HELP WITH NUMBER 5 FOR 20 POINTS

The possible answers for the restaurants are Three 8-hour shifts; four 6-hour shifts; six 4-hour shifts.

2. The seconds that they will blink together again is 45 seconds.

Here we have to determine the factors of 24 for the shifts i.e.  1, 2, 3, 4, 6, 8, 12, 24 .

A 1-hour shift does not make much sense; most employers will also not use a 2-hour or 3-hour shift.

Restaurants typically do not use 12-hour shifts either, and employers do not use 24-hour shifts either.

Since both signs blink as they are turned on and one blinks every 9 seconds. The other sign blinks every 15 seconds. The least common multiple is 45.

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Answer:

The answer would be: A = 5 1/4

In 15 years, the account will be worth $1896 if the 3.7% interest is compounded monthly on initial deposit of $1100.

It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Given Data

A =  [tex]P(1+\frac{r}{100} )^{t}[/tex]

P=$1100

r =3.7%

t = 15years

Substitute the values in formula, A = [tex]P(1+\frac{r}{100} )^{t}[/tex]

A= 1100(1+{3.7/100})¹⁵

A = 1100(1+0.037)¹⁵

A = 1100(1.037)¹⁵

A= 1100(1.724)

A= 1896.4

Round off to nearest cent - $1896

Hence, $1896 will the account be worth in 15 years

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Answer:

4.

∠ABC + ∠BCA + ∠CAB = 180

therefore, ∠ABC = 180 - ∠BCA - ∠CAB

using this formula to solve 4a, 4b and 4c:

4a. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 49 -57 = 26

∠ABC = 26

4b. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 28 -90 = 62

∠ABC = 62

4c. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 38 - 25 = 117

∠ABC = 117

5a. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 55 - 60 = 65

∠BCA = 65

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 65 = 115

∠BCD =115

5b. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 125 - 30 = 25

∠BCA = 25

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 25 = 155

∠BCD = 155

5c. ∠ABD + ∠CBD = 180

therefore ∠CBD = 180 - ∠ABD = 180 - 132 = 48

∠CBD = 48

In the Triangle BCD, ∠CBD + ∠BDC + ∠BCD = 180

therefore ∠BCD = 180 - ∠CBD - ∠BDC = 180 - 48 - 71 = 61

∠BCD =61

6. 4 angles of a quadrilateral = 360

∠a+110+60+80=360

∠a=360-110-60-80=110

∠a = 110

7. four angles of a quadrilateral = 360

using his formula to solve for ∠a, ∠b and ∠c.

for angle a: ∠a+110+95+63=360

∠a=360-110-95-63=92

∠a = 92

for angle b: ∠b+40+62+35=360

∠b=360-40-62-35=223

∠b=223

for angle c: ∠c+100+172+35=360

∠c=360-100-172-35=53

∠c=53

Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2) then the coordinates of the vertices of the image after a reflection in the y-axis will be:

P'' (-3,-8)

P' (3,8)

Q'' (-5,7)

Q'' (-5,-7)

R'' (2,0)

R'' (0,2).

A reflection around the axis and is given by the following rule:

(x, y) ----> (-x, y)

Applying the rule to each vertices of the reflection y - axis we have:

A) P' (3,-8) ----> P'' (-3,-8)

B) P (-3,8)  ----> P' (3,8)

C) Q' (5,7)  ----> Q'' (-5,7)

D) Q' (5,-7)  ----> Q'' (-5,-7)

E) R¹ (-2,0) ----> R'' (2,0)

F) R¹ (0,2) ----> R'' (0,2)

Therefore,

Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2) then the coordinates of the vertices of the image after a reflection in the y-axis will be:

P'' (-3,-8)

P' (3,8)

Q'' (-5,7)

Q'' (-5,-7)

R'' (2,0)

R'' (0,2).

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Answer:

7.25 feet/2 feet = 3.625 pieces so you can have 3 pieces of 2 feet each and 1 piece left over that is less than 2 feet.

Answer:

Ratio is a comparison between 2 numbers.

Hope this helps :)

The values of m and b are 6 and 2 respectively and the value of m + b is 8.

It is given that the equation y = mx + b   ....(1) for the line parallel to the graph of  y = 6x + -2    ...(2) means that slope of the equation y = mx + b which is parallel to the graph y = 6x + -2  is same i. e on comparing equation (1) and (2) , we get m = 6

On the other hand , the equation y = mx + b has the same y- intercept as the graph of y = 36x + 2   .....(3)

On  comparing equation (1) and (3) , we get b = 2

Therefore , m + b = 6 + 2

                             = 8

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Answer:

-6

Step-by-step explanation:

y=6

-y=-6

The scale of the map is 1:4000000

From the question, we are to determine the scale of the map

From the given information,

3cm on the map correspond to 120 km

First, we will convert 120 km to cm

120 km = 120000 m

120000 m = 12000000 cm

Thus,

3cm on the map correspond to 12000000 cm

Then,

The scale of the map is

3:12000000

Reducing to the lowest term

1:4000000

Hence, the scale of the map is 1:4000000

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Answer:

11 with a remainder of 26

Step-by-step explanation:

Accoding to the given statements;

Sasha have left 2480 mm of rope.

According to the given values;

Sasha has 520 cm of rope

She used 2m 72 mm of rope

So, 1 cm = 10mm

And 1m = 1000mm

So, 520 × 10 = 5200mm

2.72× 1000 = 2720mm

5200 - 2720 = 2480mm

Sasha have left 2480 mm of rope.

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Jasper had 362.25 in his account after two years, per the given statement.

The interest you earn upon interest is known as compound interest. This may be demonstrated with simple math: if you have $100 and that it earns 5% interest every year, you will have $105 at the end of the first year. You'll have $110.25 by the end of the second year.

Given:

Jaspar deposits £2,500

interest rate = 7

Time = 2 year

Compound interest is interest calculated on the aggregate amount rather than the principle amount alone.

Amount = P(1+r/100)^n

=2500(1+7/100)²

=2500(100+7/100)²

= 2500(107/100)²

= 2862.25

C.I.= Amount - Principal

= 2862.25-2500

= 362.25

According to the given statement jasper have 362.25 in his account after 2 years.

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Answer:
X-intercepts: -1 and 3

Y-intercepts: 3
Vertex: (1, 4)
Axis of Symmetry: y= -1x + 3x + 4 (I think this is right it might not be and im sorry if it isnt).

Step-by-step explanation: Hope this helps even a little bit <33

Domain: (-infinity, 5)

Range: [-3, infinity)

The values of the expressions in the table following their evaluation are;

1. 73

2. 97

3. x = 108

4. -13/6

5. 1 and 97

6. 1 and 41

7. The graph of the number line

8. She needs to add 5/36 cup of sugar

The length of the actual is 6 miles

1. The given expression is 5•x + 14 - 6

The value of x at which the expression is evaluated is x = 13

Which gives;

5×13 + 14 - 6 = 73

2. Twelve times six plus 25 can be expressed as 12 × 6 + 25

12 × 6 + 25 = 97

3. x/9 = 12

Multiplying across gives;

x × 1 = 9 × 12 = 108

x = 108

4. The expression is 3/16 - 3/8

= (3 - 2× 3)/16

3/16 - 3/8 = (3 - 2× 3)/16 = -3/16

(3 - 2× 3)/16 = -3/16

5. The prime factors of 97 are; 1 and 97

6. 41 is a prime number.

The factors of 41 are; 1 and 41

7. The graph of x = -1/3

8. Quantity of sugar required = 3¼

Quantity added = 3⅑

Quantity needed = 3¼ - 3⅑ = 5/36

9. 4 inches is equivalent to 2 miles

Therefore;

12 inches = 3 × 4 inches is equivalent to 3 × 2 mi = 6 mi

The length of the actual trail is 6 miles

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The properties of algebra used here are

For first point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For Second point the algebraic properties used is  Associative Property of Addition

For third point the algebraic properties used is Associative Property of Multiplication.

For fourth point the algebraic properties used is  Commutative Property of Multiplication

For fifth point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For sixth point the algebraic properties used is Associative Property of Addition

The correct question is Write the property that justifies each mathematical statement. Look carefully!!

1. a(c-d) = ac - ad

2. 2x + y = y + 2x

3. — 3(4c) = (- 3 * 4)c

4. 3(4ab) = (4ab)3

5. - 9(3 + 2x) = -9(3) - 9(2x)

6. 3+ (2 + n) = (3 + 2) + n

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Answer:

$30.25

Step-by-step explanation:

1100 (.03) [tex](\frac{11}{12})[/tex]

Answer:

C. 5/10

Step-by-step explanation:

Using a calculator:

Divide each numerator by each denominator. The answer must be 0.5

A. 1/50 = 0.02

B. 1/5 = 0.2

C. 5/10 = 0.5

D. 5/9 = 0.555...

Answer: C. 5/10

Without a calculator.

0.5 as a fraction is 1/2. Notice the denominator, 2, is twice the numerator, 1.

The answer also must have a denominator that is twice the numerator.

A. 1/50      2 × 1 = 2, not 50

B. 1/5         2 × 1 = 2, not 5

C. 5/10      2 × 5 = 10; this is it.

D. 5/9       2 × 5 = 10, not 9

Answer: C. 5/10

Answer:

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

For the relation to the function, each value of x must map onto no more than one value of y.

Answer:

Domain: -2≥x≥2

Range: -2≥x≥2

Not a function

Step-by-step explanation:

The number in standard notation is 143,000.

The number in scientific notation is 4.39 x 10^-4

Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example:

• The number : 1 x 10² is equivalent to 100

• The number 5 x 10³ is equivalent to 500

When changing a number that is less than 1 to scientific notation, there would be a negative sign before the power.

0.000439 = 4.39 x 10^-4

In order to convert a number from scientific notation to standard notation, multiply the number by its power.

1.43 x 10^5

= 1.43 x 100,000 = 143,000

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Answer:

Step-by-step explanation:

2/4 is equal to 0.5

4/8 is equal to 0.5

10/20 is equal to 0.5

16.5 is 30% of 55

1650/55 = 30

Answer:

A frequency table of grades has five classes A B C D F

Step-by-step explanation:

A frequency table of grades has five classes A B C D F

The value of x is 6

A line segment can be defined as the partition formed by end points of a line.

From the information given, we have that line JL is the line with segments JK, KL and JL and K and the midpoint between J and L

This can be represented as;

JK + KL = JL

Where;

Substitute the values into the formula, we have;

5x -8 + 7x - 12 = 52

Now, collect like terms

12x = 52 + 20

Add like terms

12x = 72

Make 'x' the subject of formula

x = 72/12

x = 6

Thus, the value of x is 6

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Answer: y=2x-14

Step-by-step explanation:

Solve for x

x/2+7 = y

x/2+7-7=y-7

x/2=y-7

2x/2=2(y-7)

x=2y-14

y=2x-14  ==> switch the x and y variables

Step-by-step explanation:

mm/kyc-kbiy-rvk come.

Answer:

Step-by-step explanation: Gold will cost €2.06 per gram.

The range of possible sizes for side x is 2.3 < x < 8.7.

Herein we have a triangle, of which two of its sides are known and we can now the set of all possible values by using the law of the cosine:

x² = 3.2² + 5.5² - 2 · 3.2 · 5.5 · cos θ

x = √(40.49 - 35.2 · cos θ)

The cosine is bounded between - 1 and 1, then the possible sizes for the side x are:

2.3 < x < 8.7

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