Solve the system y = 2x – 4 and y = (x – 1)² – 5

Answer: V= 65.4 units³

Step-by-step explanation:

The formula for volume for a sphere is [tex]V=\frac{4}{3} \pi r^3[/tex].

Since we are given our diameter, we can find our radius.

2r=d

2r=5

r=2.5

Now that we have the radius, we can plug it into the formula to find volume.

[tex]V=\frac{4}{3} \pi (2.5)^3[/tex]

[tex]V=65.4[/tex]

Answer:

A

Step-by-step explanation:

[tex]3(x-1)+2= \\\\3((5)-1)+2= \\\\3(4)+2= \\\\ 12+2=\\\\14[/tex]

Hope this helps!

Answer:

[tex]14[/tex]

Step-by-step explanation:

[tex]3(x - 1) + 2[/tex]

[tex]x= 5[/tex]

[tex]3(5 - 1) + 2[/tex]

[tex]3(4) + 2[/tex]

[tex]12 + 2[/tex]

[tex]=14[/tex]

Answer:

[tex]\fbox{\begin{minipage}{4em}Yes, it is\end{minipage}}[/tex]

Step-by-step explanation:

3x - 6y = 24

Divide both sides by 6:

(3/6)x - (6/6)y = 24/6

Simplify:

(1/2)x - y = 4

Move y to the right side, 4 to the left side, and change sign of y and 4:

(1/2)x - 4 = y

Rearrange both sides:

y= (1/2)x - 4

Hope this helps!

:)

The formula to use is

A = P(1+r)^t

where,

A = final amount after t years

P = initial amount = 4100

r = rate of increase or decay = -3.75% = -3.75/100 = -0.0375

t = number of years = 11

The value of r is negative to indicate exponential decay. Also notice that I divided by 100 to convert from -3.75% to -0.0375

Using those values, we plug them into the formula to get,

A = P(1+r)^t

A = 4100(1+(-0.0375))^11

A = 4100(1-0.0375)^11

A = 4100(0.9625)^11

A = 4100*0.65676215615721

A = 2692.72484024457

A = 2693

Rounding to the nearest whole number, the answer is approximately 2693 km^2.

Answer:

y>0

Step-by-step explanation:

Since your X is a real number, meaning a positive number, you can try and substitute multiple positive values in your equation. You would notice that you will only receive positive values of Y. Speaking of =ve/-ve values, you can't square root a negative value anyways, this further proves that your Y can't be a negative number.

Answer:

It isn't plausible enough to at least say that the distribution is approximately normal because the percentiles given, when plotted on a number line aren't in any way symmetric about the mean as is required for a normal distribution.

Step-by-step explanation:

To investigate whether these values given for the distribution are plausible enough to at least say that the distribution is approximately normal, we will plot the given percentiles on a number line and indicate the median and mean too on that number line.

The spread of the other percentiles about the mean especially and to an extent, the median will show if the distribution is symmetric/ almost symmetric about the mean and the median.

The plot of these percentiles and the mean is presented in the attached image to this answer. The percentiles are indicated with deep dots and the mean is shown with a light square.

The plot shows that the distribution isn't symmetric about the mean and the median. The distribution appears to be skewed to the right.

Hence, it isn't plausible enough to at least say that the distribution is approximately normal because the percentiles given, when plotted on a number line aren't in any way symmetric about the mean as is required for a normal distribution.

Hope this Helps!!!

It isn't plausible that the waist size distribution is at least approximately normal.

The distribution of the mean is determined by taking random samples from data and calculating the mean individually.

The given data

5th 10th 25th 50th 75th 90th 95th

69.6 70.9 75.2 81.3 95.4 107.1 116.4

To determine whether these values given for the distribution are plausible enough for the distribution to be approximately normal, we will plot the given percentiles on a number line and indicate the median and mean.

The plot of these percentiles and the mean shows percentiles that are indicated with deep dots and the mean is shown with a light square.

The plot shows that the distribution isn't symmetric between the mean and the median. The distribution appears to be skewed to the right.

Hence, It isn't plausible that the waist size distribution is at least approximately normal.

Learn more about mean;

https://brainly.com/question/794921

Answer:

y-10=5(x-15)

Step-by-step explanation:

Slope =5

15-10/16-15=5

Then plug in 10 as the y1 and 15 as y2.

Answer:

In a relation h(x) = y, the values of x are the domain and the values of y are the range.

Here the domain is:

D = {-6, -1, 7}

The range is:

R = {-9, 0 , 9}

Now, a relation f(x) = y is a function only if for every x in the domain we have only and only one value in the range.

Here we can see that for the value -1 in the domain we have two different values in the range:

(-1, 0) and (-1, 9)

So this can not be a function.

(If you want to take the variable as y, you also have that the value y = 0 leads to two different values in x, so this cant be a function either)

Answer:

The answer is C.

Step-by-step explanation:

In the graph above, it is a positive gradient so option A and B cannot be applied.

Next you have to look at the y-intercept where the line touches the y-axis so -1 is the y-intercept.

The slope-form equation is y = mx + b where m represents gradient amd b is y-intercept :

Option A,

[tex] - 2x - y - 1 = 0[/tex]

[tex]y = - 2x - 1 \: (incorrect \: m)[/tex]

Option B,

[tex]2x + y - 1 = 0[/tex]

[tex]y = - 2x + 1 \: (incorrect \: m \: and \: b)[/tex]

Option C,

[tex]2x - y - 1 = 0[/tex]

[tex]y = 2x - 1 \: (correct \: m \: and \: b)[/tex]

Complete Question:

Ellen is opening. Cookie shop eat a local middle school . She randomly surveys students to determine The types of cookies they would buy at the cookie shop the results of the surveys are below based on the survey. Which statement is not true?

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

B) 22½% of the students surveyed would buy a sugar cookie.

C) If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

(Table showing the results of her survey is in the attachment below)

Answer:

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

Step-by-step Explanation:

STEP 1:

In order to ascertain which of the statements given in the options that is NOT TRUE, let's express the given number of students that would buy the different types of cookies in their PROPORTIONS AND PERCENTAGES in the survey result.

Thus:

Type of Cookie==> no of students => Proportion (no of students of a cookie type ÷ total no of students) => % (each proportion for a cookie type)

Chocolate Chip==> 25 => 0.3125 (25÷80) => 31.25% (0.3125 × 100)

Oatmeal Raisin==> 15 => 0.1875 (15÷850) => 18.75% (0.1875 × 100)

Peanut Butter== 22 => 0.275 (22÷80) => 27.5% (0.275 × 100)

Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100)

STEP 2:

Next step is to consider each statement given in the question to see if they are true or not.

==>OPTION A: If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

To find out if this is true, multiply the proportion of students who would be buy a sugar cookie (0.255) by 160 = 0.255 × 160 = 36.

If 160 buy a cookie, approximately 36 students would buy a sugar.

Option A IS NOT TRUE.

OPTION B: 22½% of the students surveyed would buy a sugar cookie.

From our calculation in STEP 2, we have:

Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100).

Option B is TRUE. 22.5% of the students would go for sugar cookie.

OPTION C: If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

Number of students that would buy the peanut butter if 240 students were to get a cookie = proportion of students that opt for peanut butter cookie in the survey (0.275) × 240 = 0.275 × 240 = 66.

Option C is TRUE.

OPTION D: D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

Proportion of students who prefer chocolate chips or oatmeal raisin cookies = 0.3125 + 0.1785 = 0.491

This is approximately 0.5 = ½ of the total number of students.

Option D is TRUE.

Therefore, we can conclude that the statement, "A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie" is NOT TRUE.

Answer:

the volume of the box is increasing

dV = +310,000 ft^3/s

Step-by-step explanation:

Volume of a rectangular box with side a,b and c can be expressed as;

V = abc

The change in volume dV can be expressed as;

dV = d(abc)/da + d(abc)/db + d(abc)/dc

dV = bc.da + ac.db + ab.dc ......1

Given:

a= 150 feet,

b= 80 feet, and

c= 50 feet

ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec

da = +100 feet/s

db = -20 feet/s

dc = +5 feet/s

Substituting the values into the equation 1;

dV = (80×50×+100) + (150×50×-20) + (150×80×+5)

dV = +400000 - 150000 + 60000 ft^3/s

dV = +310,000 ft^3/s

Since dV is positive, the volume of the box is increasing at that instant.

Answer:

432 cubic meters

Step-by-step explanation:

The volume formula is V = [tex]\frac{1}{2}[/tex]blh

V = [tex]\frac{1}{2}[/tex](9)(16)(6)

V= 432 cubic meters

Answer:

Its D

Step-by-step explanation:

becasue the X is not repeating. the other are.

To the nearest whole number it would be 35

Step-by-step explanation:

Answer:

A) sample mean = $1.36 million

B) standard deviation = $0.9189 million

C) variance confidence interval = ($0.40 million, $2.81 million)

D) standard deviation confidence interval = ($1.93 million , $0.79 million)

*since the sample size is very small, the confidence interval is not valid.

Step-by-step explanation:

samples:

sample mean = $1.36 million

the standard deviation:

variance 0.8444

standard deviation = √0.8444 = 0.9189

in order to calculate the confidence interval for the population variance we are going to use a chi-square distribution with 2.5% on each tail ⇒ table values 2.7004 and 19.023 enclose 95% of the distribution.

[(n - 1) x variance] / 2.7004 = (9 x 0.8444) / 2.7004 = 2.81

[(n - 1) x variance] / 19.023 = (9 x 0.8444) / 19.023 = 0.40

95% confidence interval = mean +/- 1.96 standard deviations/√n:

$1.36 million + [(1.96 x $0.9189 million)/√10] = $1.36 million + $0.57 million = $1.93 million

$1.36 million - $0.57 million = $0.79 million

Answer:

b

Step-by-step explanation:

Answer: B. Eighty-two percent is a statistic and 63% is a parameter

Step-by-step explanation:

Parameters are the values which are used to describe a given property for the entire population. On the other hand, statistics are the values which can be used to describe a given property for the sample.

In this scenario the 82% of users is pertaining to the 900 users sample and, therefore is a statistic while the 63% of users is pertaining to the whole population of the users and, thus, it is the parameter.

Therefore, the answer is option B. Eighty-two percent is a statistic and 63% is a parameter.

Answer:

B) Eighty-two percent is a statistic and 63% is a parameter.

that is the correct answer on flvs

Step-by-step explanation:

Answer:

This can be done in 120 ways.

Step-by-step explanation:

Number of arrangments:

The number of arrangments of n elements is given by the following formula:

[tex]A_{n} = n![/tex]

In this question:

7 elements.

Two conditions: Counselor in the third sear, and the camper who has the tendency to engage in food fights in the fourth.

For the other 5 seats, the other 5 campers can be arranged in:

[tex]A_{5} = 5! = 120[/tex]

Ways.

This can be done in 120 ways.

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y-axis: X₁: Calories of a fast food menu.

X-axis: X₂: Fat of a fast food menu (grams)

The coefficient of correlation (r)

This coefficient shows ​​the degree of correlation between the variables and its range of values is between -1 and 1

If r = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is zero

If r < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.

If r > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)  

The closer to 1 or -1 the coefficient is, the stronger the association between variables. Using the absolute value of the correlation coefficients you can compare them, the greater the value, the stronger is the association between variables.

Looking at the scatter plot you can see that the number of calories grows with the fat content of the menu forming an approximately straight line, which means that there must be a strong positive correlation between these two variables. (using for example one of the options +0.90)

Meaning: To ↑x₁ corresponds ↑x₂ and to ↓x₁ corresponds ↓x₂

Now if the restaurant adds n=6 new menus with high calories (↑x₁) and low fat content (↓x₂) these new me nus won't follow a direct relationship, but an indirect one (negative correlation), so you'd expect the value of the correlation coefficient to drop (get closer to zero)

The coefficient won't get close to -1 since that would be a complete negative correlation (all foods having low fat and high calories), which could happen if the restaurant changed all menus.

Since they are only adding new ones, the new possible values for the coefficient of correlation could be A. +0.2 or D -0.1

I hope this helps!

Answer:

Evaluate f(7)

[tex] f(7) = 240(0.7)^7 = 19.765[/tex]

Determine x when f(×)=120

[tex] 120 = 240 (0.7)^x[/tex]

We can derive both sides by 240 and we got:

[tex] 0.5 = 0.7^x[/tex]

Now we can apply natural log on both sides and we got:

[tex] ln(0.5)= x ln(0.7)[/tex]

And if we solve for the value of x we got:

[tex] x =\frac{ln(0.5)}{ln(0.7)}= 1.943[/tex]

And then the value of x = 1.943

Step-by-step explanation:

We have the following function given:

[tex]f(x) = 240(0.7)^x [/tex]

Evaluate f(7)

And we want to find [tex] f(7) [/tex] so we just need to replace x=7 and we got:

[tex] f(7) = 240(0.7)^7 = 19.765[/tex]

Determine x when f(×)=120

And for the second part we want to find a value of x who satisfy that the function would be equal to 120 and we can set up this:

[tex] 120 = 240 (0.7)^x[/tex]

We can derive both sides by 240 and we got:

[tex] 0.5 = 0.7^x[/tex]

Now we can apply natural log on both sides and we got:

[tex] ln(0.5)= x ln(0.7)[/tex]

And if we solve for the value of x we got:

[tex] x =\frac{ln(0.5)}{ln(0.7)}= 1.943[/tex]

And then the value of x = 1.943

Answer:

Step-by-step explanation:

For focus-to-vertex distance "p", the equation of a parabola with vertex (h, k) can be written as ...

  y = 1/(4p)(x -h)^2 +k

Comparing this to your equation, we see that ...

  1/(4p) = 1

  h = -2

  k = -3

Solving for p, we find ...

  1/(4p) = 1

  1/4 = p . . . . . multiply by p

The parabola opens upward, so this means the focus is 1/4 unit above the vertex, and the directrix is 1/4 unit below the vertex.

Answer:

The focus is at (–2,–212) and the directrix is at y = –312.

Step-by-step explanation:

Find the focus and directrix of the parabola y=12(x+2)2−3.

got the answer right in the test.

Answer:

A. If you send me an e-mail message, then I will remember to send you the address.

B. If you were born in the United States, then you can be a citizen of the United States.

C. If you keep your textbook, then it will be a useful reference in your future courses.

D. If the Red Wings’s goalie plays well, then they will win the Stanley Cup.

E. If you get the job, then you had the best credentials.

F. If there is a storm, then beach erodes.

G. If you can log on to the server, then you must have a valid password.

H. If you begin your climb too late, then you will not reach the summit

Step-by-step explanation:

The statement which is written in the form, "if p, then q" symbolized by p-->q is known as a conditional statement. p is known as the hypothesis, while q is the conclusion. In such statements, the hypothesis and the conclusion may or may not have a correlation. But for the statement to be true, the conclusion must be true even if the hypothesis is wrong.

In statements A, the condition for sending the address is if I receive an email message.

In statement B, the condition for being a citizen is if one is born in the United States.

In statement C, the condition for my books to be a useful reference is if I keep them.

In statement D, the condition for winning the Stanley Cup by the Red Wings is if their Goalie plays well.

In statement E, the condition I get the job is if I had the best credentials.

In statement F, the condition for the beach eroding is if there's a storm.

In statement G, the only way I can log on to the server is if I have the correct password. In each of these statements, the conclusions correlates with the hypothesis. The conditions in the hypothesis need to be met for the conclusion to be true.

Statement H gives a conclusion which depends on not meeting the conditions of the hypothesis which is that if I don't start climbing the mountain early (if I start late), I will not reach the summit.

Answer:

[tex]V=122.5in^3[/tex]

Step-by-step explanation:

The volume of a right circular cone is given by:

[tex]V=\frac{\pi r^2h}{3}[/tex]

where r is the radius of the circle and h is the height of the cone, and [tex]\pi[/tex] is a constant [tex]\pi=3.1416[/tex].

According to the problem the height is:

[tex]h=8.1 in[/tex]

and we don't have the radius but we have the diameter, which is useful to find it. We just divide the diameter by 2 to find the radius:

[tex]r=\frac{d}{2}=\frac{7.6in}{3}=3.8in[/tex]

Now, we can find the volume by substituting all the known values:

[tex]V=\frac{\pi r^2h}{3}[/tex]

[tex]V=\frac{(3.1416)(3.8in)^2(8.1in)}{3} \\\\V=\frac{(3.1416)(14.44in^2)(8.1in)}{3} \\\\V=\frac{367.454in^3}{3} \\\\V=122.485[/tex]

Rounding the volume to the nearest tenth of cubic inch we get:

[tex]V=122.5in^3[/tex]

Answer:

At a price of $p, a quantity, q, of the item is sold.

If q = f(p)

(a) f(150) = 2000 means at price = 150$, the number of items sold is 2000

(b) f'(150) = -25 means rate of sale is negative or the number of items sold will be decreases in future

Corrected Question

Given a triangle with two sides 4.1 cm and 6.7cm and an Included angle of [tex]35^\circ[/tex]. Use the Law of Cosines to determine the length of the third side of the triangle.

Answer:

(D) 4.1cm

Step-by-step explanation:

Given a triangle with two sides 4.1 cm and 6.7 cm and an included angle of [tex]35^\circ[/tex].

Using Law of Cosines

[tex]a^2=b^2+c^2-2bc\cos A\\a^2=4.1^2+6.7^2-2*4.1*6.7\cos 35^\circ\\a^2=16.6958\\a=\sqrt{16.6958}\\a=4.09\\a \approx 4.1$ cm[/tex]

The correct option is D.

Answer:

true

Step-by-step explanation:

hope it helps .

all the best

Answer:

a. [tex]\mathbf{Y(s) = L \{y(t)\} = \dfrac{7}{s(s+1)}+ \dfrac{e^{-3s}}{s+1}}[/tex]

b. [tex]\mathbf{y(t) = \{7e^t + e^3 u (t-3)-7\}e^{-t}}[/tex]

Step-by-step explanation:

The initial value problem is given as:

[tex]y' +y = 7+\delta (t-3) \\ \\ y(0)=0[/tex]

Applying  laplace transformation on the expression [tex]y' +y = 7+\delta (t-3)[/tex]

to get  [tex]L[{y+y'} ]= L[{7 + \delta (t-3)}][/tex]

[tex]l\{y' \} + L \{y\} = L \{7\} + L \{ \delta (t-3\} \\ \\ sY(s) -y(0) +Y(s) = \dfrac{7}{s}+ e ^{-3s} \\ \\ (s+1) Y(s) -0 = \dfrac{7}{s}+ e^{-3s} \\ \\ \mathbf{Y(s) = L \{y(t)\} = \dfrac{7}{s(s+1)}+ \dfrac{e^{-3s}}{s+1}}[/tex]

Taking inverse of Laplace transformation

[tex]y(t) = 7 L^{-1} [ \dfrac{1}{(s+1)}] + L^{-1} [\dfrac{e^{-3s}}{s+1}] \\ \\ y(t) = 7L^{-1} [\dfrac{(s+1)-s}{s(s+1)}] +L^{-1} [\dfrac{e^{-3s}}{s+1}] \\ \\ y(t) = 7L^{-1} [\dfrac{1}{s}-\dfrac{1}{s+1}] + L^{-1}[\dfrac{e^{-3s}}{s+1}] \\ \\ y(t) = 7 [1-e^{-t} ] + L^{-1} [\dfrac{e^{-3s}}{s+1}][/tex]

[tex]L^{-1}[\dfrac{e^{-3s}}{s+1}][/tex]

[tex]L^{-1}[\dfrac{1}{s+1}] = e^{-t} = f(t) \ then \ by \ second \ shifting \ theorem;[/tex]

[tex]L^{-1}[\dfrac{e^{-3s}}{s+1}] = \left \{ {{f(t-3) \ \ \ t>3} \atop {0 \ \ \ \ \ \ \ \ \ t <3}} \ \ \ \right.[/tex]

[tex]L^{-1}[\dfrac{e^{-3s}}{s+1}] = \left \{ {{e^{(-t-3)} \ \ \ t>3} \atop {0 \ \ \ \ \ \ \ \ \ t <3}} \ \ \ \right.[/tex]

[tex]= e^{-t-3} \left \{ {{1 \ \ \ \ \ t>3} \atop {0 \ \ \ \ \ t<3}} \right.[/tex]

= [tex]e^{-(t-3)} u (t-3)[/tex]

Recall that:

[tex]y(t) = 7 [1-e^{-t} ] + L^{-1} [\dfrac{e^{-3s}}{s+1}][/tex]

Then

[tex]y(t) = 7 -7e^{-t} +e^{-(t-3)} u (t-3)[/tex]

[tex]y(t) = 7 -7e^{-t} +e^{-t} e^{-3} u (t-3)[/tex]

[tex]\mathbf{y(t) = \{7e^t + e^3 u (t-3)-7\}e^{-t}}[/tex]

Answer:

The growth is linear.

It will be worth $124,500 in three years.

Step-by-step explanation:

The value of a house is increasing by $1500 per year.

Fixed increase, that is, each year the value increases the same. So the growth is linear.

Value after t years:

The equation has the following format:

[tex]V(t) = V(0) + a*t[/tex]

In which V(0) is the current value and a is the yearly increase.

The value of a house is increasing by $1500 per year. It is worth $120,000 today.

Then [tex]V(0) = 120000, a = 1500[/tex]

So

[tex]V(t) = V(0) + a*t[/tex]

[tex]V(t) = 120000 + 1500*t[/tex]

What will it be worth in three years?​

This is V(3).

[tex]V(t) = 120000 + 1500*t[/tex]

[tex]V(3) = 120000 + 1500*3[/tex]

[tex]V(3) = 124500[/tex]

It will be worth $124,500 in three years.

The growth is linear. The worth of the house after 3 years from now will be $124500.

Given information:

The value of a house is increasing by $1500 per year.

It is worth $120000 today.

The value of the house increases at a fixed rate of $1500 per year. So, it is a linear growth function.

Let the worth of the house after t years be V. The given situation can be written in equation form as,

[tex]V=V_0+rt\\V=120000+1500t[/tex]

Above equation represents the worth of house after t years.

So, the worth of the house after 3 years will be calculated as,

[tex]V=120000+1500t\\V(3)=120000+1500\times 3\\V(3)=120000+4500\\V(3)=124500[/tex]

Therefore, the worth of the house after 3 years from now will be $124500.

For more details, refer to the link:

https://brainly.com/question/24972665