Two thirds of the employees at an office stated that they preferred soft cookies over crispy cookies. More than 36 employees stated their preference. Ren was asked to write, solve, and graph an inequality to find the number of employees working at the office. His work is shown below.

Answers

Answer 1

Answer:

Step 3 is wrong, he used the wrong circle

Step-by-step explanation:

Answer 2

Final answer:

To determine the minimum number of employees, solve the inequality 2/3 x > 36 to find x > 54. In Miguel's cookie choice, the events are dependent. According to the law of large numbers, probabilities stabilize as the number of trials increases.

Explanation:

The question involves solving and graphing an inequality to find the minimum number of employees in an office based on their preferences for soft cookies. Since two thirds prefer soft cookies and more than 36 employees stated their preference, we can write this as an inequality where x represents the total number of employees: 2/3 x > 36. To solve for x, we multiply both sides of the inequality by 3/2, giving us x > 54. This tells us that there must be more than 54 employees in the office.

To graph the inequality, we would draw a number line, plot a point just above 54, and shade to the right to indicate all the numbers that are greater than 54. The question of dependent probabilities relates to Miguel's cookie selection where each choice affects the next; the events are not independent. Finally, the law of large numbers indicates that as the number of trials n increases, the experimental probabilities tend to get closer to the theoretical probabilities.

Related Questions

Three couples go to the movies and sit in six consecutive seats. if the couples must sit together, in how many ways can they be seated

Answers

Since each couple must sit together, let's think of each couple as a single unit. That gives us three ways to arrange three units. It helps to draw a diagram. We can see that each coupe can sit in three distinct ways. [tex](3)(3)=9[/tex].

9

(2)
For this problem I did 2.5/8 = 1.5/4.8, then I cross multiplied and got 12=12 so I would assume that the polygons are infact similar? It must be B or C based on this, but I am pretty confused about the whole ratio part.

Answers

You are correct in saying that the figures are similar; however, the ratio you picked is incorrect. The ratio is 8:4.8 which represents the ratio of JK to PQ

Notice how JK and PQ are the first two letters of JKML and PQRS respectively. So they correspond to one another. Furthermore, notice that 8/4.8 = 1.667 approximately. Also, KM/QR = 2.5/1.5 = 1.667 approximately as well. KM and QR are the two middle letters of JKML and PQRS respectively. The fact we get 1.667 approximately both times, and because of the congruent angles, proves the figures to be similar.

In short, the actual answer is choice B

For polygons to be similar, they must have the same angles and the ratio of the lengths of the corresponding sides must be the same.

First you should rotate the second polygon 90 degrees clockwise (so angle S is on the left) to make it easier to visualize corresponding sides. Now with the shapes in the same orientation, it seems they could be similar. But we have to verify their angles and lengths.

If the two polygons are similar, then the similarity statement might be JKML~PQRS. Notice the order the angles are listed are the same for both shapes (e.g. top left angle is listed first for both shapes). That being said, you could also have written a similarity statement LMKJ ~ SRQP, or another combination of letters with corresponding angles listed in the same order.

First let's check the corresponding sides.
The ratio between corresponding sides JK and PQ is JK/PQ = 8/4.8 = 1.667
The ratio between corresponding sides JL and PS JL/PS = 2.5/1.5 = 1.667
LM/SR and KM/QR also equal 1.667.
Corresponding sides are proportional. We are halfway there.

Now let's check angles. Angle J equals 115 degrees, and its corresponding angle P also equals 115 degrees, so Angle J = Angle P.

The other angles are also similar. Quick proof here: draw a diagonal from angle L to K and from S to Q to split the shape to two triangles. The left triangles are similar by SAS similarity and the right triangles are congruent by SSS similarity. Similar triangles have the same angles, so the two entire polygons have the same angles.

Since the polygons JKML and PQRS have the proportional lengths and same angles, they are similar polygons.

Now, the second part in the answer choices is the ratio between JKML and PQRS. In our example of JK and PQ we found the ratio to be JK/PQ = 8/4.8 = 1.667, and every corresopnding side to also be 1.667. So the entire polygon ratio of JKML to PQRS has the ratio 8/4.8.

What is the greatest common factor of the polynomial's terms? 14a3b4−7ab7+21a2b

Answers

The Answer is 7(ab).

I did the quiz.

Answer: 7ab

Step-by-step explanation:

The given polynomial : [tex]14a^3b^4-7ab^7+21a^2b[/tex]

The terms of the above polynomial can be written as :

[tex]14a^3b^4=(7\times2)a^{2+1}b^{3+1}=(7\times2)a^2(a)b^3b\\\\-7ab^7=-7ab^{6+1}=-7ab^6(b)\\\\21a^2b=(7\times3)a^{1+1}b=(7\times3)a(a)b[/tex]

Now, we can see that the greatest common factor of the polynomial's terms= [tex]7ab[/tex]

what is the product (7x^3y^3)(3x^5y^8)

a)10x^5y^15
b)10x^10y^24
c)21x^7y^11
d)21x^10y^24

Answers

You have studied polynomials consisting of constants and/or variables combined by addition or subtraction. The variables may include exponents. The examples so far have been limited to expressions such as 5x4 + 3x3 – 6x2 + 2x containing one variable, but polynomials can also contain multiple variables. An example of a polynomial with two variables is 4x2y – 2xy2 + x – 7.

Many formulas are polynomials with more than one variable, such as the formula for the surface area of a rectangular prism: 2ab + 2bc + 2ac, where a, b, and c are the lengths of the three sides. By substituting in the values of the lengths, you can determine the value of the surface area. By applying the same principles for polynomials with one variable, you can evaluate or combine like terms in polynomials with more than one variable.

The product of (7x²y³) and (3x⁵y⁸) is obtained by multiplying the coefficients and adding the exponents of like terms, resulting in c) 21x⁷y¹¹.

To find the product of the two algebraic expressions (7x²y³) and (3x⁵y⁸), we simply multiply the coefficients and add the exponents of corresponding variables:

Multiply the coefficients: 7 * 3 = 21

Add the exponents of x: x² * x⁵ = x²⁺⁵ = x⁷

Add the exponents of y: y³ * y⁸ = y³⁺⁸ = y¹¹

Therefore, the product is 21x⁷y¹¹, which corresponds to option (c).

How to estimate the square root of a number that is not a perfect square?

Answers

To estimate the square root of a number that is not a perfect square, you would find the perfect squares that the number is between and you know the square roots of those, so the answer will be somewhere between them. The closer you are to the number below the number you are estimating for, the smaller the decimal (_.1, _.2, etc.) and then it is opposite as you get closer to the number above the number you are estimating for.

Moving a figure around a fixed point in the plane is called making a ___.

Answers

Answer:

Rotation.

Step-by-step explanation:

There are three rigid motions (which do not change the shape and size of the figures): rotation, translation and reflection.

You make a rotation of a figure when you turn it about a fixed point (which can be inside, on an edge or outside the figure) and it is measured in degrees. The rotation can be clockwise or counterclockwise.

Answer:

The answer is Reflection

Angle 2 and angle 3 are vertical angles. true or false

Answers

Answer: If you don't know the answer don't put one down but i do believe the answer is false.

Step-by-step explanation:

Final answer:

The statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their position, as vertical angles are those directly opposite from each other at the intersection of two lines.

Explanation:

The question is asking about vertical angles. Vertical angles are pairs of non-adjacent angles formed when two lines intersect. This means they are the angles that are directly opposite from each other where the two lines intersect. So if Angle 2 and Angle 3 are directly opposite each other at the point where two lines cross, then they are indeed vertical angles. So, the statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their placed positions.

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The home that you are interested in purchasing is listed at $135,000. In order to get financing, you have to place a 15% down payment. From the given information, determine the amount of the down payment. a. $2,025 c. $114,750 b. $135,000 d. $20,250

Answers

135,000x15%=20,250 D. 20,250.

Answer:

its D

Step-by-step explanation:

Find an equation for the circle that has center (−1, 4) and passes through the point (3, −5).

Answers

The correct answer for the equation of the circle with center (-1,4) and passes through point (3,-5) is [tex](x+1)^2 + (y-4)^2 = 97[/tex].

Given Co-ordinates:

Centre:

(-1,4)

Point of intersection:

(3,-5)

The standard equation of circle with center (h, k) is:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

(h, k) are co-ordinates of center

Given in question:

h= -1

k = 4

Find radius of the circle:

distance between the center(-1,4) and the given point (3, -5).

[tex]r = [\sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2 }[/tex]

[tex]r = [\sqrt{((3- (-1))^2 + (-5-4)^2 }[/tex]

[tex]= \sqrt{(4)^2 + (-9)^2 }[/tex]

[tex]= \sqrt{16 + 81}[/tex]

[tex]= \sqrt{97}[/tex]

Now, Equation of circle:

[tex](x-(-1))^2 + (y-4)^2 = (\sqrt{97})^2[/tex]

[tex](x+1)^2 + (y-4)^2 = 97[/tex]

The equation of circle is [tex](x+1)^2 + (y-4)^2 = 97[/tex].

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Final answer:

The equation of the circle with center (-1, 4) and passing through the point (3, -5) is (x + 1)² + (y - 4)² = 97.

Explanation:

The subject of this question is geometry, specifically about the equations of circles. We start by noting that the general equation of a circle is (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the circle's center and r is the radius of the circle.

Here, the center of the circle is at (-1, 4). We don't know the radius yet, but we know that the circle passes through the point (3, -5). The radius is the distance from the center of the circle to any point on the circle. We can find this using the distance formula which is d = sqrt[(x₂ - x₁)² + (y₂ - y₁)²].

Substituting the given points into the distance formula, we get: r = sqrt[(3 - (-1))² + (-5 - 4)²] which simplifies to r = sqrt[(4)² + (-9)²] = sqrt[16 + 81] = sqrt[97].

Now we can write the equation of the circle, substituting the center and radius values into the equation. This gives us: (x - (-1))² + (y - 4)² = sqrt[97]² which simplifies to (x + 1)² + (y - 4)² = 97.

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What is the following quotient? sqrt 120 / sqrt 30

Answers

are you asking the square root after you divide
cuz if so when you divide 120/30 you get 4 and the square root of 4 is 2

Answer:

[tex]2[/tex]

Step-by-step explanation:

we have

[tex]\frac{\sqrt{120}}{\sqrt{30}}[/tex]

we know that

[tex]\frac{\sqrt{120}}{\sqrt{30}}=\sqrt{\frac{120}{30}}=\sqrt{4} =2[/tex]

Mrs. Smith and her daughter Laura want to learn ballet. The cost of beginning ballet classes for kids is $3,200 per year, and it increases by 2% every year. The cost of beginning ballet classes for adults is $4,800 per year, and it increases by 2.7% per year. Which function can Mrs. Smith use to determine the total cost of their ballet classes, T(x), after x years?

Answers

We will set up two functions to begin with: C(x) for children and A(x) for adults. T(x) will be the total, and T(x) = C(x) + A(x).
Since it increases by a percentage every year we will use an exponential function.
C(x) = 3200(1+0.02)ˣ. This comes from the $3200 for the first year, and 2% increase every year is 0.02. Add this to 1 because we have all of the first year's cost, 100%, and the additional 2%.
A(x) = 4800(1+0.027)ˣ. This comes from the $4800 for the first year, and 2.7% increase every year is 0.027. Add this to 1 because we have 100% of the first year's cost with an additional 2.7%.
T(x) = 3200(1+0.02)ˣ+4800(1+0.027)ˣ=3200(1.02)ˣ+4800(1.027)ˣ

Use the number line to find the ratio BG/AD Simplify the ratio.

Answers

The simplified ratio of BG/AD is 10/7.

The simplified ratio is 10/7

Which of the following statements is always true?

A: All rational numbers are whole numbers.

B: All real numbers are rational numbers.

C: All irrational numbers are real numbers.

D: All square roots are irrational numbers.

Answers

Hi!

The correct answer is B: All real numbers are rational numbers.

Hope this helps!

Answer:

Step-by-step explanation:

took the test got it right

What is the probability that the card is either a face card or a spade?

Answers

50% is what I believe it is. Please mark MOST brianlest.

Thomas is saving pennies in a jar. The first day he saves 3 pennies, the second day 12 pennies, the third day 48 pennies, and so on. How many pennies does Thomas have on the eighth day?

Answers

It looks to me as if the amount of pennies is increasing times four. So I think you just keep multiplying by four until you reach the eighth day?

Describe the number and type of roots for the polynomial (how many real and complex?). x3 + 5x2 – 4x – 2 = 0

Answers

Descartes' rule of signs tells you the one sign change in the coefficients means there's one positive real root. If you change the sign of the odd-power terms, the signs become -++-, so have two sign changes. This means there are 0 or 2 negative real roots.

A graph shows there to be 3 real roots, two of which are negative. Thus there are no complex roots.

The explicit rule for a sequence is

an=17−5n .

