After four years in college, Josie owes $9500 in student loans. The interest rate on the federal loans is 11% and the rate on the private bank loans is 7%. The total interest she owed for one year was $901.00. What is the amount of each loan?

Answer:

  32x^3

Step-by-step explanation:

  [tex](2x+1)^4=(2x)^4+4(2x)^3(1)+6(2x)^2(1)^2+4(2x)(1)^3+(1)^4\\\\=16x^4 +\boxed{32x^3} +24x^2+8x+1[/tex]

_____

Comment on the question

It is helpful if you designate exponents with a caret (^). We expect the expanded form of (2x+1)4 to be 8x+4. (2x+1)^4 is entirely different. Similarly, 8x3 = 24x, whereas 8x^3 is something else.

32x^3

It is helpful if you designate exponents with a caret (^). We expect the expanded form of (2x+1)4 to be 8x+4. (2x+1)^4 is entirely different. Similarly, 8x3 = 24x, is the answer to the question

how to read pathater in himdi

Answer:

241 minutes

Step-by-step explanation:

Given:

Height of cylinder, h = 15 ft

Radius, r = [tex] \frac{d}{2} = \frac{12}{2} = 6 [/tex] (both cylinder and cone have same radius)

Let's find the height of cone, since angle of inclination = 25°C.

[tex] tan25 = \frac{h}{r} [/tex]

[tex] h = r tan25 [/tex]

[tex] h = 6 tan25 = 2.8 [/tex]

Height of cone = 2.8 ft

Let's find colume of tower.

Volume = Volume of cone + volume of cylinder.

Formula for volume of cone = ⅓πr²h

Volume of cylinder = πr²h

Therefore,

V = ⅓πr²h + πr²h

V = ⅓π*6²*2.8 + π*6²*15

V = 105.558 + 1696.46

V = 1802.02 ft³

Since volume is 1802.02 ft³, and there are 7.48 gallons in a cubic ft, the total gallon =

1802.02 * 7.48 = 13479.11 gallons

Water is used at an average rate of 56 gallons per minute.

Amount if time to drain the water:

Total gallons / average rate

[tex] = \frac{13479.11}{56} = 240.698 [/tex]

≈ 241 minutes

Answer:

a) 10

b) 0.1 = 10%

Step-by-step explanation:

The combinations formula is used to solve this question, since the horses are chosen without replacement.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

a. Use this information to determine the number of possible samples (without replacement) of size 2 that can be obtained from the population of size 5.

Combinations of 2 objects from a set of 5. So

[tex]C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]

b. If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are:________

In this procedure, the samples are all equally as likely to be chosen.

So

1/10 = 0.1 = 10%

Answer:

(x+3)^2 + (y-4)^2 = 64

Step-by-step explanation:

We can write the equation of a circle as

(x-h)^2 + (y-k)^2 = r^2  where ( h-k) is the center and r is the radius

(x--3)^2 + (y-4)^2 = 8^2

(x+3)^2 + (y-4)^2 = 64

Answer:

[tex]\large \boxed{\text{60 s}}[/tex]

Step-by-step explanation:

Assume your graph looks like the one below.

1. Calculate the equation of the straight line

The slope-intercept equation for a straight line is

y = mx + b

where m is the slope of the line and b is the y-intercept.

The line passes through the points (0,2600) and (30, 2300)

(a) Calculate the slope of the line

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{2300 - 2600}{30 - 0}\\\\& = & \dfrac{-300}{30}\\\\& = & \text{-10 ft/s}\\\\\end{array}[/tex]

(b) Locate the y-intercept

The y-intercept is at 2600 ft

(c) Write the equation for the line

h = -10t + 2600

(d) Calculate the time to 2000 ft

[tex]\begin{array}{rcl}h & = & -10t + 2600\\2000 & = & -10t + 2600\\-600 & = & -10t\\t & = & \dfrac{-600}{-10}\\\\& = & \text{60 s}\\\end{array}\\[/tex]

Shelley will be at 2000 ft 60 s after opening the parachute.

Let the given line pass through the point that is [tex]\bold{(0,2600)\ \ and\ \ (20, 2400)}[/tex]

[tex]\therefore[/tex]

[tex]\to \bold{\frac{H-2400}{t-20}} \bold{= \frac{2600-2400}{0-20}}\\\\[/tex]

                [tex]\bold{=\frac{200}{-20} }\\\\ \bold{= -\frac{200}{20}}\\\\ \bold{= - 10}\\\\[/tex]

[tex]\to \bold{H-2400=-10t+200}\\\\\to \bold{H+10t=2400+200}\\\\\to \bold{H+10t=2600}\\\\\to \bold{H=2600-10t}\\\\[/tex]

Let

time (t) in second

Height (h) in feet

for [tex]\bold{\ H=2000\ feet\\}[/tex]

[tex]\to \bold{2000=2600-10t}\\\\\to \bold{10t = 2600- 2000}\\\\\to \bold{10t = 600}\\\\\to \bold{t=\frac{600}{10}}\\\\\to \bold{t= 60\ second}\\\\[/tex]

Learn more:

brainly.com/question/3012638

75g/400ml: Simplify per unit

÷ by bottom.

0.1875g/ml nearest hundredth

0.19g/ml

Answer:

7 school buses will be needed to take the children of Anderson school on a field trip

Step-by-step explanation:

number of children = 390

We are told that each bus carries 60 people

Therefore

60 people = 1 bus

1 person = (1 ÷ 60)

∴ 390 people = [tex]\frac{1}{60}[/tex] × [tex]\frac{390}{1}[/tex] = [tex]\frac{390}{60}[/tex] =  6.5 (approx. 7 buses)

Therefore, 7 school buses will be needed to take the children of Anderson school on a field trip, but the seventh bus will be half-filled with children.

Answer:

Step-by-step explanation:

Given the expression 18x²-8, the best method to factor this expression are Factor by grouping and by factoring out the greatest common factor.

Step 1: Factor by grouping

Factor by grouping is done by creating a smaller groups from each term in the expression as shown;

18x² = (2*3*3* x²)

8 =  2*2*2

18x²-8 = (2*3*3* x²) - (2*2*2)

Step 2: Then we will factor out the greatest common factor (GCF) in the expression. GCF is the value that is common to both terms of the expression. The only common term in this case is 2.

Answer:

Factor out the GCF, and Use the difference of squares rule.

Step-by-step explanation:

The terms in the expression have a common factor of 2, so the first step is to factor out the GCF:

2(9x2 − 4).

Then, factor the remaining expression using the difference of squares rule.

Answer:

= 5x-5y

Step-by-step explanation:

Multiply 5to x and y

Answer:

5x-5y

Step-by-step explanation:

multiply both the terms x and y by 5.

Answer:

225 feet below sea level (or -225 feet)

Step-by-step explanation:

My apologies in advance if this does not format the way its supposed to. The way I did it includes arrows and may work best on a computer.

Problem: A submarine that is 245 feet below sea level descends 83 feet and then ascends 103 feet. Which represents the location of the submarine compared to sea level.

Math: Ok, so we know that whenever something descends, that means it is going down, so let's use a negative sign. These means when something ascends, it goes up. Let's use a positive sign here. Also, note the fact that we start 245 feet below sea level. This means we should start at -245.

Now, using the data we have, let's create a math problem.

A submarine that is 245 feet below sea level descends 83 feet and then ascends 103 feet. Which represents the location of the submarine compared to sea level.

-245      <---- beginning level

-83        <---- the submarine descends

+103      <---- the submarine ascends

_______

?

So grab a calculator to do this part, or do it on your own. Once you finish, plug in the answer.

-245                                                   -245

-83                                                     -83

+103                             --------------->  +103

______                                          ________

?                                                      -225 feet

So as you can see, the final answer would be -225 feet or 225 feet below sea level.

Hope this helped! Have a great day!

Answer:

There is no graph to find an inequality on...

Step-by-step explanation:

Answer:

these are my answers:

8-5=3

2÷6=3

5-2=3

2+1=3

3÷9=3

Answer:

  9 +6 +1 -8 -5 = 3

Step-by-step explanation:

There are numerous possibilities. Among them are ...

  9 +6 +1 -8 -5 = 3

  (9-5)·1·6/8 = 3

  (9·8)/(6·(5-1)) = 3

Answer:

If both sides are integers, one side will be 4 feet and the other will be 6 feet. The other solution is the symmetrical solution (4 feet instead of 6 feet, and 6 feet instead of 4 feet).

Step-by-step explanation:

We have a rectangular blanket, that has a diagonal that measures h=7.21 feet.

The two sides of the rectangle a and b can be related to the diagonal h by the Pithagorean theorem:

[tex]a^2+b^2=h^2[/tex]

Then, we can express one side in function of the other as:

[tex]a^2+b^2=h^2\\\\a^2=h^2-b^2\\\\a=\sqrt{h^2-b^2}=\sqrt{7.21-b^2}=\sqrt{52-b^2}[/tex]

Then, if we define b, we get the value of a that satisfies the equation.

A graph of values of a and b is attached.

If both side a and b are integers, we can see in the graph that are only two solutions: (b=4, a=6) and (a=4, b=6).

