A __________ names part of a whole, part of a set,
or a location on a number line.

A: decimal
B: fraction

Answer:

D

Step-by-step explanation:

D

Answer:

14÷2=7

7 is your answer. hope this helps

Ashley and her sister decide to split the cost of dinner , which is $14 . How much will each sister pay?

$7

look at the attached picture :)

Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.

\(\rule{130}1\)

Solution :

Let the two consecutive positive odd numbers be x and (x + 2)

\(\rule{130}1\)

☯ \(\underline{\boldsymbol{According\: to \:the\: Question\:now :}}\)

\(:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup\)

When,

\(\bullet\: \textsf {x = } \textbf {15} \)

\(\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17} \)

\(\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.\)

To calculate the value of X that Ellen should deposit in the bank, we need to determine the present value of the future payments that will accumulate to $50,000 in six years.

Using the formula for compound interest, the present value can be calculated as follows:

PV = X/(1 + r)^1 + X/(1 + r)^2 + X/(1 + r)^3,

where r is the annual interest rate (5%) expressed as a decimal.

To find the value of X, we set the present value equal to $50,000 and solve for X:

50,000 = X/(1 + 0.05)^1 + X/(1 + 0.05)^2 + X/(1 + 0.05)^3.

Once we determine the value of X, we can proceed to the next step.

For the second part of the question, after four years, the bank raises the interest rate to 6%.

From year four to year six, Ellen's money will continue to accumulate interest.

To find the amount donated, we calculate the future value of the remaining amount after deducting the down payment of $50,000:

Remaining amount = X/(1 + 0.06)^2 + X/(1 + 0.06)^3 + X/(1 + 0.06)^4.

The donated amount is then the difference between the remaining amount and the total accumulated after six years.

By evaluating these expressions, we can determine the value of X and the amount donated by Ellen.

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The population of the world is estimated to be 7.9 billion in 2022. Let's assume the current population of the world as P1 = 7.9 billion people.

Given, the rate of growth of the world's population has been gradually declined over many years. But, the population rate is assumed not to change from its current estimate of 1.1%.The population of the world is estimated to be 7.9 billion in 2022.

Let's assume the current population of the world as P1 = 7.9 billion people.After t years, the population of the world can be represented as P1 × (1 + r/100)^tWhere r is the rate of growth of the population, and t is the time for which we have to find out the population. The population we are looking for is P2 = 10 billion people.Putting the values in the above formula,P1 × (1 + r/100)^t = P2

⇒ 7.9 × (1 + 1.1/100)^t = 10

⇒ (101/100)^t = 10/7.9

⇒ t = log(10/7.9) / log(101/100)

⇒ t ≈ 18.4 years

So, it will take approximately 18.4 years for the world's population to reach 10 billion people if the rate of growth remains 1.1%.Therefore, the correct option is 18.4.

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Multiply the first equation by 4:

Subtract the second equation:

This is:

Simplify:

Substitute y = 1 in the first equation:

Ans solve for x:

Answer:

x = 3

y = 1

The term used to denote a number raised to the power of three is cubed.

When a number is cubed, it is multiplied by itself three times. For example, 2 cubed (written as 2³) is equal to 2 x 2 x 2, which equals 8.

Cubing a number is a common mathematical operation that is used in a variety of applications, including geometry, physics, and engineering. It is also used in basic arithmetic, such as finding the volume of a cube.

Cubing a number is similar to squaring a number, which is when a number is raised to the power of two. However, cubing a number results in a much larger value than squaring the same number. For example, 2 squared (written as 2²) is equal to 2 x 2, which equals 4, while 2 cubed (written as 2³) is equal to 2 x 2 x 2, which equals 8.

In summary, the term used to denote a number raised to the power of three is "cubed". Cubing a number involves multiplying the number by itself three times, and is a common operation in various fields of mathematics and science.

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Acute angle ⇒ 0⁰ < m < 90⁰

Straight angle ⇒  m = 180⁰

Obtuse angle ⇒ 90⁰ < m < 180⁰

Right angle ⇒ m = 90⁰

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees. In other words, an obtuse angle is an angle that is wider than a right angle (90 degrees), but not as wide as a straight angle (180 degrees).

When two rays or line segments intersect at a point, they form an angle. If the angle formed is less than 90 degrees, it is called an acute angle. If the angle is exactly 90 degrees, it is called a right angle.

If the angle is greater than 90 degrees but less than 180 degrees, it is called an obtuse angle. Finally, if the angle measures exactly 180 degrees, it is called a straight angle.

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Answer:

it is B

Step-by-step explanation:

I had this on my work it should be right

Answer:

C

Step-by-step explanation:

thats the only one that makes sense.

in other words 0.9 + 0.02 = 0.92

Answer:

160 in²

Step-by-step explanation:

20 * 16 / 2

if we wouldn't devide with 2, we would calculate the rectangle around the quadrilateral

Answer:

G, 160 in^2

Step-by-step explanation:

Let us start with the general equation to find the area of this quadrilateral, which is noticably a rhombus, \(A=\frac{d_1d_2}{2}\), where the two d represent the two diagonals of the rhombus.

Notice that the longer diagonal consists of two 10in. portions. Let's add them up to find the total length:

\(10+10=20\)in.

Now let's find the smaller diagonal consisting of two 8 in. portions:

\(8+8=16\)in.

Great! Let's plug in to solve for the area:

\(A=\frac{20*16}{2} \\A=\frac{320}{2} \\A=160\)

Therefore, the area of the quadrilateral is G, 160 in^2.

I hope this helps! Let me know if you have any questions :)

Answer:

529

Step-by-step explanation:

892=x+363.

We want to get x by itself so we know what it equals.

Because 363 is adding to x we subtract it to the other side.

892-363=529

529=x

So the other number is 529

The other number is 529.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The sum of two numbers is 892.

Let the two unknown numbers be x and y.

Now, x+y=892

One of the numbers is 363.

x+363=892

x=892-363

x=529

Therefore, the other number is 529.

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Answer:

17 cm

Step-by-step explanation:

The equilateral triangle has its three equal sides, if it is required to calculate the lenght of each side and the perimeter is known, you just have to divide by three:

\(\frac{51}{3} =17\)

I hope this help you

Answer:

in form of what?and what's the question

The area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

To get the area of the shaded region, we subtract the area of the sector from the area of the triangle as follows:

The angle m∠AOB = 180° - (34 + 90) {sum of interior angles of a triangle}

m∠AOB = 56°

area of sector = 56/360 × 22/7 × 26 cm × 26 cm

area of sector =14872/45 cm²

area of sector = 330.4888 cm²

area of the triangle = 1/2 × 26 cm × 39 cm

area of the triangle = 507 cm²

area of the shaded region = 507 cm² - 330.4888 cm²

area of the shaded region = 176.5111 cm²

Therefore, the area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

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Not possible since the value of sin(a) must lie between -1 and 1. Therefore, there is no solution for this problem.

We know that:

csc(a) = 3/2

Since csc(a) = 1/sin(a), we can find sin(a) as:

1/sin(a) = 3/2

Cross-multiplying, we get:

2sin(a) = 3

Dividing by 2, we get:

sin(a) = 3/2

This is not possible since the value of sin(a) must lie between -1 and 1. Therefore, there is no solution for this problem.

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Answer:

2x6 and 6x2

Step-by-step explanation:

because 12/6 gets you 2 and 6x2 equals 12

Answer:

2

Step-by-step explanation:

Clarie and Tyler thought about 12 divided by 6 because if you thought how much weight would give me 12?, You would think you need to divide to know that and if you multiply 2x6 it gives you the product of 12 so 12 divided by 6 is 2 therefore the missing number is 2.

Answer:

(x+7)(x+6)

Step-by-step explanation:

x²+13x+42

x²+6x+7x+42

x(x+6)+7(x+6)

(x+6)(x+7)

Answer:

a) (x+7) (x+6)

Step-by-step explanation:

That is the correct answer because you get it when you factor the current equation.

Hope it helps

The height of the cell phone tower in feet will be 135 feet high.

The utilization of two or more additional numbers that compares is known as the ratio.

The cell tower that casts a shadow is 100 feet long.

Lia casts shadows 3 feet and 4 inches long.

If Lia is 4 feet 6 inches tall.

Let 'h' be the height of the tower. Then the height of the tower is given as,

h / 100 = (4 + 6/12) / (3 + 4/12)

h / 100 = 4.5 / 3.33

h / 100 = 1.35

h = 135 feet

The height of the cell phone tower in feet will be 135 feet high.

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Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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Answer:

acceleration = 9.8 m/s^2

Step-by-step explanation:

The problem expects the user to do the rate of change between any two pairs of (time, velocity) from the table, and see that they all render the same value. Notice as well that the rate of change of a difference in velocities divided a difference in time, will render units of acceleration (in this case \(\frac{m}{s^2}\)

Let's use for example (0 s ,0 m/s) and the following point: (1 s, 9.8 m/s)

the rate of change is: \(acceleration= \frac{9.8-0}{1-0} \frac{m}{s^2} =9.8 \, \frac{m}{s^2}\)

In fact you can use any two pairs of the table, and will get the same result.

So this is the acceleration is \(9.8 \, \frac{m}{s^2}\)

The acceleration due to gravity is 9.8 m/s^2.

If you add a small imperfection to a system that has saddle-node bifurcation, the system will experience a phenomenon known as "imperfect bifurcation."

This means that the bifurcation will not occur at a single, well-defined point, but rather over a range of parameter values. This can lead to a change in the dynamics of the system, such as the appearance of new attractors or the disappearance of existing ones. In general, imperfect bifurcation can make the behavior of a system more complex and difficult to predict.

Moreover, the specific effect of the imperfection will depend on its size, location, and nature, and can vary between different types of saddle-node bifurcations, such as fold or transcritical bifurcations. Therefore, the analysis of imperfect bifurcation requires a detailed understanding of the system's dynamics and the effects of perturbations.

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If Devin is collecting signatures for a petition to open a new park in her town. She needs to collect at least 1,000 signatures before she can schedule a meeting with the mayor. The inequality best shows how many more pages (p) Devin needs is: B) 8 ≤ p

Inequality  is used to show the show the mathematical expression that are not equal to one another.

First step is to calculate the signature left

Signature left= 1,000 - 380

Signature left = 620

Now let determine the number of pages

Number of pages =620 / 80

Number of pages = 7.75

Number of pages = 8 (rounded)

Inequality

8 ≤ p

Therefore the correct option is B.

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The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Absolute maximum point: (π/10, 2).

Absolute minimum point: (π/6, -3).

Given function is: f(t) = -2sin(5t) - sin(10t)The function is defined on the closed interval [0,π/10]. We need to find the absolute maximum and absolute minimum values of the given function in the interval [0,π/10].

Absolute extrema are the highest and lowest points on a function, either over its entire domain or within a certain range (interval). If the given interval is closed and bounded, the function will have both an absolute maximum and an absolute minimum in that interval.

First, we need to find the critical points of the function f(t) in the given interval. Critical points of f(t) in the interval [0,π/10] are obtained by equating the derivative of f(t) to zero.∴ f'(t) = -10 cos(5t) - 10 cos(10t) = 0⇒ cos(5t) + cos(10t) = 0.

Using the formula 2cosAcosB = cos(A+B) + cos(A-B), we can simplify the above equation.∴ cos(5t) + cos(10t) = 2cos(7.5t)cos(2.5t) = 0⇒ cos(7.5t) = 0 or cos(2.5t) = 0Solving for cos(7.5t) = 0, we get t = π/30, 5π/30 = π/6, and 7π/30.Solving for cos(2.5t) = 0, we get t = π/10, 3π/10, 7π/10, and 9π/10.

Now, we can find the absolute extrema of f(t) in the given interval by calculating the function values at the critical points and the endpoints of the interval.∴ f(0) = -2sin(0) - sin(0) = 0∴ f(π/10) = -2sin(π/2) - sin(π) = 2∴ f(π/6) = -2sin(5π/6) - sin(π) = -3∴ f(π/30) = -2sin(π/6) - sin(π/3) = -3/2∴ f(3π/10) = -2sin(3π/2) - sin(3π) = 2∴ f(π/2) = -2sin(5π/2) - sin(5π) = 0.

The maximum value of f(t) in the interval [0,π/10] is 2, and the minimum value is -3. The absolute maximum point is (π/10, 2), and the absolute minimum point is (π/6, -3).Therefore, the required answers are:Absolute maximum point: (π/10, 2)Absolute minimum point: (π/6, -3)

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The constant variation of Y 8 when X 16 is 2.

What is Direct Proportion?

"When the relationship between two quantities is such that if we increase one, the other will also rise, and if we decrease one, the other quantity will also drop, then the two quantities are in a direct proportion," according to the definition of direct proportion. For instance, suppose there are two numbers, x and y, where x is the number of candies and y is the total amount of money spent. If we purchase more candy, we will be required to pay more, and if we purchase fewer candies, we will be required to pay less. This means that x and y are directly proportional to one another in this situation. The symbol for it is x y. Direct variation is another name for direct proportion.

So,

In the given question, we have:

y as 8 and x as 16;

So,

In order to find the proportional value, we have to divide the x quantity by the y quantity.

So, after dividing we get:

\(\frac{X}{Y} = \frac{16}{8}\)

\(\frac{X}{Y} = 2\)

So,

The constant proportion will be 2.

Hence,

The constant proportion will be 2.

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