Using combinations we know that 24 combinations of the flags can be used.
What are combinations?Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial.
Combos' components can be chosen in any hierarchy.
Combinations and permutations can coexist.
The expression "Selection of things" refers to a circumstance in which the chronology of occurrences is unimportant.
So, we know that we have 3 types of flags which are:
4 flags for the top position.
3 flags for the middle position.
2 flags for the bottom position.
Now, different combinations would be:
4 * 3 * 2 = 24
Therefore, using combinations we know that 24 combinations of the flags can be used.
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a classroom is arranged with 8 seats in the front row 10 seats in the middle row and 12 seats in the back what is the probability that that the first student who enters the room will be assigned to the front row
The probability that the first student who enters the room will be assigned to the front row is 4/15.
What is probability?The probability of an event is calculated by dividing the total number of possible outcomes by the number of possible outcomes.
given that ,
A classroom is arranged with 8 seats in the front row 10 seats in the middle row and 12 seats
The total number of seats in the classroom is 8 + 10 + 12 = 30.
There are thirty seats to choose from because there is only one student entering the room.
However, we want to determine the likelihood that the student will be assigned to one of the eight seats in the front row.
Therefore, the probability of assigning the front row to the first student who enters the room is:
P(front row) = 8/30
Simplifying this fraction gives:
P(front row) = 4/15
As a result, there is a probability of 4/15, or roughly 0.267, that the first student who enters the room will be assigned to the front row.
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What are the steps to finding out 4. 25 - 7. 06?
The result of subtracting 7.06 from 4.25 is -2.81.
Let's see how these steps apply to the problem at hand:
4.25
-7.06
In this case, we don't need to borrow because the top number 4.25 is already smaller than the bottom number 7.06.
Starting from the rightmost column, we subtract 5 from 6. Since 6 is larger than 5, we can subtract 5 from 6 and get 1. We write down 1 in the hundredths column.
Next, we move to the tenths column and subtract 2 from 0. We can't do this, so we need to borrow 1 from the digit in the ones column. The 4 in the ones column becomes 3, and the 2 in the tenths column becomes 12.
Now we can subtract 2 from 12, which gives us 10. We write down 0 in the tenths column and carry 1 to the ones column.
In the ones column, we have 3 - 7 - 1 (the borrowed 1) = -5. Since we can't have a negative number in this position, we need to borrow again from the digit in the tens column. The 2 in the tens column becomes 12, and we bring down the borrowed 1 to the ones column.
Now we can subtract 7 from 12, which gives us 5. We write down 5 in the ones column.
Step 4: Bring down any digits that have not been used.
We don't have any digits left to bring down, so we have finished the subtraction.
Therefore, the result of subtracting 7.06 from 4.25 is -2.81.
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One cubic foot of a chemical weighs 50 pounds. How many pounds of the chemical can a container with the dimensions shown hold?
The container can contains 3,000 pounds of chemicals.
How many pounds can the container hold?One cubic foot of a chemical weighs 50 pounds which means 1 ft³ of chemical = 60 pounds
We must find how many pounds in the container whose dimension 6 ft, 4 ft and 2.5 ft. So, the l = 6 ft, b = 4 ft and h = 2.5 ft.
Volume of box = L*B*H
Volume of box = 6 x 4 x 2.5
Volume of box = 60 ft³
From 1 ft³ of chemical = 60 pounds; then, the 50 ft³ of chemical will be:
= 50 x 60
= 3,000 pounds
Full question "One cubic foot of a chemical weighs 60 pounds. How many pounds of the chemical can a container with the dimensions shown hold? The base is 6, the width is 4, and the height is 2.5"
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What is the smallest rational number:
The smallest rational number among all the given numbers is equal to 0.2345678.
The rational number are equal to,
-√5 , (1/4), √25 , -√27 , 0.2345678
First simplify each of the given numbers we have,
√5 is an irrational number,
so it is not rational.
1/4 is a rational number.
√25 = 5,
which is a rational number.
-√27 = -3√3,
which is an irrational number, so it is not rational.
0.2345678 is a rational number.
Arrange the rational number in ascending order to get the smallest rational number .
Value of 1/4 = 0.25
0.2345678 < 0.25 < 5
Therefore, the smallest rational number among the given options is 0.2345678.
