Jeanette took home a net pay of $ 1 , 100 on her paycheck this week. She worked 40 hours during this specific pay period and had deductions that totaled $ 100 , what is her hourly rate of pay?

The y-intercept represents the hours Rebecca must work.

Linear equation can be represented in slope intercept from, point slope form and standard form.

Therefore, in slope intercept form it can be represented as follows:

Hence,

y = mx + b

where

She must complete 15 hours of volunteer work. She does 3 hours each day. Let's represent Rebecca situation in linear form.

where,

y = hours Rebecca still has to work

x = the number of days

Therefore,

y = 15 - 3x

The y-intercept is 15 which implies the number of hours she must complete.

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The number of hours Rebecca must work is represented by the y-intercept in the linear equation.

An equation is said to be linear if the power output of the variable is consistently one.

The linear equation is y = mx + c, where m denotes the slope and c is its intercept.

Given that she is required to put in 15 hours of volunteer work. Each day, she works three hours.

As per the given situation,

If x represents the number of days and y represents the number of hours she must work

So the linear representation shows Rebecca's situation will be:

y = 15 - 3x

Therefore, the number of hours Rebecca must work is represented by the y-intercept in the linear equation.

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Answer:

$7,925.53

Step-by-step explanation:

We'll have to use the compound interest formula: A = P(1 + r/n)ⁿˣ

A = final amount (?)

P = starting amount (5700)

r = rate

n = times applied (12 since its monthly and there 12 months in a year)

x = years (12)

A = 5700(1 + 0.0275/12)¹⁴⁴

A = 7925.525498629932

The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

Fleet of 17 means that \(N = 17\)

4 are carrying nucleas weapons, which means that \(k = 4\)

9 are destroyed, which means that \(n = 9\)

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

\(P(X > 1) = 1 - P(X \leq 1)\)

In which

\(P(X \leq 1) = P(X = 0) + P(X = 1)\)

So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294\)

\(P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118\)

Then

\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412\)

\(P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588\)

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Answer:

The rate is 5 dollars per student.

Step-by-step explanation:

The rate per student can be found with \(\frac{dollars}{student}\):

\(\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}\)

The rate is 5 dollars per student.

The number 2 represents two quantites

Answer: x= 23/30

Step-by-step explanation:

\(\frac{5}{6}\) = \(\frac{10}{2}x -3\)    reduce 10/2 to 5 because 10/2  is 5.

5/6 = 5x -3

+ 3         +3

23/6 = 5x   divide both sides by 5.

x= 23/30

Answer: 4/33

Step-by-step explanation:

just divide

Answer:

The answer is 4/33.

Step-by-step explanation:

to get this you just have to divide.

you're welcome.

The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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Answer:

A, C, E

Step-by-step explanation:

A. by alt int angles

C. <3 is a supplement of 72°, so m<3 = 108°; <6 is corresponding to <3, so it is congruent to <3.

E. by alt ext angles

The expression which is equivalent to -5(b - 6) as required to be determined in the task content is; -5b + 30.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Since the expression given is; -5(b- 6).

By using the distributive property of numbers

= (-5 × b) + (-5 × -6)

= -5b + 30

Thus, the linear expression which is equivalent to -5(b - 6) as required is; -5b + 30.

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The Question attached seems to be incomplete/ inappropriate. the complete Question is:

Which expression is equivalent to -5(b - 6).

Answer:

the last option

Step-by-step explanation:

Answer:

-2m-6

Step-by-step explanation:

-2 x 1 m= -2m

-2 x 3= -6

-2m-6

Answer:

-2m-6

Step-by-step explanation:

-2(m+3) =

-2*m + -2*3 =

-2m -6

Answer:

\(y=-\frac{4}{5}x-\frac{21}{5}\)

Step-by-step explanation:

The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):

\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

The maximum error in calculating the area of the disk is approximately 0.25 cm * 2π * 26 cm = 16.3 cm².

The maximum error in the calculated area of the disk can be estimated using differentials. A = r2, where r is the circle's radius, is the formula for calculating a circle's area.. Differentiating this equation with respect to r gives us A' = 2πr. Plugging in the given values, we get A' = 2π * 26 cm = 161.6 cm². If the possible error in measuring the radius is 0.25 cm, then the maximum error in calculating the area of the disk is 0.25 cm * A' = 0.25 cm * 161.6 cm² = 16.3 cm². Therefore, the maximum error in the calculated area of the disk is approximately 16.3 cm².

