Number 8 a&b please!

Answer:

Slope: The percent that voted falls by 0.1271 units per year.

Step-by-step explanation:

The slope of a regression line represent the average rate of change in the dependent variable (y) based upon the changes in the independent variable (x).

In this case the regression equation provided is:

y = -0.1271 x + 307.53

The slope of the line is -0.1271.

The dependent variable is the percent that voted and the independent variable is the year.

The slope of -0.1271 indicates that every year, on average, the percent that voted decreases by 0.1271 units.

Or the percent that voted falls by 0.1271 units per year.

Answer:

1/5

Step-by-step explanation:

i had a similar question

For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average). 

So the cost for one play is 2 dollars and your win is 10/6. 

Value is -2+10/6=-1/3 dollars

So you lose 1/3 dollars on average with each game

since you have no limited rolls u put 1/5

this from another question but both same just different numbers

Answer:

23,098; 23,208 ; 234,358

Step-by-step explanation:

Hope this helps

Answer:

(0.0706, 0.1294)

Step-by-step explanation:

Confidence interval of a proportion is:

CI = p ± CV × SE

where p is the proportion,

CV is the critical value (z score or t score),

and SE is the standard error.

The sample is large enough to estimate as normal.  For 95% confidence level, CV = z = 1.96.

Standard error for a proportion is:

SE = √(pq/n)

SE = √(0.1 × 0.9 / 400)

SE = 0.015

The confidence interval is:

CI = 0.1 ± (1.96)(0.015)

CI = (0.0706, 0.1294)

Round as needed.

Answer:

c. The P-value of 0.022 provides strong evidence that the 2015 average is greater than the average amount spent in 2012.

Step-by-step explanation:

The P-value indicates the probability of having this sample results given that the null hypothesis is true. If the P-value is low enough (smaller than the significance level), we have evidence to reject the null hypothesis, as there is little chance the null hypothesis is true and this sample result is due to chance.

Answer: A≈226.98 ft²

Step-by-step explanation:

The formula for area of a circle is A=πr². The formula doesn't include diameter , but we can certainly find the radius from the diameter.

d=2r

17=2r

r=17/2=8.5 ft

Now that we have the radius, we can plug it in to area formula.

A=πr²

A=π(8.5ft)²

A=π72.25ft²

A≈226.98 ft²

Area of a circle: A = πr²

Get the radius by dividing the diameter by 2.

17 / 2 = 8.5

Now, solve with the given values.

A = π(8.5)²

A = 72.25π

A = 226.865

Therefore, the area is 226.865ft³

Best of Luck!

Answer:  tank has  spherical shape . The distance from  the centre of mass =

h+r = 12 

Weight of water in tank = 9.8×π×9³×1000×4/3

 = 29.926×10⁶ N 

 to empty the tank Work done  = 12 × 29.926 × 10⁶

 = 359 × 10⁶ J

 = 359 MJ. hope this helps

Step-by-step explanation:

Answer:

  2625 kJ

Step-by-step explanation:

We assume the energy is proportional to the volume:

  energy/volume = 1050 kJ/(500 mL) = E/(1250 mL)

Multiply by 1250 mL:

  E = (1250/500)(1050 kJ) = 2625 kJ

The number of kJ in 1.25 L of Lemon Squash is 2625 kJ.

Answer:

Step-by-step explanation:

1. constraints with "[tex]\geq[/tex]" we should subtract surplus variable S1, S2, S3 and add artificial variable A1, A2, A3

Hence Z = 20 x1 + 32x2 + 40x3 + 0S1 + 0S2 + 0S3 + MA1 + MA2 + MA3

subject to

[tex]3x_1 +x_2+6x_3-S_1+A_1=9[/tex]

[tex]x_1+x_2-S_2+A_2=9[/tex]

[tex]4x_2+x_3-S_3+A_3=12[/tex]

and [tex]x_1,x_2,x_3,S_1,S_2,S_3,A_1,A_2,A_3\geq 0[/tex]

Answer:

3.3

Step-by-step explanation:

18x-5x=13+20

13x=33

x=2.5

Answer:

a. Calculate the prevalence rate of autism for these children for the two age categories.

b. Convert the prevalence rate to a rate per 1,000

Step-by-step explanation:

Generally prevalence is calculated using the following formula:

(number of people with autism / number of people measured) x 100%

age category

3-5: prevalence rate = (19/3,479) x 100% = 0.55%

6-10: prevalence rate = (17/5,417) x 100% = 0.31%

if you want to convert to a rate per 1,000, allyou need to do is multiply by 1,000 instead of 100

3-5: prevalence rate = (19/3,479) x 1,000 = 5.5

6-10: prevalence rate = (17/5,417) x 1,000 = 3.1

Answer:

1) 23/2

2) 529/25

Step-by-step explanation:

Transformation:

[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]

[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]

A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]

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

Transformation:

[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]

A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]

Answer:

(2) Real and equal (i.e., repeated roots), if D = 0.

Step-by-step explanation:

.In a quadratic equation ax2 + bx + c = 0, if discriminant is D= b2 - 4ac, then roots of the quadratic equation are

Real and equal (i.e., repeated roots), if D = 0.

If the D > b² - 4ac then it's real and distinct.

Answer:

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

100%

Answer:

[tex] 303.3 \leq \mu \leq 413.6[/tex]

We need to remember that the confidence interval for the true mean is given by:

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

Since the upper limit for the confidence interval is lower than the value of 425 we don't have enough evidence to conclude that the the mean skidding distance is at least 425 meters at the 5% of signficance used so then the confidence interval not support the loggers claim

Step-by-step explanation:

We know that they use a sample size of n =20 and the confidence interval for the true mean skidding distance along a new road in a European forest is given by:

[tex] 303.3 \leq \mu \leq 413.6[/tex]

We need to remember that the confidence interval for the true mean is given by:

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

Since the upper limit for the confidence interval is lower than the value of 425 we don't have enough evidence to conclude that the the mean skidding distance is at least 425 meters at the 5% of signficance used so then the confidence interval not support the loggers claim

Answer:

The students should request an examination with 5 examiners.

Step-by-step explanation:

Let X denote the event that the student has an “on” day, and let Y denote the

denote the event that he passes the examination. Then,

[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]

The events ([tex]Y|X[/tex]) follows a Binomial distribution with probability of success 0.80 and the events ([tex]Y|X^{c}[/tex]) follows a Binomial distribution with probability of success 0.40.

It is provided that the student believes that he is twice as likely to have an off day as he is to have an on day. Then,

[tex]P(X)=2\cdot P(X^{c})[/tex]

Then,

[tex]P(X)+P(X^{c})=1[/tex]

⇒

[tex]2P(X^{c})+P(X^{c})=1\\\\3P(X^{c})=1\\\\P(X^{c})=\frac{1}{3}[/tex]

Then,

[tex]P(X)=1-P(X^{c})\\=1-\frac{1}{3}\\=\frac{2}{3}[/tex]

Compute the probability that the students passes if request an examination with 3 examiners as follows:

[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]

        [tex]=[\sum\limits^{3}_{x=2}{{3\choose x}(0.80)^{x}(1-0.80)^{3-x}}]\times\frac{2}{3}+[\sum\limits^{3}_{x=2}{{3\choose x}(0.40)^{3}(1-0.40)^{3-x}}]\times\frac{1}{3}[/tex]

       [tex]=0.715[/tex]

The probability that the students passes if request an examination with 3 examiners is 0.715.

Compute the probability that the students passes if request an examination with 5 examiners as follows:

[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]

        [tex]=[\sum\limits^{5}_{x=3}{{5\choose x}(0.80)^{x}(1-0.80)^{5-x}}]\times\frac{2}{3}+[\sum\limits^{5}_{x=3}{{5\choose x}(0.40)^{x}(1-0.40)^{5-x}}]\times\frac{1}{3}[/tex]

       [tex]=0.734[/tex]

The probability that the students passes if request an examination with 5 examiners is 0.734.

As the probability of passing is more in case of 5 examiners, the students should request an examination with 5 examiners.

Answer:

[tex]10[/tex]

Step-by-step explanation:

[tex]05[/tex]

If the units place is higher than 5, then add 1 to the tens place.

Answer:

Step-by-step explanation:

Given that :

The probability of winning is 0.8

i.e P(winning) = 0.8

Then P(losing) = 0.2

a) Y ~ Geometric distribution

[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]

b) Y ~ Negative Binomial Distribution

[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]

c) Y ~ Binomial Distribution;

n = 100 ; P = 0.8

[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]

Answer:

a) 15

b) 65

Step-by-step explanation:

Adjunto se encuentra el diagrama asociado a esta situación. Comenzamos por ubicar aquellas afirmaciones que relacionan todos los deportes. Sabemos que 10 personas no prefieren ningún deporte. Luego, ubicamos 10 fuera de los conjuntos mostrados. Sabemos que 30 personas prefieren sólo surf y 20 personas prefieren sólo Tenis. Es decir, hay 30 personas en el conjunto S que no intersectan a los otros dos.  En este momento, hemos ubicado a 60 personas. Nos hacen falta 30 personas. La afirmación "15 personas prefieren Golf" significa que la suma de los números dentro del conjunto G es 15.  La afirmación "ninguno de los que prefieren los deportes Tenis o Surf prefieren el golf. Es decir, que la intersección de G con T y con S son vacías. Es decir que las 15 personas que prefieren golf, lo prefieren únicamente. Esto nos deja con 15 personas por ubicar. El único lugar donde podemos ubicar a dichas 15 personas es en en la intersección de T y S.

a). ¿cuántas personas prefieren dos de estos deportes? Por el diagrama, son aquellas personas que prefieren Tenis o Surf. Es decir, 15.

b) ¿Cuánto prefieren sólo uno de estos deportes? Es la suma de aquellos que prefieren sólo un deporte. Es decir, sólo G, sólo T o sólo S. Es decir 15+20+30 = 65.

Answer:

y = 4 sin(2π/11 x) + 2

Step-by-step explanation:

y = A sin(2π/T x + B) + C

where A is the amplitude,

T is the period,

B is the phase shift,

and C is the midline.

A = 4, T = 11, and C = 2.  We'll assume B = 0.

y = 4 sin(2π/11 x) + 2

The sine function with the desired characteristics is given by:

[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]

The standard sine function is given by:

[tex]y = A\sin{Bx} + C[/tex]

In this problem:

Then, the equation for the sine function is:

[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]

A similar problem is given at https://brainly.com/question/18055768

Answer:

El área a cubrir es de 4800 cm^2.

Step-by-step explanation:

La pregunta está incompleta:

Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo cuánto es centímetros cuadrados. Las medidas son 80 cm de largo y 60 cm de ancho.

Tenemos que calcular el área que representa la puerta, cuyos lados son 80 cm y 60 cm.

El área A se calcula multiplicando ambos lados:

[tex]A=80\,cm\cdot60\,cm=4800\,cm^2[/tex]

Answer:

9.90 units (3 s.f.)

Step-by-step explanation:

distance formula

[tex] = \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]

Length of WX

[tex] = \sqrt{(2 - ( - 5))^{2} + (6 - ( - 1)^{2} } \\ = \sqrt{(2 + 5)^{2} + (6 + 1)^{2} } \\ = \sqrt{7 ^{2} + 7^{2} } \\ = \sqrt{98} \\ = 9.90 \: units \: (3 \: s.f.)[/tex]

Answer:

The answer is 7 square root 2

Step-by-step explanation:

trust

Answer:

10.1%

Step-by-step explanation:

The first thing we should do is calculate the total volume of the solution when mixing them would be:

0.7 + 0.3 = 1

Now, we have that the resulting concentration (x) would be equal to the sum of the multiplications between the volumes and the concentrations to be mixed, as follows:

x * 1 = 0.7 * 0.05 + 0.3 * 0.22

x = 0.035 + 0.066

x = 0.101

That is, the concentration of the resulting mixture would be 10.1% (0.101 * 100)

Answer:

6n+1

Step-by-step explanation:

first term=13-6=7

nth term=7+(n-1)6=7+6n-6=6n+1

Answer:

aₙ= 6n +1

Step-by-step explanation:

Second term a₂= 13

Common difference d= 6

Then first term

nth term:

Answer:

Answer is given below.

Step-by-step explanation:

let us solve the numerator first

=4x²-14x+6

=2(2x²)+2(-7x)+2(3)

= GCF of the terms of the numerator is 2.

denominator

x³-7x²+12x

x(x²)+x(-7x)+x(12)

GCF of the terms of the denominator is x.

factorise the numerator

4x²-14x+6

4x²-2x-12x + 6  (by splitting the middle term; the numbers should produce the product  4*6 and when the no.s are added they should give -14)

(4x²-2x) + (-12x+6)

2x(2x-1) -6(2x-1)

(2x-6)(2x-1)

factors are

(2x-6), (2x-1)

denominator

this can also be done by splitting the middle term

x³-7x²+12x

x³-3x²-4x²+12x

(x³-3x²) + (-4x²+12x)

x²(x-3) -4x(x-3)

(x²-4x)(x-3)

factors are

(x²-4x), (x-3)

Answer:

2 is the answer

Step-by-step explanation:

area=1/2*base*height

as height = 2*base and area =4 it comes

1/2*2*base*base=4

so base *base=4

so base = 2

Answer:

There is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy

Step-by-step explanation:

Sample size, n = 150

Number of people that plan on voting for the levy, X = 78

Proportion of people that plan on voting for the levy:

[tex]\bar{p} = X/n\\\bar{p} = 78/150\\\bar{p} = 0.52[/tex]

The study is to determine whether or not the data supports the idea that more than 50%(0.5) of people plan on voting for the levy

The null and alternative hypotheses are:

[tex]H_0: p \leq 0.5\\H_a: p > 0.5[/tex]

Calculate the test statistics:

[tex]t_s = \frac{\bar{p} - p}{\sqrt{\frac{p(1-p)}{n} } } \\t_s = \frac{0.52-0.5}{\sqrt{\frac{0.5(1-0.5)}{150} } } \\t_s = 0.49[/tex]

For a test statistic [tex]t_s = 0.49[/tex], the p-value = 0.3121

The significance value, [tex]\alpha = 0.10[/tex]

Since the p-value(0.3121) is greater than α(0.10), the null hypothesis [tex]H_0[/tex] will be accepted.

This means that there is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy

Answer:

765 J

Step-by-step explanation:

We are given;

Mass of bucket = 30 kg

Mass of rope = 0.3 kg/m

height of building= 30 meter

Now,

work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand

Or W = W1 + W2

Work done in lifting the rope is given as,

W1 = Force x displacement

W1 = (30,0)∫(0.2x .dx)

Integrating, we have;

W1 = [0.2x²/2] at boundary of 30 and 0

W1 = 0.1(30²)

W1 = 90 J

work done in lifting the sand is given as;

W2 = (30,0)∫(F .dx)

F = mx + c

Where, c = 30 - 15 = 15

m = (30 - 15)/(30 - 0)

m = 15/30 = 0.5

So,

F = 0.5x + 15

Thus,

W2 = (30,0)∫(0.5x + 15 .dx)

Integrating, we have;

W2 = (0.5x²/2) + 15x at boundary of 30 and 0

So,

W2 = (0.5 × 30²)/2) + 15(30)

W2 = 225 + 450

W2 = 675 J

Therefore,

work done lifting the bucket (sand and rope) to the top of the building,

W = 90 + 675

W = 765 J

Answer:

5x^2+5x+3/3x^2+3x

Step-by-step explanation: