The sum of two consecutive numbers is 535

Answer:

h = V / ar

Step-by-step explanation:

V = arh

arh = V   (divide both sides by "ar" )

h = V / ar

Deborah spends 240 hours per month on consulting work. This was calculated by understanding 48 hours is 1/5 of her time, and multiplying it by 5 to find the total hours.

The subject of this question is mathematics, and it involves the concept of fractions to solve a real-world problem. Deborah spends 1/5, or 20% of her time, writing grant proposals. If she spends 48 hours per month on this task, 48 hours represents 1/5 of her total consulting time.

To find the total consulting time, we need to do these steps: divide 48 by 1 to get 48 (since 48 hours is the 1/5), then multiply 48 by 5 (the denominator of the fraction, which represents the whole).

So, 48 (hours) divided by 1 equals 48, and 48 multiplied by 5 equals 240. Therefore, Deborah spends 240 hours per month on consulting work.

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Answer:

D. 16.8

Step-by-step explanation:

It is right trust me!!!

Answer:

Additional amount of clearance between the truck and overpass is 16.8 inches.

Step-by-step explanation:

A law states that a a freight truck must have the clearance of at least 3 feet to travel under the a overpass.

Sign on an overpass states that the overpass is 18 feet above the road's surface.

Height of the truck is 13.6 feet.

As per rule height of overpass from the road must be height of the truck + clearance.

Additional amount of clearance between the truck and the overpass

= Distance between the road and the overpass - (height of the truck + clearance)

= 18 - (13.6 + 3)

= 18 - 16.6

= 1.4 feet

Since 1.4 feet = 12 inches

1.4 feet = 12×1.4 = 16.8 inches

Therefore, additional amount of clearance between the truck and overpass is 16.8 inches.

Answer:

[tex]\dfrac{1}{3} \left (\dfrac{1}{b} - 1 \right )[/tex]

Step-by-step explanation:

[tex]f(x) = \dfrac{1}{3b} - \dfrac{1}{3}[/tex]

1. Find the least common multiple of the denominators

The least common multiple of 3 and 3 is 3.

2. Factor out ⅓.

[tex]\dfrac{1}{3b} - \dfrac{1}{3} = \mathbf{\dfrac{1}{3} \left (\dfrac{1}{b} - 1 \right )}[/tex]

x = -6 is the solution to the equation 6x + 7 = 13 + 7x

To solve the equation 6x + 7 = 13 + 7x, you can follow these steps:

Group the x terms on one side and the constant terms on the other side:

6x - 7x = 13 - 7

Combine like terms:

-x = 6

Multiply both sides of the equation by -1 to isolate x:

-1*(-x) = -1*6

This simplifies to:

x = -6

Therefore, the solution to the equation 6x + 7 = 13 + 7x is x = -6.

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Answer:

5,500,000 = (5 x 100000000) + (0 x 10000000) + (5 x 1000000) + (0 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1)

Step-by-step explanation:

The expanded form of 5,500,000 is  (5 x 1000000) + (5 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).

The expanded form of the number is the splitting of numbers based on the place value, such as ones, tens, hundreds, thousands, ten thousands,and so on. The number that is represented by the sum of each digit multiplied by its place value is called the expanded form of the number.

Now the given number is,

5,500,000

Now each digit place value is given as,

5 =  (5 x 1000000)  

5 =  (5 x 100000)

0 =  (0 x 10000)

0 =  (0 x 1000)  

0 =  (0 x 100)

0 =  (0 x 10)

0 =  (0 x 1)

Adding this together, we get

5,500,000 = (5 x 1000000) + (5 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).

Hence, The expanded form of 5,500,000 is  (5 x 1000000) + (5 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).

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Answer:

[tex]x = 19[/tex]

Step-by-step explanation:

If two lines are perpendicular, they create 4 90° angles. Meaning, in this case, that m<DBC = 90 and m<DBA = 90.

We're given that m<DBE = 2x - 1 and that m<CBE = 5x - 42.

The sum of angles DBE and CBE = m<DBC = 90°

We can add the two angles and set it equal to 90 to find x

[tex]2x - 1 + 5x - 42 = 90\\7x - 43 = 90\\7x = 133\\x = \frac{133}{7} =19[/tex]

Answer:

4.32       46

Step-by-step explanation:

ok im lazy and just googled it here

Answer:

Rafael gets $4,32 In tips. The old lady gets $41.68 in change.

Step-by-step explanation:

Step 1: To calculate the tip we must take into account that it is 8% of the total amount of the bill.

$54 * 8%/100% = $4,32

Rafael gets $4,32 In tips.

Step 2: Now we must calculate the change the old lady receives. For this, we must subtract from the $100 that she gives the part corresponding to the payment for food and the part corresponding to the tip.

$100 - $54 - $4,32 = $41,68

The old lady gets $41.68 in change.

Have a nice day!

Answer:

{y|10 < y}; ○ y > 10

Step-by-step explanation:

Whenever you have a Rational-Radical function, the answer will ALWAYS result in greater than.

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Answer: -12

Step-by-step explanation:

[2+(-4)] becomes (2-4), or -2, and 5-[(-11)x(-2)]-(-7) becomes 5-22+7, so the entire thing is -2+5-22+7, so it is -12.

The given expression [2+(-4)]+5-[(-11)x(-2)]-(-7) simplifies to -12.

To simplify the given expression, we follow the order of operations (PEMDAS/BODMAS):

Step 1: Evaluate the innermost parentheses:

[2 + (-4)] + 5 - [(-11) x (-2)] - (-7)

[2 - 4] + 5 - [(-11) x (-2)] - (-7)

Step 2: Complete the operations inside the brackets:

[-2] + 5 - [22] - (-7)

Step 3: Simplify the subtraction and negation:

-2 + 5 - 22 + 7

Step 4: Perform addition and subtraction from left to right:

(5 - 2) - 22 + 7

3 - 22 + 7

Step 5: Continue performing addition and subtraction:

-19 + 7

Step 6: Final result:

-12

The expression simplifies to -12.

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Answer:

Step-by-step explanation:

16 feet

Answer:

Option C.

Step-by-step explanation:

Let x be the distance from holes center in feet and y be the depth from level ground in feet.

The given table represents a quadratic functions.

x :    -2             0           2

y :    -6            -8          -6

The depth from level ground in feet is same at x=-2 and x=2 it means the hole is symmetric about the line x=0.

The value of a quadratic function is on its extreme at line of symmetry.

In the given function the line of symmetry is x=0. So, the depth of the hole is defined on x=0.

From the table it is clear that at x=0 the depth from level ground is 8 feet.

Therefore, the correct option is C.

Answer:

What is the circumference of a circle with an area of 50.24 cm²?

Use 3.14 for pi.

Enter your answer as a decimal in the box.

25.12cm

Answer:

r = -29/20 or r = -1.45

Step-by-step explanation:

I believe you are saying that the equation is -2 1/4 = r - 4/5. If so, then I would solve it in this way:

-2 1/4 = r - 4/5

-9/4 = r - 4/5

-9/4 (20) = r (20) - 4/5 (20)

-45 = 20r - 16

20r = -29

r = -29/20

r = -1.45

Check:

-2 1/4 = r - 4/5

-9/4 = r - 4/5

-2.25 = r - 0.8

-2.25 = -1.45 - 0.8

-2.25 = -2.25

-9/4 = -9/4

The calculated value of variable r is r = -1.45.

An equation is a mathematical statement that shows the equality between two expressions. It typically consists of variables, constants, and mathematical operations (e.g., addition, subtraction, multiplication, division) with an equal sign (=) in between.

To solve for r in the equation -21/4 = r - 4/5

Step 1: Add 4/5 to both sides of the equation to isolate r:

r = -2.25 + 4/5

Convert -2.25 to a fraction with a common denominator of 5:

r = (-11.25/5) + (4/5)

Add the fractions:

r = (-11.25 + 4)/5

Simplify:

r = -7.25/5

r = -1.45

So, r = -1.45.

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Answer:

In order for the average to equal 3,000 then the total attendance must equal 9,000.

Show 1 = 2,580

Show 2 = 2,920

2 show total = 5,500

Therefore, third show total must equal 9,000 minus 5,500 =

3,500

Double-Check

2,580 + 2,920 + 3,500 = 9,000

Step-by-step explanation:

Answer:

Well there is a lot of different numbers he could be thinking of because we are only given 2 useful pieces of information: Four Digits, and, a 3 in the tens place (30).

.

This means that the other spaces could be any number.

.

If X represents a random number it would be XX3X.

.

Eg 1234

Answer:

125i

Step-by-step explanation:

The simplification of the complex number (5i)³ is; -125i

We are given the complex number; (5i)³

Expanding the given complex number gives;

(5i)³ = 5³ * i³

⇒ 125i * i²

From complex number multiplication, we know that i² = -1. Thus;

125i * i² = -125i

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Answer:

Rose wins the game, with 6 points over Lilly's 1 point.

Step-by-step explanation:

Let's find Lilly's score. In this example we will add together the gains first, so we wouldn't have to deal with negative numbers, and after, we subtract the losses of each person.

Lilly's points:

[tex]0 + 5 + 5 + 3 - 12 = 1[/tex]

Rose's points:

[tex]0 + 6 + 7 - 3 - 3 - 1 = 6[/tex]

Rose wins the game with a 5 point lead.

Lilly's score is 1 and Rose's score is 6. Therefore, Rose wins the game because 6 is greater than 1.

To find Lilly and Rose's score, we will create and solve an expression that reflects each player's game moves.

Lilly gains 5 points two times, loses 12 points, and then gains 3 points. We can express this as (5*2) - 12 + 3. First, we multiply 5 by 2, which equals 10. Then, we subtract 12 from 10, which gives -2. Finally, we add 3 to -2, resulting in a final score of 1 for Lilly.

Rose loses 3 points two times, loses 1 point, gains 6 points, and gains 7 points. We can write this as (-3*2) - 1 + 6 + 7. First, we multiply -3 by 2, which equals -6. Then, we subtract 1 from -6 yielding -7. After that, we add 6 to -7, getting -1. Lastly, we add 7 to -1, resulting in a final score of 6 for Rose.

Rose won the game because her final score of 6 is higher than Lilly's final score of 1.

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Check the picture below.

make sure your calculator is in Degree mode.

Answer:

[tex]4\frac{1}{6}\ cups[/tex]

Step-by-step explanation:

we know that

The recipe calls for 1 2/3 of sugar

To make 2 1/2 times the recipe

Multiply 2 1/2 by 1 2/3

Convert mixed numbers to an improper fraction

[tex]1\frac{2}{3}=\frac{1*3+2}{3}=\frac{5}{3}\ cups[/tex]

[tex]2\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}[/tex]

so

[tex]\frac{5}{2}(\frac{5}{3})=\frac{25}{6}\ cups[/tex]

Convert to mixed number

[tex]\frac{25}{6}=\frac{24}{6}+\frac{1}{6}=4\frac{1}{6}\ cups[/tex]

Final answer:

To find out how much sugar is needed for the new recipe that is 2 1/2 times as much, follow the three-step process.

Explanation:

To find the amount of sugar needed:

Calculate 1 2/3 cups of sugar is equal to 5/3 cups of sugar.

Multiply 5/3 by 2 1/2, which equals 25/6.

Convert 25/6 to a mixed number, which is 4 1/6 cups of sugar needed for the new recipe.

Answer:

False

Step-by-step explanation:

The absolute value always returns a positive value, however the expression inside can be positive or negative, that is

Given

| z - 7 | - 2 = 2 ( add 2 to both sides )

| z - 7 | = 4, then

z - 7 = 4 OR - (z - 7) = 4

z = 4 + 7 = 11 OR

- z + 7 = 4

- z = 4 - 7 = - 3 ( multiply both sides by - 1 )

z = 3

As a check

z = 11

| 11 - 7 | - 2 = | 4 | - 2 = 4 - 2 = 2 ←  True

z = 3

| 3 - 7 | - 2 = | - 4 | - 2 = 4 - 2 = 2 ← True

Hence z = 11 or z = 3 are the solutions

Answer:

68

Step-by-step explanation:

4^3-(24÷6)+8

4³-(4)+8= 68

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Answer:

68

Step-by-step explanation:

[tex] {4}^{3} - (24 \div 6) + 8 = 64 - 4 + 8 = 60 + 8 = 68[/tex]

According to the Order of Operations [GEMS\BOMDAS\PEMDAS etc.], in this case, you deal with the grouping symbols first before anything else, then comes the exponents, and finally comes Subtraction & Addition from right to left [or left to right, if you know what you are doing correctly]. Doing all of these will give sixty-eight.

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Answer:

That is written in standard form. Hope this helps.

(N-5)*7

The N-5 is in parenthesis, so this needs to be done first, then the multiplication is done.

To say this verbally:

Subtract five from N, then multiply by seven.

Answer:

-18

Step-by-step explanation:

Follow PEMDAS. So first you do 2x2=4 then 4-7x= -3-15= -18

Good evening ,

_______

Answer:

x’=5

x’’=(-3)/2

____________________

Step-by-step explanation:

Δ=(-7)²-4×(2)×(-15)=49+120=169

√Δ=√169=13

then

x’=(7+13)/4=20/4=5

x’’=(7-13)/4=(-6)/4=(-3)/2.

:)

Answer:

see explanation

Step-by-step explanation:

27 = 3 × 9 ← is one way

27 = 3³ ← is another way

The two (2) ways you can represent the number 27 using the number 3 are shown below.

In this exercise, you're required to represent the number 27 by using the number 3. This simply means that you will represent the number 27 in terms of 3.

First way;

Since 3 is a factor of 27, we would multiply it to get 27.

[tex]27 = 3 * 3 * 3[/tex]

Second way;

From the above, we can see that the product of 3 is equal to 27.

[tex]27 = 3^{3}[/tex]

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Answer:3.3

Step-by-step explanation:

You want to look at the 3.2 because the 2 in the hundredths place so you will round it up because 6 is higher than 5 so it will be 3.3

Rounded to the nearest hundredth is 3.26

Answer:

Negative Twelve Times a Number Plus Two

Step-by-step explanation:

By setting up the question as an algebraic equation, 1/2 * x = 21, and solving for x, it's determined that half of 42 is equal to 21.

The question we're looking to solve is: "1/2 of what number is 7 times 3?" First, let's understand that 7 times 3 equals 21. The question asks which number, when halved, gives us 21. This can easily be set up as an algebraic equation: 1/2 * x = 21, where x represents the number we're trying to find.

To solve for x, we first multiply both sides of the equation by 2 to get rid of the fraction (1/2). This leaves us with: x = 21 * 2. Therefore, x = 42. The number, when cut in half, that results in 21, is 42.

Answer:

the answer is C

Step-by-step explanation:

You can solve this by changing everything to fractional powers. 4th root of x^3 can be written as x^3/4. Since you are dividing you will subtract their powers, so 3/4 - 1/12 will give you the power raised by x. You can rewrite to 9/12 - 1/12 to get 8/12 which will end up as x^2/3

I tried to answer the last time you asked but you closed the question haha, I hope you understand!

Answer:

x = 180

Step-by-step explanation:

First, you need to know

1. Double-angle formula:

cos(2x) = [tex]cos^{2}x - sin^{2}x[/tex]

2. Pythagorean identity:

[tex]cos^{2}x + sin^{2}x = 1[/tex]

Back to your problem, replacing the variable by the above:

[tex]5cosx-sin\frac{x}{2}+7 = 0[/tex]

[tex]5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0[/tex] By Double-angle formula

[tex]5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0[/tex] By Pythagorean identity

Given [tex]y = \frac{x}{2}[/tex]

[tex]5(1-2sin^{2}y) - 2siny + 7 = 0[/tex]

[tex]10sin^{2}y+2siny-12=0[/tex]

[tex]5sin^{2}y+siny-6=0[/tex]

[tex](5siny + 6)(siny - 1)=0[/tex], we know -1 < sinx < 1, for every x ∈ R

[tex]siny = 1, y =90 [/tex]

[tex]y = \frac{x}{2}[/tex]

[tex]x = 180[/tex]