Lacey has two pieces of ribbon, one 30 inches long and the other 48 inches long. To decorate an album, she wants to cut them up to produce many pieces of ribbon that are all of the same length, with no ribbon left over. What is the greatest length, in inches, that she can make them?

A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 5.57x cm and 11.14x cm, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that circumference of the circle is 35x cm. Therefore, the radius and the diameter of the circle can be written as,

Circumference of circle = 2 × π × (Radius of the circle)

35x cm = 2 × π × (Radius of the circle)

(Radius of the circle) = 35x/ (2 × π)

The radius of the circle = 5.57x cm

Diameter of circle = 2 × (Radius of the circle)

                             = 2 × 5.57x cm

                             = 11.14x cm

Hence, the radius and the diameter of the circle are 5.57x cm and 11.14x cm, respectively.

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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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If Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.

Given that Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day.

We are required to write the inequality that represent the situation of Elon.

Inequality is just like an equation that shows the relationship between two variables but in greater than, less than,greater than or equal to,less than or equal to signs.

Suppose the number of hours that Elon works be x hours each day.

The earning of Elon will be 45x.

Since the expenditure is $75,the saving will be 45x-75 and if he wants to make $260 a day, the inequality will be 45x-75≥260.

45x≥260+75

45x≥335

x≥335/45

x≥7.55

Hence if Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.

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Answer:

Mr Tan's daughter received $620

Step-by-step explanation:

the son received $460

$460 × 2 = $920

the wife received $920

$920 - $300 = $620

$460 + $920 + $620 = $2000

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:

< A = 60 degrees.

< B = 44 degrees

<C = 76 degrees.

Step-by-step explanation:

A + B + C = 180    --------(1)

2A = B + C            -------(2)

B = C - 32             -------(3)

We see from equation 2 that B + C = 2A so we

replace The A + B in equation (1) by 2A:

A + 2A = 180

3A = 180

A = 60.

Substitute A = 60 in equation (2):

120 = B + C

Rearranging equation (3):

32 = -B + C

Adding theses last 2 equations:

152 = 2C

C = 152/2 = 76.

Substituting for A and C in equation (1):

60 + 76 + B = 180

B = 180 - 60 - 76 = 44 degrees.

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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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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Answer:

Yes

Step-by-step explanation:

A right triangle is a triangle that has one angle whose measure is 90°. A right triangle CANNOT have two 90º angles. This is because the angles of a triangle must add up to 180°. With one angle measuring 90°, the other two angles in the right triangle must add up to 90°

The geometric mean of 1/5 and 60 is 2√3.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 1/5 and 60 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 1/5, and x2 = 60

GM = √(1/5)(60)

GM = √12

GM = 2√3

Hence, the geometric mean of 1/5 and 60 is 2√3.

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Answer:17/38

Step-by-step explanation:

5/19+7/38

\frac{5}{19}+\frac{7}{38}

Answer:

[tex]\frac{17}{38}[/tex]

Step-by-step explanation:

[tex]\frac{5 * 2}{19 * 2} +\frac{7}{38}[/tex]

[tex]\frac{10+ 7 }{38}[/tex]  10 +7 =17

[tex]\frac{17}{38}[/tex]

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:

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:

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!

Please mark as brainliest if correct!

Have a great day!

Identify the centers and radii of the two circles. To find the transformation rule, we need to find how many units horizontally and vertically to move the center of one circle to the center of the other circle.

The equation for the shifted circle is

(x+2) ^2+(y+4) ^2=36.

Description: The standard shape of a circle is

(x−h)2+(y−k)2=r2,

where r is the circle's radius and (h,k) is the circle's center.x2+y2=36 centered at (0,0). If the circle is shifted two units to the left, it means that the new center is h = -2. If we move the circle down four units, the new center is k = −4. So, the shifted circle has the equation (x+2)2+(y+4)2=36.

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The length of GH is 8 units.

The image is not given. Attached a sample image below.

Given,

We can assume that the figure may be a line.

G is between points E and H

F is the midpoint of EG

The length of EH = 14 units

The length of FG = 3 units

We have to find the length of GH.

Here,

EH = EG + GH

Length of EG = FG + EF

F is the mid point of E and G. So, EF = FG ⇒ 3 units

Now,

EG = FG + EF

EG = 3 + 3

EG = 6 units

Now, we can find GH.

GH = EH - EG

EG = 6 units

EH = 14 units

Therefore,

GH = 14 - 6

GH = 8 units.

The length of GH is 8 units.

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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.

Answer:x

2

(

15

x

3

+

4

x

−

24

)

Step-by-step explanation:

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

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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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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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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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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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

Answer:

The answer is 2

Step-by-step explanation:

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! :)

- 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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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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