Mathematics High School

I need help solving this problem I'm stuck on.

Answers

Answer 1

Answer:

S = -90t + 550

Step-by-step explanation:

First we must note a few key things the question tells us:

1. The tickets sell at a constant rate, thus implying a linear relationship.

2. Tickets start selling at 10

3. The independent variable (t) is in hours after 10

4. The number of tickets (S) is declining, thus we should expect a negative gradient.

5. The number of tickets is our dependent variable since it is reliant on time.

y = mx+c is our general linear expression which we will call "Eq 0"

Lets substitute our knowns into this to find m and c. We know that "t" is independent and that "S" is dependent on "t" therefore, we know that our x-axis will be representing values for "t" and that our y-axis will represent values for "S"

We must use simultaneous equations to find m and c

Eq 1: 550 = m(0) + c -> 550 = c

Eq 2: 280 = m(3) + c -> 280 = 3m + c

From Eq 1. we already know that our y intercept is at 550.

To find our gradient, we must substitute our known (550 being the y-intercept) into the next equation.

Thus,

280 = 3m + 550

To isolate our variable (m) we subtract both sides by 550

280 - 550 = 3m + 550 - 550

-270 = 3m

To finally find m, we divide both sides by 3

-270/3 = 3m/3

-90 = m

Now we substitue both our knows into Eq 0, note that our gradient (m) is negative as expected.

y = -90x + 550

Or, in terms of S and t

S = -90t + 550

Related Questions

A circle is represented by the equation x2 + 8x + y2 – 12y = –29. Describe the algebraic technique(s) needed to rewrite the equation in standard form. Identify the center and radius of the circle. Show your work

Answers

The equation of the circle can be written in standard form and in a general form

The center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]

How to identify the radius and the center of the circle

The equation of the circle is given as:

[tex]x^2 + 8x + y^2 - 12y = -29[/tex]

Rewrite as:

[tex]x^2 + 8x + k - k + y^2 - 12y + k - k= -29[/tex]

Express k as the square of the half of the coefficients of x and y.

So, we have:

[tex]x^2 + 8x + (4)^2 - (4)^2 + y^2 - 12y + (6)^2 - (6)^2= -29[/tex]

Evaluate the exponents

[tex]x^2 + 8x + 16 - 16 + y^2 - 12y + 36 - 36 = -29[/tex]

Collect like terms

[tex]x^2 + 8x + 16 + y^2 - 12y + 36 = -29 + 16 + 36[/tex]

Express as perfect squares

[tex](x + 4)^2 + (y - 6)^2 = -29 + 16 + 36[/tex]

[tex](x + 4)^2 + (y - 6)^2 = 23[/tex]

The standard equation of a circle is:

[tex](x - a)^2 + (y - b)^2 + r^2[/tex]

Where:

Center = (a,b)

Radius = r

So, we have:

Center = (-4,6)

Radius = [tex]\sqrt{23[/tex]

Hence, the center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]

Answers

Answer: Unlikely

She is unlikely to win the raffle because she didn’t buy any tickets.

Find the equation of a line that passes through the point (4,2) and has a gradient of -2. Leave your answer in the form y=mx+c

Answers

Answer:

y = - 2x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c

to find c substitute (4, 2 ) into the equation

2 = - 8 + c ⇒ c = 2 + 8 = 10

y = - 2x + 10 ← equation of line

Answer:

y = - 2x + 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c

To find c we must substitute (4, 2 ) into the equation

2 = - 8 + c, c = 2 + 8 = 10

y = - 2x + 10

HELP PLEASE ASAP. I really need help so it would be amazing if you could help me.

Answers

Answer:

ans at lower left

Step-by-step explanation:

scale up every element in the matrix in the question by 2 will get you the ans.

Which segments are congruent? eh and ef gh and fe fg and eh ef and gf

Answers

If the two sides of the triangle are equal then these two triangles are similar. The sides EF and GF are congruent to each other. Then the correct option is D.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In ΔEDF and ΔGDF

DF = DF = radius (common side)

ED = GD = radius

If the two sides of the triangle are equal then these two triangles are similar.

Thus, EF and GF are congruent to each other.

More about the triangle link is given below.

https://brainly.com/question/25813512

Answer:

the answer is D

Step-by-step explanation:

EF and GF

Help please! This is an assignment!

Answers

Answer: Answer: l = s/n – r2

Solve the following system of equations graphically on the set of axes below.
y = 2x – 1
x + 3y = 18

Answers

Answer:

(x, y) = (3, 5)

Step-by-step explanation:

To solve these equations graphically, you plot each one, then identify the coordinates of the point of intersection.

The first equation can be graphed using the y-intercept of -1 and the slope of 2.

The second equation has a y-intercept of 18/3 = 6, and a slope of -1/3. The x-intercept of 18 is off the chart, so the slope and intercept are a good way to plot this line, too.

The slope is the "rise" divided by the "run". A slope of 2 means the line goes up 2 units for each unit to the right. A slope of -1/3 means the line goes down 1 unit for each 3 units to the right.

The solution is (x, y) = (3, 5).

9 athletes from a high school weightlifting team were randomly selected to begin a new resistance weight program. After 8 weeks, the difference in how much weight they could lift (after - before) was recorded below in kg 4, 13.5, 15, 6, 12, 14, 19.5, 7.5, 13, Assume the population distribution is approximately normal. Find a 95% confidence interval for the mean strength gain of all students from this school if they joined the program.

Answers

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the mean strength gain of all students from this school if they joined the program is (7.85, 15.37).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 9 - 1 = 8 df, is t = 2.306.

The other parameters are given as follows, with the help of a calculator.

[tex]\overline{x} = 11.61, s = 4.89, n = 9[/tex]

Hence:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 11.61 - 2.306\frac{4.89}{\sqrt{9}} = 7.85[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 11.61 + 2.306\frac{4.89}{\sqrt{9}} = 15.37[/tex]

The 95% confidence interval for the mean strength gain of all students from this school if they joined the program is (7.85, 15.37).

More can be learned about the t-distribution at https://brainly.com/question/16162795

Which graph represents the solution set of the compound inequality?
−5
please help!!!

Answers

Answer:

the first

Step-by-step explanation:

it just is. Be smarter.

A coat and a pair of boots are on sale for 20% off. The regular price of the coat is $225. The regular price of the boots is $130. Part A find the sale price of the coat —————-Part B what is the sale price of the boots?

Answers

Answer:

Part A = $180

Part B = $104

Step-by-step explanation:

Part A:

You do 255÷5=51

51 x 4 = 180

Part B:

You do 130÷5=26

26 x 4 = 104

Answer:

$180 for the coat, $104 for the boots

Step-by-step explanation:

first: percent = decimal (20 = 0.20)

for the coat:

225-(225x0.20)

225-40 = 180

for the boots:

130- (130x0.20)

130-26 = 104

You move up 5 units. You end at (3, 9). Where did you start?

Answers

Answer:

You started at (3, 4)

4 + 5 = 9, the only option to get there in this case.factorized, 3 x 3(x) and replace for y.

Eduardo is making a friendship bracelet with 6 different colors of thread. He uses 22 inches of each color. How many feet of thread does he use in all?

Answers

11 ft in all I believe

Write a function rule for the table.

Answers

Answer:

C. p = h + 16

Step-by-step explanation:

Write −x^2+2xy−y^2 as the opposite of the square of a binomial.
PLEASE HELP ME PLEASE I WILL GIVE BRAINLYEST

Answers

Answer:

[tex]-(x-y)^2[/tex]

Step-by-step explanation:

Original expression:

[tex]-x^2+2xy-y^2[/tex]

Factor out -1:

[tex]\implies -(x^2-2xy+y^2)[/tex]

Factor [tex]x^2-2xy+y^2[/tex]:

[tex]\implies -(x-y)(x-y)[/tex]

Apply exponent rule [tex]aa=a^2[/tex]:

[tex]\implies -(x-y)^2[/tex]

A point at (54, -27) is rotated 720° clockwise about the
origin. What are the new coordinates for the point?
a. (54,-27)
b. (-27, -54)
c. (-54, 27)
d. (27,54)

Answers

La respuesta para esa es B

In a football club there are 2 balls for every 12 players. How many footballs will

be needed for 48 players?

Answers

Answer:

Step-by-step explanation:

Given:

In a football club there are 2 balls for every 12 players.

To Find:

How many footballs will be needed for 48 players?

Solve:

Since there are 2 balls for every 12 players..

Let's b = balls and P = Players

2b = 12p

4b = 24p

6b = 36p

8b = 48

Hence, we can conclude that there will be 8 footballs needed for 48 players

~Learn with Lenvy~

Answer:

8 balls

Step-by-step explanation:

We can use ratios to solve.

2 balls x balls

------------- = -----------------

12 players 48 players

Using cross products

2 * 48 = 12 *x

96 = 12x

Divide each side by 12

96/12 =12x/12

8=x

They needs 8 balls

Need it sooner than later
A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males.

Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)

Answers

Using the z-distribution, as we are working with a proportion, it is found that:

A. The 98% confidence interval is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.

B. Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.

What is the mean and the standard error for the distribution of differences?

For each sample, they are given by:

[tex]p_F = \frac{53}{150} = 0.3533, s_F = \sqrt{\frac{0.3533(0.6467)}{150}} = 0.039[/tex]

[tex]p_M = \frac{89}{275} = 0.3236, s_M = \sqrt{\frac{0.3236(0.6764)}{275}} = 0.0282[/tex]

Hence, for the distribution of differences:

[tex]p = p_F - p_M = 0.3533 - 0.3236 = 0.0297[/tex]

[tex]s = \sqrt{s_F^2 + s_M^2} = \sqrt{0.039^2 + 0.0282^2} = 0.048[/tex]

What is the confidence interval:

It is given by:

[tex]p \pm zs[/tex]

98% confidence interval, hence, using a z-distribution calculator, the critical value is of z = 2.327.

Then:

[tex]p - zs = 0.0297 - 2.327(0.048) = -0.082[/tex]

[tex]p + zs = 0.0297 + 2.327(0.048) = 0.141[/tex]

The 98% confidence interval is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.

Item b:

Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.

To learn more about the z-distribution, you can check https://brainly.com/question/25890103

Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
2, 5, 8, ...

Answers

3, 12, 48 ... =
3(4)^0, 3(4)^1, 3(4)^2 ... =
3(1), 3(4), 3(16) ....
3, 12, 48 ...

The function y = 58. 7(1. 03)^t gives a country’s population, y (in millions), where t is the number of years since January 1994. According to this function, what was the approximate population of the country in January 2002

Answers

Answer:

Approximate population ≈ 74.36 million.

Step-by-step explanation:

The given problem involves modeling of an exponential growth or decay function of a population.

Definition:Exponential growth ( relative growth ) occurs when a population grows or increases exponentially by the same factor, over the same amount of time. Exponential decay occurs when a population decreases continuously by a constant factor, over the same amount of time.

We can model the exponential growth of a population using the following Exponential Growth Model:

⇒ [tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex]

Where:

P( t ) = population after "t" years P₀ = initial population r = relative growth rate; positive "r" value means that the population is increasing; negative "r" value implies that the population is decreasing. t = time (typically in years)

Solution:

Based from the given equation, [tex]\displaystyle\mathsf{y\:=\:58.7(1.03)^t }[/tex] , we can infer that:

⇒ [tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex] or [tex]\displaystyle\mathsf{y\:=\:P_0 (1\:+\:r)^t }[/tex]

Where:

P( t ) or y = population after "t" yearsP₀ = initial population = 58.7r = relative growth rate = 0.03 or 3% = the population is increasing (exponential growth).t = time (typically in years) = 8 years (difference between January 2002 and January 1994).

Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :

[tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex]

⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1\:+\:.03)^8 }[/tex]

Step 2: Follow the order of operations, addition inside the parenthesis:

⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.03)^8 }[/tex]

Step 3: Follow the order of operations, applying the exponent into the parenthesis (do not round off the digits inside the parenthesis):

⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.266770081) }[/tex]

Step 4: Follow the order of operations, multiplying 58.7 (P₀) into the parenthesis:

⇒ [tex]\displaystyle\mathsf{P(8)\:\approx \:74.35940378\quad or \quad 74.36\:\:million}[/tex]

Final Answer:

Therefore, the approximate population of the country in January 2002 is 74.36 million.

________________________Keywords:

Exponential functions

Exponential growth

Exponential decay

Exponential growth model

____________________________

Learn more about exponential functions here:

https://brainly.com/question/25802424

Express as a sum :
15-7

PLS HELP WILL MARK BRAINLIST

Answers

8 is correct answer according to my brain smarts

On a map scale, I inch = 53 miles. Two attractions are eight inches apart on the map. How far are they apart in miles?

Answers

Answer:

424 miles

Step-by-step explanation:

53 x 8 = 424 miles

Find the size angle XYZ
Give your answer to 1 decimal place

Answers

Answer:

∠ XYZ ≈ 72.9°

Step-by-step explanation:

using the tangent ratio in the right triangle

tan XYZ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{XY}[/tex] = [tex]\frac{13}{4}[/tex] , then

∠ XYZ = [tex]tan^{-1}[/tex] ( [tex]\frac{13}{4}[/tex] ) ≈ 72.9° ( to 1 dec. place )

Jameelah got 4 kilograms of candy. Since she didn’t want to eat it all, she decided to share it with her 4 friends. If the 5 of them share the 4 kilograms, how much will each of them have?
help me

Answers

Answer:

Each of them will have 0.8 kg of the candy.

Step-by-step explanation:

Don't have one sorry!

The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentage

If their wage went from $6.80 to $10.19 in 7 years what is the doubling time?

(nearest year)

Answers

The doubling time of the hourly wage of the workers is an illustration of an exponential function that has a rate of 2

The doubling time of the wage is 4 years

How to determine the doubling time

A doubling function is represented as:

[tex]p = w \times 2^{\frac{x}{t}}[/tex]

Where:

p represents the final amount i.e. p = 10.19w represents the initial amount i.e. w = 6.80t represents the duration i.e. t = 7x represents the doubling time

So, we have:

[tex]10.19 = 6.80 \times 2^{\frac{x}{7}}[/tex]

Divide both sides by 6.80

[tex]1.50 = 2^{\frac{x}{7}}[/tex]

Take the logarithm of both sides

[tex]\log(1.50) = \log(2^{\frac{x}{7}})[/tex]

Apply the law of logarithm

[tex]\log(1.50) = \frac{x}{7}}\log(2)[/tex]

Multiply both sides by 7

[tex]7 \times \log(1.50) = x\log(2)[/tex]

Divide both sides by log(2)

[tex]x = 7 \times \log(1.50) \div \log(2)[/tex]

[tex]x = 4.09[/tex]

Approximate

[tex]x \approx 4[/tex]

Hence, the doubling time is 4 years

Answers

The sum of all the probabilities must be one. Then the probability that the gymnast scores a 9 or 9.95 is 0.14.

What is a probability distribution?

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

Researching on the internet, the probability of the gymnast getting each score is given by:

P(X = 5) = 0.02P(X = 5.5) = 0.02P(X = 6) = 0.06P(X = 6.5) = 0.1P(X = 7) = 0.16P(X = 7.5) = 0.14P(X = 8) = 0.18P(X = 8.5) = 0.18P(X = 9) = xP(X = 9.5) = 0.02

Considering that it is a distribution, the sum of all the probabilities must be one.

0.02 + 0.02 + 0.06 + 0.1 + 0.16 + 0.14 + 0.18 + 0.18 + x + 0.02 = 1

0.88 + x = 1

x = 0.12

The probability that the gymnast scores a 9 or 9.95 will be

P(9 or 9.5) = (X = 9) + P(X = 9.5) = 0.12 + 0.02 = 0.14

More about the probability distribution link is given below.

https://brainly.com/question/795909

Answer: D

Step-by-step explanation:

trust me bro I got it right

A 5 cm object is 18. 0 cm from a convex lens, which has a focal length of 10. 0 cm. What is the distance of the image from the lens? Round your answer to three significant figures. Cm What is the height of the image? Round your answer to three significant figures. Cm.

Answers

The distance of the image from the lens V=22.5cm and the height of the image h=6.25cm.

What will be the distance and the height of the image placed in front of the convex lens?

It is given that

Hieght of an object H = 5cm

Distance of an object =18cm

Focal lenght of lens = 10cm

As we know that the lens formula is given by

[tex]\dfrac{1}{f} =\dfrac{1}{v} +\dfrac{1}{u}[/tex]

[tex]\dfrac{1}{v} =\dfrac{1}{10} -\dfrac{1}{18}=\dfrac{8}{180}[/tex]

so now

[tex]v= \dfrac{180}{8} =22.5\ cm[/tex]

Now to find the height of the image

[tex]\rm magnification =\dfrac{v}{u} =\dfrac{-Image\ Hieght }{object\ height}[/tex]

[tex]\rm magnification =\dfrac{22.5}{18} =\dfrac{-x}{5}[/tex]

[tex]x=-6.25\ cm[/tex]

Thus the distance of the image from the lens is V=22.5cm and the height of the image h=6.25cm.

To know more about convex lenses follow

https://brainly.com/question/6639542

(a) Complete the table.

There are 18 red counters in the bag.
(b) Work out the total number of counters in the bag.

Answers

Answer:

a) Red = 0.2 Blue= 0.4 and White =0.4

b) 90 counters in total

Step-by-step explanation:

a)Firstly we know that the probability of mutually exclusive events is equal to 1 and the question states that the probability of blue and white counter is the same so we subtract 1-0.2 = 0.8 and we divide that by 2 as a result 0.4 .

b) P= Favourable outcomes / total number of outcomes

P(red) = 0.2

total number of red counters = 18

0.2 = 18/t cross multiplying have 0.2t= 18

Dividing throughout by 0.2 having 90

Two hot-air balloons, one red and one blue, took off at the same time from different platforms. Each began ascending at a constant rate.
The following equation gives the height (in meters) of the red hot-air balloon as a function of time (in seconds).
h = \dfrac{1}{2} t + 4h=
2
1

t+4h, equals, start fraction, 1, divided by, 2, end fraction, t, plus, 4
The height (in meters) of the blue hot-air balloon as a function of time (in seconds) is given by the following table of values:
\text{Time}Timestart text, T, i, m, e, end text (seconds) \text{Height}Heightstart text, H, e, i, g, h, t, end text (meters)
444 555
666 666
888 777
Which balloon started at a greater height?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
The red one

(Choice B)
B
The blue one

(Choice C)
C
They both started at the same height
Which balloon ascended faster?

Answers

The answer is A the red one

The distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30°. the light forms a second-order bright band. how large is the path difference? 1047 nm 1571 nm 3142 nm 6284 nm

Answers

The path difference if the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30° is 1.57 × 10⁻⁶ m.

What is constructive interference?

When the maxima of two waves add up (the two waves are in phase), the amplitude of the resultant wave equals the total of the separate amplitudes, this is known as constructive interference.

We know that for constructive interference, therefore, the formation of bright fringe through a diffraction grating is given by:

d sin θ = n λ

where d is the distance between slits, θ is the angle of diffraction, n is the order of fringe, and λ is the path difference.

As it is given that the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30°, therefore, the path difference can be written as,

[tex]\begin{aligned}\lambda &= \dfrac{(d sin \theta)}{ n} \\\\&=\dfrac{0.60 \times 10^{-3 }m) \times sin (0.30)}{2}\\\\ &= 1.57 \times 10^{-6}\rm\ m\end{aligned}[/tex]

Hence, the path difference is 1.57 × 10⁻⁶ m.

Learn more about Constructive interference:

https://brainly.com/question/16098226

5/4 × (3 × 1/4 I NEED HELP

Answers

Answer: 15/16

Step-by-step explanation:

5/4 * (3 * 1/4) =

Mutiply 3 * 1/4

5/4 * 3/4 =

Mutiply 5/4 * 3/4

5/4 * 3/4 = 15/16

Answer:

[tex]\frac{15}{16}[/tex]

Step-by-step explanation:

[tex]\frac{5}{4}\cdot \:3\cdot \frac{1}{4}[/tex]

[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:3=\frac{3}{1}[/tex]

[tex]=\frac{5}{4}\cdot \frac{3}{1}\cdot \frac{1}{4}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]

[tex]=\frac{5\cdot \:3\cdot \:1}{4\cdot \:1\cdot \:4}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:5\cdot \:3\cdot \:1=15[/tex]

[tex]=\frac{15}{4\cdot \:1\cdot \:4}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:1\cdot \:4=16[/tex]

[tex]\frac{15}{16}[/tex]

Hence, 15/16 is the correct Answer.

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