write an expression by expanding -5(-2d + 6)

Answer:

Step-by-step explanation:

First off, we need to remember that the arc measure is equal to the angle measure inside the circle. That means m(arc) MN is 70 degrees. Knowing this, we can find the measures of the other arcs:

m(arc)NP = 180 - 70 - 30 = 80

m(arc)QR = 70 based on vertical angles principle

m(arc)MR = 80+30 = 110 based on vertical angles and angle sum principles

Now we can list the answers using this:

1. 70

2. 70

3. 180

4. 210

5. 110

6. 110

Hope this helps!

The coordinates of the other endpoint, Q, are (3,-8).

The midpoint formula is used to find the coordinates of the midpoint of a line segment. The formula is as follows:
M = ((x1+x2)/2, (y1+y2)/2)

In this case, the midpoint M=(1,-2) and one endpoint P=(-1,4) are given. We can plug these values into the formula to find the coordinates of the other endpoint, Q:
(1,-2) = ((-1+x2)/2, (4+y2)/2)

Solving for x2 and y2, we get:
x2 = 2(1) + 1 = 3
y2 = 2(-2) - 4 = -8

Therefore, the coordinates of the other endpoint, Q, are (3,-8).

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product of diagonal elements is 10 x -2 = -20.

To find the value of the determinant of the coefficient matrix, perform row operations to reduce it to an echelon form. First, multiply the first row by -3, the second row by 5, and the third row by 2. This yields the following matrix:

(-9)x + (0)y - 18z = -33

(25)x - 10y + 15z = 85

(4)x - (2)y - 14z = -6

Next, subtract the first row from the second row and the first row from the third row. This yields the following matrix:

(0)x + (10)y - (18)z = 52

(4)x - (2)y - (14)z = -6

Finally, subtract 4 times the second row from the third row. This yields the following matrix:

(0)x + (10)y - (18)z = 52

(0)x - (0)y - (2)z = -24

This matrix is in echelon form. The value of the determinant is simply the product of diagonal elements, which is 10 x -2 = -20.

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Answer:D

Step-by-step explanation:

It’s D because 18 chocolate chip muffins and there are 9 blueberry muffins so for every blueberry muffin there is 2 chocolate chip muffins you could also do 18/9 and 2

Y = 4114/5114

3 (a) To solve 2557⋅X=457 for X∈Z57 using Euclid's algorithm, take the GCD of 2557 and 457. That is, the GCD is:

GCD(2557, 457) = GCD(2557 - 457, 457)

                  = GCD(2157, 457)

                  = GCD(757, 457)

                  = GCD(357, 457)

                  = GCD(157, 457)

                  = 457


Therefore, the GCD of 2557 and 457 is 457, and thus the solution to the equation is X = 457/2557.

3 (b) To find all solutions to the equation 50114⋅Y=8114 for Y∈Z114, we need to rewrite the equation in terms of ordinary integers, since the inverse of 50114 does not exist. The equation can be rewritten as Y = 8114/50114 = 8114/(5114⋅2114) = 4114/5114. This equation is the same as the one in part (a), with 25 replaced by 5. Thus, the solution to this equation is Y = 4114/5114, which is the same solution found in part (a). Therefore, there is only one solution to this equation, and this solution is Y = 4114/5114.

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The value of perimeter of CAR is  12 + 6√2 + 6√3. (C)

The value of the perimeter of triangle CAR can be found by adding the lengths of all three sides of the triangle.

In this case, the perimeter would be the sum of side CA, side AR, and side CR.

To find the perimeter, we can use the formula P = CA + AR + CR.

If we plug in the given values for each side, we can solve for the perimeter:

P = 6 + 6√2 + 6√3

P = 12 + 6√2 + 6√3

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The actual distance between City C and City D is 4,224,000 feet.

What is total distance?

Whole distance refers to the actual travel distance between the origin and destination locations of the item.

We can use the given scale to convert the distance between City A and City B to feet:

500 miles = 500 * 5280 feet = 2,640,000 feet

Since 1.6 feet represents this distance on the wall map, we have:

1.6 feet = 2,640,000 feet / x

where x is the actual distance represented by 1.6 feet on the map. Solving for x, we get:

x = 2,640,000 feet / 1.6 feet = 1,650,000 feet per foot

Therefore, the  total distance between City C and City D, which is 2.56 feet on the map, corresponds to:

2.56 feet * 1,650,000 feet per foot = 4,224,000 feet

So the actual distance between City C and City D is 4,224,000 feet.

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Answer:

Step-by-step explanation:

I'm guessing you meant to say Lewis had $30 starting.

Well since we have an inequality already, that saves time on me and I can show you how to solve!

[tex]30+11w\geq 89.99[/tex]

[tex]11w\geq59.99[/tex]

[tex]w\geq 5.4536[/tex]

If Lewis waited 5 weeks, he'd only have 85, so we need to round up to 6 weeks, where he'd have $96. Hope this helps!

The projected number of people affected by Alzheimer's Disease at t=20 is 6.7336.

The projected number of people affected by Alzheimer's Disease can be found by plugging in the value of t into the given equation P(t)=-0.0002083(20)^(3)+0.0142(20)^(2)-0.099(20)+4.7.

Plug in the value of t=20 into the equation:
P(20)=-0.0002083(20)^(3)+0.0142(20)^(2)-0.099(20)+4.7

Simplify the equation by solving the exponents and multiplying the coefficients:
P(20)=-0.0002083(8000)+0.0142(400)-1.98+4.7

Simplify the equation further by performing the arithmetic operations:
P(20)=-1.6664+5.68+2.72

Simplify the equation to get the final answer:
P(20)=6.7336
Therefore, the projected number of people affected by Alzheimer's Disease at t=20 is 6.7336.

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For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed.

The single mass - single energy absorber model of a 2021 Volkswagen ID.4 subjected to a frontal crash can be solved using a piecewise equation which will consist of three phases: loading, unloading and separation. The loading stiffness is 993.5 N/mm, the unloading stiffness is 18,027 N/mm and the vehicle mass is 2305 kg. The closed form solution for displacement, velocity and acceleration as a function of vehicle mass, initial velocity and energy absorber spring constants can be written as follows:

Displacement:

Loading phase:

$x_1(t) = \frac{F_{crash}}{m}t^2 + v_{in}t$

Unloading phase:

$x_2(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2$

Separation phase:

$x_3(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2 - \frac{K_u}{m}t^3$

Velocity:

Loading phase:

$v_1(t) = \frac{2F_{crash}}{m}t + v_{in}$

Unloading phase:

$v_2(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t$

Separation phase:

$v_3(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t - \frac{3K_u}{m}t^2$

Acceleration:

Loading phase:

$a_1(t) = \frac{2F_{crash}}{m}$

Unloading phase:

$a_2(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m}$

Separation phase:

$a_3(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m} - \frac{6K_u}{m}t$

For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed and plotted versus time. The peak displacement, peak acceleration, rebound velocity, time of max displacement, and time of vehicle-barrier separation can be tabulated and compared. The results of the model at 35 mph can be validated graphically and by tabulating the parameters listed above.

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S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

Let S1, S2 ⊂ V be two sets of vectors which are each linearly independent. To show that S1 ∩ S2 is linearly independent, we need to show that any linear combination of vectors in S1 ∩ S2 is equal to the zero vector only if all the coefficients are zero.

Let v1, v2, ..., vn be the vectors in S1 ∩ S2 and let a1, a2, ..., an be the coefficients in the linear combination a1v1 + a2v2 + ... + anvn = 0.

Since v1, v2, ..., vn are in S1 ∩ S2, they are also in S1 and S2. Therefore, the linear combination a1v1 + a2v2 + ... + anvn = 0 is also a linear combination of vectors in S1 and S2.

Since S1 and S2 are both linearly independent, this means that all the coefficients a1, a2, ..., an must be zero. Therefore, S1 ∩ S2 is also linearly independent.

In conclusion, if S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

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The margin of error of a study showed that 387 out of 900 people eat fast food regularly. We want to construct a 90% confidence interval for the population proportion of people who east fast food is   0.0234.The correct answer is option b. 0.0234.

To find the margin of error for a 90% confidence interval, we can use the formula:

Margin of error = z*√(p*(1-p)/n)

Where z is the z-score for a 90% confidence level, p is the sample proportion, and n is the sample size.

In this case, the z-score for a 90% confidence level is 1.645, the sample proportion is 387/900 = 0.43, and the sample size is 900.

Plugging these values into the formula, we get:

Margin of error = 1.645*√(0.43*(1-0.43)/900)

Margin of error = 0.0234

Therefore, the margin of error for the 90% confidence interval is 0.0234. Answer is b. 0.0234

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Answer:

2

Step-by-step explanation:

The sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

To split the given rational expression into a sum of two rational expressions with unlike denominators, we will use the partial fraction decomposition method. Here are the steps:

1. Factor the denominator of the given rational expression: (x^(2)+3x+2) = (x+1)(x+2)
2. Set up the partial fraction decomposition: (2x+3)/(x+1)(x+2) = A/(x+1) + B/(x+2)
3. Multiply both sides of the equation by the common denominator to get rid of the denominators: 2x+3 = A(x+2) + B(x+1)
4. Set up a system of equations by equating the coefficients of the like terms: 2x+3 = (A+B)x + (2A+B)
5. Solve the system of equations to find the values of A and B: A=1, B=1
6. Substitute the values of A and B back into the partial fraction decomposition: (2x+3)/(x+1)(x+2) = 1/(x+1) + 1/(x+2)

Therefore, the sum of two rational expressions with unlike denominators is 1/(x+1) + 1/(x+2).

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The angular speed of the pulley in rad/sec is 7.95 rad/sec, and the linear speed of the chain in cm/sec is 495.6 cm/sec.

First, we need to convert the pulley's rotational speed from RPM (revolutions per minute) to rad/s (radians per second). To do this, we can use the formula:

angular speed (in rad/s) = 2π × rotational speed (in RPM) / 60

Substituting the given values, we get:

angular speed (in rad/s) = 2π × 38 / 60 = 7.95 rad/s

Next, we can use the formula for linear speed of a point on the circumference of a circle:

linear speed = radius × angular speed

Substituting the values we have, we get:

linear speed = 26 cm × 7.95 rad/s = 206.7 cm/s

However, this is the linear speed of the pulley's circumference. Since the chain is attached to the pulley, its linear speed will be the same as the pulley's linear speed. Thus, the final answer for the linear speed of the chain is:

linear speed of chain = 206.7 cm/s × 2.4 = 495.6 cm/s

Here, 2.4 is the gear ratio of the chain to pulley.

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The correct option is For every 2 white marbles, Hal has 3 black marbles​.

The size, number, or amount of one thing or group as compared to the size, number, or amount of another, is called proportion.

A proportion is a mathematical comparison between two numbers. Often, these numbers can represent a comparison between things or people.

Proportion is an equation that defines that the two given ratios are equivalent to each other.

Proportions are actually equations with equal ratios.

A proportion or proportional situation occurs when two things are related in such a way that the ratios of corresponding parts are equal.

Given that, Hal compared the number of black marbles he had to the number of white marbles he had.

Number of black marble = 9

Number of white marble = 2

The proportion is 9 /2

= 3/2

Hence, the correct option is For every 2 white marbles, Hal has 3 black marbles​.

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The sequence follows a difference of 9.

According to the information, ball B is the one that reaches the highest height because after 1.5 seconds it has a height of 13m, while ball A has a height of 12m.

To identify the ball that reaches the highest we must solve the function shown. Additionally, to know what is the greatest height we must replace the value of x by 1.5 as shown below:

According to the above we can infer that this function gives a height less than the one shown in the table because the height of the ball is 12 and that of the table is 13. So 12 < 13.

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The requried measure of the angle x in at the point of intersection of tangent and secant of the circle is 30°.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

Here,
From the figure the,
From a point, a tangent and a secant are drawn to the circle.
Since an equilateral triangle is formed with the help of a cord intersects the tangent and secant on the circumference of triangle.

Again from the figure, the sum of the angle in the triangle is equal to 180°.
90 - 60 + 180 - 60 + x = 180
30 + 120 + x = 180
x = 30°

Thus, the requried measure of the angle x at the point of intersection of tangent and secant of the circle is 30°.

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Two pairs of consecutive interior angles are ∠5 and ∠9; ∠6 and ∠7.

The correct option is C,

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.

The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles. On the internal side of a transversal, two consecutive interior angles are situated adjacent to one another. To recognize them, the characteristics of successive inner angles.

Thus, only one pair of the angle from the options is satisfying the third and fourth characteristics. So, the correct option is C) ∠5 and ∠9; ∠6 and ∠7.

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Assuming the number of people who listen to the video increases by 45% each day, there would be approximately 24 new people who listen to the video on the 7th day after the initial 8 people.

According to the problem, the number of people listening to the video increases by 45% each day. Therefore, we can use the formula for compound interest to calculate the number of new people who listen to the video on the 7th day.

Let P be the initial number of people who listened to the video, which is 8.

Let r be the daily increase rate, which is 45% or 0.45 as a decimal.

Let n be the number of days, which is 7.

Then, the formula for compound interest is:

A = P(1 + r)^n

where A is the final number of people who listen to the video.

Plugging in the values, we get:

A = 8(1 + 0.45)^7

A ≈ 32

Therefore, the number of new people who listen to the video on the 7th day is approximately 32 - 8 = 24 people.

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The covariance of X and Y is Cov(X,Y) = 2/9; 7) The correlation coefficient of X and Y is Corr(X,Y) = 1.

Question: There is given a 2D joint probability density function f(x,y) = a(2x+y) + b if 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Find: 1) Coefficient a; 2) Marginal p.d.f. of X, marginal p.d.f. of Y; 3) E(X), E(Y), E (XY); 4) Var(X), Var(Y); 5) 0(X), (Y); 6) Cov(X,Y); 7) Corr(X,Y).

Answer: 1) The coefficient a is 163; 2) The marginal probability density functions of X and Y are fx(x) = a(2x + 1) and fy(y) = a(y + 2); 3) The expected values of X, Y, and XY are E(X) = 1/3, E(Y) = 2/3, and E(XY) = 4/3; 4) The variances of X and Y are Var(X) = 1/9, Var(Y) = 4/9; 5) The standard deviations of X and Y are 0(X) = 1/3, 0(Y) = 2/3; 6)

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The statement about cosecant, secant, and cotangent values that is correct is Kayla's: The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.

In Trigonometry, the sine of an acute angle is a ratio of the length of an opposite side of a right-angled triangle to the length of its hypotenuse. Also, the sine of an angle generally lies between -1 and 1.

In Trigonometry, the cosecant (cosec) of an acute angle is a ratio of the length of its hypotenuse to the length of an opposite side of a right-angled triangle. Thus, the cosecant of an angle is the reciprocal of the sine function and as such lies outside -1 and 1.

The cotangent of an acute angle is a ratio of the length of its adjacent side to the length of an opposite side of a right-angled triangle.

In conclusion, Kayla's statement about the values of cosecant, secant, and cotangent is correct.

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Answer:

Step-by-step explanation:

The simplified form of the expression log( 14/3 ) + log( 11/5 ) - log( 22/15 ) is log( 7 ).

Given the expression in the question;

log( 14/3 ) + log( 11/5 ) - log( 22/15 ) = ?

To simplify the expression, we use the property of logarithm.

log(a) + log(b) = log(ab)

log(a) - log(b) = log(a/b)

log( 14/3 ) + log( 11/5 ) - log( 22/15 )

log[ ( 14/3 ) × ( 11/5 ) ] - log( 22/15 )

Simplify

log[ 154/15 ] - log( 22/15 )

log[ 154/15 ] - log( 22/15 )

Now, using the quotient property of logarithm

log[ 154/15 ÷ 22/15 ]

log[ 154/15 × 15/22 ]

log[ 2310/330 ]

log( 7 )

Therefore, the simplified form is log( 7 ).

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The Correct statement is

ST and KT intersect at 90 degree.

The basic qualities listed below make it simple to identify parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

Parallel lines, no matter how far they are extended in either direction, never intersect.

Given:

We have given that ST || JK

First ST and JK have no perpendicular relation.

Now, ST and KT intersect at 90 degree.

Now, ST is not parallel to JT but it is given that ST || JK.

and, KT is act as transversal not JK.

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The smallest number among the given options is 0.125.

To determine the smallest number, we can compare each of the given numbers.

0.625 > 0.25 > 0.375 > 0.5 > 0.125

As we can see, the smallest number is 0.125, which is option E.

Comparison symbols are those that tell us whether one number is greater than, less than, or equal to another. The symbols are:

To sort in descending order, you must first place the number with the largest denomination until you reach the number with the smallest denomination.

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Answer:

Step-by-step explanation:

If the surface area of a cube is 160 in2, then which best describes the length of an edge of the cube?

The time taken to read 3 books is 8 weeks.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Christian read 1/4 book every 2/3 week.

Time taken to read 1 complete book is

1 × 2/3 ÷ 1/4

= 2/3 ÷ 1/4

= 2/3 × 4/1 (To divide two fractions, keep the first fraction same and change division to multiplication and inverse the second fraction)

= 8/3

Now, time taken to read 3 complete is

= 8/3 ×3

= 8

Therefore, time taken to read 3 books is 8 weeks.

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