James and Karlee caught a lizard in their backyard. Its length from head to the end of the tail is
3/5 meters and the length of its tail is1/5

Answer:

The result gives the equation: 9x = -7

solution:  (-7/9, 4/3)

Step-by-step explanation:

6 x + 2y = − 2

and

3 x − 2y = − 5

add together

6x + 3x + 2y - 2y = -2 + -5

9x + 0 = -7

9x = -7

then x = -7/9

and y = -3x - 1:

y = -3*(-7/9) - 1

y = 7/3 - 1 =  4/3

solution:  (-7/9, 4/3)

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

6x+2y= -2   and 3x−2y ​ =−5 ​

6x + 3x  + 2y - 2y = -2 + -5

Answer:

x-coordinate of the circle's center = -2

y-coordinate of the circle's center = 5

Radius = 3

Step-by-step explanation:

Look at the picture

Answer:

What is the radius of the circle? 3

What is the x-coordinate of the circle’s center? -2

What is the y-coordinate of the circle’s center? 5

Step-by-step explanation:

Answer:

8.81% probability that the student answers exactly 4 questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A multiple choice exam has ten questions.

This means that [tex]n = 10[/tex]

The probability of answering any question correctly is 0.20.

This means that [tex]p = 0.2[/tex]

What is the probability that the student answers exactly 4 questions correctly

This is P(X = 4).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881[/tex]

8.81% probability that the student answers exactly 4 questions correctly

To estimate the mean age of the citizens in your community with a confidence interval of 95% and a margin of error of 4 years, you need a sample size of at least 25 citizens.

To estimate the mean age of the citizens in your community with a confidence interval of 95% and a margin of error of 4 years, you need to determine the required sample size. The formula for sample size calculation in this case is:

n = (Z * σ / E)²

where:

Substituting the values into the formula, we get:

n = (1.96 * 25 / 4)² = 3.8416 * 6.25 = 24.0101 ≈ 25

Therefore, you would need a sample size of at least 25 citizens to estimate the mean age of your community with a 95% confidence level and a margin of error of 4 years.

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150 citizens should be included in the sample to achieve the desired precision and confidence level.

The sample size required to estimate the mean age of the citizens within 4 years of the actual mean with a 95% confidence level, we can use the formula for the sample size in the context of a confidence interval for a population mean when the population standard deviation is known: [tex]\[ n = \left(\frac{z \sigma}{E}\right)^2 \][/tex]

where:

[tex]- \( n \)[/tex] is the sample size,

[tex]- \( z \)[/tex] is the z-score corresponding to the desired confidence level,

[tex]- \( \sigma \)[/tex] is the population standard deviation, and

[tex]- \( E \)[/tex] is the margin of error (half the width of the confidence interval).

Given:

[tex]- \( \sigma = 25 \)[/tex] years (population standard deviation),

[tex]- \( E = 4 \)[/tex] years (margin of error),

- Confidence level = 95% (corresponding to a z-score of 1.96 for a two-tailed test).

Plugging in the values:

[tex]\[ n = \left(\frac{1.96 \times 25}{4}\right)^2 \] \[ n = \left(\frac{49}{4}\right)^2 \] \[ n = (12.25)^2 \] \[ n \approx 149.0625 \][/tex]

Since we cannot have a fraction of a citizen in our sample, we round up to the nearest whole number:

[tex]\[ n = 150 \][/tex]

The sample size required is 150 citizens.

Answer:

Single-payment variable annuity

Step-by-step explanation:

The type of Annuity is single-payment variable annuity.

An annuity is a contract between you and an insurance company in which the insurer agrees to pay you either immediately or in the future. An Annuity plan guarantees you a predetermined sum of money for the remainder of your life in exchange for a lump sum payment or a series of instalments.

Annuities are a type of insurance in which a portion of the money is paid each year to ensure the future.

There are two kinds of annuities:

Single payment variable annuity - This annuity pays out at the end of each period for a set amount of time. Payments are made monthly, quarterly, semi-annually, or annually in this annuity.

Annuity due is the inverse of a single payment variable annuity in that payments are made at the start of each period.

In the given situation the annuity is single payment variable annuity because the investment is done each year for 5 years.

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Answer:

12 units squared

Step-by-step explanation:

12.39 = 2 (3.14)r

12.39 / 6.28 = 6.28r / 6.28

1.97= r

A= (3.14) (1.97)^2

A= 12.18

The triangle's side lengths of 2, 5, and 5.39 units. So the area is 4.1506 square units.

To compute the area of a triangle, we employ formula, which utilizes the semi-perimeter [tex]\(s\)[/tex] (half of the perimeter):

[tex]\[ s = \frac{a + b + c}{2} \][/tex]

The area [tex]\(A\)[/tex] is:

[tex]\[ A = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]

Triangle's sides as 2 units, 5 units, and 5.39 units:

[tex]\[ a = 2 \][/tex]

[tex]\[ b = 5 \][/tex]

[tex]\[ c = 5.39 \][/tex]

The semi-perimeter [tex]\(s\)[/tex]:

[tex]\[ s = \frac{2 + 5 + 5.39}{2} = \frac{12.39}{2} = 6.195 \][/tex]

Apply formula:

[tex]\[ A = \sqrt{s(s-a)(s-b)(s-c)} \\A= \sqrt{6.195(6.195-2)(6.195-5)(6.195-5.39)} \][/tex]

[tex]\[ A = \sqrt{6.195 \times 4.195 \times 1.195 \times 0.805} \][/tex]

Square root:

[tex]=\[ 6.195 \times 4.195 \times 1.195 \times 0.805\\= 25.201572[/tex]

The square root:

[tex]\[ A = \sqrt{25.201572} =5.02 \text{ square units} \][/tex]

Complete question:

A triangle has sides that measure 2 units, 5 units, and 5.39 units. What is the area?

Loan length affects total interest by spreading payments; interest rate directly impacts borrowing cost. Relative effect depends on borrower's goals.

The cost of interest for a loan is influenced by both the loan length (term) and the interest rate, but the degree of impact each has depends on several factors, including the specific terms of the loan and the borrower's financial situation. Let's break down their effects:

1. Loan Length (Term):

  - Longer loan terms typically result in lower monthly payments since they spread the principal amount over more payments.

  - However, longer terms also mean more time for interest to accrue, resulting in higher overall interest costs over the life of the loan.

  - For example, if Claudia takes out a loan with a longer term, she may pay less each month but end up paying more in total interest over the entire term compared to a shorter-term loan with the same interest rate.

2. Interest Rate:

  - The interest rate directly impacts the cost of borrowing. Higher interest rates mean higher monthly payments and more interest paid over the life of the loan.

  - Lower interest rates, on the other hand, result in lower monthly payments and less interest paid overall.

  - Even a small difference in interest rates can significantly affect the total interest paid over the life of the loan, especially for large loan amounts or longer terms.

Now, to determine which factor has a greater effect on the cost of interest for Claudia's loan, we need to consider her specific situation:

- If Claudia prioritizes minimizing her monthly payments, she might opt for a longer loan term despite potentially paying more interest in the long run.

- If Claudia is focused on minimizing the total interest paid over the life of the loan, she might prioritize securing a lower interest rate, even if it means higher monthly payments.

Ultimately, the relative importance of loan length and interest rate in determining the cost of interest depends on Claudia's financial goals, her ability to make monthly payments, and her overall financial situation. It's essential for her to carefully consider both factors and choose the loan terms that best align with her needs and financial objectives.

Answer:

D

Step-by-step explanation:

Look at the graph. You want to see how much distance he is at 9 minutes. Go all the way to 9 minutes, then go up. What coordinate does it fall in? (9,80). He travelled 80 meters in 9 minutes. (D)

Answer:

Pr(neither of two groups) = 0.0225

Step-by-step explanation:

Given:

15% of the students have never taken a statistics class = Pr(none)

Pr(none) = 0.15

40% have taken only one semester of statistics =Pr(one semester)

Pr(one semester) = 0.40

the rest have taken two or more semesters of statistics = Pr(two or more semester)

Pr(two or more semester) = 1 - [Pr(one semester) + Pr(none) ]

Pr(two or more semester) = 1-(0.40+0.15) = 1 - 0.55

Pr(two or more semester) = 0.45

Where Pr = probability

Let probability that neither of your two group mates has studied statistics = Pr(neither of two groups)

=Pr(none in group 1) ×Pr(none in group 2)

= 0.15 × 0.15

Pr(neither of two groups) = 0.0225

Answer:

y-8+8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer: She can travel 450 miles with 18 gallons.

Step-by-step explanation:

[tex]\frac{4.8}{120}[/tex] =  [tex]\frac{18}{x}[/tex]   solve by cross product

4.8x = 2160

x= 450

Kelsey's car gets 25 miles per gallon, and with an 18-gallon tank, she can travel a total of 450 miles on a full tank.

To calculate how far Kelsey can travel on a full tank of fuel, first we need to determine her car's fuel efficiency and then apply it to the full tank capacity. We are given that her car can travel 120 miles on 4.8 gallons of gas. This gives us a fuel efficiency rate we can use to find out the total distance she can travel on 18 gallons.

Therefore, Kelsey can travel 450 miles on a full tank of fuel.

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Answer:

The equation of the line is [tex]f\left(x\right)=-\frac{1}{9}x^{2}+1.8[/tex]

Step-by-step explanation:

I graphed the equation on the graph below and found the equation of the line.

If this answer is correct, please make me Brainliest!

Graphing the function [tex]\(f(x) = -\frac{1}{9}x^2 + 1.8\)[/tex] involves identifying the vertex, axis of symmetry, and plotting key points by selecting suitable x-values.

To graph the quadratic function [tex]\(f(x) = -\frac{1}{9}x^2 + 1.8\)[/tex], start by finding the vertex.

The vertex form [tex]\(f(x) = a(x - h)^2 + k\)[/tex] helps identify it, where \((h, k)\) is the vertex.

Here, [tex]\(a = -\frac{1}{9}\)[/tex].

The x-coordinate of the vertex is given by [tex]\(h = -\frac{b}{2a}\)[/tex] from the standard quadratic form [tex]\(ax^2 + bx + c\)[/tex], and [tex]\(b = 0\)[/tex] here since [tex]\(f(x)\)[/tex] has no linear term. So, [tex]\(h = 0\)[/tex]. Thus, the vertex is at [tex]\((0, 1.8)\)[/tex].

Next, find the axis of symmetry, which passes through the vertex. The axis of symmetry is the vertical line [tex]\(x = h\)[/tex], so in this case, [tex]\(x = 0\)[/tex].

To plot additional points, choose x-values on either side of the axis. Calculate corresponding y-values using the function.

For instance, when [tex]\(x = 3\)[/tex], [tex]\(f(3) = -\frac{1}{9}(3)^2 + 1.8\)[/tex], which equals [tex]\(1.3\)[/tex]. Repeat this process for a few more x-values.

Plot the vertex, axis of symmetry, and other points on a coordinate plane.

The resulting graph is a downward-opening parabola with the vertex as the highest point.

Label the axes, points, and use arrows to indicate the direction of opening.

This visual representation provides insight into the behavior of the function for different x-values.

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Answer:

Failure

Step-by-step explanation:

A synonym is a word that has a similar or exact same meaning as another given word. The synonym for malfunction, would therefore, be failure.

Answer:

It is failure

Step-by-step explanation:

a malfunction is a computer error. also known as a failure

Answer:

Negative correlation

Step-by-step explanation:

In a negative correlation, as one variable increases, the other variable decreases, and as one variable decreases, the other variable increases. In positive correlation, as one variable increases, so does the other and as one variable decreases, so does the other.

In the given question, as the number of student interruptions during class decreases, student scores on in-class quizzes increase. So, this an example of a negative correlation.

Answer:

  (x, y) = (0, -1)

Step-by-step explanation:

Since we have an expression for y, it is convenient to substitute that into the second equation:

  4x -7(-7x -1) = 7

  4x +49x +7 = 7

  53x = 0

  x = 0

Substituting into the first equation gives ...

  y = -7·0 -1

  y = -1

The solution is (x, y) = (0, -1).

Answer:

The standard deviation of the number of people who believe that the product is in fact improved is 1.50.

Step-by-step explanation:

The random variable X can be defined as the number of people who believe that a product is improved when they are told so.

The probability of a person believing that a product is improved is, p = 0.25.

A random sample of n = 8 people who are given a sales talk about a new, improved product are selected.

The event of a person believing that the product is improved is independent of others.

The random variable X follows a Binomial distribution with parameters n = 8 and p = 0.25.

The success is defined as a person believing that a product is improved.

The mean and standard deviation of a Binomial distribution is given by:

μ = n × p

σ = √[n × p × (1 - p)]

Compute the standard deviation as follows:

σ = √[n × p × (1 - p)]

  = √[8 × 0.25 × (1 - 0.25)]

  = √(2.25)

  = 1.50

Thus, the standard deviation of the number of people who believe that the product is in fact improved is 1.50.

Answer:

The distance to the nearest exit door is no more than 150 feet.

Use d to represent the distance (in feet) to the nearest exit door.

For this case we can create the following inequality based in the notation and condition given, when they says no more means that the possible value nees to be equal or lower than the specified value.

[tex] d \leq 150[/tex]

To ride a roller coaster, a visitor must be taller than 60 inches.

Use h to represent the height (in inches) of a visitor able to ride.

For this case we can create the following inequality based in the notation and condition given, when they says must be taller means that the possible value nees to be higher than the specified value.

[tex] h > 60[/tex]

Step-by-step explanation:

The distance to the nearest exit door is no more than 150 feet.

Use d to represent the distance (in feet) to the nearest exit door.

For this case we can create the following inequality based in the notation and condition given, when they says no more means that the possible value nees to be equal or lower than the specified value.

[tex] d \leq 150[/tex]

To ride a roller coaster, a visitor must be taller than 60 inches.

Use h to represent the height (in inches) of a visitor able to ride.

For this case we can create the following inequality based in the notation and condition given, when they says must be taller means that the possible value nees to be higher than the specified value.

[tex] h > 60[/tex]

Answer:

B, the second one

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

y=3(4)-4

y=12-4

y=8

Answer:

There is enough evidence to support the claim that the zinc concentration is higher on the bottom than the surface of the water source.

Step-by-step explanation:

We have the data

Zinc conc. bottom water (X)  | Zinc conc. in surface water (Y)

1 .430 .415

2 .266 .238

3 .567 .390

4 .531 .410

5 .707 .605

6 .716 .609

7 .651 .632

8 .589 .523

9 .469 .411

10 .723 .612

We can calculate the difference Di=(Xi-Yi) for each pair and calculate the mean and standard deviation of D.

If we calculate Di for each pair, we get the sample:

D=[0.015 0.028 0.177 0.121 0.102 0.107 0.019 0.066 0.058 0.111 ]

This sample, of size n=10, has a mean M=0.0804 and a standard deviation s=0.0523.

All the values are positive, what shows that the concentration water appearse to be higher than the concentration on the bottom.

We can test this with a t-model.

The claim is that the zinc concentration is greater on the bottom than the surface of the water source.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=0\\\\H_a:\mu> 0[/tex]

The significance level is 0.01.

The sample has a size n=10.

The sample mean is M=0.0804.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.0523.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.0523}{\sqrt{10}}=0.017[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.0804-0}{0.017}=\dfrac{0.08}{0.017}=4.861[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

This test is a right-tailed test, with 9 degrees of freedom and t=4.861, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>4.861)=0.00045[/tex]

As the P-value (0.00045) is smaller than the significance level (0.01), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the zinc concentration is greater on the bottom than the surface of the water source.

To determine if the zinc concentration is less on the bottom than the surface of the water source, a paired t-test can be performed. The t-test helps to compare the mean difference in zinc concentrations between the bottom and surface water. By comparing the calculated t-value with the critical t-value at the α = 0.1 level of significance, we can determine if the data supports the hypothesis.

To determine if the zinc concentration is less on the bottom than the surface of the water source, we can perform a hypothesis test. We'll use a paired t-test since we have paired data. We want to test if there is a significant difference between the bottom and surface zinc concentrations.

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Answer:

it would move upwards.

Step-by-step explanation:

there is no such thing as a negative exponent because, if you were suppose to graph that you have the parabola go up and down, and that is not how it works.

Answer:

would have a larger margin of error than a 90% confidence interval.

Step-by-step explanation:

Margin of error in statistics can be defined as a small amount that is allowed for in case of miscalculation or change of circumstances.

For a statistical data margin of error can be expressed as;

M.E = zr/√n

Where;

Given that;

r = Standard deviation

z = z score at a particular confidence interval

n = sample size

z at 99% = 2.58

z at 90% = 1.645

Since z at 99% is higher than z at 90% Confidence interval, the Margin of error M.E at 99% confidence interval will be higher than that of 90% confidence interval.

Answer:

When x=0 y=6

When x=3 y=0

Step-by-step explanation:

-6x-3y ≤-18

Let x = 0

-6x-3y =-18

-3y =-18

Divide each side by -3

-3y/-3 = -18/-3

y = 6

Let y = 0

-6x-3y =-18

-6x =-18

Divide each side by -6

-6x/-6 = -18/-6

x = 3

Answer:

Vertical component of velocity is [tex]81.35 ft/sec.[/tex]

Horizontal component of velocity is  [tex]182.6 ft/sec[/tex].

Step-by-step explanation:

Horizontal component of velocity is defined as:

[tex]v_{x} = v\times cos\theta[/tex]

Vertical component of velocity is defined as:

[tex]v_{y} = v\times sin\theta[/tex]

Where [tex]v_{x} , v_{y}[/tex] are the horizontal and vertical components of velocity.

[tex]v[/tex] is the actual velocity and

[tex]\theta[/tex] is the angle with horizontal axis at which the object was thrown.

Here, we are provided with the following:

[tex]v = 200 ft/sec[/tex]

[tex]\theta = 24^\circ[/tex]

[tex]v_{x} = 200 \times cos24^\circ\\\Rightarrow 200 \times 0.913\\\Rightarrow v_{x} = 182.6 ft/sec[/tex]

[tex]v_{y} = 200 \times sin24^\circ\\\Rightarrow 200 \times 0.407\\\Rightarrow v_{y} = 81.35 ft/sec[/tex]

So, Vertical component of velocity is [tex]81.35 ft/sec.[/tex]

Horizontal component of velocity is  [tex]182.6 ft/sec[/tex].

Answer:

1. Parametrization: [tex](2\cos(t), 2\sin(t))[/tex] and [tex]t\in [0,\pi][/tex]

2. In case that [tex]t\in [0,4\pi][/tex], the desired parametrization is [tex](2\cos(\frac{t}{4}), 2\sin(\frac{t}{4}))[/tex]

Step-by-step explanation:

Consider the particle at the point (2,0) and the circle of equation [tex]x^2+y^2=4[/tex]. Recall that the general equation of a circle of radius r is given by [tex]x^2+y^2=r^2[/tex]. Then, in our case, we know that the circle has radius 2.

One classic way to parametrize the movement of a particle that starts at point (r,0) and moves in a counterclockwise manner over a circular path of radius r is given by the following parametrization [tex](r\cos(t),r\sen(t)), t\in [0, 2\pi][/tex]. Since, for all t we have that

[tex](r\cos(t))^2+(r\sin(t))^2 = r^2(\cos^2(t)+\sin^2(t)) = r^2[/tex]

If we want to draw only the upper half of the circle, we must have [tex] t\in[0,\pi][/tex].

So, with r=2 the desired parametrization is [tex](2\cos(t), 2\sin(t))[/tex] and [tex]t\in [0,\pi][/tex]. Recall that in this parametrization when t=0 the particle is at (2,0) and when t=pi the particle is at (-2,0).

In the case that we want the parameter s [tex]\in[0,4\pi][/tex] but keeping the same particle's motion, we must do a transformation. We know that if parameter t is in the interval[tex][0,\pi][/tex] we get the desired motion. Note that in this case we are multiplying this interval by 4. So, we have that s = 4t.  If we solve for the parameter t, we get that t=s/4. Then, with the parameter s in the interval [tex][0,4\pi][/tex] we get the parametrization [tex](2\cos(\frac{s}{4}), 2\sin(\frac{s}{4}))[/tex] which is obtained by replacing t in the previous parametrization.

Note that since when [tex]s=4\pi[/tex] we have that [tex]t=\pi[/tex] and that when s=0, we have t=0, then the motion of the particle is the same (it changes only the velocity in which the particle moves a cross the path).

Parametric equations for the particle's motion are x(t) = 2cos(t) and y(t) = 2sin(t), with a parameter interval from 0 to 4π radians to trace the top half of the circle x2 + y2 = 4 four times.

To find the parametric equations that describe the motion of a particle tracing the top half of the circle x2 + y2 = 4 four times, we start from the standard parametric equations for a circle with radius 2 centered at the origin: x(t) = 2cos(t) and y(t) = 2sin(t). Since the problem specifies the top half of the circle and repeats this motion four times, we adjust our parameter t to cover the desired motion from 0 ≤ t ≤ 4π.

The parametric equations for the particle's motion are then: x(t) = 2cos(t) and y(t) = 2sin(t) with the parameter interval of 0 ≤ t ≤ 4π. Here, the parameter t represents the angle of rotation in radians, where the values of t from 0 to π cover the upper semicircle and the values of t from π to 2π would cover the lower semicircle, which we're ignoring in this case. Our chosen interval ensures that the top half is traced four times.

Answer:

10+26x

Step-by-step explanation:

To solve this, work your way from the inner most parentheses to the outer most:

Answer:

D = 141

Step-by-step explanation:

The given quadratic equation is

[tex]5x^2+9x=3\\\\5x^2+9x-3=0[/tex].

It is required to find the value of the discriminant. The value of discriminant  of any quadratic equation is given by :

[tex]D=b^2-4ac[/tex]

Here, a = 5, b = 9 and c = -3

On plugging all the values, we get :

[tex]D=(9)^2-4\times 5\times (-3)\\\\D=141[/tex]

So, the value of discriminant for y is 141.

Answer:

Step-by-step explanation:

The shape of the cottage is cube

The edge of the cube is of length is 26ft

L_1 = 26ft.

The roof is in form of a square with with length 17ft.

L_2 = 17ft.

The roof is made up of 4 congruent isosceles triangles. Since the roof extends 2 ft over the edge of the cottage on each side, then the base of each triangle is 26 + 2 = 28 ft.

L_2 = 28 ft

Then, area of the roof is

A = 28²

A = 784 ft²

The triangular pyramid.

The triangular has four sides

Then,

Each of the area can be calculated using

A = ½ × b × h

Then, the four area of the triangular pyramid

A_total = 4 × ½ × b × h

A_total = 2 × b × h

The base of the triangle is 28ft.

The calculate the height of the triangle

Let's calculate the area of one of the triangles and then just multiply by 4. See attachment. Drop a perpendicular from the vertex of a triangle to its base. We now have the triangle broken up into two right triangles. The hypotenuse is 17 ft and one of the legs of the right triangle is 28 / 2 = 14 ft. Then the height is using Pythagoras theorem

a² = b² + c²

17² = 14² + h²

17² - 14² = h²

h² = 93

h = √93

Then, the area of the triangular pyramid is

A = 2 × b × h

A = 2 × 28 × √93

A = 540.04 ft²

Then, the area of the pyramid is approximately 540 ft², since the base of the pyramid cannot be seen.

But if we include the base, then, the total surface area is

A_t = A_triangular + A_base

A_t = 540 + 784

A_t = 1324 ft²

The circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Since a circle fails the vertical line test, it cannot be a function. In other words, we can create a vertical line that crosses a circle's graph more than once.

Not every parabola is a function. Only parabolas with upward or downward openings are regarded as functions.

Thus, the circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.

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The only graph that represents a function is the: Third Graph

What graph depicts a function?

To check whether the graph represents a function or not, we perform vertical line test.

Vertical Line test:

The Vertical Line Test is a method used to determine whether a given graph represents a function or not. To apply the test, draw a vertical line through the graph and observe the points of intersection. If the vertical line intersects the graph at exactly one point for each value of x, then the graph represents a function. If the vertical line intersects the graph more than once for any value of x, then the graph does not represent a function

Looking into the graphs, the vertical line intersects the graph C at only one point.

Hence, graph C represents a function.