\pi rh + \pi r^2[/tex]
Where, S = surface area, r = radius, and h = height
As given in the question,
height (h) = 7 units
diameter (d) = 8 units
Since, r = d/2
So, r = 8/2 = 4 units
putting these values in the formula:
[tex]S = (2\times 3.14 \times 4 \times 7)+( 3.14 \times 4^2)[/tex]
[tex]S = (2\times 3.14 \times 4 \times 7)+( 3.14 \times 16)[/tex]
[tex]S = 175.84 + 50.24\\[/tex]
S = 226.08 units
Therefore, Surface area of the cylinder is 226.08 units
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Together, Nora and Addison own 152 shares of stock. Nora has 4 less than three times Addison's amount. How many shares does each girl have?
The number of shares that Nora has is 113.
The number of shares that Addison has is 39.
How many shares do they have?Let x represent the amount of shares that Addison has
Shares that Nora has = 3x - 4
The sum of shares they both have : 3x - 4 + x = 152
In order to determine the value of x, take the following steps:
Combine similar terms together: 3x + x = 152 + 4
Add similar terms: 4x = 156
Divide both sides by 4 : x = 156/ 4 = 39
Shares that Nora has = 3(39) - 4
117 - 4 = 113
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use the function f=8v to find the value of f when v =8
EXPLANATION
Given the function f= 8v
And the v-value = 8
Replacing this on the equation:
f= 8*8 = 16
Answer: f=16
NEED HELP ASAP
The graph compares the ages of 100 randomly selected visitors at a beach in January and in July. Select from the drop-down menu to correctly complete the statement. On average, visitors in January were Choose... years older than visitors in July.
From the given box and whisker plot, On average, visitors in January were 10 years older than visitors in July.
How to Interpret Box and Whisker Plot?A box and whisker plot is a graph plot that indicates whether a distribution is skewed and whether there are potential unusual observations (outliers) in the data set.
Now, the way to interpret it is as follows;
The left side of the box is the lower quartile. The right side of the box is the upper quartile. The box covers the interquartile interval, where 50% of the data is found.The vertical line that split the box in two is referred to as the median. The whiskers are the two lines outside the box, that go from the minimum to the lower quartile and then from the upper quartile to the maximum.Now, looking at the box and whisker plot for January and July, we can say that those in January are approximately 10 years older than those in July.
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The diagram represents a ramp in the shape of a right triangle and the lengths of two of its sides in feet. What is the length of the round in feet?
Answer:
61 feet
Explanation:
The length of the ramp is the hypotenuse of the right triangle formed.
To find the hypotenuse, use the Pythagorean Theorem:
[tex]\begin{gathered} Hypotenuse^2=Base^2+Altitude^2 \\ x^2=60^2+11^2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} x=\sqrt{60^2+11^2} \\ x=\sqrt{3721} \\ x=61\text{ ft} \end{gathered}[/tex]The length of the ramp is 61 feet.
Bobby can work at most 20 hours next week, but she needs to earn at least $150. Herdog-walking job pays her $6 per hour and her iob as a car wash attendant pays her $10 perhour. If d is the number of hours she walks dogs this week and w is the number of hours sheworks at the car wash, write a system of inequalities that represents Bobby's situation.
Solution:
Let d represent the number of hours Bobby walks dogs,
and w be the number of hours she works at the car wash.
Given that she can work at most 20 hours next week, this implies that the total number of hours she works is expressed as
[tex]d+w\leq20[/tex]If her dog-walking job pays her $6 per hour, this implies that for d number of hours, she will earn
[tex]\begin{gathered} \frac{\$6}{1\text{ hour}}\times d\text{ hours} \\ =\$\text{ 6d} \end{gathered}[/tex]and her iob as a car wash attendant pays her $10 per hour, similarly for w number of hours, she will earn
[tex]\begin{gathered} \frac{\$10}{1\text{ hour}}\times w\text{ hours} \\ =\$10w \end{gathered}[/tex]Given that she needs to earn at least $150, this implies that her total earnings will be expressed as
[tex]6d+10w\ge150[/tex]Hence, the system of inequalities that represents Bobby's situation is:
[tex]\begin{gathered} d+w\leq20 \\ 6d+10w\ge150 \end{gathered}[/tex] Andre graphed the parent function f(x) and
1
a new line d(x). If d(x) will have a slope of 4
and a y-intercept of 9, write a function to
represent d(x) as a transformation of f(x).
