To make a batch of salad dressing, combine 9 tablespoons of oil with 18 tablespoons of vinegar. How many tablespoons of vinegar are needed for every tablespoon of oil?

Step-by-step explanation:

[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]

[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]

[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]

Question :

Required solution :

Here we would be considering L.H.S. and solving.

Identities as we know that,

By using the identities we gets,

[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]

Now, here we would be using the identity of square relations.

By using the identity we gets,

[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]

[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]

The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.

You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].

So let us take a look at the possible options.

Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.

Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.

So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].

Hope this helps :)

Answer:

First term a = 3

Sum of first 20 term = 440

Step-by-step explanation:

Given:

8th term of AP = 17

12th term of AP = 25

Find:

First term a

Sum of first 20 term

Computation:

8th term of AP = 17

a + 7d = 17 ....... EQ1

12th term of AP = 25

a + 11d = 25 ...... EQ2

From EQ1 and EQ2

4d = 8

d = 2

a + 7d = 17

a + 7(2) = 17

First term a = 3

Sum of first 20 term

Sn = [n/2][2a + (n-1)d]

S20 = [20/2][(2)(3) + (20-1)2]

S20 = [10][(6) + 38]

S20 = [10][44]

S20 = 440

Sum of first 20 term = 440

Answer:

The answer is "".

Step-by-step explanation:

Please find the complete question in the attached file.

We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval

[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]

Using formula:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]  

The probability that perhaps the mean shells length of the sample is over 4.03 pounds is

[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]

Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution

[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]

the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]

Answer: A (x+1)(x+2)(x+5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3

Answer:

D. 65°

Step-by-step explanation:

It is so because the triangle is isosceles, two identical sides and two equal angles.

9514 1404 393

Answer:

  (b)  -1

Step-by-step explanation:

The graph shows the difference between the two expressions is zero at x=-1.

__

Additional comment

For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.

Answer:

The answer is b: -1

Step-by-step explanation:

good luck!

If 6ˣ = 5, then

(6ˣ)³ = 6³ˣ = 5³ = 125,

and

6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500

Given:

The heights (in inches) of students in a third-grade class are:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

To find:

The median height.

Solution:

The given data set is:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

Arrange the data set in ascending order.

37, 39, 40, 42, 42, 45, 47, 47, 48, 48, 48, 49, 49, 51, 52, 53

Here, the number of observations is 16. So, the median of the given data set is:

[tex]Median=\dfrac{\dfrac{n}{2}\text{th term}+\left(\dfrac{n}{2}+1\right)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{\dfrac{16}{2}\text{th term}+\left(\dfrac{16}{2}+1\right)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{8\text{th term}+9\text{th term}}{2}[/tex]

[tex]Median=\dfrac{47+48}{2}[/tex]

[tex]Median=\dfrac{95}{2}[/tex]

[tex]Median=47.5[/tex]

Therefore, the median height of the students is 47.5 inches.

Answer:

2x + 1.

Step-by-step explanation:

Average = sum of the expression / number of expressions

= [(4 - 2x) + (-7 - 3x) + (11x + 6)] / 3

= (-2x - 3x + 11x + 4 - 7 + 6) / 3

= 6x + 3 / 3

= 2x + 1

Answer:

2x+1

Step-by-step explanation:

(4-2x), (-7-3x),(11x+6)

Add the three expressions

(4-2x)+ (-7-3x)+(11x+6)

Combine like terms

-2x-3x+11x+4-7+6

6x+3

Divide by the number of expressions which was 3

(6x+3)/3

2x+1

The average is 2x+1

Answer:

25

Step-by-step explanation:

40/24 = x/15

x = 15•40/24

x = 25

Answer:

25

Step-by-step explanation:

just use the facts that both triangles are similar

9514 1404 393

Answer:

  x = 7

  y = 5

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

__

For a=-j and b=7,

  (-j)^-7 = 1/(-j)^7   ⇒   x = 7

For a=k and b=-5,

  k^-5 = 1/k^5   ⇒   y = 5

Given:

Distance traveled by sprinter = 200 m

Time taken by sprinter = 20.03 seconds

To find:

The sprinter's average speed rounded to 4 sf.

Solution:

We know that,

[tex]\text{Average speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

It is given that, the sprinter travels a distance of 200 m in a time of 20.03 seconds.

[tex]\text{Average speed}=\dfrac{200}{20.03}[/tex]

[tex]\text{Average speed}=9.985022466[/tex]

[tex]\text{Average speed}\approx 9.985[/tex]

Therefore, the average speed of the sprinter is 9.985 m/sec.

Answer:

9.985

Step-by-step explanation:

Answer:

X(-12,-7)

Step-by-step explanation:

This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.

Answer:

1 / 9

Step-by-step explanation:

Choosing with replacement means that the first draw from the lot is replaced before another is picked '.

