Heating oil is to be poured at the constant rate of 4.5 gallons per minute into a 400-gallon tank that already contains 115 gallons of heating oil. What fraction of the tank's total capacity will be full in 30 minutes?

Answer:

[tex]-4\pm 3\sqrt{3}[/tex]

Step-by-step explanation:

[tex]3(x+4)^2-81=0 \\\\3(x^2+8x+16)-81=0 \\\\3x^2+24x+48-81=0 \\\\3x^2+24x-33=0 \\\\x=\dfrac{-24\pm\sqrt{24^2+4(3)(33)}}{2(3)}= \\\\\dfrac{-24\pm\sqrt{972}}{6}= \\\\\dfrac{-24\pm 18\sqrt{3}}{6}= \\\\-4\pm 3\sqrt{3}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

For military scholarship,

Mean, x1 = (850 + 925 + 980 + 1080 + 1200 + 1220 + 1240 + 1300)/8

x1 = 1099.375

Standard deviation = √(summation(x - mean)²/n

n1 = 8

Summation(x - mean)² = (850 - 1099.375)^2 + (925 - 1099.375)^2 + (980 - 1099.375)^2 + (1080 - 1099.375)^2 + (1200 - 1099.375)^2 + (1220 - 1099.375)^2 + (1240 - 1099.375)^2 + (1300 - 1099.375)^2 = 191921.875

Standard deviation, s1 = √(191921.875/8

s1 = 154.89

For no military scholarship,

Mean, x2 = (820 + 850 + 980 + 1010 + 1020 + 1080 + 1100 + 1120 + 1120 + 1200 + 1220 + 1330)/12

x2 = 1070.83

Standard deviation = √(summation(x - mean)²/n

n2 = 12

Summation(x - mean)² = (820 - 1070.83)^2 + (850 - 1070.83)^2 + (980 - 1070.83)^2 + (1010 - 1070.83)^2 + (1020 - 1070.83)^2 + (1080 - 1070.83)^2 + (1100 - 1070.83)^2 + (1120 - 1070.83)^2 + (1120 - 1070.83)^2 + (1200 - 1070.83)^2 + (1220 - 1070.83)^2 + (1330 - 1070.83)^2 = 238091.6668

Standard deviation, s2 = =√(238091.6668/12

s2 = 140.86

Part A)

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean score of students with military scholarship and μ2 be the mean score of students without military scholarship.

The random variable is μ1 - μ2 = difference in the mean score between students with military scholarship and without military scholarship

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (1099.375 - 1070.83)/√(154.89²/8 + 140.86²/12)

t = 0.42

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [154.89²/8 + 140.86²/12]²/[(1/8 - 1)(154.89²/8)² + (1/12 - 1)(140.86²/12)²] = 21644133.914878543/1533280.3458504018

df = 14

We would determine the probability value from the t test calculator. It becomes

p value = 0.68

Since alpha, 0.05 < than the p value, 0.68, then we would fail to reject the null hypothesis. Therefore, at a significance level of 5%, these data do not provide convincing evidence of a difference in SAT scores between students with and without a military scholarship

Part B)

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (8 - 1) + (12 - 1) = 18

z = 2.101

x1 - x2 = 1099.375 - 1070.83 = 28.545

Margin of error = 2.101√(154.89²/8 + 140.86²/12) = 143.3

The 95% confidence interval is 28.545 ± 143.3

Answer: C

Step-by-step explanation:

Since the sides are marked with the little lines, you know they are congruent with each other. Since the sides are congruent, you know the hypotenuse will be congruent.

You can argue that these triangles are similar, but the difference is that similar triangles are the same shape, but not the same size. These triangles are congruent because they are the same size and shape. Therefore, the hypotenuse is congruent.

Answer: student tickets = 208

Adult tickets = 97

Step-by-step explanation:

x + y = 305

x = 305 - y

5x + y = 693

Substituting

5 (305 - y) + y = 693

1525 - 5y + y = 693

-4y = -832

y = 832 / 4 = 208

Answer:

3 x^2 y^2

Step-by-step explanation:

Simplify the following:

3 x y x y

3 x y x y = 3 x^2 y^2:

Answer: 3 x^2 y^2

Answer:

Step-by-step explanation:

We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]

Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

In our case, a = 1, b = -4 and c =2. Then the solutions are

[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]

[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]

We have that x = u-1. So the original solutions are

[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]

[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]

Answer: x+4

Step-by-step explanation: part one- x+4

Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4

Answer:

B

Step-by-step explanation:

OP = OQ

Answer:

B

Step-by-step explanation:

Look at the shape closely observe the following the imaginary lines;

OC = OA , OB = OD {these is the raduis of the circle;

note also line CQ = CD { the perpendicular line bisects line CD in two equal halves;

Similarly ;

note also line AP= PB { the perpendicular line bisects line OP in two equal halves}

Hence;

OP is congruent to the OQ

In maths we say something is congruent when they are the same shape and have same angles but we are allowed to flip it's side.

Answer:

Step-by-step explanation:

hello

from 4x-y=8 we can say that y = 4x-8

we substitute in the first equation to get

5x + 4 (4x-8) = 10

then

5x + 16 x -32 = 10

<=> 21x = 32+10=42

<=> x = 42/21 = 2

and then y = 8-8=0

don t hesitate if you need any further explanation

thanks

Answer: x = 2, y = 0 or (2 , 0)

Step-by-step explanation:

Solving using substitution is where you solve for a variable in one of the two equations in the system then plug it into the other.

For an easier plug in we can take the second equation. 4x-y = 8.

From here we need to isolate the y variable which is easier to isolate than x, in my opinion.

Subtract the 4x over.

-y = 8-4x

Now divide by a -1 so y is positive.

y= -8 + 4x

Now plug this in for y in the other equation.

5x + 4(-8 + 4x) = 10

Distribute the 4.

5x - 32 + 16x = 10

Combine like terms

21x - 32 = 10

Add the 32.

21x = 42

Divide by 21.

x = 2

Now that we have solved for one variable we can plug this into either equation and solve for the other.

I will plug it into the second equation.

4(2) - y = 8

Simplify.

8 - y = 8

Subtract 8.

-y = 0

Divide by -1.

y = 0

So the x and y values are.

x = 2

y = 0

Answer:

14.50 cm  

Step-by-step explanation:

The Midsegment Theorem states that the midsegment connecting the two sides of a triangle is parallel to the third side, and its length is half that of the third side.  

Thus, ∆XYZ  is similar to ∆QRS with a scale factor of 2.

Also, the perimeter of ∆XYZ  is twice that of ∆QRS.

For ∆QRS, P = 2.93 cm + 2.04 cm + 2.28 cm = 7.25 cm

∴ The perimeter of ∆XYZ = 2 × 7.25 cm =14.50 cm

The Perimeter of triangle WXY is 14.5cm

The formula for calculating the perimeter of the triangle WXY is given as:

Perimeter of triangle WXY = XY + YZ + XY

From the given triangle;

Also,

Perimeter of triangle WXY = 2QR + 2QS + 2RS

Perimeter of triangle WXY = 2(2.93) + 2(2.28) + 2(2.04)

Perimeter of triangle WXY = 5.86 + 4.56 + 4.08

Perimeter of triangle WXY = 14.5cm

Hence the Perimeter of triangle WXY is 14.5cm

Learn more on perimeter of triangles here:  https://brainly.com/question/24382052

Answer:

12.5 hours

Step-by-step explanation:

The data which represents the battery life, in hours, experienced by six users is given below:

10 14 14 16 13 8

To determine the point estimate for the web browsing battery life of the iPad, we find the mean number of hours.

[tex]Mean=\dfrac{10+14+14+16+13+8}{6} \\\\=\dfrac{75}{6} \\\\=12.5[/tex]

The point estimate for the web browsing battery life of the iPad is: 12.5 hours

Answer:

i

Step-by-step explanation:

It's imaginary, or it can also be referred to as i.

Answer:

y =34

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

63+ 2y+ y+15 = 180

Combine like terms

78+ 3y = 180

Subtract 78 from each side

78+3y-78 = 180-78

3y = 102

Divide each side by 3

3y/3 = 102/3

y =34

Answer:

[tex]y = 34[/tex]

Step-by-step explanation:

Sum of the angles in a triangle is 180 degrees

[tex]2y + 63 + y + 15 = 180 \\ 3y + 63 + 15= 180 \\ 3y +7 8 = 180 \\ 3y = 180 - 78 \\ 3y =10 2 \\ \frac{3y}{3} = \frac{102}{3} \\ y = 34 [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer: See below

Step-by-step explanation:

–2(3x – 1) = –6x – 1

       -6x + 2 = -6x - 1 (IMPOSSIBLE, ZERO)

2(3x – 1) = 6x – 2

      6x - 2 = 6x - 2 (INFINITE)

2(3x – 1) = –6x – 2

      6x - 2 = -6x - 2 (ONE, x can be the number 0)

Answer:

s must be 21 and r is 20

Step-by-step explanation:

Represent the two numbers using variables r and s.

Then r + s = 41, and r = s - 1

Substituting the 2nd equation for r into the first equation, we get:

s - 1 + s = 41, or 2s = 42.  Then s must be 21 and r is 20.

Answer:

The answer depends on the shape of the trapezoid...

Step-by-step explanation:

A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. (trapezium)

Area = (a+b/2) * h

IF the sides are a = 3 ,b = 3 and height  = 4

THEREFORE:

(3+3/2) * 4

6/2 * 4

3 * 4

12

Hope it helped.... Please mark as brainliest..thanks!!!

Answer:

14.69% of men are SHORTER than 67 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches.

This means that [tex]\mu = 69.8, \sigma = 2.67[/tex]

What percentage of men are SHORTER than 67 inches

This is the pvalue of Z when X = 67. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{67 - 69.8}{2.67}[/tex]

[tex]Z = -1.05[/tex]

[tex]Z = -1.05[/tex] has a pvalue of 0.1469

14.69% of men are SHORTER than 67 inches

Answer:

[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.

Step-by-step explanation:

Information given

[tex]\bar X=98.2[/tex] represent the sample mean

[tex]\sigma=0.62[/tex] represent the population standard deviation

[tex]n=60[/tex] sample size  

[tex]\mu_o =98.6[/tex] represent the value that we want to test

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the true mean is equal to 98.6 F, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 98.6[/tex]  

Alternative hypothesis:[tex]\mu \neq 98.6[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

The degrees of freedom, on this case:  

[tex]df=n-1=60-1=59[/tex]  

The p value would be given by:

[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.

Answer:

153

Step-by-step explanation:

Answer:

= 180 yd^3

Step-by-step explanation:

The volume of a triangle prism is

V= Bh where B is the area of the base

B = area of the triangle

   = 1/2 *8* 5

    = 20 yd^2

V = 20 yd^2 * 9 yd

  = 180 yd^3

Answer:

$5350

Step-by-step explanation:

see attachment

Answer:

Its 53.50

Step-by-step explanation:

Answer:

24 g

Step-by-step explanation:

We first find the mass of 24 % alcohol in 400 g of hand sanitizer. Let x be the mass of alcohol. So, x/400 × 100 % = 24 %

x/400 = 0.24

x = 0.24 × 400

  = 96 g

The mass of the other chemicals is thus 400 g - 96 g = 304 g

We now find the mass of 30 % alcohol in 400 g of hand sanitizer. Let y be the mass of alcohol. So, y/400 × 100 % = 30 %

y/400 = 0.30

y = 0.30 × 400

  = 120 g

The mass of the other chemicals is thus 400 g - 120 g = 280 g

The mass of other chemicals that needs to be evaporated is thus 304 g - 280 g = 24 g

Answer:

648

Step-by-step explanation:

Number of Assaults, n(A)=430

Number of Robberies, n(R)=146

Number of Drug Sales Offenses, n(D)=131

Number involved in both assault and robbery= [tex]n(A\cap R)=26[/tex]

Number involved in both assault and drug sales= [tex]n(A\cap D)=33[/tex]

Therefore, to find the greatest possible number of offenders for May who satisfy these statistics, we remove the number of those who were involved in more than one crime.

This gives us:

[tex]=n(A)+n(R)+n(D)-n(A\cap R)-n(A\cap D)\\=430+146+131-26-33\\=648[/tex]

The greatest possible numbers of offenders in May is 648.

Answer:

0.35

Step-by-step explanation:

.5x.7

Answer:

43°

Step-by-step explanation:

Answer:

a) Residents of San Antonia, Texas

b) Response variable

c) Explanatory variable

d) Observational study

e) Response bias

f) The appropriate scope of interest is the " relationship between age and the weekly average usage of local parks in San Antonia"

Step-by-step explanation:

a) In this study, the objects or entities on which observation is done are the residents of San Antonia, hence they are the observational units.

b) In this observation, the number of visits per week is the response variable because it is the outcome of the observation. It is a dependent variable that varies due to variation in the ages.

c) Age is the variable that helps to predict the average number of visits to the park, it can then be called the predictor variable. It is independent of any external variable.

d) This is an observational study because it is meant to observe the relationship between the ages and the average number of visits to the park per week. The variables are not randomly assigned.

e ) The type of bias that is most concerning in this study is response bias. This is because it is a paper survey and their can be invalid responses either due to unfaithfulness or ignorance of the respondents.

f) The appropriate scope of the inference in this study is the relationship between the ages and the weekly average usage of local parks in San Antonia.

Answer:

D. 6x-4 9/10<= 18 1/8

Step-by-step explanation:

Sorry I'm a little late :(

Answer:

x = 6

Step-by-step explanation:

Assuming these rectangles are similar, you can set up a proportion like this:

[tex]\frac{15}{10} =\frac{x}{4}[/tex]

→Cross multiply:

[tex]\frac{60}{10x}[/tex]

→Divide 60 by 10:

x = 6

Answer:

  10

Step-by-step explanation:

Using the distance formula, the distance is ...

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((-2-4)^2 +(-4-4)^2) = √((-6)^2 +(-8)^2) = √(36 +64)

  d = √100 = 10

The distance between the two points is 10 units.

Answer:

1.12

2.85

3.60

Step-by-step explanation:

1.

if m = 12 you solve by dividing 144/12

144/12 = 12

2.

when m = 11 you solve by computing 7(11) + 8

7(11) = 77 so you solve from there 77 + 8 which equals 85

3.

When g = 4 you solve my multiplying 15(4)

15(4) = 60

Answer:

first question: 12

second question: 85

third question: 60

Step-by-step explanation:

first question: plug in 12 for m and you would get 144/12 which equals 12.

Second question: plug in 11 for m and you have 7(11) + 8.

77+8 = 85

third question: plug in 4 for g and you have 15(4)

15 x 4 = 60.

*parentheses mean multiplication when next to a number

ex: 7(11)

not ex: 3 + (2/3) since it isn't directly next to the first number, instead its adding

Answer:

The set of all output values of a function. Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then the range is {1,4,9,...}