khan academy - 6th grade advanced

Answer:

Step-by-step explanation:

for double fractions,   invert the bottom one and then multiply them

[tex]\frac{3}{8}[/tex] * [tex]\frac{5}{2}[/tex]

= [tex]\frac{15}{16}[/tex]

= 0.9375

10800 mm³ is the volume of the unsharpened pencil.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm².

The length of hexagonal prism is  20 cm.

Let us convert cm to mm

1 cm = 10 mm

20 cm =200 mm.

Volume of hexagonal prism V=Ah.

A is the base area and h is the height.

V=54×200

=10800 mm³.

Hence,  volume of an unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm² and length of 20 cm is 10800 mm³.

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The solution is Option D.

The value of the equation A = ( 9x⁴ )^1/2 is A = 3x²

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = quantity 9 times x to the fourth power end quantity to the one-half power

On simplifying the expression , we get

Quantity 9 times x to the fourth power = 9x⁴

Quantity 9 times x to the fourth power end quantity to the one-half power is written as = ( 9x⁴ )^1/2

On further simplification , we get

A = ( 9x⁴ )^1/2

A = √9x⁴

Taking the square root of the value of A , we get

The value of A = 3x²

Therefore , the value of is 3x²

Hence , The value of the equation is A = 3x²

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Answer:

16

Step-by-step explanation:

Since x is negative, lets instead thing of the problem as

y + (-x)

and find the bounds of -x to be

[tex] - 2 < = - x < = 4[/tex]

now, the max value of y is 12 and the max value of -x is 4

12 + 4 = 16

The percent that the average score on the test increased during the two months is 12.5%.

It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..

The average of the increase will be:

= (10% + 15%) / 2

= 25% / 2

= 12.5%

The average is 12.5%.

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The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.

Therefore the answer is (5, -6).

The graph f(x) = |x - 5| - 6 is symmetrical about the axis  x = 5.

A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is

(5, -6)

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x - 5| - 6?"

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Answer:

10

Step-by-step explanation:

each 10 peanut butter sandwiches takes 10 ounces

Answer:

10

Step-by-step explanation:

The answer is c). The probability that the basketball player makes his first three-point shot on the third attempt is 0.38.

The geometric distribution is a probability distribution that describes the number of independent trials required to get a success. In this case, the basketball player has a 25% accuracy rate at making three-point shots, which means that the probability of success (making a three-point shot) is p=0.25 and the probability of failure (missing a three-point shot) is 1-p=0.75. Using the geometric distribution formula, the probability that the basketball player makes his first three-point shot on the third attempt is:

This means that there is a 38% probability that the basketball player will make his first three-point shot on the third attempt.

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Yes, ΔQRS  can be translate to so that Q is mapped to point A, then reflect across line containing QS.

we have two triangles ΔQRS and ΔABC in which we have ,

QR=AB = 16 cm

RS=BC= 24 cm

∠R=∠B=90°

By SAS postulate of congruence , ΔQRS ≅ ΔABC.

There are three main rigid transformations which produces congruent images.

1) Translations 2) Rotation 3) Reflection

When we look the given picture, it can be seen that ΔABC is the mirror image of ΔQRS.

But line QS is at some distance from AC , so we first translate ΔQRS to so that Q is mapped to point A, then reflect across line containing QS.

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Answer:

(1.5, -3)

Step-by-step explanation:

Both equations are in slope intercept form which means that:

for y = mx + b

m = slope

b = y-intercept

The slope can help us go from the y-intercept to the next point on the graph to make the line

For the equation

y = 2x - 6

the y-intercept is -6, so plot a point there.

The slope is 2 which means you will go up 2 then to the right by 1  to the next point on the graph.

Use the same process to find the line for y = -4x + 3, but you have to keep in mind that when the "m" value is negative, that means the line will point to the left of the graph instead of the right.

Once the lines are draw, the point where they intercept will be the solution.

The histograms is shown below.

One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution.

Given:

The standard deviation for 4 we have the highest value and range for graph C have highest standard deviation.

and, the standard deviation for 1 have lowest deviation and range for graph A have lowest standard deviation.

and, for row 2 the second histogram is the answer and for row 4 the fourth histogram is the answer.

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Without spectacles, Witney Pete has a 5/10 chance of hitting the bullseye. Witney Pete could strike the bullseye with his spectacles 0.7 of the time. This likelihood is far higher than hitting the bullseye without glasses. the probability that Pete hits five or fewer of his next ten shots is approximately 2.487.

Generally, To find the probability that Pete hits five or fewer of his next ten shots, we need to find the probability that he hits exactly 0, 1, 2, 3, 4, or 5 bull's eyes.

The probability that Pete hits exactly k bull's eyes in n throws is given by the binomial distribution:

P(k bull's eyes in n throws) = (n choose k) * p^k * (1-p)^(n-k)

where p is the probability of hitting a bull's eye on a single throw and n choose k is the binomial coefficient, which is equal to n!/(k!(n-k)!).

Substituting the given values, we get:

P(0 bull's eyes in 10 throws) = (10 choose 0) * (0.7)^0 * (0.3)^10 = 0.028 P(1 bull's eyes in 10 throws) = (10 choose 1) * (0.7)^1 * (0.3)^9 = 0.189 P(2 bull's eyes in 10 throws) = (10 choose 2) * (0.7)^2 * (0.3)^8 = 0.462 P(3 bull's eyes in 10 throws) = (10 choose 3) * (0.7)^3 * (0.3)^7 = 0.605 P(4 bull's eyes in 10 throws) = (10 choose 4) * (0.7)^4 * (0.3)^6 = 0.501 P(5 bull's eyes in 10 throws) = (10 choose 5) * (0.7)^5 * (0.3)^5 = 0.302

The probability that Pete hits five or fewer bull's eyes in his next ten shots is the sum of the probabilities of hitting exactly 0, 1, 2, 3, 4, or 5 bull's eyes:

P(hitting 5 or fewer bull's eyes in 10 shots) = 0.028 + 0.189 + 0.462 + 0.605 + 0.501 + 0.302 = 2.487

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On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = [tex]-1 < y < 1[/tex]

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The Range of the given function, f(x) = sin(x)

[tex]-1 < y < 1[/tex]

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The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25

How to find which has a quotient?

Quotient * Dividend  =  Divisor

A. 4.15 ÷ 2.5

Quotient = 1.66

Divisor = Quotient * 2.5

= 1.66 * 2.5

= 4.15

So, Option A is a correct answer.

B. 0.415÷0.25

Divisor = Quotient * 0.25

= 1.66 * 0.25

= 0.415

So, Option B is a correct answer.

C. 41.5÷0.25

Divisor = Quotient * 0.25

= 1.66 * 0.25

= 0.415 ≠ 41.5

So, Option C is not a correct answer.

D. 4.15÷0.25

Divisor = Quotient * 0.25

= 1.66 * 0.25

= 0.415 ≠  4.15

So, Option D is not a correct answer.

E. 0.415 ÷ 2

Divisor = Quotient * 0.25

= 1.66 * 2

= 3.32 ≠  0.415

So, Option E is not a correct answer.

Hence, The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25

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Experimental probability of correctly answering both questions by guessing = 1/4 .

Tail (T) = True

Head (H) = False

Number of possible outcome = 2

Head (H) or Tail (T).

Probability = number of occurrence/number of possible outcome.

Since we can only have one T or F in a toss.

number of occurrence = 1

Probability of answering first question correctly = 1/2

Probability of answering second question correctly = 1/2

Probability of answering both questions correctly = Probability of answering first question correctly * Probability of answering second question correctly

Probability of answering both questions correctly = 1/2 x 1/2

Probability of answering both questions correctly = 1/4

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Answer:3 and  10 and 3/10

Step-by-step explanation:

The steps of copying involve selecting the text you want to copy, copying the text using the option from the right click menu or alternatively using the keyboard shortcut ctrl + c.

The clipboard is a section of memory that the computer temporarily saves data when you copy or cut it from its original location. When you paste something, the previously copied or cut data is retrieved from the clipboard and added to the new location.

Text that is copied remains in its original location; a copy of the original text is created and kept in the clipboard. When you cut text, the original text is removed from its original location and put in the clipboard. When you copy or trim text, the original text is kept, but the original location is lost. In all cases, the copied or chopped text can be put into another location.

These steps can be used to copy text or other objects in a computer program:

By highlighting it with your pointer, you may choose the text or object that you wish to copy.

Use the keyboard shortcut "Ctrl+C" or the context menu when you right-click the highlighted text or object to choose "Copy" from the context menu.

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3/5 is the quotient of these fractions in lowest form when 3/10 divides by 2/4

When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the  fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.

so in order to find quotient when 3/10 is divided by 2/4 we get:

quotient = (3/10) / (2/4)

=> (3/10) * (4/2)

=> 12/20

so the quotient of this division is 12/20

now we have to find the lowest form of quotient

so gcd(12,20) = 4

where gcd is greatest common divisor

so lowest form of 12/24 = (12/4) / (20/4)

=> 3 /5

so lowest form of the quotient is 3/5

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press menu and select option,press 2 to select to a polynomial degree of 2,select the number that matches the inequality u are about to solve and lastly input the values of coefficient of x into the expression and press equal to sign on the calculator

A relationship between two expressions or values that are not equal to each other is called 'inequality. '

Inequality can be greater than >, less than < , great than or equal to ≥ , less than or equal to ≤.

like other equations, inequality can be solved on a calculator. This process shows how inequality can be solved on a calculator. For example if 3x²+4x+5≥0 is to be solved on a calculator, the following steps are to be taken

Step 1 : press menu and select option B( inequality option)

Step2 : press 2 to select to a polynomial degree of 2

step 3 : select the number that matches the inequality u are about to solve

step 4: input the values of coefficient of x into the expression

step 5 : press the equal to sign on the calculator.

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6.50 is the sample variance of the following numbers.

How to interpret a standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

            Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

X = ∑x/n

   = 3 + 4 + 2 + 7 + 1/5

    = 20/5 = 4

s² = [∑(Xi - x)²/N-1]

   = (6-4)² + ( 4 - 4 )²+ ( 4 - 4 )² + ( 7 - 4 )² + ( 1 - 4 )²/5 - 1

    = 26/4

    = 6.50

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Answer:

a. 648

Step-by-step explanation:

Deposit= Principal= p

Interest rate = R

Time= T

Simple Interest = P x T X R X 0.01

= 5400 x 6 x 2 x 0.01

=648

Answer: 31 cm

The radius of a 62 cm circle is 31 cm because the radius of a circle is half of the diameter.

D=diameter

R=radius

D=R2

R=D/2

Answer:

[tex]R = 31[/tex][tex]cm[/tex]

Step-by-step explanation:

[tex]D = 62[/tex]

[tex]R=\frac{D}{2} \\R=\frac{62}{2} \\R=31[/tex][tex]cm\\[/tex]

Jackson should correctly phrase both the alternative hypothesis and the null hypothesis as follows:

b. )

p = 0.20 indicates a null result.

A different result: p ≠ 0.20

What exactly is null hypothesis?

A specific type of statistical hypothesis known as a null hypothesis claims that no statistical significance can be established in a given set of facts. One can assess the truthfulness of a hypothesis through the use of sample data in hypothesis testing. It is represented by the letter H0 and is also sometimes referred to as the "null."

The conjecture, also known as the null hypothesis, is a tool used in quantitative analysis to examine the validity of beliefs about markets, economies, and investment strategies.

A null hypothesis is a form of speculation that asserts that specific characteristics of a population or data collection method are not distinct from one another in statistics.

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Answer: B

I have to add extra words to answer you but it’s B :))

Answer: One by two

Step-by-step explanation:

Because the mu is half or 0.5, so the word in the blank will be one by two!

Therefore , squaring a number and taking the square root of a number  is an opposite operation as we can see in the following explanation.

A number's square root, which is the result of multiplication by itself, yields the original number. Some examples of exponents are squares and square roots. Imagine the number twenty five. Additionally, this can be expressed as expression of  5x5.

Here,

In order to square an integer, you must multiply it by itself.

The opposite of squaring a number is the act of getting the square root.

Calculating the side length of a square whose area is a certain number can be compared to finding the square root of that number.

For example: √25=  √5*5 = 5

where as square of 5 : 5*5 = 25

Therefore , squaring a number and taking the square root of a number  is an opposite operation as we can see in the following explanation.

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To determine whether an inequality represents a relationship of "greater than" or "less than" by looking at a graph, you can look at the direction of the solid line. If the line is pointing upwards towards the right, it represents a "greater than" relationship. If the line is pointing downwards towards the right, it represents a "less than" relationship.

For example, consider the graph of the inequality "y > x + 2." The points on the graph that satisfy this inequality are those that are above the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points above the line are greater than the values on the line, so the inequality "y > x + 2" represents a "greater than" relationship.

On the other hand, consider the graph of the inequality "y < x + 2." The points on the graph that satisfy this inequality are those that are below the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points below the line are less than the values on the line, so the inequality "y < x + 2" represents a "less than" relationship.

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Answer:

Y-intercept: 3

Step-by-step explanation:

The equation is y = mx + b

m is the slope

b is the y-intercept

In this case, the y-intercept is 3

Answer:

Step-by-step explanation: a) To calculate the total cost of the couch when paid with a credit card, we need to calculate the amount of interest that will be charged. To do this, we first need to calculate the monthly interest rate by dividing the annual interest rate by 12. In this case, the monthly interest rate is 20/12 = 1.67%.

Next, we need to multiply the cost of the couch by the monthly interest rate to find the amount of interest that will be charged. In this case, the amount of interest is 999 * 1.67% = 16.67.

Finally, we need to add the amount of interest to the cost of the couch to find the total cost when paid with a credit card. In this case, the total cost is 999 + 16.67 = 1015.67.

To calculate the total cost of the couch when paid with the store promotion, we simply need to add up all 15 monthly payments. In this case, the total cost is 15 * 70 = 1050.00.

b) To calculate the annual interest rate being charged with Option 2, we need to divide the total cost of the couch by the number of monthly payments and then multiply by 12. In this case, the annual interest rate is (1050/15)*12 = 96%.

The notation f (x) = y means that the functional value at the point x is y.

In the notation f (x) = y, we understand that the value x is to be plugged in the function given to us (which is f here) which on solving gives y as the answer or solution 'y' of that function at a point x.

For example, let us consider the function f (x) = 2x + 3 = y

Then if we find f (2), then 2 will be plugged in the function 2x +3 such that

f (2) = 2(2) + 3 = 7,

which means that 7 is the functional value, 'y' at the point 2 which is considered as x.

The question is incomplete, the complete question is f (x) = y.

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