Can somebody help awnser these questions

The length of the midsegment of trapezoid is 24 units.

An open, flat figure with four successive sides and one pair of parallel sides is termed to as a trapezoid or trapezium.

The parallel and non-parallel sides of a trapezium are called as the bases and the legs, respectively. A trapezium may also have parallel legs. The parallel sides can be slanted, vertical, or horizontal.

The altitude is the evaluation of the angle perpendicular to the parallel sides.

Now in the given question,

a = 15

b = 23

length of mid segment EF,

[tex]l=\frac{a+b}{2} \\\\l=\frac{15+23}{2} \\\\l=\frac{48}{2} \\\\l=24[/tex]

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Answer:

9.968

Step-by-step explanation:

[tex]c^2=a^2+b^2 -2ab*cos(C)[/tex]

and more generally, a side squared of a triangle is equal to the other two sides squared then added, minus double the product of the other two sides and the cosine of the opposite angle, generally denoted as the capital letter of the side. (c is the side, C is the opposite angle)

in this case the other two sides are 7 and 10, so we can say that a=7, b=10 if  it helps understand this a bit more, but "a" and "b" really just represent the other two sides.

the opposite angle is: [tex]\frac{5\pi}{13}[/tex] and the unknown is "a", but we can just express it as "c" for the sake of simplicity. Now plugging in all the known values we get the following equation:

[tex]c^2=7^2+10^2-2(7)(10)cos(\frac{5\pi}{13})\\\\c^2=49+100-140cos(\frac{5\pi}{13})\\\\c^2=149-140cos(\frac{5\pi}{13})[/tex]

Now from here we can just use a calculator to approximate the cosine, but make sure it's in radian mode! otherwise your answer may be incorrect as degrees are different than radians.

[tex]c^2=149-140(0.3546)\\\\c^2=149-49.64468\\\\c^2=99.355315814\\\\c=\sqrt{99.355315814}\\\\c=9.96771367035\\\\c\approx 9.968[/tex]

So the side is approximately 9.968 units in length.

The length of CD can be found to be 7. 21 units .

The length of CD can be found by using the distance formula which is :

= √ [ ( x ₂ - x ₁ ) ² + ( y ₂ - y ₁ ) ² ]

Given the points, ( 3, - 2 ) and ( 7, - 8 ).

The length of CD is :

= √ [ ( 7 - 3 ) ² + ( - 8 - (- 2 ) ) ² ]

= 7. 21

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The true statement is (d) The area of triangle XYZ is equal to the area of triangle X'Y′Z

From the question, we have the following parameters that can be used in our computation:

Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y'Z'.

The rotation is a rigid transformation

This means that it does not change the side length and angles of a shape when applies

Using the above as a guide, we have the following:

The image and the preiamage have the same area

Hence, the true statement is (d)

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Complete question

Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y′Z'.

y. z. y. x. x.

Which statement is true?

The sum of the angle measures of triangle XYZ is 90° less than the sum of the angle measures of triangle X'Y′Z'.

The angle measures of triangle XYZ are less than the corresponding angle measures of triangle X'Y′Z'.

Triangle XYZ is not congruent to triangle X'Y′Z'.

The area of triangle XYZ is equal to the area of triangle X'Y′Z

Answer: a. From the perspective of the 30-year-old male, the monetary value corresponding to surviving the year is -$154 (the cost of the insurance policy). The monetary value corresponding to not surviving the year is $99,805 (the death benefit payout).

b. If the 30-year-old male purchases the policy, his expected value can be calculated using the formula:

Expected Value = (Probability of Event A) * (Value of Event A) + (Probability of Event B) * (Value of Event B)

In this case, the probability of surviving the year and not surviving the year can be assumed to be the same, as we don't have any specific information on the individual's health or life expectancy. Therefore, the probabilities can be assumed to be 0.5 each.

Plugging in the values, we get:

Expected Value = (0.5) * (-$154) + (0.5) * ($99,805) = ($50,326)

So, the expected value for the 30-year-old male purchasing the policy is $50,326.

Step-by-step explanation:

The boolean expression that evaluates to True if "x is non-negative and y is negative" is: (x >= 0) ∧ (y < 0).

A boolean expression is a logical expression that evaluates to either true or false. Boolean expressions can be composed of one or more boolean operators, such as AND, OR, and NOT, and can involve one or more variables.

We need to find boolean expression for: "x is non-negative and y is negative", then output is true.

The boolean expression is:

(x >= 0) ∧ (y < 0), or (x>=0) AND (y<0)

In this expression, the ∧ symbol represents the logical AND operator. The expression (x >= 0) checks if x is greater than or equal to 0 (i.e. non-negative), and the expression (y < 0) checks if y is less than 0 (i.e. negative).

If both conditions are true, the overall expression evaluates to true, indicating that x is non-negative and y is negative.

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Answer:12

Step-by-step explanation:30-6=24

24 divided by 2 =12

The positive coterminal angle less than 360° is, 55°

Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).

To find a positive angle that is coterminal with -1025°,

we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.

Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:

= -1,025° + 1080°

=   55°

Since this angle is less than 360°,

Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.

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The interpret the numbers in this model is -17,732 is a constant amount credited from the savings account, 367 is the amount saved per year of age, 1300 is the amount saved per year of education.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.

Given that;

The equation of savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth.

Now,

-17,732 is a constant amount credited from the savings acount

367 is the amount saved per year of age

1300 is the amount saved per year of education

0.116 is the amount save per household wealth

Therefore, the following are the interpretations of the equation.

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Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:

P= 100%[([tex]1.03^{t}[/tex]) - 1]

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

An increasing exponential function is modeled by:

A(t)= A(0)[tex](1+r)^{t}[/tex]

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

As a percentage, the increase is modeled by:

P= 100%[[tex](1+r)^{t}[/tex] - 1]

In this problem, the growth rate is of r = 0.03, hence:

P= 100%[      [tex](1+0.03)^{t}[/tex]- 1]

P= 100%[[tex](1.03)^{t}[/tex]- 1]

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Answer:

4 cups of fruit sorbet.

Step-by-step explanation:

There are 128 cups in 1 gallon. So, 1 gallon of fruit sorbet is equal to 128 cups.

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

The solution is, each person get 4 cups of fruit sorbet.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Hugo is serving fruit sorbet at his party.

He has 1 gallon of fruit sorbet to serve to 32 friends .

now. we get,

There are 128 cups in 1 gallon.

So, 1 gallon of fruit sorbet is equal to 128 cups.

so, we have,

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

If each person receives the same amount,

then, each person will receive 4 cups of fruit sorbet.

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By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.

In the next step, we need to Identify the solution to the system.

If the lines are intersected, the point of intersection is the solution.

If the lines are parallel, the system will have no solution.

If the lines are the same or coincident, then the system will have an infinite number of solutions.  

Here we have

y = x  ----- (1)

y = 2x+2 ---- (2)

From (1) and (2)

=> y = 2y + 2

=> 2y - y = -2

=> y = - 2

Hence, the solution of the given system of the equation is (-2, -2)

We can check it by graphing the lines as shown figure.  

Therefore,

By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

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15) Evaluating the mathematical expression -10 -144/(-12) shows that 144 is being divided by 12 before subtracting 10, following the application of PEMDAS.

16) The value of the algebraic expression is 2.

The evaluation of an expression is finding its value by substituting variables and applying the PEMDAS rule.

PEMDAS means the order of algebraic operations that applies parentheses, exponents, multiplication, division, addition, and subtraction.

-10 -144/(-12)

-10 + (144/12)

-10 + 12

= 2

Thus, we have evaluated the expression to have a value of 2.

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answer c)

cross x  at x = -2, x = 3, and x = 1

the square root tells us that it bounces off that location rather than intercepting

Answer:

2+1=3, 7+8=15, 0+1=1, 8+7=15, 2+9=11, 1+3=4, 2+0=0, 4+5=9, 3+4=7

A student would have to score approximately 0.84 standard deviations above the mean to be publicly recognized.

The dispersion of asset prices from their average price, or market volatility, can be calculated with the use of standard deviation. A large standard deviation indicates a dangerous investment when prices move erratically. Low standard deviation indicates stable prices, which lowers the risk associated with investments.

The remaining 79 percent of pupils are not recognised if just the top 21% of students receive public recognition. Since a normal distribution is assumed, the conventional normal distribution and its corresponding z-scores can be used to provide the solution.

The percentage of scores that are higher than a certain z-score is shown by the area under the standard normal distribution to its right. Finding the z-score that represents the top 21% of scores is equivalent to locating the z-score that represents the bottom 79% of scores. By using a calculator or a table of the ordinary normal distribution, we can determine that the z-score for the bottom 79 percent of scores is roughly 0.84.

In order to be officially acknowledged, a student would need to get a score that is roughly 0.84 standard deviations above the mean.

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The values of the operations between the two functions are, respectively:

In this problem we find the representations of two functions, each on one Cartesian plane: f(r), h(r). Based on that information we can determine the result of operations between functions, which are defined below:

Addition

(f + h)(x) = f(x) + h(x)

Subtraction

(f - h)(x) = f(x) - h(x)

Multiplication  

(f · h)(x) = f(x) · h(x)

Division

(f / h)(x) = f(x) / h(x)

Now we proceed to determine each operation:

(f + h)(5) = f(5) + h(5) = 3 + 4 = 7

(h - f)(2) = h(2) - f(2) = 1 - 1 = 0

(f · h)(3) = f(3) · h(3) = 4 · 0 = 0

(h / f)(0) = h(0) / f(0) = 3 / 5

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9.19% of the total is made up of Green.

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of green cars = 120

Number of green planes = 250

Number of green trains = 500

Total = 870

Now,

The total number of all colors of the car, plane, and train.

= 870 + 1250 + 820 + 800 + 990 + 4730

= 9460

Now,

The percentage of green cars, planes, and trains.

= 870/9460 x 100

= 9.19%

Thus,

9.19% of the total is made up of Green.

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The others operate in a similar manner. The following must be done, however, in order to determine the probability of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:  1 - P(kit-kat)

You only need to multiply the quantity of the selected candy by the total number of candies if you choose to put each piece of candy back after choosing it.

In this case, the desired confectionery is P(snickers). 12 in number.

In total, the bag contains 20 sweets.

P(snickers) = 12/20 = 3/5

The others function in the same way. The following must be done, however, in order to determine the likelihood of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:

1 - P(kit-kat)

The complete question is:

Suppose a bag of candy contains 12 Snickers, 5 Kit-Kats, and 3 Three Musketeers. Find each probability if you choose one piece of candy at random.

a) P(Snickers) b) P(Kit-Kat) c)P(Three Musketeers) d) P(not Kit-Kat)

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The needed amount of each solution is given as follows:

The amounts are obtained using a system of equations, for which the variables are given as follows:

Faith needs 300 milliliters of the solution, hence:

x + y = 300.

x = 300 - y.

The percentage is of 57%, hence:

0.5x + 0.6y = 0.57 x 300

0.5x + 0.6y = 171.

Replacing the first equation into the second, the value of y is obtained as follows:

0.5(300 - y) + 0.6y = 171

0.1y = 21

y = 21/0.1

y = 210.

The value of x is then given as follows:

x = 300 - 210

x = 90.

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Answer: To find the monthly rent during the 11th year, we need to calculate the total increase in rent over the course of 10 years and then add that to the original monthly rent of $900.

The total increase in rent over 10 years is $120 per year * 10 years = $1200.

So, the monthly rent during the 11th year would be $900 + $1200 = $2100.

Therefore, the monthly rent during the 11th year would be $2100.

Step-by-step explanation:

Answer:

smaller value = 4yd

larger value = 8yd

Step-by-step explanation:

Let's call the garden's width and length W and L respectively.

The area of the garden is 36yd². We can write this mathematically as W*L=36

If 26yd is enough fencing to perfectly enclose the garden, then this must be the garden's perimeter. Written mathematically, this is 2W+2L=26. We can simplify this by dividing each term by two to get W+L=13

If W and L multiply to get 36, they must be both a factor pair of 36. The factor pairs of 36 (the pairs of numbers which multiply to get 36) are '1 and 36', '2 and 18', '3 and 12', '4 and 9', and '6 and 6'.

W and L must also add to 13, and the only factor pairs of 36 which add to 13 are '4 and 9' so these are our dimensions.

Answer:

smaller value = 4yd

larger value = 8yd

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The relations that represent functions are given as follows:

A relation represents a function when each input value is mapped to a single output value.

Hence the two items that are not functions in this problem are given as follows:

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Answer: The present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

PV = PMT * [ (1 - (1 + r)^-n) / r ] * (1 + r)

where:

PMT = $300 (the monthly payment)

r = 0.06/12 (the monthly interest rate)

n = 10*12 (the number of periods over 10 years, with 12 months in a year)

Plugging in the values into the formula, we get:

PV = $300 * [ (1 - (1 + 0.06/12)^-n) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - (1 + 0.06/12)^-(10*12)) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 1.06^-120) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 0.379362539) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (0.620637561) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * 10.34300138

PV = $31,029.

So the present value of the annuity due is $31,029. This means that if you were to invest $31,029 today, you would receive a monthly payment of $300 for 10 years at 6% interest compounded monthly.

Step-by-step explanation:

The height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.

What is called height?

Height, altitude, and elevation mean the vertical distance either between the top and bottom of something or between a base and something above it. height refers to something measured vertically whether high or low.

Each time the ball bounces, it reaches a height of 75% of its previous height.

Since the ball was dropped from a height of 2 meters, its height after the first bounce will be:

2 meters x 0.75 = 1.5 meters

After the second bounce, the height of the ball will be:

1.5 meters x 0.75 = 1.125 meters

After the third bounce, the height of the ball will be:

1.125 meters x 0.75 = 0.84375 meters

After the fourth bounce, the height of the ball will be:

0.84375 meters x 0.75 = 0.6328125 meters

After the fifth bounce, the height of the ball will be:

0.6328125 meters x 0.75 = 0.474609375 meters

Therefore, the height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.

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Answer:

1,3 or 4,2

Step-by-step explanation:

On solving the provided question we can say that here, trigonometry, f(x) = -7cos(1x) + -3 => f(1) = -7

Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.

Trigonometry is used here.

f(x) = -7cos(1x) plus -3

f(1) = -7

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Answer:

the answer is 25c²

Step-by-step explanation:

(5c-3d)²-9d²

5²c²+3²d²-9d²

25c²+9d²-9d²

25c²

Answer:

= 25c² - 30cd

Step-by-step explanation:

(5c-3d)²-9d²

[tex](5c - 3d)(5c - 3d) - 9 {d}^{2} \\ 5c(5c - 3d) - 3d(5c - 3d) - 9{d}^{2} \ \\ 25 {c}^{2} - 15cd - 15cd + 9 {d}^{2} - 9 {d}^{2} \\25 {c}^{2} - 30cd[/tex]

Answer:

Of the shapes you mentioned (circle, square, triangle, rectangle), the only one that has only one line of symmetry is the triangle. All other shapes have multiple lines of symmetry.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given a family net income of $13150, Lisa's current annual gross of $76200, deductions of 20% of Lisa's gross salary, you want to know Lisa's monthly net income and the new family net income if Lisa makes 35% less by working part-time.

Lisa's current annual income is $76200, and her annual net income is 80% of that, or $60960. On a monthly basis, her net income is ...

  $60960/12 = $5080 . . . . . . Lisa's current net monthly income

If her income is reduced by 35%, the reduction is ...

  0.35 × $5080 = $1778

Then Lisa's part-time monthly net income will be ...

  $5080 -1778 = $3302 . . . . . Lisa's part-time monthly net income

The family net income will be reduced by the same amount:

  $13150 -1778 = $11372 . . . . . new family monthly net income

__

Additional comment

It appears the total of budgeted items is $10343, so those items can be paid even if Lisa works part-time. The family's current surplus income of $2807 would be reduced to $1029, about a 63% reduction. That gives a lot less cushion to pay for off-budget expenses that may come up.