The temperatures at several times of the day are shown in the coordinate plane below. The x-axis represents the number of hours before or after noon. For example, -1 would represent 11 a.m. The y-axis represents the temperature in degrees Celsius. At 5 p.m.5, start text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p.m.}2 p.m.2, start text, space, p, point, m, point, end text and the temperature at 8 \text{ p.m.}8 p.m.8, start text, space, p, point, m, point, end text What coordinates represent the temperature at 5pm?

Answer:

The statements that are true are:

b) n equals 30

c) The number of samples is 8

d) The sample size is 30

f) Each day she collects a total of 240 observations.

Step-by-step explanation:

She takes a sample every hour, so she takes 8 samples during the day.

Each samples consist of 30 individuals (pizzas).

This adds a total of 240 observations during the day.

The statements that are true are:

b) n equals 30

c) The number of samples is 8

d) The sample size is 30

f) Each day she collects a total of 240 observations.

Answer: Total time taken by them would be 60 minutes = 1 hour before the tank overflows.

Step-by-step explanation:

Since we have given that

Time taken by an inlet pipe =10 minutes

Time taken by a drain = 12 minutes

So, if both are open together,

Total work done by them would be

[tex]\dfrac{1}{10}-\dfrac{1}{12}\\\\=\dfrac{6-5}{60}\\\\=\dfrac{1}{60}[/tex]

So, total time taken by them would be 60 minutes = 1 hour before the tank overflows.

Answer:

Yes, Dayson can completely cover the package with wrapping paper.

Step-by-step explanation:

Given: The rectangular prism is 50 centimeters by 20 centimeters by 18 centimeters.

Area of wrapping paper is 1 square meter.

To find: whether he can completely cover the package with wrapping paper

Solution:

Total surface area of the rectangular prism = 2(lb + bh +hl)

where l denotes length, b denotes breadth and h denotes height

Total surface area of the rectangular prism = [tex]2\left [ (50)(20)+(20)(18)+(18)(50) \right ][/tex]

[tex]=2\left ( 1000+360+900 \right )\\=2(2260)\\=4520\,\,cm^2[/tex]

As [tex]1\,m^2=10000\,cm^2[/tex],

Total surface area of the rectangular prism = [tex]4520\,cm^2=0.4520\,m^2[/tex]

As Dayson has [tex]1\,m^2> 0.4520\,m^2[/tex] of wrapping paper, he can completely cover the package with wrapping paper.

Answer:

up/down

Step-by-step explanation:

Answer:

-1 -2i

Step-by-step explanation:

(-7+6) + (6i-8i) = -1 -2i

Answer:

(-1 - 2i)

Step-by-step explanation:

You simply add them.

-7 + 6 = -1

6i + (-8i) = 6i - 8i = -2i

Answer:

a = 4

Step-by-step explanation:

[tex]A = \frac{b * c * sen 45}{2} \\\\A = 8 * \sqrt{2} * \frac{\sqrt{2} }{2} * \frac{1}{2} \\\\\\\\A = 4[/tex]

Answer:

4

Step-by-step explanation:

Answer:

[tex](C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]

Step-by-step explanation:

The reference angle is the angle that the given angle makes with the x-axis.

For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.

From the given options:

[tex](A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]

We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The record of the statistics and the summary statistics which are the missing files in the question are attached below.

From the given information:

The null hypothesis and the alternative hypothesis can be represented by :

[tex]\mathbf{H_o:}[/tex] There is no difference between the average time  spend by men and women at gym each week

[tex]\mathbf{H_i:}[/tex] The average time  spend by men is greater than the average time spend by women at the gym each week

From the summary statistics in the attached file below:

The p-value = 0.3253

Level of significance = 5% = 0.05

Therefore; it is obvious that the p-value is greater than the level of significance  i.e (0.3253 > 0.05)

Hence; there is no enough evidence to reject the null hypothesis

CONCLUSION: We conclude that the mean number of minutes exercised per week is larger for men than women at the  this gym.

Answer:

1. The least squares regression is y = -0.1015·x + 6.51

2. The independent variable is b) age

Please see attached table

Step-by-step explanation:

The least squares regression formula is given as follows;

[tex]\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}}[/tex]

We have;

[tex]\bar x[/tex] = 24

[tex]\bar y[/tex] = 4

[tex]\Sigma (x_i - \bar x) (y_i - \bar y)[/tex] = -79

[tex]\Sigma (x_i - \bar x)^2[/tex] = 778

[tex]\therefore \hat \beta =\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}} = \frac{-79}{778} = -0.1015[/tex]

The least squares regression is y = -0.1015·x + α

∴ α = y  -0.1015·x = 6 - (-0.1015 × 5) = 6.51

The least squares regression is thus;

y = -0.1015·x + 6.51

2. The independent variable is the age b)

3. Steps to create an ANOVA table with α = 0.05

The overall mean = (43  + 30  + 22  + 20  + 5  + 1  + 6  + 4  + 3  + 6 )/10 = 14

There are 2 different treatment = [tex]df_{treat} = 2 - 1 = 1[/tex]

There are 10 different treatment measurement = [tex]df_{tot} = 10 - 1 = 9[/tex]

[tex]df_{res} = 9 - 1 = 8[/tex]

[tex]df_{treat} + df_{res} = df_{tot}[/tex]

The estimated effects are;

[tex]\hat A_1 = 24 - 14 = 10[/tex]

[tex]\hat A_2 = 4 - 14 = -10[/tex]

[tex]SS_{treat} = 10^2 \times 5 + (-10)^2 \times 5 =1000[/tex]

[tex]\sum_{i}\SS_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y)= [(1 - 4)^2 + (6 - 4)^2 + (4 - 4)^2 + (3 - 4)^2 + (6 - 4)^2] = 18[/tex]

[tex]\sum_{i} S S_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y) ^2= [(43 - 24)^2 + (30 - 24)^2 + (22 - 24)^2 + (20 - 24)^2 + (5 - 24)^2] = 778[/tex]

[tex]S S_{res} = \sum_{i} S S_{row}_i = 778 + 18 = 796[/tex]

[tex]SS_{tot}[/tex] = (43  - 14)² + (30  - 14)² + (22  - 14)² + (20  - 14)² + (5  - 14)² + (1 - 14)1² + (6  - 4 )² + (3  - 14)² + (6  - 14)² = 1796

[tex]MS_{treat} = \dfrac{SS_{treat} }{df_{treat} } = \dfrac{1000}{1} = 1000[/tex]

[tex]MS_{res} = \dfrac{SS_{res} }{df_{res} } = \dfrac{796}{8} = 99.5[/tex]

F- value is given by the relation;

[tex]F = \dfrac{MS_{treat} }{MS_{res} } = \frac{1000}{99.5} = 10.05[/tex]

We then look for the critical values at degrees of freedom 1 and 8 at α = 0.05 on the F-distribution tables 5.3177

Hence; [tex]F = 10.05 > F_{1,8}^{Krit}(5\%) = 5.3177[/tex], we reject the null hypothesis.

Answer:

(a)h(g(133))

(b)f(j(6.82))

Step-by-step explanation:

(a)Area of a circle whose circumference is 133 cm.

Since g(C) represents the radius (in cm) of a circle whose circumference is C cm.

h(r) represents the area [tex](in$ cm^2)[/tex] of a circle whose radius is r cm.

Therefore, the area of a circle whose circumference is 133 cm is:

h(g(133))

(b)Circumference of a circle whose area is [tex]6.82 cm^2[/tex]

j(A) represents the radius (in cm) of a circle whose area is A [tex]cm^2[/tex].

f(r) represents the circumference (in cm) of a circle whose radius is r cm.

Therefore:

The circumference of a circle whose area is [tex]6.82 cm^2[/tex] =f(j(6.82))

The inverse of the function g(x)=-2x -3.

A function assigns the value of each element of one set to the other specific element of another set.

Given function:

f(x) = -1/2 x - 3/2

Since the function is inverse, so

g(f(x)) = a(-1x/2 - 3/2) + b

x = -ax/2 - 3x/2 + b

-a/2 = 1

a = -2

and, -3a/2 + b = 0

b= -3

Hence, the inverse of the function g(x)=-2x -3.

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Answer:

Step-by-step explanation:

Question:

Consider xdy = 3ydx.

(a) Apply Theorem 1 and show the equation has unique solution in xy-plane where x ≠ 0

(b) Theorem 1 will be inconclusive about existence and uniqueness of solution where x = 0 (that is on y-axis). For points on the y-axis (i) Show there are infinitely many different solutions for xdy = 3ydx y(0) = 0. (ii) Show there is no solution for xdy = 3ydx,

y(0) = b, b ≠0.

Theorem 1 is attached.

Answer:

Given:

xdy = 3ydx

a) Given theorem 1 :

dy/dx = f (x, y)

we have:

[tex] f(x, y) = \frac{3y}{x}[/tex]

[tex] \frac{d}{dy} f(x, y) = \frac{3}{x}[/tex]

[tex] \frac{d}{dy} [/tex] is at interior of all angles except at point x=0.

