To go on a summer trip, Felipe borrows $200. He makes no payments until the end of 3 years, when he pays off the entire loan. The lender charges sim
Interest at an annual rate of 2%.

Explanation is in the file

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Answer:

X = 8

Step-by-step explanation:

A triangle's degrees always add up to 180, this is a right triangle meaning that one of the degrees is 90, and we see the other one is 54, so we add these together and subtract them from 180 and set that equall to 3x+12.  

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

2x+2y=52

x*y=120

Step-by-step explanation:

well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)

Answer:

75%

Step-by-step explanation:

16.5/22 = 0.75

0.75 x 100 = 75

∴ 75% of the tank is full.

Answer:

first you do the mutpiton in the first perentes then you do addition

Step-by-step explanation:

Answer:

b. the average calorie count of a large number of fruit smoothie brands has a sampling distribution that is close to Normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Applying to this question:

The distribution of the number of calories in fruit smoothies is strongly skewed to the right. However, in a sample with a large number of fruit smoothies, the sampling distribution will be approximately normal, so the correct answer is given by option B.

Answer:

B

Step-by-step explanation:

The perimeter of the shaded figure is 12 units

The area of the shaded figure is 8 square units

Given,

Length of the shaded figure = 4 units

Width of the shaded figure = 2 units.

The shaded figure resembles a rectangle

So,

Perimeter of the shaded figure = 2( length + width)

Perimeter, P = 2 ( 4 + 2)

P = 2 × 6

P = 12 units

Now,

Area of the shaded figure = length × width

Area, A = 4 × 2

A = 6 square units

Therefore,

The perimeter of the shaded figure is 12 units

The area of the shaded figure is 8 square units

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Median = 6

Q₁ or first quartile = 4

Q₂ or third quartile = 8

Smallest data point  = 2

Maximum data point = 11

Box plots draw boxes from the first quartile to the third quartile. At the median, a vertical line passes through the box. The whiskers move from each quartile to the minimum or maximum.

The given numbers are: 2 , 3 ,5, 6 , 7 , 8 ,11

Number of terms = 9

Middle term = 9 + 1 / 2 = 5th term =7

The first quartile is the median of the data points to the left of the median.

2,3,5,6,

Number of Terms = 4

Median = 3 + 5 /2

             = 4th term = 6

The smallest data point is 2 and the largest data point is 11 .

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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Answer:

b = 19

Step-by-step explanation:

- 2(b-1)=3(7-b) (distributive property)

-2b+2 = 21 - 3b

-2b+3b = 21-2

b = 19

It is to be noted that the boat traveled a distance of 8.39 miles South, and 12.44 miles west. This is solved using trigonometric ratios principles.

Using the trigonometric ratio involving the right triangle, we can answer how far the boat moved northward and westward, or the vertical and horizontal components of the displacement vector.

Solving for the horizontal component Vₓ, we'll be using the ratio of the sine function with regard to angle 34°

Thus,

Sin 34° = Vₓ/ 15

Vₓ = 15 * (Sin 34°)

= 15 * 0.55919290

Vₓ  = 8.39 miles.

Solving for the vertical component of, V\(_{y}\) we'll be using the ratio of Cosine Function with respect to the angle 34°

Cos 34° = V\(_{y}\) / 15

V\(_{y}\) = 15 * Cos 34°

V\(_{y}\)= 15 * 0.82903757255

V\(_{y}\) = 12.44 miles.

Thus, the boat traveled a distance of 8.39 miles South, and 12.44 miles west.

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so, we know the diameter is 8, so that means its radius is half that, or 4.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2\)

Answer:

he will have saved 45$

Step-by-step explanation:

if you take 2 from every 5 and 5 x 15 = 150, you would do 2 x 15 and get 30. So, the answer is 30$

Answer:

60

Step-by-step explanation:

turn it into a fraction.

2/5

/150

150*2=300

300/5=60

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

130$

Step-by-step explanation:

put 4 instead of the h

50+4.20

50+80

130

Answer:

The word "ENTERTAIN" has 9 letters, but it contains repeated letters. Specifically, it has 3 E's, 2 N's, and 2 T's.

To find the number of distinct permutations, we can use the formula for permutations with repeated elements.

The number of distinct permutations is given by:

n! / (n1! * n2! * ... * nk!)

where n is the total number of elements and n1, n2, ..., nk are the frequencies of each repeated element.

In this case, we have:

n = 9

n1 = 3 (for E)

n2 = 2 (for N)

n3 = 2 (for T)

Plugging these values into the formula, we get:

9! / (3! * 2! * 2!)

Calculating this expression gives us:

(9 * 8 * 7 * 6 * 5 * 4) / (3 * 2) =

(30240) / (12) =

2520

Therefore, there are a total of 2520 distinct permutations that can be formed using the letters of the word "ENTERTAIN".

Answer:

30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using:  distance = speed x time

\(\implies t=\dfrac{d}{v}\)

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

\(\implies t=\dfrac{18}{v} \ \ \textsf{and} \ \ t=\dfrac{18}{v+15}\)

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

\(\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1\)

Now all we have to do is solve the equation for v:

\(\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1\)

\(\implies \dfrac{18(v+15)+18v}{v(v+15)}=1\)

\(\implies 18(v+15)+18v=v(v+15)\)

\(\implies 18v+270+18v=v^2+15v\)

\(\implies v^2-21v-270=0\)

\(\implies (v-30)(v+9)=0\)

\(\implies v=30, v=-9\)

As v is positive, v = 30 only

So the average speed driving to the airport was 30 mph

(and the average speed driving from the airport was 45 mph)

Let s represent the speed on the return trip

So, The initial speed will be (s-15)

Equation of time:

\( \boxed{ \tt \: time = \frac{distance}{speed} }\)

return time + initial time = 1 hr

\( \sf\frac{18}{s} + \frac{18}{s - 15} = 1\)

⚘Solution for the complete equation in attachment!!~

\(\rule{300pt}{2pt}\)

Answer:

10:35 because they both start at the same time. 20 minutes of tour, 15 minute to watch a movie

The volume of the cube with a side edge of 3 inches will be 27 cubic inches.

Suppose that: The side length of the considered cube is L units. Then, we get:

Volume of that cube = L³ cubic units.

Terrance has a shape that actions 3 inches long along each side.

The edge length of the cube is 3 inches. Then the volume of the cube  will be given as,

V = (3)³

V = 27 cubic inches

The volume of the cube with a side edge of 3 inches will be 27 cubic inches.

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The quadratic functiοn in standard fοrm that wοuld represent the data in the table is y = 2x² + x - 9.

A quadratic functiοn is a type οf pοlynοmial functiοn that can be written in the fοrm οf f(x) = ax² + bx + c, where a, b, and c are cοnstants, and x is an unknοwn variable. The graph οf a quadratic functiοn is a parabοla, and the rοοts οf the equatiοn (the x-intercepts) are the pοints where the parabοla crοsses the x-axis. Quadratic functiοns are used tο mοdel a variety οf natural phenοmena, such as the trajectοry οf a prοjectile οr the grοwth οf a pοpulatiοn οver time.

This can be determined by putting the given values intο the standard fοrm equatiοn: y = ax²  + bx + c  and sοlving fοr a, b and c.

When x = 2, y = 3. Therefοre, 3 = 2a + b - 9, which gives b = 11.

When x = 4, y = 1. Therefοre, 1 = 8a + 11 - 9, which gives a = -1/4.

When x = 6, y = 3. Therefοre, 3 = 18a - 1/4 + 11 - 9, which gives c = -5/4.

The quadratic equatiοn in standard fοrm, y = 2x²  + x - 9, can then be written using the values οf a, b and c fοund.

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Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°