Question 5


Not yet answered


An ice-cream parlor used a scatterplot to record their total sales, in dollars, each day (s) and


the corresponding average temperature, in ºf, on that day (t). They then found a trend line of


this data to be s = 12. 75t + 32. What is the predicted total sales the ice-cream parlor makes


if the average temperature of the day is 72°f?


Marked out of


1. 00


P Flag question


O a.


$950. 00


O b. $820. 00


O c. $1,275. 00


O d. $740. 00

Answer:

Cylinder B has a greater volume

Step-by-step explanation:

Volume of a cylinder\(=\pi r^2h\)

Cylinder A

h=5m, r=3m

Volume

\(=3.14 *3^2*5\\=141.3m^3\)

Cylinder B

h=3m, r=5m

Volume

\(=3.14 *5^2*3\\=235.5m^3\)

Cylinder B has a greater volume.

Answer:

x = t(a+p)/4

Step-by-step explanation

Given the expression

​a=4x/t - p

We are to make x the subject of the formula

a=4x/t - p

Add p to both sides

a+p = 4x/t - p+p

a+p = 4x/t

Cross multiply

t(a+p) = 4x

Rearrange

4x = t(a+p)

Divide both sides by 4

4x/4 = t(a+p)/4

x = t(a+p)/4

Considering the given functions, we have that:

1) The inverse of function f(x) is defined by: \(f^{-1}(x) = \frac{4x^2}{9} + 1\)

2) It is shown in the Item 2 section that the function is one-to-one.

3) The functions are not inverses, due to the result of their composition.

The find the inverse of a function, we exchange x and y on the original function, and then isolate y.

The original function is given by:

\(y = 3\frac{\sqrt{x - 1}}{2}\)

Exchanging x and y, we have that:

\(x = 3\frac{\sqrt{y - 1}}{2}\)

Now we do the procedures to isolate y, as follows:

\(3\sqrt{y - 1} = 2x\)

\(\sqrt{y - 1} = \frac{2x}{3}\)

\((\sqrt{y-1})^2 = \left(\frac{2x}{3}\right)^2\)

\(y - 1 = \frac{4x^2}{9}\)

\(y = \frac{4x^2}{9} + 1\)

\(f^{-1}(x) = \frac{4x^2}{9} + 1\)

To verify if the function is one-to-one, we first find the numeric values at x = a and x = b, then:

Now we have to verify how many outcomes of a and b are possible for them to be equal. Since they have the same numerator, they will be equal when the denominators are equal, that is:

2a - 1 = 2b - 1.

Simplifying the one and then by 2:

a = b.

Only equal when a = b, hence the function is one-to-one. (this is the algebraic proof).

The functions will be inverses if the composition of the functions result in x, that is, if inputting function g(x) into function f(x) results in x.

The result of the composition is given by:

f(g(x)) = f(x/3 + 5) = 3(x/3 + 5) - 5 = x + 15 - 5 = x + 10.

x + 10 is different of x, hence the two functions are not inverses.

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Using the Integral Test, the correct choice is B. Since the integral ∫(k+7)dx diverges, the series also diverges.

We are supposed to use Integral Test to determine the convergence or divergence of the series, ∑(k+7)dx.

We can use the Integral Test to test for the convergence of series if the function in the series is continuous, positive, and decreasing for all x greater than or equal to some value N.

The Integral Test states that a series converges if and only if the integral of the series term is convergent, i.e. if the integral of u(x)dx is convergent. Also, if the integral of u(x)dx diverges, the series is divergent.

So we need to check whether the function in the given series is continuous, positive, and decreasing for all x greater than or equal to some value N.

If we integrate the series, ∑(k+7)dx, we get:∫(k+7)dx= ∫k

dx + ∫7dx= (k²/2) + 7x+ C

where C is the constant of integration.

Since the value of C is not given, we cannot say anything about the exact value of the integral.

However, the value of the constant of integration does not matter in this case as we only need to determine whether the integral converges or diverges.

Therefore, we can use the Integral Test to determine the convergence or divergence of the series.

Using the Integral Test, the correct choice is B.

Since the integral ∫(k+7)dx diverges, the series also diverges.

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Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Answer:

Step-by-step explanation:

you want to divide 36 by 8 because you have 36 people and the recipie only makes it for 8.

You know that you will need to make the recipe 4.5 times.

So, multiply all the ingredient numbers by 4.5

2 x 4.5 = 9 quarts of water

3 x 4.5 = 13.5 sticks of cinnamon

1 x 4.5 = 4.5 tablespoons of coffee

Answer: Im pretty sure you need 16 quartz of water, 24 sticks of cinnamon, and 8 tablespoons of coffee.

Step-by-step explanation:

If this figure was a parallelogram, then the opposite angles would be congruent. This would make angles B and D the same measure

angle B = angle D

x^2+20 = 7x+50

x^2+20-7x-50 = 0 .... get everything to one side

x^2-7x-30 = 0

(x-10)(x+3) = 0 ... see note below

x-10 = 0 or x+3 = 0

x = 10 or x = -3

Note: In this step is where the factoring occurs. To factor, we need to find two numbers that multiply to -30 which is the last term, and also add to -7 which is the middle coefficient. This is a trial and error process. You should find that -10 and 3 both multiply to -30 and add to -7. I suggest making a table as shown below (attached image) to list out all the possible choices.

Perhaps a much more efficient route is to use the quadratic formula.

-----------------

We found two possible solutions for x. If x = 10, then 7x+50 is 7(10)+50 = 120 which is an obtuse angle. If x = -3, then 7x+50 = 7(-3)+50 = 29 which is acute.

Assuming the diagram is drawn to scale, this means angle D is obtuse and we'll go with x = 10 and 7x+50 = 120

Angles A and D add to 180 degrees. This is true for any pair of adjacent angles in a parallelogram.

A+D = 180

A+120 = 180

A = 180-120

-----------------

This answer is based on the assumption that the diagram is drawn to scale and that this quadrilateral is a parallelogram.

Answer:

\(\angle A=60\textdegree\)

Step-by-step explanation:

So we have the following parallelogram and we wish to solve for ∠A.

To do so, we will need to solve for x first. Look carefully at the parallelogram...

Notice that ∠A and ∠D are consecutive angles. In other words:

\(\angle A+\angle D=180\)

Since we have an equation for ∠D, substitute:

\(\angle A+7x+50=180\)

Notice that ∠A and ∠B are also consecutive angles. So:

\(\angle A+\angle B=180\)

We know the equation for ∠B. Substitute:

\(\angle A+x^2+20=180\)

Since both equations equal 180, we can set them equal to each other:

\(\angle A+7x+50=x^2+20+\angle A\)

Let's subtract ∠A from both sides. This gives us:

\(7x+50=x^2+20\)

Now, we can solve for x. This is a quadratic, so let's move all the terms to one side. To start off, let's subtract 50 from both sides:

\(7x=x^2-30\)

Now, let's subtract 7x from both sides:

\(0=x^2-7x-30\)

Solve for x. We can factor.

Here's the trick to factoring. If we have the following:

\(0=ax^2+bx+c\)

The we will need to find two numbers, p and q, such that:

\(p+q=b\text{ and } pq=ac\)

In our equation, a is 1, b is -7, and c is -30.

So, we want two numbers that sum to -7 and multiply to (1)(-30)=-30.

We can use -10 and 3. -10+3 is -7 and -10(3) is -30. So, let's substitute our b term for -10x and 3x. In other words, we have:

\(0=x^2-7x-30\)

Substitute -7x for 3x-10x. This gives us:

\(0=x^2+3x-10x-30\)

This is equivalent to our old equation.

Now, we can factor. Factor out a x from the first two terms:

\(0=x(x+3)-10x-30\)

And factor out a -10 from the two last terms:

\(0=x(x+3)-10(x+3)\)

Since the expressions within the parentheses are the same, we can use grouping to acquire:

\(0=(x-10)(x+3)\)

Note that this is essentially the distribute property. If we distribute, we will get the same as above.

Zero Product Property:

\(x-10=0\text{ or }x+3=0\)

Solve for x:

\(x=10\text{ or } x=-3\)

So, we have two cases for x. Each case will yield a different answer for ∠A.

Case I: x=10

Use our original equation of:

\(\angle A+7x+50=180\)

Substitue 10 for x:

\(\angle A+7(10)+50=180\)

Multiply:

\(\angle A+70+50=180\)

Add:

\(\angle A+120=180\)

Subtract 120 from both sides:

\(\angle A=60\textdegree\)

So, in our first case, ∠A is 60°

Case II: x=-3

Again, same equation:

\(\angle A+7x+50=180\)

This time, substitute -3 for x. This yields:

\(\angle A+7(-3)+50=180\)

Multiply:

\(\angle A-21+50=180\)

Add:

\(\angle A+29=180\)

Subtract 29 from both sides:

\(\angle A=151\textdegree\)

So, in our second case, ∠A is 151°

However, 151° doesn't seem likely with how the figure is drawn.

