Sally invested some money into a savings account that earns 7.2%
annual simple interest. At the end of 9 years, she earned $745.20 in
interest. How much money did she put into the account initially?
Round to the nearest dollar.

Answers

Answer 1

Sally would have invested $1150 initially in the savings account to satisfy the conditions in the question.

What is a savings account?

A savings account is a type of bank account that helps people save money over time. It offers a safe and secure way to store money while earning interest on the balance. Unlike checking accounts, savings accounts are intended for long-term storage of funds, with a higher interest rate and regular compounding to help the balance grow. Savings accounts offer flexibility in terms of access to funds and usually allow withdrawals at any time with limits on the number of withdrawals without incurring a fee.

To determine how much money Sally initially invested in a savings account that earns 7.2% annual simple interest, we can use the formula for simple interest: I = Prt. Here, I represents the interest earned, P is the initial principal, r is the annual interest rate as a decimal, and t is the time in years.

Given that Sally earned $745.20 in interest over a period of 9 years with an annual interest rate of 7.2%, we can substitute the values into the formula and solve for P:

I = $745.20

r = 7.2% = 0.072 (decimal)

t = 9 years

Now, P = I / (rt)

P = 745.20 / (0.072 * 9)

P = $1150

Therefore, Sally initially invested $1150 in the savings account.

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Related Questions

Show that cosh2x−sinh2x=1 � � � ℎ 2 � − � � � ℎ 2 � = 1 Differentiate with respect to x � e3xx2+1 � 3 � � 2 + 1 y=secx � = sec ⁡ � y=tanx2 � = tan ⁡ � 2 Differentiate with respect to x � y=ln(x+sinx) � = ln ⁡ ( � + sin ⁡ � ) y=cosxx2 � = cos ⁡ � � 2 Find dydx � � � � given siny+x2y3−cosx=2y sin ⁡ � + � 2 � 3 − cos ⁡ � = 2 � Differentiate from first principles y=cosx � = cos ⁡ � x3+2x2+3x+4 � 3 + 2 � 2 + 3 � + 4 Find d2ydx2 � 2 � � � 2 Given 3x3−6x2+2x−1 3 � 3 − 6 � 2 + 2 � − 1

Answers

We can conclude that cosh2x−sinh2x=1.

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.

Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.

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Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

We will show that [tex]\cosh^2x-sinh^2x=1[/tex].

Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]

Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]

Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]

Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]

[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]

Hence, [tex]cosh^2x-sinh^2x=1[/tex]

Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]

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The correct form of question is Show that cosh2x−sinh2x=1 .

your friend is binging half of a crate of popsicles to the picnic. of you put what is left in the crate evenly into 6 ice buckets, what fraction of the crate will go into each of ice bucket​

Answers

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

Explain about the fraction:

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.

Given data:

fraction of crate brought by friend = 1/2

Total number of ice buckets = 6

Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets

Fraction of crate in each bucket = (1/2) / 6

Fraction of crate in each bucket =  1 / (2*6)

Fraction of crate in each bucket = 1/12

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

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Monique claims the surface area of the cylinder is about 1001.66 square feet explain Monique's error find the correct surface area.

Answers

Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.

To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.

However, we can use Monique's estimate to estimate the values of r and h.

1001.66 = 2πr^2 + 2πrh

Dividing both sides by 2π, we get:

500.83 = r^2 + rh

We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.

For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:

500.83 = 5^2 + 5h

495.83 = 5h

h = 99.166

So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:

S = 2π(5^2) + 2π(5)(99.166)

S = 1570.8 square feet

This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.

Step-by-step explanation:

HELP W NUMBER 11PLSSS
Use the circle below linu
for questions 11.
XV= 24 meters
X
Y
Z
72°
108°
11. Find the length ofw. Round to the nearest hundredth.
Veienwollot
to ribiw

Answers

The length of arc XW is 9,60 metres

The length of arc YVU is 44.93 metres

How to solve

A. M<XZW = 180 degrees - M<VZW

= 180 - 108

= 72 degrees.

XV = 180/360 x 2\pi r =

r = 7.639

XW= 72/360 x 2\pi r

= 9.60 metres.

B. M<UZY = M<XZW = 72 degrees

MYVU= 85 + 180 + 72 = 337 degrees

YVU = 337/360 x 2 pi r

=44.93 metres

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Solve for x please

Choices are...
10
5
25
90

Answers

Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10

identify the following equations as increasing linear, decreasing linear, positive quadratic, negative quadratic, exponential growth, or exponential decay.
(please help )

Answers

The types of equations in the question based on the values of the base, the slope and leading coefficients of the equations are;

11. Exponential growth

12. Exponential growth

13. Decreasing linear

14. Positive quadratic

15. Increasing linear

16. Exponential growth

17. Exponential decay

18. Exponential decay'

19. Positive quadratic

20. Linear increasing

21. Exponential growth

22. Negative quadratic

23. Negative quadratic

24. Exponential decay

What is an equation?

An equation is a statement that indicates that of two expressions are equivalent, by joining them with an '=' sign.

11. The exponential equation is; y = (5/2)ˣ

The growth or decay factor, which is the base is; (5/2) > 1, therefore, the equation is an exponential growth equation

12. The exponential equation is; y = (1/4) × 3ˣ

3 > 1, therefore the equation is an exponential growth function

13. The equation y = -2·x -10 is a linear equation with a negative slope of -2, indicating that the value of y is decreasing as x increases, therefore, the equation is decreasing linear

14. The equation, y = 2·x² + 5·x - 7, which is a quadratic equation

The leading coefficient, 2, is positive, therefore, the equation is a positive quadratic equation

15. The equation y = 4·x - 3 has a positive slope, of 4, therefore, it is an increasing linear equation

16. The exponential equation (2/5)·9ˣ, with 9 > 1, is an exponential growth equation

17. The equation  3·(1/4)ˣ, with (1/4) < 1, is an exponential decay equation

18. The equation 2·(0.1)ˣ, with 0.1 < 1, is an exponential decay equation

19. The equation y = (x + 2)² is a quadratic equation

(x + 2)² = x² + 4·x + 4

The leading coefficient is 1, therefore, the equation is a positive quadratic equation

20. The linear equation 4·x + y = 7 with a positive slope of +4 indicates that the y-value of the function is increasing as the x-value of the equation is increasing, therefore, the function is an increasing linear equation

21. The exponential equation, y = 2·5ˣ, with 5 > 1, and 2 > 0, is an exponential growth equation.

22. The equation y = -(x - 3)² is a quadratic equation. The minus sign in front of the expression (x - 3) indicates that the leading coefficient, obtained by expansion, is negative

y = -(x - 3)² = -(x² - 6·x + 9) = -x² + 6·x - 9

The leading coefficient is -1, therefore the equation negative quadratic

23. The equation, y = -6·x² -5·x + 4, with a leading coefficient of -6 is a negative quadratic equation

24. The exponential equation, y = (1/7)·(3/8)ˣ, with (1/7) > 0 and (3/8) < 1 is an exponential decay equation

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A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. Which of these best describes the volume of this rectangular prism? (5 points)


1 unit cube and 15 smaller cubes of volume fraction 1/125 cubic inch each

1 unit cube and 75 smaller cubes of volume fraction 1/125 cubic inch each

7 unit cubes and 25 smaller cubes of volume fraction 1/125 cubic inch each

7 unit cubes and 125 smaller cubes of volume fraction 1/125 cubic inch each

Answers

The volume of the rectangular prism is 1.6 cubic inches.

Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have

L = 1/5 × x

W = 1/5 × y

H = 1/5 × z

where x, y, and z are integers.

Since the rectangular prism is completely packed with 200 cubes, we have

x × y × z = 200

We want to find the volume of the rectangular prism, which is given by

V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z

Substituting x × y × z = 200, we get

V = 1/125 × 200 = 8/5 = 1.6 cubic inches

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The given question is incomplete, the complete question is:

A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the  volume of this rectangular prism

find the value of 3√1 over 16​

Answers

Answer:3/16

Step-by-step explanation:

√1 is the same thing as 1

so (3*1)/16

3/16

the teacher has a small class with only 7 students. the teacher grades their homework and reports scores of: 10, 7, 8, 12, 9, 11, and 13. what is the median?

Answers

Answer:

10

Step-by-step explanation:

To find the median in a set of data, organize the data from least to greatest.

Here, our data is the homework scores, those being:

10, 7, 8, 12, 9, 11, 13

Let's organize them in ascending order, like so:

7, 8, 9, 10, 11, 12, 13

The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.

We can find that the number in the middle is 10.

Thus, the median of the scores is 10.

a client is receiving an iv solution of 2 grams of medication diluted in 100 ml of normal saline over a one hour time period. how many mg of medication is the client receiving per minute? (enter numeric value only. if rounding is required, round to the nearest whole number.)

Answers

The client will be receiving 1.67 ml of medication in one minute and it will have 0.334 g of medication per minute.

Here 2g  of medication is diluted with 100 ml of normal saline. So concentration of 1ml of normal saline would be,

Concentration of 1 ml = 2/100 = 0.02 g/ml

It is delivered over a period of 1 hour. So, the amount delivered per minute will be,

Amount per minute = Volume/ time = 100/60 = 1.67 ml

Amount of medication in 1.67 ml = Volume × Amount per ml

                                                     = 1.67 × 0.02 = 0.334 g

So 0.334 g of medication will be received per minute. So the rate will be 1.67 ml per minute.

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A=P(1+r/n)^nt Find how long it takes for $1400 to double if it is invested at 7% interest compounded monthly. Use the formula A = P to solve the compound interest problem. TE The money will double in value in approximately years. (Do not round until the final answer. Then round to the nearest tenth as needed.)​

Answers

It will take 10 years to double the amount.

Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,

[tex]A = P(1+r/n)^{nt}[/tex]

[tex]2800 = 1400(1+0.0058)^{12t}[/tex]

[tex]2= (1.0058)^{12t[/tex]

㏒ 2 = 12t ㏒ (1.0058)

0.03 = 12t (0.0025)

12t = 120

t = 10

Hence, it will take 10 years to double the amount.

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Which equation could be solved using this application of the quadratic formula?
-(12) ± √(12)²-4(2)(-9)
2(2)
O 12x² - 4x + 13 = 4
12x² - 4x + 4 = 13
2x² + 12x + 13 = 4
2x² + 12x + 4 = 13
x =

Answers

An equation that could be solved using this application of the quadratic formula include the following: D. 2x² + 12x + 4 = 13.

What is a quadratic equation?

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

For the given quadratic equation 2x² + 12x + 4 = 13, we have:

2x² + 12x + 4 = 13

2x² + 12x + 4 - 13 = 0

2x² + 12x - 9 = 0

By substituting, we have;

[tex]x = \frac{-(12)\; \pm \;\sqrt{(12)^2 - 4(2)(-9)}}{2(2)}[/tex]

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what is the ratio of the area of triangle to the area of triangle ? express your answer as a common fraction.

Answers

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

Explain about the ratios:

An instrument for comparing the sizes of two or more quantities in proportion to one another is called a ratio. A list of the structured equivalent ratios of every given ratio is called a ratio table. By multiplying as well as dividing the 2 terms of such a ratio by an identical number, equivalent ratios can be created.

Given data:

Dimension of  larger triangle: base B = 10 cm, Height H = 5 cm.Dimension of  smaller triangle : base b = 5 cm, Height H = 2 cm.

Area of triangle = 1/2* base * height

Ratios:

area of larger triangle / area of smaller triangle = (1/2*B*H) / (1/2*b*h)

area of larger triangle / area of smaller triangle = B*H / b*h

area of larger triangle / area of smaller triangle = 10*5 / 5*2

area of larger triangle / area of smaller triangle = 50 / 10

area of larger triangle / area of smaller triangle = 5/ 1 = 5:1

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

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Complete question:

what is the ratio of the area of larger triangle to the area of smaller triangle ? express your answer as a common fraction.

Dimension of  larger triangle: base B = 10 cm, Height H = 5 cm.

Dimension of  smaller triangle : base b = 5 cm, Height H = 2 cm.

Peter needs to borrow $10,000 to repair his roof. He will take out a 317-loan on April 15th at 4% interest from the bank. He will make a payment of $3,500 on October 12th and a payment of $2,500 on January 11th.

a) What is the due date of the loan?

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th pa payment.

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

Please only serious answers ​

Answers

Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

14. An airplane flew 2,800 miles from Los Angeles to New York. The airplane flies at approximately 500
mi/hr. How many hours did it take the plane to reach New York?

Answers

Answer:

Speed= 500ml/hr

total distance= 2800 m

total time = d/t

2800/500= 5.6hrs

Step-by-step explanation:

The use of heuristics rather than algorithms is most likely to _____.
A. yield more accurate solutions to problems
B. save time in arriving at solutions to problems
C. minimize the overconfidence phenomenon
D. involve greater reliance on language skills

Answers

B. save time in arriving at solutions to problems. Heuristics are problem-solving shortcuts or rules of thumb that can save time when arriving at solutions to problems.

The use of heuristics rather than algorithms is most likely to save time in arriving at solutions to problems. Heuristics are mental shortcuts or rules of thumb that are used to solve problems quickly and efficiently, whereas algorithms are step-by-step procedures for solving problems. While algorithms may produce more accurate solutions, they can be time-consuming to apply. Heuristics, on the other hand, allow for quick problem-solving and are often based on our language skills and prior knowledge. However, relying too heavily on heuristics can sometimes lead to errors or the overconfidence phenomenon.


They might not always yield the most accurate solutions compared to algorithms, which are step-by-step, systematic procedures that guarantee a correct solution. Heuristics usually rely less on language skills and do not necessarily minimize the overconfidence phenomenon.

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Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently.

B. save time in arriving at solutions to problems . The correct answer is:

Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently. They are simple and often automatic strategies that allow individuals to make judgments or decisions without engaging in a lengthy, deliberate, and systematic process of problem-solving.

One of the main advantages of using heuristics is that they can save time in arriving at solutions to problems. Instead of analyzing all available information and considering all possible alternatives, heuristics allow individuals to quickly narrow down options and make decisions based on simplified cognitive processes. This can be especially useful in situations where time is limited or when individuals need to make decisions on the spot.

However, heuristics are not always foolproof and can sometimes lead to errors or biases in decision-making.

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Which statement about subnetting is correct?
A. Subnetting applies only to IPv4 networks, unless you are using classless interdomain routing.
B. Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage.
C. Subnetting in IPv4 involves the CIDR protocol, which runs at Layer 3; in IPv6, this protocol, and hence subnetting, is not used.
D. Because the subnet mask field is so much larger in IPv6, it is easier to subnet in this newer protocol stack than in IPv4.

Answers

The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.

Hence, the correct option is B.

In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.

IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.

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In the graph below, line k with equation y = -k makes a 45° angle with the x- and y- axes.

Rx: (2, 5)

1. (-2, 5)
2. (-2, -5)
3. (2, -5)

Answers

In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).

What is a graph?

The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.

The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)

Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).

Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).

The point (2,5) will change to if it is reflected across the line y=x (5,2).

Therefore, the correct option is 1. (-2, 5).

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Find the solution to the system of equations. Write the solution as an ordered pair. If there are no solutions, write 'no solutions'. If there are infinitely many, write 'infinitely many'.

y = −72
x + 11

7x + 2y = 20

Answers

The solution to the system of equations is (23, -72).

How to find system of equations ?

The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.

Substituting y = -72 in the second equation, we get:

7x + 2(-72) = 20

Simplifying this equation, we get:

7x - 144 = 20

Adding 144 to both sides, we get:

7x = 164

Dividing both sides by 7, we get:

x = 23.428571...

So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).

However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:

(x, y) = (23, -72)

Therefore, the solution to the system of equations is (23, -72).

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6) Practice: Using Visual Cues Label each part of the diagram. Then use your labels to complete the sentences. Square Root Notation √6 1. The expression √ means "the of b". 2. The exponent 1 symbol (√) stands for the 3. The number or expression under the radical symbol is called the​

Answers

1. The expression √b means "the square root of b".

2. The radical symbol (√) stands for the exponent 1/2.

3. The number or expression under the radical symbol is called the radicand.

What is radicand?

A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.

The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.

The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.

The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.

The exponent of the radical symbol is 1/2, which implies that the expression is a square root.

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electric utility poles in the form of right cylinders are made out of wood that costs $23.89 per cubic foot. calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 30 ft. round your answer to the nearest cent.

Answers

The cost of the utility pole is approximately $1273.99 when rounded to the nearest cent.

To calculate the cost of the utility pole, we need to find its volume first. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is its height.

Here, the diameter of the utility pole is given as 1.5 ft. We need to find the radius, which is half of the diameter, so r = 0.75 ft. The height is given as 30 ft.

Using the formula, we get:

V = πr^2h = π(0.75 ft)^2(30 ft) = 53.36 ft^3

Now, we can calculate the cost of the utility pole by multiplying its volume by the cost of wood per cubic foot, which is $23.89 per cubic foot.

Cost = 53.36 ft^3 x $23.89/ft^3 ≈ $1273.99

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a doctor can complete 3 examinations in 2 hours. how many examinations can the doctor complete in 4 hours? hint: use the proportion 3 exams : 2 hours :: x exams : 4 hours. 5 exams 5 exams 6 exams 6 exams 7 exams 7 exams 8 exams

Answers

Answer:

6 examinations

Step-by-step explanation:

We Know

A doctor can complete 3 examinations in 2 hours.

How many examinations can the doctor complete in 4 hours?

We see

4 hours is 2 hours times 2

We take

3 x 2 = 6 examinations

So, the doctor can complete 6 exams in 4 hours.

An expression is shown.

12 • 12 • 12 • 12 + 7(3 • 3 • 3 • 3 + 3)

Answers

The last answer should be correct because 12 is listed 4 times and 3 is listed 5 times so it would be 12 with an exponent of 4 + 7 and then 3 with an exponent of 5

josse is collecting signatures for a petition.
He currently has 520signatures.
He has 6 more weeks to collect the signatures he needs.
He needs at least 1000 signatures before he can submit his petition

explain pliss

Answers

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

What is number line?

A number line is a diagram that depicts numbers on a straight line. It is a tool for comparing and sorting numbers. It can represent any real number, including whole numbers and natural numbers.

Jesse currently has 520 signatures and needs at least 1000 signatures, which means he still needs to collect 1000 - 520 = 480 signatures.

He has 6 more weeks to collect the signatures he needs, so he wants to collect the same number of signatures each week. Let's call this number x, representing the number of signatures he collects each week. Then, the total number of signatures he collects in the remaining 6 weeks would be 6x.

We want to find the range of values for x that would allow Jesse to collect at least 480 signatures in the remaining 6 weeks. In other words, we want to solve the inequality:

6x ≥ 480

Dividing both sides by 6, we get:

x ≥ 80

This means that Jesse needs to collect at least 80 signatures per week in order to have enough signatures to submit the petition.

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

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Keyana puts beads at the ends of her braids. On a single braid, she places 7 beads that are
each 1.03 centimeters long. Then she adds a final bead that is 0.9 centimeter long. The
expression below can be used to find the total length of the beads on one of Keyana's braids.
7 x 1.03 +0.9
What is the total length of the beads on one braid?
A 7.3 centimeters
B.8.11 centimeters
C.9.19 centimeters
D: 10.0 centimeters

Answers

The total length of the beads on one braid is 8.11 centimeters

What is the length?

Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.

To find the total length of the beads on one braid, we need to evaluate the expression:

7 x 1.03 + 0.9

Multiplying 7 by 1.03 gives us:

7 x 1.03 = 7.21

Then, adding 0.9 gives us:

7.21 + 0.9 = 8.11

Therefore, the total length of the beads on one braid is 8.11 centimeters.

So, the correct answer is B.8.11 centimeters.

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a kite flying in the air has a 94- string attached to it, and the string is pulled taut. the angle of elevation of the kite is . find the height of the kite. round your answer to the nearest tenth.

Answers

The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

52 no one can win more than one prize? multiple choice 16,129,423 16,497,400 15,281,283 16,300,400

Answers

The closest choice to the actual number of ways to choose 52 different winners out of 52 contestants is 16,497,400,

To solve this problem, we can use the formula for permutations, which is:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, 52), and r is the number of objects we are choosing (in this case, the number of prizes, which is also 52).

Since no one can win more than one prize, we need to choose 52 different winners for the prizes. Therefore, the number of ways to do this is:

52P52 = 52! / (52 - 52)! = 52!

Using a calculator or computer program, we can find that 52! is approximately equal to 8.0658 × 10^67.

Therefore, the answer is 16,497,400, which is the closest choice to the actual number of ways to choose 52 different winners out of 52 contestants.

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Leah uses 20 ounces of beeswax to make 6 identical small candles. How many ounces of beeswax does leah need to make 15 more small candles

Answers

The ounces of  beeswax needed by Leah to make 15 more small candles is equal to 49.95 ounces.

Let us consider 'x' be the ounces of beeswax required by Leah to make 15 candles.

To make 6 small candles, Leah uses 20 ounces of beeswax.

So, to make one small candle,

Ounces of beeswax used by Leah ,

= 20 ounces / 6 candles

= 3.33 ounces/candle (rounded to two decimal places)

To make 15 more small candles,

Ounces of beeswax Leah will need is equals to,

⇒ x = 15 candles x 3.33 ounces/candle

⇒ x = 49.95 ounces (rounded to two decimal places)

Therefore, Leah needs 49.95 ounces of beeswax to make 15 more small candles.

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Find the mean, median, and mode for the data set. Express your answers as decimals rounded to the nearest tenth, if necessary.
13, 14, 15, 17, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24

Answers

The median is 20, the mean is 19.57 and the mode is 21

Find the value of ‘x’
x =

Answers

The value of x, in the image given is calculated by applying the intersecting chords theorem, which is: x = 16.

What is the Intersecting Chords Theorem?

The Intersecting Chords Theorem, also known as the Ptolemy's Theorem, states that in a circle, if two chords intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

In mathematical terms, if two chords, AB and CD, intersect at point E inside a circle, then:

AE × EB = CE × ED

Applying the theorem, we have:

5(x) = (x - 6)8

5x = 8x - 48

5x - 8x = -48

-3x = -48

x = 16

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