George has scored 88%, 67%, 90% and 75% on his four tests. He needs to average 70% in order to not lose the keys to his car. He has one test left; what does he need to score to average 70%?

​

The value of the given summation is:

\(\sum (29a_i - 13b_i) ]= -30\)

Here we know that the sums are:

\(\sum a_i = -10\\\\\sum b_i = -20\)

And we want to find the value of the sum:

\(\sum (29a_i - 13b_i)\)

First we can distribute the sum to get:

\(\sum 29a_i + \sum - 13b_i\)

And take the coefficients out of the sum:

\(29\sum a_i -13\sum b_i\)

Now replace the known values:

\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)

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We first need to find the encoding and decoding functions used by Boris and Natasha. We know that these two must be linear functions with 1 as the coefficient of x. Then the encoding function must have the form:

Where x is the number associated with the letter and b is a constant that we don't know. The decoding function is its inverse:

Now let's take a look at the table that associates the letters with numbers. The minimum number is 1 associated with A and the maximum is 27 associated with Blank. Now let's write the encoded version of these two:

And let's find the difference between their encoded values:

So the difference between their encoded values is the same as the difference between their decoded values. Since 1 and 27 are the minimum and maximum decoded values their difference is the greatest of all the difference between two decoded values. Then there's no other pair of decoded values with a difference equal to 26 and since the difference between two encoded values is the same as the difference between two decoded values we can assure that 26 is the maximum difference between two encoded values and it corresponds to the pair A - Blank.

This implies that if the difference between the minimum and maximum value in the message sent by Boris and Natasha is 26 we can assure that this pair of values is the one corresponding to A and Blank.

The minimum and maximum values in the message are 15 and 41 and their difference is 41 - 15 = 26. This means that 15 is the encoded value of A and 41 is that of Blank. Then we can construct two equations using the encoding function:

By substracting 1 from both sides of the first equation and 27 from both sides of the second equation we obtain b:

So b=14 and the encoding function is f(x)=x+14.

Then the decoding function is f⁻¹(x) = x - 14.

Now we need to decode the message. We simply need to evaluate the decoding function at all the numbers in the encoded message:

Then we replace each encoded value by its respective decoded value so the message in numbers is:

11 5 5 16 27 3 1 12 13 27 1 14 4 27 4 15 27 20 8 5 27 13 1 20 8

Using the table associating numbers and letters we obtain the final message:

KEEP CALM AND DO THE MATH

The circumference of the circle is 55.9 m

The radius is given as 8.9 m

The formula for calculating circumference of a circle is

= 2πr

= 2 × 3.142 × 8.9

= 55.9

Hence the circumference of the circle is 55.9m

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After cοmpleting the task, we can state that The whοle number clοsest tο  expressiοn 7.141 is 7. Therefοre, √51 is clοsest tο the whοle number 7.

The whοle numbers are the part οf the number system which includes all the pοsitive integers frοm 0 tο infinity. These numbers exist in the number line. Hence, they are all real numbers. We can say, all the whοle numbers are real numbers, but nοt all the real numbers are whοle numbers.

Thus, we can define whοle numbers as the set οf natural numbers and 0. Integers are the set οf whοle numbers and negative οf natural numbers. Hence, integers include bοth pοsitive and negative numbers including 0. Real numbers are the set οf all these types οf numbers, i.e., natural numbers, whοle numbers, integers and fractiοns.

√51 is apprοximately equal tο 7.141. The whοle number clοsest tο 7.141 is 7.

Therefοre, √51 is clοsest tο the whοle number 7.

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Answer:

X    |   y

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

-2   |   3

-1   |   0

0   |  -3

1   |  -6

Answer:

x+5

Step-by-step explanation:

When you move to the right or left , that's on the x axis. And since it's to the right, the x- coordinate becomes larger. Hope this helps!

Answer:

x+5

Step-by-step explanation:

The answer is x+5!

Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.

To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.

The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:

Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).

Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.

Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.

If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.

In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.

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Answer:

10miles I think

Step-by-step explanation:

The required distance between, Nate's house and the restaurant is 7.5 miles.

From the graph,

Consider point C on the graph, which is 6  and 8 units apart from A and B respectively.

The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units

Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles

Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.

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The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.

In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.

Hence, the statement relates the symbols and sequences.

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Answer:

Express your length and width as algebraic expressions:

width = x

length = 4x

Use the formula for the perimeter of a rectangle to solve for x:

perimeter = 2(length) + 2(width)

50 = 2(4x) + 2(x)

50 = 8x + 2x

50 = 10x

5 = x

The width (x) is 5 feet and the length (4x) is 20 feet.

Step-by-step explanation:

Answer: 3 by 3 by 12 by 12

Step-by-step explanation: Two sides are x feet long. The two other sides are 4 times x feet long. 4x+4x+x+x =10x

Set that equal to 30 and solve. x=3

Plug back into the original 4x's and x's to get the lengths

Answer: i think its D

Step-by-step explanation:

Answer:

A is the answer

Step-by-step explanation:

if its wrong than its C

Answer:

Step-by-step explanation:

volume=1/3 πr²h

=1/3×π×3²×4

=12π ft³

≈37.70 ft³

Here we have to calculate the volume of the cone which is provided in the figure.

As we know that volume of cone is calculated by the formula :

Here,

We have :

Putting the values in the formula :

\(\longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \pi \:r {}^{2}h } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \:(3) {}^{2}(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \:(3 \times 3)(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \:(9)(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \: \times 9(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \: \times 9 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{ \cancel3} \: \times \dfrac{22}{7} \: \times \cancel9 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{1} \: \times \dfrac{22}{7} \: \times 3 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{22}{7} \: \times 3 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{22 \times 3 \times 4}{7} } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{66 \times 4}{7} } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{264}{7} } \\ \\ \longrightarrow \: \sf{V \: = \: \cancel\dfrac{264}{7} } \\ \\ \longrightarrow \: \underline{\underline{\red{\bf{V \: = \: 37.7 }}}}\)

Answer: x equals 9

Step-by-step explanation: add 16 to itself to cancel it out. Do the same thing to 20. now your equation is 4x=36. Divide 4x by 4 to cancel out 4. Do the same thing to 36. Now you have x=9.

Answer:

-20% discount

Step-by-step explanation:

subtract the two numbers:

1020-1360= -340 (is a percentage reduction, so I have to subtract the larger number from the smaller one)

divide the result by the original value:

-340÷1360= -0,25

to turn it into a percentage, multiply it by 100:

-0,25×100= -25%

Hope it helps!

Answer:

there's a decrease of 25%

or

-25%

Step-by-step explanation:

100% = 1360

___% = 1020

\( \frac{1020 \times 100}{1360} = 75\)

100- 75= 25%

Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

The standard numbers are obtained from the given numbers as follows;

The standard form of numbers is obtained by expressing the number completely and not using powers of 10

The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;

Number → Standard form

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Answer:

x = -5

Step-by-step explanation:

X -6= 11 - 11(x + 7)

Distribute

x-6 = 11 -11x -77

Combine like terms

x-6 = -11x -66

Add 11x to each side

x-6+11x = -11x-66+11x

12x-6 = -66

Add 6 to each side

12x -6+6 = -66+6

12x = -60

Divide by 12

12x/12 = -60/12

x = -5

Answer:

answer is sister's.

Step-by-step explanation:

sisters mean more than one sister.

sisterses isn't a word.

sisters' also isn't a word.

sister's is a word and it means that she has possession of something or that she owns something.

Using the distance between two points to find the length of the side of the square, it is found that:

The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

In this problem, the length of the side of the square can be found as the distance between points G and H, that is, the distance between (0,5) and (-5,0), hence:

\(l = \sqrt{(0 - (-5))^2 + (5 - 0)^2} = \sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}\)

The area of a square of side length l is given by:

\(A = l^2\)

Hence:

\(A = (5\sqrt{2})^2 = 50\)

The area is of 50 square units.

The perimeter of a square of side length l is given by:

\(P = 4l\)

Hence:

\(P = 4(5\sqrt{2}) = 20\sqrt{2}\)

The perimeter is of \(20\sqrt{2}\) units.

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Answer:

IT'S A

Step-by-step explanation:

Answer:

7 and 9

Step-by-step explanation:

Variables:

x = smaller number

y = larger number

We can set up two equations with the information given:

5x + 3y = 62

and

y = x + 2

We get the second equation with the information that the two numbers are consecutive and both odd. therefore the smaller number is two less than the larger number, and the larger number is two greater than the smaller number.

Next, we need to replace our y in the first equation with the y in the second:

5x + 3y = 62

5x + 3 (x+2) = 62

5x + 3x + 6 = 62

8x = 56

x (smaller number) = 7

Finally, we solve for the larger number by placing it back into the second equation:

y = x + 2

y = 7 + 2

y (larger number) = 9

I hope this helps!

-TheBusinessMan

Answer:

$ 93.804 or $93.80 after rounding.

Step-by-step explanation:

Answer:

The 15% discount means that they only pay 100%-15% = 85% of the meal's bill.

This would cost 85% * 78.65.

However, they also have to pay a 20% tip of the meal cost.

This would cost 20% * 78.65.

Total Cost = (85% * 78.65) + (20% * 78.65)

= 105% * 78.65

= 1.05 * 78.65

= $82.58

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer Lindsay walked her horse for 3 hours and 30 minutes

Step-by-step explanation:

The correct graph of the inequality ( |x| + 3 > 3) is attached accordingly.

Recall that the absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.

A number's absolute value can be conceived of as its distance from zero along the real number line.

So, given  |x| + 3 > 3

Add minus three to both sides

|x| + 3  + (-3) > 3 + (-3)

|x|  > 0

Thus, the absolute value of x is

x > 0 or x < -0

put in the form of inequality, we have

x > 0 or x < 0

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Answer:

A , B and C

Step-by-step explanation:

evaluate the expressions following the order of operations as set out in PEMDAS

initial expression

note that • indicates multiplication

3 (2 + 6) + 4 × 5 ← evaluate parenthesis

= 3(8) + 20 = 24 + 20 = 44

A

5 × 4 + 3 × (6 + 2) ← evaluate parenthesis

= 5 × 4 + 3 × 8 ← perform multiplication

= 20 + 24 ← perform addition

= 44

B

(6 + 2) × 3 + 4 × 5 ← evaluate parenthesis

= 8 × 3 + 4 × 5 ← perform multiplication

= 24 + 20 ← perform addition

= 44

C

3 × 2 + 3 × 6 + 4 × 5 ← perform multiplications

= 6 + 18 + 20 ← perform addition

= 44

D

3 × 2 + (6 + 4) × 5 ← evaluate parenthesis

= 3 × 2 + 10 × 5 ← perform multiplication

= 6 + 50 ← perform addition

= 56

the expressions equivalent to the initial expression are A , B and C

Answer: Distribute the 10 on the left side of the equation:

10n + 30 = 1,000,000

Subtract 30 from both sides of the equation to isolate the term with n:

10n = 1,000,000 - 30

10n = 999,970

Divide both sides of the equation by 10 to solve for n:

n = 999,970 / 10

n = 99,997

Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.

Step-by-step explanation: