At the beginning of year 1, Bode invests $250 at an annual simple interest rate of 3%. He makes no deposits to or withdrawals from the account.Which explicit formula can be used to find the account’s balance at the beginning of year 14? What is the balance?



A.A(n) = (250)(n – 1)(0.03); $97.50 B.A(n) = 250 + (n)(0.03 • 250); $355.00 C.A(n) = 250 + (n – 1)(0.03); $250.39 D.A(n) = 250 + (n – 1)(0.03 • 250); $347.50

Answer:

24 girls.

Step-by-step explanation:

If the number of boys is x then:

x + 4/7 x = 66

x = 66  / 1 4/7

x = 66 *  7/11

= 6 * 7

= 42.

So the number of  girls is 66 - 42

= 24.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

The number of girls students is 24.

In the fifth grade at Lenape Elementary School, there are 4/7 as many girls as there are boys.

There are 66 students in the fifth grade.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

There are 66 students in fifth grade, and there is a 4:7 girl to boy ratio.

[tex]= \dfrac{66}{11}\\\\= 6[/tex]

Then,

the number of girls is = [tex]6 \times 4=24[/tex]

The number of boys is = [tex]6 \times 7 = 42[/tex]

Hence, the number of girls students is 24.

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Answer:

180,000 m

Step-by-step explanation:

There are 60 seconds in a minute, so:

2 min × 60 s/min = 120 s

Distance = rate × time

d = 1500 m/s × 120 s

d = 180,000 m

Answer:

(C) 1 : 511

Step-by-step explanation:

Possible outcome for every throw = 2 (head or tail)

Total possible outcome for 9 throws

= 2⁹

= 512

Odd of getting all head

= 1 : 511

The odds in favor of getting all heads on nine coin tosses is 1 to 512.

The odds in favor of getting all heads on nine coin tosses can be calculated as the number of favorable outcomes divided by the number of possible outcomes. In this case, we want all nine coin tosses to result in heads, which is only 1 favorable outcome. The total number of possible outcomes for nine coin tosses is 2^9 = 512.

Therefore, the odds in favor of getting all heads on nine coin tosses is 1 to 512. Comparing this to the options given, the correct answer is A. 1 to 508.

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Answer:

Option A. [tex]\frac{29}{4}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=x^{2} +7[/tex]

[tex]g(x)=\frac{x+2}{x}[/tex]

we know that

[tex](fog)=(\frac{x+2}{x})^{2} +7[/tex]

Evaluate the expression for x=-4

[tex](fog)(-4)=(\frac{-4+2}{-4})^{2} +7[/tex]

[tex]=(\frac{1}{2})^{2} +7[/tex]

[tex]=(\frac{1}{4})+7[/tex]

[tex]=\frac{29}{4}[/tex]

I. need. more info. to solve it sorry

For this case we must solve the following questions:

Question 1:

We should simplify the following expression:

[tex]\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =[/tex]

Applying double C we have:

[tex]\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =[/tex]

By definition of multiplication of powers of the same base we have to place the same base and add the exponents:[tex]\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =[/tex]

Canceling common terms:

[tex]\frac {mn ^ 5} {p ^ 4}[/tex]

Answer:

Option A

Question 2:

We should simplify the following expression:

[tex]\frac {3xyz ^ 2} {6y ^ 4} * \frac {2y} {xz ^ 4}[/tex]

So, we have:

[tex]\frac {3xyz ^ 2 * 2y} {6y ^ 4 * xz ^ 4} =\\\frac {6xy ^ 2z ^ 2} {6y ^ 4xz ^ 4} =[/tex]

Simplifying common terms:

[tex]\frac {1} {y ^ 2z ^ 2}[/tex]

Answer:

Option D

Question 3:

We factor the following expressions to rewrite the experience:

[tex]r ^ 2 + 7r + 10[/tex]: We look for two numbers that multiplied give 10 and added 7:

[tex](r + 5) (r + 2)[/tex]

[tex]r ^ 2-5r-50:[/tex] We look for two numbers that multiplied give -50 and added -5:

[tex](r-10) (r + 5)[/tex]

[tex]3r-30 = 3 (r-10)[/tex]

Rewriting the given expression we have:

[tex]\frac {(r + 5) (r + 2) * 3 (r-10)} {3 (r-10) (r + 5)} =[/tex]

We simplify common terms in the numerator and denominator we have:

[tex](r + 2)[/tex]

Answer:

Option D

Answer:

17. The correct answer option is A.

18. The correct answer option is D.

19. The correct answer option is D.

Step-by-step explanation:

17. [tex]\frac{m^2n^3}{p^3} \times \frac{mp}{n^2}[/tex]

Changing division to multiplication by taking reciprocal of the latter fraction to get:

[tex]\frac{m^2n^3}{p^3} \times \frac{n^2}{mp}[/tex]

[tex]\frac{mn^5}{p^4}[/tex]

The correct answer option is A. [tex]\frac{mn^5}{p^4}[/tex].

18. [tex]\frac{3xyz^2}{6y^4} \times \frac{2y}{xz^4}[/tex]

[tex]\frac{1}{y^2z^2}[/tex]

The correct answer option is D. [tex]\frac{1}{y^2z^2}[/tex].

19. [tex]\frac{r^2+7r+10}{3} \times \frac{3r-30}{r^2-5r-50}[/tex]

Factorizing the terms to get:

[tex]\frac{(r+2)(r+5)}{3} \times \frac{3(r-10)}{(r+5)(r-10)}[/tex]

Cancelling the like terms to get:

[tex]r+2[/tex]

The correct answer option is D. [tex]r+2[/tex].

25% of the arrows are further than approximately 24.32 cm from the target's center.

To find the distance from the center of a target that 25% of arrows are further than, we need to determine the z-score that corresponds to the 75th percentile (since 100% - 25% = 75%).

Using a z-table or technology, we find that the z-score for an area of 0.75 is approximately 0.675.

Next, we use the z-score formula: z = (X - μ) / σ, where µ is the mean (20 cm) and σ is the standard deviation (6.4 cm). Setting z to 0.675, we solve for X:

0.675 = (X - 20) / 6.4

Multiplying both sides by 6.4:

4.32 = X - 20

Adding 20 to both sides gives us:

X ≈ 24.32 cm

Thus, approximately 25% of the arrows are further than 24.32 cm from the center.

f(x)= 10x

It seems like c and d are the same.

Answer:

10 mph

Step-by-step explanation:

Let x mph be Devontre rate uphill, then x+20 mph its his rate downhill.

1. Time uphill:

[tex]\dfrac{5}{x}\ hours[/tex]

2. Time downhill:

[tex]\dfrac{5}{x+20}\ hours[/tex]

3. If it took him 20 minutes (1/3 hour) longer to ride uphill than downhill, then

[tex]\dfrac{5}{x}-\dfrac{5}{x+20}=\dfrac{1}{3}[/tex]

Solve this equation:

[tex]\dfrac{5(x+20)-5x}{x(x+20)}=\dfrac{1}{3}\\ \\\dfrac{100}{x(x+20)}=\dfrac{1}{3}\\ \\300=x(x+20)\\ \\x^2+20x-300=0\\ \\D=20^2-4\cdot (-300)=400+1200=1600\\ \\x_{1,2}=\dfrac{-20\pm \sqrt{1600}}{2}=\dfrac{-20\pm 40}{2}=-30,\ 10.[/tex]

The rate cannot be negative, thus, x=10 mph (rate uphill).

2*3=6 girls

Hope this helps :)

Answer:

[tex]\boxed{\text{144.33 m}^{2}}[/tex]

Step-by-step explanation:

The scale factor (C) is the ratio of corresponding parts of the two pyramids.  

The ratio of the areas is the square of the scale factor.

[tex]\dfrac{A_{1}}{ A_{2}} = C^{2}\\\\\dfrac{\text{327 m}^{2}}{A_{2}} = \left (\dfrac{1}{\frac{2}{3}}\right)^{2}\\\\ \dfrac{\text{327 m}^{2}}{A_{2}}= \dfrac{9}{4}\\\\\text{1308 m}^{2}= 9A_{2}\\\\A_{2} = \text{145.33 m}^{2}\\\text{The surface area of the smaller pyramid is \boxed{\text{145.33 m}^{2}}}[/tex]

Answer:

$3.55/workout

Step-by-step explanation:

Total cost:  $39 + ($27.50/month)(12 months) = $369

Number of visits per year:  (2 visits/week)(52 weeks/year) = 104 visits/year

Dividing the total cost by 104 visits/year results in:

 $369

--------------- = 3.55

104 visits

Each workout cost him $3.55. Each workout cost is obtained by the total cost and the number of the visit per year.

It is the sum of the variable cost and the fixed cost. The total cost is the minimum dollar cost of producing some quantity of output.

Registration fee = $39

Monthly fee = $27.50

No of visit a week for a year= 2

Total cost is found as;

Total cost = registration fee+monthly fee ×no of month

Total cost =  $39 + ($27.50/month)(12 months)

Total cost =$369

Number of visits per year= visits/week×no of week

Number of visits per year= (2 visits/week)(52 weeks/year)

Number of visits per year = 104 visits/year

When you divide the entire cost by 104 visits per year, you get:

Each workout cost = $369/104

Each workout cost =$3.55

Hence, each workout cost him $3.55

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Answer:

A bill's chances are the same as Sandra's

Step-by-step explanation:

Bill's chances are the same as Sandra's chances.

To be lucky means to be favored by some unforeseen event. Thus, the fact that a person is lucky or not has no relation to the luck that another person may or may not have. That is, there is no link between the chances of one person and those of another, when they are in the same situation.

Therefore, neither Bill nor Sandra have a different chance of rolling doubles on the next roll of the dice.

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Answer:

9 blocks

Step-by-step:  

One way in which to do this problem is to find the volume of the rectangular prism and then divide that by the volume of one  cubic block of side length 1/6 inch.

V = (length)(width)(height) = (1/2 cm)(1/6 cm)(1/2 cm) = 1/24 cm³.

Volume of one cubic block of side length 1/6 cm is (1/6 cm)³ = 1/216 cm³.

Dividing 1/24 cm³ by 1/216 cm³ yields 216/24 blocks, or 9 blocks.

Answer:

3.2.1

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

√(-49)

Let's rewrite this as:

√(-1) √(49)

√49 is 7, and √-1 is i.  Therefore:

7i

Answer D.

The expression √(-49) can be rewritten using the Imaginary unit "i" as follows:

[tex]\sqrt(-49) = \sqrt(49 \times (-1)) = \sqrt49 \times \sqrt(-1) = 7i[/tex]

So, the correct answer is option D) 7i.

Here, rewrite the expression √(-49) using the imaginary unit "i," you can express it as the square root of (-1) multiplied by the square root of 49. This is because the square root of -1 is represented as "i."

[tex]\sqrt(-49) = \sqrt((-1) \times 49)[/tex]

Now, we can factor out the square root of 49, which is 7:

[tex]\sqrt(-1 \times 49) = \sqrt(-1) \times \sqrt(49) = i \times 7[/tex]

So, √(-49) can be expressed as 7i.

The correct answer is:

D) 7i

Thus, √(-49) is equal to 7i, indicating that it is a complex number with a real part of 0 and an imaginary part of 7. option D) 7i is correct choice .

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Answer:

g/f

Step-by-step explanation:

Cosine is adjacent over hypotenuse.  The side adjacent to H is g.  The hypotenuse is f.  Therefore:

cos H = g / f

For this case we have by definition of trigonometric relations of rectangular triangles that, the cosine of an angle is equal to the leg adjacent to the angle on the hypotenuse of the triangle.

Then, according to the given figure we have:

[tex]cos (H) = \frac {g} {f}[/tex]

Answer:

[tex]cos (H) = \frac {g} {f}[/tex]

Answer:

[tex] y^2 + 8y + 16 [/tex]

Step-by-step explanation:

[tex] (6y^2 + 2y + 5) - (5y^2 - 6y - 11) = [/tex]

The first set of parentheses is unnecessary, so it can just be removed.

[tex] = 6y^2 + 2y + 5 - (5y^2 - 6y - 11) [/tex]

To remove the second set of parentheses, you must distribute the negative sign that is to its left. It changes every sign inside the parentheses.

[tex] = 6y^2 + 2y + 5 - 5y^2 + 6y + 11 [/tex]

Now you combine like terms.

[tex] = 6y^2 - 5y^2 + 2y + 6y + 5 + 11 [/tex]

[tex] = y^2 + 8y + 16 [/tex]

Answer:

100, 120

Step-by-step explanation:

The mean of the given data is 500/4, or 125.

If a score of 0 were added to this data, the mean would be smaller, because we'd have to divide the five scores by 5.  The mean would now be 100.

The median of the given data is the average of the middle two scores, that is, of 120 and 130.  It's 125.

If we were to add the score of 0 to the four data points, obtaining

0, 100, 120, 130, 150,

the median would be the middle number:  120.

Mean is the average of the data set and mode is the middle terms or average of the middle terms of the data set.

Given information-

The given data consists the values 100,120,130,150.

Total number of values is four.

Mean is the average of the given data.

The mean of the given data can be calculated as,

[tex]m=\dfrac{100+120+130+150}{4} [/tex]

[tex]m=\dfrac{500}{4} [/tex]

[tex]m=125[/tex]

For even terms the medium is the average of the middle terms.

The medium of the given data can be calculates as,

[tex]M=\dfrac{120+130}{2} [/tex]

[tex]M=125[/tex]

Adding a score of 0.

The data consists of the values will be 0,100,120,130,150.

Total number of values is five.

The mean of the given data can be calculated as,

[tex]m=\dfrac{0+100+120+130+150}{5} [/tex]

[tex]m=\dfrac{500}{5} [/tex]

[tex]m=100[/tex]

Medium for the odd terms is equal to the middle terms.

The medium of the given data can be calculates as,

For the

[tex]M=120[/tex]

Thus adding a score of 0 the mean of the given data is reduced with number 25 and the mode reduced with number 5.

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A z-score is a standardized value that represents the number of standard deviations a given score is above or below the mean in a normal distribution. In this case, the area under the standard normal curve is 0.1271, and the corresponding z-score is approximately -1.14.

A z-score is a standardized value that represents the number of standard deviations a given score is above or below the mean in a normal distribution.

It allows for comparison of scores from different data sets with different means and standard deviations. In this case, we are given the area under the standard normal curve and asked to find the corresponding z-score.

To find the z-score, we can use a z-table, which shows the area under the normal curve to the left of each z-score. In the given problem, the area under the curve is 0.1271.

By looking up the closest area in the z-table, we find that the z-score is approximately -1.14.

Final answer:

The z-score represents the number of standard deviations a value is from the mean in a standard normal distribution.

Explanation:

The z-score represents the number of standard deviations a value is from the mean in a standard normal distribution. To find the z-score, we can use the z-table or a calculator. In this case, the area under the standard normal curve is given as 0.1271. Using the z-table, we can find the z-score that corresponds to this area and enter it in the box.

Answer:

Kameron has 5 quarters in his wallet

Step-by-step explanation:

Let

x----> the number of nickels

y----> the number of quarters

remember that

1 nickel=$0.05

1 quarter=$0.25

we know that

x=3y -----> equation A

0.05x+0.25y=2

Multiply by 100 both sides

5x+25y=200

Simplify

x+5y=40 -----> equation B

Substitute equation A in equation B

(3y)+5y=40

8y=40

y=5 quarters

x=3(5)=15 nickels

Final answer:

By setting up and solving equations based on the value of quarters and nickels and their proportions, we can determine that Kameron has 5 quarters in his wallet.

Explanation:

Finding the Number of Quarters in Kameron's Wallet

To solve Kameron's problem, we can set up two equations based on the given information. Let's define Q as the number of quarters and N as the number of nickels Kameron has. Since we know that the number of nickels is three times the number of quarters, we can express this as N = 3Q.

Next, we calculate the monetary value of the quarters and nickels. Each quarter is worth 25 cents, and each nickel is worth 5 cents. Since the total amount is two dollars, which is 200 cents, we can write the equation 25Q + 5N = 200.

Substituting N with 3Q in the second equation, we get 25Q + 5(3Q) = 200, which simplifies to 40Q = 200. Solving for Q gives us Q = 200 / 40 = 5, so Kameron has 5 quarters in his wallet.

Answer:

Step-by-step explanation:

Basically, just replace the x and y coordinates for the equation. For example... A. (0,-8).... -8=-4(0)-8= y=-4x-8.  A would be an answer choice.... Hope that helps !!!

Answer:

d. ≈ 37,106 ft

Step-by-step explanation:

The angle of depression to the plane to the airport is the same as the angle of elevation from the airport to the plane. Therefore, the angle of elevation form the airport to the plane is 6°.

Notice that the height of the plane is the opposite side of the angle of elevation and the ground distance is the adjacent side of the angle of elevation. To find ground distance we need to use a trig function to relate the opposite side and the adjacent side; that trig function is tangent:

[tex]tan(\alpha )=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan(6)=\frac{3900ft}{ground-distance}[/tex]

[tex]ground-distance=\frac{3900ft}{tan(6)}[/tex]

[tex]ground-distance=37106ft[/tex]

We can conclude that the plane's ground distance to the airport is approximately 37,106 feet

Point A is at (12,12)

Point B is at (48,24)

Use the distance formula √((x2-x1)^2 + (y2-y1)^2)

Length = √((48-12)^2 + (24-12)^2)

Length = √(36^2 + 12^2)

Length = √(1296 + 144)

Length = √1440

The answer is E.

Answer:

[tex]\sqrt{-12} = i\sqrt{12} = i\sqrt{4\cdot 3} = 2i\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

Option A. 2/3

Step-by-step explanation:

we know that

If angle theta is in Quadrant 1

then

The value of cos(theta) is positive and the value of tan(theta) is positive

Remember that

tan(theta)=sin(theta)/cos(theta)

In this problem we have

tan(theta)*cos(theta)=[sin(theta)/cos(theta)]*cos(theta)=sin(theta)

therefore

tan(theta)*cos(theta)=sin(theta)=2/3

Final answer:

The value of (tan theta)(cos theta) is 2/3.

Explanation:

To find the value of (tan theta)(cos theta), we can use the given value of sin theta and the fact that sin² θ + cos² θ = 1.

Since the value of sin theta is known to be 2/3, we can square this value to find sin² θ = (2/3)² = 4/9.

Using the identity sin² θ + cos² θ = 1, we can solve for cos² θ by subtracting sin² θ from 1. This gives us cos²θ = 1 - 4/9 = 5/9.

Finally, we can calculate (tan θ)(cos θ) by multiplying tan θ = sin θ/ cos θ = (2/3) / [tex]\sqrt{5/9[/tex] = (2/3) / ([tex]\sqrt{5[/tex]/3) = 2 / [tex]\sqrt{5[/tex] and cos θ = [tex]\sqrt{5/9[/tex]. Therefore, (tan θ )(cos θ ) = (2 / [tex]\sqrt{5[/tex]) * [tex]\sqrt{5/9[/tex] = 2 / 3.

Answer:

u² – 11u + 24 = 0 where u = (x² – 1)

Step-by-step explanation:

Given the equation;

(x² – 1)² – 11(x² – 1) + 24 = 0

We can let;

u = x² - 1

Substituting the value of u in the equation we get;

(u)² - 11 (u) + 24 = 0

u²- 11u + 24 = 0

Therefore;

The quadratic equation that is equivalent to the equation is;

u² – 11u + 24 = 0 where u = (x² – 1)

Answer:

option 1

Step-by-step explanation:

Answer:

4, 6, 8

Step-by-step explanation:

The possible degrees of a polynomial function can be determined by observing the highest power of the variable in the polynomial. Each curve or turn in the graph represents a change in direction of the polynomial. The highest number of curves or turns is equal to the degree of the polynomial.

The possible degrees of a polynomial function in the graph can be determined by observing the highest power of the variable in the polynomial. The degree of a polynomial is the highest exponent of the variable. For example, if the highest power of the variable is 3, then the polynomial has a degree of 3.

In the graph, we can determine the degree by looking at the x-axis and counting the number of curves or turns. Each curve or turn represents a change in direction of the graph. The highest number of curves or turns is equal to the degree of the polynomial.

For example, if the graph has one curve or turn, then the polynomial has a degree of 1, which means it is a linear function. If the graph has two curves or turns, then the polynomial has a degree of 2, which means it is a quadratic function.

To horizontally stretch the linear parent function f(x) = x by a factor of 2, we replace 'x' in the original function with 'x/2'. Therefore, g(x) = x becomes g(x) = x/2 or g(x) = 1/2x.

When we talk about stretching the "linear parent function" f(x) = x horizontally by a factor of 2, we are essentially changing the 'x' values of the function, and the equation of the function changes accordingly. When a function is stretched horizontally by a factor of 'b', the new function becomes f(x/b). So, in this case, as the stretch factor is 2, the new function will be f(x/2).

This means that wherever you see 'x' in the original function, you replace it with 'x/2'. So, f(x) = x becomes g(x) = x/2. Therefore, the correct answer to your question is g(x) = 1/2x.

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We have three pythagoras:

4² + y² = z²

16² + y² = x²

x² + z² = 20²

Now let's think:

4² + y² = z²

y² = z² - 4²

16² + y² = x²

16² + z² - 4² = x²

x² + z² = 20²

16² + z²- 4² + z² = 20²

2z² = 20² - 16² + 4²

2z² = (2.10)² - (2^4)² + (2²)²

2z² = 2².10² - 2^8 + 2^4

z² = 2.10² - 2^7 + 2^3

z² = 200 - 128 + 8

z² = 208 - 128

z² = 80

z = √80

80 | 2

40 | 2

20 | 2

10 | 2

5 | 5

1

80 = 5.2^4

So

√80 = 4√5

z = 4√5

Answer:

Step-by-step explanation:

B. Vertically stretch by a factor of 3, and

D. Shift down 1 unit.

To determine which transformations were applied to the linear parent function f(x) = x to obtain the given function g(x) = 3x - 1, we need to examine the changes made to the function. Let's analyze each choice:
A. Horizontally stretch by a factor of 3.
A horizontal stretch would mean that the x-values are being multiplied by a constant factor. However, in g(x) = 3x - 1, it's the output values (y-values) that have been multiplied by 3 when compared to f(x) = x. Thus choice A is not correct.
B. Vertically stretch by a factor of 3.
In g(x) = 3x - 1, each output value has been multiplied by 3 relative to the parent function f(x) = x. In other words, y has been replaced by 3y, which causes a vertical stretch or scaling by a factor of 3. So choice B is correct.
C. Shift left 1 unit.
A horizontal shift of the graph would involve an addition or subtraction inside the function's argument (x). For instance, f(x - 1) would indicate a shift to the right by 1 unit, and f(x + 1) would be a shift to the left by 1 unit. Since there is no such term in g(x) = 3x - 1, no horizontal shift has occurred. Choice C is not correct.
D. Shift down 1 unit.
A downward shift is indicated by a subtraction outside the function. In g(x) = 3x - 1, there is indeed a "-1" applied to the entire function, which results in every point on the graph being shifted down 1 unit. Therefore, choice D is correct.
In summary, the transformations applied to f(x) = x to get g(x) = 3x - 1 are:
B. Vertically stretch by a factor of 3.
D. Shift down 1 unit.