Jack earned a base pay of $600 plus a 5% commission on his sales. If his sales were $25,000 for the week, what was his total paycheck?

15x + 25 y = 230 and x - y = 2 is a system of equations that could be used to calculate the number of hours Mamadou worked and Brianna worked.

Given:

Mamadou can iron 15 shirts in one hour, whereas Brianna can do 25. Mamadou put in two more hours of work than Brianna, and the two of them combined to iron 230 shirts.

Let y be the number of hours Brianna, works, and x be the number of hours Mamadou  works.

In y hours, Brianna would iron 25y shirts.

In x hours, Mamadou would iron 15x shirts.

Combining total number of shirts,

15x + 25 y = 230

Since, Mamadou put in two more hours of work than Brianna.

x = y +2

x - y = 2

Therefore, for the number of hours Mamadou and Brianna worked, a system of equations 15x + 25 y = 230 and x - y = 2 could be utilised.

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Answer:

15x + 25 y = 230 and x - y = 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

For the pairs of sides to be proportional to each other, they must have the same scale factor. In other words, similar figures have congruent angles and sides with the same scale factor. A scale factor of 2 means that each side of the larger figure is twice as long as its corresponding side is in the smaller figure.

Answer:

2754

Step-by-step explanation:

Answer:

9 Hours

Step-by-step explanation:

162 X 12 / 216 = 9 Hours

Answer:

Put a pretend dot at number 2 and number -4, then since the line is undefined, it will simply be vertical and look like this:

If \(x^{2}\) ≡ n (mod 65) has a solution, then so does \(x^{2}\) ≡ -n (mod 65).

Let \(x^{2}\) ≡ n (mod 65). By definition, there exists an integer k such that\(x^{2}\) = n + 65k. Now, we want to prove that \(x^{2}\)≡ -n (mod 65) has a solution.

We know that 65 is an even number, therefore\(-1^{2}\) ≡ 1 (mod 65).

Therefore, (-1)\(x^{2}\) ≡ -n (mod 65).

Now, multiplying both sides of the equation \(x^{2}\)= n + 65k by (-1) yields (-1)\(x^{2}\) = -n - 65k.Adding 65k to both sides, we have (-1)\(x^{2}\)+ 65k = -n.

Therefore, (-1)\(x^{2}\)≡ -n (mod 65).If \(x^{2}\) ≡ n (mod 65) has a solution, then so does\(x^{2}\) ≡ -n (mod 65).

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Answer:

45t = distance

Step-by-step explanation:

Distance = speed * time

Distance= 45 mph * t hours = 45t

Answer:

2y=-2x

Step-by-step explanation:

2y=4-6x

2y=-2x

y=-1

Answer:

ASA

Step-by-step explanation:

the angles of the vertex are vertical angles, so they are congruent.

We have a congruent side between two congruent angles

\(\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}\)

Given to points to us are :-

Now , we can use Distance Formula , which is :-

\(\boxed{\purple{\tt Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}\)

Here ,

→ Substituting the respective values ,

⇒ Distance = √ [ ( 6 - 1)² + ( 3 +9)² ] .

⇒ Distance = √ 5² + 12²

⇒ Distance = √ 25 + 144

⇒ Distance = √ 169 .

⇒ Distance = 13 units .

Hence the distance between two points is 13u.

Answer:

0.71. ,14%. ,7/40

Step-by-step explanation:

At first we have to find value of 14% and 7/40

which is 14/100=0.14 and

7/40 = 0.175.

so arranging in descending order which is bigger value to smaller value so,

0.71. , 0.14. , 0.175

Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

The optimal solution is x = 2, y = 0, and the maximum value of Z is Z = 2 - 2(0) = 2. To solve the given linear programming (LP) model using the graphical method, we need to graphically represent the feasible region and find the optimal solution by maximizing the objective function.

Step 1: Graph the Constraints

We start by graphing each constraint individually on a coordinate plane.

The first constraint is x - y ≥ 0, which represents the line y = x. We can draw this line on the plane.

The second constraint is x + 2y ≤ 4. To graph this, we can rewrite it as 2y ≤ -x + 4 and then solve for y, which gives y ≤ (-1/2)x + 2. We can plot this line on the graph as well.

The third constraint x ≥ 0 represents the x-axis, and the fourth constraint y ≥ -1 represents the horizontal line y = -1.

Step 2: Identify the Feasible Region

The feasible region is the area where all constraints are satisfied. It is the intersection of the shaded regions formed by the constraints.

Step 3: Identify the Optimal Solution

To find the optimal solution, we need to maximize the objective function Z = x - 2y. The objective function is represented by a line with a positive slope.

By sliding the objective function line parallel to itself from left to right or right to left, we can observe the points of intersection between the objective function line and the feasible region. The point that gives the maximum value of Z within the feasible region is the optimal solution.

Step 4: Determine the Optimal Solution

By visually inspecting the graph, we can see that the objective function line will intersect the feasible region at the corner point (2, 0). This is the optimal solution for the given LP model.

Therefore, the optimal solution is x = 2, y = 0, and the maximum value of Z is Z = 2 - 2(0) = 2.

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a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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Answer:

\(slope = \frac{7 - 0}{0 - ( - 2)} \\ = \frac{7}{2} \\{ \boxed{slope = \frac{7}{2} }} \\ y = mx + c \\ 0 = - 7 + c \\ { \boxed{y - intercept = 7}} \\ { \boxed{y = \frac{7}{2} x + 7}}\)

Answer:

A) Slope-Intercept form is: Y= 7/2X +7

B) M= 7/2

C) b= 7

The number of days in a row Makenzie could wear a different outfit using only her favorite clothes is 24 days.

