Step-by-step explanation:
We use the power rule a^(x+y) = a^x * a^y:
3^(2x+1) = 3^(2x) * 3
We can re-write 3^(2x) as (3^x)^2, and we know that 3^x = a, so:
3a^2 is the final answer. There is not exact value, it's all just about re-writing.
\(3a^2 \) is a required answer.
Answer:
solution given:
\(3^{2x+1}=? \)
if \( 3^x=a\)
By using power rule, we can write
\(3^{2x+1}\) as
\(3^{2x+1}=(3^x)^2*3^1 \)
\(a^2*3=3a^2 \)
Charles can type 675 words in 9 minutes. How many words can he type per minute?
Group of answer choices
6075 words per minute
75 words per minute
86 words per minute
75 minutes per word
Answer:
675 devided bye 9 = 75
Step-by-step explanation:
Answer: 75 words per minute
Step-by-step explanation:
We can set this problem up similar to a ratio
675:9
Knowing that this is for 9 minutes, dividing by 9 will give you the amount per one minute
675/9 9/9
75:1 or 75 words per minute
Name three collinear points.
Answer:
D, G and F or I, G and J------------------------
Collinear points are the points on the same line.
There are two lines in the diagram.
The collinear points:
D, G and F on one lineI, G and J on the second lineThe points that are collinear are D,G and E and another set of points which are collinear are L,G and J.
The points which lie on the same straight line are known as collinear points.
Similarly, if three or more number of points are collinear then they form a straight line.
If we observe the figure, the points D,G and E are collinear points as they are on same line.
Similarly the points L, G and H are in the straight line which makes them collinear.
Therefore , the points L,G and J are collinear points.
Hence, the points that are collinear are D,G and E and another set of points which are collinear are L,G and J
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What is the GCF of 12, 30, and 18?
Answer:
6
Step-by-step explanation:
Answer: 6
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Then the greatest common factor is 6.
4) Grace has $39. She has $8 less than her
brother. How much money does Grace's
brother have?
Write the equation
Answer:
Grace's brother has $47
Step-by-step explanation:
Just add 8 to 39
Answer:
39+8=47
Step-by-step explanation:
if you know the difference between numbers then you can find the unknown number by adding or subtracting the difference
pleaseee help I have no idea how to do this
Answer: D
Step-by-step explanation: on desmos you put in f(x)= x^2 then try all the options and see which graph resembles g(x)
Work out the equation of the line which has a gradient of ½ and
passes through the point (4, -2).
pls help i will give 10 points to the first person to answer this question
The coordinates of the points on the number line are given as follows:
A = -2/3.B = -1/6.C = 1/2.D = 4/3.How to obtain the coordinates on the number line?Point C is exactly halfway between 0 and 1, hence it's coordinate is given as follows:
C = 0.5.
C is also the third dot between 0 and 0.5, hence the amount represented by each space is given as follows:
0.5/3 = 1/6.
Point B is one space to the left of 0, hence it's coordinate is given as follows:
B = -1/6.
Point A is three spaces to the left of point B, hence it's coordinate is given as follows:
A = -1/6 - 3 x 1/6 = -4/6 = -2/3.
Point D is two spaces to the right of 1, hence:
D = 1 + 2x 1/6 = 1 + 1/3 = 4/3.
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Skyler is out shopping and sees that striped shirts are on sale for
$19.00 each, and plaid pants are on sale for $19.50 each. He
buys 8 shirts and 6 pairs of pants. What is the total of his
purchase?
The total was $_______
Answer:
His total is $269
Step-by-step explanation:
8x19 = 152
6x19.50 = 117
152+117 = 269
Noise in a quiet room is 500 times as intense as the threshold of sound. What is the decibel measurement for the quiet room?
The decibel measurement for the quiet room is 54 dB.
To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.
Next, we can use the formula for decibel measurement:
dB = 10 log (I/I0)
where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.
Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:
dB = 10 log (500/1)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.
To correct this mistake, we need to use the formula for decibel measurement with the correct values:
dB = 10 log (500 * I0/I0)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.
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How many degrees is the measurement of the missing angle? (Only numeric answer, no words or symbols at all)
Answer:
The answer is 135
Step-by-step explanation:
all angles in a triangle equal to 180.
so, 25+22= 45
then, 180-45= 135
the missing angles measure is 135 degrees
hope this helps!
Explain the Pythagorean identity in terms of the unit circle.
The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:
sin² θ + cos² θ = 1
tan² θ + 1 = sec² θ
1 + cot² θ = csc² θ
where angle θ is any angle in standard position in the xy-plane.
Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.
The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.
This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:
c² = a² + b² becomes:
r² = y² + x² = 1²
y² + x² = 1
We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:
(sin θ)² + (cos θ)² = 1
1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.
Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:
(sin² θ + cos² θ)/cos² θ = 1/cos² θ
(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ
(sin θ/cos θ)² + 1 = (1/cos θ)²
(tan θ)² + 1 = (sec θ)²
2.) tan² θ + 1 = sec² θ
Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:
(sin² θ + cos² θ)/sin² θ = 1/sin² θ
(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ
1 + (cos θ/sin θ)² = (1/sin θ)²
1 + (cot θ)² = (csc θ)²
3.) 1 + cot² θ = csc² θ
Question 3
A group of 5 people went to the movies and spent $44 on food and drink. The total amount spent, including
tickets, was $98.50.
What was the price, in dollars, of one ticket?
Answer:
One ticket cost $10.90.
Step-by-step explanation:
The total spent was $98.50--food, drinks, admission--everything.
$44.00 was for food and drinks.
We can take the 44 away from the total.
98.50 - 44.00
= 54.50
They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.
54.50 ÷ 5 = 10.90
The price of one ticket was $10.90
To make this look like algebra class...
let x = the price of one ticket
5x = the price of 5 tickets
5x + 44 = 98.50
subtract 44
5x = 54.50
divide by 5
x = 10.90
Solve for the value of v
Answer:
v = 31
Step-by-step explanation:
The 2 angles are adjacent and lie on a straight line, so sum to 180° , that is
4v - 2 + 2v - 4 = 180
6v - 6 = 180 ( add 6 to both sides )
6v = 186 ( divide both sides by 6 )
v = 31
Our product is 72. The Difference between us is one. What numbers are we?
Answer:
8 and 9
Step-by-step explanation:
8 times 9 is 72
√√96
√8
Ο 213
Ο 4
Ο 222
D. 12
Answer:
2sqr3, the first option
Step-by-step explanation:
A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and $9700 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business has a Poisson distribution with mean 1.5.
Find the expected amount paid to the company under this policy during a one-year period.
Therefore, the expected amount paid to the company under this policy during a one-year period is $4850.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probabilities can be calculated using different methods, depending on the nature of the event and the available information. In many cases, probabilities are estimated based on observations or data, and statistical methods are used to quantify the uncertainty or variability in the estimates. Probability theory is used in many areas of science, engineering, economics, finance, and other fields to model and analyze complex systems and phenomena, make predictions, and make decisions under uncertainty.
Here,
Let X be the random variable that represents the number of major snowstorms that shut down business in a year. Since X has a Poisson distribution with mean 1.5, we have:
P(X = 0) = \(e^{-1.5}\)* (1.5⁰ / 0!)
≈ 0.2231
P(X = 1) = \(e^{-1.5}\) * (1.5¹ / 1!)
≈ 0.3347
P(X = 2) = \(e^{-1.5}\) * (1.5² / 2!)
≈ 0.2510
P(X = 3) = \(e^{-1.5}\) * (1.5³ / 3!)
≈ 0.1255
The expected value of X is E(X) = λ = 1.5, which means the expected number of major snowstorms per year that shut down business is 1.5.
The policy pays nothing for the first snowstorm, so the expected amount paid for the first snowstorm is 0. For each subsequent snowstorm, the policy pays $9700. Therefore, the expected amount paid to the company under this policy during a one-year period is:
E(amount paid) = 0 + 9700 * E(X-1)
= 9700 * (E(X) - 1)
= 9700 * (1.5 - 1)
= $9700 * 0.5
= $4850
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Which equation represents a line passing through the point (8, 33) with a slope of 3?
A. y = 3x – 15
C. y = 3x – 8
B. y = 3x + 33
D. y = 3x + 9
Answer:
Is ka answers D ha.........
Answer:
The answer is D.
Step-by-step explanation:
(8 ,33) = (\(x_{1} , y_{1} )\)
m = 3
To find the equation, use the formula:
y - \(y_{1}\) = m(x - \(x_{1}\))
Put the values in the equation
y - 33 = 3(x - 8)
y - 33 = 3x - 24
Now to get only the y, put the \(y_{1}\)
y - 33 = 3x - 24
33 33
------------------------
y = 3x + 9
The National Assessment of Educational Progress (NAEP) is a nationwide assessment of students’ proficiency in nine subjects: mathematics, reading, writing, science, the arts, civics, economics, geography, and U.S. history. The main NAEP assessments are conducted annually on samples of students from grades 4, 8, and 12.
In 2002, the reading scores for female students had a mean of 269 with a standard deviation of 33. Assume that these scores are normally distributed with the given mean and standard deviation.
Identify the scores that are three standard deviationsabove and below the mean of the population. For this example, the limits will be 269 ± (33)(3). The lower limit is . The upper limit is . The probability that a female student will have a score between these limits is .
A score of 302 is above the mean. As a result, the percentage of female students with scores below 302 is .
You can infer that 97.72% of the female students have scores above .
"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits
To calculate the scores that are three standard deviations above and below the mean, we use the formula:
Lower limit = Mean - (Standard Deviation * 3)
Upper limit = Mean + (Standard Deviation * 3)
Given:
Mean = 269
Standard Deviation = 33
Using the formula, we can calculate the limits:
Lower limit = 269 - (33 * 3) = 269 - 99 = 170
Upper limit = 269 + (33 * 3) = 269 + 99 = 368
Therefore, the lower limit is 170 and the upper limit is 368.
To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.
Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.
For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:
Percentage = (1 - Probability) * 100
= (1 - 0.9972) * 100
= 0.0028 * 100
= 0.28%
Therefore, approximately 0.28% of the female students have scores below 302.
It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits
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Consider 3(4x − 2y − 5).
Which is equivalent to the given expression?
A. 12x − 2y −5
B. 7x −2y − 5
C. 12x − 6y − 15
D. 7x −5y −2
Which expression is equivalent to 18x + 9y − 6?
A. 9(2x − y + 3)
B. 2(9x + 3y − 2)
C. 3(6x + 3y − 2)
D. 9(2x − y + 3)
Answer:
both answers are c ............
May I ask for u to give brainlist?asking if u don't want its ok
Answer:
C
C
Step-by-step explanation:
For number 1:
times everything inside the brackets by 3
For number 2:
find a common factor all the numbers have
In the diagram at right, DE is a midsegment of triangle ABC. If the area of triangle ABC is 96 square units, what is the area of triangle ADE? Explain how you know.
The area of triangle ADE is,
⇒ A = 48 square units
We have to given that,
In the diagram , DE is a midsegment of triangle ABC.
And, The area of triangle ABC is 96 square units
Now, We know that,
Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.
Hence, the area of triangle ADE is half the area of triangle ABC,
That is,
A = 96 / 2
A = 48 square units
Thus, The area of triangle ADE is,
⇒ A = 48 square units
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Let g(x)=x^5+x^4. On which intervals is g decreasing
g(x) is decreasing function on the interval (-4/5, 0).
What is calculus?Calculus is a branch of mathematics that deals with the study of rates of change and the accumulation of small changes to find the overall effect. It provides a framework for modeling and analyzing a wide range of phenomena, from the motion of objects to the behavior of complex systems.
Calculus is divided into two main branches: differential calculus and integral calculus. Differential calculus deals with the study of rates of change, slopes of curves, and the computation of derivatives. Integral calculus deals with the study of accumulation of small changes, computation of areas, and the computation of integrals.
To determine where g(x) is decreasing, we need to find where its derivative is negative.
The derivative of g(x) is:
g'(x) = 5x⁴ + 4x³
To find where g'(x) < 0, we can factor out a common term of x³ to get:
g'(x) = x³(5x + 4)
So, g'(x) < 0 when:
x³ < 0 and 5x + 4 < 0
This condition is not possible, as x³ is never negative.
x³ > 0 and 5x + 4 < 0
This condition is satisfied when -4/5 < x < 0.
Therefore, g(x) is decreasing function on the interval (-4/5, 0).
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2. A bicycling club has 58 members, of which 4 are males and the rest are females. What is the ratio of females to males?
please help is ratio
Answer: 54:4
Step-by-step explanation:
The test scores for a group of students are shown.
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Calculate the five number summary of the data set? Minimum = First Quartile (Q1) = Median = Third Quartile (Q3) = Maximum = What is the interquartile range (IQR) Which test score is an outlier?
60
69
90
100
Answer:
Minimum=60
First Quartile(Q1)=79
Median=86
Third Quartile (Q3)=89
Interquartile range (IQR)=10
Please help I’ll upvote your work and give you brainliest.
The exponential function defined in this problem is given as follows:
y = 81(1/3)^x - 3.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The exponential function in this problem has an horizontal asymptote at y = 3, hence it is defined as follows:
y = ab^x - 3.
When x increases by 1, y is divided by 3, hence the parameter b is given as follows:
b = 1/3.
Hence:
y = a(1/3)^x - 3.
When x = 3, y = 0, hence the parameter a is given as follows:
0 = a(1/3)³ - 3
a/27 = 3
a = 81.
Hence the function is defined as follows:
y = 81(1/3)^x - 3.
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Choose the best selection for the
quadrilateral with vertices at the
following points:
(-3,0), (-3,-3), (0,-3), (0,0)
Hint: Start by graphing the points.
Distance Formula: d = √(x2-x₁)² + (Y2 − ₁)²
A. Trapezoid
C. Rectangle
B. Rhombus
D. Square
Answer:
D. Square
Step-by-step explanation:
You want the best name for the quadrilateral with vertices (-3, 0), (-3, -3), (0, -3), and (0, 0).
GraphA graph of the points is shown in the attachment. We notice the vertices are aligned with the grid, so the corner angles are all right angles.
The differences of x-coordinates and y-coordinates are both 3, so the side lengths of this rectangle are all 3 units.
The figure is all of a rectangle, rhombus, and square.
The most specific name for the figure is Square.
__
Additional comment
A trapezoid has one pair of parallel sides. This figure has two pairs of parallel sides, so is not a trapezoid.
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Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own only a cat?
a) 18
b) 15
c) None of these answers
d) 8
Answer:
c) None of these answers
Step-by-step explanation:
8 students own a cat
In this, we count the students who own both a dog and a cat, and the students who own only a cat.
5 students own both a cat and a dog.
So of the 8 who own a cat, 5 own both a cat and a dog, and 8 - 5 = 3 own only a cat.
So the correct answer is given by option c, as 3 is not an option.
Identify whether each function is linear or exponential.
Function A:
Function C
Function D:
You have $200 in
a savings
account that
earns 1% annual
interest
b. Which function has the greatest growth factor? Justify your response.
Answer:
A)
Function A: Exponential
Function B: Linear
Function C: Exponential
Function D: Exponential
B) Function A
Step-by-step explanation:
Function A: This is exponential because- (1, 3)(2,9)(3,27)
It is not going up by the same number each time. However, it is multiplying by 3 each time which means it is exponential.
Function B: This is linear because- (1, 64)(1, 80)(1, 96)
It is going up by 16 each time, (a constant number) which means it is linear.
Function C: This is exponential because- there is a curve, linear is always a straight line. But, this has a curve which means it is exponential.
Function D: This is exponential because- It is increasing by a percentage and not a constant number. It is increasing by 1% which means it is exponential.
The function that has the greatest growth factor is Function A because, Function A multiplies by 3 each time. Function B is linear, exponential functions always pass linear functions despite how "steep" they are. Eventually, the exponential function will surpass it. Function C is also exponential but is not as "steep" as Function A. Function A multiplies by 3 each time but Function C increases less. Function D is also exponential, and for the same reasons as Function C, Function A has the greatest growth factor.
Write an equation for the function graphed below
The rational function graphed in this problem is defined as follows:
y = -2(x - 1)/(x² - x - 2).
How to define the rational function?The vertical asymptotes of the rational function for this problem are given as follows:
x = -1 and x = 2.
Hence the denominator of the function is given as follows:
(x + 1)(x - 2) = x² - x - 2.
The intercept of the function is given as follows:
x = 1.
Hence the numerator of the function is given as follows:
a(x - 1)
In which a is the leading coefficient.
Hence:
y = a(x - 1)/(x² - x - 2).
When x = 0, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a/2
a = -2.
Thus the function is given as follows:
y = -2(x - 1)/(x² - x - 2).
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4. Lincoln began his speech, “Four score and seven years ago....” How many years is four score and seven? (Hint: A score is 20 years.) Can someone help me?
which of the following shows the proper steps for constructing an angle bisector
Answer:
Hello There!
~~~~~~~~~~~~~~~~~
Your answer would be (B)
Step-by-step explanation:
It is the only one that shows an angle bisector. An angle bisector is a line that split an angle into two.
Hope this helped you! Brainliest would be nice!
☆_____________❤︎______________☆
Answer:
Step-by-step explanation:
Hello there so
n plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.[1] Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.
Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.
The word angle comes from the Latin word angulus, meaning "corner"; cognate words are the Greek ἀγκύλος (ankylοs), meaning "crooked, curved," and the English word "ankle". Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".[2]
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.[3]