Marie has $180 in a savings account in week 1. She plans to deposit $12 each following week. Assuming that she does not withdraw any money from her account, what will her balance be in week 20?

Answer:-32

Step-by-step explanation:

-12+(-20)

-12-20

-32

Answer: -32

Step-by-step explanation:

−12+(−20)=

-12 - 20= ==> adding a negative number is equal to subtracting by the positive version of that number. ?-20=?+(-20)

-(12+20)=-32

The pool will have 14, 477 gallons of water.

The amount of water that has leaked in 91 days = rate of leakage × number of days

Keep the values in formula

The amount of water that has leaked in 91 days = 11 × 91

Performing multiplication

The amount of water that has leaked in 91 days = 1001 gallons

Amount of water remaining after 91 days = total amount of water - the amount of water that has leaked in 91 days

Amount of water remaining after 91 days = 15,478 - 1001

Performing subtraction

Amount of water remaining after 91 days = 14, 477 gallons

Hence, after 91 days there will be 14, 477 gallons of water in the pool.

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Answer:

Step-by-step explanation:

We start by developing an equation for Line 1, and then use that to find the equation for Line 2.  We'll use the form of an equation for a straight line:

 y = mx + b,

where m is the slope and b the y-intercept (the value of y when x=0).

Line 1

Determine the slope, m, by calculating the "Rise/Run" between the two points (-3,-7) and (5,3).

Line up the two points from left to right (based on x) and then calculate:

  Rise:  (3 - (-7)) = 10

   Run:  (5 -(-3) = 8

The slope, m, is Rise/Run or (10/8)

The equation becomes y = (5/4)x + b

We could calculate b, the y-intercept, by entering one of the two given points and solving for b, but the only thing we need from this line is it's slope, m.  Slope is (5/4), which we'll use in the next step:  Line 2.

[Note:  Out of curiosity, here is the calculation for b:  Use point (5,3) in y = (5/4)x + b and solve for b.   3 = (5/4)*5 + b.  3 = (25/4) + b  b = -13/4.  This means that Line 1 is y = (5/4)x -(13/4)]

Line 2

The slope of a line perpendicular to the first is the "negative inverse" of the first line.  In this case, line 1's slope of (13/8) would become a slope of -(8/13) for line 2.

    Line 2:  y = -(8/13)x + b

We'll calculate b for this line by enetering the single point provided,  (-4,-2), and solving for b:

          y = -(8/13)x + b

        -2 = -(8/13)*(-4) + b

          -2 = (32/13) + b

          -2 - (32/13) =  b

b = -(26/13) - (32/13)

b = -(58/13)

The new line perpendicular to Line 1 and passing through (-4,-2) is:

          y = -(8/13)x -(58/13)

See attached graph.

Answer:

since the degree of the adjacent angles is 180°, we find the answer from that

Answer:

Step-by-step explanation:

it is a right triangle, the bottom right one is, from the drawing, 90 °, the sum of the internal angles of all the triangles is 180 °, so making 180 - 90 - 38 we have the missing internal angle of 52 °.

Then we find the outer angle, the inner-outer sum is 180 °, 180 - 52 = 128 ° (your answer)

Answer:

x=3 y=4

Step-by-step explanation:

-4x= -6y+12      -1

8x-4y = 8         -2

-4x+6y=12        -1

8x-4y = 8         -2

multiply first equation by 2:

2(-4x+6y=12)

= -8x+12y=24

add with 2nd equation;

-8x+12y=24

       +

8x-4y=8

-8x+8x=0

+12-4y=8y

24+8=32

0+8y=32

y=32/8

y=4

input y into any equation to get x:

-4x= -6(4)+12

-4x = -24+12

-4x= -12

-x= -12/4

x=3

Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.

Let the radius of the sphere be R.

So, the volume of the sphere is given by,

V = [tex]\frac{4}{3}\pi r^3[/tex]

Differentiating the above relation with respect to time 't' we get,

dV/dt = 4[tex]\pi r^2[/tex]. dr/dt

Given that, the change of radius (dr/dt) = 4 mm/s

When the diameter is 80 mm, then the radius = 80/2 = 40 mm

So the volume change when the diameter is 80 mm is given by,

dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s

Hence the volume increase in 802424.77 cubic mm/s.