Answer:

x^2 -2x = 4x+1

2x^2 +12x = 0

9x^2 +6x -3=0

Step-by-step explanation:

A quadratic equation has the highest power of x being squared

x^2 -2x = 4x+1

2x^2 +12x = 0

9x^2 +6x -3=0

These are all quadratic equations

Using only the trig ratios of 45 and 60 degrees, we use angle-sum to compute [tex]\tan 105^\circ=\tan(60^\circ+45^\circ)=\frac{\tan 60^\circ+\tan 45^\circ}{1-\tan 60^\circ\tan 45^\circ}=\frac{\sqrt{3}+1}{1-\sqrt{3}}=-2-\sqrt{3},[/tex] so [tex]\cot 105^\circ=\frac{1}{\tan 105^\circ}=-2+\sqrt{3}[/tex] and [tex]\tan 105^\circ-\cot105^\circ=\boxed{-2\sqrt{3}}.[/tex]

Answer:I believe the answer is -1,-4 lies on the graph

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

5 or more add one more

4 or less let it rest

so it becomes 1000

Answer:

[tex]\frac{98000 ft}{1 second}\times \frac{? second}{1 hour}\times \frac{1 mile}{5280 ft}[/tex]

Step-by-step explanation:

If you cancel out the same unit, one from numerator and one from denominator, you will get mile/ hour as asked. The leftover is doing your math.

You finish your work!!

I don't care about the evaluation. I do care if you can work by yourself and understand the work

Answer:

Step-by-step explanation:

Hello!

This is an example of an ANOVA hypothesis test, where you'll compare the population means of the number of broken Mimbres in three different excavation sites.

The variable of interest is

Y: Number of broken pieces of prehistoric Native American clay vessels, called Mimbres in an excavation site.

Factor: Site

Treatments: 1, 2, 3

You are asked to identify the level of significance of the test. This value is the probability of committing Type I error, that is, when you fail to reject a false null hypothesis and is always represented with the Greek letter alpha "α"

This level is determined by the researcher when he is designing the experiment and statistical analysis. Normally you'd want this level to be as small as possible to be sure you didn't commit any mistake when deciding over the hypotheses.

The mos common values are 0.01, 0.05 or 0.1 and it can also be expressed as percentages 1%, 5% or 10%. Having a probability of making a mistake greater than 10% is too high so normally you would not encounter significance levels greater than 10%

With this in mind options b. 1% and c. 5% are valid values for α.

Have a nice day!

Next time check that all the information is copied!

Answer:

The expected number of people that lives in rural areas and is in favor of continuing using daylight savings time is 287.

Step-by-step explanation:

Hello!

There were 1285 residents from rural and urban areas surveyed about their opinion about using savings time. There are two variables of interest:

X₁: Area where the resident lives, categorized: "Rural area", "Urban area".

X₂: Opinion about using daylight savings time, categorized: "Stop", "Continue".

To know how many people who live in a rural area would you expect to be in favor of continuing to use daylight savings time, you have to calculate the expected frequency for that cell (See table in attachment)

The formula to calculate the expected frequencies is:

[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]

i: categories in rows i=1, 2

j: categories in columns j= 1, 2

Oi.: total observations for the i-row

O.j: total observations for the j-row

The category "rural" is in the first row, so its marginal is symbolized O₁.

The category "Continue" is in the second column, so its marginal is symbolized O.₂

The expected frequency for the people that live n rural areas and is in favor of continuing using daylight savings time is:

[tex]E_{12}= \frac{O_{1.}*O.2}{n}= \frac{622*591}{1285} = 286.07= 287[/tex]

I hope this helps!

Solution,

Diameter (d)=24 cm

Radius (r)=24/2 =12 cm

Circumference of circle= 2 pi r

=2*3.14*12

= 75.36 cm

Hope it helps

Good luck on your assignment

Answer:

[tex]c = 75.36cm[/tex]

Step-by-step explanation:

[tex]d = 2r \\ 24 = 2r \\ \frac{24}{2} = \frac{2r}{2} \\ r = 12cm[/tex]

[tex]circumference \\ = 2\pi \: r \\ = 2 \times 3.14 \times 12 \\ = 75.36cm[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

25

Step-by-step explanation:

Answer:

B and C

Step-by-step explanation:

AP = BP

OC = OD

Answer:

89

Step-by-step explanation:

2/3 times 267 is 178 after that you have to sub 178 from 267

Answer:

Option C) is correct

Step-by-step explanation:

Given: Endpoints of the diameter of the circle are A(-1, -2) and B(3,10)

To find: slope of the tangent drawn to the circle at point B

Solution:

Let [tex](x_1,y_1)=(-1,-2)\,,\,(x_2,y_2)=(3,10)[/tex]

Centre of the circle = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{-1+3}{2},\frac{-2+10}{2})=(1,4)[/tex]

Let [tex](h,k)=(1,4)[/tex]

Distance formula states that distance between points (a,b) and (c,d) is given by [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

Radius of the circle = Distance between points [tex](-1,-2)[/tex] and [tex](1,4)[/tex] = [tex]\sqrt{(1+1)^2+(4+2)^2}=\sqrt{4+36}=\sqrt{40}[/tex] units

Let r = [tex]\sqrt{40}[/tex] units

Equation of a circle is given by [tex](x-h)^2+(y-k)^2=r^2[/tex]

[tex](x-1)^2+(y-4)^2=\left ( \sqrt{40} \right )^2\\(x-1)^2+(y-4)^2=40[/tex]

Differentiate with respect to x

[tex]2(x-1)+2(y-4)\frac{\mathrm{d} y}{\mathrm{d} x}=0\\\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{1-x}{y-4}[/tex]

Put [tex](x,y)=(3,10)[/tex]

[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{1-3}{10-4}=\frac{-2}{6}=\frac{-1}{3}[/tex]

So,

slope of the tangent drawn to this circle at point B = [tex]\frac{-1}{3}[/tex]

Answer:

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.  

Step-by-step explanation:

Answer:

The answer is:

B. Both expression should be evaluated with one value if the final values of the expressions are the same then the two expressions must be equivalent

Answer:

a) $700+/-$18.07

Therefore,the 90% confidence interval (a,b)

= ($681.93, $718.07)

b) 4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $700

Standard deviation r = $65

Number of samples n = 35

Confidence interval = 90%

z(at 90% confidence) = 1.645

a. Develop a 90% confidence interval estimate for the mean audit cost.

Substituting the values we have;

$700+/-1.645($65/√35)

$700+/-1.645($10.98700531147)

$700+/-$18.07362373736

$700+/-$18.07

Therefore,the 90% confidence interval (a,b) = ($681.93, $718.07)

b) Since, $690 is contained between the 90% confidence interval of ($681.93, $718.07). It implies that the mean cost has not changed.

4. The interval contains historical data mean $690, which does not support the claim the mean cost has changed.

Answer:

a) The point estimate of the difference between the populations is Md=-0.14.

b) The margin of error at 95% confidence is 0.212.

c) The 95% confidence interval for the difference between means is (-0.352, 0.072).

Step-by-step explanation:

We have to calculate a 95% confidence interval for the difference between means.

The sample 1 (ships under 500 passengers), of size n1=20 has a mean of 6.93 and a standard deviation of 0.31.

The sample 2 (ships over 500 passengers), of size n2=55 has a mean of 7.07 and a standard deviation of 0.6.

The difference between sample means is Md=-0.14.

[tex]M_d=M_1-M_2=6.93-7.07=-0.14[/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{0.31^2}{20}+\dfrac{0.6^2}{55}}\\\\\\s_{M_d}=\sqrt{0.005+0.007}=\sqrt{0.011}=0.11[/tex]

The critical t-value for a 95% confidence interval is t=1.993.

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

[tex]MOE=t\cdot s_{M_d}=1.993 \cdot 0.11=0.212[/tex]

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

[tex]LL=M_d-t \cdot s_{M_d} = -0.14-0.212=-0.352\\\\UL=M_d+t \cdot s_{M_d} = -0.14+0.212=0.072[/tex]

The 95% confidence interval for the difference between means is (-0.352, 0.072).

Answer:

The probability of the length of a randomly selected Cane being between 360 and 370 cm  P(360 ≤X≤370)    = 0.6851

Step-by-step explanation:

step(i):-

Let 'X' be the random Normal variable

mean of the Population = 365.45

Standard deviation of the population = 4.9 cm

Let X₁ =  360

[tex]Z= \frac{x-mean}{S.D}= \frac{360-365.45}{4.9}[/tex]

Z₁ = -1.112

Let X₂ =  370

[tex]Z= \frac{x-mean}{S.D}= \frac{370-365.45}{4.9}[/tex]

Z₂ = 0.911

Step(ii):-

The probability of the length of a randomly selected Cane being between 360 and 370 cm

                  P(x₁≤x≤x₂) =    P(z₁≤Z≤z₂)

               P(360 ≤X≤370)   =    P(-1.11≤Z≤0.911)

                                     =    P(Z≤0.911)-P(Z≤-1.11)

                                     =   0.5 +A(0.911) - (0.5-A(1.11)

                                       =    0.5 +A(0.911) - 0.5+A(1.11)

                                      =     A(0.911) + A(1.11)

                                    =    0.3186 + 0.3665

                                     = 0.6851

The probability of the length of a randomly selected Cane being between 360 and 370 cm  P(360 ≤X≤370)    = 0.6851