Solving this problem would involve combinations. In mathematics, combination refers to a mathematical technique used to determine the number of possible arrangements in a collection of items, irrespective of the arrangements.

We are given that the number of t-shirts is four, the number of pairs of designer jeans is three, and the number of pairs of sandals is two. The number of days in a row Makenzie could wear a different outfit using only her favorite clothes is calculated as follows:

(4C₁) (3C₁) (2C₁) =

4 × 3 × 2 =

24

We have confirmed that the number of days in a row Makenzie could wear a different outfit using only her favorite clothes is indeed 24 days.

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Answer: 6

Step-by-step explanation:

1.75 X 8 = 14

20-14=6

Try that.

Answer:

D

Step-by-step explanation:

I dont think this needs explained

Answer:

The last option, it is greater than the distance from the Movie Theater to the Arcade

Step-by-step explanation:

Distance from food court to store is 6 units

Distance from movie theater to arcade is 5 units

The number of sides equals the number of the line of symmetry. Then the correct option is B.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The relationship between the number of sides a regular polygon has and the number of lines of symmetry will be

In a regular polygon, the amount of symmetry lines is equal to the total of sides.

Then the correct option is B.

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Answer:

B They are the same value!

Step-by-step explanation:

Why? Well go look in your lesson although because i got this correct i forgot ago and yeah (TRUST++)

Answer:

2x⁴ + x³ - 3x² - 4x + 2

4

Step-by-step explanation:

Given functions:

     f(x) = 2x⁴ - 3x² - 2x + 5

     g(x)  = x³ - 2x - 3

Unknown:

Sum of the polynomials = ?

Order of the sum  = ?

Solution:

The sum of the polynomial is expressed as;

    f(x) + g(x) = 2x⁴ - 3x² - 2x + 5 +  x³ - 2x - 3

                   = 2x⁴ + x³ - 3x² - 2x - 2x + 5 -3

                   = 2x⁴ + x³ - 3x² - 4x + 2

The order of the sum is the highest power which 4.

This polynomial is of the 4th order.

Answer:

36 total cookies

Step-by-step explanation:

2 dozen = 2/3 of the total cookies

24 = 2/3 of the total cookies

24/x = 2/3

cross multiply

24(3) = 2x

72 = 2x

x = 36

Check the math: 2/3 x 36 = 72/3 = 24

The least squares prediction equation for this data can be written as: y = 0.0006x + 6.697

where "y" is the number of software millionaire birthdays in a decade, "x" is the total number of births in the country, and the coefficients 0.0006 and 6.697 represent the slope and y-intercept, respectively. To fit a simple linear regression model relating the number (y) of software millionaire birthdays in a decade to the total number (x) of births in the country, you'll need to use the least squares method. The least squares prediction equation for linear regression is given by:
y = b0 + b1 * x
where y is the number of software millionaire birthdays, x is the total number of births, b0 is the intercept, and b1 is the slope. To find b0 and b1, you would use the following formulas:
b1 = Σ[(x - X)(y - Y)] / Σ(x - X)²
b0 = Y - b1 * X
Here, X is the mean of x values, and y is the mean of y values. After calculating b0 and b1 using your data, you can plug them into the equation to create your least squares prediction equation for the linear regression model.

To fit a simple linear regression model relating the number (y) of software millionaire birthdays in a decade to the total number (x) of births in the country, we can use the least squares method. The least squares method aims to minimize the sum of the squares of the differences between the observed values and the predicted values.
The prediction equation for this linear regression model can be written as:
y = a + bx
Where y represents the number of software millionaire birthdays in a decade, x represents the total number of births in the country, a represents the y-intercept, and b represents the slope of the line.
To find the values of a and b, we need to calculate the total number of births and the total number of software millionaire birthdays in the decade. We can then use these values to calculate the slope and y-intercept of the line.
Once we have the values of a and b, we can plug them into the equation to get the least squares prediction equation for the data. This equation will give us an estimate of the number of software millionaire birthdays in a decade based on the total number of births in the country.
Therefore, the least squares prediction equation for this data can be written as:
y = 0.0006x + 6.697 where "y" is the number of software millionaire birthdays in a decade, "x" is the total number of births in the country, and the coefficients 0.0006 and 6.697 represent the slope and y-intercept, respectively.

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When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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Answer:

22 hens and 78 sheep

Step-by-step explanation:

Let the number of hens = x

Number of sheep = y

Total heads = 100

x +  y = 100      --------------------(I)

 x = 100 - y

Number of legs of 'x' hen = 2*x = 2x

Number of legs of 'y' sheep = 4*y = 4y

total legs = 356

2x + 4y =  356 -----------------------(II)

Substitute x = 100 -y in equation (II)

2(100 - y) + 4y = 356

2*100 - 2*y + 4y = 356

200 - 2y + 4y    = 356 {Combine like terms}

        200  + 2y = 356          {Subtract 200 from both sides}

                   2y = 356 - 200

                  2y = 156       {Divide both sides by 2}

                    y = 156/2

                  y = 78

Plugin  y = 78 in equation (I)

x + 78 = 100

       x = 100 - 78

       x = 22

22 hens and 78 sheep

The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).

Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.

We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:

P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4

Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:

P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563

P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015

P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159

P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747

P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340

P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824

Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

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Answer:

(c)

Step-by-step explanation:

3+2+4 = 9,  4+2= 6- 3= 3

at a particular restaurant, each pizza roll has 65 and each chicken wing is 11 pizza rolls and 6 chicken wings.

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Answer:

SLOPE: 1

Y-Intercept: (0,4)

Step-by-step explanation:

Answer:

m=1

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Perpendicular lines intersect at a 90° angle.

Answer:

D. Segments that intersect at a right angle

Step-by-step explanation: