If c(x) = 4x-2 and d(x) = x2 + 5x, what is (c x d) (x)

Answer:

P-value = 0.0367

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of residents who favor construction is significantly over 42%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.42\\\\H_a:\pi>0.42[/tex]

The sample has a size n=900.

The sample proportion is p=0.45.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.42*0.58}{900}}\\\\\\ \sigma_p=\sqrt{0.000271}=0.016[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.45-0.42-0.5/900}{0.016}=\dfrac{0.029}{0.016}=1.79[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.79)=0.0367[/tex]

Answer:

solution,

Highest score=9

lowest score=1

now,

range= highest score-lowest score

=9-1

=8

Hope this helps...

Answer:

8

Step-by-step explanation:

The range of the sequence is the largest number - the smallest number.

The largest number is 9.

The smallest number is 1.

9 - 1

= 8

The range of the sequence is 8.

Answer:

Step-by-step explanation:

Let's organise our information :

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

Now let's solve this equation :

Δ=1²-4*(1/2)*(-4)

 = 9

So we have two solutions :

So the solutions are -4 and 2

Answer:

fg t f h 10

Step-by-step explanation:

Answer:

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X¿ 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s¿4.2 represent the sample standard deviation

n¿65 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=65-1=64[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]    

Answer:

828

Step-by-step explanation:

Missing leg of triangle:

√15²-12²= √225-144=√81=9

Triangle faces= 2*1/2*12*9= 108

Base= 20*9= 180

Front face= 20*15= 300

Back face= 20*12= 240

Total= 108+180+300+240= 828

Second choice

Answer:c

Step-by-step explanation:

hyp=6[tex]\sqrt{2}[/tex]

adj=6

hyp:adj=6[tex]\sqrt{2}[/tex]  :2

hyp:adj=[tex]\frac{6\sqrt{2} }{6} \\[/tex]

[tex]=\frac{\sqrt{2} }{1} \\hyp:adj=\sqrt{2} :1[/tex]

Answer:

True

Step-by-step explanation:

3y=5x

Put x as 3 and y as 5.

3(5) = 5(3)

15 = 15

Hence, true.

Answer:

X=3

y=15

[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]

Proved.

Hope it helps..

Answer:

36 cups

3/12 = 9/c

Step-by-step explanation

3 ÷ 12 = .25

each cup = 25 cents

9 ÷ .25 = 36

Marco sold 36 cups of lemonade.

3/12 = 9/c

Answer:

36 cups

Step-by-step explanation:

We can set up a proportion:

12/3=c/9

Cross multiply.

12*9=3*c

108=3c

Divide both sides by 3.

c=36

The error that the proportion Kaycee set up was

cups/price=price/cups

This is not proportionate.

Possible proportions include:

cups/price=cups/price

price/cups=price/cups

cups/cups=price/price

price/price=cups/cups

Answer:

The individually paid $1.5 for the tip and $8.5 for the food

Step-by-step explanation:

Total money spent =  $40

Food bill =  $34

if the situation is represented by the equation [tex]\frac{1}{4}(t+34) = \frac{40}{4}[/tex] where t is the amount of the tip, the amount for the tip can be calculated as shown;

[tex]\frac{1}{4}(t+34) = \frac{40}{4}\\ t+34 = 40\\t = 40-34\\t = 6[/tex]

Amount of the tip = $6

If they decided to split the bill and tip evenly among themselves, amount paid by each friend for the food and the tip can be gotten using the equation representing the situation where t = $6 as shown;

[tex]= \frac{1}{4}(t+34) \\= \frac{1}{4}(6+34)\\= \frac{1}{4}(6)+\frac{1}{4}(34)\\= 1.5+8.5\\[/tex]

From the result above, it can be seen that each friend paid $1.5 for their tip and $8.5 for their food

Answer:

A) Each friend paid $8.50 for the food and $1.50 for the tip.

Answer:

Option C is the correct option

Step-by-step explanation:

g = 8 ( given )

Now,

[tex] \frac{g}{2} + 3[/tex]

Plugging the value of g

[tex] \frac{8}{2} + 3[/tex]

[tex] \frac{8 + 3 \times 2}{2} [/tex]

[tex] \frac{8 + 6}{2} [/tex]

[tex] \frac{14}{2} [/tex]

[tex]7[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

[tex]r \approx 2.41\%[/tex]

Step-by-step explanation:

The computation of the approximate new interest rate is shown below:

As we know that there are four quarters in a year so

The new equation is

[tex]A = 250(1 + r)^{4t}[/tex]

Now to determine the value of interest rate,i.e r, so place this to the first equation.

So,

[tex]250(1.1)^{t} = 250(1 + r)^{4t}[/tex]

[tex]1.1^{t} = (1 + r)^{4t}[/tex]

1.1 = (1 + r)^4

[tex]\sqrt[4]{1.1} = 1 + r[/tex]

[tex]r = -1 + \sqrt[4]{1.1}[/tex]

[tex]r \approx 0.0241[/tex]

[tex]r \approx 2.41\%[/tex]

We simply applied the above formula so that the interest rate could come

Answer:

The answer is 1/27

Step-by-step explanation:

According to the rules of indices

a^-b can be written as 1/a^b

So 3^- 3 can be written as 1/3³

And

1/3³ = 1/27

Hope this helps you

Answer:

8

Step-by-step explanation:

the value of x is 8 because the sides are the same

Answer:

Test statistic t = 3.12

P-value = 0.001

As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year (Gina's claim).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=55000\\\\H_a:\mu> 55000[/tex]

The significance level is 0.05.

The sample has a size n=61.

The sample mean is M=56500.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3750.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3750}{\sqrt{61}}=480.138[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{56500-55000}{480.138}=\dfrac{1500}{480.138}=3.12[/tex]

The degrees of freedom for this sample size are:

df=n-1=61-1=60

This test is a right-tailed test, with 60 degrees of freedom and t=3.12, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>3.12)=0.001[/tex]

As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.

Answer:

[29 over 2 divided by 5 over 4] = 29/2 ÷ 5/4 (A)

[29 over 2 times 4 over 5] = 29/2 × 4/5 (C)

Step-by-step explanation:

The total amount of water a tank can hold is 14 and one and one-half gallons = 14½

We are to determine the number of 1/4 gallon buckets of water that can be used to fill the tank.

To find this, we would divide 14½ by 1¼ = 14½ ÷ 1¼

Convert 14½ and 1¼ to improper fraction

14½ = [(14×2)+1]/2 = 29/2

1¼ = [(1×4)+1]/4 = 5/4

14½ ÷ 1¼ =29/2 ÷ 5/4

Then we find the inverse of ¼ to convert the division to multiplication

= 29/2 × 4/5 = 116/10

= 11.6

14½ ÷ ¼ = 11.6

Therefore 11.6 gallons of ¼ buckets of water can be used to fill the tank.

But the two expressions that could be used to represent this scenario to get the answer from the options = 29/2 ÷ 5/4 (A)

[29 over 2 divided by 5 over 4]

29/2 × 4/5 (C)

[29 over 2 times 4 over 5]

Answer:

I believe it is A and C.

Answer:

Hope it helps you :)

And i hope you understand  

For store 1, it can be placed on 16 sites. Store 2 can be placed on 15 sites( since store 1 is already on site 1). Store 3 can be placed on 14 sites and so on until store 5 which has 12 sites.

Therefore the number of way is

C= 16*15*14*13*12

c=524,160 possibilities

Answer:

a)0.654

b)-0.34

Step-by-step explanation:

a)2 3 4 5 6 7

[tex]\mu = 4[/tex]

[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{2+3+4+5+6+7}{6}\\Mean =4.5[/tex]

Standard deviation [tex]=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]

Standard deviation [tex]=\sqrt{\frac{(2-4.5)^2+(3-4.5)^2+(4-4.5)^2+(5-4.5)^2+(6-4.5)^2+(7-4.5)^2}{6-1}}=1.87[/tex]

[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\t=\frac{4.5-4}{\frac{1.87}{\sqrt{6}}}\\t=0.654[/tex]

Df = n-1 = 6-1 = 5

Assume α=0.05

So[tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]

So, t critical = 2.57

So, t calculated < t critical

b)1 2 2 5 5 7

[tex]\mu = 4 \\Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{1+2+2+5+5+7}{6}\\Mean =3.67[/tex]

Standard deviation =[tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]

Standard deviation =[tex]\sqrt{\frac{(1-3.67)^2+(2-3.67)^2+(2-3.67)^2+(5-3.67)^2+(5-3.67)^2+(7-3.67)^2}{6-1}}=2.338[/tex]

[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}t=\frac{3.67-4}{\frac{2.338}{\sqrt{6}}}t=-0.34[/tex]

Df = n-1 = 6-1 = 5

Assume α=0.05

So, [tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]

So, t critical = 2.57

So, t calculated < t critical

Answer:

x = 270 gallons

270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze

Step-by-step explanation:

Let x represent the number of gallons of the 50% antifreeze solution.

The volume of the 10% antifreeze is = 90 gallons

The volume of the mixture that is 40% antifreeze = 90+x

The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;

50% of x + 10% of 90 = 40% of (90+x)

0.50(x) + 0.10(90) = 0.40(90+x)

0.50x + 9 = 36 + 0.40x

Collecting the like terms;

0.50x - 0.40x = 36-9

0.10x = 27

x = 27/0.10

x = 270 gallons

270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze

Answer: graphing calculator!

Step-by-step explanation: if you’re looking for the square root of a # that isn’t a perfect square (ie. sqrt4, sqrt 36) then you have to use a calculator for that. however the idea behind square roots is just a # multiplied by itself to give the original #. just ask yourself “what can i multiply by itself to get the original number”. hope that helped !

Answer:

By multiplying the number by its power 2.

E.g= 4^2

Answer:

6.85

Step-by-step explanation:

6 17/20

Convert to improper fraction.

137/20

Divide.

= 6.85

Answer:

6.85

Step-by-step explanation:

17/20 = 85/100

17 x 5 = 85

20 x 5 = 100

so,

6 + 85/100 = 6.85

Answer:

3: 2

Step-by-step explanation:

game Apps: education apps:

3: 2

Step-by-step explanation:

a. 3.14 * 4² = 50.24 cm²

b. 16 cm

c. V = B * h = 50.24 * 16 = 803.84 cm²

Answer:

She is saving 10 cents per pound

Step-by-step explanation:

First, we need to find how much she would pay without the sale:

12.5(1.8) = 22.5

Now, we can calculate how much she saved:

22.5 - 21.25 = 1.25

To find how much she's saving per pound, we divide the difference by the number of pounds:

1.25/12.5 = 0.1

She is saving 10 cents per pound

Answer:

A

Step-by-step explanation:

I took the test and got it right

Answer:

Step-by-step explanation:

a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.

__

b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.

Answer:

Step-by-step explanation:

Answer:

53/28

Step-by-step explanation:

100 g jam

Blackberry / sugar= 53/28

Answer:

Solution,

Amount of sugar=100-(19+53)

=100-72

=28 gram

Ratio of blackberries to sugar=53/28

=53:28

Hope this helps..

Good luck on your assignment..

Answer:

A)x=2pi/3 and x=-2pi/3

Step-by-step explanation:

The function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values where the tan(a) has vertical asymptotes.

we know that tan(a) has vertical asymptotes in [tex]a=\frac{\pi }{2}[/tex] and  [tex]a=\frac{-\pi }{2}[/tex], if we made [tex]a=\frac{3x}{4}[/tex] and solve for x, we get:

for [tex]a=\frac{\pi }{2}[/tex]

[tex]\frac{\pi }{2} =\frac{3x}{4}\\x = \frac{2\pi }{3}[/tex]

for [tex]a=\frac{-\pi }{2}[/tex]

[tex]\frac{-\pi }{2} =\frac{3x}{4}\\x = \frac{-2\pi }{3}[/tex]

Finally, the function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values x=2pi/3 and x=-2pi/3

Answer:

A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

I would have to say it is two bc Everitt had 30% where Desery had 20%.

Answer:

v = Δs/Δt

Step-by-step explanation:

Velocity is equal to the displacement/distance (delta symbol s) over the change of time (delta symbol t).

Answer:

(3,2)

(-9,-6)

Step-by-step explanation:

Given that the graph is a direct variation.

The equation of variation is:

[tex]x=ky[/tex]

Since point (6, 4) is on the graph

[tex]6=4k\\\\k=\dfrac64[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac64y[/tex]

[tex]\text{When y=2},x=\dfrac64 \times 2 =3\\\\\text{When y =}-6,x=\dfrac64 \times -6 =-9\\\\\text{When y =}8,x=\dfrac64 \times 8 =12\\\\\text{When y =}-3,x=\dfrac64 \times -3 =-4.5[/tex]

Therefore, the points that are also on the graph are:

(3,2) and  (-9,-6)

Answer:

(-9, -6) and (3, 2)

Step-by-step explanation: