Mr Johnson has 4 boxes of pencils with 7 pencils
in each box. If he gives each of his 26 students a
pencil, how many pencils will he have left?

Answer:

Collect Like terms...Then Take the LCM

1/4x -1/3x +3 - 2

-1/12x + 1

Or

1 - 1/12x .

Option D.

The probability that a randomly selected passenger has a waiting time less than 0.75 minutes is 0.107.

The waiting times between subway departures and passenger arrivals are uniformly distributed between 0 and 7 minutes. To find the probability that a randomly selected passenger has a waiting time less than 0.75 minutes, we need to calculate the proportion of the total interval that falls within the desired range.

Since the distribution is uniform, the probability is equal to the length of the desired range divided by the length of the total interval. In this case, the desired range is 0.75 minutes and the total interval is 7 minutes. Therefore, the probability is 0.75 / 7 = 0.107 (rounded to three decimal places).


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Answer:

y= 4x + 9

Step-by-step explanation:

y= 4x+5

y= 4(x+ 5/4)

m, gradient= 4

rule if parallel: their gradients are equal

rule if perpendicular : m1*m2=-1

parallel gradient, m1=4

passes through (-2, 1) so x= -2,  y= 1

y - 1= 4(x -- 2)

y= 4x + 9

The line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

The given equation is:

y = 4x + 5

Compare y = 4x + 5 with the equation y = mx + c

m = 4, c = 5

The equation parallel to y = 4x + 5 will also have a slope, m = 4

The point-slope form of the equation of a line is given as:

y - y₁ = m(x - x₁)

substitute m = 4, x₁ = -2 and y = 1 into the equation above

y - 1 = 4(x - (-2)

y - 1 = 4(x + 2)

y - 1 = 4x + 8

y = 4x + 8 + 1

y = 4x + 9

Therefore the line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

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The factored form of the equation are as follows;

Converting a quadratic function to factored form is called factoring.

Therefore,

let's factor the equation,

a.

d² - 7d + 6 = 0

d² - d - 6d + 6 = 0

d(d - 1) - 6(d - 1) = 0

(d - 6)(d - 1) = 0

b.

x² + 18x + 81 = 0

x² + 9x + 9x + 81 = 0

x(x + 9) + 9(x + 9) = 0

(x + 9)(x + 9) = 0

c.

u² + 7u - 60 = 0

u² - 5u + 12u - 60 = 0

u(u - 5) 12(u - 5) = 0

(u + 12)(u - 5) = 0

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Answer:

the post looks blurry on my end, can you repost so i can help you

Step-by-step explanation:

Answer:

Equation 75 X .45 = P

P = 33.75

Answer:

i need help with something like that aswell

Step-by-step explanation:

Answer:

d= 17.03

Step-by-step explanation:

\(d=\sqrt{ (x_{2}-x_{1})+(y_{2}-y_{1})^{2}}\\\\d=\sqrt{(8--3)+(-6-7)^{2}}\\\\d=\sqrt{(11)+(-13)^{2}} \\\\d=\sqrt{121+169}\\\\d= \sqrt{290} \\\\d=17.03\)

never going to left you go

never going to left you down

Answer:

               \(\bold{d=\dfrac{13}4=3\dfrac14}\)

Step-by-step explanation:

\(a_{10}\,,\ _{\{+d\}}\ \ a_{11}\,,\ _{\{+d\}}\ \ a_{12}\,,\ _{\{+d\}}\ \ a_{13}\,,\ _{\{+d\}}\ \ a_{14}\quad\implies\quad\ a_{14}-a_{10}=4d\\\\4d=a_{14}-a_{10}\\\\4d=30-17\\\\4d=13\\{}\ ^{\div4\quad\div4}\\d=\dfrac{13}4=3\dfrac14\)

Answer:

$656.77 is left

Step-by-step explanation:

-$1,500 budget

Spends: $225.30, $482.25, 135.68.

Now subtract all these values with 1,500.

1500 - 482.25 - 225.30 - 135.68 = 656.77

Answer: C

Step-by-step explanation:

I took this before

The opportunity cost is merely the expense of not making a decision.

As a result, if you chose Project P placed above a white Project Q, the opportunity cost for such a decision is 75,000 times the estimated NPV of Project Q.

The distinction between current value of money over time value of cash outflows over time is defined as net present value (NPV).

Some key features regarding the Net Present Value (NPV) are-

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The inequality expression 9|x - 8| < 36 when solved for x is 4 < x < 12

To solve the inequality 9|x - 8| < 36, we can divide both sides by 9:

|x - 8| < 4

This means that the distance between x and 8 is less than 4. So, the solution can be expressed in two parts:

x is less than 4 units away from 8 to the left:

x < 8 - 4 = 4

x is less than 4 units away from 8 to the right:

x > 8 + 4 = 12

Therefore, the solution is 4 < x < 12, or in interval notation: (4, 12).

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Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

To find out how far she will have run in total after 16 days, we can use the formula for calculating compound interest:

A = P(1 + r/100)^n

Where:

A = Total distance run after n days

P = Initial distance (4.8 kilometers)

r = Rate of increase per day (6.9%)

n = Number of days (16)

Plugging in the given values, we can calculate the total distance:

A = 4.8(1 + 6.9/100)^16

Using a calculator or performing the calculations step by step, we get:

A ≈ 4.8(1.069)^16 ≈ 4.8(2.092473)^16 ≈ 4.8(2.628)

A ≈ 12.6144

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

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The probability that both are yellow is 3/10.

Using the probability method, we get

P(y1 and y2) =  P(y1) P(y2|y1)

= 3/5 x 2/4

= 6 / 20

= 3 / 10

The probability that both are yellow is 3/10.

Probability is sincerely how in all likelihood something is to manifest. each time we're uncertain approximately the final results of an occasion, we will speak about the possibilities of sure effects—how probably they're. The analysis of activities ruled by using possibility is known as statistics.

A series of actions where the outcomes are continually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a dice. occasion. It is a single final result of an experiment.

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Answer:

Substitution

Answer:

\(f(x)=x^2-11x+30\)

Step-by-step explanation:

The factored form of a quadratic is given by:

\(f(x)=a(x-p)(x-q)\)

Where p and q are the zeros, and a is the leading coefficient.

The quadratic relation has zeros of 5 and 6, and it has a y-intercept of 30.

Since the zeros are 5 and 6, p and q are 5 and 6. Thus:

\(f(x)=a(x-5)(x-6)\)

The y-intercept is 30. In other words, when x = 0, f(x) = 30:

\(30=a(0-5)(0-6)\)

Solve for a:

\(30=a(-5)(-6)\Rightarrow 30=30a\Rightarrow a=1\)

Therefore, our quadratic in factored form is:

\(f(x)=(x-5)(x-6)\)

To find the standard form, expand:

\(\begin{aligned} f(x)&=(x-5)(x-6)\\&= (x-5)x+(x-5)(-6)\\&=(x^2-5x)+(-6x+30)\\&=x^2-11x+30\end{aligned}\)

Answer:

4 months

Step-by-step explanation:

y=179+40x.  Equation 1

y=31+77x.     Equation 2

179+40x=31+77x. Replace y from equation 1 and replace y of equation 2

148=37x

4=x

Answer: (x-2),(2x+3), and (2x-1)

Step-by-step explanation: I just took the test and guessed but now I know the answer, so I'm helping everyone :)

Answer:

20 + 5x = 50

Step-by-step explanation:

Let the number of cakes Sam baked this week be x

Total amount he received this week = $50

Amount he receives each week = $20

Amount he receives for baking one cake = $5

Amount he would receive for baking x cakes = $5x

Equation: 5x + 20 = 50

Answer:

20 + 5x = 50

Step-by-step explanation:

Let x be the number of cakes

Amount paid per cake = $5

Amount paid for "x" cakes = 5*x = 5x

Basic payment per week = $20

Amount paid that week = 20 + 5x

20 + 5x = 50

On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, the equation is -

1200=300+5x

900 = 5x

x=180

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Answer:

width = 10ft

length = 18ft

Step-by-step explanation:

Area = length * width

Then:

e * w = 180       eq. 1

e = 8+w      eq. 2

Replacing eq. 2 in eq. 1

(8+w)  * w = 180

8*w + w*w = 180

w² + 8w - 180 = 0

w = {-8±√((8²)-(4*1*-180))} / (2*1)

w = {-8±√(64+720)} / 2

w = {-8±√784} / 2

w = {-8±28} / 2

w = {-8 + 28}/2 = 20/2 = 10

from the eq. 2

e = 8+w

e = 8 + 10

e = 18

Check:

from the eq. 1

10*18 = 180

Answer:

52 degrees

Step-by-step explanation:

The 38 degree angle and the angle marked with a question mark are complimentary, which means they add up to 90 degrees. Knowing this, subtract 38 from 90 to find the mystery angle.

The types of triangles which can be used as a counterexample to the statement " all angles in a triangle are acute " are:

Obtuse

Right

Counter example in math's is defined as an attempt at showing that a mathematical statement is false.

Now, in this case we want to find the counter example that all angles in a triangle are acute angles.

Now, an acute angle is defined as an angle that is less than 90 degrees.

Now, A right angle fits the counter example statement because at least one angle is not less than 90 degrees.

Similarly, an Isosceles triangle does not fit the counter example argument because in an isosceles triangle, two angles are equal and it is possible for three of the angles to be less than 90 degrees.

An obtuse triangle means that one of the angles are greater than 90 degrees and as such this fits our counter example.

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Two unit vectors that are normal to the plane determined by the points A(0, -2, 1), B(1, -1, -2), and C(-1, 1, 0) are:

v₁ = (-2, -1, 1) / √6

v₂ = (-1, 3, 1) / √11

To find unit vectors that are normal to a plane determined by three points, we can use the cross product of two vectors that lie in the plane.

Start with the given points A, B, and C: A(0, -2, 1), B(1, -1, -2), and C(-1, 1, 0).

Calculate two vectors that lie in the plane. We can take the vectors AB and AC:

Vector AB = B - A = (1, -1, -2) - (0, -2, 1) = (1, 1, -3)

Vector AC = C - A = (-1, 1, 0) - (0, -2, 1) = (-1, 3, -1)

Take the cross product of vectors AB and AC to find a vector normal to the plane:

n = AB × AC

n = (1, 1, -3) × (-1, 3, -1)

= (-4, -2, -4)

Normalize the vector n to obtain unit vectors that are normal to the plane:

v₁ = n / ||n||

||n|| = √((-4)^2 + (-2)^2 + (-4)^2) = √36 = 6

v₁ = (-4/6, -2/6, -4/6) = (-2/3, -1/3, -2/3) = (-2, -1, -2) / √6

Similarly, we can find another unit vector perpendicular to the plane:

v₂ = (-1, 3, -1) / ||(-1, 3, -1)||

||(-1, 3, -1)|| = √((-1)^2 + 3^2 + (-1)^2) = √11

v₂ = (-1/√11, 3/√11, -1/√11) = (-1, 3, -1) / √11

Two unit vectors that are normal to the plane determined by the points A(0, -2, 1), B(1, -1, -2), and C(-1, 1, 0) are v₁ = (-2, -1, -2) / √6 and v₂ = (-1, 3, -1) / √11.

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Answer:

648

Step-by-step explanation:

The probability of the weighted coin flipping on tails is 81/100. Using this, if we multiply this ratio by 8 (to account for the 800 flips) , 81 * 8 = 648

The probability of rolling a 6 on a 6-sided die is 1/6.

Rolling a 6-sided die gives us six possible outcomes: 1, 2, 3, 4, 5, or 6. Since we're interested in the event of rolling a 6, there is only one favorable outcome, which is rolling a 6. The total number of outcomes is six (one for each face of the die). Therefore, the probability of rolling a 6 is calculated by dividing the number of favorable outcomes (1) by the total number of outcomes (6), resulting in 1/6.

Probability is a measure of how likely an event is to occur. In this case, we have a fair 6-sided die, which means each face has an equal chance of landing face-up. The probability of rolling a specific number, such as 6, is determined by dividing the number of ways that event can occur (1 in this case) by the total number of equally likely outcomes (6 in this case). So, in a single roll of the die, there is a 1/6 chance of rolling a 6.

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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