Jerome has $3,000 to invest in an account that yields 2.1% annual interest which is compounded quarterly. If he leaves the money untouched in the account for 4 years, how much money will he have?

Answer:

12

Step-by-step explanation:

h(-3)= -(-3)(1-(-3))=

3(4)=12

The fraction of the total price that the torch is is 4/5.

Let x be the cost of the battery.

We know that the torch cost is 1.50 more than the battery cost. So, the cost of the torch is

x + 1.50

The total cost is the sum of the cost of the battery and the torch, so:

x + (x + 1.50) = 2.50

2x + 1.50 = 2.50

Solving this equation we get,

x = 0.50

Therefore the cost of the battery is 0.50 and the cost of the torch is 2.00.

To find the fraction of the total price that the torch is, we divide the cost of the torch by the total cost:

= (2.00) / (2.50)

= 4/5

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Zell invested $80,000 in two different types of stocks. Solving for x gives us the amount invested in the 9% stock:

x = $45000

Generally, Let x be the amount invested in the 9% stock.

Then (80,000 - x) is the amount invested in the 12% stock.

The profit on the 9% stock is 0.09 * x and the profit on the 12% stock is

0.12 * (80,000 - x).

We know that the profit on the 12% stock is $150 more than the profit on the 9% stock.

So we can set up the following equation:

0.12 * (80,000 - x)

= 0.09 * x + 150

x=45000

Therefore, Zell invested $80,000 in two different types of stocks. the amount invested in the 9% stock is $45000

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Answer:

$45,000

Step-by-step explanation:

An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.

An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.An equilateral triangle always has angles that are 60° in length.

It is referred to as an isosceles triangle when a triangle's two sides are identical. When the corresponding sides and angles of two angles match, the angles are said to be congruent.

When stacked, two angles are also congruent if they match.

If they line up with each other after turning or moving it, then.

Also creating equivalent vertex angles are a parallelogram's diagonals.

Congruent sides - L and X, G and Y, and F and T.

Congruent angles - ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.

ΔLGF ≅ ΔXYT

Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.

Congruent sides are L and X, G and Y, and F and T.

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Answer: its 1.6667.

Answer:

Step-by-step explanation

3*X=5

X=5/3

X=1.67

Table A represents a function, but Table B does not represent a function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.

As, each element of X is associated with unique element of Y, so this is a function.

Table A    

          X               Y

          3                 1

           2                 0

           1                  0

As, each element of X is associated with a unique element of Y, so this is a function.

Table B

X            Y

3           -2

5              1

5              2

Hence, Table A represents a function, but Table B does not represent a function.

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Answer: 1.7

Step-by-step explanation: First, let's see how many decimeters are in 1 cm. To find it, we must divide the cm by 10. So, we can do 17 / 10 or move the decimal one spot left. They should both = 1.7. I hope this helped!

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

2x + 4y - 12 = 0 ( subtract 2x - 12 from both sides )

4y = - 2x + 12 ( divide through by 4 )

y = - [tex]\frac{2}{4}[/tex] x + [tex]\frac{12}{4}[/tex]

y = - [tex]\frac{1}{2}[/tex] x + 3 ← in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the parallel line

to find c substitute (- 2, 5 ) into the partial equation

5 = - [tex]\frac{1}{2}[/tex] (- 2) + c = 1 + c ( subtract 1 from both sides )

4 = c

y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of parallel line

Answer:

y = -(1/2)x + 4

Step-by-step explanation:

Lets look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = zero).  Lets rewrite the given equation to conform to this format:

2x+4y-12=0

4y = -2x+12

y = -(2/4)x +(12/4)

y = -(1/2)x +3

This line has a slope of -(1/2).  Parallel lines have the same slope as the reference line.  So the new line will also have a slope of -(1/2) and we can write the new line equation as:

 y = -(1/2)x + b

Any line with a slope of -(1/2) will be parallel.  Any value of b is acceptable.  But we want this line to intersect the point (-2,5), so we need to pick a value of b that forces the line through this point.  To find the value of b to make that happen, enter the point (-2,5) in the parallel line equation from above:

y = -(1/2)x + b

5 = -(1/2)*(-2) + b  for point (-2,5)

5 = 1+b

b = 4

The parallel line that intersects (-2,5) is

  y = -(1/2)x + 4

See the attached graph.

Answer:

Step-by-step explanation:

B

The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.

In the given question, a school has a square courtyard and wants to create diagonal walkways.

The length of each side of the courtyard is 25 meters.

We have to find how long is each walkway.

By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.

According the Pythagorean Theorem

[tex]a^2+b^2 = c^2[/tex]

[tex](25)^2+(25)^2=c^2[/tex]

Now solving,

625 + 625 = [tex]c^2[/tex]

[tex]c^2[/tex] = 1250

Taking square root on both side, we get

c = 35.36 meters.

Hence, 35.36 meters long is each walkway.

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We can use the incenter to find the best location, because the point that is equidistant to all sides of a triangle is called the incenter.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We know that;

The incenter is equidistant from the sides of the triangle and the point that is equidistant to all sides of a triangle.

Hence, We can use the incenter to find the best location, to place a streetlight so it was equidistant from three sidewalks.

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The solution to f(g(h(x))) = [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]

f(x) = [tex]x^{4} + 6[/tex]

g(x) = [tex]x-3[/tex]

h(x) = [tex]\sqrt{x}[/tex]

Therefore to find f(g(h(x))),

fogoh(x) = f(g(h(x)))

We first substitute the value of h(x) as above,

f(g([tex]\sqrt{x}[/tex]  ))   ....... as h(x) = [tex]\sqrt{x}[/tex]

Now, we substitute the value of g(x) where x is [tex]\sqrt{x}[/tex]

f([tex]\sqrt{x} -3[/tex]) ....... as g(x) =  [tex]x-3[/tex]

Then we substitute the value of x in f(x) with [tex]\sqrt{x} -3[/tex]

[tex](\sqrt{x} -3)^{4} + 6[/tex]

Now we further solve to find a simpler form of the equation,

[tex](\sqrt{x} -3)^{4} + 6[/tex]

= [tex](x^{2} -12x^{3/2} +54x- 108\sqrt{x} +81) + 6[/tex]

=  [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]

Therefore, fogoh(x) = f(g(h(x))= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]

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On solving the provided question, we can say that be equation the value we obtain Number of citizens × total percentage = 140,000 x (23%+11%) = 47,600

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

number of citizens who chose cat or fish is 47,600

Number of citizens × total percentage

140,000 x (23%+11%)

140,000 x 34%

= 47,600

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Answer: 960cm^2

Step-by-step explanation: 12 x 8 = 96 x 10 = 960

Answer:

a) 1728 [tex]cm^{3}[/tex]

b) 512 [tex]cm^{3}[/tex]

c) 1000 [tex]cm^{3}[/tex]

Step-by-step explanation:

(I think your question is ...a little mixed up as a square has same length for all of its respective sides. So I will attempt to do them a little differently as I believe the question must have had three different sub questions)

a) [tex]V = s^{3}[/tex]

   "s" here represents the respective length for the sides.

The answer for if a side was 12 centimeters, then the volume would be

[tex]V = 12^{3}[/tex]

Which would give us a volume of 1728 [tex]cm^{3}[/tex]

b)[tex]V = s^{3}[/tex]

   "s" here represents the respective length for the sides.

The answer for if a side was 8 centimeters, then the volume would be

[tex]V = 8^{3}[/tex]

Which would give us a volume of 512 [tex]cm^{3}[/tex]

c)[tex]V = s^{3}[/tex]

   "s" here represents the respective length for the sides.

The answer for if a side was 10 centimeters, then the volume would be

[tex]V = 10^{3}[/tex]

Which would give us a volume of 1000 [tex]cm^{3}[/tex]

The length of segment PX in this problem is given as follows:

PX = 9.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

In this problem, all the horizontal lines are parallel, hence the side is divided proportionality, as the resulting triangles in the context of this problem are all similar.

PX is three-fourths of the length of the segment PW = 12, hence it's length is given as follows:

PX = 3 x 12/4

PX = 3 x 3

PX = 9 units.

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The inequality which can be used to determine too, the number of outfits Wyatt can purchase while staying within his budget is:

                         780 ≥ 472.44 + 46.60x

Inequality:

In mathematics, equations are not always balanced on both sides using equal signs. It can also be about "not equal" relationships, such as one being greater than the other or less than the other. In mathematics, an inequality refers to a relationship in which two numbers or other mathematical expressions do not compare equally. These formulas belong to algebra and are called inequalities.

An inequality means that two things are not the same. One of them may be less than, greater than, less than or equal to, greater than or equal to the other.

According to the question:

As based on the information,

he can't spent more than $780.

Four cycle reflector cost = 2 × $19.41

                                         = $38.82

Let maximum number of outfit = x

and Cost = 46.60x

and the the pair of glove is for $35.27.

Therefore,

New bicycle + Bicycle reflectors + Biker gloves + Biking Outfit  ≤ 780

⇒ $398.35 + $ 38.82 + $ 35.27 + $46.60 x ≤ 780

⇒  472.44 + $ 46.60x ≤ 780

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Answer:

For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.

The required number of containers are two.

105 minutes per process cycle.

We must first determine the utilization rate of the process in order to determine the number of containers required for the parts. Usage rate is the typical unit utilised each hour.

The scenario specifies that the procedure uses 88 components every hour.

The net cycle time per part per hour is determined as follows: (99/60) x 105 = 173.25

0.31 is the efficiency factor.

We can determine the total number of things Kanban can maintain using the information provided:

= 173.25/(1 - 0.31)

= 119.54

We may calculate the total number of containers required by dividing the container capacity by the entire number of parts after we know how many total pieces will be stored.

Each container can hold 8 dozens, or 96 pieces.

=  119.54

Consequently, two containers are required.

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The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.

In this case, the 4 is being multiplied by the formula, which makes it a coefficient.

A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.

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The data from the 9 students represents the number of hours that they spend on the computer on a typical day. It forms a distribution known as a frequency distribution.

A frequency distribution is a tabular representation of data that shows how often each value or set of values of a variable occurs in a data set. The data set is typically divided into a number of classes or bins, and the frequency of each class is recorded.

In this case, the data represents the number of hours that 9 students spend on the computer on a typical day. Each student is represented by one data point, and the frequency of each value (the number of hours) is recorded.

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Answer:

Step-by-step explanation:

Given : In a GP the first term is 7

            the last term is              448

             and the sum                 889

To find : Common ratio ? The number of terms is 7.

The common ratio is 2

Answer:

common ratio (r) = 2

Step-by-step explanation:

solution in picture

Answer: The area under the curve refers to the area between the curve of a function and the x-axis. To find the area under the curve of a function, you would typically integrate the function with respect to x and then evaluate the definite integral between a set of limits.

For example, to find the area under the curve of f(x) = x^2 + 2x from x=0 to x=a, we would integrate the function with respect to x,

∫[0,a] (x^2 + 2x) dx = (1/3)x^3 + x^2 evaluated from x=0 to x=a,

Similarly, to find the area under the curve of g(x) = x + 2 from x=0 to x=a, we would integrate the function with respect to x,

∫[0,a] (x + 2) dx = (1/2)x^2 + 2x evaluated from x=0 to x=a

It's important to note that the definite integral is only defined if the function is continuous and has no vertical asymptotes on the interval.

Step-by-step explanation:

So, on solving the provided question, we can say that percentage  = 1/15 X 100 = 15%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

car gas mileage is normally distributed with a mean of = 25 miles per gallon

67% of cars get at least 23 miles per gallon

percentage of cars get less than 30 miles per gallon

25-23/30

2/30

1/15

percentage  = 1/15 X 100 = 15%

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The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.

It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.

The function illustrated shows that the weights are the same.

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Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour

Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.

Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

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Answer:x-5.50=20

Step-by-step explanation:

The dimensions size on the scale drawing is 6.5 inches by 3.5 inches.

Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.

In Geometry we can have different dimensions, The number of dimensions is how many values are needed to locate points on a shape.

Multiplying the actual dimensions by the scale gives the scale dimensions:

 (0.5 in)/(6 ft) × {78 ft, 42 ft}

 = {39/6 in, 21/6 in}

 = {6.5 in, 3.5 in}

Therefore, the dimensions size on the scale drawing is 6.5 inches by 3.5 inches.

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Using the law of sines, the length of l is: 12.1 cm.

The Law of Sines is a theorem in triangle geometry that relates the lengths of the sides of a triangle to the sine of its angles. It states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides.

Given the following:

k = 1.2 cm

m<L = 93°

m<M = 6°

m<K = 180 - 93 - 6 = 81°

Using the law of sines, sin K/k = sin L/l:

sin 81/1.2 = sin 93/l

Find l:

(sin 81)(l) = (sin 93)(12)

l = (sin 93)(12)/(sin 81)

l = 12.1 cm

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[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \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}{(-3)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +3= -\cfrac{4}{3} (x -3) \\\\\\ y+3=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x+1 \end{array}}[/tex]

According to the given possibility the event of more than 4 elk surviving to adulthood is not surprising and the appropriate probability is 0.1402.

Here we have given that  it be for more than 4 elk in the sample to survive to adulthood.

Then the probability is calculated by using the binomial probability,

And here we have to use the addition rule for mutually exclusive event, then we get,

=> P(AUB) = P(A or B) = P(A) + P(B)

At the possibility of k = 5 we have the binomial probability to be evaluated as follows:

=> P(X = 5) = 21 (0.44)⁵ (0.56)² ≈ 0.1086

At the possibility k = 6 then the binomial probability to be calculated as,

=> P(X = 6) = 7(0.44)⁶ (0.56)¹ ≈ 0.0284

Finally at the value of k = 7 then the binomial probability to be evaluated as,

=> P(X = 7) = 1 (0.44)⁷(0.56)° ≈ 0.0032

Therefore the two different numbers of successes are impossible on same simulation is by applying the addition rule for mutually exclusive events is calculated as,

=> P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)

=> 0.1086 +0.0284 + 0.0032

=> 0.1402

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