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Answer:

Step-by-step explanation:

This is a proof.  You need to use theorems and definitions to get to your answer.  You cannot make any assumptions without a definition for it.  You can you use the information that you have proven from previous statements.

m<1 = m<2                               Given

QP = QR                                   Given

m<3 = m<4                               Vertical Angles

m<1 + m<3 + m<P = 180          Triangle Sum Theorem

m<P = 180 - m<1 - m<3            Subtraction

m<P = 180 - m<2 - m<3           Substitution

m<2 + m<4 + m<R = 180         Triangle Sum Theorem

m<R = 180 - m<2 - m<4           Subtraction

m<R = 180 - m<2 - m<3           Substitution

m<P = m<R                               Transitive

m<Q = m<Q                             Reflexive

ΔQTP ≅ ΔQTR                        ASA

We proved that the triangles are congruent by proving an angle, a side and another angle are the same.

<Q and <Q same

QR and QP same, this was give

<R = <P same through proof    

The area of the composite figure is 122.5 square inches

Based on the problem statement, we have the following dimensions from the question

The area of the composite figure is the sum of individual areas

So, we have

Area = Isosceles right triangle + Rectangle + Another isosceles triangle

By applying the formulas, we have

Area = 0.5 * 11 * 11 + 14 * 4 + 0.5 * 4 * 3

Evaluate

Area = 122.5

Hence the area is 122.5 sq inches

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Answer:

D is the correct answer.

Step-by-step explanation:

5* [10 ; 5] = [50 ; 25].

by the way the semi column stands for that the next elememt is on the next row.

for A and C choices, they are wrong since we can't multiply two matrices even if the number of columns of the first matrix is equal to the number of rows of the second.

Answer:

Option (3). \(m(\widehat{ACB})=220\)

Step-by-step explanation:

Option (1).

Since measure of an inscribed angle = \(\frac{1}{2}(\text{measure of the intercepted arc})\)

m∠ABC = \(\frac{1}{2}m(\widehat{AC})\)

\(m(\widehat{AC})\) = 2(m∠ABC)

           = 2(30°)

           = 60°

Therefore, this option is not true.

Option (2),

Since, \(m(\widehat{AB})+m(\widehat{BC})+m(\widehat{AC})=360\)

\(m(\widehat{AB})+160+60=360\)

m(arc AB) = 360 - 220

                = 140°

Therefore, this option is not correct.

Option (3),

\(m(\widehat{ACB})=m(\widehat{AC})+m(\widehat{BC})\)

               = 60° + 160°

               = 220°

Option (3) is the correct option.

Option (4),

\(m(\widehat{CBA})= 360-m(\widehat{AC})\)

               = 360° - 60°

               = 300°

Therefore, this option is not correct.

Answer:

To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.

Step-by-step explanation:

a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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The difference between Tom and Alfie is  1 kg

Let's call the weight of Tom T, the weight of Harry H, the weight of Freddie F, and the weight of Alfie A. We are given that T = H + 5, H = F + 3, and F = A - 2.

Substituting the second and third equations into the first equation gives us:

T = (A - 2) + 3 + 5

T = A - 2 + 3 + 5

T = A + 1

So the difference between Tom and Alfie is T - A = A + 1 - A = 1 kg.

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Answer:

Now to secrtly stalk this man

Step-by-step explanation:

They have used after 5 days, 1 full box and 1/4 of another box.

Fractions are used to represent smaller pieces of a whole.

Given that, Each day, a company used 2 / 8 of a box of paper.

They are using 1/4 box of paper each day,

So, after 5 days = 5*1/4 = 5/4 = 1+ 1/4

Hence, They have used after 5 days, 1 full box and 1/4 of another box.

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Answer:

75

Step-by-step explanation:

4:3

4x25=100

3x25=75

In the given case- An inverse of a Laplace transform, which is the sum of two distinct components, is the sum of the inverse transforms of each term separately.

What does inverse Laplace transform refer to?

A Laplace transform that is the sum of two different terms has an inverse that is the sum of the inverse transforms of each term taken separately. A Laplace transform, which also has an inverse of the constant multiplied by the inverse of the function, is produced when a constant is multiplied by a function.

A given derivative function with a real variable (t) is transformed into a complex function with a variable (s) by the Laplace transform, which is an integral transformation. Assuming that f(t) complies with a number of later-explained conditions,

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Answer:

f(n) = 3(n-3).

f(5)=3(5-3)

f(5)=6

The investment amount is $37263.09.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.

Formula of continuous compound interest rate;

P(t) = P₀ \(e^{rt}\) , where P₀ is the principal amount, r is the interest rate and t is the time period.

Given that the Alang is going to invest with the continuous compound interest rate 5.7%.

Using the formula of continuous compound interest rate,

P(t) = P₀ \(e^{rt}\)

P(t) = $113000 x    \(e^{(5.7)(5)}\)

P(t) = $37263.09

Therefore, the investment amount is $37263.09.

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Answer:

2x−y=5

Step-by-step explanation: