write the following ratios in the simplest form

80cm to 2m
76 cents to 3 dollars
2h to 45 min

Answer:

one regular ticket costs $30

Step-by-step explanation:

The total number of people = 4

Without  the $20 coupon, the total cost would have been =100+20 = $120

Assume the price of one regular ticket is x;

4x = 120

Divide both sides by 4 to solve for x

x = 120/4

x = 30

Therefore, one regular ticket costs $30

Answer:

$30

Step-by-step explanation:

Since you pay 100 after discount, you add the 20 dollar discount to the 100 ($120)

Then since there are 4 of you in total, (you+ 3 friends), you divide by 4.

And Voila, your answer is $30 per person.

Hope this helps :)

The projection of the point (4,4) onto the line passing through (3,1) is the point on the line that is closest to (4,4). To find this projection, we need to first find the direction vector of the line, which is (3-1, 1-0) = (2,1).

Next, we need to find the vector from the point (3,1) to the point (4,4), which is (4-3, 4-1) = (1,3).

Then, we can use the formula for projecting a vector onto another vector:

proj_v u = ((u · v) / (v · v)) v

where u is the vector we want to project, v is the vector we want to project onto, and · denotes the dot product.

Applying this formula, we get:

proj_v u = ((1,3) · (2,1)) / ((2,1) · (2,1)) (2,1)

= (5/5) (2,1)

= (2,1)

So the projection of (4,4) onto the line passing through (3,1) is the point (3,1) + (2,1) = (5,2).

To find the projection of vector (4, 4) onto vector (3, 1), you can follow these steps:

Step 1: Calculate the dot product of the two vectors.
Dot product = (4 * 3) + (4 * 1) = 12 + 4 = 16

Step 2: Calculate the magnitude squared of the vector you are projecting onto (3, 1).
Magnitude squared = (3 * 3) + (1 * 1) = 9 + 1 = 10

Step 3: Divide the dot product by the magnitude squared.
Scalar = 16 / 10 = 1.6

Step 4: Multiply the scalar by the vector you are projecting onto (3, 1) to find the projection.
Projection = 1.6 * (3, 1) = (4.8, 1.6)

So, the projection of (4, 4) onto (3, 1) is (4.8, 1.6).

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The absolute extrema of the function on the given interval using the graphing utility, are as follows:

Absolute maximum value = 3

Absolute minimum value = -5.255

A graphing utility, also known as a graphing calculator or graphing software, is a tool that allows users to create visual representations of mathematical functions, equations, and data. It enables users to plot graphs and analyze various mathematical concepts and relationships visually.

To use a graphing utility to graph the function and find the absolute extrema of the function on the given interval, follow these steps:

1.Graph the function on the given interval using a graphing utility. We get this graph:

2.Observe the endpoints of the interval. At x = -1, f(x) = 3 and at x = 3, f(x) = -23.

3.Find critical points of the function, which are points where the derivative is zero or does not exist.

Differentiate the function: f'(x) = -4x³ - 6x² + 1.

We set f'(x) = 0 and solve for x.

Then we factor the equation. -4x³ - 6x² + 1 = 0 → x = -0.962, -0.308, 1.256.

These are the critical points.

4.Find the value of the function at each of the critical points.

We use the first derivative test or the second derivative test to determine whether each critical point is a maximum, a minimum, or an inflection point.

When x = -0.962, f(x) = 1.373.When x = -0.308, f(x) = 1.079.

When x = 1.256, f(x) = -5.255.5.

Compare the values at the endpoints and the critical points to find the absolute maximum and minimum of the function on the interval [-1, 3].

The absolute maximum value is 3, which occurs at x = -1.

The absolute minimum value is -5.255, which occurs at x = 1.256.

Therefore, the absolute extrema of the function on the given interval are as follows:

Absolute maximum value = 3

Absolute minimum value = -5.255

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22+2y

Mark me as brainliest

Answer: 11 + (2 + Y) type that in and submit

Answer:

Jenny will have 3 apples

Step-by-step explanation:

5-2=3

Answer:

Chloe would have 2 apples

Step-by-step explanation:

If the question is how many does Chloe have its 2 because that's how many Jenny gave her

Answer:

SAS

Step-by-step explanation: every triangle contains a total of 180 degrees if you substract 180 by 60+70(which is 130) you would get 50 degrees which is the exact degree missing in the first triangle, so after confirming that both triangles have an equal degrees on each side the answer would be SAS (which stands for Side-Angle-Side), SAS is the answer you would give to triangles that are congruent(equal)

D. The set W would be a subspace of set of real numbers R cubed.

For a set to be considered a vector space, it must satisfy the following conditions:

1. It contains the zero vector (the additive identity).

2. It is closed under vector addition.

3. It is closed under scalar multiplication.

Since the set W is a subset of R cubed, it inherits the properties of R cubed, including the zero vector. Therefore, option C is not true.

Options A and B are not necessarily true for all subsets of R cubed. They may hold for some specific subsets, but they are not general properties that apply to all subsets.

Option D is the correct answer because it states that the set W would be a subspace of R cubed. A subspace is a subset of a vector space that is itself a vector space, satisfying all the properties of a vector space. Since W is a subset of R cubed, it would be a subspace if it satisfies the three conditions mentioned above.

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The equation represents the relationship between the number of raspberry smoothies and the number of strawberry smoothies Joel made

\(\frac{2}{3}x+\frac{3}{2}y=10\)

Given :

Each raspberry smoothie uses 2/3 cup of yogurt , and each Strawberry smoothie uses 1 1/2 cups of yogurt Joel used a total of 10 cups of yogurt.

Let x represents number of raspberry and y represents the number of strawberry smoothies made.

Each raspberry smoothie uses \(\frac{2}{3}\) cup of yogurt

x   raspberry smoothie uses \(\frac{2}{3} x\) cup of yogurt

each Strawberry smoothie uses \(1\frac{1}{2} =\frac{3}{2}\) cups of yogurt

y  Strawberry smoothie uses \(\frac{3}{2} y\) cups of yogurt

Total of 10 cups of yogurt used

raspberry smoothie(yogurt) + strawberry smoothie (yogurt)=10 cups

\(\frac{2}{3}x+\frac{3}{2}y=10\)

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T

How to determine the hypotenuse?

Step 1 and 2: Draw an isosceles right triangle

See attachment (figure 1) for this triangle

The legs of this triangle have a length of 1 inch

Step 3: The hypotenuse

This is calculated using the following Pythagoras theorem

h^2 = 1^2 + 1^2h

2

=1

2

+1

2

This gives

h = \sqrt 2h=

2

Step 4: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 2) for this triangle

The legs of this triangle have lengths of 1 inch and 2 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

h^2 = 2^2 + 1^2h

2

=2

2

+1

2

This gives

h = \sqrt 5h=

5

Step 5: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 3) for this triangle

The legs of this triangle have lengths of 1 inch and 3 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

h^2 = 3^2 + 1^2h

2

=3

2

+1

2

This gives

$$h = \sqrt {10$$

Step 6: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 4) for this triangle

The legs of this triangle have lengths of 1 inch and 4 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

h^2 = 4^2 + 1^2h

2

=4

2

+1

2

This gives

$$h = \sqrt{[17$$

See that the hypotenuse is the square root of 17

Hence, the right triangle whose legs are 1 inch and 4 inches has an hypotenuse of √17

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Answer:

Step-by-step explanation:

x + 12 = y

x = y - 12

The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the Central Limit Theorem

The Central Limit Theorem is a statistical theorem that states that, given a sufficiently large sample size, the distribution of the mean of any sample will be approximately normal, regardless of the shape of the distribution from which the sample was drawn.

In other words, the theorem states that the mean of a large sample will be close to the mean of the population, and that the standard deviation of the distribution of the sample mean will be small.

The theorem is important because it provides a way to approximate the distribution of any sample statistic, as long as the sample size is large enough. This is useful because many statistical tests, such as hypothesis tests and confidence intervals, require that the data be normally distributed.

The theorem is also important because it provides a way to quantify the amount of error that is introduced when a sample is used to estimate a population parameter. This is known as the standard error, and it is equal to the standard deviation of the distribution of the sample mean divided by the square root of the sample size.

The Central Limit Theorem is one of the most important theorems in statistics, and it is widely used in many different fields.

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Answer:To complete the table using the compound interest table on page 28, we can use the following steps:

Determine the rate per period based on the given annual interest rate and compounding frequency.

Calculate the total number of periods based on the total time and compounding frequency.

Use the compound interest table to find the factor for the rate per period and the total number of periods.

Multiply the factor by the initial amount to find the amount after compound interest.

Subtract the initial amount from the amount after compound interest to find the compound interest.

Using these steps, we can complete the table as follows:

Annual

Interest Compounded

Rate

$900.00 5.50% Quarterly 1.375% 2 years 8

$640.00 6.00% Semiannually 3.00% 4 years 8

$1,340.00 5.00% Quarterly 1.25% 3 years 12

$6,231.40 5.75% Semiannually 2.875% 4 years 8

$3,871.67 12.00% Monthly 1.000% 4 years 48

$9,000.00 18.00% Monthly 1.500% 2 years 24

Quarterly 0.016%

Semiannually 0.033%

Monthly 0.058%

Monthly 0.058%

Monthly 1.500%

Quarterly 0.450%

Total

Time

2 years

4 years

3 years

4 years

4 years

2 years

Total

Number of

Periods

8

8

12

8

48

24

C.

$1,042.36

$812.65

$1,519.39

$7,305.10

$8,980.54

$20,790.56

Amount

Compound

Interest

d.

$42.36

$172.65

$119.39

$3,074.70

$4,109.87

$11,790.56

Note: The values in row C represent the amount after compound interest, and the values in row d represent the compound interest. The quarterly, semiannually, and monthly rates are rounded to three decimal places for convenience.

Step-by-step explanation:

Answer:

0.98 - rounded to the nearest decimal <3

Step-by-step explanation:

Answer:

the width is 10ft, the length is 25ft, and the area is 250 sq ft

Answer:

The width = 10 ft./ The lenght = 25 ft./ The area = 250 ft.²

Step-by-step explanation:

use X as the width

so we'll get 2X+5 as the length

the perimeter = 2(length) + 2(width)

70 = 2(2X+5) + 2(X)

70 = 4x+10 + 2x

70 = 6x+10

60 = 6x

x = 10

as the beginning x is the width

so the width is 10 ft.

the lenght is 2x+5

2(10)+5 = 25

so the length is 25 ft.

The area of rectangle is width x length

so 10 x 25 = 250 ft.²

Answer:

dimes:$8  quarters:$15

Step-by-step explanation:

im still in 6th grade

Answer:

55 dimes and 70 quarters

Step-by-step explanation:

Using a simple strategy of guess and check we know that the quarters will always be 15 more than dimes.  From this we know it has to be around the 50s as 40s would bring us numbers too low and 60s too high.  55 happens to be answer for dimes as that brings in $5.50. 23-5.5=17.5 multiply that by 4 as each quarter is only valued at $0.25 you get the answer 70 which just so happens to meet the requirements of being 15 more than 55.

According to the information we can infer that Dora's conclusion may be incorrect because the information provided only states that the number of people who spent time reading falls within specific ranges (0-2 hours, 2-4 hours, and 2-10 hours), but it does not give a specific count for those who spent at least 4 hours. Therefore, Dora's assumption that "most people spent at least 4 hours a week reading" is not supported by the given data.

The range of the time spent reading cannot be determined from the information provided because the ranges are overlapping. For example, a person who spent exactly 2 hours reading could fall into both the first range (0-2 hours) and the second range (2-4 hours). Without more specific data or non-overlapping ranges, it is not possible to determine the exact range of time spent reading.

To estimate the mean time spent reading by Dora's friends, we can calculate the midpoint of each range and use it as an approximate value. The midpoint for the first range (0-2 hours) is 1 hour, for the second range (2-4 hours) is 3 hours, and for the third range (2-10 hours) is 6 hours. We can then calculate the estimated mean by taking the weighted average of these midpoints using the respective number of people as weights.

Estimated mean = [(4 * 1) + (5 * 3) + (11 * 6)] / (4 + 5 + 11) = 4.53 hours (approximately)

So, an estimate of the mean time spent reading by Dora's friends is approximately 4.53 hours.

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Answer:

a variable expression

Step-by-step explanation:

because it consists unknown variable d

We will try to leave the letter \(r\) alone by modifying the given equation.

This equation is defined with the following expressions.

Ans: \(r=\frac{3t}{t-1}\)

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Answer:

5 cups

Step-by-step explanation:

Answer:

1/2 : 1

2 : 4

3 : 6

Notice that every ratio consists of a number and double the number.

For 1/2 cup lemon juice, use 1 cup sugar.

The amount of sugar is twice the amount of lemon juice.

The ratio is 1:2

Since you are told the ratio is 1:r, that means r is 2.

The unit rate is 2 cups sugar per cup of lemon juice.

Step-by-step explanation:

Answer:

6x² + 12y² + 17xy - 25xz

Step-by-step explanation:

(2x + 3y) (3x + 4y - 5z)

= 6x² + 8xy - 10xz + 9xy + 12y² - 15yz

= 6x² + 12y² + 8xy + 9xy - 10xz- 15yz

= 6x² + 12y² + xy (8 + 9) - xz (10 + 15)

= 6x² + 12y² + 17xy - 25xz

Answer:

what

Step-by-step explanation:

which questions you are telling there is no question to answer you!!

If Andrea ate the same amount of calories both days, Each cookie has 100 calories.

To find out how many calories are in each cookie, we need to determine the total number of calories consumed and divide it by the total number of cookies.

On Friday, Andrea ate 4 cookies and 1700 calories with her meals, resulting in a total of 1700 + (4 * C) calories, where C represents the calories per cookie.

On Saturday, Andrea ate 5 cookies and 1650 calories with her meals, resulting in a total of 1650 + (5 * C) calories.

Since Andrea ate the same amount of calories both days, we can set up an equation:

1700 + (4 * C) = 1650 + (5 * C)

Simplifying the equation, we get:

50 = C

Therefore, each cookie has 50 calories.

It's worth noting that the solution assumes that the calorie content of the meals on both days is the same and only the calorie content from the cookies varies.

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Answer:

The answer is D

Step-by-step explanation:

Believe me, dawg!

The series is (d)

A series is the cumulative sum of a given sequence of terms.

Given:

2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87

If we look at the power it is always one less the term i.e., for first term the value of k=0.

So, the series in the form of summation can be written as

\(^{88}\sum_{k=1}\) 2.5 (1.2)^(k-1)

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The value of the car in 2000 is expected to be $3800, given a starting value of $7700 in 1990 and a decrease of $390 per year for 10 years.

To find the value of the car in each subsequent year, we can subtract $390 from the previous year's value. Let's calculate the value of the car for each year from 1990 to 2000.

Year 1990: $7700

Year 1991: $7700 - $390 = $7310

Year 1992: $7310 - $390 = $6920

Year 1993: $6920 - $390 = $6530

Year 1994: $6530 - $390 = $6140

Year 1995: $6140 - $390 = $5750

Year 1996: $5750 - $390 = $5360

Year 1997: $5360 - $390 = $4970

Year 1998: $4970 - $390 = $4580

Year 1999: $4580 - $390 = $4190

Year 2000: $4190 - $390 = $3800

Therefore, the value of the car is expected to be $3800 in the year 2000.

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Answer:

The dimensions that match Alice's rectangle are 7 cm and 8 cm.

Step-by-step explanation:

The perimeter of the rectangle is given by:

\( P = 2(a + b) = 30 cm \)    (1)                              

Where a and b are the sides of the rectangle

Also, the area of the rectangle is:

\( A = a\times b = 56 cm^{2} \)   (2)

By solving equation (1) for a, we have:

\( a = 15 cm - b \)      (3)                      

Now, by entering equation (3) into (2) we can find one side of the rectangle:

\( 56 cm^{2} = (15 cm - b)\times b \)          

\( b^{2} - 15b + 56 = 0 \)                                                        

Solving the above quadratic equation we have:

b₁ = 7 cm  and b₂ = 8 cm                      

Now, the other side of the rectangle can be calculated with equation (3):

\( a = 15 cm - b_{1} = 15 - 7 cm = 8 cm \)                          

or    

\( a = 15 cm - b_{2} = 15 - 8 cm = 7 cm \)            

Taking the first solution (b₁) or the second (b₂), we find that the dimensions that match Alice's rectangle are 7 cm and 8 cm.          

Therefore, the dimensions that match Alice's rectangle are 7 cm and 8 cm.

I hope it helps you!                            

Answer:

( 0 , -5 )

Step-by-step explanation:

The coordinates of the focus of the parabola is at (0, -5)

The standard formula of a parabola is given as:

y² = 4ax

Given a parabola represented by the equation x² = -20y

The standard equation of the parabola facing downward is 4p(y-k)=(x-h)^2 where (h, k) is the focus.

Comparing with the given equation, the focus will be at (0, -5)

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Answer:

As a fraction: 3/50

It cannot be turned into a mixed number