Answer:
Peter opens an account with a $600 deposit that earns 8% simple interest annually. He makes no other deposits or withdrawals.
Complete the sentences:
This situation can be modeled by a linear function that grows in interest.
Peter will earn $48 in interest each year.
Explanation:
Simple interest is calculated as a percentage of the principal amount and does not compound over time. Therefore, the amount of interest earned each year is constant, and the growth of the account is linear.
To calculate the amount of interest earned each year, we multiply the initial deposit by the interest rate:
$600 x 0.08 = $48
Therefore, Peter will earn $48 in interest each year. After four years, he will have earned:
4 x $48 = $192
So his total balance will be:
$600 + $192 = $792
Since the growth of the account is linear, we can model it with a linear function of the form:
y = mx + b
Where y is the total balance, x is the number of years, m is the slope (or rate of growth), and b is the initial balance.
In this case, the slope is the amount of interest earned each year, which is $48, and the initial balance is $600. So the linear function that models this situation is:
y = 48x + 600
Find the length of each segment.
12. AB and AC
Applying the Angle Bisector Theorem, the length of the segments are:
AB = 15; AC = 20.
What is the Angle Bisector Theorem?The Angle Bisector Theorem states that in a triangle, if a line segment bisects an angle of the triangle and intersects the opposite side, then it divides that side into two segments that are proportional to the lengths of the other two sides of the triangle.
Therefore, we would have the following equation based on the angle bisector theorem:
5y/8 = 4y - 1 / 6
Cross multiply:
8(4y - 1) = 6(5y)
32y - 8 = 30y
32y - 30y = 8
2y = 8
y = 4
AB = 4y - 1 = 4(4) - 1 = 15
AC = 5y = 5(4) = 20
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This table contains equivalent ratios between x and y
——————-
x
1
3
7
——————-
y
5
15
25
35
The missing values in the table that contains the equivalent ratios between X and Y would be = 5
What is an equivalent ratio?An equivalent ratio is defined as the constant that exists between two different numbers when compared.
The figures in the table is as follows:
X= 1 3 ? 7
y = 5 15 25 35
If X = 1 when y = 5, X= ? when y= 25
That is;
1 =5
?= 25
? = 25/5 = 5
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8.G.B.6
The better definition of squares is
A number multiplied by itself.
What is square?
In mathematics, a square is a number that is obtained by multiplying a number by itself. It is also a geometric shape with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for calculating the area of a square is A = s^2, where A is the area and s is the length of one side.
Squares have many important applications in mathematics, including in algebra, geometry, trigonometry, and calculus. They are used in the Pythagorean theorem, which relates to the sides of a right triangle, and they are used to represent variables in algebraic equations. Squares are also important in geometry, where they are used to construct geometric shapes and to calculate their areas and perimeters.
The better definition of squares is:
A number multiplied by itself.
In mathematics, a square refers to the product of a number multiplied by itself. For example, the square of 4 is 16, because 4 multiplied by 4 equals 16. Squares have a variety of important applications in mathematics, including in geometry, algebra, and calculus.
While a result that has been proved to be true is sometimes referred to as a "square" in certain contexts, it is not the primary definition of the term. Similarly, a triangle with a right angle is referred to as a "right triangle" or a "right-angled triangle," but not a square.
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the radius of the apple increases 1/8 inch per week for the next five weeks. how does the volume change during the five-week period?
the volume of the apple would increase by ΔVtotal over the five-week period
The volume of the apple is directly proportional to the cube of its radius. Therefore, if the radius increases by 1/8 inch per week for five weeks, the total increase in radius would be 5/8 inches.
To calculate the change in volume, we can use the formula V = (4/3)πr^3.
Initially, let's assume the radius of the apple is r.
After the first week, the radius would be r + 1/8 inches. Therefore, the new volume would be:
[tex]V_1 = (4/3)\pi(r + 1/8)^3[/tex]
To calculate the change in volume, we can subtract the initial volume from the new volume:
[tex]\DeltaV_1 = V_1 - V_0[/tex]
where V0 is the initial volume of the apple.
Similarly, after the second week, the radius would be r + 2/8 inches, and the new volume would be:
[tex]V2 = (4/3)\pi(r + 2/8)^3[/tex]
The change in volume after the second week would be:
ΔV2 = V2 - V1
We can repeat this process for the remaining three weeks and find the total change in volume by adding all the individual changes:
ΔVtotal = ΔV1 + ΔV2 + ΔV3 + ΔV4 + ΔV5
By simplifying this equation, we get:
[tex]\Delta V_{total }= (4/3) \pi r^3[(r + 1/8)^3 + (r + 2/8)^3 + (r + 3/8)^3 + (r + 4/8)^3 + (r + 5/8)^3 - 5r^3][/tex]
Therefore, the volume of the apple would increase by ΔVtotal over the five-week period.
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The volume of the apple will increase by [tex](4/3)π[(r0 + 5/8)^3 - r0^3][/tex] during the five-week period.
Assuming that the apple is a perfect sphere, we can use the formula for the volume of a sphere:
[tex]V = (4/3)πr^3[/tex]
where V is the volume of the sphere and r is the radius of the sphere.
Let's start by finding the initial volume of the apple. We are not given the initial radius, so let's assume it to be r0.
[tex]V0 = (4/3)πr0^3[/tex]
After one week, the radius increases by 1/8 inch, so the new radius is r1 = r0 + 1/8. The new volume is:
[tex]V1 = (4/3)π(r0 + 1/8)^3[/tex]
After two weeks, the radius increases by another 1/8 inch, so the new radius is r2 = r0 + 2/8. The new volume is:
[tex]V2 = (4/3)π(r0 + 2/8)^3[/tex]
Similarly, after three weeks, the new radius is r3 = r0 + 3/8 and the new volume is:
[tex]V3 = (4/3)π(r0 + 3/8)^3[/tex]
After four weeks, the new radius is r4 = r0 + 4/8 and the new volume is:
[tex]V4 = (4/3)π(r0 + 4/8)^3[/tex]
Finally, after five weeks, the new radius is r5 = r0 + 5/8 and the new volume is:
[tex]V5 = (4/3)π(r0 + 5/8)^3[/tex]
To find how the volume changes during the five-week period, we need to subtract the initial volume from the final volume:
ΔV = V5 - V0
[tex]ΔV = (4/3)π(r0 + 5/8)^3 - (4/3)πr0^3[/tex]
Simplifying this expression, we get:
[tex]ΔV = (4/3)π[(r0 + 5/8)^3 - r0^3][/tex]
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The population of your town is about 30,000. This is about 1/10 the population of your friend’s town about what is the population of your friend’s town?
The population of your friend's town is 300,000 if the population of your town is about 30,000.
To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.
If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.
So, the population of your friend's town is
30,000 x 10 = 300,000
Therefore, your friend's town has a population of about 300,000.
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Rewrite in simplest terms: − 0. 4 ( − 6 g − 9 h ) − 2 h − 0. 2 ( − 5 h + 3 g ) −0. 4(−6g−9h)−2h−0. 2(−5h+3g)
The value of the given expression -0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g ) in the simplest form is equal to 1.8g + 2.6h.
The expression is equal to,
-0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g )
Apply distributive law multiplication over addition.
A ( B + C ) = A × B + A × C
Simplify the expression by first distributing the -0.4 and -0.2 coefficients to the terms inside the parentheses,
= (-0.4 × -6g + 0.4 × 9h ) -2h - ( 0.2 × -5h + 0.2 × 3g )
= 2.4g + 3.6h - 2h + h - 0.6g
Combine like terms,
= (2.4g - 0.6g) + (3.6h - 2h + h)
= 1.8g + 2.6h
Therefore, the simplest form of the expression is 1.8g + 2.6h.
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The above question is incomplete, the complete question is:
Rewrite in simplest terms:
− 0. 4 ( − 6 g − 9 h ) − 2 h − 0. 2 ( − 5 h + 3 g )
the inequality 4/5-1/2p>9/5 is givin. solve the inequality for p
Answer:
p < -2
Step-by-step explanation:
Answer:
The answer is -2
Step-by-step explanation:
4/5-1/2p>9/5
C.L.T
-1/2p>9/5-4/5
-1/2p>5/5
-1/2p=1
-p/2>1
-p=2
p= -2
what is the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin?0.14260.13570.24610.0321
The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.
Option C is correct
The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is given by the binomial probability formula:
P(X = k) = (n choose k) [tex]* p^k * (1-p)^(n-k)[/tex]
where X is the random variable representing the number of heads, n is the total number of coin flips, k is the number of heads obtained, and p is the probability of getting a head on any individual flip.
Since we are assuming that the coin is fair, p = 0.5. Let's say you flipped the coin n times and obtained k heads. Then the probability of obtaining exactly k heads with a fair coin is:
P(X = k) = (n choose k [tex]* 0.5^k * ()1-0.5)^(n-k)[/tex]
We don't know what n or k are, so we can't compute the exact probability. However, we can use the fact that the coin is fair to get an estimate. If we assume that the number of heads obtained is roughly half of the total number of flips, then k = n/2. Plugging this into the formula, we get:
[tex]P(X = n/2) = (n choose n/2) * 0.5^(n/2) * (1-0.5)^(n/2)[/tex]
Simplifying this expression, we get:
[tex]P(X = n/2) = (n choose n/2) * 0.5^n[/tex]
Now, we want to find the probability of obtaining exactly as many heads as we just obtained. Let's say we flipped the coin 10 times and obtained 5 heads. Then we want to find P(X = 5), which is:
P(X = 5) = (10 choose 5) [tex]* 0.5^5 * (1-0.5)^(10-5)[/tex] = 0.2461
Therefore, the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.
Option C is correct
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Which parent function is represented by the table? A √x) = x² B. f(x) = |x| C. f(x) = x. D. f(x) = 2^x
The parent function which is represented by the given table as required in the task content is; Choice B. f(x) = |x|.
Which answer choice represents the parent function of the table?It follows from the task content that the parent function which is represented by the table is to be determined.
On this note, by observation of the function; the values of y represent the positive version of x.
Consequently, it follows that the table represents the absolute value function.
Therefore, Choice B; f(x) = |x| is correct.
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act scores have a mean of 21.4 and 15 percent of the scores are above 26 . the scores have a distribution that is approximately normal. find the standard deviation. round your answer to the nearest tenth, if necessary.
The standard deviation of the ACT scores is approximately 4.2.
What is Standard deviation?Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.
According to the given information:
To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.
Given:
Mean (μ) = 21.4
Percentage of scores above 26 = 15%
Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.
Z-score formula:
Z = (X - μ) / σ
Where:
Z = Z-score
X = Value (in this case, 26)
μ = Mean (21.4)
σ = Standard deviation (to be found)
We can rearrange the formula to solve for σ:
σ = (X - μ) / Z
Substituting the given values:
X = 26
μ = 21.4
Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)
Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:
σ = (26 - 21.4) / 1.04
σ = 4.4 / 1.04
σ ≈ 4.2 (rounded to the nearest tenth)
So, the standard deviation of the ACT scores is approximately 4.2.
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Can anyone help me please
Answer:
25
Step-by-step explanation:
Add. Express your answer in simplest form. 2/5 + 5/6
A. 1/3
B. 7/11
C. 7/30
D. 1 7/30
Answer:
d. 1 7/30...............
Answer:
D
Step-by-step explanation:
2/5 + 5/6
Make the denominator same
(2×6)/30 + (5×5)/30
12+25/30
37/30
1 7/30
discuss possible sources of measurement error in this experiment. are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
The "possible-sources" of in the measurement error of an experiment are Instrument error, Human error, sampling error and environmental factors, these sources "may" or "may-not" be enough to account for the percent differences calculated from the data.
There are several possible sources of "measurement-error" in an experiment which affect the accuracy and precision of the results.
These sources include instrument error, human error, environmental factors, and sampling error.
(i) "Instrument-Error" : is defined as inaccuracies in the measuring instruments used in the experiment. This include issues such as calibration errors, sensitivity of the instruments.
(ii) "Human-Error" can arise from mistakes made by experimenters during data collection or analysis, such as misreading measurements or recording data incorrectly.
(iii) "Environmental-Factors", such as temperature, humidity, or electromagnetic interference, can also cause error into experiment if they affect performance of measuring instruments.
(iv) "Sampling-Error" occur when a subset of the population is used for the experiment, and the results are generalized to the entire population.
Depending on the magnitude of these sources of error, they may or may not be enough to account for the percent differences calculated from the data.
If the measurement errors are small and within an acceptable range for the experiment, they may not significantly impact the results.
If the errors are large or systematic, they can introduce significant bias into the data and affect the percent differences calculated.
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The given question is incomplete, the complete question is
Discuss the possible sources of measurement error in an experiment. Are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
write in expanded form
2d with an exponent of -5
The expanded form of 2d with an exponent of -5 is 32d⁵
How to solve exponents?2d with an exponent of -5
[tex] {(2d)}^{ - 5} [/tex]
[tex] = \frac{1}{ {(2d)}^{5} } [/tex]
expand
[tex] = \frac{1}{2d \times2d \times2d \times2d \times2d } [/tex]
[tex] = {32d}^{5} [/tex]
Therefore, 2d with an exponent of -5 is 32d⁵
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A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below. Firework B is launched 0.25 s before
Firework A. How many seconds after Firework B launches will both fireworks explode?
Firework A: 300 ft/s
Firework B: 280 ft/s
Both fireworks will explode seconds after
Firework B launches.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
The fireworks will explode after 1.125 seconds of launching Firework B.
How to find when the fireworks will explode?Distance = Speed × time
Let time = t
Firework A:
[tex]D(t) = 360t - - - (1)[/tex]
Firework B:
[tex]D(t) = 280(0.25) + 280t[/tex]
[tex]D(t) = 70 + 280t - - - (2)[/tex]
Equate 1 and 2 :
[tex]360t = 280t + 70[/tex]
Collection of like terms
[tex]360t - 280t = 70[/tex]
[tex]80t = 70[/tex]
[tex]t = 70/80[/tex]
[tex]t = 0.875 seconds[/tex]
[tex]0.875 + 0.25 = 1.125 seconds[/tex]
Therefore, the fireworks will explode after 1.125 seconds of launching Firework B.
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Solve for X. I don’t know how to solve
The value of x is approximately 10.57 and the value of y is approximately 15.25.
Describe Chords?In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.
The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.
In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:
105 + (7y + 1) + (7x + 1) + (4y + 14) = 180
Simplifying and solving for x and y, we get:
7x + 4y + 122 = 180
7x + 4y = 58 ......(1)
Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:
105 + (4y + 14) = 180 ......(2)
(7y + 1) + (7x + 1) = 180 ......(3)
Simplifying and solving for y in equation (2), we get:
4y + 119 = 180
4y = 61
y = 15.25
Substituting this value of y in equation (3) and solving for x, we get:
(7x + 1) + (7*15.25 + 1) = 180
7x + 106 = 180
7x = 74
x = 10.57
Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.
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which model represents the factors of x2 9x 8? an algebra tile configuration. 7 tiles are in the factor 1 spot: 1 is labeled x and 6 are labeled . 4 tiles are in the factor 2 spot: 1 is labeled x and 3 are labeled . 28 tiles are in the product spot: 1 is labeled x squared, 9 are labeled x, 9 are labeled , and 9 are labeled negative.
The product of 7 and 4 is 28, which is equal to the number of tiles in the product area.
Therefore, this configuration represents the factors of the quadratic expression [tex]x^2 + 9x + 8.[/tex]
To represent the factors of the quadratic expression x^2 + 9x + 8 using algebra tiles, we need to arrange the tiles into two rectangular areas representing the two factors, and the total number of tiles in the product area should be equal to the product of the number of tiles in each factor area.
Based on the information given, we can arrange the tiles as follows:
Factor 1 area: 7 tiles, with 1 x-tile and 6 blank tiles (represented by underscores):
Copy code
x
_
_
_
_
_
_
Factor 2 area: 4 tiles, with 1 x-tile and 3 blank tiles (represented by underscores):
Copy code
x
_
_
_
Product area: 28 tiles, with 1 x^2-tile, 9 x-tiles, 9 negative tiles (represented by red tiles), and 9 blank tiles (represented by underscores):
Copy code
x^2 - - -
x x x x
_ _ _ _
_ _ _ _
_ _ _ _
_ _ _ _
_ _ _ _
To check that this configuration represents the given quadratic expression, we can count the number of tiles in each area and verify that the product of the two factors equals the number of tiles in the product area:
Factor 1 area: 7 tiles
Factor 2 area: 4 tiles
Product area: 28 tiles.
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Question # 5
Question # 6
Question # 7
Question # 8
Question # 9
Question # 10
Question # 11
Answer: question#7 is 7/12
question#8 is 1 3/8
question#5 is 1/2
question#6 is 12
question#9 is 1 1/6
question#10 is 31/40
question#11 is 3/4
Step-by-step explanation: give brainliest
Question #5: Option A, [tex]\frac{1}{2}[/tex]
Question #6: Option A, 12
Question #7: Option A, [tex]\frac{7}{12}[/tex]
Question #8: Option D, [tex]1\frac{3}{8}[/tex]
Question #9: Option D, [tex]1\frac{1}{6}[/tex]
Question #10: [tex]\frac{31}{40}[/tex]
Question #11: [tex]\frac{3}{4}[/tex]
Pls mark brainliest
laptop: $199.99, 13% markup what is the markup
Answer:
≈ $26
Step-by-step explanation:
13% = 0.13
199.99 x 0.13 = $25.9987
So, 13% markup is ≈ $26
Zain's current credit card balance is $9,160.00 with a minimum payment of $325.00. Over the next month he spends $1,098.00. If the APR is 18.99% (billed monthly), what will the new balance be, including interest?
Answer: To find the new balance including interest, we need to take into account the interest charged on the current balance and the new purchase.
First, let's calculate the interest charged on the current balance. The monthly interest rate is 18.99% / 12 = 1.5825%.
The interest charged on the current balance is therefore:
interest on current balance = 0.015825 * 9160.00 = 144.98
So the total balance including interest for the current month is:
current balance including interest = 9160.00 + 144.98 = 9304.98
Next, let's calculate the interest charged on the new purchase of $1,098.00. The interest charged on the new purchase is:
interest on new purchase = 0.015825 * 1098.00 = 17.39
So the total balance including interest for the new purchase is:
new balance including interest = 1098.00 + 17.39 = 1115.39
Finally, we add the current balance including interest and the new balance including interest to get the total balance including interest:
total balance including interest = current balance including interest + new balance including interest
total balance including interest = 9304.98 + 1115.39
total balance including interest = 10420.37
Therefore, the new balance including interest is $10,420.37.
Step-by-step explanation:
what number is the greatest common factor of 90 and 315 divided by the least common multiple of 5 and 15?
The greatest common factor of 90 and 315 when divided by the least common multiple of 5 and 15 is 45.
When we multiply all the common prime factors, we get the greatest common factor of the numbers.
These prime factors should come from the prime factorization of the numbers given. These should be in all the unique combinations possible.
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(15 POINTS) HELP ASAP TY!!
How are solving systems of two linear equations or inequalities and solving systems of two quadratic equations or inequalities alike? How are they different?
Ten seventh graders and 15 eighth graders were selected for the elite choir ensemble.
a. Write the ratio of seventh graders to eighth graders who were selected for the
elite choir.
b. Write the ratio of seventh graders to total students who were selected for the
elite choir.
c. Write the ratio of eighth graders to total students who were selected for the elite
choir.
Answer:
Your answer should be A
HELPP PLS ILL MARK U BRAINLIST
Maybe 9/12? I counted the amount of times 6 or 9 shows up on the graph. :D. Hope that helps.
a teacher wants to see if a new unit on factoring is helping students learn. she has five randomly selected students take a pre-test and a post test on the material. the scores are out of 20. has there been improvement? (pre-post) what value of t would you use for the 90% confidence interval? student 1 2 3 4 5 pre-test 12 14 11 12 13 post- test 15 17 15 20 13 group of answer choices 2.776 2.132 4.604 3.747 1.645
The paired t-test results suggest that there is no significant improvement in students' learning after the new unit on factoring, based on a 90% confidence level.
How to find the value of t?To determine if there has been an improvement in students' learning after a new unit on factoring, we can perform a paired t-test on the pre-test and post-test scores of the five randomly selected students.
The differences between the pre-test and post-test scores for each student are: 3, 3, 4, 8, 0.
The mean of the differences is 3.6, and the sample standard deviation is 2.39.
The t-value for a 90% confidence interval with 4 degrees of freedom is 2.776. Since the calculated t-value of 2.68 (calculated as the mean of the differences divided by the standard error of the mean of the differences) is less than the critical t-value of 2.776, we fail to reject the null hypothesis that there is no improvement in students' learning.
Therefore, there is not enough evidence to conclude that the new unit on factoring has helped students learn based on the sample data.
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I need help with this please
The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.
Since (5/2)^x is always greater than 0 for any x, the minimum value of f(x) is -5.To find the maximum value of f(x), we can take the limit as x approaches infinity:
lim (x → ∞) (5/2)^x - 5 = ∞ - 5 = ∞Therefore, the range of f(x) is (-5, ∞).TIME SENSITIVE! please help !
Consider the word PENCIL. If all the letters are used, and the first letter can’t be N or L, how many ways can the letters be arranged?
A) 720
B) 480
C) 360
D) 96
The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.
The word PENCIL has 6 letters, here we have to use permutation method. If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,
So there are 5! = 120 ways to arrange them.
Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is
4 x 5! = 4 x 120 = 480
Therefore, the correct option is (B) 480.
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!!!!!!I NEED THIS ASAP!!!!!
Find x,y, and z
Thus, the values of x,y, and z for the similar triangles are obtained:
Part A: y = 6.70; z = 13.41 and x = 6.
Part B: z = 17.88 ; y = 35.77 and x = 32.
Explain about the similarity of the triangle:Congruent triangles and similar triangles are two distinct but closely related concepts. There are two different kinds of similar triangle problems: those that ask you to determine whether a set of triangles is similar and those that ask you to determine the angles and side length of similar triangles that are missing.
Part A: using similarity of the triangle, taking the ratios of corresponding side.
y/15 = x/z = 3/y
Consider
y/15 = 3/y
y² = 15*3
y² = 45
y = 6.70
Now,
applying Pythagorean theorem:
y² = 3² + x²
x² = y² - 3²
x² = 45 - 9
x² = 36
x = 6
And,
z² = 12² + x²
z² = 144 + 36
z² = 180
z = 13.41
Part B:using similarity of the triangle, taking the ratios of corresponding side.
z/(x + 8) = 16/y = 8/x ... eq 1
applying Pythagorean theorem:
z² = 16² + 8²
z² = 256 + 64
z² = 320
z = 17.88
Now, from eq 1
z² = 8(8 +x)
320 = 64 + 8x
8x = 320 - 64
x = 256/8
x = 32
Now,
applying Pythagorean theorem:
y² = 16² + x²
y² = 256 + 32²
y² = 1280
y = 35.77
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In a triangle PQR,the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively.
Thus, the in a triangle PQR, with the sides PQ, QR and PR formed a right angled triangle.
Explain about the Pythagorean theorem:If we know the lengths of two of the sides of a right triangle, we can apply the Pythagorean theorem to determine the third side.
According to the Pythagorean theorem, the hypotenuse squared equals the total of the squared legs. The vertical and horizontal sides, which make a 90° angle, are the legs of a right triangle. The longest side, or hypotenuse, is located on the other side of the right angle.Given data:
Triangle :PQR, PQ = 15 inQR = 20 inand PR = 25 inIN right triangle, the longest side is called the hypotenuse.
So,
hypotenuse H = 25
Now using Pythagorean theorem:
(PR)² = (PQ)² + (QR)²
(25)² = (20)² + (15)²
625 = 400 + 225
625 = 625
LHS = RHS
Thus, the in a triangle PQR, with the sides PQ, QR and PR formed a right angled traingle.
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Complete question:
In a triangle PQR,the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively. prove that triangle PQR, is the right traingle.
The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? Round to the nearest tenth.
1. 460.1 ft
2. 301.9 ft
3. 262.4 ft
4. 459.3 ft