Find the slope of the line passing through the two points.

(2.1, 3.8), (3.1, 7.6)

The weight of the last child is 36 lbs.

The average weight of the three children is 60 lbs. The total weight will be:

= 60 × 3

= 180 lbs.

When another child is added, the weight is 54lb. The total weight will be:

= 54 × 4

= 216 lbs

The weight of the last child will be:

= 216 - 180

= 36 lbs.

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Answer:

5 is the base

4 is the exponent.

5⁴ = 625

Explanation:

Given the general expression in indices;

a is known as the base of the expression

n is the exponent

Comparing with the given expression 5⁴, you will see that a = 5 and b = 4. Hence;

5 is the base

4 is the exponent.

5⁴ = 5 * 5 * 5 * 5

5⁴ = 25 * 25

5⁴ = 625

Hence the value of 5⁴ is 625

Answer:

5^4 = 625

a) 5

b) 4

c) 5 x 5 x 5 x 5

Step-by-step explanation:

The base is the number you multiply, the larger one.

The exponent is the amount of times you multiply that number by itself, or the smaller one.

Answer:

5

Step-by-step explanation:

Ask your self which equation you should use. Since it says F(3) then we have to find an equation that would fit this correctly. For example if we look at -X^2, X<-2 we could see that 3 is clearly not less than -2, leading to the conclusion that this is not the right equation.. If you look at the last equation it says that x has to be greater/equal to 0 which is true. So then we are left with the equation...

F(3)=x+2

F(3)=3+2

F(3)=5

The ball is initially 3 feet above the ground when it is tossed, The time the ball is in the air is approximately 1.13 seconds,The maximum height of the ball is approximately 10.875 fee,

The initial height of the ball can be determined by substituting t = 0 into the equation for height, h = -16t^2 + 24t + 3.

Plugging in t = 0, we get:

h = -16(0)^2 + 24(0) + 3

h = 0 + 0 + 3

h = 3

Therefore, the ball is initially 3 feet above the ground when it is tossed.

To find the time the ball is in the air, we need to determine when its height is equal to zero. We can set the height equation equal to zero and solve for t:

-16t^2 + 24t + 3 = 0

Using the quadratic formula, we can solve for t. The time the ball is in the air will be the positive root of the equation.

The time the ball is in the air is approximately 1.13 seconds (rounded to one decimal place).

To find the time at which the ball reaches its maximum height, we need to find the vertex of the parabolic equation. The x-coordinate of the vertex can be found using the formula: t = -b / (2a), where a = -16 and b = 24.

t = -24 / (2 * -16)

t = -24 / -32

t ≈ 0.75 seconds

Therefore, the ball reaches its maximum height approximately 0.75 seconds after it is tossed.

To find the maximum height, we can substitute the time of reaching the maximum height (t = 0.75) into the height equation:

h = -16(0.75)^2 + 24(0.75) + 3

h ≈ 10.875

The maximum height of the ball is approximately 10.875 feet (rounded to the nearest whole number).

After the ball reaches the maximum height, its height decreases at a decreasing rate. This can be determined by examining the coefficient of the t^2 term in the height equation, which is negative (-16). As t increases, the negative quadratic term causes the height to decrease, but at a decreasing rate due to the negative coefficient.

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If land securities borrowed £25,000,000 five years ago at a fixed rate for ten years of 5.80 per cent with annual payments, the payoff of the loan today would be approximately £13,723,037.

To determine the payoff of the loan today, we need to calculate the present value of the remaining payments.

The loan has an initial principal of £25,000,000, and the fixed interest rate is 5.80% per annum with annual payments. The loan is a 10-year loan, and it has been 5 years since it was borrowed.

We can calculate the present value of the remaining payments using the formula for the present value of an annuity:

PV = C * ((1 - (1 + r)^-n) / r)

where PV is the present value of the remaining payments, C is the annual payment, r is the annual interest rate, and n is the number of years remaining on the loan.

The annual payment is calculated using the loan amount, interest rate, and loan term. Using these values, we can calculate that the annual payment is approximately £3,251,670.

Substituting these values into the formula, we get:

PV = £3,251,670 * ((1 - (1 + 0.058)^-5) / 0.058)

Solving for PV, we get a present value of approximately £13,723,037.

This is the amount that Land Securities would need to pay to fully satisfy the loan, without any pre-payment penalty.

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Answer:

The expression x = \(\frac{13}{8}+\frac{5}{4}\) could be used to determine the amount of water drank altogether.

