2.The number of hours that the employees at the local Fry's grocery store worked last week is normallydistributed with a mean of 28 hours and a standard deviation of 4. What percentage of employees workedfewer than 32 hours?Answer:

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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Answer:

10

Step-by-step explanation:

7+15/5

Answer:

10

Step-by-step explanation:

subsitute

7+15/5=10

Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).

To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.

With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.

Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.

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Answer:

Step-by-step explanation:

Line B passes through (3.75, 0) and (0, negative 5) represents the line -3y = 15 – 4x. the slope of the line is = 4/3 and the y-intercept is -5.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

A line can be defined by the shortest distance between two points is called as a line.

Given the expression of the line,
–3y = 15 – 4x

Now by putting every given point of the lines given with their passing points in –3y = 15 – 4x , it is found that point (3.75, 0) and (0, -5) lies on the line.

Hence, the expression –3y = 15 – 4x represents line B.

Now, the slope and y-intercept of the equation.
Rearrange the equation into standard form,
y = 4/3 x - 5
Now compare the above equation with the standard form line
y = mx +c

m = 4/3 and c = -5

Thus, line B passes through (3.75, 0) and (0, negative 5) represents the line -3y = 15 – 4x. the slope of the line is = 4/3 and the y-intercept is -5.

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Answer:

Step-by-step explanation:

When they ask you to solve graphically they want you to construct those functions and note where the two lines intersect as that is the solution to the system of equations. Solving mathematically they will be equal when y=y so we can say

x-4=-x+6 add x to both sides

2x-4=6. add 4 to each side

2x=10. divide each side by 2

x=5, since y=x-4

y=5-4

y=1

So the lines will intersect at the point (5,1)

Answer:   (p - 1) • (5p + 3)

Step-by-step explanation: Changes made to your input should not affect the solution:

(1): "p2"   was replaced by   "p^2".  

STEP

1

:

Equation at the end of step 1

 (5p2 -  2p) -  3

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  5p2-2p-3  

The first term is,  5p2  its coefficient is  5 .

The middle term is,  -2p  its coefficient is  -2 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   5 • -3 = -15  

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   -2 .

     -15    +    1    =    -14  

     -5    +    3    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  3  

                    5p2 - 5p + 3p - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   5p • (p-1)

             Add up the last 2 terms, pulling out common factors :

                   3 • (p-1)

Step-5 : Add up the four terms of step 4 :

                   (5p+3)  •  (p-1)

            Which is the desired factorization

The 8 is in the ones place.

The 1 is in the tenths place.

The 3 is in the hundredths place.

The 9 is in the thousandths place.

hope it helps!

Answer:

By using opposite angles of two intersecting straight lines are congruent we proved that x = 28°

Step-by-step explanation:

Opposite angles of two intersecting straight lines are congruent

Therefore ∠DLE = ∠GLH

Here ∠DLE = 2x = ∠GLH

Sum of all angles on a straight line is 180°

Therefore ∠ELG + ∠GLH = 180°

Given that ∠ELG = 124°

124° + ∠GLH = 180°

124° + 2x  = 180°

2x = 180° -  124°

2x = 56°

x = 28°

hence proved that x = 28°

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Answer:

ounces = 16(6+2) + 16

Step-by-step explanation:

First you would have to find the conversion rate of pounds to ounces which is 16 ounces for 1 pound. That means that you would have to multiply 16 by the amount of pounds you have. Then you would have to add the amount of ounces you have onto the equation so A would be the one that does that.

Step-by-step explanation:

C you are gonna have 3,120.00 pesos

Answer:

\(-\frac{9}{1}\)

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

Answer: (c)

Step-by-step explanation:

Given

A person has a 30% chance of winning a lottery ticket.

Probability of not getting the lottery ticket is 70%

For person to win at fifth ticket, it must fail in first four

So, the probability associated with it is

\(\Rightarrow P=(0.70)\times (0.70)\times (0.70)\times (0.70)\times (0.30)\\\\\Rightarrow P=(0.70)^4\cdot (0.3)\)

Hence, option (c) is correct.

Given the quadratic equation:

Recall that the standard form of a quadratic equation is:

The given equation is already in standard form, therefore, we can now proceed identifying what is a, b and c.

We get,

Therefore,

a = 1

b = -8

c = 15

Answer: -0.530662 or 1.13066

Step-by-step explanation:

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

The formula of the parabola is y = 2/35(x + 7)(x - 5)

The parameters in the question are given as

These parameters can be represented as

x₁ = -7 and x₂ = 5

(x, y) = (0, -2)

The quadratic function can be represented as

y = a(x - x₁)(x - x₂)

Substitute the known values in the above equation So, we have the following equation

y = a(x + 7)(x - 5)

At (x, y) = (0, -2), we have

-2 = a(0 + 7)(0 - 5)

Evaluate

a = -2/-35

Divide

a = 2/35

So, we have

y = 2/35(x + 7)(x - 5)

Hence, the equation is y = 2/35(x + 7)(x - 5)

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Answer:

1 to the left and 7 up

Step-by-step explanation:

The x coordinate goes from 3 to 2, so that is your 1 to the left.

The y coordinate goes from -4 to 3, so that is your 7 up.

The fraction of the package of raisins Ashley left with will be equal to 7/18.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Amount of raisins used for fruit cake = 1/2

Amount of raisins used for muffins = 1/9

Then, the amount of raisins left will be,

1 - (1/2 + 1/9)

= [18 - (9 + 2)]/18

= (18 - 11)/18

= 7/18

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X = 31, Y = 63 satisfy the case of 0 ≤ Y < 100 as an expression.

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

Assume Kaimi was supposed to be paid X dollars Y cents (0 ≤ Y ≤ 100)

But the teller gave him Y dollars X cents.

Thus kaimi has 100Y + X cents.

A nickel is worth 5 cents.

Hence, after buying the piece of candy for a nickel, Kaimi would be left with 100Y + X - 5 cents.

This is twice his paycheck:

⇒ 100Y + X - 5 = 2(100X + Y)

⇒ 100Y + X - 5 = 200X + 2Y

⇒ 98Y - 199X = 5

199 = 98 × 2 + 3 ⇒ 3 = 199 - 98 × 2

98 = 3 × 32 + 2 ⇒ 2 = 98 - 3 × 32

3 = 2 × 1 + 1 ⇒ 1 = 3 - 2 × 1

2 = 1 × 2 + 0 ⇒ ged(199, 98) = 1

1 = 3 - 2 × 1

= 3 - (98 - 3 × 32) × 1                [∵ 2 = 98 - 3 × 32]

= 3 - 98 × 1 + 3 × 32

= 3 × 33 - 98 × 1

= (199 - 98 × 2) × 33 - 98 × 1    [∵ 3 = 199 - 98 × 2]

= 199 × 33 - 98 × 67

⇒ 1 = 199 × 33 - 98 × 67

⇒ 5(1) = 5 (199 × 33 - 98 × 67)

⇒ 5 = 199(165) - 98(335)         [∵ 5 ×33 = 165, 5 × 67 = 335]

⇒ 199(165) - 98(335) = 5

⇒ 98(-335) - 199(-165) = 5

Hence, (X,Y) = (-165, -335) is a solution to 98Y - 199X = 5

But it is required that 0 ≤ Y < 100

Now since it is the difference of two quantities, 98Y and 199X, that is a constant, 5, either both of these quantities will increase simultaneously or both will decrease simultaneously.

Hence, either both X, Y will increase or both, X, Y will decrease.

To bring Y = -335 in the range of 0 ≤ Y < 100, it needs to be increased.

Hence, both X, Y will increase.

X will increase by the absolute value of the coefficient of Y and vice-versa. Hence, X will increase by 98 and Y will increased by 199 to give

(X, Y) = (-165 + 98, -335 +199) = (-67, -136)

Still, it is not the case that 0 ≤ Y < 100

Hence, again X will increase by 98 and Y will increase by 199 to give

(X, Y) = (-67 +98, -136 +199) = (31, 63)

Now, it is the case that 0 ≤ Y = 63 < 100

∴ X = 31, Y = 63

Note that the increasing X again by 98 and Y by 199 will violate

0 ≤ Y < 100. Hence, this is the unique solution.

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Answer:

27

Step-by-step explanation:

let us assign variables and create an equation

15x+14x=29x=6003

x=27

thanks

Answer: 0.4337

Step-by-step explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean \(\mu=78\), Standard deviation  \(\sigma=36\)

Then, the probability that it is greater than 84 will be

\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)

Hence, the required probability = 0.4337

Answer:

50 minutes.

Step-by-step explanation:

We solve this question by proportions, using rule of three.

One hour is 60 minutes.

5/6 hour

This is:

\(\frac{5}{6}*60 = \frac{5*60}{6} = 5*10 = 50\)

50 minutes.

The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.

At Mega Mart, a 5kg cake costs $2500.

Therefore, the price per kilogram for this cake is:

Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.

At the same time, a 2kg chocolate cake costs $1200.

So, the price per kilogram for this cake is:

Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.

Now, let's calculate the total price for 10kg of cake from each option:

Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.

Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.

Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.

Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.

Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.

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The length of time that it will take for each of the workout sessions would be: Plan A = 1.5 hours, and Plan B =  0.5 hours.

The length of the sessions can be obtained by first obtaining drawing a system of equations for the two cases. On Wednesday, we can represent the sessions as follows:

2A + 12B = 9 hours

On Thursday, we would have

5A + 3B = 9 hours

2A + 12B = 9  Eqn 1

5A + 3B = 9   Eqn 2

Multiply equation 2 by -4

2A + 12B = 9

-20A - 12B = -36

2A - 20A = 9 -36

-18A = -27

Divide both sides by -18

A = 1.5 hours

For B, substitute A in the first equation

2(1.5) + 12B = 9

3 + 12B = 9

12B = 9 - 3

12B = 6

Divide both sides by 12

B = 0.5

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Complete Question:

Ann the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 2 clients who did Plan A and 12 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Ann trained her Wednesday clients for a total of 9 hours and her Thursday clients for a total of 9 hours. How long does each of the workout plans last?