Therefore for x≠0

[tex] \frac{d}{dy} f(x, y) = \frac{3}{2}[/tex]

Thus, from theorem 1, there is a unique solution in the xy plane where x≠0

b) i) xdy = 3ydx y(0) = 0

We have:

[tex] \frac{dy}{y} = \frac{3}{x} dx [/tex]

Integrating, we have:

∫[tex] \frac{dy}{y}[/tex] =∫[tex] \frac{3}{x} dx [/tex]

ln y = 3lnx + lnC

y = Cx³

Hence, y(0)=0 is satisfied for all values of C

Thus, there are infinitely many solutions for xdy = 3ydx

ii) xdy = 3ydx

y(0) = b, b ≠ 0.

From our part (i) above, we already know that, y = Cx³

Let's now take initial value of y as b,

ie, y(0) = b

b = 0

From the question, b≠0.

Thus, it means it has no solution.

Answer:

You will earn $483.55 in interest.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

$3,000 T - note with a 3% annual rate

This means that [tex]P = 3000, r = 0.03[/tex]

Paid quarterly

Quarterly is 4 times per year, so [tex]n = 4[/tex]

Maturity in 5 years.

This means that [tex]t = 5[/tex]

How much interest will you earn?

Interest is the final amount subtracted by the principal.

Final amount:

A(5).

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(5) = 3000(1 + \frac{0.03}{4})^{4*5}[/tex]

[tex]A(5) = 3483.55[/tex]

Interest:

$3,483.55 - $3,000 = $483.55

You will earn $483.55 in interest.

Answer:

95

Step-by-step explanation:

just did it on ed

Answer:

f(-1) = 2

f(0) = 3

Step-by-step explanation:

f(a) = 3a - a²

Answer:

The 3rd and the 4th statement are not the true statements.

Step-by-step explanation:

In the 3rd statement, if you put a=-1 into the equation f(a), it would be

=3x(-1) - (-1)2

=-3 - 1

=-4.

In the 4th statement, if you put a=0 into the equation f(a), it would be

=3x(0) - (0)2

=0 - 0

=0.

For the other statements, they show the correct results.

Answer:

zero goats and 120 Ilamas to get profit of $15,120

Step-by-step explanation:

Goats: G

Ilamas: l

Explicit constraints:

2G + 5l ≤ 400

100G+ 80l≤ 13,200

Implicit constraints

G≥0

I≥0

P= 84G+ 126l

See attachment for optimal area

substituting coordinats of optimal region in profit equation to get profit

When G= 132, l=0

P=84(132) + 126(0)

P=11,088

When G=0, l=120

P=84(0)+ 126(120)

P = 15120

When G= 100, l=40

P=84(100)+126(40)

P=13440

Answer:

4 oz

Step-by-step explanation:

one cup is 8 oz

1/2 cup is 8/2 oz which is 4 oz

Answer:

4 fluid ounces

Step-by-step explanation:

One cup is 8 oz so we would have to divide 8 by 2 to get 4 because one half of 8 is 4.

Answer:

35

Step-by-step explanation:

35 is not divisible by 3 as all the other numbers are

Answer: The number to show he is incorrect is 35 because 35 divided by 3 is 11.6666666667 which is not a whole number.

Step-by-step explanation:

Answer:

[tex]2.83,2.8,2.59,2.48[/tex]

Step-by-step explanation:

Given:

Numbers are [tex]\frac{28}{10}\,m,\,2.48\,m,\,\frac{259}{100}\,m,\,2.83 \,m[/tex]

To express: each length as a decimal number in order from greatest to least

Solution:

A number which consists of a whole number part and the fractional part separated by a decimal point is known as a decimal number.

[tex]\frac{28}{10}=2.8\\ 2.48=2.48\\\frac{259}{100}=2.59\\ 2.83=2.83[/tex]

Numbers arranged in order from greatest to least: [tex]2.83,2.8,2.59,2.48[/tex]

Answer:

5 × 10⁶

Step-by-step explanation:

To convert a long number to a scientific notation:

Count the number of zeros in the number

Use the count as the power of 10.

5,000,000 has six zeros

So:

× 10⁶

Now 5 will be left to be added to the notation.

5 × 10⁶

Answer:

5 x 10'6

Step-by-step explanation:

Corrected Question

One cylinder has a volume that is 8cm less than 7/8 of the volume of a second cylinder. If the first cylinder’s volume is 216cm³, what is the correct equation and value of x, the volume of the second cylinder?

