The vertical intercept for the table showing the relationship for Jada's grandparents starting a savings account for her is starting savings amount in the account of $ 600.
What is the vertical intercept in a graph ?The vertical intercept in a graph is the point where a line intersects the vertical axis of the coordinate plane. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
The vertical intercept would therefore be first amount in the savings account by Jada's grandparents which is the $ 600. This is the amount when x = 0 or rather when x was the starting year of 2006.
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What is the sum of all the numbers between 1 and 100 which are divisible by 4 or 7?
Answer:
The sum of all numbers between 1 and 100 that are divisible by 4 or 7 can be found by using the concept of multiples. First, let's find all the multiples of 4 between 1 and 100. These are 4, 8, 12, 16, ..., 96. To find the number of multiples of 4 between 1 and 100, we can divide 100 by 4 and round down to the nearest whole number. That gives us 25. So, we have 25 multiples of 4 between 1 and 100.
Next, let's find all the multiples of 7 between 1 and 100. These are 7, 14, 21, 28, ..., 98. To find the number of multiples of 7 between 1 and 100, we can divide 100 by 7 and round down to the nearest whole number. That gives us 14. So, we have 14 multiples of 7 between 1 and 100.
Now we need to add up all the multiples of 4 and 7, but we have to make sure not to count any number twice, since some numbers may be divisible by both 4 and 7. For example, 28 is divisible by both 4 and 7. To avoid double counting, we need to find the multiples of 4 * 7 = 28. These are 28, 56, 84. There are 3 multiples of 28 between 1 and 100. So, we subtract these 3 numbers from the sum of all multiples of 4 and 7.
Finally, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is:
(4 + 8 + 12 + ... + 96) + (7 + 14 + 21 + ... + 98) - (28 + 56 + 84)
= (4 * 25) + (7 * 14) - (28 * 3)
= 100 + 98 - 84
= 114
So, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is 114.
A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
Does the region form a right triangle? Justify your answer.
Answer: no it does not
Step-by-step explanation: Because 1,007 squared is 1,014,049 and the sum of 911 squared is 829,921 and then 829 squared is 687,241 then add 829,921+687,241=1,517,162 when it should equal 1,014,049 which is the amount of 1,007 squared to make it a right triangle.
The solution is : no, it does not form a right triangle.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
given that,
A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
now, we get,
Because 1,007 squared is 1,014,049
and the sum of 911 squared is 829,921
and then 829 squared is 687,241
then add 829,921+687,241=1,517,162
when it should equal 1,014,049
which is the amount of 1,007 squared to make it a right triangle.
as we know that,
in right triangle,
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.
so, we get,
The solution is : no, it does not form a right triangle.
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increase the number 22.5 by 0.4 of it
Answer:
Step-by-step explanation:
22.9
16. The dolphins at the Harrison Aquarium are
fed 1/3 of a bucket of fish each day. The sea otters
ce
are fed 1/3 as much as the dolphins. How many
buckets of fish are the sea otters fed each day?
Answer:
1/9 buckets of fish
---------------
The dolphins are fed 1/3 of a bucket of fish and the sea otters are fed 1/3 as much as the dolphins.
That is 1/3 of 1/3 buckets:
1/3*1/3 = 1/9pg 558selling online according to a recent pew research center report, many american adults have made money by selling something online. in a random sample of 4579 american adults, 914 reported that they earned money by selling something online in the previous year.15 assume the conditions for inference are met. determine the critical value z* for a 98% confidence interval for a proportion. construct a 98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year. interpret the interval from part (b).
The true proportion of all American adults who would report having earned money by selling something online in the previous year lies between 0.178 and 0.221.
A confidence interval is computed from the sample data and provides a range of values within which the true population parameter is expected to lie. The confidence level is the probability that the confidence interval contains the population parameter.
Using this critical value, we can construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year. To do this, we use the formula:
confidence interval = sample proportion ± z* (standard error)
The sample proportion is the number of adults who reported earning money by selling something online (914) divided by the total sample size (4579), which gives us a proportion of 0.1997.
The standard error is calculated as:
standard error = √ [(sample proportion)(1 - sample proportion) / sample size]
Substituting the values, we get:
standard error = √ [(0.1997)(1 - 0.1997) / 4579] = 0.009
Plugging in the values, we get:
confidence interval = 0.1997 ± 2.33(0.009)
This gives us a confidence interval of 0.178 to 0.221.
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the satellite is in the shape of a rectangular prism. which polynomial represents the volume of the satellite? a rectangular prism with length 4 x minus 3 feet, a width of x plus 1 feet, and a height of x plus 2 feet.
The volume of the rectangular prism will be (4x - 3)(x + 1)( x+2) cubic feet.
What is the volume?The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.
Given that the length, width, and height of the rectangular prism are,
The volume of the rectangular prism will be calculated as,
Volume = Length x width x Height
Volume = (4x - 3)(x + 1)( x+2) cubic feet
Therefore, the polynomial for the volume will be (4x - 3)(x + 1)( x+2) cubic feet.
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5x+2y=-7 and 10x+4y= -14 no solution, solution, or infinite solution?
The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).
In general, a system of linear equations can have one of three possible outcomes:
One unique solution (as in this case)
No solution (if the equations are inconsistent)
Infinitely many solutions (if the equations are dependent)
To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.
First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:
-10x - 4y = 14
5x + 2y = -7
-5x = 7
Now we can solve for x:
-5x = 7
x = -7/5
We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:
5x + 2y = -7
5(-7/5) + 2y = -7
-7 + 2y = -7
2y = 0
y = 0
Therefore, the solution to the system of equations is (x,y) = (-7/5,0).
This is called a unique solution, meaning there is only one possible solution for the system of equations.
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Complete Question:
Solve
5x + 2y = -7
10x + 4y = -14
And find the number of solutions for the equation
y=-1/2x-1
y=1/4x-4
graphing method
I need help is due today!!!
The length of a living room is 12 feet and it’s width is 10 1/2 feet. The length of the room is being expanded by x feet. Select all the expressions that represent the area of the living room in square feet.
A. 10.5 (12x) square feet
B. (10.5 + 12 + x) square feet
C.10.5( 12 + x) square feet
D.126x square feet
E.(126 + 10.5) square feet
F.( 22.5 + x) square feet
Answer:
answer is A
Step-by-step explanation:
because area of a rectangle is L × B
or length × width
since the length is expanded by x
10.5 (12x)
Answer:
Option C
Step-by-step explanation:
The original length of the room = 12 feet
After expansion, the new length = [tex](12 + x)[/tex] feet
Width of the room = 10[tex]\frac{1}{2}[/tex] feet = 10.5 feet
Area of a rectangle = Length × Width
The shape of the living room is a rectangle.
∴Area of living room = [tex](12 + x)[/tex] feet × [tex](10.5)[/tex] feet
[tex]= 10.5(12 + x)[/tex] square feet
Expand the brackets or parenthesis by applying the Distributive Law:
[tex]= (12)(10.5) + (10.5)(x)[/tex] square feet
= [tex](125 + 10x)[/tex] square feet
∴Option C
With the information given, can you prove
that this quadrilateral is a parallelogram?
Yes
No
We can see here that with the information given, one can prove that this quadrilateral is a parallelogram. Thus, it is yes>
What is a quadrilateral?A polygon with four sides and four vertices (corners) is called a quadrilateral. Its internal angles add up to 360 degrees.
Squares, rectangles, parallelograms, trapezoids, and rhombuses are all examples of quadrilaterals.
We can see that looking at the quadrilateral, we can deduce that it is parallelogram. This is because the opposites sides are equal. Also, their opposite angles are equal.
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if \cos \theta =(4)/(9), tan\theta <0, sin\theta =?
Answer: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
Step-by-step explanation:
cosθ = 4/9
tan < 0
This means our reference angle is either in Quadrants II or IV, (where tangent is negative). Since cosine is positive, it must be Quadrant IV.
Therefore we know that sinθ will be negative.
we also know that [tex]cos^2(\theta) + sin^2(\theta) = 1[/tex], from the Pythagorean identities
.: 16/81 + sin^2(θ) = 1,
.: sinθ = [tex]\sqrt{\frac{65}{81} }[/tex]= [tex]\frac{\sqrt{65}}{9}[/tex]
But since this angle is in Quadrant IV, sinθ will be negative.
.: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
Suppose the following sequence of matrix operations was used to translate AABC.
The horizontal and vertical translations applied to ΔABC:
A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
What is matrix ?It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.
Given that,
[tex]\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right][/tex] = ?
After using matrix operation it can be further solved as,
[tex]\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right][/tex]
Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
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Help me with thiss Pllllllllll
Step-by-step explanation:
the answer for -1/4(-8x+12y)
2x-3y
Answer:
2x-3y
Step-by-step explanation:
For this equation we are using distributive property
-1/4(-8x) -1/4(12y)
↓ ↓
2x -3y
So, 2x-3y is the answer.
How many positive whole numbers less than 2016 have digit sum of 8?
The total number of numbers less than 2016 with a digit sum of 8 is 116 numbers.
How many positive whole numbers less than 2016 are there that have a digit sum of 8?The sum of the digits in the positive whole numbers is to be 8.
So the possibilities are obtained by means of permutation as follows:
Three 0's and an 8; ⁴P₁ = 4
One 1 and one 7, ⁴P₂ = 12
One 2 and one 6; ⁴P₂ = 12
One 3 and one 5; ⁴P₂ = 12
Two 1's and a 6; (⁴P₃/2!) = 12
One 1, one 2, and one 5; ⁴P₃ = 24
Two 2's and a 4; (⁴P₃/2!) = 12
Two 3's and a 2; (⁴P₃/2!) = 12
Two 4's and a 0; (⁴P₃/2!) = 12
Three 1's and a 5; (⁴P₃/3!) = 4
Total = 116 numbers
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Find the integral : [tex]\frac{x+1}{x(1+x.e^x)}[/tex]
The value of the equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex] after taking the integral is [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].
What is meant by the integral of an equation?
Calculating areas, volumes, and their extensions require the use of integrals, which are the continuous equivalent of sums. One of calculus' two fundamental operations is integration, which involves computing integrals. The other essential operation is differentiation. The area under the graph of a function for some interval can be expressed numerically as the integral (definite integral), or a new function can be created whose derivative is the original function (indefinite integral).
Given equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex]
Multiply and divide the equation by eˣ
The equation becomes [tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx[/tex]
Now substitute eˣx = a
Differentiating both sides
[eˣ + xeˣ]dx = da
eˣ[1+x]dx = da
Substituting the above in the equation
[tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx = \frac{da}{a(1+a)}[/tex]
Now add and subtract a in the numerator
[tex]\frac{1 da}{a(1+a)} = \frac{a-a+1}{a(1+a)} da = \frac{a+1-a}{a(1+a)} da = \frac{1}{a} da - \frac{1}{a+1} da[/tex]
Now taking integral
[tex]\int \frac{1}{a} da -\int \frac{1}{a+1} da = ln(a) - ln(a+1) + c = ln ( \frac{a}{a+1} ) + c[/tex]
Now substituting back the value of a = eˣx
Therefore the value of the equation after taking the integral is [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].
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A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 62. 7 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.
The density and mass are related to each other with the formula -
Density = mass/volume
So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.
Volume of hemisphere = 2/3πr³, where r represents radius.
Volume = 2/3×π×5³
Performing multiplication, division and taking cube
Volume = 261.8 feet³
Now, mass = density × volume
Mass = 62.7 × 261.8
Performing multiplication
Mass = 16,414.86 pounds
Rounding off
Mass = 16,415 pounds
Thus, the mass of liquid will be 16,415 pounds.
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how many times larger is a centigram than a milligram
A centigram is 100 times larger than miligram as evident through comparison of the two values.
We know that centi can be represented as 1/100 and milli will be represented as 1/1000. Now, the magnitudes representing each of these will be in relation to gram. So, further calculating the times with which centigram is larger than miligram.
For this, the expression to be used is -
Value = centigram/milligram
Keep the values in formula to find the comparison
Value = 1/100 ÷ 1/1000
Rewriting the expression
Value = 1000/100
Performing division on Right Hand Side of the equation
Value = 100
So, we see that centigram is 100 times larger than miligram.
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Jamal mows lawns and wants to save money. Jamal currently
has $25 and plans to save an additional $25 per month. Which
graph represents the number of months it will take Jamal to
save at least $250?
Answer: eat grass whor
Step-by-step explanation:
Samantha drove 468 miles from Omaha, Nebraska to Chicago, Illinois. She drove 251 miles during the first day. Set up an equation (where D represents the distance traveled during the second day) that could be used to find the distance Samantha traveled during the second day. Then, SOLVE the equation.
Answer:
the equation: 251+D=468
the answer: 217 miles
Step-by-step explanation:
Samantha drove a total of 468 miles, and she drove 251 miles on the first day. D would represent the distance traveled on the second day. The added distance traveled on both days will equal the total amount driven.
So, our equation will be 251 + D = 468.
To solve the equation, we can use the inverse operations method in order to isolate D(the variable) To do that, we have to subtract 251 from both sides(both sides so that the equation still has the same value).
D=468-251.
Now we can simplify the equation to:
D=217.
The answer is: 217 miles will be traveled on the second day.
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms. 8d-2-4d^3
For the polynomial "8d⁻² - 4d³" , the standard form is "-4d³ + 8d⁻²" , the degree is "3" and the leading coefficient is "-4" and the number of terms is "2" .
The polynomial is ⇒ 8d⁻² - 4d³.
To write the polynomial in standard form, we first rearrange the terms by putting the terms with the highest degree first ;
So , the standard form is ⇒ -4d³ + 8d⁻² ;
The degree of the polynomial is 3, because it is the highest power of the variable "d" in the polynomial "-4d³ + 8d⁻²" .
The leading coefficient of the polynomial is "-4" , because it is the coefficient of the term with the highest degree.
The polynomial has 2 terms, so it is a binomial.
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The given question is incomplete , the complete question is
Write the polynomial " 8d⁻² - 4d³ " in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.
A school T-shirt costs $7.84. The cost of 4 school T-shirts and a school sweater is $1.40 less that the cost of 2 school sweaters. Create an equation that can be used to find the cost of the sweater?
Answer:
4a + b - $1.40 = 2b
Step-by-step explanation:
Different style of problem here, so here's my guess
Let...
A = Tshirts
B = Sweaters
4a + b - $1.40 = 2b
4a + b indicates 4 shirts plus 1 sweater
The -$1.40 at the end indicates $1.40 less than
=2b indicates 2 sweaters
Melitha would like to purchase a music system worth of R12 000.And she is offered an interest rate of 7.5 p.a on a hire purchase agreement.The terms or the agreement on the loan are that 10% deposit is paid initially and the loan will be paid back monthly over a period of 3 years.
a.Calculate the cash deposit Melitha paid.
b.Calculate how much Melitha will have to pay over 3 years.
c.Calculate the monthly installment which Melitha will have to make.
d.What is the total amount that Melitha paid for the music system?
a) The cash deposit (down payment) that Melitha paid is R1,200.
b) The total amount (sum of periodic payments) that Melitha paid over 3 years is R12,094.20.
c) The monthly installment Melitha made is R335.95.
d) The total amount that Melitha paid for the music system is R13,294.20, including the total installments and initial deposit.
What is the down payment?The down payment is the initial cash deposit made for the purchase of an item on credit.
The down payment provides financial evidence of the transaction and testifies about the borrower's ability to undertake the credit arrangement.
a) Cash deposit = R1,200 (R12,000 x 10%)
N (# of periods) = 36 months
I/Y (Interest per year) = 7.5%
PV (Present Value) = R10,800 (R12,000 - R1,200)
FV (Future Value) = R0
Results:
Monthly Payment (PMT) = R335.95
Sum of all periodic payments = R12,094.20
Total Interest = R1,294.20
Total amount paid for the music system = R13,294.20 (R1,200 + R12,094.20)
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ratio of pirates to sailors was 18 to 19. If there were 198 sailors, how many pirates were there?
There were 198 sailors and the ratio of18 pirates, so 198 divided by 19 equals 10.4, meaning there were approximately 176 pirates.
Find the ratio of pirates to sailors
Ratio of pirates to sailors
= 18 : 19
Convert the ratio to a fraction
Ratio of pirates to sailors
= 18/19
Find the number of pirates
Number of pirates
= (18/19) × 198
Number of pirates = 176
The ratio of pirates to sailors is 18 to 19. This means that for every 19 sailors, there are 18 pirates. To figure out how many pirates there are when there are 198 sailors, we can use a proportion. First, set up the proportion with the ratio given. The ratio is 18:19, so the proportion is 18/19 = x/198. Then, cross multiply, 18 x 198 = 19x. Now, divide both sides by 19, and we get 18 x 198/19 = x. Then, solve for x by multiplying both sides by 19, and we get 18 x 198 = 19x. Finally, divide both sides by 198 to get x, and x =176. So, there were approximately 176 pirates.
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A line goes through points (-3,1) and (7,6). What is the equation of the line?????????
Answer:
y= 1/2x + 5/2
Step-by-step explanation:
................
The temperature at noon was $-4\degree$ C. By midnight, the temperature dropped $8\degree$ C. Which expression represents the temperature at midnight?
The temperature at midnight would be -4°C - 8°C since the temperature at noon was -4°C and at midnight it dropped 8°C.
The temperature at midnight would be -4°C minus 8°C, which can be expressed as:
-4°C - 8°C = -12°C
Therefore, the temperature at midnight would be -12°C.
Temperature is a measure of the degree of hotness or coldness of a body or an environment. It is a physical quantity that expresses the amount of thermal energy in a substance or a system, typically measured using a thermometer in units such as Celsius (°C) or Fahrenheit (°F). In general, the higher the temperature, the more thermal energy is present in the system, and the lower the temperature, the less thermal energy is present.
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HELLLPPPP PLEASEEEEEEEEEEEEE
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Answer: the home of it is 78 degrees
Step-by-step explanation:
as the angular bisector is shown then we can say that its right
Solve the following system equation, showing your work in the space
provided.
y = 5x + 3
-2x-4y= 10
Step-by-step explanation:
the first equation is already (without any transformation) expressing y in terms of x.
we can use that identity in the second equation :
-2x - 4(5x + 3) = 10
-2x - 20x - 12 = 10
-22x = 22
x = -22/22 = -1
and then we use the first equation to solve for y :
y = 5×-1 + 3 = -5 + 3 = -2
so,
x = -1
y = -2
f(-3) if f(x) =-4x -8
Answer:
f(-3)=4
Step-by-step explanation:
The answer is 4. To get f(-3), you must plug in -3 into the x.
Therefore, -4(-3)-8=f(-3).
Then you multiply -4 and -3. 12-8=f(-3)
Finally, you subtract 8 and get the answer:
f(-3)=4
pls help i don’t understand
Which graph shows the solution to the system of linear equations?
y = 2x − 2
4x − 2y = 4
- Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0.
- Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
- Coordinate plane with one line that passes through the points 0 comma 1 and 1 comma 2.
- Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0 and another line that passes through the points 0 comma 1 and 1 comma 2.
Answer:
A
Step-by-step explanation:
Answer: the answer is A
Step-by-step explanation: