PLEASE HELP DUE TODAY!!!

#of ice cream treats sold: Day 1=16, Day 2=19, Day 3=28, Day 4=27, Day 5=28, Day 6=36, Day 7=38, Day 8=41, Day 9=41, Day 10=48

#of coffee drinks sold: Day 1=55, Day 2=43, Day 3=51, Day 4=46, Day 5=32, Day 6=36, Day 7=43, Day 8=25, Day 9=10, Day 10=33

5. What is the slope of the line that best fits the data? Use mathematical reasoning and show work.

6. Interpret what the slope means in terms of the situation.

8. Write the equation of the line that best fits the data.

9. Using the equation of the line of best fit, estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold. Write an explanation that justifies your conclusion.

PLEASE HELP DUE TODAY!!! #of Ice Cream Treats Sold: Day 1=16, Day 2=19, Day 3=28, Day 4=27, Day 5=28,

Answers

Answer 1

The slope of the line that best suits the data is -0.1463.

slope = [tex]\sum (( x -\bar x )( y - \bar y )) / \sum ( x - \bar x ) ^2[/tex]

where x is the number of ice cream treats sold, y is the number of coffee drinks sold, x bar is the mean of the number of ice cream treats sold, and ȳ is the mean of the number of coffee drinks sold.

Using the given data, we find that:

[tex]\bar x =[/tex] (16 + 19 + 28 + 27 + 28 + 36 + 38 + 41 + 41 + 48) / 10 = 32.2

[tex]\bar y =[/tex] (55 + 43 + 51 + 46 + 32 + 36 + 43 + 25 + 10 + 33) / 10 = 36.4

Next, we calculate the terms needed for the formula:

[tex]\sum (( x - \bar x )( y - \bar y ))[/tex] = (16 - 32.2)(55 - 36.4) + (19 - 32.2)(43 - 36.4) + ... + (48 - 32.2)(33 - 36.4) = -686.6

[tex]\sum ( x - \bar x )^2[/tex] = (16 - 32.2)² + (19 - 32.2)² + ... + (48 - 32.2)² = 4690.6

Plugging these values into the formula, we get:

slope = [tex]\sum (( x - \bar x )( y - \bar y )) / \sum ( x - \bar x )^2[/tex] = -686.6 / 4690.6 = -0.1463

Therefore, the slope of the line that best fits the data is -0.1463.

Interpreting the slope in terms of the situation, we can say that for every additional ice cream treat sold, the number of coffee drinks sold decreases by an average of 0.1463.

To write the equation of the line that best fits the data, we use the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. We already know the value of m, so we just need to find b. To do this, we can use the mean values of x and y:

y = mx + b

36.4 = (-0.1463)(32.2) + b

b = 41.9

Therefore, the equation of the line that best fits the data is:

y = -0.1463x + 41.9

To estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold using the equation of the line of best fit, we simply substitute x = 32 into the equation and solve for y:

y = -0.1463(32) + 41.9

y ≈ 36.9

So we can estimate that approximately 36.9 coffee drinks were sold on a day that 32 ice cream treats were sold. This conclusion is justified because we used the equation of the line that best fits the data to make the estimate, which takes into account the overall trend of the data and the relationship between the number of ice cream treats sold and the number of coffee drinks sold. However, it's important to note that this is only an estimate and there may be other factors that could affect the actual number of coffee drinks sold on a particular day.

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Related Questions

Brianna goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Brianna decides to leave a tip of 19% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Brianna paid.

Answers

Brianna left a tip οf 19% οn the entire bill, which includes the tax. Therefοre, the tοtal amοunt Brianna paid is 1.2495(xx), so the expressiοn in terms οf xx that represents the tοtal amοunt Brianna paid is 1.2495(xx).

What is the equivalent expressiοn?

Equivalent expressiοns are expressiοns that perfοrm the same functiοn despite their appearance. If twο algebraic expressiοns are equivalent, they have the same value when we use the same variable value.

The tax οn the bill is 5% οf xx, which can be expressed as 0.05(xx). Therefοre, the tοtal bill including tax is:

xx + 0.05(xx) = 1.05(xx)

Brianna left a tip οf 19% οn the entire bill, which includes the tax. Therefοre, the tοtal amοunt Brianna paid is:

1.05(xx) + 0.19(1.05(xx)) = 1.05(xx) + 0.1995(xx)

Simplifying the expressiοn, we get:

Tοtal amοunt Brianna paid = 1.2495(xx)

Therefοre, the expressiοn in terms οf xx that represents the tοtal amοunt Brianna paid is 1.2495(xx).

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A bag contains 3 blue, 9 green, and 8 red
marbles. Find the probability of picking 3 red
marbles if each marble is NOT returned to the
bag before the next marble is picked.
P(red and red and red)

1/6840

1/8000

8/125

14/285

Answers

the probability of picking 3 red marbles if each marble is NOT returned to the bag before the next marble is picked is14/285.

Define probability

Probability is a measure of the likelihood or chance that a particular event will occur, expressed as a number between 0 and 1. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

After the first red marble is drawn, there will be 19 marbles left in the bag, of which 7 are red.

So, the probability of picking a red marble on the second draw, given that the first marble was red and not returned to the bag, is 7/19.

Similarly, after the second red marble is drawn, there will be 18 marbles left in the bag, of which 6 are red.

So, the probability of picking a red marble on the third draw, given that the first two marbles were red and not returned to the bag, is 6/18 or 1/3.

Therefore, the probability of picking 3 red marbles in a row is:

(8/20) x (7/19) x (6/18) = 14/285

So, the answer is 14/285.

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negative five and one seven divided by negative two and two fifths

Answers

Answer:

Step-by-step explanation:

[tex]-5\frac{1}{7} \div 2\frac{2}{5} =-\frac{36}{7}\div \frac{12}{5}[/tex]

                [tex]=-\frac{36}{7} \times \frac{5}{12}[/tex]

                [tex]=-\frac{3}{7} \times \frac{5}{1}[/tex]           (÷ top and bottom by 12)

                [tex]=-\frac{15}{7}[/tex]

                [tex]=-2\frac{1}{7}[/tex]

How do I make x the subject of y= a√x-b

Answers

Divide both sides by y

the picture has the question and the options !!

Answers

Answer:

8g + 11h + 14f

Step-by-step explanation:

To find the perimeter just add the value of all the sides

P =9f + g + 5f + 9h + 2h + 7g

Combine like terms

P = 8g + 11h + 14f

What is statistical​ inference? Why is it​ important?

(In your own words, please! ) Thanks!

Answers

Statistical inference is the process of using data from a sample to make generalizations or draw conclusions about a larger population.

What is statistical Inference?

Based on the sample data, assumptions are made about the fundamental traits of the population, and the uncertainty in those assumptions is quantified using statistical techniques.

Because it enables us to forecast the future and make judgements based on incomplete data, statistical inference is crucial. For instance, with a sample of data, it enables us to confidently estimate population parameters such as averages and proportions. This can be helpful in a variety of contexts, including marketing analysis, surveys of public opinion, clinical trials, and manufacturing quality control.

By comparing the results of several groups or treatments, statistical inference also enables us to assess the efficacy of interventions or treatments.This can inform decisions about which treatments are most effective or which interventions should be implemented.

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Question 5(Multiple Choice Worth 1 points)
(08.02 LC)

Complete the square to transform the expression x2 − 2x − 2 into the form a(x − h)2 + k.

(x − 1)2 + 3
(x − 1)2 − 3
(x − 2)2 − 3
(x − 2)2 + 3

Answers

The expression  x2 − 2x − 2 can be transformed into the form (x − 1)2 +-3.

Completing the square is a technique used to convert a quadratic expression of the form ax^2 + bx + c into the form a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex of the quadratic function.

To complete the square, we need to add and subtract the square of half of the coefficient of x from the expression.

Starting with x2 − 2x − 2:

x2 − 2x − 2 = x2 - 2x + (-2)

We take half of the coefficient of x, which is -1, and square it to get 1.

x2 - 2x + 1 - 1 - 2 = (x - 1)2 - 3

Therefore, the expression x2 − 2x − 2 can be transformed into the form (x − 1)2 − 3, which is an option (B).

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Please try to explain it

Answers

The table of value of the function and it's graph are attached below

What is the table of value

Here's the table of values for the function m(x) = 0.5x^2 with x ranging from -5 to 5

All we need to do is simply substitute the corresponding value of x into the function to get the value of y.

m(x) = 0.5x^2

m(-5) = 0.5(-5)^2

m(-5) = 12.5

Doing this for all other values, we will have our table below

x m(x)

-5 12.5

-4 8.0

-3 4.5

-2 2.0

-1 0.5

0 0.0

1 0.5

2 2.0

3 4.5

4 8.0

5 12.5

You can use this table to plot the function using a graphing calculator.

Kindly find the attached graph below;

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Find the length of the segment indicated. Round your answer to the nearest tenth if necessary. (Please show step by step on how to figure this out! I want to understand!)

Answers

The value of x is 7.3

Define the term Circle identities?

The six trigonometric functions of an angle in a right-angled triangle are related by a set of fundamental identities in trigonometry known as the Circle identities.

Given below figure; diameter AC = 33.4 and length AM = 13.8

So, radius OA = 33.4/2 = 16.7

Here the right angle triangle ΔAMO;

So, OA² = AM² + OM²

or, , OM² = OA² - AM²

By putting all values and find OM,

OM² = (16.7)² - (13.8)²

OM² = 278.89 - 190.44

OM = √88.45

OM = 9.40

here, ON = OA = 16.7   (both are radius of circle)

ON = OM + x    

x = ON - OM     (Put the values here and find x value)

x = 16.7 - 9.40 = 7.3

Therefore, the value of x is 7.3

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Out of 160 workers surveyed at a​ company, 23 walk to work.
a.
What is the experimental probability that a randomly selected worker at that company walks to​ work?
b.
Predict about how many of the 2600 workers at the company walk to work.

Answers

A. The experimental probability of a randomly selected worker walking to work is approximately 0.144. B. We can predict that about 374 workers walk to work out of the 2600 workers at the company.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

According to the given information:

a. The experimental probability of a randomly selected worker walking to work can be calculated as:

Experimental probability = Number of workers who walk to work / Total number of workers surveyed

Experimental probability = 23/160

Experimental probability ≈ 0.144

Therefore, the experimental probability that a randomly selected worker at that company walks to work is approximately 0.144.

b. To predict how many of the 2600 workers at the company walk to work, we can use the experimental probability found in part (a) and multiply it by the total number of workers:

Number of workers who walk to work = Experimental probability x Total number of workers

Number of workers who walk to work = 0.144 x 2600

Number of workers who walk to work ≈ 374.4

Therefore, we can predict that about 374 workers walk to work out of the 2600 workers at the company.

Therefore,a. The experimental probability of a randomly selected worker walking to work is approximately 0.144.b. We can predict that about 374 workers walk to work out of the 2600 workers at the company.

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What would the area of this shape be?

Answers

Answer:

3,081.6 square feet

Step-by-step explanation:

Draw the diagonal that divides this figure into two right triangles. We then have:

[tex] \frac{1}{2} (24)(76.8) + \frac{1}{2} (60)(72) = 921.6 + 2160 = 3081.6[/tex]

URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS!!!!

Answers

1,2,4 are all linear

Need help fill in the box please

Answers

The value of function f(x) will be 2,-1/2,-1,5/2,4 when x is equal to 0,1,2,-1,-2 respectively.

The given function is f(x) = (-3/2)x + 2

We want to find the value of f(x) for all values of x, we simply substitute different values of x in the given function and evaluate it. For example:

If x = 0, then [tex]$f(0)=-{\frac{3}{2}}\times(0)+2=2$[/tex]

If x = 1, then  [tex]$f(1)=-{\frac{3}{2}}\times(1)+2=-{\frac{1}{2}}$[/tex]

If x = 2, then [tex]$f(2)={\frac{-3}{2}}\times(2)+2=-1$[/tex]

If x = -1, then [tex]$f(-1)=-{\frac{3}{2}}\times(-1)+2={\frac{5}{2}}$[/tex]

If x = -2, then [tex]$f(-2)=-{\frac{3}{2}}\times(-2)+2=4$[/tex]

So, the value of f(x) for all values of x is given by f(x) = (-3/2)x + 2

Similarly, we can find the value of f(x) for any value of x.

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The value of function f(x) will be 2,[tex]\frac{1}{2}[/tex],-1,[tex]\frac{7}{2}[/tex],5 when x is 0,1,2,-1,-2 respectively.

What is the function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function of s domain and co domain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

What Does a Function's Table of Values Mean?

In mathematics ,The list of numbers used to replace the variable is defined by the table of values. The   value of function at a solution is determined by the optimization problem of value function, which only depends on the problem's parameters.

The given function is f(x) =[tex]\frac{-3}{2} x[/tex] + 2

We find the value of f(x) ∀ x,

we substitute different values of x in the given function and evaluate it. For example:

If x = 0, then

f(x) =[tex]\frac{-3}{2} *0+2[/tex] ⇒f(x)=2

If x = 1, then  

f(x)

[tex]=(\frac{-3}{2} *1)+2\\=\frac{-3}{2} +2\\=\frac{-3+4}{2}\\=\frac{1}{2}\\[/tex]

If x = 2, then f(x)=

[tex]=(\frac{-3}{2} *2)+2\\=\frac{-6}{2} +2\\=\frac{-6+4}{2}\\=\frac{-2}{2}\\=-1[/tex]

If x = -1, then

[tex]f(x)=(\frac{-3}{2} *(-1))+2\\=\frac{3}{2} +2\\=\frac{3+4}{2}\\=\frac{7}{2}\\[/tex]

If x = -2, then

[tex]f(x)=(\frac{-3}{2} *(-2))+2\\=\frac{6}{2} +2\\=\frac{6+4}{2}\\=\frac{10}{2}\\=5[/tex]

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Four points are shown on a number line, which point represents - one and 3/4

Answers

Answer:

Step-by-step explanation:

I really need help pls!​

Answers

The integer that should be added to y² + 7y to make it factorable is 49/4.

What integer should be added?

To factor y² + 7y, we need to find two numbers that multiply to give us the coefficient of y (which is 7) and add up to give us the coefficient of y² (which is 1).

We can use the technique of completing the square to find the missing number.

To complete the square, we add the square of half of the coefficient of y (which is (7/2)² = 49/4) to both sides of the equation.

So, we have:

y² + 7y + 49/4 = y² + 7y + 49/4 + 49/4

= (y + 7/2)²

Therefore, to factor y² + 7y, we need to add 49/4 to it.

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Which statement is true?

Answers

The correct answer is (D) It is between 0.00007 and 0.0007 square miles

What is exponent ?

An exponent, also known as a power, is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript to the right of the quantity being raised to a power. For example, in the expression 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, or 2 x 2 x 2 = 8. Exponents are commonly used in mathematics, physics, engineering, and other sciences to represent very large or very small numbers, as well as to simplify calculations involving repeated multiplication.

According to the question:
To convert 7.4E-4 to a standard decimal, we move the decimal point four places to the left since the exponent is negative. This gives us:

7.4E-4 = 0.00074

Therefore, the area of the piece of land is 0.00074 square miles.

The correct answer is (D) It is between 0.00007 and 0.0007 square miles.

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The table below shows the number of credit cards owned by a group of individuals. If one person was chosen at random, find the probability that the person had no credit cards

Answers

The prοbability that a persοn chοsen at randοm has nο credit cards is:

P(nο credit cards) = 8/20 = 0.4 οr 40%

What is prοbability?

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, with 0 representing an impοssible event and 1 representing a certain event. The prοbability οf an event is calculated by dividing the number οf ways the event can οccur by the tοtal number οf pοssible οutcοmes.

Since we knοw the tοtal number οf credit cards and the number οf peοple whο οwn them, we can find the prοbability that a persοn chοsen at randοm has nο credit cards by dividing the number οf peοple with nο credit cards by the tοtal number οf peοple in the grοup:

Number οf peοple with nο credit cards: 8

Tοtal number οf peοple: 20

Therefοre, the prοbability that a persοn chοsen at randοm has nο credit cards is:

P(nο credit cards) = 8/20 = 0.4 οr 40%

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Complete Question:

Please help!!! WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!

Golf Skydiving Fishing 100-yard dash
Drag racing

1. Brainstorm: Which of the above sports do you think the graph could represent? Why?

2. Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?

(Photo of graph is added)
Please!!!!! 30 points added!

Answers

Answer:The graph represent skydiving, Because when you jump out of the plane you have a bunch of speed and when you pull your parachute the speed will drop exceedingly.

Step-by-step explanation:

DUE TODAY, I WILL MARK BRAINLIEST
screenshot provided!!

Answers

Answer:

6% for open side up

14% for closed side up

80% for landing on side

Determine what fraction of the figure is shaded.

Answers

Answer:

I would say that it would be 1/3 because there are 3 parts

Answer:

3/7

Step-by-step explanation:

There are 4 small squares inside the figure.

The partial squares are all half squares, so each two triangles have the same are as 1 small square. There are 6 small triangles which add to 3 squares.

4 + 3 = 7

Total area = 7 squares

Shaded area = 2 squares + 2 half squares = 3 squares

Fraction of shaded area = 3/7

the circumference of a circle is 20 π centimeters what is the area in square centimeters express your answer in terms of Pi​

Answers

Answer:

A = 100π cm²

Step-by-step explanation:

the area (A)  of a circle is calculated as

A = πr² ( r is the radius )

we require to find r

the circumference (C) of a circle is calculated as

C = 2πr

given

C = 20π , then

2πr = 20π ( divide both sides by 2π )

r = 10

Then

A = π × 10² = 100π cm²

4. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits.
b. If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?
My thoughts are that if she only invests 1200 she cant be loosing 10000 like the other people said about this question in here. The business would be loosing that amount of money not her right? but that question had a like 4.8 stars so i just want to confirm that it is correct they said it is 4 years to earn the money back but i think its less than a year. approx 0.6 Thanks to anyone who helps :)

Answers

a. Yes, she will make a profit of around $300.

b. It will take 4 years to earn back her initial investment.

How to solve

According to the given data, there is a 20% chance that the new business will lose $10,000, a 40% chance it will break even, a 30% chance it will make $5,000 in profits, and a 10% chance it will make $8,000 in profits.

By calculating the expected value, we get an estimate of $300.

To find the expected value :

0.2 × (-10,000) + 0.4 × (0) + 0.3 × 5,000 + 0.1 × 8,000 = $300

a. Yes, Claire should invest in the company. she will make a profit of around  $300 in a year.

b. If Claire's expected value will be $300 and her initial investment $1200.

1200 ÷ 300 = 4 years

It will take around 4 years to earn back her initial investment.

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In a unit circle, 0 = 270°. What is the terminal point?
A. (1,0)
B. (0,1)
C. (0, -1)
D. (-1,0)

Answers

The terminal point of the unit circle of angle 270° is (0, -1). The correct answer is (C).

Understanding Unit Circle

Unit Circle is a circle with a radius of one unit. In trigonometry, it is commonly used as a reference circle to understand the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for different angles.

From the unit circle question given above,

angle 0 = 360° represents the point (1,0) on the x-axis,

angle 90° represents the point (0,1) on the y-axis.

angle 180° represents the point (-1,0) on the negative x-axis,

angle 270° represents the point (0,-1) on the negative y-axis.

Therefore, if 0 = 270° in a unit circle, the terminal point would be (0,-1), which is option C.

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O 400
560
16
460
Attempt 1 of 2
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Grace needs to make 35 pounds of turkey for dinner. The turkey packaging at the grocery store indicates how many
ounces each turkey weighs. How many ounces of turkey does Grace need in order to have enough turkey for dinner?
O 500
20 21 22
23
ASK FOR HELP
SECTION 1 OF 1
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Answers

The answer of the given question based on the  ounces of turkey does Grace need in order to have enough turkey for dinner is , Grace needs 560 ounces of turkey for dinner.

What is Weight unit?

A weight unit is a standard of measurement used to express the mass or weight of an object. The most commonly used weight unit is the kilogram, which is the base unit of mass in the International System of Units (SI). Other common weight units include pounds, ounces, grams, and tons. Weight units are used in a variety of applications, including commerce, industry, and science. They are also used in everyday life to describe the weight of objects such as food, people, and animals. Accurate measurement of weight is important in many areas, including manufacturing, transportation, and health care. Weight units can be converted from one system to another using conversion factors.

There are 16 ounces in 1 pound. To convert 35 pounds to ounces, you need to multiply by 16:

35 pounds * 16 ounces/pound = 560 ounces

Therefore, Grace needs 560 ounces of turkey for dinner.

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The answer to the question is that Grace requires 560 ounces of turkey for dinner, or the amount of turkey she needs to have enough for dinner.

What is Weight unit?

A weight unit is a unit of measurement that is used to describe an object's mass or weight. The kilogram, the base measure of mass in the International System of Units, is the most widely used weight unit. (SI). The weights in pounds, ounces, grams, and tons are other popular weight units. Numerous fields, including business, industry, and research, use weight units.

In daily living, they are also used to describe the weight of things like food, people, and animals. In a variety of contexts, including production, transportation, and health care, accurate weight measurement is crucial. Conversion factors can be used to translate weight measures between different systems.

There are 16 ounces in 1 pound. To convert 35 pounds to ounces, you need to multiply by 16:

35 pounds * 16 ounces/pound = 560 ounces

Therefore, Grace needs 560 ounces of turkey for dinner.

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The complete question is,

Grace needs to make 35 pounds of turkey for dinner. The turkey packaging at the grocery store indicates how many ounces each turkey weighs. How many ounces of turkey does Grace need in order to have enough turkey for dinner?

The bill at a restaurant comes to $40. The sales tax is 6% and you will leave a 15% tip. What is the total cost?

Answers

40+6%+15%

=$ 42.55

I hope this helps!

Keisha is playing a game using a wheel divided into 8 equal sectors, as shown in the diagram below. Each time the spinner lands on blue, she will win a prize.

If Keisha spins this wheel twice, what is the probability that she will win a prize on both spins?

show step bye step

Answers

On solving the provided question we can say that As a result, Keisha's probability chances of winning a reward on both spins are 1/64, or around 0.0156.

What is probability?

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Because the results of the two spins are independent of each other, we need to multiply the chance of winning a prize on the first spin by the likelihood of winning a prize on the second spin to obtain the probability that She will win a prize on both spins.

Because there are 8 equal sectors on the wheel and only one of them is blue, the likelihood of winning a reward on any given spin is 1/8.

Hence the odds of winning a reward on both spins are:

(1/8) x (1/8) = 1/64

As a result, Keisha's chances of winning a reward on both spins are 1/64, or around 0.0156.

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help pls show ur work

Answers

The height of the telephone pole is approximately 12.5 ft.

And the ladder will reach approximately 6 ft up the building.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It focuses on the study of the functions of angles, such as sine, cosine, tangent, cosecant, secant, and cotangent, and how they are used to solve problems involving triangles.

Part 9:-To solve the problem, we can use trigonometry. Let's draw a right triangle where the height of the pole is the opposite side, the distance from the top of the pole to the attachment point of the guy wire is the adjacent side, and the guy wire itself is the hypotenuse. We know the length of the hypotenuse is 12 ft, and the length of the adjacent side is 9.5 ft. The angle between the hypotenuse and the ground is given as 51°.

