Charlie invests $325 in an account that pays 8% simple interest for 15 years. Use the simple interest formula, I = P ∙ r ∙ t, to answer the following questions.   How much interest will Charlie’s initial investment earn over the 15-year period? How much money does Charlie have after the 15 years?
PLZ HELP ASAP

Answer:

B. 3.5

Step-by-step explanation:

line BE and CD are parallel

hence AB:AC = AE:AD

=> AB/AC = AE/AD

=> 4/(4+2) = 7/(7+x)

=> 4/6 = 7/(7+x)

=> 7+x = 7 × 3/2

=> 7+x = 21/2

=> x = 21/2 - 7

=> x = (21-14)/2 (taking 2 as LCM)

=> x = 7/2 = 3.5

Hence the answer is B.

The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

How to find volume of Right Circular Cylinder?

Right cylinders are cylinders with axes that are perpendicular to the bases.

Volume of a Right Circular Cylinder= πr²h  

where,

r = radius of the base

h = height of right circular cylinder

Maximum volume of right circular cylinder that can be inscribed in a sphere will be,    

                  \(\pi r^{2} h-\frac{\pi }{4} h^{3}\\\\= \frac{4\pi r^{3} }{3\sqrt{3} }\)

given that, radius=70cm=0.0.7 m

so,

       \(Maximum\ volume=\frac{4\pi r^{3} }{3\sqrt{3} } \\\\= \frac{4\pi (70)^{3} }{3\sqrt{3} }\\\\=2640.4\pi \ m^{3}\)

Using volume of right circular cylinder,

                \(h=\frac{2r}{\sqrt{3} }\\\\ h = \frac{2(0.07)}{\sqrt{3} }\\\\h= 0.08\ m\)

Hence, The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

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Converting feet to inches solve the problem, first we have to convert 20 yards to feet and inches and then calculate the cost per foot and inch. Here are the steps:1 yard = 3 feet (since 1 yard equals 3 feet)20 yards = 20 × 3 = 60 feet (converting yards to feet)1 foot = 12 inches (since 1 foot equals 12 inches)60 feet = 60 × 12 = 720 inches

The total cost of 20 yards of ribbon is $24. Therefore, cost per yard = $24/20 = $1.2We are given that the cost per yard is $0.83. Therefore, we can write:$1.2 = $0.83 × x where x is the cost per foot and inch. To solve for x, we can divide both sides by $0.83:$1.2/$0.83 = xor1.44 = x We can conclude that it will cost $1.44 per foot and inch of the ribbon.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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Cross product of a and b : a x b = (3 - t, t - t^2, t^3 - 3t^2)

To find the cross product a x b for a = (t, 3, 1/t) and b = (t^2, t^2, 1), follow these steps:

Write out the components of vectors a and b:

a = (t, 3, 1/t)
b = (t^2, t^2, 1)

Use the cross product formula:

a x b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)

Calculate the components of the cross product:

a x b = (3(1) - (1/t)(t^2), (1/t)(t^2) - t(1), t(t^2) - 3(t^2))

Simplify the expression:

a x b = (3 - t, t^2/t - t, t^3 - 3t^2)

Write the final cross product:

a x b = (3 - t, t - t^2, t^3 - 3t^2)

To verify that the cross product is orthogonal to both a and b, we need to check if the dot product of a x b with a and b is zero.

Calculate the dot product of a x b with a:

(3 - t)(t) + (t - t^2)(3) + (t^3 - 3t^2)(1/t)

Simplify the expression:

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

Calculate the dot product of a x b with b:

(3 - t)(t^2) + (t - t^2)(t^2) + (t^3 - 3t^2)(1)

Simplify the expression:

3t^2 - t^3 + t^3 - t^4 + t^3 - 3t^2 = 0

Since both dot products are equal to zero, the cross product a x b = (3 - t, t - t^2, t^3 - 3t^2) is orthogonal to both vectors a and b.

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Answer:

6x+16x^2

Step-by-step explanation:

You multiply 2x by both of the numbers so,

2x * 3= 6x

2x* 8x=16x^2

Answer:

A. 1/6

B. 1

Step-by-step explanation:

A. 9/j x j/54= 9/54 = 1/6

B. 6k/8m : 3k/4m = 6k/8m : 4m / 3k = 2/2 =1

Answer:

a. 3/2

b. 1

Step-by-step explanation:

A. To simplify the expression, we can cancel out the common factor of j:

9/j * j/54 = (9/1 * 1/6) = 3/2

Therefore, 9/j * j/54 simplifies to 3/2.

B. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. That is,

(a/b) ÷ (c/d) = (a/b) x (d/c)

Using this rule, we can simplify the given expression as follows:

6k/8m ÷ 3k/4m = (6k/8m) x (4m/3k)

             = (6/8) x (4/3)  

             = 2/2

             = 1

Answer: 756

Step-by-step explanation:

The president can be elected in 28 different ways. After a student is elected president, there are 27 students left to elect a vice president from. So there are 28 x 27 = 756 different arrangements.

The exterior angle with angle d is equivalent to 141 degrees, and the value of x is equal to 10.

We must keep in mind that the total of all the angles in a triangle equals 180 degrees in order to solve this puzzle.

The given angles are-

Using that formula in this case;

Thus, sum of all angles is 180°.

m < d + m < e + m < f = 180°

(2x + 19)° + (3x + 24)° + 87° = 180°

x = 10°

But if angle D is on a straight line, it is possible to find its exterior angle because angle D plus its exterior angle add up to 180 degrees.

Suppose y = external angle.

m < d + y = 180°

2x + 19 + y = 180°

And x = 10°

2(10) + 19 + y = 180°

y = 141°

Thus, the measure of the degree measure of the exterior angle is found as  141°.

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The correct question is-

In triangle DEF, m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°. Determine the degree measure of the exterior angle to ∠D.

54°

39°

141°

126°

Answer:

I would say 7, because if you think about you would know that your answer is 7

The appropriate inference procedure is a one-sample z-test for p.

A one-sample z-test for the percentage would be the proper inference method in this case.

This is due to the fact that we only have one sample of coin flips and wish to determine whether the population's genuine percentage of heads (p), which represents the proportion of heads in the population, differs substantially from 0.5 (our null hypothesis).

In a one-sample z-test for the percentage, the sample proportion (p-hat) is calculated, and the standard error formula is used to get a z-statistic, which is then compared to a normal distribution to provide a p-value.

If the p-value is less than the significance level, which is typically 0.05, the null hypothesis is rejected.

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The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

From the question, we have the following parameters that can be used in our computation:

This means that

Initial, a = 250 bacterial cultures.

Rate = 3

So, the recursive formulas is

f(n) = 3f(n - 1), where f(1) = 250

For the explicit formula, we have

f(n) = 250(3)ⁿ‐¹

Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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Answer:

2x^2+1

Step-by-step explanation:

4x^2+2-2x^2-1

Group like terms:

4x^2-2x^2+2-1

2x^2+2-1

2x^2+1

Answer:

2x^2 + 3

Step-by-step explanation:

Subtracting functions is similar to subtracting normal numbers. An easy way to do it is to put one over the other and then combine like terms.

 4x^2 + 2

- 2x^2 - 1

= 2x^2 + 3

Even though it looks like you would do 2-1, the three is because you're adding -(-1) (aka 1) to 2.

Answer:

Step-by-step explanation:

You can use law of sin and law of cos to solve for this triangle because this is not a right triangle

Law of Cosine

b² =  a² + c² − 2ac cos (B)      

b² = 26² + 13² - 2(26)(13) cos 88

b² = 821.41

b= 28.66

AC=28.66

Now use Law of Sin to find angles:

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

\(\frac{sin 88}{28.66} = \frac{sin C}{13}\)

\(13\frac{sin 88}{28.66} = sin C\)

sin C = .4533

C = 26.96

A = 180-C-B

A= 180-88-26.96

A= 65.04

Answer:

look at the picture I have sent

Answer:

1.3

Step-by-step explanation:

First you simplify 2 3/5, which can be 2.6. You will find half of it so 2.6 divided by 2 equals 1.3. She traveled 1.3 miles or 1 3/10 miles before she stopped.

Compound amount = $8867.39

compound interest = $1867.39

EXPLANATION

Given:

Principal(p) = $7000 Rate(r) = 0.12 Time(t) = 2 n= 4

We can calculate the compound amount(A) using the formula below:

Substitute the values and evaluate.

Hence, the compound amount = $8867.39

We proceed to find the compound interest.

A = P + I

⇒ I = A - P

= 8867.39 - 7000

=1867. 39

Therefore, the compound interest = $1867.39

Answer:

  y = -4/3x + 3

Step-by-step explanation:

3x − 4y = −8

-4y = -3x - 8

y = 3/4x + 2

slope m = 3/4

perpendicular version of it is opposite inverse: -4/3

y-intercept through point (0, 3):

y = mx + b

3 = -4/3(0) + b

b = 3

Use the perpendicular slope with b from above to form new perpendicular equation of line:

y = mx + b

y = -4/3x + 3

For your birthday, you plan to hang a piñata in your basement. You decide to attach two hooks on opposite walls, connect the hooks with a taut string, and hang the piñata from the point on the string exactly halfway between the hooks.

1.The first hook is located 4 feet east of the origin (x-coordinate) and 7.5 feet above the origin (z-coordinate), so its coordinates are (4, 0, 7.5).

2.The second hook is located 5 feet east of the origin (x-coordinate), 12 feet north of the origin (y-coordinate), and 8 feet above the origin (z-coordinate), so its coordinates are (5, 12, 8).

3.To find the point on the string that is exactly halfway between the hooks, we need to find the midpoint of the line segment joining the two hooks. We can use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two hooks.

Substituting the values, we get:

Midpoint = ((4 + 5)/2, (0 + 12)/2, (7.5 + 8)/2)

= (4.5, 6, 7.75)

Therefore, the coordinates of the point on the string that is exactly halfway between the hooks are (4.5, 6, 7.75).

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Answer:

V=462.076m ^3

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

The product of means that you're multiplying, which means that you need to use parentheses. That narrows it down to B or D. Since the question asks you to provide a number first (x) and then 11, that means that 11 will be subtracted from the number.

Answer:

325 adults

Step-by-step explanation:

x=#adults

y=#children

x+y=937

2x+0.75y=1109

2x+2y=1874

-2x-0.75y=1109

1.25y=765

y=612

x=937-612

x=325

ANSWER AT THE BOTTOM

Question:

There is a bag with 1 red pen, 4 black pens, and 3 blue pens. If 2 pens are chosen from the bag without replacement, what is the probability that you chose 2 black pens.

Explanation:

Right now there are a total of 8 pens. 4 of them are black. So, the probability of choosing a black pen right now is 4/8, or 1/2.

Lets assume we picked a pen and got black.

Now there are only 7 pens in the bag, and only 3 of them are black. The probability of choosing a black pen right now is 3/7.

So on the first draw, the probability is 1/2

And on the second draw, the probability is 3/7

To find the probability of 2 ocurrences happening in a row, we must multiply their individual probabilities.

For example, if we wanted to find the probability of rolling two 6's in a row on a dice, we would need to mutiply the individual probability together. The probability of rolling one 6 is 1/6, so the probability of rolling two 6's in a row is 1/6 MULTIPLIED BY 1/6, which is 1/36.

The probability of rolling two 6's in a row is 1/36.

Lets apply the same principle to our situation right now.

So on the first draw, the probability is 1/2

And on the second draw, the probability is 3/7

1/2 MULTIPLIED BY 3/7    =    3/14

3/14 in decimal form is 0.21

ANSWER:

0.21, OR 21%

Answer:

60 degress

Step-by-step explanation:

1. Find out the angel of each side. 360 divded by 6 = 60

2. Get the answer of 60

The slope of the graph is \(-8\frac{1}{2}\).

The slope of a line is the change in the independent variable with respect to the change in the dependent variable.  

The slope is rise over run.

The slope of the line in the graph be found as follows:

slope = m = y₂ - y₁ / x₂ - x₁

using (1, -8) and (-1, 9)

x₁ = 1

x₂ = - 1

y₁ = - 8

y₂ = 9

Therefore,

slope = m = 9 + 8 / -1 - 1

slope = 17 / - 2

Therefore,

slope = - 17 / 2

slope = \(-8\frac{1}{2}\)

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With the information, option (C) 128 cm² will be the correct response.

A three-dimensional shape's surface area is the total area on its surface. Add these areas of each of the six rectangular sides of a cuboid to determine its surface area. The cuboid's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula SA=2lw+2lh+2hw.

A triangular prism's lateral surface area is equal to PH.

Where P is the triangle's perimeter and H is the prism's height.

Perimeter is equal to 5 + 5 + 6 = 16 cm.

The prism is 8 cm tall.

∴ PH = 16 × 8 = 128 cm²

The triangular prism's lateral surface area is 128 cm².

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Teresa spent 33.33 dollars.
The correct answer is A. 33.33.

Heather, Teresa, and Nina went shopping for new clothes. Heather spent twice as much as Teresa, and Nina spent three times what Heather spent. If they spent a total of 300, how much did Teresa spend?

To solve this problem, let's assign a variable to Teresa's spending. Let's say Teresa spent x dollars.

According to the information given, Heather spent twice as much as Teresa, so Heather spent 2x dollars.
Nina spent three times what Heather spent, so Nina spent 3 * 2x = 6x dollars.

The total amount spent is 300 dollars, so we can write the equation: x + 2x + 6x = 300.
Combining like terms, we get 9x = 300.

To find the value of x, we divide both sides of the equation by 9:

x = 300 / 9 = 33.33.

Therefore, Teresa spent 33.33 dollars.
The correct answer is A. 33.33.

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The person is 660.35 feet away from the monument.

The height of the tower is 200 foot.

We have to find how far is the person standing from the tower.

Angle of elevation is  15°, and angle of depression is 2°.

We find the distance using tangent of an angle.

tan15°=BD/AD

tan 2°=CD/AD

BD=tan15°*AD

CD=tan 2°*AD

We have to find the value of AD. We will use the value of BC to get the value of AD.

BC=BD+CD

BC is the height of the tower.

BC=200

200=tan15°*AD + tan 2°*AD

200=(tan15°+tan 2°)AD

AD=(tan15°+tan 2°)/200

AD=660.3494.

660.3494 is the distance from tower and person.

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Complete question

A 200-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is 15°, and that the angle of depression to the bottom of the tower is 2°. How far is the person from the monument?

Answer:

104,758

Step-by-step explanation:

X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.

To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.

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