Anna is a teacher at an elementary school. She purchased 73 tickets to take the first-grade children and some parents on a field trip to the zoo. She purchased
children's tickets for $9 each and adult tickets for $15 each. She spent a total of $771. How many of each ticket did she buy?
Adults
Children
Total

Answer:

31

Step-by-step explanation:

given f(x) = 2x + 25,  

f(3) =2(3) + 25

= 6 + 25

= 31

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]9(2x+1)-4(x-6)=6(2x+1)+5(x-6)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(9)(2x)+(9)(1)+(-4)(x)+(-4)(-6)=(6)(2x)+(6)(1)+(5)(x)+(5)(-6)\\\\18x+9-4x+24=12x+6+5x-30\\\\\text{combine like terms}\\\\(18x-4x)+(9+24)=(12x+5x)+(6-30)\\\\14x+33=17x-24\qquad\text{subtract 33 from both sides}\\\\14x+33-33=17x-24-33\\\\14x=17x-57\qquad\text{subtract}\ 17x\ \text{from both sides}\\\\14x-17x=17x-17x-57\\\\-3x=-57\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-57}{-3}\\\\x=19[/tex]

Answer:

40 minutes

Step-by-step explanation:

60 pages / (1 1/2 pages/ minute)

= 60 / 3/2 minutes

= 40 minutes

Answer:

330 minutes

Step-by-step explanation:

11/2 times 60/1

so basically just do 60 times 11 equals

660 then divided by 2 equals 330

so she will read 60 pages in 330 minutes, I hope I did it right

I think I'm wrong

Algebra tiles are a useful tool to simplify expressions. Depending on their shape and decoration, they represent different parts of the expression. Review your tiles and match them to the four given expressions carefully.

The question pertains to Algebra and specifically, matching a simplified algebraic expression to a set of tiles. The exact matching algebraic expression cannot be determined as the set of tiles isn't provided in the question but here's how you would approach this kind of problem:

If you're using algebra tiles, squares typically represent x², rectangles portray x, and small squares depict constants like 2. The color or decoration of a tile may indicate a positive or negative value. For example, a square with '- ' could mean '-x²'.

So if you've got a square with '- ', a rectangle without a decoration, and two small plain squares, your expression should be '-x² - x + 2'. If the rectangle had a '-', your expression would be '-x² + x + 2' instead.

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The set of tiles shown represents the expression x² - x + 2.

The set of tiles shown represents the expression x² - x + 2.

To match the tiles to the simplified expression, look at the coefficient and exponent of x on each tile. The first tile has an exponent of 2 and a coefficient of 1. The second tile has an exponent of 1 and a coefficient of -1. The third tile has an exponent of 0 and a coefficient of 2. Therefore, the simplified expression that matches the set of tiles is x² - x + 2.

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It will take 7.30 years until Dale can by his mask

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

[tex]A=Pe^{rt}[/tex] , where

Dale invests $6000 in an account at 9.5% interest compounded continuously. The mask costs $12000. We need to find how long will it take Dale until can buy this mask

∵ Dale invests $6000

∴ P = 6000

∵ The interest rate is 9.5% ⇒ compounded continuously

∴ r = 9.5% = 9.5 ÷ 100 = 0.095

∵ The mask costs $12000

∴ A = 12000

Substitute these values in the formula above

∵ [tex]12000=6000e^{0.095t}[/tex]

- Divide both sides by 6000

∴ [tex]2=e^{0.095t}[/tex]

- Insert ㏑ for both sides

∴ [tex]ln(2)=ln(e^{0.095t}[/tex])

- Remember that [tex]ln(e^{n})=n[/tex]

∴ [tex]ln(2)=0.095t[/tex]

- Divide both sides by 0.095

∴ t = 7.29628611

∴ t = 7.30 ⇒ to the nearest hundredth year

It will take 7.30 years until Dale can by his mask

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It will take Dale 7.64 years to save enough money to buy the mask we can use the method of compound interest.

To find how long it will take Dale to save enough money to buy the mask, we can use the following formula for compound interest:

A = P * e^(rt)

where:

A is the final amount

P is the principal amount

r is the interest rate

t is the time in years

We know that A = $12000, P = $6000, and r = 9.5%. We need to solve for t.

12000 = 6000 * e^(0.095t)

e^(0.095t) = 2

ln(2) = 0.095t

t = ln(2) / 0.095

t = 7.64

Therefore, it will take Dale 7.64 years to save enough money to buy the mask.

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The inequality is:

[tex]5x+4y \leq 124[/tex]

Give one solution to the inequality:

Let x = 5 and y = 10

[tex]65\leq 124\,\,\,true[/tex]

Step-by-step explanation:

Cost of Gift cards= $5

Cost of Teddy bear = $4

Total money to spend on party = $124

The required inequality is:

Let no of gift cards= x

and no of teddy bears = y

The inequality is:

[tex]5x+4y \leq 124[/tex]

Give one solution to the inequality:

Let x = 5 and y = 10

then, the solution will be:

[tex]5x+4y \leq 124\\5(5)+4(10)\leq 124\\25+40\leq 124\\65\leq 124\,\,\,true[/tex]

Keywords: Solving inequalities

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Answer:

The inequality is 5x + 4y < and the line under the sign 124

(10,9)

Step-by-step explanation:

Answer:

x=5, y=5. (5, 5).

Step-by-step explanation:

x=3y-10

x=2y-5

--------------

3y-10=2y-5

3y-2y-10=-5

y-10=-5

y=-5+10

y=5

x=2(5)-5=10-5=5

Answer:

The money he will save if he earns $120.00 is $90.00.

Step-by-step explanation:

Given:

In the figure is the ratio of the savings and the earnings.

Now, to find out that how much savings will be if Miguel earns $120.00.

We need to get the percentage of the ratio of the earning and saving.

So, according to the table:

If he earns $10.00 then he saves $7.50.

[tex]\frac{7.50}{10}\times 100[/tex]

[tex]=0.75\times 100[/tex]

[tex]=75[/tex]

So, if Miguel earns $10.00 he save the 75% of it.

If he earns $50.00 then he saves $37.50.

As we calculate the percentage as the above process then the saving is 75% of the earning.

And, if he earns  $150.00 and save $112.50 then it is also the 75% of the earning as mentioned above.

Now, to find the saving of the earning $120.00.

So, it will be 75% of the earning as we observe in the above case:

75% of $120.00

[tex]\frac{75}{100}\times 120[/tex]

[tex]=0.75\times 120[/tex]

[tex]=90[/tex]

Therefore, the money he will save if he earns $120.00 is $90.00.

Answer:

The complete length is 115 cm.

Step-by-step explanation:

Given:

If 20%of a length is 23 cm.

Now, to find the complete length.

Let, the complete length be [tex]x[/tex].

So, according to question:

20% of [tex]x[/tex] = 23 cm

[tex]\frac{20}{100} \times x=23[/tex]

[tex]0.20\times x=23[/tex]

[tex]0.20x=23[/tex]

Dividing both sides by 0.20 we get :

[tex]x=115[/tex]

Therefore, the complete length is 115 cm.

To find the complete length when 20% is 23 cm, divide 23 cm by 0.20 to get 115 cm as the total length.

If 20% of a length is 23 cm, we want to find out what the complete length is. To do so, we recognize that 20% is the same as saying 20 per 100 or 0.20 in decimal form. If 0.20 of the length is 23 cm, it means that 23 cm represents 0.20 of the total length. We can set up the equation like this:

0.20 * Total Length = 23 cm

To find the Total Length, we divide both sides of the equation by 0.20:

Total Length = 23 cm / 0.20

Total Length = 115 cm

Therefore, the complete length is 115 cm.

I believe 50% of 284 =142

Answer:

284/50*100 = 586 or simply double 284

Step-by-step explanation:

Answer: y = 4.88 + 0.525x

The equation of the line of best fit for the data shown in the picture is y=0.894x+0.535

A straight line is a combination of endless points joined on both sides of the point.

We have a data in the table:

Let's suppose the equation for the line is:

y = mx + c

Where m is the slope of the line and c is the y-intercept.

The value of m is given by:

[tex]\rm m = \frac{S_{xy}}{S_{xx}} }[/tex]    and

[tex]\rm S_{xy} = \sum_{i=1}^{n}x_iy_i-\frac{(\sum_{i=1}^{n}x_i)(\sum_{i=1}^{n}y_i)}{n}[/tex]

[tex]\rm S_{xx} = \sum_{i=1}^{n}x_i^2-\frac{(\sum_{i=1}^{n}x_i)^2}{n}[/tex]

From the table(data is not mentioned we have assumed the data) the values of  [tex]\rm \sum_{i=1}^{n}x_iy_i= 415[/tex], [tex]\rm {\sum_{i=1}^{n}x_i= 44[/tex], [tex]\rm {\sum_{i=1}^{n}y_i= 42[/tex],

[tex]\rm {\sum_{i=1}^{n}x_i^2= 438[/tex], and n = 5.

[tex]\rm S_{xy}= 415-\frac{44\times42}{5} \Rightarrow 45.4\\\\\rm S_{xx}= 438- \frac{44^2}{5} \Rightarrow 50.8[/tex]

[tex]\rm m = \frac{45.4}{50.8} } \Rightarrow 0.8937 \approx0.894[/tex]

For c we have to calculate the means of x and y for this:

[tex]\rm \bar{x} = \frac{\sum x}{n} \Rightarrow \frac{44}{5} \Rightarrow8.8[/tex]

[tex]\rm \bar{y} = \frac{\sum y}{n} \Rightarrow \frac{42}{5} \Rightarrow8.4[/tex]

Now, put the above values in the equation of a line to find the value of c

8.4 = (0.894)(8.8)+c

c = 0.5328 ≈ 0.535

Now the line is y = 0.894x+0.535

Thus, the line of best fit for the data shown in the picture is y=0.894x+0.535

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Answer:

-5

Step-by-step explanation:

A negative number divided by a positive number will be negative.

20/4 is 5.

(5x4=20)

Therefore (-20)/4 = (-5)

Answer:

First side: 12 feet, second side: 16 feet

Step-by-step explanation:

We know that the second side is 4 feet longer than the first side. If the first side is x, then the second side is x+4

b) The total amount of the border is 28 feet, so we can say that first side+second side=28, or

x+(x+4)=28

2x+4=28

2x=24

x=12 feet is the first side

x+4 = 16 feet is the second side

We can check that 12 feet + 16 feet = 28 feet as stated by the problem

Answer:

4.  B

5.  C

Step-by-step explanation:

4.

We can say the 5 angles of the Pentagon PQRST equals 540 degrees.

We see that Angle P and Angle T are 90 degrees each.

R is given as 100

Q and S are same, let it be "x"

Now we can write an equation:

P + Q + R + S + T = 540

90 + x + 100 + x + 90 = 540

Solving for x, we get:

2x + 280 = 540

2x = 540 - 280

2x = 260

x = 260/2

x = 130

Angle Q is equal to x, so that is 130

Correct answer is B

5.

When 2 parallel lines are cut by transversal, the corresponding angles are equal.

The 60 degree angle given and the angle adjacent (beside) to angle x are same. So we can say that is equal to 60 degrees as well.

This 60 degree angle and x form a straight line. The degree measure of a straight line (or a straight angle) is 180 degrees. Thus we can write:

60 + x = 180

Now, we solve for x:

60 + x = 180

x = 180 - 60

x = 120

The correct answer is C

Answer:

7^-12 or 1/7^12

Step-by-step explanation:

To divide exponents with the same base, subtract the second exponent from the first.