Using the trigonometric function tangent, we can calculate the height of the pole as follows:

tan(51°) = height of pole / 9.5 ft

height of pole = tan(51°) × 9.5 ft

height of pole ≈ 12.5 ft

Therefore, the height of the telephone pole is approximately 12.5 ft.

Part 10:-Again, we can use trigonometry to solve the problem. Let's draw a right triangle where the height of the building is the opposite side, the distance from the base of the building to the ladder is the adjacent side, and the ladder itself is the hypotenuse. We know the length of the hypotenuse is 8 ft, and the angle between the hypotenuse and the ground is given as 46°.

Using the trigonometric function sine, we can calculate the height of the building as follows:

sin(46°) = height of building / 8 ft

height of building = sin(46°) × 8 ft

height of building ≈ 6 ft

Therefore, the ladder will reach approximately 6 ft up the building. Rounded to the nearest whole number, the answer is 6 ft.

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Draw a graph of two linear equations whose associated system has the solution (-1,-3).
Choose the correct graph.

Answers

Answer:

Step-by-step explanation:

first you sit on the tolit then think and you'll get your anwser

Core concept
EXAMPLE 4
Using the Distance Formula
Your school is 4 miles east and 1 mile south of your apartment. A recycling center,
where your class is going on a field trip, is 2 miles east and 3 miles north of your
apartment. Estimate the distance between the recycling center and your school.

Answers

The estimated distance between the recycling center and your school is approximately 4.47 miles.  

WHAT IS DISTANCE?

Distance is a numerical measurement of the amount of space between two points. In physics, distance is often described as the length of a path traveled by an object from one point to another. Distance is a scalar quantity, which means it has magnitude but not direction. It is typically measured in units such as meters (m), kilometers (km), feet (ft), or miles (mi).
Distance is an important concept in many fields, including physics, mathematics, geography, and engineering. It is used to describe the separation between two objects or locations, and to calculate various quantities such as speed, velocity, and acceleration.

To estimate the distance between the recycling center and your school, we can use the distance formula:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y) represents the coordinates of your school, (x₂, y₂) represents the coordinates of the recycling center, and the √ symbol denotes the square root.

From the problem statement, we know that:

Your school is 4 miles east and 1 mile south of your apartment. Therefore, the coordinates of your school are (4, -1).

The recycling center is 2 miles east and 3 miles north of your apartment. Therefore, the coordinates of the recycling center are (2, 3).

Substituting these values into the distance formula, we get:

distance = √((2 - 4)²+ (3 - (-1))²)

= √((-2)² + (4)²)

= √(4 + 16)

= √20

≈ 4.47 miles

Therefore, the estimated distance between the recycling center and your school is approximately 4.47 miles.

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A new water park, Tony’s Tidal Takeover, just opened. You have not heard anything specific about how much it costs to go to this park, but some of your friends have told you what they spent. The information is organized in the table below.

Answers

Since we can go on the same number of rides at both parks with $14, we would choose the park with the lower admission fee, which is Park A.

What is percent?

Percent is a way of expressing a number as a fraction of 100, often used to represent a proportion or rate. It is denoted by the symbol "%". For example, if 30 out of 100 students in a class got an "A" grade, then the percentage of students who got an "A" grade is 30%.

Here,

To determine which park to attend with only $14 to spend, we need to find out how many rides we can go on at each park with that amount of money.

For Park A, we can divide the $14 by the cost per ride, which is $2.50:

$15 - $12 = $3 for 4 rides,

$3 ÷ 4 = $0.75 per ride;

$0.75 x 2 rides = $1.50.

Thus, we can go on 2 rides at Park A.

For Park B, we can divide the $14 by the cost per ride, which is $1.50:

$16.50 - $12 = $4.50 for 6 rides,

$4.50 ÷ 6 = $0.75 per ride;

$0.75 x 2 rides = $1.50

Thus, we can go on 2 rides at Park B.

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