Grade 5 mathematics

8➗0.4=

The mean  is 24 and standard deviation is 10 of the sampling distribution.

The term in math called standard deviation is defined as the standard deviation of the sampling distribution is also known as the standard error and it is inversely proportional to the sample size in which is as the sample size increases the standard deviation of the sample means decreases.

Here we know that the value of n is 100 and the number of samples 240.

Agreed count = 38.

Here we have to assuming the expected population standard deviation to be 10, and a population size of 100, the study would require a sample size of 24 to estimate a mean with 53% confidence and a precision of 1.5.

Then the standard deviation is 10.

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By calculating , The value of x is 5√5.

What is triangle?

Triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.

From the given figure,

When we draw a line inside the figure than it becomes into rectangle and one another triangle.

so,

In the right angled triangle,

with base 10 and opposite side 5

We have to find the hypothenuse that is x .

so,

from pythagorean theorem

we can say that

Sum of squares of two sides is equal to square of hypothenuse

so,

10*10 + 5*5 = x*x

100+25 = x*x

x*x = 125

x = 5√5 .

Hence, The value of x is 5√5

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The system of linear equations is y = 800x + 5445, and y = 900x + 4995. The solution is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.

The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.

Let us suppose the number of hours = x.

Let us suppose the total number of steps = y.

Given that, Lucia has 5445 steps and Lucia averages 800 steps per hour.

For Lucia the linear equation is:

y = 800x + 5445

For Danna, Danna has 4995 steps and Danna averages 900 steps per hour.

For Danna the linear equation is:

y = 900x + 4995

The system of linear equations is:

y = 800x + 5445 (equation 1)

y = 900x + 4995 (equation 2)

Substitute the value of y of equation 1 in equation 2:

800x + 5445 = 900x + 4995

5445 - 4995 = 900x - 800x

450 = 100x

x= 4.50

B. The solution of the linear equation is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.

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Answer:

I believe you answer would b B!

The number of gallons of gas used every 1 mile traveled.

Step-by-step explanation:

Hope it helps! =D

If you invest $10000 in a bank , then the better investment plan is (a) 9% compounded monthly .

The amount to be invested in bank is = $10000  ;

the formula to calculate the final amount by compounding is given as :

A = P(1 + r/n)^(nt)   ;

Where: (A) = final amount , (P) = initial amount ,

⇒ r is interest rate (in decimal form) , n is number of times the interest is compounded per year and

⇒ t is number of years investment is made

(a) the rate of interest is 9% compounded monthly ;

in this case n = 12  , because there are 12 months in 1 year ;

So , Amount = 10000(1 + 0.09/12)^(12×t)

Amount = 10000 × (1.0075)^(12×t)  

Suppose t = 1 ;

we get , Amount = 10000 × (1.0075)¹² ≈  10938 .

(b) the rate of interest is 9% compounded annually ;

in this case n = 1  , because compounded annually ;

So , Amount = 10000 × (1 + 0.09)^(1×t)

Amount = 10000 × (1.09)^t  

Suppose t = 1 ; we get , Amount = 10000 × (1.09)¹ ≈ 10900 ;

On comparing both the interest value we observe that ,

the monthly compounding returns more value than compounding annually  .

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The area of the rectangle would be 96 square inches.

Option (D) is correct.

What is the area of the rectangle?

The formula for the area of a rectangle is:

Area = length x width

where length is the distance along the longer side of the rectangle and width is the distance along the shorter side of the rectangle.

In the given figure,

The length of the rectangle = 8 + 8 = 16 inches.

Now by using the Pythagoras theorem, we can find the height

  [tex]Height= \sqrt{(10)^2-(8)^2} \\\\=\sqrt{100-64}\\\\=\sqrt{36}\\\\=6[/tex]

So the base would be 6 inches.

Now we can find the area of the rectangle

Area = 16 * 6

Area = 96 square inches.

Hence, the area of the rectangle would be 96 square inches.

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The measurement of angles formed by intersecting line segments UT and WV are -

∠TXV = 25°

∠UXW = 25°

∠TXW = 155°

∠UXV = 155°

What is a line segment?

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

Two line segments UT and WV are given.

The line segment UT and WV are intersecting each other at a point X.

Due to the intersection many angles are formed.

To find the measure of the angles, use the protractor.

The first angle is ∠TXV.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line UT.

The measure of ∠TXV is approximately 25°.

The second angle is ∠UXW.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line WV.

The measure of ∠UXW is approximately 25°.

The third angle is ∠TXW.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line WV.

The measure of ∠TXW is approximately 155°.

The fourth angle is ∠UXV.

Keep the protractor's midpoint at point X.

Then turn the protractor so that it aligns with line UV.

The measure of ∠UXV is approximately 155°.

Therefore, all the four angles are obtained.

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√5 is the minimum distance between the line AB and CD.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given Two lines AB and CD,

Since, The minimum distance between two lines is the distance between B and C As we can see in the graph

Since, coordinates of B and C are, (1, 2) and (3, 1)

From the formula of distance between two coordinates:

Distance = √((x₂ -x₁)² + (y₂ -y₁)²)

in our case,

Distance = √((3 - 1)²  + (1-2)²)

Distance = √4 + 1)

Distance = √5

Therefore, the minimum distance between the line AB and CD is √5.

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Answer: -2, -1, 4, 4, 14, 14, 14, 30, 314, 314

The values are arranged in increasing order from least to greatest.

Check the picture below.

The proportional relationship that models this situation is given as follows:

y = 2x.

The graph is given by the image presented at the end of the answer.

A proportional relationship is modeled as follows:

y = kx.

In which k is the constant of proportionality.

Susan's plane uses 2 kilograms of fuel for every unit she flies, hence the constant is given as follows:

k = 2.

The relationship is:

y = 2x.

The domain is:

x >= 0, as the number of units flied cannot be negative.

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By using the equation of the line of best fit, the​ number of minutes Nikki would need to listen to the radio is equal to 63.275 minutes.

In order to determine the​ number of minutes Nikki would need to listen to the radio, we would have to substitute the value representing the number of commercials (y) into the linear equation and then evaluate as follows;

y = 0.338x − 1.387

When the value of y = 20 commercials, the number of minutes (x) in feet is given by;

20 = 0.338x − 1.387

By rearranging and collecting like terms, we have the following:

0.338x = 20 + 1.387

0.338x = 21.387

Number of minutes (x) = 21.387/0.338

Number of minutes (x) = 63.275 minutes.

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Complete Question:

Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit: y = 0.338x − 1.387. Based on the line of best fit, for approximately how many minutes will Nikki need to listen to the radio to hear 20 commercials?

The vector equation for the line of intersection of the planes x+4y-4z=-3 and x + z = 5 is r = <5, -2, 0> + t <-1, 5/4, 1>

The equations of the planes are:

x + 4y - 4z = -3                    ..............(1)

and x + z = 5                      .............(2)

Subtract equation (2) from equation (1),

( x + 4y - 4z + 3) - (x + z - 5 ) = 0

4y - 5z + 8 = 0

we can rewrite is as,

4y = 5z - 8

y = 5/4 z - 8/4

y = 5/4 z - 2                  ...............(3)

Here, we don't have enough equations to uniquely solve for either y or z. So, we set z = t, where t can be any real number.

The variable t is the free parameter for the parametrization of the line.

Substitute z = t in equation (3) we get,

y = 5/4 t - 2        

From equation (2),

x = 5 - z

For z = t,

x = 5 - t

Thus, the parametrization of the line would be,

(x, y, z) = (5 - t, -2 + 5/4 t , t)

           = <5, -2, 0> + t<-1, 5/4, 1>

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Answer:

9.87 Gallons

Step-by-step explanation:

Start by finding how far mr. keith here can drive with one gallon of gas.

to do this you will:

360 ÷ 12 = 30

For one gallon of gas, he can drive 30 miles.

Now that we know the rate for 1 gallon of gas, you just apply that rate to the new mileage:

296 (new distance) ÷ 30 (how many he can do in one mile) = 9.87 (how many times that 30 miles goes into 296 (recall that this is the rate))

To drive 296 miles, keith will use 9.87 gallons of gasoline.

hope this helped :)

If the mean number of home goals is 2.5 and away goals is 1.88 , then the number of home and away games have been played in total is 32 games .

From the histogram , we get that ,

the total number of home goals is = 9 + 6 + 8 + 7 = 30 goals ;

the total number of away goals is = 2 + 7 + 4 + 5 = 18 goals ;

the mean number of home goals is = 2.5 ;

the mean number of away goals is = 1.8  ;

we know formula that⇒ Mean Goal = (total goals)/(number of games) ;

For Home goals :

⇒ 2.5 = 30/n ⇒ n = 30/2.5 = 22 games .

For Away goals :

⇒ 1.8 = 18/n ⇒ n = 18/1.8 = 10 games .

So , total number of games is = 10 + 22 = 32 games ,

Therefore , In total the total number of home and away games played is 32 games .

The given question is incomplete , the complete question is

Here is some information about the goals scored in some hockey games. Each game has four quarters. the histogram is given below :

The mean number of home goals scored is 2.5  ;

The mean number of away goals scored is 1.8  ;

How many home and away games have been played in total ?

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If f(0) = 18 and f(1) = 13 then f(0) be the largest value.

A function is a relationship between a number of inputs where each input has exactly one output, according to one definition.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions denoted the idealized relationship between two changing quantities.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). If f exists typically utilized to denote a function (x).

Let the function f(x) = 18 - 5x

a) f(-4) = 18 - 5(-4) = 38

b) f(0) = 18 - 5(0) = 18

f(1) = 18 - 5(1) = 13

Therefore, f(0) be the largest value.

The complete question is:

Given the function f(x) = 18 - 5x

a. What is the value of function f given an input of -4 ?

b. Which is larger, f(0) or f(1)? Show your work to justify your answer.

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If Lysosomes break open during the process of digestion, releasing enzymes into the cytoplasm. The statement that may explain why the entire cell may not be digested is: 3. The pH of the cytoplasm causes the enzymes to function less effectively.

Lysosomes can be defined as vesicles that is made up of enzyme. This Lysosomes  enables the process of digestion to take place and the enzyme found in lysosomes also  help to break down biological molecule.

The reason why the whole cell may not be digested  in an situation where enzymes  are released into the cytoplasm  is that the pH of the cytoplasm  led to the enzymes  not to function effectively.   Optimum PH is required for cytoplasm  to function more effectively.

Therefore the correct option is B.

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For the given case The boss has failed to satisfy the condition of random sampling without replacement. This condition states that the samples must be taken randomly and with replacement, meaning that each sample is replaced after it has been selected.

In this case, the boss picked the 50 names out of the hat without replacing them, which means that the same names could have been picked more than once. This can lead to a sample bias, as the same names may be overrepresented in the sample. This lack of randomness can lead to an inaccurate estimate of the proportion of employees who are satisfied with the company's parking policy.

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Large pack with 12 plates has better value of money with $1.77 for each plate comparison to smaller pack with $1.75 for each plate.

Number of plates in smaller pack is equal to 3 .

Cost of smaller pack with three plates = $5.25

Cost of each plate in smaller pack = $5.25 / 3

                                                         = $1.75

Number of plates in larger pack is equal to 12 .

Cost of larger pack with twelve plates = $21.24

Cost of each plate in larger pack = $21.24 / 12

                                                         = $1.77

$1.77 is greater than $1.75.

Larger pack of plates have better value of money for each plate comparing the smaller pack.

Therefore, the larger pack has better value of money than the smaller pack .

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The height of the tower is equal to the length of the side opposite the angle of elevation plus the length of the side opposite the angle of depression.

The angle of elevation and angle of depression in this problem can be used to solve for the height of the tower.

Since the angle of elevation is the angle from the window to the top of the tower and the angle of depression is the angle from the window to the bottom of the tower, the height of the tower can be determined by finding the length of the side opposite the angle of elevation and adding it to the length of the side opposite the angle of depression.

Using trigonometry, we can solve for the two lengths using the sine and cosine functions. The sine of the angle of elevation is equal to the length of the side opposite the angle divided by the hypotenuse. The hypotenuse is the distance from the window to the tower, which is known to be 275 feet. Therefore, we can solve for the side opposite the angle of elevation by multiplying the sine of the angle of elevation by 275. The cosine of the angle of depression is equal to the length of the side opposite the angle divided by the hypotenuse. We can solve for the side opposite the angle of depression in the same way.

Once the two lengths are calculated, we can add them together to find the height of the tower.The height of the tower is equal to the length of the side opposite the angle of elevation plus the length of the side opposite the angle of depression.

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Answer:

The ratio of sugar to lemon juice is 2 cups sugar : 3 cups lemon juice.

The ratio of lemon juice to water is 3 cups lemon juice : 8 cups water.

The first statement is true because the recipe calls for 2 cups of sugar and 3 cups of lemon juice. The ratio of sugar to lemon juice is therefore 2:3, or 2 cups sugar : 3 cups lemon juice.

The second statement is true because the recipe calls for 3 cups of lemon juice and 8 cups of water. The ratio of lemon juice to water is therefore 3:8, or 3 cups lemon juice : 8 cups water.

It's important to note that these ratios are in the context of this specific recipe, and may differ from other lemonade recipes.

Step-by-step explanation:

On average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.

To find the expected value of the Daily 3 lottery game, we need to calculate the probability of winning and the expected payout for winning.

The probability of winning the Daily 3 game with a single ticket is 1/1000, since there are 1000 possible 3-digit number combinations and only one of them is the winning combination.

The expected payout for winning is $500, since this is the prize for matching the winning digits in the correct order.

To calculate the expected value, we can use the formula:

Expected Value = (Probability of Winning) x (Payout for Winning) - (Cost of Playing)

Plugging in the values we found, we get:

Expected Value = (1/1000) x ($500) - ($1)

= $0.50 - $1

= -$0.50

This means that, on average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.

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Answer:

a₈ = 44

Step-by-step explanation:

to find a₈, substitute n = 8 into the explicit formula

a₈ = 6(8) - 4 = 48 - 4 = 44

The supplied input should simply be replaced in the function definition for that precise interval.

An equation or set of equations, rather than a single equation, defines a piecewise-defined function. For a specific interval, each equation is valid.

Find out to which of the above intervals (or inequalities) the supplied input belongs before evaluating a piecewise function at any given input. The function definition for that specific interval should therefore just have the specified input replaced.

When a rule or relationship changes as an input value passes specific "boundaries," we refer to these instances as piecewise functions. For instance, scenarios where the price per piece of a specific item is decreased once the quantity requested exceeds a given amount are frequent in business.

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There is one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4

To find the point of intersection, we need to set the two equations equal to each other and solve for x and y.

y = x² + 3x - 2

y - x = 4

x² + 3x - 2 - x = 4

x² + 2x - 6 = 0

(x-3)(x+2)=0

x =3 or x=-2

When x = 3, we substitute it into the first equation y = x² + 3x - 2

y = 3² + 3(3) - 2

y = 9 + 9 - 2

y = 16

When x = -2, we substitute it into the first equation y = x² + 3x - 2

y = -2² + 3(-2) - 2

y = 4 -6 -2

y = -4

So the point of intersection is (3,16) or (-2,-4)

Hence there is only one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4

The probability of all 5 marbles being red is (8/26) x (7/25) x (6/24) x (5/23) x (4/22) = 0.000766.

This can also be written as P(RRRRR) = 8/26 x 7/25 x 6/24 x 5/23 x 4/22. This probability is very small, as the chances of randomly selecting only red marbles from the bag is low.

This calculation is based on the formula for combinations, which states that the probability of selecting r items from a group of n items is nCr x Pr, where nCr is the number of combinations of selecting r items from n items and Pr is the probability of selecting a specific item. In this case, n = 26 and r = 5, so the number of combinations of selecting 5 items from 26 items is 26C5. This is equal to 8x7x6x5x4/5x4x3x2x1, or 8x7x6x5x4/120. The probability of selecting a specific item is 1/26, as there are 26 items in the bag. Therefore, P(RRRRR) = 8/26 x 7/25 x 6/24 x 5/23 x 4/22.

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Jill ride 43.39 meters farther than Jessica.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.

Given, Jill and Jessica are bike riding at the park. Jill rides her bike around the two edges of the rectangular park while Jessica takes the shortcut

Given the length of the Rectangular park = 100m

The width of the park =  60m

Thus jill ride total = 60 + 100

Jill ride total = 160m

Jessica took a shortcut since she rides diagonally.

From the Pythagorean theorem:

hypotaneus² = base² + height²

Thus,

total distance Jessica covers = √(60² + 100²)

total distance Jessica covers = √3600 + 10000

total distance Jessica covers = √13600

total distance Jessica covers = 116.61

Difference between their distances = 160 - 116.61

Difference between their distances = 43.39

therefore, 43.39 m farther does Jill ride than Jessica.

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Complete question:

The value of the 47th term of the given arithmetic sequence is -55.7

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.

We are given the explicit rule for an arithmetic sequence as follows -

[tex]a_n[/tex] = 8.7 - 1.4(n-1)

We have to find the value of the 47th term in the series.

So, we have the value of n = 47

The equation will become -

[tex]a_{47}[/tex] = 8.7 - 1.4(47-1)

[tex]a_{47}[/tex] = 8.7 - 1.4(46)

[tex]a_{47}[/tex] = 8.7 - 64.4

[tex]a_{47}[/tex] = -55.7

Thus, the value of the 47th term of the given arithmetic sequence is -55.7

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Answer:

5

Step-by-step explanation:

To find out how many golf balls Rafael used at the driving range, we can use the following formula:

number of balls used at the driving range = total number of balls x percentage used

Given:

Total number of balls = 25

Percentage used = 20%

So we can substitute these values into the formula:

number of balls used at the driving range = 25 x 20% = 25 x 0.20 = 5

Therefore, Rafael used 5 golf balls at the driving range.

The concept here is the Research method, it is the main extent to which a concept, conclusion, or measurement is well-founded  The answer is validity.

Research methods are strategies, processes, or ways used to collect data or substantiation for analysis to uncover new information or better understand the content.

Validity is the lesser degree to which an idea, conclusion, or action is reasonable and likely to directly reflect reality. The word" valid" comes from the Latin Validus, which means strong.

The validity of a dimension instrument is the extent to which the instrument measures what it's intended to measure. Validity refers to the relationship between the study thing and the data the experimenter chooses to use to quantify that thing. Some confines similar to physical strength, aren't naturally related to intelligence.

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A relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).

Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial.

Combos' components can be chosen in any hierarchy.

Combinations and permutations can coexist.

Hence, the ordered pair is given:

(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)

For a relation to be a function, all of the x-values must be unique (i.e. no repetition)

From the list of alternatives, options (b) and (d), with x values (6, 7) and (d), already exist in the ordered pair (4,5)

In light of this, (b) and (d) would stop the connection from being a function.

Therefore, a relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).

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Correct question:

A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.

{(1,2),(2,3),(4,5),(6,7),(12,13)}

The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.

a. (10,13)

b. (6,8)

c. (8,12)

d. (4,3)

e. (24,18)