Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5

z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2

PLease help

The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.

The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.

There are 4 tickets purchased so the equation would be:

4 x Cost of tickets - Parking cost = Total spent

4 x - 25 = 175

The cost of each admission ticket is:

4 x - 25 = 175

x = 150 / 4

x = $ 37.50

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Step-by-step explanation:

step A is incorrect.

-40/5 does not equal to -40/-5.

-40/-5 is equal to 40/5 as we can simplify the negative 1 out.

Answer:

The correct answer is step A

The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.

Let A denote the event that a student does not have a sibling.

Let B denote the event that a student has a pet.

Then A∩B will denote the event that the student does not have a sibling but he has a pet.

Let P denote the probability of an event in this question.

Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.

P(B|A)

We know that:

[tex]P(B|A) = \frac{P(A\cap B)}{P(A)}[/tex]

Also from the table, we have:

P(A)=0.25

and P(A∩B)=0.15

Hence,

[tex]P(B|A) = \frac{0.15}{0.25}[/tex]

[tex]P(B|A) = \frac{3}{5}[/tex]

[tex]P(B|A) = 0.6[/tex]

which in percentage is:

0.6 * 100 = 60 %

Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.

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Using the property of proportionality for the equation (6-x) : (7-x) :: (18-x) : (22-x), then, x = ⁶/₇.

Solving this problem by using the property of proportionality, which states that the ratio of the first two terms in a proportion is equal to the ratio of the last two terms. In this case:

(6-x) : (7-x) :: (18-x) : (22-x)

Solving for x, cross-multiply the ratios:

(6-x) x (22-x) = (7-x) x (18-x)

Expanding both sides:

132 - 28x + x² = 126 - 25x + x²

Simplifying, we get:

7x = 6

Therefore, x = ⁶/₇.

Thus, the solution to the proportion is:

(6-x) : (7-x) :: (18-x) : (22-x)

or

⁶/₇ : ¹/₇ :: ¹²/₇ : ¹⁶/₇

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Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.

All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.

So, total months = 9 + 12 + 12 = 33

Now, using the multiplication operation, we get

⇒ Total money saved = 33 * 20

⇒ Total money saved = $660

It is given that she spent 75% of her savings on computer.

So, using the subtraction operation, we get

⇒ Amount left = 660 - 75%

⇒ Amount left = $165

Hence, Anna has $165 left in the jar.

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Step-by-step explanation:

x = -2 or x = 2

x + 2 = 0 or x - 2 = 0

(x + 2) (x - 2) = 0

x² - 4 = 0

The solutions for the system of equations " 3x²-2y²+5=0 and 2x²-y²+2=0" are :

First Solution : x = 1, y = 2

Second Solution : x = 1, y = -2

Third Solution : x = -1, y = 2

Fourth Solution : x = -1 , y = 2.

In order to solve the system of equations 3x²-2y²+5=0 and 2x²-y²+2=0, we use substitution method;

From the second equation, we solve for y² in terms of x²:

The second equation is : 2x² - y² + 2 = 0;

We get, y² = 2x² + 2

Substitute this expression for y² into the first equation:

We get,

3x² - 2(2x² + 2) + 5 = 0

3x² - 4x² - 4 + 5 = 0

-x² + 1 = 0

x² = 1

We get, x = ±1

Substitute these values of x into the equation for y²:

y² = 2x² + 2

For x = 1, y² = 4,

Which means the solution set is (1,2) and (1,-2),

For x = -1, y² = 4

the solution set is (-1,2) and (-1,-2).

Therefore, the solutions to the system of equations are (1, 2), (1,-2), (-1,2) and (-1, 2).

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It will take about 711.12 minutes or approximately 11.85 hours to test all 400 units.

To find out how long it will take to test 400 units, we need to use the information given in the problem. We know that the quality expert can test 18 units in 32 minutes. We can use this information to find out how long it will take to test one unit.

First, we need to find out how many units can be tested in one minute:

18 units / 32 minutes = 0.5625 units per minute

This means that the quality expert can test 0.5625 units per minute. To find out how long it will take to test one unit, we can divide 1 by 0.5625:

1 / 0.5625 = 1.7778 minutes per unit

So it takes about 1.7778 minutes to test one unit. To find out how long it will take to test 400 units, we can multiply this value by 400:

1.7778 minutes per unit * 400 units = 711.12 minutes

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The dilation of the object is given by the coordinates:

(-6,-8)
(-2, 0)
(-2, -8)

A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer.

