Diego’s history teacher writes a test for the class with 30 problems. The test is worth 50 points and has two types of problems: multiple choice worth 1 point each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning

The value of c in the given question is 77.5.

When something can be seen as a gauge of how important something is to a person or organization, it is frequently seen as a reflection of one's worldview and can help to shape attitudes, decisions, and behaviors. Value is a subjective concept that refers to the word of importance that an individual group of people places on something. It is frequently associated with fundamental beliefs and standards that are accepted by society. Depending on the context of the commands, believe is a relative concept.

The Triangle Angle Sum Theorem, which asserts that the sum of the angles in a triangle equals 180°, must be applied in order to find x. Segment AD cuts angle BAC in half, hence the two angles must be equivalent. In order to solve for x, we can build up the following equation:

180° = angle BAC = (x + 7) + (x + 18)

We can solve this equation by combining like terms and isolating the variable x.

180° = 2c + 25

2c = 155

C = 77.5

Therefore, the value of C is 77.5.

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Answer:

arc FA = 150°

Step-by-step explanation:

the central angle of a circle is equal to the measure of the arc that subtends it.

given BF is the diameter of the circle , then

∠ FCA + ∠ ACB = 180°

∠ FCA + 30° = 180° ( subtract 30° from both sides )

∠ FCA = 150°

then

arc FA = ∠ FCA = 150°

The Kansas City Chiefs has a better chance of winning the super bowl 2023.

In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.

The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.

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The kind of triangle which is shown in the image is Obtuse triangle. The Option B is correct.

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Characteristics of Obtuse Angled Triangle:

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The speed of both the trains would be 400 mph and 450 mph respectively.

The formula to calculate the distance travelled is -

Distance = Speed x Time

Given is that two cities are 1020 miles apart. Two trains simultaneously left these cities heading toward one another. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours, the trains had not met yet and were 170 miles apart.

Let the speed of one train be {x} mph. Then, the speed of the other train would be {x + 10} mph.

Distance covered by both the trains would be -

train { 1 } = 5x                             ... { 1 }

train { 2 } = 5(x + 10)                          ... { 2 }

Now, we can write -

1020 - {5x + 5(x + 10)} = 170

1020 - 170 = 10x + 50

10x = 800

x = 80

Speed of train { 1 } = 400 mph

Speed of train { 2 } = 450 mph

Therefore, the speed of both the trains would be 400 mph and 450 mph respectively.

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The area of the shaded region is given as follows:

0.0475.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

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

The mean and the standard deviation for the IQ scores are given as follows:

[tex]\mu = 100, \sigma = 15[/tex]

The shaded region is the area to the right of 125, hence it's area is one subtracted by the p-value of Z when X = 125, hence:

Z = (125 - 100)/15

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

Hence:

1 - 0.9525 = 0.0475.

The shaded region is the area to the right of 125.

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The amount in the college fund is $16,899.66

In order to determine the amount in the college fund, we need to find the  future value of the money.

The formula for the future value of money is:

FV = PV * (1 + r)^t

where:

FV = future value

PV = present value (initial amount)

r = interest rate (as a decimal)

t = time (in years)

PV = $5000, r = 7% = 0.07, t = 18

FV = PV * (1 + r)^t

FV = 5000 * (1 + 0.07)¹⁸

FV = 5000 * (1.07)¹⁸

FV = $16,899.66

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Complete Question

When a new baby is born to the Johnsons, the family decides to invest $5000 in an account that earns 7% interest as a way to start the baby's college fund. If they do not touch that investment for 18 years, how much will there be in the college fund?

The number of rounds that Kate has to run along the perimeter of town to complete  12 miles is 4 rounds.

What is the perimeter of a triangle?

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape. The perimeter of any polygon is equal to the sum of its side lengths. Considering a triangle, the sum of the three sides equals the perimeter.

Given the town is the shape of a triangle.

The distance covered after running one round around town is equal to the perimeter of the triangle.

The sides of the triangle are 0.7 miles, 1.4 miles and 0.9 miles.

Perimeter = 0.7+0.9+1.4 = 3 miles.

The distance covered in one round = 3 miles.

So the number of rounds required to complete 12 miles = 1/3 * 12 = 4 rounds.

Therefore the number of rounds that Kate has to run along the perimeter of town to complete  12 miles is 4 rounds.

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The side x = 9.4 approximately to nearest tenth using the cosine rule.

In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Considering the given triangle, side x is calculated with cosine rule as follows;

a² = b² + c² - 2(b)(c)cosA

x² = 8² + 15² - 2(8)(15)cos33°

x² = 64 + 225 - 240(0.8387)

x² = 289 - 201.2809

x² = 87.7191

x = 9.3658 {take square root of both sides}

With proper application of the cosine rule, we can conclude the value of the side x of the triangle is approximately 9.37 to the nearest tenth.

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We can solve steps in expressions with many operations in accordance with the order of operations. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. The fourth rule is that we always add and subtract from left to right.

Use the acronyms PEMDAS or BODMAS to determine the sequence of operations. PEMDAS: Parentheses ⇒  (3+4)

Exponents ⇒ 3², Multiply ⇒ 8*4, Divide ⇒ 12÷4, Add ⇒ 6+6, Subtract ⇒ 10-5. BODMAS: Brackets, Order, Divide, Multiply, Add, Subtract .A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Using PEMDAS, we can retain the following order: Exponents, parentheses, addition, subtraction, multiplication, and division (from left to right) Parentheses, exponents, multiplication, division, addition, and subtraction are the orders in which operations must be performed, according to the order of operations. Both BODMAS and PEMDAS are valid and in use in various parts of the globe.

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The one word that fits in each case will be slope, equal, decreasing, and increasing, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A steep line has a bigger slope than a flat line.

Equally steep lines have equal slopes.

Lines that go up from left to right have decreasing slopes.

Lines that go down from left to right have increasing slopes.

The one word that fits in each case will be slope, equal, decreasing, and increasing, respectively.

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Answers of integer expression is -4, -10, 14 and -11.

A number system is defined as a system of writing to express numbers.

The first expression is -5+8-7

-5+8-7

Add the minus terms and then add with positive eight.

-12+8

The answer of integer expression is -4

2. The second expression is -12-7+9

-19+9

When minus nineteen and plus nine are added we get minus ten.

The answer of integer expression is -10

3. 9-13+18

Add the two positive integers and then use subtraction

27-13

14

The answer of integer expression is 14

4. 7-15-3

Add the negative values and add the positive seven.

7-18

-11

The answer of integer expression is -11

Hence, answer of integer expression is -4, -10, 14 and -11.

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Answer:

HECD

Step-by-step explanation:

1. -5 + 8 - 7 = -4: H

2. -12 - 7 + 9 = -10: E

3. 9 - 13 + 8 = 4: C

4. 7 - 15 - 3 = -11: D

Code: HECD

None. There are no references in this line. This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.

This line does not contain any references, so no references can be null. Therefore, no NullPointerException can be thrown.

This line of code does not contain any references at all. Therefore, it is not possible for any references to be null, and it is impossible for a NullPointerException to be thrown in response to this line. NullPointerExceptions are only thrown when a program attempts to use a reference that is null, but this line does not contain any references, so such an exception is not possible. Consequently, no references can be null in this line and no NullPointerException can be thrown.

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Answer:

20.2%

Step-by-step explanation:

he relative difference between two values can be calculated using the formula:

Relative Difference = (|V1 - V2| / ((V1 + V2) / 2)) * 100%

where V1 is the first value and V2 is the second value.

For the U.S. per capita consumption of beef, we have V1 = 67.8 pounds in 2000 and V2 = 55.4 pounds in 2016. Plugging these values into the formula, we get:

Relative Difference = (|67.8 - 55.4| / ((67.8 + 55.4) / 2)) * 100%

Relative Difference = (12.4 / 61.6) * 100%

Relative Difference = 0.202 * 100%

Relative Difference = 20.2%

So the relative difference between the U.S. per capita consumption of beef in 2000 and 2016 is 20.2%.

Answer:

(y+2)^2

= y^2 + 4y + 4

now plug in -4 in y's

=(-4)^2 + 4(-4) + 4

=8-16+4

=-4

Answer:

Step-by-step explanation:

42*2/3=84/3=28

Your commission for a month in which your sales people sold $1,250,000 in insurance policies is $62500

We know that in order to determine the percentage, we divide the value by the total value and then multiply the resultant by 100.

The formula for the percentage would be,

percent = (number of parts / total number of possible parts) × 100%

Here, for a particular month your sales people sold $1,250,000 in insurance policies.

As we can see that your commission would be 5% of all sales over $1,000,000

Let us assume that your commission for that month be x dollars.

Since 1,250,000 > 1,000,000

We need to find 5 percent of $1,250,000

i.e., x = 5 percent of $1,250,000

Using percentage formula,

x = 1,250,000 × (5/100)

x = 62500

Therefore, your commission will be 62500 dollars.

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Answer:

it will be £960

Step-by-step explanation:

first £800×20/100

simplify £8×20

£160= VAT

Total cost=VAT+ normal cost

£160+£800

=£960

The expression "The product of m and n divided by three times their difference" can be written as (m * n) / (3 * (m - n)).

Let's break this down:

"The product of m and n" means you multiply m by n, which is written as "m * n".

"Divided by" means you divide the product by something else. In this case, we're dividing by "three times their difference".

"Their difference" refers to the difference between m and n, which is written as "m - n".

"Three times their difference" means you multiply the difference by 3, which is written as "3 * (m - n)".

So, putting it all together, we have:

(m * n) / (3 * (m - n))

This expression represents the product of m and n, divided by three times their difference.

It's important to note that this expression is undefined when m = n, because in that case, the denominator (3 * (m - n)) would be equal to zero. Division by zero is undefined, so we cannot evaluate the expression when m = n.

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The sum of the first fifteen terms of the given sequence is 220.

The given sequence can be expressed as: [tex]$2, 8, 14, \dots$[/tex], in which each term is six more than the preceding term. This is an arithmetic sequence, where the common difference between terms is 6. The formula to calculate the sum of the first n terms of an arithmetic sequence is given by [tex]$S_n = \frac{n}{2}(a_1 + a_n)$[/tex], where [tex]$a_1$[/tex] is the first term and [tex]$a_n$[/tex] is the nth term.

In the given sequence, the first term [tex]$a_1$[/tex] is 2 and the 15th term [tex]$a_n$[/tex] is 42. So, plugging these values to the formula gives us, [tex]$S_{15} = \frac{15}{2}(2+42) = \frac{15\times 44}{2} = 220$[/tex].

Therefore, the sum of the first fifteen terms of the given sequence is 220.

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Answer:

The table that represents a linear function is:

x 0 1 2 3 4

y −2 1 0 1 −2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation: The linear function is a function that has a straight line when plotted on a

graph.

The correct option;

The table of ordered pairs that represent a linear function is the option; x/y  -8/-7  0/0  8/7  16/14

Reasons why the above selection is correct:

Given;

The given data can be presented as follows;

x/y -8/22 0/1 8/22 16/102

x/y -8/-7 0/1 8/9 8/2

x/y -8/-7 0/0 8/7 16/14

x/y -8/-7 0/1 8/5 16/4

Representation of the options in tabular form;

In a tabular format, we have;

Characteristic of linear function;

In a linear function, when the x-values have a constant rate of increase the

the first difference in the y-values is constant.

Selection of the table representing a linear function;

The option that has a constant first difference along with a continuous rate of

increase in the x-value is the option with the following table;

, which is the option x/y -8/-7 0/0 8/7 16/14

we can pour no more than 541 cheerios into the bowl while maintaining a density of no more than 0.3 cheerios per square inch.

What is rectangle ?

Rectangle can be defined in which the opposite sides are equal and area of rectangle is product of length and breadth.

Given ,

I poured a bowl of cereal in a Tupperware container with the following dimensions (L=9 in, w=6 in, h=3). I want no more than a density of 0.3 cheerios per sq in in my "bowl."

We can start by calculating the surface area of the Tupperware container, which is equal to 2 times the sum of the area of the base and the area of the two rectangular sides:

Area of base = Length * Width = 9 in * 6 in = 54 in²

Area of two rectangular sides = Height * Length = 3 in * 9 in = 27 in²

Surface area = 2 * (54 in² + 27 in²) = 2 * 81 in² = 162 in²

Next, we can find the maximum number of cheerios that can be poured into the bowl by dividing the surface area by the maximum allowed density of 0.3 cheerios per square inch:

Maximum number of cheerios = Surface area / Maximum allowed density = 162 in² / 0.3 cheerios/in² = 541 cheerios

Hence, we can pour no more than 541 cheerios into the bowl while maintaining a density of no more than 0.3 cheerios per square inch.

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There are 15 employees in the office and 5 need to be chosen, so there are a total of (15 choose 5) possible ways to select the employees. This can be calculated using the formula for combinations:

(15 choose 5) = 15! / (5! * 10!) = 3003

Now, we need to find the number of ways that the specific group of you, Diana, Kyle, Nancy, and Arthur can be chosen. This is simply (5 choose 5), since we want to choose all 5 members of the group.

(5 choose 5) = 5! / (5! * 0!) = 1

Therefore, the probability of this specific group being chosen is:

(5 choose 5) / (15 choose 5) = 1 / 3003 ≈ 0.0003

So the probability of you, Diana, Kyle, Nancy, and Arthur being chosen is very low, at approximately 0.0003 or 3 in 10,000. This is because there are many other possible groups of 5 employees that could be chosen from the pool of 15, and all of these groups have an equal chance of being selected.

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Answer: it is already factored

Step-by-step explanation:

Both of these are correct. When multiplying 32 and 8, we should follow these steps:

So, the correct answer is 256.

Here is the multiplication shown step-by-step:

 32
   8

 16 --> drop down 6 and carry the 1

1
32
   8

   6

24-   --> drop down the 4 and add 1; carry the 2

 56

2

 32
    8

   6

 5 -

2 - - --> drop down the 2 since no more digits available to multiply

256 --> the answer

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total cookies first to find ratio values

8 + 9 + 7 + 6 = 30 total

first ratio is sugar cookie to total

7 / 30 chances

after eating the sugar cookie, the total reduces to 29

second ratio is the new total

8 / 29 chances.

potential bonus??

the odds of this happening in this exact order is both odds multiplied.

so (7/30) × (6/29) = 7 / 145 chances she completes this in the exact order stated.

The greatest common factor ( GCF ) of 21 , 14 and 7 is given by A = 7

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the GCF of the numbers be represented as A

Now , the equation will be

Let the first number be p = 21

Let the second number be q = 14

Let the third number be r = 7

Now , the factors of 21 = 1 , 2 , 3 , 7 and 21

The factors of 14 = 1 , 2 , 7 and 14

The factors of 7 = 1 and 7

So , the greatest common factors of 21 , 14 and 7 is 7

Hence , the GCF is 7

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Answer:

B and D

Step-by-step explanation:

the correct answer is : B and D

Let's first understand what's relative here, it refers to Point of reference , the point, in respect to which other's position are to be considered, which here is O, the Origin with coordinates (0,0) as we are talking about two-dimensional reference frame. What position vector means? Say, we have the point of Reference X, and we've the position vector of Y with respect to X, then it can be written as [tex]{\overrightarrow{XY}}[/tex]. Now, using this simple rule we can have,

Now, let's calculate [tex]{\overrightarrow{AC}}[/tex] firstly;

[tex]{:\implies \overrightarrow{AC}=\overrightarrow{OC}-\overrightarrow{OA}}[/tex]

[tex]{:\implies \overrightarrow{AC}=8\hat{i}+(\lambda -7)\hat{j}}[/tex]

Now, here [tex]{AC}[/tex] just means the the magnitude of the vector [tex{\overrightarow{AC}}[/tex], and we're aware that magnitude of a vector [tex]{\overrightarrow{X}=x\hat{i}+y\hat{j}}[/tex] is given by, [tex]{X=\sqrt{x^{2}+y^{2}}}[/tex], so according to question;

[tex]{:\implies \sqrt{64+(\lambda -7)^{2}}=17}[/tex]

Squaring both sides;

[tex]{:\implies (\lambda -7)^{2}=289-64=225}[/tex]

[tex]{:\implies \lambda -7=\pm 15}[/tex]

[tex]{:\implies \boxed{\underline{\bf{\lambda =22,\:or\:-8}}}}[/tex]