carla wants to start a college fund for her daughter lila. she puts $63,000 into an account that grows at a rate of 2.55% per year, compounded monthly. write a function, c(t), that represents the amount of money in the account t years after the account is opened, given that no more money is deposited into or withdrawn from the account.

The shape of the cross section is a triangle.

To find the shape of the cross section after slicing through the triangular prism with piano wire, follow these :

Determine the original shape of the triangular prism.

Consider the orientation of the dotted lines indicating where the piano wire sliced through the prism.

Analyze the resulting shape after the cut is made.

In this case, Christina has a triangular prism, and she sliced it with piano wire.

Based on your description, the cross section would be a triangle since the wire cut through the triangular sides of the

prism.

an emotional relationship involving a couple and a third person with whom one of them is also involved.

Therefore, the shape of the cross section is a triangle.

a plane figure with three straight sides and three angles

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The slope of the line AB is 1.5 and the ratio of the sides is 2

The slope, m of line AB is solved using the formula

m = y2 - y1  / x2 - x1

using points 'A (-9, -5) and B (3, 3)

m = -9 - 3 / -5 - 3

m = -12 / -8

m = 1.5

For a similar triangle the ratio of side lengths are equal

AB / BC = AE / BD = BE / CD

The length of AB and BC is solved as follows

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points we want to find the distance between.

For AB:

x1 = -9, y1 = -5 (coordinates of A)

x2 = 3, y2 = 3 (coordinates of B)

distance_AB = sqrt((3 - (-9))^2 + (3 - (-5))^2)

distance_AB = sqrt(144 + 64)

distance_AB = sqrt(208)

distance_AB ≈ 14.42

For BC:

x1 = 3, y1 = 3 (coordinates of B)

x2 = 9, y2 = 7 (coordinates of C)

distance_BC = sqrt((9 - 3)^2 + (7 - 3)^2)

distance_BC = sqrt(36 + 16)

distance_BC = sqrt(52)

distance_BC ≈ 7.21

From the graph,

AE = 12

BD = 6

BE = 8

CD = 4

AB / BC = 14.42 / 7.21 = 2

AE / BD = 12 / 6 = 2

BE / CD = 8 / 4 = 2

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The difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero.

Kathy needs to exchange half of her US dollars into British pounds and half of her US dollars into euros. Since it is given that pound is equal to USD and euro is also equal to USD, when she withdraws half of her US dollars as British pounds and half of it as euros, she will have the same amount of pounds and euros. Thus, the difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero. Therefore, she will have the same amount of money in both currencies, and the answer to the question is 0 (rounded to the nearest whole number).

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the percentage 68% value is calculated by adding 85 and 20, or 70; the 95% value is calculated by adding 85 and 40, or 115; and the 99.7% value is calculated by adding 85 and 60, or 150.

68%: 70

95%: 115

99.7%: 150

The 68-95-99.7 rule is used to estimate the percentage of a population that falls within a certain range of values when the data is normally distributed. The rule states that 68% of the population falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. To find the percentages, we subtract the mean (85) from the corresponding standard deviation (20, 40, and 60, respectively) and add the result to the mean. Thus, the 68% value is calculated by adding 85 and 20, or 70; the 95% value is calculated by adding 85 and 40, or 115; and the 99.7% value is calculated by adding 85 and 60, or 150.

the complete question is :

Assume the resting heart rates for a sample of individuals are normally distributed with a mean of 85 and a standard deviation of 20. Use the 68-95-99.7 rule to find the following quantities:

1.The percentage of individuals with resting heart rates between 65 and 105.

2.The percentage of individuals with resting heart rates above 125.

3.The range of resting heart rates that includes the middle 95% of the individuals in the sample.

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The 8th term of the given geometric sequence is -156250.

A sequence of numbers is called a geometric sequence if each term, except for the first term, is obtained by multiplying the previous term by a constant factor, which is called the common ratio.

The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by -5.

So, the common ratio (r) between any two consecutive terms is -5.

To find the 8th term, we can use the formula for the nth term of a geometric sequence:

[tex]an = a1 * r^{(n-1)[/tex]

where,

an = 8th term

a1 = first term = 2

r = common ratio = -5

n = 8 (since we want to find the 8th term)

Therefore, substituting the values in the formula, we get:

[tex]a8 = 2 * (-5)^{(8-1)}\\\\a8 = 2 * (-5)^7\\\\a8 = 2 * (-78125)\\\\a8 = -156250[/tex]

Hence, the 8th term of the given geometric sequence is -156250.

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Answer:

312.5

Step-by-step explanation:

125g sultans for every 40g sugar

40 times 2 is 80, 125 times two is 250, then divide 125 by two to get how many for 20g of sugar

250+62.5=312.5

Answer:

The problem is the answer to your equation

Step-by-step explanation:

Im sorry to disappoint but these questions don't really have a name.

The difference between the two expressions is:

(k³-7k+2)-(k²-12) = k³ - k² - 7k + 14

What is an expression?

We can begin by simplifying the left side of the equation:

(k³ - 7k + 2) - (k² - 12)

= k³ - 7k + 2 - k² + 12 // Distribution of the negative sign

= k³ - k² - 7k + 14 // Combining like terms

So the difference between the two expressions is:

k³ - k² - 7k + 14

An expression is a combination of one or more values, variables, and operators that can be evaluated to produce a result. Expressions can be as simple as a single number or variable, or they can be complex, combining multiple operators and functions.

What are variables?

A variable is a symbol or a named memory location that can hold a value. It is used to store and manipulate data during the execution of a program. Variables can be assigned different types of values, such as numbers, text, or Boolean (true/false) values. The value of a variable can change during the execution of a program, and it can be used in expressions and statements to perform calculations, make decisions, or control the flow of the program.

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Complete question is: (k³-7k+2)-(k²-12) = k³ - k² - 7k + 14

Option C : The slope of Function A is 6 and the slope of the line graphed in Function B, going through the ordered pairs (1, 4) and (-1, -2), is 3.

To compare the slopes of Function A and Function B, we need to determine the slopes of the line graphed in Function B and the slope of Function A, and then compare them using the answer choices provided.

The slope of the line going through the ordered pairs (1, 4) and (-1, -2) can be found using the slope formula:

slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-1 - 1) = -6/-2 = 3

So the slope of Function B is 3.

The equation for Function A is f(x) = 6x - 1, which means its slope is 6.

Now we can compare the slopes using the answer choices provided:

Slope of Function B = 2 x Slope of Function A: 3 = 2 x 6 is not true

Slope of Function A = Slope of Function B: 6 = 3 is not true

Slope of Function A = 2 x Slope of Function B: 6 = 2 x 3 is true

Slope of Function B = − Slope of Function A: 3 = -6 is not true

Therefore, the equation that best compares the slopes of the two functions is "Slope of Function A = 2 x Slope of Function B".

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The equation represents Function A, and the graph represents Function B: Function A f(x) = 6x - 1 Function B graph of line going through ordered pairs 1, 4 and negative 1, negative 2 and negative 2, negative 5 Which equation best compares the slopes of the two functions? (1 point)

A. Slope of Function B = 2 x Slope of Function A

B. Slope of Function A = Slope of Function B

C. Slope of Function A = 2 x Slope of Function B

D. Slope of Function B = − Slope of Function A

Answer:

Step-by-step explanation:

Answer: A. You cannot use any theorem along with option A. For B, you can use SAS. For option C, you can use SAS. For option D, you can use SSS. For option D, you can use ASA. So, the answer is A.

Answer:

x² + y² = 16

Step-by-step explanation:

the circle has its centre at the origin (0, 0 )

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

the radius r of the circle is 4 , then

x² + y² = 4² , that is

x² + y² = 16

The formula NEXT = NOW - 8 is neither recursive or explicit.

In a recursive fοrmula, we can find the value οf a term in the sequence using the value οf the previοus term. Hοwever, in an explicit fοrmula, we can find the value οf a term in the sequence using its pοsitiοn. Hence, this is anοther difference between recursive and explicit.

Recursive formula = [tex]\rm a_{n}=a_{n-1}+ d[/tex]

Explicit formula = [tex]\rm a_n= a_1 + (n - 1) d[/tex]

Here, NEXT = NOW - 8 resembles Recursive formula, but the value of Next isn't given. Even if it starts at 50, The value of n isn't specified.

Therefore, The formula NEXT = NOW - 8 is neither recursive or explicit.

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Complete question:

Is the formula recursive, explicit, or neither?

NEXT = NOW - 8, starting at 50.

The function has a local maximum at x = 1/3 and a local minimum at x = -4/3.

A quadratic equation is a second-order polynomial equation in a single variable x

ax²+bx+c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots x can be found by completing the square,

ax²+bx+c=0

To analyze the function F(x) = -2x² - 6x³ + 4x + 1, we can begin by finding its derivative:

F'(x) = -4x - 18x² + 4

Then, we can find the critical points of the function by setting F'(x) equal to zero and solving for x:

-4x - 18x² + 4 = 0

Using the quadratic formula, we get:

x = (-(-4) ± ((-4)² - 4(-18)(4))) / (2(-18))

Simplifying, we get:

x = (-(-4) ± (400)²) / (-36)

x = (-(-4) ± 20) / (-36)

x = 1/3 or x = -4/3

So the critical points of the function are x = 1/3 and x = -4/3.

To determine the nature of these critical points, we can use the second derivative test.

F''(x) = -4 - 36x

Plugging in x = 1/3, we get:

F''(1/3) = -4 - 36(1/3) = -16 < 0

So x = 1/3 is a local maximum.

Plugging in x = -4/3, we get:

F''(-4/3) = -4 - 36(-4/3) = 40 > 0

So x = -4/3 is a local minimum.

Therefore, the function has a local maximum at x = 1/3 and a local minimum at x = -4/3.

complete question  F(X) = 6x³ - 4x² + 1. Find The Equation Of The Tangent Line To F(X)When X = 2.

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Complete question:

Find the local maximum and minimum of f(x) = -2x² - 6x³ + 4x + 1.

All the given options applies to the statement. A related-samples design reduces problems due to individual differences; can have an order effect; have less sample variance, increases the likelihood of rejecting the null hypothesis; needs few participants for same degree of power.

1. A related-samples design decreases or eliminates problems that is caused by individual differences such as age, IQ, gender, or personality.

2. Related samples (specifically, one sample of participants with repeated measures) can have an order effect such that a change observed between one measurement and the next might be attributable to the order in which the measurements were taken rather than to a treatment effect.

3. Related samples have less sample variance, which increases the likelihood of dismissing the null hypothesis if it is false (that is, increasing power).

4. Related samples (specifically, one sample of participants with repeated measures) needs very less participants for the same degree of power.

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Answer: The answer is 286.4! (Not rounded: 286.391)

Step-by-step explanation:

I hope this helped you! <333

Answer:

[tex]{ \tt{ - 1 > - 1 \frac{1}{4} }} \\ [/tex]

Answer:

A≈615.75cm²

Step-by-step explanation:

A=πr2=π·142≈615.75216cm²

1. The center of circle is (5, -10)

2. The new center of circle is (4, -12)

3. Equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]

The Circle identities defines a set of fundamental identities in trigonometry that depends on the six trigonometric functions of an angle in a right-angled triangle.

Given circle equation is [tex](x-5)^2+(y+10)^2 = 64[/tex]

after translated 1 left and 2 down, by simply add 1 in x and add 2 in y axis, So, the new circle equation will be,

[tex](x-4)^2+(y+12)^2 = 64[/tex]

1. The center of the given circle [tex](x-5)^2+(y+10)^2 = 64[/tex]

Generally the equation of circle is [tex](x-h)^2 +(y-k)^2 =r^2[/tex]

where, (h, k)is center of circle and r is radius.

by comparing the given equation, we get, h = 5, k = -10

So, the center of circle is (5, -10)

2. New center after translation

equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]

comparing the given equation, we get, h = 4, k = -12

So, the new center of circle is (4, -12)

3. Equation of the resulting circle is [tex](x-4)^2+(y+12)^2 = 64[/tex]

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The right choice is Choice D: Lines AC and RS are skew lines. Skew lines are two lines that never cross and are not equal moreover.

A line is characterized as a bunch of focuses that broaden endlessly in one or the other heading. A line is the briefest distance between any two focuses.

What are skew lines?

Skew lines are two lines that never cross and are not equal moreover. Thus we can say that the two lines can not exist in a similar plane.

From the figure obviously

Line AC and RS are in various planes and they are likewise not crossing one another, subsequently, as per the meaning of skew lines, they are skew lines.

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the complete question is:

Lines AC and RS are:

Coplanar

Parallel

Perpendicular

Skew

Step-by-step explanation:

For the second triangle, you can find X by subtracting 32+85 from 180, which leaves X as 63.

Next, since Y is the same as X, it means that Z is equal to 180-(45+63)

X=63

Y=63

Z=72

I'm sorry, but I need more information to answer your question.

The equation y = -10x + 216 represents a linear relationship between two variables, where y represents the number of students who drop out and x represents the year. However, I don't have any information about the values of x for previous years or any other data that can be used to make a prediction for the year 2012.

If you have additional information, such as the number of dropouts for previous years, you can substitute those values into the equation and solve for the value of y in 2012.

Answers:

Explanation:

An integer is any positive or negative whole number. Zero is also an integer. Examples include 12, 15, and -27.

Non-integer values are anything with a fractional or decimal part. An example is 2.47; another example is 2/3 (since it turns into roughly 0.667).

Answer:

$20.64

Step-by-step explanation:

When you take 40% of 33, you are left with 19.8. You then translate the sales tax into 84 cents and add it to 19.8. That will give you $20.64 as the after tax price.

A unit square is a square with sides of length 1 unit. When we talk about the area of a unit square, we mean the amount of space that the square covers, which is equal to 1 square unit.

To demonstrate that 0.1 of 1 is the same as 0.1 x 1 using a unit square area model, we can imagine dividing the unit square into 10 equal parts vertically and horizontally. This creates a grid of 100 smaller squares, each with an area of 0.01 square units.

Now, let's consider the expression 0.1 of 1. This means taking 0.1 times the area of a unit square. Since the area of the unit square is 1 square unit, 0.1 of 1 is equal to 0.1 times 1, which is 0.1.

Similarly, we can represent the expression 0.1 x 1 visually on the unit square area model by shading in 0.1 of the unit square, as before. Since 0.1 x 1 is also equal to 0.1, the shaded area will once again cover 0.1 square units, confirming that these two expressions are equal.

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Answer:

3(x^2+3x-1)

Step-by-step explanation:

3x^2+9x-3

3(x^2+3x-1)

5) Triangles QRN and MNL are not similar.

6) Triangle ECD is similar to triangle MNL

What is similarity of triangle?

Similarity of triangles is a concept in geometry that describes the relationship between two triangles that have the same shape but possibly different sizes. Two triangles are considered similar if their corresponding angles are congruent (equal in measure) and their corresponding sides are proportional (having the same ratio).

This can be expressed using the following notation: if triangle ABC is similar to triangle DEF, we can write it as:

∆ABC ~ ∆DEF

The symbol "~" means "is similar to."

5) To determine whether the two triangles QRN and MNL are similar, we can use the SSS~ (side-side-side) similarity criterion or the SAS~ (side-angle-side) similarity criterion.

Let's first check if the triangles satisfy the SSS~ criterion:

SSS~ criterion: If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

The sides of triangles QRN and MNL are:

QR = QN + RN = 56 + 48 = 104

RN = 48

QN = 56

MN = ML + NL = 60 + 70 = 130

NL = 70

ML = 60

We can see that the ratios of the corresponding sides are not equal:

QR/MN = 104/130 = 0.8

RN/NL = 48/70 = 0.686

QN/ML = 56/60 = 0.933

Since the ratios of the corresponding sides are not equal, the triangles QRN and MNL are not similar by the SSS~ criterion.

Now let's check if the triangles satisfy the SAS~ criterion:

SAS~ criterion: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

We can see that the included angles are not congruent, since we don't have any angle measures given. Therefore, we cannot use the SAS~ criterion to determine similarity.

Since the triangles do not satisfy either the SSS~ or SAS~ similarity criterion, we can conclude that they are not similar by either criterion.

6) In triangle ECD, we have:

angle ECD = 180 - angle CED - angle CDE

= 180 - (angle MNL + angle LNM) - angle CDE (since MNL is given as similar to ECD)

= 180 - (angle MNL + angle LNM) - angle CDM (since triangle CDM is similar to triangle LNM)

= 180 - 45 - 36 = 99 degrees

Similarly, in triangle MNL, we have:

angle MNL = 180 - angle LNM - angle MLN

= 180 - angle LNM - (angle ECD + angle CDE) (since MNL is given as similar to ECD)

= 180 - angle LNM - (angle CDM + angle CDE) (since triangle CDM is similar to triangle LNM)

= 180 - 36 - 45 = 99 degrees

Therefore, the triangles have two congruent angles: angle ECD is congruent to angle MNL, and angle CED is congruent to angle MLN.

Next, we need to check if the corresponding sides are proportional. We can do this by finding the ratios of the corresponding sides:

EC/MN = 96/36 = 8/3

CD/NL = 64/45

ED/ML = 80/54 = 40/27

If we simplify these ratios, we get:

EC/MN = 8/3

CD/NL = 64/45 = 16/9

ED/ML = 40/27

Since the ratios of the corresponding sides are not equal, the triangles are not similar by SSS~ or SAS~.

However, we can see that the triangles are similar by AA~, since they have two congruent angles. Therefore, a valid similarity statement would be:

Triangle ECD is similar to triangle MNL by AA~.

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Answer:

[tex] \begin{gathered} \mathfrak{\large\bold \bf \mapsto {\underline{ \boxed{ \sf{\ \: p \: = 1 }}}}} \: \purple \: \bigstar \\ \end{gathered}[/tex]

Step-by-step explanation:

[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5 ( 5p - 1) = 20 }}} \: \\ \end{gathered}[/tex]

[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p - 1 = \frac{20}{5} }}} \: \\ \end{gathered}[/tex]

[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p - 1= 4 }}} \: \\ \end{gathered}[/tex]

[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p = 4 + 1 }}} \: \\ \end{gathered} \\ \\ \begin{gathered} \large\bold \bf \mapsto { { \sf{\ 5p = 5 }}} \: \\ \end{gathered}[/tex]

[tex]\begin{gathered} \large\bold \bf \mapsto { { \sf{\ p \: = \frac{5}{5} }}} \: \\ \end{gathered}[/tex]

[tex]\begin{gathered} \large\bold \bf \mapsto { \pink{ \bf{\ p \: = 1 }}} \: \\ \end{gathered}[/tex]

[tex] \underline{ \rule{250pt}{7pt}}[/tex]

The solution to the equation 5(5p-1) = 20 is p = 1.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To solve this equation, we can follow these steps:

Simplify the left side of the equation by using the distributive property of multiplication:

5(5p-1) = 25p - 5

Solve for the unknown variable by isolating it on one side of the equation. In this case, we want to get p by itself, so we'll add 5 to both sides of the equation:

25p - 5 + 5 = 20 + 5

25p = 25

Finally, divide both sides of the equation by 25 to get the value of p:

25p/25 = 25/25

p = 1

Therefore,

The solution to the equation 5(5p-1) = 20 is p = 1.

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Lines AB and CD are parallel. If 6 measures (4x - 31)°, and 5 measures 111°, the value of x will be 21 if both angles are supplementary.

If lines AB and CD are parallel, then we can assume that m<5 and m<6 are supplementary that is the sum of both angles is 180 degrees

Therefore we can say that;

then 3x - 31 + 148 = 180

then 3x + 117 = 180

we need to then subtract 117 from both sides

therefore, 3x+117-117 = 180 - 117

then 3x = 180 - 117

then 3x = 63

then x = 63/3

therefore, x = 21

Hence the value of x will be 21 if both angles are supplementary.

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The P(Z > 2.90) = 1 - P(Z ≤ 2.90)= 1 - 0.9986= 0.0014Thus, the proportion of overweight children with left atrial diameters greater than the mean of healthy children is 0.0014, rounded to four decimal places.Answer: 0.0014

According to the given question, we have to find what proportion of overweight children have left atrial diameters greater than the mean for healthy children. To calculate the answer, we need to use the z-score of the left atrial diameter. We have to find the z-score value corresponding to the mean of healthy children and the standard deviation of the left atrial diameter of healthy children. Then, we will have to use the z-score formula.

Let’s solve it.Step-by-step explanation:Given that we need to calculate the proportion of overweight children with left atrial diameters greater than the mean of healthy children. Here, we can use the standard normal distribution to solve this problem. To solve this problem, we need to calculate the z-score for the mean of healthy children and the left atrial diameter of healthy children.1. Find the z-score for the mean of healthy children.z = (x - μ) / σz = (0 - 0) / 1z = 0 Thus, the z-score for the mean of healthy children is 0.2.

Find the z-score for the left atrial diameter of healthy children.z = (x - μ) / σz = (3.95 - 2.5) / 0.5z = 2.90Thus, the z-score for the left atrial diameter of healthy children is 2.90.Using the z-score formula, we can find the proportion of overweight children with left atrial diameters greater than the mean of healthy children. Let’s use the formula for it.P(Z > 2.90) = 1 - P(Z ≤ 2.90)From the z-score table, we can find that the value of P(Z ≤ 2.90) is 0.9986.

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