1000, 200, 40, .... Find the 50th term:​

The required answers are

a) b = -4

b) x = 23.45

c) p = 201

The distributive property implies that multiplying a number by the sum of two or more addends yields the same result as dividing the multiplier, multiplying each addend individually, and combining the products . It can be given as,

a (b+c) = d

[tex](a*b) + (a*c) = d[/tex]

Now in the given question,

a) −1/2(b−6)= 5

by distributive property , we have

[tex](\frac{-1}{2} *b)-(\frac{-1}{2}*6 )=5\\\frac{-1}{2}b+3=5\\\frac{-1}{2}b=2\\b=-4[/tex]

b) 0.4(x−0.45)= 9.2

by distributive property , we have

0.4x - 0.4(0.45) =9.2

0.4x -0.18 = 9.2

0.4x = 9.38

x = 23.45

c) −4(p−212)=44

by distributive property , we have

-4p +4 (212) = 44

-4p + 848 =44

-4p = 44 - 848

-4p = -804

p = 201

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Answer:

Step-by-step explanation:

because if you multipled 7 times 8 you will get 56 and if you add it with 45 you will get 101

i hope this help

After 8 weeks of saving, Alexa will have a total of $101. The expression to show the money Alexa saves in 'w' weeks is 45 + 7w.

The subject of this question is

Mathematics

and it is geared towards

Middle School

grades. To solve this problem, we need to use

algebraic expressions

. Based on the problem given, Alexa has $45 initially and saves $7 per week additionally from her after school job. So if she saves for 8 weeks, Alexa would have accumulated an additional $7 times 8 = $56. Therefore, the total amount of money Alexa would have after 8 weeks is her initial amount of $45 plus the additional $56, which equals $101. To represent this in terms of an expression, where 'w' stands for weeks, you can write 45 + 7w. This expression lets us calculate the total savings for any number of weeks 'w'.

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Answer:

if the angle has the arrow on top pointing straight up thats a right angle if it is leaning towards the left instead it is obtuse and if is getting closer to the right side it is acute.

Step-by-step explanation:

i can't tell you anything else if there is no picture to base this question.

Answer:

x = 8 - 3y - 2z

Step-by-step explanation:

Step-by-step explanation:

x + 3y + 2z = 8

3x + y + 3z = -10

-2x - 2y - z = 10

we solve this by eliminating variables or expressing sine variables by others, and then solve for the remaining one. with that value we then cancer back to solve for the other variables.

in our case the easiest way is the elimination via combinations of equations.

let's first multiply equating 1 by -3 and then add that to equation 2 :

-3x - 9y - 6z = -24

3x + y + 3z = -10

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

0 - 8y - 3z = -34

8y + 3z = 34

then multiply equation 1 by 2 and add it to equation 3 :

2x + 6y + 4z = 16

-2x - 2y - z = 10

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

0 4y + 3z = 26

now we subtract this result from the previous result :

8y + 3z = 34

- 4y + 3z = 26

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

4y 0 = 8

y = 8/4 = 2

4×2 + 3z = 26

3z = 18

z = 18/3 = 6

x + 3×2 + 2×6 = 8

x = -10

so,

x = -10

y = 2

z = 6

Answer:aaaa

Step-by-step explanation:because

The correct option is SE is 0.04. In statistics, a sample proportion is a statistic that represents the proportion of individuals in a sample who have a particular characteristic or belong to a certain category.

The standard error of the sample proportion can be calculated as follows:

SE = sqrt(p * (1 - p) / n)

Where p is the sample proportion and n is the sample size. In this case, the sample proportion is 0.2, and the sample size is 200. So, plugging these values into the formula, we get:

SE = sqrt(0.2 * (1 - 0.2) / 200)

SE = sqrt(0.16 / 200)

SE = 0.04

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Answer: [tex]-\frac{9}{8}[/tex]

Step-by-step explanation:

If you are given two points of a line, the slope is defined as rise/run. Rise is the difference in y coordinates, (think about it, going UP is RISING), and Run is the difference in x coordinates, (again its pretty intuitive.)

So Slope = [tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]

This can be calculated with the coordinates of the two points, (order wont matter youll get the same answer).

Slope = (-3-6)/(6-(-2)) = -9/8

OR, (going the other way)

Slope = (6-(-3))/(-2-6) = 9/-8 = -9/8

Easy!

Answer:

Step-by-step explanation:

First, we need to evaluate the expression inside the parenthesis: 4(12) = 4 * 12 = 48.

Next, we can simplify the expression: 42 - 6 * 48 = 42 - 288 = -246.

Finally, we raise the result to the third power: (-246)^3 = (-246) * (-246) * (-246) = -158,048.

So, the result is -158,048.

a. The two firing angles of the projectile are 5.65° and 174.35°

b. The time it takes the projectile to hit the ground is 4.02 s

A projectile is an object that follows a parabolic path when thrown into the air.

Given that a projectile travels a distance of 800 meters with an initial velocity of 200 m/s, to find the firing angles, we use the formula for the range of a projectile.

The range of a projectile is its horizontal distance. It is given by R = u²sin2Ф/g where

Given that we require Ф, the angle of projection. Making it subject of the formula, we have that

Ф = [sin⁻¹(gR/u²)]/2

Given that

Substituting the values of the variables into the equation, we have

Ф = [sin⁻¹(gR/u²)]/2

Ф = [sin⁻¹(9.8 m/s² × 800 m/(200 m/s)²)]/2

Ф = [sin⁻¹(9.8 m/s² × 800 m/(40000 m²/s²)]/2

Ф = [sin⁻¹(9.8 m²/s² × 1/50 m²/s²)]/2

Ф = [sin⁻¹(0.196)]/2

Ф = 11.30°/2

Ф = 5.65°

Since sin is positive in the second qudrant also, the second angle is

Ф = 180° - 5.65°

= 174.35°

So, the angle are 5.65° and 174.35°

To find how long it takes the projectile to hit the ground, we use the formula for time of flight of a projectile.

T = 2usinФ/g where

Since

Substituting the values of the variables into the equation, we have

T = 2usinФ/g

T = 2(200 m/s)sin5.65° ÷ 9.8 m/s²

T = 400 m/s × 0.09845 ÷ 9.8 m/s²

T = 39.381 m/s ÷ 9.8 m/s²

T = 4.02 s

So, the time it takes the projectile to hit the ground is 4.02 s

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An irrational number is created by adding two rational numbers, according to the answer to the given question. If the oppositely irrational numbers a and b.

Rational numbers are those that may be written as a ratio (or fraction) of two integers. A fraction with a non-zero denominator is said to be rational.

A few instances of rational numbers are 1/2, 1/5, and 3/4. A rational number, “0,” can also be stated in a number of different ways, such as 0/1, 0/2, and 0/3. But 1/0, 2/0, 3/0, and so forth.

The number seven makes sense. A rational number is produced when two integers are split. To get the rational number 7, divide the whole number 7 by the whole number 1. Since 7 can be obtained by dividing two integers, it is referred to as a rational number.

Two rational integers added together yield an irrational number. Ab is irrational if and only if a and b are mutually exclusive irrational numbers.

Therefore, a = 2 and b = ab = 2 is an irrational number.

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To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.

Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:

a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.

Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.

b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.

Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.

c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).

Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.

d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).

Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.

Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.

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Answer:

37

Step-by-step explanation:

AAA   1 way

AAB, AAC, AAD      3 ways each     3*3=9  ways

ABB, ACC, ADD      3 ways each     3*3=9 ways

ABC, ABD, ACD       3*2=6 ways each     3*6=18ways

1+9+9+18 = 37 ways

In the given case where 860 observations are drawn from a bell-shaped distribution, there are 2 observations of more than 112.

Total number of observations = 860

Mean of the observations = 76

Standard deviation = 18

The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the observations utilizing the Z- score -

Z = X - u/a

Calculating the observations -

Where X = 112 u = 76 and a = 18

Z = 112 - 76/18

= 36/18

= 2

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The profit that they will make if they have 24 dogs for adoption is given as follows:

$160.

The profit is obtained with the subtraction of the revenue by the costs.

The revenue and the costs for this problem are obtained as follows:

Hence the profit made is obtained as follows:

Profit = 45 x 24 - 920

Profit = $160.

