Evaluate the expression and enter your answer in the box below.
[(5+11) 4]+9. (6-4)
÷
Answer here

Answer:

y = 1100 - 115x

Step-by-step explanation:

Let the monthly payment be $p

In two months Zach would have paid 2p dollars

Balance would be  1100 - 2p = y

We know after 2 months, balance y was actually 870

Substituting y = 870 we get
1100 - 2p = 870

Subtract 1100 on both sides

1100 - 1100 - 2p = 870 -1100

==> -2p = - 230

Divide by -2 on both sides

-2p/-2 = -230/-2

p = 115 which represents the monthly payment .

So the balance y after m months is given by the equation
y = 1100 - 115x

We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent

Answer:

7

Step-by-step explanation:

(2t+3r) divide 4

so if r=2 and t=11 the new equation will be :

(2times11 + 3times 2) divide 4

(22+6) divide 4

= 28 divide 4 = 7

The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.

The formula of the n-th term of a geometric sequence is:

a(n) = a₁ . r^(n-1)

Where:

a₁ is the first term

r  is the ratio = a(n)/a(n-1)

Parameters given in the problem:

a₁ =1024, r=0.5

Plug these parameters into the formula, then we get the explicit formula of the n-th term:

a(n) = 1024 . (0.5)ⁿ⁻¹

The first 5 terms:

a₁ = 1024

a(2) = 1024 . (0.5)²⁻¹

       = 1024 . (0.5)¹ = 512

a(3) = 1024 . (0.5)³⁻¹

       = 1024 . (0.5)² = 256

a(4) = 1024 . (0.5)⁴⁻¹

       = 11024 . (0.5)³ = 128

a(5) = 1024 . (0.5)⁵⁻¹

       = 1024 . (0.5)⁴ = 64

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Answer:

The answer is 2

Step-by-step explanation:

Answer:x

2

(

15

x

3

+

4

x

−

24

)

Step-by-step explanation:

Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.

Simple interest is simply a method to determine the amount of interest charged on a sum at a given rate and for a given period of time.

It is expressed as;

I = prt

Given the data in the question;

Plug the given values into the formula above and solve for I.

I = p × r × t

I = $625 × 0.025 × 0.5

I = $7.81

Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.

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The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.

The sequence we are provided is 2, 4, 7, 10, …

Here, [tex] a_{1}[/tex] = 2, [tex] a_{2}[/tex] = 4 and [tex] a_{3}[/tex] = 7.

A sequence is considered as an Arithmetic sequence if their difference is equal. Represented as -

[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = [tex] a_{4}[/tex] - [tex] a_{3}[/tex] and so on

Now, in the given sequence

⇒[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 4 - 2

[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 2

⇒ [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 7 - 4

[tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 3

⇒ [tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 10 - 7

[tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 3

Since, the difference between the given sequence of terms are not same.

∴ The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.

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Reason:

Angle R is the reference angle since we're computing tan(R)

Side r is opposite angle R. This is the opposite side because it's furthest away from angle R.

Side t is opposite angle T. This is the adjacent side because it's nearest to reference angle R.

The tangent involves the ratio of opposite over adjacent

tan(angle) = opposite/adjacent

tan(R) = r/t

Writing the propositions using p and q with logical connectives, including negations, in each of the statement will give;

(a) you do not drive over 65 miles per hour-

        ¬ p

(b) you drive over 65 miles per hour, but you do not get a speeding ticket

        p ∨ ¬ q

(c) you will get a speeding ticket if you drive over 65 miles per hour-  

         p → q

We are to represent each statement using letters; p and q

The letters p and q are then connected with the logical connectives symbols; example negation, conjunction, disjunction and implication symbols.

Thus, each statement given in the question is logically written as;

(a) ¬ p

(b) p ∨ ¬ q

(c) p → q

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The simplified answer to 5.3. √2 will be 7.495.

It should be noted that we are to find the simplified answer to 5.3. √2 .

This means that we have to multiply them. This will be:

= 5.3 × ✓2

= 5.3 × 1.1414

= 7.495

Note that the options given aren't complete.

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- 40.18 is the solution of this function .

What does a math cube root mean?

[tex]2( -15) - \sqrt[3]{18( -15 ) - 1061}[/tex]

= [tex]2 ( -15 ) - \sqrt[3]{3 - 1061}[/tex]

= [tex]-30 - \sqrt[3]{ - 1058}[/tex]

=  - 30 - 10.18

=  - 40.18

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Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

Given the data in the question;

A bisector divides a line or angle into two equal halves.

Hence

Segment JM = Segment MK

7x + 5 = 8x

Solve for x

8x - 7x = 5

x = 5

Now, numerical value of segment JM will be;

Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40

Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80

Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

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The portion of wooden strip that is left from the original strip is 1/4

Samantha is using a wooden strip that measures 7/8 yard

Samantha cuts off a piece of the wood that is 3/4 long

The fraction that represents the proportion of the original strip that is left can be calculated as follows

7/8 - 3/4

The LCM of both fractions is 8

7 - 6/8

= 2/8

convert to the lowest term

1/4

Hence the proportion of the original wooden strip that remains is 1/4

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On a number line, the value of x is six places away from zero. Any of the following numbers, from 1 to 5, could serve as the x.

When X is 6 numbers away from -1, it has a value of 5.

The values from -1 after 6 is -1,0,1,2,3,4,5 so 5 is the 6th number from -1

A number line is a straight line with numbers spaced at equal segments or intervals in mathematics.

A number line is often shown horizontally and can be extended indefinitely in any direction.

Moving from left to right causes the numbers on the number line to climb, whilst moving from right to left causes them to fall.

On a number line, both positive and negative integers can be shown.

Comparing numbers is made simpler by writing them on a number line. The number line's leftmost numerals are smaller than its right most digits.

A number line can be used to do addition, subtraction, and multiplication. We always move to the right, to the left, or by skipping a count while adding, subtracting, or multiplying.

Hence, x could be any one of the following Numbers: 5, 4, 3, 2, or 1.

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750 items were sold that day

The first step is to calculate the total revenue

Total revenue= 935 - 125

= 810

Therefore the number of items sold can be calculated as follows

810= 1x + 8/100

810= 1x + 0.08x

810= 1.08x

x= 810/1.08

x= 750

Hence 750 items were sold that day

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Answer:

0.245

Step-by-step explanation:

Divide both the numerator and denominator by 2.

49/200 will be 24.5/100

If you divide a number by 100, you move the decimal place 2 digits to the left. 24.5/100 will become 0.245

The sequence -5,15,-45,135,-405,. . . . is a geometric sequence and its 10th term is a(10) = 98,415

To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.

The given sequence is:

    -5,15,-45,135,-405,....

In this sequence:

a(1) = -5

a(2) = 15

a(3) = -45

and so on.

Notice that:

15 = -5 . (-3)  ⇒ a(2) = a(1) . (-3)

-45 = 15 . (-3) ⇒ a(3) = a(2) . (-3)

Since the n-th term is obtained by multiplying the (n-1)-th term by a constant, r = -3, hence, the given sequence is a geometric sequence.

The formula for the nth term in a geometric sequence is given by:

a(n) = a(1) . rⁿ⁻¹

Substitute n = 10, r = -3, and a(1) = -5

a(10) = (-5) . (-3)¹⁰⁻¹

a(10) = (-5) . (-3)⁹

        = 98,415

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The value of h based on the information illustrated is 24 1/2.

It should be noted that the fraction given is illustrated as:

3/4h - 12 = 8 5/8

Add 12 to both sides

3/4h - 12 + 12 = 8 5/8 + 12

3/4h = 20 5/8

Multiply both side by 4/3

3/4h × 4/3 = 20 5/8 × 4/3

h = 165/8 × 4/3

h = 27 1/2

Therefore, the value of h is 24 1/2.

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Answer:

C.

-3-6=-9

Step-by-step explanation:

-3-6=-9

C. The blue arrow goes to negative 3. Then the red arrow goes from negative 3 to negative 9.

Hope this helps!

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The possible parking spot numbers can be either 12th spot or 26th spot.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that the parking spot was smudged on the ticket.

Let's assume the possible parking spot numbers can be given by x which is represented by an inequality.

Your parking spot is 7 spaces away from your friend's spot which is number 19 in the same row. So , the possible parking spot numbers can be given by ;

19 - 7 ≤ x ≤ 19 + 7

12 ≤ x ≤ 26

Therefore , the possible parking spot numbers can be either 12th spot or 26th spot.

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Answer:2,4,8,16,32,64,128,256,512,1024,2048,4096

Step-by-step explanation:

You just mutiply the number with 2

The numbers in the order of least to greatest is :

₋1.8 , ₋1/4 , 1/2 , 1.41 , 7.2 , 9.1 , 121

Given, the numbers are in decimal and fraction form.

1/2 , -1/4 , 7.2 , 121 , 1.41 , -1.8 , 9.1

we need to convert the fractions and then arrange the numbers in the ascending order.

Writing the numbers in an ordered list according to their values means arranging them from least to greatest. The smallest number should be put on the left, followed by the next smallest number, which should be written directly to its right.

for 1/2:

1/2 = 0.5

for ₋1/4:

₋1/4 = 0.25

now arrange the numbers according to the least to greatest form.

we have numbers:

0.5 , 0.25 , 7.2 , 121 , 1.41 , ₋1.8 , 9.1

least to greatest form:

₋1.8 , 0.25 , 0.5 , 1.41 , 9.1 , 121

i.e , ₋1.8 , 1/4 , 1/2 , 1.41 , 9.1 , 121

Hence we get the required form.

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   The binomial expansion of the given expression is:

x³ - y³ - 3x²y + 3y²x

   A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.

 Depending on the number of terms it can be :

 We solve first by perfect square trinomial, then we apply the distributive property.

(x-  y)³ = (x - y)²(x - y)

(x - y)² = x² - 2xy + y²

(x - y)( x² - 2xy + y²)

x³ - 2x²y + y²x - x²y + 2y²x - y³

x³ - y³ - 3x²y + 3y²x

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Answer:

Mean:  160

Median:  150

Mode:  none

Range:  105

Standard deviation:  35.3

Step-by-step explanation:

Given:

If each value in the data set is multiplied by a constant value, the mean, median, mode, range, and standard deviation will all be scaled by the same amount.

Therefore, if each value in the data set is multiplied by 0.5:

Proof

Data set: {1, 2, 3, 4, 5}

[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{1+2+3+4+5}{5} = 3[/tex]

[tex]\sf Median = 3[/tex]

[tex]\sf Mode = none[/tex]

[tex]\sf Range = 5-1=4[/tex]

[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{10}{5}}=\sqrt{2}[/tex]

If we multiply each value by 0.5, the new data set is:

{0.5, 1, 1.5, 2, 2.5}

[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{0.5+1+1.5+2+2.5}{5} = 1.5[/tex]

[tex]\sf Median = 1.5[/tex]

[tex]\sf Mode = none[/tex]

[tex]\sf Range = 2.5-0.5=2[/tex]

[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{2.5}{5}}=\dfrac{\sqrt{2}}{2}[/tex]

Therefore, if each value in the data set is multiplied by 0.5, the mean, median, mode, range, and standard deviation are all scaled by the same amount.

Answer:

m∠FQR = 23°

Step-by-step explanation:

Since m∠KQF = 90°, it's a complementary angle and is equal to 90°

Step 1: Write the equation. Since The whole angle equals 90° add everything together to equal 90°

(3x - 23)° + (2/3x + 3)° = 90

3x - 23 + (2/3)x + 3 = 90

Combine like terms

multiply the denominator by 3. (3 × 3) = 9 + 2 = 11

(11/3)x - 20 = 90

          + 20   +20

(11/3)x = 110

÷(11/3)  ÷(11/3)

x = 30°

Step 2: Find m∠FQR

m∠FQR = ((2/3)x + 3))

(2/3)(30) + 3

20 + 3 = 23

m∠FQR = 23°

I hope this helps!

Answer:

Step-by-step explanation:

(2/3x+3) + (3x-23)=90

(2/3+3)x -20 =90

11/3x =90 + 20

x= 110 * 3/11 =30

FQR = 2/3x+3= 2/3 (30) +3 = 20 +3 =23

Answer:

4400

Step-by-step explanation:

4001→4000 (you need to round the number to the nearest thousand)

283→300 (you need to round the number to the nearest hundred)

97→100 (you need to round the number to the nearest ten, in this case 100)

4000+300+100= 4400

Hope this helps! :)

According to the question, when die is rolled check the number is greater than two and it should be [tex]6[/tex].

The total number of outcomes : [tex]n(E)= {1,2,3,4,5,6}[/tex]

And getting a number greater than [tex]2[/tex] [tex]= {3,4,5,6}[/tex]

Finally, getting a number as [tex]6 = {6}[/tex]

Therefore, the probability can be written as:

[tex]P(E) = \frac{1}{6}[/tex]

Hence, the calculated probability is [tex]\frac{1}{6} .[/tex]

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Answer:

-11.

Step-by-step explanation:

h(x) = -4x - 3, find h(2).​

Replace the x by 2:

h(2) = -4(2) - 3

       = -8 - 3

       = -11.

 The final answer is the combination of both solutions   x = 3,− 3.

What are quadratic in math?

Use the quadratic formula to find the solutions

x = - b + √b² - 4ac / 2a

Substitute the values

a = 1, b = 0, and c = − 9 into the quadratic formula and solve for x.

x = 0  +  √ 0² - 4 . ( 1 . 9 ) / 2. 1

Simplify

    The final answer is the combination of both solutions.

          x = 3,− 3

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