Question 1 (5 points)
(03.06A LC)
How many solutions does the equation 4p + 7 = 3 + 4 + 4p have? (5 points)

a
One

b
Two

c
Infinitely many

d
None

Question 2 (5 points)
(03.06A HC)
The work of a student to solve the equation 2(3x − 4) = 8 + 2x + 4 is shown below:

Step 1: 2(3x − 4) = 8 + 2x + 4
Step 2: 5x − 6 = 12 + 2x
Step 3: 5x − 2x = 12 + 6
Step 4: 3x = 18
Step 5: x = 6

In which step did the student first make an error and what is the correct step? (5 points)

a
Step 2; 6x − 6 = 2(6 + x + 2)

b
Step 2; 6x − 8 = 12 + 2x

c
Step 3; 5x − 2x = 12 − 6

d
Step 3; 5x + 2x = 12 + 6

Question 3 (5 points)
(03.06A LC)

Which statement is true about the equation fraction 3 over 4 z − fraction 1 over 4 z + 3 = fraction 2 over 4 z + 5? (5 points)

a
It has no solution.

b
It has one solution.

c
It has two solutions.

d
It has infinitely many solutions.

Question 4 (5 points)
(03.06A MC)
What is the solution to the equation 1.6m − 4.8 = −1.6m? (5 points)

a
m = 0.5

b
m = 0.7

c
m = 1.5

d
m = 3

Question 5 (5 points)
(03.07A MC)
Two lines, C and D, are represented by the equations given below:

Line C: y = x + 14
Line D: y = 3x + 2

Which of the following shows the solution to the system of equations and explains why? (5 points)

a
(6, 20), because both lines pass through this point

b
(6, 20), because the point does not lie on any axis

c
(3, 11), because one of the lines passes through this point

d
(3, 11), because the point lies between the two axes

Question 6 (5 points)
(03.07A LC)

The coordinate grid shows the graph of four equations:

A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.

Which set of equations has (3, 1) as its solution? (5 points)

a
A and B

b
C and D

c
B and D

d
A and D

Question 7 (5 points)
(03.07A MC)
Two equations are given below:

a − 3b = 16
a = b − 2

What is the solution to the set of equations in the form (a, b)? (5 points)

a
(−2, −6)

b
(−7, −9)

c
(−11, −9)

d
(−12, −10)

Question 8 (5 points)
(03.07A LC)
Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's age (p) and Winnie's age (w):

p = w + 2
p = 7w − 16

Which is a possible correct method to find Peter's and Winnie's ages? (5 points)

a
Solve w + 2 = 7w − 16 to find the value of w.

b
Solve p + 2 = 7p − 16 to find the value of p.

c
Write the points where the graphs of the equations intersect the x axis.

d
Write the points where the graphs of the equations intersect the y axis.

Question 9 (10 points)
(03.07A MC)
A pair of equations is shown below:

y = 7x − 8
y = 5x − 2

Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)

Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)

Answer:

(4, -6)

Step-by-step explanation:

(x1+x2)/2 + (y1+y2)/2 = midpoint

(11+-3)/2 = 8/2 = 4.     x = 4

(-5 + -7)/2 = -12/2.      y = -6

4, -6 is the midpoint

give brainliest please! hope this helps :)

Answer:

V≈0.064

Tip:

just to help you for future note with finding volume with fractions is you use a calculator and do the top divided by the bottom and it should give you a decimal

John William is entitled to purchase 15,000 shares before the offering is made to the public.

a. To calculate the percentage of the total vote John William will control, we need to find the proportion of shares he owns out of the total shares represented at the meeting.

John William owns 6,000 shares out of the 20,000 shares offered so far. Therefore, the proportion of shares he owns is 6,000/20,000, which simplifies to 3/10 or 0.3.

To convert this proportion to a percentage, we multiply by 100:

Percentage of the total vote = 0.3 * 100 = 30%

Thus, John William will control 30% of the total vote at the.         shareholder meeting.    

b. Preemptive rights allow existing shareholders to purchase new shares before they are offered to the public. To determine the number of shares John William is entitled to purchase, we need to calculate the proportion of his current ownership.

John William owns 6,000 shares out of the total shares offered so far, which is 20,000. Therefore, his ownership proportion is 6,000/20,000, or 3/10.

If Peixotto Media plans to issue 50,000 new shares, John William's entitlement would be:

Entitlement = (3/10) * 50,000 = 15,000 shares.

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Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  160

Step-by-step explanation:

The problem statement tells us ...

  (# in museum) = 4 × (# waiting)

  (# in museum) = 4 × 40 . . . . . . . . . . . . the number waiting is 40

  # in museum = 160

Marian had a balance of $102

Then she made two deposits, one of $75 and the other for $50

We can calculate the balance of her checking account after the deposits were done

New balance = $102 + $75 + $50 = $227

The account needs to have at least $300 to avoid a service fee, so we calculate how much is needed to complete that amount

New deposit = $300 - $227 = $73

So, if Marian deposits at least $73, the account balance will be $300 or more

Answer: She must deposit at least $73

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

First we are going to calculate how much she paid for the $150000 when she was 35 years old

Now we calculate how much she is going to pay now that she is 45

Then she will pay 1294.5-925.5=369 dollars more

Answer:

17 days

Step-by-step explanation:

238/14 = 17

Answer:

4/3

Step-by-step explanation:

You use Rise over Run.

It runs 3 blocks to the left (+).

It rises 4 blocks up (+).

Answer:

is the change in y over the change in x

Notes are commonly issued on discounted value when the issuer needs to raise funds quickly and is willing to accept a lower price for the note in exchange for immediate cash.

Notes can be issued either at their face value or at a discounted value.

A note is issued at its face value, the price of the note is the same as the face value of the note.

This is known as issuing the note at par value or face value.

A note is issued at a discounted value, the price of the note is lower than the face value of the note.

This is known as issuing the note at a discount.

The difference between the face value of the note and the discounted value is called the discount.

The investor who purchases the note at a discounted value will receive the face value of the note when it matures.

Notes may be issued at face value or at a discount from that amount.

The price of a note is equal to its face value when it is issued, or at face value.

The note will then be issued at face value or par value.

A note is sold for less than its face value when it is issued at a reduced price.

This is referred to as discounting the note's issuance.

The discount is the amount that separates the note's face value from its reduced value.

The face value of the note will be paid to the investor who paid the reduced price when the note matures.

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Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))

To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.

The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.

The total number of possible arrangements is given by the factorial of the total number of letters:

Total arrangements = 10!

However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:

Total arrangements = 10! / (2!)

To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.

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The equation of a graph is a mathematical statement true only for points of that graph. The equation of specified circle is: x² + y² −41 = 0

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as: (x-h)²+(y-k)² = r²

For given case, we have h = 0, and k = 0,

We know that,

The shortest distance (straight line segment's length connecting both given points) between points (p, q) and (x, y) is:

D = √(x-p)² + (y-q)²  units.

Also,

Radius = distance between O and B as length of radius, which is

r = √[(4-0)² + (5-0)²] = √[16+25] = √41   units.

Thus, we have the equation as:

(x-h)² + (y-k)² = r²

x²+ y² = (√41)²

x² + y² = 41

x² + y² - 41 = 0

Hence, The equation of specified circle is: Option b) x² + y² - 41 = 0

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Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

The solution to the equations are b = 15, b = 22, c = 21 and n = 28

From the question, we have the following equations that can be used in our computation:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Answer:

Acute

Step-by-step explanation:

All triangles have to have a acute or it would be to big

Answer:

yes it is because its a triangle and its acute

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Then you can state that angle DEF is congruent to angle GHJ.

The postulate or theorem that allows you to state that angle DEF is congruent to angle GHJ is the Angle-Angle (AA) Postulate.

This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles must also be congruent.

In this case, if you have two triangles, one with angles DEF and the other with angles GHJ, and

you know that angle D is congruent to angle G and angle E is congruent to angle H, then by the AA Postulate, you can conclude that angle F is congruent to angle J.

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Answer:

50,12

Step-by-step explanation:

any number that has 5 in the tensplace is correct

1/10 of 100 is 10

Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.

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The answer is 20.

4 isn't divisible by 5 and 5 isn't divisible by 4.

4 8 12 16 24 28

5 10 15 20 25

Answer:

Step-by-step explanation:

2/5 and 3/4

5*4 = 20

Hope that helps!

You will find it easiest if you write the integral in the form.

∫??∫??13 ,∫??∫??1r3drdθ ,that is, with θ on the "outside" integral. Looking at your diagram, the minimum θ value in the region of integration is =0θ=0, which occurs along the x axis. The maximum θ value occurs at the point (1,1)(1,1), giving =/4θ=π/4. So we have∫/40∫??13 .∫0π/4∫??1r3drdθ .For any fixed θ value, the values of r in the region go from the vertical line =1x=1 to the semicircle. At =1x=1 we have =secr=sec⁡θ as you have noted. The easiest way to get the maximum r value is to draw a line from the origin at angle θ until it hits the semicircle, and a line from there to (2,0)(2,0). Then you can see in the diagram a right-angled triangle (because the angle in a semicircle is a right angle) with hypotenuse 22, and so we get max=2cosrmax=2cos⁡θ. So the integral is∫/40∫2cossec13 .∫0π/4∫sec⁡θ2cos⁡θ1r3drdθ .For sketching the graph,=2−2‾‾‾‾‾‾‾√⇒2−2+2=0⇒(−1)2+2=1 ,y=2x−x2⇒x2−2x+y2=0⇒(x−1)2+y2=1 ,and not forgetting that ≥0y≥0.

Answer:

there are 5 boys

Step-by-step explanation:

Answer:

waitttttttttttttttt- MY DAD IS A TEACHER!?!?!?!??!?!??!??!?!?!?!?

Step-by-step explanation:

I DIDNT KNOW MY DAD WAS A TEACHER-

Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

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The equation which represents the relationship between X values and Y values can be found by deriving the equation of line using slope intercept form. The equation of line is 3x - 5y = 25.

How to find equation of line using slope intercept form?

Equation of line using slope intercept form is y = mx + b

where m is slope of the line and b is y-intercept

The slope intercept can be used to form equation of line using two points on the line.

According to the given question:

The two points which lie on the line are (x, y) = (5, -2) and (x', y') = (0, -5)

Slope of the line m = y' - y/x' - x

                               = (-5 +2)/(0 - 5)

                               = 3/5

Now y intercept b = y - mx

                              = -2 - (3/5. 5)

                              = -5

Therefore the required equation of line is y = 3/5x - 5

On simplifying further 3x - 5y = 25

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Answer:

-7(5-u)

Step-by-step explanation:

-7(5-u)

-7x5  -7x-u

-35+7u

Answer:

-35+ 7u

Step-by-step explanation:

Distribution Property

distribute the first time by the 2 terms in the parenthesis

-7×5 and -7u

-35 - (-7u)

-35+ 7u

Answer:

B: 3/2x - 7 + 3 = 0

Step-by-step explanation:

Answer: C

Step-by-step explanation:

General form is in Ax+By+C. To do this, you move everything onto one side.

\(\frac{3}{2}x -y+3=0\)

This should be the general form, but this is not correct in these answer choices! Let's try this another way to get Ax+By+C by making Ax not a fraction.

\(y=\frac{3}{2} x-3\)

\(y+3=\frac{3}{2} x\)

\(2(y+3)=3x\)

\(2y+6=3x\)

\(3x-2y-6=0\)

This may seem incorrect, but we can always check our answer by plugging in numbers.

In our slope intercept form, let's say x=2. What would be our y?

\(y=\frac{3}{2} (2)-3\)

\(y=3-3\)

\(y=0\)

Now we know our coordinates should be (2, 0). When we rewrite the slope-intercept form, we should still get 0 when we plug in x=2 and y=0. Let's check on all answer choices to see which one works.

A. Correct

-3(2)+2(0)+6

-6-6=0

0=0

B. Incorrect

3/2(2)-(0)+3

3+3=6

6≠0

C. Correct

3(2)-2(0)-6

6-6=0

0=0

D. Incorrect; not general form

2(0)=3(2)-6

0=6-6

Now, you can see that A and C are both correct, but the main difference, is that you want to make A positive. The only option where A is positive is in answer C.