Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning.

If interest rates stay at 4​% APR and I continue to make my monthly ​$50 deposits into my retirement​ plan, I should have at least ​$30 comma 000 saved when I retire in 25 years.

The statement ___________ because I will have ​$ ___________ nothing in my retirement account when I retire in 25 years.
​(Round to the nearest cent as​ needed.)

Answer:

A

Step-by-step explanation:

right on Edge.2020

The graph that shows the solution set for -4.4 ≥ 1.6x - 3.6 is A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded, the correct option is A.

An Inequality is a statement that is formed when two expressions are joined using an inequality operator.

-4.4 ≥ 1.6x - 3.6

The value of x is

-4.4+3.6 ≥ 1.6x

x ≤ -0.5

The number line of any length, which has a closed circle at -0.5 and the left side of the point -0.5 is shaded is the graph of the inequality.

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Answer:

A, 61 degrees

Step-by-step explanation:

Since the two angles are supplementary, this means that they add up to 180 degrees. m=180-119=61 degrees, or option A. Hope this helps!

Answer:

A. 61

Step-by-step explanation:

The line AOB is a 180 degree line. That means that both the angles have to add up to 180. Angle AOc is 119. 180-119= 61. You can check by doing 119 + 61 does it equal 180.

Hope this helps!

Answer:

375

Step-by-step explanation:500 equals 100% divide by 4 its 125 times 3 equals 375, your welcome

Answer:

They will need 375 hamburgers.

Step-by-step explanation:

Keeping the ratio in mind, we solve this problem by cross multiplying. Set up the ratio 4/3 and set it equal to the greater ratio of 500/(an unknown number of hamburgers, represented by x). Cross multiply to end up with the equation 4x=1500. (Cross multiplying is multiplying each numerator by the opposite denominator). Solve for x in the above equation using SADMEG. You divide 1500 by 4 and end up with 375 hamburgers.

The rate of interest is 13%.

Step-by-step explanation:

Given,

Principal (P) = $560

Interest (I) = $145.60

Time (T) = 2 years

To find the rate of interest

Formula

If P principal was invested for T years at r% simple interest, the interest will be I = [tex]\frac{PTr}{100}[/tex]

So,

Putting the values of P, I, T we get,

145.60 =  [tex]\frac{560X2Xr}{100}[/tex]

or, r = [tex]\frac{145.60X100}{2X560}[/tex]

or, r = 13%

Hence,

The rate of interest is 13%.

Answer:

You give it a nudge and it solves itself.

Step-by-step explanation:

Answer: Here is an example.

Step-by-step explanation:

Given: parallelogram ABCD, sides as marked.

Find AD.

Solution: 6x - 10 = 3x + 5 (opposite sides)

3x - 10 = 5;    3x = 15;    x = 5

AD = 4x - 5 = 4(5) - 5 = 15

 Remember:

• This is where the properties of a parallelogram are needed. You know the opposite sides of a parallelogram are congruent, so set the opposite sides equal to one another.

• Be sure to pair up the opposite sides correctly. The side labeled 4x - 5 will not be used when solving for x, but will be used to solve for AD.

Two polygons are congruent if they are the same size and shape

Answer:2(B) and 4(D) are your answers!!

Step-by-step explanation:

hope this helped youu!!have a terrific Tuesday!

Answer:

93

Step-by-step explanation:

Let's say President Reagan was x years old when he died. He was 69 years old at his first inauguration

(2*69)-x = 45

Wait. But how will we find x in that equation?

--> (2*69)-45 = x

That's better.

2*69 = 138

138-45 = 93

x=93

Answer 3.5 inches

Step-by-step explanation:

Answer:

A. 3.5

Step-by-step explanation:

Given:

Triangle ABC is similar to triangle XYZ.

The measures of the sides are AB = 6 cm, BC = 18 cm and XY = 12 cm

We need to determine the measure of side YZ.

Measure of YZ:

Since, ABC and XYZ are similar triangles, by using similar triangles property, we have;

[tex]\frac{AB}{XY}=\frac{BC}{YZ}[/tex]

Let the length of YZ be x.

Substituting the values, we get;

[tex]\frac{6}{12}=\frac{18}{x}[/tex]

Cross multiplying, we get;

[tex]6x=12 \times 18[/tex]

[tex]6x=216[/tex]

Dividing both sides by 6, we have;

[tex]x=36[/tex]

Thus, the value of x is 36.

Hence, the measure of the side YZ is 36 cm.

The soldiers used 562 cartridges in combat, while the subofficers used 138, using the total amount of ammunition and the difference between cartridges used.

The total amount of ammunition for the section is 175 per soldier for a total of 20 soldiers, so we have 175 * 20 = 3500 cartridges. A fifth of this ammunition is used in combat, that is, 3500/5 = 700 cartridges. According to the question, the number of cartridges used by the soldiers exceeds that of the subordinates by 424 cartridges, so we can establish a system of equations:

We can then solve this system and find that the soldiers used 562 cartridges and the subofficers used 138.

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Answer:

A, C and D are correct.

\

Step-by-step explanation:

A is correct.

B is false; that space is the "area" of the circle.

C is true.  C = πd

D is true.  C = 2πr

E is false.  Way off.

Final answer:

Circumference is the distance around a circle, calculated as C = πd or C = 2πr, depending on whether the diameter or radius is known. (Option A,C,D)

Explanation:

Circumference is the term used to describe the distance around a circle. When calculating the circumference, you can use different formulas depending on the information you have about the circle. If you know the diameter (d), the circumference (C) can be found by multiplying the diameter by pi (π), using the formula C = πd. Alternatively, if you know the radius (r) of the circle, you can use the formula C = 2πr since the diameter is twice the radius (d = 2r).

The correct answers to the question are:

It's important to note that the space inside the circle is referred to as the area, not the circumference, and the formula for circumference is not C = pi + r as stated in option E, but rather C = πd or C = 2πr.

Answer:

48

Step-by-step explanation:

6*5+6*3=30+18=48

distubutive property

Answer:

349,257,830

Step-by-step explanation:

Multiply 349,257.83 by 1000

The required number where the digit 8 has a value that is 1,000 times greater than the digit 8 in the number 349,257.83 is 349,257,830.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the number x,
According to the question, [An approximate calculation]

x / 1000 = 349,257.83
x = 1000 [349,257.83]
x = 349,257,830

Thus, the required number where the digit 8 has a value that is 1,000 times greater than the digit 8 in the number 349,257.83 is 349,257,830.

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Total possible outcomes if a coin is flipped and a normal dice is rolled are   12

Probability of getting a tail and a five will be 1/12

The probability of getting a number less than five and a head  is 1/3

∴ Total possible outcomes  = (6 x 2) = 12

∴ Probability of getting a tail and a five will be 1/12

∴ The probability of getting a number less than five and a head =               (1/2)(4/6) = 4/12 = 1/3

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Answer: 1: 3x

2: area

3: six

4: 3/2

Step-by-step explanation:

The height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.

The pyramid has a hexagonal base with six isosceles triangular faces known as a hexagonal base pyramid. It is also called a heptahedron.

We have,

The length of the base edge of a pyramid = x units

The height of the pyramid is three times longer than the base edge ie.

The height of the pyramid = 3x

The area of an equilateral triangle with base length x units is [tex]\rm x\sqrt{3}[/tex] square units square(let's assume)

Then the area of the hexagon base = 6×[tex]\rm x\sqrt{3}[/tex] ⇒  6[tex]\rm x\sqrt{3}[/tex] square units.

Because the hexagon base has a six-equilateral triangle.

Let's assume the area of a hexagonal base is Y times the equilateral triangle.

[tex]\rm 6x\sqrt{3} = Y \times x\sqrt{3}[/tex]

Y = 6 times

We know the volume of a hexagonal pyramid = [tex]\frac{\sqrt{3} }{2} a^2h[/tex]

Where a is the base length and h is the height of the hexagonal pyramid.

Here a = x units and h = 3x units

Then Volume:

[tex]\frac{\sqrt{3} }{2} x^2(3x)\\\\\frac{{3} }{2} \sqrt{3}x^2[/tex]

Thus, the height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.

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A 99% confidence interval for the mean body temperature can be calculated using the sample mean, standard deviation, and the t-score corresponding to the confidence level. The findings may suggest that the commonly accepted average body temperature of 98.6°F could be reconsidered if it does not fall within this interval.

Constructing a 99% Confidence Interval

To construct a 99% confidence interval for the mean body temperature of all healthy humans, we use the sample mean, standard deviation, and the t-distribution since the population standard deviation is not known. With a mean of 98.9°F, a standard deviation of 0.67°F, and a sample size of 103, we can calculate the margin of error using a t-score that corresponds to the 99% confidence level.

First, we find the t-score from the t-distribution table for 102 degrees of freedom (n-1) that corresponds to a 99% confidence level. Then, we calculate the margin of error using the formula:

Margin of Error (E) = t-score * (standard deviation / sqrt(n))

This margin of error is then added and subtracted from the sample mean to obtain the confidence interval:

Lower Limit = Mean - Margin of Error

Upper Limit = Mean + Margin of Error

This confidence interval provides a range within which we can be 99% confident that the true mean body temperature of all healthy humans lies.

Implications for 98.6°F as Average Body Temperature

The sample suggests that the mean body temperature of 98.6°F might not be accurate for all individuals. If the constructed 99% confidence interval does not contain the traditional mean of 98.6°F, it could indicate that the average body temperature is different than what has been historically taught.

The 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.

To construct a 99% confidence interval for the mean body temperature of all healthy humans, we'll use the formula:

[tex]\[ \text{Confidence Interval} = \bar{x} \pm z \left( \frac{s}{\sqrt{n}} \right) \][/tex]

Let's calculate the confidence interval:

[tex]\[ \text{Confidence Interval} = 98.9 \pm 2.576 \left( \frac{0.67}{\sqrt{103}} \right) \]First, let's calculate \(\frac{s}{\sqrt{n}}\):\[ \frac{s}{\sqrt{n}} = \frac{0.67}{\sqrt{103}} \approx 0.0662 \][/tex]

Now, we can find the margin of error:

[tex]\[ \text{Margin of Error} = 2.576 \times 0.0662 \approx 0.1706 \]Finally, construct the confidence interval:\[ \text{Confidence Interval} = 98.9 \pm 0.1706 \][/tex]

So, the 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.

Answer:

B) -4

Step-by-step explanation:

(5/2)x + y = 2

x + (2/3)y = 4

y = 2 - (5/2)x

x + (2/3)(2 - (5/2)x) = 4

x + 4/3 - (5/3)x = 4

(-2/3)x = 8/3

-2x = 8

x = -4

Answer:

well is a 50 50 chains that  Allen will get a red marble and

a 50 50 that the coin will land heads up.

Step-by-step explanation:

Answer:

It is a combination answer

495 ways

Step-by-step explanation:

In this question, we are tasked with calculating the number of ways in which a manager can select 4 people out of 12 for the Sunday evening shift.

Firstly, the question talks about selecting a particular number from a mix, this is a combination question since the key word SELECT is mentioned.

Now, how do we go about it? To select a partial number from a mix , we use the combination formula as stated.

Mathematically, say we are selecting a number r from a total of numbers n, the number of ways we can do this is nCr = n!/(n-r)!r!

In this case however, we are simply selecting 4 out of 12

Our combinational equation thus becomes 12C4 = 12!/(12-4)!4! = 12!/8!4! = 495 ways

Final answer:

The manager can choose 4 from 12 employees in 495 different ways for the Sunday evening shift, using a combination rather than a permutation since the order of selection does not matter.

Explanation:

To determine the number of ways the manager can choose 4 out of 12 employees for the Sunday evening shift, we need to decide whether the order in which the employees are chosen matters. If the order does not matter, we will use a combination. If the order does matter, we would use a permutation. In this case, because the task is simply to choose 4 employees and the order in which they are chosen does not affect the outcome, we use a combination.

The formula for finding the number of combinations when choosing k objects out of a total of n objects without repetition is given by:

C(n, k) = n! / (k! * (n-k)!)

In this situation, we have n=12 and k=4, so we calculate:

C(12, 4) = 12! / (4! * (12-4)!) = 12! / (4! * 8!) = (12*11*10*9) / (4*3*2*1) = 495

Therefore, there are 495 different ways for the manager to choose 4 employees for the Sunday evening shift.

Answer:

y=2x+15

Step-by-step explanation:

h=9

The equation to find the number of hours the boat was rented is $33 = $15 + ($2  imes h). After subtracting the deposit fee and dividing by the cost per hour, the solution is h = 9, indicating the boat was rented for 9 hours.

The equation to find out how many hours, h, the boat was rented for when the total cost was $33 can be represented as follows:

Total cost = Deposit fee + (Cost per hour  imes Number of hours)

Substituting the given values, we have:

$33 = $15 + ($2  imes h)

To solve for h, we subtract $15 from both sides of the equation:

$33 - $15 = $15 - $15 + ($2  imes h)

So, $18 = $2  imes h

Next, we divide both sides of the equation by $2 to solve for h:

$18 \/ $2 = ($2  imes h) \/ $2

h = 9

This means they rented the boat for 9 hours.

Answer:

Sphere=48 beads

Cylinder=24 beads

Step-by-step explanation:

Let the number of cylinder beads be y and since she has twice as many sphere beads, the sphere beads will be 2y

The sum of sphere and cylinder beads will be y+2y=3y

This sum is equivalent to the total number given as 72

Therefore, equating 3y to be equal to 72 we obtain the equation

3y=72

Dividing by 3 on both sides we obtain that

Y=72/3=24 beads for cylinder

Since the sphere is 2y then 2*24=48

To confirm, it is evident that 48+24=72

Also, the number 48 is double/twice the number 24

Answer:

$18 is the cost per ticket ordered

Step-by-step explanation:

We proceed as follows;

Let the cost per ticket be $x while the fixed fee be $y

For the person that ordered 5 tickets, we can have his mathematical representation as;

5(x) + y = 93 •••••••••(i)

For the person that ordered 3 tickets, we can have his mathematical representation as;

3(x) + y = 57 ••••••••(ii)

From the first equation, we can have;

y = 93 - 5x

Let’s plug this into ii

3x + 93 - 5x = 57

-2x = 57 -93

2x = 36

x = 36/2

x = $18

This means that the cost per ticket ordered is $18

Answer:

The net will have 1 square face

The net will have 4 triangular faces

The triangular faces are identical

The net will have a total of 5 faces.

Step-by-step explanation:

If you look at the picture, count the triangular faces, you will see 4.

Count the square on the bottom, its 1.

All the triangular faces are identical, if they weren't the picture would be all over the place.

Add 1+4 and it equals 5. The net will have a total of 5 faces.

(Hope you got it right, cause I took it and got it right!! Also I'm not good at explaining math lol)

Stay safe and social distance :DD

The net will have one square face, four triangular faces, the triangular faces are identical.

The net will have a total of five faces.

"It is a three-dimensional geometric shape that has a square base and four triangular sides that are joined at a vertex."

"It is a two-dimensional structure which forms a three-dimensional geometric structure by folding."

According to the problem,

The base of the square pyramid has a square and if a three dimensional structure of a net formed into a pyramid is looked at, we can see 1 face of the square at the base.

A pyramid is comprised of 4 triangles joined together at the vertex.

Again, if a three dimensional structure of a pyramid is looked at, we can see 4 faces of the pyramid.

Now in order to align into a single unit to be joined at the vertex, the triangles have to be identical. They will have similar faces with the same base and slant height.

Therefore, 1 square face and 4 triangular faces adds up to five total faces.

Hence, we can conclude that the net will have one square face, four triangular faces and a total of five faces with the triangular faces being similar.

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Answer:

The decimal multiplier is 1.1663

Step-by-step explanation:

Since the increases are done successively we can find decimal numbers for each one and multiply both to have a single decimal representing the whole operation. When there's a increase this means that we have the original value (100%) summed by some other value, in this case 7%, so the new value would be 100% + 7% = 107%, we can transform this to a decimal number by dividing it by 100, so 107/100 = 1.07. The same applies to the 9% increase, so we would have 109/100 = 1.09. We can now multiply both to obtain a single decimal multiplier, we have:

1.07*1.09 = 1.1663

Answer:

  A)  dV/dt=-1.2x^2

Step-by-step explanation:

The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...

  dV/dt = -1.2x^2

Answer:

C

Step-by-step explanation:

V(t) = [x(t)]³

A(t) = 6[x(t)]²

dV/dt = k × 6[x(t)]²

Where k < 0

From the options,

taking k = -0.2

dV/dt = -1.2[x(t)]²

Answer:

11/32

Step-by-step explanation:

4/16 + 2/16 - 1/32

simplify and solve

The position of the university marked x is shown in the attachment.

Given that university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital.

so we can say that the university position is gotten relative to the the position of the stadium and hospital.

The university is 50° from the stadium and then 350° from the hospital.

I.e it is N 50° E from the stadium and N 60° W from hospital.

The angle forms will be 50+60 = 110°

The point where the two lines intersect is the position of the university. Mark this point with a cross on the map.

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Answer:

Weight of large box = 18.5 Kg

Weight of small box = 13 Kg

Step-by-step explanation:

Let the weight of large box be X kg

Let the weight of small box be Y kg

So weight of 8 large boxes = 8X

weight of 3 small box be =  3Y

According to question

8 large boxes and 3 small boxes has a total weight of 187

mathematically it can be represented as

8X + 3 Y = 187

_________________________________________________

Second condition

weight of 2 large boxes = 2X

weight of 5 small box be =  5Y

According to question

2 large boxes and 5 small boxes has a total weight of 102 kilograms

mathematically it can be represented as

2X + 5Y = 102

--------------------------------------------------------------------------

we have two equation

8X + 3 Y = 187   -------------------A

2X + 5Y = 102   -------------------B

multiplying equation B with 4  on both side of equation we have

4*(2X + 5Y) = 4*102

=> 8X + 20Y = 408   -------------------C

Now subtracting equation A and C on both sides we have

8X + 3 Y - (8X + 20Y ) = 187 -408

8X - 8X + 3 Y -  20Y = -221

-17Y = -221

=> Y = -221/-17 = 13

Now substituting value of Y in equation B we have

2X + 5*13 = 102

=> 2X + 65 = 102

=> X = (102-65)/2  = 18.5

______________________________

Weight of large box = 18.5 Kg

Weight of small box = 13 Kg

The large box weighs 17 kg and the small box weighs 13 kg.

Let's denote the weight of a large box as x and the weight of a small box as y. We can set up a system of equations to solve for the weights:

8x + 3y = 187 (equation 1)

2x + 5y = 102 (equation 2)

To solve the system, we can multiply equation 1 by 2 and equation 2 by 8 to eliminate x:

16x + 6y = 374 (equation 3)

16x + 40y = 816 (equation 4)

Subtracting equation 3 from equation 4, we get:

34y = 442

Solving for y, we find y = 13.
Substituting this value back into one of the original equations, we find x = 17.

Therefore, the large box weighs 17 kilograms, and the small box weighs 13 kilograms.

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