6. Part D
Another method of proving diagonals of a parallelogram bisect each other
uses a coordinate grid.
A.
P (r, t)
S (0, 0)
R (s, 0)
What could be shown about the diagonals of parallelogram PQRS to com
the proof?
PR and SQ have the same length.
PR is a perpendicular bisector of SQ.
PR and SQ have the same midpoint.
D. Angles formed by the intersection of PR and SQ each measu
B.
Q
(r+s, t)

Answer:

  77.5°

Step-by-step explanation:

You want the measures of the angles formed when ray OX bisects the 155° angle AOB.

The angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...

  155°/2 = 77.5°

Answer:

3 inches is approximately equal to 76.2 millimeters.

Step-by-step explanation:

Answer:

3 inches = 76.2 millimeters

Step-by-step explanation:

Answer: the weight of the wheat still in the truck is 5000 pounds.

Step-by-step explanation:

Here are the steps to calculate the weight of the wheat still in the truck:

Convert the weight of the unloaded wheat to tons. To convert from pounds to tons, divide by 2,000:

1000 lbs / 2000 lbs/ton = 0.5 tons

Subtract the weight of the unloaded wheat from the original weight:

3 tons - 0.5 tons = 2.5 tons

Convert the answer back to pounds:

2.5 tons * 2000 lbs/ton = 5000 lbs

Therefore, the weight of the wheat still in the truck is 5000 pounds.

Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

What is meant by budget?

Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.

We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.

So we can set up the following system of equations:

x + y = 168 (total amount of punch)

1.57x + 2.41y = 1.66(168) (total cost of punch)

Simplifying the second equation:

1.57x + 2.41y = 278.88

Now we can use substitution or elimination method to solve for x and y.

Using substitution:

x = 168 - y

1.57(168 - y) + 2.41y = 278.88

264.36 - 1.57y + 2.41y = 278.88

0.84y = 14.52

y = 17.29

So Hannah needs 17.29 gallons of fruit drink.

Using x + y = 168, we can find that she needs 150.71 gallons of soda.

Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

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The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator.

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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The predicted number of principals in attendance at the conference can be 161

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

A recent conference had 850 people in attendance.

In one exhibit room of 60 people, there were 46 teachers and 14 principals.

The predicated number of principals = ?

The ratio of teachers to principals  = 60/14

                                                          = 30/7

In the same ratio there will be total teachers and principals:

Suppose, the number of teachers = x

the number of principals = y

x + y = 850

x/y = 30/7

x = (30/7)y

(30/7)y + y = 850

37y = 850 x 7

y  = 161 (approx)

Hence, the number of principals cab be 161

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Answer:

D

Step-by-step explanation:

There were about 198 principals in attendance. EZ

Using Euler's formula, the expressions can be rewritten as Im = sin(e^j) - sinh(1), exp(e^j) = e^(cos(1) + j*sin(1)) and e^[(1/2)√(2)e^(j(π/4+2π*n))] respectively

1.

Cos(e^j) can be expressed using Euler's formula as:

Cos(e^j) = (e^(je^j) + e^(-je^j)) / 2

= (cos(e^j) + cosh(1)) + j(sin(e^j) - sinh(1))

Re = cos(e^j) + cosh(1)

Im = sin(e^j) - sinh(1)

2.

exp(e^j) can also be expressed using Euler's formula as:

exp(e^j) = e^(cos(1) + j*sin(1))

3.

(sqrt(j))^sqrt(j) can be written as:

(sqrt(j))^sqrt(j) = e^[(1/2)√(2)e^(j(π/4+2π*n))]

where n is an integer. This is because the logarithm of a complex number has infinitely many possible values due to the periodicity of the exponential function.

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Answer:

2,19/3 this is answer this is correct

Answer:

RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.

For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.

For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.

For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.

For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.

So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340

The value of x is 9 by using the concept of corresponding angles.

Corresponding angles are the angles formed when two parallel lines are crossed by any other line. It may also be generated in matching edges(corners) or corresponding corners with the transversal.

From the information given:

(8x + 9) is corresponding to the opposite side of the transversal with an angle of 99 degrees.

Using the sum of angles on a straight line.

Step 1: (8x + 9)° + 99 = 180°

Step 2: 8x + 108 = 180

Step 3: 8x = 72

Step 4: x = 9

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Answer:

the answer to this question is 936

Solving the provided question, we can say that equatiοn of slope intercept will me as y -y1 = m(x-x1) => 3x - y = -1

In mathematics, the intersectiοn point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crοsses on a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equation fοr the straight line to show this.

The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept fοrm. When an equatiοn has the intercept form (y=mx+b), the slοpe is m and the y-intercept is b. Sοme equations can also be rewritten such that they seem to be slοpe intercepts. If y=x is rewritten as y=1x+0, fοr instance, the slοpe and y-intercept are bοth changed to 1.

Here,

coordinates are

M(2,5) and P(a,-2)

equation of slope intercept will me as

y -y1 = m(x-x1)

y - 5 = 3x-4

3x - y = -1

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Answer:

Step-by-step explanation:

Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:

Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:

y0 = 3,500

Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:

r = 0.05

Write the equation for exponential growth. The formula for exponential growth is given by:

y = y0 × (1 + r)^x

where x is the number of years after the nature center is built.

So, the equation for the function in this case would be:

f(x) = 3,500 × (1 + 0.05)^x

This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.

12 hours

If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours

Answer:

5.333 hours.

Step-by-step explanation:

Put this on a chart:

6 people = 8 hours

4 people = ? hours

To find ? Use crisscross multiplication and solve:

? = (4 * 8) / 6

? = 32 / 6

? = 5.333

Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.

Answer:

1: 9 polar bears and 38 penguins

2: 47 snowglobes

3: 130 snowballs

4: 97 penguins

Step-by-step explanation:

i did the math

The average daily balance for Pete's credit card last month was a dollars. The finance charge was f dollars. APR algebraically is: 12f/a.

Finance charge = Monthly interest rate · Average daily balance

Monthly interest rate = APR/12

Where:

Finance charge = f

Average daily balance = a

f= Monthly interest rate · a

f = APR/12 · a

f/a  = APR/12

12.f/a = APR

Therefore APR algebraically is: 12f/a.

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The y-intercept b of the equation of the line is 30.

The graph represent a linear relationship between the temperature in degree farad and time in minutes.

Therefore, let's find the y-intercept b of the equation.

Hence, using slope intercept form,

y = mx + b

where

Therefore,

y = 20x + b

where

Using (6, 150) let's find b as follows:

y = 20x + b

150 = 20(6) + b

150 - 120 = b

Therefore,

b = 30

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Answer:

This system of equations can be solved using substitution or elimination methods.

Using substitution, we can solve for one of the variables in one of the equations and substitute that expression into the other equation.

Solving for x in the second equation:

x + 3y = 1

x = 1 - 3y

Substituting this expression for x into the first equation:

-4(1 - 3y) - 15y = -10

Expanding and solving for y:

-4 + 12y - 15y = -10

12y - 4 = -10

12y = -6

y = -1/2

Now that we know y = -1/2, we can substitute this value back into the expression for x:

x = 1 - 3(-1/2) = 1 + 3/2 = 7/2

So the solution to the system of equations is (7/2, -1/2).

Checking the solution in both equations:

-4(7/2) - 15(-1/2) = -4(7/2) + 15/

Step-by-step explanation:

The angle of the base and the ladder is 69. 34 degrees

Note that the six trigonometric identities are;

From the information given, we have that;

Hypotenuse = 17 meters

Adjacent = 6 meters

The identity to use is the cosine

cos θ = adjacent/hypotenuse

Substitute the  values

cos θ = 6/17

cos θ =,0. 3529

Take inverse of cos

θ = 69. 34 degrees

Hence, the value is 69. 34 degrees

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Answer:

89392i + 788

Step-by-step explanation:

The divide by 5 and the multiply by 5 cancel out, and we cannot simplify 89392i + 788 any further, since we don't know what i is. Therefore the answer is 89392i + 788.

Hope that helps!

The probability that the hiker will reach his destination is, 1/2

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the hiker chooses one of the four trails with equal probability by rolling a fair 4-sided die,

the probability of taking any one trail is 1/4.

Once the hiker is on a trail, there are two sub-trails, and the hiker chooses one of them by flipping a fair coin.

The probability of taking the correct sub-trail is 1/2.

P(reaching destination) = P(trail 1) x P(correct sub-trail on trail 1) + P(trail 2) x P(correct sub-trail on trail 2) + P(trail 3) x P(correct sub-trail on trail 3) + P(trail 4) x P(correct sub-trail on trail 4)

P(reaching destination) = (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2)

P(reaching destination) = 4/8

P(reaching destination) = 1/2

Therefore, the probability that the hiker will reach his destination is 1/2, or 50%.

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One reason to compute a correlation coefficient to measure the strength of the relationship between two variables is that quantify the strength and direction of the correlation in a precise and standardized way..

When we have two variables that are related, we say that there is a correlation between them. The most common way to visually represent a correlation is by plotting the data on a scatter plot, where each point represents a pair of values for the two variables.

While a scatter plot is a useful tool to visualize the relationship between two variables, it doesn't tell us how strong or weak the correlation is. For instance, two variables might show a positive correlation, but the scatter plot might be quite dispersed, indicating that there is a lot of variability in the data. In this case, we would say that the correlation is weak. On the other hand, if the scatter plot is tightly clustered around the line, we would say that the correlation is strong.

This is where the correlation coefficient comes in. The correlation coefficient is a mathematical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation.

To compute the correlation coefficient, we first need to calculate the covariance between the two variables. Covariance is a measure of how much the two variables vary together, and it is defined as the sum of the products of the deviations of the values from their respective means. Once we have the covariance, we can divide it by the product of the standard deviations of the two variables to get the correlation coefficient.

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The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.

What's meant by rate?

Areas If the scale factor of the sides of two analogous polygons is m/ n

 also the rate of the areas is (m/n)^2.

Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.

It's given that, the rate of peripheries of two analogous quadrilateral is 2 4

 now,  

to find the rate of area, we can take two quadrilaterals, say square.

Square ABCD of side 2 units and Square PQRS of side 4 units.

now rate of areas,

[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]

[tex]=\frac{2 \times 2}{4 \times 4}[/tex]

= 4/16

= 1/4

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Liters of 10% solution = 1 liters

Liters of 70% solution = 5 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x +3 = 8 is an equation.

We have,

10% solution = x

70% solution = y

Now,

A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution.

This means,

We can make two equations.

0.10x + 0.70y = 6 x 0.20

0.10x + 0.70y = 1.2 ______(1)

x + y = 6 ______(2)

Solve for x and y.

From (2),

x = 6 - y

Substituting in (1) we get,

0.10x + 0.70y = 1.2

0.10 (6 - y) + 0.70y = 1.2

0.6 - 0.10y + 0.70y = 1.2

0.6 + 0.60y = 1.2

0.60y = 1.2 - 0.6

0.60y = 0.6

y = 1

And,

x = 6 - y

x = 6 - 1

x = 5

Thus,

10% solution = 1 liter

70% solution = 5 liters

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Answer:

The height of the triangle is 14 m,

Step-by-step explanation:

Let the base be x, then the height is:

The area is half the product of base and height.

Set up equation and solve for x:

The first root is discarded as negative. The second root is the answer.

The base is 3 m, so the height is:

Answer:

The height of the triangle is 14 m.

Step-by-step explanation:

The area of a triangle can be found by using the following formula:

[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]

where:

If the height of a triangle is 8 m more than twice the length of the base, then an expression for h in terms of b is:

[tex]h = 2b + 8[/tex]

Rewrite this equation to make b the subject:

[tex]\implies 2b=h-8[/tex]

[tex]\implies b=\dfrac{1}{2}h-4[/tex]

Given the area of the triangle is 21 m², substitute this value along with the found expression for b into the formula for area of a triangle:

[tex]\implies \dfrac{1}{2}\left(\dfrac{1}{2}h-4\right)h=21[/tex]

To find the height of the triangle, solve the equation for h.

[tex]\implies \dfrac{1}{4}h^2-2h=21[/tex]

[tex]\implies h^2-8h=84[/tex]

[tex]\implies h^2-8h-84=0[/tex]

[tex]\implies h^2-14h+6h-84=0[/tex]

[tex]\implies h(h-14)+6(h-14)=0[/tex]

[tex]\implies (h+6)(h-14)=0[/tex]

Apply the zero-product property:

[tex]h+6=0 \implies h=-6[/tex]

[tex]h-14=0 \implies h=14[/tex]

As length cannot be negative, the height of the triangle is 14 m.