What is -9 + m + (-6) in simplest form?

As per the unitary method, there are 10 chairs and there are 2 tables.

In math the term called unitary method is known as  a process of finding the value of a single unit, and based on this value we can find the value of the required number of units.

Here we have given that tom and jerry have one day to work, but two tasks to focus on building chairs and tables.

Here we also know that  if tom spends all day building chairs, then he will make 16 chairs.

And if he instead devotes his day to building tables, then tom will make 4 tables.

Where as if jerry spends his day building chairs, then he will make 14 chairs on the other hand if he spends the day building tables, then he will make 7 tables.

Based on the given details, here by using the unitary method, for one day, he will product 10 chairs and 2 tables.

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Answer:

The best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

Step-by-step explanation:

Best point estimate:

The best point estimate of a population mean is the sample mean.

In this question:

The sample mean amount of money spent for textbooks was $121.60, which means that the best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

The rate of the area with the circle is increased after each of the following.

a. after 1s 15,707.963cm^2/s b. after 4s 62,800.889cm^2/s c. after 7 s 109,955.74 cm^2/s

50cm/s is the radius of the ripple per second, that is, radius(r) of the ripple after t seconds = speed * time(t)

Speed = 50cm/s

r = 50t

Area of a circle(A) = πr^2

The rate of change of area with radius is measured by:

dA/dt = π2r . dr/dt

Speed of ripple 50cm/s.

This can be the rate at which the radius changes with time (dr/dt)

dr/dt = 50cm/s

The rate at which the area is increased with time:

dA/dt = π2r . dr/dt

dA/dt = π2(50t).50

dA/dt = 5000πt

After 1 second:

dA/dt = 5000π(1)

= 15,707.963cm^2/s

After 4 seconds:

dA/dt = 5000π(4)

= 62,800.889cm^2/s

After 7 seconds:

dA/dt = 5000π(7)

= 109,955.74cm^2/s

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The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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The initial value problem's solution becomes closer to 0, the problem's limit, as time gets closer to infinity.

1. Determine both sides of the equation's Laplace transform: d2y + 4dy + 13y = u5(t) Y(s) = s2Y(s) + 4sY(s) + 13Y(s) = U5 (s)

2. Rewrite the equation to Y(s) = U5(s) / (s2 + 4s + 13) to find the value of Y(s).

3. Consider the reverse Finding y(t) using the Laplace transform on both sides

y(t) = (1/12)e(-t) + (1/24)sin(3t) + (1/8)cos (3t)

4. As t approaches infinity, determine the limit:

Laplace transformations are used to resolve the initial value issue d2y + 4dy + 13y = u5(t), where y(0) = 0 and y′(0) = 1. Y(s) = s2Y(s) + 4sY(s) + 13Y(s) = U5 is the result of first doing the Laplace transform of both sides of the equation (s). To find Y(s), we rewrite the equation as Y(s) = U5(s) / (s2 + 4s + 13). Then, to get y(t), we use the inverse Laplace transform of both sides: y(t) = (1/24)e(-2t) + (1/12)e(-t) + (1/24)sin(3t) + (1/8)cos (3t). Finally, when t approaches infinity, we compute the limit: limt[infinity]y(t) = 0. As a result, as time gets closer to infinity, the initial value problem's solution gets closer to 0.

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After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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Answer:

81.64 cm

Step-by-step explanation:

c = 2(3.14) x 13

c = 6.28 x 13

c = 81.64

Answer:

200

Step-by-step explanation:

you subtract

Inequalities help us to compare two unequal expressions. The inequality that represents the given statement is 45≤x≤ 65.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the maximum legal speed on the highway is 65 MPH, therefore, the value of x must not exceed 65 MPH.

x ≤ 65

Also, the minimum legal speed on the highway is 45 MPH, therefore, the value of x must not be less than 45 MPH.

45≤x

By combining the two inequalities, we will get,

45≤x≤ 65

Hence, the inequality that represents the given statement is 45≤x≤ 65.

The complete question is:

Write an inequality that accurately represents the following statement: "Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."

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There are 3+4+3=10 chocolates in total

Now the chances of getting a milk or dark chocolate is 3+4/10=7/10

which is 0.7 so none of the choices are correct!

Answer:

ur probaby gonna randomly get dark chocolte its healthy

Step-by-step explanation:

Answer:

-7+x=38,

Step-by-step explanation:

Answer:

Step-by-step explanation:

should be both line GJ and JK as well as line HK and JK

Answer:

Its 5!

Step-by-step explanation:

You add up all the numbers then divide by the total of number of numbers you added up!

The amount of money increases by $125,000 due to the decrease in the reserve rate. The correct answer is B. It increases the amount by $125,000.

When the Federal Reserve decreases the reserve rate, it allows banks to hold a smaller portion of their deposits as reserves and lend out a larger portion. This change stimulates lending and increases the money supply in the economy through the process of fractional-reserve banking.

In this scenario, the initial deposit of $15,000 can be multiplied by the money multiplier, which is the reciprocal of the reserve rate. Initially, with a reserve rate of 6%, the money multiplier is 1/0.06 = 16.67. Therefore, the initial deposit can lead to a maximum increase in the money supply of $15,000 x 16.67 = $250,050.

When the reserve rate is decreased to 4%, the money multiplier becomes 1/0.04 = 25. Therefore, the same initial deposit of $15,000 can now result in a maximum increase in the money supply of $15,000 x 25 = $375,000.

The difference between the two scenarios is $375,000 - $250,050 = $124,950, which is approximately $125,000. Hence, the amount of money increases by $125,000 due to the decrease in the reserve rate.

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Answer:

The mode is 20 because it is has been seen 3 times and the median is 20 because it is in the middle

Step-by-step explanation:

12, 15, 16, 19, 20, 20, 20, 23, 24, 25, 25, 105, 209

The formula of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis as g(x) = 8x⁴ + 5x³- 2x²-6x + 5 .

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Reflection across the y-axis is defined as reflecting a point across they = x,  the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).

So reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

We have to determine the equation of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis.

Since reflected across the y-axis: f(x) → f(-x), So substitute the value x = -x

⇒ f(-x) = 8(-x)⁴-5(-x)³-2(-x)²+6(-x)+5

⇒ f(-x) = 8x⁴ + 5x³- 2x²-6x + 5 = g(x)

Hence, the equation of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis as g(x) = 8x⁴ + 5x³- 2x²-6x + 5 .

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(a)  75% stocks of B is large tree diagram is given below

(b) Probability of a tin chosen at random from the stock will be a small size is 29%.

(c) Probability of a small tin chosen at random from the stock will be of brand A is 51.7%.

(a) \(A = \frac{60}{40} = 150\%\)

\(B = 60\%\)

\(S_A = 25/35 = 71.42\%\)

\(S_B = 25\%\)

\(L_A = 75/65 = 115\%\)

\(L_B = 75\%\)

Refer attached, for tree diagram.

(b) \(P(S) = P(A) \times P(S_A) \times P(B) \times P(S_B)\)

\(= 60\% \times 25\% \times 40\% \times 35\%\)

\(= 29\%\)

(c) \(P(A|S) = \frac{P(A) \times P(S_A)}{P(S)}\)

\(= \frac{60\% \times 25\%}{29\%}\)

\(= 51.7 \%\)

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Given

The floor plan of a house is,

After installing new hardwood flooring , you also need to install base board around the bottom of the walls.

To find: How many feet of base board will you need to buy?

Explanation:

It is given that,

The floor plan of a house is,

After installing new hardwood flooring , you also need to install base board around the bottom of the walls.

That implies,

The perimetr of the base board is,

Hence, we need to buy 108ft of base board.

The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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Answer:

a quotient is the result obtained by dividing one quantity by another.

Check the picture below.

so let's use those two points for that domain.

\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0}\implies \cfrac{0~~ - ~~(-6)}{2}\implies \cfrac{6}{2}\implies 3\)

Answer:

-4/3

Step-by-step explanation:

Answer:

\(x = -\frac{4}{3}\)

Step-by-step explanation:

3(x + 4) - 1 = 7

3x + 12 - 1 = 7

3x + 11 = 7

3x + 11 - 11 = 7 - 11

3x = -4

\(\frac{3x}{3} =-\frac{4}{3} \\\\x = -\frac{4}{3}\)

The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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1) The expression 2⁻ˣ⁺³ = 3 is matched with graph B.

2 The expression  3ˣ⁺¹=3 is matched with graph C.

3) The expression 4ˣ = 3 is matched with graph

4 ) The expression 1ˣ/4 = 3 is matched with graph

1) The graph of the expression 2⁻ˣ⁺³ = 3  represents an exponential function where the y-coordinate is 3 when the base 2 raised to the power of (-x+3).

2) The graph of the expression 3ˣ⁺¹=3represents an exponential function where the y-coordinate is 3 when the base 3 raised to the power of (x+1). This graph is a straight line with a slope of 1.

3)  The graph of the equation 4ˣ = 3 represents an exponential function where the base 4 raised to the power of x is equal to 3. This equation has a single solution, which can be determined using logarithms.

4) The graph of the expression 1ˣ/4 = 3 represents an exponential function where the base 1 raised to the power of (x/4) is equal to 3.

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Answer:

5x

Step-by-step explanation:

-6 + 2x + 4 + 3x - (-2)

rearrange to make it easier to solve

2x + 3x - 6 + 4 - (-2)

add like terms, negative time negative is positive

5x - 2 + 2

5x

(6x + 9y) + (7x - 4y)

Remove parenthesis:

6x + 9y + 7x - 4y

Add like terms:

(6x + 7x) + (9y - 4y)

(13x) + (5y)

13x + 5y

(6x + 9y) - (7x - 4y)

Remove parenthesis (keep in mind law of signs)

6x + 9y - 7x + 4y

Add like terms:

(6x - 7x) + (9y + 4y)

(-x) + (13y)

-x + 13y

or

13y - x

Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

Answer:

D. x - 4

Step-by-step explanation:

x² - 3x - 4 = ( x - 4 )( x + 1 )

main formula: x² + ( a + b )x + ab = ( x + a )( x + b )

The polynomial with the given zeros is:;

P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)

Remember that if a polynomial has the zeros a, b, c, and d, then we can write it as:

P(x) = K*(x - a)*(x - b)*(x - c)*(x - d)

Where K is a coefficient.

Here the zeros are 0, -1, 1, 3/2

Then we can write:

P(x) =K*(x - 0)*(x + 1)*(x - 1)*(x - 3/2)

P(x) =K*x*(x + 1)*(x - 1)*(x - 3/2)

We also know that when x = -3, P(x) = 300

Then we can write:

300 = K*(-3)*(-3 + 1)*(-3 - 1)*(-3 - 3/2)

300 = K*(-3)*(-2)*(-4)*(-9/2)

300 = K*108

300/108 = K

Then the polynomial is:

P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)

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