where a and b are integers.

Find the values of a and b.

Optional working

+

a

b =

**Step-by-step explanation:**

This is a quadratic with vertex at (2,1) ....write the equation first in vertex form, then expand to the form requested

y = ( x -2)^2 + 1

y = x^2 -4x +4 + 1

** y = x^2 -4x + 5 Done. a = -4 b = 5 **

johnny can build in 3 1/2 lego planes in 60 minutes. how many can he build in 40 minutes?

The number of **lego **planes that can be **build **in 40 minutes is A = 2.33

Given data ,

Johnny can **build **in 3 1/2 **lego **planes in 60 minutes

On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:

From the **proportion **, we get

To find out how many planes he can build in 40 minutes, we can multiply the amount he can **build **in one minute by 40:

3.5 / 60 = A / 40

Multiply by 40 on both sides , we get

A = 2.33

Hence , Johnny can build approximately 2.33 **lego **planes in 40 minutes

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every year 5 rows and 5columns are increased . derive the formula for the number of students in each row

The number of students in each row after any number of years, as long as the increase in **rows and columns** is uniform every year.

Assuming that the** increase** in rows and columns is uniform every year, we can derive the formula for the number of students in each row as follows:

Let's start with the initial number of rows and columns, which we'll call R0 and C0, respectively, and the number of students in each row, which we'll call S.

After one year, the number of rows and columns will increase by 5, so we'll have R1 = R0 + 5 and C1 = C0 + 5. The total number of students will be R1 x S. We can also **express** this in terms of the initial number of rows and columns as:

R1 x S = (R0 + 5) x S

Expanding the brackets, we get:

R1 x S = R0 x S + 5 x S

**Subtracting **R0 x S from both sides, we get:

(R1 - R0) x S = 5 x S

**Dividing** both sides by 5 x (R1 - R0), we get:

S = 5 / (R1 - R0)

We can use this formula to calculate the number of students in each row after any number of years, as long as the increase in rows and columns is uniform every year.

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Please help I’ll mark you as brainliest if correct!

Using **similar side theorem**, the side with equivalent **proportion** to the given side is RQ/SQ

**Similar triangles** are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

In this problem, we can use this same theory to find the equivalent side of the given **proportion**.

OQ / PQ = RQ / SQ

The equivalent side is RQ/SQ

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Joe King thinks he is "top notch" and buys a bouquet of flowers to pass out to all the ladies... The bouquet has 7 purple tulips, 9 yellow daisies and 12 pink roses. He grabs a flower from the bouquet and gives it to Anita Bath. Then Joe grabs another flower and gives it to Lois Price.

What is the probability that Anita gets a purple tulip and Lois gets a pink rose?

The **probability **that Anita gets a purple tulip and Lois gets a pink rose is 1/9.

**Total number** of flowers in the bouquet = 7 purple tulips + 9 yellow daisies + 12 pink roses = 28 flowers.

P(Anita gets a purple tulip) = 7 purple tulips / 28 total flowers = 7/28 = 1/4.

P(Lois gets a pink rose) = 12 pink roses / 27 remaining flowers = 12/27 = 4/9.

P(Anita gets a **purple tulip** and Lois gets a pink rose) = P(Anita gets a purple tulip) * P(Lois gets a pink rose)

= (1/4) * (4/9) = 1/9.

Therefore, the **probability **that Anita gets a purple tulip and Lois gets a pink rose is 1/9.

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The circle graph shows how Josh's family budgets a total of $6200 for the month.

Housing

$1178

Category

Clothing

Insurance

Transportation

Taxes

$1364

Taxes

Food

$868

$248 Insurance

$186

Utilities

$496

Savings

$434

Find the percentage of the total budgeted for each category listed below.

Percentage

0%

0%

0%

Clothing

Entertainment

$682

The **percentage **of the total **budgeted **category is given by

a) Clothing : 12 %

b) Insurance : 3 %

c) Taxes : 22 %

Given data ,

Let the **percentage **value be represented as A

Now , the value of A is

Let the total **budgeted **amount be = $ 6,200

Now , the amount for clothing = $ 744

So , the **percentage **for clothing = 744 / 6200 = 12 %

And , the amount for insurance = $ 186

Now , the **percentage **for insurance = 186 / 6200 = 3 %

And , the amount for taxes = $ 1,364

So , the **percentage **for taxes = 1364 / 6200 = 22 %

Hence , the **percentages **are solved

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A cone has a volume of 2560 Pi cm cubed and a height of 30cm. Find the radius

First the given question is

•A volume of 2560 pi cm cube

•A height of 30 centimeters

The the required one

•The radius of the cone

Then find the solution

Using the formula

V=πr squared * h/3

Solving for

r=3V 3·2560

π·30≈9.02703

πh=

•A volume of 2560 pi cm cube

•A height of 30 centimeters

The the required one

•The radius of the cone

Then find the solution

Using the formula

V=πr squared * h/3

Solving for

r=3V 3·2560

π·30≈9.02703

πh=

A chambered nautilus is a marine animal that lives in the outermost chamber of its shell

The chambered nautilus is a fascinating marine animal that belongs to the family of **cephalopods**.

It is notable for its unique, **spiral-shaped** shell that is divided into a series of chambers.

The nautilus lives in the outermost chamber of its shell, which it can control by adjusting the amount of **gas and fluid** inside it. This allows the nautilus to regulate its buoyancy and move up or down in the water column.

The nautilus has been around for millions of years and is sometimes called a "**living fossil**" because of its ancient lineage.

Unfortunately, due to overfishing and habitat destruction, many species of nautilus are **now endangered**.

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The given question is incomplete, the complete question is:

A chambered nautilus is a marine animal form which family?

Three students share pawpaw as follows: Mark get 1/4 of the total and the remainder is shared between Eric and Francis in a ratio 2:3. If Eric get 48 pawpaws does Mark and Francis had ?

The **total number **of pawpaws was 160, which can be found by using simple **equations **considering the amount taken by Eric and the proportion.

Let's start by finding out how many **pawpaws **are left after Mark takes 1/4 of the total. Let T be the total number of pawpaws. **Mark **gets 1**/**4 of T, which means there are 3/4 of T left:

3/4T = Total number of pawpaws - Mark's share

3/4T = T - 1/4T

3/4T = 3/4T

So, 3/4T is the amount shared between **Eric **and **Francis**. The ratio of Eric's share to Francis' share is 2:3. Let's call Eric's share E and Francis's share F.

E/F = **2/3**

We can use this ratio to write an equation for Eric's share in terms of F:

E/F = 2/3

E = (2/3)F

We know Eric's share is **48**, so we can substitute that into the **equation **and solve for F:

E = (2/3)F

48 = (2/3)F

F = (48*3)/2

F = 72

So, Francis has 72 pawpaws.

We can now find out how many pawpaws Mark got:

Mark's share + Eric's share + Francis's share = **Total number **of pawpaws

1/4T + E + F = T

1/4T + 48 + 72 = T

T = 480/3

T = **160**

So, the total number of pawpaws is 160. Mark got 1/4 of the total, which is:

Mark's share = (1/4)*160 = 40

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Can someone please help me with this? Explaining would really help thank you

The **solution** of the **equation** is x=1/2 and y=1/3

The given **equations** are

18x+12y=13...(1)

30x+24y=23...(2)

Let us form the matrix form to solve the equation

[tex]\left[\begin{array}{ccc}18&12\\30&24\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}13\\23\end{array}\right][/tex]

Multiply equation (1) with 2

36x+24y=26..(3)

Subtract **equation **3 from equation 2

30x+24y-36x-24y=23-26

-6x=-3

x=1/2

Now plug in the value of x in equation 1

18(1/2)+12y=13

9+12y=13

12y=4

y=4/12

y=1/3

Hence, the **solution** of the equation is x=1/2 and y=1/3

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how do u graph the solution y=2x-1 iready

**Answer:**

**Step-by-step explanation:**

y=mx+b

m= slope and b= y intercept

you'll start with a point on the y axis on -1

and the slope will go up so towards the right corner up but 2/1 points

please help with geometric series

**Answer:**

[tex]C. -5.15\cdot10^{13}[/tex]

**Step-by-step explanation:**

[tex]Common\ ratio\ (r)=\frac{a_{n+1}}{a_n}=(-3)\\\\Sum\ (S_n)=\frac{a(r^n-1)}{r-1}\ \ (r\neq1)\\\\\implies S_n=\frac{1\ (\ (-3)^{30}-1\ )}{-4}\\\\\implies S_n=\frac{205891132094649-1}{-4}\\\\\approx\frac{206\cdot10^{12}}{-4}\\\\\approx-5.15\cdot10^{13}[/tex]

Solve.

10 - 9x^2 + 4x = -6x^210−9x

2

+4x=−6x

2

**Answer: **the solutions to the equation are x = √(10/3) and x = -√(10/3).

**Step-by-step explanation:**

To solve the equation 10 - 9x^2 + 4x = -6x^2 + 4x, we can simplify it and then solve for x.

Rearranging the equation, we have:

10 - 9x^2 + 4x = -6x^2 + 4x

Combining like terms, we get:

10 - 9x^2 = -6x^2

Subtracting -6x^2 from both sides, we have:

10 - 9x^2 + 6x^2 = 0

Simplifying further, we get:

10 - 3x^2 = 0

To solve for x, we can isolate the term with x^2:

-3x^2 = -10

Dividing both sides by -3, we have:

x^2 = 10/3

Taking the square root of both sides, we get:

x = ±√(10/3)

Therefore, the solutions to the equation are x = √(10/3) and x = -√(10/3).

Write the equation of the circle for which ý(22, 21) and p(6, 23) are the endpoints of

a diameter of the circle.

**Answer:**

[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]

**Step-by-step explanation:**

If the two given points are the extremes of the diameter, the center of the circle has to be its middle point - that we can find by taking the average of the coordinates. The center thus sits in

[tex](\frac{22+6}2; \frac{21+23}2)[/tex]* *or [tex](14; 22)[/tex]. At this point we either find the length of the diameter and halve it, or the distance between the center and either point. Let's go for the diameter.

[tex]r=\sqrt{(22-6)^2+(21-23)^2}=\sqrt{16^2+2^2} = \sqrt {260}=2\sqrt{65}[/tex]. That makes our radius half of that. We can easily write the equation of the circle now:

[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]

Now, in theory you can improve it by multiplying it out and taking every term to the LHS, but I think it's good enough like that.

jasmine bikes the same distance every day. in 8 days, she biked a total of 32 miles. How far will she bike in 5 days?

**Answer:**

20

**Step-by-step explanation:**

She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.

How is the graph of y(x-1)²-3 transformed to produce the graph of y(x+4)²

O The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.

O The graph is stretched vertically by a factor of 2, translated left 5 units, and translated up 3 units.

The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units.

O The graph is stretched horizontally by a factor of 2, translated left 5 units, and translated down 3 units.

Mark this and return

Save and Exit

Next

Submit

The** transformations** are:

Shift up 3 units.

Shift left 5 units.

Vertical **compression** of scale factor 2.

The correct option is the first one.

Here, we have,

Here we start with the original **function**:

y = (x - 1)^2 - 3

And it will be transformed into the new **function:**

y = (1/2)*(x + 4)^2

So let's start with the first **function**, and apply t**ransformations** until we reach the new one.

y = (x - 1)^2 - 3

If we shift it up by 3 units, then we get:

y = [ (x - 1)^2 - 3 ] + 3 = (x - 1)^2

If now we shift it to the left 5 units, then we get:

y = ( (x + 5) - 1)^2 = (x + 4)^2

finally, we **compress** the graph by a factor of 2, so we get:

y = (1/2)*(x + 4)^2

The order may be different, but from that we conclude that the correct option is the first option.

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complete question:

graph of y = (x- 1)2 -3 transformed to produce the graph of y = - 1/2(X+-4)2?

O The graph is translated left 5 units, compressed vertically by a factor a of 2, and translated up 3 units.

The graph is stretched vertically by a factor of 2, translated left 5 units, and translated up 3 units.

• The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units.

• The graph is stretched horizontally by a factor of 7, translated left 5 units, and translated down 3 units:

WHAT IS THE FIRST STEP TO SOLVE 3(4x + 5) = 12

First step:

Multiplying 3 by each term inside the parentheses, we get:

12x + 15 = 12

Multiplying 3 by each term inside the parentheses, we get:

12x + 15 = 12

-8.915444681 round to nearest hundred miles

On rounding the given number to nearest **hundred** miles will give the result -8.92.

**Rounding** to nearest hundred miles refers to changing the number present on **hundreds place**. We see that the number 8 is at unit's place, 9 is at tenth's place and 2 is at hundred's place.

Based on the **rules** of rounding, we will check the number to the right of number on hundred's place. Since the next number is 5, the number we will round the number 1 present at hundred's place. Hence, the final number will be -8.92.

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What is the scale of the x-axis in this coordinate graph?

A. 1 tick mark represents 0.1 unit

B. 1 tick mark represents 0.2 unit

C. 1 tick mark represents 0.3 unit

D. 1 tick mark represents 0.4 unit

**Answer:**

B. 1 tick mark represents 0.2 unit

**Step-by-step explanation:**

Looking at the axis and going over **2 tick marks is .4**

.4 /2 = .2

Each tick mark is .2 units

Which of the following can be used to evaluate the series 8∑k=1 5(2/3)^k-1?

The evaluation of the **geometric series** is found as:

[tex]5(1- \frac{2}{3}^{8} / 1- \frac{2}{3} )[/tex]

The given series is

[tex]8∑k=1 5(2/3)^k-1[/tex]

A **geometric series **is described as the sum of an infinite number of terms that have a constant ratio between successive terms.

Since this is a** geometric series**, we apply formula for the sum of the first k terms.

[tex]S= a( 1- r^{k} / 1-r )[/tex]

From the series, first term a = 5, common ratio r = 2/3 , k = 8

We substitute the values to obtain:

he evaluation of the series is found as:

[tex]5(1- \frac{2}{3}^{8} / 1- \frac{2}{3} )[/tex]

**Geometric series** finds its applications in Physics, **engineering**, biology, economics, computer science, queueing theory, and finance.

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complete question is attached in image

NO LINKS!!! URGENT HELP PLEASE!!!

3. A virus has infected 400 people in the town and is spreading to 25% more people each day. Write an exponential function to model this situation, then find the number of 3000 people are infected.

4. The population of a small town was 10,800 in 2002. Since then, the population has decreased at a rate of 2.5% each year. Write an exponential function to model the situation, then find when the popuation reaches half the 2002 value?

**Step-by-step explanation:**

3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:

P(t) = 400 * 1.25^t

Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.

To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:

P(t) = 400 * 1.25^t

P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))

P(t) ≈ 2,343

Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.

4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:

P(t) = 10,800 * 0.975^t

Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.

To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:

5,400 = 10,800 * 0.975^t

0.5 = 0.975^t

log(0.5) = t * log(0.975)

t ≈ 28.2

Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.

**Answer:**

3) 9.03 days

4) 27.38 years

**Step-by-step explanation:**

To model the spread of the virus over time, we can use an **exponential function** in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

P(t) is the number of infected people after t days.P₀ is the initial number of infected people.r is the daily growth rate (as a decimal).t is the time elapsed (in days).Given the virus has infected 400 people in the town and is spreading to 25% more people each day:

P₀ = 400r = 25% = 0.25**Substitute **these values into the **formula **to create a **function for P in terms of t**:

[tex]P(t) = 400(1 + 0.25)^t[/tex]

[tex]P(t) = 400(1.25)^t[/tex]

To find **how many days** it will take for **3000 people** to be infected, set P(t) equal to 3000 and** solve for t**:

[tex]\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}[/tex]

Therefore, it will take approximately **9.03 days** for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.

Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.

[tex]\hrulefill[/tex]

Question 4To model the population of the town over time, we can use an **exponential function** in the form:

[tex]\large\boxed{P(t) = P_0(1 - r)^t}[/tex]

where:

P(t) is population after t days.P₀ is the initial population.r is the annual decay rate (as a decimal).t is the time elapsed (in days).Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:

P₀ = 10,800r = 2.5% = 0.025**Substitute **these values into the **formula **to create a **function for P in terms of t**:

[tex]P(t) = 10800(1 -0.025)^t[/tex]

[tex]P(t) = 10800(0.975)^t[/tex]

To find **how many days** it will take for the **population to halve**, set P(t) equal to 5400 and** solve for t**:

[tex]\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}[/tex]

Therefore, it will take approximately **27.38 years** for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.

What is the end behavior for f(x) = 2x^3 -3x -4x^4+1

Based on the given** polynomial function**, as x approaches positive or negative infinity, the **function** f(x) = 2x³ - 3x - 4x⁴ + 1 approaches negative infinity.

The end behavior of a** polynomial function** is determined as follows:

Examine the leading term of the function f(x) = -4x⁴ + 2x³ - 3x + 1

The leading term of the function is -4x⁴.

For large positive values of x, as x approaches positive infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the **end behavior **of the **function** as x approaches positive infinity is that f(x) approaches negative infinity.

Similarly, for large negative values of x, as x approaches negative infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the end behavior of the function as x approaches negative infinity is that f(x) approaches negative infinity.

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PLS HELP ME OUT MARKING AS BRAINlist

**Answer:**

The answer is 176

**Step-by-step explanation:**

First lets find the area of rectangle by multiplying 16 by 8 to get 128.

Now lets find the area of each triangle. We know that one side is 6 cm and the base of both is 16.

So to find the base of one triangle we divide 16 by 2 to get 8.

Now we know that the base of one triangle is 8, so lets sub. that into the equation for a triangle. 1/2(b)(h) to get

1/2(6)(8)=24

Since there are two triangle 24+24=48 for area of both triangles

Now lets add that to the answer for the rectangle to get area for whole structure

128+48 = 176

So the answer is 176

HOPE THAT HELPS :)

Using the present value approach, solve the following:

Tom has $100 in a bank account that pays a guaranteed 5% interest rate each year. How much would Tom have at the end of Year 3?

**Answer:**

**Step-by-step explanation:**

$100x0.5x1=$5

Pretest: Unit 5

Question 6 of 25

If a sample proportion is 0.65, which range of possible values best describes

an estimate for the population parameter?

OA. (0.6, 0.69)

B. (0.65, 0.7)

O C. (0.5, 0.89)

OD. (0.5, 0.8)

SUBMIT

The range of possible values for the population parameter can be estimated using the margin of error, which is calculated as the critical value times the standard error.

Assuming a 95% confidence level, the critical value is approximately 1.96. The standard error for a sample proportion can be calculated as:

SE = sqrt[(p * (1 - p)) / n]

Where p is the sample proportion and n is the sample size. Substituting the values given in the question, we get:

SE = sqrt[(0.65 * 0.35) / n]

We do not know the sample size, so we cannot calculate the standard error exactly. However, we can use a rule of thumb that states that if the sample size is at least 30, we can use the normal distribution to estimate the margin of error.

With a sample proportion of 0.65, the margin of error can be estimated as:

ME = 1.96 * sqrt[(0.65 * 0.35) / n]

We do not know the sample size, so we cannot calculate the margin of error exactly. However, we can use the rule of thumb that a margin of error of about ±5% is typical for a 95% confidence level.

Using this margin of error, we can construct the following range of possible values for the population parameter:

0.65 ± 0.05

This range can be expressed as (0.6, 0.7), which corresponds to option A.

Therefore, the correct answer is option A) (0.6, 0.69).

The population of bees worldwide has been in decline. There are estimated to be 2,000,000,000 bees worldwide and each year there is estimated to be 10% less. How many bees worldwide will there be in 10 years?

**ANSWER: 100% of 2000000000 is 2000000000**

**What is 100 Percent of 2000000000?**

100 percent *2000000000

= (100/100)*2000000000

= (100*2000000000)/100

= 200000000000/100 = 2000000000

Now we have: 100 percent of 2000000000 = 2000000000

Question: What is 100 percent of 2000000000?

We need to determine 100% of 2000000000 now and the procedure explaining it as such

Step 1: In the given case Output Value is 2000000000.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 2000000000 = 100%.

Step 4: In the Same way, x = 100%.

Step 5: On dividing the pair of simple equations we got the equation as under

2000000000 = 100% (1).

x = 100% (2).

(2000000000%)/(x%) = 100/100

Step 6: Reciprocal of both the sides results in the following equation

x%/2000000000% = 100/100

Step 7: Simplifying the above obtained equation further will tell what is 100% of 2000000000

x = 2000000000%

Therefore, **100% of 2000000000 is 2000000000**

Can someone help me find the surface area of these cylinders??

The** surface area **for each of the cylinders is given as follows:

**13.** 126 yd².

**14. **490 m².

**15. **283 mm².

**16. **297 cm².

The surface area of a cylinder of **radius r and height h** is given by the equation presented as follows, which combines the base area with the lateral area:

S = 2πrh + 2πr²

S = 2πr(h + r)

**Item 13:**

r = 2 yd and h = 8 yd, hence the **surface area **is given as follows:

S = 2π x 2(2 + 8)

S = 126 yd².

**Item 14:**

r = 6 m and h = 7 m, hence the **surface area **is given as follows:

S = 2π x 6(6 + 7)

S = 490 m².

**Item 15:**

r = 3 mm and h = 12 mm, hence the **surface area **is given as follows:

S = 2π x 3(3 + 12)

S = 283 mm².

**Item 16:**

r = 3.5 mm and h = 10 mm, hence the **surface area **is given as follows:

S = 2π x 3.5(3.5 + 10)

S = 297 cm².

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Ivy Corporation gave 74 people a bonus. If Ivy had given 3 more people bonuses, Ivy would have rewarded 13

of the workforce. How large is Ivy’s workforce?

If Ivy had given 3 more people **bonuses**, Ivy would have rewarded 13 of the workforce, Ivy Corporation's workforce has 592 employees.

Let's assume that the total **workforce** at Ivy Corporation is represented by "x".

According to the problem statement, Ivy Corporation gave a bonus to 74 people. Therefore, the remaining non-bonus-receiving **employees** would be (x-74).

If Ivy had given 3 more people bonuses, then the number of employees that would receive the bonus would be (74+3)=77.

According to the problem, 77 is **equal** to 13% of the total workforce (x):

77 = 0.13x

We can solve for x by **dividing** both sides by 0.13:

x = 592

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100 tickets are sold for $1 each there is $25 prizes and a $10 prize what is the expected value for a person that buys a ticket round to the nearest cent

The **expected value** for a person buying a **ticket** is $0.35 rounded to the nearest cent.

The expected value is calculated considering the probabilities of winning each prize and the corresponding values of each prize.

Assuming:

P($25) as the **probability** of winning the $25 prize

P($10) as the probability of winning the $10 prize

There are 100 **tickets** sold, therefore, the probabilities can be found as follows:

P($25) = 1/100 (since there is only 1 $25 prize)

P($10) = 1/100 (since there is only 1 $10 prize)

The **expected value (E)**, will then be:

E = P($25) * $25 + P($10) * $10

E = (1/100) * $25 + (1/100) * $10

E = $0.25 + $0.10

E = $0.35

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Diondra wants to know the most popular movie of this year but is unsure of the best way to determine this answer. Which of the following questions would Diondra ask that does NOT allow for variability?

Which movie did her best friend like the most?

How many awards did each movie win?

What is the total dollar amount that each movie made from ticket sales?

How many weeks did each movie play in the theater?

The question that **Diondra **would ask that does not allow for **variability **is A. Which movie did her best friend like the most?

The other three **questions **("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a **movie's popularity **could be measured, and those measurements could vary from movie to movie.

However, the question about her best **friend's favorite movie **depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.

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What are the solutions to the system of equations graphed?

**Answer:**

(- 2, 0 ) , (1, - 3 )

**Step-by-step explanation:**

the solutions to the system of equations are at the points of intersection with the curve and the straight line.

points of intersection are at (- 2, 0 ) and (1, - 3 ) , then

solutions are (- 2, 0 ) , (1, - 3 )

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