Therefore, the equation for which g = 5 is not the solution is 4g = 20.
What is equation?An equation is a mathematical statement that shows the equality between two expressions or values. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations can be used to solve problems or to describe relationships between quantities. They are commonly written in the form of "expression 1 = expression 2" or "expression 1 - expression 2 = 0", where the goal is to find the value(s) of the variable(s) that make the equation true.
To check for which equation g = 5 is not the solution, we can substitute g = 5 into each equation and see which ones result in a false statement.
[tex]8g = 40[/tex]
Substituting g = 5 gives: 8(5) = 40, which is true. Therefore, g = 5 is a solution to this equation.
4g = 20
Substituting g = 5 gives: 4(5) = 20, which is false. Therefore, g = 5 is not a solution to this equation.
g - 2 = 3
Substituting g = 5 gives: 5 - 2 = 3, which is true. Therefore, g = 5 is not a solution to this equation.
2g = 25
Substituting g = 5 gives: 2(5) = 25, which is false. Therefore, g = 5 is not a solution to this equation.
Therefore, the equation for which g = 5 is not the solution is 4g = 20.
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determine the failure rate for a 100-hr test of 11 samples, where 3 items failed at 35, 64 and 72 hrs., respectively.
The failure rate for the 100-hour test with 11 samples is 2.73%. It can be expressed as the proportion of failed samples over the total time of the test and the number of samples.
How to determine the failure rate?To determine the failure rate for a 100-hr test of 11 samples, where 3 items failed at 35, 64, and 72 hours, respectively, we can use the following formula:
Failure rate = (Number of failures / Total time of the test) * (1 / Number of samples)
Number of failures = 3
Total time of the test = 100 hours
Number of samples = 11
So, the failure rate would be:
Failure rate = (3 / 100) * (1 / 11) = 0.0273 or 2.73%
Therefore, the failure rate for this 100-hour test with 11 samples is 2.73%.
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I need help on this I can’t figure it out
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
The length of arc XW is 9,60 metres
The length of arc YVU is 44.93 metres
How to solveA. 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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4. A bag of candy has 22 twix, 14 reeces, and 16 hersheys. Give a reduced ratio of non-twix to ALL candy.
Answer: 30/52 or 58%
Step-by-step explanation:
The non-Twix candies to all candies is 30 pieces of non-Twix to 52 total candies. This is a ratio of 30:52 or 58%. I hope this helps you. <3
Answer: 15 non-twix to 26 total candy
Step-by-step explanation:
non twix: 14+16=30
all candy: 22+14+16=52
30:52
simplify
15:26
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.)
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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Solve for x please
Choices are...
10
5
25
90
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
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
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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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
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
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
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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A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 6 feet. The portion from a point to a vertical line created by two vertices is 6 feet.
Which of the following represents the total area of the figure?
968 ft2
616 ft2
484 ft2.
352ft2
Area of figure is 484ft².
Define area of rectangle and triangleThe area of a rectangle is the amount of space that is enclosed by its sides. It is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is:
Area = length x width
where "length" refers to the longer side of the rectangle, and "width" refers to the shorter side.
The formula for the area of a triangle is:
Area = (base x height) / 2
where "base" refers to the length of the side of the triangle that is parallel to the ground, and "height" refers to the length of a line that is perpendicular to the base and connects the base to the opposite vertex.
Area of figure=Area of 1st triangular part+ Area of rectangular part+ Area of 2nd triangle
=1/2× 22× 8 + 16 ×22 + 1/2 ×4×22
=88+352+44
=484ft².
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Can someone help me asap? It’s due tomorrow. I will give brainliest if it’s correct.
The simulation that represents the context is given as follows:
2,5, 8 of diamonds: gold plastic ring.3, 6, 9 of diamonds: silver plastic ring.4, 7, 10 of diamonds: black plastic ring.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
In the context of this problem, we have an equal number of gold rings, silver rings and black rins, thus each outcome should have the same probability, which is represented by the last option.
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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
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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Liv collected information about the length and width of a random sample of
48
4848 petals of iris flowers. Here are the results:
Width is less than
2
cm
2 cm2, start text, space, c, m, end text Width is more than
2
cm
2 cm2, start text, space, c, m, end text Total
Length is less than
5.2
cm
5.2 cm5, point, 2, start text, space, c, m, end text
14
1414
3
33
17
1717
Length is
5.2
cm
5.2 cm5, point, 2, start text, space, c, m, end text to
5.7
cm
5.7 cm5, point, 7, start text, space, c, m, end text
4
44
11
1111
15
1515
Length is more than
5.7
cm
5.7 cm5, point, 7, start text, space, c, m, end text
7
77
9
9
start box, 9, end box
16
1616
Total
25
2525
23
2323
48
4848
Liv wants to perform a
χ
2
χ
2
\chi, squared test of independence between petal length and width.
What is the expected count for the cell corresponding to petals whose length is more than
5.7
cm
5.7 cm5, point, 7, start text, space, c, m, end text and whose width is more than
2
cm
2 cm2, start text, space, c, m, end text?
You may round your answer to the nearest hundredth.
The expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm is approximately 7.67.
What is the frequency?
The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.
To find the expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm, we need to calculate the expected frequency for that cell using the formula:
Expected frequency = (row total * column total) / grand total
For this particular cell, the row total is 16 (from the table) and the column total is 23.
The grand total is 48 (also from the table). So, we can calculate the expected frequency as:
Expected frequency = (16 * 23) / 48 = 7.67
Rounding this to the nearest hundredth, we get the expected count as 7.67.
Therefore, the expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm is approximately 7.67.
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Find the value of ‘x’
x =
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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what is the answer to this question? (please i need help)
Answer:
-5d + 5.5 < 17
-5d < 11.5
d > -2.3
A is the correct solution.
identify the following equations as increasing linear, decreasing linear, positive quadratic, negative quadratic, exponential growth, or exponential decay.
(please help )
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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Monique claims the surface area of the cylinder is about 1001.66 square feet explain Monique's error find the correct surface area.
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:
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 =
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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I need HELP on ALL these questions
THEN the 4 question is” what is the shape”
(1) Area of triangle = 6in²
Area of rectangle of first kind=18in²
Area of rectangle of second kind= 30in²
(2) 90in²
(3) 0 as it is 2-D body
Define surface area?Surface area refers to the total area that covers the surface of a three-dimensional object, including all of its faces, sides, and any other surfaces that are exposed. It is measured in square units, such as square meters or square feet, and is calculated by adding up the areas of each individual surface of the object. The surface area is a fundamental property used to describe the physical characteristics of an object, and it is important in many different fields, including mathematics, physics, and engineering.
What is volume?Volume is a measure of the amount of space that a substance or object occupies, typically in cubic units such as liters or cubic meters. It is commonly used to describe the size or amount of a liquid, gas, or solid.
(1) Area of triangle = 6in²
Area of rectangle of first kind=18in²
Area of rectangle of second kind= 30in²
(2) The surface area of entire figure =( 6×2+18+2×30)in²
= 90in²
(3) Volume is =0 as it is a 2-D body
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An expression is shown.
12 • 12 • 12 • 12 + 7(3 • 3 • 3 • 3 + 3)
the value of r-squared always falls between ________ and ________, inclusive.
The value of r-squared always falls between 0 and 1, inclusive, as it represents the proportion of the variation in the dependent variable that is explained by the independent variable(s).
The value of R-squared, also known as the coefficient of determination, is a measure of the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a linear regression model.
The value of R-squared ranges from 0 to 1, with 0 indicating that the model does not explain any of the variance in the dependent variable, and 1 indicating that the model explains all of the variance in the dependent variable. Thus, the value of R-squared always falls between 0 and 1, inclusive. A higher value of R-squared indicates a better fit of the model to the data.
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The value of r-squared, also known as the coefficient of determination, always falls between 0 and 1, inclusive.
R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that is
explained by the independent variable(s).
It ranges from 0 to 1, where 0 indicates that the independent variable(s) does not explain any of the variation in the
dependent variable, and 1 indicates that the independent variable(s) explain all of the variation in the dependent
variable.
An R-squared value of 1 is therefore a perfect fit of the model to the data.
therefore, The value of R-squared always falls between 0 and 1, inclusive.
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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
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
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.)
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 of the following ratios is in proportion to the ratio 3:4? (choose any that work)
5:6
12:14
12:16
6:7
4:5
6:8
Answer: 12:16
Step-by-step explanation: If you simply the ratio by dividing each side by 4 you are left with 3:4
Answer: 12:16,6:8
Step-by-step explanation:
simplify
12:16=3:4
6:8=3:4
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
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 .
solve for x round to the hundredth placement
Answer:
Set your calculator to degree mode.
[tex] \ \sin(25) = \frac{6}{x} [/tex]
[tex]x \sin(25) = 6[/tex]
[tex]x = \frac{6}{ \sin(25) } = 14.20[/tex]
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
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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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?
Answer:
Speed= 500ml/hr
total distance= 2800 m
total time = d/t
2800/500= 5.6hrs
Step-by-step explanation:
Joanna rented a bike for Friday and Saturday. The cost of renting a bike on the weekdays is $7. She used a coupon and paid half the amount on Friday. The amount she paid on Saturday was $4 less than twice the regular cost of renting a bike on weekdays.
How much did she spend on renting the bike?
A.
$13.50
B.
$32.00
C.
$21.50
D.
$24.00
The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.
what is amount ?The term "amount" designates a sum or number, typically expressed in terms of monetary value or a tangible good. It can also be used to describe the whole amount of anything, such as the total time that is spent on a work or the total amount of rain that falls in a specific location. "Amount" is frequently used synonymously with "amount" or "total."
given
A two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.
Joanna paid $7/2 ($3.50) on Friday thanks to a voucher she utilised to pay half the price.
The normal Saturday bike rental fee should be "x." Then, according to the issue, Joanna paid $4 less than double what renting a bike normally costs during the workweek. As a result, she spent $10 on Saturday (2($7) - $4).
As a result, she spent the following sum overall to rent the bike:
$3.50 + $10 = $13.50
The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.
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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.
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.