Number of Blue marbles = 2

Number of red marbles = 4

Total number of marbles = (2 + 4) = 6

Probability = required outcome / Total possible outcomes

1st draw :

Probability of picking blue = 2 / 6 = 1 /3

2nd draw :

Probability of picking blue = 2 / 6 = 1/3

P(1st draw) * P(2nd draw)

1/3 * 1/3 = 1/9

Answer:

(x+7)^2+(y-10)^2=9

Step-by-step explanation:

The distance between the two points is sqrt((-7+7)^2+(10-7)^2)=3 which is in turn the radius of the circle

Answer:

f

Step-by-step explanation:

Answer:

S = 62.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan S = opp side / adj side

tan S = sqrt(42)/ sqrt (11)

tan S = sqrt(42/11)

Taking the inverse tan of each side

tan ^ -1( tan S) =  tan ^-1(sqrt(42/11))

S=62.89816

Rounding to the nearest tenth

S = 62.9

Answer:

b. The actual count of bike riders is too small.

d. n*p is not greater than 10.

Step-by-step explanation:

Confidence interval for a proportion:

To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]

Of the 123 students surveyed 5 ride a bike to campus.

Less than 10 successes, that is:

The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.

Answer:

A sample of 784 is required to estimate the mean usage of water.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The standard deviation is 2 gallons

This means that [tex]\sigma = 2[/tex]

They would like the estimate to have a maximum error of 0.14 gallons. How large of a sample is required to estimate the mean usage of water?

This is n for which M = 0.14. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.14 = 1.96\frac{2}{\sqrt{n}}[/tex]

[tex]0.14\sqrt{n} = 1.96*2[/tex]

[tex]\sqrt{n} = \frac{1.96*2}{0.14}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*2}{0.14})^2[/tex]

[tex]n = 784[/tex]

A sample of 784 is required to estimate the mean usage of water.

Answer:

"0.250" is the appropriate answer.

Step-by-step explanation:

Given:

New car sample,

= 1453

Preferred foreign,

= 363

Now,

The amount of new automobile purchasers preferring foreign cars will be approximated as:

= [tex]\frac{363}{1453}[/tex]

= [tex]0.250[/tex]

Answer:

AB is correct as It is the shorter parallel line

as the line measures 6 units.

Step-by-step explanation:

The polygon is a trapezoid / (trapezium Eng/Europe)

We see the given coordinates  (2, 6) - (-4, 6) = x-6 y 0 = x = 6units

as x always is shown as x - 6  as  x= 6

We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6

y = 0  x = 6 = 6 units as its horizontal line.

when y is 6-6 = 0 then we know the line is horizontal for y = 0.

The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.

When looking at diagonal lines we still group the x's and y's and make the fraction whole.

When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.

Answer:

x > 21

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

x + 34 > 55

Step 2: Solve for x

Answer:(2,5)

Step-by-step explanation:   watch this video

https://youtu.be/l78P2Xi68-k

Answer:

a) 0.321 = 32.1% probability of obtaining a negative daily return, on any given day.

b) 0.103 = 10.3% probability of having a negative daily return for two days in a row.

c) (-$1449.68, $3109.68)

d) A bonus of $4,488.174 is needed.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with mean = $830 and standard deviation = $1,781.

This means that [tex]\mu = 830, \sigma = 1781[/tex]

(a) What is the probability of obtaining a negative daily return, on any given day?

This is the p-value of Z when X = 0, so:

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

[tex]Z = \frac{0 - 830}{1781}[/tex]

[tex]Z = -0.466[/tex]

[tex]Z = -0.466[/tex] has a p-value 0.321.

0.321 = 32.1% probability of obtaining a negative daily return, on any given day.

(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row?

Each day, 0.3206 probability, so:

[tex](0.321)^2 = 0.103[/tex]

0.103 = 10.3% probability of having a negative daily return for two days in a row.

(c) Give the boundaries of the interval containing the middle 80% of daily returns

Between the 50 - (80/2) = 10th percentile and the 50 + (80/2) = 90th percentile.

10th percentile:

X when Z has a p-value of 0.1, so X when Z = -1.28.

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

[tex]-1.28 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = -1.28*1781[/tex]

[tex]X = -1449.68[/tex]

90th percentile:

X when Z has a p-value of 0.9, so X when Z = 1.28.

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

[tex]1.28 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = 1.28*1781[/tex]

[tex]X = 3109.68[/tex]

So

(-$1449.68, $3109.68)

d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus?

The 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.

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

[tex]2.054 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = 2.054*1781[/tex]

[tex]X = 4488.174 [/tex]

A bonus of $4,488.174 is needed.

Answer:

A

Step-by-step explanation:

Recall that for a quadratic equation of the form:

[tex]0=ax^2+bx+c[/tex]

The number of solutions it has can be determined using its discriminant:  

[tex]\Delta = b^2-4ac[/tex]

Where:

We have the equation:

[tex]2x^2+5x-k=0[/tex]

Thus, a = 2, b = 5, and c = -k.

In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:

[tex]b^2-4ac=0[/tex]

Substitute:

[tex](5)^2-4(2)(-k)=0[/tex]

Solve for k. Simplify:

[tex]25+8k=0[/tex]

Solve:

[tex]\displaystyle k = -\frac{25}{8}[/tex]

Thus, our answer is indeed A.

Answer:

No

Step-by-step explanation:

If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.

[tex]6^{2}+8^{2}=c^2[/tex]

If the triangle is a right triangle, c would equal 11

Solve.

[tex]36+64=100[/tex]

Then find the square root of 100.

The square root of 100 is 10, not 11.

So this is not a right triangle.

I hope this helps!