What is the recursive rule for the sequence?

can you explain also

Answers

The general form of an explicit rule for an arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex], where a₁ is the first term of the sequence and d is the common difference. Since we have [tex]a_n=17-5n[/tex], we know that n is multiplied by 5. That means that d must be 5, since that is the only thing that n gets multiplied in our general form. This gives us:
[tex]a_n=a_1+5(n-1) \\ \\a_n=a_1+5*n-5*1 \\ \\a_n=a_1+5n-5[/tex]
We know that we add something to 5n and then subtract 5 to get 17. Cancelling this process, we can add 5 to 17 to get 22. This gives us
[tex]a_n=22+5(n-1)[/tex]
We know that our first term, a₁, is 22 and our common difference, d, is 5.
The general form of a recursive formula for an arithmetic sequence is
[tex]a_n=a_n_-_1+d[/tex], where d is the common difference and [tex]a_n_-_1[/tex] is the previous term. We know that d is 5, so our recursive formula is
[tex]a_n=a_n_-_1+5[/tex]

A quadrilateral has angles that measure 71°, 74°, 113°, and x°. What is the measure of x?

Answers

The answer would be 360 minus 258 because 71 plus 74 and 113 is 258 and you have to minus that by 360

Bascially for answer 360-258

IT would be 360-258 that is the answer to your question

please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

We can solve this question with an equation. Knowing that the numbers in the sequence are EVEN, we know that they are two apart. So...

x + (x+2) + (x + 4) + (x + 6) + (x + 8) = 310

Combine like terms and you'll get this:

5x + 20 = 310

Using subtraction of equality:

5x = 290

Using division of equality:

x = 58

NOW, the question isn't asking for the value of x but the value of the 3rd number in the sequence. Go back to the original equation and plug in x to the 3rd number.

the 3rd number = x + 4 = 58 + 4 = 62

Voila! Hope this helps!

Which of the following data sets represents a positive correlation?

A
B
C

Answers

B as you can see the points go upwards as they go across :) Hope this helps!

B)
It is B) because the y-value is increasing as the x-value is increasing.

Find the area of the shaded region?

Answers

10 x 12 = 120
3 x4 = 12
4x 1 = 4
120 - 12 = 108
108-4 = 104 square feet

HELP!!!!!!!!!!!!!
To solve the equation 3x−2=4x−1 , Veronica graphs the functions f(x)=3x−2 and g(x)=4x−1

on the same set of coordinate axes.

Which statement describes the solution of the equation 3x−2=4x−1?

(A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

(B) The solution of the equation cannot be found graphically. Veronica should solve the equation algebraically.

(C) The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect.

(D) The solution of the equation is the y-intercept of the linear equations.

Answers

we have that

f(x)=3x-2

g(x)=4x-1

3x-2=4x-1-------------> 4x-3x=-2+1--- > x=-1

find the value of f(x) or g(x) for x=-1

f(x)=3x-2 -------> f(-1)=3*(-1)-2 ------> f(-1)=-5

the solution is the point (-1,-5)

using a graph tool

see the attached figure

the answer is

case (A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

I need help on how to convert the radian into degrees for 7pi/10 !!

Answers

Each pi has 180° in it. So, if you multiply:
[tex] \frac{7}{10} \pi * \frac{180}{\pi}= 126 [/tex]

We divide by pi to get rid of it because we want the answer in degrees:
So your answer is 126°.

Randy bought a zero coupon bond and a TIPS 5 years ago for $2,500 each. Both had 10 years to maturity. The TIPS's coupon was 2% while the zero coupon bond will be redeemed for $3,000. What should the maximum real value of his bonds be if he tries to sell them today? Select the best answer from the choices provided. $250 $750 $5,250 $5,750

Answers

So, we have that the final value of the zero coupon bond after ten years will be 3000$. The TIPS mature after 10 years, but the interest will be calculated only for 5 years. Each year of interest, the TIPS gains 2%*2500=2*25=50$. Hence the TIPS gains 50$ for each year of interest. Since the interest is not compounding, it will gain 5*50=250$ in value. Hence its total value after ten years is 2500+250=2750$. The total maximum value of the two assets combined is 3000+2750=5750$ and it is attained after 10 years. If one things that money is more important now than in 10 years, the assets could be sold at a lower price; nonetheless their max value never exceeds choice d)=5.750$

The simplest form of square root of eighty can be written as a times square root of b, where a

Answers

sqrt(80 ) = sqrt (16 * 5) = 4 sqrt(5)
a = 4
b = 5 I'm guessing.

A cruise ship travels 1900 miles per trip. There are a total of 4 stops the ship makes, and the distance to the first stop is 460 miles. If the variable d stands for the distance left to travel after the first stop, which of the following units could apply to this variable?
A. ships
B. days
C. stops
D. miles

Answers

I believe the answer is D. miles just seems to sound the best to me.

I think the answer is D

What is the question

Answers

To solve for this problem, we need to combine like-terms. Let's list our current variables:
2x - 2y - 5y + 5z - 2x - y + 3z; now, we need to list like-terms together and simplify.
2x - 2x; 0
2y - y; -3y
5z + 3z; 8z

Now, let's put this into an expression;
-3y + 8z.

From our answer choices in the image above, the last option "D.) -3y + 8z" is the correct answer.

I hope this helps!

Given f(x)=5x^2−2x and g(x)=3x ^2+x−4 .

Answers

add both together by combing like terms to get 8x^2-x-4

The addition of the two functions f(x) and g(x) is 8x² − x − 4. Then the correct option is C.

What is a function?

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The functions are given below.

[tex]\rm f(x)=5x^2-2x \\\\g(x)=3x ^2+x-4[/tex]

The addition of the functions is given as

f(x) + g(x) = 5x² − 2x + 3x² + x − 4

f(x) + g(x) = 8x² − x − 4

More about the function link is given below.

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The sum of 4 interior angles of a pentagon is 402. Find the measure of the fifth interior angle.

108
62
138
42

Answers

complete interior angle = 540

5th angle = 540 - 402 = 138

your answer is 138 because u have to divide the 4th interior by the fith and plug in 458

A sample has a mean of m = 90. if each score in the sample is multiplied by 5, then what is the mean for the new distribution?

Answers

In the sample has a mean of m=90 and each score in the sample is multiply by 5 and you want to calculate the mean for the new distribution, you only have to multiply the mean (m=90) by 5.

Then:

m= 90x5
m=450

Therefore, the answer is: The mean for the new distribution is 450 (m=450).

Final answer:

When each score in a sample is multiplied by a constant, the mean of the new distribution will also be multiplied by that constant, resulting in a new mean value of 450.

Explanation:

The mean of a sample is a measure of the average value of the data points in that sample.

When each score in a sample is multiplied by a constant, like 5 in this case, the resulting mean of the new distribution will also be multiplied by that constant.

In this scenario, since each score is multiplied by 5, the mean of the new distribution will be 5 times the original mean, giving a new mean of 450.

Other Questions

Apply the distributive property to create an equivalent expression.1/2 (2a-6b+8) =? Which of the following would describe Lamarcks ideas about evolution?Horses and zebras are similar. They have a common ancestor.A mouse loses its tail in a fight. Its offspring will not have tails.Wolves eat most of the rabbits in a field. A few smart rabbits find hiding places. They survive and reproduce.( which is correct? ) Erik erikson proposed that at what stage of life do people struggle to form close relationships and to gain the capacity for intimate love? what is C=24x+80 R=44x breakeven point According to dr king what are two types of laws helppppppppppppppppppppp Why did the U.S. delay entry to World War I until 1917? Which of the following is the best evidence that work has been done on or by an object? Read this newspaper article, which discusses the Endurance Expedition. What differences do you note between the voice and point of view of the newspaper article compared to the chapter Across South Georgia from Shackleton's memoir? What important practice can help prevent hardware trouble? A.Repairs B.Troubleshooting C.Maintenance D.Diagnosis In part a reaction to protestantism, the period of spiritual renewal in catholicism in the seventeenth century is known as the __________. a principle that seems to underlie the three stages model of memory is that ____. Which is not a problem that Native Americans face on reservations today?lack of jobspovertywar with settlersalcoholism give the reason why the horizontal component of the velocity of a projectile remains the same at every point of its flight You should ____ your important files daily. A.) backup B.) back up C.) back-up A right triangle has a leg of 13 cm and a hypotenuse of 21 cm. What is the length of the other leg? Round to the nearest tenthA. 8.0 cmB.16.5 cmC. 24.7 cm D. 272.0 cm Explain the advantage of creating a linear function from a set of data; why bother to do this? Read the excerpt below and answer the question. " He had a latten cross set full of stones And in a bottle had he some pigs bones, But with these relics, when he came upon. Some simple parson, then this paragon In that one day more money stood to gain (The Canterbury Tales; General Prologue, lines 701-705) " Based upon the above context, Chaucer chooses the word paragon to show _____. Find the area of a circle with a circumference of \color{blue}{6\pi}6start color blue, 6, pi, end color blue. Sues Corner Market has a markup of 60% on bottled water. If the market sells a bottle of water for $2, find the original amount that Sue pays.