Nicole has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. There is a combined total of 980 cans and bottles in her truck. Let x be the number of 14 -ounce cans in her truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in her truck.

1) The reflection image of figure 1 with respect to line m is figure 2.

2) The  pair of figures for which the second figure a translation image of the first is: Figures 1 and 3

How to find the transformation?

There are different types of transformation such as:

Translation

Rotation

Reflection

Dilation

1) The reflection transformation is a mirror image of the original image.

Thus, the reflection image of figure 1 with respect to line m is figure 2.

2) The  pair of figures for which the second figure a translation image of the first is:

Figures 1 and 3

Answer:

GLH is congruent to JLK as the quadrilateral is a parallelogram,

KJ = GH OR HJ = GK

GL = LJ OR. HL = LK

triangle JKG = GHJ

triangle HGK = KJH

Answer:

A parallelogram has two pairs of opposite parallel congruent sides.

Given :

Quadrilateral GKJH is a parallelogram,

To prove :

Δ GLH ≅ Δ JLK

Proof :

          Statement                                     Reason

1.   GH ║ KJ                                      Definition of parallelogram

2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ     Alternate interior angle theorem

3. GH ≅ KJ                                        Definition of parallelogram

4.  Δ GLH ≅ Δ JLK                            ASA postulate of congruence

Hence, proved...

Answer:

amount of total cash payment is $5450

Step-by-step explanation:

Given data

amount = $15000

principal = $5000

rate = 3% = 0.03

to find out

the amount of total cash payment

solution

we know according to question is Each yearly installment will include both principal repayment of​ $5,000 and interest payment for the preceding​ one-year period

so first we calculate interest i.e.

interest = rate × amount

interest = 0.03 × 15000

interest = 450

so interest is $450 for 1 year

now we calculate the amount of total cash payment i.e.

interest + principal

so the amount of total cash payment = 450 +5000 = 5450

amount of total cash payment is $5450

Mandy will make total cash payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.

Further explanation:

Mandy issued a 3% long-term notes payable for [tex]\$\text{ }15000[/tex] over a 3-year term in [tex]\$\text{ }5000[/tex] principal installments on March 1 each year.

Then the interest payment for the first year will apply on total amount of [tex]\$\text{ }15000[/tex].

The formula for simple interest at principal value [tex]P[/tex] and rate percentage of [tex]R[/tex] in the time of [tex]T[/tex] years is,

[tex]\fbox{\begin{minispace}\\ \math{I}=\dfrac{P\times R\times T}{100}\\\end{minispace}}[/tex]

So, the interest amount payable at the end of one year is calculated as,

[tex]I=\dfrac{15000\times 3\times 1}{100}\\I=150\times 3\\I=450[/tex]

The total cash payment to be done by Mandy after a year on March 1, 2019, is the sum of the principal installment of [tex]\$\text{ }5000[/tex] and the interest applied on the total amount.

Hence the total cash payment is obtained as,

[tex]\fbox{\begin{minispace}\\\text{Total cash payment}=5000+450=5450\end{minispace}}[/tex]

Therefore, Mandy has to make a total payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.

Learn more:  

1. Linear equation https://brainly.com/question/1682776

2. Domain of the function https://brainly.com/question/3852778

3. Equation of circle https://brainly.com/question/1506955

Answer details  

Grade: High school  

Subject: Mathematics  

Chapter: Simple Interest

Keywords: installments, one year, Mandy, principal, long-term, payable, March 1, amount, total cash, total cash payments, each year, payments, simple interest, rate percentage, sum, total amount, time, interest applied.

Answer:

  $240

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

[tex]m=\dfrac{12,000+12,000rt}{12t}=\dfrac{12,000+12,000\cdot 0.04\cdot 5}{12\cdot 5}\\\\m=\dfrac{14,400}{60}=240[/tex]

Keri's monthly loan payment is $240 per month.

Answer: 300 per month

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A:

The solution of a system is not just the x coordinates; it is the whole coordinate pair that is the solution, where both x and y are the same.  Normally, when you have a system and are solving them simultaneously, you are looking for the point at which they are equal.  This is a very useful concept in business and finance, both in the home for personal information, and in the office setting where companies are.  Where the 2 equations intersect is a point where they are equal.  

Part B:

The graphs do not intersect right at a perfect integer of x.  Therefore, we will solve these equations simultaneously to solve first for x, then we will plug in x to solve for y.  Since we have the equations set to equal each other, we can solve for x by getting everything on one side of the equation and then setting it equal to 0.  

2 - x = 4x + 3 so

5x + 1 = 0.  Solving for x,

5x = -1 so

[tex]x=-\frac{1}{5}[/tex]

The y coordinate can be found by subbing in this value of x into either equation.  If y = 2 - x, and x = -1/5, then

y = 2 -(-1/5) and y = 2 + 1/5 and y = 10/5 + 1/5 gives us that y = 11/5

Thus, the coordinate pair that is the solution to that system is

[tex](-\frac{1}{5},\frac{11}{5})[/tex]

Part C:

You would solve the system graphically by graphing both lines on the same window.  However, since their intersection is not an integer pair, but are fractions, you would not be able to tell EXACTLY where they intersect.  From the graphing window, you would hit your 2nd button then "trace" which is in the row at the very top of the buttons below the window.  Then hit 5:  intersect.  You'll be back to your graph of the lines, and there will be a cursor blinking along the line you graphed under Y1.  Move the cursor til it is right over the intersection of the lines and hit "enter".  Then you'll be back to the graphs with a blinking cursor over the line you entered in Y2.  Move that cursor along the line til it is dead-center over the other point on the first line and hit "enter" again.  At the bottom, you will see the x and y coordinates that are the intersection of this system.

The solution of the inequality is:

                       [tex]x\leq 3[/tex]

We are given a inequality in terms of variable x as:

[tex]2(4+2x)\geq 5x+5[/tex]

Now we are asked to find the solution of the inequality i.e. we are asked to find the possible values of x such that the inequality holds true.

We may simplify this inequality as follows:

On using the distributive property of multiplication in the left hand side of the inequality we have:

[tex]2\times 4+2\times 2x\geq 5x+5\\\\i.e.\\\\8+4x\geq 5x+5\\\\i.e.\\\\8-5\geq 5x-4x\\\\i.e.\\\\x\leq 3[/tex]

The solution is:      [tex]x\leq 3[/tex]

Answer:

Option C.

Step-by-step explanation:

The given inequality is given as

2(4 + 2x) ≥ 5x + 5

8 + 4x ≥ 5x + 5 [Simplify the parenthesis by distributive law]

Subtract 5 from each side of the inequality

(8 + 4x) - 5 ≥ (5x + 5) - 5

3 + 4x ≥ 5x

subtract 4x from each side of the inequality

(4x + 3) - 4x ≥ 5x - 4x

3 ≥ x

Or x ≤ 3

Option C. x ≤ 3 is the correct option.

Answer:

D. A stratified sample because the population is divided into separate groups and each group is randomly sampled.

Step-by-step explanation:

The researcher plans to take a random sample of 100 recent graduates of public universities and 100 recent graduates of private universities.

Her method is stratified sampling. This is because she divided the selected samples in two groups and will conduct the survey group wise.

These groups are also called strata.

Final answer:

Cluster sampling is used in the researcher's study design by dividing the population into clusters and randomly selecting all members from chosen clusters that is option A is correct.

Explanation:

Cluster sampling is utilized in the researcher's study design. In cluster sampling, the population is divided into separate clusters, and all subjects from a randomly selected cluster are selected. This method is practical when the population is dispersed geographically, making simple random sampling challenging.