Answer:

The equation is: [tex]216=\frac{7}{8}x-8[/tex]

Volume of the second cylinder= [tex]256cm^3[/tex]

Step-by-step explanation:

Volume of the first cylinder=[tex]216cm^3[/tex]

Let the volume of the second cylinder=x

7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x[/tex]

8 less than 7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x-8[/tex]

Therefore, the equation is:

[tex]216=\frac{7}{8}x-8[/tex]

Next, we solve for x

[tex]216=\frac{7}{8}x-8\\216+8=\frac{7}{8}x\\224=\frac{7}{8}x\\$Cross multiply\\7x=224*8\\Divide both sides by 7\\x=256cm^3[/tex]

The volume of the second cylinder is [tex]256cm^3[/tex]

Answer:

The answer is D

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Since diameter AB divides MN into two equal parts hence

MO = NO

NOW,

5x+34 = -2(1-7x)

5x+34 = -2+14x

34+2 = 14x-5x

36 = 9x

Dividing both sides by 9

x = 4

Now,

NO = -2(1-7(4))

NO = -2+56

NO = -2+56

NO = 54

Answer:12 gallons

Step-by-step explanation: It is enough to fill 40

The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

A motor oil retailer needs to fill 40 one-quart bottles.

We know that in 1 gallon, there are 4 quarts. Then the number of gallons in 40 quarts will be given as,

⇒ 40 / 4

⇒ 10 gallons

The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.

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Answer:

Interest= $10000

Step-by-step explanation:

So we are to calculate the interest at 5% annum of $200000.

Ok , we'll use the formula

PRT/100 = interest

Where P = principal

R = rate

T= time

(200000* 5*1)/100 = interest

1000000/100 = interest

10000 = interest

Interest= $10000

Answer:

555

Step-by-step explanation:

(357+452+589+602+775)/5

Step-by-step explanation:

I HAVE DONE AT HERE YOU HAVE ASK WHE\E *O PUT 120°

Answer:

B.

Step-by-step explanation:

Volume of fudge cubes = 1 ×1×1

= 1 inch³

The cylinder contains 12.6 fudge cubes

So,

Volume of cylinder = 12.6 inches³

Height of cylinder = 1 inch

Base area of cylinder = Volume / Height

= 12.6 / 1

= 12.6 inches²

Answer:

Yes, there is enough evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city (P-value=0.0000263).

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that dog owners in the country (sample 2) spend more time walking their dogs than do dog owners in the city (sample 1).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=20 has a mean of 10 and a standard deviation of 3.

The sample 2, of size n2=21 has a mean of 15 and a standard deviation of 4.

The difference between sample means is Md=-5.

[tex]M_d=M_1-M_2=10-15=-5[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{20}+\dfrac{4^2}{21}}\\\\\\s_{M_d}=\sqrt{0.45+0.762}=\sqrt{1.212}=1.101[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-5-0}{1.101}=\dfrac{-5}{1.101}=-4.54[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-1=20+21-2=39[/tex]

This test is a left-tailed test, with 39 degrees of freedom and t=-4.54, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-4.54)=0.0000263[/tex]

As the P-value (0.0000263) 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 dog owners in the country spend more time walking their dogs than do dog owners in the city.

Using the t-distribution, it is found that since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.

At the null hypothesis, we test if dog owners in the country and in the city spend the same amount of time walking their dogs, that is:

[tex]H_0: \mu_{Co} - \mu_{Ci} = 0[/tex]

At the alternative hypothesis, we test if dog owners in the country spend more time, that is:

[tex]H_1: \mu_{Co} - \mu_{Ci} > 0[/tex]

The standard errors are:

[tex]s_{Co} = \frac{4}{\sqrt{21}} = 0.8729[/tex]

[tex]s_{Ci} = \frac{3}{\sqrt{20}} = 0.6708[/tex]

The distribution of the differences has:

[tex]\overline{x} = \mu_{Co} - \mu_{Ci} = 15 - 10 = 5[/tex]

[tex]s = \sqrt{s_{Co}^2 + s_{Ci}^2} = \sqrt{0.8729^2 + 0.6708^2} = 1.1009[/tex]

We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu[/tex] is the value tested at the null hypothesis, for this problem [tex]\mu = 0[/tex], hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{5 - 0}{1.1009}[/tex]

[tex]t = 4.54[/tex]

Since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.

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Answer:

C. x = 27

Step-by-step explanation:

To solve we must undo what is being done to the variable. It is being modified in several ways in this equation so we must do the opposites of each step to both sides of the equation.

1. 1/3x + 9 = 7 + 11

2. 1/3x = 18 - 9

3. (1/3x) * 3 = 9 * 3

4. x = 27

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