The function is d(t) = 6cos(πt/6 + π/4) + 6. It models the water depth in meters as a cosine function of time after midnight.
The amplitude of the cosine curve is the difference between the high and low tide water depths, which is 6 m. The period of the cosine curve is the same as the natural oscillation period, which is 12 hours. The high tide occurred at 4:45 a.m., so the phase shift is π/4.Therefore, the function is d(t) = 6cos(πt/6 + π/4) + 6.The cosine function models the water depth d(t) in meters as a function of time t (in hours after midnight) on a particular day. The amplitude of the cosine curve is the difference between the high and low tide water depths, which is 6 m. The period of the cosine curve is the same as the natural oscillation period, which is 12 hours. The phase shift is π/4, as the high tide occurred at 4:45 a.m. Therefore, the function is d(t) = 6cos(πt/6 + π/4) + 6.
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What is the area of this polygon? 28. 5 units² 34. 5 units² 37. 5 units² 40. 5 units² 6 sided polygon on a coordinate plane with vertices at (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2)
After solving the polygon, the area of this polygon is 34.5 unit². So the option 2 is correct.
an equilateral triangle is a plane shape with at least three straight sides and angles, and usually five or more.
The total length of all the sides equals the perimeter. Apothem is the term for the segment that connects the midpoint of any perpendicular side to any side's midpoint in a polygon.
Let A(-6, -2), B(-5, 1), C(-1, 4), D(1, 1), E(5, 3), and F(1, -2) are the vertices of polygon.
Divide the shape into 3 triangles and 1 rectangle to get 4 separate forms.
Area of a triangle = 1/2 x base x height
Area of rectangle = length x width
Calculate the areas of each of the four forms, then add them.
The area of Shape 1 from the diagram:
Area of shape 1 = 1/2 × 1 × 3
Area of shape 1 = 1.5
Area of shape 2 = 1/2 × 6 × 3
Area of shape 2 = 9
Area of shape 3 = 1/2 × 3 × 4
Area of shape 3 = 6
Area of shape 4 = 3 × 6
Area of shape 4 = 18
Total Area = 1.5 + 9 + 6 + 18
Total Area = 34.5
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The complete question is given below:
Jackie made the same
amount of bracelets for
8 days. Write an expression
for the number of bracelets
made.
Jackie made 12 bracelets each day and the equation used to represent this is 8x = 96. The solution has been obtained using the concept of simplification.
What is simplification?
In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
We are given that Jackie made bracelets for 8 days and when he was done he had 96 bracelets with him.
Let 'x' be the number of bracelets made by Jackie each day
So, we get
⇒8x = 96
⇒x = 96/8
⇒x = 12
Hence, Jackie made 12 bracelets each day and the equation used to represent this is 8x = 96.
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Question: Jackie made bracelets for 8 days. When he was done he had 96 bracelets Write equation to express how many bracelets Jackie made each day.
a tablet pc manufacturer wishes to estimate the proportion of people who want to purchase tablet pcs which cost more than $700. find the required sample size when its 95% error margin is 0.03.
The required sample size when its 95% error margin is 0.03 with 385 samples.
Sample Size RequiredTo estimate the proportion of people who want to purchase tablet PCs that cost more than $700 with a 95% confidence level and an error margin of 0.03, you can use the formula for sample size:
n = (z² * p * (1-p)) / E²
where:
n is the sample sizez is the standard normal deviate (1.96 for a 95% confidence level)p is the proportion of people who want to purchase tablet PCs that cost more than $700 (unknown)E is the error margin (0.03)Since we don't know the proportion of people who want to purchase tablet PCs that cost more than $700, you can use a reasonable estimate or a conservative estimate (e.g., 0.50) in the formula.
n = (1.96² * 0.50 * (1 - 0.50)) / (0.03²)
n = 384.16
The sample size required is 385.
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The figure is made up of a cylinder and a hemisphere.
To the nearest whole number, what is the volume of this figure?
Use 3. 14 to approximate π. Round only your final answer to the nearest whole number.
Enter your answer in the box.
in³
A 7 inch cylinder with a dome on top of it that has a 5 inch diameter
Approximate volume of the figure formed with the cylinder with a dome of hemispherical shape with diameter 5 inch is equal to 170 cubic inch ( nearest whole number ).
Figure attached.
Diameter of the hemisphere = 5 inch
Height of the cylinder 'h'= 7 inch
Radius of the cylinder and hemisphere is same 'r' = 2.5 inch
Volume of the figure
= Volume of the cylinder + volume of the hemisphere
= πr²h + (2/3)πr³
= πr² [h + (2/3)r ]
Substitute the values we get,
= 3.14 ( 2.5 )² [ 7 + (2/3)2.5 ]
= 3.14 (6.25 ) [ 7 + 1.67 ]
= 170.14
= 170 cubic inch ( nearest whole number )
Therefore, the volume of the given figure of the cylinder with dome in hemispherical shape is equal to 170 cubic inch ( nearest whole number ).
The above question is incomplete, the complete question is:
The figure is made up of a cylinder and a hemisphere.
To the nearest whole number, what is the volume of this figure?
Use 3. 14 to approximate π. Round only your final answer to the nearest whole number. Enter your answer in the box in³ .
A 7 inch cylinder with a dome on top of it that has a 5 inch diameter.
Figure is attached.
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shade exactly two of the nine smaller squares so that the resulting figure has a. only one vertical and one horizontal line of symmetry. b. only two lines of symmetry about the diagonals. c. only one horizontal line of symmetry. d. only one line of symmetry about a diagonal. e. no line of symmetry.
The attached figures(a., b., c., d., and e.) define the line of symmetry of the given options.
a) In order to have exactly one vertical and one horizontal line of symmetry, you can shade one square in the first row and one square in the centre column.
b) To have only two lines of symmetry about the diagonals, you can shade two squares that are diagonally opposite from each other.
c) To have only one horizontal line of symmetry, you can shade one square in the centre row.
d) To have only one line of symmetry about a diagonal, you can shade two squares that are on the same diagonal.
e) To have no line of symmetry, you can shade two squares that are not on the same row, column, or diagonal.
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--The given question is incomplete; the complete question is
"Use Figure 2 to answer the problem.
Shade exactly two of the nine smaller squares so that the resulting figure has
a. Only one vertical and one horizontal line of symmetry.
b. Only two lines of symmetry about the diagonals.
c. Only one horizontal line of symmetry.
d. Only one line of symmetry about a diagonal.
e. No line of symmetry."--
Analyzing a Proof Click here to see a proof of the converse of the parallelogram angle theorem. As you read through the proof, look for how to complete the statements on the right. Complete the statements by choosing the correct answer from the drop-down menu. Are being used to get the equation in step 6. Are being used to get the equation in step 8. Are being used to get the equation in step 9. In step 14, "similar argument" means to draw segment and follow the same logic in steps 3-12
The converse of the parallelogram angle theorem is proved.
The term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.
Here we have to prove the the converse of the parallelogram angle theorem.
Here we have given that LM ≅ ON and LO ≅ MN
Here we have also know that ∠LNO and ∠NLM are alternative and interior angles
Where as the angles ∠OLN and ∠MNL are alternative interior angles
Then according to the reflexive property, it can be written as
=> LN ≅ LN
Then as per the SSS similarity the given triangle is written as,
=> ΔLNO ≅ ΔNLM
Here we have also it can be written as
=> ∠OLN ≅ ∠MNL and ∠LNO ≅ ∠NLM
Then it can be written as LM || ON and LO || MN
Then the LMNO is a parallelogram
Complete Question:
Analyzing a Proof Click here to see a proof of the converse of the parallelogram angle theorem. Complete the statements by choosing the correct answer from the proof of theorem.
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What is the value of x? x =
24
7
X
Answer:
x = 25
Step-by-step explanation:
Following the Pythagoras' Theorem,
a² + b² = c²
24² + 7² = c²
c² = 625
∴ c = 25
In this case, since the length of the hypotenuse is x cm, ∴ c = x.
∴ x = 25
Answer:
25
Step-by-step explanation:
According to Pythagoras theorem,
H²=P²+B²
(H-hypotenuse, P-perpendicular, B-Base)
X²=24²+7²
X²=576+49
X²=625
X²=25²
X=25
The sides of a triangle are measured at a = 4, b = 5 and c = 6. What is the length of Median A?
Five years ago, a computer that worked half as fast as a current computer cost twice as much money. The current computer's speed to price ratio is what percent of the older computer's speed to price ratio? I'm confused on what the ratio is
The current computer's speed to price ratio is 400% of the older computer's speed to price ratio.
How to obtain the speed to price ratios?
The speed to price ratios, along with the percentage, is obtained applying the proportions in the context of this problem.
Five years ago, the ratio was given as follows:
0.5x/2y = 0.25x/y.
The current ratio is given as follows:
x/y.
The current ratio is 4 times greater than the ratio of five years ago, hence it's a percentage of 400% the old ratio.
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at what intercepts is the function f(x)=-1/4x^3 constant ?
The function f(x) = 1/4x³ is constant when the intercept is 0
What are polynomial graph?Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.
the graph of a polynomial function is a smooth continuous curve.
The y-intercept is the point where the graph crosses the y-axis and can be found by substituting x = 0. The x-intercepts are points where the graph crosses the x-axis and can be found by making the function equal to zero and solving for x.
therefore f(0) = 1/4 0³ = 0
therefore the y- intercept of the function is 0
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Help, it's something that has to do with Slope-intercept form
Answer:
y = 1/2x + 7/6
Step-by-step explanation:
Blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box?
The greatest number of blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box = 84
Let h represents the height, w represents the width and l represents the length of the box.
The box is 6 units tall, 7 units wide, and 8 units deep.
⇒ h = 6 units, w = 7 units and l = 8 units
The volume of the box would be,
V = l × w × h
V = 6 × 7 × 8
V = 336 cu. units
The four block has unit-cubes.
The volume of unit each unit cube would be, 1 × 1 × 1 = 1 cubic unit
so, the volume of 4 blocks would be,
V₁ = 4 × 1
V₁ = 4 cu. units
The number of blocks that can be placed in the box would be,
n = V / V₁
n = 336 / 4
n = 84
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The complete question is:
There is an ample supply of identical blocks (as shown). Each block is constructed from four 1 × 1 × 1 unit-cubes glued whole-face to whole-face. What is the greatest number of such blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box?
explain why the exponents can not be added in the product 12 to the power of 3 then * 11 to the power of three
Answer:
In the product 12 to the power of 3 * 11 to the power of 3, the exponents (3 and 3) indicate that 12 is multiplied by itself 3 times, and 11 is multiplied by itself 3 times.
When two or more numbers with the same base are multiplied together, the exponents can be added, because it's the same as multiplying the base numbers together. For example, (12^3) * (12^2) = 12^(3+2) = 12^5
However, in this case, the bases of 12 and 11 are different, and therefore, the exponents cannot be added. The product of 12 to the power of 3 * 11 to the power of 3 is different from (1211) to the power of 3, the result is (1211)^3= 1332^3
5. Segment AB has endpoints at A(-4,-8) and B(10, 13). If point P lies on AB such that AP: BP = 2:5 then find the coordinates of P. Show all your work.
Answer:
To find the coordinates of P, we can use the concept of proportional division of line segments. Given that AP:BP = 2:5, it means that the ratio of the length of AP to BP is 2:5.
Let's first find the vector that represents the direction of AB, which is the vector pointing from A to B. We can find this by subtracting the coordinates of A from the coordinates of B:
(10,13) - (-4,-8) = (14, 21)
This is the vector <14,21>
Now, we can find the point P, which is located two fifths of the way from A to B, by multiplying the vector <14,21> by 2/7 and adding the result to the coordinates of A:
P = A + (2/7) * <14,21>
= (-4,-8) + (2/7) * <14,21>
= (-4,-8) + <8,6>
= (4,-2)
So, the coordinates of P are (4,-2)
We can observe that point P is two fifth of the way from A to B.
Given BE ≅ BD and AD ≅ CE, prove triangle ABE ≅ triangle CBD
Answer: To prove that triangle ABE is congruent to triangle CBD, we will use the SAS (Side-Angle-Side) Congruence Theorem.
This theorem states that if two triangles have two sides and the included angle congruent, then the triangles are congruent.
Given:
BE ≅ BD (congruent sides)
AD ≅ CE (congruent sides)
We have congruent sides AB and BC, and congruent angles A and C (included angles)
By SAS congruence theorem, we can prove that:
Triangle ABE ≅ triangle CBD
Therefore, triangle ABE is congruent to triangle CBD
Alternatively, if we use the ASA (Angle-Side-Angle) congruence theorem, where we have congruent angles and congruent sides between those angles, we can also prove that triangle ABE ≅ triangle CBD
Step-by-step explanation:
Solve log (4x + 8) − log 3 = 2.
The value of x for the expression is 73.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
log (4x + 8) - log 3 = 2
[ log (a/b) = log a - log b ]
So,
log (4x + 8) - log 3 = 2 can be written as,
log (4x + 8)/3 = 2
Taking exponents on both sides.
(4x + 8)/3 = [tex]10^2[/tex]
4x + 8 = 100 x 3
4x + 8 = 300
4x = 292
x = 73
Thus,
The value of x is 73.
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a polling agency is investigating the voter support for a ballot measure in an upcoming city election. the agency will select a random sample of 500 voters from one region, region a, of the city. assume that the population proportion of voters who would support the ballot measure in region a is 0.47.
According to the normal distribution and the central limit theorem the ballot measure is greater than 0.50.
The term called normal distribution is defined as a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Here we know that t a random sample of 500 voters from one region, region a, of the city and the ballot measure in region a is 0.47.
Here we have to find the mean and the standard deviation are calculated as,
=> mean = 0.47
=> Standard deviation = √0.47(1-0.47)/500
When we simplify this then we get,
=> Standard deviation = 0.0223
By using the Central Limit Theorem the probability is calculated as,
=> Z = (0.5 - 0.47) / 0.0223
=> Z = 1.34
When we use the z table, then we get the p - value as 0.9099
Then the probability is calculated as,
=> P = 1 - 0.9099
=> P = 0.0901
Hence 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
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Create a diagram based on the given symbolic statement. Be sure enough information is provided in the diagram to validate each statement.
△FUN≅△CAR
According to the diagram,
The two triangles are right-angle triangles.
ΔFUN and ΔCAR
where angle CAR and angle FUN are 90° each.
According to RHS congruency
NU = CA (each 3 cm)
FUN = CAR (each 90°)
FN = CR (each 5cm)
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if a lawyer charges $120 an hour (or any fraction of an hour), how much is a bill for 3 hours and 20 minutes? what is the equation for this problem?
Answer: If a lawyer charges $120 an hour (or any fraction of an hour), how much is a bill for 3 hours and 20 minutes? What is the equation for this problem? answer choices l (x) = 120x l (x) = 120 [x-1] l (x) = 120 [x] l (x) = 120 [x+1]
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Graham is hiking a trail that is 512 miles long. He has hiked 358 miles so far.
Which expression shows how many miles he has left to hike?
Answer:
512-358= how manyy miles left
Step-by-step explanation:
The expression that shows how many miles Graham has left to hike would be 512 - 358 = 154 miles.
In an isosceles triangle ABC with AC = BC, point M is on the side BC , and point N is on the segment MC. It is known that MN=AM, and m∠BAM=m∠NAC. Find m∠MAC.
Please answer correctly in less than 10 min
The measure of angle MAC is 90°.
What does the isosceles triangle mean?
When two of a triangle's sides are congruent, or the same length, the triangle is said to be isosceles. This means that if you draw a line through the middle of an isosceles triangle, it will split in half, with the two parts having equal-length sides.
The angles on either side of the congruent side of an isosceles triangle are also congruent. As a result, in the ABC triangle, mBAM = mCAB = mNAC.
Angle MAC is congruent to itself since angles BAM and NAC are complementary to it and are also congruent with each other.
Therefore, m∠MAC = m∠MAC = 180 - m∠BAM = 180 - m∠NAC.
Since m∠BAM = m∠NAC, we can conclude that
m∠MAC = 180 - m∠NAC = 90°
Hence, the measure of angle MAC is 90°.
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________ is measured in square units because it has two dimensions: length and width.
A. Area
B. Height
C. Perimeter
D. Volume
The quantity that is measured in square units is area ( option C )
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area.
The area of a rectangle is given as Length × width . The area of a triangle is 1/2 bh.
Height has only one dimension. it is measured in meters. Perimeter has only one dimension, it is also measure in meters. Volume has three dimensions i.e l × b× h = m³
Therefore Out of the options only area has two dimension i.e l× w= m× m = m²
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a longitudinal study is able to help resolve which of the following limitations of a traditional correlational study? a. whether there is a third, unmeasured variable causing both of the measured variables b. the direction of a possible causal relationship between the variables c. whether the sample size is sufficient to detect a relationship between variables d. whether the relationship between variables is statistically significant
A longitudinal study is a type of research method used to observe changes in a given behavior or condition of a group of individuals over a period of time.
It is especially useful in resolving the limitation of a traditional correlational study in that it can provide evidence for the direction of a possible causal relationship between the variables. This is because the study is conducted over a period of time, which allows for the observation of changes in the variables over time, and the ability to determine which variable is causing the changes in the other. This can be done through the use of statistical tests, such as regression analysis, which can measure the strength of the correlation and the direction of the relationship. Additionally, longitudinal studies can also help to determine whether the sample size is sufficient, as well as whether the relationship between the variables is statistically significant.
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Drag numbers to the table so it shows a proportional relationship between x
and y
A proportional relationship between x and y is
y/x = 8.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
A table is given below.
To show a proportional relationship:
y/x = k
6/0.75 = 8
So, 1.5 x 8 = 12
And 3 x 8 = 24
So, the complete table is given in the attached image.
Therefore, the complete table is given in the attached image.
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whats the answer for 45,688 -5.65
Answer:
Step-by-step explanation:
true or false: the residuals from a linear regression analysis on any possible dataset (with more than 1 observation) will add up to 0.
The statement is False. The residuals will not necessarily add up to 0.
The residuals from a linear regression analysis are the differences between the observed values of the dependent variable and the predicted values of the dependent variable. Therefore, the sum of the residuals will depend on the data and the model used. If the model is a perfect fit, then the sum of the residuals will be 0. However, in most cases, the model will not be a perfect fit and the sum of the residuals will not be 0. Therefore, it is not true that the residuals from a linear regression analysis on any possible dataset (with more than 1 observation) will add up to 0.
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Find the probability of drawing a single card from a 52 card deck for the following
a. Diamond or a 10.
b. A spade or a queen.
Answer: a. The probability of drawing a single card from a 52 card deck that is a diamond or a 10 is 13/52 or 1/4. There are 13 diamonds in a standard deck of 52 cards and 4 of them are 10s. So, the chance of drawing a diamond 10 is 4/52 and the chance of drawing a diamond is 13/52. The probability of drawing a diamond or a 10 is the sum of the individual probabilities, which is (4/52) + (13/52) = 17/52 or 1/3.
b. The probability of drawing a single card from a 52 card deck that is a spade or a queen is 13/52 or 1/4. There are 13 spades in a standard deck of 52 cards and 4 of them are queens. So, the chance of drawing a spade queen is 4/52 and the chance of drawing a spade is 13/52. The probability of drawing a spade or a queen is the sum of the individual probabilities, which is (4/52) + (13/52) = 17/52 or 1/4.
Step-by-step explanation:
Taye wants to find 352+116. Show how he can use place value to find the sum
Answer:
Step-by-step explanation:
well if you 6+2 is 8 that is the one's place then 50+10 is 60 that is the tens place then 300+100 is 400 that is the hundreds place and add 400+60+8 is 468
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A pipe takes 6 minutes to fill 3.4 of a water tank how long would it take to fill the entire tank?
x = 20.4 it take to fill the entire tank.
How to calculate how long would it take to fill the entire tank?Calculate a tank's total capacity and the volume that is filled in gallons and litres for tanks like water and oil storage. assumes the tank's interior measurements.
You can enter metric dimensions in metres (m) or centimetres, or U.S. dimensions in feet (ft) or inches (in) (cm). Results are given in fluid US gallons, fluid Imperial (UK) gallons, fluid cubic feet (ft3), fluid metric litres (fl), and fluid cubic metres (m3).
x = total volume of the entire tank.
We can suggest the following equation:
6 minutes
6 minutes to fill 3.4
x=6*3.4=20.4
x=20.4
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Fred bought a soft drink for 2 dollars and 7 candy bars. He spent a total of 16 dollars. How much did each candy bar cost ?
Answer:
$2 for each candy bar
Step-by-step explanation:
16 - 2 = 14
14 / 7 = 2
Answer:
$2
Step-by-step explanation:
16-2=14
14/7=2
he spent $14 total on candy bars, divide that by 7, and each candy bar costs $2