Sophie earns a weekly retainer of $355 plus a commission of 10% on sales. What are Sophie’s total earnings for each week if she made the following sale: $760

Answer:

Step-by-step explanation:

Ratio and proportion:

   \(\sf \dfrac{x}{3}=\dfrac{6}{9}\\\\ x = \dfrac{6*3}{9}\\\\x = 2\)

\(\sf \dfrac{8}{y}=\dfrac{6}{9}\\\\Cross \ multiply,\\\\y*6=9*8\\\\y=\dfrac{9*8}{6}\\\\y=3*4\\\\\bf y = 12\)

\(\sf \dfrac{a}{15}=\dfrac{6}{9}\\\\a =\dfrac{6}{9}*15\\\\a=2*5\\\\\bf a = 10\)

Answer:

The number is 13 /24

Step-by-step explanation:

Let the number = x

x - (- 11/12) = 3x - 1/6

x + 11/12 = 3x - 1/6

Collect like terms ;

x - 3x = - 1/6 - 11/12

-2x = (-2 - 11) / 12

-2x = - 13 / 12

-2x(12) = - 13

-24x = - 13

x = 13 / 24

The equation 2y² - 32y + 128 = 0 has one Real Root, which is y = 8.

To find the roots of the quadratic function 2y² - 32y + 128 = 0 using the quadratic formula, we can follow these steps:

Step 1: Identify the coefficients of the quadratic equation. In this case, we have:

a = 2

b = -32

c = 128

Step 2: Substitute the values of a, b, and c into the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

Step 3: Calculate the discriminant, which is the value inside the square root:

Discriminant = b² - 4ac

In this case, the discriminant is:

b² - 4ac = (-32)² - 4(2)(128) = 1024 - 1024 = 0

Step 4: Determine the number of distinct roots based on the discriminant.

- If the discriminant is positive, there are two distinct real roots.

- If the discriminant is zero, there is one real root (the graph touches the x-axis at a single point).

- If the discriminant is negative, there are no real roots (the graph does not intersect the x-axis).

Since the discriminant is 0 in this case, we have one real root.

Step 5: Substitute the values of a, b, and c into the quadratic formula to find the root(s):

y = (-(-32) ± √(0)) / (2(2))

y = (32 ± 0) / 4

y = 32 / 4

y = 8

Therefore, the equation 2y² - 32y + 128 = 0 has one real root, which is y = 8.

For more questions on Root.

https://brainly.com/question/428672

#SPJ8

The calculated value of x is 6

The measure of the arc lengths is 50 degrees

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

There is a theorem that states that angles in thesame segment are equal.

This means that;

3x+7 = 6x -11

Collecting like terms

3x - 6x = -11 - 7

Evaluate the like terms

-3x = -18

Divide both sides by -3

So, we have

x = -18/-3

Evaluate

x = 6

Therefore the value of the angles

is 3 × 6 + 7= 25°

By definition, the measure of the arc is twice the measure of the angle it subtends provided the angle is at the circumference

So, we have

Arc = 2 * 25

Evaluate

Arc = 50 degrees

Hence, the measure of both arcs are 50 degrees

Learn more about circle geometry from

https://brainly.com/question/24375372

#SPJ1

The value of x is 6 and the arc length value is 50°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

In circle geometry , there is a law that states that angle in the same segments are equal.

This means that;

3x +7 = 6x -11

collecting like terms

3x -6x = -11 -7

-3x = -18

divide both sides by -3

x = -18/-3

x = 6

therefore the value of x is 6

There is another theorem that states that the angle at the centre is twice the angle at the circumference.

Therefore the angle at the center = 2(3x+7)

= 2 × ( 18+7)

= 2 × 25

= 50°

the angle at the centre is the measure of the arc length. Therefore;

arc length = 50°

learn more about circle geometry from

https://brainly.com/question/24375372

#SPJ1

Answer:

The linear equation for tip barista gets in a day is f(n)=0.5n+20.

Step-by-step explanation:

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

It is required to find how much will she have in her tip jar if she serves n more customers during her shift. m=0.5. Bases on this write the equation for n more customers.

Step 1 of 1

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

To solve this let f(n) is the total tip barista has in her tip jar after a day.

When n is equal to 0 , that barista has $20,

Then if barista make 0.5 from each customer, then for the linear function m=0.5,

Bases on this write the equation for n more customers,

\($$f(n)=0.5 n+20 .$$\)

Answer:

Alex

Step-by-step explanation:

Representing the position of each person with respect to sea level :

Jack = surface of the ocean = 0 m

Max = Deck of a ship = elevation is above sea level = positive distance or elevation

Alex = Searching for sea life = below ocean surface = negative distance or elevation

Given an elevation of - 5m, then the person who could be at this elevation is Alex

(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

Read more about Linear Function at; https://brainly.com/question/4025726

#SPJ1

If we take a sample of size n from a random variable X with mean μ and variance σ^2, the distribution of X - μ will have a mean of 0 and the same variance σ^2 as X.

The random variable X - μ represents the deviation of X from its mean μ. The distribution of X - μ can be characterized by its mean and variance.

Mean of X - μ:

The mean of X - μ can be calculated as follows:

E(X - μ) = E(X) - E(μ) = μ - μ = 0

Variance of X - μ:

The variance of X - μ can be calculated as follows:

Var(X - μ) = Var(X)

From the properties of variance, we know that for a random variable X, the variance remains unchanged when a constant is added or subtracted. Since μ is a constant, the variance of X - μ is equal to the variance of X.

Therefore, the distribution of X - μ has a mean of 0 and the same variance as X. This means that X - μ has the same distribution as X, just shifted by a constant value of -μ. In other words, the distribution of X - μ is centered around 0 and has the same spread as the original distribution of X.

In summary, if we take a sample of size n from a random variable X with mean μ and variance σ^2, the distribution of X - μ will have a mean of 0 and the same variance σ^2 as X.

Learn more about Random variable here

https://brainly.com/question/30789758

#SPJ11

Two tiny parallel horizontal lines serve as the "equality sign" connecting 1 kilogramme of NaCl to 27 ml of a solvent.

To learn more about equality sign refer to :

https://brainly.com/question/30197153

#SPJ1

Answer:

2

=

|

3

x

|

5

−

x

>

x

+

1

−

3

x

5

+

1

5

=

2

5

Step-by-step explanation:

Answer:

Angle a = 114 Angle b = 114 Angle c = 66 Angle d = 66

Step-by-step explanation:

180 - 48 = 132

132/2= 66

180 - 66 = 114

daisy will received 30 on her 5th birthday

Answer:

20

Step-by-step explanation:

= 0.25 (20−(22) (3) (\(\frac{2}{5}\)(25)

= 0.25 (20−(4) (3) (\(\frac{2}{5}\)(25)

= 0.25 (20−12) (\(\frac{2}{5}\)(25)

= (0.25) (8) (\(\frac {2} {5}\)(25)

= 2 (\(\frac {2} {5}\)(25)

= (2) (10)

= 2 x 10 = 20

Answer:

In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".

Step-by-step explanation:

Answer:

The independent variable

Step-by-step explanation:

Answer:

168 ft

Step-by-step explanation:

Formula = Length x height x width

14x6x2= 168

Im 100% sure this is right. Pls mark me as brainliest!

:))

Answer:

168

Step-by-step explanation:

V = 14 x 6 x 2 = 168

To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

To learn more about distribution : brainly.com/question/29664127

#SPJ11

The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

To learn more about probability visit

https://brainly.com/question/9793303

#SPJ4

The answer is 6x^2. To find this, just find the greatest factor of each question, aka the greatest "common" factor (GCF), of both since it is the greatest factor they each have in common. Hope this helps!

Answer:

11

Step-by-step explanation:

Answer:

a=5.5 I hope this helped you

Answer:

the answer a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The solution to the equation 9(b - 2) = -7 + 0 is b = 11/9.

Given the equation in the question:

9( b - 2 ) = -7 + 0

To solve the equation, first apply distributive property to remove the poarenthesis:

9( b - 2 ) = -7 + 0

9×b + 9×-2 = -7 + 0

9b - 18 = -7 + 0

Next, we simplify the right side of the equation:

9b - 18 = -7

To isolate the variable 'b,' we need to get rid of the constant term (-18) on the left side. We can do this by adding 18 to both sides of the equation:

9b - 18 + 18 = -7 + 18

Simplifying further:

9b = -7 + 18

Add -7 and 18

9b = 11

Now, we want to solve for 'b,' so we divide both sides of the equation by 9:

9b/9 = 11/9

b = 11/9

Therefore, the value of b is 11/9.

Learn more about equations here: https://brainly.com/question/9236233

#SPJ1

The value of the linear equation is 1.2

A linear equation is an algebraic equation for a straight line, where the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0, where x is a variable, A is a coefficient, and B is a constant

The given equation is 9(b-2) = -7 + 0

Opening the brackets we have

9b -18 = -7 + 0

Collecting like terms

9b = -7+18

9b = 11

Dividing both sides by 9 we have

b = 11/9

b = 1.2

Therefore the value of b is 1.2

Learn more about linear equations on https://brainly.com/question/12974594

#SPJ1

Julie has spent 40.25 + 10.56 = <<40.25+10.56=50.81>>50.81 seconds on wall climbing and the ropes.

She needs to complete the course in 74.6 - 50.81 = <<74.6-50.81=23.79>>23.79 seconds to match Lisa's record. Answer: \boxed{23.79}.

Using Poisson distribution ,

a) The probability that two next inspected disk will have no missing pulse is 0.905...

b) The probability that the next inspected disk will have more than one missing pulse is 0.005..

c) The probabihty that neither of the next two inspected disks will contain any missing pulse is 0.819..

Poisson distribution:

It can be defined as a probability distribution resulting from a Poisson experiment. A Poisson experiment is a statistical experiment that divides the experiment into two categories Success or Failure. The Poisson distribution is a restricted process of the binomial distribution.

A Poisson random variable “x” defines the number of successes in the experiment.

Poisson Probability function is represent as given below i.e Mathematically,

P(x, lamda ) = (e ⁻λ (λ ))/x!

where, λ --> an average rate of value

x --> Poission random variable

e ----> base for the logarithm

we have given that,

The quality of computer disk is measured .

averaged missing pluse per disk in a computer disk brand (λ) = 0.1

let x be Poisson random variable which represents the number of missing pulse.

a) we want to find the probability that two next inspected disk will have no missing pulse

P(x= 0 ) = (e⁰·¹ )(0.1)^0/0! = 1/e⁰·¹ ×1/1

=> P(x=0) = 0.905

b) The probability that the next inspected disk will have more than one missing pulse, P(x>1)

P(x>1) = 1 - P(x=0) - P(x=1) = 1 - 0.905 - e⁰·¹(0.1)/1!

= 1 - 0.905 - 0.0905 = 0.0045 ~ 0.005

c) We can assume the disks are independent. the probabihty that neither of the next two inspected disks will contain any missing pulse

P(X = 0 on first disk and x = 0 on second disk) = P(X = 0).P(X = 0) =(0.905)².

= 0.819

Hence, we got all the required probabilities for different cases that is for a) 0.905 b) 0.005 c) 0.81

To learn more about Poisson distribution, refer:

https://brainly.com/question/7879375?

#SPJ4

Answer:

the answer is 43 have a great day

Step-by-step explanation:

The equation to illustrate the information is I(s)=0.0057s

It should be noted that an equation shows the relationship between the variables

I=ks

For I =16, s =2800

k= 16/2800 =0.0057

Hence,

I(s)= 0.0057s

Learn more about equations on:

https://brainly.com/question/2972832

#SPJ4

If interest rates suddenly decline, existing bonds that have a call feature are more likely to be called.

A call feature is a provision in a bond that allows the issuer to redeem the bond before its maturity date. When interest rates decline, issuers can typically issue new bonds with lower coupon rates, which reduces their interest expense. In this situation, the issuer may choose to call the existing bonds with higher coupon rates to refinance their debt at a lower cost.

When interest rates decline, the market value of existing bonds with higher coupon rates increases because they offer a higher yield than newly issued bonds with lower coupon rates. This means that issuers have an incentive to call these bonds and refinance them at a lower cost. As a result, existing bonds that have a call feature are more likely to be called when interest rates decline.

Therefore, the correct answer is a) decline; more. If interest rates increase, issuers are less likely to call their existing bonds because they would have to issue new bonds with higher coupon rates, which would increase their interest expense. If interest rates remain stable, the call probability of existing bonds will depend on other factors such as the issuer's financial condition and the bond's call protection provisions.

To learn more about rate click here: brainly.com/question/14731228

#SPJ11

Answer:

Yes

Step-by-step explanation:

If you subsitute for x, x will only repeat if it has the same y value.

Yes, The given relation is a function.

Here,

The relation is given as; Y = 3x

We have to find the given relation is a function or not.

What is Function?

A relation is said to be function if there is exactly one value for each value of y.

Now,

The given relation is,

Y = 3x

When, we put x = 1 then y = 3

And, when x = 2 then y = 6 and so on.

Clearly, there is exactly one value of x for value of y.

So, The given relation is a function.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ2