A student creates a scale model of a dinosaur in science class. In the model, the length of the dinosaur's tail is 2 inches.
the dinosaur's tail is 5 feet.
Which scale does the student use to create the scale model of the dinosaur?
1 inch represents 2.5 feet
2.5 inches represent 0.4 foot
1 inch represents 0.4 foot
2.5 inches represent 1 foot

Answer:

8 weeks

Step-by-step explanation:

48 is 75%

x is 100%

48×100=4800

75x=4800

x=4800:75

x=64

64-48=16

16:2=8

Answer is 8 weeks

The graph of the functions f(x) = (-5x)³ and f(x) = x³ - 4 are drawn below.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

The parent function is given below.

f(x) = x³

The function is stretched by 5 units and gets reflected over the y-axis. Then the function is given as,

f(x) = (-5x)³

The function is shifted by 4 units downward then subtract 4 from the function. Then the function is given as,

f(x) = x³ - 4

The graph of the functions f(x) = (-5x)³ and f(x) = x³ - 4 are drawn below.

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Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

The cost of a apple is $0.75 and that of orange is $1.5.

Given is that 4 apples and 6 oranges cost $12 while 6 apples and 3 oranges cost $9.

We can write the system of equations as -

4x + 6y = 12

6x + 3y  = 9

Reducing the equations, we get -

2x + 3y = 6

2x + y = 3

We can write -

2x + y = 3

2x = 3 - y

Using the value of [2x], we get -

3 - y + 3y = 6

3 + 2y = 6

2y = 3

y = 1.5

and

2x = 3 - 1.5

x = 1.5/2

x = 0.75

Therefore, the cost of a apple is $0.75 and that of orange is $1.5.

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Answer:

Give her brainiest

Step-by-step explanation:

B) The system of equations has a solution

Answer:

1) m = 9/2, n = 9

3) x = y = (3√2)/2

Step-by-step explanation:

1) We have a 30°-60°-90° right triangle, so the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is (9√3)/2, so m, the length of the shorter leg, is 9/2, and n, the length of the hypotenuse, is 18/2, or 9.

3) We have an isosceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. The length of the hypotenuse is 3, so x and y, the lengths of the two congruent legs, are 3/√2, or (3√2)/2.

There are 640 juniors enrolled in Eagle Mountain High school.

Percentage can be define as the way of shown a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "by the hundred." Percentages are commonly used to represent proportions or rates, and they are denoted using the symbol "%".

Let's denote the total number of juniors in the high school as "x".

From the problem, we know that 90% of the juniors have a driver's license. We can express this as:

0.9x = 576

To solve for x, we can divide both sides by 0.9:

x = 576 / 0.9

x = 640

Therefore, there are 640 juniors enrolled in Eagle Mountain High school.

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The expression 1 2/5 + 2 2/3 using fifteenths is 3 + 6/15 + 10/15

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

1 2/5 + 2 2/3

3 + 2/5 + 2/3

To rewrite the expression using fifteenths, we multiply the numerator and the denominator of the fractions by the same number

In this case, we use 3 and 5

So, we have

3 + 2/5 * 3/3 + 2/3 * 5/5

Evaluate the products

3 + 6/15 + 10/15

Hence, the expression using fifteenths is 3 + 6/15 + 10/15

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Answer:

false

Step-by-step explanation:

A negative number divided by a negative number results in a positive number.

Answer:

2-sqrt(3)

Step-by-step explanation:

google said

Answer:

33

Step-by-step explanation:

each upper cell is the sum of the two cells under it. For example 4 and 5 make 9 so 16+17=33

Answer:

1460

Step-by-step explanation:

rounding to the nearest ten, that is nearest to 1456 which would be 1460 (hope this helps! ) ♡

Answer:

1460

Step-by-step explanation:

Original number is 1 4 5 6

To round to the nearest ten, look at the digit in the 10's place and the digit immediately to the right of it

The digit in the tens place is 5

If the digit to the immediate right of this digit is 5 or greater, round the digit in the tens place up by one digit and set the immediate right digit to 0

So 5 rounds up to 6

The 6 to the immediate right(units place becomes 0)

1 4 5 6 rounded to nearest ten==> 1 4 6 0

Answer:

13,101,108

as in Thirteen million ,hundred and one thousand, one hundred and eight

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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The given box plots, we can conclude that Fast Chicken typically has a longer median wait time compared to Super Fast Food, but we cannot make any conclusions about the mean wait time without additional information.

What is data collection ?

Data collection is the process of gathering and measuring information on a particular subject or variable of interest. In order to conduct data collection, researchers typically use various methods and techniques, such as surveys, experiments, observations, and interviews, to collect data from individuals, groups, or organizations.

Data collection is a critical component of the research process, as the quality and accuracy of the data collected can significantly impact the outcomes of the study. The data collected can be quantitative or qualitative, and may include a wide range of variables such as age, gender, income, education level, health outcomes, attitudes, behaviors, and many more.

Once the data is collected, researchers typically analyze and interpret the data using statistical methods and techniques to derive meaningful insights and conclusions from the data. These insights can be used to address research questions or to inform decision-making in various fields such as business, healthcare, social sciences, and many more.

Overall, data collection is an important step in the research process that helps to provide a foundation for accurate and reliable information and analysis.

Based on the given box plots, we can compare the wait time data collected from the two different drive-thru restaurants: Fast Chicken and Super Fast Food. The box plot for Fast Chicken has a median wait time of 12.5 minutes, which is higher than the median wait time of 12 minutes for Super Fast Food. Therefore, we can infer that on average, customers at Fast Chicken experience a longer wait time than customers at Super Fast Food.

Additionally, we can also compare the ranges of the wait time data for the two restaurants. The box plot for Fast Chicken has a range of 15 minutes (from 10 to 25 minutes), while the range for Super Fast Food is 24 minutes (from 8.5 to 32.5 minutes). This indicates that the variability in wait times is higher for Super Fast Food compared to Fast Chicken.

However, we cannot determine the mean wait time for each drive-thru from the given box plots, as the mean is not typically included in a box plot. Instead, box plots show the median and quartiles of the data set. The median represents the middle value in the data set, while the quartiles divide the data into four equal parts, with the upper quartile (Q3) representing the 75th percentile of the data set and the lower quartile (Q1) representing the 25th percentile.

Therefore, based on the given box plots, we can conclude that Fast Chicken typically has a longer median wait time compared to Super Fast Food, but we cannot make any conclusions about the mean wait time without additional information.

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Answer:

yes

Step-by-step explanation:

2 = (3)(18) + (6)(7)

54 + 42 = (9)(10) + 6

54 + 42 = 90 + 6

O 54 + 42 = 6(9 + 7)

The equation of the sphere with center coordinates  (4, −12, 8) and radius 10 is x² -8x + y² + 24y + z² -16z + 124 =0 .

And different plane equations are :

Intersection with xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

Intersection with yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

Intersection with zx plane :( x - 4 )² +  ( z - 8 )² = -44

Equation of the sphere with center coordinates (4, −12, 8) and radius 'r' = 10 is :

( x - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒ x² -8x + y² + 24y + z² -16z + 224 = 100

⇒x² -8x + y² + 24y + z² -16z + 124 =0

Intersection with xy-plane

z = 0

( x - 4 )² + ( y + 12 )² + ( 0 - 8 )² = 10²

⇒( x - 4 )² + ( y + 12 )² = 6²

Circle with center ( 4,-12) and radius 6.

Intersection with yz-plane

x = 0

( 0 - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒( y + 12 )² + ( z - 8 )² = (√84)²

Circle with center ( -12, 8) and radius √84.

Intersection with zx-plane

y = 0

( x - 4 )² + ( 0 + 12 )² + ( z - 8 )² = 10²

⇒( x - 4 )² +  ( z - 8 )² = -44

Not possible as radius cannot be negative.

Therefore, the equation of the sphere with the given center and radius is equal to x² -8x + y² + 24y + z² -16z + 124 =0 and equation of the intersection of different planes are:

xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

zx plane :( x - 4 )² +  ( z - 8 )² = -44

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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By composite compostion f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions

A function is a relationship between inputs where each input is related to exactly one output.

Given: f(x) = 5x-6 and f⁻¹(x) = (x+6)/5

To show the inverse relationship exists using composite composition, f(f⁻¹(x)) must be equal to f⁻¹(f(x))

Let's check:

f(f⁻¹(x)) = f((x+6)/5)

Substitute x = (x+6)/5  into  f(x) = 5x-6:

f(f⁻¹(x)) = 5((x+6)/5) - 6

f(f⁻¹(x)) = (x+6)- 6

f(f⁻¹(x)) = x

Also,

f⁻¹(f(x)) = f⁻¹(5x-6)

Substitute x = 5x-6 into f⁻¹(x) = (x+6)/5:

f⁻¹(f(x)) =  ((5x-6)+6)/5

f⁻¹(f(x)) =  5x/5

f⁻¹(f(x)) =  x

Since f(f⁻¹(x)) = f⁻¹(f(x)). Therefore, f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions

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Answer:

The explicit arithmetic formula can be used to find the 39th term of this sequence.

\(a_{n} = a_{1} + d(n-1)\)

In order to use this formula, we must know a_1, the first term, and , the common difference.

In this case, the first term is given as -15.

The difference can be found by looking at the difference between each following term. In this case, d = +5.

(Notice to get from -15 to -10, we add 5, to get from -10 to -5, we add 5, etc.)

Now that we have everything we need, we can plug everything in to find the 39th term:

\(a_{39} = -15 + 5(39-1)\\a_{39} = -15 + 190\\a_{39} = 175\)

The 39th term of this sequence is 175.

*Note n represents the term number we are trying to find. That's why we substituted 39 for n when plugging everything into the formula. \(a_{39}\) denotes the 39th term

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

Some examples of parallel lines cut by a transversal: Zebra crossing on the road. Road and railway crossing. Railway tracks with sleepers.

Answer:

8 square inches

Step-by-step explanation:

when finding the area of a rectangle you multiply the length and width

so the area is equal to 2 x 4

2 x 4 = 8 so the area of the rectangle is 8 square inches

The correct option is (b) as the expected value and variance of daily revenue are 37.5 and 4.5 respectively.

What is meant by variance?

Consider the expected value to be the average value. The expected value of X when it is a discrete random variable is the exact mean of the relevant data.

The difference between the actual numbers and the average should be viewed as the variance. A greater range of values is indicated by a higher variance. A spread of measure for a random variable distribution that quantifies how much a random variable's values deviate from its expected value is called variance. Frequently, V(X) is used to represent the variance of random variable X.

Given,

  Cost of soft drink c = $0.30

   Expected value of the number of cans sold per day E(X) = 125

  Variance of number of cans sold per day V(X) = 50

 So,

    Expected value of daily revenue E(Y) = c *  E(X) = 0.3 * 125 = 37.5

  Variance of daily revenue V(Y) = c² * V(X) = 0.3² * 50 = 4.5

Therefore the expected value and variance of daily revenue are 37.5 and 4.5 respectively. The correct option is (b).

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Answer:

Points scored in a basketball game vary directly with shots taken.

This means that this question can be solved

by proportions, using a rule of three.

How many would she have scored if she takes 60 shots?

Using a rule of three:

50 points - 40 shots

x points - 60 shots

Applying cross multiplication:

4x = 50 × 60

Divide from both sides

x = 50 × 1.25 = 75

Answer is 75

Step-by-step explanation:

Here is a easier explanation if you didn't understand clearly:

It asked for how many 60 shots would score.

You would look at the first time he scored which is 50 and took 40 shots. Divide them

50 ÷ 40 = 1.25 or 1.5

So now you know each point scores 1.25 or 1.5

Now you multiply 1.25 or 1.5 with how many shots to see how much was scored and in this case 60 shots.

60 × 1.25 or 60 × 1.5

& They both end up equaling just the same, 75.

Hope it made sense :)