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Answer:

He subtracted a term of [tex]2x[/tex] from both sides of the equation.

Answer: 4.5m

Step-by-step explanation:

because 12.5 can - by 2.5

then 9.0=9 -5.5=4.5

Answer:

Step-by-step explanation:

Comment

The graph below shows or implies that you start at very close to 4 and move downward and to your right

To find the beginning of the range, substitute 4 into the given equation

f(4) = 11 - 4

f(4) = 7

The range is

7 <y <-∞

Answer:

83.978 the thousandth digit is 3, 78.934 the thousandth digit is 8,84.765 the thousandth digit is 4

Answer:

Step-by-step explanation:

Ok:

1. Identify the thousandths digit

The numbers to the left of the decimal point are the ones and hundreds digits

The first number to the right of the point is the tenths digits

The second to the right of point i s the Hundreths

The third number to the right of point is the thounsandths which is what we are looking for!

2. Apply to problem!

1. 83.978 : Thousandths digit is 8

2. 78.934 : Thousandths digit is 4

3. 84.765 : Thousandths digit it 5

Extra tips and tricks writing as fractions!Ps: Some are not simplified!

1. 83.978= 83 978/1000 as fraction

2. 78.932= 78 932/1000 as fraction

3. 84.765= 84 765/1000 as fraction

The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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Ty has  2 5/6 pounds of coffee left after giving 5/6 pounds of coffee to his grandma

Fraction is a numerical quantity that is not a whole number

From the question,

Ty bought 3 4/6 pounds of coffee

converting 3 4/6 to improper fraction

we have 22/6

Ty gave his friend 5/6 pound of coffee to his grandma

To estimate how much coffee Ty has left

We substract Coffee given to his grandma from Coffee bought

That is,

22/6 - 5/6

= 17/6

= 2 5/6 pounds of coffee left

Ty has 2 5/6 pounds of toffee left. He gave 5/6 of what he bought to his grandma.

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Please find attached the graph of the image of ΔIJK following a translation transformation of (-17, 5), and a reflection across the line y = 5

A transformation is an operation that changes the location, size and shape of geometric figures.

The coordinates of the vertex of ΔIJK are; I(14, 8), J(8, 5), K(14, 2)

The translation transformation is 17 units left and 5 units up = T₍₋₁₇, ₅₎

The location of the vertices of the image of ΔIJK following the translation transformation are;

[tex]I(14,\, 8)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ I'(-3,\, 13)[/tex]

[tex]J(8, 5)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ j'(-9,\, 10)[/tex]

[tex]K(14, 2)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ K'(-3,\, 7)[/tex]

The coordinates of a point following a reflection across the line y = 1 are as follows;

The coordinates of the vertices of the image I'J'K' relative to the line y = 1 are;

I'(-3, 13), Relative point I'(-3, 12)

J'(-9, 10) has a relative point at (-9, 9)

K'(-3, 7) has a relative point (-3, 6)

The coordinates of the vertices of the reflected image are therefore;

(x, y)  [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex]  (x, -(y - 1))

Which gives;

I'(-3, 12)  [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-3, -12 + 1) = I''(-3, -11)

J'(-9, 9) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-9, -9 + 1) = I''(-9, -8)

k'(-3, 6)  [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] k''(-3, -6 + 1) = k''(-3, -5)

Please find attached the image of the ΔIJK following the translation and reflection transformation

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Answer:

1/9 > m

Step-by-step explanation:

-2(7+3m)+6m>3(3m-5)

Distribute.

-14-6m+6m>9m-15

Combine like terms.

-14>9m-15

1>9m

Get m to be alone.

1/9>m

       -2(7+3m) + 6m > 3(3m-5)

       -2(3m+7) + 6m > 3(3m-5)

The final answer is m < 1/9

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Part (a)

Each year is independent of any other. This allows us to simply multiply the probability values for each increase. Recall that P(A and B) = P(A)*P(B) if and only if events A & B are independent.

(0.65)*(0.65)*(0.65) = (0.65)^3 = 0.274625

=========================================

Part (b)

We calculated the probability of an increase for each of the 3 years back in part (a). Let's calculate we have a decrease 3 times in a row.

0.65 is the probability of increase for any given year, which makes 1-0.65 = 0.35 the probability of decrease for any given year.

Therefore (0.35)^3 = 0.042875 represents the probability of 3 decreases in a row.

Add this result to what we got in part (a)

0.274625+0.042875 = 0.3175

This is done because we could have 3 increases OR 3 decreases (pick one). Think of it like this P(A or B) = P(A) + P(B) where A & B are mutually exclusive events.

=========================================

Part (c)

In the previous part we calculated 0.042875 as the probability of 3 decreases in a row.

1-0.042875 = 0.957125 is the probability of at least one increase. Note how the events "no increases" and "at least one increase" are complementary events. They are opposite. One or the other must happen, which allows us to subtract from 1.

You can think of it like this

P(no increases) + P(at least one increase) = 1

P(at least one increase) = 1 - P(no increases)

Side note: none of the final answers have been rounded.

The reduced fraction is 7 using GCF method.The GCF is also known as the Highest Common Factor (HCF)

The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

The fraction = 14/66

The factors of 14 = 2×2×2×3

The factors of 28 = 11*3*2

The gcf is 2 × 2 = 4

Divide the denominator and numerator by 4

14 ÷2 = 7

14÷ 2 = 7

We get,

The fraction = 14/2 =7

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================================================

Explanation:

Part A)  Find P(-2)

We'll divide P(x) over (x+2) to get a quotient Q(x) and remainder 8 like so

P(x)/(x+2) = quotient + remainder/(x+2)

P(x)/(x+2) = Q(x) + 8/(x+2)

When multiplying both sides by (x+2), it clears out the fractions and we're left with this

P(x) = (x+2)*Q(x) + 8

From here, plug in x = -2 and simplify

P(x) = (x+2)*Q(x) + 8

P(-2) = (-2+2)*Q(-2) + 8

P(-2) = (0)*Q(-2) + 8

P(-2) = 0 + 8

P(-2) = 8

Luckily we don't need the value of Q(-2) since it cancels out with the zero.

-----------------------------------

Part B) Find P(2)

This time we'll plug in x = 2 and we'll get...

P(x) = (x+2)*Q(x) + 8

P(2) = (2+2)*Q(2) + 8

P(2) = 4*Q(2) + 8

P(2) = 4*5 + 8

P(2) = 20+8

P(2) = 28

Answer:

width = 35 m

Step-by-step explanation:

w is the width, then l = w + 5

Perimeter P = 2(l + w)

=> 150 =2(w + 5 + w)

75 = 2w + 5

2w = 70

w = 35

x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

What is, axis of symmetry, vertex and x - intercept?

A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.

A line's x-intercept is the location at which the x-axis is crossed.

Consider, the given equation,

[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]

Let,

[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex]             ..(1)

To find x - intercept, plug y = 0 in above equation,

[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]

Therefore, x = 1 and x = -7 are the x - intercepts.

Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.

So,

[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]

Plug x = -3 in equation (1)

[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]

Therefore, the vertex is, (-3, -4).

The x - coordinate of the vertex is the axis of symmetry.

Therefore, axis of symmetry is x = -3.

Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

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Answer: 47

Step-by-step explanation:

The value of Simple interest for the given data comes as $2550.

Given,

The Principal amount is equal to 12,000 dollars.

The Rate of Interest is stated at 4.25%.

The Total time period given for the question is 5 years.

Let the principal amount be considered as (P), the Rate of Interest per annum be (R), the Time period is (T), and Simple Interest is (S.I).

So, according to the given question,

P = $12,000

R = 4.25%

T = 5 years

We know, Simple interest can be calculated by multiplying the Principal amount with the Rate of Interest as well as the Time period.

If we write it mathematically, the formula will be,

S.I = PRT/100

=> S.I = (12,000* 4.25* 5)/100

=> S.I = (2,55,000)/100

=> S.I = $2550.

Hence, the value of Simple Interest will be 2550 dollars.

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Answer:

360 of 10%

360 x 10/100

36

now, 360 - 36 = 324

therefore, 324 students attended haley elementry this yr.

Throughput is often a dependent variable with "bits per second" as its unit.

what is unit and measurment?

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the sum of two odd integers will always be resulted in an odd digit.

Odd numbers are entire numbers that can't be isolated precisely into matches. Odd numbers, when separated by 2, leave a rest of 1. , 3, 5, , 9, 11, , 15  are consecutive odd numbers.

These are added together to get n + n+1, or 2n+1. Since +1 make it odd, 2n is even. Any two successive integer sums are hence odd. According to the solution is "2n + (2n + 1) = 4n +1."

Even numbers result from the addition of two fractions, but still only digits result from the addition of one odd number with one even number. In order to only receive an odd number, add one odd as well as one even.

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The remainder of the long division problem (x + 1)/x is given as follows:

1.

The representation of a long division problem is given as follows:

di(x)/d(x) = q(x) + (r(x)/b(x))

In which the meaning of each symbol is listed as follows:

In the context of this problem, the operation is presented as follows:

(x + 1)/x.

This division can be separated into two divisions that are added, hence:

(x + 1)/x = x/x + 1/x = 1 + 1/x.

Comparing to the standard symbols, we have that:

The expression is:

(x + 1)/x.

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Answer:

B 1

Step-by-step explanation:

The equation which has infinitely many solutions include the following: B. -6x + 35 = -6x + 35

In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal.

This ultimately implies that, an equation would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and intercept for the two lines are the same.

In this scenario, we can reasonably and logically deduce that the following equations satisfy the condition for an equation which has infinitely many solutions:

-6x + 35 = -6x - 35 (False).

-6x + 35 = -6x + 35 (True).

6x + 35 = -6x + 35 (False).

6x + 35 = -6x - 35 (False).

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Complete Question:

Which of the following equations have infinitely many solutions?

Choose all answers that apply:

A. -6x + 35 = -6x - 35

B. -6x + 35 = -6x + 35

C. 6x + 35 = -6x + 35

D. 6x + 35 = -6x - 35

The amounts are given as follows, using proportions:

i) Amount spent on entertainment: $240.

c) Monthly salary: $840.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem along with basic arithmetic operations such as multiplication or division to find the desired amounts.

The ratio of food : travelling : entertainment = 4 : 2 : 3 means that:

The amount spent on food $160 more than travelling, the total amount is obtained as follows:

(4/9 - 2/9)x = 160

2/9x = 160

2x = 160 x 9

x = 80 x 9

x = 720.

Then the amount invested in entertainment was of:

3/9 x 720 = 1/3 x 720 = $240.

He invests 6/7 of his monthly salary, as 1/7 is deposited, hence:

6x/7 = 720

6x = 720 x 7

x = 120 x 7 (simplifying both sides of the equality by 6)

x = $840.

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The vertex of the graph is (2, -1), the axis of symmetry of the graph is x = 2 and the parabola opens downward

The vertex

The graph represents the given parameter

From the graph, we can see that:

The maximum point on the graph is located at

(2, -1)

The vertex of a graph is the maximum or the minimum  of the graph

This means that

Vertex = (2, -1)

The axis of symmetry

The graph represents the given parameter

In (a), we have

Vertex = (2, -1)

Remove the y-coordinate

x = 2

The axis of symmetry of a graph is the x coordinate of the vertex

This means that the axis of symmetry is x = 2

From the graph, we can see that the parabola opens downward

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The height of the TV is 31 inches . This can be calculated using Pythagoras theorem.

What is Pythagoras theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

Main Body:

according to the question --

hypotenuse = 52 in

base = 42 in

height =?

Pythagoras theorem = [tex]{P^{2} +B^{2} }[/tex] = [tex]H^{2}[/tex]

inserting the values --

52² = 42² +H²

H² = 2704- 1764

H² = 940

H≈31 inches

Hence the height of TV is 31 inches

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