Step-by-step explanation:

Given that:

Amount of water drank during practice = \(1\frac{5}{8} = \frac{13}{8}\)  liters

Amount of water drank on the ride home = \(1\frac{1}{4} = \frac{5}{4}\) liters

Let,

x be the total amount of water drank by Ramona.

x = Water drank during practice + Water drank on the ride home

x = \(\frac{13}{8}+\frac{5}{4}\)

Hence,

The expression x = \(\frac{13}{8}+\frac{5}{4}\) could be used to determine the amount of water drank altogether.

Answer:

A. True

B. True

C. False

Step-by-step explanation:

Hope that helps!

An inequality which represents this situation, and if the fires continue to decrease the area of the forests at the same rate, will the state be able to keep their funding from the nonprofit wildlife organization in 5 years is: C. 24,000(0.908)^t > 15,000; no.

From the information provided, we can logically deduce that only an exponential function would model or represent the rate at which the forest fires decrease, and this is given by this mathematical expression:

y = a(b)^t

Where:

For the value of b, we have:

b = 100% - 9.2%

b = 90.8%

b = 90.8/100

b = 0.908.

Substituting the given parameters into the formula, we have;

y = a(b)^t

y = 24,000(0.908)^t

Therefore, an inequality that represent the situation is given by:

24,000(0.908)^t > 15,000.

When the value of t = 5 years, the area of the forest in square miles is given by:

y = 24,000(0.908)^t

y = 24,000(0.908)^5

y = 24,000 × 0.61720472567

y = 14,812.913 ≈ 14,813 square miles.

Therefore, the verdict is as follows:

14,813 > 15,000 (False and No).

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Complete Question:

There are 24,000 square miles of forest in a western state. Forest fires decrease this area by 9.2% each year. The state needs to have more than 15,000 square miles of forest to keep their funding from a nonprofit wildlife organization.

Which inequality represents this situation, and if the fires continue to decrease the area of the forests at the same rate, will the state be able to keep their funding from the nonprofit wildlife organization in 5 years?

A. 24,000(1.092)^t > 15,000; no

B. 24,000(0.092)^t > 15,000; yes

C. 24,000(0.908)^t > 15,000; no

D. 24,000(1.098)^t > 15,000; yes​

Answer:

24,000(0.908)t > 15,000; no

Step-by-step explanation:

The area of forest remaining in the state decreases at a rate of 9.2% each year. Thus, the area remaining after t years can be represented by an exponential expression, a(b)t, where a is the initial area of forest and b is the base of the exponent.

Since the area of forest remaining in the state decreases at a rate of 9.2% each year, the variable r represents the decay rate. Thus, for this situation, r is 9.2%, or r = 0.092. Substitute this value into the decay rate equation below, and solve for b.

\(1-b=r\\1-b=0.092\\-b=0.092-1\\-b=-0.908\\\frac{-b}{-1}=\frac{-0.908}{-1} \\b=0.908\)

The area of forest after t years needs to be greater than or equal to 15,000 square miles for the state to keep their funding, so use the greater than symbol and compare to 15,000 square miles. The initial area of forest is 24,000 square miles. So, substitute a = 24,000 and b = 0.908 into the exponential inequality to represent this situation.

\(a(b)^{t} > 15,000\\ 24,000(0.908)^{t} > 15,000\)

Thus, the inequality that represents this situation is 24,000(0.908)t > 15,000.

To find if the state will be able to keep their funding in 5 years, substitute t = 5 into the inequality and determine if this value yields a true statement.

\(24,000(0.908)^{5} > 15,000 \\ 14,812.91 > 15,000\)

Since, 14,812.91 is not greater than 15,000, the inequality is false. Thus, in five years, no, the state will not be able to keep their funding from the nonprofit wildlife organization.

The joint probability of a and b upto 2 decimal places is 0.12

The conditional probability P(B/A)  arises only in the case of dependent events. It gives the conditional probability of B given that A has occurred.

p(a) = 0. 40 and p(b | a) = 0. 30.

P(B/A) = P(A∩B) / P(A)

0.30 = P(A∩B) / 0.40

P(A∩B) = 0.30 x 0.40

P(A∩B) = 0.12

Therefore, the joint probability of a and b upto 2 decimal places is 0.12

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Answer:

∠ PTR = 140°

Step-by-step explanation:

∠ PTQ and ∠ RTS are vertical and congruent, thus

2x + 16 = x + 28 ( subtract x from both sides )

x + 16 = 28 ( subtract 16 from both sides

x = 12

Thus ∠PTQ = x + 28 = 12 + 28 = 40°

∠ PTQ and ∠ PTR are adjacent and supplementary, thus

∠ PTR = 180° - 40° = 140°

Answer:

its 17.3 or 18.0 feet

Step-by-step explanation:

Answer:

C. 66°

Step-by-step explanation:

Given:

m∠FAB = 48°,

m∠ECB = 18°,

Required:

m∠ABC

SOLUTION:

∠CHB ≅ ∠FAB (alternate interior angles theorem)

m∠CHB = ∠FAB

m∠CHB = 48° (substitution)

m∠CHB + m∠ECB + m∠CBH = 180° (sum of angles in a ∆)

48° + 18° + m∠CBH = 180° (substitution)

66° + m∠CBH = 180°

Subtract 66° from each side

m∠CBH = 180° - 66°

m∠CBH = 114°

Thus,

m∠CBH + m∠ABC = 180° (Linear pair)

114° + m∠ABC = 180° (substitution)

Subtract 114° from both sides

m∠ABC = 180° - 114°

m∠ABC = 66°

The angle m∠ABC will be equal to 66° the correct answer is option C.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Given:

m∠FAB = 48°,

m∠ECB = 18°,

Required:

m∠ABC

The angle ABC will be calculated as follows:-

∠CHB ≅ ∠FAB (alternate interior angles theorem)

m∠CHB = ∠FAB

m∠CHB = 48° (substitution)

m∠CHB + m∠ECB + m∠CBH = 180° (sum of angles in a ∆)

48° + 18° + m∠CBH = 180° (substitution)

66° + m∠CBH = 180°

Subtract 66° from each side

m∠CBH = 180° - 66°

m∠CBH = 114°

Thus,

m∠CBH + m∠ABC = 180° (Linear pair)

114° + m∠ABC = 180° (substitution)

Subtract 114° from both sides

m∠ABC = 180° - 114°

m∠ABC = 66°

Therefore the angle m∠ABC will be equal to 66° the correct answer is option C.

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Answer:

6/8

Step-by-step explanation:

3/4

Multiply by 2/2

3/4 *2/2 = 6/8

Answer:

3

8

Step-by-step explanation:

probability= no. of blue marbles

total no. of marbles

= 3

8

If the charge on a single-use bag is 25 fils, then the notations that shows the amount of dirhams that the store will get after one year can be expressed as 0.25x.

Given that the charge on single-use bag is 25 fils.

We are required to give the express the amount of dirhams that the store will get after one year.

Equation is the relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be a linear equation,quadratic equation,cubic equation and many more depending on the powers of variables that are present in the equation.

let the number that single use bag used in 1 year be x.

We know that there are 100 files in a dirham, so 25 fils will be 0.25 dirham.

Equation that shows the number of dirham that the store will get after one year=0.25x.

Hence if the charge on a single-use bag is 25 fils, then the notation that shows the amount of dirham that store will get after one year can be expressed as 0.25x.

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Answer:

88,900

Step-by-step explanation:

:) hope this helps! give it a like!

Answer:

88,900

Step-by-step explanation:

you are rounding 88,855 to the nearest hundred so you really just need to look at the hundred's place

855 rounded to the nearest hundred is 900 (round your 8 to 9 since the tens place is a 5 or above)

Answer:

x=1

Step-by-step explanation:

Answer:

  (x, y) = (0.2, -1.6) or (67.8, 9.6)

Step-by-step explanation:

You want the solution to the system of equations ...

using substitution for x.

The first equation can be used to write an expression for x:

  x = 6y +10 . . . . . . add 6y to both sides

This can be substituted for x in the second equation:

  3y² = 4(6y +10) +7

  3y² = 24y +40 +7

  3y² -24y -47 = 0 . . . . . . . subtract (24y+47) to get standard form

We can use the quadratic formula to solve this equation:

  \(y=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-24)\pm\sqrt{(-24)^2-4(3)(-47)}}{2\cdot3}\\\\y=\dfrac{24\pm\sqrt{24^2+12\cdot47}}{6}\approx\{9.6,-1.6\}\)

Then x can be found from the equation above as ...

  x = 6y +10 = 34 ± √1140 ≈ {67.8, 0.2}

The solutions are (x, y) = (0.2, -1.6) or (67.8, 9.6).

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Answer:

12 mathletes is needed to solve 30 problems in 5 minutes

Step-by-step explanation:

8 athletes can solve 20 problems in 10 minutes

30-20=10

now we need 10 more problems to be solved so

20/2=10. 8/2=4 so we need more 4 mathletes to solve all the problems

Borrowers can make more accurate comparisons between different loan options and understand the overall cost they will incur over the life of the loan.

In the given scenario, there are two banks offering 20-year, $210,000 mortgages at 4.4 percent interest. The banks charge a $3,100 loan application fee. However, there is a difference between the banks regarding the refundability of the application fee.

Insecurity Bank and Trust: This bank charges a $3,100 loan application fee, which is refundable if the loan application is denied. In this case, the fee is considered part of the loan rather than a separate fee.

I. M. Greedy and Sons Mortgage Bank: This bank also charges a $3,100 loan application fee, but it is nonrefundable, meaning it will not be returned if the loan application is rejected.

The disclosure law requires that any fees that will be refunded if the applicant is rejected must be included in calculating the Annual Percentage Rate (APR). This is because these fees are considered part of the loan amount and have an impact on the overall cost of borrowing.

On the other hand, nonrefundable fees like the one charged by I. M. Greedy and Sons Mortgage Bank are not required to be included in the APR calculation. This is because these fees are treated as separate costs that are not directly part of the loan.

When comparing mortgage offers and determining the true cost of borrowing, it is important to consider not only the interest rate but also any associated fees. By including refundable fees in the APR calculation, borrowers can make more accurate comparisons between different loan options and understand the overall cost they will incur over the life of the loan.

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Answer:

m∠B = 100°

a = 4.6

b = 7.36

Step-by-step explanation:

By applying sine rule in the given triangle,

\(\frac{\text{sin(A)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(C)}}{c}\)

Now substitute the values in the expression,

\(\frac{\text{sin(38)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(42)}}{5}\)

\(\frac{\text{sin(38)}}{a}= \frac{\text{sin(42)}}{5}\)

\(a=\frac{5\text{sin(38)}}{\text{sin(42)}}\)

a = 4.6

By applying triangle sum theorem in ΔABC,

m∠A + m∠B + m∠C = 180°

38° + m∠B + 42° = 180°

m∠B = 180° - 80°

m∠B = 100°

\(\frac{\text{sin(100)}}{b}= \frac{\text{sin(42)}}{5}\)

\(b=\frac{5\text{sin(100)}}{\text{sin(42)}}\)

b = 7.36

Answer:6340000

Step-by-step explanation:

Answer:

  yes; 1.25

Step-by-step explanation:

The length to width ratios of the rectangles are ...

  A: 12/8 = 1.5

  B: 15/10 = 1.5

  C: 30/15 = 2.0

__

Rectangles A and B have the same aspect ratio, so are similar. Rectangle B is a scaled copy of A with a scale factor of 10/8 = 1.25.

The lifting force if the speed is 220 miles per hour is F' = 708.53 N.

The force of light, or simply light, is the sum of all forces on an object that cause the object to move perpendicular to the direction of flow.

The most common type of lift is the wing lift. But there are many other common uses, such as propellers on airplanes and ships, rotors on helicopters, fan blades, sails on sailboats, and wind turbines.

We have,

The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. It, means that,

\(F=kAv^{2}\)

Where

k is constant

If, A = 190 Ft², v = 220 mph, F = 950 pounds

Now, find k first from the above data. So,

    \(k=\frac{F}{Av^{2} }\)

⇒ \(k=\frac{950}{190* (220)^2}\)

⇒ k = 0.0001033

It is required to find the lifting force on the wing if the plane slows down to 190 miles per hour.

Let F' is a new force. So,

    F' = 0.0001033 × 190 × (190)²

⇒ F' = 708.53 pounds.

So, the lifting force is 708.53 pounds if the plane slows down to 190 miles per hour.

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The smallest number of eggs that could have been in the box is 1134

The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:

Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:

n ≡ 1 (mod 2)

n ≡ 1 (mod 3)

n ≡ 1 (mod 4)

n ≡ 1 (mod 5)

n ≡ 1 (mod 6)

n ≡ 0 (mod 7)

For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.

Plugging these values into the formula and simplifying modulo 5040, we get:

n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040

n = (−8946) mod 5040

n = (−3906) mod 5040

n = 1134 mod 5040

Therefore, the smallest number of eggs that could have been in the box is 1134

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Answer:

continental shelf

Step-by-step explanation:

The continental shelf extends from the edge of the continent into the sea. The shelf extends from the shoreline into the continental slope. Sea floor profile begins with the boundary between the land the ocean which spans the entire space of the continental shelf. The shelf area is flat and gently sloping into the sea.

It subjected to a high tidal change during a single day.

TT is equal to T-1, so the given matrix is an orthogonal matrix.

What is an orthogonal matrix?

Here, the determinant of T,

 |T| = cos²∅ + sin²∅

      = 1

Now, its cofactors,

\(T_{11}\) = cos ∅

\(T_{12\) = sin ∅

       \(T_{21\)= -sin ∅

\(T_{22\) = cos ∅

Now, the adjoint matrix of cofactors matrix transpose \(T^T\) is equal to \(T^{-1.\)

Hence, the given matrix is an orthogonal matrix.

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\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}\)