Answer:Its d(x)=1/4f(x)+9, mate
Step-by-step explanation:I just guessed and got it correct lol, also its "1/4" as a fraction
Which expression is equivalent to -5/3 x
Answer:
-1 2/3 x
Step-by-step explanation:
This is not that difficult. But I suggest that you provide answer options.
pls mark brainliest
11. It takes 4 hours to type 8 memos. How long will it take to type 56 memos?
Answer:28
Step-by-step explanation:if the unknown hour is x
then it would be
4hr=8memos
x hr=56 memos
cross multiply that would be
4×56÷8=28
and to check this answer you can find how many hours it would take to write one memo and multiply it by 28(your answer) that would be
x hr=1 memo
4hr =8 memo
cross multiply that would be
8÷4=
and then check it by doing 28 × 2=56
The time taken to type 56 memos will be 28 hours.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that it takes 4 hours to type 8 memos. The time taken to type 56 memos will be calculated as,
8 memos = 4 hours
56 memos = ( 56 x 4 ) /8
56 memos = 28 hors
Therefore, it will take 28 hours to type 56 memos.
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Write an equivalent expression for (x+2)+(x+2)
We will proceed as follows in order to get an equivalent expression:
[tex](x+2)+(x+2)=(x+x)+(2+2)=2x+4[/tex]So, one equivalent expression is 2x + 4.
Hiro picks up four digits card, he says: I can make a multiple of 10 with these cards. I can also make a number that rounds to 5300 and a number where the digit 8 is worth 800?
i need help with this question
In the given expression
[tex]x^5+32y^3=\ln y[/tex]To differentiate it with respect to it, we will writ y' for every term of y
The differentiation of
[tex]x^5=5x^{5-1}=5x^4[/tex]The differentiation of
[tex]32y^3=32(3)y^{3-1}y^{\prime}=96y^2y^{\prime}[/tex]The differentiation of
[tex]\ln y=\frac{1}{y}(y^{\prime})=y^{-1}y^{\prime}[/tex]Now let us write all of them in one line
[tex]5x^4+96y^2y^{\prime}=y^{-1}y^{\prime}[/tex]Put the terms of y' on one side and the other term on the other side
[tex]96y^2y^{\prime}-y^{-1}y^{\prime}=-5x^4[/tex]Take y' as a common factor
[tex]y^{\prime}(96y^2-y^{-1})=-5x^4[/tex]Divide both sides by the bracket
[tex]y^{\prime}=\frac{-5x^4}{(96y^2-y^{-1})}[/tex]Since the given point is (-2, 1), then
x = -2 and y = 1
Substitute them to find y'
[tex]\begin{gathered} y^{\prime}=\frac{-5(-2)^4}{(96\lbrack1\rbrack^2-\lbrack1\rbrack^{-1})}=\frac{-5(16)}{(96-1)}=\frac{-80}{95} \\ y^{\prime}=-\frac{16}{19} \end{gathered}[/tex]The value of y' is -16/19
Using the idea of the Empirical Rule for a normal distribution, explain what percent of individuals would fall in the given range. iܒܫܡܗ Si The range of IQ scores from 80 to 120, when the mean IQ score is 100 and the standard deviation is 10.
SOLUTION
Answer = 95.5%
From this information given.
We have a mean value of 100 and a standard deviation value of 10
To obtain the range from 80 to 120.
This will be moving 2(S.D) to the left and 2(S.D) to the right of the mean.
From theory, values within 2S.D from the mean, represent 95.5% of the given data.
Therefore, the percent of individuals that would fall in the given range is
95.5%
The points R, S, T and U all lie on the same line segment, in that order, such that the ratio of RS:ST:TURS:ST:TU is equal to 1:1:4.1:1:4. If RU=54,RU=54, find RS.RS.
The segment RS has a length of 9 units
How to determine the length of the segment RS?From the question, the partition of the line segment is given as
RS : ST : TU = 1 : 1 : 4
Where the endpoints of the line segments are R and U
This means that the length RS can be calculated using the following equation
Length RS = Ratio of RS/Sum of the ratios x The length of RU
Substitute the known values in the above equation
So, we have
Length RS = 1/(1 + 1 + 4) x 54
Evaluate the sum
Length RS = 1/6 x 54
Evaluate the products
Length RS = 9
Hence, the length of the segment RS is 9 units
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PLS HELP I HAVE LESS THAN 20 MINUTES!!!!
The statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
Given is the following statement - "Samuel will get 25 or more for mowing the lawn".
The given statement is -
Samuel will get $25 or more for mowing the lawn.
Assume that Samuel gets $x for mowing the lawn.
Then according to the question, we can write the inequality as -
x ≥ 25
" ≥ " sign to represent either 25 or more.
So, the inequality can be written as x ≥ 25 and the graph number [2] represents the correct graph.
Therefore, the statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
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Find the mean of these numbers: 5, 11, 2, 12, 4, 2Need solution :D
SOLUTION
We want to find the mean of the numbers 5, 11, 2, 12, 4, 2
To do this, we add the numbers and divide by the total numbers.
The numbers are 6 in numbers, so the mean
[tex]\begin{gathered} mean=\frac{5+11+2+12+4+2}{6} \\ =\frac{36}{6} \\ =6 \end{gathered}[/tex]Hence the answer is 6
Simplify completely (7x²+11x-6)/(7x²-10x+3)
One way of simplifying the given expression is by factoring them, and then simplifying the common terms.
So, we need to write:
[tex]\begin{gathered} 7x^{2}+11x-6=7(x-a)(x-b) \\ \text{and} \\ 7x^{2}-10x+3=7(x-c)(x-d) \end{gathered}[/tex]The constants a and b are the zeros of the first expression, and the constants c and d are the zeros of the second expression.
So, we can find those zeros using the quadratic formula. We obtain, for the first expression:
[tex]\begin{gathered} x=\frac{-11\pm\sqrt[]{11^{2}-4(7)(-6)}}{2(7)} \\ \\ x=\frac{-11\pm\sqrt[]{289}}{14} \\ \\ x=\frac{-11\pm17}{14} \\ \\ a=\frac{-11-17}{14}=-2 \\ \\ b=\frac{-11+17}{14}=\frac{6}{14}=\frac{3}{7} \end{gathered}[/tex]And, for the second expression, we obtain:
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{(-10)^{2}-4(7)(3)}}{2(7)} \\ \\ x=\frac{10\pm\sqrt[]{16}}{14} \\ \\ x=\frac{10\pm4}{14} \\ \\ c=\frac{10-4}{14}=\frac{6}{14}=\frac{3}{7} \\ \\ d=\frac{10+4}{14}=1 \end{gathered}[/tex]Then, we can write:
[tex]\begin{gathered} 7x^2+11x-6=7(x-(-2))(x-\frac{3}{7})=7(x+2)(x-\frac{3}{7}) \\ \\ 7x^2-10x+3=7(x-\frac{3}{7})(x-1) \end{gathered}[/tex]Thus, the given function can be simplified as follows:
[tex]\frac{7x²+11x-6}{7x²-10x+3}=\frac{7(x+2)(x-\frac{3}{7})}{7(x-\frac{3}{7})(x-1)}=\frac{x+2}{x-1}[/tex]Therefore, the answer is:
[tex]\mathbf{\frac{x+2}{x-1}}[/tex]The ------------- of a circle is a line segment that joins two points on the circumference of the circle and passes through the centre of the circle
Solution
The Diameter of a circle is a line segment that joins two points on the circumference of the circle and passes through the centre of the circle
Reflect (1, -3) over the y-axis.
Then translate the result down 1 unit.
What are the coordinates of the final point?
Answer:
(-1 , -4)
Step-by-step explanation:
Hello!
Refer to the graph for the reflection and translation.
The coordinates of the final point would be (-1,-4), given the x and y-values of the point.
What's 2,412 Divided by 25
Answer:
96.48
Step-by-step explanation:
The answer is 96.48.
Answer:
96.48
Step-by-step explanation:
2,412 divided by 25 equals 96.48
A group of 60 students arerandom randomly selected to take a one minute fitness test using a jump rope 30 students are in first grade and 30 students are in 7th grade the following following status information is calculated using the number of jumps completed him one minute they sell me samples what interest rate can be used
we get that the final price of a 16-ounce smoothie is:
[tex]3.69+1.06+0.94-0.75=4.94[/tex]$4.94
Factor the following expression completely.x4 - 16
Given:
[tex]x^4-16[/tex]Required:
To factor the given expression.
Explanation:
Consider the given expression
[tex]x^4-16[/tex]Now
[tex]\begin{gathered} x^4-16=(x^2)^2-(4^)^2 \\ \\ =(x^2-4)(x^2+4) \\ \\ =(x^2-2^2)(x^2+4) \\ \\ =(x-2)(x+2)(x^2+4) \end{gathered}[/tex]Final Answer:
[tex]x^4-16=(x-2)(x+2)(x^2+4)[/tex]My answer I correct or no please help
The product of 8 and a number k increased by 12 , 8K+12
What is algebraic expression?Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables. Variables and constants can both be used in an algebraic expression. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + can algebraic symbol or set of symbols that includes one or more integers, variables, and arithmetic operationsTo learn more about Algebraic expression refer to:
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PLEASE HELP
A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random, find the probability that it is yellow or green.
p(Yellow or not green)= ?
Answer:
I think the answer is 94/139
Step-by-step explanation:
Answer:
65/139
Step-by-step explanation:
Total number of candies - 139
No of yellow and green - 65
Thus probability - 65/139
How do you know when an equation has one solution? A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define an equation with one solution
You can tell that an equation has one solution if you solve the equation and get a variable equal to a number. A system of linear equations has one solution when the graphs intersect at a point.
STEP 2: Examine the options
An equation is said to have "no solution" when the coefficients are the same and the constants are different as seen below:
[tex]\begin{gathered} 4x+12=24+4x \\ 4x-4x=24-12 \\ 0=12 \end{gathered}[/tex]When the coefficients are the same and the constants are the same, the equation is said to have "infinitely many solutions as seen below:
[tex]\begin{gathered} 4x-14=-6-8+4x \\ 4x-14=-14+4x \\ 4x-4x=-14+14 \\ 0=0 \end{gathered}[/tex]When the coefficients are different, the equation is said to have one solution as seen below:
[tex]\begin{gathered} 2x+56=3x-12 \\ 2x-3x=-12-56 \\ -x=-68 \\ x=68 \end{gathered}[/tex]Hence, the answer is:
"When the coefficients are different"
Dean started with 5 metersof yarn. He used 300millimeters of yarn each dayfor 5 days. How manymeters of yarn does Deanhave left?
Given:
Dean started a yarn with 5 meters. He used 300millimeters of yarn each day for 5 days.
Required:
Find how many meters of yarn Dean has left.
Explanation:
We know that 1 meter = 1000milimeters
Dean used meters of yarn in the five days
[tex]\begin{gathered} =\frac{300\times5}{1000} \\ =\frac{3}{2}\text{ meter} \end{gathered}[/tex]The left meters are:
[tex]\begin{gathered} =5-\frac{3}{2} \\ =\frac{10-3}{2} \\ =\frac{7}{2} \\ =3.5 \end{gathered}[/tex]Final Answer:
Thus 3.5 meters of yarn left
Write a rational expression to determine how many cubbies high the book shelf will be.
Answer:
[tex]\frac{x^2-8x-65}{x+1}[/tex]
Explanation:
The height of each small division is x + 1, and the total height is x² + 6x + 5. Then, the number of small division is the total height divided by the small division height.
what is the exact value of tan (-3pi/4)
Answer:
1
Step-by-step explanation:
= 186x – 30y5х – 25y= 15
Answer:
There are infinitely many solutions
Explanation:
Given the system of linear equations:
[tex]\mleft\{\begin{aligned}6x-30y=18 \\ 5x+25y=15\end{aligned}\mright.[/tex]To solve using Matrices, we write the equation in the form:
Ax = b
Where A represent the matrix of the coefficient of the variables x and y
x represent the matrix of the variables x and y
and b represents the matrix of the constants on the right hand side.
In matrix form, we have:
[tex]\begin{bmatrix}{6} & {-30} \\ {5} & {-25}\end{bmatrix}\begin{bmatrix}{x} \\ {y}\end{bmatrix}=\begin{bmatrix}{18} \\ {15}\end{bmatrix}[/tex]We must have a nonzero determinant for A
The determinant of A is:
[tex]\begin{gathered} (-25\times6)-(-30\times5) \\ =-150+150 \\ =0 \end{gathered}[/tex]The determinant of A is zero, without going far, we conclude that the system has infinite number of solutions.
2. Which pair of numbers has the least common multiple with the greatest value?
4 and 8
4 and 9
5 and 7
6 and 8
Answer:
4 and 9
Step-by-step explanation:
4 x 8 = 32
4 x 9 = 36
5 x 7 = 35
(6 x 4 = 24 and 8 x 3 = 24)