an artist designed a badge for a school club. Figure ABCD on the coordinate grid below shows the shape of the badge:​

Answer:

a=b

Step-by-step explanation:

When the denominator is zero, the expression is undefined

a-b=0

a=b

Answer:

True.

95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

Step-by-step explanation:

True.

The confidence level represents the proportion of possible confidence intervals that contain the true mean. In this case, 95% of all confidence intervals of sample size n=10 constructed similarly to this one will contain the population mean.

Answer:

49/99

Step-by-step explanation:

I'm assuming you want to find the fraction that gives the decimal 0.494949...

If that is the case, the 49/99 is your answer.

Answer:

4

Step-by-step explanation:

Answer:

C. 1/3(3x)

Step-by-step explanation:

In order to verify if functions are inverses, you need to plug one into the other. In this case, it would be g of f(x) or g(f(x)). You will be able to see that g(f(x)) = 1/3(3x)

Answer:

[tex]x\approx 50^\circ[/tex]

Step-by-step explanation:

[tex]c^2 = a^2 + b^2 - 2ab(cos(C))[/tex]

See the figure below to get the values as:

[tex]7^2=7^2+9^2-2\left(7\right)\left(9\right)cos\left(x\right)\\\\cos(x)=\frac{7^2+9^2-7^2}{2\cdot \:7\cdot \:9}\\\\x\approx 50^\circ[/tex]

There are multiple concepts to solve this problem. This is one of the concept used in high school. Other concept to solve this problem is to use the concept of isosceles triangle. An isosceles triangle is a triangle with (at least) two equal sides. The angles shared by the two equal sides are also equal. So that the sum of all the three angles will add up to 180.

[tex]x+x+80=180\\\\2x=100\\\\x=50^{\circ}[/tex]

Best Regards!

Answer:

f(-11/5) = -5

Step-by-step explanation:

f(n) = 5n + 6

Let x = -11/5

f(-11/5) = 5*-11/5 +6

          = -11 +6

           = -5

Answer:

24.5

Step-by-step explanation:

24 = 24

1/2 -->

convert to a decimal => 1 divided by 2

0.5

24+0.5 = 24.5

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

47.25 pounds

Step-by-step explanation:

[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]

First, we determine the Rate In

Rate In=(concentration of salt in inflow)(input rate of brine)

[tex]=(0.5\frac{lbs}{gal})( 6\frac{gal}{min})\\R_{in}=3\frac{lbs}{min}[/tex]

Change In Volume of the tank, [tex]\frac{dV}{dt}=6\frac{gal}{min}-4\frac{gal}{min}=2\frac{gal}{min}[/tex]

Therefore, after t minutes, the volume of fluid in the tank will be: 100+2t

Rate Out

Rate Out=(concentration of salt in outflow)(output rate of brine)

[tex]R_{out}=(\frac{A(t)}{100+2t})( 4\frac{gal}{min})\\\\R_{out}=\frac{4A(t)}{100+2t}[/tex]

Therefore:

[tex]\dfrac{dA}{dt}=3-\dfrac{4A(t)}{100+2t}\\\\\dfrac{dA}{dt}=3-\dfrac{4A(t)}{2(50+t)}\\\\\dfrac{dA}{dt}=3-\dfrac{2A(t)}{50+t}\\\\\dfrac{dA}{dt}+\dfrac{2A(t)}{50+t}=3[/tex]

This is a linear differential equation in standard form, therefore the integrating factor:

[tex]e^{\int \frac{2}{50+t}dt}=e^{2\ln|50+t|}=e^{\ln(50+t)^2}=(50+t)^2[/tex]

Multiplying the DE by the integrating factor, we have:

[tex](50+t)^2\dfrac{dA}{dt}+(50+t)^2\dfrac{2A(t)}{50+t}=3(50+t)^2\\\{(50+t)^2A(t)\}'=3(50+t)^2\\$Taking the integral of both sides\\\int \{(50+t)^2A(t)\}'= \int 3(50+t)^2\\(50+t)^2A(t)=(50+t)^3+C $ (C a constant of integration)\\Therefore:\\A(t)=(50+t)+C(50+t)^{-2}[/tex]

Initially, 20 pounds of salt was dissolved in the tank, therefore: A(0)=20

[tex]20=(50+0)+C(50+0)^{-2}\\20-50=C(50)^{-2}\\C=-\dfrac{30}{(50)^{-2}} =-30X50^2=-75000[/tex]

Therefore, the amount of salt in the tank at any time t is:

[tex]A(t)=(50+t)-75000(50+t)^{-2}[/tex]

After 15 minutes, the amount of salt in the tank is:

[tex]A(15)=(50+15)-75000(50+15)^{-2}\\=47.25$ pounds[/tex]

Following are the solution to the given question:

Using formula:

[tex]\to \frac{dA}{dt} =R_{in}-R_{out}\\\\[/tex]

Find:

[tex]\to R_{in}\ and \ R_{out}\ =? \\\\[/tex]

Solution:

[tex]\to R_{ in} = \text{(concentration of salt in inflow)}[/tex][tex]\times \text{(i\1nput rate of brine)}\\[/tex]

[tex]\therefore\\ R_{in} = (\frac{1}{2}\frac{lb}{gal})\cdot (3\frac{gal}{min}) = 3\frac{lb}{min}\\[/tex]

Since in this question the solution is pumped out at a slower rate, therefore the water amount in the tank accumulates at the rate of[tex](6- 4) = 2 \ \frac{gal}{min} Thus,[/tex]

after t minutes there will be [tex]100+ 2t[/tex]gallons in the tank.

[tex]\because R_{out}=\text{(concentration of salt in outflow)}\cdot \text{(o\1utput rate of brine)}[/tex]

[tex]\therefore R_{out} =\frac{A(t)}{100+2t} \frac{lb}{gal} \cdot (4\frac{gal}{min})= \frac{4A(t)}{100+2t}\ \frac{lb}{min}[/tex]

Now, we substitute these results in the DE to get

[tex]\to \frac{dA}{dt}=3-\frac{4A(t)}{100+2t}\\\\\to \frac{dA}{dt}= 3 -\frac{2A(t)}{50+t} \\\\\to \frac{dA}{dt}+\frac{2}{50+t}\ A(t) -3\\\\[/tex]

Which is a linear DE in the standard form Thus, the integrating factor is

[tex]e ^{\frac{2}{ 50+t} \ dt} + e^{2\ln|(50+t)|} =e^{\ln(50 + t)^2}=(50+t)^2[/tex]

Multiplying the DE by integrated factor:

[tex](50+t)^2 \frac{dA}{dt} +2(50 + t) A(t) = 3(50 +t)^2\\\\ \therefore \frac{d}{dt}(50+t)^2 \frac{dA}{dt}-3(50+t)^2\\\\\therefore (50+t)^2\ A(t) -3(50+t)^2 \ dt \\\\\therefore (50+t)^2\ A(t) -\frac{3}{3}(50+t)^3 + c \\\\\therefore \ A(t) -(50+t) + c(50+t)^{-2} \\\\[/tex]

Now, applying the initial condition [tex]A(0) = 20[/tex]to get

[tex]\to 20 = (50) +\frac{c}{2500}\\\\\to 20 - 50=\frac{c}{2500}\\\\[/tex]

[tex]\therefore \\\\\to \frac{c}{2500} = -30\\\\ \to c= -30 \times 2500 \\\\\ \to c= -75000\\\\[/tex]

Now, substitute by this result in the solution to get

[tex]\to A(t) = (50 +t) - \frac{-75000}{(50 +t)^2}[/tex]

Now, after 15 minutes we find that

[tex]\to A(30) = 50 + 15-\frac{-75000}{(50+15)^2 } = 65+\frac{75000}{65^2} \\\\[/tex]

therefore

[tex]\to A(30)=65 +\frac{75000}{4225} \\\\[/tex]

            [tex]=65 +\frac{15000}{845} \\\\ =65+\frac{3000}{169}\\\\= 65+17.75 \\\\= 82.75 \ \frac{lb}{gal} \\\\[/tex]

Learn more:

brainly.com/question/23611819

Answer:

0.637

Step-by-step explanation:

The average value of a whole sinusoidal waveform over one complete cycle is zero as the two halves cancel each other out

Answer:

it determins the atmosphere out of space and how its gonna end up

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

The area of a square depends upon the length of its sides

For side a, The area of the square is a²

Therefore a(s) = s²

Therefore, a square of 3 feet has an area of 9 square feet

Option D

Answer:

8 nickels, 5 dimes and 7 quarters

Step-by-step explanation:

Each nickel is $0.05, each dime is $0.10 and each quarter is $0.25.

So, if we have n nickes, d dimes and q quarters, we can write the system of equations:

[tex]n + d + q = 20\ (eq1)[/tex]

[tex]0.05n + 0.1d + 0.25q = 2.65\ (eq2)[/tex]

[tex]7n + 5d + 20q = 221\ (eq3)[/tex]

If we multiply (eq2) by 140 and (eq1) by 7, we have:

[tex]7n + 14d + 35q = 371\ (eq4)[/tex]

[tex]7n + 7d + 7q = 140\ (eq5)[/tex]

Now, making (eq4) - (eq3) and (eq5) - (eq3), we have:

[tex]9d + 15q = 150\ (eq6)[/tex]

[tex]2d - 13q = -81\ (eq7)[/tex]

Multiplying (eq7) by 4.5, we have:

[tex]9d - 58.5q = -364.5\ (eq8)[/tex]

Subtracting (eq6) by (eq8), we have:

[tex]73.5q = 514.5[/tex]

[tex]q = 7[/tex]

Finding 'd' using (eq6), we have:

[tex]9d + 15*7 = 150[/tex]

[tex]9d = 150 - 105[/tex]

[tex]d = 5[/tex]

Finding 'n' using (eq1), we have:

[tex]n + 5 + 7 = 20[/tex]

[tex]n = 8[/tex]

So we have 8 nickels, 5 dimes and 7 quarters.

Answer:

C. [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

You can use the formula to find the slope: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

(-1.5, 1.5) & (1.5, 0)

[tex]\frac{0-(-1.5)}{1.5-(-1.5)} =\\\\\frac{0+1.5}{1.5+1.5} =\\\\\frac{1.5}{3} =\\\\\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex]

Answer:

10

Step-by-step explanation:

Let the first number be x, and the second number be y.

x + y = 5

x - y = 2

Solve for x in first equation.

x + y = 5

x = 5 - y

Put x as 5-y in the second equation, and solve for y.

(5-y) - y = 2

5 - 2y = 2

-2y = -3

y = 3/2

Put y as 3/2 in the first equation and solve for x.

x + y = 5

x + 3/2 = 5

x = 7/2

The difference of their squares would be:

(7/2)² - (3/2)²

49/4 - 9/4

40/4 = 10

Answer:

5 full sandwich

Step-by-step explanation:

Total roasted beef kelly has =  4 3/8 ounces

lets convert it into improper fraction for ease of calculation

Total roasted beef kelly has = ( 4*8+ 3)/8 ounces = 35/8 ounces.

weight of beef in 1 sandwich = 3/4 ounce

let the no. of sanwich be x

Total weight of beef in x sandwich = 3/4 *x ounce

given that total weight of roasted beef is 35/8 ounces. so

3/4 *x  = 35/8

=> 3x = 35*4/8 = 35/2

=> x = 35/2*3 = 35/6

=> x = 5  5/6

Thus, kelly can make 5 full sandwich and 5/6 part of full sandwich.

If answer should be for full sandwich , then kelly can make 5 sandwich.

Answer: $468

Step-by-step explanation:

SI = (prt) / 100

SI = ( 975 x 6 x 8) / 100

SI = 468

Answer:

(A)the frequencies found in the sample data.

Step-by-step explanation:

In a given experiment or trial, the frequency of the item under consideration is referred to as the observed frequency. The experiment is carried out on only a sample of the population.

Observed frequencies are the frequencies actually found in the data while expected frequencies are calculated from the observations given assuming the null hypothesis to be true.

Therefore, the term observed frequency refers to the frequencies found in the sample data.

Answer:

a. The margin of error is 2.29.

b. 19.23 to 23.81

Step-by-step explanation:

The sample size is n=64.

We start by calculating the sample mean and standard deviation with the following formulas:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}[/tex]

The sample mean is M=21.52.

The sample standard deviation is s=6.89.

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{6.89}{\sqrt{64}}=\dfrac{6.89}{8}=0.861[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=64-1=63[/tex]

The t-value for a 99% confidence interval and 63 degrees of freedom is t=2.656.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.656 \cdot 0.861=2.29[/tex]

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 21.52-2.29=19.23\\\\UL=M+t \cdot s_M = 21.52+2.29=23.81

The 99% confidence interval for the mean is (19.23, 23.81).

Answer:

(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b) The expected number of available places when the limousine departs is 0.338.

Step-by-step explanation:

Let the random variable Y represent the number of passenger reserving the trip shows up.

The probability of the random variable Y is, p = 0.70.

The success in this case an be defined as the number of passengers who show up for the trip.

The random variable Y follows a Binomial distribution with probability of success as 0.70.

(a)

It is provided that n = 6 reservations are made.

Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:

P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)

[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]

Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b)

The formula to compute the expected value is:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]

Compute the expected number of available places when the limousine departs as follows:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

         [tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]

Thus, the expected number of available places when the limousine departs is 0.338.

Answer:

(a) There are 20 ways to  select both a council president and a vice president.

(b) There are 60 ways to  select both a president, a vice president, and a secretary.

(c) There are 10 ways to select two members for the President’s Council.

Step-by-step explanation:

All the five engineering majors have one student representative at the Student Engineers Council at a California university.

(a)

Compute the number of ways to select both a council president and a vice president as follows:

As order of selection is important, the number of ways to select both a council president and a vice president is:

[tex]^{5}P_{2}=\frac{5!}{(5-2)!}=20[/tex]

Thus, there are 20 ways to  select both a council president and a vice president.

(b)

Compute the number of ways to select president, a vice president, and a secretary as follows:

Again as the order of selection is important, the number of ways to select both a president, a vice president, and a secretary is:

[tex]^{5}P_{3}=\frac{5!}{(5-3)!}=60[/tex]

Thus, there are 60 ways to  select both a president, a vice president, and a secretary.

(c)

Now for two members for the President's Council are to be selected.

As the order of selection is not important, two members can be selected in:

[tex]{5\choose 2}=\frac{5!}{(5-2)!\cdot\ 2!}=\frac{5!}{3!\ \times\ 2!}=10[/tex]

Thus, there are 10 ways to select two members for the President’s Council.

Answer:

  (x, y) = (-4, 3)

Step-by-step explanation:

For midpoint M of segment AB, we must have ...

  M = (A+B)/2

  2M = A+B

  B = 2M -A

In terms of x and y, for the given points, we have ...

  (x, y) = 2(3, 9) -(10, 15) = (6-10, 18-15)

  (x, y) = (-4, 3)

True.

Isometry is such transformation where the shape of observed body is not manipulated on itself but rather the position of it is manipulated.

Hope this helps.

Answer:

mark the other brainliest

Step-by-step explanation:

Answer:

C. 20(1/2)

Step-by-step explanation:

Let's find the value of the expression before looking for the nearest estimate

(19 4/5) (4/6) = 19 *(4/5)(4/6)

(19 4/5) (4/6) = 19(16/30)

(19 4/5) (4/6) = 19(8/15)

(19 4/5) (4/6) = (19*8)/15

(19 4/5) (4/6) = 152/15

(19 4/5) (4/6) = 10(2/15)

A. 16(1/3) =5.33

B. 19(2/3) = 12.667

C. 20(1/2) = 10

D. 20(1)= 20

The nearest to the expression is C. 20(1/2)

Answer:

  g(7) = 16

Step-by-step explanation:

The domain definitions in this piecewise function tell you that the third (bottom) piece applies when x=7.

  g(7) = (7+1)(7-5) = (8)(2)

  g(7) = 16

Answer:

C. Between 175 and 295 dollars.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 235

Standard deviation = 20

According to the Standard Deviation Rule, almost all (99.7%) of the students spent on textbooks in a semester:

Within 3 standard deviations of the mean.

235 - 3*20 = 175

235 + 3*20 = 295

So the correct answer is C.

Answer:

[tex]44.7-2.052\frac{6.96}{\sqrt{28}}=42.001[/tex]    

[tex]44.7+2.052\frac{6.96}{\sqrt{28}}=47.399[/tex]    

And the confidence interval would be between 42.001 and 47.399

Step-by-step explanation:

Information given

[tex]\bar X=44.7[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean

s=6.96 represent the sample standard deviation

n=28 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=28-1=27[/tex]

The Confidence interval is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex],the critical value for this case would be [tex]t_{\alpha/2}=2.052[/tex]

And replacing we got:

[tex]44.7-2.052\frac{6.96}{\sqrt{28}}=42.001[/tex]    

[tex]44.7+2.052\frac{6.96}{\sqrt{28}}=47.399[/tex]    

And the confidence interval would be between 42.001 and 47.399

Answer:

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex] = 1

Step-by-step explanation:

You have to calculate the following limit:

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}[/tex]

To solve the previous limit, you can factor x from numerator and denominator of the function, and use the fact that c/∞ = 0 with c a constant.

[tex]\lim_{x \to \infty} \frac{x+6}{x+7}= \lim_{x \to \infty}\frac{x(1+\frac{6}{x})}{x(1+\frac{7}{x})}=\lim_{x \to \infty}\frac{1+6/x}{1+7/x}=\frac{1+0}{1+0}=1[/tex]

Hence, the limit is 1, L = 1

Answer:

The probability that a randomly selected call time will be less than 30 seconds is 0.7443.

Step-by-step explanation:

We are given that the caller times at a customer service center has an exponential distribution with an average of 22 seconds.

Let X = caller times at a customer service center

The probability distribution (pdf) of the exponential distribution is given by;

[tex]f(x) = \lambda e^{-\lambda x} ; x > 0[/tex]

Here, [tex]\lambda[/tex] = exponential parameter

Now, the mean of the exponential distribution is given by;

Mean =  [tex]\frac{1}{\lambda}[/tex]  

So,  [tex]22=\frac{1}{\lambda}[/tex]  ⇒ [tex]\lambda=\frac{1}{22}[/tex]

SO, X ~ Exp([tex]\lambda=\frac{1}{22}[/tex])  

To find the given probability we will use cumulative distribution function (cdf) of the exponential distribution, i.e;

    [tex]P(X\leq x) = 1 - e^{-\lambda x}[/tex]  ; x > 0

Now, the probability that a randomly selected call time will be less than 30 seconds is given by = P(X < 30 seconds)

        P(X < 30)  =  [tex]1 - e^{-\frac{1}{22} \times 30}[/tex]

                         =  1 - 0.2557

                         =  0.7443

Answer:

9

Step-by-step explanation:

Since the scale factor is 12/8 = 1.5, to find LA we have to multiply FI by 1.5 which is 6 * 1.5 = 9.