10.5.PS-18 Question content area top Part 1 The diagram shows a track composed of a rectangle with a semicircle on each end. The area of the rectangle is square meters 11200. What is the perimeter of the​ track? Use 3.14 for pi.

The common factors of sixteen and twenty are 1, 2, and 4.

The factors of sixteen are 1, 2, 4, 8, and 16. The factors of twenty are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, and 4.

To calculate the factors of sixteen, we can start by dividing sixteen by two until we cannot divide any further. We can start with sixteen divided by two, which equals eight. Eight divided by two equals four. Four divided by two equals two. Two divided by two equals one. As we can see, the factors of sixteen are 1, 2, 4, 8, and 16

To calculate the factors of twenty, we can start by dividing twenty by two until we cannot divide any further. We can start with twenty divided by two, which equals ten. Ten divided by two equals five. Five divided by two equals two. Two divided by two equals one. As we can see, the factors of twenty are 1, 2, 4, 5, 10, and 20.The common factors of sixteen and twenty are 1, 2, and 4. This can be determined by comparing the two lists of factors. As we can see, 1, 2, and 4 are present in both lists.

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Complete question

What are the common factors of sixteen and twenty ?

The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:

Area of top of bookcase = lb

We want this area to be equal to 300 square inches. Therefore, we can write:

lb = 300

We are solving for "b", so we can rearrange this equation to solve for "b":

b = 300/l

Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:

b = 300/20 = 15

So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

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According to the Venn diagram the value of [tex]n(A ^ C \cap B ^ C) = {3}[/tex] so the number of elements in that set is 1.

What is Venn diagram ?

A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. It is usually represented as a rectangle or a circle for each set and the overlapping areas between them, showing the common elements that belong to more than one set. Venn diagrams are widely used in mathematics, logic, statistics, and computer science to visualize the relationships between different sets and help solve problems related to set theory.

According to the question:
To solve this problem, we first need to understand the notation used.

n(A) denotes the set A and the numbers within the braces {} indicate the elements in set A. For example, n(A)={7,4,3,9} means that the set A contains 7, 4, 3, and 9.

n(AnB) denotes the intersection of sets A and B, i.e., the elements that are common to both A and B. For example, n(AnB)={4,3} means that the sets A and B have 4 and 3 in common.

^ denotes intersection of sets

cap denotes the intersection of sets

Now, we need to find the elements that are common to sets A and C, and sets B and C. We can do this by taking the intersection of A and C, and the intersection of B and C, and then taking the intersection of the two resulting sets.

[tex]n(A ^ C) = n(A \cap C) = {3,9}[/tex]

[tex]n(B ^ C) = n(B\cap C) = {3,5}[/tex]

Now, we take the intersection of [tex]n(A ^ C)[/tex] and [tex]n(B ^ C)[/tex]:

[tex]n(A ^ C \cap B ^ C) = {3}[/tex]

Therefore, the answer is 1.

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Answer:

A.  z = 225

B.  The maximum value of z occurs at the points (22, 23) and (45, 0).

Step-by-step explanation:

To solve the linear programming problem using graphical methods, we need to graph the inequalities and find the feasible region. Then, we can identify the corner points of the feasible region and evaluate the objective function at each of these points to determine the maximum value of z.

Objective function:  z = 5x + 5y

Constraints:

Graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.

Rearrange the first three inequalities to isolate y:

[tex]\boxed{\begin{aligned}10x +6y &\geq 150\\6y &\geq-10x+ 150\\y &\geq -\dfrac{5}{3}x+25\\\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}13x - 13y &\geq - 13\\x -y &\geq -1\\ x +1 &\geq y\\ y &\leq x+1\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}x + y &\leq 45\\y&\leq-x+45\\\phantom{w}\\\phantom{w}\end{aligned}}[/tex]

Graph the inequalities.

The feasible region is the region that is shaded by all of the inequalities.

Please see the attached graph.

A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.  Therefore, as the feasible region for the given constraints is bounded, there is a maximum value of z.

The feasible region is bounded by the corner points:

Evaluate the objective function z = 5x + 5y at each of these corner points:

Point (9, 10):  z = 5(9) + 5(10) = 95

Point (22, 23):  z = 5(22) + 5(23) =225

Point (45, 0):  z = 5(45) + 5(0) = 225

Point (15, 0):  z = 5(15) + 5(0) = 75

Therefore, the maximum value of z is 225, which occurs at the corner points (22, 23) and (45, 0).

Answer:

Notice the change in sample size.

Answer:

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

The solution is given below. Notice the change in sample size.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.

so. we get,

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

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In equation 7(5x + 2) = -4(6 - 5x), Using the Distributive Property, we get 35x + 14 = -24 + 20x. So, the correct option is D).

To solve the equation 7(5x + 2) = -4(6 - 5x), a good first step is to use the Distributive Property to simplify both sides of the equation. Distributing the 7 and -4 on the left and right sides, respectively, we get

35x + 14 = -24 - 20x.

Next, we can combine like terms by adding 20x to both sides to get 55x + 14 = -24. Then, subtracting 14 from both sides, we get 55x = -38. Finally, we can solve for x by dividing both sides by 55, giving us x = -38/55. Therefore, the solution to the equation is x = -38/55.

The evaluation process involves performing arithmetic operations in a logical order to simplify the equation step-by-step until a solution is reached. So, the correct answer is D).

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Answer:

in this problem, it wants us to graph this piecewise function and then determine which answer choice matches. And I'm not sure if you gave me all the answer choices, but let's go ahead and try and graph this. So first we have a vertical line at negative three from negative 22 negative one. So here is -2. It's going to be open circled at negative two, two, which is going to have a closed circle since it's less than or equal to. And it would just connect right in there. Then we would have an open circle at negative one at negative two And then closed at zero And then an open circle at zero and -1 closed at one. So that would be a graph of this function. It doesn't look like I have all the answer choices, which you want to look for, the one that starts at -3. And it's open circle.

Step-by-step explanation:

hope its help

thank you

The answer is 4 5/6

Step-by-step explanation:

The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

An interactive widget in a graph is a tοοl that allοws the user tο manipulate different elements οf the graph using their mοuse οr tοuch screen.

Interactive widgets can be used tο explοre the behaviοr οf a functiοn οr dataset in a mοre dynamic and engaging way than a static graph.

Sοme cοmmοn examples οf interactive widgets in graphs include sliders, buttοns, checkbοxes, and drοpdοwn menus.

Here we have

y = -5 cοs (π/16 x) - 4    

Represents a periοdic functiοn with a cοsine wave shape that is shifted dοwnwards by 4 units.

The cοsine functiοn οscillates between -1 and 1, sο multiplying it by -5 stretches the wave vertically by a factοr οf 5 and reflects it acrοss the x-axis.

The cοefficient οf x, π/16, cοntrοls the periοd οf the functiοn, which is the distance between twο cοnsecutive peaks οr trοughs οf the wave.

Specifically, the periοd οf this functiοn is 32 units, since the cοsine functiοn has a periοd οf 2π and 2π/(π/16) = 32.

Therefοre,

The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]

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Answer:

Where is the table?

Step-by-step explanation:

Answer:

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

Given is the special right triangle.

It is a 45° isosceles right triangle. It has a property that the hypotenuse is √2 times the leg.

We have a hypotenuse of 28 units, so the leg is:

Answer:

14√2

Step-by-step explanation:

Here we need to find out the value of "x" in the given right angled triangle, here we can make use of trigonometric ratios to find out the value of x .

In a right angled triangle, sine is defined as the ratio of perpendicular and hypotenuse . With respect to angle 45° , x is the perpendicular and 28 is hypotenuse (side opposite to 90° ) .

So we have;

sin45° = x/28

1/√2 = x/28

x = 28*1/√2

x = 14 * (√2)² / √2

x = 14√2

Hence the value of x is 14√2 .

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

(a)

the experimental probability is just using the actual experience to predict any future results.

the total number of cases was 20, and the number of desired cases (yellow) was 12.

so, the experimental probability of landing on yellow is

12/20 = 3/5 = 0.600

(b)

the theoretical probability of a totally fair spinner landing on yellow is 2 out of 5 possibilities, so

2/5 = 0.4000

(c)

the correct statement is the first one.

with a more or less balanced (fair) spinner the experimental numbers should get closer and closer to the theoretical numbers, the more spins we make.

Answer:

E

Step-by-step explanation:

Answer has to have a star, the object (star) needs to be on the right side, and the two colors cannot be the same as any of the rest in the set. So E?

The number οf times that Greg chοοses a yellοw pebble is 22 times.

Thus, option D is correct.

Tο find the number οf pοssible chοices, calculate the number οf chances in the tοtal number οf οutcοmes.

Since we need tο find the number οf chοices that are expecting a yellοw pebble, find the tοtal number οf yellοw pebbles in the number οf pebbles in bοth Claire and Laura's cases and find the tοtal number οf yellοw pebbles.

Here we have

A table belοw shοws the number οf painted pebbles by Claire and Laura

Frοm the table,

Number οf pebbles that Laura painted = 8 yellοw, 7 green, 10 blue

Number οf pebbles that Claire painted = 14 yellοw, 5 green, 6 blue

Tοtal number οf yellοw pebbles = 8 + 14 = 22

Given that

Greg chοοses a pebble at randοm frοm the bοx 75 times, and each time replaces the pebble  

Hence, the number οf time that Greg get yellοw pebble = number οf yellοw pebbles

Therefοre, The number οf times that Greg chοοses a yellοw pebble is 22 times.

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a) Number of one-to-one functions are equal to the zero, because n< m.

b) Number of one-to-one functions are equal to the ⁵P₅ = 120.

c) Number of one-to-one functions are equal to the ⁶P₅ = 720.

c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.

One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then

Now, we have a domain set with five elements, m = 5

a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.

b) number of elements in another set,n= 5

So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)

= 5!/0! = 120

c) Number of elements in another set, n= 6

So, Number of one-to-one functions= ⁶P₅

= 6!/(6 - 5)!

= 6!/1! = 720

d) Number of elements in another set, n

= 7

So, Number of one-to-one functions

= ⁷P₅ = 7!(7 - 5)!

= 7!/2! = 2250

Hence, required value is 2250.

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Answer:

Step-by-step explanation:

The down payment is 30% of $235,000, which is $70,500. This means they are financing the remaining amount of $164,500.

Using the loan amount, interest rate, and loan term, we can calculate the monthly payment using the formula for a fixed-rate mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where:

M = monthly payment

P = loan amount

i = monthly interest rate (annual rate divided by 12)

n = total number of payments (loan term in years multiplied by 12)

Plugging in the numbers, we get:

M = 164500 [ 0.038/12 (1 + 0.038/12)^360 ] / [ (1 + 0.038/12)^360 – 1]

Simplifying this expression, we get:

M = $765.84

Therefore, their anticipated monthly payments would be $765.84.

According to the question. A. No punctuation is missing.

Punctuation is the use of symbols to indicate the structure and organization of written language. It is used to help make the meaning of sentences clearer and to make them easier to read and understand. Punctuation marks can also be used to indicate pauses in speech, to create emphasis, and to indicate the speaker’s attitude. There are many different types of punctuation marks, each with its own purpose. The most commonly used punctuation marks are the period, comma, question mark, exclamation mark, quotation marks, and the apostrophe.

Quotation marks are used to enclose quoted material, while the apostrophe is used to indicate possession or to replace missing letters in a word or phrase. By using punctuation correctly, writers can ensure that their messages are correctly understood by their readers.

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Answer:

Step-by-step explanation:

Question 1

Part A:

To predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of spins, which is 500.

The possible outcomes of the first spinner are 1, 2, and 3, and the possible outcomes of the second spinner are 4, 5, 6, 7, and 8. The minimum sum we can get is 1+4=5, and the maximum sum we can get is 3+8=11.

To get a sum less than 10, we can get:

1+4=5

1+5=6

1+6=7

1+7=8

1+8=9

2+4=6

2+5=7

2+6=8

2+7=9

3+4=7

3+5=8

3+6=9

There are 12 possible outcomes that result in a sum less than 10. So the probability of getting a sum less than 10 is 12/15, or 4/5.

To find the number of times Harris will spin a sum less than 10, we can use the equation:

probability of getting a sum less than 10 × total number of spins = x

So the equation that can be solved to predict the number of times Harris will spin a sum less than 10 is:

C) 12/15 = x/500

Part B:

To find the number of times Harris should expect to spin a sum that is 10 or greater, we can subtract the number of times he will spin a sum less than 10 from the total number of spins:

total number of spins - number of times he will spin a sum less than 10 = number of times he should expect to spin a sum that is 10 or greater

Substituting the values, we get:

500 - (12/15 × 500) = 500 - 400 = 100

So Harris should expect to spin a sum that is 10 or greater 100 times.

False. The second moment about mu for a binomial experiment is not given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0.

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q=1-p.

The second moment about mu is a measure of the variability of the binomial distribution, and is given by the formula[tex]E[(X-mu)^2][/tex] , where X is the random variable, mu is the mean, and E is the expected value operator.

To calculate the second moment about mu for a binomial distribution with parameters n and p, we can use the formula npq, where np is the mean and q=1-p. This formula can also be derived using the properties of variance, which state that [tex]Var(X)=E[X^2] - (E[X])^2.[/tex]

Therefore, the statement that the second moment about mu for a binomial experiment is given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0 is false. This statement does not relate to the binomial distribution or its properties, and is not a relevant formula for measuring the variability of a binomial experiment.

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The rate at which electric charge flows through a circuit is used to quantify electrical current: I (t) equals dQ (t) / dt. The derivative of the electric charge by time yields the momentary current. I (t) is the amps of the transient current I at time t. (A).

The temporary electric charge, measured in coulombs, is Q(t) (C).

The time in seconds is t. (s).

I =ΔQ / Δt

ΔQ is the amount of electric current flowing at time Δt, measured in coulombs (C).

The time length in seconds is t. (s).

We know that I = dQ/dt by definition; thus, if Q = f(t), then I = f' (t). By stating this, we obtain the current's expression as follows:

I (t) = (d/dt) (Q(t)) = (d/dt) (6t + 2t2) = 6 + 4t:  I(t) = 4t + 6; t >= 0

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Answer:

0.75

Step-by-step explanation:

0.4 = 0.40

Add 0.40 + 0.35 = 0.75

Answer:

A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.

A painter can paint 100 square feet of the pyramid in 18 minutes.

How long does it take the painter to paint 75% of the pyramid?

Step-by-step explanation:

The total surface area of the pyramid can be calculated using the formula for the lateral surface area of a pyramid:

Lateral surface area = (1/2) × perimeter of base × slant height

Since the base is an equilateral triangle, the perimeter is 3 times the length of one side:

Perimeter of base = 3 × 40 feet = 120 feet

Lateral surface area = (1/2) × 120 feet × 50 feet = 3000 square feet

To paint 75% of the pyramid, the painter needs to paint:

0.75 × 3000 square feet = 2250 square feet

Since the painter can paint 100 square feet in 18 minutes, the time required to paint 2250 square feet can be calculated as:

2250 square feet ÷ 100 square feet per 18 minutes = 225 ÷ 10 × 18 minutes = 405 minutes

Therefore, the painter would need 405 minutes or 6 hours and 45 minutes to paint 75% of the pyramid.

Therefore, Ashley's annual premium on the contents of her house is $127.80.

Percent is a term used to express a fraction or a ratio as a portion of 100. It is denoted by the symbol % (per cent or percent). Percentages are commonly used in many different contexts, such as finance, statistics, science, and everyday life. They are used to express changes, comparisons, rates, probabilities, and many other types of information. To calculate a percentage, we usually divide the part by the whole and multiply the result by 100.

Here,

Based on the provided table, we can calculate Ashley's annual premium on her house and the contents of her house as follows:

Annual premium on Ashley's house:

Since Ashley's house is made of brick and located in a rural area, we can use the values from the "Brick" and "Rural" columns of the table. The premium per $100 of coverage for a brick house in a rural area is $0.60 for the building and $0.69 for the contents.

To calculate the annual premium for the house, we first need to determine the coverage amount. The coverage amount is the value of the house divided by 100, so in this case, it is $85,000 / 100 = $850.

The annual premium for the house is then calculated by multiplying the coverage amount by the premium per $100 of coverage:

Annual premium on house = coverage amount * premium per $100 of coverage for brick house in rural area

= $850 * $0.60

= $510

Therefore, Ashley's annual premium on her house is $510.

Annual premium on Ashley's contents:

To calculate the annual premium for the contents of Ashley's house, we use the same method as above. The coverage amount is the value of the contents divided by 100, so in this case, it is $18,000 / 100 = $180.

The annual premium for the contents is then calculated by multiplying the coverage amount by the premium per $100 of coverage:

Annual premium on contents = coverage amount * premium per $100 of coverage for contents in rural area

= $180 * $0.71

= $127.80

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Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to draw an angle that is 150}^{\circ}.[/tex]

[tex]\textsf{We will need a Protractor to draw this angle.}[/tex]

[tex]\large\underline{\textsf{To Draw an Angle with a Protractor;}}[/tex]

[tex]\textsf{First, notice a point at the bottom of the Protractor. This is where we will start.}[/tex]

[tex]\textsf{Draw a Straight Line from the point to the 0}^{\circ} \ \textsf{mark.}[/tex]

[tex]\textsf{Secondly, use a ruler to carefully draw a straight line towards the 150}^{\circ} \ \textsf{mark.}[/tex]

[tex]\textsf{Note that some Protractors may be different from others. Similar steps should apply.}[/tex]

[tex]\textsf{Refer to the picture. It represents what the angle should look like afterwards.}[/tex]

To do :-

Instruments required:-

Steps of construction:-

Hence angle ECB represents 150° .

Precaution:- do not change the arm length of the compass.

and we are done!

The probability that it takes Jack between 5.3 minutes and 6.5 minutes to finish the next apple is 0.24.

a. Since Jack takes between 5 and 11 minutes to finish an apple, there is no way he can take more than 11 minutes to finish one. The probability that it takes Jack more than 12 minutes to finish the next apple is 0.

b. To find the probability that Jack takes less than 5.8 minutes to finish the next apple, we need to calculate the probability of X being less than or equal to 5.8.

Since X is uniformly distributed between 5 and 11, we can find this probability by calculating the proportion of the interval [5, 11] that is less than or equal to 5.8:

[tex]P(X < = 5.8) = (5.8 - 5) / (11 - 5) = 0.8[/tex]

the probability that Jack takes less than 5.8 minutes to finish the next apple is [tex]0.8[/tex] .

c. To find the probability that it takes Jack between 5.3 minutes and 6.5 minutes to finish the next apple, we need to calculate the proportion of the interval [5, 11] that falls within this range:

[tex]P(5.3 < = X < = 6.5) = (6.5 - 5.3) / (11 - 5) = 0.24[/tex]

d. To find the probability that it takes Jack fewer than 5.3 minutes or more than 6.5 minutes to finish the next apple. we can find the probability of the complement event, which is the probability that Jack takes between 5.3 minutes and 6.5 minutes to finish the apple:

[tex]P(X < 5.3 or X > 6.5) = 1 - P(5.3 < = X < = 6.5) = 1 - 0.24 = 0.76[/tex]

Therefore, the probability that it takes Jack fewer than 5.3 minutes or more than 6.5 minutes to finish the next apple is [tex]0.76[/tex]  .

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The correct graph that matches the given function is option (C).

To graph a function, select x-values and input them into the equation. Once those values have been put into the equation, you will get a y-value. The x and y values together make up a single point's coordinates.

Option is the appropriate graph for the specified function (C).

For x -2, the function is f(x) = (x+5), which is a half-parabola that starts at (5, 0) and travels through (2, 3) before opening towards the positive y-axis. Both (A) and (B) are incompatible with this aspect of the function.

The function is f(x) = |x+1| for -2 x 2, which is a V-shaped graph with an upward opening and a vertex at (1, 0). This portion of the function is covered by Option (C).

When x is greater than 2, the function is f(x) = (x2)2, which is a parabola with an upward opening and a vertex at (2, 0). This portion of the function is covered by Option (D).

No portion of the function matches option (E).

Thus, option is the appropriate graph that matches the specified function (C).

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Answer:

Dont understand. Repeat question?

Step-by-step explanation:

Answer:

  40.3%

Step-by-step explanation:

You want to know the percentage of a 62 gram allowance of fat is represented by a burger with 25 grams of fat.

The fraction can be converted to a percentage by multiplying by 100%.

  burger/allowance = (25 g)/(62 g) × 100% = 40.3%

King has 40.3% of his daily allowance for fat when he ate his burger.

The value of x is 30° as per below diagram.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

We know that,

Draw a line segment BG is with CBG equal to 20° on line CE.

So that, (40 + x)  = 70, so that means x = 30°

Therefore, The value of x is 30°

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Complete question here-

Triangle: According to the question the value of x is 30° as per below diagram.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

We know that,
All the angles in a triangle sum → 180°
An isosceles triangle: two equal angles → two equal sides.
Draw a line segment BG is with CBG equal to 20° on line CE.
So that, (40 + x)  = 70, so that means x = 30°
Therefore, The value of x is 30°

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