A group of 2 adults and 4 children spent $38 on tickets to a museum. A group of 3 adults and 3 children spent $40.50 on tickets to the museum. Based on this information, how much is an adult ticket, and how much is a child ticket?


2a + 4c = 38.00

3a + 3c = 40.50

What values of a and c represent the solution to the system?

a = c =

[tex]\{x|x < -5\}\ \cap\ \{x|x > 5\}=\O[/tex]

Look at the picture.

The common part does not exist.

so if the original price of the bicycle is $360 and the sale price is 5/6 of that you would multiple $360 by 5/6 which equals 300 now thats NOT your final price you have one more step which is to subtract the sale (money off) the original price 360-60 so the sale price of the bicyle is $300

answer:

$300

step-by-step explanation:

our original price is $360 and we need find 5/6 of 360

our first step is to multiply 360 by 5 which is equal to 1,800

our next step is it divide by 6 which is equal to 300

so our sale price is $300

Final answer:

The ratio of seniors graduating with honors to the total number of seniors is 46/310, which simplifies to 23/155.

Explanation:

To find the ratio of seniors graduating with honors to the total number of seniors, you would divide the number of seniors graduating with honors by the total number of seniors. In this case, 46 seniors graduate with honors out of a total of 310 seniors.

Therefore, the ratio is 46/310, which can be simplified to 23/155 when reduced to the lowest terms.

First, change the mixed fraction into improper fraction. Change the whole number into a fraction, and add.

1 8/11 = 11/11 + 8/11 = 19/11

To find the reciprocal, flip the fraction.

The reciprocal of 19/11 is 11/19

hope this helps

Final answer:

The reciprocal of 1 ⁸/₁₁ is 11/19, which is calculated by first converting the mixed number to an improper fraction (19/11) and then flipping the numerator and denominator to get the reciprocal.

Explanation:

To find the reciprocal of 1 ⁸/₁₁ , you first need to convert the mixed number to an improper fraction. To do this, multiply the whole number by the denominator, add the numerator, and then write the result over the original denominator. In this case, 1 ⁸/₁₁ becomes (1×11 + 8)/11, which simplifies to 19/11.

Now, the reciprocal of a fraction is obtained by flipping the numerator and denominator. So the reciprocal of 19/11 is 11/19. Therefore, the reciprocal of 1 ⁸/₁₁ is 11/19.

Understanding the concept of reciprocals is important in mathematics because dividing by a number is the same as multiplying by its reciprocal. In this context, dividing by 1 8/11 is equivalent to multiplying by 11/19.

The ratio of 16 days to 2 weeks, when converted to the same units and reduced to its simplest form, is 8:7.

To write the comparison of 16 days to 2 weeks as a ratio in the lowest terms, we first need to express both quantities in the same units. There are 7 days in a week, so 2 weeks equal 14 days. The ratio between 16 days and 14 days is therefore 16:14. This ratio can be reduced to lowest terms by dividing both numbers by their greatest common divisor, which is 2. This gives us the reduced ratio of 8:7.

So, the ratio of 16 days to 2 weeks, reduced to lowest terms, is 8:7.

The number of cubic yards of concrete that are needed to fill the sidewalk is 7.40741 cubic yards

where

l = length

w = width

h = height

Therefore,

l = 200 ft

w = 4 feet

h = 0.25 feet

v = 200 × 4 × 0.25

v = 200 ft³

In yards the concrete will fill the following volume:

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To find the volume of concrete needed for the sidewalk, multiply the length, width, and depth of the sidewalk. Convert the volume from cubic feet to cubic yards by dividing by 27.

To find the volume of concrete needed, we need to multiply the length, width, and depth of the sidewalk. The length is given as 200 feet, the width is 4 feet, and the depth is 0.25 foot. Multiplying these values together gives us the volume in cubic feet. To convert this to cubic yards, we divide the volume in cubic feet by 27 (since there are 27 cubic feet in a cubic yard).

The volume of the sidewalk in cubic feet is 4 ft * 200 ft * 0.25 ft = 200 cubic feet. Dividing this by 27, we get the volume in cubic yards: 200 cubic feet / 27 = 7.41 cubic yards. Therefore, approximately 7.41 cubic yards of concrete are needed for the sidewalk.

if the lines are parallel the slopes are the same so the slope is -2

the equation for a line given a point and a slope is

y-y1 = m(x-x1)

y-3= -2(x-4)

y-3 = -2x+8

y = -2x+11

a. sum of angles in triangle

b. supplementary angles

c. sum of angles is triangle=180 and supplementary angles =180

d. Parts whole postulate/subtraction

e. exterior angle equals the sum of the 2 remote interior angles

Bob passed 4 activities, so 4 x 10 = 40 points. He failed 3, so 3 x 5 = 15

Total points = 40-15 = 25 points.

Tom passed 7, so 7 x 10 = 70 points. He failed 4, so 4 x 5  = 20

Total points = 70-20 = 50 points.

Tom got a higher score.

There are 11 numbers divisible by 9 between 1 and 100, and 25 numbers divisible by 4 between 1 and 100. So there are 11 + 25 = 36, so 36 numbers divisible by one or the other, but this also includes every number which is divisible by both 9 and 4 twice.

Answer:34

Step-by-step explanation:

I had the answer on khaun academy

Hello AskMeBosh

The missing number in this equation is 7

This is because 9 * 7 is 63

So your answer would be 7

:)

63/7=9 the missing number is 7

I believe it is 360 sorry if i am wrong i truely sorry

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\sqrt{\dfrac{1}{144}}=\dfrac{\sqrt1}{\sqrt{144}}=\dfrac{1}{12}\\\\\\\sqrt1=1\ because\ 1^2=1\\\\\sqrt{144}=12\ because\ 12^2=144[/tex]

0.00961538461

I typed this for 20 characters

Nine plus a unknown number equals unknown.

Answer:

The sum of 9 and a number.

Step-by-step explanation:

Sum = Add.

9 = 9

Number = n

Hope this helps :-)

A variable can be used to represent an unknown amount. Then you write an equation using the variable and based on the information you are given, and you solve the equation to find the unknown amount.

Here is an example.

Mary has money in a bank account. She received $20 for her birthday. She deposited the $20 in her account. After the deposit, she was told the account had a balance of $85. How much money did she have in the account before depositing the $20?

We don't know the amount she had before depositing the $20, so we will call that amount x. x is a letter used as a variable to represent an unknown amount.

She had x dollars in her account before depositing the $20.

After she deposited the $20, she now has x plus 20, or x + 20.

We are told her account now has $85, so x + 20 must equal 85.

That allows us to write an equation which we can then solve to find the amount of money she had in the account before depositing the $20.

x + 20 = 85

Subtract 20 from both sides.

x + 20 - 20 = 85 - 20

x + 0 = 65

x = 65

Since the variable x represents the amount of money in the account before depositing the $20 birthday money, we can now answer the question.

Mary had $65.

you can use varibales in real life problems by using them to describe the constants

$24.80 is the new retail price for the hat

Answer:

$24.8

Step-by-step explanation:

Hello, i think I can help you with  this,you can easily solve this by using a rule of three

Step 1

define

the retail price for the hat will be the originally paid value plus 55%, it is equal to 155% of the original price

if

$16 ⇒100%

$x? ⇒155%

the relation is

[tex]\frac{16}{100}=\frac{x}{155}\\solve\ for\ x \\\frac{155*16}{100}=x\\x=\frac{2480}{100}\\ x=24.8[/tex]

the retail price is $24.8

Have  great day.

Answer:

If both dealers sold 70 total cars, Car Dealer B sold 14 more blue cars.

Step-by-step explanation:

If dealer A sold 70 cars, this means they sold

0.3(70) = 21 blue cars.

If dealer B sold 70 cars, this means they sold

0.5(70) = 35 blue cars.

This is 35-21 = 14 more blue cars than dealer A.

Answer:

If both dealers sold 70 total cars, Car Dealer B sold 14 more blue cars.

Step-by-step explanation:

math

:0

The full recipe for the banana oat muffins requires 3/4 (or 0.75) cups of old fashion oats. But you are planning to make only 1/3 of the recipe.

To find the amount of oats required for 1/3 of the recipe, we need to multiply the amount required for the full recipe (3/4 cups) by the proportion of the recipe you are making (1/3).

Let's start with the full amount, which is 3/4 cups of oats. Then, we are going to use only 1/3 of this amount. So, we multiply 3/4 by 1/3.

The result of this calculation is 0.25.

So, you will need 0.25 cups of old fashion oats to make 1/3 of the banana oat muffins recipe.

8.31 because it goes after the decimal tenth then hundreth the for is in the thousandths

The answer is 8.3 Hope this helps

By graphing the given points we understood that (0,12) is on the y-axis and (12,0) is on the x-axis.

We need to explain how is graphing (0,12) different from graphing (12,0).

Given a point, (a, b), you plot the point in the Cartesian plane by finding the number a on the horizontal, or x-axis; then you trace directly up or down from that spot, moving parallel to the vertical, or y-axis until you reach the height of the number b.

Now, plot  (0,12) and (12,0) on the Cartesian plane.

In the graph plotted we can see (0,12) is on the y-axis and (12,0) is on the x-axis.

Therefore, by graphing the given points we understood that (0,12) is on the y-axis and (12,0) is on the x-axis.

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1+7

because when there are two negatives together you turn it into a positive and add

1 + 7

Because two negatives makes a positive. Hope this helps!

Assuming each movement is in a straight​ line, the composition

represents the moves.

Each movement is in a straight line, the composition represents the moves <-5, 1>, <-3, 4>, <1, 4> and <2, 7>.

Given that, a robot travels from position A to B to C to D.

We need to find what composition of rigid motions represents those moves.

Any way of moving all the points in the plane such that

a) the relative distance between points stays the same and

b) the relative position of the points stays the same.

There are four types of rigid motions that we will consider: translation, rotation, reflection, and glide reflection.

In a translation, everything is moved by the same amount and in the same direction. Every translation has a direction and a distance.

Therefore, each movement is in a straight line, the composition represents the moves <-5, 1>, <-3, 4>, <1, 4> and <2, 7>.

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The slope of this line is 1/4, because slope is rise/run. This line rises 1 for every 4 it runs. The slope is positive because the line is moving upward.

It is B because they show the X variable next to the .50 cents meaning that this can change depending on how many the rider buys in this Equation.

Answer:

no the answer is a $10. i took the usatestprep :)

Step-by-step explanation:

The correct answer is B. The function has a constant rate of change, decreasing for all x at a rate of 6.

In order to find the rate of change, we have to identify the slope. The slope is always the coefficient of x when in slope intercept form. In this case it is -6, which means it decreases at a rate of 6.

To describe the rate of change of the function \( f(x) = -6x - 7 \), we first need to understand that the rate of change in the context of a function, particularly a linear function, is another term for its slope.

Now, let's recall what the slope of a linear function means. A linear function is of the form \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept. The slope \( m \) determines how steep the line is, and it represents the change in the y-value (the output of the function) for a unit change in the x-value (the input of the function).

Looking at the given function \( f(x) = -6x - 7 \), we can see it is in the same form as \( y = mx + b \), with the slope \( m = -6 \) and the y-intercept \( b = -7 \).

The slope being -6 means that for every one unit increase in \( x \), the function's value decreases by 6 units. This is a constant rate of change because it does not matter what the value of \( x \) is; the function will always decrease by 6 for every one unit increase in \( x \).

Now, let's examine the given statements:

 A. The function has a varying rate of change when \( x < 7 \).
    - This statement is incorrect because the slope is constant at -6, regardless of the value of \( x \).
 
 B. The function has a constant rate of change, decreasing for all \( x \) at a rate of 6.
    - This statement is correct; it accurately describes the behavior of a linear function with a slope of -6.
 
 C. The function has a varying rate of change when \( x < 6 \).
    - This statement is also incorrect because, once again, the rate of change (slope) is constant for all values of \( x \).
 
 D. The function has a constant rate of change, decreasing for all \( x \) at a rate of 7.
    - This statement is incorrect; the coefficient of \( x \) in the function, which represents the slope, is -6, not -7.

Based on our analysis, the correct answer is:

 B. The function has a constant rate of change, decreasing for all \( x \) at a rate of 6.

Answer:

2.38% annual interest rate

Step-by-step explanation:

We have the initial value that is $6139 and the final value that is $8,624.97 the initial value is a 100% and the final value is 100%+17x%  where x is the annual interest rate, then:

[tex]\dfrac{8624,97\cdot 100\%}{6139\cdot (100\%+17x\%)}=1[/tex]

[tex]\dfrac{8624,97\cdot 100\%}{6139}=100\%+17x\%[/tex]

[tex]\dfrac{862497\%}{6139}-100\%=17x\%[/tex]

[tex]140.49\%-100\%=17x\%[/tex]

[tex]40.49\%=17x\%[/tex]

[tex]\dfrac{40.49\%}{17}=x\%[/tex]

[tex]2.38\%=x\%[/tex]

To find the interest rate of the account, you can use the formula for continuous compound interest, which is A = Pe^(rt). By plugging in the given values, you can solve for r and find that the interest rate is approximately 1.77%.

To find the interest rate of the account, we can use the formula for continuous compound interest:

A = Pe^(rt)

Where:

Given that Adam invested $6139 and the balance after 17 years is $8624.97, we can plug in these values and solve for r:

8624.97 = 6139 * e^(17r)

Divide both sides of the equation by 6139:

e^(17r) = 8624.97 / 6139

Now, take the natural logarithm (ln) of both sides:

ln(e^(17r)) = ln(8624.97 / 6139)

Use the logarithmic property ln(e^x) = x to simplify the equation:

17r = ln(8624.97 / 6139)

Finally, divide both sides of the equation by 17 to solve for r:

r = ln(8624.97 / 6139) / 17

Using a calculator, we find that the interest rate of the account is approximately 0.0177, or 1.77%.

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