So:

7^-5/7^7 = 7^-5-7 = 7^-12

You can also write 7^-12 as 1/7^12.

Answer:

[tex]\large\boxed{5x-6y=16}[/tex]

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

We have the equation in the point-slope form. Convert:

[tex]y+1=\dfrac{5}{6}(x-2)\qquad\text{multiply both sides by 6}\\\\6y+6=6\!\!\!\!\diagup^1\cdot\dfrac{5}{6\!\!\!\!\diagup_1}(x-2)\\\\6y+6=5(x-2)\qquad\text{use the distributive property}\\\\6y+6=(5)(x)+(5)(-2)\\\\6y+6=5x-10\qquad\text{subtract 6 from both sides}\\\\6y+6-6=5x-10-6\\\\6y=5x-16\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+6y=5x-5x-16\\\\-5x+6y=-16\qquad\text{change the signs}\\\\\boxed{5x-6y=16}[/tex]

Answer: 2hrs

Step-by-step explanation:

paid 10 dollars at first and then 6 every hour he rode

so let x represent the # of hour rented

6x+10=22

x=2hrs

The number is -40

Step-by-step explanation:

Let x be the number that we have to find

Then according to the given statement

the square of the sum of the number and 5 is equal to 1225.

[tex](x+5)^2 = 1225[/tex]

Taking square root on both sides

[tex]\sqrt{(x+5)^2} = \sqrt{1225}\\x+5 = -35 and x+5 = -35\\[/tex]

Subtracting 4 from both sides

[tex]x+5-5 = 35-5\ and\\ x+5 = -35-5\\x = 30\ and\ x = -40[/tex]

As it is mentioned in the equation, that the number is a negative number

So,

x = -40

Keywords: Radicals, Linear equations

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Answer:

11j + 4

Step-by-step explanation:

Disregard parentheses in this situation.

3j + 11 + 8j - 7

Add the j's

11j + 11 - 7

11j + 4

To make a minimum profit of $100 with each snack priced at $4.00, a total of 47 snacks need to be sold at the concession stand. This includes 22 snacks to cover the total cost of $86.56 and an additional 25 snacks to achieve the profit goal.

The question is about finding out how many snacks need to be sold at a concession stand to achieve a minimum profit. To get the answer, we first need to determine how many snacks would make up the total cost, and then calculate how many additional snacks would be necessary to attain the profit goal.

Given that each snack at the concession stand costs $4.00 and that the total cost of the snacks is $86.56, we can find out how many snacks were initially purchased by dividing the total cost by the price of each snack: $86.56 ÷ $4.00 = 21.64 snacks. Since we can't sell a fraction of snack, we round up to 22 snacks to cover the total cost.

To calculate the number of additional snacks needed to attain a $100 profit, we divide the profit goal by the price of each snack: $100 ÷ $4 = 25 snacks.

Therefore, to cover the total cost and also make a minimum profit of $100, the concession stand needs to sell 22 snacks for the cost and additional 25 snacks for the profit, totaling 47 snacks altogether.

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Answer:

72 degrees

Step-by-step explanation:

Congruent supplements Theorem.

The symbol m∠LNM denotes the measure of the angle formed by points L, N, M. The 'm' stands for measure, '∠' denotes an angle, and LNM are the points forming the angle. In this context, m∠LNM is 72 degrees.

The term m∠LNM refers to the measure of angle LNM. In mathematical notation, the symbol '∠' is often used to denote an angle, and LNM refers to the points forming the angle. For instance, if you have a triangle or any other polygon, and points L, N, and M are three vertices (corners) of the shape, then ∠LNM would be the angle at vertex N, formed by the intersection of line segments LN and NM. Given that m∠LNM is said to be 72°, this indicates that the measure of angle LNM is 72 degrees.