Therefore, our final answer is 60°.

And we're done!

Edit: Fixed Incorrect Answer

Answer:

36 back

Step-by-step explanation:

100 - 64 = 36

Answer:

36¢

Step-by-step explanation:

1.00-0.64=0.36

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

To find an angle that is coterminal with 1260 degrees, we need to subtract or add a multiple of 360 degrees until we get an angle between 0 and 360 degrees.

Let's subtract multiples of 360 degrees from 1260 until we get an angle between 0 and 360:

1260 - 360 = 900 (not between 0 and 360)

900 - 360 = 540 (between 0 and 360)

Therefore, an angle that is coterminal with 1260 degrees and between 0 and 360 degrees is 540 degrees.

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Answer:

The answer to the expression in simplest form is:

\(\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}\)

Step-by-step explanation:

Given the function

\(\frac{\frac{1}{3}}{\frac{1}{4}}\)

solving to get the simplest form

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}\)

\(\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{1\cdot \:4}{3\cdot \:1}\)

\(\mathrm{Apply\:rule}\:a\cdot 1=a\)

\(=\frac{4}{3}\)

Thus, the answer to the expression in simplest form is:

\(\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}\)

Answer:

25

Step-by-step explanation:

The air speed of the plane to cover 360 miles against the wind and with the wind in the given time is equal to 200 miles per hour.

Let 'x' be the speed of the plane fly in still air.

And 'y' be the speed of the wind.

Speed against the wind = x - y

Speed with the wind = x + y

Total distance covered by plane = 360 miles

Time taken against the wind = 2 hours 15 minutes

                                               = 2 ( 1/4 ) hours

                                               = 9 / 4 hours

Time taken with the wind = 1 hour 30 minutes

                                          = 1 ( 1/2 ) hours

                                          = 3 /2 hours

Speed = distance / time

Against the wind :

x - y = 360 / (9 /4 )

⇒x - y = 160___(1)

With the wind:

x + y = 360 / (3 /2)

⇒x + y = 240 ___(2)

Add (1) and (2) we get,

2x = 400

⇒ x= 200miles per hour

⇒y = 40 miles per hour

Therefore, the air speed of the plane as per given condition is equal to 200miles per hour.

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Therefore, the limit of the given expression lim(x→0) (sin 4x cos 11x) (5x + 9xcos 3x) is 0.

To evaluate the limit of the expression lim(x→0) (sin 4x cos 11x) (5x + 9xcos 3x), we can factor the denominator first.

The denominator can be factored as:

5x + 9xcos 3x = x(5 + 9cos 3x)

Now, we can rewrite the expression as:

lim(x→0) [(sin 4x cos 11x) / (x(5 + 9cos 3x))]

Next, let's analyze each term separately:

The term sin 4x approaches 0 as x approaches 0.

The term cos 11x approaches 1 as x approaches 0.

The term x approaches 0 as x approaches 0.

However, the term (5 + 9cos 3x) needs further evaluation.

As x approaches 0, the term cos 3x approaches cos(3 * 0) = cos(0) = 1.

Therefore, we can substitute the value of cos 3x in the denominator:

(5 + 9cos 3x) = 5 + 9(1) = 5 + 9 = 14

Now, we can simplify the expression further:

lim(x→0) [(sin 4x cos 11x) / (x(5 + 9cos 3x))] = lim(x→0) [(sin 4x cos 11x) / (14x)]

To evaluate this limit, we can consider the following properties:

sin 4x approaches 0 as x approaches 0.

cos 11x approaches 1 as x approaches 0.

The term 14x approaches 0 as x approaches 0.

Therefore, we have:

lim(x→0) [(sin 4x cos 11x) / (14x)] = 0/0

This form of the expression is an indeterminate form. To proceed further, we can apply L'Hôpital's rule.

Differentiating the numerator and denominator with respect to x:

lim(x→0) [(sin 4x cos 11x) / (14x)] = lim(x→0) [(4cos 4x cos 11x - 11sin 4x sin 11x) / 14]

Again, evaluating this limit will result in 0/0, indicating another indeterminate form. We can apply L'Hôpital's rule again.

Differentiating the numerator and denominator once more:

lim(x→0) [(4cos 4x cos 11x - 11sin 4x sin 11x) / 14] = lim(x→0) [(-44sin 4x cos 11x - 44sin 4x cos 11x) / 14]

= lim(x→0) [(-88sin 4x cos 11x) / 14]

= lim(x→0) [-4sin 4x cos 11x]

Now, as x approaches 0, sin 4x approaches 0 and cos 11x approaches 1. Hence, we have:

lim(x→0) [-4sin 4x cos 11x] = -4(0)(1) = 0

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The random variable is the number of brown MOM's in a package of 50 MOM's. The given numbers are n = 50 and p = 0.13. The probabilities of exactly none, exactly 44, at least 43, and at most 45 MOM's being brown can be calculated using the binomial probability formula.

a) The random variable in this scenario is the number of brown MOM's in a package of 50 MOM's.

b) The given numbers with correct symbols are:

n = 50 (number of MOM's in the package)

p = 0.13 (proportion of brown MEM's)

c) This is a binomial experiment because the following conditions are met:

- There are only two outcomes for each MOM: brown or not brown.

- The number of MOM's is fixed at 50.

- The probability of selecting a brown MOM remains constant at 13% for each randomly selected MOM.

- The selection of one MOM being brown does not affect the probability of another MOM being brown.

d) The probability that exactly none of the MOM's are brown can be calculated using the binomial probability formula as P(X = 0) = C(50, 0) * (0.13)^0 * (1 - 0.13)^(50 - 0).

e) The probability that exactly 44 MOM's are brown can be calculated using the binomial probability formula as P(X = 44) = C(50, 44) * (0.13)^44 * (1 - 0.13)^(50 - 44).

f) The probability that at least 43 MOM's are brown can be calculated by summing the individual probabilities of having 43, 44, 45, ..., 50 MOM's brown. This can be calculated as P(X ≥ 43) = P(X = 43) + P(X = 44) + ... + P(X = 50).

g) The probability that at most 45 MOM's are brown can be calculated by summing the individual probabilities of having 0, 1, 2, ..., 45 MOM's brown. This can be calculated as P(X ≤ 45) = P(X = 0) + P(X = 1) + ... + P(X = 45).

By substituting the appropriate values into the binomial probability formula and performing the calculations, we can find the probabilities (d), (e), (f), and (g) to 4 decimal places.

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Miki has a dozen oranges of the same size and a dozen pears of the same size.

Miki uses her juicer to extract 88 ounces of pear juice from 33 pears and 88 ounces of orange juice from 22 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is pear juice?The ratio of ounces of orange juice to the number of oranges is: 88/22 = 4. The ratio of ounces of pear juice to the number of pears is 88/33 = 2.67.The number of pears and oranges used in the blend is equal and since 2.67 is not equal to 4, we know that neither 22 nor 33 is the number of pieces used for the blend.

To find out the number of pieces used in the blend, we need to find a common multiple of 22 and 33, which is 66.The amount of pear juice used in the blend is (66/2) × (2.67/12) = 5.5 ounces.The amount of orange juice used in the blend is (66/2) × (4/12) = 22 ounces.The percentage of pear juice in the blend is: (5.5 / (5.5 + 22)) × 100% = 20%.Therefore, the percent of pear juice in the blend is 20%.

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Answer:

red

Step-by-step explanation:

1 and 21  1 1 1 1 1111111111

= 2 π r

Answer: The formula to find the circumference C of a circle of radius r is C = 2 π r.

The minimum score an applicant needs to qualify for the final stage 1056

In this question we have been given that students sit for a special standardized test and score on the top 10% of the test to be admitted into the final stage of hiring. the mean of the score of the test is 800 and the population standard deviation is known to be 200.

We need to find the minimum score an applicant needs to qualify for the final stage.

Z score is given by:

z = (raw score - mean) / standard deviation

here: mean = 800

and a standard deviation = 200

P(z > c) = 10% = 0.1

1 - P(z < c) = 0.1

P(z < c) = 0.9

P(z < c) = 1.282

So, substituting these values in above formula,

1.282 = (x - 800)/200

x - 800 = 256.4

x = 1056.4

x ≈ 1056

Therefore, the lowest possible score to qualify in the top 10% is approximately 1056

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The simplified expression of |(1/4-1/5)+(-3/4+1/8)| is |-0.57|.

In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD). As an illustration, LCM (4, 5) = 20. In this case, the LCM 20 may be divided by both 4 and 5, hence these two numbers are referred to as the divisors of 20.

When the fractions' denominators differ, LCM can also be used to add or subtract any two fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction.

The given expression is:

|(1/4-1/5)+(-3/4+1/8)|

Take the LCM:

|(5 - 4)/ 20 + (-24 + 4)  32|

|1/20 - 20/32|

Take the LCM:

|(32 - 400) / 640|

|-368 / 640|

|-0.57|

Hence, the simplified expression of |(1/4-1/5)+(-3/4+1/8)| is |-0.57|.

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Answer:

i think it is 80sq cm

Step-by-step explanation:

Collecting soil evidence from a house that has been burglarized involves careful and systematic procedures to ensure the integrity and preservation of the samples. Here is a brief description of how you could go about collecting soil samples:

1.Assess the scene: Before collecting any samples, carefully assess the crime scene to identify potential areas of interest. This could include entry points, areas where the suspect may have walked or left traces, or areas where soil may have been disturbed.

2.Use proper tools: Equip yourself with the necessary tools for sample collection. This typically includes clean gloves, clean containers or evidence bags, a clean trowel or spatula, and clean disposable paper or plastic sheets.

3.Document the location: Before collecting any samples, thoroughly document the location and context of each sample. Take photographs and detailed notes to provide a visual and written record of where each sample was collected from.

4.Collect control samples: Start by collecting control samples from unaffected areas of the house or the surrounding environment. These control samples will serve as a reference for comparison with the samples collected from potential evidence areas.

5.Collect suspected samples: Collect soil samples from areas where you suspect the burglar or intruder may have left traces. This could include areas around windows, doors, or other potential entry points, as well as any areas of disturbed soil or footprints.

6.Follow proper collection techniques: Use the clean trowel or spatula to carefully scrape the soil sample into a clean container or evidence bag. Ensure that the container is properly sealed and labeled with the relevant information, including the location, date, and time of collection.

7.Preserve and transport the samples: To preserve the integrity of the samples, avoid mixing different samples together and ensure they are stored in a cool, dry, and secure location. Properly package and seal the samples for transport to the laboratory, following chain of custody protocols to maintain their evidentiary value.

8.Maintain documentation: Throughout the process, maintain accurate and detailed documentation of all collected samples, including their collection method, location, and handling procedures. This documentation is crucial for maintaining the chain of custody and providing a comprehensive record of the evidence collection process.

It is important to note that this is a general overview, and the specific procedures and protocols may vary depending on the jurisdiction and the nature of the crime. It is advisable to consult with forensic experts or follow the guidelines provided by the appropriate law enforcement agencies to ensure proper and legally valid collection of soil evidence.

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The first 4 terms in the expansion of (1 + x²)⁸ using the binomial theorem are: (1 + x²)⁸ = 1 + 8x² + 28x⁴ + 56x⁶ + ...

The question asks us to find the first 4 terms in the expansion of (1 + x^2)⁸. To expand this binomial, we can use the binomial theorem, which states that for any positive integer n:

To find the value of (1.01)⁸, we substitute x = 0.01 in the above expression:

(1.01)⁸ = (1 + 0.01²)⁸

= 1 + 8(0.01²) + 28(0.01⁴) + 56(0.01⁶) + ...

Using a calculator, we can evaluate this expression to get:

(1.01)⁸ ≈ 1.0824

Therefore, the value of (1.01)⁸ is approximately 1.0824.

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Answer:

4

8

12

16

...............

Answer:

4,8,12,16

Step-by-step explanation:

.20×20=4 .40×20=8 and so on

Answer:

-4.14130434783

Step-by-step explanation:

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer:

part a= -1

part b= -4

Step-by-step explanation:

f(x) is y. plug in -4 for y and check x

Answer:

f(x) is y. plug in -4 for y and check x

Step-by-step explanation:

Answer:

send the complete question . there are some missing signs .

Answer:

Below

Step-by-step explanation:

To find the volume of a sphere you can use this formula!

     V = 4/3πr^3

Plugging in the values....

V = 4/3π(49.5)^3

V = 5.08047 × 10^5

V = 5.1 x 10^5 in^3

If you wanted to write this is standard form it would be

V = 508047 in^3

Hope this helps!