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A store sells pajamas in two sizes.
• The child size is for people less than `60` inches tall.
• The adult size is for people `60` inches tall or more.
Juan’s height is `145` centimeters.
Would he fit the child or adult size
What is the answer
he would fit the child size
his height is 145cm and we want to convert it into inches so the formula is
length/2.54=
145cm/2.54=57.08in
so juan is 57.08 inches, so he fits the child size.
Kendrick attends a private school where he must wear a uniform. Last year, the price of the uniform was $52. This year's uniform price was $65. What is the percent of increase in the cost of the uniform?
The percent increase in the cost of the uniform from last year to this year is 25%.
What is the percent of increase in the cost of the uniform?To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.
The difference between this year's price and last year's price is:
$65 - $52 = $13
The original price (last year's price) is $52.
So the percent increase in the cost of the uniform is:
percent increase = (difference / original price) x 100
percent increase = ($13 / $52) x 100
percent increase = 0.25 x 100
percent increase = 25%
Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.
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a circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 79 cm long. 1/360th of the circumference of the circle is 0.5 cm long. what is the measure of this angle in degrees?
The measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.
Since 1/360th of the circumference of the circle is 0.5 cm long, the circumference of the circle is 360 times longer, or 180 cm long.
The arc subtended by the angle is 79 cm long, which is a fraction of the entire circumference. To find the angle in degrees, we need to convert the arc length to an angle measure using the formula:
angle measure = (arc length / circumference) x 360 degrees
Substituting the values we know, we get:
angle measure = (79 cm / 180 cm) x 360 degrees
Simplifying the fraction, we get:
angle measure = 1.9833 x 360 degrees
Rounding to the nearest degree, we get:
angle measure ≈ 713 degrees
Therefore, the measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.
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How do you find the legs of a 45-45-90 triangle if you know the length of the hypotenuse?
Each leg of the triangle has a length of 5√(2) units
Since the triangle is 45-45-90, each of the two legs has the same length, which we'll call x. By the Pythagorean theorem, we know that:
x² + x² = h²
Simplifying this equation, we get:
2x² = h²
To solve for x, we can divide both sides by 2 and then take the square root:
x = h / √(2)
This tells us that each leg of a 45-45-90 triangle is equal to the hypotenuse divided by the square root of 2.
Let's say you have a 45-45-90 triangle with a hypotenuse of length 10. To find the length of each leg, you would use the formula:
x = h / √(2)
Substituting h = 10, we get:
x = 10 / √(2)
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √(2):
x = (10 / √(2)) * (√(2) / √(2))
= 10√(2) / 2
= 5√(2)
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Eric needs to read 5 novels each month. Let n be the number of novels Eric needs to read in m months. write you equation and graph it.
Tasha has a gift card to buy tickets to the movie theater. The initial value of the gift card is $120 . The function M(x)=120-12x represents the amount of money, M , in dollars, that is still left on the gift card after purchasing x movie tickets at a cost of $12 each.
Complete the statements.
The value of is 60/-60 which is viable/not viable in terms of the given context.
The solution to the linear function M(x) = 180 is of x = -5.
What is a Linear Function Equation?The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.
In this problem, the function is defined as follows:
M(x) = 120 - 12x.
M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.
The domain of the situation is given as follows:
x ≥ 0. {discrete}
As the number of tickets cannot assume negative neither decimal values.
The equation is:
M(x) = 180.
The solution is calculated as:
120 - 12x = 180
12x = -60
x = -60/12
x = -5.
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Which scatter plot shows a positive linear association? A. Scatter plot graph in quadrant 1 of a coordinate plane. 11 points are plotted approximated at (2, 5), (1.5, 11.5), (3.1, 6.1), (4, 9), (5.9, 12.5), (7, 6), (7.5, 8.5), (8, 11), (8.9, 4.1), (9, 8), and (11, 10). B. Scatter plot in quadrant 1 of a coordinate plane. 14 points are plotted at (3, 11), (3, 12), (4, 11), (4.2, 11), (5, 10.8), (5.5, 12), (6, 10), (6.5, 11), (7, 9), (7.1, 6), (7.1, 7.5), (7.5, 9), (8, 7.5), and (8.1, 6.1). C. Scatter plot graph in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 11), (2.5, 9), (3, 10), (4, 8), (5, 8.2), (5.5, 6.5), (6.5, 7), (6.5, 5), (8, 5.8), and (9, 4). D. Scatter plot graph in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 3), (2.8, 4.2), (3.8, 3.2), (4, 4.7), (4, 6), (5, 5), (6, 8), (7, 7), (7.8, 9.2), and (8.9, 9.1).
So, from the given options, the scatter plot that shows a positive linear association is option B.
What is scatter plot?A scatter plot is a type of graph that displays the relationship between two variables. Each data point in the scatter plot represents a pair of values for the two variables being plotted, with one variable on the x-axis and the other on the y-axis. Scatter plots are used to examine the correlation or relationship between the variables. If the points on the scatter plot form a pattern that slopes upwards as you move from left to right, it indicates a positive linear association between the variables. If the pattern slopes downwards, it indicates a negative linear association. If there is no pattern or trend, it indicates no correlation between the variables.
Here,
A scatter plot that shows a positive linear association is one where the points on the graph form a pattern that goes upward and to the right.
In option A, the data points do not show a clear upward trend, so this scatter plot does not show a positive linear association.
In option B, there is a clear upward trend in the data points as you move from left to right, so this scatter plot does show a positive linear association.
In option C, the data points do not show a clear upward trend, so this scatter plot does not show a positive linear association.
In option D, the data points do not show a clear upward trend, so this scatter plot does not show a positive linear association.
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Jordan reads a comic book at a rate of 21 pages in 6 minutes. At this rate, how many pages does he read each minute?
Answer:
x = 3.5 pages per minute
Step-by-step explanation:
We make the relationship
21 pages ------ 6 min
x pages -------- 1 min
So x= (21x1)/(6)
x = 3.5 pages per minute
which integer conversion specifier would display the hexadecimal digit a? a) H b) h c) Xd) x
The integer conversion specifier that would display the hexadecimal digit "a" is "x".
d) x
To display the hexadecimal digit "a" using an integer conversion specifier.
The "x" specifier is used for displaying an integer value in hexadecimal format with lowercase letters (i.e., a, b, c, etc.), while "X" would display the value in uppercase letters (i.e., A, B, C, etc.).
Options "H" and "h" are not standard integer conversion specifiers for displaying hexadecimal values.
Hence d) x is correct.
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Ryan has 2,000 grams of Flerovium-289, which has a half life of 30 seconds. Use
the formula y = ab* to figure out how much Flerovium-289 you will have after
5 minutes. (Hint: x is the the total number of half lives in 5 minutes)
(.5)_
a.) 62.5 grams
b.) 1.95 grams
c.) 353.55 grams
d.) 1,000 grams
y =____
Which of the following sets of parametric equations represents (x - 1)2 + (y + 4)2 = 9?
the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:
x = 1 + 3 cosθ
y = -4 + 3 sinθ
How to the sets of parametric equation?( x -1)^2 = (r cosθ)^2
x - 1 = r cosθ
= 3 cosθ
x = 1 + 3 cosθ
y + 4 = 3 sinθ
= y = -4 + 3 sinθ
There, the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:
the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:
x = 1 + 3 cosθ
y = -4 + 3 sinθ
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The question is incomplete, see missing part in the attached image.
A company is designing a new cylindrical water bottle. The volume of the bottle will be 220 cm cubed 3. The height of the water bottle is 8. 9 cm. What is the radius of the water bottle? Use 3. 14 for π
The radius of the cylindrical water bottle is approximately 2.34 cm.
The company designing the water bottle has given us the volume of the bottle, which is 220 cm³, and the height of the bottle, which is 8.9 cm. We can use the formula for the volume of a cylinder to relate the radius, height, and volume of the water bottle. The formula is:
Volume of a cylinder = π × radius² × height
We are given the volume of the cylinder as 220 cm³ and the height as 8.9 cm, so we can substitute these values into the formula to get:
220 = π × radius² × 8.9
To solve for the radius, we need to isolate it on one side of the equation. We can start by dividing both sides by π × 8.9:
220 ÷ (π × 8.9) = radius²
Now, we can take the square root of both sides to find the value of the radius:
√(220 ÷ (π × 8.9)) = radius
Using 3.14 for π, we can simplify the expression to get:
radius ≈ 2.34 cm
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The price of the daily dinner special at Deb’s Dinner increases from $7.00 to $8.75. By what percent does the price of the dinner special increase?
The percent increase for the dinner is 25%
The first step is to calculate the increase
The price rose from $7 to $8.75
Increase= 8.75-7
= 1.75
Therefore the percent increase can be calculated as follows
1.75/7 × 100
= 0.25 × 100
= 25
Hence the percent increase is 25%
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Please answer the questions in the picture below and show work
The value of the variables as identified from the reciprocal function are;
a = 5
h = -6
k = 7
2. The correct option is Option A
What is a reciprocal function?A reciprocal function is a mathematical function that can be represented as f(x) = 1/x, where x ≠ 0.
The graph of a reciprocal function is a hyperbola with two branches that approach the x and y axes, but never touch them.
From the information given, we have the function as;
y = a/x - h + k
Given that the function with numbers is written as;
y = 5/x + 6 + 7
To determine the values of a, h and k, we get;
The variable, a = 5
The variable, k = 7
The variable, h = -(6) = -6
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The diameter of a circle is 170 inches. The circle has two chords of length 26 inches. What is the distance from each chord to the center of the circle?
the distance from each chord to the center of the circle is 85 inches.
what is chord ?
In geometry, a chord is a line segment that connects two points on the circumference of a circle. It is the straight line that intersects a circle at two points. In other words, a chord is a line segment that lies entirely inside the circle and connects two points on the circle.
In the given question,
If we draw a diagram of the circle with diameter 170 inches, we can see that the chords of length 26 inches divide the circle into two regions. We are interested in finding the distance from each chord to the center of the circle.
To solve this problem, we can use the following formula:
distance from chord to center = 1/2 * √(4r² - c²)
where r is the radius of the circle and c is the length of the chord.
First, we need to find the radius of the circle. The radius is half of the diameter, so:
r = 1/2 * diameter = 1/2 * 170 = 85 inches
Next, we can use the formula above to find the distance from each chord to the center of the circle. Plugging in the values we have:
distance from chord to center = 1/2 * √(4r² - c²)
distance from chord to center = 1/2 * √(4(85)² - 26²)
distance from chord to center = 1/2 * √(28,900)
distance from chord to center = 1/2 * 170
distance from chord to center = 85
Therefore, the distance from each chord to the center of the circle is 85 inches.
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10. Jill's bank statement shows a balance of $539.22. Checks outstanding were #841 for $29.67, #843 for $89.02, and #844 for $9.76. A $130 deposit was outstanding. Reconcile Jill's bank statement.
Answer:
Step-by-step explanation:
539.22 dollars
In circle H with m/GHJ = 46 and GH = 4 units find area of sector GHJ. Round
to the nearest hundredth.
G
1
H
rann
Area of sector GHJ ≈ 2.04 square units
Area of sector calculation.
Since we are given the central angle GHJ in degrees and the radius GH of circle H, we can find the area of sector GHJ using the formula:
Area of sector GHJ = (θ/360) × πr^2
where θ is the central angle in degrees and r is the radius.
Substituting the given values, we get:
Area of sector GHJ = (46/360) × π(4)^2
= (0.1278) × 16π
= 2.0448 square units
Rounding to the nearest hundredth, we get:
Area of sector GHJ ≈ 2.04 square units
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A useful computational shortcut for the ANOVA test is expressed asa. dfw = dfb + SST
b. SSB SSW-SST
c. SST = SSB/SSW
d. SSW SST-SSB
The correct answer is (b). SSB = SST - SSW
The ANOVA (analysis of variance) test is a statistical method used to compare the means of two or more groups. One useful computational shortcut for this test is expressed as SSB = SST - SSW, where SSB is the sum of squares between groups, SST is the total sum of squares, and SSW is the sum of squares within groups.
The useful computational shortcut for the ANOVA test is expressed as:
SSB = SST - SSW
where SSB is the sum of squares between groups, SST is the total sum of squares, and SSW is the sum of squares within groups.
Option (b) is the closest, but it has a typo. It should be:
SSB = SST - SSW
Therefore, the correct answer is (b).
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The useful computational shortcut for the ANOVA test is SSW = SST - SSB
therefore,option d. SSW = SST - SSB is correct.
ANOVA (Analysis of Variance) is a statistical test used to analyze differences between group means.
The test involves partitioning the total variation into two components:
variation between groups (SSB, sum of squares between) and variation within groups (SSW, sum of squares within).
The total sum of squares (SST) represents the overall variability in the dataset.
The computational shortcut for ANOVA states that the sum of squares within groups (SSW) can be calculated by
subtracting the sum of squares between groups (SSB) from the total sum of squares (SST).
So, SSW = SST - SSB.
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.
5
one fifth
12
one twelfth
A population has a mean μ=71 and a standard deviation Ï=20. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=249.
The mean and standard deviation of a sampling distribution of sample means with sample size 249 are 71 and approximately 1.267 respectively when the population has a mean of 71 and standard deviation of 20.
We know that, if the population has mean [tex]=\mu[/tex] and standard deviation [tex]=\sigma[/tex] and if the sampling distribution has sample size of n then
mean of the sampling distribution will be [tex](\mu_{\bar{x}})=\mu[/tex]
and the standard deviation of sampling distribution will be [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}[/tex]
Here in this problem,
Mean of the population [tex](\mu)[/tex] = 71
Standard Deviation of the population [tex](\sigma)[/tex] = 20
And the sample size of the sampling distribution (n) = 249
So, the mean of sampling distribution [tex](\mu_{\bar{x}})=\mu[/tex] = 71
Standard Deviation of sampling distribution [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{249}} \approx 1.267[/tex] (Correct up to three decimal places)
Hence, the mean and standard deviation of the sampling distribution of sample means with sample size 249 are 71 and 1.267 (approximately) respectively.
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messages are sent over a communications channel using two different signals. one signal requires 2 microseconds for transmittal, and the other signal requires 3 microseconds for transmittal. each signal of a message is followed immediately by the next signal. a) find a recurrence relation for the number of different signals that can be sent in n microseconds. b) what are the initial conditions of the recurrence rela?tion in part (a)? c) how many different messages can be sent in 12 microseconds?
a) A recurrence relation, aₙ = aₙ₋₂ + aₙ₋₃
is for the different signals that can be sent in n microseconds.
b) Initial conditions are a₀ = 0, a₁ = a₂ = 1
c) The number of messages sent in 12 microseconds are equal to 16.
A recurrence relation is an equation form for nth term of a sequence of numbers which is equal to some combination of the previous terms. We have a messages are sent over a communications channel using two different signals. Let an be different number of messages that can be transmitted in n microseconds. In case of First signal, it required 2 microsecondes time to tramissmit the signals. So, the different number of signals that can be transmitted in 2 microseconds are [tex]a_{n - 2} [/tex]
In case of second signal , Time required by second signal to to transmit signal = 3
microsecondes
So, different number of messages that can be transmitted in 3 microseconds are
[tex]a_{n - 3} [/tex]
Each signal of a message is transmitted one by one.
a) A recurrence relation for the number of different signals that can be sent in n microseconds is written as
[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]
hat is an us sum of different signals transmitted by each signals.
b) recurrence relation is
[tex]a_n = a_{n - 2} + a_{n - 3}[/tex]
so, the initial conditions of the recurrence relation in part (a) is n = 3 , [tex]a_3 = a_1 + a_0 [/tex]
a₀ = 0, a₁ = 1 , a₂ = 1
c) Different messages can be sent in 12 microseconds is determined by plugging the value in recurrence relation, a₃
= a₁ + a₀ = 1 + 0 = 1
a₄ = 1 + 1 = 2
a₅ = 1 + 1 = 2
a₆ = 2 + 1 = 3
a₇ = 2 + 2 = 4
a₈ = 3 + 2 =5
a₉= 4 + 3 = 7
a₁₀= 5 + 4 = 9
a ₁₁ = 7 + 5 = 12
a₁₂ = 9 + 7 = 16
Hence, required value is 16.
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The angle of elevation to a nearby tree from a point on the ground is measured to be 32^{\circ}
∘
. How tall is the tree if the point on the ground is 71 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
The height of the tree is 44.4 feet.
What is height?Height is the vertical distance between two points.
To calculate the height of the tree, we use the formula below
Formula:
h = dtan∅.................... Equation 1Where:
h = height of the treed = Distance from the point on the ground to the tree∅ = Angle of elevationFrom the question,
Given:
d = 71 feet∅ = 32°Substitute these values into equation 1
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Does tripling the length of time for the investment double the interest earned with
compound?
No, tripling the length of time for the investment does not double the interest earned with compound interest.
Explaining if tripling the length double the interestWhen interest is compounded, the interest earned depends not only on the length of time, but also on the interest rate and the number of compounding periods.
For example, if an investment of $100 earns 5% annual interest compounded annually for 1 year, the interest earned would be:
Interest = $100 x 0.05 = $5
If the same investment is compounded for 2 years instead of 1, the interest earned would be:
Interest = $100 x (1 + 0.05)^2 - $100 = $10.25
As we can see, doubling the length of time for the investment does not double the interest earned with compound interest.
The interest earned depends on the interest rate and the number of compounding periods as well.
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Y'all I really need some help here. 100 points.
Answer:
42 degrees
Step-by-step explanation:
So, first to find <QUT, which is a vertical angle, we have to figure out either QUR or TUS. So:
9x+3=11x-27
solve for x:
x=15
Then, plug it into one of the equations. Let's use 9x+3.
9(15)+3=138
So, we know that QUR is 138 degrees.
That means that TUS is ALSO 138.
138x2=276
Now we know that QUT and RUS have to equal whatever 360-276 is:
360-276=84
QUT and RUS have to equal 84 degrees, so we DIVIDE by 2.
84/2=42
So, QUT=42 degrees
Answer:
42 Degrees
Step-by-step explanation
Becuase (11x-27) and (9x+3) are vertical angles that means they are equal to each other
(11x - 27) = (9x + 3)
First you will add 27 to both sides
11x -27 = 9x +3
+27 +27
Making it to:
11x = 9x + 30
Now you need to subtract 9x from both sides
11x = 9x +30
-9x -9x
Turning it into this
2x= 30
Now Lastly, divide both sides by 2
2x = 30
2x 2x
And the answer is...... X=15
Now that you have the x value, we go back to the 11x-27 and replace the X with 15
11(15) -27 = 138 degress
Now because angle QUT and 138 degrees make a straight line that means together they will be 180 degress so you will subtract 180 by 138
Giving you the final answer of
42 Degrees
find the antiderivative:x/square root of x
The antiderivative of f(x) = x/√x is [tex](2/3)x^{3/2} + C[/tex],
where C is the constant of integration.
To find the antiderivative of the given function.
The function is: f(x) = x/√x
First, let's rewrite the function in a more convenient form for integration:
f(x) = x / √x
[tex]= x / x^{1/2}[/tex]
[tex]= x^{1 - 1/2}[/tex]
[tex]= x^{1/2}[/tex]
Now, let's find the antiderivative using the power rule for integration:
∫[tex]x^{1/2} dx[/tex]
To apply the power rule, we need to add 1 to the exponent and then divide by the new exponent:
Antiderivative = [tex](x^{(1/2) + 1)) / ((1/2) + 1} ) + C[/tex]
Antiderivative =[tex](x^{3/2/ 3/2} + C)[/tex]
Finally, multiply by the reciprocal to simplify the expression:
Antiderivative = [tex](2/3)x^{3/2} + C.[/tex].
An antiderivative, also known as an indefinite integral, is a function that, when differentiated, yields a given function. In other words, an antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x).
For example, if f(x) = 2x, then an antiderivative of f(x) would be F(x) = x^2 + C,
where C is a constant of integration.
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One angle of a parallelogram measures 37°. What are the measures of the other three angles in the parallelogram?
The measures of the other two angles in the parallelogram are both 143 degrees.
what is a parallelogram?A parallelogram is a quadrilateral with two sides that are parallel to one another. A parallelogram has equal-length opposite sides and equal-length opposite angles. The internal angles that are extra to the transversal on the same side. A parallelogram's total interior angles add up to 360 degrees.
A parallelogram is formed by the junction of two parallel lines, and its opposite angles are equal.
Then, there are two 35 degree angles. Two further angles that are equivalent are noted: A parallelogram's angles add up to 360 degrees. Following that, x+x+37+37=360
2x=360-74
2x=286
x=143.
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