Answer:

15/2 x^2y - 5xy

Step-by-step explanation:

First find the area of the rectangle

A = l*w

   = 5xy * 2x

    10x^2y

The find the area of the triangle

A = 1/2 bh

   = 1/2 (5xy) (x+2)

   = 1/2((5x^2y + 10xy)

   = 5/2 x^2y +5xy

The shaded region is the area of the rectangle minus the area of the triangle

10x^2y -  (5/2 x^2y +5xy)

Distribute the minus sign

10x^2y -5/2 x^2y -5xy

Combining like terms by getting a common denominator

20/2x^2y -5/2 x^2y -5xy

15/2 x^2y - 5xy

A.) Yes. The input and output are both possible.

In this problem, a dentist sees patients each day to clean their teeth. So we represent this function as [tex]g(x)[/tex] where:

x: Represents the number of people who saw the dentist.

g(x): Represents the number of teeth cleaned.

So we are given a point that is solution to our function, which is [tex](20, 20)[/tex] but what does this point represent? This tells us that the dentist saw 20 patients and cleaned 20 teeth, that is, he cleaned an only teeth per patient. So this will make sense under the conditions that make it possible, for example, a volunteer dentist can see more people than a common dentist and it is likely that that volunteer person sees fewer teeth. However, it's very difficult that that dentist finds 20 people with an only tooth each. So this situation is possible, but not realistic in the real world.

Final answer:

To convert Fahrenheit (F) to Celsius (C), subtract 32 from the Fahrenheit value, then multiply by 5/9 to get the Celsius value; the formula is C = (5/9)(F - 32).

Explanation:

Converting Fahrenheit to Celsius

To solve the formula for converting temperature from degrees Fahrenheit (F) to degrees Celsius (C), we are given the formula F = (9/5)C + 32. The student needs to find the value of C. To do this, we'll follow these steps:

Isolate the term containing C by subtracting 32 from both sides of the equation, which gives us F - 32 = (9/5)C.

Then, to solve for C, multiply both sides of the equation by the reciprocal of (9/5), which is (5/9), resulting in (5/9)(F - 32) = C.

Therefore, the converted equation for Celsius is C = (5/9)(F - 32), which can be used to find the Celsius temperature corresponding to a given Fahrenheit temperature.

The quadratic equation 4x^2 - 4x - 7 = 0 is solved using the Quadratic Formula with coefficients a = 4, b = -4, c = -7. The correct solutions obtained are x = 1/2 + √2 and x = 1/2 - √2, corresponding to option (c).

To solve the quadratic equation 4x^2 - 4x - 7 = 0 using the Quadratic Formula, we first identify the coefficients: a = 4, b = -4, and c = -7.

The Quadratic Formula is given by:

x = √((-b ± √(b^2 - 4ac)) / (2a)).

Substitute the identified coefficients into the formula:

x = √(((-(-4) ± √((-4)^2 - 4(4)(-7))) / (2(4))).

Simplify the expression:

x = √(((4 ± √(16 + 112)) / 8),

x = √(((4 ± √(128)) / 8),

x = √((4 ± 8√2) / 8).

Simplify further:

x = 1/2 ± √2.

Therefore, the correct answers are:

x = 1/2 + √2 and x = 1/2 - √2,

which corresponds to option (c).

Answer:

a. 8.4 km  b. 20 km/hr or 20,000 m/hr

Step-by-step explanation:

This is your polynomial:

[tex]d(v)=.004v^2+.2v+6[/tex]

The important thing to realize is that d(v) is the distance it takes for the boat to stop.  That will come later, in part b. Besides that, we also need to remember that v is velocity, which is speed, in km/hr.

For part a. we are looking for d(v), the stopping distance, when v = 10.  That means that we will sub in a 10 for each v in the function and solve for d(v):

[tex]d(10)=.004(10)^2+.2(10)+6[/tex] so

d(10) = 8.4 km

Now comes the part I was referring to above.  Part b is asking us the speed of the boat if it takes 11.6 meters to stop.  If d(v) is the stopping distance, we sub 11.6 in for d(v) in the function:

[tex]11.6=.004v^2+.2v+6[/tex]

The only way w can solve this for velocity is to get everything on one side of the equals sign, set the polynomial equal to 0, then plug the values into the quadratic formula.  

[tex]0=.004v^2+.2v-5.6[/tex]

Plugging that into the quadratic formula gives you 2 values of velocity:

v = 20 km/hr and -70 km/hr

We all know that neither time nor distance in math will EVER be negative so we can discount the negative number.  However, I believe that you asked for the distance in meters, so 20 km/hr is the same as 20,000 m/hr.

[tex]\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_4&18\\ s_5&18r\\ s_6&18rr\\ &18r^2 \end{array}\qquad \qquad \stackrel{s_6}{8}=18r^2\implies \cfrac{8}{18}=r^2\implies \cfrac{4}{9}=r^2 \\\\\\ \sqrt{\cfrac{4}{9}}=r\implies \cfrac{\sqrt{4}}{\sqrt{9}}=r\implies \boxed{\cfrac{2}{3}=r} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=6\\ s_6=8\\ r=\frac{2}{3} \end{cases}\implies 8=s_1\left( \frac{2}{3} \right)^{6-1} \\\\\\ 8=s_1\left( \frac{2}{3} \right)^5\implies 8=s_1\cdot \cfrac{32}{243}\implies 8\cdot \cfrac{243}{32}=s_1\implies \boxed{\cfrac{243}{4}=s_1}[/tex]

Answer:

Step-by-step explanation:

a. We assume the appropriate equation for ballistic motion is ...

  h = -4.9t^2 +1

Then h = 0 when ...

  0 = -4.9t^2 +1

  49t^2 = 10 . . . . . add 4.9t^2, multply by 10

  7t = √10 . . . . . . . take the square root

  t = (√10)/7 . . . . . . divide by the coefficient of t

The marble will be in the air about (√10)/7 ≈ 0.451754 seconds.

__

b. The average velocity is the ratio of distance to time:

  v = (1 m)/((√10)/7 s) = 0.7√10 m/s ≈ 2.214 m/s

__

c. Under the influence of gravity, the velocity is linearly increasing over the time period, so its instantaneous value when the marble hits the ground will be twice the average value:

  When it hits, the marble's velocity is 1.4√10 m/s ≈ 4.427 m/s.

a. Monthly: $14,185.30 b. Daily: $14,185.50 c. Quarterly: $14,320.00 d. Weekly: $14,372.70.

To find the balance after 5 years with different compounding frequencies, we'll use the compound interest formula:

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

Where:

- [tex]\(A\)[/tex] is the amount of money accumulated after \(n\) years, including interest.

- [tex]\(P\)[/tex] is the principal amount (the initial amount of money).

- [tex]\(r\)[/tex] is the annual interest rate (in decimal).

- [tex]\(n\)[/tex] is the number of times that interest is compounded per year.

- [tex]\(t\)[/tex] is the time the money is invested for, in years.

Given:

- [tex]\(P = $10,000\)[/tex]

- [tex]\(r = 6.92\% = 0.0692\)[/tex]

Let's calculate each scenario:

a. Monthly compounding (12 times per year):

[tex]\[n = 12\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{12}\right)^{12 \times 5}\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{12}\right)^{60}\][/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times (1.005766)^{60}[/tex]

[tex]\[A \approx10000 \times 1.41853\][/tex]

b. Daily compounding (365 times per year):

[tex]\[n = 365\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{365}\right)^{365 \times 5}\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{365}\right)^{1825}\][/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times (1.000189)^{1825}[/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times 1.41855[/tex]

[tex]\[A[/tex] ≈ [tex]\$14,185.50\][/tex]

c. Quarterly compounding (4 times per year):

[tex]\[n = 4\][/tex]

[tex]\[A[/tex] = [tex]10000 \left(1 + \frac{0.0692}{4}\right)^{4 \times 5}[/tex]

[tex]\[A[/tex] = [tex]10000 \left(1 + \frac{0.0692}{4}\right)^{20}[/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times (1.0173)^{20}[/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times 1.432[/tex]

[tex]\[A[/tex] ≈ [tex]\$14,320.00[/tex]

d. Weekly compounding (52 times per year):

[tex]\[n = 52\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{52}\right)^{52 \times 5}\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{52}\right)^{260}\][/tex]

[tex]\[A \approx 10000 \times (1.0013308)^{260}\][/tex]

[tex]\[A \approx10000 \times 1.43727\][/tex]

[tex]\[A \approx \$14,372.70\][/tex]

So, after 5 years, the balances would be:

a. Monthly compounding: [tex]\$14,185.30[/tex]

b. Daily compounding: [tex]\$14,185.50[/tex]

c. Quarterly compounding: [tex]\$14,320.00[/tex]

d. Weekly compounding: [tex]\$14,372.70[/tex]

Answer:

The next two terms after a1 is

-6 and then 18

Step-by-step explanation:

Geometric sequence means your pattern for the terms is multiplication by the same number.

So a1 is the first term and r is your common ratio.

The common ratio is what you are multiplying by each time to figure out the next term.

So the geometric sequence goes like this:

a1 ,  a1*r , (a1*r)*r or a1*r^2 , a1*r^3 ,....

So anyways you have

first term a1=2

second term a2=2(-3)=-6

third term a3=-6(-3)=18

And so on...

Answer:

f(x) is an odd function and g(x) is an even function

Step-by-step explanation:

Even Function :

A function f(x) is said to be an even function if

f(-x) = f(x) for every value of x

Odd Function :

A Function is said to be an odd function if

f(-x)= -f(x)

Part a)

[tex]f(x)=x^3+x[/tex]

let us substitute x with -x

[tex]f(-x) = (-x)^3-x\\=-x \times -x \times -x\\=-x^3-x\\=-(x^3+x)\\=-f(x)[/tex]

Hence

f(-x)=-f(x)

There fore f(x) is an odd function

[tex]g(x)=x^2+1[/tex]

Substituting x with -x  we get

[tex]g(-x)=(-x)^2+1\\=-x \times -x+1\\=x^2+1\\=g(x)[/tex]

Hence g(-x)=g(x)

Therefore g(x) is an even Function.

Part b)

hf(x)=hx^3

Answer:

[tex]y = 6 + x[/tex]

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

Assuming that the value of y is the total number of flour used in the mixture, then we would need to add both types of flour in order to find the value of y. Since we do not know the amount of white flour used, we will be substituting it for the variable x.

[tex]y = 6 + x[/tex]

The Equation above is stating that 6 cups of whole wheat flour added to the amount of white flour will equal the total amount of flour in the mixture.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Hey There!

We'd distribute the negative sign first:

[tex]y + 7 = -x - 6[/tex]

Now, we'd have to isolate the variable y by subtracting seven in both sides:

[tex]y = -x - 13[/tex]

Replace y with f(x):

[tex]f(x) = -x - 13[/tex]

Our answer would be [tex]f(x) = -x - 13[/tex]

Answer:

f(x)-x-13

Step-by-step explanation:

Answer:

the area left to 51 on normal distribution curve

Step-by-step explanation:

we have to find the probability that at most 51 it means the probability of less than 51 . The probability of at most 51 or less than 51 on the normal distribution curve will be the area lest side of 51 for example if we have to find the are of at least 51 then the area on the normal distribution curve will be right of 51

so the answer will be the area left side of 51

When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. To find the probability that at most 51 households have a gas stove, we convert the binomial random variable to a standard normal random variable and find the area to the left of 51 on the normal curve, which is extremely close to 0.

When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. In this case, we want to find the probability that at most 51 households have a gas stove. To do this, we need to find the area to the left of 51 on the normal curve.

To find this probability, we use the standard normal distribution table or a calculator. We convert the binomial random variable to a standard normal random variable using the formula z = (x - np) / √(npq), where x is the number of households, n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, np = 500 * 0.2 = 100 and npq = 500 * 0.2 * 0.8 = 80. So, z = (51 - 100) / √80 ≈ -6.325.

Looking up this value in the standard normal distribution table, we find that the area to the left of -6.325 is extremely close to 0. Therefore, the probability that at most 51 households have a gas stove is approximately 0.

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Answer:

60060 different ways that teams can be chosen

Step-by-step explanation:

Given data

employees n  = 14

team = 3

each project employees

n(1) =  8

n(2) = 3

n(3) = 3

to find out

how many different ways can the teams be chosen

solution

we know according to question all employees work on a team so

select ways are = n! / n(1) ! × n(2) ! × n(3)     ....................1

here  n! = 14! = 14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1

and n(1)! = 8! =  8 ×7 ×6 ×5 ×4 × 3× 2× 1

n(2)! = 3! =  3× 2× 1

n(3)! = 3! =  3× 2× 1

so now put all these in equation 1 and we get

select ways are = (14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) / (8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) × ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  (14 × 13 ×12 ×11 ×10 ×9 ) / ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  2162160 / 36

select ways are = 60060

60060 different ways that teams can be chosen

Answer:

60060

Step-by-step explanation:

#copyright

Answer:

c. 172.54 pi cm^3

Step-by-step explanation:

i got it right on plato

Answer:

c. 172.54 pi cm^3

Step-by-step explanation:

PLATO

Answer:

A. Increase sample size

Step-by-step explanation:

From the formula for estimating the confidence level interval for the mean:

X - Z × s/sqrt n where; X = sample mean; Z = z value corresponding to 95%;

s = standard deviation and n = sample size

It is evident from the equation that the confidence interval for the mean is inversely proportional to the sample size (n), hence increasing the sample size will result in a reduced interval width.

Answer:

  θ = 38°

Step-by-step explanation:

The lower right triangle is congruent to the upper left triangle, so we have θ and 20° being the two acute angles in the triangle. The law of sines tells you ...

  sin(θ)/9 = sin(20°)/5

  sin(θ) = (9/5)sin(20°)

  θ = arcsin(9/5·sin(20°)) ≈ 38°

___

Another solution to the triangle is θ = 180° -38° = 142°. The diagram clearly shows θ as an acute angle, so we take this second solution to be extraneous.

Answer:

69 bpm

Step-by-step explanation:

Here we start out finding the z-score corresponding to the bottom 33% of the area under the standard normal curve.  Using the invNorm( function on a basic TI-83 Plus calculator, I found that the z-score associated with the upper end of the bottom 33% is -0.43073.

Next we use the formula for z score to determine the x value representing this woman's heart rate:

       x - mean                              x - 75 bpm

z = ----------------- = -0.43073 = --------------------

       std. dev.                                    15

Thus,  x - 75 = -0.43073(15) = -6.461, so x = 75 - 6.6461, or approx. 68.54, or (to the nearest integer), approx 69 bpm

Answer:

A. -3

Step-by-step explanation:

Answer:

Its undefined or D

Step-by-step explanation:

A undefined slope is something that is vertical or horizontal. The provided images explains it! Hope it helps!

Answer:

  18°

Step-by-step explanation:

The law of cosines tells you ...

  a² = b² + c² -2bc·cos(A)

Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.

  cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140

  A = arccos(133/140) ≈ 18.2° ≈ 18°

Answer:

0.0952  or 9.52%.

Step-by-step explanation:

The standard deviation = √(40,000) = 200.

Z-scores are  917 - 800  / 200 = 0.585 and

980 - 800 / 200 = 0.90..

From the tables the required probability =

0.81594 - 0.72072

= 0.09522 (answer).

The probability of the steer's weight falling between 917lbs and 980lbs can be determined by first calculating their respective z-scores based on given mean and variance. The difference in probabilities associated with these z-scores will give the desired probability.

In this case, we are dealing with a normal distribution which is important when we are considering mean and variance. To find the probability that the weight of the steer falls between 917lbs to 980lbs, we need to first convert these weights into z-scores, because a z-score helps us understand if a data point is typical or atypical within a distribution.

Z-score is given by z = (x - μ) / σ, where μ is the mean and σ is the standard deviation, which is the square root of variance. Given that the mean (μ) is 800lbs and variance is 40,000, the standard deviation (σ) is √40,000=200.

So, the z-scores for 917 and 980 lbs are z1 = (917 - 800) / 200 = 0.585 and z2 = (980 - 800) / 200 = 0.90 respectively.

The probability that the weight of a randomly selected steer is between 917lbs and 980lbs is the probability that the z-score is between 0.585 and 0.90. We can find these values using a z-table or statistical software. The difference between these probabilities will give us the probability of a steer's weight falling between 917 and 980 lbs.

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Answer:

b.

Step-by-step explanation:

First off, let's name these endpoints.  We will call them J(3, -2) and K(8, 0).  The point we are looking for that divides this into a 3:1 ratio let's call L.  We are looking for point L that divides segment JK into a 3:1 ratio.

A 3:1 ratio means that we need to divide JK into 3 + 1 equal parts, or 4.  Point L divides JK into a 3:1 ratio.  We need to find the constant of proportionality, k, that can be used in the formula to find the coordinates of L.  k is found by putting the numerator of the 3/1 ratio over the sum of the numerator and denominator.  Therefore, our k value is 3/4.

Now we need to find the slope of the given segment.

[tex]m=\frac{0-(-2)}{8-3}=\frac{2}{5}[/tex]

The coordinates of L can be found in this formula:

[tex]L(x, y)=(x_{1}+k(run),x_{2}+k(rise))[/tex]

Filling in:

[tex]L(x,y)=(3+\frac{3}{4}(5),-2+\frac{3}4}(2))[/tex]

Simplifying we have:

[tex]L(x,y)=(3+\frac{15}{4},-2+\frac{6}{4})[/tex]

Simplifying further:

[tex]L(x,y)=(\frac{12}{4}+\frac{15}{4},\frac{-8}{4} +\frac{6}{4})[/tex]

And we have the coordinates of L to be

[tex]L(x,y)=(\frac{27}{4},-\frac{1}{2})[/tex]

27/4 does divide to 6.75

[tex]\bf \textit{Sum to Product Identities} \\\\ cos(\alpha)+cos(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ cos(\alpha)-cos(\beta)=-2sin\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{cos(4\theta )+cos(2\theta )}{cos(4\theta )-cos(2\theta )}\implies \cfrac{2cos\left( \frac{4\theta +2\theta }{2} \right)cos\left( \frac{4\theta -2\theta }{2} \right)}{-2sin\left( \frac{4\theta +2\theta }{2} \right)sin\left( \frac{4\theta -2\theta }{2} \right)} \implies \cfrac{cos\left( \frac{6\theta }{2} \right)cos\left( \frac{2\theta }{2} \right)}{-sin\left( \frac{6\theta }{2} \right)sin\left( \frac{2\theta }{2} \right)}[/tex]

[tex]\bf \cfrac{cos(3\theta )cos(\theta )}{-sin(3\theta )sin(\theta )}\implies -\cfrac{cos(3\theta )}{sin(3\theta )}\cdot \cfrac{cos(\theta )}{sin(\theta )}\implies -cot(3\theta )cot(\theta )[/tex]

The given expression is:

(cos 4θ + cos 2θ) / (cos 4θ - cos 2θ)

To simplify this expression, we can use the formula cot A sin C + cos B cos C = cot A sin B. Applying this formula gives us -cot 3θ cot θ as the simplified form of the expression.