What are all of the solutions to the equation (cos θ)(cos θ) + 1 = (sin θ)(sin θ)?
Answer: Starting with the given equation:
(cos θ)(cos θ) + 1 = (sin θ)(sin θ)
We can use the identity cos² θ + sin² θ = 1 to rewrite the right-hand side:
(cos θ)(cos θ) + 1 = 1 - (cos θ)(cos θ)
Combining like terms, we get:
2(cos θ)(cos θ) = 0
Dividing both sides by 2, we get:
(cos θ)(cos θ) = 0
Taking the square root of both sides, we get:
cos θ = 0
This equation is true for θ = π/2 + kπ, where k is any integer. So the solutions to the equation are:
θ = π/2 + kπ, where k is any integer.
Enjoy!
Step-by-step explanation:
when calculating confidence intervals in this class the product of a constant times a margin of error is added and subtracted to what value to obtain the ci range? group of answer choices mean standard deviation alpha median
The confidence interval is calculated by adding and subtracting the product of a constant (usually 1.96), the margin of error, and the mean.
The constant times the margin of error is added and subtracted from the sample mean to obtain the confidence interval range.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
The constant is determined by the confidence level of your analysis (typically 95%) and the margin of error is determined by the standard deviation and the size of your sample.
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julie buys 19 identical calculators the total cost is £143.64wirk out the total cost of 31 of these calculaters
Answer:
£234.36
Step-by-step explanation:
Smoothie activity
The smoothie chain makes mulliole SO.15 increases to the average prices of their smoothies. The table shows the average profit of the chain compared to the number of price increases. The data models a quadratic function.
y = 5x² + 25x + 100 is the quadratic function that models the data.
What does a math quadratic equation mean?x ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0.Since it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
We must employ the quadratic equation's general form in order to identify the quadratic function that best represents this data:
y = ax²+ bx + c
Three data points are available from the table: (0, 100), (1, 130), and (2, 140).
100 = a(0)² + b(0) + c
130 = a(1)² + b(1) + c
140 = a(2)² + b(2) + c
Simplifying each equation, we get:
c = 100
a + b + c = 130
4a + 2b + c = 140
Substituting c = 100 into the second and third equations, we get:
a + b = 30
4a + 2b = 40
The first equation's solution for b in terms of an is as follows:
b = 30 - a
This results from substituting this into the second equation:
4a + 2(30 - a) = 40
By condensing and figuring out a, we get at:
a = 5
Adding a = 5 to the first equation results in:
b = 25
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#HELP! I WILL MAKE U BRAINLIST!
Answer:
x = 1.5
y = 12.99
Step-by-step explanation:
let's call cost of 1 song is x and cost of 1 album is 6
6x + y = 21.99
4x + 3y = 44.97
6x + y = 21.99 => y = -6x + 21.99
Substitute into 4x + 3y = 44.97
4x + 3(-6x + 21.99) = 44.97
4x - 18x + 65.97 = 44.97
-14x = -21
x = -21/-14 = 1.5
y = -6x + 21.99 = -6(1.5) + 21.99 = 12.99
how can you convert a given number of fluid ounces to find equivalent number of cups explian
Step-by-step explanation:
There are 8 fluid ounces in a cup....
divide the number of ounces by 8 to find the number of cups
# ounces / 8 ounces/cup = cups
Question
Find the value of y
for the given value of x
.
y=x+5;x=3
Answer: y is equal to 8
Step-by-step explanation:
by substituting the x for its vale of three we can add the two values to get 8 or y=8
Determine the area of the shaded regions in the figures below. Write the final polynomial in standard form
Answer:
for the tringle:
area=[tex]p^{2} -2p-3[/tex]
for the frame:
area=[tex]8x+28[/tex]
Step-by-step explanation:
For the tringle:-
Area=1/2bh
Area=1/2(2p-6)(p+1)
Area=1/2([tex]2p^{2} -4p-6[/tex])
Area=[tex]p^{2} -2p-3[/tex]
For the picture frame:-
part 1:the area of the big frame
Area=lw
Area=(x+7)(x+4)
Area=[tex]x^{2} +11x+28[/tex]
part 2:the area of the small frame
Area=lw
Area=(x+3)(x)
Area=[tex]x^{2} +3x[/tex]
To find the area of the shaded regions:
Area of shaded region=area of the big frame-the area of the small frame
Area of shaded region=[tex](x^{2} +11x+28)-(x^{2} +3x)[/tex]
Area of shaded region=[tex]8x+28[/tex]
I need help
Which situation best represents the equation below?
26-179-9k
A. A pool of water has 26 gallons of water in it. It is filled at a rate of 9 gallons per minute, until there are 179
gallons.
B. A dairy farm has 179 cows in it. All of the cows are placed in groups of nine. There are 26 groups of cows.
C. There were 26 boxes for delivery at the post office one morning. By the end of the day, 179 boxes had been
added to the delivery pile. The boxes will be delivered in groups of k
D. A school assembly has 179 students in it. Nine teachers escort k number of students out of the assembly.
until there are 26 students remaining.
In linear equatiοn, A schοοl assembly has 179 students in it. Nine teachers escοrt k number οf students οut οf the assembly, until there are 26 students remaining.
What is a linear equatiοn in math?A linear equatiοn is an algebraic equatiοn that οnly has a cοnstant and a first-οrder (linear) term, such as y=mx+b, where m is the slοpe and b is the y-intercept. A "linear equatiοn οf twο variables" in which x and y are the variables is a term that is sοmetimes used tο refer tο the afοrementiοned situatiοn.
Mοdel equatiοn fοr the situatiοn
The equatiοn fοr the situatiοn is given as;
26 = 179 - 9k
Frοm the equatiοn abοve, 26 is the result οf the difference between "179" and "9k".
Thus, the situtatiοn that bets represent the equatiοn is, a schοοl assembly has 179 students in it. Nine teachers escοrt k number οf students οut οf the assembly, until there are 26 students remaining.
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Maria purchased 1,000 shares of stock for $35. 50 per share in 2014. She sold them in 2016 for $55. 10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent
Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.
To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.
The purchase price for 1,000 shares of stock was:
$35.50 x 1,000 = $35,500
The selling price for 1,000 shares of stock was:
$55.10 x 1,000 = $55,100
The capital gain is the difference between the selling price and the purchase price:
$55,100 - $35,500 = $19,600
To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:
($19,600 / $35,500) x 100 = 55.21%
In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.
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A right triangular prism is shown.
A right triangular prism is shown. The right triangles have sides with lengths 15 and 8. The hypotenuse has a length of 17. The height of the prism is 15.
What is the volume of the prism?
900 cubic units
1,020 cubic units
1,800 cubic units
2,312 cubic units
Therefore , the solution of the given problem of volume comes out to be the response is 900 cubic units.
What precisely is volume?A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, understanding an object's volume is necessary to calculate its measurements. It is standard practice to convert the weight of an object into mass units like grams and kilograms.
Here,
The formula V = Bh, when B is the area of the bottom and h is the height of the prism, determines the volume of a right triangle prism.
The prism has an area of because its foundation is a right triangle with 8 and 15-foot-long legs.
=> B = (1/2)bh = (1/2)(8)(15) = 60
The prism's height is specified as 15 inches.
As a result, the prism's capacity is:
=> 900 cubic units are equal to V = Bh = 60(15).
Therefore, the response is 900 cubic units.
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Answer:
900 cubic units
Step-by-step explanation:
Harmonicas. When ordering a new box of harmoniens, let X denote the time until the box arrives, and let y denote the number of harmonicas that work properly. Is X a continuous or discrete random variable? Why? Is Y a continuous or discrete random variable? Why?
X is a discrete random variable and Y is a discrete random variable because they both measure countable values rather than continuous values.
X is a discrete random variable because the time until the box arrives is measured in discrete, countable intervals such as days, weeks, or months. Y is a discrete random variable because the number of harmonicas that work properly is a countable number, rather than a continuous, measured value.
For example, the box could arrive in one week, or it could arrive in one month. Therefore,[tex]X[/tex] is discrete. Similarly, Y is discrete because there will be a certain number of harmonicas that work properly, such as 12, 15, 20, etc. So, Y is also discrete.
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El area de un rectángulo es 216 m² y su base es 6m mayor que su altura. Determina sus dimensiones recordando la ecuación de segundo grado de la forma ax² + bx + c = 0 y se resuelve con los formula general
Answer:
[tex]base = 18 m\\\\altura= 12 m[/tex]
Step-by-step explanation:
Disclaimer: My Spanish is not great so I used a translation tool. Please let me know if it is understandable. I think the equations are understandable.
Area = 216 m²
Sea base = b m y altura = h m
[tex]Area = bh[/tex]
So
[tex]bh = 216[/tex]
base = 6 m mayor que la altura
[tex]b = h + 6[/tex]
Así que sustituyendo b en la fórmula bh = 216 da
[tex]b h = 216[/tex]
⇒ [tex](h + 6)h = 216[/tex]
⇒ [tex]h^2 + 6h = 216[/tex]
⇒ [tex]h^2 + 6h - 216 = 0[/tex] [1]
Esta es una ecuación cuadrática que se puede resolver usando fórmulas cuadráticas o factorizando. Aquí se nos pide que utilicemos la fórmula general
Para una ecuación cuadrática general de la forma
[tex]ax^2 + bx + c = 0[/tex]
hay dos soluciones dadas por la fórmula cuadrática
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
En este problema, comparando [tex]ax^2 + bx + c = 0[/tex] a [tex]h^2 + 6h - 216 = 0[/tex] :
[tex]a = 1\\b = 6\\c = -216\\[/tex]
Reemplaza estos valores en las fórmulas cuadráticas y resuelve para h
[tex]h = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
[tex]h = \dfrac{ -6 \pm \sqrt{6^2 - 4(1)(-216)}}{ 2(1) }[/tex]
[tex]h = \dfrac{ -6 \pm \sqrt{36 - -864}}{ 2 }[/tex]
[tex]h = \dfrac{ -6 \pm \sqrt{900}}{ 2 }[/tex]
[tex]h = \dfrac{ -6 \pm 30\, }{ 2 }[/tex]
[tex]h = \dfrac{ 24 }{ 2 } \; \; \; h = -\dfrac{ 36 }{ 2 }[/tex]
que se convierte
[tex]h = 12[/tex]
[tex]h = -18[/tex]
Como no podemos tener altura negativa, la solución es
[tex]h = 12[/tex] m
Desde b = h + 6,
[tex]b = 12 + 6 = 18 m[/tex]
If tan theta=5/6 and tan gamma=1/11 the show that (theta + gamma)=180/4
(theta + gamma) = 45 degrees, which is equal to 180/4.
Property of right-angled triangle.tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right-angled triangle.
Let's consider a right-angled triangle ABC, where angle B is 90 degrees, and angle A(theta ) and angle C(gamma) are the angles whose tangent values are given.
Using the given information, we can say that:
tan(A) = 5/6
tan(C) = 1/11
We can now use the following trigonometric identity:
tan(A + C) = (tan(A) + tan(C)) / (1 - tan(A) * tan(C))
Substituting the given values, we get:
tan(A + C) = (5/6 + 1/11) / (1 - 5/6 * 1/11)
tan(A + C) = (55/66 + 6/66) / (66/66 - 5/66)
tan(A + C) = 61/61 = 1
Now, we know that:
tan(180/4) = tan(45) = 1
Therefore, we can conclude that:
A + C = 180/4 = 45 degrees
Hence, we have shown that (theta + gamma) = 45 degrees, which is equal to 180/4.
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Trevin puts 8 gallons of gas in his car and pays 22$. At this rate what is the cost of 9 gallons of gas
The cost of 9 gallons of gas is 24.75$
A unitary method is a mathematical technique for finding the value of a single unit and then multiplying it by any number of other units to derive the value of the provided units. Employing the unitary method, we can solve the above problem.
Given that,
The cost of 8 gallons of gas = 22$
The cost of 1 gallon of gas = 22 ÷ 8
= 2.75$
Therefore, the cost of 9 gallons of gas = 2.75 × 9
= 24.75$.
Hence, the cost of 9 gallons of gas is 24.75$.
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Solve for C.
16
17
8
C = [?]°
Round your final answer
to the nearest tenth.
Law of Cosines: c² = a² + b² - 2ab-cosC
69.1° is the value of C by Law of Cosines .
What is the cosine law?
The formula for the Law of Cosines is c2=a2+b22ab cosC. With the exception of the third component, which equals 0 if C is a right angle because the cosine of 90° is 0 and we have the Pythagorean Theorem, this is similar to the Pythagorean Theorem.
The Law of Cosines is given as
c² = a² + b² - 2ab-cosC
substitute the values in a, b, c
Plugging in given values, we get
16² = 8² + 17² - 2 . 8 . 17 . cosC
256 = 64 + 289 - 272. CosC
256 = 353 - 272 . cosC
256 - 353 = 272 . CosC
-97 = 272 . CosC
cosC = -97/-272
C = across(97/272)
C = 69.1°
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Answer:
C= 83.04
Step-by-step explanation:
1. A new bicycle sells for $300. It is on sale for off the regular price. Select
all the expressions that represent the sale price of the bicycle in dollars.
A300-1
B 300-2/
(C.) 300-(1-1)
(D.) 300 -4/1
E 300--300
Answer:
Step-by-step explanation:
e
Hester sells televisions. She earns a fixed amount for each television and an additional $25 if the buyer gets an extended warranty. If Hester sells 15 televisions with extended warranties, she earns $1,350. How much is the fixed amount Hester earns for each television?
The fixed amount Hester earns for each television is $65.
What is linear equation?A straight line in a two-dimensional coordinate system is described by a linear equation. Using m as the line's slope and b as the y-intercept, it has the generic form y = mx + b.
Mathematical applications of linear equations include algebra, geometry, and calculus. They are employed to represent and examine interactions between different variables, such as the connection between time and space in a straightforward linear motion issue.
Let us suppose the fixed amount = x.
Then, for 15 televisions she earns:
15*$25 = $375
Now, she earned a total of 1350, thus:
15x + $375 = $1,350
15x = $975
x = $65
Therefore, the fixed amount Hester earns for each television is $65.
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Plssss help due today!!!
Answer:
235.6 cm²
Step-by-step explanation:
The formula to find the area of a sector is,
[tex]\sf A=\frac{\theta}{360}*\pi r^2[/tex]
Here,
Θ = angle
r = radius
Let us find it now.
[tex]\sf A=\frac{\theta}{360}*\pi r^2\\\\\sf A=\frac{270}{360}*\pi *10*10\\\\\sf A=\frac{270}{360}*\pi *100\\\\A = 235.61 cm^2[/tex]
Find an expression that is equivalent to (a - b) ^ 3
An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.
What other expressions are the same as 2 5?The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.
One way to expand (a - b)³ is to use the binomial formula:
(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³
where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.
Simplifying the above expression, we get:
(a-b)³ = a³-3a²b+3ab²-b³.
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serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof.
Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.
Measurement of Angle:
The measurement of angles is done using basic geometric tools such as protractors and compasses. This tool helps to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles. Angles are measured in three ways: degrees, radians, and revolutions.
According to the Question:
Suppose the measure of angle is θ, then we have
Sinθ = 22.8/24
⇒ Sinθ = 0.95
Therefore,
θ = Sin⁻¹ (0.95)
= 71.8 degree.
Therefore, Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.
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What property of real numbers does each statement demonstrate? (3 + 4) + 1 = 3 + (4 + 1)
Answer: Associative property
Step-by-step explanation:
The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!
You may need to use the appropriate appendix table to answer this question. Suppose that the mean daily viewing time of television is 8.35 hours. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household (a) What is the probability that a household views television between 5 and 11 hours a day? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (b) How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. hrs (c) What is the probability that a household views television more than 3 hours a day? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect.
The probability that a household views television between 5 and 11 hours a day is approximately 0.7291, and that a household views television more than 3 hours a day is approximately 0.9830.
(a) To find the probability that a household views television between 5 and 11 hours a day, we need to find the area under the normal distribution curve between the values of 5 and 11, with a mean of 8.35 and a standard deviation of 2.5. We can use a standard normal distribution table or calculator to find the corresponding probabilities.
First, we need to standardize the values of 5 and 11 using the formula:
z = (x - μ) / σ
where z is the standardized score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For x = 5: z = (5 - 8.35) / 2.5 = -1.34
For x = 11: z = (11 - 8.35) / 2.5 = 1.06
Using a standard normal distribution table, we can find the area under the curve between z = -1.34 and z = 1.06 to be approximately 0.7291.
Therefore, the probability that a household views television between 5 and 11 hours a day is approximately 0.7291.
(b) To find how many hours of television viewing a household must have in order to be in the top 3% of all television-viewing households, we need to find the z-score corresponding to the top 3% of the distribution, and then use the formula:
z = (x - μ) / σ
to solve for x, where x is the number of hours of television viewing and μ and σ are the mean and standard deviation of the distribution, respectively.
Using a standard normal distribution table, we can find that the z-score corresponding to the top 3% of the distribution is approximately 1.88.
Therefore, we can solve for x as follows:
1.88 = (x - 8.35) / 2.5
x - 8.35 = 4.7
x = 13.05
Therefore, a household must view more than 13.05 hours of television per day to be in the top 3% of all television-viewing households.
(c) To find the probability that a household views television more than 3 hours a day, we need to find the area under the normal distribution curve to the right of the value of 3, with a mean of 8.35 and a standard deviation of 2.5. We can again use a standard normal distribution table or calculator to find the corresponding probability.
First, we need to standardize the value of 3 using the formula:
z = (x - μ) / σ
where z is the standardized score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For x = 3: z = (3 - 8.35) / 2.5 = -2.14
Using a standard normal distribution table, we can find the area under the curve to the right of z = -2.14 to be approximately 0.9830.
Therefore, the probability that a household views television more than 3 hours a day is approximately 0.9830.
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Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
X
The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.
What is surface area ?
Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.
To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.
First, let's find the area of the triangular base.
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 18 x 24
Area of triangle = 216 [tex]feet ^2[/tex]
Next, let's find the area of each rectangular face.
Area of rectangle = length x width
Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]
Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]
Area of rectangle 3 = 22 x 30 = 660 [tex]feet ^2[/tex]
Now, we can add up the areas of all three faces to get the total surface area of the prism:
Surface area = area of rectangle (1+2+3) + 2 x area of triangle
Surface area = 528 + 396 + 660 + 2(216)
Surface area = 2016 [tex]feet ^2[/tex]
Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].
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Cutting (chess) boards. Suppose we are given a standard 8 x 8 checkerboard and given a standard 8 x 8 checkerboard and an immense supply of dominoes. Each domino can cover exactly two adjacent squares on the checkerboard below). As a warm-up, verify that the checkerboard can be covered completely dominoes where each domino covers exactly two squares and the dominoes do not overlapon another. Assume next that two squares of the checkerboard have been cut off as shown (second checkerboard). Your challenge now is to determine if you can cover this cut checkerboard winnon overlapping dominoes so that again, each domino covers exactly two squares. Finally, your last challenge is to consider the same question for the truncated checkerboard (last checkerboard). Does your answer change? Justify your answers.
If the two removed squares have the same color, then it is possible to cover the truncated checkerboard with non-overlapping dominoes. If they have different colors, then it will be impossible to cover the truncated checkerboard with non-overlapping dominoes.
To prove that the chess board can be completely covered by non-overlapping dominoes, where each domino covers exactly two squares, we can color the board alternatively in black and white. The two colors will make the board have 32 black squares and 32 white squares. Each domino will cover one white and one black square. Since there are the same number of black and white squares, there is an equal number of squares that each domino can cover so it is possible to cover the entire board with dominoes without overlap.
To determine whether the cut checkerboard can be covered by non-overlapping dominoes, note that we have 62 squares, 31 of which are black, and 31 white. This means that one color will have one extra square, in this case black. Therefore, if the two removed squares are of different colors, it will be impossible to cover the cut checkerboard with non-overlapping dominoes.However, if the two removed squares have the same color, then it will be possible to cover the checkerboard with non-overlapping dominoes. This is because we will still have an equal number of black and white squares even after the removal of the two squares.The same logic applies to the truncated checkerboard.
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1) Scott and Tom rent a boat at Stow Lake. They start at 10:15 and end at 11:45. The boat
rental costs $1.50 for every 15 minutes. How much will they pay?
Answer:
$9
Step-by-step explanation:
We know
They start at 10:15 and end at 11:45. It is 1 hour 30 minutes long.
1 hour 30 minutes = 90 minutes
The boat rental costs $1.50 for every 15 minutes.
How much will they pay?
We Take
90 divided by 15, then time 1.50 = $9
So, they pay $9
Answer:
Scott and Tom will pay a total of $9 for the boat rental.
Step-by-step explanation:
If Scott and Tom rent the boat between 10:15 and 11:45, then the total time they rented the boat is 1 hour and 30 minutes.
To convert 1 hour and 30 minutes to units of 15 minutes, we can divide the total number of minutes by 15:
⇒ 1 hour = 60 minutes
⇒ 1 hour and 30 minutes = 60 + 30 = 90 minutes
⇒ 90 minutes / 15 minutes = 6
Therefore, there are 6 units of 15 minutes in 1 hour and 30 minutes.
Given the cost for renting the boat is $1.50 per 15-minute interval, the total cost for renting the boat is:
⇒ 6 × $1.50 = $9
Therefore, Scott and Tom will pay $9 for the boat rental.
The Law of Sines says that for a given triangle, _____.the sine values of all three internal angles will be the samethe sine values of all three internal angles will be proportional to each otherthe ratio between the sine of the angle and the opposite side will match for all three internal anglesthe sine values of all three angles will be different
The Law of Sines says that for a given triangle, the ratio between the sine of an angle and the length of the opposite side is the same for all three angles in a triangle. the sine values of all three internal angles will be the samethe sine values of all three internal angles will be proportional to each otherthe ratio between the sine of the angle and the opposite side will match for all three internal anglesthe sine values of all three angles will be different
In a triangle, we have three angles and three sides. The Law of Sines says that for any triangle, the ratio between the sine of an angle and the length of the opposite side will be the same for all three angles. In other words, the sine values of each angle are proportional to the length of the opposite side.
To put this in mathematical terms, let's consider a triangle with angles A, B, and C, and sides a, b, and c respectively. The Law of Sines can be written as:
sin(A)/a = sin(B)/b = sin(C)/c
This means that if we know the length of any two sides and the measure of the angle opposite one of those sides, we can use the Law of Sines to find the measure of the other angles and sides.
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given the resulting p-values, would you reject or fail to reject the null hypotheses (assuming a 0.05 significance level)? what does your decision mean in the context of this problem? would you proceed with changing the design of the arrow, or would you keep the original design?
In the context of this problem, if we reject the null hypothesis, we can conclude that the new design is more effective in terms of accuracy. If we fail to reject the null hypothesis, we can't conclude anything about the effectiveness of the new design
How do we interpret the results of the p.values?When given the resulting p-values, we reject the null hypotheses (assuming a 0.05 significance level) if the p-value is less than 0.05. We fail to reject the null hypotheses if the p-value is greater than or equal to 0.05.If we reject the null hypothesis, it means that there is strong evidence against it, and we can say that the alternative hypothesis is supported by the data. If we fail to reject the null hypothesis, it means that there is insufficient evidence to reject it, and we can't say that the alternative hypothesis is supported by the data.
In the context of this problem, if we reject the null hypothesis, we can conclude that the new design is more effective in terms of accuracy. If we fail to reject the null hypothesis, we can't conclude anything about the effectiveness of the new design.In either case, whether we reject or fail to reject the null hypothesis, we wouldn't proceed with changing the design of the arrow based solely on the statistical analysis. We would need to consider other factors such as cost, feasibility, and practicality before making any decisions about changing the design.
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Change 0.182 0.005 0.050 0.174 Table 10-3. Regression results for predicting depression at wave 2 Predictor Variable b Beta P R? Depression Score Wave 1 0.267 0.231 0.000 0.182 Sociodemographic Age -0.014 -0.024 0.538 0.187 Sex 0.165 0.034 0.370 Psychologic Health Neuroticism, wave 1 0.067 0.077 0.056 0.0237 Past history of depression 0.320 0.136 0.000 Physical Health ADL, wave 1 -0.154 0.103 0.033 0.411 ADL, Wave 2 0.275 0.283 0.012 ADL?, wave 2 -0.013 --0.150 0.076 Number of current 0.115 0.117 0.009 symptoms, wave 2 Number of medical 0.309 0.226 0.000 conditions, wave 2 BP, systolic, wave 2 -0.010 -0.092 0.010 Global health rating 0.284 0079 0.028 change Sensory impairment -0.045 -0.064 0.073 change Social support inactivity Social support-friends, -1.650 -0.095 0.015 0.442 wave 2 Social support-visits, -1.229 -0.087 0.032 wave 2 Activity level, wave 2 0.061 0.095 0.025 Services (community residents 0.207 0.135 0.001 0.438° only), wave 2 Abhreviation: BP = blood pressure 0.031 0.015€ Based on above MLRA summary Table, which of following independent variables is the strongest predictor (or factor)?
Number of medical conditions, wave 2
Number of current symptoms, wave 2
Global health rating change
Past history of depression
ADL, wave 2
The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.
The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.
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Regina is trying to figure out if AABC and ADEF are congruent. She already knows that AC is the same length as DF, and ZA is the same measure as ZD.
Jared tells her that if ZB and ZE are the same measure, she'll know the triangles are congruent.
Isaac tells her that if BC and EF are the same length, she'll know the triangles are congruent.
E
Who is correct?
A. Jared only
B. Isaac only
C. Both
D. Neither
The relationship between the sides and angles of the triangles indicates that the information provided by Jared, satisfies the Side-Angle-Angle, SAA congruence rule, therefore, Jared only is correct. The correct option is therefore;
A. Jares only
What are congruent triangles?Congruent triangles are triangles that have both the same shape and size.
The specified information are;
Regina is trying to figure out if triangles ΔABC and ΔDEF are congruent
Regina knows that side AC is the same length as DF, therefore;
AC ≅ DF
∠A is the same measure as ∠D, therefore; m∠A = m∠D
The information Jared tells Regina is; If ∠B and ∠E are the same measure, Regina will know that the triangles are congruent.
The information Isaac tells here is; If BC and EF are the same length, she'll know that the triangles are congruent
In ΔABC and ΔDEF, AC ≅ DF, m∠A = m∠D
The relationship between the triangles if ∠B and ∠E are congruent therefore is; Side-Angle-Angle, SAA, which is a condition for congruence, therefore, Jared is correct
The relationship between the triangles if BC is congruent to EF is Side-Angle-Angle, SAA, which is not a condition for congruence, therefore, Isaac is not correct
Therefore, Jared only is correct. The correct option is option A.
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