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Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles

We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles

Depth of Mariana Trench (d) = 11 km = 11 × 0.62136

                                                          = 6.835 miles

Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189

                                                              = 5.492 miles

Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by

H = Depth of Mariana Trench + Height of Mount Everest

H = d + h

H = 6.835 miles + 5.492 miles

H = 12.327 miles

H = 12.3 miles

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The baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.

Hannah’s school playground is divided into two parts, with the majority of it being covered in grass. Specifically, 3/5 of the playground is grassy and the remaining 2/5 is taken up by other materials such as pavement or gravel. Of the grassy area, 5/8 is taken up by the baseball field. This means that the baseball field occupies a total of 15/40 or 3/8 of the entire playground.

In terms of proportions, if we consider the entire playground to be 100%, then the amount of the playground taken up by the baseball field is 3/8, or 37.5%. This means that 62.5% of the playground is taken up by the other materials and the remaining grassy area not occupied by the baseball field.In terms of area, the total size of the playground can be determined by multiplying the length of the playground by its width. If we assume that the length and width are equal, then the area of the playground can be calculated as the length squared. The area of the baseball field can then be calculated by multiplying 3/8 by the total area of the playground. This will give us the total area of the baseball field.

Overall, the baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.

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Check the picture below.

so the polygon is really just a 5x7 rectangle with a triangle that has a base of 7 units(vertically) and a height of 2 units.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(5)(7)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(2)}}\implies 35~~ + ~~7\implies \text{\LARGE 42}~units^2[/tex]

Answer: Change x to a number, and that number + 1 will be y

Step-by-step explanation: the reason for this is simple, change the independent variable, which is always in the problem, and you can figure out the dependent variable.

Answer:

X +1

Step-by-step explanation:

the graph is x +1.....

We can write the equivalent expression as -

{5.95 × 10⁸ + 8.87 × 10⁸} = {10⁸ x 14.82}.

In mathematics, an expression or mathematical expression is combination of terms both constants and variables. For example -

23 + 54

2x + 5

3x + 5y + z

Given is that after gathering information, Kara decided to add up some distances. She decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. He wrote -

5.95 × 10⁸ + 8.87 × 10⁸

The given expression is -

5.95 × 10⁸ + 8.87 × 10⁸

10⁸ x (5.95 + 8.87)

10⁸ x 14.82

Therefore, we can write the equivalent expression as -

5.95 × 10⁸ + 8.87 × 10⁸ = 10⁸ x 14.82.

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{Question in english -

1) Operations with numbers written in scientific notation

a) After gathering information, Kara decided to add up some distances. decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. Here is what he wrote.

5.95×108 + 8.87×108

Do you know what the result is?}

The height of the flagpole is 110 feet.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

tan 19 = f/x

tan 21 = f/(600 - x)

Now,

tan 16 x = tan 21 x (600 - x)

0.34x = 0.38 x 600 - 0.38x

0.34x = 230 - 0.38x

0.34x + 0.38x = 230

0.72x = 230

x = 319

Now,

tan 19 = f/319

0.34 x 319 = f

f = 109.8

f = 110 feet

Thus,

110 feet is the height of the flagpole.

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Answer: A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is constant. Let's call the common ratio "r". We can use this property to find "r" and then calculate other terms in the sequence.

Given that t3 = 24 and t9 = 1536, we can use the formula for the nth term in a geometric sequence: tn = t1 * r^(n-1), where t1 is the first term in the sequence.

Since we know t3 and t9, we can find r by dividing t9 by t3:

r = t9/t3 = 1536/24 = 64

Now that we have found "r", we can use it to find t1 by dividing t3 by r^(3-1):

t1 = t3 / r^(3-1) = 24 / 64^(3-1) = 24 / 64 = 3/2

Now that we know t1 and r, we can find any term in the sequence by using the formula: tn = t1 * r^(n-1).

Therefore, there are two possible sequences with two different first terms:

Sequence 1: t1 = 3/2, r = 64

Sequence 2: t1 = -3/2, r = -64

These are the two possible geometric sequences that satisfy the conditions t3 = 24 and t9 = 1536.

Step-by-step explanation:

The probability that the first box was the one selected given that the marble is white is [tex]\frac{7}{12}[/tex] .

Probability is the likelihood that an event will occur.

The likelihood of an occurrence A provided that an earlier event B has already happened is known as conditional probability.

the two boxes are marked as B1, B2

Number of black balls: 1

Number of white balls: 1

Number of black balls in the box: 2,

Number of white balls: 1.

B and W should stand for black and white marble.

Therefore, the likelihood that either box will be selected is [tex]\frac{1}{2}[/tex]

Probability of selecting a black ball from a box: [tex]\frac{1}{2}[/tex]

Probability of selecting a black ball from a box: [tex]\frac{2}{3}[/tex]

To determine: the likelihood that the marble is black.

Solution:

The likelihood that the marble being black is equal to

[tex]\frac{1}{2} (\frac{1}{2} ) + \frac{1}{2} (\frac{2}{3} )\\= \frac{7}{12}[/tex]

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Answer: 1024

Step-by-step explanation:

2 x 2 is 4

4 x 2 is 8

8 x 2 is 16

16 x 2 is 32

32 x 2 is 64

64 x 2 is 128

128 x 2 is 256

256 x 2 is 512

512 x 2 is 1024

Answer: The tip is $14.00

Step-by-step explanation: 20% of 70 is 14.

Answer:

Step-by-step explanation:

o find the solution of a system of linear equations, we can find the point where the two lines intersect. The point of intersection represents the solution to the system of equations.

The first linear equation can be determined by finding its slope and y-intercept using the given points:

m = (7 - 6) / (3 - 1) = 1

b = 6 - m * 1 = 6 - 1 * 1 = 5

y = mx + b

y = x + 5

The second linear equation can be found similarly:

m = (8 - 6) / (5 - 3) = 1

b = 6 - m * 3 = 6 - 1 * 3 = 3

y = mx + b

y = x + 3

Since the two lines have the same slope, they are coincident and represent the same line. The solution to the system of equations is therefore any point on this line, but since we were asked for a specific point, we can choose (3,6) as the solution.

Answer:

58585

Step-by-step explanation:

i know

The mean number of days to maturity for dollars invested in these five money market funds is approximately 8.95 days.

To calculate the weighted mean of the days to maturity, we need to multiply each value of days to maturity by its corresponding dollar value, sum the products, and divide the result by the total dollar value.

The calculation for the weighted mean is as follows:

Weighted Mean = (D1 x V1 + D2 x V2 + D3 x V3 + D4 x V4 + D5 x V5) / (V1 + V2 + V3 + V4 + V5)

where D represents the days to maturity and V represents the dollar value.

Using the given values, we can plug them into the formula and get:

Weighted Mean = (15 x 15 + 11 x 10 + 7 x 25 + 5 x 15 + 4 x 10) / (15 + 10 + 25 + 15 + 10)

Weighted Mean = 8.95 (rounded to two decimal places)

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Answer: 83 3/5

Step-by-step explanation:

hope this helps !! :3

Answer: Decagon

Step-by-step explanation:

That would be a decagon because it has 10 sides. It does not matter if the shape looks wonky.

Hope this helps :)

Answer:

3√10

Step-by-step explanation:

[tex]GM=\sqrt{(3\sqrt{5})(6\sqrt{5})}=\sqrt{18*5}=\sqrt{90}=3\sqrt{10}[/tex]

Answer:   [tex]3\sqrt{10}[/tex]

Work Shown:

Part 1

[tex]g = \text{geometric mean of x and y}\\\\g = \sqrt{\text{x}\text{y}}\\\\g = \sqrt{3\sqrt{5}*6\sqrt{5}}\\\\g = \sqrt{(3*6)*(\sqrt{5}*\sqrt{5})}\\\\g = \sqrt{18\sqrt{5*5}}\\\\g = \sqrt{18\sqrt{5^2}}\\\\g = \sqrt{18*5}\\\\g = \sqrt{90}\\\\[/tex]

Part 2

[tex]g = \sqrt{90}\\\\g = \sqrt{9*10}\\\\g = \sqrt{9}*\sqrt{10}\\\\g = 3\sqrt{10}\\\\[/tex]