Ella has a mass of 56 kg, and Tyrone has a mass of 68 kg. Ella is standing at the top of a skateboard ramp that is
1.5 meters tall. Which conclusion is best supported by the given information?
If Tyrone stands at the top of the same ramp, his potential energy will be less than Ella's
If Tyrone stands at the top of a 1 m high ramp, his potential energy will be greater than Ella's.
If Tyrone stands at the top of the same ramp, his potential energy will be the same as Ella's.
If Tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than Ella's.
Hey

Answer:

b) 5:11

Step-by-step explanation:

count the orange squares and the white squares

Answer:

f (t) ≈ 12,119(0.93)t, where t represents the number of years after 1990

Step-by-step explanation:

The exponential function will be \(f(t) = 12119(0.93)^t\). The correct option is C.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Exponents are used in exponential equations, as the name suggests. We are aware that a number's exponent (or base) tells us how many times the original number has been multiplied.

In the table, the data of the building is given for 1990 the cost is 12,100 and for 1992 the cost is 10,498.

The exponential expression is written as:-

\(f(t) = 12119(0.93)^t\)

For 1992 the time will be t = 2 years

\(f(t) = 12119(0.93)^2\\f(t) = 10490\)

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Answer:

first option

Step-by-step explanation:

the standard form of a quadratic function is

f(x) = ax² + bx + c ( a ≠ 0 )

the only function in this form from the list is

f(x) = - 5x² - 3x + 9

Answer:

f(x) = -5x² - 3x +9

Step-by-step explanation:

The standard form of a quadratic function is: f(x) = ax² + bx + c

The intercept form of a quadratic function is:  f(x) = a(x - p)(x - q)

The vertex form of a quadratic function is:  f(x) = a(x - h)² + k

(when a ≠ 0)

Therefore:

f(x) = -5x² - 3x +9

f(x) = -5(x + 4)(x - 2)

f(x) = 2x - 8

f(x) = -5(x - 1)² + 6

The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

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Answer:

The median is 6

Step-by-step explanation:

Answer:

8 quaters 3 nickels

Step-by-step explanation:

The markup on the TV for Leons is $156.84. This represents a 44% increase over the cost of $357. The selling price of the TV, including the markup, would be $513.84.

To determine the markup on the TV, we need to calculate 44% of the cost.

The cost of the TV is given as $357.

To find the markup, we multiply the cost by the markup rate:

Markup = 44% of $357 = (44/100) * $357 = $156.84

Therefore, the markup on the TV is $156.84.

The markup represents the additional amount added to the cost of the TV to cover expenses and generate a profit for the retailer. In this case, Leons is applying a 44% markup rate to the cost of $357.

The markup is typically expressed as a percentage of the cost. In this case, the markup amount of $156.84 is 44% of the cost.

It's important to note that the markup is not the same as the selling price. To determine the selling price, the markup is added to the cost:

Selling Price = Cost + Markup = $357 + $156.84 = $513.84

Therefore, the selling price of the TV, considering the 44% markup, would be $513.84.

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The graph that represents Ramon's initial step is, On a coordinate plane, the point (0, 3) is graphed.

The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.

Pair in Order = (x, y) where x represents the abscissa, the measure of a point's separation from the main axis, and y represents the ordinate, the measure of a point's separation from the secondary axis.

Given, Ramon is graphing the function f(x) = 3 + (4)x.

We know the initial value of a function is determined when the independent variable is set to zero.

Here the independent variable is 'x'.

Now, at x = 0,

f(0) = 3 + (4)(0).

f(0) = 3.

So, The ordered pair is (0, 3).

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Answer:

a

Step-by-step explanation:

To determine the probability of a continuous distribution we use the integral to determine it and for the normal distribution the integral is not so simple, for that reason it is simpler to use range values from tables.

Probability can be determined from a continuous distribution in the following way:To compute the probability of a given interval for a continuous random variable, the area under the curve over the interval is determined. Integrals are used to calculate this area under the curve, which can be done either numerically or analytically using probability density functions.

For some distributions, such as the uniform distribution, calculating the area under the curve is straightforward. However, for other distributions, such as the normal distribution, it can be more difficult to calculate the integral analytically.

The normal distribution is a continuous probability distribution that is frequently used in statistics. It is defined by its probability density function, which is a bell-shaped curve with a mean and a standard deviation.

Calculating the area under the curve for the normal distribution requires the use of integrals. Integrals are difficult to solve analytically for the normal distribution because the probability density function is not simple. However, it is relatively simple to calculate the probability for a given range of values using standard statistical tables or computer software.

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The total surface area of the sphere with a radius of 6cm, correct to 3 significant figures, is approximately 452 cm^2.

The formula for the surface area of a sphere is:

A = 4πr^2

where A is the surface area and r is the radius.

Substituting π = 3.142 and r = 6cm, we get:

A = 4 x 3.142 x 6^2

= 452.39 cm^2

Rounding to 3 significant figures gives:

A ≈ 452 cm^2

Therefore, the total surface area of the sphere with a radius of 6cm, correct to 3 significant figures, is approximately 452 cm^2.

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False. Scaling, in the context of graphics, refers to the process of resizing an image or graphic while maintaining its aspect ratio. It involves changing both the vertical and horizontal size of the graphic by the same percentage.

When scaling a graphic, the goal is to resize it proportionally, preserving the original aspect ratio. This means that both the vertical and horizontal dimensions are changed by the same factor or percentage. For example, if an image is scaled by 50%, both its height and width will be reduced by 50% of their original values. This ensures that the graphic maintains its original proportions and does not appear distorted.

Scaling graphics is commonly used in various applications, such as graphic design, image editing, and web development, to resize images without distorting their appearance. It allows for consistent resizing across different devices or platforms while maintaining the integrity of the original graphic.

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Answer:

(0,1) and (1,4)

Step-by-step explanation:

Answer:

A: Function f.

Step-by-step explanation:

Let's find the maximum y-value of each function.

Function f  is given by:

\(f(x)=3\cos(2x)+4\)

Remember that the value of cosine is always between -1 and 1. In other words:

\(-1\leq \cos(x)\leq 1\)

Then assuming the greatest value for cosine, we can substitute it for one:

\(f(x)_{\text{max}}=3(1)+4=7\)

Function g is given by the graph.

Looking at the graph, we can see that the maximum y-value of g is 3.

Finally, function h is given by the table.

Looking at the table, the maximum y-value of h is -2.

Therefore, function f has the greatest maximum y-value.

Answer:

Maksim's answer and explanation are not correct

The actual domain is 2 < x < Infinity

Step-by-step explanation:

The domain of a function is the set that is made up of the possible inputs of the function

The given function is f(x) = √(x - 2)

Maksim's response for the domain of f(x) is x ∈ R ('x' is a member of the set of all real numbers

The function is not defined when x < 2, at which the expression, x - 2, will become negative, and for which the square root of the negative number is imaginary

Therefore, the domain for which the function is defined is all real numbers larger than 2, which can be presented as follows;

The domain of f(x) = 2 < x < ∞

Therefore Maksim is wrong as the actual domain is limited to 2 < x < ∞.

C.) right and isosceles, but not equilateral

Answer:

C.) right and isosceles, but not equilateral

Step-by-step explanation:

The slope of the line is 2 and Jan runs 2 laps for every minute.

The slope of the line is defined as the change in the y-coordinate with respect to the x- coordinate and the formula for slope is given by

Where (x₁, y₁) and (x₂, y₂) are points where the line passes through.

Here we have

The graph shows the number of laps that Jan runs  

From the graph,

The line that represents the situation will pass through (2, 4) and (5, 10)

Using the formula, Slope (m) = (y₂ - y₁) / (x₂ - x)  

Slope of the line = [10 - 4]/[5 - 2 ] = 6/3 = 2

This means that Jan runs 2 laps for every 1 minute  

Therefore,

The slope of the line is 2 and Jan runs 2 laps for every minute.

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Answer:

Parallel Line: -1/4x Perpendicular Line: 4x

Step-by-step explanation:

An exponential function that models the population of bluegill over the last 5 years is \(y = 2,802.62(0.6)^x\).

In this exercise, we would plot the years on the x-axis of a scatter plot while the population would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit on the scatter plot.

Based on the scatter plot shown below, which models the relationship between the years and the population, an exponential equation for the line of best fit is modeled as follows:

\(y = 2,802.62(0.6)^x\)

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The probability of each outcome in the sample space is B. 1/20.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

For given example, the total number of students:n(S) = 5. The probability of selecting one student would be: P(A) = 1/5.

Now, there are 4 students.n(S) = 4

So, probability of selecting second student from remaining 4.P(B) = 1/4

Hence, the probability of each outcome in the sample space would be:

1/5 × 1/4

= 1/20

Therefore, the probability of each outcome in the sample space is 1/20.

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Answer: 5t = 400-105

Step-by-step explanation:

Let t= Number of three–pointers Marissa has to average over the next 5 days to reach her goal. .

Goal = 400 three–pointers every week.

Marissa has already shot  = 105 three–pointers

Remaining shots to achieve target (5t) = Goal - (Marissa has already shot)

i.e. 5t = 400-105  (required equation)

⇒ 5t = 295

⇒ t = 59

hence, she need to make 59 shots per day for next 5 days.

Answer:

(-2,0)

Step-by-step explanation:

Cause I took the quiz <3

Answer:

B. d = sin2e

Step-by-step explanation:

Use the following identity: 2cos(x)sin(x)=sin(2x)

Therefore

d = 2sine cose

can be written as

d=sin(2e)

However, if you want step by step (for example if your teacher does not give you formula sheets with identities let me know.

The horizontal distance of the hop can also be written as d = sin 2e,  the correct option is B.

A trigonometric identity is used to solve a trigonometric Equation, it is based on the six trigonometric Ratios.

The horizontal distance of a hop by a frog is given by

d = 2 sine cose

By the trigonometric Identity sin 2x = 2 sinx cosx

From the above Identity, the horizontal distance of the hop can also be written as

d = sin 2e

Therefore, the correct option is B.

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Answer:

y+5-1/3x=7 find y and then x to find the corresponding values

y = 5 - 1/3x + 7

y = 5 - 1/3(x) + 7

y = 5 - (1/3)x + 7

y = (5 - 1/3x) + 7

y = (5 + 7) - (1/3)x

y = 12 - (1/3)x

For y = 12,

12 - (1/3)x = 12

(1/3)x = 0

x = 0

Therefore, when y = 12, x = 0.

For performing this analysis Brewer can use a method such as a survey for gathering the data.

Brewer would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. He will require a large amount of data to determine this.

This data that he requires can be gathered using the method of survey, and a conclusion can be drawn from the data with the help of statistical analysis and probability analysis.

Surveys can be conducted by email or in an online survey form and can include both open-ended and closed-ended questions to gather both quantitative and qualitative data on the subject.

In this case, the survey can also be conducted by using orthodox methods of gathering data, such as observing people who are going to eat at local restaurants and on campus, although this is not the most ideal method.

Surveys allow the researcher to reach a large number of participants and gather data efficiently and effectively.

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The best way for her to find this data reliably is by using survey's

She can go around campus and survey the other students, and eventually get enough data to find an answer to her question (I also took the test and this answer was right)

have a good day :)

From the F-table the critical value of \(\frac{\alpha }{2}\) at the degrees of freedom of :

\(F_\frac{\alpha }{2}, _d_f_1,_d_f_2=3.91\)

The decision rule

=> Fail to reject the null hypothesis

The first sample size \(n_1=12\)

The first sample standard deviation is \(s_1=0.038\)

The second sample size is \(n_2=10\)

The first sample standard deviation is \(s_2=0.042\)

The significance level is \(\alpha =0.05\)

The null hypothesis is \(H_0:\sigma^2_1=\sigma^2_2\)

The alternative hypothesis is \(H_0:\sigma^2_1\neq \sigma^2_2\)

The test statistics is mathematically represented as:

\(F_c_a_l=\frac{s^2_1}{s^2_2}\)

\(F_c_a_l=\frac{0.038^2}{0.042^2}\)

\(F_c_a_l=0.81859\)

The first degree of freedom is :

\(df_1=n_1-1=12-1=11\)

The second degree of freedom is :

\(df_2=n_2-1=10-1=9\)

From the F-table the critical  value of \(\frac{\alpha }{2}\) at the degrees of freedom of :

\(df_1=11\) and \(df_2=9\)

\(F_\frac{\alpha }{2}, _d_f_1,_d_f_2=3.91\)

The decision rule

Fail to reject the null hypothesis

The conclusion

This no sufficient evidence to conclude that there is a difference between the two variance.

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We are given the following equation

We are asked to solve the equation for y.

Solving for y means that we have to separate the variable y.

Step 1:

Subtract 3x from both sides of the equation

Answer:

2/5

Step-by-step explanation:

the population in 1915 and 1940 is 24264.5

the population reach 50,000 is 77 years

In 1891 the population would be 6250 x  ( 1+ 0.0275)

In 1832 the population would be [ 6250 x ( 1+0.0275 ) ] x (1+0.0275)

in 1893 the population would be [6250 x ( 1+0.0275) ] x ( 1+0.0275) x (1+0.0275)

p= 6250(1.0275)^t

where t= number of years till 1890

t=25

p= 6250(1.0275) ²⁵

= 6250 x 1.9704

= 12314.8

t=50

p= 6250(1.0275) ⁵⁰

= 6250 x 3.8823

=24264.5

To reach 50,000

50000= 6250(1.0275)^t

(1.0275)^t = 50000 /6250

(1.0275)^t =8

Take log on both sides

log (1.0275)^t = log 8

t= log8/ log (1.0275)

t=76.6%

Hence

the population in 1915 and 1940 is 24264.5

the population reach 50,000 is 77 years

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