For the first dilation

Original points are

(2,1)

(4,5)

(4,1)

Multiply by scale factor

(2,1) x 2 = (4,2)

(4,5) x 2 = (8, 10)

(4,1) x 2 = (8, 2)

This given us the coordinates of triangle B).

For the second dilation

(2,1)  

(4,5)

(4,1)
Adjust for the center of dilation which is (5,5)

(2,1)  less (5,5) = (-3, -4)

(4,5) less (5,5) = (-1, 0)

(4,1) less (5,5) =(-1, -4)

Multiply the New original point by scale factor

(-3, -4) x 2 = (-6,-8)
(-1, 0) x 2 = (-2, 0)

(-1, -4) x 2 = (-2, -8)

Thus, the new coordinates of the dilated triangle C are:

(-6,-8)
(-2, 0)
(-2, -8).

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The perimeter of the rug is 36ft

Perimeter is the total length around the outside of a shape. The perimeter can be found by adding all the sides of the shape.

Perimeter of a rectangle is expressed as ;

P = 2(l+w)

The area of the rug is 81ft²

area = l× w

length = 9ft

width of the rug = 81/9 = 9ft

Therefore the perimeter of the rug will be

P = 2(l+w)

P= 2( 9+ 9)

P = 2 × 18

P = 36 ft

therefore the perimeter of the rectangular rug is 36ft

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Answer:

A

Step-by-step explanation:

The probability of choosing a red marble is 6/17.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

To calculate this probability, we can use the formula:

P(red marble) = number of red marbles / total number of marbles

In this case, we substitute the numbers we know:

P(red marble) = 6 / 17

So the probability of choosing a red marble is 6/17 or approximately 0.35.

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Answer:

Step-by-step explanation:

(-2-3)-(4-5)+ (−1+6)−(−9+8)

-5-4+5-1+6+9-8

-9+4+15-8

-5+7

2

C: the number of leaves is multiplied by 2 each week

Step-by-step explanation

The proper expression ought to be 5(2) ^ t =5(2)^{t}

where t speak to the number weeks after it planted.

On the off chance that we put to the time(t) we are going know how numerous clears out at first are. The calculation will be:

5(2)^{t}= 5(2)^{0} =5

This appear that coefficient 5 decide how much the takes off at first are.

Let see how the number going for distinctive esteem of t. On the off chance that its 1 week after plant, the leaf will ended up:

5(2)^{t}= 5(2)^{1} = 10

At that point the number of takes off 2 weeks after planted will be:

5(2)^{t}= 5(2)^{2}= 20

The number keeps twofold each week since coefficient 2 speaks to the proportion of the development of the work and the proportion decides how much takes off duplicated each week.

So, the reply will be C.

For the given function 'g':

domain = (-4, -2) ∪ (1, 3]

range = (-5, 4]

If the function is defined as f(x) = y, then the values of x for which the value of function exists, the set of that values is said to be the domain of the function f.

If the function is defined as f(x) = y, then the set of all possible values of the function that is the set of all possible values of y is said to be the range of the function f.

Here given the graph of 'g'.

From the graph we can see that for -4 < x < -2 and 1 < x [tex]\le[/tex] 3 the function has graph.

So the domain = (-4, -2) ∪ (1, 3]

And it is clear that the value of y lies between -5 < y [tex]\le[/tex] 4.

So the range = (-5, 4].

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Answer:

23.375 in^2

Step-by-step explanation:

To find the area of a rectangle or square, you need to multiple the length by the width.

The length: 8.5

Width: 11

8.5*11 = 93.5

Now we divide by 4

93.5/4

23.375

Answer:

[tex]30d^2[/tex]

Step-by-step explanation:

An expression to show how many books would be on each table is a/10

To find out how many books would be on each table, we need to divide the total number of books by the number of tables.

First, let's express the total number of books in terms of a and d. Since we are not given any specific numbers for a and d, we can simply use variables to represent them. Therefore, the total number of books is given by a.

Next, we need to divide a by 10, the number of tables. This gives us the expression:

a/10

So, the above expression shows how many books would be on each table if Mrs. Marcus combines her books and magazines and then divides them among 10 different tables.

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Complete question is:

Mrs. Marcus combines her atlases and dictionaries and then divides them among 10 different tables. If a represents the number of atlases and d represents the number of dictionaries Mrs. Marcus has, write an expression to show how many books would be on each table.

Answer: x=3

Step-by-step explanation:

shaded part is 5/6 of the full circle, so just make an equation.

5/6 pi r^2(formula to find area)=15/2 pi(area given)

cancel out pi and simplify

r^2=9

r=+-3 but cant be negative so r=3

Answer:

The answer is going to 5

Step-by-step explanation:

I hope this helps you

The expressions are written as;

h(t)+k(t) = 10t - 1

h(t)−k(t) = -2t + 1

Note that algebraic expressions are described as expressions that are made up of coefficients, variables, terms, constants and factors.

These expressions are made up of arithmetic operations, which includes;

From the information given, we have that;

h(t)=4t

k(t)=t+5t−1

To determine the value of h(t) + k(t), we have;

4t + t + 5t - 1

add the like terms, we get;

10t - 1

To determine h(t) = k(t)

4t- t - 5t + 1

add like terms

-2t + 1

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Answer:

B. 1

Step-by-step explanation:

Let's use the formula for finding the mean of a set of data:

mean = (sum of all data values) / (number of data values)

We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:

2.2 = (sum of all 10 data values, including x) / 10

Multiplying both sides by 10, we get:

22 = sum of all 10 data values, including x

We can then subtract the sum of the known data values from both sides to find the missing value:

22 - (01 + 12 + 23 + 31 + 42 + 51) = x

22 - (0 + 2 + 6 + 3 + 8 + 5) = x

x = 22 - 24 = -2

However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:

If the missing score is 0:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10

2.2 = 18 / 10

2.2 = 1.8

This is not true, so the missing score cannot be 0.

If the missing score is 1:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10

2.2 = (18 + ?) / 10

22 = 18 + ?

? = 4

So the missing score is 1, and the answer is B.

Answer:

Answer is B

Total scores/total frequency =mean

54/24=2,25

If you added a score of 1

55/25=2,2

Step-by-step explanation:

hope that helps you

For the given function h(x) the points can be plotted on,

The given function h(x) is having four conditions and each condition can be clearly discussed below:

From, the above analysis we plotted the graph and attaching below.

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Answer:

$2,440 + $1,220 = $3,660

Step-by-step explanation:

If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:

$61,000 x 0.04 = $2,440

Since her employer has a 50% match on the first 4% of her salary, they would contribute:

$2,440 x 0.5 = $1,220

Answer:

Step-by-step explanation:

no

The value of t is given as 2.3 years.

we get the table for function as

t          f(t)

8    350

12   138

16   36

20    4

25   3.2

27    1.3

So it is better to model the data by using an exponential model

using a graphing calculator we get our model as

f(t)=a(b)^t

[tex]f(t)=\boldsymbol{3648.6915(0.7380)^t}[/tex]

we have an exponential decay, so we get a rate of decrease as

b=1-r

r=1-b=1-0.738=0.262=26.2\\%

So the number of polio cases is decreasing by 26.2% per year

The number of polio cases in 2014 is

t=2014-1980=34

f(34)=3648.6915(0.7380)^{34}=0.1991389

this is in thousands so we get the number of cases in 2014 approximately as

[tex]0.1191389*1000 \approx \boldsymbol{119} \textup{ cases}[/tex]

for 1 case of polio :

f(t)=0.001

3648.6915(0.738)^t=0.001

we get

[tex]t=\frac{\ln (\frac{0.001}{3648.6915})}{\ln(0.738)}\approx 50[/tex]

so we get year as

1980+50={2030},

to find half life

[tex]\frac{a}{2}=a(b)^t[/tex]

[tex]b^t=\frac{1}{2}[/tex]

[tex]0.738^t=\frac{1}{2}[/tex]

[tex]t=\frac{\ln (1/2)}{\ln (0.738)}\approx\boldsymbol{2.3} \textup{ years}[/tex]

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The equaltion for the line of best fit would be,

y = 0.67x + 4.05

The points on the scatter plot are: (1, 3.8), (2, 5.8), (3, 6.2) , (4, 7.5) , (5, 7.2), (6, 8.3), (7, 9.3), and (8, 8.5 )

First we find the mean of the x-values and mean of the y-values.

The mean of the x-values would be,

[tex]\bar{X}[/tex] = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8

[tex]\bar{X}[/tex] = 4.5

and the mean of the y-values would be,

[tex]\bar{Y}[/tex] = (3.8 + 5.8 + 6.2 + 7.5 + 7.2 + 8.3 + 9.3 + 8.5) / 8

[tex]\bar{Y}[/tex] = 7.075

The sum of squares (SSX) = 42

And the sum of products (SP) = 28.2

Regression Equation would be,

y = mx + c

m = SP/SSX

   = 28.2/42

   = 0.67143

And the y-intercept would be,

c =  4.05357

So, the equation for the line of best fit would be,

y = 0.67143x + 4.05357

Number of Households = 0.67143 (time) + 4.05357

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Find the complete question below.

The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.

Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.