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Answer:

$21.75

Step-by-step explanation:

Add 25% then subtract to get back to $17.40

83.78% students turned in their homework and 16.22 percent students did not turn in their homework

Step-by-step explanation:

Percentage formula will be used for this problem

Given

Total students = 74

Students who turned their homework = 62

So the percentage of students who turned in their homework will be:

[tex]Percentage\ of\ students\ who\ turned\ in\ their\ hw = \frac{62}{74} *100\\=0.8378*100\\=83.78\%[/tex]

So the students who did not turn in their homework = 100-83.78

=16.22%

Hence,

83.78% students turned in their homework and 16.22 percent students did not turn in their homework

Keywords: Percent, percentage

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Answer:

375 adult tickets and 302 student tickets

Step-by-step explanation:

s+a=677

a=s+73

s+s+73=677

2s+73=677

2s=604

s=302

a= 375

Final answer:

Explanation on finding the number of adult tickets sold for a school play when the total number of tickets sold and the relationship between adult and student tickets are known.

Explanation:

The total number of tickets sold for the school play was 677.

Let x be the number of adult tickets sold.

It is given that there were 73 fewer student tickets than adult tickets, so the number of student tickets sold would be x - 73.

Therefore, x + (x - 73) = 677.

Solving this equation, we find that 2x - 73 = 677, 2x = 750, x = 375.

So, 375 adult tickets were sold.

Answer:

-6(2b-c-3)

Step-by-step explanation:

Collect like terms

-12b+6c+12+6

Add the 2 numbers on right

-12b+6c+18

Factor -6 out of expression

-6(2b-c-3)

Answer:

2.03

Step-by-step explanation:

Answer:A

Step-by-step explanation:The answer is A because if you divide the numbers equally, then you will get 1

The number of 1/8-acre plots in a 3/4-acre garden is 6.

The question is about dividing the total area of a garden into smaller plots and finding out how many plots there will be. Here, the total size of the garden is given as 3/4 acre and each plot is 1/8 acre in size. To find out how many 1/8-acre plots make 3/4 of an acre, we perform a division: 3/4 divided by 1/8. This is the same as multiplying 3/4 by the reciprocal (the 'flipped' fraction) of 1/8, which is 8/1. So, the calculation is 3/4 * 8/1 = 24/4 = 6. Therefore, there are 6 1/8-acre plots in a 3/4-acre garden.

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Answer: 5 faces

Step-by-step explanation:

The Euler's polyhedron formula states that:

number vertices - number of edges + number of faces = 2

That is :

6 - 9 + F = 2

-3 + f = 2

f = 2 + 3

f = 5

Therefore , it has 5 faces

For this case we must find an expression equivalent to:

[tex]36y-18x-108y + 54[/tex]

We add similar terms:

[tex]36y-108y-18x + 54 =[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]-72y-18x + 54[/tex]

Thus, an equivalent expression is:

[tex]-72y-18x + 54\\-18x-72y + 54[/tex]

Answer:

[tex]-18x-72y + 54[/tex]

Final answer:

To find equivalent expressions, we combine like terms in the given expression 36y - 18x - 108y + 54.

Explanation:

To find expressions equivalent to 36y - 18x - 108y + 54, we can combine like terms.

First, combine the y terms: 36y - 108y = -72y.

Next, combine the x terms: -18x.

Combining the constants, we have: 54.

Putting it all together, the equivalent expression is: -18x - 72y + 54.

Answer:

B.) Open circle on 3 and all numbers to the left shaded

Answer:

[tex]\large\boxed{\dfrac{1}{10}x-\dfrac{7}{10}=\dfrac{1}{10}(x-7)}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{10}x=\left(\dfrac{1}{10}\right)(x)\\\\\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(7)\\\\\dfrac{1}{10}x-\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(x)-\left(\dfrac{1}{10}\right)(7)=\left(\dfrac{1}{10}\right)(x-7)[/tex]